// Copyright 2016 - 2022 The excelize Authors. All rights reserved. Use of
// this source code is governed by a BSD-style license that can be found in
// the LICENSE file.
//
// Package excelize providing a set of functions that allow you to write to and
// read from XLAM / XLSM / XLSX / XLTM / XLTX files. Supports reading and
// writing spreadsheet documents generated by Microsoft Excelâ„¢ 2007 and later.
// Supports complex components by high compatibility, and provided streaming
// API for generating or reading data from a worksheet with huge amounts of
// data. This library needs Go version 1.15 or later.
package excelize
import (
"bytes"
"container/list"
"errors"
"fmt"
"math"
"math/big"
"math/cmplx"
"math/rand"
"net/url"
"reflect"
"regexp"
"sort"
"strconv"
"strings"
"sync"
"time"
"unicode"
"unsafe"
"github.com/xuri/efp"
"golang.org/x/text/language"
"golang.org/x/text/message"
)
const (
// Excel formula errors
formulaErrorDIV = "#DIV/0!"
formulaErrorNAME = "#NAME?"
formulaErrorNA = "#N/A"
formulaErrorNUM = "#NUM!"
formulaErrorVALUE = "#VALUE!"
formulaErrorREF = "#REF!"
formulaErrorNULL = "#NULL!"
formulaErrorSPILL = "#SPILL!"
formulaErrorCALC = "#CALC!"
formulaErrorGETTINGDATA = "#GETTING_DATA"
// formula criteria condition enumeration.
_ byte = iota
criteriaEq
criteriaLe
criteriaGe
criteriaNe
criteriaL
criteriaG
criteriaErr
criteriaRegexp
catgoryWeightAndMass
catgoryDistance
catgoryTime
catgoryPressure
catgoryForce
catgoryEnergy
catgoryPower
catgoryMagnetism
catgoryTemperature
catgoryVolumeAndLiquidMeasure
catgoryArea
catgoryInformation
catgorySpeed
matchModeExact = 0
matchModeMinGreater = 1
matchModeMaxLess = -1
matchModeWildcard = 2
searchModeLinear = 1
searchModeReverseLinear = -1
searchModeAscBinary = 2
searchModeDescBinary = -2
maxFinancialIterations = 128
financialPrecision = 1.0e-08
// Date and time format regular expressions
monthRe = `((jan|january)|(feb|february)|(mar|march)|(apr|april)|(may)|(jun|june)|(jul|july)|(aug|august)|(sep|september)|(oct|october)|(nov|november)|(dec|december))`
df1 = `(([0-9])+)/(([0-9])+)/(([0-9])+)`
df2 = monthRe + ` (([0-9])+), (([0-9])+)`
df3 = `(([0-9])+)-(([0-9])+)-(([0-9])+)`
df4 = `(([0-9])+)-` + monthRe + `-(([0-9])+)`
datePrefix = `^((` + df1 + `|` + df2 + `|` + df3 + `|` + df4 + `) )?`
tfhh = `(([0-9])+) (am|pm)`
tfhhmm = `(([0-9])+):(([0-9])+)( (am|pm))?`
tfmmss = `(([0-9])+):(([0-9])+\.([0-9])+)( (am|pm))?`
tfhhmmss = `(([0-9])+):(([0-9])+):(([0-9])+(\.([0-9])+)?)( (am|pm))?`
timeSuffix = `( (` + tfhh + `|` + tfhhmm + `|` + tfmmss + `|` + tfhhmmss + `))?$`
)
var (
// tokenPriority defined basic arithmetic operator priority.
tokenPriority = map[string]int{
"^": 5,
"*": 4,
"/": 4,
"+": 3,
"-": 3,
"=": 2,
"<>": 2,
"<": 2,
"<=": 2,
">": 2,
">=": 2,
"&": 1,
}
month2num = map[string]int{
"january": 1,
"february": 2,
"march": 3,
"april": 4,
"may": 5,
"june": 6,
"july": 7,
"august": 8,
"september": 9,
"october": 10,
"november": 11,
"december": 12,
"jan": 1,
"feb": 2,
"mar": 3,
"apr": 4,
"jun": 6,
"jul": 7,
"aug": 8,
"sep": 9,
"oct": 10,
"nov": 11,
"dec": 12,
}
dateFormats = map[string]*regexp.Regexp{
"mm/dd/yy": regexp.MustCompile(`^` + df1 + timeSuffix),
"mm dd, yy": regexp.MustCompile(`^` + df2 + timeSuffix),
"yy-mm-dd": regexp.MustCompile(`^` + df3 + timeSuffix),
"yy-mmStr-dd": regexp.MustCompile(`^` + df4 + timeSuffix),
}
timeFormats = map[string]*regexp.Regexp{
"hh": regexp.MustCompile(datePrefix + tfhh + `$`),
"hh:mm": regexp.MustCompile(datePrefix + tfhhmm + `$`),
"mm:ss": regexp.MustCompile(datePrefix + tfmmss + `$`),
"hh:mm:ss": regexp.MustCompile(datePrefix + tfhhmmss + `$`),
}
dateOnlyFormats = []*regexp.Regexp{
regexp.MustCompile(`^` + df1 + `$`),
regexp.MustCompile(`^` + df2 + `$`),
regexp.MustCompile(`^` + df3 + `$`),
regexp.MustCompile(`^` + df4 + `$`),
}
addressFmtMaps = map[string]func(col, row int) (string, error){
"1_TRUE": func(col, row int) (string, error) {
return CoordinatesToCellName(col, row, true)
},
"1_FALSE": func(col, row int) (string, error) {
return fmt.Sprintf("R%dC%d", row, col), nil
},
"2_TRUE": func(col, row int) (string, error) {
column, err := ColumnNumberToName(col)
if err != nil {
return "", err
}
return fmt.Sprintf("%s$%d", column, row), nil
},
"2_FALSE": func(col, row int) (string, error) {
return fmt.Sprintf("R%dC[%d]", row, col), nil
},
"3_TRUE": func(col, row int) (string, error) {
column, err := ColumnNumberToName(col)
if err != nil {
return "", err
}
return fmt.Sprintf("$%s%d", column, row), nil
},
"3_FALSE": func(col, row int) (string, error) {
return fmt.Sprintf("R[%d]C%d", row, col), nil
},
"4_TRUE": func(col, row int) (string, error) {
return CoordinatesToCellName(col, row, false)
},
"4_FALSE": func(col, row int) (string, error) {
return fmt.Sprintf("R[%d]C[%d]", row, col), nil
},
}
)
// calcContext defines the formula execution context.
type calcContext struct {
sync.Mutex
entry string
iterations map[string]uint
}
// cellRef defines the structure of a cell reference.
type cellRef struct {
Col int
Row int
Sheet string
}
// cellRef defines the structure of a cell range.
type cellRange struct {
From cellRef
To cellRef
}
// formulaCriteria defined formula criteria parser result.
type formulaCriteria struct {
Type byte
Condition string
}
// ArgType is the type of formula argument type.
type ArgType byte
// Formula argument types enumeration.
const (
ArgUnknown ArgType = iota
ArgNumber
ArgString
ArgList
ArgMatrix
ArgError
ArgEmpty
)
// formulaArg is the argument of a formula or function.
type formulaArg struct {
SheetName string
Number float64
String string
List []formulaArg
Matrix [][]formulaArg
Boolean bool
Error string
Type ArgType
cellRefs, cellRanges *list.List
}
// Value returns a string data type of the formula argument.
func (fa formulaArg) Value() (value string) {
switch fa.Type {
case ArgNumber:
if fa.Boolean {
if fa.Number == 0 {
return "FALSE"
}
return "TRUE"
}
return fmt.Sprintf("%g", fa.Number)
case ArgString:
return fa.String
case ArgError:
return fa.Error
}
return
}
// ToNumber returns a formula argument with number data type.
func (fa formulaArg) ToNumber() formulaArg {
var n float64
var err error
switch fa.Type {
case ArgString:
n, err = strconv.ParseFloat(fa.String, 64)
if err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
case ArgNumber:
n = fa.Number
}
return newNumberFormulaArg(n)
}
// ToBool returns a formula argument with boolean data type.
func (fa formulaArg) ToBool() formulaArg {
var b bool
var err error
switch fa.Type {
case ArgString:
b, err = strconv.ParseBool(fa.String)
if err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
case ArgNumber:
if fa.Boolean && fa.Number == 1 {
b = true
}
}
return newBoolFormulaArg(b)
}
// ToList returns a formula argument with array data type.
func (fa formulaArg) ToList() []formulaArg {
switch fa.Type {
case ArgMatrix:
var args []formulaArg
for _, row := range fa.Matrix {
args = append(args, row...)
}
return args
case ArgList:
return fa.List
case ArgNumber, ArgString, ArgError, ArgUnknown:
return []formulaArg{fa}
}
return nil
}
// formulaFuncs is the type of the formula functions.
type formulaFuncs struct {
f *File
ctx *calcContext
sheet, cell string
}
// CalcCellValue provides a function to get calculated cell value. This feature
// is currently in working processing. Iterative calculation, implicit
// intersection, explicit intersection, array formula, table formula and some
// other formulas are not supported currently.
//
// Supported formula functions:
//
// ABS
// ACCRINT
// ACCRINTM
// ACOS
// ACOSH
// ACOT
// ACOTH
// ADDRESS
// AMORDEGRC
// AMORLINC
// AND
// ARABIC
// ASIN
// ASINH
// ATAN
// ATAN2
// ATANH
// AVEDEV
// AVERAGE
// AVERAGEA
// AVERAGEIF
// AVERAGEIFS
// BASE
// BESSELI
// BESSELJ
// BESSELK
// BESSELY
// BETADIST
// BETA.DIST
// BETAINV
// BETA.INV
// BIN2DEC
// BIN2HEX
// BIN2OCT
// BINOMDIST
// BINOM.DIST
// BINOM.DIST.RANGE
// BINOM.INV
// BITAND
// BITLSHIFT
// BITOR
// BITRSHIFT
// BITXOR
// CEILING
// CEILING.MATH
// CEILING.PRECISE
// CHAR
// CHIDIST
// CHIINV
// CHITEST
// CHISQ.DIST
// CHISQ.DIST.RT
// CHISQ.INV
// CHISQ.INV.RT
// CHISQ.TEST
// CHOOSE
// CLEAN
// CODE
// COLUMN
// COLUMNS
// COMBIN
// COMBINA
// COMPLEX
// CONCAT
// CONCATENATE
// CONFIDENCE
// CONFIDENCE.NORM
// CONFIDENCE.T
// CONVERT
// CORREL
// COS
// COSH
// COT
// COTH
// COUNT
// COUNTA
// COUNTBLANK
// COUNTIF
// COUNTIFS
// COUPDAYBS
// COUPDAYS
// COUPDAYSNC
// COUPNCD
// COUPNUM
// COUPPCD
// COVAR
// COVARIANCE.P
// COVARIANCE.S
// CRITBINOM
// CSC
// CSCH
// CUMIPMT
// CUMPRINC
// DATE
// DATEDIF
// DATEVALUE
// DAVERAGE
// DAY
// DAYS
// DAYS360
// DB
// DCOUNT
// DCOUNTA
// DDB
// DEC2BIN
// DEC2HEX
// DEC2OCT
// DECIMAL
// DEGREES
// DELTA
// DEVSQ
// DGET
// DISC
// DMAX
// DMIN
// DOLLARDE
// DOLLARFR
// DPRODUCT
// DSTDEV
// DSTDEVP
// DSUM
// DURATION
// DVAR
// DVARP
// EFFECT
// EDATE
// ENCODEURL
// EOMONTH
// ERF
// ERF.PRECISE
// ERFC
// ERFC.PRECISE
// ERROR.TYPE
// EUROCONVERT
// EVEN
// EXACT
// EXP
// EXPON.DIST
// EXPONDIST
// FACT
// FACTDOUBLE
// FALSE
// F.DIST
// F.DIST.RT
// FDIST
// FIND
// FINDB
// F.INV
// F.INV.RT
// FINV
// FISHER
// FISHERINV
// FIXED
// FLOOR
// FLOOR.MATH
// FLOOR.PRECISE
// FORMULATEXT
// F.TEST
// FTEST
// FV
// FVSCHEDULE
// GAMMA
// GAMMA.DIST
// GAMMADIST
// GAMMA.INV
// GAMMAINV
// GAMMALN
// GAMMALN.PRECISE
// GAUSS
// GCD
// GEOMEAN
// GESTEP
// GROWTH
// HARMEAN
// HEX2BIN
// HEX2DEC
// HEX2OCT
// HLOOKUP
// HOUR
// HYPERLINK
// HYPGEOM.DIST
// HYPGEOMDIST
// IF
// IFERROR
// IFNA
// IFS
// IMABS
// IMAGINARY
// IMARGUMENT
// IMCONJUGATE
// IMCOS
// IMCOSH
// IMCOT
// IMCSC
// IMCSCH
// IMDIV
// IMEXP
// IMLN
// IMLOG10
// IMLOG2
// IMPOWER
// IMPRODUCT
// IMREAL
// IMSEC
// IMSECH
// IMSIN
// IMSINH
// IMSQRT
// IMSUB
// IMSUM
// IMTAN
// INDEX
// INDIRECT
// INT
// INTRATE
// IPMT
// IRR
// ISBLANK
// ISERR
// ISERROR
// ISEVEN
// ISFORMULA
// ISLOGICAL
// ISNA
// ISNONTEXT
// ISNUMBER
// ISODD
// ISREF
// ISTEXT
// ISO.CEILING
// ISOWEEKNUM
// ISPMT
// KURT
// LARGE
// LCM
// LEFT
// LEFTB
// LEN
// LENB
// LN
// LOG
// LOG10
// LOGINV
// LOGNORM.DIST
// LOGNORMDIST
// LOGNORM.INV
// LOOKUP
// LOWER
// MATCH
// MAX
// MAXA
// MAXIFS
// MDETERM
// MDURATION
// MEDIAN
// MID
// MIDB
// MIN
// MINA
// MINIFS
// MINUTE
// MINVERSE
// MIRR
// MMULT
// MOD
// MODE
// MODE.MULT
// MODE.SNGL
// MONTH
// MROUND
// MULTINOMIAL
// MUNIT
// N
// NA
// NEGBINOM.DIST
// NEGBINOMDIST
// NETWORKDAYS
// NETWORKDAYS.INTL
// NOMINAL
// NORM.DIST
// NORMDIST
// NORM.INV
// NORMINV
// NORM.S.DIST
// NORMSDIST
// NORM.S.INV
// NORMSINV
// NOT
// NOW
// NPER
// NPV
// OCT2BIN
// OCT2DEC
// OCT2HEX
// ODD
// ODDFPRICE
// OR
// PDURATION
// PEARSON
// PERCENTILE.EXC
// PERCENTILE.INC
// PERCENTILE
// PERCENTRANK.EXC
// PERCENTRANK.INC
// PERCENTRANK
// PERMUT
// PERMUTATIONA
// PHI
// PI
// PMT
// POISSON.DIST
// POISSON
// POWER
// PPMT
// PRICE
// PRICEDISC
// PRICEMAT
// PRODUCT
// PROPER
// PV
// QUARTILE
// QUARTILE.EXC
// QUARTILE.INC
// QUOTIENT
// RADIANS
// RAND
// RANDBETWEEN
// RANK
// RANK.EQ
// RATE
// RECEIVED
// REPLACE
// REPLACEB
// REPT
// RIGHT
// RIGHTB
// ROMAN
// ROUND
// ROUNDDOWN
// ROUNDUP
// ROW
// ROWS
// RRI
// RSQ
// SEC
// SECH
// SECOND
// SERIESSUM
// SHEET
// SHEETS
// SIGN
// SIN
// SINH
// SKEW
// SKEW.P
// SLN
// SLOPE
// SMALL
// SQRT
// SQRTPI
// STANDARDIZE
// STDEV
// STDEV.P
// STDEV.S
// STDEVA
// STDEVP
// STDEVPA
// STEYX
// SUBSTITUTE
// SUM
// SUMIF
// SUMIFS
// SUMPRODUCT
// SUMSQ
// SUMX2MY2
// SUMX2PY2
// SUMXMY2
// SWITCH
// SYD
// T
// TAN
// TANH
// TBILLEQ
// TBILLPRICE
// TBILLYIELD
// T.DIST
// T.DIST.2T
// T.DIST.RT
// TDIST
// TEXTJOIN
// TIME
// TIMEVALUE
// T.INV
// T.INV.2T
// TINV
// TODAY
// TRANSPOSE
// TREND
// TRIM
// TRIMMEAN
// TRUE
// TRUNC
// T.TEST
// TTEST
// TYPE
// UNICHAR
// UNICODE
// UPPER
// VALUE
// VAR
// VAR.P
// VAR.S
// VARA
// VARP
// VARPA
// VDB
// VLOOKUP
// WEEKDAY
// WEEKNUM
// WEIBULL
// WEIBULL.DIST
// WORKDAY
// WORKDAY.INTL
// XIRR
// XLOOKUP
// XNPV
// XOR
// YEAR
// YEARFRAC
// YIELD
// YIELDDISC
// YIELDMAT
// Z.TEST
// ZTEST
//
func (f *File) CalcCellValue(sheet, cell string) (result string, err error) {
return f.calcCellValue(&calcContext{
entry: fmt.Sprintf("%s!%s", sheet, cell),
iterations: make(map[string]uint),
}, sheet, cell)
}
func (f *File) calcCellValue(ctx *calcContext, sheet, cell string) (result string, err error) {
var (
formula string
token formulaArg
)
if formula, err = f.GetCellFormula(sheet, cell); err != nil {
return
}
ps := efp.ExcelParser()
tokens := ps.Parse(formula)
if tokens == nil {
return
}
if token, err = f.evalInfixExp(ctx, sheet, cell, tokens); err != nil {
return
}
result = token.Value()
isNum, precision := isNumeric(result)
if isNum && (precision > 15 || precision == 0) {
num := roundPrecision(result, -1)
result = strings.ToUpper(num)
}
return
}
// getPriority calculate arithmetic operator priority.
func getPriority(token efp.Token) (pri int) {
pri = tokenPriority[token.TValue]
if token.TValue == "-" && token.TType == efp.TokenTypeOperatorPrefix {
pri = 6
}
if isBeginParenthesesToken(token) { // (
pri = 0
}
return
}
// newNumberFormulaArg constructs a number formula argument.
func newNumberFormulaArg(n float64) formulaArg {
if math.IsNaN(n) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return formulaArg{Type: ArgNumber, Number: n}
}
// newStringFormulaArg constructs a string formula argument.
func newStringFormulaArg(s string) formulaArg {
return formulaArg{Type: ArgString, String: s}
}
// newMatrixFormulaArg constructs a matrix formula argument.
func newMatrixFormulaArg(m [][]formulaArg) formulaArg {
return formulaArg{Type: ArgMatrix, Matrix: m}
}
// newListFormulaArg create a list formula argument.
func newListFormulaArg(l []formulaArg) formulaArg {
return formulaArg{Type: ArgList, List: l}
}
// newBoolFormulaArg constructs a boolean formula argument.
func newBoolFormulaArg(b bool) formulaArg {
var n float64
if b {
n = 1
}
return formulaArg{Type: ArgNumber, Number: n, Boolean: true}
}
// newErrorFormulaArg create an error formula argument of a given type with a
// specified error message.
func newErrorFormulaArg(formulaError, msg string) formulaArg {
return formulaArg{Type: ArgError, String: formulaError, Error: msg}
}
// newEmptyFormulaArg create an empty formula argument.
func newEmptyFormulaArg() formulaArg {
return formulaArg{Type: ArgEmpty}
}
// evalInfixExp evaluate syntax analysis by given infix expression after
// lexical analysis. Evaluate an infix expression containing formulas by
// stacks:
//
// opd - Operand
// opt - Operator
// opf - Operation formula
// opfd - Operand of the operation formula
// opft - Operator of the operation formula
// args - Arguments list of the operation formula
//
// TODO: handle subtypes: Nothing, Text, Logical, Error, Concatenation, Intersection, Union
//
func (f *File) evalInfixExp(ctx *calcContext, sheet, cell string, tokens []efp.Token) (formulaArg, error) {
var err error
opdStack, optStack, opfStack, opfdStack, opftStack, argsStack := NewStack(), NewStack(), NewStack(), NewStack(), NewStack(), NewStack()
var inArray, inArrayRow bool
var arrayRow []formulaArg
for i := 0; i < len(tokens); i++ {
token := tokens[i]
// out of function stack
if opfStack.Len() == 0 {
if err = f.parseToken(ctx, sheet, token, opdStack, optStack); err != nil {
return newEmptyFormulaArg(), err
}
}
// function start
if isFunctionStartToken(token) {
if token.TValue == "ARRAY" {
inArray = true
continue
}
if token.TValue == "ARRAYROW" {
inArrayRow = true
continue
}
opfStack.Push(token)
argsStack.Push(list.New().Init())
opftStack.Push(token) // to know which operators belong to a function use the function as a separator
continue
}
// in function stack, walk 2 token at once
if opfStack.Len() > 0 {
var nextToken efp.Token
if i+1 < len(tokens) {
nextToken = tokens[i+1]
}
// current token is args or range, skip next token, order required: parse reference first
if token.TSubType == efp.TokenSubTypeRange {
if opftStack.Peek().(efp.Token) != opfStack.Peek().(efp.Token) {
refTo := f.getDefinedNameRefTo(token.TValue, sheet)
if refTo != "" {
token.TValue = refTo
}
// parse reference: must reference at here
result, err := f.parseReference(ctx, sheet, token.TValue)
if err != nil {
return result, err
}
if result.Type != ArgString {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE), errors.New(formulaErrorVALUE)
}
opfdStack.Push(result)
continue
}
if nextToken.TType == efp.TokenTypeArgument || nextToken.TType == efp.TokenTypeFunction {
// parse reference: reference or range at here
refTo := f.getDefinedNameRefTo(token.TValue, sheet)
if refTo != "" {
token.TValue = refTo
}
result, err := f.parseReference(ctx, sheet, token.TValue)
if err != nil {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE), err
}
if result.Type == ArgUnknown {
return newEmptyFormulaArg(), errors.New(formulaErrorVALUE)
}
// when current token is range, next token is argument and opfdStack not empty,
// should push value to opfdStack and continue
if nextToken.TType == efp.TokenTypeArgument && !opfdStack.Empty() {
opfdStack.Push(result)
continue
}
argsStack.Peek().(*list.List).PushBack(result)
continue
}
}
if isEndParenthesesToken(token) && isBeginParenthesesToken(opftStack.Peek().(efp.Token)) {
if arg := argsStack.Peek().(*list.List).Back(); arg != nil {
opfdStack.Push(arg.Value.(formulaArg))
argsStack.Peek().(*list.List).Remove(arg)
}
}
// check current token is opft
if err = f.parseToken(ctx, sheet, token, opfdStack, opftStack); err != nil {
return newEmptyFormulaArg(), err
}
// current token is arg
if token.TType == efp.TokenTypeArgument {
for opftStack.Peek().(efp.Token) != opfStack.Peek().(efp.Token) {
// calculate trigger
topOpt := opftStack.Peek().(efp.Token)
if err := calculate(opfdStack, topOpt); err != nil {
argsStack.Peek().(*list.List).PushFront(newErrorFormulaArg(formulaErrorVALUE, err.Error()))
}
opftStack.Pop()
}
if !opfdStack.Empty() {
argsStack.Peek().(*list.List).PushBack(opfdStack.Pop().(formulaArg))
}
continue
}
// current token is logical
if token.TType == efp.TokenTypeOperand && token.TSubType == efp.TokenSubTypeLogical {
argsStack.Peek().(*list.List).PushBack(newStringFormulaArg(token.TValue))
}
if inArrayRow && isOperand(token) {
arrayRow = append(arrayRow, tokenToFormulaArg(token))
continue
}
if inArrayRow && isFunctionStopToken(token) {
inArrayRow = false
continue
}
if inArray && isFunctionStopToken(token) {
argsStack.Peek().(*list.List).PushBack(opfdStack.Pop())
arrayRow, inArray = []formulaArg{}, false
continue
}
if err = f.evalInfixExpFunc(ctx, sheet, cell, token, nextToken, opfStack, opdStack, opftStack, opfdStack, argsStack); err != nil {
return newEmptyFormulaArg(), err
}
}
}
for optStack.Len() != 0 {
topOpt := optStack.Peek().(efp.Token)
if err = calculate(opdStack, topOpt); err != nil {
return newEmptyFormulaArg(), err
}
optStack.Pop()
}
if opdStack.Len() == 0 {
return newEmptyFormulaArg(), ErrInvalidFormula
}
return opdStack.Peek().(formulaArg), err
}
// evalInfixExpFunc evaluate formula function in the infix expression.
func (f *File) evalInfixExpFunc(ctx *calcContext, sheet, cell string, token, nextToken efp.Token, opfStack, opdStack, opftStack, opfdStack, argsStack *Stack) error {
if !isFunctionStopToken(token) {
return nil
}
prepareEvalInfixExp(opfStack, opftStack, opfdStack, argsStack)
// call formula function to evaluate
arg := callFuncByName(&formulaFuncs{f: f, sheet: sheet, cell: cell, ctx: ctx}, strings.NewReplacer(
"_xlfn.", "", ".", "dot").Replace(opfStack.Peek().(efp.Token).TValue),
[]reflect.Value{reflect.ValueOf(argsStack.Peek().(*list.List))})
if arg.Type == ArgError && opfStack.Len() == 1 {
return errors.New(arg.Value())
}
argsStack.Pop()
opftStack.Pop() // remove current function separator
opfStack.Pop()
if opfStack.Len() > 0 { // still in function stack
if nextToken.TType == efp.TokenTypeOperatorInfix || (opftStack.Len() > 1 && opfdStack.Len() > 0) {
// mathematics calculate in formula function
opfdStack.Push(arg)
} else {
argsStack.Peek().(*list.List).PushBack(arg)
}
} else {
val := arg.Value()
if arg.Type == ArgMatrix && len(arg.Matrix) > 0 && len(arg.Matrix[0]) > 0 {
val = arg.Matrix[0][0].Value()
}
opdStack.Push(newStringFormulaArg(val))
}
return nil
}
// prepareEvalInfixExp check the token and stack state for formula function
// evaluate.
func prepareEvalInfixExp(opfStack, opftStack, opfdStack, argsStack *Stack) {
// current token is function stop
for opftStack.Peek().(efp.Token) != opfStack.Peek().(efp.Token) {
// calculate trigger
topOpt := opftStack.Peek().(efp.Token)
if err := calculate(opfdStack, topOpt); err != nil {
argsStack.Peek().(*list.List).PushBack(newErrorFormulaArg(err.Error(), err.Error()))
opftStack.Pop()
continue
}
opftStack.Pop()
}
argument := true
if opftStack.Len() > 2 && opfdStack.Len() == 1 {
topOpt := opftStack.Pop()
if opftStack.Peek().(efp.Token).TType == efp.TokenTypeOperatorInfix {
argument = false
}
opftStack.Push(topOpt)
}
// push opfd to args
if argument && opfdStack.Len() > 0 {
argsStack.Peek().(*list.List).PushBack(opfdStack.Pop().(formulaArg))
}
}
// calcPow evaluate exponentiation arithmetic operations.
func calcPow(rOpd, lOpd formulaArg, opdStack *Stack) error {
lOpdVal := lOpd.ToNumber()
if lOpdVal.Type != ArgNumber {
return errors.New(lOpdVal.Value())
}
rOpdVal := rOpd.ToNumber()
if rOpdVal.Type != ArgNumber {
return errors.New(rOpdVal.Value())
}
opdStack.Push(newNumberFormulaArg(math.Pow(lOpdVal.Number, rOpdVal.Number)))
return nil
}
// calcEq evaluate equal arithmetic operations.
func calcEq(rOpd, lOpd formulaArg, opdStack *Stack) error {
opdStack.Push(newBoolFormulaArg(rOpd.Value() == lOpd.Value()))
return nil
}
// calcNEq evaluate not equal arithmetic operations.
func calcNEq(rOpd, lOpd formulaArg, opdStack *Stack) error {
opdStack.Push(newBoolFormulaArg(rOpd.Value() != lOpd.Value()))
return nil
}
// calcL evaluate less than arithmetic operations.
func calcL(rOpd, lOpd formulaArg, opdStack *Stack) error {
if rOpd.Type == ArgNumber && lOpd.Type == ArgNumber {
opdStack.Push(newBoolFormulaArg(lOpd.Number < rOpd.Number))
}
if rOpd.Type == ArgString && lOpd.Type == ArgString {
opdStack.Push(newBoolFormulaArg(strings.Compare(lOpd.Value(), rOpd.Value()) == -1))
}
if rOpd.Type == ArgNumber && lOpd.Type == ArgString {
opdStack.Push(newBoolFormulaArg(false))
}
if rOpd.Type == ArgString && lOpd.Type == ArgNumber {
opdStack.Push(newBoolFormulaArg(true))
}
return nil
}
// calcLe evaluate less than or equal arithmetic operations.
func calcLe(rOpd, lOpd formulaArg, opdStack *Stack) error {
if rOpd.Type == ArgNumber && lOpd.Type == ArgNumber {
opdStack.Push(newBoolFormulaArg(lOpd.Number <= rOpd.Number))
}
if rOpd.Type == ArgString && lOpd.Type == ArgString {
opdStack.Push(newBoolFormulaArg(strings.Compare(lOpd.Value(), rOpd.Value()) != 1))
}
if rOpd.Type == ArgNumber && lOpd.Type == ArgString {
opdStack.Push(newBoolFormulaArg(false))
}
if rOpd.Type == ArgString && lOpd.Type == ArgNumber {
opdStack.Push(newBoolFormulaArg(true))
}
return nil
}
// calcG evaluate greater than or equal arithmetic operations.
func calcG(rOpd, lOpd formulaArg, opdStack *Stack) error {
if rOpd.Type == ArgNumber && lOpd.Type == ArgNumber {
opdStack.Push(newBoolFormulaArg(lOpd.Number > rOpd.Number))
}
if rOpd.Type == ArgString && lOpd.Type == ArgString {
opdStack.Push(newBoolFormulaArg(strings.Compare(lOpd.Value(), rOpd.Value()) == 1))
}
if rOpd.Type == ArgNumber && lOpd.Type == ArgString {
opdStack.Push(newBoolFormulaArg(true))
}
if rOpd.Type == ArgString && lOpd.Type == ArgNumber {
opdStack.Push(newBoolFormulaArg(false))
}
return nil
}
// calcGe evaluate greater than or equal arithmetic operations.
func calcGe(rOpd, lOpd formulaArg, opdStack *Stack) error {
if rOpd.Type == ArgNumber && lOpd.Type == ArgNumber {
opdStack.Push(newBoolFormulaArg(lOpd.Number >= rOpd.Number))
}
if rOpd.Type == ArgString && lOpd.Type == ArgString {
opdStack.Push(newBoolFormulaArg(strings.Compare(lOpd.Value(), rOpd.Value()) != -1))
}
if rOpd.Type == ArgNumber && lOpd.Type == ArgString {
opdStack.Push(newBoolFormulaArg(true))
}
if rOpd.Type == ArgString && lOpd.Type == ArgNumber {
opdStack.Push(newBoolFormulaArg(false))
}
return nil
}
// calcSplice evaluate splice '&' operations.
func calcSplice(rOpd, lOpd formulaArg, opdStack *Stack) error {
opdStack.Push(newStringFormulaArg(lOpd.Value() + rOpd.Value()))
return nil
}
// calcAdd evaluate addition arithmetic operations.
func calcAdd(rOpd, lOpd formulaArg, opdStack *Stack) error {
lOpdVal := lOpd.ToNumber()
if lOpdVal.Type != ArgNumber {
return errors.New(lOpdVal.Value())
}
rOpdVal := rOpd.ToNumber()
if rOpdVal.Type != ArgNumber {
return errors.New(rOpdVal.Value())
}
opdStack.Push(newNumberFormulaArg(lOpdVal.Number + rOpdVal.Number))
return nil
}
// calcSubtract evaluate subtraction arithmetic operations.
func calcSubtract(rOpd, lOpd formulaArg, opdStack *Stack) error {
lOpdVal := lOpd.ToNumber()
if lOpdVal.Type != ArgNumber {
return errors.New(lOpdVal.Value())
}
rOpdVal := rOpd.ToNumber()
if rOpdVal.Type != ArgNumber {
return errors.New(rOpdVal.Value())
}
opdStack.Push(newNumberFormulaArg(lOpdVal.Number - rOpdVal.Number))
return nil
}
// calcMultiply evaluate multiplication arithmetic operations.
func calcMultiply(rOpd, lOpd formulaArg, opdStack *Stack) error {
lOpdVal := lOpd.ToNumber()
if lOpdVal.Type != ArgNumber {
return errors.New(lOpdVal.Value())
}
rOpdVal := rOpd.ToNumber()
if rOpdVal.Type != ArgNumber {
return errors.New(rOpdVal.Value())
}
opdStack.Push(newNumberFormulaArg(lOpdVal.Number * rOpdVal.Number))
return nil
}
// calcDiv evaluate division arithmetic operations.
func calcDiv(rOpd, lOpd formulaArg, opdStack *Stack) error {
lOpdVal := lOpd.ToNumber()
if lOpdVal.Type != ArgNumber {
return errors.New(lOpdVal.Value())
}
rOpdVal := rOpd.ToNumber()
if rOpdVal.Type != ArgNumber {
return errors.New(rOpdVal.Value())
}
if rOpdVal.Number == 0 {
return errors.New(formulaErrorDIV)
}
opdStack.Push(newNumberFormulaArg(lOpdVal.Number / rOpdVal.Number))
return nil
}
// calculate evaluate basic arithmetic operations.
func calculate(opdStack *Stack, opt efp.Token) error {
if opt.TValue == "-" && opt.TType == efp.TokenTypeOperatorPrefix {
if opdStack.Len() < 1 {
return ErrInvalidFormula
}
opd := opdStack.Pop().(formulaArg)
opdStack.Push(newNumberFormulaArg(0 - opd.Number))
}
if opt.TValue == "-" && opt.TType == efp.TokenTypeOperatorInfix {
if opdStack.Len() < 2 {
return ErrInvalidFormula
}
rOpd := opdStack.Pop().(formulaArg)
lOpd := opdStack.Pop().(formulaArg)
if err := calcSubtract(rOpd, lOpd, opdStack); err != nil {
return err
}
}
tokenCalcFunc := map[string]func(rOpd, lOpd formulaArg, opdStack *Stack) error{
"^": calcPow,
"*": calcMultiply,
"/": calcDiv,
"+": calcAdd,
"=": calcEq,
"<>": calcNEq,
"<": calcL,
"<=": calcLe,
">": calcG,
">=": calcGe,
"&": calcSplice,
}
fn, ok := tokenCalcFunc[opt.TValue]
if ok {
if opdStack.Len() < 2 {
return ErrInvalidFormula
}
rOpd := opdStack.Pop().(formulaArg)
lOpd := opdStack.Pop().(formulaArg)
if rOpd.Type == ArgError {
return errors.New(rOpd.Value())
}
if lOpd.Type == ArgError {
return errors.New(lOpd.Value())
}
if err := fn(rOpd, lOpd, opdStack); err != nil {
return err
}
}
return nil
}
// parseOperatorPrefixToken parse operator prefix token.
func (f *File) parseOperatorPrefixToken(optStack, opdStack *Stack, token efp.Token) (err error) {
if optStack.Len() == 0 {
optStack.Push(token)
} else {
tokenPriority := getPriority(token)
topOpt := optStack.Peek().(efp.Token)
topOptPriority := getPriority(topOpt)
if tokenPriority > topOptPriority {
optStack.Push(token)
} else {
for tokenPriority <= topOptPriority {
optStack.Pop()
if err = calculate(opdStack, topOpt); err != nil {
return
}
if optStack.Len() > 0 {
topOpt = optStack.Peek().(efp.Token)
topOptPriority = getPriority(topOpt)
continue
}
break
}
optStack.Push(token)
}
}
return
}
// isFunctionStartToken determine if the token is function start.
func isFunctionStartToken(token efp.Token) bool {
return token.TType == efp.TokenTypeFunction && token.TSubType == efp.TokenSubTypeStart
}
// isFunctionStopToken determine if the token is function stop.
func isFunctionStopToken(token efp.Token) bool {
return token.TType == efp.TokenTypeFunction && token.TSubType == efp.TokenSubTypeStop
}
// isBeginParenthesesToken determine if the token is begin parentheses: (.
func isBeginParenthesesToken(token efp.Token) bool {
return token.TType == efp.TokenTypeSubexpression && token.TSubType == efp.TokenSubTypeStart
}
// isEndParenthesesToken determine if the token is end parentheses: ).
func isEndParenthesesToken(token efp.Token) bool {
return token.TType == efp.TokenTypeSubexpression && token.TSubType == efp.TokenSubTypeStop
}
// isOperatorPrefixToken determine if the token is parse operator prefix
// token.
func isOperatorPrefixToken(token efp.Token) bool {
_, ok := tokenPriority[token.TValue]
return (token.TValue == "-" && token.TType == efp.TokenTypeOperatorPrefix) || (ok && token.TType == efp.TokenTypeOperatorInfix)
}
// isOperand determine if the token is parse operand.
func isOperand(token efp.Token) bool {
return token.TType == efp.TokenTypeOperand && (token.TSubType == efp.TokenSubTypeNumber || token.TSubType == efp.TokenSubTypeText)
}
// tokenToFormulaArg create a formula argument by given token.
func tokenToFormulaArg(token efp.Token) formulaArg {
if token.TSubType == efp.TokenSubTypeNumber {
num, _ := strconv.ParseFloat(token.TValue, 64)
return newNumberFormulaArg(num)
}
return newStringFormulaArg(token.TValue)
}
// parseToken parse basic arithmetic operator priority and evaluate based on
// operators and operands.
func (f *File) parseToken(ctx *calcContext, sheet string, token efp.Token, opdStack, optStack *Stack) error {
// parse reference: must reference at here
if token.TSubType == efp.TokenSubTypeRange {
refTo := f.getDefinedNameRefTo(token.TValue, sheet)
if refTo != "" {
token.TValue = refTo
}
result, err := f.parseReference(ctx, sheet, token.TValue)
if err != nil {
return errors.New(formulaErrorNAME)
}
if result.Type != ArgString {
return errors.New(formulaErrorVALUE)
}
token.TValue = result.String
token.TType = efp.TokenTypeOperand
token.TSubType = efp.TokenSubTypeText
}
if isOperatorPrefixToken(token) {
if err := f.parseOperatorPrefixToken(optStack, opdStack, token); err != nil {
return err
}
}
if isBeginParenthesesToken(token) { // (
optStack.Push(token)
}
if isEndParenthesesToken(token) { // )
for !isBeginParenthesesToken(optStack.Peek().(efp.Token)) { // != (
topOpt := optStack.Peek().(efp.Token)
if err := calculate(opdStack, topOpt); err != nil {
return err
}
optStack.Pop()
}
optStack.Pop()
}
if token.TType == efp.TokenTypeOperatorPostfix && !opdStack.Empty() {
topOpd := opdStack.Pop().(formulaArg)
opdStack.Push(newNumberFormulaArg(topOpd.Number / 100))
}
// opd
if isOperand(token) {
opdStack.Push(tokenToFormulaArg(token))
}
return nil
}
// parseReference parse reference and extract values by given reference
// characters and default sheet name.
func (f *File) parseReference(ctx *calcContext, sheet, reference string) (arg formulaArg, err error) {
reference = strings.ReplaceAll(reference, "$", "")
refs, cellRanges, cellRefs := list.New(), list.New(), list.New()
for _, ref := range strings.Split(reference, ":") {
tokens := strings.Split(ref, "!")
cr := cellRef{}
if len(tokens) == 2 { // have a worksheet name
cr.Sheet = tokens[0]
// cast to cell coordinates
if cr.Col, cr.Row, err = CellNameToCoordinates(tokens[1]); err != nil {
// cast to column
if cr.Col, err = ColumnNameToNumber(tokens[1]); err != nil {
// cast to row
if cr.Row, err = strconv.Atoi(tokens[1]); err != nil {
err = newInvalidColumnNameError(tokens[1])
return
}
cr.Col = MaxColumns
}
}
if refs.Len() > 0 {
e := refs.Back()
cellRefs.PushBack(e.Value.(cellRef))
refs.Remove(e)
}
refs.PushBack(cr)
continue
}
// cast to cell coordinates
if cr.Col, cr.Row, err = CellNameToCoordinates(tokens[0]); err != nil {
// cast to column
if cr.Col, err = ColumnNameToNumber(tokens[0]); err != nil {
// cast to row
if cr.Row, err = strconv.Atoi(tokens[0]); err != nil {
err = newInvalidColumnNameError(tokens[0])
return
}
cr.Col = MaxColumns
}
cellRanges.PushBack(cellRange{
From: cellRef{Sheet: sheet, Col: cr.Col, Row: 1},
To: cellRef{Sheet: sheet, Col: cr.Col, Row: TotalRows},
})
cellRefs.Init()
arg, err = f.rangeResolver(ctx, cellRefs, cellRanges)
return
}
e := refs.Back()
if e == nil {
cr.Sheet = sheet
refs.PushBack(cr)
continue
}
cellRanges.PushBack(cellRange{
From: e.Value.(cellRef),
To: cr,
})
refs.Remove(e)
}
if refs.Len() > 0 {
e := refs.Back()
cellRefs.PushBack(e.Value.(cellRef))
refs.Remove(e)
}
arg, err = f.rangeResolver(ctx, cellRefs, cellRanges)
return
}
// prepareValueRange prepare value range.
func prepareValueRange(cr cellRange, valueRange []int) {
if cr.From.Row < valueRange[0] || valueRange[0] == 0 {
valueRange[0] = cr.From.Row
}
if cr.From.Col < valueRange[2] || valueRange[2] == 0 {
valueRange[2] = cr.From.Col
}
if cr.To.Row > valueRange[1] || valueRange[1] == 0 {
valueRange[1] = cr.To.Row
}
if cr.To.Col > valueRange[3] || valueRange[3] == 0 {
valueRange[3] = cr.To.Col
}
}
// prepareValueRef prepare value reference.
func prepareValueRef(cr cellRef, valueRange []int) {
if cr.Row < valueRange[0] || valueRange[0] == 0 {
valueRange[0] = cr.Row
}
if cr.Col < valueRange[2] || valueRange[2] == 0 {
valueRange[2] = cr.Col
}
if cr.Row > valueRange[1] || valueRange[1] == 0 {
valueRange[1] = cr.Row
}
if cr.Col > valueRange[3] || valueRange[3] == 0 {
valueRange[3] = cr.Col
}
}
// cellResolver calc cell value by given worksheet name, cell reference and context.
func (f *File) cellResolver(ctx *calcContext, sheet, cell string) (string, error) {
var value string
ref := fmt.Sprintf("%s!%s", sheet, cell)
if formula, _ := f.GetCellFormula(sheet, cell); len(formula) != 0 {
ctx.Lock()
if ctx.entry != ref && ctx.iterations[ref] <= f.options.MaxCalcIterations {
ctx.iterations[ref]++
ctx.Unlock()
value, _ = f.calcCellValue(ctx, sheet, cell)
return value, nil
}
ctx.Unlock()
}
return f.GetCellValue(sheet, cell, Options{RawCellValue: true})
}
// rangeResolver extract value as string from given reference and range list.
// This function will not ignore the empty cell. For example, A1:A2:A2:B3 will
// be reference A1:B3.
func (f *File) rangeResolver(ctx *calcContext, cellRefs, cellRanges *list.List) (arg formulaArg, err error) {
arg.cellRefs, arg.cellRanges = cellRefs, cellRanges
// value range order: from row, to row, from column, to column
valueRange := []int{0, 0, 0, 0}
var sheet string
// prepare value range
for temp := cellRanges.Front(); temp != nil; temp = temp.Next() {
cr := temp.Value.(cellRange)
if cr.From.Sheet != cr.To.Sheet {
err = errors.New(formulaErrorVALUE)
}
rng := []int{cr.From.Col, cr.From.Row, cr.To.Col, cr.To.Row}
_ = sortCoordinates(rng)
cr.From.Col, cr.From.Row, cr.To.Col, cr.To.Row = rng[0], rng[1], rng[2], rng[3]
prepareValueRange(cr, valueRange)
if cr.From.Sheet != "" {
sheet = cr.From.Sheet
}
}
for temp := cellRefs.Front(); temp != nil; temp = temp.Next() {
cr := temp.Value.(cellRef)
if cr.Sheet != "" {
sheet = cr.Sheet
}
prepareValueRef(cr, valueRange)
}
// extract value from ranges
if cellRanges.Len() > 0 {
arg.Type = ArgMatrix
for row := valueRange[0]; row <= valueRange[1]; row++ {
var matrixRow []formulaArg
for col := valueRange[2]; col <= valueRange[3]; col++ {
var cell, value string
if cell, err = CoordinatesToCellName(col, row); err != nil {
return
}
if value, err = f.cellResolver(ctx, sheet, cell); err != nil {
return
}
matrixRow = append(matrixRow, formulaArg{
String: value,
Type: ArgString,
})
}
arg.Matrix = append(arg.Matrix, matrixRow)
}
return
}
// extract value from references
for temp := cellRefs.Front(); temp != nil; temp = temp.Next() {
cr := temp.Value.(cellRef)
var cell string
if cell, err = CoordinatesToCellName(cr.Col, cr.Row); err != nil {
return
}
if arg.String, err = f.cellResolver(ctx, cr.Sheet, cell); err != nil {
return
}
arg.Type = ArgString
}
return
}
// callFuncByName calls the no error or only error return function with
// reflect by given receiver, name and parameters.
func callFuncByName(receiver interface{}, name string, params []reflect.Value) (arg formulaArg) {
function := reflect.ValueOf(receiver).MethodByName(name)
if function.IsValid() {
rt := function.Call(params)
if len(rt) == 0 {
return
}
arg = rt[0].Interface().(formulaArg)
return
}
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("not support %s function", name))
}
// formulaCriteriaParser parse formula criteria.
func formulaCriteriaParser(exp string) (fc *formulaCriteria) {
fc = &formulaCriteria{}
if exp == "" {
return
}
if match := regexp.MustCompile(`^(\d+)$`).FindStringSubmatch(exp); len(match) > 1 {
fc.Type, fc.Condition = criteriaEq, match[1]
return
}
if match := regexp.MustCompile(`^=(.*)$`).FindStringSubmatch(exp); len(match) > 1 {
fc.Type, fc.Condition = criteriaEq, match[1]
return
}
if match := regexp.MustCompile(`^<>(.*)$`).FindStringSubmatch(exp); len(match) > 1 {
fc.Type, fc.Condition = criteriaNe, match[1]
return
}
if match := regexp.MustCompile(`^<=(.*)$`).FindStringSubmatch(exp); len(match) > 1 {
fc.Type, fc.Condition = criteriaLe, match[1]
return
}
if match := regexp.MustCompile(`^>=(.*)$`).FindStringSubmatch(exp); len(match) > 1 {
fc.Type, fc.Condition = criteriaGe, match[1]
return
}
if match := regexp.MustCompile(`^<(.*)$`).FindStringSubmatch(exp); len(match) > 1 {
fc.Type, fc.Condition = criteriaL, match[1]
return
}
if match := regexp.MustCompile(`^>(.*)$`).FindStringSubmatch(exp); len(match) > 1 {
fc.Type, fc.Condition = criteriaG, match[1]
return
}
if strings.Contains(exp, "?") {
exp = strings.ReplaceAll(exp, "?", ".")
}
if strings.Contains(exp, "*") {
exp = strings.ReplaceAll(exp, "*", ".*")
}
fc.Type, fc.Condition = criteriaRegexp, exp
return
}
// formulaCriteriaEval evaluate formula criteria expression.
func formulaCriteriaEval(val string, criteria *formulaCriteria) (result bool, err error) {
var value, expected float64
var e error
prepareValue := func(val, cond string) (value float64, expected float64, err error) {
percential := 1.0
if strings.HasSuffix(cond, "%") {
cond = strings.TrimSuffix(cond, "%")
percential /= 100
}
if value, err = strconv.ParseFloat(val, 64); err != nil {
return
}
if expected, err = strconv.ParseFloat(cond, 64); err != nil {
return
}
expected *= percential
return
}
switch criteria.Type {
case criteriaEq:
return val == criteria.Condition, err
case criteriaLe:
value, expected, e = prepareValue(val, criteria.Condition)
return value <= expected && e == nil, err
case criteriaGe:
value, expected, e = prepareValue(val, criteria.Condition)
return value >= expected && e == nil, err
case criteriaNe:
return val != criteria.Condition, err
case criteriaL:
value, expected, e = prepareValue(val, criteria.Condition)
return value < expected && e == nil, err
case criteriaG:
value, expected, e = prepareValue(val, criteria.Condition)
return value > expected && e == nil, err
case criteriaRegexp:
return regexp.MatchString(criteria.Condition, val)
}
return
}
// Engineering Functions
// BESSELI function the modified Bessel function, which is equivalent to the
// Bessel function evaluated for purely imaginary arguments. The syntax of
// the Besseli function is:
//
// BESSELI(x,n)
//
func (fn *formulaFuncs) BESSELI(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "BESSELI requires 2 numeric arguments")
}
return fn.bassel(argsList, true)
}
// BESSELJ function returns the Bessel function, Jn(x), for a specified order
// and value of x. The syntax of the function is:
//
// BESSELJ(x,n)
//
func (fn *formulaFuncs) BESSELJ(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "BESSELJ requires 2 numeric arguments")
}
return fn.bassel(argsList, false)
}
// bassel is an implementation of the formula functions BESSELI and BESSELJ.
func (fn *formulaFuncs) bassel(argsList *list.List, modfied bool) formulaArg {
x, n := argsList.Front().Value.(formulaArg).ToNumber(), argsList.Back().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return x
}
if n.Type != ArgNumber {
return n
}
max, x1 := 100, x.Number*0.5
x2 := x1 * x1
x1 = math.Pow(x1, n.Number)
n1, n2, n3, n4, add := fact(n.Number), 1.0, 0.0, n.Number, false
result := x1 / n1
t := result * 0.9
for result != t && max != 0 {
x1 *= x2
n3++
n1 *= n3
n4++
n2 *= n4
t = result
r := x1 / n1 / n2
if modfied || add {
result += r
} else {
result -= r
}
max--
add = !add
}
return newNumberFormulaArg(result)
}
// BESSELK function calculates the modified Bessel functions, Kn(x), which are
// also known as the hyperbolic Bessel Functions. These are the equivalent of
// the Bessel functions, evaluated for purely imaginary arguments. The syntax
// of the function is:
//
// BESSELK(x,n)
//
func (fn *formulaFuncs) BESSELK(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "BESSELK requires 2 numeric arguments")
}
x, n := argsList.Front().Value.(formulaArg).ToNumber(), argsList.Back().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return x
}
if n.Type != ArgNumber {
return n
}
if x.Number <= 0 || n.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
var result float64
switch math.Floor(n.Number) {
case 0:
result = fn.besselK0(x)
case 1:
result = fn.besselK1(x)
default:
result = fn.besselK2(x, n)
}
return newNumberFormulaArg(result)
}
// besselK0 is an implementation of the formula function BESSELK.
func (fn *formulaFuncs) besselK0(x formulaArg) float64 {
var y float64
if x.Number <= 2 {
n2 := x.Number * 0.5
y = n2 * n2
args := list.New()
args.PushBack(x)
args.PushBack(newNumberFormulaArg(0))
return -math.Log(n2)*fn.BESSELI(args).Number +
(-0.57721566 + y*(0.42278420+y*(0.23069756+y*(0.3488590e-1+y*(0.262698e-2+y*
(0.10750e-3+y*0.74e-5))))))
}
y = 2 / x.Number
return math.Exp(-x.Number) / math.Sqrt(x.Number) *
(1.25331414 + y*(-0.7832358e-1+y*(0.2189568e-1+y*(-0.1062446e-1+y*
(0.587872e-2+y*(-0.251540e-2+y*0.53208e-3))))))
}
// besselK1 is an implementation of the formula function BESSELK.
func (fn *formulaFuncs) besselK1(x formulaArg) float64 {
var n2, y float64
if x.Number <= 2 {
n2 = x.Number * 0.5
y = n2 * n2
args := list.New()
args.PushBack(x)
args.PushBack(newNumberFormulaArg(1))
return math.Log(n2)*fn.BESSELI(args).Number +
(1+y*(0.15443144+y*(-0.67278579+y*(-0.18156897+y*(-0.1919402e-1+y*(-0.110404e-2+y*(-0.4686e-4)))))))/x.Number
}
y = 2 / x.Number
return math.Exp(-x.Number) / math.Sqrt(x.Number) *
(1.25331414 + y*(0.23498619+y*(-0.3655620e-1+y*(0.1504268e-1+y*(-0.780353e-2+y*
(0.325614e-2+y*(-0.68245e-3)))))))
}
// besselK2 is an implementation of the formula function BESSELK.
func (fn *formulaFuncs) besselK2(x, n formulaArg) float64 {
tox, bkm, bk, bkp := 2/x.Number, fn.besselK0(x), fn.besselK1(x), 0.0
for i := 1.0; i < n.Number; i++ {
bkp = bkm + i*tox*bk
bkm = bk
bk = bkp
}
return bk
}
// BESSELY function returns the Bessel function, Yn(x), (also known as the
// Weber function or the Neumann function), for a specified order and value
// of x. The syntax of the function is:
//
// BESSELY(x,n)
//
func (fn *formulaFuncs) BESSELY(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "BESSELY requires 2 numeric arguments")
}
x, n := argsList.Front().Value.(formulaArg).ToNumber(), argsList.Back().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return x
}
if n.Type != ArgNumber {
return n
}
if x.Number <= 0 || n.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
var result float64
switch math.Floor(n.Number) {
case 0:
result = fn.besselY0(x)
case 1:
result = fn.besselY1(x)
default:
result = fn.besselY2(x, n)
}
return newNumberFormulaArg(result)
}
// besselY0 is an implementation of the formula function BESSELY.
func (fn *formulaFuncs) besselY0(x formulaArg) float64 {
var y float64
if x.Number < 8 {
y = x.Number * x.Number
f1 := -2957821389.0 + y*(7062834065.0+y*(-512359803.6+y*(10879881.29+y*
(-86327.92757+y*228.4622733))))
f2 := 40076544269.0 + y*(745249964.8+y*(7189466.438+y*
(47447.26470+y*(226.1030244+y))))
args := list.New()
args.PushBack(x)
args.PushBack(newNumberFormulaArg(0))
return f1/f2 + 0.636619772*fn.BESSELJ(args).Number*math.Log(x.Number)
}
z := 8.0 / x.Number
y = z * z
xx := x.Number - 0.785398164
f1 := 1 + y*(-0.1098628627e-2+y*(0.2734510407e-4+y*(-0.2073370639e-5+y*0.2093887211e-6)))
f2 := -0.1562499995e-1 + y*(0.1430488765e-3+y*(-0.6911147651e-5+y*(0.7621095161e-6+y*
(-0.934945152e-7))))
return math.Sqrt(0.636619772/x.Number) * (math.Sin(xx)*f1 + z*math.Cos(xx)*f2)
}
// besselY1 is an implementation of the formula function BESSELY.
func (fn *formulaFuncs) besselY1(x formulaArg) float64 {
if x.Number < 8 {
y := x.Number * x.Number
f1 := x.Number * (-0.4900604943e13 + y*(0.1275274390e13+y*(-0.5153438139e11+y*
(0.7349264551e9+y*(-0.4237922726e7+y*0.8511937935e4)))))
f2 := 0.2499580570e14 + y*(0.4244419664e12+y*(0.3733650367e10+y*(0.2245904002e8+y*
(0.1020426050e6+y*(0.3549632885e3+y)))))
args := list.New()
args.PushBack(x)
args.PushBack(newNumberFormulaArg(1))
return f1/f2 + 0.636619772*(fn.BESSELJ(args).Number*math.Log(x.Number)-1/x.Number)
}
return math.Sqrt(0.636619772/x.Number) * math.Sin(x.Number-2.356194491)
}
// besselY2 is an implementation of the formula function BESSELY.
func (fn *formulaFuncs) besselY2(x, n formulaArg) float64 {
tox, bym, by, byp := 2/x.Number, fn.besselY0(x), fn.besselY1(x), 0.0
for i := 1.0; i < n.Number; i++ {
byp = i*tox*by - bym
bym = by
by = byp
}
return by
}
// BIN2DEC function converts a Binary (a base-2 number) into a decimal number.
// The syntax of the function is:
//
// BIN2DEC(number)
//
func (fn *formulaFuncs) BIN2DEC(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "BIN2DEC requires 1 numeric argument")
}
token := argsList.Front().Value.(formulaArg)
number := token.ToNumber()
if number.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, number.Error)
}
return fn.bin2dec(token.Value())
}
// BIN2HEX function converts a Binary (Base 2) number into a Hexadecimal
// (Base 16) number. The syntax of the function is:
//
// BIN2HEX(number,[places])
//
func (fn *formulaFuncs) BIN2HEX(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "BIN2HEX requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "BIN2HEX allows at most 2 arguments")
}
token := argsList.Front().Value.(formulaArg)
number := token.ToNumber()
if number.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, number.Error)
}
decimal, newList := fn.bin2dec(token.Value()), list.New()
if decimal.Type != ArgNumber {
return decimal
}
newList.PushBack(decimal)
if argsList.Len() == 2 {
newList.PushBack(argsList.Back().Value.(formulaArg))
}
return fn.dec2x("BIN2HEX", newList)
}
// BIN2OCT function converts a Binary (Base 2) number into an Octal (Base 8)
// number. The syntax of the function is:
//
// BIN2OCT(number,[places])
//
func (fn *formulaFuncs) BIN2OCT(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "BIN2OCT requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "BIN2OCT allows at most 2 arguments")
}
token := argsList.Front().Value.(formulaArg)
number := token.ToNumber()
if number.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, number.Error)
}
decimal, newList := fn.bin2dec(token.Value()), list.New()
if decimal.Type != ArgNumber {
return decimal
}
newList.PushBack(decimal)
if argsList.Len() == 2 {
newList.PushBack(argsList.Back().Value.(formulaArg))
}
return fn.dec2x("BIN2OCT", newList)
}
// bin2dec is an implementation of the formula function BIN2DEC.
func (fn *formulaFuncs) bin2dec(number string) formulaArg {
decimal, length := 0.0, len(number)
for i := length; i > 0; i-- {
s := string(number[length-i])
if i == 10 && s == "1" {
decimal += math.Pow(-2.0, float64(i-1))
continue
}
if s == "1" {
decimal += math.Pow(2.0, float64(i-1))
continue
}
if s != "0" {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
return newNumberFormulaArg(decimal)
}
// BITAND function returns the bitwise 'AND' for two supplied integers. The
// syntax of the function is:
//
// BITAND(number1,number2)
//
func (fn *formulaFuncs) BITAND(argsList *list.List) formulaArg {
return fn.bitwise("BITAND", argsList)
}
// BITLSHIFT function returns a supplied integer, shifted left by a specified
// number of bits. The syntax of the function is:
//
// BITLSHIFT(number1,shift_amount)
//
func (fn *formulaFuncs) BITLSHIFT(argsList *list.List) formulaArg {
return fn.bitwise("BITLSHIFT", argsList)
}
// BITOR function returns the bitwise 'OR' for two supplied integers. The
// syntax of the function is:
//
// BITOR(number1,number2)
//
func (fn *formulaFuncs) BITOR(argsList *list.List) formulaArg {
return fn.bitwise("BITOR", argsList)
}
// BITRSHIFT function returns a supplied integer, shifted right by a specified
// number of bits. The syntax of the function is:
//
// BITRSHIFT(number1,shift_amount)
//
func (fn *formulaFuncs) BITRSHIFT(argsList *list.List) formulaArg {
return fn.bitwise("BITRSHIFT", argsList)
}
// BITXOR function returns the bitwise 'XOR' (exclusive 'OR') for two supplied
// integers. The syntax of the function is:
//
// BITXOR(number1,number2)
//
func (fn *formulaFuncs) BITXOR(argsList *list.List) formulaArg {
return fn.bitwise("BITXOR", argsList)
}
// bitwise is an implementation of the formula functions BITAND, BITLSHIFT,
// BITOR, BITRSHIFT and BITXOR.
func (fn *formulaFuncs) bitwise(name string, argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 2 numeric arguments", name))
}
num1, num2 := argsList.Front().Value.(formulaArg).ToNumber(), argsList.Back().Value.(formulaArg).ToNumber()
if num1.Type != ArgNumber || num2.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
max := math.Pow(2, 48) - 1
if num1.Number < 0 || num1.Number > max || num2.Number < 0 || num2.Number > max {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
bitwiseFuncMap := map[string]func(a, b int) int{
"BITAND": func(a, b int) int { return a & b },
"BITLSHIFT": func(a, b int) int { return a << uint(b) },
"BITOR": func(a, b int) int { return a | b },
"BITRSHIFT": func(a, b int) int { return a >> uint(b) },
"BITXOR": func(a, b int) int { return a ^ b },
}
bitwiseFunc := bitwiseFuncMap[name]
return newNumberFormulaArg(float64(bitwiseFunc(int(num1.Number), int(num2.Number))))
}
// COMPLEX function takes two arguments, representing the real and the
// imaginary coefficients of a complex number, and from these, creates a
// complex number. The syntax of the function is:
//
// COMPLEX(real_num,i_num,[suffix])
//
func (fn *formulaFuncs) COMPLEX(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "COMPLEX requires at least 2 arguments")
}
if argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, "COMPLEX allows at most 3 arguments")
}
realNum, i, suffix := argsList.Front().Value.(formulaArg).ToNumber(), argsList.Front().Next().Value.(formulaArg).ToNumber(), "i"
if realNum.Type != ArgNumber {
return realNum
}
if i.Type != ArgNumber {
return i
}
if argsList.Len() == 3 {
if suffix = strings.ToLower(argsList.Back().Value.(formulaArg).Value()); suffix != "i" && suffix != "j" {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
}
return newStringFormulaArg(cmplx2str(complex(realNum.Number, i.Number), suffix))
}
// cmplx2str replace complex number string characters.
func cmplx2str(num complex128, suffix string) string {
realPart, imagPart := fmt.Sprint(real(num)), fmt.Sprint(imag(num))
isNum, i := isNumeric(realPart)
if isNum && i > 15 {
realPart = roundPrecision(realPart, -1)
}
isNum, i = isNumeric(imagPart)
if isNum && i > 15 {
imagPart = roundPrecision(imagPart, -1)
}
c := realPart
if imag(num) > 0 {
c += "+"
}
if imag(num) != 0 {
c += imagPart + "i"
}
c = strings.TrimPrefix(c, "(")
c = strings.TrimPrefix(c, "+0+")
c = strings.TrimPrefix(c, "-0+")
c = strings.TrimSuffix(c, ")")
c = strings.TrimPrefix(c, "0+")
if strings.HasPrefix(c, "0-") {
c = "-" + strings.TrimPrefix(c, "0-")
}
c = strings.TrimPrefix(c, "0+")
c = strings.TrimSuffix(c, "+0i")
c = strings.TrimSuffix(c, "-0i")
c = strings.NewReplacer("+1i", "+i", "-1i", "-i").Replace(c)
c = strings.ReplaceAll(c, "i", suffix)
return c
}
// str2cmplx convert complex number string characters.
func str2cmplx(c string) string {
c = strings.ReplaceAll(c, "j", "i")
if c == "i" {
c = "1i"
}
c = strings.NewReplacer("+i", "+1i", "-i", "-1i").Replace(c)
return c
}
// conversionUnit defined unit info for conversion.
type conversionUnit struct {
group uint8
allowPrefix bool
}
// conversionUnits maps info list for unit conversion, that can be used in
// formula function CONVERT.
var conversionUnits = map[string]conversionUnit{
// weight and mass
"g": {group: catgoryWeightAndMass, allowPrefix: true},
"sg": {group: catgoryWeightAndMass, allowPrefix: false},
"lbm": {group: catgoryWeightAndMass, allowPrefix: false},
"u": {group: catgoryWeightAndMass, allowPrefix: true},
"ozm": {group: catgoryWeightAndMass, allowPrefix: false},
"grain": {group: catgoryWeightAndMass, allowPrefix: false},
"cwt": {group: catgoryWeightAndMass, allowPrefix: false},
"shweight": {group: catgoryWeightAndMass, allowPrefix: false},
"uk_cwt": {group: catgoryWeightAndMass, allowPrefix: false},
"lcwt": {group: catgoryWeightAndMass, allowPrefix: false},
"hweight": {group: catgoryWeightAndMass, allowPrefix: false},
"stone": {group: catgoryWeightAndMass, allowPrefix: false},
"ton": {group: catgoryWeightAndMass, allowPrefix: false},
"uk_ton": {group: catgoryWeightAndMass, allowPrefix: false},
"LTON": {group: catgoryWeightAndMass, allowPrefix: false},
"brton": {group: catgoryWeightAndMass, allowPrefix: false},
// distance
"m": {group: catgoryDistance, allowPrefix: true},
"mi": {group: catgoryDistance, allowPrefix: false},
"Nmi": {group: catgoryDistance, allowPrefix: false},
"in": {group: catgoryDistance, allowPrefix: false},
"ft": {group: catgoryDistance, allowPrefix: false},
"yd": {group: catgoryDistance, allowPrefix: false},
"ang": {group: catgoryDistance, allowPrefix: true},
"ell": {group: catgoryDistance, allowPrefix: false},
"ly": {group: catgoryDistance, allowPrefix: false},
"parsec": {group: catgoryDistance, allowPrefix: false},
"pc": {group: catgoryDistance, allowPrefix: false},
"Pica": {group: catgoryDistance, allowPrefix: false},
"Picapt": {group: catgoryDistance, allowPrefix: false},
"pica": {group: catgoryDistance, allowPrefix: false},
"survey_mi": {group: catgoryDistance, allowPrefix: false},
// time
"yr": {group: catgoryTime, allowPrefix: false},
"day": {group: catgoryTime, allowPrefix: false},
"d": {group: catgoryTime, allowPrefix: false},
"hr": {group: catgoryTime, allowPrefix: false},
"mn": {group: catgoryTime, allowPrefix: false},
"min": {group: catgoryTime, allowPrefix: false},
"sec": {group: catgoryTime, allowPrefix: true},
"s": {group: catgoryTime, allowPrefix: true},
// pressure
"Pa": {group: catgoryPressure, allowPrefix: true},
"p": {group: catgoryPressure, allowPrefix: true},
"atm": {group: catgoryPressure, allowPrefix: true},
"at": {group: catgoryPressure, allowPrefix: true},
"mmHg": {group: catgoryPressure, allowPrefix: true},
"psi": {group: catgoryPressure, allowPrefix: true},
"Torr": {group: catgoryPressure, allowPrefix: true},
// force
"N": {group: catgoryForce, allowPrefix: true},
"dyn": {group: catgoryForce, allowPrefix: true},
"dy": {group: catgoryForce, allowPrefix: true},
"lbf": {group: catgoryForce, allowPrefix: false},
"pond": {group: catgoryForce, allowPrefix: true},
// energy
"J": {group: catgoryEnergy, allowPrefix: true},
"e": {group: catgoryEnergy, allowPrefix: true},
"c": {group: catgoryEnergy, allowPrefix: true},
"cal": {group: catgoryEnergy, allowPrefix: true},
"eV": {group: catgoryEnergy, allowPrefix: true},
"ev": {group: catgoryEnergy, allowPrefix: true},
"HPh": {group: catgoryEnergy, allowPrefix: false},
"hh": {group: catgoryEnergy, allowPrefix: false},
"Wh": {group: catgoryEnergy, allowPrefix: true},
"wh": {group: catgoryEnergy, allowPrefix: true},
"flb": {group: catgoryEnergy, allowPrefix: false},
"BTU": {group: catgoryEnergy, allowPrefix: false},
"btu": {group: catgoryEnergy, allowPrefix: false},
// power
"HP": {group: catgoryPower, allowPrefix: false},
"h": {group: catgoryPower, allowPrefix: false},
"W": {group: catgoryPower, allowPrefix: true},
"w": {group: catgoryPower, allowPrefix: true},
"PS": {group: catgoryPower, allowPrefix: false},
"T": {group: catgoryMagnetism, allowPrefix: true},
"ga": {group: catgoryMagnetism, allowPrefix: true},
// temperature
"C": {group: catgoryTemperature, allowPrefix: false},
"cel": {group: catgoryTemperature, allowPrefix: false},
"F": {group: catgoryTemperature, allowPrefix: false},
"fah": {group: catgoryTemperature, allowPrefix: false},
"K": {group: catgoryTemperature, allowPrefix: false},
"kel": {group: catgoryTemperature, allowPrefix: false},
"Rank": {group: catgoryTemperature, allowPrefix: false},
"Reau": {group: catgoryTemperature, allowPrefix: false},
// volume
"l": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: true},
"L": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: true},
"lt": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: true},
"tsp": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"tspm": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"tbs": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"oz": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"cup": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"pt": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"us_pt": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"uk_pt": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"qt": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"uk_qt": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"gal": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"uk_gal": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"ang3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: true},
"ang^3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: true},
"barrel": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"bushel": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"in3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"in^3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"ft3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"ft^3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"ly3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"ly^3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"m3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: true},
"m^3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: true},
"mi3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"mi^3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"yd3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"yd^3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"Nmi3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"Nmi^3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"Pica3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"Pica^3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"Picapt3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"Picapt^3": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"GRT": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"regton": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
"MTON": {group: catgoryVolumeAndLiquidMeasure, allowPrefix: false},
// area
"ha": {group: catgoryArea, allowPrefix: true},
"uk_acre": {group: catgoryArea, allowPrefix: false},
"us_acre": {group: catgoryArea, allowPrefix: false},
"ang2": {group: catgoryArea, allowPrefix: true},
"ang^2": {group: catgoryArea, allowPrefix: true},
"ar": {group: catgoryArea, allowPrefix: true},
"ft2": {group: catgoryArea, allowPrefix: false},
"ft^2": {group: catgoryArea, allowPrefix: false},
"in2": {group: catgoryArea, allowPrefix: false},
"in^2": {group: catgoryArea, allowPrefix: false},
"ly2": {group: catgoryArea, allowPrefix: false},
"ly^2": {group: catgoryArea, allowPrefix: false},
"m2": {group: catgoryArea, allowPrefix: true},
"m^2": {group: catgoryArea, allowPrefix: true},
"Morgen": {group: catgoryArea, allowPrefix: false},
"mi2": {group: catgoryArea, allowPrefix: false},
"mi^2": {group: catgoryArea, allowPrefix: false},
"Nmi2": {group: catgoryArea, allowPrefix: false},
"Nmi^2": {group: catgoryArea, allowPrefix: false},
"Pica2": {group: catgoryArea, allowPrefix: false},
"Pica^2": {group: catgoryArea, allowPrefix: false},
"Picapt2": {group: catgoryArea, allowPrefix: false},
"Picapt^2": {group: catgoryArea, allowPrefix: false},
"yd2": {group: catgoryArea, allowPrefix: false},
"yd^2": {group: catgoryArea, allowPrefix: false},
// information
"byte": {group: catgoryInformation, allowPrefix: true},
"bit": {group: catgoryInformation, allowPrefix: true},
// speed
"m/s": {group: catgorySpeed, allowPrefix: true},
"m/sec": {group: catgorySpeed, allowPrefix: true},
"m/h": {group: catgorySpeed, allowPrefix: true},
"m/hr": {group: catgorySpeed, allowPrefix: true},
"mph": {group: catgorySpeed, allowPrefix: false},
"admkn": {group: catgorySpeed, allowPrefix: false},
"kn": {group: catgorySpeed, allowPrefix: false},
}
// unitConversions maps details of the Units of measure conversion factors,
// organised by group.
var unitConversions = map[byte]map[string]float64{
// conversion uses gram (g) as an intermediate unit
catgoryWeightAndMass: {
"g": 1,
"sg": 6.85217658567918e-05,
"lbm": 2.20462262184878e-03,
"u": 6.02214179421676e+23,
"ozm": 3.52739619495804e-02,
"grain": 1.54323583529414e+01,
"cwt": 2.20462262184878e-05,
"shweight": 2.20462262184878e-05,
"uk_cwt": 1.96841305522212e-05,
"lcwt": 1.96841305522212e-05,
"hweight": 1.96841305522212e-05,
"stone": 1.57473044417770e-04,
"ton": 1.10231131092439e-06,
"uk_ton": 9.84206527611061e-07,
"LTON": 9.84206527611061e-07,
"brton": 9.84206527611061e-07,
},
// conversion uses meter (m) as an intermediate unit
catgoryDistance: {
"m": 1,
"mi": 6.21371192237334e-04,
"Nmi": 5.39956803455724e-04,
"in": 3.93700787401575e+01,
"ft": 3.28083989501312e+00,
"yd": 1.09361329833771e+00,
"ang": 1.0e+10,
"ell": 8.74890638670166e-01,
"ly": 1.05700083402462e-16,
"parsec": 3.24077928966473e-17,
"pc": 3.24077928966473e-17,
"Pica": 2.83464566929134e+03,
"Picapt": 2.83464566929134e+03,
"pica": 2.36220472440945e+02,
"survey_mi": 6.21369949494950e-04,
},
// conversion uses second (s) as an intermediate unit
catgoryTime: {
"yr": 3.16880878140289e-08,
"day": 1.15740740740741e-05,
"d": 1.15740740740741e-05,
"hr": 2.77777777777778e-04,
"mn": 1.66666666666667e-02,
"min": 1.66666666666667e-02,
"sec": 1,
"s": 1,
},
// conversion uses Pascal (Pa) as an intermediate unit
catgoryPressure: {
"Pa": 1,
"p": 1,
"atm": 9.86923266716013e-06,
"at": 9.86923266716013e-06,
"mmHg": 7.50063755419211e-03,
"psi": 1.45037737730209e-04,
"Torr": 7.50061682704170e-03,
},
// conversion uses Newton (N) as an intermediate unit
catgoryForce: {
"N": 1,
"dyn": 1.0e+5,
"dy": 1.0e+5,
"lbf": 2.24808923655339e-01,
"pond": 1.01971621297793e+02,
},
// conversion uses Joule (J) as an intermediate unit
catgoryEnergy: {
"J": 1,
"e": 9.99999519343231e+06,
"c": 2.39006249473467e-01,
"cal": 2.38846190642017e-01,
"eV": 6.24145700000000e+18,
"ev": 6.24145700000000e+18,
"HPh": 3.72506430801000e-07,
"hh": 3.72506430801000e-07,
"Wh": 2.77777916238711e-04,
"wh": 2.77777916238711e-04,
"flb": 2.37304222192651e+01,
"BTU": 9.47815067349015e-04,
"btu": 9.47815067349015e-04,
},
// conversion uses Horsepower (HP) as an intermediate unit
catgoryPower: {
"HP": 1,
"h": 1,
"W": 7.45699871582270e+02,
"w": 7.45699871582270e+02,
"PS": 1.01386966542400e+00,
},
// conversion uses Tesla (T) as an intermediate unit
catgoryMagnetism: {
"T": 1,
"ga": 10000,
},
// conversion uses litre (l) as an intermediate unit
catgoryVolumeAndLiquidMeasure: {
"l": 1,
"L": 1,
"lt": 1,
"tsp": 2.02884136211058e+02,
"tspm": 2.0e+02,
"tbs": 6.76280454036860e+01,
"oz": 3.38140227018430e+01,
"cup": 4.22675283773038e+00,
"pt": 2.11337641886519e+00,
"us_pt": 2.11337641886519e+00,
"uk_pt": 1.75975398639270e+00,
"qt": 1.05668820943259e+00,
"uk_qt": 8.79876993196351e-01,
"gal": 2.64172052358148e-01,
"uk_gal": 2.19969248299088e-01,
"ang3": 1.0e+27,
"ang^3": 1.0e+27,
"barrel": 6.28981077043211e-03,
"bushel": 2.83775932584017e-02,
"in3": 6.10237440947323e+01,
"in^3": 6.10237440947323e+01,
"ft3": 3.53146667214886e-02,
"ft^3": 3.53146667214886e-02,
"ly3": 1.18093498844171e-51,
"ly^3": 1.18093498844171e-51,
"m3": 1.0e-03,
"m^3": 1.0e-03,
"mi3": 2.39912758578928e-13,
"mi^3": 2.39912758578928e-13,
"yd3": 1.30795061931439e-03,
"yd^3": 1.30795061931439e-03,
"Nmi3": 1.57426214685811e-13,
"Nmi^3": 1.57426214685811e-13,
"Pica3": 2.27769904358706e+07,
"Pica^3": 2.27769904358706e+07,
"Picapt3": 2.27769904358706e+07,
"Picapt^3": 2.27769904358706e+07,
"GRT": 3.53146667214886e-04,
"regton": 3.53146667214886e-04,
"MTON": 8.82866668037215e-04,
},
// conversion uses hectare (ha) as an intermediate unit
catgoryArea: {
"ha": 1,
"uk_acre": 2.47105381467165e+00,
"us_acre": 2.47104393046628e+00,
"ang2": 1.0e+24,
"ang^2": 1.0e+24,
"ar": 1.0e+02,
"ft2": 1.07639104167097e+05,
"ft^2": 1.07639104167097e+05,
"in2": 1.55000310000620e+07,
"in^2": 1.55000310000620e+07,
"ly2": 1.11725076312873e-28,
"ly^2": 1.11725076312873e-28,
"m2": 1.0e+04,
"m^2": 1.0e+04,
"Morgen": 4.0e+00,
"mi2": 3.86102158542446e-03,
"mi^2": 3.86102158542446e-03,
"Nmi2": 2.91553349598123e-03,
"Nmi^2": 2.91553349598123e-03,
"Pica2": 8.03521607043214e+10,
"Pica^2": 8.03521607043214e+10,
"Picapt2": 8.03521607043214e+10,
"Picapt^2": 8.03521607043214e+10,
"yd2": 1.19599004630108e+04,
"yd^2": 1.19599004630108e+04,
},
// conversion uses bit (bit) as an intermediate unit
catgoryInformation: {
"bit": 1,
"byte": 0.125,
},
// conversion uses Meters per Second (m/s) as an intermediate unit
catgorySpeed: {
"m/s": 1,
"m/sec": 1,
"m/h": 3.60e+03,
"m/hr": 3.60e+03,
"mph": 2.23693629205440e+00,
"admkn": 1.94260256941567e+00,
"kn": 1.94384449244060e+00,
},
}
// conversionMultipliers maps details of the Multiplier prefixes that can be
// used with Units of Measure in CONVERT.
var conversionMultipliers = map[string]float64{
"Y": 1e24,
"Z": 1e21,
"E": 1e18,
"P": 1e15,
"T": 1e12,
"G": 1e9,
"M": 1e6,
"k": 1e3,
"h": 1e2,
"e": 1e1,
"da": 1e1,
"d": 1e-1,
"c": 1e-2,
"m": 1e-3,
"u": 1e-6,
"n": 1e-9,
"p": 1e-12,
"f": 1e-15,
"a": 1e-18,
"z": 1e-21,
"y": 1e-24,
"Yi": math.Pow(2, 80),
"Zi": math.Pow(2, 70),
"Ei": math.Pow(2, 60),
"Pi": math.Pow(2, 50),
"Ti": math.Pow(2, 40),
"Gi": math.Pow(2, 30),
"Mi": math.Pow(2, 20),
"ki": math.Pow(2, 10),
}
// getUnitDetails check and returns the unit of measure details.
func getUnitDetails(uom string) (unit string, catgory byte, res float64, ok bool) {
if len(uom) == 0 {
ok = false
return
}
if unit, ok := conversionUnits[uom]; ok {
return uom, unit.group, 1, ok
}
// 1 character standard metric multiplier prefixes
multiplierType := uom[:1]
uom = uom[1:]
conversionUnit, ok1 := conversionUnits[uom]
multiplier, ok2 := conversionMultipliers[multiplierType]
if ok1 && ok2 {
if !conversionUnit.allowPrefix {
ok = false
return
}
unitCategory := conversionUnit.group
return uom, unitCategory, multiplier, true
}
// 2 character standard and binary metric multiplier prefixes
if len(uom) > 0 {
multiplierType += uom[:1]
uom = uom[1:]
}
conversionUnit, ok1 = conversionUnits[uom]
multiplier, ok2 = conversionMultipliers[multiplierType]
if ok1 && ok2 {
if !conversionUnit.allowPrefix {
ok = false
return
}
unitCategory := conversionUnit.group
return uom, unitCategory, multiplier, true
}
ok = false
return
}
// resolveTemperatureSynonyms returns unit of measure according to a given
// temperature synonyms.
func resolveTemperatureSynonyms(uom string) string {
switch uom {
case "fah":
return "F"
case "cel":
return "C"
case "kel":
return "K"
}
return uom
}
// convertTemperature returns converted temperature by a given unit of measure.
func convertTemperature(fromUOM, toUOM string, value float64) float64 {
fromUOM = resolveTemperatureSynonyms(fromUOM)
toUOM = resolveTemperatureSynonyms(toUOM)
if fromUOM == toUOM {
return value
}
// convert to Kelvin
switch fromUOM {
case "F":
value = (value-32)/1.8 + 273.15
case "C":
value += 273.15
case "Rank":
value /= 1.8
case "Reau":
value = value*1.25 + 273.15
}
// convert from Kelvin
switch toUOM {
case "F":
value = (value-273.15)*1.8 + 32
case "C":
value -= 273.15
case "Rank":
value *= 1.8
case "Reau":
value = (value - 273.15) * 0.8
}
return value
}
// CONVERT function converts a number from one unit type (e.g. Yards) to
// another unit type (e.g. Meters). The syntax of the function is:
//
// CONVERT(number,from_unit,to_unit)
//
func (fn *formulaFuncs) CONVERT(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "CONVERT requires 3 arguments")
}
num := argsList.Front().Value.(formulaArg).ToNumber()
if num.Type != ArgNumber {
return num
}
fromUOM, fromCategory, fromMultiplier, ok1 := getUnitDetails(argsList.Front().Next().Value.(formulaArg).Value())
toUOM, toCategory, toMultiplier, ok2 := getUnitDetails(argsList.Back().Value.(formulaArg).Value())
if !ok1 || !ok2 || fromCategory != toCategory {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
val := num.Number * fromMultiplier
if fromUOM == toUOM && fromMultiplier == toMultiplier {
return newNumberFormulaArg(val / fromMultiplier)
} else if fromUOM == toUOM {
return newNumberFormulaArg(val / toMultiplier)
} else if fromCategory == catgoryTemperature {
return newNumberFormulaArg(convertTemperature(fromUOM, toUOM, val))
}
fromConversion := unitConversions[fromCategory][fromUOM]
toConversion := unitConversions[fromCategory][toUOM]
baseValue := val * (1 / fromConversion)
return newNumberFormulaArg((baseValue * toConversion) / toMultiplier)
}
// DEC2BIN function converts a decimal number into a Binary (Base 2) number.
// The syntax of the function is:
//
// DEC2BIN(number,[places])
//
func (fn *formulaFuncs) DEC2BIN(argsList *list.List) formulaArg {
return fn.dec2x("DEC2BIN", argsList)
}
// DEC2HEX function converts a decimal number into a Hexadecimal (Base 16)
// number. The syntax of the function is:
//
// DEC2HEX(number,[places])
//
func (fn *formulaFuncs) DEC2HEX(argsList *list.List) formulaArg {
return fn.dec2x("DEC2HEX", argsList)
}
// DEC2OCT function converts a decimal number into an Octal (Base 8) number.
// The syntax of the function is:
//
// DEC2OCT(number,[places])
//
func (fn *formulaFuncs) DEC2OCT(argsList *list.List) formulaArg {
return fn.dec2x("DEC2OCT", argsList)
}
// dec2x is an implementation of the formula functions DEC2BIN, DEC2HEX and
// DEC2OCT.
func (fn *formulaFuncs) dec2x(name string, argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 1 argument", name))
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s allows at most 2 arguments", name))
}
decimal := argsList.Front().Value.(formulaArg).ToNumber()
if decimal.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, decimal.Error)
}
maxLimitMap := map[string]float64{
"DEC2BIN": 511,
"HEX2BIN": 511,
"OCT2BIN": 511,
"BIN2HEX": 549755813887,
"DEC2HEX": 549755813887,
"OCT2HEX": 549755813887,
"BIN2OCT": 536870911,
"DEC2OCT": 536870911,
"HEX2OCT": 536870911,
}
minLimitMap := map[string]float64{
"DEC2BIN": -512,
"HEX2BIN": -512,
"OCT2BIN": -512,
"BIN2HEX": -549755813888,
"DEC2HEX": -549755813888,
"OCT2HEX": -549755813888,
"BIN2OCT": -536870912,
"DEC2OCT": -536870912,
"HEX2OCT": -536870912,
}
baseMap := map[string]int{
"DEC2BIN": 2,
"HEX2BIN": 2,
"OCT2BIN": 2,
"BIN2HEX": 16,
"DEC2HEX": 16,
"OCT2HEX": 16,
"BIN2OCT": 8,
"DEC2OCT": 8,
"HEX2OCT": 8,
}
maxLimit, minLimit := maxLimitMap[name], minLimitMap[name]
base := baseMap[name]
if decimal.Number < minLimit || decimal.Number > maxLimit {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
n := int64(decimal.Number)
binary := strconv.FormatUint(*(*uint64)(unsafe.Pointer(&n)), base)
if argsList.Len() == 2 {
places := argsList.Back().Value.(formulaArg).ToNumber()
if places.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, places.Error)
}
binaryPlaces := len(binary)
if places.Number < 0 || places.Number > 10 || binaryPlaces > int(places.Number) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newStringFormulaArg(strings.ToUpper(fmt.Sprintf("%s%s", strings.Repeat("0", int(places.Number)-binaryPlaces), binary)))
}
if decimal.Number < 0 && len(binary) > 10 {
return newStringFormulaArg(strings.ToUpper(binary[len(binary)-10:]))
}
return newStringFormulaArg(strings.ToUpper(binary))
}
// DELTA function tests two numbers for equality and returns the Kronecker
// Delta. i.e. the function returns 1 if the two supplied numbers are equal
// and 0 otherwise. The syntax of the function is:
//
// DELTA(number1,[number2])
//
func (fn *formulaFuncs) DELTA(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "DELTA requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "DELTA allows at most 2 arguments")
}
number1 := argsList.Front().Value.(formulaArg).ToNumber()
if number1.Type != ArgNumber {
return number1
}
number2 := newNumberFormulaArg(0)
if argsList.Len() == 2 {
if number2 = argsList.Back().Value.(formulaArg).ToNumber(); number2.Type != ArgNumber {
return number2
}
}
return newBoolFormulaArg(number1.Number == number2.Number).ToNumber()
}
// ERF function calculates the Error Function, integrated between two supplied
// limits. The syntax of the function is:
//
// ERF(lower_limit,[upper_limit])
//
func (fn *formulaFuncs) ERF(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ERF requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "ERF allows at most 2 arguments")
}
lower := argsList.Front().Value.(formulaArg).ToNumber()
if lower.Type != ArgNumber {
return lower
}
if argsList.Len() == 2 {
upper := argsList.Back().Value.(formulaArg).ToNumber()
if upper.Type != ArgNumber {
return upper
}
return newNumberFormulaArg(math.Erf(upper.Number) - math.Erf(lower.Number))
}
return newNumberFormulaArg(math.Erf(lower.Number))
}
// ERFdotPRECISE function calculates the Error Function, integrated between a
// supplied lower or upper limit and 0. The syntax of the function is:
//
// ERF.PRECISE(x)
//
func (fn *formulaFuncs) ERFdotPRECISE(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ERF.PRECISE requires 1 argument")
}
x := argsList.Front().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return x
}
return newNumberFormulaArg(math.Erf(x.Number))
}
// erfc is an implementation of the formula functions ERFC and ERFC.PRECISE.
func (fn *formulaFuncs) erfc(name string, argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 1 argument", name))
}
x := argsList.Front().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return x
}
return newNumberFormulaArg(math.Erfc(x.Number))
}
// ERFC function calculates the Complementary Error Function, integrated
// between a supplied lower limit and infinity. The syntax of the function
// is:
//
// ERFC(x)
//
func (fn *formulaFuncs) ERFC(argsList *list.List) formulaArg {
return fn.erfc("ERFC", argsList)
}
// ERFCdotPRECISE function calculates the Complementary Error Function,
// integrated between a supplied lower limit and infinity. The syntax of the
// function is:
//
// ERFC(x)
//
func (fn *formulaFuncs) ERFCdotPRECISE(argsList *list.List) formulaArg {
return fn.erfc("ERFC.PRECISE", argsList)
}
// GESTEP unction tests whether a supplied number is greater than a supplied
// step size and returns. The syntax of the function is:
//
// GESTEP(number,[step])
//
func (fn *formulaFuncs) GESTEP(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "GESTEP requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "GESTEP allows at most 2 arguments")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type != ArgNumber {
return number
}
step := newNumberFormulaArg(0)
if argsList.Len() == 2 {
if step = argsList.Back().Value.(formulaArg).ToNumber(); step.Type != ArgNumber {
return step
}
}
return newBoolFormulaArg(number.Number >= step.Number).ToNumber()
}
// HEX2BIN function converts a Hexadecimal (Base 16) number into a Binary
// (Base 2) number. The syntax of the function is:
//
// HEX2BIN(number,[places])
//
func (fn *formulaFuncs) HEX2BIN(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "HEX2BIN requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "HEX2BIN allows at most 2 arguments")
}
decimal, newList := fn.hex2dec(argsList.Front().Value.(formulaArg).Value()), list.New()
if decimal.Type != ArgNumber {
return decimal
}
newList.PushBack(decimal)
if argsList.Len() == 2 {
newList.PushBack(argsList.Back().Value.(formulaArg))
}
return fn.dec2x("HEX2BIN", newList)
}
// HEX2DEC function converts a hexadecimal (a base-16 number) into a decimal
// number. The syntax of the function is:
//
// HEX2DEC(number)
//
func (fn *formulaFuncs) HEX2DEC(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "HEX2DEC requires 1 numeric argument")
}
return fn.hex2dec(argsList.Front().Value.(formulaArg).Value())
}
// HEX2OCT function converts a Hexadecimal (Base 16) number into an Octal
// (Base 8) number. The syntax of the function is:
//
// HEX2OCT(number,[places])
//
func (fn *formulaFuncs) HEX2OCT(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "HEX2OCT requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "HEX2OCT allows at most 2 arguments")
}
decimal, newList := fn.hex2dec(argsList.Front().Value.(formulaArg).Value()), list.New()
if decimal.Type != ArgNumber {
return decimal
}
newList.PushBack(decimal)
if argsList.Len() == 2 {
newList.PushBack(argsList.Back().Value.(formulaArg))
}
return fn.dec2x("HEX2OCT", newList)
}
// hex2dec is an implementation of the formula function HEX2DEC.
func (fn *formulaFuncs) hex2dec(number string) formulaArg {
decimal, length := 0.0, len(number)
for i := length; i > 0; i-- {
num, err := strconv.ParseInt(string(number[length-i]), 16, 64)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
if i == 10 && string(number[length-i]) == "F" {
decimal += math.Pow(-16.0, float64(i-1))
continue
}
decimal += float64(num) * math.Pow(16.0, float64(i-1))
}
return newNumberFormulaArg(decimal)
}
// IMABS function returns the absolute value (the modulus) of a complex
// number. The syntax of the function is:
//
// IMABS(inumber)
//
func (fn *formulaFuncs) IMABS(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMABS requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newNumberFormulaArg(cmplx.Abs(inumber))
}
// IMAGINARY function returns the imaginary coefficient of a supplied complex
// number. The syntax of the function is:
//
// IMAGINARY(inumber)
//
func (fn *formulaFuncs) IMAGINARY(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMAGINARY requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newNumberFormulaArg(imag(inumber))
}
// IMARGUMENT function returns the phase (also called the argument) of a
// supplied complex number. The syntax of the function is:
//
// IMARGUMENT(inumber)
//
func (fn *formulaFuncs) IMARGUMENT(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMARGUMENT requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newNumberFormulaArg(cmplx.Phase(inumber))
}
// IMCONJUGATE function returns the complex conjugate of a supplied complex
// number. The syntax of the function is:
//
// IMCONJUGATE(inumber)
//
func (fn *formulaFuncs) IMCONJUGATE(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMCONJUGATE requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(cmplx2str(cmplx.Conj(inumber), value[len(value)-1:]))
}
// IMCOS function returns the cosine of a supplied complex number. The syntax
// of the function is:
//
// IMCOS(inumber)
//
func (fn *formulaFuncs) IMCOS(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMCOS requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(cmplx2str(cmplx.Cos(inumber), value[len(value)-1:]))
}
// IMCOSH function returns the hyperbolic cosine of a supplied complex number. The syntax
// of the function is:
//
// IMCOSH(inumber)
//
func (fn *formulaFuncs) IMCOSH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMCOSH requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(cmplx2str(cmplx.Cosh(inumber), value[len(value)-1:]))
}
// IMCOT function returns the cotangent of a supplied complex number. The syntax
// of the function is:
//
// IMCOT(inumber)
//
func (fn *formulaFuncs) IMCOT(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMCOT requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(cmplx2str(cmplx.Cot(inumber), value[len(value)-1:]))
}
// IMCSC function returns the cosecant of a supplied complex number. The syntax
// of the function is:
//
// IMCSC(inumber)
//
func (fn *formulaFuncs) IMCSC(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMCSC requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
num := 1 / cmplx.Sin(inumber)
if cmplx.IsInf(num) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newStringFormulaArg(cmplx2str(num, value[len(value)-1:]))
}
// IMCSCH function returns the hyperbolic cosecant of a supplied complex
// number. The syntax of the function is:
//
// IMCSCH(inumber)
//
func (fn *formulaFuncs) IMCSCH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMCSCH requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
num := 1 / cmplx.Sinh(inumber)
if cmplx.IsInf(num) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newStringFormulaArg(cmplx2str(num, value[len(value)-1:]))
}
// IMDIV function calculates the quotient of two complex numbers (i.e. divides
// one complex number by another). The syntax of the function is:
//
// IMDIV(inumber1,inumber2)
//
func (fn *formulaFuncs) IMDIV(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "IMDIV requires 2 arguments")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber1, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
inumber2, err := strconv.ParseComplex(str2cmplx(argsList.Back().Value.(formulaArg).Value()), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
num := inumber1 / inumber2
if cmplx.IsInf(num) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newStringFormulaArg(cmplx2str(num, value[len(value)-1:]))
}
// IMEXP function returns the exponential of a supplied complex number. The
// syntax of the function is:
//
// IMEXP(inumber)
//
func (fn *formulaFuncs) IMEXP(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMEXP requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(cmplx2str(cmplx.Exp(inumber), value[len(value)-1:]))
}
// IMLN function returns the natural logarithm of a supplied complex number.
// The syntax of the function is:
//
// IMLN(inumber)
//
func (fn *formulaFuncs) IMLN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMLN requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
num := cmplx.Log(inumber)
if cmplx.IsInf(num) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newStringFormulaArg(cmplx2str(num, value[len(value)-1:]))
}
// IMLOG10 function returns the common (base 10) logarithm of a supplied
// complex number. The syntax of the function is:
//
// IMLOG10(inumber)
//
func (fn *formulaFuncs) IMLOG10(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMLOG10 requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
num := cmplx.Log10(inumber)
if cmplx.IsInf(num) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newStringFormulaArg(cmplx2str(num, value[len(value)-1:]))
}
// IMLOG2 function calculates the base 2 logarithm of a supplied complex
// number. The syntax of the function is:
//
// IMLOG2(inumber)
//
func (fn *formulaFuncs) IMLOG2(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMLOG2 requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
num := cmplx.Log(inumber)
if cmplx.IsInf(num) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newStringFormulaArg(cmplx2str(num/cmplx.Log(2), value[len(value)-1:]))
}
// IMPOWER function returns a supplied complex number, raised to a given
// power. The syntax of the function is:
//
// IMPOWER(inumber,number)
//
func (fn *formulaFuncs) IMPOWER(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "IMPOWER requires 2 arguments")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
number, err := strconv.ParseComplex(str2cmplx(argsList.Back().Value.(formulaArg).Value()), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
if inumber == 0 && number == 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
num := cmplx.Pow(inumber, number)
if cmplx.IsInf(num) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newStringFormulaArg(cmplx2str(num, value[len(value)-1:]))
}
// IMPRODUCT function calculates the product of two or more complex numbers.
// The syntax of the function is:
//
// IMPRODUCT(number1,[number2],...)
//
func (fn *formulaFuncs) IMPRODUCT(argsList *list.List) formulaArg {
product := complex128(1)
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgString:
if token.Value() == "" {
continue
}
val, err := strconv.ParseComplex(str2cmplx(token.Value()), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
product = product * val
case ArgNumber:
product = product * complex(token.Number, 0)
case ArgMatrix:
for _, row := range token.Matrix {
for _, value := range row {
if value.Value() == "" {
continue
}
val, err := strconv.ParseComplex(str2cmplx(value.Value()), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
product = product * val
}
}
}
}
return newStringFormulaArg(cmplx2str(product, "i"))
}
// IMREAL function returns the real coefficient of a supplied complex number.
// The syntax of the function is:
//
// IMREAL(inumber)
//
func (fn *formulaFuncs) IMREAL(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMREAL requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(fmt.Sprint(real(inumber)))
}
// IMSEC function returns the secant of a supplied complex number. The syntax
// of the function is:
//
// IMSEC(inumber)
//
func (fn *formulaFuncs) IMSEC(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMSEC requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(cmplx2str(1/cmplx.Cos(inumber), value[len(value)-1:]))
}
// IMSECH function returns the hyperbolic secant of a supplied complex number.
// The syntax of the function is:
//
// IMSECH(inumber)
//
func (fn *formulaFuncs) IMSECH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMSECH requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(cmplx2str(1/cmplx.Cosh(inumber), value[len(value)-1:]))
}
// IMSIN function returns the Sine of a supplied complex number. The syntax of
// the function is:
//
// IMSIN(inumber)
//
func (fn *formulaFuncs) IMSIN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMSIN requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(cmplx2str(cmplx.Sin(inumber), value[len(value)-1:]))
}
// IMSINH function returns the hyperbolic sine of a supplied complex number.
// The syntax of the function is:
//
// IMSINH(inumber)
//
func (fn *formulaFuncs) IMSINH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMSINH requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(cmplx2str(cmplx.Sinh(inumber), value[len(value)-1:]))
}
// IMSQRT function returns the square root of a supplied complex number. The
// syntax of the function is:
//
// IMSQRT(inumber)
//
func (fn *formulaFuncs) IMSQRT(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMSQRT requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(cmplx2str(cmplx.Sqrt(inumber), value[len(value)-1:]))
}
// IMSUB function calculates the difference between two complex numbers
// (i.e. subtracts one complex number from another). The syntax of the
// function is:
//
// IMSUB(inumber1,inumber2)
//
func (fn *formulaFuncs) IMSUB(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "IMSUB requires 2 arguments")
}
i1, err := strconv.ParseComplex(str2cmplx(argsList.Front().Value.(formulaArg).Value()), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
i2, err := strconv.ParseComplex(str2cmplx(argsList.Back().Value.(formulaArg).Value()), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(cmplx2str(i1-i2, "i"))
}
// IMSUM function calculates the sum of two or more complex numbers. The
// syntax of the function is:
//
// IMSUM(inumber1,inumber2,...)
//
func (fn *formulaFuncs) IMSUM(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMSUM requires at least 1 argument")
}
var result complex128
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
num, err := strconv.ParseComplex(str2cmplx(token.Value()), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
result += num
}
return newStringFormulaArg(cmplx2str(result, "i"))
}
// IMTAN function returns the tangent of a supplied complex number. The syntax
// of the function is:
//
// IMTAN(inumber)
//
func (fn *formulaFuncs) IMTAN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IMTAN requires 1 argument")
}
value := argsList.Front().Value.(formulaArg).Value()
inumber, err := strconv.ParseComplex(str2cmplx(value), 128)
if err != nil {
return newErrorFormulaArg(formulaErrorNUM, err.Error())
}
return newStringFormulaArg(cmplx2str(cmplx.Tan(inumber), value[len(value)-1:]))
}
// OCT2BIN function converts an Octal (Base 8) number into a Binary (Base 2)
// number. The syntax of the function is:
//
// OCT2BIN(number,[places])
//
func (fn *formulaFuncs) OCT2BIN(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "OCT2BIN requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "OCT2BIN allows at most 2 arguments")
}
token := argsList.Front().Value.(formulaArg)
number := token.ToNumber()
if number.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, number.Error)
}
decimal, newList := fn.oct2dec(token.Value()), list.New()
newList.PushBack(decimal)
if argsList.Len() == 2 {
newList.PushBack(argsList.Back().Value.(formulaArg))
}
return fn.dec2x("OCT2BIN", newList)
}
// OCT2DEC function converts an Octal (a base-8 number) into a decimal number.
// The syntax of the function is:
//
// OCT2DEC(number)
//
func (fn *formulaFuncs) OCT2DEC(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "OCT2DEC requires 1 numeric argument")
}
token := argsList.Front().Value.(formulaArg)
number := token.ToNumber()
if number.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, number.Error)
}
return fn.oct2dec(token.Value())
}
// OCT2HEX function converts an Octal (Base 8) number into a Hexadecimal
// (Base 16) number. The syntax of the function is:
//
// OCT2HEX(number,[places])
//
func (fn *formulaFuncs) OCT2HEX(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "OCT2HEX requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "OCT2HEX allows at most 2 arguments")
}
token := argsList.Front().Value.(formulaArg)
number := token.ToNumber()
if number.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, number.Error)
}
decimal, newList := fn.oct2dec(token.Value()), list.New()
newList.PushBack(decimal)
if argsList.Len() == 2 {
newList.PushBack(argsList.Back().Value.(formulaArg))
}
return fn.dec2x("OCT2HEX", newList)
}
// oct2dec is an implementation of the formula function OCT2DEC.
func (fn *formulaFuncs) oct2dec(number string) formulaArg {
decimal, length := 0.0, len(number)
for i := length; i > 0; i-- {
num, _ := strconv.Atoi(string(number[length-i]))
if i == 10 && string(number[length-i]) == "7" {
decimal += math.Pow(-8.0, float64(i-1))
continue
}
decimal += float64(num) * math.Pow(8.0, float64(i-1))
}
return newNumberFormulaArg(decimal)
}
// Math and Trigonometric Functions
// ABS function returns the absolute value of any supplied number. The syntax
// of the function is:
//
// ABS(number)
//
func (fn *formulaFuncs) ABS(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ABS requires 1 numeric argument")
}
arg := argsList.Front().Value.(formulaArg).ToNumber()
if arg.Type == ArgError {
return arg
}
return newNumberFormulaArg(math.Abs(arg.Number))
}
// ACOS function calculates the arccosine (i.e. the inverse cosine) of a given
// number, and returns an angle, in radians, between 0 and π. The syntax of
// the function is:
//
// ACOS(number)
//
func (fn *formulaFuncs) ACOS(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ACOS requires 1 numeric argument")
}
arg := argsList.Front().Value.(formulaArg).ToNumber()
if arg.Type == ArgError {
return arg
}
return newNumberFormulaArg(math.Acos(arg.Number))
}
// ACOSH function calculates the inverse hyperbolic cosine of a supplied number.
// of the function is:
//
// ACOSH(number)
//
func (fn *formulaFuncs) ACOSH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ACOSH requires 1 numeric argument")
}
arg := argsList.Front().Value.(formulaArg).ToNumber()
if arg.Type == ArgError {
return arg
}
return newNumberFormulaArg(math.Acosh(arg.Number))
}
// ACOT function calculates the arccotangent (i.e. the inverse cotangent) of a
// given number, and returns an angle, in radians, between 0 and π. The syntax
// of the function is:
//
// ACOT(number)
//
func (fn *formulaFuncs) ACOT(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ACOT requires 1 numeric argument")
}
arg := argsList.Front().Value.(formulaArg).ToNumber()
if arg.Type == ArgError {
return arg
}
return newNumberFormulaArg(math.Pi/2 - math.Atan(arg.Number))
}
// ACOTH function calculates the hyperbolic arccotangent (coth) of a supplied
// value. The syntax of the function is:
//
// ACOTH(number)
//
func (fn *formulaFuncs) ACOTH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ACOTH requires 1 numeric argument")
}
arg := argsList.Front().Value.(formulaArg).ToNumber()
if arg.Type == ArgError {
return arg
}
return newNumberFormulaArg(math.Atanh(1 / arg.Number))
}
// ARABIC function converts a Roman numeral into an Arabic numeral. The syntax
// of the function is:
//
// ARABIC(text)
//
func (fn *formulaFuncs) ARABIC(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ARABIC requires 1 numeric argument")
}
text := argsList.Front().Value.(formulaArg).Value()
if len(text) > MaxFieldLength {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
text = strings.ToUpper(text)
number, actualStart, index, isNegative := 0, 0, len(text)-1, false
startIndex, subtractNumber, currentPartValue, currentCharValue, prevCharValue := 0, 0, 0, 0, -1
for index >= 0 && text[index] == ' ' {
index--
}
for actualStart <= index && text[actualStart] == ' ' {
actualStart++
}
if actualStart <= index && text[actualStart] == '-' {
isNegative = true
actualStart++
}
charMap := map[rune]int{'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000}
for index >= actualStart {
startIndex = index
startChar := text[startIndex]
index--
for index >= actualStart && (text[index]|' ') == startChar {
index--
}
currentCharValue = charMap[rune(startChar)]
currentPartValue = (startIndex - index) * currentCharValue
if currentCharValue >= prevCharValue {
number += currentPartValue - subtractNumber
prevCharValue = currentCharValue
subtractNumber = 0
continue
}
subtractNumber += currentPartValue
}
if subtractNumber != 0 {
number -= subtractNumber
}
if isNegative {
number = -number
}
return newNumberFormulaArg(float64(number))
}
// ASIN function calculates the arcsine (i.e. the inverse sine) of a given
// number, and returns an angle, in radians, between -π/2 and π/2. The syntax
// of the function is:
//
// ASIN(number)
//
func (fn *formulaFuncs) ASIN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ASIN requires 1 numeric argument")
}
arg := argsList.Front().Value.(formulaArg).ToNumber()
if arg.Type == ArgError {
return arg
}
return newNumberFormulaArg(math.Asin(arg.Number))
}
// ASINH function calculates the inverse hyperbolic sine of a supplied number.
// The syntax of the function is:
//
// ASINH(number)
//
func (fn *formulaFuncs) ASINH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ASINH requires 1 numeric argument")
}
arg := argsList.Front().Value.(formulaArg).ToNumber()
if arg.Type == ArgError {
return arg
}
return newNumberFormulaArg(math.Asinh(arg.Number))
}
// ATAN function calculates the arctangent (i.e. the inverse tangent) of a
// given number, and returns an angle, in radians, between -Ï€/2 and +Ï€/2. The
// syntax of the function is:
//
// ATAN(number)
//
func (fn *formulaFuncs) ATAN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ATAN requires 1 numeric argument")
}
arg := argsList.Front().Value.(formulaArg).ToNumber()
if arg.Type == ArgError {
return arg
}
return newNumberFormulaArg(math.Atan(arg.Number))
}
// ATANH function calculates the inverse hyperbolic tangent of a supplied
// number. The syntax of the function is:
//
// ATANH(number)
//
func (fn *formulaFuncs) ATANH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ATANH requires 1 numeric argument")
}
arg := argsList.Front().Value.(formulaArg).ToNumber()
if arg.Type == ArgError {
return arg
}
return newNumberFormulaArg(math.Atanh(arg.Number))
}
// ATAN2 function calculates the arctangent (i.e. the inverse tangent) of a
// given set of x and y coordinates, and returns an angle, in radians, between
// -Ï€/2 and +Ï€/2. The syntax of the function is:
//
// ATAN2(x_num,y_num)
//
func (fn *formulaFuncs) ATAN2(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "ATAN2 requires 2 numeric arguments")
}
x := argsList.Back().Value.(formulaArg).ToNumber()
if x.Type == ArgError {
return x
}
y := argsList.Front().Value.(formulaArg).ToNumber()
if y.Type == ArgError {
return y
}
return newNumberFormulaArg(math.Atan2(x.Number, y.Number))
}
// BASE function converts a number into a supplied base (radix), and returns a
// text representation of the calculated value. The syntax of the function is:
//
// BASE(number,radix,[min_length])
//
func (fn *formulaFuncs) BASE(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "BASE requires at least 2 arguments")
}
if argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, "BASE allows at most 3 arguments")
}
var minLength int
var err error
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
radix := argsList.Front().Next().Value.(formulaArg).ToNumber()
if radix.Type == ArgError {
return radix
}
if int(radix.Number) < 2 || int(radix.Number) > 36 {
return newErrorFormulaArg(formulaErrorVALUE, "radix must be an integer >= 2 and <= 36")
}
if argsList.Len() > 2 {
if minLength, err = strconv.Atoi(argsList.Back().Value.(formulaArg).Value()); err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
}
result := strconv.FormatInt(int64(number.Number), int(radix.Number))
if len(result) < minLength {
result = strings.Repeat("0", minLength-len(result)) + result
}
return newStringFormulaArg(strings.ToUpper(result))
}
// CEILING function rounds a supplied number away from zero, to the nearest
// multiple of a given number. The syntax of the function is:
//
// CEILING(number,significance)
//
func (fn *formulaFuncs) CEILING(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "CEILING requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "CEILING allows at most 2 arguments")
}
number, significance, res := 0.0, 1.0, 0.0
n := argsList.Front().Value.(formulaArg).ToNumber()
if n.Type == ArgError {
return n
}
number = n.Number
if number < 0 {
significance = -1
}
if argsList.Len() > 1 {
s := argsList.Back().Value.(formulaArg).ToNumber()
if s.Type == ArgError {
return s
}
significance = s.Number
}
if significance < 0 && number > 0 {
return newErrorFormulaArg(formulaErrorVALUE, "negative sig to CEILING invalid")
}
if argsList.Len() == 1 {
return newNumberFormulaArg(math.Ceil(number))
}
number, res = math.Modf(number / significance)
if res > 0 {
number++
}
return newNumberFormulaArg(number * significance)
}
// CEILINGdotMATH function rounds a supplied number up to a supplied multiple
// of significance. The syntax of the function is:
//
// CEILING.MATH(number,[significance],[mode])
//
func (fn *formulaFuncs) CEILINGdotMATH(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "CEILING.MATH requires at least 1 argument")
}
if argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, "CEILING.MATH allows at most 3 arguments")
}
number, significance, mode := 0.0, 1.0, 1.0
n := argsList.Front().Value.(formulaArg).ToNumber()
if n.Type == ArgError {
return n
}
number = n.Number
if number < 0 {
significance = -1
}
if argsList.Len() > 1 {
s := argsList.Front().Next().Value.(formulaArg).ToNumber()
if s.Type == ArgError {
return s
}
significance = s.Number
}
if argsList.Len() == 1 {
return newNumberFormulaArg(math.Ceil(number))
}
if argsList.Len() > 2 {
m := argsList.Back().Value.(formulaArg).ToNumber()
if m.Type == ArgError {
return m
}
mode = m.Number
}
val, res := math.Modf(number / significance)
if res != 0 {
if number > 0 {
val++
} else if mode < 0 {
val--
}
}
return newNumberFormulaArg(val * significance)
}
// CEILINGdotPRECISE function rounds a supplied number up (regardless of the
// number's sign), to the nearest multiple of a given number. The syntax of
// the function is:
//
// CEILING.PRECISE(number,[significance])
//
func (fn *formulaFuncs) CEILINGdotPRECISE(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "CEILING.PRECISE requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "CEILING.PRECISE allows at most 2 arguments")
}
number, significance := 0.0, 1.0
n := argsList.Front().Value.(formulaArg).ToNumber()
if n.Type == ArgError {
return n
}
number = n.Number
if number < 0 {
significance = -1
}
if argsList.Len() == 1 {
return newNumberFormulaArg(math.Ceil(number))
}
if argsList.Len() > 1 {
s := argsList.Back().Value.(formulaArg).ToNumber()
if s.Type == ArgError {
return s
}
significance = s.Number
significance = math.Abs(significance)
if significance == 0 {
return newNumberFormulaArg(significance)
}
}
val, res := math.Modf(number / significance)
if res != 0 {
if number > 0 {
val++
}
}
return newNumberFormulaArg(val * significance)
}
// COMBIN function calculates the number of combinations (in any order) of a
// given number objects from a set. The syntax of the function is:
//
// COMBIN(number,number_chosen)
//
func (fn *formulaFuncs) COMBIN(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "COMBIN requires 2 argument")
}
number, chosen, val := 0.0, 0.0, 1.0
n := argsList.Front().Value.(formulaArg).ToNumber()
if n.Type == ArgError {
return n
}
number = n.Number
c := argsList.Back().Value.(formulaArg).ToNumber()
if c.Type == ArgError {
return c
}
chosen = c.Number
number, chosen = math.Trunc(number), math.Trunc(chosen)
if chosen > number {
return newErrorFormulaArg(formulaErrorVALUE, "COMBIN requires number >= number_chosen")
}
if chosen == number || chosen == 0 {
return newNumberFormulaArg(1)
}
for c := float64(1); c <= chosen; c++ {
val *= (number + 1 - c) / c
}
return newNumberFormulaArg(math.Ceil(val))
}
// COMBINA function calculates the number of combinations, with repetitions,
// of a given number objects from a set. The syntax of the function is:
//
// COMBINA(number,number_chosen)
//
func (fn *formulaFuncs) COMBINA(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "COMBINA requires 2 argument")
}
var number, chosen float64
n := argsList.Front().Value.(formulaArg).ToNumber()
if n.Type == ArgError {
return n
}
number = n.Number
c := argsList.Back().Value.(formulaArg).ToNumber()
if c.Type == ArgError {
return c
}
chosen = c.Number
number, chosen = math.Trunc(number), math.Trunc(chosen)
if number < chosen {
return newErrorFormulaArg(formulaErrorVALUE, "COMBINA requires number > number_chosen")
}
if number == 0 {
return newNumberFormulaArg(number)
}
args := list.New()
args.PushBack(formulaArg{
String: fmt.Sprintf("%g", number+chosen-1),
Type: ArgString,
})
args.PushBack(formulaArg{
String: fmt.Sprintf("%g", number-1),
Type: ArgString,
})
return fn.COMBIN(args)
}
// COS function calculates the cosine of a given angle. The syntax of the
// function is:
//
// COS(number)
//
func (fn *formulaFuncs) COS(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "COS requires 1 numeric argument")
}
val := argsList.Front().Value.(formulaArg).ToNumber()
if val.Type == ArgError {
return val
}
return newNumberFormulaArg(math.Cos(val.Number))
}
// COSH function calculates the hyperbolic cosine (cosh) of a supplied number.
// The syntax of the function is:
//
// COSH(number)
//
func (fn *formulaFuncs) COSH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "COSH requires 1 numeric argument")
}
val := argsList.Front().Value.(formulaArg).ToNumber()
if val.Type == ArgError {
return val
}
return newNumberFormulaArg(math.Cosh(val.Number))
}
// COT function calculates the cotangent of a given angle. The syntax of the
// function is:
//
// COT(number)
//
func (fn *formulaFuncs) COT(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "COT requires 1 numeric argument")
}
val := argsList.Front().Value.(formulaArg).ToNumber()
if val.Type == ArgError {
return val
}
if val.Number == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(1 / math.Tan(val.Number))
}
// COTH function calculates the hyperbolic cotangent (coth) of a supplied
// angle. The syntax of the function is:
//
// COTH(number)
//
func (fn *formulaFuncs) COTH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "COTH requires 1 numeric argument")
}
val := argsList.Front().Value.(formulaArg).ToNumber()
if val.Type == ArgError {
return val
}
if val.Number == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg((math.Exp(val.Number) + math.Exp(-val.Number)) / (math.Exp(val.Number) - math.Exp(-val.Number)))
}
// CSC function calculates the cosecant of a given angle. The syntax of the
// function is:
//
// CSC(number)
//
func (fn *formulaFuncs) CSC(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "CSC requires 1 numeric argument")
}
val := argsList.Front().Value.(formulaArg).ToNumber()
if val.Type == ArgError {
return val
}
if val.Number == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(1 / math.Sin(val.Number))
}
// CSCH function calculates the hyperbolic cosecant (csch) of a supplied
// angle. The syntax of the function is:
//
// CSCH(number)
//
func (fn *formulaFuncs) CSCH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "CSCH requires 1 numeric argument")
}
val := argsList.Front().Value.(formulaArg).ToNumber()
if val.Type == ArgError {
return val
}
if val.Number == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(1 / math.Sinh(val.Number))
}
// DECIMAL function converts a text representation of a number in a specified
// base, into a decimal value. The syntax of the function is:
//
// DECIMAL(text,radix)
//
func (fn *formulaFuncs) DECIMAL(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "DECIMAL requires 2 numeric arguments")
}
text := argsList.Front().Value.(formulaArg).Value()
var err error
radix := argsList.Back().Value.(formulaArg).ToNumber()
if radix.Type != ArgNumber {
return radix
}
if len(text) > 2 && (strings.HasPrefix(text, "0x") || strings.HasPrefix(text, "0X")) {
text = text[2:]
}
val, err := strconv.ParseInt(text, int(radix.Number), 64)
if err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
return newNumberFormulaArg(float64(val))
}
// DEGREES function converts radians into degrees. The syntax of the function
// is:
//
// DEGREES(angle)
//
func (fn *formulaFuncs) DEGREES(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "DEGREES requires 1 numeric argument")
}
val := argsList.Front().Value.(formulaArg).ToNumber()
if val.Type == ArgError {
return val
}
if val.Number == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(180.0 / math.Pi * val.Number)
}
// EVEN function rounds a supplied number away from zero (i.e. rounds a
// positive number up and a negative number down), to the next even number.
// The syntax of the function is:
//
// EVEN(number)
//
func (fn *formulaFuncs) EVEN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "EVEN requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
sign := math.Signbit(number.Number)
m, frac := math.Modf(number.Number / 2)
val := m * 2
if frac != 0 {
if !sign {
val += 2
} else {
val -= 2
}
}
return newNumberFormulaArg(val)
}
// EXP function calculates the value of the mathematical constant e, raised to
// the power of a given number. The syntax of the function is:
//
// EXP(number)
//
func (fn *formulaFuncs) EXP(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "EXP requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
return newStringFormulaArg(strings.ToUpper(fmt.Sprintf("%g", math.Exp(number.Number))))
}
// fact returns the factorial of a supplied number.
func fact(number float64) float64 {
val := float64(1)
for i := float64(2); i <= number; i++ {
val *= i
}
return val
}
// FACT function returns the factorial of a supplied number. The syntax of the
// function is:
//
// FACT(number)
//
func (fn *formulaFuncs) FACT(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "FACT requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
if number.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(fact(number.Number))
}
// FACTDOUBLE function returns the double factorial of a supplied number. The
// syntax of the function is:
//
// FACTDOUBLE(number)
//
func (fn *formulaFuncs) FACTDOUBLE(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "FACTDOUBLE requires 1 numeric argument")
}
val := 1.0
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
if number.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
for i := math.Trunc(number.Number); i > 1; i -= 2 {
val *= i
}
return newStringFormulaArg(strings.ToUpper(fmt.Sprintf("%g", val)))
}
// FLOOR function rounds a supplied number towards zero to the nearest
// multiple of a specified significance. The syntax of the function is:
//
// FLOOR(number,significance)
//
func (fn *formulaFuncs) FLOOR(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "FLOOR requires 2 numeric arguments")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
significance := argsList.Back().Value.(formulaArg).ToNumber()
if significance.Type == ArgError {
return significance
}
if significance.Number < 0 && number.Number >= 0 {
return newErrorFormulaArg(formulaErrorNUM, "invalid arguments to FLOOR")
}
val := number.Number
val, res := math.Modf(val / significance.Number)
if res != 0 {
if number.Number < 0 && res < 0 {
val--
}
}
return newStringFormulaArg(strings.ToUpper(fmt.Sprintf("%g", val*significance.Number)))
}
// FLOORdotMATH function rounds a supplied number down to a supplied multiple
// of significance. The syntax of the function is:
//
// FLOOR.MATH(number,[significance],[mode])
//
func (fn *formulaFuncs) FLOORdotMATH(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "FLOOR.MATH requires at least 1 argument")
}
if argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, "FLOOR.MATH allows at most 3 arguments")
}
significance, mode := 1.0, 1.0
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
if number.Number < 0 {
significance = -1
}
if argsList.Len() > 1 {
s := argsList.Front().Next().Value.(formulaArg).ToNumber()
if s.Type == ArgError {
return s
}
significance = s.Number
}
if argsList.Len() == 1 {
return newNumberFormulaArg(math.Floor(number.Number))
}
if argsList.Len() > 2 {
m := argsList.Back().Value.(formulaArg).ToNumber()
if m.Type == ArgError {
return m
}
mode = m.Number
}
val, res := math.Modf(number.Number / significance)
if res != 0 && number.Number < 0 && mode > 0 {
val--
}
return newNumberFormulaArg(val * significance)
}
// FLOORdotPRECISE function rounds a supplied number down to a supplied
// multiple of significance. The syntax of the function is:
//
// FLOOR.PRECISE(number,[significance])
//
func (fn *formulaFuncs) FLOORdotPRECISE(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "FLOOR.PRECISE requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "FLOOR.PRECISE allows at most 2 arguments")
}
var significance float64
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
if number.Number < 0 {
significance = -1
}
if argsList.Len() == 1 {
return newNumberFormulaArg(math.Floor(number.Number))
}
if argsList.Len() > 1 {
s := argsList.Back().Value.(formulaArg).ToNumber()
if s.Type == ArgError {
return s
}
significance = s.Number
significance = math.Abs(significance)
if significance == 0 {
return newNumberFormulaArg(significance)
}
}
val, res := math.Modf(number.Number / significance)
if res != 0 {
if number.Number < 0 {
val--
}
}
return newNumberFormulaArg(val * significance)
}
// gcd returns the greatest common divisor of two supplied integers.
func gcd(x, y float64) float64 {
x, y = math.Trunc(x), math.Trunc(y)
if x == 0 {
return y
}
if y == 0 {
return x
}
for x != y {
if x > y {
x = x - y
} else {
y = y - x
}
}
return x
}
// GCD function returns the greatest common divisor of two or more supplied
// integers. The syntax of the function is:
//
// GCD(number1,[number2],...)
//
func (fn *formulaFuncs) GCD(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "GCD requires at least 1 argument")
}
var (
val float64
nums []float64
)
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgString:
num := token.ToNumber()
if num.Type == ArgError {
return num
}
val = num.Number
case ArgNumber:
val = token.Number
}
nums = append(nums, val)
}
if nums[0] < 0 {
return newErrorFormulaArg(formulaErrorVALUE, "GCD only accepts positive arguments")
}
if len(nums) == 1 {
return newNumberFormulaArg(nums[0])
}
cd := nums[0]
for i := 1; i < len(nums); i++ {
if nums[i] < 0 {
return newErrorFormulaArg(formulaErrorVALUE, "GCD only accepts positive arguments")
}
cd = gcd(cd, nums[i])
}
return newNumberFormulaArg(cd)
}
// INT function truncates a supplied number down to the closest integer. The
// syntax of the function is:
//
// INT(number)
//
func (fn *formulaFuncs) INT(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "INT requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
val, frac := math.Modf(number.Number)
if frac < 0 {
val--
}
return newNumberFormulaArg(val)
}
// ISOdotCEILING function rounds a supplied number up (regardless of the
// number's sign), to the nearest multiple of a supplied significance. The
// syntax of the function is:
//
// ISO.CEILING(number,[significance])
//
func (fn *formulaFuncs) ISOdotCEILING(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "ISO.CEILING requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "ISO.CEILING allows at most 2 arguments")
}
var significance float64
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
if number.Number < 0 {
significance = -1
}
if argsList.Len() == 1 {
return newNumberFormulaArg(math.Ceil(number.Number))
}
if argsList.Len() > 1 {
s := argsList.Back().Value.(formulaArg).ToNumber()
if s.Type == ArgError {
return s
}
significance = s.Number
significance = math.Abs(significance)
if significance == 0 {
return newNumberFormulaArg(significance)
}
}
val, res := math.Modf(number.Number / significance)
if res != 0 {
if number.Number > 0 {
val++
}
}
return newNumberFormulaArg(val * significance)
}
// lcm returns the least common multiple of two supplied integers.
func lcm(a, b float64) float64 {
a = math.Trunc(a)
b = math.Trunc(b)
if a == 0 && b == 0 {
return 0
}
return a * b / gcd(a, b)
}
// LCM function returns the least common multiple of two or more supplied
// integers. The syntax of the function is:
//
// LCM(number1,[number2],...)
//
func (fn *formulaFuncs) LCM(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "LCM requires at least 1 argument")
}
var (
val float64
nums []float64
err error
)
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgString:
if token.String == "" {
continue
}
if val, err = strconv.ParseFloat(token.String, 64); err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
case ArgNumber:
val = token.Number
}
nums = append(nums, val)
}
if nums[0] < 0 {
return newErrorFormulaArg(formulaErrorVALUE, "LCM only accepts positive arguments")
}
if len(nums) == 1 {
return newNumberFormulaArg(nums[0])
}
cm := nums[0]
for i := 1; i < len(nums); i++ {
if nums[i] < 0 {
return newErrorFormulaArg(formulaErrorVALUE, "LCM only accepts positive arguments")
}
cm = lcm(cm, nums[i])
}
return newNumberFormulaArg(cm)
}
// LN function calculates the natural logarithm of a given number. The syntax
// of the function is:
//
// LN(number)
//
func (fn *formulaFuncs) LN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "LN requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
return newNumberFormulaArg(math.Log(number.Number))
}
// LOG function calculates the logarithm of a given number, to a supplied
// base. The syntax of the function is:
//
// LOG(number,[base])
//
func (fn *formulaFuncs) LOG(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "LOG requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "LOG allows at most 2 arguments")
}
base := 10.0
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
if argsList.Len() > 1 {
b := argsList.Back().Value.(formulaArg).ToNumber()
if b.Type == ArgError {
return b
}
base = b.Number
}
if number.Number == 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorDIV)
}
if base == 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorDIV)
}
if base == 1 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(math.Log(number.Number) / math.Log(base))
}
// LOG10 function calculates the base 10 logarithm of a given number. The
// syntax of the function is:
//
// LOG10(number)
//
func (fn *formulaFuncs) LOG10(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "LOG10 requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
return newNumberFormulaArg(math.Log10(number.Number))
}
// minor function implement a minor of a matrix A is the determinant of some
// smaller square matrix.
func minor(sqMtx [][]float64, idx int) [][]float64 {
var ret [][]float64
for i := range sqMtx {
if i == 0 {
continue
}
var row []float64
for j := range sqMtx {
if j == idx {
continue
}
row = append(row, sqMtx[i][j])
}
ret = append(ret, row)
}
return ret
}
// det determinant of the 2x2 matrix.
func det(sqMtx [][]float64) float64 {
if len(sqMtx) == 2 {
m00 := sqMtx[0][0]
m01 := sqMtx[0][1]
m10 := sqMtx[1][0]
m11 := sqMtx[1][1]
return m00*m11 - m10*m01
}
var res, sgn float64 = 0, 1
for j := range sqMtx {
res += sgn * sqMtx[0][j] * det(minor(sqMtx, j))
sgn *= -1
}
return res
}
// newNumberMatrix converts a formula arguments matrix to a number matrix.
func newNumberMatrix(arg formulaArg, phalanx bool) (numMtx [][]float64, ele formulaArg) {
rows := len(arg.Matrix)
for r, row := range arg.Matrix {
if phalanx && len(row) != rows {
ele = newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
return
}
numMtx = append(numMtx, make([]float64, len(row)))
for c, cell := range row {
if ele = cell.ToNumber(); ele.Type != ArgNumber {
return
}
numMtx[r][c] = ele.Number
}
}
return
}
// newFormulaArgMatrix converts the number formula arguments matrix to a
// formula arguments matrix.
func newFormulaArgMatrix(numMtx [][]float64) (arg [][]formulaArg) {
for r, row := range numMtx {
arg = append(arg, make([]formulaArg, len(row)))
for c, cell := range row {
arg[r][c] = newNumberFormulaArg(cell)
}
}
return
}
// MDETERM calculates the determinant of a square matrix. The
// syntax of the function is:
//
// MDETERM(array)
//
func (fn *formulaFuncs) MDETERM(argsList *list.List) (result formulaArg) {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "MDETERM requires 1 argument")
}
numMtx, errArg := newNumberMatrix(argsList.Front().Value.(formulaArg), true)
if errArg.Type == ArgError {
return errArg
}
return newNumberFormulaArg(det(numMtx))
}
// cofactorMatrix returns the matrix A of cofactors.
func cofactorMatrix(i, j int, A [][]float64) float64 {
N, sign := len(A), -1.0
if (i+j)%2 == 0 {
sign = 1
}
var B [][]float64
B = append(B, A...)
for m := 0; m < N; m++ {
for n := j + 1; n < N; n++ {
B[m][n-1] = B[m][n]
}
B[m] = B[m][:len(B[m])-1]
}
for k := i + 1; k < N; k++ {
B[k-1] = B[k]
}
B = B[:len(B)-1]
return sign * det(B)
}
// adjugateMatrix returns transpose of the cofactor matrix A with Cramer's
// rule.
func adjugateMatrix(A [][]float64) (adjA [][]float64) {
N := len(A)
var B [][]float64
for i := 0; i < N; i++ {
adjA = append(adjA, make([]float64, N))
for j := 0; j < N; j++ {
for m := 0; m < N; m++ {
for n := 0; n < N; n++ {
for x := len(B); x <= m; x++ {
B = append(B, []float64{})
}
for k := len(B[m]); k <= n; k++ {
B[m] = append(B[m], 0)
}
B[m][n] = A[m][n]
}
}
adjA[i][j] = cofactorMatrix(j, i, B)
}
}
return
}
// MINVERSE function calculates the inverse of a square matrix. The syntax of
// the function is:
//
// MINVERSE(array)
//
func (fn *formulaFuncs) MINVERSE(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "MINVERSE requires 1 argument")
}
numMtx, errArg := newNumberMatrix(argsList.Front().Value.(formulaArg), true)
if errArg.Type == ArgError {
return errArg
}
if detM := det(numMtx); detM != 0 {
datM, invertM := 1/detM, adjugateMatrix(numMtx)
for i := 0; i < len(invertM); i++ {
for j := 0; j < len(invertM[i]); j++ {
invertM[i][j] *= datM
}
}
return newMatrixFormulaArg(newFormulaArgMatrix(invertM))
}
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
// MMULT function calculates the matrix product of two arrays
// (representing matrices). The syntax of the function is:
//
// MMULT(array1,array2)
//
func (fn *formulaFuncs) MMULT(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "MMULT requires 2 argument")
}
numMtx1, errArg1 := newNumberMatrix(argsList.Front().Value.(formulaArg), false)
if errArg1.Type == ArgError {
return errArg1
}
numMtx2, errArg2 := newNumberMatrix(argsList.Back().Value.(formulaArg), false)
if errArg2.Type == ArgError {
return errArg2
}
array2Rows, array2Cols := len(numMtx2), len(numMtx2[0])
if len(numMtx1[0]) != array2Rows {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
var numMtx [][]float64
var row1, row []float64
var sum float64
for i := 0; i < len(numMtx1); i++ {
numMtx = append(numMtx, []float64{})
row = []float64{}
row1 = numMtx1[i]
for j := 0; j < array2Cols; j++ {
sum = 0
for k := 0; k < array2Rows; k++ {
sum += row1[k] * numMtx2[k][j]
}
for l := len(row); l <= j; l++ {
row = append(row, 0)
}
row[j] = sum
numMtx[i] = row
}
}
return newMatrixFormulaArg(newFormulaArgMatrix(numMtx))
}
// MOD function returns the remainder of a division between two supplied
// numbers. The syntax of the function is:
//
// MOD(number,divisor)
//
func (fn *formulaFuncs) MOD(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "MOD requires 2 numeric arguments")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
divisor := argsList.Back().Value.(formulaArg).ToNumber()
if divisor.Type == ArgError {
return divisor
}
if divisor.Number == 0 {
return newErrorFormulaArg(formulaErrorDIV, "MOD divide by zero")
}
trunc, rem := math.Modf(number.Number / divisor.Number)
if rem < 0 {
trunc--
}
return newNumberFormulaArg(number.Number - divisor.Number*trunc)
}
// MROUND function rounds a supplied number up or down to the nearest multiple
// of a given number. The syntax of the function is:
//
// MROUND(number,multiple)
//
func (fn *formulaFuncs) MROUND(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "MROUND requires 2 numeric arguments")
}
n := argsList.Front().Value.(formulaArg).ToNumber()
if n.Type == ArgError {
return n
}
multiple := argsList.Back().Value.(formulaArg).ToNumber()
if multiple.Type == ArgError {
return multiple
}
if multiple.Number == 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if multiple.Number < 0 && n.Number > 0 ||
multiple.Number > 0 && n.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
number, res := math.Modf(n.Number / multiple.Number)
if math.Trunc(res+0.5) > 0 {
number++
}
return newNumberFormulaArg(number * multiple.Number)
}
// MULTINOMIAL function calculates the ratio of the factorial of a sum of
// supplied values to the product of factorials of those values. The syntax of
// the function is:
//
// MULTINOMIAL(number1,[number2],...)
//
func (fn *formulaFuncs) MULTINOMIAL(argsList *list.List) formulaArg {
val, num, denom := 0.0, 0.0, 1.0
var err error
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgString:
if token.String == "" {
continue
}
if val, err = strconv.ParseFloat(token.String, 64); err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
case ArgNumber:
val = token.Number
}
num += val
denom *= fact(val)
}
return newNumberFormulaArg(fact(num) / denom)
}
// MUNIT function returns the unit matrix for a specified dimension. The
// syntax of the function is:
//
// MUNIT(dimension)
//
func (fn *formulaFuncs) MUNIT(argsList *list.List) (result formulaArg) {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "MUNIT requires 1 numeric argument")
}
dimension := argsList.Back().Value.(formulaArg).ToNumber()
if dimension.Type == ArgError || dimension.Number < 0 {
return newErrorFormulaArg(formulaErrorVALUE, dimension.Error)
}
matrix := make([][]formulaArg, 0, int(dimension.Number))
for i := 0; i < int(dimension.Number); i++ {
row := make([]formulaArg, int(dimension.Number))
for j := 0; j < int(dimension.Number); j++ {
if i == j {
row[j] = newNumberFormulaArg(1.0)
} else {
row[j] = newNumberFormulaArg(0.0)
}
}
matrix = append(matrix, row)
}
return newMatrixFormulaArg(matrix)
}
// ODD function ounds a supplied number away from zero (i.e. rounds a positive
// number up and a negative number down), to the next odd number. The syntax
// of the function is:
//
// ODD(number)
//
func (fn *formulaFuncs) ODD(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ODD requires 1 numeric argument")
}
number := argsList.Back().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
if number.Number == 0 {
return newNumberFormulaArg(1)
}
sign := math.Signbit(number.Number)
m, frac := math.Modf((number.Number - 1) / 2)
val := m*2 + 1
if frac != 0 {
if !sign {
val += 2
} else {
val -= 2
}
}
return newNumberFormulaArg(val)
}
// PI function returns the value of the mathematical constant π (pi), accurate
// to 15 digits (14 decimal places). The syntax of the function is:
//
// PI()
//
func (fn *formulaFuncs) PI(argsList *list.List) formulaArg {
if argsList.Len() != 0 {
return newErrorFormulaArg(formulaErrorVALUE, "PI accepts no arguments")
}
return newNumberFormulaArg(math.Pi)
}
// POWER function calculates a given number, raised to a supplied power.
// The syntax of the function is:
//
// POWER(number,power)
//
func (fn *formulaFuncs) POWER(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "POWER requires 2 numeric arguments")
}
x := argsList.Front().Value.(formulaArg).ToNumber()
if x.Type == ArgError {
return x
}
y := argsList.Back().Value.(formulaArg).ToNumber()
if y.Type == ArgError {
return y
}
if x.Number == 0 && y.Number == 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if x.Number == 0 && y.Number < 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(math.Pow(x.Number, y.Number))
}
// PRODUCT function returns the product (multiplication) of a supplied set of
// numerical values. The syntax of the function is:
//
// PRODUCT(number1,[number2],...)
//
func (fn *formulaFuncs) PRODUCT(argsList *list.List) formulaArg {
val, product := 0.0, 1.0
var err error
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgString:
if token.String == "" {
continue
}
if val, err = strconv.ParseFloat(token.String, 64); err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
product = product * val
case ArgNumber:
product = product * token.Number
case ArgMatrix:
for _, row := range token.Matrix {
for _, value := range row {
if value.Value() == "" {
continue
}
if val, err = strconv.ParseFloat(value.String, 64); err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
product *= val
}
}
}
}
return newNumberFormulaArg(product)
}
// QUOTIENT function returns the integer portion of a division between two
// supplied numbers. The syntax of the function is:
//
// QUOTIENT(numerator,denominator)
//
func (fn *formulaFuncs) QUOTIENT(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "QUOTIENT requires 2 numeric arguments")
}
x := argsList.Front().Value.(formulaArg).ToNumber()
if x.Type == ArgError {
return x
}
y := argsList.Back().Value.(formulaArg).ToNumber()
if y.Type == ArgError {
return y
}
if y.Number == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(math.Trunc(x.Number / y.Number))
}
// RADIANS function converts radians into degrees. The syntax of the function is:
//
// RADIANS(angle)
//
func (fn *formulaFuncs) RADIANS(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "RADIANS requires 1 numeric argument")
}
angle := argsList.Front().Value.(formulaArg).ToNumber()
if angle.Type == ArgError {
return angle
}
return newNumberFormulaArg(math.Pi / 180.0 * angle.Number)
}
// RAND function generates a random real number between 0 and 1. The syntax of
// the function is:
//
// RAND()
//
func (fn *formulaFuncs) RAND(argsList *list.List) formulaArg {
if argsList.Len() != 0 {
return newErrorFormulaArg(formulaErrorVALUE, "RAND accepts no arguments")
}
return newNumberFormulaArg(rand.New(rand.NewSource(time.Now().UnixNano())).Float64())
}
// RANDBETWEEN function generates a random integer between two supplied
// integers. The syntax of the function is:
//
// RANDBETWEEN(bottom,top)
//
func (fn *formulaFuncs) RANDBETWEEN(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "RANDBETWEEN requires 2 numeric arguments")
}
bottom := argsList.Front().Value.(formulaArg).ToNumber()
if bottom.Type == ArgError {
return bottom
}
top := argsList.Back().Value.(formulaArg).ToNumber()
if top.Type == ArgError {
return top
}
if top.Number < bottom.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
num := rand.New(rand.NewSource(time.Now().UnixNano())).Int63n(int64(top.Number - bottom.Number + 1))
return newNumberFormulaArg(float64(num + int64(bottom.Number)))
}
// romanNumerals defined a numeral system that originated in ancient Rome and
// remained the usual way of writing numbers throughout Europe well into the
// Late Middle Ages.
type romanNumerals struct {
n float64
s string
}
var romanTable = [][]romanNumerals{
{
{1000, "M"},
{900, "CM"},
{500, "D"},
{400, "CD"},
{100, "C"},
{90, "XC"},
{50, "L"},
{40, "XL"},
{10, "X"},
{9, "IX"},
{5, "V"},
{4, "IV"},
{1, "I"},
},
{
{1000, "M"},
{950, "LM"},
{900, "CM"},
{500, "D"},
{450, "LD"},
{400, "CD"},
{100, "C"},
{95, "VC"},
{90, "XC"},
{50, "L"},
{45, "VL"},
{40, "XL"},
{10, "X"},
{9, "IX"},
{5, "V"},
{4, "IV"},
{1, "I"},
},
{
{1000, "M"},
{990, "XM"},
{950, "LM"},
{900, "CM"},
{500, "D"},
{490, "XD"},
{450, "LD"},
{400, "CD"},
{100, "C"},
{99, "IC"},
{90, "XC"},
{50, "L"},
{45, "VL"},
{40, "XL"},
{10, "X"},
{9, "IX"},
{5, "V"},
{4, "IV"},
{1, "I"},
},
{
{1000, "M"},
{995, "VM"},
{990, "XM"},
{950, "LM"},
{900, "CM"},
{500, "D"},
{495, "VD"},
{490, "XD"},
{450, "LD"},
{400, "CD"},
{100, "C"},
{99, "IC"},
{90, "XC"},
{50, "L"},
{45, "VL"},
{40, "XL"},
{10, "X"},
{9, "IX"},
{5, "V"},
{4, "IV"},
{1, "I"},
},
{
{1000, "M"},
{999, "IM"},
{995, "VM"},
{990, "XM"},
{950, "LM"},
{900, "CM"},
{500, "D"},
{499, "ID"},
{495, "VD"},
{490, "XD"},
{450, "LD"},
{400, "CD"},
{100, "C"},
{99, "IC"},
{90, "XC"},
{50, "L"},
{45, "VL"},
{40, "XL"},
{10, "X"},
{9, "IX"},
{5, "V"},
{4, "IV"},
{1, "I"},
},
}
// ROMAN function converts an arabic number to Roman. I.e. for a supplied
// integer, the function returns a text string depicting the roman numeral
// form of the number. The syntax of the function is:
//
// ROMAN(number,[form])
//
func (fn *formulaFuncs) ROMAN(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "ROMAN requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "ROMAN allows at most 2 arguments")
}
var form int
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
if argsList.Len() > 1 {
f := argsList.Back().Value.(formulaArg).ToNumber()
if f.Type == ArgError {
return f
}
form = int(f.Number)
if form < 0 {
form = 0
} else if form > 4 {
form = 4
}
}
decimalTable := romanTable[0]
switch form {
case 1:
decimalTable = romanTable[1]
case 2:
decimalTable = romanTable[2]
case 3:
decimalTable = romanTable[3]
case 4:
decimalTable = romanTable[4]
}
val := math.Trunc(number.Number)
buf := bytes.Buffer{}
for _, r := range decimalTable {
for val >= r.n {
buf.WriteString(r.s)
val -= r.n
}
}
return newStringFormulaArg(buf.String())
}
type roundMode byte
const (
closest roundMode = iota
down
up
)
// round rounds a supplied number up or down.
func (fn *formulaFuncs) round(number, digits float64, mode roundMode) float64 {
var significance float64
if digits > 0 {
significance = math.Pow(1/10.0, digits)
} else {
significance = math.Pow(10.0, -digits)
}
val, res := math.Modf(number / significance)
switch mode {
case closest:
const eps = 0.499999999
if res >= eps {
val++
} else if res <= -eps {
val--
}
case down:
case up:
if res > 0 {
val++
} else if res < 0 {
val--
}
}
return val * significance
}
// ROUND function rounds a supplied number up or down, to a specified number
// of decimal places. The syntax of the function is:
//
// ROUND(number,num_digits)
//
func (fn *formulaFuncs) ROUND(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "ROUND requires 2 numeric arguments")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
digits := argsList.Back().Value.(formulaArg).ToNumber()
if digits.Type == ArgError {
return digits
}
return newNumberFormulaArg(fn.round(number.Number, digits.Number, closest))
}
// ROUNDDOWN function rounds a supplied number down towards zero, to a
// specified number of decimal places. The syntax of the function is:
//
// ROUNDDOWN(number,num_digits)
//
func (fn *formulaFuncs) ROUNDDOWN(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "ROUNDDOWN requires 2 numeric arguments")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
digits := argsList.Back().Value.(formulaArg).ToNumber()
if digits.Type == ArgError {
return digits
}
return newNumberFormulaArg(fn.round(number.Number, digits.Number, down))
}
// ROUNDUP function rounds a supplied number up, away from zero, to a
// specified number of decimal places. The syntax of the function is:
//
// ROUNDUP(number,num_digits)
//
func (fn *formulaFuncs) ROUNDUP(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "ROUNDUP requires 2 numeric arguments")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
digits := argsList.Back().Value.(formulaArg).ToNumber()
if digits.Type == ArgError {
return digits
}
return newNumberFormulaArg(fn.round(number.Number, digits.Number, up))
}
// SEC function calculates the secant of a given angle. The syntax of the
// function is:
//
// SEC(number)
//
func (fn *formulaFuncs) SEC(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "SEC requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
return newNumberFormulaArg(math.Cos(number.Number))
}
// SECH function calculates the hyperbolic secant (sech) of a supplied angle.
// The syntax of the function is:
//
// SECH(number)
//
func (fn *formulaFuncs) SECH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "SECH requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
return newNumberFormulaArg(1 / math.Cosh(number.Number))
}
// SERIESSUM function returns the sum of a power series. The syntax of the
// function is:
//
// SERIESSUM(x,n,m,coefficients)
//
func (fn *formulaFuncs) SERIESSUM(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "SERIESSUM requires 4 arguments")
}
var x, n, m formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if n = argsList.Front().Next().Value.(formulaArg).ToNumber(); n.Type != ArgNumber {
return n
}
if m = argsList.Front().Next().Next().Value.(formulaArg).ToNumber(); m.Type != ArgNumber {
return m
}
var result, i float64
for _, coefficient := range argsList.Back().Value.(formulaArg).ToList() {
if coefficient.Value() == "" {
continue
}
num := coefficient.ToNumber()
if num.Type != ArgNumber {
return num
}
result += num.Number * math.Pow(x.Number, n.Number+(m.Number*i))
i++
}
return newNumberFormulaArg(result)
}
// SIGN function returns the arithmetic sign (+1, -1 or 0) of a supplied
// number. I.e. if the number is positive, the Sign function returns +1, if
// the number is negative, the function returns -1 and if the number is 0
// (zero), the function returns 0. The syntax of the function is:
//
// SIGN(number)
//
func (fn *formulaFuncs) SIGN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "SIGN requires 1 numeric argument")
}
val := argsList.Front().Value.(formulaArg).ToNumber()
if val.Type == ArgError {
return val
}
if val.Number < 0 {
return newNumberFormulaArg(-1)
}
if val.Number > 0 {
return newNumberFormulaArg(1)
}
return newNumberFormulaArg(0)
}
// SIN function calculates the sine of a given angle. The syntax of the
// function is:
//
// SIN(number)
//
func (fn *formulaFuncs) SIN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "SIN requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
return newNumberFormulaArg(math.Sin(number.Number))
}
// SINH function calculates the hyperbolic sine (sinh) of a supplied number.
// The syntax of the function is:
//
// SINH(number)
//
func (fn *formulaFuncs) SINH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "SINH requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
return newNumberFormulaArg(math.Sinh(number.Number))
}
// SQRT function calculates the positive square root of a supplied number. The
// syntax of the function is:
//
// SQRT(number)
//
func (fn *formulaFuncs) SQRT(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "SQRT requires 1 numeric argument")
}
value := argsList.Front().Value.(formulaArg).ToNumber()
if value.Type == ArgError {
return value
}
if value.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(math.Sqrt(value.Number))
}
// SQRTPI function returns the square root of a supplied number multiplied by
// the mathematical constant, π. The syntax of the function is:
//
// SQRTPI(number)
//
func (fn *formulaFuncs) SQRTPI(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "SQRTPI requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
return newNumberFormulaArg(math.Sqrt(number.Number * math.Pi))
}
// STDEV function calculates the sample standard deviation of a supplied set
// of values. The syntax of the function is:
//
// STDEV(number1,[number2],...)
//
func (fn *formulaFuncs) STDEV(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "STDEV requires at least 1 argument")
}
return fn.stdev(false, argsList)
}
// STDEVdotS function calculates the sample standard deviation of a supplied
// set of values. The syntax of the function is:
//
// STDEV.S(number1,[number2],...)
//
func (fn *formulaFuncs) STDEVdotS(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "STDEV.S requires at least 1 argument")
}
return fn.stdev(false, argsList)
}
// STDEVA function estimates standard deviation based on a sample. The
// standard deviation is a measure of how widely values are dispersed from
// the average value (the mean). The syntax of the function is:
//
// STDEVA(number1,[number2],...)
//
func (fn *formulaFuncs) STDEVA(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "STDEVA requires at least 1 argument")
}
return fn.stdev(true, argsList)
}
// calcStdevPow is part of the implementation stdev.
func calcStdevPow(result, count float64, n, m formulaArg) (float64, float64) {
if result == -1 {
result = math.Pow(n.Number-m.Number, 2)
} else {
result += math.Pow(n.Number-m.Number, 2)
}
count++
return result, count
}
// calcStdev is part of the implementation stdev.
func calcStdev(stdeva bool, result, count float64, mean, token formulaArg) (float64, float64) {
for _, row := range token.ToList() {
if row.Type == ArgNumber || row.Type == ArgString {
if !stdeva && (row.Value() == "TRUE" || row.Value() == "FALSE") {
continue
} else if stdeva && (row.Value() == "TRUE" || row.Value() == "FALSE") {
num := row.ToBool()
if num.Type == ArgNumber {
result, count = calcStdevPow(result, count, num, mean)
continue
}
} else {
num := row.ToNumber()
if num.Type == ArgNumber {
result, count = calcStdevPow(result, count, num, mean)
}
}
}
}
return result, count
}
// stdev is an implementation of the formula functions STDEV and STDEVA.
func (fn *formulaFuncs) stdev(stdeva bool, argsList *list.List) formulaArg {
count, result := -1.0, -1.0
var mean formulaArg
if stdeva {
mean = fn.AVERAGEA(argsList)
} else {
mean = fn.AVERAGE(argsList)
}
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgString, ArgNumber:
if !stdeva && (token.Value() == "TRUE" || token.Value() == "FALSE") {
continue
} else if stdeva && (token.Value() == "TRUE" || token.Value() == "FALSE") {
num := token.ToBool()
if num.Type == ArgNumber {
result, count = calcStdevPow(result, count, num, mean)
continue
}
} else {
num := token.ToNumber()
if num.Type == ArgNumber {
result, count = calcStdevPow(result, count, num, mean)
}
}
case ArgList, ArgMatrix:
result, count = calcStdev(stdeva, result, count, mean, token)
}
}
if count > 0 && result >= 0 {
return newNumberFormulaArg(math.Sqrt(result / count))
}
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
// POISSONdotDIST function calculates the Poisson Probability Mass Function or
// the Cumulative Poisson Probability Function for a supplied set of
// parameters. The syntax of the function is:
//
// POISSON.DIST(x,mean,cumulative)
//
func (fn *formulaFuncs) POISSONdotDIST(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "POISSON.DIST requires 3 arguments")
}
return fn.POISSON(argsList)
}
// POISSON function calculates the Poisson Probability Mass Function or the
// Cumulative Poisson Probability Function for a supplied set of parameters.
// The syntax of the function is:
//
// POISSON(x,mean,cumulative)
//
func (fn *formulaFuncs) POISSON(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "POISSON requires 3 arguments")
}
var x, mean, cumulative formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if mean = argsList.Front().Next().Value.(formulaArg).ToNumber(); mean.Type != ArgNumber {
return mean
}
if cumulative = argsList.Back().Value.(formulaArg).ToBool(); cumulative.Type == ArgError {
return cumulative
}
if x.Number < 0 || mean.Number <= 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
if cumulative.Number == 1 {
summer := 0.0
floor := math.Floor(x.Number)
for i := 0; i <= int(floor); i++ {
summer += math.Pow(mean.Number, float64(i)) / fact(float64(i))
}
return newNumberFormulaArg(math.Exp(0-mean.Number) * summer)
}
return newNumberFormulaArg(math.Exp(0-mean.Number) * math.Pow(mean.Number, x.Number) / fact(x.Number))
}
// SUM function adds together a supplied set of numbers and returns the sum of
// these values. The syntax of the function is:
//
// SUM(number1,[number2],...)
//
func (fn *formulaFuncs) SUM(argsList *list.List) formulaArg {
var sum float64
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgError:
return token
case ArgString:
if num := token.ToNumber(); num.Type == ArgNumber {
sum += num.Number
}
case ArgNumber:
sum += token.Number
case ArgMatrix:
for _, row := range token.Matrix {
for _, value := range row {
if num := value.ToNumber(); num.Type == ArgNumber {
sum += num.Number
}
}
}
}
}
return newNumberFormulaArg(sum)
}
// SUMIF function finds the values in a supplied array, that satisfy a given
// criteria, and returns the sum of the corresponding values in a second
// supplied array. The syntax of the function is:
//
// SUMIF(range,criteria,[sum_range])
//
func (fn *formulaFuncs) SUMIF(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "SUMIF requires at least 2 arguments")
}
criteria := formulaCriteriaParser(argsList.Front().Next().Value.(formulaArg).String)
rangeMtx := argsList.Front().Value.(formulaArg).Matrix
var sumRange [][]formulaArg
if argsList.Len() == 3 {
sumRange = argsList.Back().Value.(formulaArg).Matrix
}
var sum, val float64
var err error
for rowIdx, row := range rangeMtx {
for colIdx, col := range row {
var ok bool
fromVal := col.String
if col.String == "" {
continue
}
ok, _ = formulaCriteriaEval(fromVal, criteria)
if ok {
if argsList.Len() == 3 {
if len(sumRange) > rowIdx && len(sumRange[rowIdx]) > colIdx {
fromVal = sumRange[rowIdx][colIdx].String
}
}
if val, err = strconv.ParseFloat(fromVal, 64); err != nil {
continue
}
sum += val
}
}
}
return newNumberFormulaArg(sum)
}
// SUMIFS function finds values in one or more supplied arrays, that satisfy a
// set of criteria, and returns the sum of the corresponding values in a
// further supplied array. The syntax of the function is:
//
// SUMIFS(sum_range,criteria_range1,criteria1,[criteria_range2,criteria2],...)
//
func (fn *formulaFuncs) SUMIFS(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "SUMIFS requires at least 3 arguments")
}
if argsList.Len()%2 != 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
var args []formulaArg
sum, sumRange := 0.0, argsList.Front().Value.(formulaArg).Matrix
for arg := argsList.Front().Next(); arg != nil; arg = arg.Next() {
args = append(args, arg.Value.(formulaArg))
}
for _, ref := range formulaIfsMatch(args) {
if ref.Row >= len(sumRange) || ref.Col >= len(sumRange[ref.Row]) {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if num := sumRange[ref.Row][ref.Col].ToNumber(); num.Type == ArgNumber {
sum += num.Number
}
}
return newNumberFormulaArg(sum)
}
// sumproduct is an implementation of the formula function SUMPRODUCT.
func (fn *formulaFuncs) sumproduct(argsList *list.List) formulaArg {
var (
argType ArgType
n int
res []float64
sum float64
)
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
if argType == ArgUnknown {
argType = token.Type
}
if token.Type != argType {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
switch token.Type {
case ArgString, ArgNumber:
if num := token.ToNumber(); num.Type == ArgNumber {
sum = fn.PRODUCT(argsList).Number
continue
}
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
case ArgMatrix:
args := token.ToList()
if res == nil {
n = len(args)
res = make([]float64, n)
for i := range res {
res[i] = 1.0
}
}
if len(args) != n {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
for i, value := range args {
num := value.ToNumber()
if num.Type != ArgNumber && value.Value() != "" {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
res[i] = res[i] * num.Number
}
}
}
for _, r := range res {
sum += r
}
return newNumberFormulaArg(sum)
}
// SUMPRODUCT function returns the sum of the products of the corresponding
// values in a set of supplied arrays. The syntax of the function is:
//
// SUMPRODUCT(array1,[array2],[array3],...)
//
func (fn *formulaFuncs) SUMPRODUCT(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "SUMPRODUCT requires at least 1 argument")
}
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
if token := arg.Value.(formulaArg); token.Type == ArgError {
return token
}
}
return fn.sumproduct(argsList)
}
// SUMSQ function returns the sum of squares of a supplied set of values. The
// syntax of the function is:
//
// SUMSQ(number1,[number2],...)
//
func (fn *formulaFuncs) SUMSQ(argsList *list.List) formulaArg {
var val, sq float64
var err error
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgString:
if token.String == "" {
continue
}
if val, err = strconv.ParseFloat(token.String, 64); err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
sq += val * val
case ArgNumber:
sq += token.Number * token.Number
case ArgMatrix:
for _, row := range token.Matrix {
for _, value := range row {
if value.Value() == "" {
continue
}
if val, err = strconv.ParseFloat(value.Value(), 64); err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
sq += val * val
}
}
}
}
return newNumberFormulaArg(sq)
}
// sumx is an implementation of the formula functions SUMX2MY2, SUMX2PY2 and
// SUMXMY2.
func (fn *formulaFuncs) sumx(name string, argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 2 arguments", name))
}
array1 := argsList.Front().Value.(formulaArg)
array2 := argsList.Back().Value.(formulaArg)
left, right := array1.ToList(), array2.ToList()
n := len(left)
if n != len(right) {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
result := 0.0
for i := 0; i < n; i++ {
if lhs, rhs := left[i].ToNumber(), right[i].ToNumber(); lhs.Number != 0 && rhs.Number != 0 {
switch name {
case "SUMX2MY2":
result += lhs.Number*lhs.Number - rhs.Number*rhs.Number
case "SUMX2PY2":
result += lhs.Number*lhs.Number + rhs.Number*rhs.Number
default:
result += (lhs.Number - rhs.Number) * (lhs.Number - rhs.Number)
}
}
}
return newNumberFormulaArg(result)
}
// SUMX2MY2 function returns the sum of the differences of squares of two
// supplied sets of values. The syntax of the function is:
//
// SUMX2MY2(array_x,array_y)
//
func (fn *formulaFuncs) SUMX2MY2(argsList *list.List) formulaArg {
return fn.sumx("SUMX2MY2", argsList)
}
// SUMX2PY2 function returns the sum of the sum of squares of two supplied sets
// of values. The syntax of the function is:
//
// SUMX2PY2(array_x,array_y)
//
func (fn *formulaFuncs) SUMX2PY2(argsList *list.List) formulaArg {
return fn.sumx("SUMX2PY2", argsList)
}
// SUMXMY2 function returns the sum of the squares of differences between
// corresponding values in two supplied arrays. The syntax of the function
// is:
//
// SUMXMY2(array_x,array_y)
//
func (fn *formulaFuncs) SUMXMY2(argsList *list.List) formulaArg {
return fn.sumx("SUMXMY2", argsList)
}
// TAN function calculates the tangent of a given angle. The syntax of the
// function is:
//
// TAN(number)
//
func (fn *formulaFuncs) TAN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "TAN requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
return newNumberFormulaArg(math.Tan(number.Number))
}
// TANH function calculates the hyperbolic tangent (tanh) of a supplied
// number. The syntax of the function is:
//
// TANH(number)
//
func (fn *formulaFuncs) TANH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "TANH requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
return newNumberFormulaArg(math.Tanh(number.Number))
}
// TRUNC function truncates a supplied number to a specified number of decimal
// places. The syntax of the function is:
//
// TRUNC(number,[number_digits])
//
func (fn *formulaFuncs) TRUNC(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "TRUNC requires at least 1 argument")
}
var digits, adjust, rtrim float64
var err error
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type == ArgError {
return number
}
if argsList.Len() > 1 {
d := argsList.Back().Value.(formulaArg).ToNumber()
if d.Type == ArgError {
return d
}
digits = d.Number
digits = math.Floor(digits)
}
adjust = math.Pow(10, digits)
x := int((math.Abs(number.Number) - math.Abs(float64(int(number.Number)))) * adjust)
if x != 0 {
if rtrim, err = strconv.ParseFloat(strings.TrimRight(strconv.Itoa(x), "0"), 64); err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
}
if (digits > 0) && (rtrim < adjust/10) {
return newNumberFormulaArg(number.Number)
}
return newNumberFormulaArg(float64(int(number.Number*adjust)) / adjust)
}
// Statistical Functions
// AVEDEV function calculates the average deviation of a supplied set of
// values. The syntax of the function is:
//
// AVEDEV(number1,[number2],...)
//
func (fn *formulaFuncs) AVEDEV(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "AVEDEV requires at least 1 argument")
}
average := fn.AVERAGE(argsList)
if average.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
result, count := 0.0, 0.0
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
num := arg.Value.(formulaArg).ToNumber()
if num.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
result += math.Abs(num.Number - average.Number)
count++
}
return newNumberFormulaArg(result / count)
}
// AVERAGE function returns the arithmetic mean of a list of supplied numbers.
// The syntax of the function is:
//
// AVERAGE(number1,[number2],...)
//
func (fn *formulaFuncs) AVERAGE(argsList *list.List) formulaArg {
var args []formulaArg
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
args = append(args, arg.Value.(formulaArg))
}
count, sum := fn.countSum(false, args)
if count == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(sum / count)
}
// AVERAGEA function returns the arithmetic mean of a list of supplied numbers
// with text cell and zero values. The syntax of the function is:
//
// AVERAGEA(number1,[number2],...)
//
func (fn *formulaFuncs) AVERAGEA(argsList *list.List) formulaArg {
var args []formulaArg
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
args = append(args, arg.Value.(formulaArg))
}
count, sum := fn.countSum(true, args)
if count == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(sum / count)
}
// AVERAGEIF function finds the values in a supplied array that satisfy a
// specified criteria, and returns the average (i.e. the statistical mean) of
// the corresponding values in a second supplied array. The syntax of the
// function is:
//
// AVERAGEIF(range,criteria,[average_range])
//
func (fn *formulaFuncs) AVERAGEIF(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "AVERAGEIF requires at least 2 arguments")
}
var (
criteria = formulaCriteriaParser(argsList.Front().Next().Value.(formulaArg).Value())
rangeMtx = argsList.Front().Value.(formulaArg).Matrix
cellRange [][]formulaArg
args []formulaArg
val float64
err error
ok bool
)
if argsList.Len() == 3 {
cellRange = argsList.Back().Value.(formulaArg).Matrix
}
for rowIdx, row := range rangeMtx {
for colIdx, col := range row {
fromVal := col.Value()
if col.Value() == "" {
continue
}
ok, _ = formulaCriteriaEval(fromVal, criteria)
if ok {
if argsList.Len() == 3 {
if len(cellRange) > rowIdx && len(cellRange[rowIdx]) > colIdx {
fromVal = cellRange[rowIdx][colIdx].Value()
}
}
if val, err = strconv.ParseFloat(fromVal, 64); err != nil {
continue
}
args = append(args, newNumberFormulaArg(val))
}
}
}
count, sum := fn.countSum(false, args)
if count == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(sum / count)
}
// AVERAGEIFS function finds entries in one or more arrays, that satisfy a set
// of supplied criteria, and returns the average (i.e. the statistical mean)
// of the corresponding values in a further supplied array. The syntax of the
// function is:
//
// AVERAGEIFS(average_range,criteria_range1,criteria1,[criteria_range2,criteria2],...)
//
func (fn *formulaFuncs) AVERAGEIFS(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "AVERAGEIFS requires at least 3 arguments")
}
if argsList.Len()%2 != 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
var args []formulaArg
sum, sumRange := 0.0, argsList.Front().Value.(formulaArg).Matrix
for arg := argsList.Front().Next(); arg != nil; arg = arg.Next() {
args = append(args, arg.Value.(formulaArg))
}
count := 0.0
for _, ref := range formulaIfsMatch(args) {
if num := sumRange[ref.Row][ref.Col].ToNumber(); num.Type == ArgNumber {
sum += num.Number
count++
}
}
if count == 0 {
return newErrorFormulaArg(formulaErrorDIV, "AVERAGEIF divide by zero")
}
return newNumberFormulaArg(sum / count)
}
// getBetaHelperContFrac continued fractions for the beta function.
func getBetaHelperContFrac(fX, fA, fB float64) float64 {
var a1, b1, a2, b2, fnorm, cfnew, cf, rm float64
a1, b1, b2 = 1, 1, 1-(fA+fB)/(fA+1)*fX
if b2 == 0 {
a2, fnorm, cf = 0, 1, 1
} else {
a2, fnorm = 1, 1/b2
cf = a2 * fnorm
}
cfnew, rm = 1, 1
fMaxIter, fMachEps := 50000.0, 2.22045e-016
bfinished := false
for rm < fMaxIter && !bfinished {
apl2m := fA + 2*rm
d2m := rm * (fB - rm) * fX / ((apl2m - 1) * apl2m)
d2m1 := -(fA + rm) * (fA + fB + rm) * fX / (apl2m * (apl2m + 1))
a1 = (a2 + d2m*a1) * fnorm
b1 = (b2 + d2m*b1) * fnorm
a2 = a1 + d2m1*a2*fnorm
b2 = b1 + d2m1*b2*fnorm
if b2 != 0 {
fnorm = 1 / b2
cfnew = a2 * fnorm
bfinished = math.Abs(cf-cfnew) < math.Abs(cf)*fMachEps
}
cf = cfnew
rm += 1
}
return cf
}
// getLanczosSum uses a variant of the Lanczos sum with a rational function.
func getLanczosSum(fZ float64) float64 {
num := []float64{
23531376880.41075968857200767445163675473,
42919803642.64909876895789904700198885093,
35711959237.35566804944018545154716670596,
17921034426.03720969991975575445893111267,
6039542586.35202800506429164430729792107,
1439720407.311721673663223072794912393972,
248874557.8620541565114603864132294232163,
31426415.58540019438061423162831820536287,
2876370.628935372441225409051620849613599,
186056.2653952234950402949897160456992822,
8071.672002365816210638002902272250613822,
210.8242777515793458725097339207133627117,
2.506628274631000270164908177133837338626,
}
denom := []float64{
0,
39916800,
120543840,
150917976,
105258076,
45995730,
13339535,
2637558,
357423,
32670,
1925,
66,
1,
}
var sumNum, sumDenom, zInv float64
if fZ <= 1 {
sumNum = num[12]
sumDenom = denom[12]
for i := 11; i >= 0; i-- {
sumNum *= fZ
sumNum += num[i]
sumDenom *= fZ
sumDenom += denom[i]
}
} else {
zInv = 1 / fZ
sumNum = num[0]
sumDenom = denom[0]
for i := 1; i <= 12; i++ {
sumNum *= zInv
sumNum += num[i]
sumDenom *= zInv
sumDenom += denom[i]
}
}
return sumNum / sumDenom
}
// getBeta return beta distribution.
func getBeta(fAlpha, fBeta float64) float64 {
var fA, fB float64
if fAlpha > fBeta {
fA = fAlpha
fB = fBeta
} else {
fA = fBeta
fB = fAlpha
}
const maxGammaArgument = 171.624376956302
if fA+fB < maxGammaArgument {
return math.Gamma(fA) / math.Gamma(fA+fB) * math.Gamma(fB)
}
fg := 6.024680040776729583740234375
fgm := fg - 0.5
fLanczos := getLanczosSum(fA)
fLanczos /= getLanczosSum(fA + fB)
fLanczos *= getLanczosSum(fB)
fABgm := fA + fB + fgm
fLanczos *= math.Sqrt((fABgm / (fA + fgm)) / (fB + fgm))
fTempA := fB / (fA + fgm)
fTempB := fA / (fB + fgm)
fResult := math.Exp(-fA*math.Log1p(fTempA) - fB*math.Log1p(fTempB) - fgm)
fResult *= fLanczos
return fResult
}
// getBetaDistPDF is an implementation for the Beta probability density
// function.
func getBetaDistPDF(fX, fA, fB float64) float64 {
if fX <= 0 || fX >= 1 {
return 0
}
fLogDblMax, fLogDblMin := math.Log(1.79769e+308), math.Log(2.22507e-308)
fLogY := math.Log(0.5 - fX + 0.5)
if fX < 0.1 {
fLogY = math.Log1p(-fX)
}
fLogX := math.Log(fX)
fAm1LogX := (fA - 1) * fLogX
fBm1LogY := (fB - 1) * fLogY
fLogBeta := getLogBeta(fA, fB)
if fAm1LogX < fLogDblMax && fAm1LogX > fLogDblMin && fBm1LogY < fLogDblMax &&
fBm1LogY > fLogDblMin && fLogBeta < fLogDblMax && fLogBeta > fLogDblMin &&
fAm1LogX+fBm1LogY < fLogDblMax && fAm1LogX+fBm1LogY > fLogDblMin {
return math.Pow(fX, fA-1) * math.Pow(0.5-fX+0.5, fB-1) / getBeta(fA, fB)
}
return math.Exp(fAm1LogX + fBm1LogY - fLogBeta)
}
// getLogBeta return beta with logarithm.
func getLogBeta(fAlpha, fBeta float64) float64 {
var fA, fB float64
if fAlpha > fBeta {
fA, fB = fAlpha, fBeta
} else {
fA, fB = fBeta, fAlpha
}
fg := 6.024680040776729583740234375
fgm := fg - 0.5
fLanczos := getLanczosSum(fA)
fLanczos /= getLanczosSum(fA + fB)
fLanczos *= getLanczosSum(fB)
fLogLanczos := math.Log(fLanczos)
fABgm := fA + fB + fgm
fLogLanczos += 0.5 * (math.Log(fABgm) - math.Log(fA+fgm) - math.Log(fB+fgm))
fTempA := fB / (fA + fgm)
fTempB := fA / (fB + fgm)
fResult := -fA*math.Log1p(fTempA) - fB*math.Log1p(fTempB) - fgm
fResult += fLogLanczos
return fResult
}
// getBetaDist is an implementation for the beta distribution function.
func getBetaDist(fXin, fAlpha, fBeta float64) float64 {
if fXin <= 0 {
return 0
}
if fXin >= 1 {
return 1
}
if fBeta == 1 {
return math.Pow(fXin, fAlpha)
}
if fAlpha == 1 {
return -math.Expm1(fBeta * math.Log1p(-fXin))
}
var fResult float64
fY, flnY := (0.5-fXin)+0.5, math.Log1p(-fXin)
fX, flnX := fXin, math.Log(fXin)
fA, fB := fAlpha, fBeta
bReflect := fXin > fAlpha/(fAlpha+fBeta)
if bReflect {
fA = fBeta
fB = fAlpha
fX = fY
fY = fXin
flnX = flnY
flnY = math.Log(fXin)
}
fResult = getBetaHelperContFrac(fX, fA, fB) / fA
fP, fQ := fA/(fA+fB), fB/(fA+fB)
var fTemp float64
if fA > 1 && fB > 1 && fP < 0.97 && fQ < 0.97 {
fTemp = getBetaDistPDF(fX, fA, fB) * fX * fY
} else {
fTemp = math.Exp(fA*flnX + fB*flnY - getLogBeta(fA, fB))
}
fResult *= fTemp
if bReflect {
fResult = 0.5 - fResult + 0.5
}
return fResult
}
// prepareBETAdotDISTArgs checking and prepare arguments for the formula
// function BETA.DIST.
func (fn *formulaFuncs) prepareBETAdotDISTArgs(argsList *list.List) formulaArg {
if argsList.Len() < 4 {
return newErrorFormulaArg(formulaErrorVALUE, "BETA.DIST requires at least 4 arguments")
}
if argsList.Len() > 6 {
return newErrorFormulaArg(formulaErrorVALUE, "BETA.DIST requires at most 6 arguments")
}
x := argsList.Front().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return x
}
alpha := argsList.Front().Next().Value.(formulaArg).ToNumber()
if alpha.Type != ArgNumber {
return alpha
}
beta := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if beta.Type != ArgNumber {
return beta
}
if alpha.Number <= 0 || beta.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
cumulative := argsList.Front().Next().Next().Next().Value.(formulaArg).ToBool()
if cumulative.Type != ArgNumber {
return cumulative
}
a, b := newNumberFormulaArg(0), newNumberFormulaArg(1)
if argsList.Len() > 4 {
if a = argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber(); a.Type != ArgNumber {
return a
}
}
if argsList.Len() == 6 {
if b = argsList.Back().Value.(formulaArg).ToNumber(); b.Type != ArgNumber {
return b
}
}
return newListFormulaArg([]formulaArg{x, alpha, beta, cumulative, a, b})
}
// BETAdotDIST function calculates the cumulative beta distribution function
// or the probability density function of the Beta distribution, for a
// supplied set of parameters. The syntax of the function is:
//
// BETA.DIST(x,alpha,beta,cumulative,[A],[B])
//
func (fn *formulaFuncs) BETAdotDIST(argsList *list.List) formulaArg {
args := fn.prepareBETAdotDISTArgs(argsList)
if args.Type != ArgList {
return args
}
x, alpha, beta, cumulative, a, b := args.List[0], args.List[1], args.List[2], args.List[3], args.List[4], args.List[5]
if x.Number < a.Number || x.Number > b.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if a.Number == b.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
scale := b.Number - a.Number
x.Number = (x.Number - a.Number) / scale
if cumulative.Number == 1 {
return newNumberFormulaArg(getBetaDist(x.Number, alpha.Number, beta.Number))
}
return newNumberFormulaArg(getBetaDistPDF(x.Number, alpha.Number, beta.Number) / scale)
}
// BETADIST function calculates the cumulative beta probability density
// function for a supplied set of parameters. The syntax of the function is:
//
// BETADIST(x,alpha,beta,[A],[B])
//
func (fn *formulaFuncs) BETADIST(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "BETADIST requires at least 3 arguments")
}
if argsList.Len() > 5 {
return newErrorFormulaArg(formulaErrorVALUE, "BETADIST requires at most 5 arguments")
}
x := argsList.Front().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return x
}
alpha := argsList.Front().Next().Value.(formulaArg).ToNumber()
if alpha.Type != ArgNumber {
return alpha
}
beta := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if beta.Type != ArgNumber {
return beta
}
if alpha.Number <= 0 || beta.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
a, b := newNumberFormulaArg(0), newNumberFormulaArg(1)
if argsList.Len() > 3 {
if a = argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber(); a.Type != ArgNumber {
return a
}
}
if argsList.Len() == 5 {
if b = argsList.Back().Value.(formulaArg).ToNumber(); b.Type != ArgNumber {
return b
}
}
if x.Number < a.Number || x.Number > b.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if a.Number == b.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(getBetaDist((x.Number-a.Number)/(b.Number-a.Number), alpha.Number, beta.Number))
}
// d1mach returns double precision real machine constants.
func d1mach(i int) float64 {
arr := []float64{
2.2250738585072014e-308,
1.7976931348623158e+308,
1.1102230246251565e-16,
2.2204460492503131e-16,
0.301029995663981195,
}
if i > len(arr) {
return 0
}
return arr[i-1]
}
// chebyshevInit determines the number of terms for the double precision
// orthogonal series "dos" needed to insure the error is no larger
// than "eta". Ordinarily eta will be chosen to be one-tenth machine
// precision.
func chebyshevInit(nos int, eta float64, dos []float64) int {
i, e := 0, 0.0
if nos < 1 {
return 0
}
for ii := 1; ii <= nos; ii++ {
i = nos - ii
e += math.Abs(dos[i])
if e > eta {
return i
}
}
return i
}
// chebyshevEval evaluates the n-term Chebyshev series "a" at "x".
func chebyshevEval(n int, x float64, a []float64) float64 {
if n < 1 || n > 1000 || x < -1.1 || x > 1.1 {
return math.NaN()
}
twox, b0, b1, b2 := x*2, 0.0, 0.0, 0.0
for i := 1; i <= n; i++ {
b2 = b1
b1 = b0
b0 = twox*b1 - b2 + a[n-i]
}
return (b0 - b2) * 0.5
}
// lgammacor is an implementation for the log(gamma) correction.
func lgammacor(x float64) float64 {
algmcs := []float64{
0.1666389480451863247205729650822, -0.1384948176067563840732986059135e-4,
0.9810825646924729426157171547487e-8, -0.1809129475572494194263306266719e-10,
0.6221098041892605227126015543416e-13, -0.3399615005417721944303330599666e-15,
0.2683181998482698748957538846666e-17, -0.2868042435334643284144622399999e-19,
0.3962837061046434803679306666666e-21, -0.6831888753985766870111999999999e-23,
0.1429227355942498147573333333333e-24, -0.3547598158101070547199999999999e-26,
0.1025680058010470912000000000000e-27, -0.3401102254316748799999999999999e-29,
0.1276642195630062933333333333333e-30,
}
nalgm := chebyshevInit(15, d1mach(3), algmcs)
xbig := 1.0 / math.Sqrt(d1mach(3))
xmax := math.Exp(math.Min(math.Log(d1mach(2)/12.0), -math.Log(12.0*d1mach(1))))
if x < 10.0 {
return math.NaN()
} else if x >= xmax {
return 4.930380657631324e-32
} else if x < xbig {
tmp := 10.0 / x
return chebyshevEval(nalgm, tmp*tmp*2.0-1.0, algmcs) / x
}
return 1.0 / (x * 12.0)
}
// logrelerr compute the relative error logarithm.
func logrelerr(x float64) float64 {
alnrcs := []float64{
0.10378693562743769800686267719098e+1, -0.13364301504908918098766041553133,
0.19408249135520563357926199374750e-1, -0.30107551127535777690376537776592e-2,
0.48694614797154850090456366509137e-3, -0.81054881893175356066809943008622e-4,
0.13778847799559524782938251496059e-4, -0.23802210894358970251369992914935e-5,
0.41640416213865183476391859901989e-6, -0.73595828378075994984266837031998e-7,
0.13117611876241674949152294345011e-7, -0.23546709317742425136696092330175e-8,
0.42522773276034997775638052962567e-9, -0.77190894134840796826108107493300e-10,
0.14075746481359069909215356472191e-10, -0.25769072058024680627537078627584e-11,
0.47342406666294421849154395005938e-12, -0.87249012674742641745301263292675e-13,
0.16124614902740551465739833119115e-13, -0.29875652015665773006710792416815e-14,
0.55480701209082887983041321697279e-15, -0.10324619158271569595141333961932e-15,
0.19250239203049851177878503244868e-16, -0.35955073465265150011189707844266e-17,
0.67264542537876857892194574226773e-18, -0.12602624168735219252082425637546e-18,
0.23644884408606210044916158955519e-19, -0.44419377050807936898878389179733e-20,
0.83546594464034259016241293994666e-21, -0.15731559416479562574899253521066e-21,
0.29653128740247422686154369706666e-22, -0.55949583481815947292156013226666e-23,
0.10566354268835681048187284138666e-23, -0.19972483680670204548314999466666e-24,
0.37782977818839361421049855999999e-25, -0.71531586889081740345038165333333e-26,
0.13552488463674213646502024533333e-26, -0.25694673048487567430079829333333e-27,
0.48747756066216949076459519999999e-28, -0.92542112530849715321132373333333e-29,
0.17578597841760239233269760000000e-29, -0.33410026677731010351377066666666e-30,
0.63533936180236187354180266666666e-31,
}
nlnrel := chebyshevInit(43, 0.1*d1mach(3), alnrcs)
if x <= -1 {
return math.NaN()
}
if math.Abs(x) <= 0.375 {
return x * (1.0 - x*chebyshevEval(nlnrel, x/0.375, alnrcs))
}
return math.Log(x + 1.0)
}
// logBeta is an implementation for the log of the beta distribution
// function.
func logBeta(a, b float64) float64 {
corr, p, q := 0.0, a, a
if b < p {
p = b
}
if b > q {
q = b
}
if p < 0 {
return math.NaN()
}
if p == 0 {
return math.MaxFloat64
}
if p >= 10.0 {
corr = lgammacor(p) + lgammacor(q) - lgammacor(p+q)
f1 := q * logrelerr(-p/(p+q))
return math.Log(q)*-0.5 + 0.918938533204672741780329736406 + corr + (p-0.5)*math.Log(p/(p+q)) + math.Nextafter(f1, f1)
}
if q >= 10 {
corr = lgammacor(q) - lgammacor(p+q)
val, _ := math.Lgamma(p)
return val + corr + p - p*math.Log(p+q) + (q-0.5)*logrelerr(-p/(p+q))
}
return math.Log(math.Gamma(p) * (math.Gamma(q) / math.Gamma(p+q)))
}
// pbetaRaw is a part of pbeta for the beta distribution.
func pbetaRaw(alnsml, ans, eps, p, pin, q, sml, x, y float64) float64 {
if q > 1.0 {
xb := p*math.Log(y) + q*math.Log(1.0-y) - logBeta(p, q) - math.Log(q)
ib := int(math.Max(xb/alnsml, 0.0))
term := math.Exp(xb - float64(ib)*alnsml)
c := 1.0 / (1.0 - y)
p1 := q * c / (p + q - 1.0)
finsum := 0.0
n := int(q)
if q == float64(n) {
n = n - 1
}
for i := 1; i <= n; i++ {
if p1 <= 1 && term/eps <= finsum {
break
}
xi := float64(i)
term = (q - xi + 1.0) * c * term / (p + q - xi)
if term > 1.0 {
ib = ib - 1
term = term * sml
}
if ib == 0 {
finsum = finsum + term
}
}
ans = ans + finsum
}
if y != x || p != pin {
ans = 1.0 - ans
}
ans = math.Max(math.Min(ans, 1.0), 0.0)
return ans
}
// pbeta returns distribution function of the beta distribution.
func pbeta(x, pin, qin float64) (ans float64) {
eps := d1mach(3)
alneps := math.Log(eps)
sml := d1mach(1)
alnsml := math.Log(sml)
y := x
p := pin
q := qin
if p/(p+q) < x {
y = 1.0 - y
p = qin
q = pin
}
if (p+q)*y/(p+1.0) < eps {
xb := p*math.Log(math.Max(y, sml)) - math.Log(p) - logBeta(p, q)
if xb > alnsml && y != 0.0 {
ans = math.Exp(xb)
}
if y != x || p != pin {
ans = 1.0 - ans
}
} else {
ps := q - math.Floor(q)
if ps == 0.0 {
ps = 1.0
}
xb := p*math.Log(y) - logBeta(ps, p) - math.Log(p)
if xb >= alnsml {
ans = math.Exp(xb)
term := ans * p
if ps != 1.0 {
n := int(math.Max(alneps/math.Log(y), 4.0))
for i := 1; i <= n; i++ {
xi := float64(i)
term = term * (xi - ps) * y / xi
ans = ans + term/(p+xi)
}
}
}
ans = pbetaRaw(alnsml, ans, eps, p, pin, q, sml, x, y)
}
return ans
}
// betainvProbIterator is a part of betainv for the inverse of the beta
// function.
func betainvProbIterator(alpha1, alpha3, beta1, beta2, beta3, logBeta, maxCumulative, prob1, prob2 float64) float64 {
var i, j, prev, prop4 float64
j = 1
for prob := 0; prob < 1000; prob++ {
prop3 := pbeta(beta3, alpha1, beta1)
prop3 = (prop3 - prob1) * math.Exp(logBeta+prob2*math.Log(beta3)+beta2*math.Log(1.0-beta3))
if prop3*prop4 <= 0 {
prev = math.Max(math.Abs(j), maxCumulative)
}
h := 1.0
for iteratorCount := 0; iteratorCount < 1000; iteratorCount++ {
j = h * prop3
if math.Abs(j) < prev {
i = beta3 - j
if i >= 0 && i <= 1.0 {
if prev <= alpha3 {
return beta3
}
if math.Abs(prop3) <= alpha3 {
return beta3
}
if i != 0 && i != 1.0 {
break
}
}
}
h /= 3.0
}
if i == beta3 {
return beta3
}
beta3, prop4 = i, prop3
}
return beta3
}
// calcBetainv is an implementation for the quantile of the beta
// distribution.
func calcBetainv(probability, alpha, beta, lower, upper float64) float64 {
minCumulative, maxCumulative := 1.0e-300, 3.0e-308
lowerBound, upperBound := maxCumulative, 1.0-2.22e-16
needSwap := false
var alpha1, alpha2, beta1, beta2, beta3, prob1, x, y float64
if probability <= 0.5 {
prob1, alpha1, beta1 = probability, alpha, beta
} else {
prob1, alpha1, beta1, needSwap = 1.0-probability, beta, alpha, true
}
logBetaNum := logBeta(alpha, beta)
prob2 := math.Sqrt(-math.Log(prob1 * prob1))
prob3 := prob2 - (prob2*0.27061+2.3075)/(prob2*(prob2*0.04481+0.99229)+1)
if alpha1 > 1 && beta1 > 1 {
alpha2, beta2, prob2 = 1/(alpha1+alpha1-1), 1/(beta1+beta1-1), (prob3*prob3-3)/6
x = 2 / (alpha2 + beta2)
y = prob3*math.Sqrt(x+prob2)/x - (beta2-alpha2)*(prob2+5/6.0-2/(x*3))
beta3 = alpha1 / (alpha1 + beta1*math.Exp(y+y))
} else {
beta2, prob2 = 1/(beta1*9), beta1+beta1
beta2 = prob2 * math.Pow(1-beta2+prob3*math.Sqrt(beta2), 3)
if beta2 <= 0 {
beta3 = 1 - math.Exp((math.Log((1-prob1)*beta1)+logBetaNum)/beta1)
} else {
beta2 = (prob2 + alpha1*4 - 2) / beta2
if beta2 <= 1 {
beta3 = math.Exp((logBetaNum + math.Log(alpha1*prob1)) / alpha1)
} else {
beta3 = 1 - 2/(beta2+1)
}
}
}
beta2, prob2 = 1-beta1, 1-alpha1
if beta3 < lowerBound {
beta3 = lowerBound
} else if beta3 > upperBound {
beta3 = upperBound
}
alpha3 := math.Max(minCumulative, math.Pow(10.0, -13.0-2.5/(alpha1*alpha1)-0.5/(prob1*prob1)))
beta3 = betainvProbIterator(alpha1, alpha3, beta1, beta2, beta3, logBetaNum, maxCumulative, prob1, prob2)
if needSwap {
beta3 = 1.0 - beta3
}
return (upper-lower)*beta3 + lower
}
// betainv is an implementation of the formula functions BETAINV and
// BETA.INV.
func (fn *formulaFuncs) betainv(name string, argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 3 arguments", name))
}
if argsList.Len() > 5 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at most 5 arguments", name))
}
probability := argsList.Front().Value.(formulaArg).ToNumber()
if probability.Type != ArgNumber {
return probability
}
if probability.Number <= 0 || probability.Number >= 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
alpha := argsList.Front().Next().Value.(formulaArg).ToNumber()
if alpha.Type != ArgNumber {
return alpha
}
beta := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if beta.Type != ArgNumber {
return beta
}
if alpha.Number <= 0 || beta.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
a, b := newNumberFormulaArg(0), newNumberFormulaArg(1)
if argsList.Len() > 3 {
if a = argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber(); a.Type != ArgNumber {
return a
}
}
if argsList.Len() == 5 {
if b = argsList.Back().Value.(formulaArg).ToNumber(); b.Type != ArgNumber {
return b
}
}
if a.Number == b.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(calcBetainv(probability.Number, alpha.Number, beta.Number, a.Number, b.Number))
}
// BETAINV function uses an iterative procedure to calculate the inverse of
// the cumulative beta probability density function for a supplied
// probability. The syntax of the function is:
//
// BETAINV(probability,alpha,beta,[A],[B])
//
func (fn *formulaFuncs) BETAINV(argsList *list.List) formulaArg {
return fn.betainv("BETAINV", argsList)
}
// BETAdotINV function uses an iterative procedure to calculate the inverse of
// the cumulative beta probability density function for a supplied
// probability. The syntax of the function is:
//
// BETA.INV(probability,alpha,beta,[A],[B])
//
func (fn *formulaFuncs) BETAdotINV(argsList *list.List) formulaArg {
return fn.betainv("BETA.INV", argsList)
}
// incompleteGamma is an implementation of the incomplete gamma function.
func incompleteGamma(a, x float64) float64 {
max := 32
summer := 0.0
for n := 0; n <= max; n++ {
divisor := a
for i := 1; i <= n; i++ {
divisor *= a + float64(i)
}
summer += math.Pow(x, float64(n)) / divisor
}
return math.Pow(x, a) * math.Exp(0-x) * summer
}
// binomCoeff implement binomial coefficient calculation.
func binomCoeff(n, k float64) float64 {
return fact(n) / (fact(k) * fact(n-k))
}
// binomdist implement binomial distribution calculation.
func binomdist(x, n, p float64) float64 {
return binomCoeff(n, x) * math.Pow(p, x) * math.Pow(1-p, n-x)
}
// BINOMdotDIST function returns the Binomial Distribution probability for a
// given number of successes from a specified number of trials. The syntax of
// the function is:
//
// BINOM.DIST(number_s,trials,probability_s,cumulative)
//
func (fn *formulaFuncs) BINOMdotDIST(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "BINOM.DIST requires 4 arguments")
}
return fn.BINOMDIST(argsList)
}
// BINOMDIST function returns the Binomial Distribution probability of a
// specified number of successes out of a specified number of trials. The
// syntax of the function is:
//
// BINOMDIST(number_s,trials,probability_s,cumulative)
//
func (fn *formulaFuncs) BINOMDIST(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "BINOMDIST requires 4 arguments")
}
var s, trials, probability, cumulative formulaArg
if s = argsList.Front().Value.(formulaArg).ToNumber(); s.Type != ArgNumber {
return s
}
if trials = argsList.Front().Next().Value.(formulaArg).ToNumber(); trials.Type != ArgNumber {
return trials
}
if s.Number < 0 || s.Number > trials.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if probability = argsList.Back().Prev().Value.(formulaArg).ToNumber(); probability.Type != ArgNumber {
return probability
}
if probability.Number < 0 || probability.Number > 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if cumulative = argsList.Back().Value.(formulaArg).ToBool(); cumulative.Type == ArgError {
return cumulative
}
if cumulative.Number == 1 {
bm := 0.0
for i := 0; i <= int(s.Number); i++ {
bm += binomdist(float64(i), trials.Number, probability.Number)
}
return newNumberFormulaArg(bm)
}
return newNumberFormulaArg(binomdist(s.Number, trials.Number, probability.Number))
}
// BINOMdotDISTdotRANGE function returns the Binomial Distribution probability
// for the number of successes from a specified number of trials falling into
// a specified range.
//
// BINOM.DIST.RANGE(trials,probability_s,number_s,[number_s2])
//
func (fn *formulaFuncs) BINOMdotDISTdotRANGE(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "BINOM.DIST.RANGE requires at least 3 arguments")
}
if argsList.Len() > 4 {
return newErrorFormulaArg(formulaErrorVALUE, "BINOM.DIST.RANGE requires at most 4 arguments")
}
trials := argsList.Front().Value.(formulaArg).ToNumber()
if trials.Type != ArgNumber {
return trials
}
probability := argsList.Front().Next().Value.(formulaArg).ToNumber()
if probability.Type != ArgNumber {
return probability
}
if probability.Number < 0 || probability.Number > 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
num1 := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if num1.Type != ArgNumber {
return num1
}
if num1.Number < 0 || num1.Number > trials.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
num2 := num1
if argsList.Len() > 3 {
if num2 = argsList.Back().Value.(formulaArg).ToNumber(); num2.Type != ArgNumber {
return num2
}
}
if num2.Number < 0 || num2.Number > trials.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
sum := 0.0
for i := num1.Number; i <= num2.Number; i++ {
sum += binomdist(i, trials.Number, probability.Number)
}
return newNumberFormulaArg(sum)
}
// binominv implement inverse of the binomial distribution calculation.
func binominv(n, p, alpha float64) float64 {
q, i, sum, max := 1-p, 0.0, 0.0, 0.0
n = math.Floor(n)
if q > p {
factor := math.Pow(q, n)
sum = factor
for i = 0; i < n && sum < alpha; i++ {
factor *= (n - i) / (i + 1) * p / q
sum += factor
}
return i
}
factor := math.Pow(p, n)
sum, max = 1-factor, n
for i = 0; i < max && sum >= alpha; i++ {
factor *= (n - i) / (i + 1) * q / p
sum -= factor
}
return n - i
}
// BINOMdotINV function returns the inverse of the Cumulative Binomial
// Distribution. The syntax of the function is:
//
// BINOM.INV(trials,probability_s,alpha)
//
func (fn *formulaFuncs) BINOMdotINV(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "BINOM.INV requires 3 numeric arguments")
}
trials := argsList.Front().Value.(formulaArg).ToNumber()
if trials.Type != ArgNumber {
return trials
}
if trials.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
probability := argsList.Front().Next().Value.(formulaArg).ToNumber()
if probability.Type != ArgNumber {
return probability
}
if probability.Number <= 0 || probability.Number >= 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
alpha := argsList.Back().Value.(formulaArg).ToNumber()
if alpha.Type != ArgNumber {
return alpha
}
if alpha.Number <= 0 || alpha.Number >= 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(binominv(trials.Number, probability.Number, alpha.Number))
}
// CHIDIST function calculates the right-tailed probability of the chi-square
// distribution. The syntax of the function is:
//
// CHIDIST(x,degrees_freedom)
//
func (fn *formulaFuncs) CHIDIST(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "CHIDIST requires 2 numeric arguments")
}
x := argsList.Front().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return x
}
degrees := argsList.Back().Value.(formulaArg).ToNumber()
if degrees.Type != ArgNumber {
return degrees
}
logSqrtPi, sqrtPi := math.Log(math.Sqrt(math.Pi)), 1/math.Sqrt(math.Pi)
var e, s, z, c, y float64
a, x1, even := x.Number/2, x.Number, int(degrees.Number)%2 == 0
if degrees.Number > 1 {
y = math.Exp(-a)
}
args := list.New()
args.PushBack(newNumberFormulaArg(-math.Sqrt(x1)))
o := fn.NORMSDIST(args)
s = 2 * o.Number
if even {
s = y
}
if degrees.Number > 2 {
x1 = (degrees.Number - 1) / 2
z = 0.5
if even {
z = 1
}
if a > 20 {
e = logSqrtPi
if even {
e = 0
}
c = math.Log(a)
for z <= x1 {
e = math.Log(z) + e
s += math.Exp(c*z - a - e)
z += 1
}
return newNumberFormulaArg(s)
}
e = sqrtPi / math.Sqrt(a)
if even {
e = 1
}
c = 0
for z <= x1 {
e = e * (a / z)
c = c + e
z += 1
}
return newNumberFormulaArg(c*y + s)
}
return newNumberFormulaArg(s)
}
// CHIINV function calculates the inverse of the right-tailed probability of
// the Chi-Square Distribution. The syntax of the function is:
//
// CHIINV(probability,deg_freedom)
//
func (fn *formulaFuncs) CHIINV(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "CHIINV requires 2 numeric arguments")
}
probability := argsList.Front().Value.(formulaArg).ToNumber()
if probability.Type != ArgNumber {
return probability
}
if probability.Number <= 0 || probability.Number > 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
deg := argsList.Back().Value.(formulaArg).ToNumber()
if deg.Type != ArgNumber {
return deg
}
if deg.Number < 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(gammainv(1-probability.Number, 0.5*deg.Number, 2.0))
}
// CHITEST function uses the chi-square test to calculate the probability that
// the differences between two supplied data sets (of observed and expected
// frequencies), are likely to be simply due to sampling error, or if they are
// likely to be real. The syntax of the function is:
//
// CHITEST(actual_range,expected_range)
//
func (fn *formulaFuncs) CHITEST(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "CHITEST requires 2 arguments")
}
actual, expected := argsList.Front().Value.(formulaArg), argsList.Back().Value.(formulaArg)
actualList, expectedList := actual.ToList(), expected.ToList()
rows := len(actual.Matrix)
columns := len(actualList) / rows
if len(actualList) != len(expectedList) || len(actualList) == 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
var result float64
var degrees int
for i := 0; i < len(actualList); i++ {
a, e := actualList[i].ToNumber(), expectedList[i].ToNumber()
if a.Type == ArgNumber && e.Type == ArgNumber {
if e.Number == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
if e.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
result += (a.Number - e.Number) * (a.Number - e.Number) / e.Number
}
}
if rows == 1 {
degrees = columns - 1
} else if columns == 1 {
degrees = rows - 1
} else {
degrees = (columns - 1) * (rows - 1)
}
args := list.New()
args.PushBack(newNumberFormulaArg(result))
args.PushBack(newNumberFormulaArg(float64(degrees)))
return fn.CHIDIST(args)
}
// getGammaSeries calculates a power-series of the gamma function.
func getGammaSeries(fA, fX float64) float64 {
var (
fHalfMachEps = 2.22045e-016 / 2
fDenomfactor = fA
fSummand = 1 / fA
fSum = fSummand
nCount = 1
)
for fSummand/fSum > fHalfMachEps && nCount <= 10000 {
fDenomfactor = fDenomfactor + 1
fSummand = fSummand * fX / fDenomfactor
fSum = fSum + fSummand
nCount = nCount + 1
}
return fSum
}
// getGammaContFraction returns continued fraction with odd items of the gamma
// function.
func getGammaContFraction(fA, fX float64) float64 {
var (
fBigInv = 2.22045e-016
fHalfMachEps = fBigInv / 2
fBig = 1 / fBigInv
fCount = 0.0
fY = 1 - fA
fDenom = fX + 2 - fA
fPkm1 = fX + 1
fPkm2 = 1.0
fQkm1 = fDenom * fX
fQkm2 = fX
fApprox = fPkm1 / fQkm1
bFinished = false
)
for !bFinished && fCount < 10000 {
fCount = fCount + 1
fY = fY + 1
fDenom = fDenom + 2
var (
fNum = fY * fCount
f1 = fPkm1 * fDenom
f2 = fPkm2 * fNum
fPk = math.Nextafter(f1, f1) - math.Nextafter(f2, f2)
f3 = fQkm1 * fDenom
f4 = fQkm2 * fNum
fQk = math.Nextafter(f3, f3) - math.Nextafter(f4, f4)
)
if fQk != 0 {
fR := fPk / fQk
bFinished = math.Abs((fApprox-fR)/fR) <= fHalfMachEps
fApprox = fR
}
fPkm2, fPkm1, fQkm2, fQkm1 = fPkm1, fPk, fQkm1, fQk
if math.Abs(fPk) > fBig {
// reduce a fraction does not change the value
fPkm2 = fPkm2 * fBigInv
fPkm1 = fPkm1 * fBigInv
fQkm2 = fQkm2 * fBigInv
fQkm1 = fQkm1 * fBigInv
}
}
return fApprox
}
// getLogGammaHelper is a part of implementation of the function getLogGamma.
func getLogGammaHelper(fZ float64) float64 {
_fg := 6.024680040776729583740234375
zgHelp := fZ + _fg - 0.5
return math.Log(getLanczosSum(fZ)) + (fZ-0.5)*math.Log(zgHelp) - zgHelp
}
// getGammaHelper is a part of implementation of the function getLogGamma.
func getGammaHelper(fZ float64) float64 {
var (
gamma = getLanczosSum(fZ)
fg = 6.024680040776729583740234375
zgHelp = fZ + fg - 0.5
// avoid intermediate overflow
halfpower = math.Pow(zgHelp, fZ/2-0.25)
)
gamma *= halfpower
gamma /= math.Exp(zgHelp)
gamma *= halfpower
if fZ <= 20 && fZ == math.Floor(fZ) {
gamma = math.Round(gamma)
}
return gamma
}
// getLogGamma calculates the natural logarithm of the gamma function.
func getLogGamma(fZ float64) float64 {
fMaxGammaArgument := 171.624376956302
if fZ >= fMaxGammaArgument {
return getLogGammaHelper(fZ)
}
if fZ >= 1.0 {
return math.Log(getGammaHelper(fZ))
}
if fZ >= 0.5 {
return math.Log(getGammaHelper(fZ+1) / fZ)
}
return getLogGammaHelper(fZ+2) - math.Log(fZ+1) - math.Log(fZ)
}
// getLowRegIGamma returns lower regularized incomplete gamma function.
func getLowRegIGamma(fA, fX float64) float64 {
lnFactor := fA*math.Log(fX) - fX - getLogGamma(fA)
factor := math.Exp(lnFactor)
if fX > fA+1 {
return 1 - factor*getGammaContFraction(fA, fX)
}
return factor * getGammaSeries(fA, fX)
}
// getChiSqDistCDF returns left tail for the Chi-Square distribution.
func getChiSqDistCDF(fX, fDF float64) float64 {
if fX <= 0 {
return 0
}
return getLowRegIGamma(fDF/2, fX/2)
}
// getChiSqDistPDF calculates the probability density function for the
// Chi-Square distribution.
func getChiSqDistPDF(fX, fDF float64) float64 {
if fDF*fX > 1391000 {
return math.Exp((0.5*fDF-1)*math.Log(fX*0.5) - 0.5*fX - math.Log(2) - getLogGamma(0.5*fDF))
}
var fCount, fValue float64
if math.Mod(fDF, 2) < 0.5 {
fValue = 0.5
fCount = 2
} else {
fValue = 1 / math.Sqrt(fX*2*math.Pi)
fCount = 1
}
for fCount < fDF {
fValue *= fX / fCount
fCount += 2
}
if fX >= 1425 {
fValue = math.Exp(math.Log(fValue) - fX/2)
} else {
fValue *= math.Exp(-fX / 2)
}
return fValue
}
// CHISQdotDIST function calculates the Probability Density Function or the
// Cumulative Distribution Function for the Chi-Square Distribution. The
// syntax of the function is:
//
// CHISQ.DIST(x,degrees_freedom,cumulative)
//
func (fn *formulaFuncs) CHISQdotDIST(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "CHISQ.DIST requires 3 arguments")
}
var x, degrees, cumulative formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if degrees = argsList.Front().Next().Value.(formulaArg).ToNumber(); degrees.Type != ArgNumber {
return degrees
}
if cumulative = argsList.Back().Value.(formulaArg).ToBool(); cumulative.Type == ArgError {
return cumulative
}
if x.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
maxDeg := math.Pow10(10)
if degrees.Number < 1 || degrees.Number >= maxDeg {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if cumulative.Number == 1 {
return newNumberFormulaArg(getChiSqDistCDF(x.Number, degrees.Number))
}
return newNumberFormulaArg(getChiSqDistPDF(x.Number, degrees.Number))
}
// CHISQdotDISTdotRT function calculates the right-tailed probability of the
// Chi-Square Distribution. The syntax of the function is:
//
// CHISQ.DIST.RT(x,degrees_freedom)
//
func (fn *formulaFuncs) CHISQdotDISTdotRT(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "CHISQ.DIST.RT requires 2 numeric arguments")
}
return fn.CHIDIST(argsList)
}
// CHISQdotTEST function performs the chi-square test on two supplied data sets
// (of observed and expected frequencies), and returns the probability that
// the differences between the sets are simply due to sampling error. The
// syntax of the function is:
//
// CHISQ.TEST(actual_range,expected_range)
//
func (fn *formulaFuncs) CHISQdotTEST(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "CHISQ.TEST requires 2 arguments")
}
return fn.CHITEST(argsList)
}
// hasChangeOfSign check if the sign has been changed.
func hasChangeOfSign(u, w float64) bool {
return (u < 0 && w > 0) || (u > 0 && w < 0)
}
// calcInverseIterator directly maps the required parameters for inverse
// distribution functions.
type calcInverseIterator struct {
name string
fp, fDF, nT float64
}
// callBack implements the callback function for the inverse iterator.
func (iterator *calcInverseIterator) callBack(x float64) float64 {
if iterator.name == "CHISQ.INV" {
return iterator.fp - getChiSqDistCDF(x, iterator.fDF)
}
return iterator.fp - getTDist(x, iterator.fDF, iterator.nT)
}
// inverseQuadraticInterpolation inverse quadratic interpolation with
// additional brackets.
func inverseQuadraticInterpolation(iterator calcInverseIterator, fAx, fAy, fBx, fBy float64) float64 {
fYEps := 1.0e-307
fXEps := 2.22045e-016
fPx, fPy, fQx, fQy, fRx, fRy := fAx, fAy, fBx, fBy, fAx, fAy
fSx := 0.5 * (fAx + fBx)
bHasToInterpolate := true
nCount := 0
for nCount < 500 && math.Abs(fRy) > fYEps && (fBx-fAx) > math.Max(math.Abs(fAx), math.Abs(fBx))*fXEps {
if bHasToInterpolate {
if fPy != fQy && fQy != fRy && fRy != fPy {
fSx = fPx*fRy*fQy/(fRy-fPy)/(fQy-fPy) + fRx*fQy*fPy/(fQy-fRy)/(fPy-fRy) +
fQx*fPy*fRy/(fPy-fQy)/(fRy-fQy)
bHasToInterpolate = (fAx < fSx) && (fSx < fBx)
} else {
bHasToInterpolate = false
}
}
if !bHasToInterpolate {
fSx = 0.5 * (fAx + fBx)
fQx, fQy = fBx, fBy
bHasToInterpolate = true
}
fPx, fQx, fRx, fPy, fQy = fQx, fRx, fSx, fQy, fRy
fRy = iterator.callBack(fSx)
if hasChangeOfSign(fAy, fRy) {
fBx, fBy = fRx, fRy
} else {
fAx, fAy = fRx, fRy
}
bHasToInterpolate = bHasToInterpolate && (math.Abs(fRy)*2 <= math.Abs(fQy))
nCount++
}
return fRx
}
// calcIterateInverse function calculates the iteration for inverse
// distributions.
func calcIterateInverse(iterator calcInverseIterator, fAx, fBx float64) float64 {
fAy, fBy := iterator.callBack(fAx), iterator.callBack(fBx)
var fTemp float64
var nCount int
for nCount = 0; nCount < 1000 && !hasChangeOfSign(fAy, fBy); nCount++ {
if math.Abs(fAy) <= math.Abs(fBy) {
fTemp = fAx
fAx += 2 * (fAx - fBx)
if fAx < 0 {
fAx = 0
}
fBx = fTemp
fBy = fAy
fAy = iterator.callBack(fAx)
} else {
fTemp = fBx
fBx += 2 * (fBx - fAx)
fAx = fTemp
fAy = fBy
fBy = iterator.callBack(fBx)
}
}
if fAy == 0 || fBy == 0 {
return 0
}
return inverseQuadraticInterpolation(iterator, fAx, fAy, fBx, fBy)
}
// CHISQdotINV function calculates the inverse of the left-tailed probability
// of the Chi-Square Distribution. The syntax of the function is:
//
// CHISQ.INV(probability,degrees_freedom)
//
func (fn *formulaFuncs) CHISQdotINV(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "CHISQ.INV requires 2 numeric arguments")
}
var probability, degrees formulaArg
if probability = argsList.Front().Value.(formulaArg).ToNumber(); probability.Type != ArgNumber {
return probability
}
if degrees = argsList.Back().Value.(formulaArg).ToNumber(); degrees.Type != ArgNumber {
return degrees
}
if probability.Number < 0 || probability.Number >= 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if degrees.Number < 1 || degrees.Number > math.Pow10(10) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(calcIterateInverse(calcInverseIterator{
name: "CHISQ.INV",
fp: probability.Number,
fDF: degrees.Number,
}, degrees.Number/2, degrees.Number))
}
// CHISQdotINVdotRT function calculates the inverse of the right-tailed
// probability of the Chi-Square Distribution. The syntax of the function is:
//
// CHISQ.INV.RT(probability,degrees_freedom)
//
func (fn *formulaFuncs) CHISQdotINVdotRT(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "CHISQ.INV.RT requires 2 numeric arguments")
}
return fn.CHIINV(argsList)
}
// confidence is an implementation of the formula functions CONFIDENCE and
// CONFIDENCE.NORM.
func (fn *formulaFuncs) confidence(name string, argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 3 numeric arguments", name))
}
alpha := argsList.Front().Value.(formulaArg).ToNumber()
if alpha.Type != ArgNumber {
return alpha
}
if alpha.Number <= 0 || alpha.Number >= 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
stdDev := argsList.Front().Next().Value.(formulaArg).ToNumber()
if stdDev.Type != ArgNumber {
return stdDev
}
if stdDev.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
size := argsList.Back().Value.(formulaArg).ToNumber()
if size.Type != ArgNumber {
return size
}
if size.Number < 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
args := list.New()
args.Init()
args.PushBack(newNumberFormulaArg(alpha.Number / 2))
args.PushBack(newNumberFormulaArg(0))
args.PushBack(newNumberFormulaArg(1))
return newNumberFormulaArg(-fn.NORMINV(args).Number * (stdDev.Number / math.Sqrt(size.Number)))
}
// CONFIDENCE function uses a Normal Distribution to calculate a confidence
// value that can be used to construct the Confidence Interval for a
// population mean, for a supplied probability and sample size. It is assumed
// that the standard deviation of the population is known. The syntax of the
// function is:
//
// CONFIDENCE(alpha,standard_dev,size)
//
func (fn *formulaFuncs) CONFIDENCE(argsList *list.List) formulaArg {
return fn.confidence("CONFIDENCE", argsList)
}
// CONFIDENCEdotNORM function uses a Normal Distribution to calculate a
// confidence value that can be used to construct the confidence interval for
// a population mean, for a supplied probability and sample size. It is
// assumed that the standard deviation of the population is known. The syntax
// of the function is:
//
// CONFIDENCE.NORM(alpha,standard_dev,size)
//
func (fn *formulaFuncs) CONFIDENCEdotNORM(argsList *list.List) formulaArg {
return fn.confidence("CONFIDENCE.NORM", argsList)
}
// CONFIDENCEdotT function uses a Student's T-Distribution to calculate a
// confidence value that can be used to construct the confidence interval for
// a population mean, for a supplied probablity and supplied sample size. It
// is assumed that the standard deviation of the population is known. The
// syntax of the function is:
//
// CONFIDENCE.T(alpha,standard_dev,size)
//
func (fn *formulaFuncs) CONFIDENCEdotT(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "CONFIDENCE.T requires 3 arguments")
}
var alpha, standardDev, size formulaArg
if alpha = argsList.Front().Value.(formulaArg).ToNumber(); alpha.Type != ArgNumber {
return alpha
}
if standardDev = argsList.Front().Next().Value.(formulaArg).ToNumber(); standardDev.Type != ArgNumber {
return standardDev
}
if size = argsList.Back().Value.(formulaArg).ToNumber(); size.Type != ArgNumber {
return size
}
if alpha.Number <= 0 || alpha.Number >= 1 || standardDev.Number <= 0 || size.Number < 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if size.Number == 1 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(standardDev.Number * calcIterateInverse(calcInverseIterator{
name: "CONFIDENCE.T",
fp: alpha.Number,
fDF: size.Number - 1,
nT: 2,
}, size.Number/2, size.Number) / math.Sqrt(size.Number))
}
// covar is an implementation of the formula functions COVAR, COVARIANCE.P and
// COVARIANCE.S.
func (fn *formulaFuncs) covar(name string, argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 2 arguments", name))
}
array1 := argsList.Front().Value.(formulaArg)
array2 := argsList.Back().Value.(formulaArg)
left, right := array1.ToList(), array2.ToList()
n := len(left)
if n != len(right) {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
l1, l2 := list.New(), list.New()
l1.PushBack(array1)
l2.PushBack(array2)
result, skip := 0.0, 0
mean1, mean2 := fn.AVERAGE(l1), fn.AVERAGE(l2)
for i := 0; i < n; i++ {
arg1 := left[i].ToNumber()
arg2 := right[i].ToNumber()
if arg1.Type == ArgError || arg2.Type == ArgError {
skip++
continue
}
result += (arg1.Number - mean1.Number) * (arg2.Number - mean2.Number)
}
if name == "COVARIANCE.S" {
return newNumberFormulaArg(result / float64(n-skip-1))
}
return newNumberFormulaArg(result / float64(n-skip))
}
// COVAR function calculates the covariance of two supplied sets of values. The
// syntax of the function is:
//
// COVAR(array1,array2)
//
func (fn *formulaFuncs) COVAR(argsList *list.List) formulaArg {
return fn.covar("COVAR", argsList)
}
// COVARIANCEdotP function calculates the population covariance of two supplied
// sets of values. The syntax of the function is:
//
// COVARIANCE.P(array1,array2)
//
func (fn *formulaFuncs) COVARIANCEdotP(argsList *list.List) formulaArg {
return fn.covar("COVARIANCE.P", argsList)
}
// COVARIANCEdotS function calculates the sample covariance of two supplied
// sets of values. The syntax of the function is:
//
// COVARIANCE.S(array1,array2)
//
func (fn *formulaFuncs) COVARIANCEdotS(argsList *list.List) formulaArg {
return fn.covar("COVARIANCE.S", argsList)
}
// calcStringCountSum is part of the implementation countSum.
func calcStringCountSum(countText bool, count, sum float64, num, arg formulaArg) (float64, float64) {
if countText && num.Type == ArgError && arg.String != "" {
count++
}
if num.Type == ArgNumber {
sum += num.Number
count++
}
return count, sum
}
// countSum get count and sum for a formula arguments array.
func (fn *formulaFuncs) countSum(countText bool, args []formulaArg) (count, sum float64) {
for _, arg := range args {
switch arg.Type {
case ArgNumber:
if countText || !arg.Boolean {
sum += arg.Number
count++
}
case ArgString:
if !countText && (arg.Value() == "TRUE" || arg.Value() == "FALSE") {
continue
} else if countText && (arg.Value() == "TRUE" || arg.Value() == "FALSE") {
num := arg.ToBool()
if num.Type == ArgNumber {
count++
sum += num.Number
continue
}
}
num := arg.ToNumber()
count, sum = calcStringCountSum(countText, count, sum, num, arg)
case ArgList, ArgMatrix:
cnt, summary := fn.countSum(countText, arg.ToList())
sum += summary
count += cnt
}
}
return
}
// CORREL function calculates the Pearson Product-Moment Correlation
// Coefficient for two sets of values. The syntax of the function is:
//
// CORREL(array1,array2)
//
func (fn *formulaFuncs) CORREL(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "CORREL requires 2 arguments")
}
array1 := argsList.Front().Value.(formulaArg)
array2 := argsList.Back().Value.(formulaArg)
left, right := array1.ToList(), array2.ToList()
n := len(left)
if n != len(right) {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
l1, l2, l3 := list.New(), list.New(), list.New()
for i := 0; i < n; i++ {
if lhs, rhs := left[i].ToNumber(), right[i].ToNumber(); lhs.Number != 0 && rhs.Number != 0 {
l1.PushBack(lhs)
l2.PushBack(rhs)
}
}
stdev1, stdev2 := fn.STDEV(l1), fn.STDEV(l2)
if stdev1.Number == 0 || stdev2.Number == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
mean1, mean2, skip := fn.AVERAGE(l1), fn.AVERAGE(l2), 0
for i := 0; i < n; i++ {
lhs, rhs := left[i].ToNumber(), right[i].ToNumber()
if lhs.Number == 0 || rhs.Number == 0 {
skip++
continue
}
l3.PushBack(newNumberFormulaArg((lhs.Number - mean1.Number) * (rhs.Number - mean2.Number)))
}
return newNumberFormulaArg(fn.SUM(l3).Number / float64(n-skip-1) / stdev1.Number / stdev2.Number)
}
// COUNT function returns the count of numeric values in a supplied set of
// cells or values. This count includes both numbers and dates. The syntax of
// the function is:
//
// COUNT(value1,[value2],...)
//
func (fn *formulaFuncs) COUNT(argsList *list.List) formulaArg {
var count int
for token := argsList.Front(); token != nil; token = token.Next() {
arg := token.Value.(formulaArg)
switch arg.Type {
case ArgString, ArgNumber:
if arg.ToNumber().Type != ArgError {
count++
}
case ArgMatrix:
for _, row := range arg.Matrix {
for _, value := range row {
if value.ToNumber().Type != ArgError {
count++
}
}
}
}
}
return newNumberFormulaArg(float64(count))
}
// COUNTA function returns the number of non-blanks within a supplied set of
// cells or values. The syntax of the function is:
//
// COUNTA(value1,[value2],...)
//
func (fn *formulaFuncs) COUNTA(argsList *list.List) formulaArg {
var count int
for token := argsList.Front(); token != nil; token = token.Next() {
arg := token.Value.(formulaArg)
switch arg.Type {
case ArgString:
if arg.String != "" {
count++
}
case ArgNumber:
count++
case ArgMatrix:
for _, row := range arg.ToList() {
switch row.Type {
case ArgString:
if row.String != "" {
count++
}
case ArgNumber:
count++
}
}
}
}
return newNumberFormulaArg(float64(count))
}
// COUNTBLANK function returns the number of blank cells in a supplied range.
// The syntax of the function is:
//
// COUNTBLANK(range)
//
func (fn *formulaFuncs) COUNTBLANK(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "COUNTBLANK requires 1 argument")
}
var count float64
for _, cell := range argsList.Front().Value.(formulaArg).ToList() {
if cell.Value() == "" {
count++
}
}
return newNumberFormulaArg(count)
}
// COUNTIF function returns the number of cells within a supplied range, that
// satisfy a given criteria. The syntax of the function is:
//
// COUNTIF(range,criteria)
//
func (fn *formulaFuncs) COUNTIF(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "COUNTIF requires 2 arguments")
}
var (
criteria = formulaCriteriaParser(argsList.Front().Next().Value.(formulaArg).String)
count float64
)
for _, cell := range argsList.Front().Value.(formulaArg).ToList() {
if ok, _ := formulaCriteriaEval(cell.Value(), criteria); ok {
count++
}
}
return newNumberFormulaArg(count)
}
// formulaIfsMatch function returns cells reference array which match criteria.
func formulaIfsMatch(args []formulaArg) (cellRefs []cellRef) {
for i := 0; i < len(args)-1; i += 2 {
var match []cellRef
matrix, criteria := args[i].Matrix, formulaCriteriaParser(args[i+1].Value())
if i == 0 {
for rowIdx, row := range matrix {
for colIdx, col := range row {
if ok, _ := formulaCriteriaEval(col.Value(), criteria); ok {
match = append(match, cellRef{Col: colIdx, Row: rowIdx})
}
}
}
} else {
for _, ref := range cellRefs {
value := matrix[ref.Row][ref.Col]
if ok, _ := formulaCriteriaEval(value.Value(), criteria); ok {
match = append(match, ref)
}
}
}
if len(match) == 0 {
return
}
cellRefs = match[:]
}
return
}
// COUNTIFS function returns the number of rows within a table, that satisfy a
// set of given criteria. The syntax of the function is:
//
// COUNTIFS(criteria_range1,criteria1,[criteria_range2,criteria2],...)
//
func (fn *formulaFuncs) COUNTIFS(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "COUNTIFS requires at least 2 arguments")
}
if argsList.Len()%2 != 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
var args []formulaArg
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
args = append(args, arg.Value.(formulaArg))
}
return newNumberFormulaArg(float64(len(formulaIfsMatch(args))))
}
// CRITBINOM function returns the inverse of the Cumulative Binomial
// Distribution. I.e. for a specific number of independent trials, the
// function returns the smallest value (number of successes) for which the
// cumulative binomial distribution is greater than or equal to a specified
// value. The syntax of the function is:
//
// CRITBINOM(trials,probability_s,alpha)
//
func (fn *formulaFuncs) CRITBINOM(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "CRITBINOM requires 3 numeric arguments")
}
return fn.BINOMdotINV(argsList)
}
// DEVSQ function calculates the sum of the squared deviations from the sample
// mean. The syntax of the function is:
//
// DEVSQ(number1,[number2],...)
//
func (fn *formulaFuncs) DEVSQ(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "DEVSQ requires at least 1 numeric argument")
}
avg, count, result := fn.AVERAGE(argsList), -1, 0.0
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
for _, number := range arg.Value.(formulaArg).ToList() {
num := number.ToNumber()
if num.Type != ArgNumber {
continue
}
count++
if count == 0 {
result = math.Pow(num.Number-avg.Number, 2)
continue
}
result += math.Pow(num.Number-avg.Number, 2)
}
}
if count == -1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
return newNumberFormulaArg(result)
}
// FISHER function calculates the Fisher Transformation for a supplied value.
// The syntax of the function is:
//
// FISHER(x)
//
func (fn *formulaFuncs) FISHER(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "FISHER requires 1 numeric argument")
}
token := argsList.Front().Value.(formulaArg)
switch token.Type {
case ArgString:
arg := token.ToNumber()
if arg.Type == ArgNumber {
if arg.Number <= -1 || arg.Number >= 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
return newNumberFormulaArg(0.5 * math.Log((1+arg.Number)/(1-arg.Number)))
}
case ArgNumber:
if token.Number <= -1 || token.Number >= 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
return newNumberFormulaArg(0.5 * math.Log((1+token.Number)/(1-token.Number)))
}
return newErrorFormulaArg(formulaErrorVALUE, "FISHER requires 1 numeric argument")
}
// FISHERINV function calculates the inverse of the Fisher Transformation and
// returns a value between -1 and +1. The syntax of the function is:
//
// FISHERINV(y)
//
func (fn *formulaFuncs) FISHERINV(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "FISHERINV requires 1 numeric argument")
}
token := argsList.Front().Value.(formulaArg)
switch token.Type {
case ArgString:
arg := token.ToNumber()
if arg.Type == ArgNumber {
return newNumberFormulaArg((math.Exp(2*arg.Number) - 1) / (math.Exp(2*arg.Number) + 1))
}
case ArgNumber:
return newNumberFormulaArg((math.Exp(2*token.Number) - 1) / (math.Exp(2*token.Number) + 1))
}
return newErrorFormulaArg(formulaErrorVALUE, "FISHERINV requires 1 numeric argument")
}
// GAMMA function returns the value of the Gamma Function, Γ(n), for a
// specified number, n. The syntax of the function is:
//
// GAMMA(number)
//
func (fn *formulaFuncs) GAMMA(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "GAMMA requires 1 numeric argument")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, "GAMMA requires 1 numeric argument")
}
if number.Number <= 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
return newNumberFormulaArg(math.Gamma(number.Number))
}
// GAMMAdotDIST function returns the Gamma Distribution, which is frequently
// used to provide probabilities for values that may have a skewed
// distribution, such as queuing analysis.
//
// GAMMA.DIST(x,alpha,beta,cumulative)
//
func (fn *formulaFuncs) GAMMAdotDIST(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "GAMMA.DIST requires 4 arguments")
}
return fn.GAMMADIST(argsList)
}
// GAMMADIST function returns the Gamma Distribution, which is frequently used
// to provide probabilities for values that may have a skewed distribution,
// such as queuing analysis.
//
// GAMMADIST(x,alpha,beta,cumulative)
//
func (fn *formulaFuncs) GAMMADIST(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "GAMMADIST requires 4 arguments")
}
var x, alpha, beta, cumulative formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if x.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if alpha = argsList.Front().Next().Value.(formulaArg).ToNumber(); alpha.Type != ArgNumber {
return alpha
}
if beta = argsList.Back().Prev().Value.(formulaArg).ToNumber(); beta.Type != ArgNumber {
return beta
}
if alpha.Number <= 0 || beta.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if cumulative = argsList.Back().Value.(formulaArg).ToBool(); cumulative.Type == ArgError {
return cumulative
}
if cumulative.Number == 1 {
return newNumberFormulaArg(incompleteGamma(alpha.Number, x.Number/beta.Number) / math.Gamma(alpha.Number))
}
return newNumberFormulaArg((1 / (math.Pow(beta.Number, alpha.Number) * math.Gamma(alpha.Number))) * math.Pow(x.Number, alpha.Number-1) * math.Exp(0-(x.Number/beta.Number)))
}
// gammainv returns the inverse of the Gamma distribution for the specified
// value.
func gammainv(probability, alpha, beta float64) float64 {
xLo, xHi := 0.0, alpha*beta*5
dx, x, xNew, result := 1024.0, 1.0, 1.0, 0.0
for i := 0; math.Abs(dx) > 8.88e-016 && i <= 256; i++ {
result = incompleteGamma(alpha, x/beta) / math.Gamma(alpha)
e := result - probability
if e == 0 {
dx = 0
} else if e < 0 {
xLo = x
} else {
xHi = x
}
pdf := (1 / (math.Pow(beta, alpha) * math.Gamma(alpha))) * math.Pow(x, alpha-1) * math.Exp(0-(x/beta))
if pdf != 0 {
dx = e / pdf
xNew = x - dx
}
if xNew < xLo || xNew > xHi || pdf == 0 {
xNew = (xLo + xHi) / 2
dx = xNew - x
}
x = xNew
}
return x
}
// GAMMAdotINV function returns the inverse of the Gamma Cumulative
// Distribution. The syntax of the function is:
//
// GAMMA.INV(probability,alpha,beta)
//
func (fn *formulaFuncs) GAMMAdotINV(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "GAMMA.INV requires 3 arguments")
}
return fn.GAMMAINV(argsList)
}
// GAMMAINV function returns the inverse of the Gamma Cumulative Distribution.
// The syntax of the function is:
//
// GAMMAINV(probability,alpha,beta)
//
func (fn *formulaFuncs) GAMMAINV(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "GAMMAINV requires 3 arguments")
}
var probability, alpha, beta formulaArg
if probability = argsList.Front().Value.(formulaArg).ToNumber(); probability.Type != ArgNumber {
return probability
}
if probability.Number < 0 || probability.Number >= 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if alpha = argsList.Front().Next().Value.(formulaArg).ToNumber(); alpha.Type != ArgNumber {
return alpha
}
if beta = argsList.Back().Value.(formulaArg).ToNumber(); beta.Type != ArgNumber {
return beta
}
if alpha.Number <= 0 || beta.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(gammainv(probability.Number, alpha.Number, beta.Number))
}
// GAMMALN function returns the natural logarithm of the Gamma Function, Γ
// (n). The syntax of the function is:
//
// GAMMALN(x)
//
func (fn *formulaFuncs) GAMMALN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "GAMMALN requires 1 numeric argument")
}
x := argsList.Front().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, "GAMMALN requires 1 numeric argument")
}
if x.Number <= 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
return newNumberFormulaArg(math.Log(math.Gamma(x.Number)))
}
// GAMMALNdotPRECISE function returns the natural logarithm of the Gamma
// Function, Γ(n). The syntax of the function is:
//
// GAMMALN.PRECISE(x)
//
func (fn *formulaFuncs) GAMMALNdotPRECISE(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "GAMMALN.PRECISE requires 1 numeric argument")
}
x := argsList.Front().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return x
}
if x.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(getLogGamma(x.Number))
}
// GAUSS function returns the probability that a member of a standard normal
// population will fall between the mean and a specified number of standard
// deviations from the mean. The syntax of the function is:
//
// GAUSS(z)
//
func (fn *formulaFuncs) GAUSS(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "GAUSS requires 1 numeric argument")
}
args := list.New().Init()
args.PushBack(argsList.Front().Value.(formulaArg))
args.PushBack(formulaArg{Type: ArgNumber, Number: 0})
args.PushBack(formulaArg{Type: ArgNumber, Number: 1})
args.PushBack(newBoolFormulaArg(true))
normdist := fn.NORMDIST(args)
if normdist.Type != ArgNumber {
return normdist
}
return newNumberFormulaArg(normdist.Number - 0.5)
}
// GEOMEAN function calculates the geometric mean of a supplied set of values.
// The syntax of the function is:
//
// GEOMEAN(number1,[number2],...)
//
func (fn *formulaFuncs) GEOMEAN(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "GEOMEAN requires at least 1 numeric argument")
}
product := fn.PRODUCT(argsList)
if product.Type != ArgNumber {
return product
}
count := fn.COUNT(argsList)
min := fn.MIN(argsList)
if product.Number > 0 && min.Number > 0 {
return newNumberFormulaArg(math.Pow(product.Number, 1/count.Number))
}
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
// getNewMatrix create matrix by given columns and rows.
func getNewMatrix(c, r int) (matrix [][]float64) {
for i := 0; i < c; i++ {
for j := 0; j < r; j++ {
for x := len(matrix); x <= i; x++ {
matrix = append(matrix, []float64{})
}
for y := len(matrix[i]); y <= j; y++ {
matrix[i] = append(matrix[i], 0)
}
matrix[i][j] = 0
}
}
return
}
// approxSub subtract two values, if signs are identical and the values are
// equal, will be returns 0 instead of calculating the subtraction.
func approxSub(a, b float64) float64 {
if ((a < 0 && b < 0) || (a > 0 && b > 0)) && math.Abs(a-b) < 2.22045e-016 {
return 0
}
return a - b
}
// matrixClone return a copy of all elements of the original matrix.
func matrixClone(matrix [][]float64) (cloneMatrix [][]float64) {
for i := 0; i < len(matrix); i++ {
for j := 0; j < len(matrix[i]); j++ {
for x := len(cloneMatrix); x <= i; x++ {
cloneMatrix = append(cloneMatrix, []float64{})
}
for k := len(cloneMatrix[i]); k <= j; k++ {
cloneMatrix[i] = append(cloneMatrix[i], 0)
}
cloneMatrix[i][j] = matrix[i][j]
}
}
return
}
// trendGrowthMatrixInfo defined matrix checking result.
type trendGrowthMatrixInfo struct {
trendType, nCX, nCY, nRX, nRY, M, N int
mtxX, mtxY [][]float64
}
// prepareTrendGrowthMtxX is a part of implementation of the trend growth prepare.
func prepareTrendGrowthMtxX(mtxX [][]float64) [][]float64 {
var mtx [][]float64
for i := 0; i < len(mtxX); i++ {
for j := 0; j < len(mtxX[i]); j++ {
if mtxX[i][j] == 0 {
return nil
}
for x := len(mtx); x <= j; x++ {
mtx = append(mtx, []float64{})
}
for y := len(mtx[j]); y <= i; y++ {
mtx[j] = append(mtx[j], 0)
}
mtx[j][i] = mtxX[i][j]
}
}
return mtx
}
// prepareTrendGrowthMtxY is a part of implementation of the trend growth prepare.
func prepareTrendGrowthMtxY(bLOG bool, mtxY [][]float64) [][]float64 {
var mtx [][]float64
for i := 0; i < len(mtxY); i++ {
for j := 0; j < len(mtxY[i]); j++ {
if mtxY[i][j] == 0 {
return nil
}
for x := len(mtx); x <= j; x++ {
mtx = append(mtx, []float64{})
}
for y := len(mtx[j]); y <= i; y++ {
mtx[j] = append(mtx[j], 0)
}
mtx[j][i] = mtxY[i][j]
}
}
if bLOG {
var pNewY [][]float64
for i := 0; i < len(mtxY); i++ {
for j := 0; j < len(mtxY[i]); j++ {
fVal := mtxY[i][j]
if fVal <= 0 {
return nil
}
for x := len(pNewY); x <= j; x++ {
pNewY = append(pNewY, []float64{})
}
for y := len(pNewY[j]); y <= i; y++ {
pNewY[j] = append(pNewY[j], 0)
}
pNewY[j][i] = math.Log(fVal)
}
}
mtx = pNewY
}
return mtx
}
// prepareTrendGrowth check and return the result.
func prepareTrendGrowth(bLOG bool, mtxX, mtxY [][]float64) (*trendGrowthMatrixInfo, formulaArg) {
var nCX, nRX, M, N, trendType int
nRY, nCY := len(mtxY), len(mtxY[0])
cntY := nCY * nRY
newY := prepareTrendGrowthMtxY(bLOG, mtxY)
if newY == nil {
return nil, newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
var newX [][]float64
if len(mtxX) != 0 {
nRX, nCX = len(mtxX), len(mtxX[0])
if newX = prepareTrendGrowthMtxX(mtxX); newX == nil {
return nil, newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if nCX == nCY && nRX == nRY {
trendType, M, N = 1, 1, cntY // simple regression
} else if nCY != 1 && nRY != 1 {
return nil, newErrorFormulaArg(formulaErrorREF, formulaErrorREF)
} else if nCY == 1 {
if nRX != nRY {
return nil, newErrorFormulaArg(formulaErrorREF, formulaErrorREF)
}
trendType, M, N = 2, nCX, nRY
} else if nCX != nCY {
return nil, newErrorFormulaArg(formulaErrorREF, formulaErrorREF)
} else {
trendType, M, N = 3, nRX, nCY
}
} else {
newX = getNewMatrix(nCY, nRY)
nCX, nRX = nCY, nRY
num := 1.0
for i := 0; i < nRY; i++ {
for j := 0; j < nCY; j++ {
newX[j][i] = num
num++
}
}
trendType, M, N = 1, 1, cntY
}
return &trendGrowthMatrixInfo{
trendType: trendType,
nCX: nCX,
nCY: nCY,
nRX: nRX,
nRY: nRY,
M: M,
N: N,
mtxX: newX,
mtxY: newY,
}, newEmptyFormulaArg()
}
// calcPosition calculate position for matrix by given index.
func calcPosition(mtx [][]float64, idx int) (row, col int) {
rowSize := len(mtx[0])
col = idx
if rowSize > 1 {
col = idx / rowSize
}
row = idx - col*rowSize
return
}
// getDouble returns float64 data type value in the matrix by given index.
func getDouble(mtx [][]float64, idx int) float64 {
row, col := calcPosition(mtx, idx)
return mtx[col][row]
}
// putDouble set a float64 data type value in the matrix by given index.
func putDouble(mtx [][]float64, idx int, val float64) {
row, col := calcPosition(mtx, idx)
mtx[col][row] = val
}
// calcMeanOverAll returns mean of the given matrix by over all element.
func calcMeanOverAll(mtx [][]float64, n int) float64 {
var sum float64
for i := 0; i < len(mtx); i++ {
for j := 0; j < len(mtx[i]); j++ {
sum += mtx[i][j]
}
}
return sum / float64(n)
}
// calcSumProduct returns uses the matrices as vectors of length M over all
// element.
func calcSumProduct(mtxA, mtxB [][]float64, m int) float64 {
sum := 0.0
for i := 0; i < m; i++ {
sum += getDouble(mtxA, i) * getDouble(mtxB, i)
}
return sum
}
// calcColumnMeans calculates means of the columns of matrix.
func calcColumnMeans(mtxX, mtxRes [][]float64, c, r int) {
for i := 0; i < c; i++ {
var sum float64
for k := 0; k < r; k++ {
sum += mtxX[i][k]
}
putDouble(mtxRes, i, sum/float64(r))
}
}
// calcColumnsDelta calculates subtract of the columns of matrix.
func calcColumnsDelta(mtx, columnMeans [][]float64, c, r int) {
for i := 0; i < c; i++ {
for k := 0; k < r; k++ {
mtx[i][k] = approxSub(mtx[i][k], getDouble(columnMeans, i))
}
}
}
// calcSign returns sign by given value, no mathematical signum, but used to
// switch between adding and subtracting.
func calcSign(val float64) float64 {
if val > 0 {
return 1
}
return -1
}
// calcColsMaximumNorm is a special version for use within QR
// decomposition. Maximum norm of column index c starting in row index r;
// matrix A has count n rows.
func calcColsMaximumNorm(mtxA [][]float64, c, r, n int) float64 {
var norm float64
for row := r; row < n; row++ {
if norm < math.Abs(mtxA[c][row]) {
norm = math.Abs(mtxA[c][row])
}
}
return norm
}
// calcFastMult returns multiply n x m matrix A with m x l matrix B to n x l matrix R.
func calcFastMult(mtxA, mtxB, mtxR [][]float64, n, m, l int) {
var sum float64
for row := 0; row < n; row++ {
for col := 0; col < l; col++ {
sum = 0.0
for k := 0; k < m; k++ {
sum += mtxA[k][row] * mtxB[col][k]
}
mtxR[col][row] = sum
}
}
}
// calcRowsEuclideanNorm is a special version for use within QR
// decomposition. Euclidean norm of column index c starting in row index r;
// matrix a has count n rows.
func calcRowsEuclideanNorm(mtxA [][]float64, c, r, n int) float64 {
var norm float64
for row := r; row < n; row++ {
norm += mtxA[c][row] * mtxA[c][row]
}
return math.Sqrt(norm)
}
// calcRowsSumProduct is a special version for use within QR decomposition.
// <A(a);B(b)> starting in row index r;
// a and b are indices of columns, matrices A and B have count n rows.
func calcRowsSumProduct(mtxA [][]float64, a int, mtxB [][]float64, b, r, n int) float64 {
var result float64
for row := r; row < n; row++ {
result += mtxA[a][row] * mtxB[b][row]
}
return result
}
// calcSolveWithUpperRightTriangle solve for X in R*X=S using back substitution.
func calcSolveWithUpperRightTriangle(mtxA [][]float64, vecR []float64, mtxS [][]float64, k int, bIsTransposed bool) {
var row int
for rowp1 := k; rowp1 > 0; rowp1-- {
row = rowp1 - 1
sum := getDouble(mtxS, row)
for col := rowp1; col < k; col++ {
if bIsTransposed {
sum -= mtxA[row][col] * getDouble(mtxS, col)
} else {
sum -= mtxA[col][row] * getDouble(mtxS, col)
}
}
putDouble(mtxS, row, sum/vecR[row])
}
}
// calcRowQRDecomposition calculates a QR decomposition with Householder
// reflection.
func calcRowQRDecomposition(mtxA [][]float64, vecR []float64, k, n int) bool {
for col := 0; col < k; col++ {
scale := calcColsMaximumNorm(mtxA, col, col, n)
if scale == 0 {
return false
}
for row := col; row < n; row++ {
mtxA[col][row] = mtxA[col][row] / scale
}
euclid := calcRowsEuclideanNorm(mtxA, col, col, n)
factor := 1.0 / euclid / (euclid + math.Abs(mtxA[col][col]))
signum := calcSign(mtxA[col][col])
mtxA[col][col] = mtxA[col][col] + signum*euclid
vecR[col] = -signum * scale * euclid
// apply Householder transformation to A
for c := col + 1; c < k; c++ {
sum := calcRowsSumProduct(mtxA, col, mtxA, c, col, n)
for row := col; row < n; row++ {
mtxA[c][row] = mtxA[c][row] - sum*factor*mtxA[col][row]
}
}
}
return true
}
// calcApplyColsHouseholderTransformation transposed matrices A and Y.
func calcApplyColsHouseholderTransformation(mtxA [][]float64, r int, mtxY [][]float64, n int) {
denominator := calcColsSumProduct(mtxA, r, mtxA, r, r, n)
numerator := calcColsSumProduct(mtxA, r, mtxY, 0, r, n)
factor := 2 * (numerator / denominator)
for col := r; col < n; col++ {
putDouble(mtxY, col, getDouble(mtxY, col)-factor*mtxA[col][r])
}
}
// calcRowMeans calculates means of the rows of matrix.
func calcRowMeans(mtxX, mtxRes [][]float64, c, r int) {
for k := 0; k < r; k++ {
var fSum float64
for i := 0; i < c; i++ {
fSum += mtxX[i][k]
}
mtxRes[k][0] = fSum / float64(c)
}
}
// calcRowsDelta calculates subtract of the rows of matrix.
func calcRowsDelta(mtx, rowMeans [][]float64, c, r int) {
for k := 0; k < r; k++ {
for i := 0; i < c; i++ {
mtx[i][k] = approxSub(mtx[i][k], rowMeans[k][0])
}
}
}
// calcColumnMaximumNorm returns maximum norm of row index R starting in col
// index C; matrix A has count N columns.
func calcColumnMaximumNorm(mtxA [][]float64, r, c, n int) float64 {
var norm float64
for col := c; col < n; col++ {
if norm < math.Abs(mtxA[col][r]) {
norm = math.Abs(mtxA[col][r])
}
}
return norm
}
// calcColsEuclideanNorm returns euclidean norm of row index R starting in
// column index C; matrix A has count N columns.
func calcColsEuclideanNorm(mtxA [][]float64, r, c, n int) float64 {
var norm float64
for col := c; col < n; col++ {
norm += (mtxA[col][r]) * (mtxA[col][r])
}
return math.Sqrt(norm)
}
// calcColsSumProduct returns sum product for given matrix.
func calcColsSumProduct(mtxA [][]float64, a int, mtxB [][]float64, b, c, n int) float64 {
var result float64
for col := c; col < n; col++ {
result += mtxA[col][a] * mtxB[col][b]
}
return result
}
// calcColQRDecomposition same with transposed matrix A, N is count of
// columns, k count of rows.
func calcColQRDecomposition(mtxA [][]float64, vecR []float64, k, n int) bool {
var sum float64
for row := 0; row < k; row++ {
// calculate vector u of the householder transformation
scale := calcColumnMaximumNorm(mtxA, row, row, n)
if scale == 0 {
return false
}
for col := row; col < n; col++ {
mtxA[col][row] = mtxA[col][row] / scale
}
euclid := calcColsEuclideanNorm(mtxA, row, row, n)
factor := 1 / euclid / (euclid + math.Abs(mtxA[row][row]))
signum := calcSign(mtxA[row][row])
mtxA[row][row] = mtxA[row][row] + signum*euclid
vecR[row] = -signum * scale * euclid
// apply Householder transformation to A
for r := row + 1; r < k; r++ {
sum = calcColsSumProduct(mtxA, row, mtxA, r, row, n)
for col := row; col < n; col++ {
mtxA[col][r] = mtxA[col][r] - sum*factor*mtxA[col][row]
}
}
}
return true
}
// calcApplyRowsHouseholderTransformation applies a Householder transformation to a
// column vector Y with is given as Nx1 Matrix. The vector u, from which the
// Householder transformation is built, is the column part in matrix A, with
// column index c, starting with row index c. A is the result of the QR
// decomposition as obtained from calcRowQRDecomposition.
func calcApplyRowsHouseholderTransformation(mtxA [][]float64, c int, mtxY [][]float64, n int) {
denominator := calcRowsSumProduct(mtxA, c, mtxA, c, c, n)
numerator := calcRowsSumProduct(mtxA, c, mtxY, 0, c, n)
factor := 2 * (numerator / denominator)
for row := c; row < n; row++ {
putDouble(mtxY, row, getDouble(mtxY, row)-factor*mtxA[c][row])
}
}
// calcTrendGrowthSimpleRegression calculate simple regression for the calcTrendGrowth.
func calcTrendGrowthSimpleRegression(bConstant, bGrowth bool, mtxY, mtxX, newX, mtxRes [][]float64, meanY float64, N int) {
var meanX float64
if bConstant {
meanX = calcMeanOverAll(mtxX, N)
for i := 0; i < len(mtxX); i++ {
for j := 0; j < len(mtxX[i]); j++ {
mtxX[i][j] = approxSub(mtxX[i][j], meanX)
}
}
}
sumXY := calcSumProduct(mtxX, mtxY, N)
sumX2 := calcSumProduct(mtxX, mtxX, N)
slope := sumXY / sumX2
var help float64
var intercept float64
if bConstant {
intercept = meanY - slope*meanX
for i := 0; i < len(mtxRes); i++ {
for j := 0; j < len(mtxRes[i]); j++ {
help = newX[i][j]*slope + intercept
if bGrowth {
mtxRes[i][j] = math.Exp(help)
} else {
mtxRes[i][j] = help
}
}
}
} else {
for i := 0; i < len(mtxRes); i++ {
for j := 0; j < len(mtxRes[i]); j++ {
help = newX[i][j] * slope
if bGrowth {
mtxRes[i][j] = math.Exp(help)
} else {
mtxRes[i][j] = help
}
}
}
}
}
// calcTrendGrowthMultipleRegressionPart1 calculate multiple regression for the
// calcTrendGrowth.
func calcTrendGrowthMultipleRegressionPart1(bConstant, bGrowth bool, mtxY, mtxX, newX, mtxRes [][]float64, meanY float64, RXN, K, N int) {
vecR := make([]float64, N) // for QR decomposition
means := getNewMatrix(K, 1) // mean of each column
slopes := getNewMatrix(1, K) // from b1 to bK
if len(means) == 0 || len(slopes) == 0 {
return
}
if bConstant {
calcColumnMeans(mtxX, means, K, N)
calcColumnsDelta(mtxX, means, K, N)
}
if !calcRowQRDecomposition(mtxX, vecR, K, N) {
return
}
// Later on we will divide by elements of vecR, so make sure that they aren't zero.
bIsSingular := false
for row := 0; row < K && !bIsSingular; row++ {
bIsSingular = bIsSingular || vecR[row] == 0
}
if bIsSingular {
return
}
for col := 0; col < K; col++ {
calcApplyRowsHouseholderTransformation(mtxX, col, mtxY, N)
}
for col := 0; col < K; col++ {
putDouble(slopes, col, getDouble(mtxY, col))
}
calcSolveWithUpperRightTriangle(mtxX, vecR, slopes, K, false)
// Fill result matrix
calcFastMult(newX, slopes, mtxRes, RXN, K, 1)
if bConstant {
intercept := meanY - calcSumProduct(means, slopes, K)
for row := 0; row < RXN; row++ {
mtxRes[0][row] = mtxRes[0][row] + intercept
}
}
if bGrowth {
for i := 0; i < RXN; i++ {
putDouble(mtxRes, i, math.Exp(getDouble(mtxRes, i)))
}
}
}
// calcTrendGrowthMultipleRegressionPart2 calculate multiple regression for the
// calcTrendGrowth.
func calcTrendGrowthMultipleRegressionPart2(bConstant, bGrowth bool, mtxY, mtxX, newX, mtxRes [][]float64, meanY float64, nCXN, K, N int) {
vecR := make([]float64, N) // for QR decomposition
means := getNewMatrix(K, 1) // mean of each row
slopes := getNewMatrix(K, 1) // row from b1 to bK
if len(means) == 0 || len(slopes) == 0 {
return
}
if bConstant {
calcRowMeans(mtxX, means, N, K)
calcRowsDelta(mtxX, means, N, K)
}
if !calcColQRDecomposition(mtxX, vecR, K, N) {
return
}
// later on we will divide by elements of vecR, so make sure that they aren't zero
bIsSingular := false
for row := 0; row < K && !bIsSingular; row++ {
bIsSingular = bIsSingular || vecR[row] == 0
}
if bIsSingular {
return
}
for row := 0; row < K; row++ {
calcApplyColsHouseholderTransformation(mtxX, row, mtxY, N)
}
for col := 0; col < K; col++ {
putDouble(slopes, col, getDouble(mtxY, col))
}
calcSolveWithUpperRightTriangle(mtxX, vecR, slopes, K, true)
// fill result matrix
calcFastMult(slopes, newX, mtxRes, 1, K, nCXN)
if bConstant {
fIntercept := meanY - calcSumProduct(means, slopes, K)
for col := 0; col < nCXN; col++ {
mtxRes[col][0] = mtxRes[col][0] + fIntercept
}
}
if bGrowth {
for i := 0; i < nCXN; i++ {
putDouble(mtxRes, i, math.Exp(getDouble(mtxRes, i)))
}
}
}
// calcTrendGrowthRegression is a part of implementation of the calcTrendGrowth.
func calcTrendGrowthRegression(bConstant, bGrowth bool, trendType, nCXN, nRXN, K, N int, mtxY, mtxX, newX, mtxRes [][]float64) {
if len(mtxRes) == 0 {
return
}
var meanY float64
if bConstant {
copyX, copyY := matrixClone(mtxX), matrixClone(mtxY)
mtxX, mtxY = copyX, copyY
meanY = calcMeanOverAll(mtxY, N)
for i := 0; i < len(mtxY); i++ {
for j := 0; j < len(mtxY[i]); j++ {
mtxY[i][j] = approxSub(mtxY[i][j], meanY)
}
}
}
switch trendType {
case 1:
calcTrendGrowthSimpleRegression(bConstant, bGrowth, mtxY, mtxX, newX, mtxRes, meanY, N)
case 2:
calcTrendGrowthMultipleRegressionPart1(bConstant, bGrowth, mtxY, mtxX, newX, mtxRes, meanY, nRXN, K, N)
default:
calcTrendGrowthMultipleRegressionPart2(bConstant, bGrowth, mtxY, mtxX, newX, mtxRes, meanY, nCXN, K, N)
}
}
// calcTrendGrowth returns values along a predicted exponential trend.
func calcTrendGrowth(mtxY, mtxX, newX [][]float64, bConstant, bGrowth bool) ([][]float64, formulaArg) {
getMatrixParams, errArg := prepareTrendGrowth(bGrowth, mtxX, mtxY)
if errArg.Type != ArgEmpty {
return nil, errArg
}
trendType := getMatrixParams.trendType
nCX := getMatrixParams.nCX
nRX := getMatrixParams.nRX
K := getMatrixParams.M
N := getMatrixParams.N
mtxX = getMatrixParams.mtxX
mtxY = getMatrixParams.mtxY
// checking if data samples are enough
if (bConstant && (N < K+1)) || (!bConstant && (N < K)) || (N < 1) || (K < 1) {
return nil, errArg
}
// set the default newX if necessary
nCXN, nRXN := nCX, nRX
if len(newX) == 0 {
newX = matrixClone(mtxX) // mtxX will be changed to X-meanX
} else {
nRXN, nCXN = len(newX[0]), len(newX)
if (trendType == 2 && K != nCXN) || (trendType == 3 && K != nRXN) {
return nil, errArg
}
}
var mtxRes [][]float64
switch trendType {
case 1:
mtxRes = getNewMatrix(nCXN, nRXN)
case 2:
mtxRes = getNewMatrix(1, nRXN)
default:
mtxRes = getNewMatrix(nCXN, 1)
}
calcTrendGrowthRegression(bConstant, bGrowth, trendType, nCXN, nRXN, K, N, mtxY, mtxX, newX, mtxRes)
return mtxRes, errArg
}
// trendGrowth is an implementation of the formula functions GROWTH and TREND.
func (fn *formulaFuncs) trendGrowth(name string, argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 1 argument", name))
}
if argsList.Len() > 4 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s allows at most 4 arguments", name))
}
var knowY, knowX, newX [][]float64
var errArg formulaArg
constArg := newBoolFormulaArg(true)
knowY, errArg = newNumberMatrix(argsList.Front().Value.(formulaArg), false)
if errArg.Type == ArgError {
return errArg
}
if argsList.Len() > 1 {
knowX, errArg = newNumberMatrix(argsList.Front().Next().Value.(formulaArg), false)
if errArg.Type == ArgError {
return errArg
}
}
if argsList.Len() > 2 {
newX, errArg = newNumberMatrix(argsList.Front().Next().Next().Value.(formulaArg), false)
if errArg.Type == ArgError {
return errArg
}
}
if argsList.Len() > 3 {
if constArg = argsList.Back().Value.(formulaArg).ToBool(); constArg.Type != ArgNumber {
return constArg
}
}
var mtxNewX [][]float64
for i := 0; i < len(newX); i++ {
for j := 0; j < len(newX[i]); j++ {
for x := len(mtxNewX); x <= j; x++ {
mtxNewX = append(mtxNewX, []float64{})
}
for k := len(mtxNewX[j]); k <= i; k++ {
mtxNewX[j] = append(mtxNewX[j], 0)
}
mtxNewX[j][i] = newX[i][j]
}
}
mtx, errArg := calcTrendGrowth(knowY, knowX, mtxNewX, constArg.Number == 1, name == "GROWTH")
if errArg.Type != ArgEmpty {
return errArg
}
return newMatrixFormulaArg(newFormulaArgMatrix(mtx))
}
// GROWTH function calculates the exponential growth curve through a given set
// of y-values and (optionally), one or more sets of x-values. The function
// then extends the curve to calculate additional y-values for a further
// supplied set of new x-values. The syntax of the function is:
//
// GROWTH(known_y's,[known_x's],[new_x's],[const])
//
func (fn *formulaFuncs) GROWTH(argsList *list.List) formulaArg {
return fn.trendGrowth("GROWTH", argsList)
}
// HARMEAN function calculates the harmonic mean of a supplied set of values.
// The syntax of the function is:
//
// HARMEAN(number1,[number2],...)
//
func (fn *formulaFuncs) HARMEAN(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "HARMEAN requires at least 1 argument")
}
if min := fn.MIN(argsList); min.Number < 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
number, val, cnt := 0.0, 0.0, 0.0
for token := argsList.Front(); token != nil; token = token.Next() {
arg := token.Value.(formulaArg)
switch arg.Type {
case ArgString:
num := arg.ToNumber()
if num.Type != ArgNumber {
continue
}
number = num.Number
case ArgNumber:
number = arg.Number
}
if number <= 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
val += 1 / number
cnt++
}
return newNumberFormulaArg(1 / (val / cnt))
}
// checkHYPGEOMDISTArgs checking arguments for the formula function HYPGEOMDIST
// and HYPGEOM.DIST.
func checkHYPGEOMDISTArgs(sampleS, numberSample, populationS, numberPop formulaArg) bool {
return sampleS.Number < 0 ||
sampleS.Number > math.Min(numberSample.Number, populationS.Number) ||
sampleS.Number < math.Max(0, numberSample.Number-numberPop.Number+populationS.Number) ||
numberSample.Number <= 0 ||
numberSample.Number > numberPop.Number ||
populationS.Number <= 0 ||
populationS.Number > numberPop.Number ||
numberPop.Number <= 0
}
// prepareHYPGEOMDISTArgs prepare arguments for the formula function
// HYPGEOMDIST and HYPGEOM.DIST.
func (fn *formulaFuncs) prepareHYPGEOMDISTArgs(name string, argsList *list.List) formulaArg {
if name == "HYPGEOMDIST" && argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "HYPGEOMDIST requires 4 numeric arguments")
}
if name == "HYPGEOM.DIST" && argsList.Len() != 5 {
return newErrorFormulaArg(formulaErrorVALUE, "HYPGEOM.DIST requires 5 arguments")
}
var sampleS, numberSample, populationS, numberPop, cumulative formulaArg
if sampleS = argsList.Front().Value.(formulaArg).ToNumber(); sampleS.Type != ArgNumber {
return sampleS
}
if numberSample = argsList.Front().Next().Value.(formulaArg).ToNumber(); numberSample.Type != ArgNumber {
return numberSample
}
if populationS = argsList.Front().Next().Next().Value.(formulaArg).ToNumber(); populationS.Type != ArgNumber {
return populationS
}
if numberPop = argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber(); numberPop.Type != ArgNumber {
return numberPop
}
if checkHYPGEOMDISTArgs(sampleS, numberSample, populationS, numberPop) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if name == "HYPGEOM.DIST" {
if cumulative = argsList.Back().Value.(formulaArg).ToBool(); cumulative.Type != ArgNumber {
return cumulative
}
}
return newListFormulaArg([]formulaArg{sampleS, numberSample, populationS, numberPop, cumulative})
}
// HYPGEOMdotDIST function returns the value of the hypergeometric distribution
// for a specified number of successes from a population sample. The function
// can calculate the cumulative distribution or the probability density
// function. The syntax of the function is:
//
// HYPGEOM.DIST(sample_s,number_sample,population_s,number_pop,cumulative)
//
func (fn *formulaFuncs) HYPGEOMdotDIST(argsList *list.List) formulaArg {
args := fn.prepareHYPGEOMDISTArgs("HYPGEOM.DIST", argsList)
if args.Type != ArgList {
return args
}
sampleS, numberSample, populationS, numberPop, cumulative := args.List[0], args.List[1], args.List[2], args.List[3], args.List[4]
if cumulative.Number == 1 {
var res float64
for i := 0; i <= int(sampleS.Number); i++ {
res += binomCoeff(populationS.Number, float64(i)) *
binomCoeff(numberPop.Number-populationS.Number, numberSample.Number-float64(i)) /
binomCoeff(numberPop.Number, numberSample.Number)
}
return newNumberFormulaArg(res)
}
return newNumberFormulaArg(binomCoeff(populationS.Number, sampleS.Number) *
binomCoeff(numberPop.Number-populationS.Number, numberSample.Number-sampleS.Number) /
binomCoeff(numberPop.Number, numberSample.Number))
}
// HYPGEOMDIST function returns the value of the hypergeometric distribution
// for a given number of successes from a sample of a population. The syntax
// of the function is:
//
// HYPGEOMDIST(sample_s,number_sample,population_s,number_pop)
//
func (fn *formulaFuncs) HYPGEOMDIST(argsList *list.List) formulaArg {
args := fn.prepareHYPGEOMDISTArgs("HYPGEOMDIST", argsList)
if args.Type != ArgList {
return args
}
sampleS, numberSample, populationS, numberPop := args.List[0], args.List[1], args.List[2], args.List[3]
return newNumberFormulaArg(binomCoeff(populationS.Number, sampleS.Number) *
binomCoeff(numberPop.Number-populationS.Number, numberSample.Number-sampleS.Number) /
binomCoeff(numberPop.Number, numberSample.Number))
}
// KURT function calculates the kurtosis of a supplied set of values. The
// syntax of the function is:
//
// KURT(number1,[number2],...)
//
func (fn *formulaFuncs) KURT(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "KURT requires at least 1 argument")
}
mean, stdev := fn.AVERAGE(argsList), fn.STDEV(argsList)
if stdev.Number > 0 {
count, summer := 0.0, 0.0
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgString, ArgNumber:
num := token.ToNumber()
if num.Type == ArgError {
continue
}
summer += math.Pow((num.Number-mean.Number)/stdev.Number, 4)
count++
case ArgList, ArgMatrix:
for _, row := range token.ToList() {
if row.Type == ArgNumber || row.Type == ArgString {
num := row.ToNumber()
if num.Type == ArgError {
continue
}
summer += math.Pow((num.Number-mean.Number)/stdev.Number, 4)
count++
}
}
}
}
if count > 3 {
return newNumberFormulaArg(summer*(count*(count+1)/((count-1)*(count-2)*(count-3))) - (3 * math.Pow(count-1, 2) / ((count - 2) * (count - 3))))
}
}
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
// EXPONdotDIST function returns the value of the exponential distribution for
// a give value of x. The user can specify whether the probability density
// function or the cumulative distribution function is used. The syntax of the
// Expondist function is:
//
// EXPON.DIST(x,lambda,cumulative)
//
func (fn *formulaFuncs) EXPONdotDIST(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "EXPON.DIST requires 3 arguments")
}
return fn.EXPONDIST(argsList)
}
// EXPONDIST function returns the value of the exponential distribution for a
// give value of x. The user can specify whether the probability density
// function or the cumulative distribution function is used. The syntax of the
// Expondist function is:
//
// EXPONDIST(x,lambda,cumulative)
//
func (fn *formulaFuncs) EXPONDIST(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "EXPONDIST requires 3 arguments")
}
var x, lambda, cumulative formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if lambda = argsList.Front().Next().Value.(formulaArg).ToNumber(); lambda.Type != ArgNumber {
return lambda
}
if cumulative = argsList.Back().Value.(formulaArg).ToBool(); cumulative.Type == ArgError {
return cumulative
}
if x.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if lambda.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if cumulative.Number == 1 {
return newNumberFormulaArg(1 - math.Exp(-lambda.Number*x.Number))
}
return newNumberFormulaArg(lambda.Number * math.Exp(-lambda.Number*x.Number))
}
// FdotDIST function calculates the Probability Density Function or the
// Cumulative Distribution Function for the F Distribution. This function is
// frequently used to measure the degree of diversity between two data
// sets. The syntax of the function is:
//
// F.DIST(x,deg_freedom1,deg_freedom2,cumulative)
//
func (fn *formulaFuncs) FdotDIST(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "F.DIST requires 4 arguments")
}
var x, deg1, deg2, cumulative formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if deg1 = argsList.Front().Next().Value.(formulaArg).ToNumber(); deg1.Type != ArgNumber {
return deg1
}
if deg2 = argsList.Front().Next().Next().Value.(formulaArg).ToNumber(); deg2.Type != ArgNumber {
return deg2
}
if cumulative = argsList.Back().Value.(formulaArg).ToBool(); cumulative.Type == ArgError {
return cumulative
}
if x.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
maxDeg := math.Pow10(10)
if deg1.Number < 1 || deg1.Number >= maxDeg {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if deg2.Number < 1 || deg2.Number >= maxDeg {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if cumulative.Number == 1 {
return newNumberFormulaArg(1 - getBetaDist(deg2.Number/(deg2.Number+deg1.Number*x.Number), deg2.Number/2, deg1.Number/2))
}
return newNumberFormulaArg(math.Gamma((deg2.Number+deg1.Number)/2) / (math.Gamma(deg1.Number/2) * math.Gamma(deg2.Number/2)) * math.Pow(deg1.Number/deg2.Number, deg1.Number/2) * (math.Pow(x.Number, (deg1.Number-2)/2) / math.Pow(1+(deg1.Number/deg2.Number)*x.Number, (deg1.Number+deg2.Number)/2)))
}
// FDIST function calculates the (right-tailed) F Probability Distribution,
// which measures the degree of diversity between two data sets. The syntax
// of the function is:
//
// FDIST(x,deg_freedom1,deg_freedom2)
//
func (fn *formulaFuncs) FDIST(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "FDIST requires 3 arguments")
}
var x, deg1, deg2 formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if deg1 = argsList.Front().Next().Value.(formulaArg).ToNumber(); deg1.Type != ArgNumber {
return deg1
}
if deg2 = argsList.Back().Value.(formulaArg).ToNumber(); deg2.Type != ArgNumber {
return deg2
}
if x.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
maxDeg := math.Pow10(10)
if deg1.Number < 1 || deg1.Number >= maxDeg {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if deg2.Number < 1 || deg2.Number >= maxDeg {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
args := list.New()
args.PushBack(newNumberFormulaArg(deg1.Number * x.Number / (deg1.Number*x.Number + deg2.Number)))
args.PushBack(newNumberFormulaArg(0.5 * deg1.Number))
args.PushBack(newNumberFormulaArg(0.5 * deg2.Number))
args.PushBack(newNumberFormulaArg(0))
args.PushBack(newNumberFormulaArg(1))
return newNumberFormulaArg(1 - fn.BETADIST(args).Number)
}
// FdotDISTdotRT function calculates the (right-tailed) F Probability
// Distribution, which measures the degree of diversity between two data sets.
// The syntax of the function is:
//
// F.DIST.RT(x,deg_freedom1,deg_freedom2)
//
func (fn *formulaFuncs) FdotDISTdotRT(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "F.DIST.RT requires 3 arguments")
}
return fn.FDIST(argsList)
}
// prepareFinvArgs checking and prepare arguments for the formula function
// F.INV, F.INV.RT and FINV.
func (fn *formulaFuncs) prepareFinvArgs(name string, argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 3 arguments", name))
}
var probability, d1, d2 formulaArg
if probability = argsList.Front().Value.(formulaArg).ToNumber(); probability.Type != ArgNumber {
return probability
}
if d1 = argsList.Front().Next().Value.(formulaArg).ToNumber(); d1.Type != ArgNumber {
return d1
}
if d2 = argsList.Back().Value.(formulaArg).ToNumber(); d2.Type != ArgNumber {
return d2
}
if probability.Number <= 0 || probability.Number > 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if d1.Number < 1 || d1.Number >= math.Pow10(10) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if d2.Number < 1 || d2.Number >= math.Pow10(10) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newListFormulaArg([]formulaArg{probability, d1, d2})
}
// FdotINV function calculates the inverse of the Cumulative F Distribution
// for a supplied probability. The syntax of the F.Inv function is:
//
// F.INV(probability,deg_freedom1,deg_freedom2)
//
func (fn *formulaFuncs) FdotINV(argsList *list.List) formulaArg {
args := fn.prepareFinvArgs("F.INV", argsList)
if args.Type != ArgList {
return args
}
probability, d1, d2 := args.List[0], args.List[1], args.List[2]
return newNumberFormulaArg((1/calcBetainv(1-probability.Number, d2.Number/2, d1.Number/2, 0, 1) - 1) * (d2.Number / d1.Number))
}
// FdotINVdotRT function calculates the inverse of the (right-tailed) F
// Probability Distribution for a supplied probability. The syntax of the
// function is:
//
// F.INV.RT(probability,deg_freedom1,deg_freedom2)
//
func (fn *formulaFuncs) FdotINVdotRT(argsList *list.List) formulaArg {
args := fn.prepareFinvArgs("F.INV.RT", argsList)
if args.Type != ArgList {
return args
}
probability, d1, d2 := args.List[0], args.List[1], args.List[2]
return newNumberFormulaArg((1/calcBetainv(1-(1-probability.Number), d2.Number/2, d1.Number/2, 0, 1) - 1) * (d2.Number / d1.Number))
}
// FINV function calculates the inverse of the (right-tailed) F Probability
// Distribution for a supplied probability. The syntax of the function is:
//
// FINV(probability,deg_freedom1,deg_freedom2)
//
func (fn *formulaFuncs) FINV(argsList *list.List) formulaArg {
args := fn.prepareFinvArgs("FINV", argsList)
if args.Type != ArgList {
return args
}
probability, d1, d2 := args.List[0], args.List[1], args.List[2]
return newNumberFormulaArg((1/calcBetainv(1-(1-probability.Number), d2.Number/2, d1.Number/2, 0, 1) - 1) * (d2.Number / d1.Number))
}
// FdotTEST function returns the F-Test for two supplied arrays. I.e. the
// function returns the two-tailed probability that the variances in the two
// supplied arrays are not significantly different. The syntax of the Ftest
// function is:
//
// F.TEST(array1,array2)
//
func (fn *formulaFuncs) FdotTEST(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "F.TEST requires 2 arguments")
}
array1 := argsList.Front().Value.(formulaArg)
array2 := argsList.Back().Value.(formulaArg)
left, right := array1.ToList(), array2.ToList()
collectMatrix := func(args []formulaArg) (n, accu float64) {
var p, sum float64
for _, arg := range args {
if num := arg.ToNumber(); num.Type == ArgNumber {
x := num.Number - p
y := x / (n + 1)
p += y
accu += n * x * y
n++
sum += num.Number
}
}
return
}
nums, accu := collectMatrix(left)
f3 := nums - 1
if nums == 1 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
f1 := accu / (nums - 1)
if f1 == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
nums, accu = collectMatrix(right)
f4 := nums - 1
if nums == 1 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
f2 := accu / (nums - 1)
if f2 == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
args := list.New()
args.PushBack(newNumberFormulaArg(f1 / f2))
args.PushBack(newNumberFormulaArg(f3))
args.PushBack(newNumberFormulaArg(f4))
probability := (1 - fn.FDIST(args).Number) * 2
if probability > 1 {
probability = 2 - probability
}
return newNumberFormulaArg(probability)
}
// FTEST function returns the F-Test for two supplied arrays. I.e. the function
// returns the two-tailed probability that the variances in the two supplied
// arrays are not significantly different. The syntax of the Ftest function
// is:
//
// FTEST(array1,array2)
//
func (fn *formulaFuncs) FTEST(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "FTEST requires 2 arguments")
}
return fn.FdotTEST(argsList)
}
// LOGINV function calculates the inverse of the Cumulative Log-Normal
// Distribution Function of x, for a supplied probability. The syntax of the
// function is:
//
// LOGINV(probability,mean,standard_dev)
//
func (fn *formulaFuncs) LOGINV(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "LOGINV requires 3 arguments")
}
var probability, mean, stdDev formulaArg
if probability = argsList.Front().Value.(formulaArg).ToNumber(); probability.Type != ArgNumber {
return probability
}
if mean = argsList.Front().Next().Value.(formulaArg).ToNumber(); mean.Type != ArgNumber {
return mean
}
if stdDev = argsList.Back().Value.(formulaArg).ToNumber(); stdDev.Type != ArgNumber {
return stdDev
}
if probability.Number <= 0 || probability.Number >= 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if stdDev.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
args := list.New()
args.PushBack(probability)
args.PushBack(newNumberFormulaArg(0))
args.PushBack(newNumberFormulaArg(1))
norminv := fn.NORMINV(args)
return newNumberFormulaArg(math.Exp(mean.Number + stdDev.Number*norminv.Number))
}
// LOGNORMdotINV function calculates the inverse of the Cumulative Log-Normal
// Distribution Function of x, for a supplied probability. The syntax of the
// function is:
//
// LOGNORM.INV(probability,mean,standard_dev)
//
func (fn *formulaFuncs) LOGNORMdotINV(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "LOGNORM.INV requires 3 arguments")
}
return fn.LOGINV(argsList)
}
// LOGNORMdotDIST function calculates the Log-Normal Probability Density
// Function or the Cumulative Log-Normal Distribution Function for a supplied
// value of x. The syntax of the function is:
//
// LOGNORM.DIST(x,mean,standard_dev,cumulative)
//
func (fn *formulaFuncs) LOGNORMdotDIST(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "LOGNORM.DIST requires 4 arguments")
}
var x, mean, stdDev, cumulative formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if mean = argsList.Front().Next().Value.(formulaArg).ToNumber(); mean.Type != ArgNumber {
return mean
}
if stdDev = argsList.Back().Prev().Value.(formulaArg).ToNumber(); stdDev.Type != ArgNumber {
return stdDev
}
if cumulative = argsList.Back().Value.(formulaArg).ToBool(); cumulative.Type == ArgError {
return cumulative
}
if x.Number <= 0 || stdDev.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if cumulative.Number == 1 {
args := list.New()
args.PushBack(newNumberFormulaArg((math.Log(x.Number) - mean.Number) / stdDev.Number))
args.PushBack(newNumberFormulaArg(0))
args.PushBack(newNumberFormulaArg(1))
args.PushBack(cumulative)
return fn.NORMDIST(args)
}
return newNumberFormulaArg((1 / (math.Sqrt(2*math.Pi) * stdDev.Number * x.Number)) *
math.Exp(0-(math.Pow(math.Log(x.Number)-mean.Number, 2)/(2*math.Pow(stdDev.Number, 2)))))
}
// LOGNORMDIST function calculates the Cumulative Log-Normal Distribution
// Function at a supplied value of x. The syntax of the function is:
//
// LOGNORMDIST(x,mean,standard_dev)
//
func (fn *formulaFuncs) LOGNORMDIST(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "LOGNORMDIST requires 3 arguments")
}
var x, mean, stdDev formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if mean = argsList.Front().Next().Value.(formulaArg).ToNumber(); mean.Type != ArgNumber {
return mean
}
if stdDev = argsList.Back().Value.(formulaArg).ToNumber(); stdDev.Type != ArgNumber {
return stdDev
}
if x.Number <= 0 || stdDev.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
args := list.New()
args.PushBack(newNumberFormulaArg((math.Log(x.Number) - mean.Number) / stdDev.Number))
return fn.NORMSDIST(args)
}
// MODE function returns the statistical mode (the most frequently occurring
// value) of a list of supplied numbers. If there are 2 or more most
// frequently occurring values in the supplied data, the function returns the
// lowest of these values The syntax of the function is:
//
// MODE(number1,[number2],...)
//
func (fn *formulaFuncs) MODE(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "MODE requires at least 1 argument")
}
var values []float64
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
cells := arg.Value.(formulaArg)
if cells.Type != ArgMatrix && cells.ToNumber().Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
for _, cell := range cells.ToList() {
if num := cell.ToNumber(); num.Type == ArgNumber {
values = append(values, num.Number)
}
}
}
sort.Float64s(values)
cnt := len(values)
var count, modeCnt int
var mode float64
for i := 0; i < cnt; i++ {
count = 0
for j := 0; j < cnt; j++ {
if j != i && values[j] == values[i] {
count++
}
}
if count > modeCnt {
modeCnt = count
mode = values[i]
}
}
if modeCnt == 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
return newNumberFormulaArg(mode)
}
// MODEdotMULT function returns a vertical array of the statistical modes
// (the most frequently occurring values) within a list of supplied numbers.
// The syntax of the function is:
//
// MODE.MULT(number1,[number2],...)
//
func (fn *formulaFuncs) MODEdotMULT(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "MODE.MULT requires at least 1 argument")
}
var values []float64
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
cells := arg.Value.(formulaArg)
if cells.Type != ArgMatrix && cells.ToNumber().Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
for _, cell := range cells.ToList() {
if num := cell.ToNumber(); num.Type == ArgNumber {
values = append(values, num.Number)
}
}
}
sort.Float64s(values)
cnt := len(values)
var count, modeCnt int
var mtx [][]formulaArg
for i := 0; i < cnt; i++ {
count = 0
for j := i + 1; j < cnt; j++ {
if values[i] == values[j] {
count++
}
}
if count > modeCnt {
modeCnt = count
mtx = [][]formulaArg{}
mtx = append(mtx, []formulaArg{newNumberFormulaArg(values[i])})
} else if count == modeCnt {
mtx = append(mtx, []formulaArg{newNumberFormulaArg(values[i])})
}
}
if modeCnt == 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
return newMatrixFormulaArg(mtx)
}
// MODEdotSNGL function returns the statistical mode (the most frequently
// occurring value) within a list of supplied numbers. If there are 2 or more
// most frequently occurring values in the supplied data, the function returns
// the lowest of these values. The syntax of the function is:
//
// MODE.SNGL(number1,[number2],...)
//
func (fn *formulaFuncs) MODEdotSNGL(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "MODE.SNGL requires at least 1 argument")
}
return fn.MODE(argsList)
}
// NEGBINOMdotDIST function calculates the probability mass function or the
// cumulative distribution function for the Negative Binomial Distribution.
// This gives the probability that there will be a given number of failures
// before a required number of successes is achieved. The syntax of the
// function is:
//
// NEGBINOM.DIST(number_f,number_s,probability_s,cumulative)
//
func (fn *formulaFuncs) NEGBINOMdotDIST(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "NEGBINOM.DIST requires 4 arguments")
}
var f, s, probability, cumulative formulaArg
if f = argsList.Front().Value.(formulaArg).ToNumber(); f.Type != ArgNumber {
return f
}
if s = argsList.Front().Next().Value.(formulaArg).ToNumber(); s.Type != ArgNumber {
return s
}
if probability = argsList.Front().Next().Next().Value.(formulaArg).ToNumber(); probability.Type != ArgNumber {
return probability
}
if cumulative = argsList.Back().Value.(formulaArg).ToBool(); cumulative.Type != ArgNumber {
return cumulative
}
if f.Number < 0 || s.Number < 1 || probability.Number < 0 || probability.Number > 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if cumulative.Number == 1 {
return newNumberFormulaArg(1 - getBetaDist(1-probability.Number, f.Number+1, s.Number))
}
return newNumberFormulaArg(binomCoeff(f.Number+s.Number-1, s.Number-1) * math.Pow(probability.Number, s.Number) * math.Pow(1-probability.Number, f.Number))
}
// NEGBINOMDIST function calculates the Negative Binomial Distribution for a
// given set of parameters. This gives the probability that there will be a
// specified number of failures before a required number of successes is
// achieved. The syntax of the function is:
//
// NEGBINOMDIST(number_f,number_s,probability_s)
//
func (fn *formulaFuncs) NEGBINOMDIST(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "NEGBINOMDIST requires 3 arguments")
}
var f, s, probability formulaArg
if f = argsList.Front().Value.(formulaArg).ToNumber(); f.Type != ArgNumber {
return f
}
if s = argsList.Front().Next().Value.(formulaArg).ToNumber(); s.Type != ArgNumber {
return s
}
if probability = argsList.Back().Value.(formulaArg).ToNumber(); probability.Type != ArgNumber {
return probability
}
if f.Number < 0 || s.Number < 1 || probability.Number < 0 || probability.Number > 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(binomCoeff(f.Number+s.Number-1, s.Number-1) * math.Pow(probability.Number, s.Number) * math.Pow(1-probability.Number, f.Number))
}
// NORMdotDIST function calculates the Normal Probability Density Function or
// the Cumulative Normal Distribution. Function for a supplied set of
// parameters. The syntax of the function is:
//
// NORM.DIST(x,mean,standard_dev,cumulative)
//
func (fn *formulaFuncs) NORMdotDIST(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "NORM.DIST requires 4 arguments")
}
return fn.NORMDIST(argsList)
}
// NORMDIST function calculates the Normal Probability Density Function or the
// Cumulative Normal Distribution. Function for a supplied set of parameters.
// The syntax of the function is:
//
// NORMDIST(x,mean,standard_dev,cumulative)
//
func (fn *formulaFuncs) NORMDIST(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "NORMDIST requires 4 arguments")
}
var x, mean, stdDev, cumulative formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if mean = argsList.Front().Next().Value.(formulaArg).ToNumber(); mean.Type != ArgNumber {
return mean
}
if stdDev = argsList.Back().Prev().Value.(formulaArg).ToNumber(); stdDev.Type != ArgNumber {
return stdDev
}
if cumulative = argsList.Back().Value.(formulaArg).ToBool(); cumulative.Type == ArgError {
return cumulative
}
if stdDev.Number < 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
if cumulative.Number == 1 {
return newNumberFormulaArg(0.5 * (1 + math.Erf((x.Number-mean.Number)/(stdDev.Number*math.Sqrt(2)))))
}
return newNumberFormulaArg((1 / (math.Sqrt(2*math.Pi) * stdDev.Number)) * math.Exp(0-(math.Pow(x.Number-mean.Number, 2)/(2*(stdDev.Number*stdDev.Number)))))
}
// NORMdotINV function calculates the inverse of the Cumulative Normal
// Distribution Function for a supplied value of x, and a supplied
// distribution mean & standard deviation. The syntax of the function is:
//
// NORM.INV(probability,mean,standard_dev)
//
func (fn *formulaFuncs) NORMdotINV(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "NORM.INV requires 3 arguments")
}
return fn.NORMINV(argsList)
}
// NORMINV function calculates the inverse of the Cumulative Normal
// Distribution Function for a supplied value of x, and a supplied
// distribution mean & standard deviation. The syntax of the function is:
//
// NORMINV(probability,mean,standard_dev)
//
func (fn *formulaFuncs) NORMINV(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "NORMINV requires 3 arguments")
}
var prob, mean, stdDev formulaArg
if prob = argsList.Front().Value.(formulaArg).ToNumber(); prob.Type != ArgNumber {
return prob
}
if mean = argsList.Front().Next().Value.(formulaArg).ToNumber(); mean.Type != ArgNumber {
return mean
}
if stdDev = argsList.Back().Value.(formulaArg).ToNumber(); stdDev.Type != ArgNumber {
return stdDev
}
if prob.Number < 0 || prob.Number > 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
if stdDev.Number < 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
inv, err := norminv(prob.Number)
if err != nil {
return newErrorFormulaArg(err.Error(), err.Error())
}
return newNumberFormulaArg(inv*stdDev.Number + mean.Number)
}
// NORMdotSdotDIST function calculates the Standard Normal Cumulative
// Distribution Function for a supplied value. The syntax of the function
// is:
//
// NORM.S.DIST(z)
//
func (fn *formulaFuncs) NORMdotSdotDIST(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "NORM.S.DIST requires 2 numeric arguments")
}
args := list.New().Init()
args.PushBack(argsList.Front().Value.(formulaArg))
args.PushBack(formulaArg{Type: ArgNumber, Number: 0})
args.PushBack(formulaArg{Type: ArgNumber, Number: 1})
args.PushBack(argsList.Back().Value.(formulaArg))
return fn.NORMDIST(args)
}
// NORMSDIST function calculates the Standard Normal Cumulative Distribution
// Function for a supplied value. The syntax of the function is:
//
// NORMSDIST(z)
//
func (fn *formulaFuncs) NORMSDIST(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "NORMSDIST requires 1 numeric argument")
}
args := list.New().Init()
args.PushBack(argsList.Front().Value.(formulaArg))
args.PushBack(formulaArg{Type: ArgNumber, Number: 0})
args.PushBack(formulaArg{Type: ArgNumber, Number: 1})
args.PushBack(formulaArg{Type: ArgNumber, Number: 1, Boolean: true})
return fn.NORMDIST(args)
}
// NORMSINV function calculates the inverse of the Standard Normal Cumulative
// Distribution Function for a supplied probability value. The syntax of the
// function is:
//
// NORMSINV(probability)
//
func (fn *formulaFuncs) NORMSINV(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "NORMSINV requires 1 numeric argument")
}
args := list.New().Init()
args.PushBack(argsList.Front().Value.(formulaArg))
args.PushBack(formulaArg{Type: ArgNumber, Number: 0})
args.PushBack(formulaArg{Type: ArgNumber, Number: 1})
return fn.NORMINV(args)
}
// NORMdotSdotINV function calculates the inverse of the Standard Normal
// Cumulative Distribution Function for a supplied probability value. The
// syntax of the function is:
//
// NORM.S.INV(probability)
//
func (fn *formulaFuncs) NORMdotSdotINV(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "NORM.S.INV requires 1 numeric argument")
}
args := list.New().Init()
args.PushBack(argsList.Front().Value.(formulaArg))
args.PushBack(formulaArg{Type: ArgNumber, Number: 0})
args.PushBack(formulaArg{Type: ArgNumber, Number: 1})
return fn.NORMINV(args)
}
// norminv returns the inverse of the normal cumulative distribution for the
// specified value.
func norminv(p float64) (float64, error) {
a := map[int]float64{
1: -3.969683028665376e+01, 2: 2.209460984245205e+02, 3: -2.759285104469687e+02,
4: 1.383577518672690e+02, 5: -3.066479806614716e+01, 6: 2.506628277459239e+00,
}
b := map[int]float64{
1: -5.447609879822406e+01, 2: 1.615858368580409e+02, 3: -1.556989798598866e+02,
4: 6.680131188771972e+01, 5: -1.328068155288572e+01,
}
c := map[int]float64{
1: -7.784894002430293e-03, 2: -3.223964580411365e-01, 3: -2.400758277161838e+00,
4: -2.549732539343734e+00, 5: 4.374664141464968e+00, 6: 2.938163982698783e+00,
}
d := map[int]float64{
1: 7.784695709041462e-03, 2: 3.224671290700398e-01, 3: 2.445134137142996e+00,
4: 3.754408661907416e+00,
}
pLow := 0.02425 // Use lower region approx. below this
pHigh := 1 - pLow // Use upper region approx. above this
if 0 < p && p < pLow {
// Rational approximation for lower region.
q := math.Sqrt(-2 * math.Log(p))
return (((((c[1]*q+c[2])*q+c[3])*q+c[4])*q+c[5])*q + c[6]) /
((((d[1]*q+d[2])*q+d[3])*q+d[4])*q + 1), nil
} else if pLow <= p && p <= pHigh {
// Rational approximation for central region.
q := p - 0.5
r := q * q
f1 := ((((a[1]*r+a[2])*r+a[3])*r+a[4])*r + a[5]) * r
f2 := (b[1]*r + b[2]) * r
f3 := ((math.Nextafter(f2, f2)+b[3])*r + b[4]) * r
f4 := (math.Nextafter(f3, f3) + b[5]) * r
return (math.Nextafter(f1, f1) + a[6]) * q /
(math.Nextafter(f4, f4) + 1), nil
} else if pHigh < p && p < 1 {
// Rational approximation for upper region.
q := math.Sqrt(-2 * math.Log(1-p))
return -(((((c[1]*q+c[2])*q+c[3])*q+c[4])*q+c[5])*q + c[6]) /
((((d[1]*q+d[2])*q+d[3])*q+d[4])*q + 1), nil
}
return 0, errors.New(formulaErrorNUM)
}
// kth is an implementation of the formula functions LARGE and SMALL.
func (fn *formulaFuncs) kth(name string, argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 2 arguments", name))
}
array := argsList.Front().Value.(formulaArg).ToList()
argK := argsList.Back().Value.(formulaArg).ToNumber()
if argK.Type != ArgNumber {
return argK
}
k := int(argK.Number)
if k < 1 {
return newErrorFormulaArg(formulaErrorNUM, "k should be > 0")
}
var data []float64
for _, arg := range array {
if numArg := arg.ToNumber(); numArg.Type == ArgNumber {
data = append(data, numArg.Number)
}
}
if len(data) < k {
return newErrorFormulaArg(formulaErrorNUM, "k should be <= length of array")
}
sort.Float64s(data)
if name == "LARGE" {
return newNumberFormulaArg(data[len(data)-k])
}
return newNumberFormulaArg(data[k-1])
}
// LARGE function returns the k'th largest value from an array of numeric
// values. The syntax of the function is:
//
// LARGE(array,k)
//
func (fn *formulaFuncs) LARGE(argsList *list.List) formulaArg {
return fn.kth("LARGE", argsList)
}
// MAX function returns the largest value from a supplied set of numeric
// values. The syntax of the function is:
//
// MAX(number1,[number2],...)
//
func (fn *formulaFuncs) MAX(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "MAX requires at least 1 argument")
}
return fn.max(false, argsList)
}
// MAXA function returns the largest value from a supplied set of numeric
// values, while counting text and the logical value FALSE as the value 0 and
// counting the logical value TRUE as the value 1. The syntax of the function
// is:
//
// MAXA(number1,[number2],...)
//
func (fn *formulaFuncs) MAXA(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "MAXA requires at least 1 argument")
}
return fn.max(true, argsList)
}
// MAXIFS function returns the maximum value from a subset of values that are
// specified according to one or more criteria. The syntax of the function
// is:
//
// MAXIFS(max_range,criteria_range1,criteria1,[criteria_range2,criteria2],...)
//
func (fn *formulaFuncs) MAXIFS(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "MAXIFS requires at least 3 arguments")
}
if argsList.Len()%2 != 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
var args []formulaArg
max, maxRange := -math.MaxFloat64, argsList.Front().Value.(formulaArg).Matrix
for arg := argsList.Front().Next(); arg != nil; arg = arg.Next() {
args = append(args, arg.Value.(formulaArg))
}
for _, ref := range formulaIfsMatch(args) {
if num := maxRange[ref.Row][ref.Col].ToNumber(); num.Type == ArgNumber && max < num.Number {
max = num.Number
}
}
if max == -math.MaxFloat64 {
max = 0
}
return newNumberFormulaArg(max)
}
// calcListMatrixMax is part of the implementation max.
func calcListMatrixMax(maxa bool, max float64, arg formulaArg) float64 {
for _, row := range arg.ToList() {
switch row.Type {
case ArgString:
if !maxa && (row.Value() == "TRUE" || row.Value() == "FALSE") {
continue
} else {
num := row.ToBool()
if num.Type == ArgNumber && num.Number > max {
max = num.Number
continue
}
}
num := row.ToNumber()
if num.Type != ArgError && num.Number > max {
max = num.Number
}
case ArgNumber:
if row.Number > max {
max = row.Number
}
}
}
return max
}
// max is an implementation of the formula functions MAX and MAXA.
func (fn *formulaFuncs) max(maxa bool, argsList *list.List) formulaArg {
max := -math.MaxFloat64
for token := argsList.Front(); token != nil; token = token.Next() {
arg := token.Value.(formulaArg)
switch arg.Type {
case ArgString:
if !maxa && (arg.Value() == "TRUE" || arg.Value() == "FALSE") {
continue
} else {
num := arg.ToBool()
if num.Type == ArgNumber && num.Number > max {
max = num.Number
continue
}
}
num := arg.ToNumber()
if num.Type != ArgError && num.Number > max {
max = num.Number
}
case ArgNumber:
if arg.Number > max {
max = arg.Number
}
case ArgList, ArgMatrix:
max = calcListMatrixMax(maxa, max, arg)
case ArgError:
return arg
}
}
if max == -math.MaxFloat64 {
max = 0
}
return newNumberFormulaArg(max)
}
// MEDIAN function returns the statistical median (the middle value) of a list
// of supplied numbers. The syntax of the function is:
//
// MEDIAN(number1,[number2],...)
//
func (fn *formulaFuncs) MEDIAN(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "MEDIAN requires at least 1 argument")
}
var values []float64
var median, digits float64
var err error
for token := argsList.Front(); token != nil; token = token.Next() {
arg := token.Value.(formulaArg)
switch arg.Type {
case ArgString:
num := arg.ToNumber()
if num.Type == ArgError {
return newErrorFormulaArg(formulaErrorVALUE, num.Error)
}
values = append(values, num.Number)
case ArgNumber:
values = append(values, arg.Number)
case ArgMatrix:
for _, row := range arg.Matrix {
for _, value := range row {
if value.String == "" {
continue
}
if digits, err = strconv.ParseFloat(value.String, 64); err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
values = append(values, digits)
}
}
}
}
sort.Float64s(values)
if len(values)%2 == 0 {
median = (values[len(values)/2-1] + values[len(values)/2]) / 2
} else {
median = values[len(values)/2]
}
return newNumberFormulaArg(median)
}
// MIN function returns the smallest value from a supplied set of numeric
// values. The syntax of the function is:
//
// MIN(number1,[number2],...)
//
func (fn *formulaFuncs) MIN(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "MIN requires at least 1 argument")
}
return fn.min(false, argsList)
}
// MINA function returns the smallest value from a supplied set of numeric
// values, while counting text and the logical value FALSE as the value 0 and
// counting the logical value TRUE as the value 1. The syntax of the function
// is:
//
// MINA(number1,[number2],...)
//
func (fn *formulaFuncs) MINA(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "MINA requires at least 1 argument")
}
return fn.min(true, argsList)
}
// MINIFS function returns the minimum value from a subset of values that are
// specified according to one or more criteria. The syntax of the function
// is:
//
// MINIFS(min_range,criteria_range1,criteria1,[criteria_range2,criteria2],...)
//
func (fn *formulaFuncs) MINIFS(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "MINIFS requires at least 3 arguments")
}
if argsList.Len()%2 != 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
var args []formulaArg
min, minRange := math.MaxFloat64, argsList.Front().Value.(formulaArg).Matrix
for arg := argsList.Front().Next(); arg != nil; arg = arg.Next() {
args = append(args, arg.Value.(formulaArg))
}
for _, ref := range formulaIfsMatch(args) {
if num := minRange[ref.Row][ref.Col].ToNumber(); num.Type == ArgNumber && min > num.Number {
min = num.Number
}
}
if min == math.MaxFloat64 {
min = 0
}
return newNumberFormulaArg(min)
}
// calcListMatrixMin is part of the implementation min.
func calcListMatrixMin(mina bool, min float64, arg formulaArg) float64 {
for _, row := range arg.ToList() {
switch row.Type {
case ArgString:
if !mina && (row.Value() == "TRUE" || row.Value() == "FALSE") {
continue
} else {
num := row.ToBool()
if num.Type == ArgNumber && num.Number < min {
min = num.Number
continue
}
}
num := row.ToNumber()
if num.Type != ArgError && num.Number < min {
min = num.Number
}
case ArgNumber:
if row.Number < min {
min = row.Number
}
}
}
return min
}
// min is an implementation of the formula functions MIN and MINA.
func (fn *formulaFuncs) min(mina bool, argsList *list.List) formulaArg {
min := math.MaxFloat64
for token := argsList.Front(); token != nil; token = token.Next() {
arg := token.Value.(formulaArg)
switch arg.Type {
case ArgString:
if !mina && (arg.Value() == "TRUE" || arg.Value() == "FALSE") {
continue
} else {
num := arg.ToBool()
if num.Type == ArgNumber && num.Number < min {
min = num.Number
continue
}
}
num := arg.ToNumber()
if num.Type != ArgError && num.Number < min {
min = num.Number
}
case ArgNumber:
if arg.Number < min {
min = arg.Number
}
case ArgList, ArgMatrix:
min = calcListMatrixMin(mina, min, arg)
case ArgError:
return arg
}
}
if min == math.MaxFloat64 {
min = 0
}
return newNumberFormulaArg(min)
}
// pearsonProduct is an implementation of the formula functions PEARSON, RSQ
// and SLOPE.
func (fn *formulaFuncs) pearsonProduct(name string, argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 2 arguments", name))
}
var array1, array2 []formulaArg
if name == "SLOPE" {
array1 = argsList.Back().Value.(formulaArg).ToList()
array2 = argsList.Front().Value.(formulaArg).ToList()
} else {
array1 = argsList.Front().Value.(formulaArg).ToList()
array2 = argsList.Back().Value.(formulaArg).ToList()
}
if len(array1) != len(array2) {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
var sum, deltaX, deltaY, x, y, length float64
for i := 0; i < len(array1); i++ {
num1, num2 := array1[i].ToNumber(), array2[i].ToNumber()
if !(num1.Type == ArgNumber && num2.Type == ArgNumber) {
continue
}
x += num1.Number
y += num2.Number
length++
}
x /= length
y /= length
for i := 0; i < len(array1); i++ {
num1, num2 := array1[i].ToNumber(), array2[i].ToNumber()
if !(num1.Type == ArgNumber && num2.Type == ArgNumber) {
continue
}
sum += (num1.Number - x) * (num2.Number - y)
deltaX += (num1.Number - x) * (num1.Number - x)
deltaY += (num2.Number - y) * (num2.Number - y)
}
if deltaX == 0 || deltaY == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
if name == "RSQ" {
return newNumberFormulaArg(math.Pow(sum/math.Sqrt(deltaX*deltaY), 2))
}
if name == "PEARSON" {
return newNumberFormulaArg(sum / math.Sqrt(deltaX*deltaY))
}
return newNumberFormulaArg(sum / deltaX)
}
// PEARSON function calculates the Pearson Product-Moment Correlation
// Coefficient for two sets of values. The syntax of the function is:
//
// PEARSON(array1,array2)
//
func (fn *formulaFuncs) PEARSON(argsList *list.List) formulaArg {
return fn.pearsonProduct("PEARSON", argsList)
}
// PERCENTILEdotEXC function returns the k'th percentile (i.e. the value below
// which k% of the data values fall) for a supplied range of values and a
// supplied k (between 0 & 1 exclusive).The syntax of the function is:
//
// PERCENTILE.EXC(array,k)
//
func (fn *formulaFuncs) PERCENTILEdotEXC(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "PERCENTILE.EXC requires 2 arguments")
}
array := argsList.Front().Value.(formulaArg).ToList()
k := argsList.Back().Value.(formulaArg).ToNumber()
if k.Type != ArgNumber {
return k
}
if k.Number <= 0 || k.Number >= 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
var numbers []float64
for _, arg := range array {
if arg.Type == ArgError {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
num := arg.ToNumber()
if num.Type == ArgNumber {
numbers = append(numbers, num.Number)
}
}
cnt := len(numbers)
sort.Float64s(numbers)
idx := k.Number * (float64(cnt) + 1)
base := math.Floor(idx)
next := base - 1
proportion := math.Nextafter(idx, idx) - base
return newNumberFormulaArg(numbers[int(next)] + ((numbers[int(base)] - numbers[int(next)]) * proportion))
}
// PERCENTILEdotINC function returns the k'th percentile (i.e. the value below
// which k% of the data values fall) for a supplied range of values and a
// supplied k. The syntax of the function is:
//
// PERCENTILE.INC(array,k)
//
func (fn *formulaFuncs) PERCENTILEdotINC(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "PERCENTILE.INC requires 2 arguments")
}
return fn.PERCENTILE(argsList)
}
// PERCENTILE function returns the k'th percentile (i.e. the value below which
// k% of the data values fall) for a supplied range of values and a supplied
// k. The syntax of the function is:
//
// PERCENTILE(array,k)
//
func (fn *formulaFuncs) PERCENTILE(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "PERCENTILE requires 2 arguments")
}
array := argsList.Front().Value.(formulaArg).ToList()
k := argsList.Back().Value.(formulaArg).ToNumber()
if k.Type != ArgNumber {
return k
}
if k.Number < 0 || k.Number > 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
var numbers []float64
for _, arg := range array {
if arg.Type == ArgError {
return arg
}
num := arg.ToNumber()
if num.Type == ArgNumber {
numbers = append(numbers, num.Number)
}
}
cnt := len(numbers)
sort.Float64s(numbers)
idx := k.Number * (float64(cnt) - 1)
base := math.Floor(idx)
if idx == base {
return newNumberFormulaArg(numbers[int(idx)])
}
next := base + 1
proportion := math.Nextafter(idx, idx) - base
return newNumberFormulaArg(numbers[int(base)] + ((numbers[int(next)] - numbers[int(base)]) * proportion))
}
// percentrank is an implementation of the formula functions PERCENTRANK and
// PERCENTRANK.INC.
func (fn *formulaFuncs) percentrank(name string, argsList *list.List) formulaArg {
if argsList.Len() != 2 && argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 2 or 3 arguments", name))
}
array := argsList.Front().Value.(formulaArg).ToList()
x := argsList.Front().Next().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return x
}
var numbers []float64
for _, arg := range array {
if arg.Type == ArgError {
return arg
}
num := arg.ToNumber()
if num.Type == ArgNumber {
numbers = append(numbers, num.Number)
}
}
cnt := len(numbers)
sort.Float64s(numbers)
if x.Number < numbers[0] || x.Number > numbers[cnt-1] {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
pos, significance := float64(inFloat64Slice(numbers, x.Number)), newNumberFormulaArg(3)
if argsList.Len() == 3 {
if significance = argsList.Back().Value.(formulaArg).ToNumber(); significance.Type != ArgNumber {
return significance
}
if significance.Number < 1 {
return newErrorFormulaArg(formulaErrorNUM, fmt.Sprintf("%s arguments significance should be > 1", name))
}
}
if pos == -1 {
pos = 0
cmp := numbers[0]
for cmp < x.Number {
pos++
cmp = numbers[int(pos)]
}
pos--
pos += (x.Number - numbers[int(pos)]) / (cmp - numbers[int(pos)])
}
pow := math.Pow(10, significance.Number)
digit := pow * pos / (float64(cnt) - 1)
if name == "PERCENTRANK.EXC" {
digit = pow * (pos + 1) / (float64(cnt) + 1)
}
return newNumberFormulaArg(math.Floor(digit) / pow)
}
// PERCENTRANKdotEXC function calculates the relative position, between 0 and
// 1 (exclusive), of a specified value within a supplied array. The syntax of
// the function is:
//
// PERCENTRANK.EXC(array,x,[significance])
//
func (fn *formulaFuncs) PERCENTRANKdotEXC(argsList *list.List) formulaArg {
return fn.percentrank("PERCENTRANK.EXC", argsList)
}
// PERCENTRANKdotINC function calculates the relative position, between 0 and
// 1 (inclusive), of a specified value within a supplied array.The syntax of
// the function is:
//
// PERCENTRANK.INC(array,x,[significance])
//
func (fn *formulaFuncs) PERCENTRANKdotINC(argsList *list.List) formulaArg {
return fn.percentrank("PERCENTRANK.INC", argsList)
}
// PERCENTRANK function calculates the relative position of a specified value,
// within a set of values, as a percentage. The syntax of the function is:
//
// PERCENTRANK(array,x,[significance])
//
func (fn *formulaFuncs) PERCENTRANK(argsList *list.List) formulaArg {
return fn.percentrank("PERCENTRANK", argsList)
}
// PERMUT function calculates the number of permutations of a specified number
// of objects from a set of objects. The syntax of the function is:
//
// PERMUT(number,number_chosen)
//
func (fn *formulaFuncs) PERMUT(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "PERMUT requires 2 numeric arguments")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
chosen := argsList.Back().Value.(formulaArg).ToNumber()
if number.Type != ArgNumber {
return number
}
if chosen.Type != ArgNumber {
return chosen
}
if number.Number < chosen.Number {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
return newNumberFormulaArg(math.Round(fact(number.Number) / fact(number.Number-chosen.Number)))
}
// PERMUTATIONA function calculates the number of permutations, with
// repetitions, of a specified number of objects from a set. The syntax of
// the function is:
//
// PERMUTATIONA(number,number_chosen)
//
func (fn *formulaFuncs) PERMUTATIONA(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "PERMUTATIONA requires 2 numeric arguments")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
chosen := argsList.Back().Value.(formulaArg).ToNumber()
if number.Type != ArgNumber {
return number
}
if chosen.Type != ArgNumber {
return chosen
}
num, numChosen := math.Floor(number.Number), math.Floor(chosen.Number)
if num < 0 || numChosen < 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
return newNumberFormulaArg(math.Pow(num, numChosen))
}
// PHI function returns the value of the density function for a standard normal
// distribution for a supplied number. The syntax of the function is:
//
// PHI(x)
//
func (fn *formulaFuncs) PHI(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "PHI requires 1 argument")
}
x := argsList.Front().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return x
}
return newNumberFormulaArg(0.39894228040143268 * math.Exp(-(x.Number*x.Number)/2))
}
// QUARTILE function returns a requested quartile of a supplied range of
// values. The syntax of the function is:
//
// QUARTILE(array,quart)
//
func (fn *formulaFuncs) QUARTILE(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "QUARTILE requires 2 arguments")
}
quart := argsList.Back().Value.(formulaArg).ToNumber()
if quart.Type != ArgNumber {
return quart
}
if quart.Number < 0 || quart.Number > 4 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
args := list.New().Init()
args.PushBack(argsList.Front().Value.(formulaArg))
args.PushBack(newNumberFormulaArg(quart.Number / 4))
return fn.PERCENTILE(args)
}
// QUARTILEdotEXC function returns a requested quartile of a supplied range of
// values, based on a percentile range of 0 to 1 exclusive. The syntax of the
// function is:
//
// QUARTILE.EXC(array,quart)
//
func (fn *formulaFuncs) QUARTILEdotEXC(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "QUARTILE.EXC requires 2 arguments")
}
quart := argsList.Back().Value.(formulaArg).ToNumber()
if quart.Type != ArgNumber {
return quart
}
if quart.Number <= 0 || quart.Number >= 4 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
args := list.New().Init()
args.PushBack(argsList.Front().Value.(formulaArg))
args.PushBack(newNumberFormulaArg(quart.Number / 4))
return fn.PERCENTILEdotEXC(args)
}
// QUARTILEdotINC function returns a requested quartile of a supplied range of
// values. The syntax of the function is:
//
// QUARTILE.INC(array,quart)
//
func (fn *formulaFuncs) QUARTILEdotINC(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "QUARTILE.INC requires 2 arguments")
}
return fn.QUARTILE(argsList)
}
// rank is an implementation of the formula functions RANK and RANK.EQ.
func (fn *formulaFuncs) rank(name string, argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 2 arguments", name))
}
if argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at most 3 arguments", name))
}
num := argsList.Front().Value.(formulaArg).ToNumber()
if num.Type != ArgNumber {
return num
}
var arr []float64
for _, arg := range argsList.Front().Next().Value.(formulaArg).ToList() {
n := arg.ToNumber()
if n.Type == ArgNumber {
arr = append(arr, n.Number)
}
}
sort.Float64s(arr)
order := newNumberFormulaArg(0)
if argsList.Len() == 3 {
if order = argsList.Back().Value.(formulaArg).ToNumber(); order.Type != ArgNumber {
return order
}
}
if order.Number == 0 {
sort.Sort(sort.Reverse(sort.Float64Slice(arr)))
}
if idx := inFloat64Slice(arr, num.Number); idx != -1 {
return newNumberFormulaArg(float64(idx + 1))
}
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
// RANKdotEQ function returns the statistical rank of a given value, within a
// supplied array of values. If there are duplicate values in the list, these
// are given the same rank. The syntax of the function is:
//
// RANK.EQ(number,ref,[order])
//
func (fn *formulaFuncs) RANKdotEQ(argsList *list.List) formulaArg {
return fn.rank("RANK.EQ", argsList)
}
// RANK function returns the statistical rank of a given value, within a
// supplied array of values. If there are duplicate values in the list, these
// are given the same rank. The syntax of the function is:
//
// RANK(number,ref,[order])
//
func (fn *formulaFuncs) RANK(argsList *list.List) formulaArg {
return fn.rank("RANK", argsList)
}
// RSQ function calculates the square of the Pearson Product-Moment Correlation
// Coefficient for two supplied sets of values. The syntax of the function
// is:
//
// RSQ(known_y's,known_x's)
//
func (fn *formulaFuncs) RSQ(argsList *list.List) formulaArg {
return fn.pearsonProduct("RSQ", argsList)
}
// skew is an implementation of the formula functions SKEW and SKEW.P.
func (fn *formulaFuncs) skew(name string, argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 1 argument", name))
}
mean := fn.AVERAGE(argsList)
var stdDev formulaArg
var count, summer float64
if name == "SKEW" {
stdDev = fn.STDEV(argsList)
} else {
stdDev = fn.STDEVP(argsList)
}
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgNumber, ArgString:
num := token.ToNumber()
if num.Type == ArgError {
return num
}
summer += math.Pow((num.Number-mean.Number)/stdDev.Number, 3)
count++
case ArgList, ArgMatrix:
for _, row := range token.ToList() {
numArg := row.ToNumber()
if numArg.Type != ArgNumber {
continue
}
summer += math.Pow((numArg.Number-mean.Number)/stdDev.Number, 3)
count++
}
}
}
if count > 2 {
if name == "SKEW" {
return newNumberFormulaArg(summer * (count / ((count - 1) * (count - 2))))
}
return newNumberFormulaArg(summer / count)
}
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
// SKEW function calculates the skewness of the distribution of a supplied set
// of values. The syntax of the function is:
//
// SKEW(number1,[number2],...)
//
func (fn *formulaFuncs) SKEW(argsList *list.List) formulaArg {
return fn.skew("SKEW", argsList)
}
// SKEWdotP function calculates the skewness of the distribution of a supplied
// set of values. The syntax of the function is:
//
// SKEW.P(number1,[number2],...)
//
func (fn *formulaFuncs) SKEWdotP(argsList *list.List) formulaArg {
return fn.skew("SKEW.P", argsList)
}
// SLOPE returns the slope of the linear regression line through data points in
// known_y's and known_x's. The slope is the vertical distance divided by the
// horizontal distance between any two points on the line, which is the rate
// of change along the regression line. The syntax of the function is:
//
// SLOPE(known_y's,known_x's)
//
func (fn *formulaFuncs) SLOPE(argsList *list.List) formulaArg {
return fn.pearsonProduct("SLOPE", argsList)
}
// SMALL function returns the k'th smallest value from an array of numeric
// values. The syntax of the function is:
//
// SMALL(array,k)
//
func (fn *formulaFuncs) SMALL(argsList *list.List) formulaArg {
return fn.kth("SMALL", argsList)
}
// STANDARDIZE function returns a normalized value of a distribution that is
// characterized by a supplied mean and standard deviation. The syntax of the
// function is:
//
// STANDARDIZE(x,mean,standard_dev)
//
func (fn *formulaFuncs) STANDARDIZE(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "STANDARDIZE requires 3 arguments")
}
x := argsList.Front().Value.(formulaArg).ToNumber()
if x.Type != ArgNumber {
return x
}
mean := argsList.Front().Next().Value.(formulaArg).ToNumber()
if mean.Type != ArgNumber {
return mean
}
stdDev := argsList.Back().Value.(formulaArg).ToNumber()
if stdDev.Type != ArgNumber {
return stdDev
}
if stdDev.Number <= 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
return newNumberFormulaArg((x.Number - mean.Number) / stdDev.Number)
}
// stdevp is an implementation of the formula functions STDEVP, STDEV.P and
// STDEVPA.
func (fn *formulaFuncs) stdevp(name string, argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 1 argument", name))
}
fnName := "VARP"
if name == "STDEVPA" {
fnName = "VARPA"
}
varp := fn.vars(fnName, argsList)
if varp.Type != ArgNumber {
return varp
}
return newNumberFormulaArg(math.Sqrt(varp.Number))
}
// STDEVP function calculates the standard deviation of a supplied set of
// values. The syntax of the function is:
//
// STDEVP(number1,[number2],...)
//
func (fn *formulaFuncs) STDEVP(argsList *list.List) formulaArg {
return fn.stdevp("STDEVP", argsList)
}
// STDEVdotP function calculates the standard deviation of a supplied set of
// values.
//
// STDEV.P( number1, [number2], ... )
//
func (fn *formulaFuncs) STDEVdotP(argsList *list.List) formulaArg {
return fn.stdevp("STDEV.P", argsList)
}
// STDEVPA function calculates the standard deviation of a supplied set of
// values. The syntax of the function is:
//
// STDEVPA(number1,[number2],...)
//
func (fn *formulaFuncs) STDEVPA(argsList *list.List) formulaArg {
return fn.stdevp("STDEVPA", argsList)
}
// STEYX function calculates the standard error for the line of best fit,
// through a supplied set of x- and y- values. The syntax of the function is:
//
// STEYX(known_y's,known_x's)
//
func (fn *formulaFuncs) STEYX(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "STEYX requires 2 arguments")
}
array1 := argsList.Back().Value.(formulaArg).ToList()
array2 := argsList.Front().Value.(formulaArg).ToList()
if len(array1) != len(array2) {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
var count, sumX, sumY, squareX, squareY, sigmaXY float64
for i := 0; i < len(array1); i++ {
num1, num2 := array1[i].ToNumber(), array2[i].ToNumber()
if !(num1.Type == ArgNumber && num2.Type == ArgNumber) {
continue
}
sumX += num1.Number
sumY += num2.Number
squareX += num1.Number * num1.Number
squareY += num2.Number * num2.Number
sigmaXY += num1.Number * num2.Number
count++
}
if count < 3 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
dx, dy := sumX/count, sumY/count
sigma1 := squareY - 2*dy*sumY + count*dy*dy
sigma2 := sigmaXY - dy*sumX - sumY*dx + count*dy*dx
sigma3 := squareX - 2*dx*sumX + count*dx*dx
return newNumberFormulaArg(math.Sqrt((sigma1 - (sigma2*sigma2)/sigma3) / (count - 2)))
}
// getTDist is an implementation for the beta distribution probability density
// function.
func getTDist(T, fDF, nType float64) float64 {
var res float64
switch nType {
case 1:
res = 0.5 * getBetaDist(fDF/(fDF+T*T), fDF/2, 0.5)
case 2:
res = getBetaDist(fDF/(fDF+T*T), fDF/2, 0.5)
case 3:
res = math.Pow(1+(T*T/fDF), -(fDF+1)/2) / (math.Sqrt(fDF) * getBeta(0.5, fDF/2.0))
case 4:
X := fDF / (T*T + fDF)
R := 0.5 * getBetaDist(X, 0.5*fDF, 0.5)
res = 1 - R
if T < 0 {
res = R
}
}
return res
}
// TdotDIST function calculates the one-tailed Student's T Distribution, which
// is a continuous probability distribution that is frequently used for
// testing hypotheses on small sample data sets. The syntax of the function
// is:
//
// T.DIST(x,degrees_freedom,cumulative)
//
func (fn *formulaFuncs) TdotDIST(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "T.DIST requires 3 arguments")
}
var x, degrees, cumulative formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if degrees = argsList.Front().Next().Value.(formulaArg).ToNumber(); degrees.Type != ArgNumber {
return degrees
}
if cumulative = argsList.Back().Value.(formulaArg).ToBool(); cumulative.Type != ArgNumber {
return cumulative
}
if cumulative.Number == 1 && degrees.Number < 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if cumulative.Number == 0 {
if degrees.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if degrees.Number == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(getTDist(x.Number, degrees.Number, 3))
}
return newNumberFormulaArg(getTDist(x.Number, degrees.Number, 4))
}
// TdotDISTdot2T function calculates the two-tailed Student's T Distribution,
// which is a continuous probability distribution that is frequently used for
// testing hypotheses on small sample data sets. The syntax of the function
// is:
//
// T.DIST.2T(x,degrees_freedom)
//
func (fn *formulaFuncs) TdotDISTdot2T(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "T.DIST.2T requires 2 arguments")
}
var x, degrees formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if degrees = argsList.Back().Value.(formulaArg).ToNumber(); degrees.Type != ArgNumber {
return degrees
}
if x.Number < 0 || degrees.Number < 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(getTDist(x.Number, degrees.Number, 2))
}
// TdotDISTdotRT function calculates the right-tailed Student's T Distribution,
// which is a continuous probability distribution that is frequently used for
// testing hypotheses on small sample data sets. The syntax of the function
// is:
//
// T.DIST.RT(x,degrees_freedom)
//
func (fn *formulaFuncs) TdotDISTdotRT(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "T.DIST.RT requires 2 arguments")
}
var x, degrees formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if degrees = argsList.Back().Value.(formulaArg).ToNumber(); degrees.Type != ArgNumber {
return degrees
}
if degrees.Number < 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
v := getTDist(x.Number, degrees.Number, 1)
if x.Number < 0 {
v = 1 - v
}
return newNumberFormulaArg(v)
}
// TDIST function calculates the Student's T Distribution, which is a
// continuous probability distribution that is frequently used for testing
// hypotheses on small sample data sets. The syntax of the function is:
//
// TDIST(x,degrees_freedom,tails)
//
func (fn *formulaFuncs) TDIST(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "TDIST requires 3 arguments")
}
var x, degrees, tails formulaArg
if x = argsList.Front().Value.(formulaArg).ToNumber(); x.Type != ArgNumber {
return x
}
if degrees = argsList.Front().Next().Value.(formulaArg).ToNumber(); degrees.Type != ArgNumber {
return degrees
}
if tails = argsList.Back().Value.(formulaArg).ToNumber(); tails.Type != ArgNumber {
return tails
}
if x.Number < 0 || degrees.Number < 1 || (tails.Number != 1 && tails.Number != 2) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(getTDist(x.Number, degrees.Number, tails.Number))
}
// TdotINV function calculates the left-tailed inverse of the Student's T
// Distribution, which is a continuous probability distribution that is
// frequently used for testing hypotheses on small sample data sets. The
// syntax of the function is:
//
// T.INV(probability,degrees_freedom)
//
func (fn *formulaFuncs) TdotINV(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "T.INV requires 2 arguments")
}
var probability, degrees formulaArg
if probability = argsList.Front().Value.(formulaArg).ToNumber(); probability.Type != ArgNumber {
return probability
}
if degrees = argsList.Back().Value.(formulaArg).ToNumber(); degrees.Type != ArgNumber {
return degrees
}
if probability.Number <= 0 || probability.Number >= 1 || degrees.Number < 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if probability.Number < 0.5 {
return newNumberFormulaArg(-calcIterateInverse(calcInverseIterator{
name: "T.INV",
fp: 1 - probability.Number,
fDF: degrees.Number,
nT: 4,
}, degrees.Number/2, degrees.Number))
}
return newNumberFormulaArg(calcIterateInverse(calcInverseIterator{
name: "T.INV",
fp: probability.Number,
fDF: degrees.Number,
nT: 4,
}, degrees.Number/2, degrees.Number))
}
// TdotINVdot2T function calculates the inverse of the two-tailed Student's T
// Distribution, which is a continuous probability distribution that is
// frequently used for testing hypotheses on small sample data sets. The
// syntax of the function is:
//
// T.INV.2T(probability,degrees_freedom)
//
func (fn *formulaFuncs) TdotINVdot2T(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "T.INV.2T requires 2 arguments")
}
var probability, degrees formulaArg
if probability = argsList.Front().Value.(formulaArg).ToNumber(); probability.Type != ArgNumber {
return probability
}
if degrees = argsList.Back().Value.(formulaArg).ToNumber(); degrees.Type != ArgNumber {
return degrees
}
if probability.Number <= 0 || probability.Number > 1 || degrees.Number < 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(calcIterateInverse(calcInverseIterator{
name: "T.INV.2T",
fp: probability.Number,
fDF: degrees.Number,
nT: 2,
}, degrees.Number/2, degrees.Number))
}
// TINV function calculates the inverse of the two-tailed Student's T
// Distribution, which is a continuous probability distribution that is
// frequently used for testing hypotheses on small sample data sets. The
// syntax of the function is:
//
// TINV(probability,degrees_freedom)
//
func (fn *formulaFuncs) TINV(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "TINV requires 2 arguments")
}
return fn.TdotINVdot2T(argsList)
}
// TREND function calculates the linear trend line through a given set of
// y-values and (optionally), a given set of x-values. The function then
// extends the linear trendline to calculate additional y-values for a further
// supplied set of new x-values. The syntax of the function is:
//
// TREND(known_y's,[known_x's],[new_x's],[const])
//
func (fn *formulaFuncs) TREND(argsList *list.List) formulaArg {
return fn.trendGrowth("TREND", argsList)
}
// tTest calculates the probability associated with the Student's T Test.
func tTest(bTemplin bool, mtx1, mtx2 [][]formulaArg, c1, c2, r1, r2 int) (float64, float64, bool) {
var cnt1, cnt2, sum1, sumSqr1, sum2, sumSqr2 float64
var fVal formulaArg
for i := 0; i < c1; i++ {
for j := 0; j < r1; j++ {
fVal = mtx1[i][j].ToNumber()
if fVal.Type == ArgNumber {
sum1 += fVal.Number
sumSqr1 += fVal.Number * fVal.Number
cnt1++
}
}
}
for i := 0; i < c2; i++ {
for j := 0; j < r2; j++ {
fVal = mtx2[i][j].ToNumber()
if fVal.Type == ArgNumber {
sum2 += fVal.Number
sumSqr2 += fVal.Number * fVal.Number
cnt2++
}
}
}
if cnt1 < 2.0 || cnt2 < 2.0 {
return 0, 0, false
}
if bTemplin {
fS1 := (sumSqr1 - sum1*sum1/cnt1) / (cnt1 - 1) / cnt1
fS2 := (sumSqr2 - sum2*sum2/cnt2) / (cnt2 - 1) / cnt2
if fS1+fS2 == 0 {
return 0, 0, false
}
c := fS1 / (fS1 + fS2)
return math.Abs(sum1/cnt1-sum2/cnt2) / math.Sqrt(fS1+fS2), 1 / (c*c/(cnt1-1) + (1-c)*(1-c)/(cnt2-1)), true
}
fS1 := (sumSqr1 - sum1*sum1/cnt1) / (cnt1 - 1)
fS2 := (sumSqr2 - sum2*sum2/cnt2) / (cnt2 - 1)
return math.Abs(sum1/cnt1-sum2/cnt2) / math.Sqrt((cnt1-1)*fS1+(cnt2-1)*fS2) * math.Sqrt(cnt1*cnt2*(cnt1+cnt2-2)/(cnt1+cnt2)), cnt1 + cnt2 - 2, true
}
// tTest is an implementation of the formula function TTEST.
func (fn *formulaFuncs) tTest(mtx1, mtx2 [][]formulaArg, fTails, fTyp float64) formulaArg {
var fT, fF float64
c1, c2, r1, r2, ok := len(mtx1), len(mtx2), len(mtx1[0]), len(mtx2[0]), true
if fTyp == 1 {
if c1 != c2 || r1 != r2 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
var cnt, sum1, sum2, sumSqrD float64
var fVal1, fVal2 formulaArg
for i := 0; i < c1; i++ {
for j := 0; j < r1; j++ {
fVal1, fVal2 = mtx1[i][j].ToNumber(), mtx2[i][j].ToNumber()
if fVal1.Type != ArgNumber || fVal2.Type != ArgNumber {
continue
}
sum1 += fVal1.Number
sum2 += fVal2.Number
sumSqrD += (fVal1.Number - fVal2.Number) * (fVal1.Number - fVal2.Number)
cnt++
}
}
if cnt < 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
sumD := sum1 - sum2
divider := cnt*sumSqrD - sumD*sumD
if divider == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
fT = math.Abs(sumD) * math.Sqrt((cnt-1)/divider)
fF = cnt - 1
} else if fTyp == 2 {
fT, fF, ok = tTest(false, mtx1, mtx2, c1, c2, r1, r2)
} else {
fT, fF, ok = tTest(true, mtx1, mtx2, c1, c2, r1, r2)
}
if !ok {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(getTDist(fT, fF, fTails))
}
// TTEST function calculates the probability associated with the Student's T
// Test, which is commonly used for identifying whether two data sets are
// likely to have come from the same two underlying populations with the same
// mean. The syntax of the function is:
//
// TTEST(array1,array2,tails,type)
//
func (fn *formulaFuncs) TTEST(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "TTEST requires 4 arguments")
}
var array1, array2, tails, typeArg formulaArg
array1 = argsList.Front().Value.(formulaArg)
array2 = argsList.Front().Next().Value.(formulaArg)
if tails = argsList.Front().Next().Next().Value.(formulaArg).ToNumber(); tails.Type != ArgNumber {
return tails
}
if typeArg = argsList.Back().Value.(formulaArg).ToNumber(); typeArg.Type != ArgNumber {
return typeArg
}
if len(array1.Matrix) == 0 || len(array2.Matrix) == 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if tails.Number != 1 && tails.Number != 2 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if typeArg.Number != 1 && typeArg.Number != 2 && typeArg.Number != 3 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return fn.tTest(array1.Matrix, array2.Matrix, tails.Number, typeArg.Number)
}
// TdotTEST function calculates the probability associated with the Student's T
// Test, which is commonly used for identifying whether two data sets are
// likely to have come from the same two underlying populations with the same
// mean. The syntax of the function is:
//
// T.TEST(array1,array2,tails,type)
//
func (fn *formulaFuncs) TdotTEST(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "T.TEST requires 4 arguments")
}
return fn.TTEST(argsList)
}
// TRIMMEAN function calculates the trimmed mean (or truncated mean) of a
// supplied set of values. The syntax of the function is:
//
// TRIMMEAN(array,percent)
//
func (fn *formulaFuncs) TRIMMEAN(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "TRIMMEAN requires 2 arguments")
}
percent := argsList.Back().Value.(formulaArg).ToNumber()
if percent.Type != ArgNumber {
return percent
}
if percent.Number < 0 || percent.Number >= 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
var arr []float64
arrArg := argsList.Front().Value.(formulaArg).ToList()
for _, cell := range arrArg {
num := cell.ToNumber()
if num.Type != ArgNumber {
continue
}
arr = append(arr, num.Number)
}
discard := math.Floor(float64(len(arr)) * percent.Number / 2)
sort.Float64s(arr)
for i := 0; i < int(discard); i++ {
if len(arr) > 0 {
arr = arr[1:]
}
if len(arr) > 0 {
arr = arr[:len(arr)-1]
}
}
args := list.New().Init()
for _, ele := range arr {
args.PushBack(newNumberFormulaArg(ele))
}
return fn.AVERAGE(args)
}
// vars is an implementation of the formula functions VAR, VARA, VARP, VAR.P
// VAR.S and VARPA.
func (fn *formulaFuncs) vars(name string, argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 1 argument", name))
}
summerA, summerB, count := 0.0, 0.0, 0.0
minimum := 0.0
if name == "VAR" || name == "VAR.S" || name == "VARA" {
minimum = 1.0
}
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
for _, token := range arg.Value.(formulaArg).ToList() {
if token.Value() == "" {
continue
}
num := token.ToNumber()
if token.Value() != "TRUE" && num.Type == ArgNumber {
summerA += num.Number * num.Number
summerB += num.Number
count++
continue
}
num = token.ToBool()
if num.Type == ArgNumber {
summerA += num.Number * num.Number
summerB += num.Number
count++
continue
}
if name == "VARA" || name == "VARPA" {
count++
}
}
}
if count > minimum {
summerA *= count
summerB *= summerB
return newNumberFormulaArg((summerA - summerB) / (count * (count - minimum)))
}
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
// VAR function returns the sample variance of a supplied set of values. The
// syntax of the function is:
//
// VAR(number1,[number2],...)
//
func (fn *formulaFuncs) VAR(argsList *list.List) formulaArg {
return fn.vars("VAR", argsList)
}
// VARA function calculates the sample variance of a supplied set of values.
// The syntax of the function is:
//
// VARA(number1,[number2],...)
//
func (fn *formulaFuncs) VARA(argsList *list.List) formulaArg {
return fn.vars("VARA", argsList)
}
// VARP function returns the Variance of a given set of values. The syntax of
// the function is:
//
// VARP(number1,[number2],...)
//
func (fn *formulaFuncs) VARP(argsList *list.List) formulaArg {
return fn.vars("VARP", argsList)
}
// VARdotP function returns the Variance of a given set of values. The syntax
// of the function is:
//
// VAR.P(number1,[number2],...)
//
func (fn *formulaFuncs) VARdotP(argsList *list.List) formulaArg {
return fn.vars("VAR.P", argsList)
}
// VARdotS function calculates the sample variance of a supplied set of
// values. The syntax of the function is:
//
// VAR.S(number1,[number2],...)
//
func (fn *formulaFuncs) VARdotS(argsList *list.List) formulaArg {
return fn.vars("VAR.S", argsList)
}
// VARPA function returns the Variance of a given set of values. The syntax of
// the function is:
//
// VARPA(number1,[number2],...)
//
func (fn *formulaFuncs) VARPA(argsList *list.List) formulaArg {
return fn.vars("VARPA", argsList)
}
// WEIBULL function calculates the Weibull Probability Density Function or the
// Weibull Cumulative Distribution Function for a supplied set of parameters.
// The syntax of the function is:
//
// WEIBULL(x,alpha,beta,cumulative)
//
func (fn *formulaFuncs) WEIBULL(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "WEIBULL requires 4 arguments")
}
x := argsList.Front().Value.(formulaArg).ToNumber()
alpha := argsList.Front().Next().Value.(formulaArg).ToNumber()
beta := argsList.Back().Prev().Value.(formulaArg).ToNumber()
if alpha.Type == ArgNumber && beta.Type == ArgNumber && x.Type == ArgNumber {
if alpha.Number < 0 || alpha.Number <= 0 || beta.Number <= 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
cumulative := argsList.Back().Value.(formulaArg).ToBool()
if cumulative.Boolean && cumulative.Number == 1 {
return newNumberFormulaArg(1 - math.Exp(0-math.Pow(x.Number/beta.Number, alpha.Number)))
}
return newNumberFormulaArg((alpha.Number / math.Pow(beta.Number, alpha.Number)) *
math.Pow(x.Number, alpha.Number-1) * math.Exp(0-math.Pow(x.Number/beta.Number, alpha.Number)))
}
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
// WEIBULLdotDIST function calculates the Weibull Probability Density Function
// or the Weibull Cumulative Distribution Function for a supplied set of
// parameters. The syntax of the function is:
//
// WEIBULL.DIST(x,alpha,beta,cumulative)
//
func (fn *formulaFuncs) WEIBULLdotDIST(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "WEIBULL.DIST requires 4 arguments")
}
return fn.WEIBULL(argsList)
}
// ZdotTEST function calculates the one-tailed probability value of the
// Z-Test. The syntax of the function is:
//
// Z.TEST(array,x,[sigma])
//
func (fn *formulaFuncs) ZdotTEST(argsList *list.List) formulaArg {
argsLen := argsList.Len()
if argsLen < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "Z.TEST requires at least 2 arguments")
}
if argsLen > 3 {
return newErrorFormulaArg(formulaErrorVALUE, "Z.TEST accepts at most 3 arguments")
}
return fn.ZTEST(argsList)
}
// ZTEST function calculates the one-tailed probability value of the Z-Test.
// The syntax of the function is:
//
// ZTEST(array,x,[sigma])
//
func (fn *formulaFuncs) ZTEST(argsList *list.List) formulaArg {
argsLen := argsList.Len()
if argsLen < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "ZTEST requires at least 2 arguments")
}
if argsLen > 3 {
return newErrorFormulaArg(formulaErrorVALUE, "ZTEST accepts at most 3 arguments")
}
arrArg, arrArgs := argsList.Front().Value.(formulaArg), list.New()
arrArgs.PushBack(arrArg)
arr := fn.AVERAGE(arrArgs)
if arr.Type == ArgError {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
x := argsList.Front().Next().Value.(formulaArg).ToNumber()
if x.Type == ArgError {
return x
}
sigma := argsList.Back().Value.(formulaArg).ToNumber()
if sigma.Type == ArgError {
return sigma
}
if argsLen != 3 {
sigma = fn.STDEV(arrArgs).ToNumber()
}
normsdistArg := list.New()
div := sigma.Number / math.Sqrt(float64(len(arrArg.ToList())))
if div == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
normsdistArg.PushBack(newNumberFormulaArg((arr.Number - x.Number) / div))
return newNumberFormulaArg(1 - fn.NORMSDIST(normsdistArg).Number)
}
// Information Functions
// ERRORdotTYPE function receives an error value and returns an integer, that
// tells you the type of the supplied error. The syntax of the function is:
//
// ERROR.TYPE(error_val)
//
func (fn *formulaFuncs) ERRORdotTYPE(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ERROR.TYPE requires 1 argument")
}
token := argsList.Front().Value.(formulaArg)
if token.Type == ArgError {
for i, errType := range []string{
formulaErrorNULL, formulaErrorDIV, formulaErrorVALUE, formulaErrorREF,
formulaErrorNAME, formulaErrorNUM, formulaErrorNA,
} {
if errType == token.String {
return newNumberFormulaArg(float64(i) + 1)
}
}
}
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
// ISBLANK function tests if a specified cell is blank (empty) and if so,
// returns TRUE; Otherwise the function returns FALSE. The syntax of the
// function is:
//
// ISBLANK(value)
//
func (fn *formulaFuncs) ISBLANK(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISBLANK requires 1 argument")
}
token := argsList.Front().Value.(formulaArg)
result := "FALSE"
switch token.Type {
case ArgUnknown:
result = "TRUE"
case ArgString:
if token.String == "" {
result = "TRUE"
}
}
return newStringFormulaArg(result)
}
// ISERR function tests if an initial supplied expression (or value) returns
// any Excel Error, except the #N/A error. If so, the function returns the
// logical value TRUE; If the supplied value is not an error or is the #N/A
// error, the ISERR function returns FALSE. The syntax of the function is:
//
// ISERR(value)
//
func (fn *formulaFuncs) ISERR(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISERR requires 1 argument")
}
token := argsList.Front().Value.(formulaArg)
result := false
if token.Type == ArgError {
for _, errType := range []string{
formulaErrorDIV, formulaErrorNAME, formulaErrorNUM,
formulaErrorVALUE, formulaErrorREF, formulaErrorNULL,
formulaErrorSPILL, formulaErrorCALC, formulaErrorGETTINGDATA,
} {
if errType == token.String {
result = true
}
}
}
return newBoolFormulaArg(result)
}
// ISERROR function tests if an initial supplied expression (or value) returns
// an Excel Error, and if so, returns the logical value TRUE; Otherwise the
// function returns FALSE. The syntax of the function is:
//
// ISERROR(value)
//
func (fn *formulaFuncs) ISERROR(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISERROR requires 1 argument")
}
token := argsList.Front().Value.(formulaArg)
result := false
if token.Type == ArgError {
for _, errType := range []string{
formulaErrorDIV, formulaErrorNAME, formulaErrorNA, formulaErrorNUM,
formulaErrorVALUE, formulaErrorREF, formulaErrorNULL, formulaErrorSPILL,
formulaErrorCALC, formulaErrorGETTINGDATA,
} {
if errType == token.String {
result = true
}
}
}
return newBoolFormulaArg(result)
}
// ISEVEN function tests if a supplied number (or numeric expression)
// evaluates to an even number, and if so, returns TRUE; Otherwise, the
// function returns FALSE. The syntax of the function is:
//
// ISEVEN(value)
//
func (fn *formulaFuncs) ISEVEN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISEVEN requires 1 argument")
}
var (
token = argsList.Front().Value.(formulaArg)
result = "FALSE"
numeric int
err error
)
if token.Type == ArgString {
if numeric, err = strconv.Atoi(token.String); err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
if numeric == numeric/2*2 {
return newStringFormulaArg("TRUE")
}
}
return newStringFormulaArg(result)
}
// ISFORMULA function tests if a specified cell contains a formula, and if so,
// returns TRUE; Otherwise, the function returns FALSE. The syntax of the
// function is:
//
// ISFORMULA(reference)
//
func (fn *formulaFuncs) ISFORMULA(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISFORMULA requires 1 argument")
}
arg := argsList.Front().Value.(formulaArg)
if arg.cellRefs != nil && arg.cellRefs.Len() == 1 {
ref := arg.cellRefs.Front().Value.(cellRef)
cell, _ := CoordinatesToCellName(ref.Col, ref.Row)
if formula, _ := fn.f.GetCellFormula(ref.Sheet, cell); len(formula) > 0 {
return newBoolFormulaArg(true)
}
}
return newBoolFormulaArg(false)
}
// ISLOGICAL function tests if a supplied value (or expression) returns a
// logical value (i.e. evaluates to True or False). If so, the function
// returns TRUE; Otherwise, it returns FALSE. The syntax of the function is:
//
// ISLOGICAL(value)
//
func (fn *formulaFuncs) ISLOGICAL(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISLOGICAL requires 1 argument")
}
val := argsList.Front().Value.(formulaArg).Value()
if strings.EqualFold("TRUE", val) || strings.EqualFold("FALSE", val) {
return newBoolFormulaArg(true)
}
return newBoolFormulaArg(false)
}
// ISNA function tests if an initial supplied expression (or value) returns
// the Excel #N/A Error, and if so, returns TRUE; Otherwise the function
// returns FALSE. The syntax of the function is:
//
// ISNA(value)
//
func (fn *formulaFuncs) ISNA(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISNA requires 1 argument")
}
token := argsList.Front().Value.(formulaArg)
result := "FALSE"
if token.Type == ArgError && token.String == formulaErrorNA {
result = "TRUE"
}
return newStringFormulaArg(result)
}
// ISNONTEXT function tests if a supplied value is text. If not, the
// function returns TRUE; If the supplied value is text, the function returns
// FALSE. The syntax of the function is:
//
// ISNONTEXT(value)
//
func (fn *formulaFuncs) ISNONTEXT(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISNONTEXT requires 1 argument")
}
token := argsList.Front().Value.(formulaArg)
result := "TRUE"
if token.Type == ArgString && token.String != "" {
result = "FALSE"
}
return newStringFormulaArg(result)
}
// ISNUMBER function tests if a supplied value is a number. If so,
// the function returns TRUE; Otherwise it returns FALSE. The syntax of the
// function is:
//
// ISNUMBER(value)
//
func (fn *formulaFuncs) ISNUMBER(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISNUMBER requires 1 argument")
}
token, result := argsList.Front().Value.(formulaArg), false
if token.Type == ArgString && token.String != "" {
if _, err := strconv.Atoi(token.String); err == nil {
result = true
}
}
return newBoolFormulaArg(result)
}
// ISODD function tests if a supplied number (or numeric expression) evaluates
// to an odd number, and if so, returns TRUE; Otherwise, the function returns
// FALSE. The syntax of the function is:
//
// ISODD(value)
//
func (fn *formulaFuncs) ISODD(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISODD requires 1 argument")
}
var (
token = argsList.Front().Value.(formulaArg)
result = "FALSE"
numeric int
err error
)
if token.Type == ArgString {
if numeric, err = strconv.Atoi(token.String); err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
if numeric != numeric/2*2 {
return newStringFormulaArg("TRUE")
}
}
return newStringFormulaArg(result)
}
// ISREF function tests if a supplied value is a reference. If so, the
// function returns TRUE; Otherwise it returns FALSE. The syntax of the
// function is:
//
// ISREF(value)
//
func (fn *formulaFuncs) ISREF(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISREF requires 1 argument")
}
arg := argsList.Front().Value.(formulaArg)
if arg.cellRanges != nil && arg.cellRanges.Len() > 0 || arg.cellRefs != nil && arg.cellRefs.Len() > 0 {
return newBoolFormulaArg(true)
}
return newBoolFormulaArg(false)
}
// ISTEXT function tests if a supplied value is text, and if so, returns TRUE;
// Otherwise, the function returns FALSE. The syntax of the function is:
//
// ISTEXT(value)
//
func (fn *formulaFuncs) ISTEXT(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISTEXT requires 1 argument")
}
token := argsList.Front().Value.(formulaArg)
if token.ToNumber().Type != ArgError {
return newBoolFormulaArg(false)
}
return newBoolFormulaArg(token.Type == ArgString)
}
// N function converts data into a numeric value. The syntax of the function
// is:
//
// N(value)
//
func (fn *formulaFuncs) N(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "N requires 1 argument")
}
token, num := argsList.Front().Value.(formulaArg), 0.0
if token.Type == ArgError {
return token
}
if arg := token.ToNumber(); arg.Type == ArgNumber {
num = arg.Number
}
if token.Value() == "TRUE" {
num = 1
}
return newNumberFormulaArg(num)
}
// NA function returns the Excel #N/A error. This error message has the
// meaning 'value not available' and is produced when an Excel Formula is
// unable to find a value that it needs. The syntax of the function is:
//
// NA()
//
func (fn *formulaFuncs) NA(argsList *list.List) formulaArg {
if argsList.Len() != 0 {
return newErrorFormulaArg(formulaErrorVALUE, "NA accepts no arguments")
}
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
// SHEET function returns the Sheet number for a specified reference. The
// syntax of the function is:
//
// SHEET([value])
//
func (fn *formulaFuncs) SHEET(argsList *list.List) formulaArg {
if argsList.Len() > 1 {
return newErrorFormulaArg(formulaErrorVALUE, "SHEET accepts at most 1 argument")
}
if argsList.Len() == 0 {
return newNumberFormulaArg(float64(fn.f.GetSheetIndex(fn.sheet) + 1))
}
arg := argsList.Front().Value.(formulaArg)
if sheetIdx := fn.f.GetSheetIndex(arg.Value()); sheetIdx != -1 {
return newNumberFormulaArg(float64(sheetIdx + 1))
}
if arg.cellRanges != nil && arg.cellRanges.Len() > 0 {
if sheetIdx := fn.f.GetSheetIndex(arg.cellRanges.Front().Value.(cellRange).From.Sheet); sheetIdx != -1 {
return newNumberFormulaArg(float64(sheetIdx + 1))
}
}
if arg.cellRefs != nil && arg.cellRefs.Len() > 0 {
if sheetIdx := fn.f.GetSheetIndex(arg.cellRefs.Front().Value.(cellRef).Sheet); sheetIdx != -1 {
return newNumberFormulaArg(float64(sheetIdx + 1))
}
}
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
// SHEETS function returns the number of sheets in a supplied reference. The
// result includes sheets that are Visible, Hidden or Very Hidden. The syntax
// of the function is:
//
// SHEETS([reference])
//
func (fn *formulaFuncs) SHEETS(argsList *list.List) formulaArg {
if argsList.Len() > 1 {
return newErrorFormulaArg(formulaErrorVALUE, "SHEETS accepts at most 1 argument")
}
if argsList.Len() == 0 {
return newNumberFormulaArg(float64(len(fn.f.GetSheetList())))
}
arg := argsList.Front().Value.(formulaArg)
sheetMap := map[string]struct{}{}
if arg.cellRanges != nil && arg.cellRanges.Len() > 0 {
for rng := arg.cellRanges.Front(); rng != nil; rng = rng.Next() {
sheetMap[rng.Value.(cellRange).From.Sheet] = struct{}{}
}
}
if arg.cellRefs != nil && arg.cellRefs.Len() > 0 {
for ref := arg.cellRefs.Front(); ref != nil; ref = ref.Next() {
sheetMap[ref.Value.(cellRef).Sheet] = struct{}{}
}
}
if len(sheetMap) > 0 {
return newNumberFormulaArg(float64(len(sheetMap)))
}
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
// TYPE function returns an integer that represents the value's data type. The
// syntax of the function is:
//
// TYPE(value)
//
func (fn *formulaFuncs) TYPE(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "TYPE requires 1 argument")
}
token := argsList.Front().Value.(formulaArg)
switch token.Type {
case ArgError:
return newNumberFormulaArg(16)
case ArgMatrix:
return newNumberFormulaArg(64)
default:
if arg := token.ToNumber(); arg.Type != ArgError || len(token.Value()) == 0 {
return newNumberFormulaArg(1)
}
if arg := token.ToBool(); arg.Type != ArgError {
return newNumberFormulaArg(4)
}
return newNumberFormulaArg(2)
}
}
// T function tests if a supplied value is text and if so, returns the
// supplied text; Otherwise, the function returns an empty text string. The
// syntax of the function is:
//
// T(value)
//
func (fn *formulaFuncs) T(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "T requires 1 argument")
}
token := argsList.Front().Value.(formulaArg)
if token.Type == ArgError {
return token
}
if token.Type == ArgNumber {
return newStringFormulaArg("")
}
return newStringFormulaArg(token.Value())
}
// Logical Functions
// AND function tests a number of supplied conditions and returns TRUE or
// FALSE. The syntax of the function is:
//
// AND(logical_test1,[logical_test2],...)
//
func (fn *formulaFuncs) AND(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "AND requires at least 1 argument")
}
if argsList.Len() > 30 {
return newErrorFormulaArg(formulaErrorVALUE, "AND accepts at most 30 arguments")
}
and := true
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgUnknown:
continue
case ArgString:
if token.String == "TRUE" {
continue
}
if token.String == "FALSE" {
return newStringFormulaArg(token.String)
}
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
case ArgNumber:
and = and && token.Number != 0
case ArgMatrix:
// TODO
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
}
return newBoolFormulaArg(and)
}
// FALSE function returns the logical value FALSE. The syntax of the
// function is:
//
// FALSE()
//
func (fn *formulaFuncs) FALSE(argsList *list.List) formulaArg {
if argsList.Len() != 0 {
return newErrorFormulaArg(formulaErrorVALUE, "FALSE takes no arguments")
}
return newBoolFormulaArg(false)
}
// IFERROR function receives two values (or expressions) and tests if the
// first of these evaluates to an error. The syntax of the function is:
//
// IFERROR(value,value_if_error)
//
func (fn *formulaFuncs) IFERROR(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "IFERROR requires 2 arguments")
}
value := argsList.Front().Value.(formulaArg)
if value.Type != ArgError {
if value.Type == ArgEmpty {
return newNumberFormulaArg(0)
}
return value
}
return argsList.Back().Value.(formulaArg)
}
// IFNA function tests if an initial supplied value (or expression) evaluates
// to the Excel #N/A error. If so, the function returns a second supplied
// value; Otherwise the function returns the first supplied value. The syntax
// of the function is:
//
// IFNA(value,value_if_na)
//
func (fn *formulaFuncs) IFNA(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "IFNA requires 2 arguments")
}
arg := argsList.Front().Value.(formulaArg)
if arg.Type == ArgError && arg.Value() == formulaErrorNA {
return argsList.Back().Value.(formulaArg)
}
return arg
}
// IFS function tests a number of supplied conditions and returns the result
// corresponding to the first condition that evaluates to TRUE. If none of
// the supplied conditions evaluate to TRUE, the function returns the #N/A
// error.
//
// IFS(logical_test1,value_if_true1,[logical_test2,value_if_true2],...)
//
func (fn *formulaFuncs) IFS(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "IFS requires at least 2 arguments")
}
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
if arg.Value.(formulaArg).ToBool().Number == 1 {
return arg.Next().Value.(formulaArg)
}
arg = arg.Next()
}
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
// NOT function returns the opposite to a supplied logical value. The syntax
// of the function is:
//
// NOT(logical)
//
func (fn *formulaFuncs) NOT(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "NOT requires 1 argument")
}
token := argsList.Front().Value.(formulaArg)
switch token.Type {
case ArgString, ArgList:
if strings.ToUpper(token.String) == "TRUE" {
return newBoolFormulaArg(false)
}
if strings.ToUpper(token.String) == "FALSE" {
return newBoolFormulaArg(true)
}
case ArgNumber:
return newBoolFormulaArg(!(token.Number != 0))
case ArgError:
return token
}
return newErrorFormulaArg(formulaErrorVALUE, "NOT expects 1 boolean or numeric argument")
}
// OR function tests a number of supplied conditions and returns either TRUE
// or FALSE. The syntax of the function is:
//
// OR(logical_test1,[logical_test2],...)
//
func (fn *formulaFuncs) OR(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "OR requires at least 1 argument")
}
if argsList.Len() > 30 {
return newErrorFormulaArg(formulaErrorVALUE, "OR accepts at most 30 arguments")
}
var or bool
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgUnknown:
continue
case ArgString:
if token.String == "FALSE" {
continue
}
if token.String == "TRUE" {
or = true
continue
}
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
case ArgNumber:
or = token.Number != 0
case ArgMatrix:
// TODO
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
}
return newStringFormulaArg(strings.ToUpper(strconv.FormatBool(or)))
}
// SWITCH function compares a number of supplied values to a supplied test
// expression and returns a result corresponding to the first value that
// matches the test expression. A default value can be supplied, to be
// returned if none of the supplied values match the test expression. The
// syntax of the function is:
//
//
// SWITCH(expression,value1,result1,[value2,result2],[value3,result3],...,[default])
//
func (fn *formulaFuncs) SWITCH(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "SWITCH requires at least 3 arguments")
}
target := argsList.Front().Value.(formulaArg)
argCount := argsList.Len() - 1
switchCount := int(math.Floor(float64(argCount) / 2))
hasDefaultClause := argCount%2 != 0
result := newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
if hasDefaultClause {
result = argsList.Back().Value.(formulaArg)
}
if switchCount > 0 {
arg := argsList.Front()
for i := 0; i < switchCount; i++ {
arg = arg.Next()
if target.Value() == arg.Value.(formulaArg).Value() {
result = arg.Next().Value.(formulaArg)
break
}
arg = arg.Next()
}
}
return result
}
// TRUE function returns the logical value TRUE. The syntax of the function
// is:
//
// TRUE()
//
func (fn *formulaFuncs) TRUE(argsList *list.List) formulaArg {
if argsList.Len() != 0 {
return newErrorFormulaArg(formulaErrorVALUE, "TRUE takes no arguments")
}
return newBoolFormulaArg(true)
}
// calcXor checking if numeric cell exists and count it by given arguments
// sequence for the formula function XOR.
func calcXor(argsList *list.List) formulaArg {
count, ok := 0, false
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgError:
return token
case ArgNumber:
ok = true
if token.Number != 0 {
count++
}
case ArgMatrix:
for _, value := range token.ToList() {
if num := value.ToNumber(); num.Type == ArgNumber {
ok = true
if num.Number != 0 {
count++
}
}
}
}
}
if !ok {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
return newBoolFormulaArg(count%2 != 0)
}
// XOR function returns the Exclusive Or logical operation for one or more
// supplied conditions. I.e. the Xor function returns TRUE if an odd number
// of the supplied conditions evaluate to TRUE, and FALSE otherwise. The
// syntax of the function is:
//
// XOR(logical_test1,[logical_test2],...)
//
func (fn *formulaFuncs) XOR(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "XOR requires at least 1 argument")
}
return calcXor(argsList)
}
// Date and Time Functions
// DATE returns a date, from a user-supplied year, month and day. The syntax
// of the function is:
//
// DATE(year,month,day)
//
func (fn *formulaFuncs) DATE(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "DATE requires 3 number arguments")
}
year := argsList.Front().Value.(formulaArg).ToNumber()
month := argsList.Front().Next().Value.(formulaArg).ToNumber()
day := argsList.Back().Value.(formulaArg).ToNumber()
if year.Type != ArgNumber || month.Type != ArgNumber || day.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, "DATE requires 3 number arguments")
}
d := makeDate(int(year.Number), time.Month(month.Number), int(day.Number))
return newStringFormulaArg(timeFromExcelTime(daysBetween(excelMinTime1900.Unix(), d)+1, false).String())
}
// calcDateDif is an implementation of the formula function DATEDIF,
// calculation difference between two dates.
func calcDateDif(unit string, diff float64, seq []int, startArg, endArg formulaArg) float64 {
ey, sy, em, sm, ed, sd := seq[0], seq[1], seq[2], seq[3], seq[4], seq[5]
switch unit {
case "d":
diff = endArg.Number - startArg.Number
case "md":
smMD := em
if ed < sd {
smMD--
}
diff = endArg.Number - daysBetween(excelMinTime1900.Unix(), makeDate(ey, time.Month(smMD), sd)) - 1
case "ym":
diff = float64(em - sm)
if ed < sd {
diff--
}
if diff < 0 {
diff += 12
}
case "yd":
syYD := sy
if em < sm || (em == sm && ed < sd) {
syYD++
}
s := daysBetween(excelMinTime1900.Unix(), makeDate(syYD, time.Month(em), ed))
e := daysBetween(excelMinTime1900.Unix(), makeDate(sy, time.Month(sm), sd))
diff = s - e
}
return diff
}
// DATEDIF function calculates the number of days, months, or years between
// two dates. The syntax of the function is:
//
// DATEDIF(start_date,end_date,unit)
//
func (fn *formulaFuncs) DATEDIF(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "DATEDIF requires 3 number arguments")
}
startArg, endArg := argsList.Front().Value.(formulaArg).ToNumber(), argsList.Front().Next().Value.(formulaArg).ToNumber()
if startArg.Type != ArgNumber || endArg.Type != ArgNumber {
return startArg
}
if startArg.Number > endArg.Number {
return newErrorFormulaArg(formulaErrorNUM, "start_date > end_date")
}
if startArg.Number == endArg.Number {
return newNumberFormulaArg(0)
}
unit := strings.ToLower(argsList.Back().Value.(formulaArg).Value())
startDate, endDate := timeFromExcelTime(startArg.Number, false), timeFromExcelTime(endArg.Number, false)
sy, smm, sd := startDate.Date()
ey, emm, ed := endDate.Date()
sm, em, diff := int(smm), int(emm), 0.0
switch unit {
case "y":
diff = float64(ey - sy)
if em < sm || (em == sm && ed < sd) {
diff--
}
case "m":
yDiff := ey - sy
mDiff := em - sm
if ed < sd {
mDiff--
}
if mDiff < 0 {
yDiff--
mDiff += 12
}
diff = float64(yDiff*12 + mDiff)
case "d", "md", "ym", "yd":
diff = calcDateDif(unit, diff, []int{ey, sy, em, sm, ed, sd}, startArg, endArg)
default:
return newErrorFormulaArg(formulaErrorVALUE, "DATEDIF has invalid unit")
}
return newNumberFormulaArg(diff)
}
// isDateOnlyFmt check if the given string matches date-only format regular expressions.
func isDateOnlyFmt(dateString string) bool {
for _, df := range dateOnlyFormats {
subMatch := df.FindStringSubmatch(dateString)
if len(subMatch) > 1 {
return true
}
}
return false
}
// isTimeOnlyFmt check if the given string matches time-only format regular expressions.
func isTimeOnlyFmt(timeString string) bool {
for _, tf := range timeFormats {
subMatch := tf.FindStringSubmatch(timeString)
if len(subMatch) > 1 {
return true
}
}
return false
}
// strToTimePatternHandler1 parse and convert the given string in pattern
// hh to the time.
func strToTimePatternHandler1(subMatch []string) (h, m int, s float64, err error) {
h, err = strconv.Atoi(subMatch[0])
return
}
// strToTimePatternHandler2 parse and convert the given string in pattern
// hh:mm to the time.
func strToTimePatternHandler2(subMatch []string) (h, m int, s float64, err error) {
if h, err = strconv.Atoi(subMatch[0]); err != nil {
return
}
m, err = strconv.Atoi(subMatch[2])
return
}
// strToTimePatternHandler3 parse and convert the given string in pattern
// mm:ss to the time.
func strToTimePatternHandler3(subMatch []string) (h, m int, s float64, err error) {
if m, err = strconv.Atoi(subMatch[0]); err != nil {
return
}
s, err = strconv.ParseFloat(subMatch[2], 64)
return
}
// strToTimePatternHandler4 parse and convert the given string in pattern
// hh:mm:ss to the time.
func strToTimePatternHandler4(subMatch []string) (h, m int, s float64, err error) {
if h, err = strconv.Atoi(subMatch[0]); err != nil {
return
}
if m, err = strconv.Atoi(subMatch[2]); err != nil {
return
}
s, err = strconv.ParseFloat(subMatch[4], 64)
return
}
// strToTime parse and convert the given string to the time.
func strToTime(str string) (int, int, float64, bool, bool, formulaArg) {
var subMatch []string
pattern := ""
for key, tf := range timeFormats {
subMatch = tf.FindStringSubmatch(str)
if len(subMatch) > 1 {
pattern = key
break
}
}
if pattern == "" {
return 0, 0, 0, false, false, newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
dateIsEmpty := subMatch[1] == ""
subMatch = subMatch[49:]
var (
l = len(subMatch)
last = subMatch[l-1]
am = last == "am"
pm = last == "pm"
hours, minutes int
seconds float64
err error
)
if handler, ok := map[string]func(match []string) (int, int, float64, error){
"hh": strToTimePatternHandler1,
"hh:mm": strToTimePatternHandler2,
"mm:ss": strToTimePatternHandler3,
"hh:mm:ss": strToTimePatternHandler4,
}[pattern]; ok {
if hours, minutes, seconds, err = handler(subMatch); err != nil {
return 0, 0, 0, false, false, newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
}
if minutes >= 60 {
return 0, 0, 0, false, false, newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if am || pm {
if hours > 12 || seconds >= 60 {
return 0, 0, 0, false, false, newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
} else if hours == 12 {
hours = 0
}
} else if hours >= 24 || seconds >= 10000 {
return 0, 0, 0, false, false, newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
return hours, minutes, seconds, pm, dateIsEmpty, newEmptyFormulaArg()
}
// strToDatePatternHandler1 parse and convert the given string in pattern
// mm/dd/yy to the date.
func strToDatePatternHandler1(subMatch []string) (int, int, int, bool, error) {
var year, month, day int
var err error
if month, err = strconv.Atoi(subMatch[1]); err != nil {
return 0, 0, 0, false, err
}
if day, err = strconv.Atoi(subMatch[3]); err != nil {
return 0, 0, 0, false, err
}
if year, err = strconv.Atoi(subMatch[5]); err != nil {
return 0, 0, 0, false, err
}
if year < 0 || year > 9999 || (year > 99 && year < 1900) {
return 0, 0, 0, false, ErrParameterInvalid
}
return formatYear(year), month, day, subMatch[8] == "", err
}
// strToDatePatternHandler2 parse and convert the given string in pattern mm
// dd, yy to the date.
func strToDatePatternHandler2(subMatch []string) (int, int, int, bool, error) {
var year, month, day int
var err error
month = month2num[subMatch[1]]
if day, err = strconv.Atoi(subMatch[14]); err != nil {
return 0, 0, 0, false, err
}
if year, err = strconv.Atoi(subMatch[16]); err != nil {
return 0, 0, 0, false, err
}
if year < 0 || year > 9999 || (year > 99 && year < 1900) {
return 0, 0, 0, false, ErrParameterInvalid
}
return formatYear(year), month, day, subMatch[19] == "", err
}
// strToDatePatternHandler3 parse and convert the given string in pattern
// yy-mm-dd to the date.
func strToDatePatternHandler3(subMatch []string) (int, int, int, bool, error) {
var year, month, day int
v1, err := strconv.Atoi(subMatch[1])
if err != nil {
return 0, 0, 0, false, err
}
v2, err := strconv.Atoi(subMatch[3])
if err != nil {
return 0, 0, 0, false, err
}
v3, err := strconv.Atoi(subMatch[5])
if err != nil {
return 0, 0, 0, false, err
}
if v1 >= 1900 && v1 < 10000 {
year = v1
month = v2
day = v3
} else if v1 > 0 && v1 < 13 {
month = v1
day = v2
year = v3
} else {
return 0, 0, 0, false, ErrParameterInvalid
}
return year, month, day, subMatch[8] == "", err
}
// strToDatePatternHandler4 parse and convert the given string in pattern
// yy-mmStr-dd, yy to the date.
func strToDatePatternHandler4(subMatch []string) (int, int, int, bool, error) {
var year, month, day int
var err error
if year, err = strconv.Atoi(subMatch[16]); err != nil {
return 0, 0, 0, false, err
}
month = month2num[subMatch[3]]
if day, err = strconv.Atoi(subMatch[1]); err != nil {
return 0, 0, 0, false, err
}
return formatYear(year), month, day, subMatch[19] == "", err
}
// strToDate parse and convert the given string to the date.
func strToDate(str string) (int, int, int, bool, formulaArg) {
var subMatch []string
pattern := ""
for key, df := range dateFormats {
subMatch = df.FindStringSubmatch(str)
if len(subMatch) > 1 {
pattern = key
break
}
}
if pattern == "" {
return 0, 0, 0, false, newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
var (
timeIsEmpty bool
year, month, day int
err error
)
if handler, ok := map[string]func(match []string) (int, int, int, bool, error){
"mm/dd/yy": strToDatePatternHandler1,
"mm dd, yy": strToDatePatternHandler2,
"yy-mm-dd": strToDatePatternHandler3,
"yy-mmStr-dd": strToDatePatternHandler4,
}[pattern]; ok {
if year, month, day, timeIsEmpty, err = handler(subMatch); err != nil {
return 0, 0, 0, false, newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
}
if !validateDate(year, month, day) {
return 0, 0, 0, false, newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
return year, month, day, timeIsEmpty, newEmptyFormulaArg()
}
// DATEVALUE function converts a text representation of a date into an Excel
// date. For example, the function converts a text string representing a
// date, into the serial number that represents the date in Excels' date-time
// code. The syntax of the function is:
//
// DATEVALUE(date_text)
//
func (fn *formulaFuncs) DATEVALUE(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "DATEVALUE requires 1 argument")
}
dateText := argsList.Front().Value.(formulaArg).Value()
if !isDateOnlyFmt(dateText) {
if _, _, _, _, _, err := strToTime(dateText); err.Type == ArgError {
return err
}
}
y, m, d, _, err := strToDate(dateText)
if err.Type == ArgError {
return err
}
return newNumberFormulaArg(daysBetween(excelMinTime1900.Unix(), makeDate(y, time.Month(m), d)) + 1)
}
// DAY function returns the day of a date, represented by a serial number. The
// day is given as an integer ranging from 1 to 31. The syntax of the
// function is:
//
// DAY(serial_number)
//
func (fn *formulaFuncs) DAY(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "DAY requires exactly 1 argument")
}
arg := argsList.Front().Value.(formulaArg)
num := arg.ToNumber()
if num.Type != ArgNumber {
dateString := strings.ToLower(arg.Value())
if !isDateOnlyFmt(dateString) {
if _, _, _, _, _, err := strToTime(dateString); err.Type == ArgError {
return err
}
}
_, _, day, _, err := strToDate(dateString)
if err.Type == ArgError {
return err
}
return newNumberFormulaArg(float64(day))
}
if num.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "DAY only accepts positive argument")
}
if num.Number <= 60 {
return newNumberFormulaArg(math.Mod(num.Number, 31.0))
}
return newNumberFormulaArg(float64(timeFromExcelTime(num.Number, false).Day()))
}
// DAYS function returns the number of days between two supplied dates. The
// syntax of the function is:
//
// DAYS(end_date,start_date)
//
func (fn *formulaFuncs) DAYS(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "DAYS requires 2 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
end, start := args.List[0], args.List[1]
return newNumberFormulaArg(end.Number - start.Number)
}
// DAYS360 function returns the number of days between 2 dates, based on a
// 360-day year (12 x 30 months). The syntax of the function is:
//
// DAYS360(start_date,end_date,[method])
//
func (fn *formulaFuncs) DAYS360(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "DAYS360 requires at least 2 arguments")
}
if argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, "DAYS360 requires at most 3 arguments")
}
startDate := toExcelDateArg(argsList.Front().Value.(formulaArg))
if startDate.Type != ArgNumber {
return startDate
}
endDate := toExcelDateArg(argsList.Front().Next().Value.(formulaArg))
if endDate.Type != ArgNumber {
return endDate
}
start, end := timeFromExcelTime(startDate.Number, false), timeFromExcelTime(endDate.Number, false)
sy, sm, sd, ey, em, ed := start.Year(), int(start.Month()), start.Day(), end.Year(), int(end.Month()), end.Day()
method := newBoolFormulaArg(false)
if argsList.Len() > 2 {
if method = argsList.Back().Value.(formulaArg).ToBool(); method.Type != ArgNumber {
return method
}
}
if method.Number == 1 {
if sd == 31 {
sd--
}
if ed == 31 {
ed--
}
} else {
if getDaysInMonth(sy, sm) == sd {
sd = 30
}
if ed > 30 {
if sd < 30 {
em++
ed = 1
} else {
ed = 30
}
}
}
return newNumberFormulaArg(float64(360*(ey-sy) + 30*(em-sm) + (ed - sd)))
}
// ISOWEEKNUM function returns the ISO week number of a supplied date. The
// syntax of the function is:
//
// ISOWEEKNUM(date)
//
func (fn *formulaFuncs) ISOWEEKNUM(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ISOWEEKNUM requires 1 argument")
}
date := argsList.Front().Value.(formulaArg)
num := date.ToNumber()
weekNum := 0
if num.Type != ArgNumber {
dateString := strings.ToLower(date.Value())
if !isDateOnlyFmt(dateString) {
if _, _, _, _, _, err := strToTime(dateString); err.Type == ArgError {
return err
}
}
y, m, d, _, err := strToDate(dateString)
if err.Type == ArgError {
return err
}
_, weekNum = time.Date(y, time.Month(m), d, 0, 0, 0, 0, time.UTC).ISOWeek()
} else {
if num.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
_, weekNum = timeFromExcelTime(num.Number, false).ISOWeek()
}
return newNumberFormulaArg(float64(weekNum))
}
// EDATE function returns a date that is a specified number of months before or
// after a supplied start date. The syntax of function is:
//
// EDATE(start_date,months)
//
func (fn *formulaFuncs) EDATE(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "EDATE requires 2 arguments")
}
date := argsList.Front().Value.(formulaArg)
num := date.ToNumber()
var dateTime time.Time
if num.Type != ArgNumber {
dateString := strings.ToLower(date.Value())
if !isDateOnlyFmt(dateString) {
if _, _, _, _, _, err := strToTime(dateString); err.Type == ArgError {
return err
}
}
y, m, d, _, err := strToDate(dateString)
if err.Type == ArgError {
return err
}
dateTime = time.Date(y, time.Month(m), d, 0, 0, 0, 0, time.Now().Location())
} else {
if num.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
dateTime = timeFromExcelTime(num.Number, false)
}
month := argsList.Back().Value.(formulaArg).ToNumber()
if month.Type != ArgNumber {
return month
}
y, d := dateTime.Year(), dateTime.Day()
m := int(dateTime.Month()) + int(month.Number)
if month.Number < 0 {
y -= int(math.Ceil(-1 * float64(m) / 12))
}
if month.Number > 11 {
y += int(math.Floor(float64(m) / 12))
}
if m = m % 12; m < 0 {
m += 12
}
if d > 28 {
if days := getDaysInMonth(y, m); d > days {
d = days
}
}
result, _ := timeToExcelTime(time.Date(y, time.Month(m), d, 0, 0, 0, 0, time.UTC), false)
return newNumberFormulaArg(result)
}
// EOMONTH function returns the last day of the month, that is a specified
// number of months before or after an initial supplied start date. The syntax
// of the function is:
//
// EOMONTH(start_date,months)
//
func (fn *formulaFuncs) EOMONTH(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "EOMONTH requires 2 arguments")
}
date := argsList.Front().Value.(formulaArg)
num := date.ToNumber()
var dateTime time.Time
if num.Type != ArgNumber {
dateString := strings.ToLower(date.Value())
if !isDateOnlyFmt(dateString) {
if _, _, _, _, _, err := strToTime(dateString); err.Type == ArgError {
return err
}
}
y, m, d, _, err := strToDate(dateString)
if err.Type == ArgError {
return err
}
dateTime = time.Date(y, time.Month(m), d, 0, 0, 0, 0, time.Now().Location())
} else {
if num.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
dateTime = timeFromExcelTime(num.Number, false)
}
months := argsList.Back().Value.(formulaArg).ToNumber()
if months.Type != ArgNumber {
return months
}
y, m := dateTime.Year(), int(dateTime.Month())+int(months.Number)-1
if m < 0 {
y -= int(math.Ceil(-1 * float64(m) / 12))
}
if m > 11 {
y += int(math.Floor(float64(m) / 12))
}
if m = m % 12; m < 0 {
m += 12
}
result, _ := timeToExcelTime(time.Date(y, time.Month(m+1), getDaysInMonth(y, m+1), 0, 0, 0, 0, time.UTC), false)
return newNumberFormulaArg(result)
}
// HOUR function returns an integer representing the hour component of a
// supplied Excel time. The syntax of the function is:
//
// HOUR(serial_number)
//
func (fn *formulaFuncs) HOUR(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "HOUR requires exactly 1 argument")
}
date := argsList.Front().Value.(formulaArg)
num := date.ToNumber()
if num.Type != ArgNumber {
timeString := strings.ToLower(date.Value())
if !isTimeOnlyFmt(timeString) {
_, _, _, _, err := strToDate(timeString)
if err.Type == ArgError {
return err
}
}
h, _, _, pm, _, err := strToTime(timeString)
if err.Type == ArgError {
return err
}
if pm {
h += 12
}
return newNumberFormulaArg(float64(h))
}
if num.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "HOUR only accepts positive argument")
}
return newNumberFormulaArg(float64(timeFromExcelTime(num.Number, false).Hour()))
}
// MINUTE function returns an integer representing the minute component of a
// supplied Excel time. The syntax of the function is:
//
// MINUTE(serial_number)
//
func (fn *formulaFuncs) MINUTE(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "MINUTE requires exactly 1 argument")
}
date := argsList.Front().Value.(formulaArg)
num := date.ToNumber()
if num.Type != ArgNumber {
timeString := strings.ToLower(date.Value())
if !isTimeOnlyFmt(timeString) {
_, _, _, _, err := strToDate(timeString)
if err.Type == ArgError {
return err
}
}
_, m, _, _, _, err := strToTime(timeString)
if err.Type == ArgError {
return err
}
return newNumberFormulaArg(float64(m))
}
if num.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "MINUTE only accepts positive argument")
}
return newNumberFormulaArg(float64(timeFromExcelTime(num.Number, false).Minute()))
}
// MONTH function returns the month of a date represented by a serial number.
// The month is given as an integer, ranging from 1 (January) to 12
// (December). The syntax of the function is:
//
// MONTH(serial_number)
//
func (fn *formulaFuncs) MONTH(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "MONTH requires exactly 1 argument")
}
arg := argsList.Front().Value.(formulaArg)
num := arg.ToNumber()
if num.Type != ArgNumber {
dateString := strings.ToLower(arg.Value())
if !isDateOnlyFmt(dateString) {
if _, _, _, _, _, err := strToTime(dateString); err.Type == ArgError {
return err
}
}
_, month, _, _, err := strToDate(dateString)
if err.Type == ArgError {
return err
}
return newNumberFormulaArg(float64(month))
}
if num.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "MONTH only accepts positive argument")
}
return newNumberFormulaArg(float64(timeFromExcelTime(num.Number, false).Month()))
}
// genWeekendMask generate weekend mask of a series of seven 0's and 1's which
// represent the seven weekdays, starting from Monday.
func genWeekendMask(weekend int) []byte {
if masks, ok := map[int][]int{
1: {5, 6}, 2: {6, 0}, 3: {0, 1}, 4: {1, 2}, 5: {2, 3}, 6: {3, 4}, 7: {4, 5},
11: {6}, 12: {0}, 13: {1}, 14: {2}, 15: {3}, 16: {4}, 17: {5},
}[weekend]; ok {
mask := make([]byte, 7)
for _, idx := range masks {
mask[idx] = 1
}
return mask
}
return nil
}
// isWorkday check if the date is workday.
func isWorkday(weekendMask []byte, date float64) bool {
dateTime := timeFromExcelTime(date, false)
weekday := dateTime.Weekday()
if weekday == time.Sunday {
weekday = 7
}
return weekendMask[weekday-1] == 0
}
// prepareWorkday returns weekend mask and workdays pre week by given days
// counted as weekend.
func prepareWorkday(weekend formulaArg) ([]byte, int) {
weekendArg := weekend.ToNumber()
if weekendArg.Type != ArgNumber {
return nil, 0
}
var weekendMask []byte
var workdaysPerWeek int
if len(weekend.Value()) == 7 {
// possible string values for the weekend argument
for _, mask := range weekend.Value() {
if mask != '0' && mask != '1' {
return nil, 0
}
weekendMask = append(weekendMask, byte(mask)-48)
}
} else {
weekendMask = genWeekendMask(int(weekendArg.Number))
}
for _, mask := range weekendMask {
if mask == 0 {
workdaysPerWeek++
}
}
return weekendMask, workdaysPerWeek
}
// toExcelDateArg function converts a text representation of a time, into an
// Excel date time number formula argument.
func toExcelDateArg(arg formulaArg) formulaArg {
num := arg.ToNumber()
if num.Type != ArgNumber {
dateString := strings.ToLower(arg.Value())
if !isDateOnlyFmt(dateString) {
if _, _, _, _, _, err := strToTime(dateString); err.Type == ArgError {
return err
}
}
y, m, d, _, err := strToDate(dateString)
if err.Type == ArgError {
return err
}
num.Number, _ = timeToExcelTime(time.Date(y, time.Month(m), d, 0, 0, 0, 0, time.UTC), false)
return newNumberFormulaArg(num.Number)
}
if arg.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return num
}
// prepareHolidays function converts array type formula arguments to into an
// Excel date time number formula arguments list.
func prepareHolidays(args formulaArg) []int {
var holidays []int
for _, arg := range args.ToList() {
num := toExcelDateArg(arg)
if num.Type != ArgNumber {
continue
}
holidays = append(holidays, int(math.Ceil(num.Number)))
}
return holidays
}
// workdayIntl is an implementation of the formula function WORKDAY.INTL.
func workdayIntl(endDate, sign int, holidays []int, weekendMask []byte, startDate float64) int {
for i := 0; i < len(holidays); i++ {
holiday := holidays[i]
if sign > 0 {
if holiday > endDate {
break
}
} else {
if holiday < endDate {
break
}
}
if sign > 0 {
if holiday > int(math.Ceil(startDate)) {
if isWorkday(weekendMask, float64(holiday)) {
endDate += sign
for !isWorkday(weekendMask, float64(endDate)) {
endDate += sign
}
}
}
} else {
if holiday < int(math.Ceil(startDate)) {
if isWorkday(weekendMask, float64(holiday)) {
endDate += sign
for !isWorkday(weekendMask, float64(endDate)) {
endDate += sign
}
}
}
}
}
return endDate
}
// NETWORKDAYS function calculates the number of work days between two supplied
// dates (including the start and end date). The calculation includes all
// weekdays (Mon - Fri), excluding a supplied list of holidays. The syntax of
// the function is:
//
// NETWORKDAYS(start_date,end_date,[holidays])
//
func (fn *formulaFuncs) NETWORKDAYS(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "NETWORKDAYS requires at least 2 arguments")
}
if argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, "NETWORKDAYS requires at most 3 arguments")
}
args := list.New()
args.PushBack(argsList.Front().Value.(formulaArg))
args.PushBack(argsList.Front().Next().Value.(formulaArg))
args.PushBack(newNumberFormulaArg(1))
if argsList.Len() == 3 {
args.PushBack(argsList.Back().Value.(formulaArg))
}
return fn.NETWORKDAYSdotINTL(args)
}
// NETWORKDAYSdotINTL function calculates the number of whole work days between
// two supplied dates, excluding weekends and holidays. The function allows
// the user to specify which days are counted as weekends and holidays. The
// syntax of the function is:
//
// NETWORKDAYS.INTL(start_date,end_date,[weekend],[holidays])
//
func (fn *formulaFuncs) NETWORKDAYSdotINTL(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "NETWORKDAYS.INTL requires at least 2 arguments")
}
if argsList.Len() > 4 {
return newErrorFormulaArg(formulaErrorVALUE, "NETWORKDAYS.INTL requires at most 4 arguments")
}
startDate := toExcelDateArg(argsList.Front().Value.(formulaArg))
if startDate.Type != ArgNumber {
return startDate
}
endDate := toExcelDateArg(argsList.Front().Next().Value.(formulaArg))
if endDate.Type != ArgNumber {
return endDate
}
weekend := newNumberFormulaArg(1)
if argsList.Len() > 2 {
weekend = argsList.Front().Next().Next().Value.(formulaArg)
}
var holidays []int
if argsList.Len() == 4 {
holidays = prepareHolidays(argsList.Back().Value.(formulaArg))
sort.Ints(holidays)
}
weekendMask, workdaysPerWeek := prepareWorkday(weekend)
if workdaysPerWeek == 0 {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
sign := 1
if startDate.Number > endDate.Number {
sign = -1
temp := startDate.Number
startDate.Number = endDate.Number
endDate.Number = temp
}
offset := endDate.Number - startDate.Number
count := int(math.Floor(offset/7) * float64(workdaysPerWeek))
daysMod := int(offset) % 7
for daysMod >= 0 {
if isWorkday(weekendMask, endDate.Number-float64(daysMod)) {
count++
}
daysMod--
}
for i := 0; i < len(holidays); i++ {
holiday := float64(holidays[i])
if isWorkday(weekendMask, holiday) && holiday >= startDate.Number && holiday <= endDate.Number {
count--
}
}
return newNumberFormulaArg(float64(sign * count))
}
// WORKDAY function returns a date that is a supplied number of working days
// (excluding weekends and holidays) ahead of a given start date. The syntax
// of the function is:
//
// WORKDAY(start_date,days,[holidays])
//
func (fn *formulaFuncs) WORKDAY(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "WORKDAY requires at least 2 arguments")
}
if argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, "WORKDAY requires at most 3 arguments")
}
args := list.New()
args.PushBack(argsList.Front().Value.(formulaArg))
args.PushBack(argsList.Front().Next().Value.(formulaArg))
args.PushBack(newNumberFormulaArg(1))
if argsList.Len() == 3 {
args.PushBack(argsList.Back().Value.(formulaArg))
}
return fn.WORKDAYdotINTL(args)
}
// WORKDAYdotINTL function returns a date that is a supplied number of working
// days (excluding weekends and holidays) ahead of a given start date. The
// function allows the user to specify which days of the week are counted as
// weekends. The syntax of the function is:
//
// WORKDAY.INTL(start_date,days,[weekend],[holidays])
//
func (fn *formulaFuncs) WORKDAYdotINTL(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "WORKDAY.INTL requires at least 2 arguments")
}
if argsList.Len() > 4 {
return newErrorFormulaArg(formulaErrorVALUE, "WORKDAY.INTL requires at most 4 arguments")
}
startDate := toExcelDateArg(argsList.Front().Value.(formulaArg))
if startDate.Type != ArgNumber {
return startDate
}
days := argsList.Front().Next().Value.(formulaArg).ToNumber()
if days.Type != ArgNumber {
return days
}
weekend := newNumberFormulaArg(1)
if argsList.Len() > 2 {
weekend = argsList.Front().Next().Next().Value.(formulaArg)
}
var holidays []int
if argsList.Len() == 4 {
holidays = prepareHolidays(argsList.Back().Value.(formulaArg))
sort.Ints(holidays)
}
if days.Number == 0 {
return newNumberFormulaArg(math.Ceil(startDate.Number))
}
weekendMask, workdaysPerWeek := prepareWorkday(weekend)
if workdaysPerWeek == 0 {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
sign := 1
if days.Number < 0 {
sign = -1
}
offset := int(days.Number) / workdaysPerWeek
daysMod := int(days.Number) % workdaysPerWeek
endDate := int(math.Ceil(startDate.Number)) + offset*7
if daysMod == 0 {
for !isWorkday(weekendMask, float64(endDate)) {
endDate -= sign
}
} else {
for daysMod != 0 {
endDate += sign
if isWorkday(weekendMask, float64(endDate)) {
if daysMod < 0 {
daysMod++
continue
}
daysMod--
}
}
}
return newNumberFormulaArg(float64(workdayIntl(endDate, sign, holidays, weekendMask, startDate.Number)))
}
// YEAR function returns an integer representing the year of a supplied date.
// The syntax of the function is:
//
// YEAR(serial_number)
//
func (fn *formulaFuncs) YEAR(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "YEAR requires exactly 1 argument")
}
arg := argsList.Front().Value.(formulaArg)
num := arg.ToNumber()
if num.Type != ArgNumber {
dateString := strings.ToLower(arg.Value())
if !isDateOnlyFmt(dateString) {
if _, _, _, _, _, err := strToTime(dateString); err.Type == ArgError {
return err
}
}
year, _, _, _, err := strToDate(dateString)
if err.Type == ArgError {
return err
}
return newNumberFormulaArg(float64(year))
}
if num.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "YEAR only accepts positive argument")
}
return newNumberFormulaArg(float64(timeFromExcelTime(num.Number, false).Year()))
}
// yearFracBasisCond is an implementation of the yearFracBasis1.
func yearFracBasisCond(sy, sm, sd, ey, em, ed int) bool {
return (isLeapYear(sy) && (sm < 2 || (sm == 2 && sd <= 29))) || (isLeapYear(ey) && (em > 2 || (em == 2 && ed == 29)))
}
// yearFracBasis0 function returns the fraction of a year that between two
// supplied dates in US (NASD) 30/360 type of day.
func yearFracBasis0(startDate, endDate float64) (dayDiff, daysInYear float64) {
startTime, endTime := timeFromExcelTime(startDate, false), timeFromExcelTime(endDate, false)
sy, smM, sd := startTime.Date()
ey, emM, ed := endTime.Date()
sm, em := int(smM), int(emM)
if sd == 31 {
sd--
}
if sd == 30 && ed == 31 {
ed--
} else if leap := isLeapYear(sy); sm == 2 && ((leap && sd == 29) || (!leap && sd == 28)) {
sd = 30
if leap := isLeapYear(ey); em == 2 && ((leap && ed == 29) || (!leap && ed == 28)) {
ed = 30
}
}
dayDiff = float64((ey-sy)*360 + (em-sm)*30 + (ed - sd))
daysInYear = 360
return
}
// yearFracBasis1 function returns the fraction of a year that between two
// supplied dates in actual type of day.
func yearFracBasis1(startDate, endDate float64) (dayDiff, daysInYear float64) {
startTime, endTime := timeFromExcelTime(startDate, false), timeFromExcelTime(endDate, false)
sy, smM, sd := startTime.Date()
ey, emM, ed := endTime.Date()
sm, em := int(smM), int(emM)
dayDiff = endDate - startDate
isYearDifferent := sy != ey
if isYearDifferent && (ey != sy+1 || sm < em || (sm == em && sd < ed)) {
dayCount := 0
for y := sy; y <= ey; y++ {
dayCount += getYearDays(y, 1)
}
daysInYear = float64(dayCount) / float64(ey-sy+1)
} else {
if !isYearDifferent && isLeapYear(sy) {
daysInYear = 366
} else {
if isYearDifferent && yearFracBasisCond(sy, sm, sd, ey, em, ed) {
daysInYear = 366
} else {
daysInYear = 365
}
}
}
return
}
// yearFracBasis4 function returns the fraction of a year that between two
// supplied dates in European 30/360 type of day.
func yearFracBasis4(startDate, endDate float64) (dayDiff, daysInYear float64) {
startTime, endTime := timeFromExcelTime(startDate, false), timeFromExcelTime(endDate, false)
sy, smM, sd := startTime.Date()
ey, emM, ed := endTime.Date()
sm, em := int(smM), int(emM)
if sd == 31 {
sd--
}
if ed == 31 {
ed--
}
dayDiff = float64((ey-sy)*360 + (em-sm)*30 + (ed - sd))
daysInYear = 360
return
}
// yearFrac is an implementation of the formula function YEARFRAC.
func yearFrac(startDate, endDate float64, basis int) formulaArg {
startTime, endTime := timeFromExcelTime(startDate, false), timeFromExcelTime(endDate, false)
if startTime == endTime {
return newNumberFormulaArg(0)
}
var dayDiff, daysInYear float64
switch basis {
case 0:
dayDiff, daysInYear = yearFracBasis0(startDate, endDate)
case 1:
dayDiff, daysInYear = yearFracBasis1(startDate, endDate)
case 2:
dayDiff = endDate - startDate
daysInYear = 360
case 3:
dayDiff = endDate - startDate
daysInYear = 365
case 4:
dayDiff, daysInYear = yearFracBasis4(startDate, endDate)
default:
return newErrorFormulaArg(formulaErrorNUM, "invalid basis")
}
return newNumberFormulaArg(dayDiff / daysInYear)
}
// getYearDays return days of the year with specifying the type of day count
// basis to be used.
func getYearDays(year, basis int) int {
switch basis {
case 1:
if isLeapYear(year) {
return 366
}
return 365
case 3:
return 365
default:
return 360
}
}
// YEARFRAC function returns the fraction of a year that is represented by the
// number of whole days between two supplied dates. The syntax of the
// function is:
//
// YEARFRAC(start_date,end_date,[basis])
//
func (fn *formulaFuncs) YEARFRAC(argsList *list.List) formulaArg {
if argsList.Len() != 2 && argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "YEARFRAC requires 3 or 4 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
start, end := args.List[0], args.List[1]
basis := newNumberFormulaArg(0)
if argsList.Len() == 3 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return basis
}
}
return yearFrac(start.Number, end.Number, int(basis.Number))
}
// NOW function returns the current date and time. The function receives no
// arguments and therefore. The syntax of the function is:
//
// NOW()
//
func (fn *formulaFuncs) NOW(argsList *list.List) formulaArg {
if argsList.Len() != 0 {
return newErrorFormulaArg(formulaErrorVALUE, "NOW accepts no arguments")
}
now := time.Now()
_, offset := now.Zone()
return newNumberFormulaArg(25569.0 + float64(now.Unix()+int64(offset))/86400)
}
// SECOND function returns an integer representing the second component of a
// supplied Excel time. The syntax of the function is:
//
// SECOND(serial_number)
//
func (fn *formulaFuncs) SECOND(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "SECOND requires exactly 1 argument")
}
date := argsList.Front().Value.(formulaArg)
num := date.ToNumber()
if num.Type != ArgNumber {
timeString := strings.ToLower(date.Value())
if !isTimeOnlyFmt(timeString) {
_, _, _, _, err := strToDate(timeString)
if err.Type == ArgError {
return err
}
}
_, _, s, _, _, err := strToTime(timeString)
if err.Type == ArgError {
return err
}
return newNumberFormulaArg(float64(int(s) % 60))
}
if num.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "SECOND only accepts positive argument")
}
return newNumberFormulaArg(float64(timeFromExcelTime(num.Number, false).Second()))
}
// TIME function accepts three integer arguments representing hours, minutes
// and seconds, and returns an Excel time. I.e. the function returns the
// decimal value that represents the time in Excel. The syntax of the
// function is:
//
// TIME(hour,minute,second)
//
func (fn *formulaFuncs) TIME(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "TIME requires 3 number arguments")
}
h := argsList.Front().Value.(formulaArg).ToNumber()
m := argsList.Front().Next().Value.(formulaArg).ToNumber()
s := argsList.Back().Value.(formulaArg).ToNumber()
if h.Type != ArgNumber || m.Type != ArgNumber || s.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, "TIME requires 3 number arguments")
}
t := (h.Number*3600 + m.Number*60 + s.Number) / 86400
if t < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(t)
}
// TIMEVALUE function converts a text representation of a time, into an Excel
// time. The syntax of the function is:
//
// TIMEVALUE(time_text)
//
func (fn *formulaFuncs) TIMEVALUE(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "TIMEVALUE requires exactly 1 argument")
}
date := argsList.Front().Value.(formulaArg)
timeString := strings.ToLower(date.Value())
if !isTimeOnlyFmt(timeString) {
_, _, _, _, err := strToDate(timeString)
if err.Type == ArgError {
return err
}
}
h, m, s, pm, _, err := strToTime(timeString)
if err.Type == ArgError {
return err
}
if pm {
h += 12
}
args := list.New()
args.PushBack(newNumberFormulaArg(float64(h)))
args.PushBack(newNumberFormulaArg(float64(m)))
args.PushBack(newNumberFormulaArg(s))
return fn.TIME(args)
}
// TODAY function returns the current date. The function has no arguments and
// therefore. The syntax of the function is:
//
// TODAY()
//
func (fn *formulaFuncs) TODAY(argsList *list.List) formulaArg {
if argsList.Len() != 0 {
return newErrorFormulaArg(formulaErrorVALUE, "TODAY accepts no arguments")
}
now := time.Now()
_, offset := now.Zone()
return newNumberFormulaArg(daysBetween(excelMinTime1900.Unix(), now.Unix()+int64(offset)) + 1)
}
// makeDate return date as a Unix time, the number of seconds elapsed since
// January 1, 1970 UTC.
func makeDate(y int, m time.Month, d int) int64 {
if y == 1900 && int(m) <= 2 {
d--
}
date := time.Date(y, m, d, 0, 0, 0, 0, time.UTC)
return date.Unix()
}
// daysBetween return time interval of the given start timestamp and end
// timestamp.
func daysBetween(startDate, endDate int64) float64 {
return float64(int(0.5 + float64((endDate-startDate)/86400)))
}
// WEEKDAY function returns an integer representing the day of the week for a
// supplied date. The syntax of the function is:
//
// WEEKDAY(serial_number,[return_type])
//
func (fn *formulaFuncs) WEEKDAY(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "WEEKDAY requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "WEEKDAY allows at most 2 arguments")
}
sn := argsList.Front().Value.(formulaArg)
num := sn.ToNumber()
weekday, returnType := 0, 1
if num.Type != ArgNumber {
dateString := strings.ToLower(sn.Value())
if !isDateOnlyFmt(dateString) {
if _, _, _, _, _, err := strToTime(dateString); err.Type == ArgError {
return err
}
}
y, m, d, _, err := strToDate(dateString)
if err.Type == ArgError {
return err
}
weekday = int(time.Date(y, time.Month(m), d, 0, 0, 0, 0, time.Now().Location()).Weekday())
} else {
if num.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
weekday = int(timeFromExcelTime(num.Number, false).Weekday())
}
if argsList.Len() == 2 {
returnTypeArg := argsList.Back().Value.(formulaArg).ToNumber()
if returnTypeArg.Type != ArgNumber {
return returnTypeArg
}
returnType = int(returnTypeArg.Number)
}
if returnType == 2 {
returnType = 11
}
weekday++
if returnType == 1 {
return newNumberFormulaArg(float64(weekday))
}
if returnType == 3 {
return newNumberFormulaArg(float64((weekday + 6 - 1) % 7))
}
if returnType >= 11 && returnType <= 17 {
return newNumberFormulaArg(float64((weekday+6-(returnType-10))%7 + 1))
}
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
// weeknum is an implementation of the formula function WEEKNUM.
func (fn *formulaFuncs) weeknum(snTime time.Time, returnType int) formulaArg {
days := snTime.YearDay()
weekMod, weekNum := days%7, math.Ceil(float64(days)/7)
if weekMod == 0 {
weekMod = 7
}
year := snTime.Year()
firstWeekday := int(time.Date(year, time.January, 1, 0, 0, 0, 0, time.UTC).Weekday())
var offset int
switch returnType {
case 1, 17:
offset = 0
case 2, 11, 21:
offset = 1
case 12, 13, 14, 15, 16:
offset = returnType - 10
default:
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
padding := offset + 7 - firstWeekday
if padding > 7 {
padding -= 7
}
if weekMod > padding {
weekNum++
}
if returnType == 21 && (firstWeekday == 0 || firstWeekday > 4) {
if weekNum--; weekNum < 1 {
if weekNum = 52; int(time.Date(year-1, time.January, 1, 0, 0, 0, 0, time.UTC).Weekday()) < 4 {
weekNum++
}
}
}
return newNumberFormulaArg(weekNum)
}
// WEEKNUM function returns an integer representing the week number (from 1 to
// 53) of the year. The syntax of the function is:
//
// WEEKNUM(serial_number,[return_type])
//
func (fn *formulaFuncs) WEEKNUM(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "WEEKNUM requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "WEEKNUM allows at most 2 arguments")
}
sn := argsList.Front().Value.(formulaArg)
num, returnType := sn.ToNumber(), 1
var snTime time.Time
if num.Type != ArgNumber {
dateString := strings.ToLower(sn.Value())
if !isDateOnlyFmt(dateString) {
if _, _, _, _, _, err := strToTime(dateString); err.Type == ArgError {
return err
}
}
y, m, d, _, err := strToDate(dateString)
if err.Type == ArgError {
return err
}
snTime = time.Date(y, time.Month(m), d, 0, 0, 0, 0, time.Now().Location())
} else {
if num.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
snTime = timeFromExcelTime(num.Number, false)
}
if argsList.Len() == 2 {
returnTypeArg := argsList.Back().Value.(formulaArg).ToNumber()
if returnTypeArg.Type != ArgNumber {
return returnTypeArg
}
returnType = int(returnTypeArg.Number)
}
return fn.weeknum(snTime, returnType)
}
// Text Functions
// CHAR function returns the character relating to a supplied character set
// number (from 1 to 255). syntax of the function is:
//
// CHAR(number)
//
func (fn *formulaFuncs) CHAR(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "CHAR requires 1 argument")
}
arg := argsList.Front().Value.(formulaArg).ToNumber()
if arg.Type != ArgNumber {
return arg
}
num := int(arg.Number)
if num < 0 || num > MaxFieldLength {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
return newStringFormulaArg(fmt.Sprintf("%c", num))
}
// CLEAN removes all non-printable characters from a supplied text string. The
// syntax of the function is:
//
// CLEAN(text)
//
func (fn *formulaFuncs) CLEAN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "CLEAN requires 1 argument")
}
b := bytes.Buffer{}
for _, c := range argsList.Front().Value.(formulaArg).Value() {
if c > 31 {
b.WriteRune(c)
}
}
return newStringFormulaArg(b.String())
}
// CODE function converts the first character of a supplied text string into
// the associated numeric character set code used by your computer. The
// syntax of the function is:
//
// CODE(text)
//
func (fn *formulaFuncs) CODE(argsList *list.List) formulaArg {
return fn.code("CODE", argsList)
}
// code is an implementation of the formula functions CODE and UNICODE.
func (fn *formulaFuncs) code(name string, argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 1 argument", name))
}
text := argsList.Front().Value.(formulaArg).Value()
if len(text) == 0 {
if name == "CODE" {
return newNumberFormulaArg(0)
}
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
return newNumberFormulaArg(float64(text[0]))
}
// CONCAT function joins together a series of supplied text strings into one
// combined text string.
//
// CONCAT(text1,[text2],...)
//
func (fn *formulaFuncs) CONCAT(argsList *list.List) formulaArg {
return fn.concat("CONCAT", argsList)
}
// CONCATENATE function joins together a series of supplied text strings into
// one combined text string.
//
// CONCATENATE(text1,[text2],...)
//
func (fn *formulaFuncs) CONCATENATE(argsList *list.List) formulaArg {
return fn.concat("CONCATENATE", argsList)
}
// concat is an implementation of the formula functions CONCAT and
// CONCATENATE.
func (fn *formulaFuncs) concat(name string, argsList *list.List) formulaArg {
buf := bytes.Buffer{}
for arg := argsList.Front(); arg != nil; arg = arg.Next() {
token := arg.Value.(formulaArg)
switch token.Type {
case ArgString:
buf.WriteString(token.String)
case ArgNumber:
if token.Boolean {
if token.Number == 0 {
buf.WriteString("FALSE")
} else {
buf.WriteString("TRUE")
}
} else {
buf.WriteString(token.Value())
}
default:
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires arguments to be strings", name))
}
}
return newStringFormulaArg(buf.String())
}
// EXACT function tests if two supplied text strings or values are exactly
// equal and if so, returns TRUE; Otherwise, the function returns FALSE. The
// function is case-sensitive. The syntax of the function is:
//
// EXACT(text1,text2)
//
func (fn *formulaFuncs) EXACT(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "EXACT requires 2 arguments")
}
text1 := argsList.Front().Value.(formulaArg).Value()
text2 := argsList.Back().Value.(formulaArg).Value()
return newBoolFormulaArg(text1 == text2)
}
// FIXED function rounds a supplied number to a specified number of decimal
// places and then converts this into text. The syntax of the function is:
//
// FIXED(number,[decimals],[no_commas])
//
func (fn *formulaFuncs) FIXED(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "FIXED requires at least 1 argument")
}
if argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, "FIXED allows at most 3 arguments")
}
numArg := argsList.Front().Value.(formulaArg).ToNumber()
if numArg.Type != ArgNumber {
return numArg
}
precision, decimals, noCommas := 0, 0, false
s := strings.Split(argsList.Front().Value.(formulaArg).Value(), ".")
if argsList.Len() == 1 && len(s) == 2 {
precision = len(s[1])
decimals = len(s[1])
}
if argsList.Len() >= 2 {
decimalsArg := argsList.Front().Next().Value.(formulaArg).ToNumber()
if decimalsArg.Type != ArgNumber {
return decimalsArg
}
decimals = int(decimalsArg.Number)
}
if argsList.Len() == 3 {
noCommasArg := argsList.Back().Value.(formulaArg).ToBool()
if noCommasArg.Type == ArgError {
return noCommasArg
}
noCommas = noCommasArg.Boolean
}
n := math.Pow(10, float64(decimals))
r := numArg.Number * n
fixed := float64(int(r+math.Copysign(0.5, r))) / n
if decimals > 0 {
precision = decimals
}
if noCommas {
return newStringFormulaArg(fmt.Sprintf(fmt.Sprintf("%%.%df", precision), fixed))
}
p := message.NewPrinter(language.English)
return newStringFormulaArg(p.Sprintf(fmt.Sprintf("%%.%df", precision), fixed))
}
// FIND function returns the position of a specified character or sub-string
// within a supplied text string. The function is case-sensitive. The syntax
// of the function is:
//
// FIND(find_text,within_text,[start_num])
//
func (fn *formulaFuncs) FIND(argsList *list.List) formulaArg {
return fn.find("FIND", argsList)
}
// FINDB counts each double-byte character as 2 when you have enabled the
// editing of a language that supports DBCS and then set it as the default
// language. Otherwise, FINDB counts each character as 1. The syntax of the
// function is:
//
// FINDB(find_text,within_text,[start_num])
//
func (fn *formulaFuncs) FINDB(argsList *list.List) formulaArg {
return fn.find("FINDB", argsList)
}
// find is an implementation of the formula functions FIND and FINDB.
func (fn *formulaFuncs) find(name string, argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 2 arguments", name))
}
if argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s allows at most 3 arguments", name))
}
findText := argsList.Front().Value.(formulaArg).Value()
withinText := argsList.Front().Next().Value.(formulaArg).Value()
startNum, result := 1, 1
if argsList.Len() == 3 {
numArg := argsList.Back().Value.(formulaArg).ToNumber()
if numArg.Type != ArgNumber {
return numArg
}
if numArg.Number < 0 {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
startNum = int(numArg.Number)
}
if findText == "" {
return newNumberFormulaArg(float64(startNum))
}
for idx := range withinText {
if result < startNum {
result++
}
if strings.Index(withinText[idx:], findText) == 0 {
return newNumberFormulaArg(float64(result))
}
result++
}
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
// LEFT function returns a specified number of characters from the start of a
// supplied text string. The syntax of the function is:
//
// LEFT(text,[num_chars])
//
func (fn *formulaFuncs) LEFT(argsList *list.List) formulaArg {
return fn.leftRight("LEFT", argsList)
}
// LEFTB returns the first character or characters in a text string, based on
// the number of bytes you specify. The syntax of the function is:
//
// LEFTB(text,[num_bytes])
//
func (fn *formulaFuncs) LEFTB(argsList *list.List) formulaArg {
return fn.leftRight("LEFTB", argsList)
}
// leftRight is an implementation of the formula functions LEFT, LEFTB, RIGHT,
// RIGHTB. TODO: support DBCS include Japanese, Chinese (Simplified), Chinese
// (Traditional), and Korean.
func (fn *formulaFuncs) leftRight(name string, argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 1 argument", name))
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s allows at most 2 arguments", name))
}
text, numChars := argsList.Front().Value.(formulaArg).Value(), 1
if argsList.Len() == 2 {
numArg := argsList.Back().Value.(formulaArg).ToNumber()
if numArg.Type != ArgNumber {
return numArg
}
if numArg.Number < 0 {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
numChars = int(numArg.Number)
}
if len(text) > numChars {
if name == "LEFT" || name == "LEFTB" {
return newStringFormulaArg(text[:numChars])
}
return newStringFormulaArg(text[len(text)-numChars:])
}
return newStringFormulaArg(text)
}
// LEN returns the length of a supplied text string. The syntax of the
// function is:
//
// LEN(text)
//
func (fn *formulaFuncs) LEN(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "LEN requires 1 string argument")
}
return newStringFormulaArg(strconv.Itoa(len(argsList.Front().Value.(formulaArg).String)))
}
// LENB returns the number of bytes used to represent the characters in a text
// string. LENB counts 2 bytes per character only when a DBCS language is set
// as the default language. Otherwise LENB behaves the same as LEN, counting
// 1 byte per character. The syntax of the function is:
//
// LENB(text)
//
// TODO: the languages that support DBCS include Japanese, Chinese
// (Simplified), Chinese (Traditional), and Korean.
func (fn *formulaFuncs) LENB(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "LENB requires 1 string argument")
}
return newStringFormulaArg(strconv.Itoa(len(argsList.Front().Value.(formulaArg).String)))
}
// LOWER converts all characters in a supplied text string to lower case. The
// syntax of the function is:
//
// LOWER(text)
//
func (fn *formulaFuncs) LOWER(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "LOWER requires 1 argument")
}
return newStringFormulaArg(strings.ToLower(argsList.Front().Value.(formulaArg).String))
}
// MID function returns a specified number of characters from the middle of a
// supplied text string. The syntax of the function is:
//
// MID(text,start_num,num_chars)
//
func (fn *formulaFuncs) MID(argsList *list.List) formulaArg {
return fn.mid("MID", argsList)
}
// MIDB returns a specific number of characters from a text string, starting
// at the position you specify, based on the number of bytes you specify. The
// syntax of the function is:
//
// MID(text,start_num,num_chars)
//
func (fn *formulaFuncs) MIDB(argsList *list.List) formulaArg {
return fn.mid("MIDB", argsList)
}
// mid is an implementation of the formula functions MID and MIDB. TODO:
// support DBCS include Japanese, Chinese (Simplified), Chinese
// (Traditional), and Korean.
func (fn *formulaFuncs) mid(name string, argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 3 arguments", name))
}
text := argsList.Front().Value.(formulaArg).Value()
startNumArg, numCharsArg := argsList.Front().Next().Value.(formulaArg).ToNumber(), argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if startNumArg.Type != ArgNumber {
return startNumArg
}
if numCharsArg.Type != ArgNumber {
return numCharsArg
}
startNum := int(startNumArg.Number)
if startNum < 0 {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
textLen := len(text)
if startNum > textLen {
return newStringFormulaArg("")
}
startNum--
endNum := startNum + int(numCharsArg.Number)
if endNum > textLen+1 {
return newStringFormulaArg(text[startNum:])
}
return newStringFormulaArg(text[startNum:endNum])
}
// PROPER converts all characters in a supplied text string to proper case
// (i.e. all letters that do not immediately follow another letter are set to
// upper case and all other characters are lower case). The syntax of the
// function is:
//
// PROPER(text)
//
func (fn *formulaFuncs) PROPER(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "PROPER requires 1 argument")
}
buf := bytes.Buffer{}
isLetter := false
for _, char := range argsList.Front().Value.(formulaArg).String {
if !isLetter && unicode.IsLetter(char) {
buf.WriteRune(unicode.ToUpper(char))
} else {
buf.WriteRune(unicode.ToLower(char))
}
isLetter = unicode.IsLetter(char)
}
return newStringFormulaArg(buf.String())
}
// REPLACE function replaces all or part of a text string with another string.
// The syntax of the function is:
//
// REPLACE(old_text,start_num,num_chars,new_text)
//
func (fn *formulaFuncs) REPLACE(argsList *list.List) formulaArg {
return fn.replace("REPLACE", argsList)
}
// REPLACEB replaces part of a text string, based on the number of bytes you
// specify, with a different text string.
//
// REPLACEB(old_text,start_num,num_chars,new_text)
//
func (fn *formulaFuncs) REPLACEB(argsList *list.List) formulaArg {
return fn.replace("REPLACEB", argsList)
}
// replace is an implementation of the formula functions REPLACE and REPLACEB.
// TODO: support DBCS include Japanese, Chinese (Simplified), Chinese
// (Traditional), and Korean.
func (fn *formulaFuncs) replace(name string, argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 4 arguments", name))
}
oldText, newText := argsList.Front().Value.(formulaArg).Value(), argsList.Back().Value.(formulaArg).Value()
startNumArg, numCharsArg := argsList.Front().Next().Value.(formulaArg).ToNumber(), argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if startNumArg.Type != ArgNumber {
return startNumArg
}
if numCharsArg.Type != ArgNumber {
return numCharsArg
}
oldTextLen, startIdx := len(oldText), int(startNumArg.Number)
if startIdx > oldTextLen {
startIdx = oldTextLen + 1
}
endIdx := startIdx + int(numCharsArg.Number)
if endIdx > oldTextLen {
endIdx = oldTextLen + 1
}
if startIdx < 1 || endIdx < 1 {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
result := oldText[:startIdx-1] + newText + oldText[endIdx-1:]
return newStringFormulaArg(result)
}
// REPT function returns a supplied text string, repeated a specified number
// of times. The syntax of the function is:
//
// REPT(text,number_times)
//
func (fn *formulaFuncs) REPT(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "REPT requires 2 arguments")
}
text := argsList.Front().Value.(formulaArg)
if text.Type != ArgString {
return newErrorFormulaArg(formulaErrorVALUE, "REPT requires first argument to be a string")
}
times := argsList.Back().Value.(formulaArg).ToNumber()
if times.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, "REPT requires second argument to be a number")
}
if times.Number < 0 {
return newErrorFormulaArg(formulaErrorVALUE, "REPT requires second argument to be >= 0")
}
if times.Number == 0 {
return newStringFormulaArg("")
}
buf := bytes.Buffer{}
for i := 0; i < int(times.Number); i++ {
buf.WriteString(text.String)
}
return newStringFormulaArg(buf.String())
}
// RIGHT function returns a specified number of characters from the end of a
// supplied text string. The syntax of the function is:
//
// RIGHT(text,[num_chars])
//
func (fn *formulaFuncs) RIGHT(argsList *list.List) formulaArg {
return fn.leftRight("RIGHT", argsList)
}
// RIGHTB returns the last character or characters in a text string, based on
// the number of bytes you specify. The syntax of the function is:
//
// RIGHTB(text,[num_bytes])
//
func (fn *formulaFuncs) RIGHTB(argsList *list.List) formulaArg {
return fn.leftRight("RIGHTB", argsList)
}
// SUBSTITUTE function replaces one or more instances of a given text string,
// within an original text string. The syntax of the function is:
//
// SUBSTITUTE(text,old_text,new_text,[instance_num])
//
func (fn *formulaFuncs) SUBSTITUTE(argsList *list.List) formulaArg {
if argsList.Len() != 3 && argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "SUBSTITUTE requires 3 or 4 arguments")
}
text, oldText := argsList.Front().Value.(formulaArg), argsList.Front().Next().Value.(formulaArg)
newText, instanceNum := argsList.Front().Next().Next().Value.(formulaArg), 0
if argsList.Len() == 3 {
return newStringFormulaArg(strings.ReplaceAll(text.Value(), oldText.Value(), newText.Value()))
}
instanceNumArg := argsList.Back().Value.(formulaArg).ToNumber()
if instanceNumArg.Type != ArgNumber {
return instanceNumArg
}
instanceNum = int(instanceNumArg.Number)
if instanceNum < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "instance_num should be > 0")
}
str, oldTextLen, count, chars, pos := text.Value(), len(oldText.Value()), instanceNum, 0, -1
for {
count--
index := strings.Index(str, oldText.Value())
if index == -1 {
pos = -1
break
} else {
pos = index + chars
if count == 0 {
break
}
idx := oldTextLen + index
chars += idx
str = str[idx:]
}
}
if pos == -1 {
return newStringFormulaArg(text.Value())
}
pre, post := text.Value()[:pos], text.Value()[pos+oldTextLen:]
return newStringFormulaArg(pre + newText.Value() + post)
}
// TEXTJOIN function joins together a series of supplied text strings into one
// combined text string. The user can specify a delimiter to add between the
// individual text items, if required. The syntax of the function is:
//
// TEXTJOIN([delimiter],[ignore_empty],text1,[text2],...)
//
func (fn *formulaFuncs) TEXTJOIN(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "TEXTJOIN requires at least 3 arguments")
}
if argsList.Len() > 252 {
return newErrorFormulaArg(formulaErrorVALUE, "TEXTJOIN accepts at most 252 arguments")
}
delimiter := argsList.Front().Value.(formulaArg)
ignoreEmpty := argsList.Front().Next().Value.(formulaArg).ToBool()
if ignoreEmpty.Type != ArgNumber {
return ignoreEmpty
}
args, ok := textJoin(argsList.Front().Next().Next(), []string{}, ignoreEmpty.Number != 0)
if ok.Type != ArgNumber {
return ok
}
result := strings.Join(args, delimiter.Value())
if len(result) > TotalCellChars {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("TEXTJOIN function exceeds %d characters", TotalCellChars))
}
return newStringFormulaArg(result)
}
// textJoin is an implementation of the formula function TEXTJOIN.
func textJoin(arg *list.Element, arr []string, ignoreEmpty bool) ([]string, formulaArg) {
for arg.Next(); arg != nil; arg = arg.Next() {
switch arg.Value.(formulaArg).Type {
case ArgError:
return arr, arg.Value.(formulaArg)
case ArgString:
val := arg.Value.(formulaArg).Value()
if val != "" || !ignoreEmpty {
arr = append(arr, val)
}
case ArgNumber:
arr = append(arr, arg.Value.(formulaArg).Value())
case ArgMatrix:
for _, row := range arg.Value.(formulaArg).Matrix {
argList := list.New().Init()
for _, ele := range row {
argList.PushBack(ele)
}
if argList.Len() > 0 {
args, _ := textJoin(argList.Front(), []string{}, ignoreEmpty)
arr = append(arr, args...)
}
}
}
}
return arr, newBoolFormulaArg(true)
}
// TRIM removes extra spaces (i.e. all spaces except for single spaces between
// words or characters) from a supplied text string. The syntax of the
// function is:
//
// TRIM(text)
//
func (fn *formulaFuncs) TRIM(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "TRIM requires 1 argument")
}
return newStringFormulaArg(strings.TrimSpace(argsList.Front().Value.(formulaArg).Value()))
}
// UNICHAR returns the Unicode character that is referenced by the given
// numeric value. The syntax of the function is:
//
// UNICHAR(number)
//
func (fn *formulaFuncs) UNICHAR(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "UNICHAR requires 1 argument")
}
numArg := argsList.Front().Value.(formulaArg).ToNumber()
if numArg.Type != ArgNumber {
return numArg
}
if numArg.Number <= 0 || numArg.Number > 55295 {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
return newStringFormulaArg(string(rune(numArg.Number)))
}
// UNICODE function returns the code point for the first character of a
// supplied text string. The syntax of the function is:
//
// UNICODE(text)
//
func (fn *formulaFuncs) UNICODE(argsList *list.List) formulaArg {
return fn.code("UNICODE", argsList)
}
// UPPER converts all characters in a supplied text string to upper case. The
// syntax of the function is:
//
// UPPER(text)
//
func (fn *formulaFuncs) UPPER(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "UPPER requires 1 argument")
}
return newStringFormulaArg(strings.ToUpper(argsList.Front().Value.(formulaArg).String))
}
// VALUE function converts a text string into a numeric value. The syntax of
// the function is:
//
// VALUE(text)
//
func (fn *formulaFuncs) VALUE(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "VALUE requires 1 argument")
}
text := strings.ReplaceAll(argsList.Front().Value.(formulaArg).Value(), ",", "")
percent := 1.0
if strings.HasSuffix(text, "%") {
percent, text = 0.01, strings.TrimSuffix(text, "%")
}
decimal := big.Float{}
if _, ok := decimal.SetString(text); ok {
value, _ := decimal.Float64()
return newNumberFormulaArg(value * percent)
}
dateValue, timeValue, errTime, errDate := 0.0, 0.0, false, false
if !isDateOnlyFmt(text) {
h, m, s, _, _, err := strToTime(text)
errTime = err.Type == ArgError
if !errTime {
timeValue = (float64(h)*3600 + float64(m)*60 + s) / 86400
}
}
y, m, d, _, err := strToDate(text)
errDate = err.Type == ArgError
if !errDate {
dateValue = daysBetween(excelMinTime1900.Unix(), makeDate(y, time.Month(m), d)) + 1
}
if errTime && errDate {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
return newNumberFormulaArg(dateValue + timeValue)
}
// Conditional Functions
// IF function tests a supplied condition and returns one result if the
// condition evaluates to TRUE, and another result if the condition evaluates
// to FALSE. The syntax of the function is:
//
// IF(logical_test,value_if_true,value_if_false)
//
func (fn *formulaFuncs) IF(argsList *list.List) formulaArg {
if argsList.Len() == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "IF requires at least 1 argument")
}
if argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, "IF accepts at most 3 arguments")
}
token := argsList.Front().Value.(formulaArg)
var (
cond bool
err error
result formulaArg
)
switch token.Type {
case ArgString:
if cond, err = strconv.ParseBool(token.String); err != nil {
return newErrorFormulaArg(formulaErrorVALUE, err.Error())
}
case ArgNumber:
cond = token.Number == 1
}
if argsList.Len() == 1 {
return newBoolFormulaArg(cond)
}
if cond {
value := argsList.Front().Next().Value.(formulaArg)
switch value.Type {
case ArgNumber:
result = value.ToNumber()
default:
result = newStringFormulaArg(value.String)
}
return result
}
if argsList.Len() == 3 {
value := argsList.Back().Value.(formulaArg)
switch value.Type {
case ArgNumber:
result = value.ToNumber()
default:
result = newStringFormulaArg(value.String)
}
}
return result
}
// Lookup and Reference Functions
// ADDRESS function takes a row and a column number and returns a cell
// reference as a text string. The syntax of the function is:
//
// ADDRESS(row_num,column_num,[abs_num],[a1],[sheet_text])
//
func (fn *formulaFuncs) ADDRESS(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "ADDRESS requires at least 2 arguments")
}
if argsList.Len() > 5 {
return newErrorFormulaArg(formulaErrorVALUE, "ADDRESS requires at most 5 arguments")
}
rowNum := argsList.Front().Value.(formulaArg).ToNumber()
if rowNum.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if rowNum.Number >= TotalRows {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
colNum := argsList.Front().Next().Value.(formulaArg).ToNumber()
if colNum.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
absNum := newNumberFormulaArg(1)
if argsList.Len() >= 3 {
absNum = argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if absNum.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
}
if absNum.Number < 1 || absNum.Number > 4 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
a1 := newBoolFormulaArg(true)
if argsList.Len() >= 4 {
a1 = argsList.Front().Next().Next().Next().Value.(formulaArg).ToBool()
if a1.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
}
var sheetText string
if argsList.Len() == 5 {
sheetText = trimSheetName(argsList.Back().Value.(formulaArg).Value())
}
if len(sheetText) > 0 {
sheetText = fmt.Sprintf("%s!", sheetText)
}
formatter := addressFmtMaps[fmt.Sprintf("%d_%s", int(absNum.Number), a1.Value())]
addr, err := formatter(int(colNum.Number), int(colNum.Number))
if err != nil {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
return newStringFormulaArg(fmt.Sprintf("%s%s", sheetText, addr))
}
// CHOOSE function returns a value from an array, that corresponds to a
// supplied index number (position). The syntax of the function is:
//
// CHOOSE(index_num,value1,[value2],...)
//
func (fn *formulaFuncs) CHOOSE(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "CHOOSE requires 2 arguments")
}
idx, err := strconv.Atoi(argsList.Front().Value.(formulaArg).Value())
if err != nil {
return newErrorFormulaArg(formulaErrorVALUE, "CHOOSE requires first argument of type number")
}
if argsList.Len() <= idx {
return newErrorFormulaArg(formulaErrorVALUE, "index_num should be <= to the number of values")
}
arg := argsList.Front()
for i := 0; i < idx; i++ {
arg = arg.Next()
}
return arg.Value.(formulaArg)
}
// deepMatchRune finds whether the text deep matches/satisfies the pattern
// string.
func deepMatchRune(str, pattern []rune, simple bool) bool {
for len(pattern) > 0 {
switch pattern[0] {
default:
if len(str) == 0 || str[0] != pattern[0] {
return false
}
case '?':
if len(str) == 0 && !simple {
return false
}
case '*':
return deepMatchRune(str, pattern[1:], simple) ||
(len(str) > 0 && deepMatchRune(str[1:], pattern, simple))
}
str = str[1:]
pattern = pattern[1:]
}
return len(str) == 0 && len(pattern) == 0
}
// matchPattern finds whether the text matches or satisfies the pattern
// string. The pattern supports '*' and '?' wildcards in the pattern string.
func matchPattern(pattern, name string) (matched bool) {
if pattern == "" {
return name == pattern
}
if pattern == "*" {
return true
}
rName, rPattern := make([]rune, 0, len(name)), make([]rune, 0, len(pattern))
for _, r := range name {
rName = append(rName, r)
}
for _, r := range pattern {
rPattern = append(rPattern, r)
}
return deepMatchRune(rName, rPattern, false)
}
// compareFormulaArg compares the left-hand sides and the right-hand sides'
// formula arguments by given conditions such as case-sensitive, if exact
// match, and make compare result as formula criteria condition type.
func compareFormulaArg(lhs, rhs, matchMode formulaArg, caseSensitive bool) byte {
if lhs.Type != rhs.Type {
return criteriaErr
}
switch lhs.Type {
case ArgNumber:
if lhs.Number == rhs.Number {
return criteriaEq
}
if lhs.Number < rhs.Number {
return criteriaL
}
return criteriaG
case ArgString:
ls, rs := lhs.String, rhs.String
if !caseSensitive {
ls, rs = strings.ToLower(ls), strings.ToLower(rs)
}
if matchMode.Number == matchModeWildcard {
if matchPattern(rs, ls) {
return criteriaEq
}
}
return map[int]byte{1: criteriaG, -1: criteriaL, 0: criteriaEq}[strings.Compare(ls, rs)]
case ArgEmpty:
return criteriaEq
case ArgList:
return compareFormulaArgList(lhs, rhs, matchMode, caseSensitive)
case ArgMatrix:
return compareFormulaArgMatrix(lhs, rhs, matchMode, caseSensitive)
}
return criteriaErr
}
// compareFormulaArgList compares the left-hand sides and the right-hand sides
// list type formula arguments.
func compareFormulaArgList(lhs, rhs, matchMode formulaArg, caseSensitive bool) byte {
if len(lhs.List) < len(rhs.List) {
return criteriaL
}
if len(lhs.List) > len(rhs.List) {
return criteriaG
}
for arg := range lhs.List {
criteria := compareFormulaArg(lhs.List[arg], rhs.List[arg], matchMode, caseSensitive)
if criteria != criteriaEq {
return criteria
}
}
return criteriaEq
}
// compareFormulaArgMatrix compares the left-hand sides and the right-hand sides'
// matrix type formula arguments.
func compareFormulaArgMatrix(lhs, rhs, matchMode formulaArg, caseSensitive bool) byte {
if len(lhs.Matrix) < len(rhs.Matrix) {
return criteriaL
}
if len(lhs.Matrix) > len(rhs.Matrix) {
return criteriaG
}
for i := range lhs.Matrix {
left := lhs.Matrix[i]
right := lhs.Matrix[i]
if len(left) < len(right) {
return criteriaL
}
if len(left) > len(right) {
return criteriaG
}
for arg := range left {
criteria := compareFormulaArg(left[arg], right[arg], matchMode, caseSensitive)
if criteria != criteriaEq {
return criteria
}
}
}
return criteriaEq
}
// COLUMN function returns the first column number within a supplied reference
// or the number of the current column. The syntax of the function is:
//
// COLUMN([reference])
//
func (fn *formulaFuncs) COLUMN(argsList *list.List) formulaArg {
if argsList.Len() > 1 {
return newErrorFormulaArg(formulaErrorVALUE, "COLUMN requires at most 1 argument")
}
if argsList.Len() == 1 {
if argsList.Front().Value.(formulaArg).cellRanges != nil && argsList.Front().Value.(formulaArg).cellRanges.Len() > 0 {
return newNumberFormulaArg(float64(argsList.Front().Value.(formulaArg).cellRanges.Front().Value.(cellRange).From.Col))
}
if argsList.Front().Value.(formulaArg).cellRefs != nil && argsList.Front().Value.(formulaArg).cellRefs.Len() > 0 {
return newNumberFormulaArg(float64(argsList.Front().Value.(formulaArg).cellRefs.Front().Value.(cellRef).Col))
}
return newErrorFormulaArg(formulaErrorVALUE, "invalid reference")
}
col, _, _ := CellNameToCoordinates(fn.cell)
return newNumberFormulaArg(float64(col))
}
// calcColumnsMinMax calculation min and max value for given formula arguments
// sequence of the formula function COLUMNS.
func calcColumnsMinMax(argsList *list.List) (min, max int) {
if argsList.Front().Value.(formulaArg).cellRanges != nil && argsList.Front().Value.(formulaArg).cellRanges.Len() > 0 {
crs := argsList.Front().Value.(formulaArg).cellRanges
for cr := crs.Front(); cr != nil; cr = cr.Next() {
if min == 0 {
min = cr.Value.(cellRange).From.Col
}
if min > cr.Value.(cellRange).From.Col {
min = cr.Value.(cellRange).From.Col
}
if min > cr.Value.(cellRange).To.Col {
min = cr.Value.(cellRange).To.Col
}
if max < cr.Value.(cellRange).To.Col {
max = cr.Value.(cellRange).To.Col
}
if max < cr.Value.(cellRange).From.Col {
max = cr.Value.(cellRange).From.Col
}
}
}
if argsList.Front().Value.(formulaArg).cellRefs != nil && argsList.Front().Value.(formulaArg).cellRefs.Len() > 0 {
cr := argsList.Front().Value.(formulaArg).cellRefs
for refs := cr.Front(); refs != nil; refs = refs.Next() {
if min == 0 {
min = refs.Value.(cellRef).Col
}
if min > refs.Value.(cellRef).Col {
min = refs.Value.(cellRef).Col
}
if max < refs.Value.(cellRef).Col {
max = refs.Value.(cellRef).Col
}
}
}
return
}
// COLUMNS function receives an Excel range and returns the number of columns
// that are contained within the range. The syntax of the function is:
//
// COLUMNS(array)
//
func (fn *formulaFuncs) COLUMNS(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "COLUMNS requires 1 argument")
}
min, max := calcColumnsMinMax(argsList)
if max == MaxColumns {
return newNumberFormulaArg(float64(MaxColumns))
}
result := max - min + 1
if max == min {
if min == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "invalid reference")
}
return newNumberFormulaArg(float64(1))
}
return newNumberFormulaArg(float64(result))
}
// FORMULATEXT function returns a formula as a text string. The syntax of the
// function is:
//
// FORMULATEXT(reference)
//
func (fn *formulaFuncs) FORMULATEXT(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "FORMULATEXT requires 1 argument")
}
refs := argsList.Front().Value.(formulaArg).cellRefs
col, row := 0, 0
if refs != nil && refs.Len() > 0 {
col, row = refs.Front().Value.(cellRef).Col, refs.Front().Value.(cellRef).Row
}
ranges := argsList.Front().Value.(formulaArg).cellRanges
if ranges != nil && ranges.Len() > 0 {
col, row = ranges.Front().Value.(cellRange).From.Col, ranges.Front().Value.(cellRange).From.Row
}
cell, err := CoordinatesToCellName(col, row)
if err != nil {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
formula, _ := fn.f.GetCellFormula(fn.sheet, cell)
return newStringFormulaArg(formula)
}
// checkHVLookupArgs checking arguments, prepare extract mode, lookup value,
// and data for the formula functions HLOOKUP and VLOOKUP.
func checkHVLookupArgs(name string, argsList *list.List) (idx int, lookupValue, tableArray, matchMode, errArg formulaArg) {
unit := map[string]string{
"HLOOKUP": "row",
"VLOOKUP": "col",
}[name]
if argsList.Len() < 3 {
errArg = newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 3 arguments", name))
return
}
if argsList.Len() > 4 {
errArg = newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at most 4 arguments", name))
return
}
lookupValue = argsList.Front().Value.(formulaArg)
tableArray = argsList.Front().Next().Value.(formulaArg)
if tableArray.Type != ArgMatrix {
errArg = newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires second argument of table array", name))
return
}
arg := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if arg.Type != ArgNumber {
errArg = newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires numeric %s argument", name, unit))
return
}
idx, matchMode = int(arg.Number)-1, newNumberFormulaArg(matchModeMaxLess)
if argsList.Len() == 4 {
rangeLookup := argsList.Back().Value.(formulaArg).ToBool()
if rangeLookup.Type == ArgError {
errArg = newErrorFormulaArg(formulaErrorVALUE, rangeLookup.Error)
return
}
if rangeLookup.Number == 0 {
matchMode = newNumberFormulaArg(matchModeWildcard)
}
}
return
}
// HLOOKUP function 'looks up' a given value in the top row of a data array
// (or table), and returns the corresponding value from another row of the
// array. The syntax of the function is:
//
// HLOOKUP(lookup_value,table_array,row_index_num,[range_lookup])
//
func (fn *formulaFuncs) HLOOKUP(argsList *list.List) formulaArg {
rowIdx, lookupValue, tableArray, matchMode, errArg := checkHVLookupArgs("HLOOKUP", argsList)
if errArg.Type == ArgError {
return errArg
}
var matchIdx int
var wasExact bool
if matchMode.Number == matchModeWildcard || len(tableArray.Matrix) == TotalRows {
matchIdx, wasExact = lookupLinearSearch(false, lookupValue, tableArray, matchMode, newNumberFormulaArg(searchModeLinear))
} else {
matchIdx, wasExact = lookupBinarySearch(false, lookupValue, tableArray, matchMode, newNumberFormulaArg(searchModeAscBinary))
}
if matchIdx == -1 {
return newErrorFormulaArg(formulaErrorNA, "HLOOKUP no result found")
}
if rowIdx < 0 || rowIdx >= len(tableArray.Matrix) {
return newErrorFormulaArg(formulaErrorNA, "HLOOKUP has invalid row index")
}
row := tableArray.Matrix[rowIdx]
if wasExact || matchMode.Number == matchModeWildcard {
return row[matchIdx]
}
return newErrorFormulaArg(formulaErrorNA, "HLOOKUP no result found")
}
// HYPERLINK function creates a hyperlink to a specified location. The syntax
// of the function is:
//
// HYPERLINK(link_location,[friendly_name])
//
func (fn *formulaFuncs) HYPERLINK(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "HYPERLINK requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "HYPERLINK allows at most 2 arguments")
}
return newStringFormulaArg(argsList.Back().Value.(formulaArg).Value())
}
// calcMatch returns the position of the value by given match type, criteria
// and lookup array for the formula function MATCH.
func calcMatch(matchType int, criteria *formulaCriteria, lookupArray []formulaArg) formulaArg {
switch matchType {
case 0:
for i, arg := range lookupArray {
if ok, _ := formulaCriteriaEval(arg.Value(), criteria); ok {
return newNumberFormulaArg(float64(i + 1))
}
}
case -1:
for i, arg := range lookupArray {
if ok, _ := formulaCriteriaEval(arg.Value(), criteria); ok {
return newNumberFormulaArg(float64(i + 1))
}
if ok, _ := formulaCriteriaEval(arg.Value(), &formulaCriteria{
Type: criteriaL, Condition: criteria.Condition,
}); ok {
if i == 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
return newNumberFormulaArg(float64(i))
}
}
case 1:
for i, arg := range lookupArray {
if ok, _ := formulaCriteriaEval(arg.Value(), criteria); ok {
return newNumberFormulaArg(float64(i + 1))
}
if ok, _ := formulaCriteriaEval(arg.Value(), &formulaCriteria{
Type: criteriaG, Condition: criteria.Condition,
}); ok {
if i == 0 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
return newNumberFormulaArg(float64(i))
}
}
}
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
// MATCH function looks up a value in an array, and returns the position of
// the value within the array. The user can specify that the function should
// only return a result if an exact match is found, or that the function
// should return the position of the closest match (above or below), if an
// exact match is not found. The syntax of the Match function is:
//
// MATCH(lookup_value,lookup_array,[match_type])
//
func (fn *formulaFuncs) MATCH(argsList *list.List) formulaArg {
if argsList.Len() != 2 && argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "MATCH requires 1 or 2 arguments")
}
var (
matchType = 1
lookupArray []formulaArg
lookupArrayArg = argsList.Front().Next().Value.(formulaArg)
lookupArrayErr = "MATCH arguments lookup_array should be one-dimensional array"
)
if argsList.Len() == 3 {
matchTypeArg := argsList.Back().Value.(formulaArg).ToNumber()
if matchTypeArg.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, "MATCH requires numeric match_type argument")
}
if matchTypeArg.Number == -1 || matchTypeArg.Number == 0 {
matchType = int(matchTypeArg.Number)
}
}
switch lookupArrayArg.Type {
case ArgMatrix:
if len(lookupArrayArg.Matrix[0]) != 1 {
return newErrorFormulaArg(formulaErrorNA, lookupArrayErr)
}
lookupArray = lookupArrayArg.ToList()
default:
return newErrorFormulaArg(formulaErrorNA, lookupArrayErr)
}
return calcMatch(matchType, formulaCriteriaParser(argsList.Front().Value.(formulaArg).Value()), lookupArray)
}
// TRANSPOSE function 'transposes' an array of cells (i.e. the function copies
// a horizontal range of cells into a vertical range and vice versa). The
// syntax of the function is:
//
// TRANSPOSE(array)
//
func (fn *formulaFuncs) TRANSPOSE(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "TRANSPOSE requires 1 argument")
}
args := argsList.Back().Value.(formulaArg).ToList()
rmin, rmax := calcRowsMinMax(argsList)
cmin, cmax := calcColumnsMinMax(argsList)
cols, rows := cmax-cmin+1, rmax-rmin+1
src := make([][]formulaArg, 0)
for i := 0; i < len(args); i += cols {
src = append(src, args[i:i+cols])
}
mtx := make([][]formulaArg, cols)
for r, row := range src {
colIdx := r % rows
for c, cell := range row {
rowIdx := c % cols
if len(mtx[rowIdx]) == 0 {
mtx[rowIdx] = make([]formulaArg, rows)
}
mtx[rowIdx][colIdx] = cell
}
}
return newMatrixFormulaArg(mtx)
}
// lookupLinearSearch sequentially checks each look value of the lookup array until
// a match is found or the whole list has been searched.
func lookupLinearSearch(vertical bool, lookupValue, lookupArray, matchMode, searchMode formulaArg) (int, bool) {
var tableArray []formulaArg
if vertical {
for _, row := range lookupArray.Matrix {
tableArray = append(tableArray, row[0])
}
} else {
tableArray = lookupArray.Matrix[0]
}
matchIdx, wasExact := -1, false
start:
for i, cell := range tableArray {
lhs := cell
if lookupValue.Type == ArgNumber {
if lhs = cell.ToNumber(); lhs.Type == ArgError {
lhs = cell
}
} else if lookupValue.Type == ArgMatrix {
lhs = lookupArray
}
if compareFormulaArg(lhs, lookupValue, matchMode, false) == criteriaEq {
matchIdx = i
wasExact = true
if searchMode.Number == searchModeLinear {
break start
}
}
if matchMode.Number == matchModeMinGreater || matchMode.Number == matchModeMaxLess {
matchIdx = int(calcMatch(int(matchMode.Number), formulaCriteriaParser(lookupValue.Value()), tableArray).Number)
continue
}
}
return matchIdx, wasExact
}
// VLOOKUP function 'looks up' a given value in the left-hand column of a
// data array (or table), and returns the corresponding value from another
// column of the array. The syntax of the function is:
//
// VLOOKUP(lookup_value,table_array,col_index_num,[range_lookup])
//
func (fn *formulaFuncs) VLOOKUP(argsList *list.List) formulaArg {
colIdx, lookupValue, tableArray, matchMode, errArg := checkHVLookupArgs("VLOOKUP", argsList)
if errArg.Type == ArgError {
return errArg
}
var matchIdx int
var wasExact bool
if matchMode.Number == matchModeWildcard || len(tableArray.Matrix) == TotalRows {
matchIdx, wasExact = lookupLinearSearch(true, lookupValue, tableArray, matchMode, newNumberFormulaArg(searchModeLinear))
} else {
matchIdx, wasExact = lookupBinarySearch(true, lookupValue, tableArray, matchMode, newNumberFormulaArg(searchModeAscBinary))
}
if matchIdx == -1 {
return newErrorFormulaArg(formulaErrorNA, "VLOOKUP no result found")
}
mtx := tableArray.Matrix[matchIdx]
if colIdx < 0 || colIdx >= len(mtx) {
return newErrorFormulaArg(formulaErrorNA, "VLOOKUP has invalid column index")
}
if wasExact || matchMode.Number == matchModeWildcard {
return mtx[colIdx]
}
return newErrorFormulaArg(formulaErrorNA, "VLOOKUP no result found")
}
// lookupBinarySearch finds the position of a target value when range lookup
// is TRUE, if the data of table array can't guarantee be sorted, it will
// return wrong result.
func lookupBinarySearch(vertical bool, lookupValue, lookupArray, matchMode, searchMode formulaArg) (matchIdx int, wasExact bool) {
var tableArray []formulaArg
if vertical {
for _, row := range lookupArray.Matrix {
tableArray = append(tableArray, row[0])
}
} else {
tableArray = lookupArray.Matrix[0]
}
low, high, lastMatchIdx := 0, len(tableArray)-1, -1
count := high
for low <= high {
mid := low + (high-low)/2
cell := tableArray[mid]
lhs := cell
if lookupValue.Type == ArgNumber {
if lhs = cell.ToNumber(); lhs.Type == ArgError {
lhs = cell
}
} else if lookupValue.Type == ArgMatrix && vertical {
lhs = lookupArray
}
result := compareFormulaArg(lhs, lookupValue, matchMode, false)
if result == criteriaEq {
matchIdx, wasExact = mid, true
if searchMode.Number == searchModeDescBinary {
matchIdx = count - matchIdx
}
return
} else if result == criteriaG {
high = mid - 1
} else if result == criteriaL {
matchIdx = mid
if lhs.Value() != "" {
lastMatchIdx = matchIdx
}
low = mid + 1
} else {
return -1, false
}
}
matchIdx, wasExact = lastMatchIdx, true
return
}
// checkLookupArgs checking arguments, prepare lookup value, and data for the
// formula function LOOKUP.
func checkLookupArgs(argsList *list.List) (arrayForm bool, lookupValue, lookupVector, errArg formulaArg) {
if argsList.Len() < 2 {
errArg = newErrorFormulaArg(formulaErrorVALUE, "LOOKUP requires at least 2 arguments")
return
}
if argsList.Len() > 3 {
errArg = newErrorFormulaArg(formulaErrorVALUE, "LOOKUP requires at most 3 arguments")
return
}
lookupValue = newStringFormulaArg(argsList.Front().Value.(formulaArg).Value())
lookupVector = argsList.Front().Next().Value.(formulaArg)
if lookupVector.Type != ArgMatrix && lookupVector.Type != ArgList {
errArg = newErrorFormulaArg(formulaErrorVALUE, "LOOKUP requires second argument of table array")
return
}
arrayForm = lookupVector.Type == ArgMatrix
if arrayForm && len(lookupVector.Matrix) == 0 {
errArg = newErrorFormulaArg(formulaErrorVALUE, "LOOKUP requires not empty range as second argument")
}
return
}
// iterateLookupArgs iterate arguments to extract columns and calculate match
// index for the formula function LOOKUP.
func iterateLookupArgs(lookupValue, lookupVector formulaArg) ([]formulaArg, int, bool) {
cols, matchIdx, ok := lookupCol(lookupVector, 0), -1, false
for idx, col := range cols {
lhs := lookupValue
switch col.Type {
case ArgNumber:
lhs = lhs.ToNumber()
if !col.Boolean {
if lhs.Type == ArgError {
lhs = lookupValue
}
}
}
compare := compareFormulaArg(lhs, col, newNumberFormulaArg(matchModeMaxLess), false)
// Find exact match
if compare == criteriaEq {
matchIdx = idx
break
}
// Find the nearest match if lookup value is more than or equal to the first value in lookup vector
if idx == 0 {
ok = compare == criteriaG
} else if ok && compare == criteriaL && matchIdx == -1 {
matchIdx = idx - 1
}
}
return cols, matchIdx, ok
}
// index is an implementation of the formula function INDEX.
func (fn *formulaFuncs) index(array formulaArg, rowIdx, colIdx int) formulaArg {
var cells []formulaArg
if array.Type == ArgMatrix {
cellMatrix := array.Matrix
if rowIdx < -1 || rowIdx >= len(cellMatrix) {
return newErrorFormulaArg(formulaErrorREF, "INDEX row_num out of range")
}
if rowIdx == -1 {
if colIdx >= len(cellMatrix[0]) {
return newErrorFormulaArg(formulaErrorREF, "INDEX col_num out of range")
}
var column [][]formulaArg
for _, cells = range cellMatrix {
column = append(column, []formulaArg{cells[colIdx]})
}
return newMatrixFormulaArg(column)
}
cells = cellMatrix[rowIdx]
}
if colIdx < -1 || colIdx >= len(cells) {
return newErrorFormulaArg(formulaErrorREF, "INDEX col_num out of range")
}
return newListFormulaArg(cells)
}
// validateMatchMode check the number of match mode if be equal to 0, 1, -1 or
// 2.
func validateMatchMode(mode float64) bool {
return mode == matchModeExact || mode == matchModeMinGreater || mode == matchModeMaxLess || mode == matchModeWildcard
}
// validateSearchMode check the number of search mode if be equal to 1, -1, 2
// or -2.
func validateSearchMode(mode float64) bool {
return mode == searchModeLinear || mode == searchModeReverseLinear || mode == searchModeAscBinary || mode == searchModeDescBinary
}
// prepareXlookupArgs checking and prepare arguments for the formula function
// XLOOKUP.
func (fn *formulaFuncs) prepareXlookupArgs(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "XLOOKUP requires at least 3 arguments")
}
if argsList.Len() > 6 {
return newErrorFormulaArg(formulaErrorVALUE, "XLOOKUP allows at most 6 arguments")
}
lookupValue := argsList.Front().Value.(formulaArg)
lookupArray := argsList.Front().Next().Value.(formulaArg)
returnArray := argsList.Front().Next().Next().Value.(formulaArg)
ifNotFond := newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
matchMode, searchMode := newNumberFormulaArg(matchModeExact), newNumberFormulaArg(searchModeLinear)
if argsList.Len() > 3 {
ifNotFond = argsList.Front().Next().Next().Next().Value.(formulaArg)
}
if argsList.Len() > 4 {
if matchMode = argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber(); matchMode.Type != ArgNumber {
return matchMode
}
}
if argsList.Len() > 5 {
if searchMode = argsList.Back().Value.(formulaArg).ToNumber(); searchMode.Type != ArgNumber {
return searchMode
}
}
if lookupArray.Type != ArgMatrix || returnArray.Type != ArgMatrix {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
if !validateMatchMode(matchMode.Number) || !validateSearchMode(searchMode.Number) {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
return newListFormulaArg([]formulaArg{lookupValue, lookupArray, returnArray, ifNotFond, matchMode, searchMode})
}
// xlookup is an implementation of the formula function XLOOKUP.
func (fn *formulaFuncs) xlookup(lookupRows, lookupCols, returnArrayRows, returnArrayCols, matchIdx int,
condition1, condition2, condition3, condition4 bool, returnArray formulaArg,
) formulaArg {
var result [][]formulaArg
for rowIdx, row := range returnArray.Matrix {
for colIdx, cell := range row {
if condition1 {
if condition2 {
result = append(result, []formulaArg{cell})
continue
}
if returnArrayRows > 1 && returnArrayCols > 1 {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
}
if condition3 {
if returnArrayCols != lookupCols {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if colIdx == matchIdx {
result = append(result, []formulaArg{cell})
continue
}
}
if condition4 {
if returnArrayRows != lookupRows {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if rowIdx == matchIdx {
if len(result) == 0 {
result = append(result, []formulaArg{cell})
continue
}
result[0] = append(result[0], cell)
}
}
}
}
array := newMatrixFormulaArg(result)
cells := array.ToList()
if len(cells) == 1 {
return cells[0]
}
return array
}
// XLOOKUP function searches a range or an array, and then returns the item
// corresponding to the first match it finds. If no match exists, then
// XLOOKUP can return the closest (approximate) match. The syntax of the
// function is:
//
// XLOOKUP(lookup_value,lookup_array,return_array,[if_not_found],[match_mode],[search_mode])
//
func (fn *formulaFuncs) XLOOKUP(argsList *list.List) formulaArg {
args := fn.prepareXlookupArgs(argsList)
if args.Type != ArgList {
return args
}
lookupValue, lookupArray, returnArray, ifNotFond, matchMode, searchMode := args.List[0], args.List[1], args.List[2], args.List[3], args.List[4], args.List[5]
lookupRows, lookupCols := len(lookupArray.Matrix), 0
if lookupRows > 0 {
lookupCols = len(lookupArray.Matrix[0])
}
if lookupRows != 1 && lookupCols != 1 {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
verticalLookup := lookupRows >= lookupCols
var matchIdx int
switch searchMode.Number {
case searchModeLinear, searchModeReverseLinear:
matchIdx, _ = lookupLinearSearch(verticalLookup, lookupValue, lookupArray, matchMode, searchMode)
default:
matchIdx, _ = lookupBinarySearch(verticalLookup, lookupValue, lookupArray, matchMode, searchMode)
}
if matchIdx == -1 {
return ifNotFond
}
returnArrayRows, returnArrayCols := len(returnArray.Matrix), len(returnArray.Matrix[0])
condition1 := lookupRows == 1 && lookupCols == 1
condition2 := returnArrayRows == 1 || returnArrayCols == 1
condition3 := lookupRows == 1 && lookupCols > 1
condition4 := lookupRows > 1 && lookupCols == 1
return fn.xlookup(lookupRows, lookupCols, returnArrayRows, returnArrayCols, matchIdx, condition1, condition2, condition3, condition4, returnArray)
}
// INDEX function returns a reference to a cell that lies in a specified row
// and column of a range of cells. The syntax of the function is:
//
// INDEX(array,row_num,[col_num])
//
func (fn *formulaFuncs) INDEX(argsList *list.List) formulaArg {
if argsList.Len() < 2 || argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, "INDEX requires 2 or 3 arguments")
}
array := argsList.Front().Value.(formulaArg)
if array.Type != ArgMatrix && array.Type != ArgList {
array = newMatrixFormulaArg([][]formulaArg{{array}})
}
rowArg := argsList.Front().Next().Value.(formulaArg).ToNumber()
if rowArg.Type != ArgNumber {
return rowArg
}
rowIdx, colIdx := int(rowArg.Number)-1, -1
if argsList.Len() == 3 {
colArg := argsList.Back().Value.(formulaArg).ToNumber()
if colArg.Type != ArgNumber {
return colArg
}
colIdx = int(colArg.Number) - 1
}
if rowIdx == -1 && colIdx == -1 {
if len(array.ToList()) != 1 {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
return array.ToList()[0]
}
cells := fn.index(array, rowIdx, colIdx)
if cells.Type != ArgList {
return cells
}
if colIdx == -1 {
return newMatrixFormulaArg([][]formulaArg{cells.List})
}
return cells.List[colIdx]
}
// INDIRECT function converts a text string into a cell reference. The syntax
// of the Indirect function is:
//
// INDIRECT(ref_text,[a1])
//
func (fn *formulaFuncs) INDIRECT(argsList *list.List) formulaArg {
if argsList.Len() != 1 && argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "INDIRECT requires 1 or 2 arguments")
}
refText := argsList.Front().Value.(formulaArg).Value()
a1 := newBoolFormulaArg(true)
if argsList.Len() == 2 {
if a1 = argsList.Back().Value.(formulaArg).ToBool(); a1.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
}
R1C1ToA1 := func(ref string) (cell string, err error) {
parts := strings.Split(strings.TrimLeft(ref, "R"), "C")
if len(parts) != 2 {
return
}
row, err := strconv.Atoi(parts[0])
if err != nil {
return
}
col, err := strconv.Atoi(parts[1])
if err != nil {
return
}
cell, err = CoordinatesToCellName(col, row)
return
}
refs := strings.Split(refText, ":")
fromRef, toRef := refs[0], ""
if len(refs) == 2 {
toRef = refs[1]
}
if a1.Number == 0 {
from, err := R1C1ToA1(refs[0])
if err != nil {
return newErrorFormulaArg(formulaErrorREF, formulaErrorREF)
}
fromRef = from
if len(refs) == 2 {
to, err := R1C1ToA1(refs[1])
if err != nil {
return newErrorFormulaArg(formulaErrorREF, formulaErrorREF)
}
toRef = to
}
}
if len(refs) == 1 {
value, err := fn.f.GetCellValue(fn.sheet, fromRef)
if err != nil {
return newErrorFormulaArg(formulaErrorREF, formulaErrorREF)
}
return newStringFormulaArg(value)
}
arg, _ := fn.f.parseReference(fn.ctx, fn.sheet, fromRef+":"+toRef)
return arg
}
// LOOKUP function performs an approximate match lookup in a one-column or
// one-row range, and returns the corresponding value from another one-column
// or one-row range. The syntax of the function is:
//
// LOOKUP(lookup_value,lookup_vector,[result_vector])
//
func (fn *formulaFuncs) LOOKUP(argsList *list.List) formulaArg {
arrayForm, lookupValue, lookupVector, errArg := checkLookupArgs(argsList)
if errArg.Type == ArgError {
return errArg
}
cols, matchIdx, ok := iterateLookupArgs(lookupValue, lookupVector)
if ok && matchIdx == -1 {
matchIdx = len(cols) - 1
}
var column []formulaArg
if argsList.Len() == 3 {
column = lookupCol(argsList.Back().Value.(formulaArg), 0)
} else if arrayForm && len(lookupVector.Matrix[0]) > 1 {
column = lookupCol(lookupVector, 1)
} else {
column = cols
}
if matchIdx < 0 || matchIdx >= len(column) {
return newErrorFormulaArg(formulaErrorNA, "LOOKUP no result found")
}
return column[matchIdx]
}
// lookupCol extract columns for LOOKUP.
func lookupCol(arr formulaArg, idx int) []formulaArg {
col := arr.List
if arr.Type == ArgMatrix {
col = nil
for _, r := range arr.Matrix {
if len(r) > 0 {
col = append(col, r[idx])
continue
}
col = append(col, newEmptyFormulaArg())
}
}
return col
}
// ROW function returns the first row number within a supplied reference or
// the number of the current row. The syntax of the function is:
//
// ROW([reference])
//
func (fn *formulaFuncs) ROW(argsList *list.List) formulaArg {
if argsList.Len() > 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ROW requires at most 1 argument")
}
if argsList.Len() == 1 {
if argsList.Front().Value.(formulaArg).cellRanges != nil && argsList.Front().Value.(formulaArg).cellRanges.Len() > 0 {
return newNumberFormulaArg(float64(argsList.Front().Value.(formulaArg).cellRanges.Front().Value.(cellRange).From.Row))
}
if argsList.Front().Value.(formulaArg).cellRefs != nil && argsList.Front().Value.(formulaArg).cellRefs.Len() > 0 {
return newNumberFormulaArg(float64(argsList.Front().Value.(formulaArg).cellRefs.Front().Value.(cellRef).Row))
}
return newErrorFormulaArg(formulaErrorVALUE, "invalid reference")
}
_, row, _ := CellNameToCoordinates(fn.cell)
return newNumberFormulaArg(float64(row))
}
// calcRowsMinMax calculation min and max value for given formula arguments
// sequence of the formula function ROWS.
func calcRowsMinMax(argsList *list.List) (min, max int) {
if argsList.Front().Value.(formulaArg).cellRanges != nil && argsList.Front().Value.(formulaArg).cellRanges.Len() > 0 {
crs := argsList.Front().Value.(formulaArg).cellRanges
for cr := crs.Front(); cr != nil; cr = cr.Next() {
if min == 0 {
min = cr.Value.(cellRange).From.Row
}
if min > cr.Value.(cellRange).From.Row {
min = cr.Value.(cellRange).From.Row
}
if min > cr.Value.(cellRange).To.Row {
min = cr.Value.(cellRange).To.Row
}
if max < cr.Value.(cellRange).To.Row {
max = cr.Value.(cellRange).To.Row
}
if max < cr.Value.(cellRange).From.Row {
max = cr.Value.(cellRange).From.Row
}
}
}
if argsList.Front().Value.(formulaArg).cellRefs != nil && argsList.Front().Value.(formulaArg).cellRefs.Len() > 0 {
cr := argsList.Front().Value.(formulaArg).cellRefs
for refs := cr.Front(); refs != nil; refs = refs.Next() {
if min == 0 {
min = refs.Value.(cellRef).Row
}
if min > refs.Value.(cellRef).Row {
min = refs.Value.(cellRef).Row
}
if max < refs.Value.(cellRef).Row {
max = refs.Value.(cellRef).Row
}
}
}
return
}
// ROWS function takes an Excel range and returns the number of rows that are
// contained within the range. The syntax of the function is:
//
// ROWS(array)
//
func (fn *formulaFuncs) ROWS(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ROWS requires 1 argument")
}
min, max := calcRowsMinMax(argsList)
if max == TotalRows {
return newStringFormulaArg(strconv.Itoa(TotalRows))
}
result := max - min + 1
if max == min {
if min == 0 {
return newErrorFormulaArg(formulaErrorVALUE, "invalid reference")
}
return newNumberFormulaArg(float64(1))
}
return newStringFormulaArg(strconv.Itoa(result))
}
// Web Functions
// ENCODEURL function returns a URL-encoded string, replacing certain
// non-alphanumeric characters with the percentage symbol (%) and a
// hexadecimal number. The syntax of the function is:
//
// ENCODEURL(url)
//
func (fn *formulaFuncs) ENCODEURL(argsList *list.List) formulaArg {
if argsList.Len() != 1 {
return newErrorFormulaArg(formulaErrorVALUE, "ENCODEURL requires 1 argument")
}
token := argsList.Front().Value.(formulaArg).Value()
return newStringFormulaArg(strings.ReplaceAll(url.QueryEscape(token), "+", "%20"))
}
// Financial Functions
// validateFrequency check the number of coupon payments per year if be equal to 1, 2 or 4.
func validateFrequency(freq float64) bool {
return freq == 1 || freq == 2 || freq == 4
}
// ACCRINT function returns the accrued interest in a security that pays
// periodic interest. The syntax of the function is:
//
// ACCRINT(issue,first_interest,settlement,rate,par,frequency,[basis],[calc_method])
//
func (fn *formulaFuncs) ACCRINT(argsList *list.List) formulaArg {
if argsList.Len() < 6 {
return newErrorFormulaArg(formulaErrorVALUE, "ACCRINT requires at least 6 arguments")
}
if argsList.Len() > 8 {
return newErrorFormulaArg(formulaErrorVALUE, "ACCRINT allows at most 8 arguments")
}
args := fn.prepareDataValueArgs(3, argsList)
if args.Type != ArgList {
return args
}
issue, settlement := args.List[0], args.List[2]
rate := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
par := argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
frequency := argsList.Front().Next().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber || par.Type != ArgNumber || frequency.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if !validateFrequency(frequency.Number) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
basis := newNumberFormulaArg(0)
if argsList.Len() >= 7 {
if basis = argsList.Front().Next().Next().Next().Next().Next().Next().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
if argsList.Len() == 8 {
if cm := argsList.Back().Value.(formulaArg).ToBool(); cm.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
}
frac1 := yearFrac(issue.Number, settlement.Number, int(basis.Number))
if frac1.Type != ArgNumber {
return frac1
}
return newNumberFormulaArg(par.Number * rate.Number * frac1.Number)
}
// ACCRINTM function returns the accrued interest in a security that pays
// interest at maturity. The syntax of the function is:
//
// ACCRINTM(issue,settlement,rate,[par],[basis])
//
func (fn *formulaFuncs) ACCRINTM(argsList *list.List) formulaArg {
if argsList.Len() != 4 && argsList.Len() != 5 {
return newErrorFormulaArg(formulaErrorVALUE, "ACCRINTM requires 4 or 5 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
issue, settlement := args.List[0], args.List[1]
if settlement.Number < issue.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
rate := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
par := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber || par.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if par.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 5 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
frac := yearFrac(issue.Number, settlement.Number, int(basis.Number))
if frac.Type != ArgNumber {
return frac
}
return newNumberFormulaArg(frac.Number * rate.Number * par.Number)
}
// prepareAmorArgs checking and prepare arguments for the formula functions
// AMORDEGRC and AMORLINC.
func (fn *formulaFuncs) prepareAmorArgs(name string, argsList *list.List) formulaArg {
cost := argsList.Front().Value.(formulaArg).ToNumber()
if cost.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires cost to be number argument", name))
}
if cost.Number < 0 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires cost >= 0", name))
}
args := list.New().Init()
args.PushBack(argsList.Front().Next().Value.(formulaArg))
datePurchased := fn.DATEVALUE(args)
if datePurchased.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
args.Init()
args.PushBack(argsList.Front().Next().Next().Value.(formulaArg))
firstPeriod := fn.DATEVALUE(args)
if firstPeriod.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if firstPeriod.Number < datePurchased.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
salvage := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if salvage.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if salvage.Number < 0 || salvage.Number > cost.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
period := argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if period.Type != ArgNumber || period.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
rate := argsList.Front().Next().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber || rate.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 7 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
return newListFormulaArg([]formulaArg{cost, datePurchased, firstPeriod, salvage, period, rate, basis})
}
// AMORDEGRC function is provided for users of the French accounting system.
// The function calculates the prorated linear depreciation of an asset for a
// specified accounting period. The syntax of the function is:
//
// AMORDEGRC(cost,date_purchased,first_period,salvage,period,rate,[basis])
//
func (fn *formulaFuncs) AMORDEGRC(argsList *list.List) formulaArg {
if argsList.Len() != 6 && argsList.Len() != 7 {
return newErrorFormulaArg(formulaErrorVALUE, "AMORDEGRC requires 6 or 7 arguments")
}
args := fn.prepareAmorArgs("AMORDEGRC", argsList)
if args.Type != ArgList {
return args
}
cost, datePurchased, firstPeriod, salvage, period, rate, basis := args.List[0], args.List[1], args.List[2], args.List[3], args.List[4], args.List[5], args.List[6]
if rate.Number >= 0.5 {
return newErrorFormulaArg(formulaErrorNUM, "AMORDEGRC requires rate to be < 0.5")
}
assetsLife, amorCoeff := 1/rate.Number, 2.5
if assetsLife < 3 {
amorCoeff = 1
} else if assetsLife < 5 {
amorCoeff = 1.5
} else if assetsLife <= 6 {
amorCoeff = 2
}
rate.Number *= amorCoeff
frac := yearFrac(datePurchased.Number, firstPeriod.Number, int(basis.Number))
if frac.Type != ArgNumber {
return frac
}
nRate := float64(int((frac.Number * cost.Number * rate.Number) + 0.5))
cost.Number -= nRate
rest := cost.Number - salvage.Number
for n := 0; n < int(period.Number); n++ {
nRate = float64(int((cost.Number * rate.Number) + 0.5))
rest -= nRate
if rest < 0 {
switch int(period.Number) - n {
case 0:
case 1:
return newNumberFormulaArg(float64(int((cost.Number * 0.5) + 0.5)))
default:
return newNumberFormulaArg(0)
}
}
cost.Number -= nRate
}
return newNumberFormulaArg(nRate)
}
// AMORLINC function is provided for users of the French accounting system.
// The function calculates the prorated linear depreciation of an asset for a
// specified accounting period. The syntax of the function is:
//
// AMORLINC(cost,date_purchased,first_period,salvage,period,rate,[basis])
//
func (fn *formulaFuncs) AMORLINC(argsList *list.List) formulaArg {
if argsList.Len() != 6 && argsList.Len() != 7 {
return newErrorFormulaArg(formulaErrorVALUE, "AMORLINC requires 6 or 7 arguments")
}
args := fn.prepareAmorArgs("AMORLINC", argsList)
if args.Type != ArgList {
return args
}
cost, datePurchased, firstPeriod, salvage, period, rate, basis := args.List[0], args.List[1], args.List[2], args.List[3], args.List[4], args.List[5], args.List[6]
frac := yearFrac(datePurchased.Number, firstPeriod.Number, int(basis.Number))
if frac.Type != ArgNumber {
return frac
}
rate1 := frac.Number * cost.Number * rate.Number
if period.Number == 0 {
return newNumberFormulaArg(rate1)
}
rate2 := cost.Number * rate.Number
delta := cost.Number - salvage.Number
periods := int((delta - rate1) / rate2)
if int(period.Number) <= periods {
return newNumberFormulaArg(rate2)
} else if int(period.Number)-1 == periods {
return newNumberFormulaArg(delta - rate2*float64(periods) - math.Nextafter(rate1, rate1))
}
return newNumberFormulaArg(0)
}
// prepareCouponArgs checking and prepare arguments for the formula functions
// COUPDAYBS, COUPDAYS, COUPDAYSNC, COUPPCD, COUPNUM and COUPNCD.
func (fn *formulaFuncs) prepareCouponArgs(name string, argsList *list.List) formulaArg {
if argsList.Len() != 3 && argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 3 or 4 arguments", name))
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
if settlement.Number >= maturity.Number {
return newErrorFormulaArg(formulaErrorNUM, fmt.Sprintf("%s requires maturity > settlement", name))
}
frequency := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if frequency.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if !validateFrequency(frequency.Number) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 4 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
return newListFormulaArg([]formulaArg{settlement, maturity, frequency, basis})
}
// is30BasisMethod determine if the financial day count basis rules is 30/360
// methods.
func is30BasisMethod(basis int) bool {
return basis == 0 || basis == 4
}
// getDaysInMonthRange return the day by given year, month range and day count
// basis.
func getDaysInMonthRange(fromMonth, toMonth int) int {
if fromMonth > toMonth {
return 0
}
return (toMonth - fromMonth + 1) * 30
}
// getDayOnBasis returns the day by given date and day count basis.
func getDayOnBasis(y, m, d, basis int) int {
if !is30BasisMethod(basis) {
return d
}
day := d
dim := getDaysInMonth(y, m)
if day > 30 || d >= dim || day >= dim {
day = 30
}
return day
}
// coupdays returns the number of days that base on date range and the day
// count basis to be used.
func coupdays(from, to time.Time, basis int) float64 {
days := 0
fromY, fromM, fromD := from.Date()
toY, toM, toD := to.Date()
fromDay, toDay := getDayOnBasis(fromY, int(fromM), fromD, basis), getDayOnBasis(toY, int(toM), toD, basis)
if !is30BasisMethod(basis) {
return (daysBetween(excelMinTime1900.Unix(), makeDate(toY, toM, toDay)) + 1) - (daysBetween(excelMinTime1900.Unix(), makeDate(fromY, fromM, fromDay)) + 1)
}
if basis == 0 {
if (int(fromM) == 2 || fromDay < 30) && toD == 31 {
toDay = 31
}
} else {
if int(fromM) == 2 && fromDay == 30 {
fromDay = getDaysInMonth(fromY, 2)
}
if int(toM) == 2 && toDay == 30 {
toDay = getDaysInMonth(toY, 2)
}
}
if fromY < toY || (fromY == toY && int(fromM) < int(toM)) {
days = 30 - fromDay + 1
fromD = 1
fromDay = 1
date := time.Date(fromY, fromM, fromD, 0, 0, 0, 0, time.UTC).AddDate(0, 1, 0)
if date.Year() < toY {
days += getDaysInMonthRange(int(date.Month()), 12)
date = date.AddDate(0, 13-int(date.Month()), 0)
}
days += getDaysInMonthRange(int(date.Month()), int(toM)-1)
}
if days += toDay - fromDay; days > 0 {
return float64(days)
}
return 0
}
// COUPDAYBS function calculates the number of days from the beginning of a
// coupon's period to the settlement date. The syntax of the function is:
//
// COUPDAYBS(settlement,maturity,frequency,[basis])
//
func (fn *formulaFuncs) COUPDAYBS(argsList *list.List) formulaArg {
args := fn.prepareCouponArgs("COUPDAYBS", argsList)
if args.Type != ArgList {
return args
}
settlement := timeFromExcelTime(args.List[0].Number, false)
pcd := timeFromExcelTime(fn.COUPPCD(argsList).Number, false)
return newNumberFormulaArg(coupdays(pcd, settlement, int(args.List[3].Number)))
}
// COUPDAYS function calculates the number of days in a coupon period that
// contains the settlement date. The syntax of the function is:
//
// COUPDAYS(settlement,maturity,frequency,[basis])
//
func (fn *formulaFuncs) COUPDAYS(argsList *list.List) formulaArg {
args := fn.prepareCouponArgs("COUPDAYS", argsList)
if args.Type != ArgList {
return args
}
freq := args.List[2].Number
basis := int(args.List[3].Number)
if basis == 1 {
pcd := timeFromExcelTime(fn.COUPPCD(argsList).Number, false)
next := pcd.AddDate(0, 12/int(freq), 0)
return newNumberFormulaArg(coupdays(pcd, next, basis))
}
return newNumberFormulaArg(float64(getYearDays(0, basis)) / freq)
}
// COUPDAYSNC function calculates the number of days from the settlement date
// to the next coupon date. The syntax of the function is:
//
// COUPDAYSNC(settlement,maturity,frequency,[basis])
//
func (fn *formulaFuncs) COUPDAYSNC(argsList *list.List) formulaArg {
args := fn.prepareCouponArgs("COUPDAYSNC", argsList)
if args.Type != ArgList {
return args
}
settlement := timeFromExcelTime(args.List[0].Number, false)
basis := int(args.List[3].Number)
ncd := timeFromExcelTime(fn.COUPNCD(argsList).Number, false)
return newNumberFormulaArg(coupdays(settlement, ncd, basis))
}
// coupons is an implementation of the formula functions COUPNCD and COUPPCD.
func (fn *formulaFuncs) coupons(name string, arg formulaArg) formulaArg {
settlement := timeFromExcelTime(arg.List[0].Number, false)
maturity := timeFromExcelTime(arg.List[1].Number, false)
maturityDays := (maturity.Year()-settlement.Year())*12 + (int(maturity.Month()) - int(settlement.Month()))
coupon := 12 / int(arg.List[2].Number)
mod := maturityDays % coupon
year := settlement.Year()
month := int(settlement.Month())
if mod == 0 && settlement.Day() >= maturity.Day() {
month += coupon
} else {
month += mod
}
if name != "COUPNCD" {
month -= coupon
}
if month > 11 {
year += 1
month -= 12
} else if month < 0 {
year -= 1
month += 12
}
day, lastDay := maturity.Day(), time.Date(year, time.Month(month), 1, 0, 0, 0, 0, time.UTC)
days := getDaysInMonth(lastDay.Year(), int(lastDay.Month()))
if getDaysInMonth(maturity.Year(), int(maturity.Month())) == maturity.Day() {
day = days
} else if day > 27 && day > days {
day = days
}
return newNumberFormulaArg(daysBetween(excelMinTime1900.Unix(), makeDate(year, time.Month(month), day)) + 1)
}
// COUPNCD function calculates the number of coupons payable, between a
// security's settlement date and maturity date, rounded up to the nearest
// whole coupon. The syntax of the function is:
//
// COUPNCD(settlement,maturity,frequency,[basis])
//
func (fn *formulaFuncs) COUPNCD(argsList *list.List) formulaArg {
args := fn.prepareCouponArgs("COUPNCD", argsList)
if args.Type != ArgList {
return args
}
return fn.coupons("COUPNCD", args)
}
// COUPNUM function calculates the number of coupons payable, between a
// security's settlement date and maturity date, rounded up to the nearest
// whole coupon. The syntax of the function is:
//
// COUPNUM(settlement,maturity,frequency,[basis])
//
func (fn *formulaFuncs) COUPNUM(argsList *list.List) formulaArg {
args := fn.prepareCouponArgs("COUPNUM", argsList)
if args.Type != ArgList {
return args
}
frac := yearFrac(args.List[0].Number, args.List[1].Number, 0)
return newNumberFormulaArg(math.Ceil(frac.Number * args.List[2].Number))
}
// COUPPCD function returns the previous coupon date, before the settlement
// date for a security. The syntax of the function is:
//
// COUPPCD(settlement,maturity,frequency,[basis])
//
func (fn *formulaFuncs) COUPPCD(argsList *list.List) formulaArg {
args := fn.prepareCouponArgs("COUPPCD", argsList)
if args.Type != ArgList {
return args
}
return fn.coupons("COUPPCD", args)
}
// CUMIPMT function calculates the cumulative interest paid on a loan or
// investment, between two specified periods. The syntax of the function is:
//
// CUMIPMT(rate,nper,pv,start_period,end_period,type)
//
func (fn *formulaFuncs) CUMIPMT(argsList *list.List) formulaArg {
return fn.cumip("CUMIPMT", argsList)
}
// CUMPRINC function calculates the cumulative payment on the principal of a
// loan or investment, between two specified periods. The syntax of the
// function is:
//
// CUMPRINC(rate,nper,pv,start_period,end_period,type)
//
func (fn *formulaFuncs) CUMPRINC(argsList *list.List) formulaArg {
return fn.cumip("CUMPRINC", argsList)
}
// cumip is an implementation of the formula functions CUMIPMT and CUMPRINC.
func (fn *formulaFuncs) cumip(name string, argsList *list.List) formulaArg {
if argsList.Len() != 6 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 6 arguments", name))
}
rate := argsList.Front().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
nper := argsList.Front().Next().Value.(formulaArg).ToNumber()
if nper.Type != ArgNumber {
return nper
}
pv := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if pv.Type != ArgNumber {
return pv
}
start := argsList.Back().Prev().Prev().Value.(formulaArg).ToNumber()
if start.Type != ArgNumber {
return start
}
end := argsList.Back().Prev().Value.(formulaArg).ToNumber()
if end.Type != ArgNumber {
return end
}
typ := argsList.Back().Value.(formulaArg).ToNumber()
if typ.Type != ArgNumber {
return typ
}
if typ.Number != 0 && typ.Number != 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
if start.Number < 1 || start.Number > end.Number {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
num := 0.0
for per := start.Number; per <= end.Number; per++ {
args := list.New().Init()
args.PushBack(rate)
args.PushBack(newNumberFormulaArg(per))
args.PushBack(nper)
args.PushBack(pv)
args.PushBack(newNumberFormulaArg(0))
args.PushBack(typ)
if name == "CUMIPMT" {
num += fn.IPMT(args).Number
continue
}
num += fn.PPMT(args).Number
}
return newNumberFormulaArg(num)
}
// calcDbArgsCompare implements common arguments' comparison for DB and DDB.
func calcDbArgsCompare(cost, salvage, life, period formulaArg) bool {
return (cost.Number <= 0) || ((salvage.Number / cost.Number) < 0) || (life.Number <= 0) || (period.Number < 1)
}
// DB function calculates the depreciation of an asset, using the Fixed
// Declining Balance Method, for each period of the asset's lifetime. The
// syntax of the function is:
//
// DB(cost,salvage,life,period,[month])
//
func (fn *formulaFuncs) DB(argsList *list.List) formulaArg {
if argsList.Len() < 4 {
return newErrorFormulaArg(formulaErrorVALUE, "DB requires at least 4 arguments")
}
if argsList.Len() > 5 {
return newErrorFormulaArg(formulaErrorVALUE, "DB allows at most 5 arguments")
}
cost := argsList.Front().Value.(formulaArg).ToNumber()
if cost.Type != ArgNumber {
return cost
}
salvage := argsList.Front().Next().Value.(formulaArg).ToNumber()
if salvage.Type != ArgNumber {
return salvage
}
life := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if life.Type != ArgNumber {
return life
}
period := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if period.Type != ArgNumber {
return period
}
month := newNumberFormulaArg(12)
if argsList.Len() == 5 {
if month = argsList.Back().Value.(formulaArg).ToNumber(); month.Type != ArgNumber {
return month
}
}
if cost.Number == 0 {
return newNumberFormulaArg(0)
}
if calcDbArgsCompare(cost, salvage, life, period) || (month.Number < 1) {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
dr := 1 - math.Pow(salvage.Number/cost.Number, 1/life.Number)
dr = math.Round(dr*1000) / 1000
pd, depreciation := 0.0, 0.0
for per := 1; per <= int(period.Number); per++ {
if per == 1 {
depreciation = cost.Number * dr * month.Number / 12
} else if per == int(life.Number+1) {
depreciation = (cost.Number - pd) * dr * (12 - month.Number) / 12
} else {
depreciation = (cost.Number - pd) * dr
}
pd += depreciation
}
return newNumberFormulaArg(depreciation)
}
// DDB function calculates the depreciation of an asset, using the Double
// Declining Balance Method, or another specified depreciation rate. The
// syntax of the function is:
//
// DDB(cost,salvage,life,period,[factor])
//
func (fn *formulaFuncs) DDB(argsList *list.List) formulaArg {
if argsList.Len() < 4 {
return newErrorFormulaArg(formulaErrorVALUE, "DDB requires at least 4 arguments")
}
if argsList.Len() > 5 {
return newErrorFormulaArg(formulaErrorVALUE, "DDB allows at most 5 arguments")
}
cost := argsList.Front().Value.(formulaArg).ToNumber()
if cost.Type != ArgNumber {
return cost
}
salvage := argsList.Front().Next().Value.(formulaArg).ToNumber()
if salvage.Type != ArgNumber {
return salvage
}
life := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if life.Type != ArgNumber {
return life
}
period := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if period.Type != ArgNumber {
return period
}
factor := newNumberFormulaArg(2)
if argsList.Len() == 5 {
if factor = argsList.Back().Value.(formulaArg).ToNumber(); factor.Type != ArgNumber {
return factor
}
}
if cost.Number == 0 {
return newNumberFormulaArg(0)
}
if calcDbArgsCompare(cost, salvage, life, period) || (factor.Number <= 0.0) || (period.Number > life.Number) {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
pd, depreciation := 0.0, 0.0
for per := 1; per <= int(period.Number); per++ {
depreciation = math.Min((cost.Number-pd)*(factor.Number/life.Number), cost.Number-salvage.Number-pd)
pd += depreciation
}
return newNumberFormulaArg(depreciation)
}
// prepareDataValueArgs convert first N arguments to data value for the
// formula functions.
func (fn *formulaFuncs) prepareDataValueArgs(n int, argsList *list.List) formulaArg {
l := list.New()
var dataValues []formulaArg
getDateValue := func(arg formulaArg, l *list.List) formulaArg {
switch arg.Type {
case ArgNumber:
break
case ArgString:
num := arg.ToNumber()
if num.Type == ArgNumber {
arg = num
break
}
l.Init()
l.PushBack(arg)
arg = fn.DATEVALUE(l)
if arg.Type == ArgError {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
default:
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
return arg
}
for i, arg := 0, argsList.Front(); i < n; arg = arg.Next() {
dataValue := getDateValue(arg.Value.(formulaArg), l)
if dataValue.Type != ArgNumber {
return dataValue
}
dataValues = append(dataValues, dataValue)
i++
}
return newListFormulaArg(dataValues)
}
// DISC function calculates the Discount Rate for a security. The syntax of
// the function is:
//
// DISC(settlement,maturity,pr,redemption,[basis])
//
func (fn *formulaFuncs) DISC(argsList *list.List) formulaArg {
if argsList.Len() != 4 && argsList.Len() != 5 {
return newErrorFormulaArg(formulaErrorVALUE, "DISC requires 4 or 5 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
if maturity.Number <= settlement.Number {
return newErrorFormulaArg(formulaErrorNUM, "DISC requires maturity > settlement")
}
pr := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if pr.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if pr.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "DISC requires pr > 0")
}
redemption := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if redemption.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if redemption.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "DISC requires redemption > 0")
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 5 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
frac := yearFrac(settlement.Number, maturity.Number, int(basis.Number))
if frac.Type != ArgNumber {
return frac
}
return newNumberFormulaArg((redemption.Number - pr.Number) / redemption.Number / frac.Number)
}
// DOLLARDE function converts a dollar value in fractional notation, into a
// dollar value expressed as a decimal. The syntax of the function is:
//
// DOLLARDE(fractional_dollar,fraction)
//
func (fn *formulaFuncs) DOLLARDE(argsList *list.List) formulaArg {
return fn.dollar("DOLLARDE", argsList)
}
// DOLLARFR function converts a dollar value in decimal notation, into a
// dollar value that is expressed in fractional notation. The syntax of the
// function is:
//
// DOLLARFR(decimal_dollar,fraction)
//
func (fn *formulaFuncs) DOLLARFR(argsList *list.List) formulaArg {
return fn.dollar("DOLLARFR", argsList)
}
// dollar is an implementation of the formula functions DOLLARDE and DOLLARFR.
func (fn *formulaFuncs) dollar(name string, argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 2 arguments", name))
}
dollar := argsList.Front().Value.(formulaArg).ToNumber()
if dollar.Type != ArgNumber {
return dollar
}
frac := argsList.Back().Value.(formulaArg).ToNumber()
if frac.Type != ArgNumber {
return frac
}
if frac.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if frac.Number == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
cents := math.Mod(dollar.Number, 1)
if name == "DOLLARDE" {
cents /= frac.Number
cents *= math.Pow(10, math.Ceil(math.Log10(frac.Number)))
} else {
cents *= frac.Number
cents *= math.Pow(10, -math.Ceil(math.Log10(frac.Number)))
}
return newNumberFormulaArg(math.Floor(dollar.Number) + cents)
}
// prepareDurationArgs checking and prepare arguments for the formula
// functions DURATION and MDURATION.
func (fn *formulaFuncs) prepareDurationArgs(name string, argsList *list.List) formulaArg {
if argsList.Len() != 5 && argsList.Len() != 6 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 5 or 6 arguments", name))
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
if settlement.Number >= maturity.Number {
return newErrorFormulaArg(formulaErrorNUM, fmt.Sprintf("%s requires maturity > settlement", name))
}
coupon := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if coupon.Type != ArgNumber {
return coupon
}
if coupon.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, fmt.Sprintf("%s requires coupon >= 0", name))
}
yld := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if yld.Type != ArgNumber {
return yld
}
if yld.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, fmt.Sprintf("%s requires yld >= 0", name))
}
frequency := argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if frequency.Type != ArgNumber {
return frequency
}
if !validateFrequency(frequency.Number) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 6 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
return newListFormulaArg([]formulaArg{settlement, maturity, coupon, yld, frequency, basis})
}
// duration is an implementation of the formula function DURATION.
func (fn *formulaFuncs) duration(settlement, maturity, coupon, yld, frequency, basis formulaArg) formulaArg {
frac := yearFrac(settlement.Number, maturity.Number, int(basis.Number))
if frac.Type != ArgNumber {
return frac
}
argumments := list.New().Init()
argumments.PushBack(settlement)
argumments.PushBack(maturity)
argumments.PushBack(frequency)
argumments.PushBack(basis)
coups := fn.COUPNUM(argumments)
duration := 0.0
p := 0.0
coupon.Number *= 100 / frequency.Number
yld.Number /= frequency.Number
yld.Number++
diff := frac.Number*frequency.Number - coups.Number
for t := 1.0; t < coups.Number; t++ {
tDiff := t + diff
add := coupon.Number / math.Pow(yld.Number, tDiff)
p += add
duration += tDiff * add
}
add := (coupon.Number + 100) / math.Pow(yld.Number, coups.Number+diff)
p += add
duration += (coups.Number + diff) * add
duration /= p
duration /= frequency.Number
return newNumberFormulaArg(duration)
}
// DURATION function calculates the Duration (specifically, the Macaulay
// Duration) of a security that pays periodic interest, assuming a par value
// of $100. The syntax of the function is:
//
// DURATION(settlement,maturity,coupon,yld,frequency,[basis])
//
func (fn *formulaFuncs) DURATION(argsList *list.List) formulaArg {
args := fn.prepareDurationArgs("DURATION", argsList)
if args.Type != ArgList {
return args
}
return fn.duration(args.List[0], args.List[1], args.List[2], args.List[3], args.List[4], args.List[5])
}
// EFFECT function returns the effective annual interest rate for a given
// nominal interest rate and number of compounding periods per year. The
// syntax of the function is:
//
// EFFECT(nominal_rate,npery)
//
func (fn *formulaFuncs) EFFECT(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "EFFECT requires 2 arguments")
}
rate := argsList.Front().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
npery := argsList.Back().Value.(formulaArg).ToNumber()
if npery.Type != ArgNumber {
return npery
}
if rate.Number <= 0 || npery.Number < 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(math.Pow(1+rate.Number/npery.Number, npery.Number) - 1)
}
// EUROCONVERT function convert a number to euro or from euro to a
// participating currency. You can also use it to convert a number from one
// participating currency to another by using the euro as an intermediary
// (triangulation). The syntax of the function is:
//
// EUROCONVERT(number,sourcecurrency,targetcurrency[,fullprecision,triangulationprecision])
//
func (fn *formulaFuncs) EUROCONVERT(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "EUROCONVERT requires at least 3 arguments")
}
if argsList.Len() > 5 {
return newErrorFormulaArg(formulaErrorVALUE, "EUROCONVERT allows at most 5 arguments")
}
number := argsList.Front().Value.(formulaArg).ToNumber()
if number.Type != ArgNumber {
return number
}
sourceCurrency := argsList.Front().Next().Value.(formulaArg).Value()
targetCurrency := argsList.Front().Next().Next().Value.(formulaArg).Value()
fullPrec, triangulationPrec := newBoolFormulaArg(false), newNumberFormulaArg(0)
if argsList.Len() >= 4 {
if fullPrec = argsList.Front().Next().Next().Next().Value.(formulaArg).ToBool(); fullPrec.Type != ArgNumber {
return fullPrec
}
}
if argsList.Len() == 5 {
if triangulationPrec = argsList.Back().Value.(formulaArg).ToNumber(); triangulationPrec.Type != ArgNumber {
return triangulationPrec
}
}
convertTable := map[string][]float64{
"EUR": {1.0, 2},
"ATS": {13.7603, 2},
"BEF": {40.3399, 0},
"DEM": {1.95583, 2},
"ESP": {166.386, 0},
"FIM": {5.94573, 2},
"FRF": {6.55957, 2},
"IEP": {0.787564, 2},
"ITL": {1936.27, 0},
"LUF": {40.3399, 0},
"NLG": {2.20371, 2},
"PTE": {200.482, 2},
"GRD": {340.750, 2},
"SIT": {239.640, 2},
"MTL": {0.429300, 2},
"CYP": {0.585274, 2},
"SKK": {30.1260, 2},
"EEK": {15.6466, 2},
"LVL": {0.702804, 2},
"LTL": {3.45280, 2},
}
source, ok := convertTable[sourceCurrency]
if !ok {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
target, ok := convertTable[targetCurrency]
if !ok {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if sourceCurrency == targetCurrency {
return number
}
var res float64
if sourceCurrency == "EUR" {
res = number.Number * target[0]
} else {
intermediate := number.Number / source[0]
if triangulationPrec.Number != 0 {
ratio := math.Pow(10, triangulationPrec.Number)
intermediate = math.Round(intermediate*ratio) / ratio
}
res = intermediate * target[0]
}
if fullPrec.Number != 1 {
ratio := math.Pow(10, target[1])
res = math.Round(res*ratio) / ratio
}
return newNumberFormulaArg(res)
}
// FV function calculates the Future Value of an investment with periodic
// constant payments and a constant interest rate. The syntax of the function
// is:
//
// FV(rate,nper,[pmt],[pv],[type])
//
func (fn *formulaFuncs) FV(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "FV requires at least 3 arguments")
}
if argsList.Len() > 5 {
return newErrorFormulaArg(formulaErrorVALUE, "FV allows at most 5 arguments")
}
rate := argsList.Front().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
nper := argsList.Front().Next().Value.(formulaArg).ToNumber()
if nper.Type != ArgNumber {
return nper
}
pmt := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if pmt.Type != ArgNumber {
return pmt
}
pv, typ := newNumberFormulaArg(0), newNumberFormulaArg(0)
if argsList.Len() >= 4 {
if pv = argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber(); pv.Type != ArgNumber {
return pv
}
}
if argsList.Len() == 5 {
if typ = argsList.Back().Value.(formulaArg).ToNumber(); typ.Type != ArgNumber {
return typ
}
}
if typ.Number != 0 && typ.Number != 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
if rate.Number != 0 {
return newNumberFormulaArg(-pv.Number*math.Pow(1+rate.Number, nper.Number) - pmt.Number*(1+rate.Number*typ.Number)*(math.Pow(1+rate.Number, nper.Number)-1)/rate.Number)
}
return newNumberFormulaArg(-pv.Number - pmt.Number*nper.Number)
}
// FVSCHEDULE function calculates the Future Value of an investment with a
// variable interest rate. The syntax of the function is:
//
// FVSCHEDULE(principal,schedule)
//
func (fn *formulaFuncs) FVSCHEDULE(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "FVSCHEDULE requires 2 arguments")
}
pri := argsList.Front().Value.(formulaArg).ToNumber()
if pri.Type != ArgNumber {
return pri
}
principal := pri.Number
for _, arg := range argsList.Back().Value.(formulaArg).ToList() {
if arg.Value() == "" {
continue
}
rate := arg.ToNumber()
if rate.Type != ArgNumber {
return rate
}
principal *= 1 + rate.Number
}
return newNumberFormulaArg(principal)
}
// INTRATE function calculates the interest rate for a fully invested
// security. The syntax of the function is:
//
// INTRATE(settlement,maturity,investment,redemption,[basis])
//
func (fn *formulaFuncs) INTRATE(argsList *list.List) formulaArg {
if argsList.Len() != 4 && argsList.Len() != 5 {
return newErrorFormulaArg(formulaErrorVALUE, "INTRATE requires 4 or 5 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
if maturity.Number <= settlement.Number {
return newErrorFormulaArg(formulaErrorNUM, "INTRATE requires maturity > settlement")
}
investment := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if investment.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if investment.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "INTRATE requires investment > 0")
}
redemption := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if redemption.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if redemption.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "INTRATE requires redemption > 0")
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 5 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
frac := yearFrac(settlement.Number, maturity.Number, int(basis.Number))
if frac.Type != ArgNumber {
return frac
}
return newNumberFormulaArg((redemption.Number - investment.Number) / investment.Number / frac.Number)
}
// IPMT function calculates the interest payment, during a specific period of a
// loan or investment that is paid in constant periodic payments, with a
// constant interest rate. The syntax of the function is:
//
// IPMT(rate,per,nper,pv,[fv],[type])
//
func (fn *formulaFuncs) IPMT(argsList *list.List) formulaArg {
return fn.ipmt("IPMT", argsList)
}
// calcIpmt is part of the implementation ipmt.
func calcIpmt(name string, typ, per, pmt, pv, rate formulaArg) formulaArg {
capital, interest, principal := pv.Number, 0.0, 0.0
for i := 1; i <= int(per.Number); i++ {
if typ.Number != 0 && i == 1 {
interest = 0
} else {
interest = -capital * rate.Number
}
principal = pmt.Number - interest
capital += principal
}
if name == "IPMT" {
return newNumberFormulaArg(interest)
}
return newNumberFormulaArg(principal)
}
// ipmt is an implementation of the formula functions IPMT and PPMT.
func (fn *formulaFuncs) ipmt(name string, argsList *list.List) formulaArg {
if argsList.Len() < 4 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 4 arguments", name))
}
if argsList.Len() > 6 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s allows at most 6 arguments", name))
}
rate := argsList.Front().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
per := argsList.Front().Next().Value.(formulaArg).ToNumber()
if per.Type != ArgNumber {
return per
}
nper := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if nper.Type != ArgNumber {
return nper
}
pv := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if pv.Type != ArgNumber {
return pv
}
fv, typ := newNumberFormulaArg(0), newNumberFormulaArg(0)
if argsList.Len() >= 5 {
if fv = argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber(); fv.Type != ArgNumber {
return fv
}
}
if argsList.Len() == 6 {
if typ = argsList.Back().Value.(formulaArg).ToNumber(); typ.Type != ArgNumber {
return typ
}
}
if typ.Number != 0 && typ.Number != 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
if per.Number <= 0 || per.Number > nper.Number {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
args := list.New().Init()
args.PushBack(rate)
args.PushBack(nper)
args.PushBack(pv)
args.PushBack(fv)
args.PushBack(typ)
pmt := fn.PMT(args)
return calcIpmt(name, typ, per, pmt, pv, rate)
}
// IRR function returns the Internal Rate of Return for a supplied series of
// periodic cash flows (i.e. an initial investment value and a series of net
// income values). The syntax of the function is:
//
// IRR(values,[guess])
//
func (fn *formulaFuncs) IRR(argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, "IRR requires at least 1 argument")
}
if argsList.Len() > 2 {
return newErrorFormulaArg(formulaErrorVALUE, "IRR allows at most 2 arguments")
}
values, guess := argsList.Front().Value.(formulaArg).ToList(), newNumberFormulaArg(0.1)
if argsList.Len() > 1 {
if guess = argsList.Back().Value.(formulaArg).ToNumber(); guess.Type != ArgNumber {
return guess
}
}
x1, x2 := newNumberFormulaArg(0), guess
args := list.New().Init()
args.PushBack(x1)
for _, v := range values {
args.PushBack(v)
}
f1 := fn.NPV(args)
args.Front().Value = x2
f2 := fn.NPV(args)
for i := 0; i < maxFinancialIterations; i++ {
if f1.Number*f2.Number < 0 {
break
}
if math.Abs(f1.Number) < math.Abs(f2.Number) {
x1.Number += 1.6 * (x1.Number - x2.Number)
args.Front().Value = x1
f1 = fn.NPV(args)
continue
}
x2.Number += 1.6 * (x2.Number - x1.Number)
args.Front().Value = x2
f2 = fn.NPV(args)
}
if f1.Number*f2.Number > 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
args.Front().Value = x1
f := fn.NPV(args)
var rtb, dx, xMid, fMid float64
if f.Number < 0 {
rtb = x1.Number
dx = x2.Number - x1.Number
} else {
rtb = x2.Number
dx = x1.Number - x2.Number
}
for i := 0; i < maxFinancialIterations; i++ {
dx *= 0.5
xMid = rtb + dx
args.Front().Value = newNumberFormulaArg(xMid)
fMid = fn.NPV(args).Number
if fMid <= 0 {
rtb = xMid
}
if math.Abs(fMid) < financialPrecision || math.Abs(dx) < financialPrecision {
break
}
}
return newNumberFormulaArg(xMid)
}
// ISPMT function calculates the interest paid during a specific period of a
// loan or investment. The syntax of the function is:
//
// ISPMT(rate,per,nper,pv)
//
func (fn *formulaFuncs) ISPMT(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "ISPMT requires 4 arguments")
}
rate := argsList.Front().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
per := argsList.Front().Next().Value.(formulaArg).ToNumber()
if per.Type != ArgNumber {
return per
}
nper := argsList.Back().Prev().Value.(formulaArg).ToNumber()
if nper.Type != ArgNumber {
return nper
}
pv := argsList.Back().Value.(formulaArg).ToNumber()
if pv.Type != ArgNumber {
return pv
}
pr, payment, num := pv.Number, pv.Number/nper.Number, 0.0
for i := 0; i <= int(per.Number); i++ {
num = rate.Number * pr * -1
pr -= payment
if i == int(nper.Number) {
num = 0
}
}
return newNumberFormulaArg(num)
}
// MDURATION function calculates the Modified Macaulay Duration of a security
// that pays periodic interest, assuming a par value of $100. The syntax of
// the function is:
//
// MDURATION(settlement,maturity,coupon,yld,frequency,[basis])
//
func (fn *formulaFuncs) MDURATION(argsList *list.List) formulaArg {
args := fn.prepareDurationArgs("MDURATION", argsList)
if args.Type != ArgList {
return args
}
duration := fn.duration(args.List[0], args.List[1], args.List[2], args.List[3], args.List[4], args.List[5])
if duration.Type != ArgNumber {
return duration
}
return newNumberFormulaArg(duration.Number / (1 + args.List[3].Number/args.List[4].Number))
}
// MIRR function returns the Modified Internal Rate of Return for a supplied
// series of periodic cash flows (i.e. a set of values, which includes an
// initial investment value and a series of net income values). The syntax of
// the function is:
//
// MIRR(values,finance_rate,reinvest_rate)
//
func (fn *formulaFuncs) MIRR(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "MIRR requires 3 arguments")
}
values := argsList.Front().Value.(formulaArg).ToList()
financeRate := argsList.Front().Next().Value.(formulaArg).ToNumber()
if financeRate.Type != ArgNumber {
return financeRate
}
reinvestRate := argsList.Back().Value.(formulaArg).ToNumber()
if reinvestRate.Type != ArgNumber {
return reinvestRate
}
n, fr, rr, npvPos, npvNeg := len(values), 1+financeRate.Number, 1+reinvestRate.Number, 0.0, 0.0
for i, v := range values {
val := v.ToNumber()
if val.Number >= 0 {
npvPos += val.Number / math.Pow(rr, float64(i))
continue
}
npvNeg += val.Number / math.Pow(fr, float64(i))
}
if npvNeg == 0 || npvPos == 0 || reinvestRate.Number <= -1 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
return newNumberFormulaArg(math.Pow(-npvPos*math.Pow(rr, float64(n))/(npvNeg*rr), 1/(float64(n)-1)) - 1)
}
// NOMINAL function returns the nominal interest rate for a given effective
// interest rate and number of compounding periods per year. The syntax of
// the function is:
//
// NOMINAL(effect_rate,npery)
//
func (fn *formulaFuncs) NOMINAL(argsList *list.List) formulaArg {
if argsList.Len() != 2 {
return newErrorFormulaArg(formulaErrorVALUE, "NOMINAL requires 2 arguments")
}
rate := argsList.Front().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
npery := argsList.Back().Value.(formulaArg).ToNumber()
if npery.Type != ArgNumber {
return npery
}
if rate.Number <= 0 || npery.Number < 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(npery.Number * (math.Pow(rate.Number+1, 1/npery.Number) - 1))
}
// NPER function calculates the number of periods required to pay off a loan,
// for a constant periodic payment and a constant interest rate. The syntax
// of the function is:
//
// NPER(rate,pmt,pv,[fv],[type])
//
func (fn *formulaFuncs) NPER(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "NPER requires at least 3 arguments")
}
if argsList.Len() > 5 {
return newErrorFormulaArg(formulaErrorVALUE, "NPER allows at most 5 arguments")
}
rate := argsList.Front().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
pmt := argsList.Front().Next().Value.(formulaArg).ToNumber()
if pmt.Type != ArgNumber {
return pmt
}
pv := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if pv.Type != ArgNumber {
return pv
}
fv, typ := newNumberFormulaArg(0), newNumberFormulaArg(0)
if argsList.Len() >= 4 {
if fv = argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber(); fv.Type != ArgNumber {
return fv
}
}
if argsList.Len() == 5 {
if typ = argsList.Back().Value.(formulaArg).ToNumber(); typ.Type != ArgNumber {
return typ
}
}
if typ.Number != 0 && typ.Number != 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
if pmt.Number == 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if rate.Number != 0 {
p := math.Log((pmt.Number*(1+rate.Number*typ.Number)/rate.Number-fv.Number)/(pv.Number+pmt.Number*(1+rate.Number*typ.Number)/rate.Number)) / math.Log(1+rate.Number)
return newNumberFormulaArg(p)
}
return newNumberFormulaArg((-pv.Number - fv.Number) / pmt.Number)
}
// NPV function calculates the Net Present Value of an investment, based on a
// supplied discount rate, and a series of future payments and income. The
// syntax of the function is:
//
// NPV(rate,value1,[value2],[value3],...)
//
func (fn *formulaFuncs) NPV(argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, "NPV requires at least 2 arguments")
}
rate := argsList.Front().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
val, i := 0.0, 1
for arg := argsList.Front().Next(); arg != nil; arg = arg.Next() {
num := arg.Value.(formulaArg).ToNumber()
if num.Type != ArgNumber {
continue
}
val += num.Number / math.Pow(1+rate.Number, float64(i))
i++
}
return newNumberFormulaArg(val)
}
// aggrBetween is a part of implementation of the formula function ODDFPRICE.
func aggrBetween(startPeriod, endPeriod float64, initialValue []float64, f func(acc []float64, index float64) []float64) []float64 {
var s []float64
if startPeriod <= endPeriod {
for i := startPeriod; i <= endPeriod; i++ {
s = append(s, i)
}
} else {
for i := startPeriod; i >= endPeriod; i-- {
s = append(s, i)
}
}
return fold(f, initialValue, s)
}
// fold is a part of implementation of the formula function ODDFPRICE.
func fold(f func(acc []float64, index float64) []float64, state []float64, source []float64) []float64 {
length, value := len(source), state
for index := 0; length > index; index++ {
value = f(value, source[index])
}
return value
}
// changeMonth is a part of implementation of the formula function ODDFPRICE.
func changeMonth(date time.Time, numMonths float64, returnLastMonth bool) time.Time {
offsetDay := 0
if returnLastMonth && date.Day() == getDaysInMonth(date.Year(), int(date.Month())) {
offsetDay--
}
newDate := date.AddDate(0, int(numMonths), offsetDay)
if returnLastMonth {
lastDay := getDaysInMonth(newDate.Year(), int(newDate.Month()))
return timeFromExcelTime(daysBetween(excelMinTime1900.Unix(), makeDate(newDate.Year(), newDate.Month(), lastDay))+1, false)
}
return newDate
}
// datesAggregate is a part of implementation of the formula function
// ODDFPRICE.
func datesAggregate(startDate, endDate time.Time, numMonths float64, f func(pcd, ncd time.Time) float64, acc float64, returnLastMonth bool) (time.Time, time.Time, float64) {
frontDate, trailingDate := startDate, endDate
s1 := frontDate.After(endDate) || frontDate.Equal(endDate)
s2 := endDate.After(frontDate) || endDate.Equal(frontDate)
stop := s2
if numMonths > 0 {
stop = s1
}
for !stop {
trailingDate = frontDate
frontDate = changeMonth(frontDate, numMonths, returnLastMonth)
fn := f(frontDate, trailingDate)
acc += fn
s1 = frontDate.After(endDate) || frontDate.Equal(endDate)
s2 = endDate.After(frontDate) || endDate.Equal(frontDate)
stop = s2
if numMonths > 0 {
stop = s1
}
}
return frontDate, trailingDate, acc
}
// coupNumber is a part of implementation of the formula function ODDFPRICE.
func coupNumber(maturity, settlement, numMonths float64) float64 {
maturityTime, settlementTime := timeFromExcelTime(maturity, false), timeFromExcelTime(settlement, false)
my, mm, md := maturityTime.Year(), maturityTime.Month(), maturityTime.Day()
sy, sm, sd := settlementTime.Year(), settlementTime.Month(), settlementTime.Day()
couponsTemp, endOfMonthTemp := 0.0, getDaysInMonth(my, int(mm)) == md
endOfMonth := endOfMonthTemp
if !endOfMonthTemp && mm != 2 && md > 28 && md < getDaysInMonth(my, int(mm)) {
endOfMonth = getDaysInMonth(sy, int(sm)) == sd
}
startDate := changeMonth(settlementTime, 0, endOfMonth)
coupons := couponsTemp
if startDate.After(settlementTime) {
coupons++
}
date := changeMonth(startDate, numMonths, endOfMonth)
f := func(pcd, ncd time.Time) float64 {
return 1
}
_, _, result := datesAggregate(date, maturityTime, numMonths, f, coupons, endOfMonth)
return result
}
// prepareOddfpriceArgs checking and prepare arguments for the formula
// function ODDFPRICE.
func (fn *formulaFuncs) prepareOddfpriceArgs(argsList *list.List) formulaArg {
dateValues := fn.prepareDataValueArgs(4, argsList)
if dateValues.Type != ArgList {
return dateValues
}
settlement, maturity, issue, firstCoupon := dateValues.List[0], dateValues.List[1], dateValues.List[2], dateValues.List[3]
if issue.Number >= settlement.Number {
return newErrorFormulaArg(formulaErrorNUM, "ODDFPRICE requires settlement > issue")
}
if settlement.Number >= firstCoupon.Number {
return newErrorFormulaArg(formulaErrorNUM, "ODDFPRICE requires first_coupon > settlement")
}
if firstCoupon.Number >= maturity.Number {
return newErrorFormulaArg(formulaErrorNUM, "ODDFPRICE requires maturity > first_coupon")
}
rate := argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
if rate.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "ODDFPRICE requires rate >= 0")
}
yld := argsList.Front().Next().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if yld.Type != ArgNumber {
return yld
}
if yld.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "ODDFPRICE requires yld >= 0")
}
redemption := argsList.Front().Next().Next().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if redemption.Type != ArgNumber {
return redemption
}
if redemption.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "ODDFPRICE requires redemption > 0")
}
frequency := argsList.Front().Next().Next().Next().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if frequency.Type != ArgNumber {
return frequency
}
if !validateFrequency(frequency.Number) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 9 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
return newListFormulaArg([]formulaArg{settlement, maturity, issue, firstCoupon, rate, yld, redemption, frequency, basis})
}
// ODDFPRICE function calculates the price per $100 face value of a security
// with an odd (short or long) first period. The syntax of the function is:
//
// ODDFPRICE(settlement,maturity,issue,first_coupon,rate,yld,redemption,frequency,[basis])
//
func (fn *formulaFuncs) ODDFPRICE(argsList *list.List) formulaArg {
if argsList.Len() != 8 && argsList.Len() != 9 {
return newErrorFormulaArg(formulaErrorVALUE, "ODDFPRICE requires 8 or 9 arguments")
}
args := fn.prepareOddfpriceArgs(argsList)
if args.Type != ArgList {
return args
}
settlement, maturity, issue, firstCoupon, rate, yld, redemption, frequency, basisArg := args.List[0], args.List[1], args.List[2], args.List[3], args.List[4], args.List[5], args.List[6], args.List[7], args.List[8]
if basisArg.Number < 0 || basisArg.Number > 4 {
return newErrorFormulaArg(formulaErrorNUM, "invalid basis")
}
issueTime := timeFromExcelTime(issue.Number, false)
settlementTime := timeFromExcelTime(settlement.Number, false)
maturityTime := timeFromExcelTime(maturity.Number, false)
firstCouponTime := timeFromExcelTime(firstCoupon.Number, false)
basis := int(basisArg.Number)
monthDays := getDaysInMonth(maturityTime.Year(), int(maturityTime.Month()))
returnLastMonth := monthDays == maturityTime.Day()
numMonths := 12 / frequency.Number
numMonthsNeg := -numMonths
mat := changeMonth(maturityTime, numMonthsNeg, returnLastMonth)
pcd, _, _ := datesAggregate(mat, firstCouponTime, numMonthsNeg, func(d1, d2 time.Time) float64 {
return 0
}, 0, returnLastMonth)
if !pcd.Equal(firstCouponTime) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
fnArgs := list.New().Init()
fnArgs.PushBack(settlement)
fnArgs.PushBack(maturity)
fnArgs.PushBack(frequency)
fnArgs.PushBack(basisArg)
e := fn.COUPDAYS(fnArgs)
n := fn.COUPNUM(fnArgs)
m := frequency.Number
dfc := coupdays(issueTime, firstCouponTime, basis)
if dfc < e.Number {
dsc := coupdays(settlementTime, firstCouponTime, basis)
a := coupdays(issueTime, settlementTime, basis)
x := yld.Number/m + 1
y := dsc / e.Number
p1 := x
p3 := math.Pow(p1, n.Number-1+y)
term1 := redemption.Number / p3
term2 := 100 * rate.Number / m * dfc / e.Number / math.Pow(p1, y)
f := func(acc []float64, index float64) []float64 {
return []float64{acc[0] + 100*rate.Number/m/math.Pow(p1, index-1+y)}
}
term3 := aggrBetween(2, math.Floor(n.Number), []float64{0}, f)
p2 := rate.Number / m
term4 := a / e.Number * p2 * 100
return newNumberFormulaArg(term1 + term2 + term3[0] - term4)
}
fnArgs.Init()
fnArgs.PushBack(issue)
fnArgs.PushBack(firstCoupon)
fnArgs.PushBack(frequency)
nc := fn.COUPNUM(fnArgs)
lastCoupon := firstCoupon.Number
aggrFunc := func(acc []float64, index float64) []float64 {
lastCouponTime := timeFromExcelTime(lastCoupon, false)
earlyCoupon := daysBetween(excelMinTime1900.Unix(), makeDate(lastCouponTime.Year(), time.Month(float64(lastCouponTime.Month())+numMonthsNeg), lastCouponTime.Day())) + 1
earlyCouponTime := timeFromExcelTime(earlyCoupon, false)
nl := e.Number
if basis == 1 {
nl = coupdays(earlyCouponTime, lastCouponTime, basis)
}
dci := coupdays(issueTime, lastCouponTime, basis)
if index > 1 {
dci = nl
}
startDate := earlyCoupon
if issue.Number > earlyCoupon {
startDate = issue.Number
}
endDate := lastCoupon
if settlement.Number < lastCoupon {
endDate = settlement.Number
}
startDateTime := timeFromExcelTime(startDate, false)
endDateTime := timeFromExcelTime(endDate, false)
a := coupdays(startDateTime, endDateTime, basis)
lastCoupon = earlyCoupon
dcnl := acc[0]
anl := acc[1]
return []float64{dcnl + dci/nl, anl + a/nl}
}
ag := aggrBetween(math.Floor(nc.Number), 1, []float64{0, 0}, aggrFunc)
dcnl, anl := ag[0], ag[1]
dsc := 0.0
fnArgs.Init()
fnArgs.PushBack(settlement)
fnArgs.PushBack(firstCoupon)
fnArgs.PushBack(frequency)
if basis == 2 || basis == 3 {
d := timeFromExcelTime(fn.COUPNCD(fnArgs).Number, false)
dsc = coupdays(settlementTime, d, basis)
} else {
d := timeFromExcelTime(fn.COUPPCD(fnArgs).Number, false)
a := coupdays(d, settlementTime, basis)
dsc = e.Number - a
}
nq := coupNumber(firstCoupon.Number, settlement.Number, numMonths)
fnArgs.Init()
fnArgs.PushBack(firstCoupon)
fnArgs.PushBack(maturity)
fnArgs.PushBack(frequency)
fnArgs.PushBack(basisArg)
n = fn.COUPNUM(fnArgs)
x := yld.Number/m + 1
y := dsc / e.Number
p1 := x
p3 := math.Pow(p1, y+nq+n.Number)
term1 := redemption.Number / p3
term2 := 100 * rate.Number / m * dcnl / math.Pow(p1, nq+y)
f := func(acc []float64, index float64) []float64 {
return []float64{acc[0] + 100*rate.Number/m/math.Pow(p1, index+nq+y)}
}
term3 := aggrBetween(1, math.Floor(n.Number), []float64{0}, f)
term4 := 100 * rate.Number / m * anl
return newNumberFormulaArg(term1 + term2 + term3[0] - term4)
}
// PDURATION function calculates the number of periods required for an
// investment to reach a specified future value. The syntax of the function
// is:
//
// PDURATION(rate,pv,fv)
//
func (fn *formulaFuncs) PDURATION(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "PDURATION requires 3 arguments")
}
rate := argsList.Front().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
pv := argsList.Front().Next().Value.(formulaArg).ToNumber()
if pv.Type != ArgNumber {
return pv
}
fv := argsList.Back().Value.(formulaArg).ToNumber()
if fv.Type != ArgNumber {
return fv
}
if rate.Number <= 0 || pv.Number <= 0 || fv.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg((math.Log(fv.Number) - math.Log(pv.Number)) / math.Log(1+rate.Number))
}
// PMT function calculates the constant periodic payment required to pay off
// (or partially pay off) a loan or investment, with a constant interest
// rate, over a specified period. The syntax of the function is:
//
// PMT(rate,nper,pv,[fv],[type])
//
func (fn *formulaFuncs) PMT(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "PMT requires at least 3 arguments")
}
if argsList.Len() > 5 {
return newErrorFormulaArg(formulaErrorVALUE, "PMT allows at most 5 arguments")
}
rate := argsList.Front().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
nper := argsList.Front().Next().Value.(formulaArg).ToNumber()
if nper.Type != ArgNumber {
return nper
}
pv := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if pv.Type != ArgNumber {
return pv
}
fv, typ := newNumberFormulaArg(0), newNumberFormulaArg(0)
if argsList.Len() >= 4 {
if fv = argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber(); fv.Type != ArgNumber {
return fv
}
}
if argsList.Len() == 5 {
if typ = argsList.Back().Value.(formulaArg).ToNumber(); typ.Type != ArgNumber {
return typ
}
}
if typ.Number != 0 && typ.Number != 1 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
if rate.Number != 0 {
p := (-fv.Number - pv.Number*math.Pow(1+rate.Number, nper.Number)) / (1 + rate.Number*typ.Number) / ((math.Pow(1+rate.Number, nper.Number) - 1) / rate.Number)
return newNumberFormulaArg(p)
}
return newNumberFormulaArg((-pv.Number - fv.Number) / nper.Number)
}
// PPMT function calculates the payment on the principal, during a specific
// period of a loan or investment that is paid in constant periodic payments,
// with a constant interest rate. The syntax of the function is:
//
// PPMT(rate,per,nper,pv,[fv],[type])
//
func (fn *formulaFuncs) PPMT(argsList *list.List) formulaArg {
return fn.ipmt("PPMT", argsList)
}
// price is an implementation of the formula function PRICE.
func (fn *formulaFuncs) price(settlement, maturity, rate, yld, redemption, frequency, basis formulaArg) formulaArg {
if basis.Number < 0 || basis.Number > 4 {
return newErrorFormulaArg(formulaErrorNUM, "invalid basis")
}
argsList := list.New().Init()
argsList.PushBack(settlement)
argsList.PushBack(maturity)
argsList.PushBack(frequency)
argsList.PushBack(basis)
e := fn.COUPDAYS(argsList)
dsc := fn.COUPDAYSNC(argsList).Number / e.Number
n := fn.COUPNUM(argsList)
a := fn.COUPDAYBS(argsList)
ret := 0.0
if n.Number > 1 {
ret = redemption.Number / math.Pow(1+yld.Number/frequency.Number, n.Number-1+dsc)
ret -= 100 * rate.Number / frequency.Number * a.Number / e.Number
t1 := 100 * rate.Number / frequency.Number
t2 := 1 + yld.Number/frequency.Number
for k := 0.0; k < n.Number; k++ {
ret += t1 / math.Pow(t2, k+dsc)
}
} else {
dsc = e.Number - a.Number
t1 := 100*(rate.Number/frequency.Number) + redemption.Number
t2 := (yld.Number/frequency.Number)*(dsc/e.Number) + 1
t3 := 100 * (rate.Number / frequency.Number) * (a.Number / e.Number)
ret = t1/t2 - t3
}
return newNumberFormulaArg(ret)
}
// PRICE function calculates the price, per $100 face value of a security that
// pays periodic interest. The syntax of the function is:
//
// PRICE(settlement,maturity,rate,yld,redemption,frequency,[basis])
//
func (fn *formulaFuncs) PRICE(argsList *list.List) formulaArg {
if argsList.Len() != 6 && argsList.Len() != 7 {
return newErrorFormulaArg(formulaErrorVALUE, "PRICE requires 6 or 7 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
rate := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
if rate.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "PRICE requires rate >= 0")
}
yld := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if yld.Type != ArgNumber {
return yld
}
if yld.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "PRICE requires yld >= 0")
}
redemption := argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if redemption.Type != ArgNumber {
return redemption
}
if redemption.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "PRICE requires redemption > 0")
}
frequency := argsList.Front().Next().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if frequency.Type != ArgNumber {
return frequency
}
if !validateFrequency(frequency.Number) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 7 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
return fn.price(settlement, maturity, rate, yld, redemption, frequency, basis)
}
// PRICEDISC function calculates the price, per $100 face value of a
// discounted security. The syntax of the function is:
//
// PRICEDISC(settlement,maturity,discount,redemption,[basis])
//
func (fn *formulaFuncs) PRICEDISC(argsList *list.List) formulaArg {
if argsList.Len() != 4 && argsList.Len() != 5 {
return newErrorFormulaArg(formulaErrorVALUE, "PRICEDISC requires 4 or 5 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
if maturity.Number <= settlement.Number {
return newErrorFormulaArg(formulaErrorNUM, "PRICEDISC requires maturity > settlement")
}
discount := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if discount.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if discount.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "PRICEDISC requires discount > 0")
}
redemption := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if redemption.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if redemption.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "PRICEDISC requires redemption > 0")
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 5 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
frac := yearFrac(settlement.Number, maturity.Number, int(basis.Number))
if frac.Type != ArgNumber {
return frac
}
return newNumberFormulaArg(redemption.Number * (1 - discount.Number*frac.Number))
}
// PRICEMAT function calculates the price, per $100 face value of a security
// that pays interest at maturity. The syntax of the function is:
//
// PRICEMAT(settlement,maturity,issue,rate,yld,[basis])
//
func (fn *formulaFuncs) PRICEMAT(argsList *list.List) formulaArg {
if argsList.Len() != 5 && argsList.Len() != 6 {
return newErrorFormulaArg(formulaErrorVALUE, "PRICEMAT requires 5 or 6 arguments")
}
args := fn.prepareDataValueArgs(3, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity, issue := args.List[0], args.List[1], args.List[2]
if settlement.Number >= maturity.Number {
return newErrorFormulaArg(formulaErrorNUM, "PRICEMAT requires maturity > settlement")
}
if issue.Number >= settlement.Number {
return newErrorFormulaArg(formulaErrorNUM, "PRICEMAT requires settlement > issue")
}
rate := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
if rate.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "PRICEMAT requires rate >= 0")
}
yld := argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if yld.Type != ArgNumber {
return yld
}
if yld.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "PRICEMAT requires yld >= 0")
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 6 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
dsm := yearFrac(settlement.Number, maturity.Number, int(basis.Number))
if dsm.Type != ArgNumber {
return dsm
}
dis := yearFrac(issue.Number, settlement.Number, int(basis.Number))
dim := yearFrac(issue.Number, maturity.Number, int(basis.Number))
return newNumberFormulaArg(((1+dim.Number*rate.Number)/(1+dsm.Number*yld.Number) - dis.Number*rate.Number) * 100)
}
// PV function calculates the Present Value of an investment, based on a
// series of future payments. The syntax of the function is:
//
// PV(rate,nper,pmt,[fv],[type])
//
func (fn *formulaFuncs) PV(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "PV requires at least 3 arguments")
}
if argsList.Len() > 5 {
return newErrorFormulaArg(formulaErrorVALUE, "PV allows at most 5 arguments")
}
rate := argsList.Front().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
nper := argsList.Front().Next().Value.(formulaArg).ToNumber()
if nper.Type != ArgNumber {
return nper
}
pmt := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if pmt.Type != ArgNumber {
return pmt
}
fv := newNumberFormulaArg(0)
if argsList.Len() >= 4 {
if fv = argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber(); fv.Type != ArgNumber {
return fv
}
}
t := newNumberFormulaArg(0)
if argsList.Len() == 5 {
if t = argsList.Back().Value.(formulaArg).ToNumber(); t.Type != ArgNumber {
return t
}
if t.Number != 0 {
t.Number = 1
}
}
if rate.Number == 0 {
return newNumberFormulaArg(-pmt.Number*nper.Number - fv.Number)
}
return newNumberFormulaArg((((1-math.Pow(1+rate.Number, nper.Number))/rate.Number)*pmt.Number*(1+rate.Number*t.Number) - fv.Number) / math.Pow(1+rate.Number, nper.Number))
}
// rate is an implementation of the formula function RATE.
func (fn *formulaFuncs) rate(nper, pmt, pv, fv, t, guess formulaArg) formulaArg {
maxIter, iter, isClose, epsMax, rate := 100, 0, false, 1e-6, guess.Number
for iter < maxIter && !isClose {
t1 := math.Pow(rate+1, nper.Number)
t2 := math.Pow(rate+1, nper.Number-1)
rt := rate*t.Number + 1
p0 := pmt.Number * (t1 - 1)
f1 := fv.Number + t1*pv.Number + p0*rt/rate
n1 := nper.Number * t2 * pv.Number
n2 := p0 * rt / math.Pow(rate, 2)
f2 := math.Nextafter(n1, n1) - math.Nextafter(n2, n2)
f3 := (nper.Number*pmt.Number*t2*rt + p0*t.Number) / rate
delta := f1 / (f2 + f3)
if math.Abs(delta) < epsMax {
isClose = true
}
iter++
rate -= delta
}
return newNumberFormulaArg(rate)
}
// RATE function calculates the interest rate required to pay off a specified
// amount of a loan, or to reach a target amount on an investment, over a
// given period. The syntax of the function is:
//
// RATE(nper,pmt,pv,[fv],[type],[guess])
//
func (fn *formulaFuncs) RATE(argsList *list.List) formulaArg {
if argsList.Len() < 3 {
return newErrorFormulaArg(formulaErrorVALUE, "RATE requires at least 3 arguments")
}
if argsList.Len() > 6 {
return newErrorFormulaArg(formulaErrorVALUE, "RATE allows at most 6 arguments")
}
nper := argsList.Front().Value.(formulaArg).ToNumber()
if nper.Type != ArgNumber {
return nper
}
pmt := argsList.Front().Next().Value.(formulaArg).ToNumber()
if pmt.Type != ArgNumber {
return pmt
}
pv := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if pv.Type != ArgNumber {
return pv
}
fv := newNumberFormulaArg(0)
if argsList.Len() >= 4 {
if fv = argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber(); fv.Type != ArgNumber {
return fv
}
}
t := newNumberFormulaArg(0)
if argsList.Len() >= 5 {
if t = argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber(); t.Type != ArgNumber {
return t
}
if t.Number != 0 {
t.Number = 1
}
}
guess := newNumberFormulaArg(0.1)
if argsList.Len() == 6 {
if guess = argsList.Back().Value.(formulaArg).ToNumber(); guess.Type != ArgNumber {
return guess
}
}
return fn.rate(nper, pmt, pv, fv, t, guess)
}
// RECEIVED function calculates the amount received at maturity for a fully
// invested security. The syntax of the function is:
//
// RECEIVED(settlement,maturity,investment,discount,[basis])
//
func (fn *formulaFuncs) RECEIVED(argsList *list.List) formulaArg {
if argsList.Len() < 4 {
return newErrorFormulaArg(formulaErrorVALUE, "RECEIVED requires at least 4 arguments")
}
if argsList.Len() > 5 {
return newErrorFormulaArg(formulaErrorVALUE, "RECEIVED allows at most 5 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
investment := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if investment.Type != ArgNumber {
return investment
}
discount := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if discount.Type != ArgNumber {
return discount
}
if discount.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "RECEIVED requires discount > 0")
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 5 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
frac := yearFrac(settlement.Number, maturity.Number, int(basis.Number))
if frac.Type != ArgNumber {
return frac
}
return newNumberFormulaArg(investment.Number / (1 - discount.Number*frac.Number))
}
// RRI function calculates the equivalent interest rate for an investment with
// specified present value, future value and duration. The syntax of the
// function is:
//
// RRI(nper,pv,fv)
//
func (fn *formulaFuncs) RRI(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "RRI requires 3 arguments")
}
nper := argsList.Front().Value.(formulaArg).ToNumber()
pv := argsList.Front().Next().Value.(formulaArg).ToNumber()
fv := argsList.Back().Value.(formulaArg).ToNumber()
if nper.Type != ArgNumber || pv.Type != ArgNumber || fv.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if nper.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "RRI requires nper argument to be > 0")
}
if pv.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "RRI requires pv argument to be > 0")
}
if fv.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "RRI requires fv argument to be >= 0")
}
return newNumberFormulaArg(math.Pow(fv.Number/pv.Number, 1/nper.Number) - 1)
}
// SLN function calculates the straight line depreciation of an asset for one
// period. The syntax of the function is:
//
// SLN(cost,salvage,life)
//
func (fn *formulaFuncs) SLN(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "SLN requires 3 arguments")
}
cost := argsList.Front().Value.(formulaArg).ToNumber()
salvage := argsList.Front().Next().Value.(formulaArg).ToNumber()
life := argsList.Back().Value.(formulaArg).ToNumber()
if cost.Type != ArgNumber || salvage.Type != ArgNumber || life.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if life.Number == 0 {
return newErrorFormulaArg(formulaErrorNUM, "SLN requires life argument to be > 0")
}
return newNumberFormulaArg((cost.Number - salvage.Number) / life.Number)
}
// SYD function calculates the sum-of-years' digits depreciation for a
// specified period in the lifetime of an asset. The syntax of the function
// is:
//
// SYD(cost,salvage,life,per)
//
func (fn *formulaFuncs) SYD(argsList *list.List) formulaArg {
if argsList.Len() != 4 {
return newErrorFormulaArg(formulaErrorVALUE, "SYD requires 4 arguments")
}
cost := argsList.Front().Value.(formulaArg).ToNumber()
salvage := argsList.Front().Next().Value.(formulaArg).ToNumber()
life := argsList.Back().Prev().Value.(formulaArg).ToNumber()
per := argsList.Back().Value.(formulaArg).ToNumber()
if cost.Type != ArgNumber || salvage.Type != ArgNumber || life.Type != ArgNumber || per.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if life.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "SYD requires life argument to be > 0")
}
if per.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "SYD requires per argument to be > 0")
}
if per.Number > life.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(((cost.Number - salvage.Number) * (life.Number - per.Number + 1) * 2) / (life.Number * (life.Number + 1)))
}
// TBILLEQ function calculates the bond-equivalent yield for a Treasury Bill.
// The syntax of the function is:
//
// TBILLEQ(settlement,maturity,discount)
//
func (fn *formulaFuncs) TBILLEQ(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "TBILLEQ requires 3 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
dsm := maturity.Number - settlement.Number
if dsm > 365 || maturity.Number <= settlement.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
discount := argsList.Back().Value.(formulaArg).ToNumber()
if discount.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if discount.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg((365 * discount.Number) / (360 - discount.Number*dsm))
}
// TBILLPRICE function returns the price, per $100 face value, of a Treasury
// Bill. The syntax of the function is:
//
// TBILLPRICE(settlement,maturity,discount)
//
func (fn *formulaFuncs) TBILLPRICE(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "TBILLPRICE requires 3 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
dsm := maturity.Number - settlement.Number
if dsm > 365 || maturity.Number <= settlement.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
discount := argsList.Back().Value.(formulaArg).ToNumber()
if discount.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if discount.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(100 * (1 - discount.Number*dsm/360))
}
// TBILLYIELD function calculates the yield of a Treasury Bill. The syntax of
// the function is:
//
// TBILLYIELD(settlement,maturity,pr)
//
func (fn *formulaFuncs) TBILLYIELD(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "TBILLYIELD requires 3 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
dsm := maturity.Number - settlement.Number
if dsm > 365 || maturity.Number <= settlement.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
pr := argsList.Back().Value.(formulaArg).ToNumber()
if pr.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if pr.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(((100 - pr.Number) / pr.Number) * (360 / dsm))
}
// prepareVdbArgs checking and prepare arguments for the formula function
// VDB.
func (fn *formulaFuncs) prepareVdbArgs(argsList *list.List) formulaArg {
cost := argsList.Front().Value.(formulaArg).ToNumber()
if cost.Type != ArgNumber {
return cost
}
if cost.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "VDB requires cost >= 0")
}
salvage := argsList.Front().Next().Value.(formulaArg).ToNumber()
if salvage.Type != ArgNumber {
return salvage
}
if salvage.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "VDB requires salvage >= 0")
}
life := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if life.Type != ArgNumber {
return life
}
if life.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "VDB requires life > 0")
}
startPeriod := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if startPeriod.Type != ArgNumber {
return startPeriod
}
if startPeriod.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "VDB requires start_period > 0")
}
endPeriod := argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if endPeriod.Type != ArgNumber {
return endPeriod
}
if startPeriod.Number > endPeriod.Number {
return newErrorFormulaArg(formulaErrorNUM, "VDB requires start_period <= end_period")
}
if endPeriod.Number > life.Number {
return newErrorFormulaArg(formulaErrorNUM, "VDB requires end_period <= life")
}
factor := newNumberFormulaArg(2)
if argsList.Len() > 5 {
if factor = argsList.Front().Next().Next().Next().Next().Next().Value.(formulaArg).ToNumber(); factor.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if factor.Number < 0 {
return newErrorFormulaArg(formulaErrorVALUE, "VDB requires factor >= 0")
}
}
return newListFormulaArg([]formulaArg{cost, salvage, life, startPeriod, endPeriod, factor})
}
// vdb is a part of implementation of the formula function VDB.
func (fn *formulaFuncs) vdb(cost, salvage, life, life1, period, factor formulaArg) formulaArg {
var ddb, vdb, sln, term float64
endInt, cs, nowSln := math.Ceil(period.Number), cost.Number-salvage.Number, false
ddbArgs := list.New()
for i := 1.0; i <= endInt; i++ {
if !nowSln {
ddbArgs.Init()
ddbArgs.PushBack(cost)
ddbArgs.PushBack(salvage)
ddbArgs.PushBack(life)
ddbArgs.PushBack(newNumberFormulaArg(i))
ddbArgs.PushBack(factor)
ddb = fn.DDB(ddbArgs).Number
sln = cs / (life1.Number - i + 1)
if sln > ddb {
term = sln
nowSln = true
} else {
term = ddb
cs -= ddb
}
} else {
term = sln
}
if i == endInt {
term *= period.Number + 1 - endInt
}
vdb += term
}
return newNumberFormulaArg(vdb)
}
// VDB function calculates the depreciation of an asset, using the Double
// Declining Balance Method, or another specified depreciation rate, for a
// specified period (including partial periods). The syntax of the function
// is:
//
// VDB(cost,salvage,life,start_period,end_period,[factor],[no_switch])
//
func (fn *formulaFuncs) VDB(argsList *list.List) formulaArg {
if argsList.Len() < 5 || argsList.Len() > 7 {
return newErrorFormulaArg(formulaErrorVALUE, "VDB requires 5 or 7 arguments")
}
args := fn.prepareVdbArgs(argsList)
if args.Type != ArgList {
return args
}
cost, salvage, life, startPeriod, endPeriod, factor := args.List[0], args.List[1], args.List[2], args.List[3], args.List[4], args.List[5]
noSwitch := newBoolFormulaArg(false)
if argsList.Len() > 6 {
if noSwitch = argsList.Back().Value.(formulaArg).ToBool(); noSwitch.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
startInt, endInt, vdb, ddbArgs := math.Floor(startPeriod.Number), math.Ceil(endPeriod.Number), newNumberFormulaArg(0), list.New()
if noSwitch.Number == 1 {
for i := startInt + 1; i <= endInt; i++ {
ddbArgs.Init()
ddbArgs.PushBack(cost)
ddbArgs.PushBack(salvage)
ddbArgs.PushBack(life)
ddbArgs.PushBack(newNumberFormulaArg(i))
ddbArgs.PushBack(factor)
term := fn.DDB(ddbArgs)
if i == startInt+1 {
term.Number *= math.Min(endPeriod.Number, startInt+1) - startPeriod.Number
} else if i == endInt {
term.Number *= endPeriod.Number + 1 - endInt
}
vdb.Number += term.Number
}
return vdb
}
life1, part := life, 0.0
if startPeriod.Number != math.Floor(startPeriod.Number) && factor.Number > 1.0 && startPeriod.Number >= life.Number/2.0 {
part = startPeriod.Number - life.Number/2.0
startPeriod.Number = life.Number / 2.0
endPeriod.Number -= part
}
cost.Number -= fn.vdb(cost, salvage, life, life1, startPeriod, factor).Number
return fn.vdb(cost, salvage, life, newNumberFormulaArg(life.Number-startPeriod.Number), newNumberFormulaArg(endPeriod.Number-startPeriod.Number), factor)
}
// prepareXArgs prepare arguments for the formula function XIRR and XNPV.
func (fn *formulaFuncs) prepareXArgs(values, dates formulaArg) (valuesArg, datesArg []float64, err formulaArg) {
for _, arg := range values.ToList() {
if numArg := arg.ToNumber(); numArg.Type == ArgNumber {
valuesArg = append(valuesArg, numArg.Number)
continue
}
err = newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
return
}
if len(valuesArg) < 2 {
err = newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
return
}
args, date := list.New(), 0.0
for _, arg := range dates.ToList() {
args.Init()
args.PushBack(arg)
dateValue := fn.DATEVALUE(args)
if dateValue.Type != ArgNumber {
err = newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
return
}
if dateValue.Number < date {
err = newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
return
}
datesArg = append(datesArg, dateValue.Number)
date = dateValue.Number
}
if len(valuesArg) != len(datesArg) {
err = newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
return
}
err = newEmptyFormulaArg()
return
}
// xirr is an implementation of the formula function XIRR.
func (fn *formulaFuncs) xirr(values, dates []float64, guess float64) formulaArg {
positive, negative := false, false
for i := 0; i < len(values); i++ {
if values[i] > 0 {
positive = true
}
if values[i] < 0 {
negative = true
}
}
if !positive || !negative {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
result, epsMax, count, maxIterate, err := guess, 1e-10, 0, 50, false
for {
resultValue := xirrPart1(values, dates, result)
newRate := result - resultValue/xirrPart2(values, dates, result)
epsRate := math.Abs(newRate - result)
result = newRate
count++
if epsRate <= epsMax || math.Abs(resultValue) <= epsMax {
break
}
if count > maxIterate {
err = true
break
}
}
if err || math.IsNaN(result) || math.IsInf(result, 0) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
return newNumberFormulaArg(result)
}
// xirrPart1 is a part of implementation of the formula function XIRR.
func xirrPart1(values, dates []float64, rate float64) float64 {
r := rate + 1
result := values[0]
vlen := len(values)
firstDate := dates[0]
for i := 1; i < vlen; i++ {
result += values[i] / math.Pow(r, (dates[i]-firstDate)/365)
}
return result
}
// xirrPart2 is a part of implementation of the formula function XIRR.
func xirrPart2(values, dates []float64, rate float64) float64 {
r := rate + 1
result := 0.0
vlen := len(values)
firstDate := dates[0]
for i := 1; i < vlen; i++ {
frac := (dates[i] - firstDate) / 365
result -= frac * values[i] / math.Pow(r, frac+1)
}
return result
}
// XIRR function returns the Internal Rate of Return for a supplied series of
// cash flows (i.e. a set of values, which includes an initial investment
// value and a series of net income values) occurring at a series of supplied
// dates. The syntax of the function is:
//
// XIRR(values,dates,[guess])
//
func (fn *formulaFuncs) XIRR(argsList *list.List) formulaArg {
if argsList.Len() != 2 && argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "XIRR requires 2 or 3 arguments")
}
values, dates, err := fn.prepareXArgs(argsList.Front().Value.(formulaArg), argsList.Front().Next().Value.(formulaArg))
if err.Type != ArgEmpty {
return err
}
guess := newNumberFormulaArg(0)
if argsList.Len() == 3 {
if guess = argsList.Back().Value.(formulaArg).ToNumber(); guess.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if guess.Number <= -1 {
return newErrorFormulaArg(formulaErrorVALUE, "XIRR requires guess > -1")
}
}
return fn.xirr(values, dates, guess.Number)
}
// XNPV function calculates the Net Present Value for a schedule of cash flows
// that is not necessarily periodic. The syntax of the function is:
//
// XNPV(rate,values,dates)
//
func (fn *formulaFuncs) XNPV(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "XNPV requires 3 arguments")
}
rate := argsList.Front().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
if rate.Number <= 0 {
return newErrorFormulaArg(formulaErrorVALUE, "XNPV requires rate > 0")
}
values, dates, err := fn.prepareXArgs(argsList.Front().Next().Value.(formulaArg), argsList.Back().Value.(formulaArg))
if err.Type != ArgEmpty {
return err
}
date1, xnpv := dates[0], 0.0
for idx, value := range values {
xnpv += value / math.Pow(1+rate.Number, (dates[idx]-date1)/365)
}
return newNumberFormulaArg(xnpv)
}
// yield is an implementation of the formula function YIELD.
func (fn *formulaFuncs) yield(settlement, maturity, rate, pr, redemption, frequency, basis formulaArg) formulaArg {
priceN, yield1, yield2 := newNumberFormulaArg(0), newNumberFormulaArg(0), newNumberFormulaArg(1)
price1 := fn.price(settlement, maturity, rate, yield1, redemption, frequency, basis)
if price1.Type != ArgNumber {
return price1
}
price2 := fn.price(settlement, maturity, rate, yield2, redemption, frequency, basis)
yieldN := newNumberFormulaArg((yield2.Number - yield1.Number) * 0.5)
for iter := 0; iter < 100 && priceN.Number != pr.Number; iter++ {
priceN = fn.price(settlement, maturity, rate, yieldN, redemption, frequency, basis)
if pr.Number == price1.Number {
return yield1
} else if pr.Number == price2.Number {
return yield2
} else if pr.Number == priceN.Number {
return yieldN
} else if pr.Number < price2.Number {
yield2.Number *= 2.0
price2 = fn.price(settlement, maturity, rate, yield2, redemption, frequency, basis)
yieldN.Number = (yield2.Number - yield1.Number) * 0.5
} else {
if pr.Number < priceN.Number {
yield1 = yieldN
price1 = priceN
} else {
yield2 = yieldN
price2 = priceN
}
f1 := (yield2.Number - yield1.Number) * ((pr.Number - price2.Number) / (price1.Number - price2.Number))
yieldN.Number = yield2.Number - math.Nextafter(f1, f1)
}
}
return yieldN
}
// YIELD function calculates the Yield of a security that pays periodic
// interest. The syntax of the function is:
//
// YIELD(settlement,maturity,rate,pr,redemption,frequency,[basis])
//
func (fn *formulaFuncs) YIELD(argsList *list.List) formulaArg {
if argsList.Len() != 6 && argsList.Len() != 7 {
return newErrorFormulaArg(formulaErrorVALUE, "YIELD requires 6 or 7 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
rate := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
if rate.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "PRICE requires rate >= 0")
}
pr := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if pr.Type != ArgNumber {
return pr
}
if pr.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "PRICE requires pr > 0")
}
redemption := argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if redemption.Type != ArgNumber {
return redemption
}
if redemption.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "PRICE requires redemption >= 0")
}
frequency := argsList.Front().Next().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if frequency.Type != ArgNumber {
return frequency
}
if !validateFrequency(frequency.Number) {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 7 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
return fn.yield(settlement, maturity, rate, pr, redemption, frequency, basis)
}
// YIELDDISC function calculates the annual yield of a discounted security.
// The syntax of the function is:
//
// YIELDDISC(settlement,maturity,pr,redemption,[basis])
//
func (fn *formulaFuncs) YIELDDISC(argsList *list.List) formulaArg {
if argsList.Len() != 4 && argsList.Len() != 5 {
return newErrorFormulaArg(formulaErrorVALUE, "YIELDDISC requires 4 or 5 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
pr := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if pr.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if pr.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "YIELDDISC requires pr > 0")
}
redemption := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if redemption.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
if redemption.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "YIELDDISC requires redemption > 0")
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 5 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
frac := yearFrac(settlement.Number, maturity.Number, int(basis.Number))
if frac.Type != ArgNumber {
return frac
}
return newNumberFormulaArg((redemption.Number/pr.Number - 1) / frac.Number)
}
// YIELDMAT function calculates the annual yield of a security that pays
// interest at maturity. The syntax of the function is:
//
// YIELDMAT(settlement,maturity,issue,rate,pr,[basis])
//
func (fn *formulaFuncs) YIELDMAT(argsList *list.List) formulaArg {
if argsList.Len() != 5 && argsList.Len() != 6 {
return newErrorFormulaArg(formulaErrorVALUE, "YIELDMAT requires 5 or 6 arguments")
}
args := fn.prepareDataValueArgs(2, argsList)
if args.Type != ArgList {
return args
}
settlement, maturity := args.List[0], args.List[1]
arg := list.New().Init()
issue := argsList.Front().Next().Next().Value.(formulaArg).ToNumber()
if issue.Type != ArgNumber {
arg.PushBack(argsList.Front().Next().Next().Value.(formulaArg))
issue = fn.DATEVALUE(arg)
if issue.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
}
if issue.Number >= settlement.Number {
return newErrorFormulaArg(formulaErrorNUM, "YIELDMAT requires settlement > issue")
}
rate := argsList.Front().Next().Next().Next().Value.(formulaArg).ToNumber()
if rate.Type != ArgNumber {
return rate
}
if rate.Number < 0 {
return newErrorFormulaArg(formulaErrorNUM, "YIELDMAT requires rate >= 0")
}
pr := argsList.Front().Next().Next().Next().Next().Value.(formulaArg).ToNumber()
if pr.Type != ArgNumber {
return pr
}
if pr.Number <= 0 {
return newErrorFormulaArg(formulaErrorNUM, "YIELDMAT requires pr > 0")
}
basis := newNumberFormulaArg(0)
if argsList.Len() == 6 {
if basis = argsList.Back().Value.(formulaArg).ToNumber(); basis.Type != ArgNumber {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
dim := yearFrac(issue.Number, maturity.Number, int(basis.Number))
if dim.Type != ArgNumber {
return dim
}
dis := yearFrac(issue.Number, settlement.Number, int(basis.Number))
dsm := yearFrac(settlement.Number, maturity.Number, int(basis.Number))
f1 := dim.Number * rate.Number
result := 1 + math.Nextafter(f1, f1)
result /= pr.Number/100 + dis.Number*rate.Number
result--
result /= dsm.Number
return newNumberFormulaArg(result)
}
// Database Functions
// calcDatabase defines the structure for formula database.
type calcDatabase struct {
col, row int
indexMap map[int]int
database [][]formulaArg
criteria [][]formulaArg
}
// newCalcDatabase function returns formula database by given data range of
// cells containing the database, field and criteria range.
func newCalcDatabase(database, field, criteria formulaArg) *calcDatabase {
db := calcDatabase{
indexMap: make(map[int]int),
database: database.Matrix,
criteria: criteria.Matrix,
}
exp := len(database.Matrix) < 2 || len(database.Matrix[0]) < 1 ||
len(criteria.Matrix) < 2 || len(criteria.Matrix[0]) < 1
if field.Type != ArgEmpty {
if db.col = db.columnIndex(database.Matrix, field); exp || db.col < 0 || len(db.database[0]) <= db.col {
return nil
}
return &db
}
if db.col = -1; exp {
return nil
}
return &db
}
// columnIndex return index by specifies column field within the database for
// which user want to return the count of non-blank cells.
func (db *calcDatabase) columnIndex(database [][]formulaArg, field formulaArg) int {
num := field.ToNumber()
if num.Type != ArgNumber && len(database) > 0 {
for i := 0; i < len(database[0]); i++ {
if title := database[0][i]; strings.EqualFold(title.Value(), field.Value()) {
return i
}
}
return -1
}
return int(num.Number - 1)
}
// criteriaEval evaluate formula criteria expression.
func (db *calcDatabase) criteriaEval() bool {
var (
columns, rows = len(db.criteria[0]), len(db.criteria)
criteria = db.criteria
k int
matched bool
)
if len(db.indexMap) == 0 {
fields := criteria[0]
for j := 0; j < columns; j++ {
if k = db.columnIndex(db.database, fields[j]); k < 0 {
return false
}
db.indexMap[j] = k
}
}
for i := 1; !matched && i < rows; i++ {
matched = true
for j := 0; matched && j < columns; j++ {
criteriaExp := db.criteria[i][j].Value()
if criteriaExp == "" {
continue
}
criteria := formulaCriteriaParser(criteriaExp)
cell := db.database[db.row][db.indexMap[j]].Value()
matched, _ = formulaCriteriaEval(cell, criteria)
}
}
return matched
}
// value returns the current cell value.
func (db *calcDatabase) value() formulaArg {
if db.col == -1 {
return db.database[db.row][len(db.database[db.row])-1]
}
return db.database[db.row][db.col]
}
// next will return true if find the matched cell in the database.
func (db *calcDatabase) next() bool {
matched, rows := false, len(db.database)
for !matched && db.row < rows {
if db.row++; db.row < rows {
matched = db.criteriaEval()
}
}
return matched
}
// database is an implementation of the formula functions DAVERAGE, DMAX and DMIN.
func (fn *formulaFuncs) database(name string, argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires 3 arguments", name))
}
database := argsList.Front().Value.(formulaArg)
field := argsList.Front().Next().Value.(formulaArg)
criteria := argsList.Back().Value.(formulaArg)
db := newCalcDatabase(database, field, criteria)
if db == nil {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
args := list.New()
for db.next() {
args.PushBack(db.value())
}
switch name {
case "DMAX":
return fn.MAX(args)
case "DMIN":
return fn.MIN(args)
case "DPRODUCT":
return fn.PRODUCT(args)
case "DSTDEV":
return fn.STDEV(args)
case "DSTDEVP":
return fn.STDEVP(args)
case "DSUM":
return fn.SUM(args)
case "DVAR":
return fn.VAR(args)
case "DVARP":
return fn.VARP(args)
default:
return fn.AVERAGE(args)
}
}
// DAVERAGE function calculates the average (statistical mean) of values in a
// field (column) in a database for selected records, that satisfy
// user-specified criteria. The syntax of the Excel Daverage function is:
//
// DAVERAGE(database,field,criteria)
//
func (fn *formulaFuncs) DAVERAGE(argsList *list.List) formulaArg {
return fn.database("DAVERAGE", argsList)
}
// dcount is an implementation of the formula functions DCOUNT and DCOUNTA.
func (fn *formulaFuncs) dcount(name string, argsList *list.List) formulaArg {
if argsList.Len() < 2 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 2 arguments", name))
}
if argsList.Len() > 3 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s allows at most 3 arguments", name))
}
field := newEmptyFormulaArg()
criteria := argsList.Back().Value.(formulaArg)
if argsList.Len() > 2 {
field = argsList.Front().Next().Value.(formulaArg)
}
database := argsList.Front().Value.(formulaArg)
db := newCalcDatabase(database, field, criteria)
if db == nil {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
args := list.New()
for db.next() {
args.PushBack(db.value())
}
if name == "DCOUNT" {
return fn.COUNT(args)
}
return fn.COUNTA(args)
}
// DCOUNT function returns the number of cells containing numeric values, in a
// field (column) of a database for selected records only. The records to be
// included in the count are those that satisfy a set of one or more
// user-specified criteria. The syntax of the function is:
//
// DCOUNT(database,[field],criteria)
//
func (fn *formulaFuncs) DCOUNT(argsList *list.List) formulaArg {
return fn.dcount("DCOUNT", argsList)
}
// DCOUNTA function returns the number of non-blank cells, in a field
// (column) of a database for selected records only. The records to be
// included in the count are those that satisfy a set of one or more
// user-specified criteria. The syntax of the function is:
//
// DCOUNTA(database,[field],criteria)
//
func (fn *formulaFuncs) DCOUNTA(argsList *list.List) formulaArg {
return fn.dcount("DCOUNTA", argsList)
}
// DGET function returns a single value from a column of a database. The record
// is selected via a set of one or more user-specified criteria. The syntax of
// the function is:
//
// DGET(database,field,criteria)
//
func (fn *formulaFuncs) DGET(argsList *list.List) formulaArg {
if argsList.Len() != 3 {
return newErrorFormulaArg(formulaErrorVALUE, "DGET requires 3 arguments")
}
database := argsList.Front().Value.(formulaArg)
field := argsList.Front().Next().Value.(formulaArg)
criteria := argsList.Back().Value.(formulaArg)
db := newCalcDatabase(database, field, criteria)
if db == nil {
return newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
}
value := newErrorFormulaArg(formulaErrorVALUE, formulaErrorVALUE)
if db.next() {
if value = db.value(); db.next() {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
}
return value
}
// DMAX function finds the maximum value in a field (column) in a database for
// selected records only. The records to be included in the calculation are
// defined by a set of one or more user-specified criteria. The syntax of the
// function is:
//
// DMAX(database,field,criteria)
//
func (fn *formulaFuncs) DMAX(argsList *list.List) formulaArg {
return fn.database("DMAX", argsList)
}
// DMIN function finds the minimum value in a field (column) in a database for
// selected records only. The records to be included in the calculation are
// defined by a set of one or more user-specified criteria. The syntax of the
// function is:
//
// DMIN(database,field,criteria)
//
func (fn *formulaFuncs) DMIN(argsList *list.List) formulaArg {
return fn.database("DMIN", argsList)
}
// DPRODUCT function calculates the product of a field (column) in a database
// for selected records, that satisfy user-specified criteria. The syntax of
// the function is:
//
// DPRODUCT(database,field,criteria)
//
func (fn *formulaFuncs) DPRODUCT(argsList *list.List) formulaArg {
return fn.database("DPRODUCT", argsList)
}
// DSTDEV function calculates the sample standard deviation of a field
// (column) in a database for selected records only. The records to be
// included in the calculation are defined by a set of one or more
// user-specified criteria. The syntax of the function is:
//
// DSTDEV(database,field,criteria)
//
func (fn *formulaFuncs) DSTDEV(argsList *list.List) formulaArg {
return fn.database("DSTDEV", argsList)
}
// DSTDEVP function calculates the standard deviation of a field (column) in a
// database for selected records only. The records to be included in the
// calculation are defined by a set of one or more user-specified criteria.
// The syntax of the function is:
//
// DSTDEVP(database,field,criteria)
//
func (fn *formulaFuncs) DSTDEVP(argsList *list.List) formulaArg {
return fn.database("DSTDEVP", argsList)
}
// DSUM function calculates the sum of a field (column) in a database for
// selected records, that satisfy user-specified criteria. The syntax of the
// function is:
//
// DSUM(database,field,criteria)
//
func (fn *formulaFuncs) DSUM(argsList *list.List) formulaArg {
return fn.database("DSUM", argsList)
}
// DVAR function calculates the sample variance of a field (column) in a
// database for selected records only. The records to be included in the
// calculation are defined by a set of one or more user-specified criteria.
// The syntax of the function is:
//
// DVAR(database,field,criteria)
//
func (fn *formulaFuncs) DVAR(argsList *list.List) formulaArg {
return fn.database("DVAR", argsList)
}
// DVARP function calculates the variance (for an entire population), of the
// values in a field (column) in a database for selected records only. The
// records to be included in the calculation are defined by a set of one or
// more user-specified criteria. The syntax of the function is:
//
// DVARP(database,field,criteria)
//
func (fn *formulaFuncs) DVARP(argsList *list.List) formulaArg {
return fn.database("DVARP", argsList)
}