ref #65, new formula functions: T.INV and T.INV.2T

- Typo fixed

5 files changed, 140 insertions, 51 deletions

diff --git a/calc.go b/calc.go
index ad62596..c375b71 100644
--- a/calc.go
+++ b/calc.go
@@ -664,6 +664,8 @@ type formulaFuncs struct {
 //    TEXTJOIN
 //    TIME
 //    TIMEVALUE
+//    T.INV
+//    T.INV.2T
 //    TODAY
 //    TRANSPOSE
 //    TRIM
@@ -1265,27 +1267,6 @@ func isOperand(token efp.Token) bool {
 	return token.TType == efp.TokenTypeOperand && (token.TSubType == efp.TokenSubTypeNumber || token.TSubType == efp.TokenSubTypeText)
 }
 
-// getDefinedNameRefTo convert defined name to reference range.
-func (f *File) getDefinedNameRefTo(definedNameName string, currentSheet string) (refTo string) {
-	var workbookRefTo, worksheetRefTo string
-	for _, definedName := range f.GetDefinedName() {
-		if definedName.Name == definedNameName {
-			// worksheet scope takes precedence over scope workbook when both definedNames exist
-			if definedName.Scope == "Workbook" {
-				workbookRefTo = definedName.RefersTo
-			}
-			if definedName.Scope == currentSheet {
-				worksheetRefTo = definedName.RefersTo
-			}
-		}
-	}
-	refTo = workbookRefTo
-	if worksheetRefTo != "" {
-		refTo = worksheetRefTo
-	}
-	return
-}
-
 // parseToken parse basic arithmetic operator priority and evaluate based on
 // operators and operands.
 func (f *File) parseToken(sheet string, token efp.Token, opdStack, optStack *Stack) error {
@@ -6647,14 +6628,16 @@ func hasChangeOfSign(u, w float64) bool {
 // calcInverseIterator directly maps the required parameters for inverse
 // distribution functions.
 type calcInverseIterator struct {
-	name    string
-	fp, fDF float64
+	name        string
+	fp, fDF, nT float64
 }
 
-// chiSqDist implements inverse distribution with left tail for the Chi-Square
-// distribution.
-func (iterator *calcInverseIterator) chiSqDist(x float64) float64 {
-	return iterator.fp - getChiSqDistCDF(x, iterator.fDF)
+// 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
@@ -6682,7 +6665,7 @@ func inverseQuadraticInterpolation(iterator calcInverseIterator, fAx, fAy, fBx,
 			bHasToInterpolate = true
 		}
 		fPx, fQx, fRx, fPy, fQy = fQx, fRx, fSx, fQy, fRy
-		fRy = iterator.chiSqDist(fSx)
+		fRy = iterator.callBack(fSx)
 		if hasChangeOfSign(fAy, fRy) {
 			fBx, fBy = fRx, fRy
 		} else {
@@ -6697,7 +6680,7 @@ func inverseQuadraticInterpolation(iterator calcInverseIterator, fAx, fAy, fBx,
 // calcIterateInverse function calculates the iteration for inverse
 // distributions.
 func calcIterateInverse(iterator calcInverseIterator, fAx, fBx float64) float64 {
-	fAy, fBy := iterator.chiSqDist(fAx), iterator.chiSqDist(fBx)
+	fAy, fBy := iterator.callBack(fAx), iterator.callBack(fBx)
 	var fTemp float64
 	var nCount int
 	for nCount = 0; nCount < 1000 && !hasChangeOfSign(fAy, fBy); nCount++ {
@@ -6709,13 +6692,13 @@ func calcIterateInverse(iterator calcInverseIterator, fAx, fBx float64) float64
 			}
 			fBx = fTemp
 			fBy = fAy
-			fAy = iterator.chiSqDist(fAx)
+			fAy = iterator.callBack(fAx)
 		} else {
 			fTemp = fBx
 			fBx += 2 * (fBx - fAx)
 			fAx = fTemp
 			fAy = fBy
-			fBy = iterator.chiSqDist(fBx)
+			fBy = iterator.callBack(fBx)
 		}
 	}
 	if fAy == 0 || fBy == 0 {
@@ -9152,6 +9135,72 @@ func (fn *formulaFuncs) TDIST(argsList *list.List) formulaArg {
 	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))
+}
+
 // TRIMMEAN function calculates the trimmed mean (or truncated mean) of a
 // supplied set of values. The syntax of the function is:
 //
diff --git a/calc_test.go b/calc_test.go
index 6324344..8565038 100644
--- a/calc_test.go
+++ b/calc_test.go
@@ -1167,6 +1167,12 @@ func TestCalcCellValue(t *testing.T) {
 		// TDIST
 		"=TDIST(1,10,1)": "0.17044656615103",
 		"=TDIST(1,10,2)": "0.34089313230206",
+		// T.INV
+		"=T.INV(0.25,10)": "-0.699812061312432",
+		"=T.INV(0.75,10)": "0.699812061312432",
+		// T.INV.2T
+		"=T.INV.2T(1,10)":   "0",
+		"=T.INV.2T(0.5,10)": "0.699812061312432",
 		// TRIMMEAN
 		"=TRIMMEAN(A1:B4,10%)": "2.5",
 		"=TRIMMEAN(A1:B4,70%)": "2.5",
@@ -3048,6 +3054,19 @@ func TestCalcCellValue(t *testing.T) {
 		"=TDIST(-1,10,1)":   "#NUM!",
 		"=TDIST(1,0,1)":     "#NUM!",
 		"=TDIST(1,10,0)":    "#NUM!",
+		// T.INV
+		"=T.INV()":          "T.INV requires 2 arguments",
+		"=T.INV(\"\",10)":   "strconv.ParseFloat: parsing \"\": invalid syntax",
+		"=T.INV(0.25,\"\")": "strconv.ParseFloat: parsing \"\": invalid syntax",
+		"=T.INV(0,10)":      "#NUM!",
+		"=T.INV(1,10)":      "#NUM!",
+		"=T.INV(0.25,0.5)":  "#NUM!",
+		// T.INV.2T
+		"=T.INV.2T()":          "T.INV.2T requires 2 arguments",
+		"=T.INV.2T(\"\",10)":   "strconv.ParseFloat: parsing \"\": invalid syntax",
+		"=T.INV.2T(0.25,\"\")": "strconv.ParseFloat: parsing \"\": invalid syntax",
+		"=T.INV.2T(0,10)":      "#NUM!",
+		"=T.INV.2T(0.25,0.5)":  "#NUM!",
 		// TRIMMEAN
 		"=TRIMMEAN()":        "TRIMMEAN requires 2 arguments",
 		"=TRIMMEAN(A1,\"\")": "strconv.ParseFloat: parsing \"\": invalid syntax",
diff --git a/file.go b/file.go
index 0135e20..9707a79 100644
--- a/file.go
+++ b/file.go
@@ -63,7 +63,7 @@ func (f *File) Save() error {
 	return f.SaveAs(f.Path)
 }
 
-// SaveAs provides a function to create or update to an spreadsheet at the
+// SaveAs provides a function to create or update to a spreadsheet at the
 // provided path.
 func (f *File) SaveAs(name string, opt ...Options) error {
 	if len(name) > MaxFileNameLength {
@@ -81,7 +81,7 @@ func (f *File) SaveAs(name string, opt ...Options) error {
 		return ErrWorkbookExt
 	}
 	f.setContentTypePartProjectExtensions(contentType)
-	file, err := os.OpenFile(filepath.Clean(name), os.O_WRONLY|os.O_TRUNC|os.O_CREATE, 0o600)
+	file, err := os.OpenFile(filepath.Clean(name), os.O_WRONLY|os.O_TRUNC|os.O_CREATE, os.ModePerm)
 	if err != nil {
 		return err
 	}
diff --git a/lib.go b/lib.go
index 4205e08..723b976 100644
--- a/lib.go
+++ b/lib.go
@@ -132,7 +132,7 @@ func (f *File) saveFileList(name string, content []byte) {
 	f.Pkg.Store(name, append([]byte(xml.Header), content...))
 }
 
-// Read file content as string in a archive file.
+// Read file content as string in an archive file.
 func readFile(file *zip.File) ([]byte, error) {
 	rc, err := file.Open()
 	if err != nil {
@@ -157,8 +157,8 @@ func SplitCellName(cell string) (string, int, error) {
 	if strings.IndexFunc(cell, alpha) == 0 {
 		i := strings.LastIndexFunc(cell, alpha)
 		if i >= 0 && i < len(cell)-1 {
-			col, rowstr := strings.ReplaceAll(cell[:i+1], "$", ""), cell[i+1:]
-			if row, err := strconv.Atoi(rowstr); err == nil && row > 0 {
+			col, rowStr := strings.ReplaceAll(cell[:i+1], "$", ""), cell[i+1:]
+			if row, err := strconv.Atoi(rowStr); err == nil && row > 0 {
 				return col, row, nil
 			}
 		}
@@ -187,7 +187,7 @@ func JoinCellName(col string, row int) (string, error) {
 }
 
 // ColumnNameToNumber provides a function to convert Excel sheet column name
-// to int. Column name case insensitive. The function returns an error if
+// to int. Column name case-insensitive. The function returns an error if
 // column name incorrect.
 //
 // Example:
@@ -248,14 +248,14 @@ func ColumnNumberToName(num int) (string, error) {
 //    excelize.CellNameToCoordinates("Z3") // returns 26, 3, nil
 //
 func CellNameToCoordinates(cell string) (int, int, error) {
-	colname, row, err := SplitCellName(cell)
+	colName, row, err := SplitCellName(cell)
 	if err != nil {
 		return -1, -1, newCellNameToCoordinatesError(cell, err)
 	}
 	if row > TotalRows {
 		return -1, -1, ErrMaxRows
 	}
-	col, err := ColumnNameToNumber(colname)
+	col, err := ColumnNameToNumber(colName)
 	return col, row, err
 }
 
@@ -277,8 +277,8 @@ func CoordinatesToCellName(col, row int, abs ...bool) (string, error) {
 			sign = "$"
 		}
 	}
-	colname, err := ColumnNumberToName(col)
-	return sign + colname + sign + strconv.Itoa(row), err
+	colName, err := ColumnNumberToName(col)
+	return sign + colName + sign + strconv.Itoa(row), err
 }
 
 // areaRefToCoordinates provides a function to convert area reference to a
@@ -336,6 +336,27 @@ func (f *File) coordinatesToAreaRef(coordinates []int) (string, error) {
 	return firstCell + ":" + lastCell, err
 }
 
+// getDefinedNameRefTo convert defined name to reference range.
+func (f *File) getDefinedNameRefTo(definedNameName string, currentSheet string) (refTo string) {
+	var workbookRefTo, worksheetRefTo string
+	for _, definedName := range f.GetDefinedName() {
+		if definedName.Name == definedNameName {
+			// worksheet scope takes precedence over scope workbook when both definedNames exist
+			if definedName.Scope == "Workbook" {
+				workbookRefTo = definedName.RefersTo
+			}
+			if definedName.Scope == currentSheet {
+				worksheetRefTo = definedName.RefersTo
+			}
+		}
+	}
+	refTo = workbookRefTo
+	if worksheetRefTo != "" {
+		refTo = worksheetRefTo
+	}
+	return
+}
+
 // flatSqref convert reference sequence to cell coordinates list.
 func (f *File) flatSqref(sqref string) (cells map[int][][]int, err error) {
 	var coordinates []int
@@ -365,7 +386,7 @@ func (f *File) flatSqref(sqref string) (cells map[int][][]int, err error) {
 	return
 }
 
-// inCoordinates provides a method to check if an coordinate is present in
+// inCoordinates provides a method to check if a coordinate is present in
 // coordinates array, and return the index of its location, otherwise
 // return -1.
 func inCoordinates(a [][]int, x []int) int {
@@ -391,7 +412,7 @@ func inStrSlice(a []string, x string, caseSensitive bool) int {
 	return -1
 }
 
-// inFloat64Slice provides a method to check if an element is present in an
+// inFloat64Slice provides a method to check if an element is present in a
 // float64 array, and return the index of its location, otherwise return -1.
 func inFloat64Slice(a []float64, x float64) int {
 	for idx, n := range a {
@@ -405,7 +426,7 @@ func inFloat64Slice(a []float64, x float64) int {
 // boolPtr returns a pointer to a bool with the given value.
 func boolPtr(b bool) *bool { return &b }
 
-// intPtr returns a pointer to a int with the given value.
+// intPtr returns a pointer to an int with the given value.
 func intPtr(i int) *int { return &i }
 
 // float64Ptr returns a pointer to a float64 with the given value.
@@ -626,7 +647,7 @@ func (f *File) replaceNameSpaceBytes(path string, contentMarshal []byte) []byte
 	return bytesReplace(contentMarshal, oldXmlns, newXmlns, -1)
 }
 
-// addNameSpaces provides a function to add a XML attribute by the given
+// addNameSpaces provides a function to add an XML attribute by the given
 // component part path.
 func (f *File) addNameSpaces(path string, ns xml.Attr) {
 	exist := false
@@ -715,7 +736,7 @@ var (
 
 // bstrUnmarshal parses the binary basic string, this will trim escaped string
 // literal which not permitted in an XML 1.0 document. The basic string
-// variant type can store any valid Unicode character. Unicode characters
+// variant type can store any valid Unicode character. Unicode's characters
 // that cannot be directly represented in XML as defined by the XML 1.0
 // specification, shall be escaped using the Unicode numerical character
 // representation escape character format _xHHHH_, where H represents a
diff --git a/numfmt.go b/numfmt.go
index 685005f..b48c36a 100644
--- a/numfmt.go
+++ b/numfmt.go
@@ -33,9 +33,9 @@ type languageInfo struct {
 type numberFormat struct {
 	section                                                                 []nfp.Section
 	t                                                                       time.Time
-	sectionIdx                                                              int
-	isNumberic, hours, seconds                                              bool
-	number                                                                  float64
+	sectionIdx                int
+	isNumeric, hours, seconds bool
+	number                    float64
 	ap, afterPoint, beforePoint, localCode, result, value, valueSectionType string
 }
 
@@ -279,7 +279,7 @@ var (
 // prepareNumberic split the number into two before and after parts by a
 // decimal point.
 func (nf *numberFormat) prepareNumberic(value string) {
-	if nf.isNumberic, _ = isNumeric(value); !nf.isNumberic {
+	if nf.isNumeric, _ = isNumeric(value); !nf.isNumeric {
 		return
 	}
 }
@@ -297,7 +297,7 @@ func format(value, numFmt string) string {
 		if section.Type != nf.valueSectionType {
 			continue
 		}
-		if nf.isNumberic {
+		if nf.isNumeric {
 			switch section.Type {
 			case nfp.TokenSectionPositive:
 				return nf.positiveHandler()