Merge e5ee5e5502 into f55dd56454

.github/workflows/ci.yml

@@ -1,16 +1,16 @@
-name: ci
+name: decimal-ci
 on: [push]
 jobs:
   ci-job:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        go: [ '1.7.x', '1.18', '1.19', '1.20', '1.21', '1.x' ]
+        go: [ '1.7.x', '1.15', '1.16', '1.17', '1.x' ]
     name: Go ${{ matrix.go }}
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@v2
       - name: Use go
-        uses: actions/setup-go@v5
+        uses: actions/setup-go@v2
         with:
           go-version: ${{ matrix.go }}
       - run: go build .

README.md

@@ -1,6 +1,6 @@
 # decimal
 
-[![ci](https://github.com/shopspring/decimal/actions/workflows/ci.yml/badge.svg?branch=master)](https://github.com/shopspring/decimal/actions/workflows/ci.yml)
+[![Github Actions](https://github.com/shopspring/decimal/actions/workflows/ci.yml/badge.svg)](https://github.com/shopspring/decimal/actions/workflows/ci.yml)
 [![GoDoc](https://godoc.org/github.com/shopspring/decimal?status.svg)](https://godoc.org/github.com/shopspring/decimal) 
 [![Go Report Card](https://goreportcard.com/badge/github.com/shopspring/decimal)](https://goreportcard.com/report/github.com/shopspring/decimal)
 

const.go

@@ -1,63 +0,0 @@
-package decimal
-
-import (
-	"strings"
-)
-
-const (
-	strLn10 = "2.302585092994045684017991454684364207601101488628772976033327900967572609677352480235997205089598298341967784042286248633409525465082806756666287369098781689482907208325554680843799894826233198528393505308965377732628846163366222287698219886746543667474404243274365155048934314939391479619404400222105101714174800368808401264708068556774321622835522011480466371565912137345074785694768346361679210180644507064800027750268491674655058685693567342067058113642922455440575892572420824131469568901675894025677631135691929203337658714166023010570308963457207544037084746994016826928280848118428931484852494864487192780967627127577539702766860595249671667418348570442250719796500471495105049221477656763693866297697952211071826454973477266242570942932258279850258550978526538320760672631716430950599508780752371033310119785754733154142180842754386359177811705430982748238504564801909561029929182431823752535770975053956518769751037497088869218020518933950723853920514463419726528728696511086257149219884997874887377134568620916705849807828059751193854445009978131146915934666241071846692310107598438319191292230792503747298650929009880391941702654416816335727555703151596113564846546190897042819763365836983716328982174407366009162177850541779276367731145041782137660111010731042397832521894898817597921798666394319523936855916447118246753245630912528778330963604262982153040874560927760726641354787576616262926568298704957954913954918049209069438580790032763017941503117866862092408537949861264933479354871737451675809537088281067452440105892444976479686075120275724181874989395971643105518848195288330746699317814634930000321200327765654130472621883970596794457943468343218395304414844803701305753674262153675579814770458031413637793236291560128185336498466942261465206459942072917119370602444929358037007718981097362533224548366988505528285966192805098447175198503666680874970496982273220244823343097169111136813588418696549323714996941979687803008850408979618598756579894836445212043698216415292987811742973332588607915912510967187510929248475023930572665446276200923068791518135803477701295593646298412366497023355174586195564772461857717369368404676577047874319780573853271810933883496338813069945569399346101090745616033312247949360455361849123333063704751724871276379140924398331810164737823379692265637682071706935846394531616949411701841938119405416449466111274712819705817783293841742231409930022911502362192186723337268385688273533371925103412930705632544426611429765388301822384091026198582888433587455960453004548370789052578473166283701953392231047527564998119228742789713715713228319641003422124210082180679525276689858180956119208391760721080919923461516952599099473782780648128058792731993893453415320185969711021407542282796298237068941764740642225757212455392526179373652434440560595336591539160312524480149313234572453879524389036839236450507881731359711238145323701508413491122324390927681724749607955799151363982881058285740538000653371655553014196332241918087621018204919492651483892"
-)
-
-var (
-	ln10 = newConstApproximation(strLn10)
-)
-
-type constApproximation struct {
-	exact          Decimal
-	approximations []Decimal
-}
-
-func newConstApproximation(value string) constApproximation {
-	parts := strings.Split(value, ".")
-	coeff, fractional := parts[0], parts[1]
-
-	coeffLen := len(coeff)
-	maxPrecision := len(fractional)
-
-	var approximations []Decimal
-	for p := 1; p < maxPrecision; p *= 2 {
-		r := RequireFromString(value[:coeffLen+p])
-		approximations = append(approximations, r)
-	}
-
-	return constApproximation{
-		RequireFromString(value),
-		approximations,
-	}
-}
-
-// Returns the smallest approximation available that's at least as precise
-// as the passed precision (places after decimal point), i.e. Floor[ log2(precision) ] + 1
-func (c constApproximation) withPrecision(precision int32) Decimal {
-	i := 0
-
-	if precision >= 1 {
-		i++
-	}
-
-	for precision >= 16 {
-		precision /= 16
-		i += 4
-	}
-
-	for precision >= 2 {
-		precision /= 2
-		i++
-	}
-
-	if i >= len(c.approximations) {
-		return c.exact
-	}
-
-	return c.approximations[i]
-}

const_test.go

@@ -1,34 +0,0 @@
-package decimal
-
-import "testing"
-
-func TestConstApproximation(t *testing.T) {
-	for _, testCase := range []struct {
-		Const                 string
-		Precision             int32
-		ExpectedApproximation string
-	}{
-		{"2.3025850929940456840179914546", 0, "2"},
-		{"2.3025850929940456840179914546", 1, "2.3"},
-		{"2.3025850929940456840179914546", 3, "2.302"},
-		{"2.3025850929940456840179914546", 5, "2.302585"},
-		{"2.3025850929940456840179914546", 10, "2.302585092994045"},
-		{"2.3025850929940456840179914546", 100, "2.3025850929940456840179914546"},
-		{"2.3025850929940456840179914546", -1, "2"},
-		{"2.3025850929940456840179914546", -5, "2"},
-		{"3.14159265359", 0, "3"},
-		{"3.14159265359", 1, "3.1"},
-		{"3.14159265359", 2, "3.141"},
-		{"3.14159265359", 4, "3.1415926"},
-		{"3.14159265359", 13, "3.14159265359"},
-	} {
-		ca := newConstApproximation(testCase.Const)
-		expected, _ := NewFromString(testCase.ExpectedApproximation)
-
-		approximation := ca.withPrecision(testCase.Precision)
-
-		if approximation.Cmp(expected) != 0 {
-			t.Errorf("expected approximation %s, got %s - for const with %s precision %d", testCase.ExpectedApproximation, approximation.String(), testCase.Const, testCase.Precision)
-		}
-	}
-}

decimal.go

@@ -4,14 +4,14 @@
 //
 // The best way to create a new Decimal is to use decimal.NewFromString, ex:
 //
-//	n, err := decimal.NewFromString("-123.4567")
+//     n, err := decimal.NewFromString("-123.4567")
-//	n.String() // output: "-123.4567"
+//     n.String() // output: "-123.4567"
 //
 // To use Decimal as part of a struct:
 //
-//	type StructName struct {
+//     type Struct struct {
-//	    Number Decimal
+//         Number Decimal
-//	}
+//     }
 //
 // Note: This can "only" represent numbers with a maximum of 2^31 digits after the decimal point.
 package decimal
@@ -32,15 +32,16 @@ import (
 //
 // Example:
 //
-//	d1 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(3))
+//     d1 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(3))
-//	d1.String() // output: "0.6666666666666667"
+//     d1.String() // output: "0.6666666666666667"
-//	d2 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(30000))
+//     d2 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(30000))
-//	d2.String() // output: "0.0000666666666667"
+//     d2.String() // output: "0.0000666666666667"
-//	d3 := decimal.NewFromFloat(20000).Div(decimal.NewFromFloat(3))
+//     d3 := decimal.NewFromFloat(20000).Div(decimal.NewFromFloat(3))
-//	d3.String() // output: "6666.6666666666666667"
+//     d3.String() // output: "6666.6666666666666667"
-//	decimal.DivisionPrecision = 3
+//     decimal.DivisionPrecision = 3
-//	d4 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(3))
+//     d4 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(3))
-//	d4.String() // output: "0.667"
+//     d4.String() // output: "0.667"
+//
 var DivisionPrecision = 16
 
 // MarshalJSONWithoutQuotes should be set to true if you want the decimal to
@@ -90,12 +91,12 @@ func New(value int64, exp int32) Decimal {
 	}
 }
 
-// NewFromInt converts an int64 to Decimal.
+// NewFromInt converts a int64 to Decimal.
 //
 // Example:
 //
-//	NewFromInt(123).String() // output: "123"
+//     NewFromInt(123).String() // output: "123"
-//	NewFromInt(-10).String() // output: "-10"
+//     NewFromInt(-10).String() // output: "-10"
 func NewFromInt(value int64) Decimal {
 	return Decimal{
 		value: big.NewInt(value),
@@ -103,12 +104,12 @@ func NewFromInt(value int64) Decimal {
 	}
 }
 
-// NewFromInt32 converts an int32 to Decimal.
+// NewFromInt32 converts a int32 to Decimal.
 //
 // Example:
 //
-//	NewFromInt(123).String() // output: "123"
+//     NewFromInt(123).String() // output: "123"
-//	NewFromInt(-10).String() // output: "-10"
+//     NewFromInt(-10).String() // output: "-10"
 func NewFromInt32(value int32) Decimal {
 	return Decimal{
 		value: big.NewInt(int64(value)),
@@ -124,34 +125,15 @@ func NewFromBigInt(value *big.Int, exp int32) Decimal {
 	}
 }
 
-// NewFromBigRat returns a new Decimal from a big.Rat. The numerator and
-// denominator are divided and rounded to the given precision.
-//
-// Example:
-//
-//     d1 := NewFromBigRat(big.NewRat(0, 1), 0)    // output: "0"
-//     d2 := NewFromBigRat(big.NewRat(4, 5), 1)    // output: "0.8"
-//     d3 := NewFromBigRat(big.NewRat(1000, 3), 3) // output: "333.333"
-//     d4 := NewFromBigRat(big.NewRat(2, 7), 4)    // output: "0.2857"
-//
-func NewFromBigRat(value *big.Rat, precision int32) Decimal {
-	return Decimal{
-		value: new(big.Int).Set(value.Num()),
-		exp:   0,
-	}.DivRound(Decimal{
-		value: new(big.Int).Set(value.Denom()),
-		exp:   0,
-	}, precision)
-}
-
 // NewFromString returns a new Decimal from a string representation.
 // Trailing zeroes are not trimmed.
 //
 // Example:
 //
-//	d, err := NewFromString("-123.45")
+//     d, err := NewFromString("-123.45")
-//	d2, err := NewFromString(".0001")
+//     d2, err := NewFromString(".0001")
-//	d3, err := NewFromString("1.47000")
+//     d3, err := NewFromString("1.47000")
+//
 func NewFromString(value string) (Decimal, error) {
 	originalInput := value
 	var intString string
@@ -229,14 +211,15 @@ func NewFromString(value string) (Decimal, error) {
 //
 // Example:
 //
-//	r := regexp.MustCompile("[$,]")
+//     r := regexp.MustCompile("[$,]")
-//	d1, err := NewFromFormattedString("$5,125.99", r)
+//     d1, err := NewFromFormattedString("$5,125.99", r)
 //
-//	r2 := regexp.MustCompile("[_]")
+//     r2 := regexp.MustCompile("[_]")
-//	d2, err := NewFromFormattedString("1_000_000", r2)
+//     d2, err := NewFromFormattedString("1_000_000", r2)
+//
+//     r3 := regexp.MustCompile("[USD\\s]")
+//     d3, err := NewFromFormattedString("5000 USD", r3)
 //
-//	r3 := regexp.MustCompile("[USD\\s]")
-//	d3, err := NewFromFormattedString("5000 USD", r3)
 func NewFromFormattedString(value string, replRegexp *regexp.Regexp) (Decimal, error) {
 	parsedValue := replRegexp.ReplaceAllString(value, "")
 	d, err := NewFromString(parsedValue)
@@ -247,12 +230,13 @@ func NewFromFormattedString(value string, replRegexp *regexp.Regexp) (Decimal, e
 }
 
 // RequireFromString returns a new Decimal from a string representation
-// or panics if NewFromString had returned an error.
+// or panics if NewFromString would have returned an error.
 //
 // Example:
 //
-//	d := RequireFromString("-123.45")
+//     d := RequireFromString("-123.45")
-//	d2 := RequireFromString(".0001")
+//     d2 := RequireFromString(".0001")
+//
 func RequireFromString(value string) Decimal {
 	dec, err := NewFromString(value)
 	if err != nil {
@@ -348,7 +332,8 @@ func newFromFloat(val float64, bits uint64, flt *floatInfo) Decimal {
 //
 // Example:
 //
-//	NewFromFloatWithExponent(123.456, -2).String() // output: "123.46"
+//     NewFromFloatWithExponent(123.456, -2).String() // output: "123.46"
+//
 func NewFromFloatWithExponent(value float64, exp int32) Decimal {
 	if math.IsNaN(value) || math.IsInf(value, 0) {
 		panic(fmt.Sprintf("Cannot create a Decimal from %v", value))
@@ -433,7 +418,7 @@ func NewFromFloatWithExponent(value float64, exp int32) Decimal {
 func (d Decimal) Copy() Decimal {
 	d.ensureInitialized()
 	return Decimal{
-		value: new(big.Int).Set(d.value),
+		value: &(*d.value),
 		exp:   d.exp,
 	}
 }
@@ -445,7 +430,7 @@ func (d Decimal) Copy() Decimal {
 //
 // Example:
 //
-//	d := New(12345, -4)
+// 	d := New(12345, -4)
 //	d2 := d.rescale(-1)
 //	d3 := d2.rescale(-4)
 //	println(d1)
@@ -457,6 +442,7 @@ func (d Decimal) Copy() Decimal {
 //	1.2345
 //	1.2
 //	1.2000
+//
 func (d Decimal) rescale(exp int32) Decimal {
 	d.ensureInitialized()
 
@@ -568,11 +554,9 @@ func (d Decimal) Div(d2 Decimal) Decimal {
 
 // QuoRem does division with remainder
 // d.QuoRem(d2,precision) returns quotient q and remainder r such that
-//
+//   d = d2 * q + r, q an integer multiple of 10^(-precision)
-//	d = d2 * q + r, q an integer multiple of 10^(-precision)
+//   0 <= r < abs(d2) * 10 ^(-precision) if d>=0
-//	0 <= r < abs(d2) * 10 ^(-precision) if d>=0
+//   0 >= r > -abs(d2) * 10 ^(-precision) if d<0
-//	0 >= r > -abs(d2) * 10 ^(-precision) if d<0
-//
 // Note that precision<0 is allowed as input.
 func (d Decimal) QuoRem(d2 Decimal, precision int32) (Decimal, Decimal) {
 	d.ensureInitialized()
@@ -581,7 +565,7 @@ func (d Decimal) QuoRem(d2 Decimal, precision int32) (Decimal, Decimal) {
 		panic("decimal division by 0")
 	}
 	scale := -precision
-	e := int64(d.exp) - int64(d2.exp) - int64(scale)
+	e := int64(d.exp - d2.exp - scale)
 	if e > math.MaxInt32 || e < math.MinInt32 {
 		panic("overflow in decimal QuoRem")
 	}
@@ -615,10 +599,8 @@ func (d Decimal) QuoRem(d2 Decimal, precision int32) (Decimal, Decimal) {
 
 // DivRound divides and rounds to a given precision
 // i.e. to an integer multiple of 10^(-precision)
-//
+//   for a positive quotient digit 5 is rounded up, away from 0
-//	for a positive quotient digit 5 is rounded up, away from 0
+//   if the quotient is negative then digit 5 is rounded down, away from 0
-//	if the quotient is negative then digit 5 is rounded down, away from 0
-//
 // Note that precision<0 is allowed as input.
 func (d Decimal) DivRound(d2 Decimal, precision int32) Decimal {
 	// QuoRem already checks initialization
@@ -646,8 +628,8 @@ func (d Decimal) DivRound(d2 Decimal, precision int32) Decimal {
 
 // Mod returns d % d2.
 func (d Decimal) Mod(d2 Decimal) Decimal {
-	_, r := d.QuoRem(d2, 0)
+	quo := d.DivRound(d2, -d.exp+1).Truncate(0)
-	return r
+	return d.Sub(d2.Mul(quo))
 }
 
 // Pow returns d to the power d2
@@ -673,8 +655,9 @@ func (d Decimal) Pow(d2 Decimal) Decimal {
 //
 // Example:
 //
-//	NewFromFloat(26.1).ExpHullAbrham(2).String()    // output: "220000000000"
+//     NewFromFloat(26.1).ExpHullAbrham(2).String()    // output: "220000000000"
-//	NewFromFloat(26.1).ExpHullAbrham(20).String()   // output: "216314672147.05767284"
+//     NewFromFloat(26.1).ExpHullAbrham(20).String()   // output: "216314672147.05767284"
+//
 func (d Decimal) ExpHullAbrham(overallPrecision uint32) (Decimal, error) {
 	// Algorithm based on Variable precision exponential function.
 	// ACM Transactions on Mathematical Software by T. E. Hull & A. Abrham.
@@ -764,14 +747,15 @@ func (d Decimal) ExpHullAbrham(overallPrecision uint32) (Decimal, error) {
 //
 // Example:
 //
-//	d, err := NewFromFloat(26.1).ExpTaylor(2).String()
+//     d, err := NewFromFloat(26.1).ExpTaylor(2).String()
-//	d.String()  // output: "216314672147.06"
+//     d.String()  // output: "216314672147.06"
 //
-//	NewFromFloat(26.1).ExpTaylor(20).String()
+//     NewFromFloat(26.1).ExpTaylor(20).String()
-//	d.String()  // output: "216314672147.05767284062928674083"
+//     d.String()  // output: "216314672147.05767284062928674083"
+//
+//     NewFromFloat(26.1).ExpTaylor(-10).String()
+//     d.String()  // output: "220000000000"
 //
-//	NewFromFloat(26.1).ExpTaylor(-10).String()
-//	d.String()  // output: "220000000000"
 func (d Decimal) ExpTaylor(precision int32) (Decimal, error) {
 	// Note(mwoss): Implementation can be optimized by exclusively using big.Int API only
 	if d.IsZero() {
@@ -828,127 +812,9 @@ func (d Decimal) ExpTaylor(precision int32) (Decimal, error) {
 	return result, nil
 }
 
-// Ln calculates natural logarithm of d.
-// Precision argument specifies how precise the result must be (number of digits after decimal point).
-// Negative precision is allowed.
-//
-// Example:
-//
-//	d1, err := NewFromFloat(13.3).Ln(2)
-//	d1.String()  // output: "2.59"
-//
-//	d2, err := NewFromFloat(579.161).Ln(10)
-//	d2.String()  // output: "6.3615805046"
-func (d Decimal) Ln(precision int32) (Decimal, error) {
-	// Algorithm based on The Use of Iteration Methods for Approximating the Natural Logarithm,
-	// James F. Epperson, The American Mathematical Monthly, Vol. 96, No. 9, November 1989, pp. 831-835.
-	if d.IsNegative() {
-		return Decimal{}, fmt.Errorf("cannot calculate natural logarithm for negative decimals")
-	}
-
-	if d.IsZero() {
-		return Decimal{}, fmt.Errorf("cannot represent natural logarithm of 0, result: -infinity")
-	}
-
-	calcPrecision := precision + 2
-	z := d.Copy()
-
-	var comp1, comp3, comp2, comp4, reduceAdjust Decimal
-	comp1 = z.Sub(Decimal{oneInt, 0})
-	comp3 = Decimal{oneInt, -1}
-
-	// for decimal in range [0.9, 1.1] where ln(d) is close to 0
-	usePowerSeries := false
-
-	if comp1.Abs().Cmp(comp3) <= 0 {
-		usePowerSeries = true
-	} else {
-		// reduce input decimal to range [0.1, 1)
-		expDelta := int32(z.NumDigits()) + z.exp
-		z.exp -= expDelta
-
-		// Input decimal was reduced by factor of 10^expDelta, thus we will need to add
-		// ln(10^expDelta) = expDelta * ln(10)
-		// to the result to compensate that
-		ln10 := ln10.withPrecision(calcPrecision)
-		reduceAdjust = NewFromInt32(expDelta)
-		reduceAdjust = reduceAdjust.Mul(ln10)
-
-		comp1 = z.Sub(Decimal{oneInt, 0})
-
-		if comp1.Abs().Cmp(comp3) <= 0 {
-			usePowerSeries = true
-		} else {
-			// initial estimate using floats
-			zFloat := z.InexactFloat64()
-			comp1 = NewFromFloat(math.Log(zFloat))
-		}
-	}
-
-	epsilon := Decimal{oneInt, -calcPrecision}
-
-	if usePowerSeries {
-		// Power Series - https://en.wikipedia.org/wiki/Logarithm#Power_series
-		// Calculating n-th term of formula: ln(z+1) = 2 sum [ 1 / (2n+1) * (z / (z+2))^(2n+1) ]
-		// until the difference between current and next term is smaller than epsilon.
-		// Coverage quite fast for decimals close to 1.0
-
-		// z + 2
-		comp2 = comp1.Add(Decimal{twoInt, 0})
-		// z / (z + 2)
-		comp3 = comp1.DivRound(comp2, calcPrecision)
-		// 2 * (z / (z + 2))
-		comp1 = comp3.Add(comp3)
-		comp2 = comp1.Copy()
-
-		for n := 1; ; n++ {
-			// 2 * (z / (z+2))^(2n+1)
-			comp2 = comp2.Mul(comp3).Mul(comp3)
-
-			// 1 / (2n+1) * 2 * (z / (z+2))^(2n+1)
-			comp4 = NewFromInt(int64(2*n + 1))
-			comp4 = comp2.DivRound(comp4, calcPrecision)
-
-			// comp1 = 2 sum [ 1 / (2n+1) * (z / (z+2))^(2n+1) ]
-			comp1 = comp1.Add(comp4)
-
-			if comp4.Abs().Cmp(epsilon) <= 0 {
-				break
-			}
-		}
-	} else {
-		// Halley's Iteration.
-		// Calculating n-th term of formula: a_(n+1) = a_n - 2 * (exp(a_n) - z) / (exp(a_n) + z),
-		// until the difference between current and next term is smaller than epsilon
-		for {
-			// exp(a_n)
-			comp3, _ = comp1.ExpTaylor(calcPrecision)
-			// exp(a_n) - z
-			comp2 = comp3.Sub(z)
-			// 2 * (exp(a_n) - z)
-			comp2 = comp2.Add(comp2)
-			// exp(a_n) + z
-			comp4 = comp3.Add(z)
-			// 2 * (exp(a_n) - z) / (exp(a_n) + z)
-			comp3 = comp2.DivRound(comp4, calcPrecision)
-			// comp1 = a_(n+1) = a_n - 2 * (exp(a_n) - z) / (exp(a_n) + z)
-			comp1 = comp1.Sub(comp3)
-
-			if comp3.Abs().Cmp(epsilon) <= 0 {
-				break
-			}
-		}
-	}
-
-	comp1 = comp1.Add(reduceAdjust)
-
-	return comp1.Round(precision), nil
-}
-
 // NumDigits returns the number of digits of the decimal coefficient (d.Value)
 // Note: Current implementation is extremely slow for large decimals and/or decimals with large fractional part
 func (d Decimal) NumDigits() int {
-	d.ensureInitialized()
 	// Note(mwoss): It can be optimized, unnecessary cast of big.Int to string
 	if d.IsNegative() {
 		return len(d.value.String()) - 1
@@ -985,9 +851,10 @@ func abs(n int32) int32 {
 
 // Cmp compares the numbers represented by d and d2 and returns:
 //
-//	-1 if d <  d2
+//     -1 if d <  d2
-//	 0 if d == d2
+//      0 if d == d2
-//	+1 if d >  d2
+//     +1 if d >  d2
+//
 func (d Decimal) Cmp(d2 Decimal) int {
 	d.ensureInitialized()
 	d2.ensureInitialized()
@@ -1001,21 +868,12 @@ func (d Decimal) Cmp(d2 Decimal) int {
 	return rd.value.Cmp(rd2.value)
 }
 
-// Compare compares the numbers represented by d and d2 and returns:
-//
-//	-1 if d <  d2
-//	 0 if d == d2
-//	+1 if d >  d2
-func (d Decimal) Compare(d2 Decimal) int {
-	return d.Cmp(d2)
-}
-
 // Equal returns whether the numbers represented by d and d2 are equal.
 func (d Decimal) Equal(d2 Decimal) bool {
 	return d.Cmp(d2) == 0
 }
 
-// Deprecated: Equals is deprecated, please use Equal method instead.
+// Equals is deprecated, please use Equal method instead
 func (d Decimal) Equals(d2 Decimal) bool {
 	return d.Equal(d2)
 }
@@ -1047,6 +905,7 @@ func (d Decimal) LessThanOrEqual(d2 Decimal) bool {
 //	-1 if d <  0
 //	 0 if d == 0
 //	+1 if d >  0
+//
 func (d Decimal) Sign() int {
 	if d.value == nil {
 		return 0
@@ -1155,12 +1014,13 @@ func (d Decimal) InexactFloat64() float64 {
 //
 // Example:
 //
-//	d := New(-12345, -3)
+//     d := New(-12345, -3)
-//	println(d.String())
+//     println(d.String())
 //
 // Output:
 //
-//	-12.345
+//     -12.345
+//
 func (d Decimal) String() string {
 	return d.string(true)
 }
@@ -1170,13 +1030,14 @@ func (d Decimal) String() string {
 //
 // Example:
 //
-//	NewFromFloat(0).StringFixed(2) // output: "0.00"
+// 	   NewFromFloat(0).StringFixed(2) // output: "0.00"
-//	NewFromFloat(0).StringFixed(0) // output: "0"
+// 	   NewFromFloat(0).StringFixed(0) // output: "0"
-//	NewFromFloat(5.45).StringFixed(0) // output: "5"
+// 	   NewFromFloat(5.45).StringFixed(0) // output: "5"
-//	NewFromFloat(5.45).StringFixed(1) // output: "5.5"
+// 	   NewFromFloat(5.45).StringFixed(1) // output: "5.5"
-//	NewFromFloat(5.45).StringFixed(2) // output: "5.45"
+// 	   NewFromFloat(5.45).StringFixed(2) // output: "5.45"
-//	NewFromFloat(5.45).StringFixed(3) // output: "5.450"
+// 	   NewFromFloat(5.45).StringFixed(3) // output: "5.450"
-//	NewFromFloat(545).StringFixed(-1) // output: "550"
+// 	   NewFromFloat(545).StringFixed(-1) // output: "550"
+//
 func (d Decimal) StringFixed(places int32) string {
 	rounded := d.Round(places)
 	return rounded.string(false)
@@ -1187,13 +1048,14 @@ func (d Decimal) StringFixed(places int32) string {
 //
 // Example:
 //
-//	NewFromFloat(0).StringFixedBank(2) // output: "0.00"
+// 	   NewFromFloat(0).StringFixedBank(2) // output: "0.00"
-//	NewFromFloat(0).StringFixedBank(0) // output: "0"
+// 	   NewFromFloat(0).StringFixedBank(0) // output: "0"
-//	NewFromFloat(5.45).StringFixedBank(0) // output: "5"
+// 	   NewFromFloat(5.45).StringFixedBank(0) // output: "5"
-//	NewFromFloat(5.45).StringFixedBank(1) // output: "5.4"
+// 	   NewFromFloat(5.45).StringFixedBank(1) // output: "5.4"
-//	NewFromFloat(5.45).StringFixedBank(2) // output: "5.45"
+// 	   NewFromFloat(5.45).StringFixedBank(2) // output: "5.45"
-//	NewFromFloat(5.45).StringFixedBank(3) // output: "5.450"
+// 	   NewFromFloat(5.45).StringFixedBank(3) // output: "5.450"
-//	NewFromFloat(545).StringFixedBank(-1) // output: "540"
+// 	   NewFromFloat(545).StringFixedBank(-1) // output: "540"
+//
 func (d Decimal) StringFixedBank(places int32) string {
 	rounded := d.RoundBank(places)
 	return rounded.string(false)
@@ -1211,8 +1073,9 @@ func (d Decimal) StringFixedCash(interval uint8) string {
 //
 // Example:
 //
-//	NewFromFloat(5.45).Round(1).String() // output: "5.5"
+// 	   NewFromFloat(5.45).Round(1).String() // output: "5.5"
-//	NewFromFloat(545).Round(-1).String() // output: "550"
+// 	   NewFromFloat(545).Round(-1).String() // output: "550"
+//
 func (d Decimal) Round(places int32) Decimal {
 	if d.exp == -places {
 		return d
@@ -1241,10 +1104,11 @@ func (d Decimal) Round(places int32) Decimal {
 //
 // Example:
 //
-//	NewFromFloat(545).RoundCeil(-2).String()   // output: "600"
+//     NewFromFloat(545).RoundCeil(-2).String()   // output: "600"
-//	NewFromFloat(500).RoundCeil(-2).String()   // output: "500"
+//     NewFromFloat(500).RoundCeil(-2).String()   // output: "500"
-//	NewFromFloat(1.1001).RoundCeil(2).String() // output: "1.11"
+//     NewFromFloat(1.1001).RoundCeil(2).String() // output: "1.11"
-//	NewFromFloat(-1.454).RoundCeil(1).String() // output: "-1.4"
+//     NewFromFloat(-1.454).RoundCeil(1).String() // output: "-1.5"
+//
 func (d Decimal) RoundCeil(places int32) Decimal {
 	if d.exp >= -places {
 		return d
@@ -1266,10 +1130,11 @@ func (d Decimal) RoundCeil(places int32) Decimal {
 //
 // Example:
 //
-//	NewFromFloat(545).RoundFloor(-2).String()   // output: "500"
+//     NewFromFloat(545).RoundFloor(-2).String()   // output: "500"
-//	NewFromFloat(-500).RoundFloor(-2).String()   // output: "-500"
+//     NewFromFloat(-500).RoundFloor(-2).String()   // output: "-500"
-//	NewFromFloat(1.1001).RoundFloor(2).String() // output: "1.1"
+//     NewFromFloat(1.1001).RoundFloor(2).String() // output: "1.1"
-//	NewFromFloat(-1.454).RoundFloor(1).String() // output: "-1.5"
+//     NewFromFloat(-1.454).RoundFloor(1).String() // output: "-1.4"
+//
 func (d Decimal) RoundFloor(places int32) Decimal {
 	if d.exp >= -places {
 		return d
@@ -1291,10 +1156,11 @@ func (d Decimal) RoundFloor(places int32) Decimal {
 //
 // Example:
 //
-//	NewFromFloat(545).RoundUp(-2).String()   // output: "600"
+//     NewFromFloat(545).RoundUp(-2).String()   // output: "600"
-//	NewFromFloat(500).RoundUp(-2).String()   // output: "500"
+//     NewFromFloat(500).RoundUp(-2).String()   // output: "500"
-//	NewFromFloat(1.1001).RoundUp(2).String() // output: "1.11"
+//     NewFromFloat(1.1001).RoundUp(2).String() // output: "1.11"
-//	NewFromFloat(-1.454).RoundUp(1).String() // output: "-1.5"
+//     NewFromFloat(-1.454).RoundUp(1).String() // output: "-1.4"
+//
 func (d Decimal) RoundUp(places int32) Decimal {
 	if d.exp >= -places {
 		return d
@@ -1318,10 +1184,11 @@ func (d Decimal) RoundUp(places int32) Decimal {
 //
 // Example:
 //
-//	NewFromFloat(545).RoundDown(-2).String()   // output: "500"
+//     NewFromFloat(545).RoundDown(-2).String()   // output: "500"
-//	NewFromFloat(-500).RoundDown(-2).String()   // output: "-500"
+//     NewFromFloat(-500).RoundDown(-2).String()   // output: "-500"
-//	NewFromFloat(1.1001).RoundDown(2).String() // output: "1.1"
+//     NewFromFloat(1.1001).RoundDown(2).String() // output: "1.1"
-//	NewFromFloat(-1.454).RoundDown(1).String() // output: "-1.4"
+//     NewFromFloat(-1.454).RoundDown(1).String() // output: "-1.5"
+//
 func (d Decimal) RoundDown(places int32) Decimal {
 	if d.exp >= -places {
 		return d
@@ -1342,12 +1209,13 @@ func (d Decimal) RoundDown(places int32) Decimal {
 //
 // Examples:
 //
-//	NewFromFloat(5.45).RoundBank(1).String() // output: "5.4"
+// 	   NewFromFloat(5.45).RoundBank(1).String() // output: "5.4"
-//	NewFromFloat(545).RoundBank(-1).String() // output: "540"
+// 	   NewFromFloat(545).RoundBank(-1).String() // output: "540"
-//	NewFromFloat(5.46).RoundBank(1).String() // output: "5.5"
+// 	   NewFromFloat(5.46).RoundBank(1).String() // output: "5.5"
-//	NewFromFloat(546).RoundBank(-1).String() // output: "550"
+// 	   NewFromFloat(546).RoundBank(-1).String() // output: "550"
-//	NewFromFloat(5.55).RoundBank(1).String() // output: "5.6"
+// 	   NewFromFloat(5.55).RoundBank(1).String() // output: "5.6"
-//	NewFromFloat(555).RoundBank(-1).String() // output: "560"
+// 	   NewFromFloat(555).RoundBank(-1).String() // output: "560"
+//
 func (d Decimal) RoundBank(places int32) Decimal {
 
 	round := d.Round(places)
@@ -1369,13 +1237,11 @@ func (d Decimal) RoundBank(places int32) Decimal {
 // interval. The amount payable for a cash transaction is rounded to the nearest
 // multiple of the minimum currency unit available. The following intervals are
 // available: 5, 10, 25, 50 and 100; any other number throws a panic.
-//
+//	    5:   5 cent rounding 3.43 => 3.45
-//	  5:   5 cent rounding 3.43 => 3.45
+// 	   10:  10 cent rounding 3.45 => 3.50 (5 gets rounded up)
-//	 10:  10 cent rounding 3.45 => 3.50 (5 gets rounded up)
+// 	   25:  25 cent rounding 3.41 => 3.50
-//	 25:  25 cent rounding 3.41 => 3.50
+// 	   50:  50 cent rounding 3.75 => 4.00
-//	 50:  50 cent rounding 3.75 => 4.00
+// 	  100: 100 cent rounding 3.50 => 4.00
-//	100: 100 cent rounding 3.50 => 4.00
-//
 // For more details: https://en.wikipedia.org/wiki/Cash_rounding
 func (d Decimal) RoundCash(interval uint8) Decimal {
 	var iVal *big.Int
@@ -1444,7 +1310,8 @@ func (d Decimal) Ceil() Decimal {
 //
 // Example:
 //
-//	decimal.NewFromString("123.456").Truncate(2).String() // "123.45"
+//     decimal.NewFromString("123.456").Truncate(2).String() // "123.45"
+//
 func (d Decimal) Truncate(precision int32) Decimal {
 	d.ensureInitialized()
 	if precision >= 0 && -precision > d.exp {
@@ -1608,8 +1475,7 @@ func (d *Decimal) GobDecode(data []byte) error {
 }
 
 // StringScaled first scales the decimal then calls .String() on it.
-//
+// NOTE: buggy, unintuitive, and DEPRECATED! Use StringFixed instead.
-// Deprecated: buggy and unintuitive. Use StringFixed instead.
 func (d Decimal) StringScaled(exp int32) string {
 	return d.rescale(exp).String()
 }
@@ -1669,7 +1535,7 @@ func (d *Decimal) ensureInitialized() {
 //
 // To call this function with an array, you must do:
 //
-//	Min(arr[0], arr[1:]...)
+//     Min(arr[0], arr[1:]...)
 //
 // This makes it harder to accidentally call Min with 0 arguments.
 func Min(first Decimal, rest ...Decimal) Decimal {
@@ -1686,7 +1552,7 @@ func Min(first Decimal, rest ...Decimal) Decimal {
 //
 // To call this function with an array, you must do:
 //
-//	Max(arr[0], arr[1:]...)
+//     Max(arr[0], arr[1:]...)
 //
 // This makes it harder to accidentally call Max with 0 arguments.
 func Max(first Decimal, rest ...Decimal) Decimal {
@@ -1721,13 +1587,22 @@ func RescalePair(d1 Decimal, d2 Decimal) (Decimal, Decimal) {
 	d1.ensureInitialized()
 	d2.ensureInitialized()
 
-	if d1.exp < d2.exp {
+	if d1.exp == d2.exp {
-		return d1, d2.rescale(d1.exp)
+		return d1, d2
-	} else if d1.exp > d2.exp {
-		return d1.rescale(d2.exp), d2
 	}
 
-	return d1, d2
+	baseScale := min(d1.exp, d2.exp)
+	if baseScale != d1.exp {
+		return d1.rescale(baseScale), d2
+	}
+	return d1, d2.rescale(baseScale)
+}
+
+func min(x, y int32) int32 {
+	if x >= y {
+		return y
+	}
+	return x
 }
 
 func unquoteIfQuoted(value interface{}) (string, error) {
@@ -1739,7 +1614,8 @@ func unquoteIfQuoted(value interface{}) (string, error) {
 	case []byte:
 		bytes = v
 	default:
-		return "", fmt.Errorf("could not convert value '%+v' to byte array of type '%T'", value, value)
+		return "", fmt.Errorf("could not convert value '%+v' to byte array of type '%T'",
+			value, value)
 	}
 
 	// If the amount is quoted, strip the quotes

decimal_test.go

@@ -556,59 +556,10 @@ func TestNewFromBigIntWithExponent(t *testing.T) {
 	}
 }
 
-func TestNewFromBigRat(t *testing.T) {
-	mustParseRat := func(val string) *big.Rat {
-		num, _ := new(big.Rat).SetString(val)
-		return num
-	}
-
-	type Inp struct {
-		val  *big.Rat
-		prec int32
-	}
-
-	tests := map[Inp]string{
-		Inp{big.NewRat(0, 1), 16}:                                                     "0",
-		Inp{big.NewRat(4, 5), 16}:                                                     "0.8",
-		Inp{big.NewRat(10, 2), 16}:                                                    "5",
-		Inp{big.NewRat(1023427554493, 43432632), 16}:                                  "23563.5628642767953828", // rounded
-		Inp{big.NewRat(1, 434324545566634), 16}:                                       "0.0000000000000023",
-		Inp{big.NewRat(1, 3), 16}:                                                     "0.3333333333333333",
-		Inp{big.NewRat(2, 3), 2}:                                                      "0.67",               // rounded
-		Inp{big.NewRat(2, 3), 16}:                                                     "0.6666666666666667", // rounded
-		Inp{big.NewRat(10000, 3), 16}:                                                 "3333.3333333333333333",
-		Inp{mustParseRat("30702832066636633479"), 16}:                                 "30702832066636633479",
-		Inp{mustParseRat("487028320159896636679.1827512895753"), 16}:                  "487028320159896636679.1827512895753",
-		Inp{mustParseRat("127028320612589896636633479.173582751289575278357832"), -2}: "127028320612589896636633500",                  // rounded
-		Inp{mustParseRat("127028320612589896636633479.173582751289575278357832"), 16}: "127028320612589896636633479.1735827512895753", // rounded
-		Inp{mustParseRat("127028320612589896636633479.173582751289575278357832"), 32}: "127028320612589896636633479.173582751289575278357832",
-	}
-
-	// add negatives
-	for p, s := range tests {
-		if p.val.Cmp(new(big.Rat)) > 0 {
-			tests[Inp{p.val.Neg(p.val), p.prec}] = "-" + s
-		}
-	}
-
-	for input, s := range tests {
-		d := NewFromBigRat(input.val, input.prec)
-		if d.String() != s {
-			t.Errorf("expected %s, got %s (%s, %d)",
-				s, d.String(),
-				d.value.String(), d.exp)
-		}
-	}
-}
-
 func TestCopy(t *testing.T) {
 	origin := New(1, 0)
 	cpy := origin.Copy()
 
-	if origin.value == cpy.value {
-		t.Error("expecting copy and origin to have different value pointers")
-	}
-
 	if cpy.Cmp(origin) != 0 {
 		t.Error("expecting copy and origin to be equals, but they are not")
 	}
@@ -2192,8 +2143,6 @@ func TestDecimal_Mod(t *testing.T) {
 		Inp{"-7.5", "2"}:                        "-1.5",
 		Inp{"7.5", "-2"}:                        "1.5",
 		Inp{"-7.5", "-2"}:                       "-1.5",
-		Inp{"41", "21"}:                         "20",
-		Inp{"400000000001", "200000000001"}:     "200000000000",
 	}
 
 	for inp, res := range inputs {
@@ -2856,67 +2805,6 @@ func TestDecimal_ExpTaylor(t *testing.T) {
 	}
 }
 
-func TestDecimal_Ln(t *testing.T) {
-	for _, testCase := range []struct {
-		Dec       string
-		Precision int32
-		Expected  string
-	}{
-		{"0.1", 25, "-2.3025850929940456840179915"},
-		{"0.01", 25, "-4.6051701859880913680359829"},
-		{"0.001", 25, "-6.9077552789821370520539744"},
-		{"0.00000001", 25, "-18.4206807439523654721439316"},
-		{"1.0", 10, "0.0"},
-		{"1.01", 25, "0.0099503308531680828482154"},
-		{"1.001", 25, "0.0009995003330835331668094"},
-		{"1.0001", 25, "0.0000999950003333083353332"},
-		{"1.1", 25, "0.0953101798043248600439521"},
-		{"1.13", 25, "0.1222176327242492005461486"},
-		{"3.13", 10, "1.1410330046"},
-		{"3.13", 25, "1.1410330045520618486427824"},
-		{"3.13", 50, "1.14103300455206184864278239988848193837089629107972"},
-		{"3.13", 100, "1.1410330045520618486427823998884819383708962910797239760817078430268177216960996098918971117211892839"},
-		{"5.71", 25, "1.7422190236679188486939833"},
-		{"5.7185108151957193571930205", 50, "1.74370842450178929149992165925283704012576949094645"},
-		{"839101.0351", 25, "13.6400864014410013994397240"},
-		{"839101.0351094726488848490572028502", 50, "13.64008640145229044389152437468283605382056561604272"},
-		{"5023583755703750094849.03519358513093500275017501750602739169823", 25, "49.9684305274348922267409953"},
-		{"5023583755703750094849.03519358513093500275017501750602739169823", -1, "50.0"},
-	} {
-		d, _ := NewFromString(testCase.Dec)
-		expected, _ := NewFromString(testCase.Expected)
-
-		ln, err := d.Ln(testCase.Precision)
-		if err != nil {
-			t.Fatal(err)
-		}
-
-		if ln.Cmp(expected) != 0 {
-			t.Errorf("expected %s, got %s, for decimal %s", testCase.Expected, ln.String(), testCase.Dec)
-		}
-	}
-}
-
-func TestDecimal_LnZero(t *testing.T) {
-	d := New(0, 0)
-
-	_, err := d.Ln(5)
-
-	if err == nil {
-		t.Errorf("expected error, natural logarithm of 0 cannot be represented (-infinity)")
-	}
-}
-
-func TestDecimal_LnNegative(t *testing.T) {
-	d := New(-20, 2)
-
-	_, err := d.Ln(5)
-
-	if err == nil {
-		t.Errorf("expected error, natural logarithm cannot be calculated for nagative decimals")
-	}
-}
-
 func TestDecimal_NumDigits(t *testing.T) {
 	for _, testCase := range []struct {
 		Dec               string
@@ -2936,7 +2824,6 @@ func TestDecimal_NumDigits(t *testing.T) {
 		{"-5.26", 3},
 		{"-5.2663117716", 11},
 		{"-26.1", 3},
-		{"", 1},
 	} {
 		d, _ := NewFromString(testCase.Dec)
 

go.mod

@@ -1,3 +1,3 @@
 module github.com/shopspring/decimal
 
-go 1.7
+go 1.13