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decimal.go
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decimal.go
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// Package decimal implements an arbitrary precision fixed-point decimal.
//
// The zero-value of a Decimal is 0, as you would expect.
//
// The best way to create a new Decimal is to use decimal.NewFromString, ex:
//
// n, err := decimal.NewFromString("-123.4567")
// n.String() // output: "-123.4567"
//
// To use Decimal as part of a struct:
//
// type StructName struct {
// Number Decimal
// }
//
// Note: This can "only" represent numbers with a maximum of 2^31 digits after the decimal point.
package decimal
import (
"database/sql/driver"
"encoding/binary"
"fmt"
"math"
"math/big"
"regexp"
"strconv"
"strings"
)
// DivisionPrecision is the number of decimal places in the result when it
// doesn't divide exactly.
//
// Example:
//
// d1 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(3))
// d1.String() // output: "0.6666666666666667"
// d2 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(30000))
// d2.String() // output: "0.0000666666666667"
// d3 := decimal.NewFromFloat(20000).Div(decimal.NewFromFloat(3))
// d3.String() // output: "6666.6666666666666667"
// decimal.DivisionPrecision = 3
// d4 := decimal.NewFromFloat(2).Div(decimal.NewFromFloat(3))
// d4.String() // output: "0.667"
var DivisionPrecision = 16
// PowPrecisionNegativeExponent specifies the maximum precision of the result (digits after decimal point)
// when calculating decimal power. Only used for cases where the exponent is a negative number.
// This constant applies to Pow, PowInt32 and PowBigInt methods, PowWithPrecision method is not constrained by it.
//
// Example:
//
// d1, err := decimal.NewFromFloat(15.2).PowInt32(-2)
// d1.String() // output: "0.0043282548476454"
//
// decimal.PowPrecisionNegativeExponent = 24
// d2, err := decimal.NewFromFloat(15.2).PowInt32(-2)
// d2.String() // output: "0.004328254847645429362881"
var PowPrecisionNegativeExponent = 16
// MarshalJSONWithoutQuotes should be set to true if you want the decimal to
// be JSON marshaled as a number, instead of as a string.
// WARNING: this is dangerous for decimals with many digits, since many JSON
// unmarshallers (ex: Javascript's) will unmarshal JSON numbers to IEEE 754
// double-precision floating point numbers, which means you can potentially
// silently lose precision.
var MarshalJSONWithoutQuotes = false
// ExpMaxIterations specifies the maximum number of iterations needed to calculate
// precise natural exponent value using ExpHullAbrham method.
var ExpMaxIterations = 1000
// Zero constant, to make computations faster.
// Zero should never be compared with == or != directly, please use decimal.Equal or decimal.Cmp instead.
var Zero = New(0, 1)
var zeroInt = big.NewInt(0)
var oneInt = big.NewInt(1)
var twoInt = big.NewInt(2)
var fourInt = big.NewInt(4)
var fiveInt = big.NewInt(5)
var tenInt = big.NewInt(10)
var twentyInt = big.NewInt(20)
var factorials = []Decimal{New(1, 0)}
// Decimal represents a fixed-point decimal. It is immutable.
// number = value * 10 ^ exp
type Decimal struct {
value *big.Int
// NOTE(vadim): this must be an int32, because we cast it to float64 during
// calculations. If exp is 64 bit, we might lose precision.
// If we cared about being able to represent every possible decimal, we
// could make exp a *big.Int but it would hurt performance and numbers
// like that are unrealistic.
exp int32
}
// New returns a new fixed-point decimal, value * 10 ^ exp.
func New(value int64, exp int32) Decimal {
return Decimal{
value: big.NewInt(value),
exp: exp,
}
}
// NewFromInt converts an int64 to Decimal.
//
// Example:
//
// NewFromInt(123).String() // output: "123"
// NewFromInt(-10).String() // output: "-10"
func NewFromInt(value int64) Decimal {
return Decimal{
value: big.NewInt(value),
exp: 0,
}
}
// NewFromInt32 converts an int32 to Decimal.
//
// Example:
//
// NewFromInt(123).String() // output: "123"
// NewFromInt(-10).String() // output: "-10"
func NewFromInt32(value int32) Decimal {
return Decimal{
value: big.NewInt(int64(value)),
exp: 0,
}
}
// NewFromUint64 converts an uint64 to Decimal.
//
// Example:
//
// NewFromUint64(123).String() // output: "123"
func NewFromUint64(value uint64) Decimal {
return Decimal{
value: new(big.Int).SetUint64(value),
exp: 0,
}
}
// NewFromBigInt returns a new Decimal from a big.Int, value * 10 ^ exp
func NewFromBigInt(value *big.Int, exp int32) Decimal {
return Decimal{
value: new(big.Int).Set(value),
exp: exp,
}
}
// 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")
// d2, err := NewFromString(".0001")
// d3, err := NewFromString("1.47000")
func NewFromString(value string) (Decimal, error) {
originalInput := value
var intString string
var exp int64
// Check if number is using scientific notation
eIndex := strings.IndexAny(value, "Ee")
if eIndex != -1 {
expInt, err := strconv.ParseInt(value[eIndex+1:], 10, 32)
if err != nil {
if e, ok := err.(*strconv.NumError); ok && e.Err == strconv.ErrRange {
return Decimal{}, fmt.Errorf("can't convert %s to decimal: fractional part too long", value)
}
return Decimal{}, fmt.Errorf("can't convert %s to decimal: exponent is not numeric", value)
}
value = value[:eIndex]
exp = expInt
}
pIndex := -1
vLen := len(value)
for i := 0; i < vLen; i++ {
if value[i] == '.' {
if pIndex > -1 {
return Decimal{}, fmt.Errorf("can't convert %s to decimal: too many .s", value)
}
pIndex = i
}
}
if pIndex == -1 {
// There is no decimal point, we can just parse the original string as
// an int
intString = value
} else {
if pIndex+1 < vLen {
intString = value[:pIndex] + value[pIndex+1:]
} else {
intString = value[:pIndex]
}
expInt := -len(value[pIndex+1:])
exp += int64(expInt)
}
var dValue *big.Int
// strconv.ParseInt is faster than new(big.Int).SetString so this is just a shortcut for strings we know won't overflow
if len(intString) <= 18 {
parsed64, err := strconv.ParseInt(intString, 10, 64)
if err != nil {
return Decimal{}, fmt.Errorf("can't convert %s to decimal", value)
}
dValue = big.NewInt(parsed64)
} else {
dValue = new(big.Int)
_, ok := dValue.SetString(intString, 10)
if !ok {
return Decimal{}, fmt.Errorf("can't convert %s to decimal", value)
}
}
if exp < math.MinInt32 || exp > math.MaxInt32 {
// NOTE(vadim): I doubt a string could realistically be this long
return Decimal{}, fmt.Errorf("can't convert %s to decimal: fractional part too long", originalInput)
}
return Decimal{
value: dValue,
exp: int32(exp),
}, nil
}
// NewFromFormattedString returns a new Decimal from a formatted string representation.
// The second argument - replRegexp, is a regular expression that is used to find characters that should be
// removed from given decimal string representation. All matched characters will be replaced with an empty string.
//
// Example:
//
// r := regexp.MustCompile("[$,]")
// d1, err := NewFromFormattedString("$5,125.99", r)
//
// r2 := regexp.MustCompile("[_]")
// d2, err := NewFromFormattedString("1_000_000", r2)
//
// 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)
if err != nil {
return Decimal{}, err
}
return d, nil
}
// RequireFromString returns a new Decimal from a string representation
// or panics if NewFromString had returned an error.
//
// Example:
//
// d := RequireFromString("-123.45")
// d2 := RequireFromString(".0001")
func RequireFromString(value string) Decimal {
dec, err := NewFromString(value)
if err != nil {
panic(err)
}
return dec
}
// NewFromFloat converts a float64 to Decimal.
//
// The converted number will contain the number of significant digits that can be
// represented in a float with reliable roundtrip.
// This is typically 15 digits, but may be more in some cases.
// See https://www.exploringbinary.com/decimal-precision-of-binary-floating-point-numbers/ for more information.
//
// For slightly faster conversion, use NewFromFloatWithExponent where you can specify the precision in absolute terms.
//
// NOTE: this will panic on NaN, +/-inf
func NewFromFloat(value float64) Decimal {
if value == 0 {
return New(0, 0)
}
return newFromFloat(value, math.Float64bits(value), &float64info)
}
// NewFromFloat32 converts a float32 to Decimal.
//
// The converted number will contain the number of significant digits that can be
// represented in a float with reliable roundtrip.
// This is typically 6-8 digits depending on the input.
// See https://www.exploringbinary.com/decimal-precision-of-binary-floating-point-numbers/ for more information.
//
// For slightly faster conversion, use NewFromFloatWithExponent where you can specify the precision in absolute terms.
//
// NOTE: this will panic on NaN, +/-inf
func NewFromFloat32(value float32) Decimal {
if value == 0 {
return New(0, 0)
}
// XOR is workaround for https://github.com/golang/go/issues/26285
a := math.Float32bits(value) ^ 0x80808080
return newFromFloat(float64(value), uint64(a)^0x80808080, &float32info)
}
func newFromFloat(val float64, bits uint64, flt *floatInfo) Decimal {
if math.IsNaN(val) || math.IsInf(val, 0) {
panic(fmt.Sprintf("Cannot create a Decimal from %v", val))
}
exp := int(bits>>flt.mantbits) & (1<<flt.expbits - 1)
mant := bits & (uint64(1)<<flt.mantbits - 1)
switch exp {
case 0:
// denormalized
exp++
default:
// add implicit top bit
mant |= uint64(1) << flt.mantbits
}
exp += flt.bias
var d decimal
d.Assign(mant)
d.Shift(exp - int(flt.mantbits))
d.neg = bits>>(flt.expbits+flt.mantbits) != 0
roundShortest(&d, mant, exp, flt)
// If less than 19 digits, we can do calculation in an int64.
if d.nd < 19 {
tmp := int64(0)
m := int64(1)
for i := d.nd - 1; i >= 0; i-- {
tmp += m * int64(d.d[i]-'0')
m *= 10
}
if d.neg {
tmp *= -1
}
return Decimal{value: big.NewInt(tmp), exp: int32(d.dp) - int32(d.nd)}
}
dValue := new(big.Int)
dValue, ok := dValue.SetString(string(d.d[:d.nd]), 10)
if ok {
return Decimal{value: dValue, exp: int32(d.dp) - int32(d.nd)}
}
return NewFromFloatWithExponent(val, int32(d.dp)-int32(d.nd))
}
// NewFromFloatWithExponent converts a float64 to Decimal, with an arbitrary
// number of fractional digits.
//
// Example:
//
// 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))
}
bits := math.Float64bits(value)
mant := bits & (1<<52 - 1)
exp2 := int32((bits >> 52) & (1<<11 - 1))
sign := bits >> 63
if exp2 == 0 {
// specials
if mant == 0 {
return Decimal{}
}
// subnormal
exp2++
} else {
// normal
mant |= 1 << 52
}
exp2 -= 1023 + 52
// normalizing base-2 values
for mant&1 == 0 {
mant = mant >> 1
exp2++
}
// maximum number of fractional base-10 digits to represent 2^N exactly cannot be more than -N if N<0
if exp < 0 && exp < exp2 {
if exp2 < 0 {
exp = exp2
} else {
exp = 0
}
}
// representing 10^M * 2^N as 5^M * 2^(M+N)
exp2 -= exp
temp := big.NewInt(1)
dMant := big.NewInt(int64(mant))
// applying 5^M
if exp > 0 {
temp = temp.SetInt64(int64(exp))
temp = temp.Exp(fiveInt, temp, nil)
} else if exp < 0 {
temp = temp.SetInt64(-int64(exp))
temp = temp.Exp(fiveInt, temp, nil)
dMant = dMant.Mul(dMant, temp)
temp = temp.SetUint64(1)
}
// applying 2^(M+N)
if exp2 > 0 {
dMant = dMant.Lsh(dMant, uint(exp2))
} else if exp2 < 0 {
temp = temp.Lsh(temp, uint(-exp2))
}
// rounding and downscaling
if exp > 0 || exp2 < 0 {
halfDown := new(big.Int).Rsh(temp, 1)
dMant = dMant.Add(dMant, halfDown)
dMant = dMant.Quo(dMant, temp)
}
if sign == 1 {
dMant = dMant.Neg(dMant)
}
return Decimal{
value: dMant,
exp: exp,
}
}
// Copy returns a copy of decimal with the same value and exponent, but a different pointer to value.
func (d Decimal) Copy() Decimal {
d.ensureInitialized()
return Decimal{
value: new(big.Int).Set(d.value),
exp: d.exp,
}
}
// rescale returns a rescaled version of the decimal. Returned
// decimal may be less precise if the given exponent is bigger
// than the initial exponent of the Decimal.
// NOTE: this will truncate, NOT round
//
// Example:
//
// d := New(12345, -4)
// d2 := d.rescale(-1)
// d3 := d2.rescale(-4)
// println(d1)
// println(d2)
// println(d3)
//
// Output:
//
// 1.2345
// 1.2
// 1.2000
func (d Decimal) rescale(exp int32) Decimal {
d.ensureInitialized()
if d.exp == exp {
return Decimal{
new(big.Int).Set(d.value),
d.exp,
}
}
// NOTE(vadim): must convert exps to float64 before - to prevent overflow
diff := math.Abs(float64(exp) - float64(d.exp))
value := new(big.Int).Set(d.value)
expScale := new(big.Int).Exp(tenInt, big.NewInt(int64(diff)), nil)
if exp > d.exp {
value = value.Quo(value, expScale)
} else if exp < d.exp {
value = value.Mul(value, expScale)
}
return Decimal{
value: value,
exp: exp,
}
}
// Abs returns the absolute value of the decimal.
func (d Decimal) Abs() Decimal {
if !d.IsNegative() {
return d
}
d.ensureInitialized()
d2Value := new(big.Int).Abs(d.value)
return Decimal{
value: d2Value,
exp: d.exp,
}
}
// Add returns d + d2.
func (d Decimal) Add(d2 Decimal) Decimal {
rd, rd2 := RescalePair(d, d2)
d3Value := new(big.Int).Add(rd.value, rd2.value)
return Decimal{
value: d3Value,
exp: rd.exp,
}
}
// Sub returns d - d2.
func (d Decimal) Sub(d2 Decimal) Decimal {
rd, rd2 := RescalePair(d, d2)
d3Value := new(big.Int).Sub(rd.value, rd2.value)
return Decimal{
value: d3Value,
exp: rd.exp,
}
}
// Neg returns -d.
func (d Decimal) Neg() Decimal {
d.ensureInitialized()
val := new(big.Int).Neg(d.value)
return Decimal{
value: val,
exp: d.exp,
}
}
// Mul returns d * d2.
func (d Decimal) Mul(d2 Decimal) Decimal {
d.ensureInitialized()
d2.ensureInitialized()
expInt64 := int64(d.exp) + int64(d2.exp)
if expInt64 > math.MaxInt32 || expInt64 < math.MinInt32 {
// NOTE(vadim): better to panic than give incorrect results, as
// Decimals are usually used for money
panic(fmt.Sprintf("exponent %v overflows an int32!", expInt64))
}
d3Value := new(big.Int).Mul(d.value, d2.value)
return Decimal{
value: d3Value,
exp: int32(expInt64),
}
}
// Shift shifts the decimal in base 10.
// It shifts left when shift is positive and right if shift is negative.
// In simpler terms, the given value for shift is added to the exponent
// of the decimal.
func (d Decimal) Shift(shift int32) Decimal {
d.ensureInitialized()
return Decimal{
value: new(big.Int).Set(d.value),
exp: d.exp + shift,
}
}
// Div returns d / d2. If it doesn't divide exactly, the result will have
// DivisionPrecision digits after the decimal point.
func (d Decimal) Div(d2 Decimal) Decimal {
return d.DivRound(d2, int32(DivisionPrecision))
}
// 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)
// 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()
d2.ensureInitialized()
if d2.value.Sign() == 0 {
panic("decimal division by 0")
}
scale := -precision
e := int64(d.exp) - int64(d2.exp) - int64(scale)
if e > math.MaxInt32 || e < math.MinInt32 {
panic("overflow in decimal QuoRem")
}
var aa, bb, expo big.Int
var scalerest int32
// d = a 10^ea
// d2 = b 10^eb
if e < 0 {
aa = *d.value
expo.SetInt64(-e)
bb.Exp(tenInt, &expo, nil)
bb.Mul(d2.value, &bb)
scalerest = d.exp
// now aa = a
// bb = b 10^(scale + eb - ea)
} else {
expo.SetInt64(e)
aa.Exp(tenInt, &expo, nil)
aa.Mul(d.value, &aa)
bb = *d2.value
scalerest = scale + d2.exp
// now aa = a ^ (ea - eb - scale)
// bb = b
}
var q, r big.Int
q.QuoRem(&aa, &bb, &r)
dq := Decimal{value: &q, exp: scale}
dr := Decimal{value: &r, exp: scalerest}
return dq, dr
}
// 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
// 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
q, r := d.QuoRem(d2, precision)
// the actual rounding decision is based on comparing r*10^precision and d2/2
// instead compare 2 r 10 ^precision and d2
var rv2 big.Int
rv2.Abs(r.value)
rv2.Lsh(&rv2, 1)
// now rv2 = abs(r.value) * 2
r2 := Decimal{value: &rv2, exp: r.exp + precision}
// r2 is now 2 * r * 10 ^ precision
var c = r2.Cmp(d2.Abs())
if c < 0 {
return q
}
if d.value.Sign()*d2.value.Sign() < 0 {
return q.Sub(New(1, -precision))
}
return q.Add(New(1, -precision))
}
// Mod returns d % d2.
func (d Decimal) Mod(d2 Decimal) Decimal {
_, r := d.QuoRem(d2, 0)
return r
}
// Pow returns d to the power of d2.
// When exponent is negative the returned decimal will have maximum precision of PowPrecisionNegativeExponent places after decimal point.
//
// Pow returns 0 (zero-value of Decimal) instead of error for power operation edge cases, to handle those edge cases use PowWithPrecision
// Edge cases not handled by Pow:
// - 0 ** 0 => undefined value
// - 0 ** y, where y < 0 => infinity
// - x ** y, where x < 0 and y is non-integer decimal => imaginary value
//
// Example:
//
// d1 := decimal.NewFromFloat(4.0)
// d2 := decimal.NewFromFloat(4.0)
// res1 := d1.Pow(d2)
// res1.String() // output: "256"
//
// d3 := decimal.NewFromFloat(5.0)
// d4 := decimal.NewFromFloat(5.73)
// res2 := d3.Pow(d4)
// res2.String() // output: "10118.08037125"
func (d Decimal) Pow(d2 Decimal) Decimal {
baseSign := d.Sign()
expSign := d2.Sign()
if baseSign == 0 {
if expSign == 0 {
return Decimal{}
}
if expSign == 1 {
return Decimal{zeroInt, 0}
}
if expSign == -1 {
return Decimal{}
}
}
if expSign == 0 {
return Decimal{oneInt, 0}
}
// TODO: optimize extraction of fractional part
one := Decimal{oneInt, 0}
expIntPart, expFracPart := d2.QuoRem(one, 0)
if baseSign == -1 && !expFracPart.IsZero() {
return Decimal{}
}
intPartPow, _ := d.PowBigInt(expIntPart.value)
// if exponent is an integer we don't need to calculate d1**frac(d2)
if expFracPart.value.Sign() == 0 {
return intPartPow
}
// TODO: optimize NumDigits for more performant precision adjustment
digitsBase := d.NumDigits()
digitsExponent := d2.NumDigits()
precision := digitsBase
if digitsExponent > precision {
precision += digitsExponent
}
precision += 6
// Calculate x ** frac(y), where
// x ** frac(y) = exp(ln(x ** frac(y)) = exp(ln(x) * frac(y))
fracPartPow, err := d.Abs().Ln(-d.exp + int32(precision))
if err != nil {
return Decimal{}
}
fracPartPow = fracPartPow.Mul(expFracPart)
fracPartPow, err = fracPartPow.ExpTaylor(-d.exp + int32(precision))
if err != nil {
return Decimal{}
}
// Join integer and fractional part,
// base ** (expBase + expFrac) = base ** expBase * base ** expFrac
res := intPartPow.Mul(fracPartPow)
return res
}
// PowWithPrecision returns d to the power of d2.
// Precision parameter specifies minimum precision of the result (digits after decimal point).
// Returned decimal is not rounded to 'precision' places after decimal point.
//
// PowWithPrecision returns error when:
// - 0 ** 0 => undefined value
// - 0 ** y, where y < 0 => infinity
// - x ** y, where x < 0 and y is non-integer decimal => imaginary value
//
// Example:
//
// d1 := decimal.NewFromFloat(4.0)
// d2 := decimal.NewFromFloat(4.0)
// res1, err := d1.PowWithPrecision(d2, 2)
// res1.String() // output: "256"
//
// d3 := decimal.NewFromFloat(5.0)
// d4 := decimal.NewFromFloat(5.73)
// res2, err := d3.PowWithPrecision(d4, 5)
// res2.String() // output: "10118.080371595015625"
//
// d5 := decimal.NewFromFloat(-3.0)
// d6 := decimal.NewFromFloat(-6.0)
// res3, err := d5.PowWithPrecision(d6, 10)
// res3.String() // output: "0.0013717421"
func (d Decimal) PowWithPrecision(d2 Decimal, precision int32) (Decimal, error) {
baseSign := d.Sign()
expSign := d2.Sign()
if baseSign == 0 {
if expSign == 0 {
return Decimal{}, fmt.Errorf("cannot represent undefined value of 0**0")
}
if expSign == 1 {
return Decimal{zeroInt, 0}, nil
}
if expSign == -1 {
return Decimal{}, fmt.Errorf("cannot represent infinity value of 0 ** y, where y < 0")
}
}
if expSign == 0 {
return Decimal{oneInt, 0}, nil
}
// TODO: optimize extraction of fractional part
one := Decimal{oneInt, 0}
expIntPart, expFracPart := d2.QuoRem(one, 0)
if baseSign == -1 && !expFracPart.IsZero() {
return Decimal{}, fmt.Errorf("cannot represent imaginary value of x ** y, where x < 0 and y is non-integer decimal")
}
intPartPow, _ := d.powBigIntWithPrecision(expIntPart.value, precision)
// if exponent is an integer we don't need to calculate d1**frac(d2)
if expFracPart.value.Sign() == 0 {
return intPartPow, nil
}
// TODO: optimize NumDigits for more performant precision adjustment
digitsBase := d.NumDigits()
digitsExponent := d2.NumDigits()
if int32(digitsBase) > precision {
precision = int32(digitsBase)
}
if int32(digitsExponent) > precision {
precision += int32(digitsExponent)
}
// increase precision by 10 to compensate for errors in further calculations
precision += 10
// Calculate x ** frac(y), where
// x ** frac(y) = exp(ln(x ** frac(y)) = exp(ln(x) * frac(y))
fracPartPow, err := d.Abs().Ln(precision)
if err != nil {
return Decimal{}, err
}
fracPartPow = fracPartPow.Mul(expFracPart)
fracPartPow, err = fracPartPow.ExpTaylor(precision)
if err != nil {
return Decimal{}, err
}
// Join integer and fractional part,
// base ** (expBase + expFrac) = base ** expBase * base ** expFrac
res := intPartPow.Mul(fracPartPow)
return res, nil
}
// PowInt32 returns d to the power of exp, where exp is int32.
// Only returns error when d and exp is 0, thus result is undefined.
//
// When exponent is negative the returned decimal will have maximum precision of PowPrecisionNegativeExponent places after decimal point.
//
// Example:
//
// d1, err := decimal.NewFromFloat(4.0).PowInt32(4)
// d1.String() // output: "256"
//
// d2, err := decimal.NewFromFloat(3.13).PowInt32(5)
// d2.String() // output: "300.4150512793"
func (d Decimal) PowInt32(exp int32) (Decimal, error) {
if d.IsZero() && exp == 0 {
return Decimal{}, fmt.Errorf("cannot represent undefined value of 0**0")
}
isExpNeg := exp < 0
exp = abs(exp)
n, result := d, New(1, 0)
for exp > 0 {
if exp%2 == 1 {
result = result.Mul(n)
}
exp /= 2
if exp > 0 {
n = n.Mul(n)
}
}
if isExpNeg {
return New(1, 0).DivRound(result, int32(PowPrecisionNegativeExponent)), nil
}
return result, nil
}
// PowBigInt returns d to the power of exp, where exp is big.Int.
// Only returns error when d and exp is 0, thus result is undefined.
//
// When exponent is negative the returned decimal will have maximum precision of PowPrecisionNegativeExponent places after decimal point.
//
// Example:
//
// d1, err := decimal.NewFromFloat(3.0).PowBigInt(big.NewInt(3))
// d1.String() // output: "27"
//
// d2, err := decimal.NewFromFloat(629.25).PowBigInt(big.NewInt(5))
// d2.String() // output: "98654323103449.5673828125"
func (d Decimal) PowBigInt(exp *big.Int) (Decimal, error) {
return d.powBigIntWithPrecision(exp, int32(PowPrecisionNegativeExponent))
}
func (d Decimal) powBigIntWithPrecision(exp *big.Int, precision int32) (Decimal, error) {
if d.IsZero() && exp.Sign() == 0 {
return Decimal{}, fmt.Errorf("cannot represent undefined value of 0**0")
}
tmpExp := new(big.Int).Set(exp)
isExpNeg := exp.Sign() < 0
if isExpNeg {
tmpExp.Abs(tmpExp)
}
n, result := d, New(1, 0)
for tmpExp.Sign() > 0 {
if tmpExp.Bit(0) == 1 {
result = result.Mul(n)
}
tmpExp.Rsh(tmpExp, 1)
if tmpExp.Sign() > 0 {
n = n.Mul(n)
}
}
if isExpNeg {
return New(1, 0).DivRound(result, precision), nil
}
return result, nil
}
// ExpHullAbrham calculates the natural exponent of decimal (e to the power of d) using Hull-Abraham algorithm.
// OverallPrecision argument specifies the overall precision of the result (integer part + decimal part).
//
// ExpHullAbrham is faster than ExpTaylor for small precision values, but it is much slower for large precision values.
//
// Example:
//
// NewFromFloat(26.1).ExpHullAbrham(2).String() // output: "220000000000"
// 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.
if d.IsZero() {
return Decimal{oneInt, 0}, nil
}
currentPrecision := overallPrecision
// Algorithm does not work if currentPrecision * 23 < |x|.
// Precision is automatically increased in such cases, so the value can be calculated precisely.
// If newly calculated precision is higher than ExpMaxIterations the currentPrecision will not be changed.
f := d.Abs().InexactFloat64()
if ncp := f / 23; ncp > float64(currentPrecision) && ncp < float64(ExpMaxIterations) {
currentPrecision = uint32(math.Ceil(ncp))
}
// fail if abs(d) beyond an over/underflow threshold
overflowThreshold := New(23*int64(currentPrecision), 0)
if d.Abs().Cmp(overflowThreshold) > 0 {
return Decimal{}, fmt.Errorf("over/underflow threshold, exp(x) cannot be calculated precisely")
}
// Return 1 if abs(d) small enough; this also avoids later over/underflow
overflowThreshold2 := New(9, -int32(currentPrecision)-1)
if d.Abs().Cmp(overflowThreshold2) <= 0 {
return Decimal{oneInt, d.exp}, nil
}
// t is the smallest integer >= 0 such that the corresponding abs(d/k) < 1
t := d.exp + int32(d.NumDigits()) // Add d.NumDigits because the paper assumes that d.value [0.1, 1)
if t < 0 {
t = 0
}
k := New(1, t) // reduction factor
r := Decimal{new(big.Int).Set(d.value), d.exp - t} // reduced argument
p := int32(currentPrecision) + t + 2 // precision for calculating the sum
// Determine n, the number of therms for calculating sum
// use first Newton step (1.435p - 1.182) / log10(p/abs(r))
// for solving appropriate equation, along with directed
// roundings and simple rational bound for log10(p/abs(r))