mirror of
https://github.com/VictoriaMetrics/VictoriaMetrics.git
synced 2024-11-28 09:55:36 +01:00
497 lines
10 KiB
Go
497 lines
10 KiB
Go
package decimal
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import (
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"math"
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"sync"
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"github.com/VictoriaMetrics/VictoriaMetrics/lib/fastnum"
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)
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// CalibrateScale calibrates a and b with the corresponding exponents ae, be
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// and returns the resulting exponent e.
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func CalibrateScale(a []int64, ae int16, b []int64, be int16) (e int16) {
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if ae == be {
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// Fast path - exponents are equal.
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return ae
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}
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if len(a) == 0 {
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return be
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}
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if len(b) == 0 {
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return ae
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}
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if ae < be {
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a, b = b, a
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ae, be = be, ae
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}
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upExp := ae - be
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downExp := int16(0)
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for _, v := range a {
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maxUpExp := maxUpExponent(v)
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if upExp-maxUpExp > downExp {
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downExp = upExp - maxUpExp
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}
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}
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upExp -= downExp
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for i, v := range a {
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if v == vInfPos || v == vInfNeg {
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continue
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}
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adjExp := upExp
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for adjExp > 0 {
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v *= 10
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adjExp--
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}
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a[i] = v
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}
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if downExp > 0 {
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for i, v := range b {
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if v == vInfPos || v == vInfNeg {
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continue
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}
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adjExp := downExp
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for adjExp > 0 {
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v /= 10
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adjExp--
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}
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b[i] = v
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}
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}
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return be + downExp
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}
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// ExtendFloat64sCapacity extends dst capacity to hold additionalItems
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// and returns the extended dst.
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func ExtendFloat64sCapacity(dst []float64, additionalItems int) []float64 {
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dstLen := len(dst)
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if n := dstLen + additionalItems - cap(dst); n > 0 {
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dst = append(dst[:cap(dst)], make([]float64, n)...)
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}
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return dst[:dstLen]
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}
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// ExtendInt64sCapacity extends dst capacity to hold additionalItems
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// and returns the extended dst.
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func ExtendInt64sCapacity(dst []int64, additionalItems int) []int64 {
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dstLen := len(dst)
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if n := dstLen + additionalItems - cap(dst); n > 0 {
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dst = append(dst[:cap(dst)], make([]int64, n)...)
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}
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return dst[:dstLen]
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}
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func extendInt16sCapacity(dst []int16, additionalItems int) []int16 {
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dstLen := len(dst)
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if n := dstLen + additionalItems - cap(dst); n > 0 {
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dst = append(dst[:cap(dst)], make([]int16, n)...)
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}
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return dst[:dstLen]
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}
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// AppendDecimalToFloat converts each item in va to f=v*10^e, appends it
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// to dst and returns the resulting dst.
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func AppendDecimalToFloat(dst []float64, va []int64, e int16) []float64 {
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// Extend dst capacity in order to eliminate memory allocations below.
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dst = ExtendFloat64sCapacity(dst, len(va))
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a := dst[len(dst) : len(dst)+len(va)]
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if fastnum.IsInt64Zeros(va) {
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return fastnum.AppendFloat64Zeros(dst, len(va))
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}
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if e == 0 {
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if fastnum.IsInt64Ones(va) {
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return fastnum.AppendFloat64Ones(dst, len(va))
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}
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_ = a[len(va)-1]
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for i, v := range va {
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f := float64(v)
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if v == vInfPos {
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f = infPos
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} else if v == vInfNeg {
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f = infNeg
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}
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a[i] = f
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}
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return dst[:len(dst)+len(va)]
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}
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// increase conversion precision for negative exponents by dividing by e10
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if e < 0 {
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e10 := math.Pow10(int(-e))
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_ = a[len(va)-1]
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for i, v := range va {
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f := float64(v) / e10
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if v == vInfPos {
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f = infPos
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} else if v == vInfNeg {
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f = infNeg
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}
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a[i] = f
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}
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return dst[:len(dst)+len(va)]
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}
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e10 := math.Pow10(int(e))
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_ = a[len(va)-1]
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for i, v := range va {
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f := float64(v) * e10
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if v == vInfPos {
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f = infPos
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} else if v == vInfNeg {
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f = infNeg
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}
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a[i] = f
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}
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return dst[:len(dst)+len(va)]
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}
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// AppendFloatToDecimal converts each item in src to v*10^e and appends
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// each v to dst returning it as va.
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//
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// It tries minimizing each item in dst.
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func AppendFloatToDecimal(dst []int64, src []float64) ([]int64, int16) {
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if len(src) == 0 {
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return dst, 0
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}
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if fastnum.IsFloat64Zeros(src) {
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dst = fastnum.AppendInt64Zeros(dst, len(src))
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return dst, 0
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}
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if fastnum.IsFloat64Ones(src) {
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dst = fastnum.AppendInt64Ones(dst, len(src))
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return dst, 0
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}
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vaev := vaeBufPool.Get()
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if vaev == nil {
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vaev = &vaeBuf{
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va: make([]int64, len(src)),
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ea: make([]int16, len(src)),
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}
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}
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vae := vaev.(*vaeBuf)
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va := vae.va[:0]
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ea := vae.ea[:0]
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va = ExtendInt64sCapacity(va, len(src))
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va = va[:len(src)]
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ea = extendInt16sCapacity(ea, len(src))
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ea = ea[:len(src)]
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// Determine the minimum exponent across all src items.
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minExp := int16(1<<15 - 1)
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for i, f := range src {
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v, exp := FromFloat(f)
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va[i] = v
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ea[i] = exp
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if exp < minExp && v != vInfPos && v != vInfNeg {
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minExp = exp
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}
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}
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// Determine whether all the src items may be upscaled to minExp.
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// If not, adjust minExp accordingly.
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downExp := int16(0)
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_ = ea[len(va)-1]
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for i, v := range va {
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exp := ea[i]
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upExp := exp - minExp
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maxUpExp := maxUpExponent(v)
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if upExp-maxUpExp > downExp {
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downExp = upExp - maxUpExp
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}
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}
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minExp += downExp
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// Extend dst capacity in order to eliminate memory allocations below.
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dst = ExtendInt64sCapacity(dst, len(src))
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a := dst[len(dst) : len(dst)+len(src)]
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// Scale each item in src to minExp and append it to dst.
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_ = a[len(va)-1]
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_ = ea[len(va)-1]
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for i, v := range va {
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if v == vInfPos || v == vInfNeg {
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a[i] = v
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continue
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}
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exp := ea[i]
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adjExp := exp - minExp
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for adjExp > 0 {
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v *= 10
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adjExp--
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}
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for adjExp < 0 {
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v /= 10
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adjExp++
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}
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a[i] = v
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}
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vae.va = va
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vae.ea = ea
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vaeBufPool.Put(vae)
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return dst[:len(dst)+len(va)], minExp
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}
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type vaeBuf struct {
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va []int64
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ea []int16
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}
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var vaeBufPool sync.Pool
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const int64Max = int64(1<<63 - 1)
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func maxUpExponent(v int64) int16 {
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if v == 0 || v == vInfPos || v == vInfNeg {
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// Any exponent allowed.
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return 1024
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}
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if v < 0 {
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v = -v
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}
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if v < 0 {
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// Handle corner case for v=-1<<63
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return 0
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}
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switch {
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case v <= int64Max/1e18:
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return 18
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case v <= int64Max/1e17:
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return 17
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case v <= int64Max/1e16:
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return 16
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case v <= int64Max/1e15:
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return 15
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case v <= int64Max/1e14:
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return 14
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case v <= int64Max/1e13:
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return 13
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case v <= int64Max/1e12:
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return 12
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case v <= int64Max/1e11:
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return 11
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case v <= int64Max/1e10:
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return 10
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case v <= int64Max/1e9:
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return 9
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case v <= int64Max/1e8:
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return 8
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case v <= int64Max/1e7:
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return 7
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case v <= int64Max/1e6:
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return 6
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case v <= int64Max/1e5:
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return 5
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case v <= int64Max/1e4:
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return 4
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case v <= int64Max/1e3:
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return 3
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case v <= int64Max/1e2:
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return 2
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case v <= int64Max/1e1:
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return 1
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default:
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return 0
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}
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}
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// RoundToDecimalDigits rounds f to the given number of decimal digits after the point.
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//
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// See also RoundToSignificantFigures.
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func RoundToDecimalDigits(f float64, digits int) float64 {
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if digits <= -100 || digits >= 100 {
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return f
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}
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m := math.Pow10(digits)
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return math.Round(f*m) / m
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}
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// RoundToSignificantFigures rounds f to value with the given number of significant figures.
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//
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// See also RoundToDecimalDigits.
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func RoundToSignificantFigures(f float64, digits int) float64 {
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if digits <= 0 || digits >= 18 {
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return f
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}
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if math.IsNaN(f) || math.IsInf(f, 0) || f == 0 {
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return f
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}
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n := int64(math.Pow10(digits))
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isNegative := f < 0
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if isNegative {
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f = -f
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}
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v, e := positiveFloatToDecimal(f)
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if v > vMax {
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v = vMax
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}
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var rem int64
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for v > n {
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rem = v % 10
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v /= 10
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e++
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}
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if rem >= 5 {
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v++
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}
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if isNegative {
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v = -v
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}
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return ToFloat(v, e)
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}
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// ToFloat returns f=v*10^e.
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func ToFloat(v int64, e int16) float64 {
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if v == vInfPos {
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return infPos
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}
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if v == vInfNeg {
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return infNeg
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}
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f := float64(v)
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// increase conversion precision for negative exponents by dividing by e10
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if e < 0 {
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return f / math.Pow10(int(-e))
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}
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return f * math.Pow10(int(e))
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}
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var (
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infPos = math.Inf(1)
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infNeg = math.Inf(-1)
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)
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const (
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vInfPos = 1<<63 - 1
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vInfNeg = -1 << 63
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vMax = 1<<63 - 3
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vMin = -1<<63 + 1
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)
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// FromFloat converts f to v*10^e.
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//
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// It tries minimizing v.
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// For instance, for f = -1.234 it returns v = -1234, e = -3.
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//
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// FromFloat doesn't work properly with NaN values, so don't pass them here.
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func FromFloat(f float64) (int64, int16) {
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if f == 0 {
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return 0, 0
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}
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if math.IsInf(f, 0) {
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return fromFloatInf(f)
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}
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if f > 0 {
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v, e := positiveFloatToDecimal(f)
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if v > vMax {
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v = vMax
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}
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return v, e
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}
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v, e := positiveFloatToDecimal(-f)
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v = -v
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if v < vMin {
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v = vMin
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}
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return v, e
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}
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func fromFloatInf(f float64) (int64, int16) {
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// Limit infs by max and min values for int64
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if math.IsInf(f, 1) {
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return vInfPos, 0
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}
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return vInfNeg, 0
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}
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func positiveFloatToDecimal(f float64) (int64, int16) {
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// There is no need in checking for f == 0, since it should be already checked by the caller.
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u := uint64(f)
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if float64(u) != f {
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return positiveFloatToDecimalSlow(f)
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}
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// Fast path for integers.
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if u < 1<<55 && u%10 != 0 {
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return int64(u), 0
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}
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return getDecimalAndScale(u)
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}
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func getDecimalAndScale(u uint64) (int64, int16) {
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var scale int16
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for u >= 1<<55 {
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// Remove trailing garbage bits left after float64->uint64 conversion,
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// since float64 contains only 53 significant bits.
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// See https://en.wikipedia.org/wiki/Double-precision_floating-point_format
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u /= 10
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scale++
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}
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if u%10 != 0 {
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return int64(u), scale
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}
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// Minimize v by converting trailing zeros to scale.
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u /= 10
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scale++
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for u != 0 && u%10 == 0 {
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u /= 10
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scale++
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}
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return int64(u), scale
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}
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func positiveFloatToDecimalSlow(f float64) (int64, int16) {
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// Slow path for floating point numbers.
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var scale int16
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prec := conversionPrecision
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if f > 1e6 || f < 1e-6 {
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// Normalize f, so it is in the small range suitable
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// for the next loop.
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if f > 1e6 {
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// Increase conversion precision for big numbers.
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// See https://github.com/VictoriaMetrics/VictoriaMetrics/issues/213
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prec = 1e15
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}
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_, exp := math.Frexp(f)
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// Bound the exponent according to https://en.wikipedia.org/wiki/Double-precision_floating-point_format
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// This fixes the issue https://github.com/VictoriaMetrics/VictoriaMetrics/issues/1114
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if exp < -1022 {
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exp = -1022
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} else if exp > 1023 {
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exp = 1023
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}
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scale = int16(float64(exp) * (math.Ln2 / math.Ln10))
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f *= math.Pow10(-int(scale))
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}
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// Multiply f by 100 until the fractional part becomes
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// too small comparing to integer part.
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for f < prec {
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x, frac := math.Modf(f)
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if frac*prec < x {
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f = x
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break
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}
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if (1-frac)*prec < x {
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f = x + 1
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break
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}
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f *= 100
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scale -= 2
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}
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u := uint64(f)
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if u%10 != 0 {
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return int64(u), scale
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}
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// Minimize u by converting trailing zero to scale.
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u /= 10
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scale++
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return int64(u), scale
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}
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const conversionPrecision = 1e12
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