mirror of
https://github.com/VictoriaMetrics/VictoriaMetrics.git
synced 2024-11-21 14:44:00 +00:00
391 lines
7.9 KiB
Go
391 lines
7.9 KiB
Go
package decimal
|
|
|
|
import (
|
|
"math"
|
|
"sync"
|
|
|
|
"github.com/VictoriaMetrics/VictoriaMetrics/lib/fastnum"
|
|
)
|
|
|
|
// CalibrateScale calibrates a and b with the corresponding exponents ae, be
|
|
// and returns the resulting exponent e.
|
|
func CalibrateScale(a []int64, ae int16, b []int64, be int16) (e int16) {
|
|
if ae == be {
|
|
// Fast path - exponents are equal.
|
|
return ae
|
|
}
|
|
if len(a) == 0 {
|
|
return be
|
|
}
|
|
if len(b) == 0 {
|
|
return ae
|
|
}
|
|
|
|
if ae < be {
|
|
a, b = b, a
|
|
ae, be = be, ae
|
|
}
|
|
|
|
upExp := ae - be
|
|
downExp := int16(0)
|
|
for _, v := range a {
|
|
maxUpExp := maxUpExponent(v)
|
|
if upExp-maxUpExp > downExp {
|
|
downExp = upExp - maxUpExp
|
|
}
|
|
}
|
|
upExp -= downExp
|
|
for i, v := range a {
|
|
adjExp := upExp
|
|
for adjExp > 0 {
|
|
v *= 10
|
|
adjExp--
|
|
}
|
|
a[i] = v
|
|
}
|
|
if downExp > 0 {
|
|
for i, v := range b {
|
|
adjExp := downExp
|
|
for adjExp > 0 {
|
|
v /= 10
|
|
adjExp--
|
|
}
|
|
b[i] = v
|
|
}
|
|
}
|
|
return be + downExp
|
|
}
|
|
|
|
// ExtendFloat64sCapacity extends dst capacity to hold additionalItems
|
|
// and returns the extended dst.
|
|
func ExtendFloat64sCapacity(dst []float64, additionalItems int) []float64 {
|
|
dstLen := len(dst)
|
|
if n := dstLen + additionalItems - cap(dst); n > 0 {
|
|
dst = append(dst[:cap(dst)], make([]float64, n)...)
|
|
}
|
|
return dst[:dstLen]
|
|
}
|
|
|
|
// ExtendInt64sCapacity extends dst capacity to hold additionalItems
|
|
// and returns the extended dst.
|
|
func ExtendInt64sCapacity(dst []int64, additionalItems int) []int64 {
|
|
dstLen := len(dst)
|
|
if n := dstLen + additionalItems - cap(dst); n > 0 {
|
|
dst = append(dst[:cap(dst)], make([]int64, n)...)
|
|
}
|
|
return dst[:dstLen]
|
|
}
|
|
|
|
// AppendDecimalToFloat converts each item in va to f=v*10^e, appends it
|
|
// to dst and returns the resulting dst.
|
|
func AppendDecimalToFloat(dst []float64, va []int64, e int16) []float64 {
|
|
// Extend dst capacity in order to eliminate memory allocations below.
|
|
dst = ExtendFloat64sCapacity(dst, len(va))
|
|
|
|
if fastnum.IsInt64Zeros(va) {
|
|
return fastnum.AppendFloat64Zeros(dst, len(va))
|
|
}
|
|
if e == 0 {
|
|
if fastnum.IsInt64Ones(va) {
|
|
return fastnum.AppendFloat64Ones(dst, len(va))
|
|
}
|
|
for _, v := range va {
|
|
f := float64(v)
|
|
dst = append(dst, f)
|
|
}
|
|
return dst
|
|
}
|
|
|
|
// increase conversion precision for negative exponents by dividing by e10
|
|
if e < 0 {
|
|
e10 := math.Pow10(int(-e))
|
|
for _, v := range va {
|
|
f := float64(v) / e10
|
|
dst = append(dst, f)
|
|
}
|
|
return dst
|
|
}
|
|
e10 := math.Pow10(int(e))
|
|
for _, v := range va {
|
|
f := float64(v) * e10
|
|
dst = append(dst, f)
|
|
}
|
|
return dst
|
|
}
|
|
|
|
// AppendFloatToDecimal converts each item in src to v*10^e and appends
|
|
// each v to dst returning it as va.
|
|
//
|
|
// It tries minimizing each item in dst.
|
|
func AppendFloatToDecimal(dst []int64, src []float64) (va []int64, e int16) {
|
|
if len(src) == 0 {
|
|
return dst, 0
|
|
}
|
|
if fastnum.IsFloat64Zeros(src) {
|
|
dst = fastnum.AppendInt64Zeros(dst, len(src))
|
|
return dst, 0
|
|
}
|
|
if fastnum.IsFloat64Ones(src) {
|
|
dst = fastnum.AppendInt64Ones(dst, len(src))
|
|
return dst, 0
|
|
}
|
|
|
|
// Extend dst capacity in order to eliminate memory allocations below.
|
|
dst = ExtendInt64sCapacity(dst, len(src))
|
|
|
|
vaev := vaeBufPool.Get()
|
|
if vaev == nil {
|
|
vaev = &vaeBuf{
|
|
va: make([]int64, len(src)),
|
|
ea: make([]int16, len(src)),
|
|
}
|
|
}
|
|
vae := vaev.(*vaeBuf)
|
|
vae.va = vae.va[:0]
|
|
vae.ea = vae.ea[:0]
|
|
|
|
// Determine the minimum exponent across all src items.
|
|
v, exp := FromFloat(src[0])
|
|
vae.va = append(vae.va, v)
|
|
vae.ea = append(vae.ea, exp)
|
|
minExp := exp
|
|
for _, f := range src[1:] {
|
|
v, exp := FromFloat(f)
|
|
vae.va = append(vae.va, v)
|
|
vae.ea = append(vae.ea, exp)
|
|
if exp < minExp {
|
|
minExp = exp
|
|
}
|
|
}
|
|
|
|
// Determine whether all the src items may be upscaled to minExp.
|
|
// If not, adjust minExp accordingly.
|
|
downExp := int16(0)
|
|
for i, v := range vae.va {
|
|
exp := vae.ea[i]
|
|
upExp := exp - minExp
|
|
maxUpExp := maxUpExponent(v)
|
|
if upExp-maxUpExp > downExp {
|
|
downExp = upExp - maxUpExp
|
|
}
|
|
}
|
|
minExp += downExp
|
|
|
|
// Scale each item in src to minExp and append it to dst.
|
|
for i, v := range vae.va {
|
|
exp := vae.ea[i]
|
|
adjExp := exp - minExp
|
|
for adjExp > 0 {
|
|
v *= 10
|
|
adjExp--
|
|
}
|
|
for adjExp < 0 {
|
|
v /= 10
|
|
adjExp++
|
|
}
|
|
dst = append(dst, v)
|
|
}
|
|
|
|
vaeBufPool.Put(vae)
|
|
|
|
return dst, minExp
|
|
}
|
|
|
|
type vaeBuf struct {
|
|
va []int64
|
|
ea []int16
|
|
}
|
|
|
|
var vaeBufPool sync.Pool
|
|
|
|
func maxUpExponent(v int64) int16 {
|
|
if v == 0 {
|
|
// Any exponent allowed.
|
|
return 1024
|
|
}
|
|
if v < 0 {
|
|
v = -v
|
|
}
|
|
if v < 0 {
|
|
// Handle corner case for v=-1<<63
|
|
return 0
|
|
}
|
|
|
|
maxMultiplier := ((1 << 63) - 1) / uint64(v)
|
|
switch {
|
|
case maxMultiplier >= 1e19:
|
|
return 19
|
|
case maxMultiplier >= 1e18:
|
|
return 18
|
|
case maxMultiplier >= 1e17:
|
|
return 17
|
|
case maxMultiplier >= 1e16:
|
|
return 16
|
|
case maxMultiplier >= 1e15:
|
|
return 15
|
|
case maxMultiplier >= 1e14:
|
|
return 14
|
|
case maxMultiplier >= 1e13:
|
|
return 13
|
|
case maxMultiplier >= 1e12:
|
|
return 12
|
|
case maxMultiplier >= 1e11:
|
|
return 11
|
|
case maxMultiplier >= 1e10:
|
|
return 10
|
|
case maxMultiplier >= 1e9:
|
|
return 9
|
|
case maxMultiplier >= 1e8:
|
|
return 8
|
|
case maxMultiplier >= 1e7:
|
|
return 7
|
|
case maxMultiplier >= 1e6:
|
|
return 6
|
|
case maxMultiplier >= 1e5:
|
|
return 5
|
|
case maxMultiplier >= 1e4:
|
|
return 4
|
|
case maxMultiplier >= 1e3:
|
|
return 3
|
|
case maxMultiplier >= 1e2:
|
|
return 2
|
|
case maxMultiplier >= 1e1:
|
|
return 1
|
|
default:
|
|
return 0
|
|
}
|
|
}
|
|
|
|
// ToFloat returns f=v*10^e.
|
|
func ToFloat(v int64, e int16) float64 {
|
|
f := float64(v)
|
|
// increase conversion precision for negative exponents by dividing by e10
|
|
if e < 0 {
|
|
return f / math.Pow10(int(-e))
|
|
}
|
|
return f * math.Pow10(int(e))
|
|
}
|
|
|
|
const (
|
|
vInfPos = 1<<63 - 1
|
|
vInfNeg = -1 << 63
|
|
|
|
vMax = 1<<63 - 3
|
|
vMin = -1<<63 + 1
|
|
)
|
|
|
|
// FromFloat converts f to v*10^e.
|
|
//
|
|
// It tries minimizing v.
|
|
// For instance, for f = -1.234 it returns v = -1234, e = -3.
|
|
//
|
|
// FromFloat doesn't work properly with NaN values, so don't pass them here.
|
|
func FromFloat(f float64) (int64, int16) {
|
|
if f == 0 {
|
|
return 0, 0
|
|
}
|
|
if math.IsInf(f, 0) {
|
|
return fromFloatInf(f)
|
|
}
|
|
if f > 0 {
|
|
v, e := positiveFloatToDecimal(f)
|
|
if v > vMax {
|
|
v = vMax
|
|
}
|
|
return v, e
|
|
}
|
|
v, e := positiveFloatToDecimal(-f)
|
|
v = -v
|
|
if v < vMin {
|
|
v = vMin
|
|
}
|
|
return v, e
|
|
}
|
|
|
|
func fromFloatInf(f float64) (int64, int16) {
|
|
// Limit infs by max and min values for int64
|
|
if math.IsInf(f, 1) {
|
|
return vInfPos, 0
|
|
}
|
|
return vInfNeg, 0
|
|
}
|
|
|
|
func positiveFloatToDecimal(f float64) (int64, int16) {
|
|
// There is no need in checking for f == 0, since it should be already checked by the caller.
|
|
u := uint64(f)
|
|
if float64(u) != f {
|
|
return positiveFloatToDecimalSlow(f)
|
|
}
|
|
// Fast path for integers.
|
|
if u < 1<<55 && u%10 != 0 {
|
|
return int64(u), 0
|
|
}
|
|
return getDecimalAndScale(u)
|
|
}
|
|
|
|
func getDecimalAndScale(u uint64) (int64, int16) {
|
|
var scale int16
|
|
for u >= 1<<55 {
|
|
// Remove trailing garbage bits left after float64->uint64 conversion,
|
|
// since float64 contains only 53 significant bits.
|
|
// See https://en.wikipedia.org/wiki/Double-precision_floating-point_format
|
|
u /= 10
|
|
scale++
|
|
}
|
|
if u%10 != 0 {
|
|
return int64(u), scale
|
|
}
|
|
// Minimize v by converting trailing zeros to scale.
|
|
u /= 10
|
|
scale++
|
|
for u != 0 && u%10 == 0 {
|
|
u /= 10
|
|
scale++
|
|
}
|
|
return int64(u), scale
|
|
}
|
|
|
|
func positiveFloatToDecimalSlow(f float64) (int64, int16) {
|
|
// Slow path for floating point numbers.
|
|
var scale int16
|
|
prec := conversionPrecision
|
|
if f > 1e6 || f < 1e-6 {
|
|
// Normalize f, so it is in the small range suitable
|
|
// for the next loop.
|
|
if f > 1e6 {
|
|
// Increase conversion precision for big numbers.
|
|
// See https://github.com/VictoriaMetrics/VictoriaMetrics/issues/213
|
|
prec = 1e15
|
|
}
|
|
_, exp := math.Frexp(f)
|
|
scale = int16(float64(exp) * math.Ln2 / math.Ln10)
|
|
f *= math.Pow10(-int(scale))
|
|
}
|
|
|
|
// Multiply f by 100 until the fractional part becomes
|
|
// too small comparing to integer part.
|
|
for f < prec {
|
|
x, frac := math.Modf(f)
|
|
if frac*prec < x {
|
|
f = x
|
|
break
|
|
}
|
|
if (1-frac)*prec < x {
|
|
f = x + 1
|
|
break
|
|
}
|
|
f *= 100
|
|
scale -= 2
|
|
}
|
|
u := uint64(f)
|
|
if u%10 != 0 {
|
|
return int64(u), scale
|
|
}
|
|
|
|
// Minimize u by converting trailing zero to scale.
|
|
u /= 10
|
|
scale++
|
|
return int64(u), scale
|
|
}
|
|
|
|
const conversionPrecision = 1e12
|