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strconv: faster FormatFloat(x, *, -1, 64) using Grisu3 algorithm.
The implementation is similar to the one from the double-conversion
library used in the Chrome V8 engine.
old ns/op new ns/op speedup
BenchmarkAppendFloatDecimal 591 480 1.2x
BenchmarkAppendFloat 2956 486 6.1x
BenchmarkAppendFloatExp 10622 503 21.1x
BenchmarkAppendFloatNegExp 40343 483 83.5x
BenchmarkAppendFloatBig 2798 664 4.2x
See F. Loitsch, ``Printing Floating-Point Numbers Quickly and
Accurately with Integers'', Proceedings of the ACM, 2010.
R=rsc
CC=golang-dev, remy
https://golang.org/cl/5502079
This commit is contained in:
Rémy Oudompheng
parent
a5950df89e
commit
0575cd9de4
@ -191,6 +191,36 @@ func (f *extFloat) Assign(x float64) {
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f.exp -= 64
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}
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// AssignComputeBounds sets f to the value of x and returns
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// lower, upper such that any number in the closed interval
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// [lower, upper] is converted back to x.
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func (f *extFloat) AssignComputeBounds(x float64) (lower, upper extFloat) {
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// Special cases.
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bits := math.Float64bits(x)
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flt := &float64info
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neg := bits>>(flt.expbits+flt.mantbits) != 0
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expBiased := int(bits>>flt.mantbits) & (1<<flt.expbits - 1)
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mant := bits & (uint64(1)<<flt.mantbits - 1)
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if expBiased == 0 {
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// denormalized.
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f.mant = mant
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f.exp = 1 + flt.bias - int(flt.mantbits)
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} else {
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f.mant = mant | 1<<flt.mantbits
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f.exp = expBiased + flt.bias - int(flt.mantbits)
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}
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f.neg = neg
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upper = extFloat{mant: 2*f.mant + 1, exp: f.exp - 1, neg: f.neg}
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if mant != 0 || expBiased == 1 {
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lower = extFloat{mant: 2*f.mant - 1, exp: f.exp - 1, neg: f.neg}
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} else {
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lower = extFloat{mant: 4*f.mant - 1, exp: f.exp - 2, neg: f.neg}
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}
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return
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}
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// Normalize normalizes f so that the highest bit of the mantissa is
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// set, and returns the number by which the mantissa was left-shifted.
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func (f *extFloat) Normalize() uint {
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@ -309,3 +339,163 @@ func (f *extFloat) AssignDecimal(d *decimal) (ok bool) {
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}
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return true
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}
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// Frexp10 is an analogue of math.Frexp for decimal powers. It scales
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// f by an approximate power of ten 10^-exp, and returns exp10, so
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// that f*10^exp10 has the same value as the old f, up to an ulp,
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// as well as the index of 10^-exp in the powersOfTen table.
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// The arguments expMin and expMax constrain the final value of the
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// binary exponent of f.
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func (f *extFloat) frexp10(expMin, expMax int) (exp10, index int) {
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// it is illegal to call this function with a too restrictive exponent range.
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if expMax-expMin <= 25 {
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panic("strconv: invalid exponent range")
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}
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// Find power of ten such that x * 10^n has a binary exponent
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// between expMin and expMax
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approxExp10 := -(f.exp + 100) * 28 / 93 // log(10)/log(2) is close to 93/28.
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i := (approxExp10 - firstPowerOfTen) / stepPowerOfTen
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Loop:
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for {
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exp := f.exp + powersOfTen[i].exp + 64
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switch {
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case exp < expMin:
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i++
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case exp > expMax:
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i--
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default:
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break Loop
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}
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}
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// Apply the desired decimal shift on f. It will have exponent
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// in the desired range. This is multiplication by 10^-exp10.
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f.Multiply(powersOfTen[i])
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return -(firstPowerOfTen + i*stepPowerOfTen), i
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}
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// frexp10Many applies a common shift by a power of ten to a, b, c.
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func frexp10Many(expMin, expMax int, a, b, c *extFloat) (exp10 int) {
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exp10, i := c.frexp10(expMin, expMax)
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a.Multiply(powersOfTen[i])
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b.Multiply(powersOfTen[i])
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return
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}
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// ShortestDecimal stores in d the shortest decimal representation of f
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// which belongs to the open interval (lower, upper), where f is supposed
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// to lie. It returns false whenever the result is unsure. The implementation
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// uses the Grisu3 algorithm.
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func (f *extFloat) ShortestDecimal(d *decimal, lower, upper *extFloat) bool {
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if f.mant == 0 {
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d.d[0] = '0'
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d.nd = 1
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d.dp = 0
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d.neg = f.neg
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}
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const minExp = -60
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const maxExp = -32
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upper.Normalize()
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// Uniformize exponents.
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if f.exp > upper.exp {
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f.mant <<= uint(f.exp - upper.exp)
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f.exp = upper.exp
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}
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if lower.exp > upper.exp {
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lower.mant <<= uint(lower.exp - upper.exp)
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lower.exp = upper.exp
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}
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exp10 := frexp10Many(minExp, maxExp, lower, f, upper)
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// Take a safety margin due to rounding in frexp10Many, but we lose precision.
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upper.mant++
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lower.mant--
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// The shortest representation of f is either rounded up or down, but
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// in any case, it is a truncation of upper.
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shift := uint(-upper.exp)
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integer := uint32(upper.mant >> shift)
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fraction := upper.mant - (uint64(integer) << shift)
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// How far we can go down from upper until the result is wrong.
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allowance := upper.mant - lower.mant
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// How far we should go to get a very precise result.
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targetDiff := upper.mant - f.mant
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// Count integral digits: there are at most 10.
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var integerDigits int
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for i, pow := range uint64pow10 {
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if uint64(integer) >= pow {
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integerDigits = i + 1
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}
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}
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for i := 0; i < integerDigits; i++ {
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pow := uint64pow10[integerDigits-i-1]
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digit := integer / uint32(pow)
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d.d[i] = byte(digit + '0')
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integer -= digit * uint32(pow)
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// evaluate whether we should stop.
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if currentDiff := uint64(integer)<<shift + fraction; currentDiff < allowance {
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d.nd = i + 1
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d.dp = integerDigits + exp10
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d.neg = f.neg
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// Sometimes allowance is so large the last digit might need to be
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// decremented to get closer to f.
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return adjustLastDigit(d, currentDiff, targetDiff, allowance, pow<<shift, 2)
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}
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}
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d.nd = integerDigits
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d.dp = d.nd + exp10
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d.neg = f.neg
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// Compute digits of the fractional part. At each step fraction does not
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// overflow. The choice of minExp implies that fraction is less than 2^60.
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var digit int
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multiplier := uint64(1)
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for {
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fraction *= 10
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multiplier *= 10
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digit = int(fraction >> shift)
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d.d[d.nd] = byte(digit + '0')
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d.nd++
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fraction -= uint64(digit) << shift
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if fraction < allowance*multiplier {
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// We are in the admissible range. Note that if allowance is about to
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// overflow, that is, allowance > 2^64/10, the condition is automatically
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// true due to the limited range of fraction.
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return adjustLastDigit(d,
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fraction, targetDiff*multiplier, allowance*multiplier,
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1<<shift, multiplier*2)
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}
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}
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return false
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}
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// adjustLastDigit modifies d = x-currentDiff*ε, to get closest to
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// d = x-targetDiff*ε, without becoming smaller than x-maxDiff*ε.
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// It assumes that a decimal digit is worth ulpDecimal*ε, and that
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// all data is known with a error estimate of ulpBinary*ε.
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func adjustLastDigit(d *decimal, currentDiff, targetDiff, maxDiff, ulpDecimal, ulpBinary uint64) bool {
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if ulpDecimal < 2*ulpBinary {
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// Appromixation is too wide.
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return false
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}
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for currentDiff+ulpDecimal/2+ulpBinary < targetDiff {
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d.d[d.nd-1]--
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currentDiff += ulpDecimal
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}
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if currentDiff+ulpDecimal <= targetDiff+ulpDecimal/2+ulpBinary {
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// we have two choices, and don't know what to do.
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return false
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}
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if currentDiff < ulpBinary || currentDiff > maxDiff-ulpBinary {
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// we went too far
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return false
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}
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if d.nd == 1 && d.d[0] == '0' {
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// the number has actually reached zero.
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d.nd = 0
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d.dp = 0
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}
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return true
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}
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@ -98,29 +98,43 @@ func genericFtoa(dst []byte, val float64, fmt byte, prec, bitSize int) []byte {
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return fmtB(dst, neg, mant, exp, flt)
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}
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// Create exact decimal representation.
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// The shift is exp - flt.mantbits because mant is a 1-bit integer
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// followed by a flt.mantbits fraction, and we are treating it as
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// a 1+flt.mantbits-bit integer.
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d := new(decimal)
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d.Assign(mant)
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d.Shift(exp - int(flt.mantbits))
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// Round appropriately.
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// Negative precision means "only as much as needed to be exact."
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shortest := false
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if prec < 0 {
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shortest = true
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roundShortest(d, mant, exp, flt)
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switch fmt {
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case 'e', 'E':
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prec = d.nd - 1
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case 'f':
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prec = max(d.nd-d.dp, 0)
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case 'g', 'G':
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prec = d.nd
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shortest := prec < 0
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d := new(decimal)
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if shortest {
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ok := false
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if optimize && bitSize == 64 {
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// Try Grisu3 algorithm.
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f := new(extFloat)
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lower, upper := f.AssignComputeBounds(val)
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ok = f.ShortestDecimal(d, &lower, &upper)
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}
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if !ok {
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// Create exact decimal representation.
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// The shift is exp - flt.mantbits because mant is a 1-bit integer
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// followed by a flt.mantbits fraction, and we are treating it as
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// a 1+flt.mantbits-bit integer.
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d.Assign(mant)
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d.Shift(exp - int(flt.mantbits))
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roundShortest(d, mant, exp, flt)
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}
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// Precision for shortest representation mode.
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if prec < 0 {
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switch fmt {
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case 'e', 'E':
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prec = d.nd - 1
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case 'f':
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prec = max(d.nd-d.dp, 0)
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case 'g', 'G':
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prec = d.nd
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}
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}
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} else {
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// Create exact decimal representation.
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d.Assign(mant)
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d.Shift(exp - int(flt.mantbits))
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// Round appropriately.
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switch fmt {
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case 'e', 'E':
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d.Round(prec + 1)
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@ -6,6 +6,7 @@ package strconv_test
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import (
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"math"
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"math/rand"
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. "strconv"
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"testing"
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)
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@ -153,6 +154,25 @@ func TestFtoa(t *testing.T) {
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}
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}
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func TestFtoaRandom(t *testing.T) {
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N := int(1e4)
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if testing.Short() {
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N = 100
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}
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t.Logf("testing %d random numbers with fast and slow FormatFloat", N)
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for i := 0; i < N; i++ {
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bits := uint64(rand.Uint32())<<32 | uint64(rand.Uint32())
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x := math.Float64frombits(bits)
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shortFast := FormatFloat(x, 'g', -1, 64)
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SetOptimize(false)
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shortSlow := FormatFloat(x, 'g', -1, 64)
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SetOptimize(true)
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if shortSlow != shortFast {
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t.Errorf("%b printed as %s, want %s", x, shortFast, shortSlow)
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}
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}
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}
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func TestAppendFloatDoesntAllocate(t *testing.T) {
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n := numAllocations(func() {
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var buf [64]byte
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@ -188,6 +208,12 @@ func BenchmarkFormatFloatExp(b *testing.B) {
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}
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}
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func BenchmarkFormatFloatNegExp(b *testing.B) {
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for i := 0; i < b.N; i++ {
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FormatFloat(-5.11e-95, 'g', -1, 64)
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}
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}
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func BenchmarkFormatFloatBig(b *testing.B) {
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for i := 0; i < b.N; i++ {
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FormatFloat(123456789123456789123456789, 'g', -1, 64)
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@ -215,6 +241,13 @@ func BenchmarkAppendFloatExp(b *testing.B) {
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}
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}
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func BenchmarkAppendFloatNegExp(b *testing.B) {
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dst := make([]byte, 0, 30)
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for i := 0; i < b.N; i++ {
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AppendFloat(dst, -5.11e-95, 'g', -1, 64)
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}
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}
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func BenchmarkAppendFloatBig(b *testing.B) {
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dst := make([]byte, 0, 30)
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for i := 0; i < b.N; i++ {
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