mirror of https://go.googlesource.com/go
110 lines
3.1 KiB
Go
110 lines
3.1 KiB
Go
// Copyright 2015 The Go Authors. All rights reserved.
|
|
// Use of this source code is governed by a BSD-style
|
|
// license that can be found in the LICENSE file.
|
|
|
|
//go:build ignore
|
|
|
|
// fastlog2Table contains log2 approximations for 5 binary digits.
|
|
// This is used to implement fastlog2, which is used for heap sampling.
|
|
|
|
package main
|
|
|
|
import (
|
|
"bytes"
|
|
"fmt"
|
|
"log"
|
|
"math"
|
|
"os"
|
|
)
|
|
|
|
func main() {
|
|
var buf bytes.Buffer
|
|
|
|
fmt.Fprintln(&buf, "// Code generated by mkfastlog2table.go; DO NOT EDIT.")
|
|
fmt.Fprintln(&buf, "// Run go generate from src/runtime to update.")
|
|
fmt.Fprintln(&buf, "// See mkfastlog2table.go for comments.")
|
|
fmt.Fprintln(&buf)
|
|
fmt.Fprintln(&buf, "package runtime")
|
|
fmt.Fprintln(&buf)
|
|
fmt.Fprintln(&buf, "const fastlogNumBits =", fastlogNumBits)
|
|
fmt.Fprintln(&buf)
|
|
|
|
fmt.Fprintln(&buf, "var fastlog2Table = [1<<fastlogNumBits + 1]float64{")
|
|
table := computeTable()
|
|
for _, t := range table {
|
|
fmt.Fprintf(&buf, "\t%v,\n", t)
|
|
}
|
|
fmt.Fprintln(&buf, "}")
|
|
|
|
if err := os.WriteFile("fastlog2table.go", buf.Bytes(), 0644); err != nil {
|
|
log.Fatalln(err)
|
|
}
|
|
}
|
|
|
|
const fastlogNumBits = 5
|
|
|
|
func computeTable() []float64 {
|
|
fastlog2Table := make([]float64, 1<<fastlogNumBits+1)
|
|
for i := 0; i <= (1 << fastlogNumBits); i++ {
|
|
fastlog2Table[i] = log2(1.0 + float64(i)/(1<<fastlogNumBits))
|
|
}
|
|
return fastlog2Table
|
|
}
|
|
|
|
// log2 is a local copy of math.Log2 with an explicit float64 conversion
|
|
// to disable FMA. This lets us generate the same output on all platforms.
|
|
func log2(x float64) float64 {
|
|
frac, exp := math.Frexp(x)
|
|
// Make sure exact powers of two give an exact answer.
|
|
// Don't depend on Log(0.5)*(1/Ln2)+exp being exactly exp-1.
|
|
if frac == 0.5 {
|
|
return float64(exp - 1)
|
|
}
|
|
return float64(nlog(frac)*(1/math.Ln2)) + float64(exp)
|
|
}
|
|
|
|
// nlog is a local copy of math.Log with explicit float64 conversions
|
|
// to disable FMA. This lets us generate the same output on all platforms.
|
|
func nlog(x float64) float64 {
|
|
const (
|
|
Ln2Hi = 6.93147180369123816490e-01 /* 3fe62e42 fee00000 */
|
|
Ln2Lo = 1.90821492927058770002e-10 /* 3dea39ef 35793c76 */
|
|
L1 = 6.666666666666735130e-01 /* 3FE55555 55555593 */
|
|
L2 = 3.999999999940941908e-01 /* 3FD99999 9997FA04 */
|
|
L3 = 2.857142874366239149e-01 /* 3FD24924 94229359 */
|
|
L4 = 2.222219843214978396e-01 /* 3FCC71C5 1D8E78AF */
|
|
L5 = 1.818357216161805012e-01 /* 3FC74664 96CB03DE */
|
|
L6 = 1.531383769920937332e-01 /* 3FC39A09 D078C69F */
|
|
L7 = 1.479819860511658591e-01 /* 3FC2F112 DF3E5244 */
|
|
)
|
|
|
|
// special cases
|
|
switch {
|
|
case math.IsNaN(x) || math.IsInf(x, 1):
|
|
return x
|
|
case x < 0:
|
|
return math.NaN()
|
|
case x == 0:
|
|
return math.Inf(-1)
|
|
}
|
|
|
|
// reduce
|
|
f1, ki := math.Frexp(x)
|
|
if f1 < math.Sqrt2/2 {
|
|
f1 *= 2
|
|
ki--
|
|
}
|
|
f := f1 - 1
|
|
k := float64(ki)
|
|
|
|
// compute
|
|
s := float64(f / (2 + f))
|
|
s2 := float64(s * s)
|
|
s4 := float64(s2 * s2)
|
|
t1 := s2 * float64(L1+float64(s4*float64(L3+float64(s4*float64(L5+float64(s4*L7))))))
|
|
t2 := s4 * float64(L2+float64(s4*float64(L4+float64(s4*L6))))
|
|
R := float64(t1 + t2)
|
|
hfsq := float64(0.5 * f * f)
|
|
return float64(k*Ln2Hi) - ((hfsq - (float64(s*float64(hfsq+R)) + float64(k*Ln2Lo))) - f)
|
|
}
|