1// Copyright 2015 The Go Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style
3// license that can be found in the LICENSE file.
4
5//go:build ignore
6
7// fastlog2Table contains log2 approximations for 5 binary digits.
8// This is used to implement fastlog2, which is used for heap sampling.
9
10package main
11
12import (
13	"bytes"
14	"fmt"
15	"log"
16	"math"
17	"os"
18)
19
20func main() {
21	var buf bytes.Buffer
22
23	fmt.Fprintln(&buf, "// Code generated by mkfastlog2table.go; DO NOT EDIT.")
24	fmt.Fprintln(&buf, "// Run go generate from src/runtime to update.")
25	fmt.Fprintln(&buf, "// See mkfastlog2table.go for comments.")
26	fmt.Fprintln(&buf)
27	fmt.Fprintln(&buf, "package runtime")
28	fmt.Fprintln(&buf)
29	fmt.Fprintln(&buf, "const fastlogNumBits =", fastlogNumBits)
30	fmt.Fprintln(&buf)
31
32	fmt.Fprintln(&buf, "var fastlog2Table = [1<<fastlogNumBits + 1]float64{")
33	table := computeTable()
34	for _, t := range table {
35		fmt.Fprintf(&buf, "\t%v,\n", t)
36	}
37	fmt.Fprintln(&buf, "}")
38
39	if err := os.WriteFile("fastlog2table.go", buf.Bytes(), 0644); err != nil {
40		log.Fatalln(err)
41	}
42}
43
44const fastlogNumBits = 5
45
46func computeTable() []float64 {
47	fastlog2Table := make([]float64, 1<<fastlogNumBits+1)
48	for i := 0; i <= (1 << fastlogNumBits); i++ {
49		fastlog2Table[i] = log2(1.0 + float64(i)/(1<<fastlogNumBits))
50	}
51	return fastlog2Table
52}
53
54// log2 is a local copy of math.Log2 with an explicit float64 conversion
55// to disable FMA. This lets us generate the same output on all platforms.
56func log2(x float64) float64 {
57	frac, exp := math.Frexp(x)
58	// Make sure exact powers of two give an exact answer.
59	// Don't depend on Log(0.5)*(1/Ln2)+exp being exactly exp-1.
60	if frac == 0.5 {
61		return float64(exp - 1)
62	}
63	return float64(nlog(frac)*(1/math.Ln2)) + float64(exp)
64}
65
66// nlog is a local copy of math.Log with explicit float64 conversions
67// to disable FMA. This lets us generate the same output on all platforms.
68func nlog(x float64) float64 {
69	const (
70		Ln2Hi = 6.93147180369123816490e-01 /* 3fe62e42 fee00000 */
71		Ln2Lo = 1.90821492927058770002e-10 /* 3dea39ef 35793c76 */
72		L1    = 6.666666666666735130e-01   /* 3FE55555 55555593 */
73		L2    = 3.999999999940941908e-01   /* 3FD99999 9997FA04 */
74		L3    = 2.857142874366239149e-01   /* 3FD24924 94229359 */
75		L4    = 2.222219843214978396e-01   /* 3FCC71C5 1D8E78AF */
76		L5    = 1.818357216161805012e-01   /* 3FC74664 96CB03DE */
77		L6    = 1.531383769920937332e-01   /* 3FC39A09 D078C69F */
78		L7    = 1.479819860511658591e-01   /* 3FC2F112 DF3E5244 */
79	)
80
81	// special cases
82	switch {
83	case math.IsNaN(x) || math.IsInf(x, 1):
84		return x
85	case x < 0:
86		return math.NaN()
87	case x == 0:
88		return math.Inf(-1)
89	}
90
91	// reduce
92	f1, ki := math.Frexp(x)
93	if f1 < math.Sqrt2/2 {
94		f1 *= 2
95		ki--
96	}
97	f := f1 - 1
98	k := float64(ki)
99
100	// compute
101	s := float64(f / (2 + f))
102	s2 := float64(s * s)
103	s4 := float64(s2 * s2)
104	t1 := s2 * float64(L1+float64(s4*float64(L3+float64(s4*float64(L5+float64(s4*L7))))))
105	t2 := s4 * float64(L2+float64(s4*float64(L4+float64(s4*L6))))
106	R := float64(t1 + t2)
107	hfsq := float64(0.5 * f * f)
108	return float64(k*Ln2Hi) - ((hfsq - (float64(s*float64(hfsq+R)) + float64(k*Ln2Lo))) - f)
109}
110