1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
|
// Copyright (c) 2016 The mathutil Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package mathutil // import "modernc.org/mathutil"
import (
"math/big"
)
type float struct {
n *big.Int
fracBits int
maxFracBits int
}
func newFloat(n *big.Int, fracBits, maxFracBits int) float {
f := float{n: n, fracBits: fracBits, maxFracBits: maxFracBits}
f.normalize()
return f
}
func (f *float) normalize() {
n := f.n.BitLen()
if n == 0 {
return
}
if n := f.fracBits - f.maxFracBits; n > 0 {
bit := f.n.Bit(n - 1)
f.n.Rsh(f.n, uint(n))
if bit != 0 {
f.n.Add(f.n, _1)
}
f.fracBits -= n
}
var i int
for ; f.fracBits > 0 && i <= f.fracBits && f.n.Bit(i) == 0; i++ {
f.fracBits--
}
if i != 0 {
f.n.Rsh(f.n, uint(i))
}
}
func (f *float) eq1() bool { return f.fracBits == 0 && f.n.BitLen() == 1 }
func (f *float) ge2() bool { return f.n.BitLen() > f.fracBits+1 }
func (f *float) div2() {
f.fracBits++
f.normalize()
}
// BinaryLog computes the binary logarithm of n. The result consists of a
// characteristic and a mantissa having precision mantissaBits. The value of
// the binary logarithm is
//
// characteristic + mantissa*(2^-mantissaBits)
//
// BinaryLog panics for n <= 0 or mantissaBits < 0.
func BinaryLog(n *big.Int, mantissaBits int) (characteristic int, mantissa *big.Int) {
if n.Sign() <= 0 || mantissaBits < 0 {
panic("invalid argument of BinaryLog")
}
characteristic = n.BitLen() - 1
mantissa = big.NewInt(0)
x := newFloat(n, characteristic, mantissaBits)
for ; mantissaBits != 0 && !x.eq1(); mantissaBits-- {
x.sqr()
mantissa.Lsh(mantissa, 1)
if x.ge2() {
mantissa.SetBit(mantissa, 0, 1)
x.div2()
}
}
return characteristic, mantissa
}
|
