81 lines
1.8 KiB
Go
81 lines
1.8 KiB
Go
|
// 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
|
||
|
|
}
|