81 lines
1.8 KiB
Go
81 lines
1.8 KiB
Go
// Copyright (c) 2016 The mathutil Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package mathutil // import "modernc.org/mathutil"
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import (
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"math/big"
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)
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type float struct {
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n *big.Int
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fracBits int
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maxFracBits int
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}
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func newFloat(n *big.Int, fracBits, maxFracBits int) float {
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f := float{n: n, fracBits: fracBits, maxFracBits: maxFracBits}
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f.normalize()
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return f
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}
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func (f *float) normalize() {
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n := f.n.BitLen()
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if n == 0 {
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return
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}
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if n := f.fracBits - f.maxFracBits; n > 0 {
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bit := f.n.Bit(n - 1)
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f.n.Rsh(f.n, uint(n))
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if bit != 0 {
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f.n.Add(f.n, _1)
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}
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f.fracBits -= n
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}
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var i int
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for ; f.fracBits > 0 && i <= f.fracBits && f.n.Bit(i) == 0; i++ {
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f.fracBits--
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}
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if i != 0 {
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f.n.Rsh(f.n, uint(i))
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}
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}
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func (f *float) eq1() bool { return f.fracBits == 0 && f.n.BitLen() == 1 }
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func (f *float) ge2() bool { return f.n.BitLen() > f.fracBits+1 }
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func (f *float) div2() {
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f.fracBits++
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f.normalize()
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}
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// BinaryLog computes the binary logarithm of n. The result consists of a
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// characteristic and a mantissa having precision mantissaBits. The value of
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// the binary logarithm is
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//
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// characteristic + mantissa*(2^-mantissaBits)
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//
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// BinaryLog panics for n <= 0 or mantissaBits < 0.
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func BinaryLog(n *big.Int, mantissaBits int) (characteristic int, mantissa *big.Int) {
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if n.Sign() <= 0 || mantissaBits < 0 {
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panic("invalid argument of BinaryLog")
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}
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characteristic = n.BitLen() - 1
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mantissa = big.NewInt(0)
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x := newFloat(n, characteristic, mantissaBits)
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for ; mantissaBits != 0 && !x.eq1(); mantissaBits-- {
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x.sqr()
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mantissa.Lsh(mantissa, 1)
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if x.ge2() {
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mantissa.SetBit(mantissa, 0, 1)
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x.div2()
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}
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}
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return characteristic, mantissa
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}
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