source: code/trunk/vendor/modernc.org/mathutil/binarylog.go@ 822

// 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
}