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// Copyright 2009 The Go 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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// This file implements signed multi-precision integers.
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package big
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// An Int represents a signed multi-precision integer.
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// The zero value for an Int represents the value 0.
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type Int struct {
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neg bool // sign
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abs []Word // absolute value of the integer
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}
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// New allocates and returns a new Int set to x.
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func (z *Int) New(x int64) *Int {
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z.neg = false
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if x < 0 {
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z.neg = true
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x = -x
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}
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z.abs = newN(z.abs, uint64(x))
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return z
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}
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// NewInt allocates and returns a new Int set to x.
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func NewInt(x int64) *Int { return new(Int).New(x) }
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// Set sets z to x.
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func (z *Int) Set(x *Int) *Int {
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z.neg = x.neg
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z.abs = setN(z.abs, x.abs)
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return z
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}
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// Add computes z = x+y.
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func (z *Int) Add(x, y *Int) *Int {
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if x.neg == y.neg {
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// x + y == x + y
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// (-x) + (-y) == -(x + y)
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z.neg = x.neg
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z.abs = addNN(z.abs, x.abs, y.abs)
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} else {
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// x + (-y) == x - y == -(y - x)
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// (-x) + y == y - x == -(x - y)
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if cmpNN(x.abs, y.abs) >= 0 {
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z.neg = x.neg
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z.abs = subNN(z.abs, x.abs, y.abs)
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} else {
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z.neg = !x.neg
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z.abs = subNN(z.abs, y.abs, x.abs)
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}
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}
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if len(z.abs) == 0 {
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z.neg = false // 0 has no sign
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}
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return z
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}
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// Sub computes z = x-y.
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func (z *Int) Sub(x, y *Int) *Int {
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if x.neg != y.neg {
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// x - (-y) == x + y
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// (-x) - y == -(x + y)
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z.neg = x.neg
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z.abs = addNN(z.abs, x.abs, y.abs)
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} else {
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// x - y == x - y == -(y - x)
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// (-x) - (-y) == y - x == -(x - y)
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if cmpNN(x.abs, y.abs) >= 0 {
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z.neg = x.neg
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z.abs = subNN(z.abs, x.abs, y.abs)
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} else {
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z.neg = !x.neg
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z.abs = subNN(z.abs, y.abs, x.abs)
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}
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}
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if len(z.abs) == 0 {
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z.neg = false // 0 has no sign
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}
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return z
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}
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// Mul computes z = x*y.
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func (z *Int) Mul(x, y *Int) *Int {
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// x * y == x * y
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// x * (-y) == -(x * y)
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// (-x) * y == -(x * y)
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// (-x) * (-y) == x * y
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z.abs = mulNN(z.abs, x.abs, y.abs)
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z.neg = len(z.abs) > 0 && x.neg != y.neg // 0 has no sign
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return z
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}
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// Div calculates q = (x-r)/y where 0 <= r < y. The receiver is set to q.
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func (z *Int) Div(x, y *Int) (q, r *Int) {
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q = z
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r = new(Int)
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div(q, r, x, y)
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return
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}
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// Mod calculates q = (x-r)/y and returns r.
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func (z *Int) Mod(x, y *Int) (r *Int) {
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q := new(Int)
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r = z
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div(q, r, x, y)
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return
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}
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func div(q, r, x, y *Int) {
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q.neg = x.neg != y.neg
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r.neg = x.neg
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q.abs, r.abs = divNN(q.abs, r.abs, x.abs, y.abs)
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return
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}
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// Neg computes z = -x.
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func (z *Int) Neg(x *Int) *Int {
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z.abs = setN(z.abs, x.abs)
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z.neg = len(z.abs) > 0 && !x.neg // 0 has no sign
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return z
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}
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// Cmp compares x and y. The result is
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//
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// -1 if x < y
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// 0 if x == y
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// +1 if x > y
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//
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func (x *Int) Cmp(y *Int) (r int) {
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// x cmp y == x cmp y
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// x cmp (-y) == x
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// (-x) cmp y == y
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// (-x) cmp (-y) == -(x cmp y)
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switch {
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case x.neg == y.neg:
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r = cmpNN(x.abs, y.abs)
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if x.neg {
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r = -r
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}
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case x.neg:
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r = -1
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default:
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r = 1
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}
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return
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}
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func (z *Int) String() string {
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s := ""
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if z.neg {
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s = "-"
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}
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return s + stringN(z.abs, 10)
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}
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// SetString sets z to the value of s, interpreted in the given base.
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// If base is 0 then SetString attempts to detect the base by at the prefix of
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// s. '0x' implies base 16, '0' implies base 8. Otherwise base 10 is assumed.
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func (z *Int) SetString(s string, base int) (*Int, bool) {
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var scanned int
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if base == 1 || base > 16 {
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goto Error
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}
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if len(s) == 0 {
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goto Error
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}
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if s[0] == '-' {
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z.neg = true
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s = s[1:]
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} else {
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z.neg = false
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}
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z.abs, _, scanned = scanN(z.abs, s, base)
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if scanned != len(s) {
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goto Error
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}
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return z, true
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Error:
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z.neg = false
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z.abs = nil
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return nil, false
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}
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// SetBytes interprets b as the bytes of a big-endian, unsigned integer and
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// sets x to that value.
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func (z *Int) SetBytes(b []byte) *Int {
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s := int(_S)
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z.abs = makeN(z.abs, (len(b)+s-1)/s, false)
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z.neg = false
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j := 0
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for len(b) >= s {
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var w Word
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for i := s; i > 0; i-- {
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w <<= 8
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w |= Word(b[len(b)-i])
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}
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z.abs[j] = w
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j++
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b = b[0 : len(b)-s]
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}
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if len(b) > 0 {
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var w Word
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for i := len(b); i > 0; i-- {
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w <<= 8
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w |= Word(b[len(b)-i])
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}
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z.abs[j] = w
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}
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z.abs = normN(z.abs)
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return z
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}
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// Bytes returns the absolute value of x as a big-endian byte array.
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func (z *Int) Bytes() []byte {
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s := int(_S)
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b := make([]byte, len(z.abs)*s)
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for i, w := range z.abs {
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wordBytes := b[(len(z.abs)-i-1)*s : (len(z.abs)-i)*s]
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for j := s - 1; j >= 0; j-- {
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wordBytes[j] = byte(w)
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w >>= 8
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}
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}
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i := 0
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for i < len(b) && b[i] == 0 {
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i++
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}
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return b[i:]
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}
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// Len returns the length of the absolute value of x in bits. Zero is
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// considered to have a length of one.
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func (z *Int) Len() int {
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if len(z.abs) == 0 {
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return 0
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}
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return len(z.abs)*_W - int(leadingZeros(z.abs[len(z.abs)-1]))
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}
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// Exp sets z = x**y mod m. If m is nil, z = x**y.
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// See Knuth, volume 2, section 4.6.3.
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func (z *Int) Exp(x, y, m *Int) *Int {
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if y.neg || len(y.abs) == 0 {
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z.New(1)
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z.neg = x.neg
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return z
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}
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var mWords []Word
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if m != nil {
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mWords = m.abs
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}
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|
z.abs = expNNN(z.abs, x.abs, y.abs, mWords)
|
|
|
|
z.neg = x.neg && y.abs[0]&1 == 1
|
|
|
|
return z
|
2009-11-05 16:55:41 -07:00
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
// GcdInt sets d to the greatest common divisor of a and b, which must be
|
|
|
|
// positive numbers.
|
|
|
|
// If x and y are not nil, GcdInt sets x and y such that d = a*x + b*y.
|
|
|
|
// If either a or b is not positive, GcdInt sets d = x = y = 0.
|
|
|
|
func GcdInt(d, x, y, a, b *Int) {
|
|
|
|
if a.neg || b.neg {
|
2009-12-15 16:33:31 -07:00
|
|
|
d.New(0)
|
2009-11-05 16:55:41 -07:00
|
|
|
if x != nil {
|
2009-11-09 13:07:39 -07:00
|
|
|
x.New(0)
|
2009-11-05 16:55:41 -07:00
|
|
|
}
|
|
|
|
if y != nil {
|
2009-11-09 13:07:39 -07:00
|
|
|
y.New(0)
|
2009-11-05 16:55:41 -07:00
|
|
|
}
|
2009-12-15 16:33:31 -07:00
|
|
|
return
|
2009-11-05 16:55:41 -07:00
|
|
|
}
|
|
|
|
|
2009-12-15 16:33:31 -07:00
|
|
|
A := new(Int).Set(a)
|
|
|
|
B := new(Int).Set(b)
|
2009-11-05 16:55:41 -07:00
|
|
|
|
2009-12-15 16:33:31 -07:00
|
|
|
X := new(Int)
|
|
|
|
Y := new(Int).New(1)
|
2009-11-05 16:55:41 -07:00
|
|
|
|
2009-12-15 16:33:31 -07:00
|
|
|
lastX := new(Int).New(1)
|
|
|
|
lastY := new(Int)
|
2009-11-05 16:55:41 -07:00
|
|
|
|
2009-12-15 16:33:31 -07:00
|
|
|
q := new(Int)
|
|
|
|
temp := new(Int)
|
2009-11-05 16:55:41 -07:00
|
|
|
|
|
|
|
for len(B.abs) > 0 {
|
2009-12-15 16:33:31 -07:00
|
|
|
q, r := q.Div(A, B)
|
2009-11-05 16:55:41 -07:00
|
|
|
|
2009-12-15 16:33:31 -07:00
|
|
|
A, B = B, r
|
2009-11-05 16:55:41 -07:00
|
|
|
|
2009-12-15 16:33:31 -07:00
|
|
|
temp.Set(X)
|
|
|
|
X.Mul(X, q)
|
|
|
|
X.neg = !X.neg
|
|
|
|
X.Add(X, lastX)
|
|
|
|
lastX.Set(temp)
|
2009-11-05 16:55:41 -07:00
|
|
|
|
2009-12-15 16:33:31 -07:00
|
|
|
temp.Set(Y)
|
|
|
|
Y.Mul(Y, q)
|
|
|
|
Y.neg = !Y.neg
|
|
|
|
Y.Add(Y, lastY)
|
|
|
|
lastY.Set(temp)
|
2009-11-05 16:55:41 -07:00
|
|
|
}
|
|
|
|
|
|
|
|
if x != nil {
|
2009-11-09 13:07:39 -07:00
|
|
|
*x = *lastX
|
2009-11-05 16:55:41 -07:00
|
|
|
}
|
|
|
|
|
|
|
|
if y != nil {
|
2009-11-09 13:07:39 -07:00
|
|
|
*y = *lastY
|
2009-11-05 16:55:41 -07:00
|
|
|
}
|
|
|
|
|
2009-12-15 16:33:31 -07:00
|
|
|
*d = *A
|
2009-08-14 12:53:27 -06:00
|
|
|
}
|
2009-11-11 14:21:37 -07:00
|
|
|
|
|
|
|
|
|
|
|
// ProbablyPrime performs n Miller-Rabin tests to check whether z is prime.
|
|
|
|
// If it returns true, z is prime with probability 1 - 1/4^n.
|
|
|
|
// If it returns false, z is not prime.
|
2010-01-05 17:49:05 -07:00
|
|
|
func ProbablyPrime(z *Int, n int) bool { return !z.neg && probablyPrime(z.abs, n) }
|
2009-11-11 14:21:37 -07:00
|
|
|
|
|
|
|
|
|
|
|
// Rsh sets z = x >> s and returns z.
|
|
|
|
func (z *Int) Rsh(x *Int, n int) *Int {
|
2009-12-15 16:33:31 -07:00
|
|
|
removedWords := n / _W
|
|
|
|
z.abs = makeN(z.abs, len(x.abs)-removedWords, false)
|
|
|
|
z.neg = x.neg
|
|
|
|
shiftRight(z.abs, x.abs[removedWords:], n%_W)
|
|
|
|
z.abs = normN(z.abs)
|
|
|
|
return z
|
2009-11-11 14:21:37 -07:00
|
|
|
}
|