7a9389330e
gcc/: * gcc.c (default_compilers): Add entry for ".go". * common.opt: Add -static-libgo as a driver option. * doc/install.texi (Configuration): Mention libgo as an option for --enable-shared. Mention go as an option for --enable-languages. * doc/invoke.texi (Overall Options): Mention .go as a file name suffix. Mention go as a -x option. * doc/frontends.texi (G++ and GCC): Mention Go as a supported language. * doc/sourcebuild.texi (Top Level): Mention libgo. * doc/standards.texi (Standards): Add section on Go language. Move references for other languages into their own section. * doc/contrib.texi (Contributors): Mention that I contributed the Go frontend. gcc/testsuite/: * lib/go.exp: New file. * lib/go-dg.exp: New file. * lib/go-torture.exp: New file. * lib/target-supports.exp (check_compile): Match // Go. From-SVN: r167407
742 lines
15 KiB
Go
742 lines
15 KiB
Go
// 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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import (
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"fmt"
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"rand"
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)
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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 nat // absolute value of the integer
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}
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var intOne = &Int{false, natOne}
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// Sign returns:
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//
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// -1 if x < 0
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// 0 if x == 0
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// +1 if x > 0
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//
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func (x *Int) Sign() int {
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if len(x.abs) == 0 {
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return 0
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}
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if x.neg {
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return -1
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}
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return 1
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}
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// SetInt64 sets z to x and returns z.
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func (z *Int) SetInt64(x int64) *Int {
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neg := false
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if x < 0 {
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neg = true
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x = -x
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}
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z.abs = z.abs.setUint64(uint64(x))
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z.neg = neg
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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 {
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return new(Int).SetInt64(x)
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}
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// Set sets z to x and returns z.
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func (z *Int) Set(x *Int) *Int {
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z.abs = z.abs.set(x.abs)
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z.neg = x.neg
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return z
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}
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// Abs sets z to |x| (the absolute value of x) and returns z.
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func (z *Int) Abs(x *Int) *Int {
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z.abs = z.abs.set(x.abs)
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z.neg = false
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return z
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}
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// Neg sets z to -x and returns z.
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func (z *Int) Neg(x *Int) *Int {
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z.abs = z.abs.set(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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// Add sets z to the sum x+y and returns z.
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func (z *Int) Add(x, y *Int) *Int {
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neg := x.neg
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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.abs = z.abs.add(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 x.abs.cmp(y.abs) >= 0 {
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z.abs = z.abs.sub(x.abs, y.abs)
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} else {
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neg = !neg
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z.abs = z.abs.sub(y.abs, x.abs)
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}
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}
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z.neg = len(z.abs) > 0 && neg // 0 has no sign
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return z
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}
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// Sub sets z to the difference x-y and returns z.
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func (z *Int) Sub(x, y *Int) *Int {
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neg := x.neg
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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.abs = z.abs.add(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 x.abs.cmp(y.abs) >= 0 {
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z.abs = z.abs.sub(x.abs, y.abs)
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} else {
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neg = !neg
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z.abs = z.abs.sub(y.abs, x.abs)
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}
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}
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z.neg = len(z.abs) > 0 && neg // 0 has no sign
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return z
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}
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// Mul sets z to the product x*y and returns z.
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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 = z.abs.mul(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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// MulRange sets z to the product of all integers
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// in the range [a, b] inclusively and returns z.
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// If a > b (empty range), the result is 1.
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func (z *Int) MulRange(a, b int64) *Int {
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switch {
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case a > b:
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return z.SetInt64(1) // empty range
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case a <= 0 && b >= 0:
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return z.SetInt64(0) // range includes 0
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}
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// a <= b && (b < 0 || a > 0)
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neg := false
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if a < 0 {
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neg = (b-a)&1 == 0
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a, b = -b, -a
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}
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z.abs = z.abs.mulRange(uint64(a), uint64(b))
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z.neg = neg
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return z
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}
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// Binomial sets z to the binomial coefficient of (n, k) and returns z.
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func (z *Int) Binomial(n, k int64) *Int {
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var a, b Int
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a.MulRange(n-k+1, n)
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b.MulRange(1, k)
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return z.Quo(&a, &b)
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}
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// Quo sets z to the quotient x/y for y != 0 and returns z.
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// If y == 0, a division-by-zero run-time panic occurs.
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// See QuoRem for more details.
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func (z *Int) Quo(x, y *Int) *Int {
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z.abs, _ = z.abs.div(nil, 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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// Rem sets z to the remainder x%y for y != 0 and returns z.
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// If y == 0, a division-by-zero run-time panic occurs.
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// See QuoRem for more details.
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func (z *Int) Rem(x, y *Int) *Int {
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_, z.abs = nat(nil).div(z.abs, x.abs, y.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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// QuoRem sets z to the quotient x/y and r to the remainder x%y
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// and returns the pair (z, r) for y != 0.
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// If y == 0, a division-by-zero run-time panic occurs.
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//
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// QuoRem implements T-division and modulus (like Go):
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//
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// q = x/y with the result truncated to zero
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// r = x - y*q
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//
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// (See Daan Leijen, ``Division and Modulus for Computer Scientists''.)
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//
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func (z *Int) QuoRem(x, y, r *Int) (*Int, *Int) {
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z.abs, r.abs = z.abs.div(r.abs, x.abs, y.abs)
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z.neg, r.neg = len(z.abs) > 0 && x.neg != y.neg, len(r.abs) > 0 && x.neg // 0 has no sign
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return z, r
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}
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// Div sets z to the quotient x/y for y != 0 and returns z.
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// If y == 0, a division-by-zero run-time panic occurs.
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// See DivMod for more details.
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func (z *Int) Div(x, y *Int) *Int {
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y_neg := y.neg // z may be an alias for y
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var r Int
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z.QuoRem(x, y, &r)
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if r.neg {
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if y_neg {
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z.Add(z, intOne)
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} else {
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z.Sub(z, intOne)
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}
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}
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return z
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}
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// Mod sets z to the modulus x%y for y != 0 and returns z.
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// If y == 0, a division-by-zero run-time panic occurs.
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// See DivMod for more details.
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func (z *Int) Mod(x, y *Int) *Int {
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y0 := y // save y
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if z == y || alias(z.abs, y.abs) {
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y0 = new(Int).Set(y)
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}
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var q Int
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q.QuoRem(x, y, z)
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if z.neg {
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if y0.neg {
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z.Sub(z, y0)
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} else {
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z.Add(z, y0)
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}
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}
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return z
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}
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// DivMod sets z to the quotient x div y and m to the modulus x mod y
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// and returns the pair (z, m) for y != 0.
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// If y == 0, a division-by-zero run-time panic occurs.
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//
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// DivMod implements Euclidean division and modulus (unlike Go):
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//
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// q = x div y such that
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// m = x - y*q with 0 <= m < |q|
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//
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// (See Raymond T. Boute, ``The Euclidean definition of the functions
|
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// div and mod''. ACM Transactions on Programming Languages and
|
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// Systems (TOPLAS), 14(2):127-144, New York, NY, USA, 4/1992.
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// ACM press.)
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//
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func (z *Int) DivMod(x, y, m *Int) (*Int, *Int) {
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y0 := y // save y
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if z == y || alias(z.abs, y.abs) {
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y0 = new(Int).Set(y)
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}
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z.QuoRem(x, y, m)
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if m.neg {
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if y0.neg {
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z.Add(z, intOne)
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m.Sub(m, y0)
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} else {
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z.Sub(z, intOne)
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m.Add(m, y0)
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}
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}
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return z, m
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}
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// Cmp compares x and y and returns:
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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 = x.abs.cmp(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 (x *Int) String() string {
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s := ""
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if x.neg {
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s = "-"
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}
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return s + x.abs.string(10)
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}
|
||
|
||
|
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func fmtbase(ch int) int {
|
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switch ch {
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case 'b':
|
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return 2
|
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case 'o':
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return 8
|
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case 'd':
|
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return 10
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case 'x':
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return 16
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}
|
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return 10
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}
|
||
|
||
|
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// Format is a support routine for fmt.Formatter. It accepts
|
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// the formats 'b' (binary), 'o' (octal), 'd' (decimal) and
|
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// 'x' (hexadecimal).
|
||
//
|
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func (x *Int) Format(s fmt.State, ch int) {
|
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if x.neg {
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fmt.Fprint(s, "-")
|
||
}
|
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fmt.Fprint(s, x.abs.string(fmtbase(ch)))
|
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}
|
||
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||
|
||
// Int64 returns the int64 representation of z.
|
||
// If z cannot be represented in an int64, the result is undefined.
|
||
func (x *Int) Int64() int64 {
|
||
if len(x.abs) == 0 {
|
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return 0
|
||
}
|
||
v := int64(x.abs[0])
|
||
if _W == 32 && len(x.abs) > 1 {
|
||
v |= int64(x.abs[1]) << 32
|
||
}
|
||
if x.neg {
|
||
v = -v
|
||
}
|
||
return v
|
||
}
|
||
|
||
|
||
// SetString sets z to the value of s, interpreted in the given base,
|
||
// and returns z and a boolean indicating success. If SetString fails,
|
||
// the value of z is undefined.
|
||
//
|
||
// If the base argument is 0, the string prefix determines the actual
|
||
// conversion base. A prefix of ``0x'' or ``0X'' selects base 16; the
|
||
// ``0'' prefix selects base 8, and a ``0b'' or ``0B'' prefix selects
|
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// base 2. Otherwise the selected base is 10.
|
||
//
|
||
func (z *Int) SetString(s string, base int) (*Int, bool) {
|
||
if len(s) == 0 || base < 0 || base == 1 || 16 < base {
|
||
return z, false
|
||
}
|
||
|
||
neg := s[0] == '-'
|
||
if neg || s[0] == '+' {
|
||
s = s[1:]
|
||
if len(s) == 0 {
|
||
return z, false
|
||
}
|
||
}
|
||
|
||
var scanned int
|
||
z.abs, _, scanned = z.abs.scan(s, base)
|
||
if scanned != len(s) {
|
||
return z, false
|
||
}
|
||
z.neg = len(z.abs) > 0 && neg // 0 has no sign
|
||
|
||
return z, true
|
||
}
|
||
|
||
|
||
// SetBytes interprets b as the bytes of a big-endian, unsigned integer and
|
||
// sets z to that value.
|
||
func (z *Int) SetBytes(b []byte) *Int {
|
||
const s = _S
|
||
z.abs = z.abs.make((len(b) + s - 1) / s)
|
||
|
||
j := 0
|
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for len(b) >= s {
|
||
var w Word
|
||
|
||
for i := s; i > 0; i-- {
|
||
w <<= 8
|
||
w |= Word(b[len(b)-i])
|
||
}
|
||
|
||
z.abs[j] = w
|
||
j++
|
||
b = b[0 : len(b)-s]
|
||
}
|
||
|
||
if len(b) > 0 {
|
||
var w Word
|
||
|
||
for i := len(b); i > 0; i-- {
|
||
w <<= 8
|
||
w |= Word(b[len(b)-i])
|
||
}
|
||
|
||
z.abs[j] = w
|
||
}
|
||
|
||
z.abs = z.abs.norm()
|
||
z.neg = false
|
||
return z
|
||
}
|
||
|
||
|
||
// Bytes returns the absolute value of x as a big-endian byte array.
|
||
func (z *Int) Bytes() []byte {
|
||
const s = _S
|
||
b := make([]byte, len(z.abs)*s)
|
||
|
||
for i, w := range z.abs {
|
||
wordBytes := b[(len(z.abs)-i-1)*s : (len(z.abs)-i)*s]
|
||
for j := s - 1; j >= 0; j-- {
|
||
wordBytes[j] = byte(w)
|
||
w >>= 8
|
||
}
|
||
}
|
||
|
||
i := 0
|
||
for i < len(b) && b[i] == 0 {
|
||
i++
|
||
}
|
||
|
||
return b[i:]
|
||
}
|
||
|
||
|
||
// BitLen returns the length of the absolute value of z in bits.
|
||
// The bit length of 0 is 0.
|
||
func (z *Int) BitLen() int {
|
||
return z.abs.bitLen()
|
||
}
|
||
|
||
|
||
// Exp sets z = x**y mod m. If m is nil, z = x**y.
|
||
// See Knuth, volume 2, section 4.6.3.
|
||
func (z *Int) Exp(x, y, m *Int) *Int {
|
||
if y.neg || len(y.abs) == 0 {
|
||
neg := x.neg
|
||
z.SetInt64(1)
|
||
z.neg = neg
|
||
return z
|
||
}
|
||
|
||
var mWords nat
|
||
if m != nil {
|
||
mWords = m.abs
|
||
}
|
||
|
||
z.abs = z.abs.expNN(x.abs, y.abs, mWords)
|
||
z.neg = len(z.abs) > 0 && x.neg && y.abs[0]&1 == 1 // 0 has no sign
|
||
return z
|
||
}
|
||
|
||
|
||
// 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 {
|
||
d.SetInt64(0)
|
||
if x != nil {
|
||
x.SetInt64(0)
|
||
}
|
||
if y != nil {
|
||
y.SetInt64(0)
|
||
}
|
||
return
|
||
}
|
||
|
||
A := new(Int).Set(a)
|
||
B := new(Int).Set(b)
|
||
|
||
X := new(Int)
|
||
Y := new(Int).SetInt64(1)
|
||
|
||
lastX := new(Int).SetInt64(1)
|
||
lastY := new(Int)
|
||
|
||
q := new(Int)
|
||
temp := new(Int)
|
||
|
||
for len(B.abs) > 0 {
|
||
r := new(Int)
|
||
q, r = q.QuoRem(A, B, r)
|
||
|
||
A, B = B, r
|
||
|
||
temp.Set(X)
|
||
X.Mul(X, q)
|
||
X.neg = !X.neg
|
||
X.Add(X, lastX)
|
||
lastX.Set(temp)
|
||
|
||
temp.Set(Y)
|
||
Y.Mul(Y, q)
|
||
Y.neg = !Y.neg
|
||
Y.Add(Y, lastY)
|
||
lastY.Set(temp)
|
||
}
|
||
|
||
if x != nil {
|
||
*x = *lastX
|
||
}
|
||
|
||
if y != nil {
|
||
*y = *lastY
|
||
}
|
||
|
||
*d = *A
|
||
}
|
||
|
||
|
||
// 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.
|
||
func ProbablyPrime(z *Int, n int) bool {
|
||
return !z.neg && z.abs.probablyPrime(n)
|
||
}
|
||
|
||
|
||
// Rand sets z to a pseudo-random number in [0, n) and returns z.
|
||
func (z *Int) Rand(rnd *rand.Rand, n *Int) *Int {
|
||
z.neg = false
|
||
if n.neg == true || len(n.abs) == 0 {
|
||
z.abs = nil
|
||
return z
|
||
}
|
||
z.abs = z.abs.random(rnd, n.abs, n.abs.bitLen())
|
||
return z
|
||
}
|
||
|
||
|
||
// ModInverse sets z to the multiplicative inverse of g in the group ℤ/pℤ (where
|
||
// p is a prime) and returns z.
|
||
func (z *Int) ModInverse(g, p *Int) *Int {
|
||
var d Int
|
||
GcdInt(&d, z, nil, g, p)
|
||
// x and y are such that g*x + p*y = d. Since p is prime, d = 1. Taking
|
||
// that modulo p results in g*x = 1, therefore x is the inverse element.
|
||
if z.neg {
|
||
z.Add(z, p)
|
||
}
|
||
return z
|
||
}
|
||
|
||
|
||
// Lsh sets z = x << n and returns z.
|
||
func (z *Int) Lsh(x *Int, n uint) *Int {
|
||
z.abs = z.abs.shl(x.abs, n)
|
||
z.neg = x.neg
|
||
return z
|
||
}
|
||
|
||
|
||
// Rsh sets z = x >> n and returns z.
|
||
func (z *Int) Rsh(x *Int, n uint) *Int {
|
||
if x.neg {
|
||
// (-x) >> s == ^(x-1) >> s == ^((x-1) >> s) == -(((x-1) >> s) + 1)
|
||
t := z.abs.sub(x.abs, natOne) // no underflow because |x| > 0
|
||
t = t.shr(t, n)
|
||
z.abs = t.add(t, natOne)
|
||
z.neg = true // z cannot be zero if x is negative
|
||
return z
|
||
}
|
||
|
||
z.abs = z.abs.shr(x.abs, n)
|
||
z.neg = false
|
||
return z
|
||
}
|
||
|
||
|
||
// And sets z = x & y and returns z.
|
||
func (z *Int) And(x, y *Int) *Int {
|
||
if x.neg == y.neg {
|
||
if x.neg {
|
||
// (-x) & (-y) == ^(x-1) & ^(y-1) == ^((x-1) | (y-1)) == -(((x-1) | (y-1)) + 1)
|
||
x1 := nat{}.sub(x.abs, natOne)
|
||
y1 := nat{}.sub(y.abs, natOne)
|
||
z.abs = z.abs.add(z.abs.or(x1, y1), natOne)
|
||
z.neg = true // z cannot be zero if x and y are negative
|
||
return z
|
||
}
|
||
|
||
// x & y == x & y
|
||
z.abs = z.abs.and(x.abs, y.abs)
|
||
z.neg = false
|
||
return z
|
||
}
|
||
|
||
// x.neg != y.neg
|
||
if x.neg {
|
||
x, y = y, x // & is symmetric
|
||
}
|
||
|
||
// x & (-y) == x & ^(y-1) == x &^ (y-1)
|
||
y1 := nat{}.sub(y.abs, natOne)
|
||
z.abs = z.abs.andNot(x.abs, y1)
|
||
z.neg = false
|
||
return z
|
||
}
|
||
|
||
|
||
// AndNot sets z = x &^ y and returns z.
|
||
func (z *Int) AndNot(x, y *Int) *Int {
|
||
if x.neg == y.neg {
|
||
if x.neg {
|
||
// (-x) &^ (-y) == ^(x-1) &^ ^(y-1) == ^(x-1) & (y-1) == (y-1) &^ (x-1)
|
||
x1 := nat{}.sub(x.abs, natOne)
|
||
y1 := nat{}.sub(y.abs, natOne)
|
||
z.abs = z.abs.andNot(y1, x1)
|
||
z.neg = false
|
||
return z
|
||
}
|
||
|
||
// x &^ y == x &^ y
|
||
z.abs = z.abs.andNot(x.abs, y.abs)
|
||
z.neg = false
|
||
return z
|
||
}
|
||
|
||
if x.neg {
|
||
// (-x) &^ y == ^(x-1) &^ y == ^(x-1) & ^y == ^((x-1) | y) == -(((x-1) | y) + 1)
|
||
x1 := nat{}.sub(x.abs, natOne)
|
||
z.abs = z.abs.add(z.abs.or(x1, y.abs), natOne)
|
||
z.neg = true // z cannot be zero if x is negative and y is positive
|
||
return z
|
||
}
|
||
|
||
// x &^ (-y) == x &^ ^(y-1) == x & (y-1)
|
||
y1 := nat{}.add(y.abs, natOne)
|
||
z.abs = z.abs.and(x.abs, y1)
|
||
z.neg = false
|
||
return z
|
||
}
|
||
|
||
|
||
// Or sets z = x | y and returns z.
|
||
func (z *Int) Or(x, y *Int) *Int {
|
||
if x.neg == y.neg {
|
||
if x.neg {
|
||
// (-x) | (-y) == ^(x-1) | ^(y-1) == ^((x-1) & (y-1)) == -(((x-1) & (y-1)) + 1)
|
||
x1 := nat{}.sub(x.abs, natOne)
|
||
y1 := nat{}.sub(y.abs, natOne)
|
||
z.abs = z.abs.add(z.abs.and(x1, y1), natOne)
|
||
z.neg = true // z cannot be zero if x and y are negative
|
||
return z
|
||
}
|
||
|
||
// x | y == x | y
|
||
z.abs = z.abs.or(x.abs, y.abs)
|
||
z.neg = false
|
||
return z
|
||
}
|
||
|
||
// x.neg != y.neg
|
||
if x.neg {
|
||
x, y = y, x // | is symmetric
|
||
}
|
||
|
||
// x | (-y) == x | ^(y-1) == ^((y-1) &^ x) == -(^((y-1) &^ x) + 1)
|
||
y1 := nat{}.sub(y.abs, natOne)
|
||
z.abs = z.abs.add(z.abs.andNot(y1, x.abs), natOne)
|
||
z.neg = true // z cannot be zero if one of x or y is negative
|
||
return z
|
||
}
|
||
|
||
|
||
// Xor sets z = x ^ y and returns z.
|
||
func (z *Int) Xor(x, y *Int) *Int {
|
||
if x.neg == y.neg {
|
||
if x.neg {
|
||
// (-x) ^ (-y) == ^(x-1) ^ ^(y-1) == (x-1) ^ (y-1)
|
||
x1 := nat{}.sub(x.abs, natOne)
|
||
y1 := nat{}.sub(y.abs, natOne)
|
||
z.abs = z.abs.xor(x1, y1)
|
||
z.neg = false
|
||
return z
|
||
}
|
||
|
||
// x ^ y == x ^ y
|
||
z.abs = z.abs.xor(x.abs, y.abs)
|
||
z.neg = false
|
||
return z
|
||
}
|
||
|
||
// x.neg != y.neg
|
||
if x.neg {
|
||
x, y = y, x // ^ is symmetric
|
||
}
|
||
|
||
// x ^ (-y) == x ^ ^(y-1) == ^(x ^ (y-1)) == -((x ^ (y-1)) + 1)
|
||
y1 := nat{}.sub(y.abs, natOne)
|
||
z.abs = z.abs.add(z.abs.xor(x.abs, y1), natOne)
|
||
z.neg = true // z cannot be zero if only one of x or y is negative
|
||
return z
|
||
}
|
||
|
||
|
||
// Not sets z = ^x and returns z.
|
||
func (z *Int) Not(x *Int) *Int {
|
||
if x.neg {
|
||
// ^(-x) == ^(^(x-1)) == x-1
|
||
z.abs = z.abs.sub(x.abs, natOne)
|
||
z.neg = false
|
||
return z
|
||
}
|
||
|
||
// ^x == -x-1 == -(x+1)
|
||
z.abs = z.abs.add(x.abs, natOne)
|
||
z.neg = true // z cannot be zero if x is positive
|
||
return z
|
||
}
|