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-rw-r--r--src/pkg/math/big/int.go1011
1 files changed, 0 insertions, 1011 deletions
diff --git a/src/pkg/math/big/int.go b/src/pkg/math/big/int.go
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index 269949d61..000000000
--- a/src/pkg/math/big/int.go
+++ /dev/null
@@ -1,1011 +0,0 @@
-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// This file implements signed multi-precision integers.
-
-package big
-
-import (
- "errors"
- "fmt"
- "io"
- "math/rand"
- "strings"
-)
-
-// An Int represents a signed multi-precision integer.
-// The zero value for an Int represents the value 0.
-type Int struct {
- neg bool // sign
- abs nat // absolute value of the integer
-}
-
-var intOne = &Int{false, natOne}
-
-// Sign returns:
-//
-// -1 if x < 0
-// 0 if x == 0
-// +1 if x > 0
-//
-func (x *Int) Sign() int {
- if len(x.abs) == 0 {
- return 0
- }
- if x.neg {
- return -1
- }
- return 1
-}
-
-// SetInt64 sets z to x and returns z.
-func (z *Int) SetInt64(x int64) *Int {
- neg := false
- if x < 0 {
- neg = true
- x = -x
- }
- z.abs = z.abs.setUint64(uint64(x))
- z.neg = neg
- return z
-}
-
-// SetUint64 sets z to x and returns z.
-func (z *Int) SetUint64(x uint64) *Int {
- z.abs = z.abs.setUint64(x)
- z.neg = false
- return z
-}
-
-// NewInt allocates and returns a new Int set to x.
-func NewInt(x int64) *Int {
- return new(Int).SetInt64(x)
-}
-
-// Set sets z to x and returns z.
-func (z *Int) Set(x *Int) *Int {
- if z != x {
- z.abs = z.abs.set(x.abs)
- z.neg = x.neg
- }
- return z
-}
-
-// Bits provides raw (unchecked but fast) access to x by returning its
-// absolute value as a little-endian Word slice. The result and x share
-// the same underlying array.
-// Bits is intended to support implementation of missing low-level Int
-// functionality outside this package; it should be avoided otherwise.
-func (x *Int) Bits() []Word {
- return x.abs
-}
-
-// SetBits provides raw (unchecked but fast) access to z by setting its
-// value to abs, interpreted as a little-endian Word slice, and returning
-// z. The result and abs share the same underlying array.
-// SetBits is intended to support implementation of missing low-level Int
-// functionality outside this package; it should be avoided otherwise.
-func (z *Int) SetBits(abs []Word) *Int {
- z.abs = nat(abs).norm()
- z.neg = false
- return z
-}
-
-// Abs sets z to |x| (the absolute value of x) and returns z.
-func (z *Int) Abs(x *Int) *Int {
- z.Set(x)
- z.neg = false
- return z
-}
-
-// Neg sets z to -x and returns z.
-func (z *Int) Neg(x *Int) *Int {
- z.Set(x)
- z.neg = len(z.abs) > 0 && !z.neg // 0 has no sign
- return z
-}
-
-// Add sets z to the sum x+y and returns z.
-func (z *Int) Add(x, y *Int) *Int {
- neg := x.neg
- if x.neg == y.neg {
- // x + y == x + y
- // (-x) + (-y) == -(x + y)
- z.abs = z.abs.add(x.abs, y.abs)
- } else {
- // x + (-y) == x - y == -(y - x)
- // (-x) + y == y - x == -(x - y)
- if x.abs.cmp(y.abs) >= 0 {
- z.abs = z.abs.sub(x.abs, y.abs)
- } else {
- neg = !neg
- z.abs = z.abs.sub(y.abs, x.abs)
- }
- }
- z.neg = len(z.abs) > 0 && neg // 0 has no sign
- return z
-}
-
-// Sub sets z to the difference x-y and returns z.
-func (z *Int) Sub(x, y *Int) *Int {
- neg := x.neg
- if x.neg != y.neg {
- // x - (-y) == x + y
- // (-x) - y == -(x + y)
- z.abs = z.abs.add(x.abs, y.abs)
- } else {
- // x - y == x - y == -(y - x)
- // (-x) - (-y) == y - x == -(x - y)
- if x.abs.cmp(y.abs) >= 0 {
- z.abs = z.abs.sub(x.abs, y.abs)
- } else {
- neg = !neg
- z.abs = z.abs.sub(y.abs, x.abs)
- }
- }
- z.neg = len(z.abs) > 0 && neg // 0 has no sign
- return z
-}
-
-// Mul sets z to the product x*y and returns z.
-func (z *Int) Mul(x, y *Int) *Int {
- // x * y == x * y
- // x * (-y) == -(x * y)
- // (-x) * y == -(x * y)
- // (-x) * (-y) == x * y
- z.abs = z.abs.mul(x.abs, y.abs)
- z.neg = len(z.abs) > 0 && x.neg != y.neg // 0 has no sign
- return z
-}
-
-// MulRange sets z to the product of all integers
-// in the range [a, b] inclusively and returns z.
-// If a > b (empty range), the result is 1.
-func (z *Int) MulRange(a, b int64) *Int {
- switch {
- case a > b:
- return z.SetInt64(1) // empty range
- case a <= 0 && b >= 0:
- return z.SetInt64(0) // range includes 0
- }
- // a <= b && (b < 0 || a > 0)
-
- neg := false
- if a < 0 {
- neg = (b-a)&1 == 0
- a, b = -b, -a
- }
-
- z.abs = z.abs.mulRange(uint64(a), uint64(b))
- z.neg = neg
- return z
-}
-
-// Binomial sets z to the binomial coefficient of (n, k) and returns z.
-func (z *Int) Binomial(n, k int64) *Int {
- var a, b Int
- a.MulRange(n-k+1, n)
- b.MulRange(1, k)
- return z.Quo(&a, &b)
-}
-
-// Quo sets z to the quotient x/y for y != 0 and returns z.
-// If y == 0, a division-by-zero run-time panic occurs.
-// Quo implements truncated division (like Go); see QuoRem for more details.
-func (z *Int) Quo(x, y *Int) *Int {
- z.abs, _ = z.abs.div(nil, x.abs, y.abs)
- z.neg = len(z.abs) > 0 && x.neg != y.neg // 0 has no sign
- return z
-}
-
-// Rem sets z to the remainder x%y for y != 0 and returns z.
-// If y == 0, a division-by-zero run-time panic occurs.
-// Rem implements truncated modulus (like Go); see QuoRem for more details.
-func (z *Int) Rem(x, y *Int) *Int {
- _, z.abs = nat(nil).div(z.abs, x.abs, y.abs)
- z.neg = len(z.abs) > 0 && x.neg // 0 has no sign
- return z
-}
-
-// QuoRem sets z to the quotient x/y and r to the remainder x%y
-// and returns the pair (z, r) for y != 0.
-// If y == 0, a division-by-zero run-time panic occurs.
-//
-// QuoRem implements T-division and modulus (like Go):
-//
-// q = x/y with the result truncated to zero
-// r = x - y*q
-//
-// (See Daan Leijen, ``Division and Modulus for Computer Scientists''.)
-// See DivMod for Euclidean division and modulus (unlike Go).
-//
-func (z *Int) QuoRem(x, y, r *Int) (*Int, *Int) {
- z.abs, r.abs = z.abs.div(r.abs, x.abs, y.abs)
- z.neg, r.neg = len(z.abs) > 0 && x.neg != y.neg, len(r.abs) > 0 && x.neg // 0 has no sign
- return z, r
-}
-
-// Div sets z to the quotient x/y for y != 0 and returns z.
-// If y == 0, a division-by-zero run-time panic occurs.
-// Div implements Euclidean division (unlike Go); see DivMod for more details.
-func (z *Int) Div(x, y *Int) *Int {
- y_neg := y.neg // z may be an alias for y
- var r Int
- z.QuoRem(x, y, &r)
- if r.neg {
- if y_neg {
- z.Add(z, intOne)
- } else {
- z.Sub(z, intOne)
- }
- }
- return z
-}
-
-// Mod sets z to the modulus x%y for y != 0 and returns z.
-// If y == 0, a division-by-zero run-time panic occurs.
-// Mod implements Euclidean modulus (unlike Go); see DivMod for more details.
-func (z *Int) Mod(x, y *Int) *Int {
- y0 := y // save y
- if z == y || alias(z.abs, y.abs) {
- y0 = new(Int).Set(y)
- }
- var q Int
- q.QuoRem(x, y, z)
- if z.neg {
- if y0.neg {
- z.Sub(z, y0)
- } else {
- z.Add(z, y0)
- }
- }
- return z
-}
-
-// DivMod sets z to the quotient x div y and m to the modulus x mod y
-// and returns the pair (z, m) for y != 0.
-// If y == 0, a division-by-zero run-time panic occurs.
-//
-// DivMod implements Euclidean division and modulus (unlike Go):
-//
-// q = x div y such that
-// m = x - y*q with 0 <= m < |q|
-//
-// (See Raymond T. Boute, ``The Euclidean definition of the functions
-// div and mod''. ACM Transactions on Programming Languages and
-// Systems (TOPLAS), 14(2):127-144, New York, NY, USA, 4/1992.
-// ACM press.)
-// See QuoRem for T-division and modulus (like Go).
-//
-func (z *Int) DivMod(x, y, m *Int) (*Int, *Int) {
- y0 := y // save y
- if z == y || alias(z.abs, y.abs) {
- y0 = new(Int).Set(y)
- }
- z.QuoRem(x, y, m)
- if m.neg {
- if y0.neg {
- z.Add(z, intOne)
- m.Sub(m, y0)
- } else {
- z.Sub(z, intOne)
- m.Add(m, y0)
- }
- }
- return z, m
-}
-
-// Cmp compares x and y and returns:
-//
-// -1 if x < y
-// 0 if x == y
-// +1 if x > y
-//
-func (x *Int) Cmp(y *Int) (r int) {
- // x cmp y == x cmp y
- // x cmp (-y) == x
- // (-x) cmp y == y
- // (-x) cmp (-y) == -(x cmp y)
- switch {
- case x.neg == y.neg:
- r = x.abs.cmp(y.abs)
- if x.neg {
- r = -r
- }
- case x.neg:
- r = -1
- default:
- r = 1
- }
- return
-}
-
-func (x *Int) String() string {
- switch {
- case x == nil:
- return "<nil>"
- case x.neg:
- return "-" + x.abs.decimalString()
- }
- return x.abs.decimalString()
-}
-
-func charset(ch rune) string {
- switch ch {
- case 'b':
- return lowercaseDigits[0:2]
- case 'o':
- return lowercaseDigits[0:8]
- case 'd', 's', 'v':
- return lowercaseDigits[0:10]
- case 'x':
- return lowercaseDigits[0:16]
- case 'X':
- return uppercaseDigits[0:16]
- }
- return "" // unknown format
-}
-
-// write count copies of text to s
-func writeMultiple(s fmt.State, text string, count int) {
- if len(text) > 0 {
- b := []byte(text)
- for ; count > 0; count-- {
- s.Write(b)
- }
- }
-}
-
-// Format is a support routine for fmt.Formatter. It accepts
-// the formats 'b' (binary), 'o' (octal), 'd' (decimal), 'x'
-// (lowercase hexadecimal), and 'X' (uppercase hexadecimal).
-// Also supported are the full suite of package fmt's format
-// verbs for integral types, including '+', '-', and ' '
-// for sign control, '#' for leading zero in octal and for
-// hexadecimal, a leading "0x" or "0X" for "%#x" and "%#X"
-// respectively, specification of minimum digits precision,
-// output field width, space or zero padding, and left or
-// right justification.
-//
-func (x *Int) Format(s fmt.State, ch rune) {
- cs := charset(ch)
-
- // special cases
- switch {
- case cs == "":
- // unknown format
- fmt.Fprintf(s, "%%!%c(big.Int=%s)", ch, x.String())
- return
- case x == nil:
- fmt.Fprint(s, "<nil>")
- return
- }
-
- // determine sign character
- sign := ""
- switch {
- case x.neg:
- sign = "-"
- case s.Flag('+'): // supersedes ' ' when both specified
- sign = "+"
- case s.Flag(' '):
- sign = " "
- }
-
- // determine prefix characters for indicating output base
- prefix := ""
- if s.Flag('#') {
- switch ch {
- case 'o': // octal
- prefix = "0"
- case 'x': // hexadecimal
- prefix = "0x"
- case 'X':
- prefix = "0X"
- }
- }
-
- // determine digits with base set by len(cs) and digit characters from cs
- digits := x.abs.string(cs)
-
- // number of characters for the three classes of number padding
- var left int // space characters to left of digits for right justification ("%8d")
- var zeroes int // zero characters (actually cs[0]) as left-most digits ("%.8d")
- var right int // space characters to right of digits for left justification ("%-8d")
-
- // determine number padding from precision: the least number of digits to output
- precision, precisionSet := s.Precision()
- if precisionSet {
- switch {
- case len(digits) < precision:
- zeroes = precision - len(digits) // count of zero padding
- case digits == "0" && precision == 0:
- return // print nothing if zero value (x == 0) and zero precision ("." or ".0")
- }
- }
-
- // determine field pad from width: the least number of characters to output
- length := len(sign) + len(prefix) + zeroes + len(digits)
- if width, widthSet := s.Width(); widthSet && length < width { // pad as specified
- switch d := width - length; {
- case s.Flag('-'):
- // pad on the right with spaces; supersedes '0' when both specified
- right = d
- case s.Flag('0') && !precisionSet:
- // pad with zeroes unless precision also specified
- zeroes = d
- default:
- // pad on the left with spaces
- left = d
- }
- }
-
- // print number as [left pad][sign][prefix][zero pad][digits][right pad]
- writeMultiple(s, " ", left)
- writeMultiple(s, sign, 1)
- writeMultiple(s, prefix, 1)
- writeMultiple(s, "0", zeroes)
- writeMultiple(s, digits, 1)
- writeMultiple(s, " ", right)
-}
-
-// scan sets z to the integer value corresponding to the longest possible prefix
-// read from r representing a signed integer number in a given conversion base.
-// It returns z, the actual conversion base used, and an error, if any. In the
-// error case, the value of z is undefined but the returned value is nil. The
-// syntax follows the syntax of integer literals in Go.
-//
-// The base argument must be 0 or a value from 2 through MaxBase. If the base
-// 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 base 2. Otherwise the selected base is 10.
-//
-func (z *Int) scan(r io.RuneScanner, base int) (*Int, int, error) {
- // determine sign
- ch, _, err := r.ReadRune()
- if err != nil {
- return nil, 0, err
- }
- neg := false
- switch ch {
- case '-':
- neg = true
- case '+': // nothing to do
- default:
- r.UnreadRune()
- }
-
- // determine mantissa
- z.abs, base, err = z.abs.scan(r, base)
- if err != nil {
- return nil, base, err
- }
- z.neg = len(z.abs) > 0 && neg // 0 has no sign
-
- return z, base, nil
-}
-
-// Scan is a support routine for fmt.Scanner; it sets z to the value of
-// the scanned number. It accepts the formats 'b' (binary), 'o' (octal),
-// 'd' (decimal), 'x' (lowercase hexadecimal), and 'X' (uppercase hexadecimal).
-func (z *Int) Scan(s fmt.ScanState, ch rune) error {
- s.SkipSpace() // skip leading space characters
- base := 0
- switch ch {
- case 'b':
- base = 2
- case 'o':
- base = 8
- case 'd':
- base = 10
- case 'x', 'X':
- base = 16
- case 's', 'v':
- // let scan determine the base
- default:
- return errors.New("Int.Scan: invalid verb")
- }
- _, _, err := z.scan(s, base)
- return err
-}
-
-// Int64 returns the int64 representation of x.
-// If x cannot be represented in an int64, the result is undefined.
-func (x *Int) Int64() int64 {
- v := int64(x.Uint64())
- if x.neg {
- v = -v
- }
- return v
-}
-
-// Uint64 returns the uint64 representation of x.
-// If x cannot be represented in a uint64, the result is undefined.
-func (x *Int) Uint64() uint64 {
- if len(x.abs) == 0 {
- return 0
- }
- v := uint64(x.abs[0])
- if _W == 32 && len(x.abs) > 1 {
- v |= uint64(x.abs[1]) << 32
- }
- 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 but the returned value is nil.
-//
-// The base argument must be 0 or a value from 2 through MaxBase. If the base
-// 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 base 2. Otherwise the selected base is 10.
-//
-func (z *Int) SetString(s string, base int) (*Int, bool) {
- r := strings.NewReader(s)
- _, _, err := z.scan(r, base)
- if err != nil {
- return nil, false
- }
- _, _, err = r.ReadRune()
- if err != io.EOF {
- return nil, false
- }
- return z, true // err == io.EOF => scan consumed all of s
-}
-
-// SetBytes interprets buf as the bytes of a big-endian unsigned
-// integer, sets z to that value, and returns z.
-func (z *Int) SetBytes(buf []byte) *Int {
- z.abs = z.abs.setBytes(buf)
- z.neg = false
- return z
-}
-
-// Bytes returns the absolute value of x as a big-endian byte slice.
-func (x *Int) Bytes() []byte {
- buf := make([]byte, len(x.abs)*_S)
- return buf[x.abs.bytes(buf):]
-}
-
-// BitLen returns the length of the absolute value of x in bits.
-// The bit length of 0 is 0.
-func (x *Int) BitLen() int {
- return x.abs.bitLen()
-}
-
-// Exp sets z = x**y mod |m| (i.e. the sign of m is ignored), and returns z.
-// If y <= 0, the result is 1 mod |m|; if m == nil or m == 0, z = x**y.
-// See Knuth, volume 2, section 4.6.3.
-func (z *Int) Exp(x, y, m *Int) *Int {
- var yWords nat
- if !y.neg {
- yWords = y.abs
- }
- // y >= 0
-
- var mWords nat
- if m != nil {
- mWords = m.abs // m.abs may be nil for m == 0
- }
-
- z.abs = z.abs.expNN(x.abs, yWords, mWords)
- z.neg = len(z.abs) > 0 && x.neg && len(yWords) > 0 && yWords[0]&1 == 1 // 0 has no sign
- return z
-}
-
-// GCD sets z to the greatest common divisor of a and b, which both must
-// be > 0, and returns z.
-// If x and y are not nil, GCD sets x and y such that z = a*x + b*y.
-// If either a or b is <= 0, GCD sets z = x = y = 0.
-func (z *Int) GCD(x, y, a, b *Int) *Int {
- if a.Sign() <= 0 || b.Sign() <= 0 {
- z.SetInt64(0)
- if x != nil {
- x.SetInt64(0)
- }
- if y != nil {
- y.SetInt64(0)
- }
- return z
- }
- if x == nil && y == nil {
- return z.binaryGCD(a, b)
- }
-
- 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
- }
-
- *z = *A
- return z
-}
-
-// binaryGCD sets z to the greatest common divisor of a and b, which both must
-// be > 0, and returns z.
-// See Knuth, The Art of Computer Programming, Vol. 2, Section 4.5.2, Algorithm B.
-func (z *Int) binaryGCD(a, b *Int) *Int {
- u := z
- v := new(Int)
-
- // use one Euclidean iteration to ensure that u and v are approx. the same size
- switch {
- case len(a.abs) > len(b.abs):
- u.Set(b)
- v.Rem(a, b)
- case len(a.abs) < len(b.abs):
- u.Set(a)
- v.Rem(b, a)
- default:
- u.Set(a)
- v.Set(b)
- }
-
- // v might be 0 now
- if len(v.abs) == 0 {
- return u
- }
- // u > 0 && v > 0
-
- // determine largest k such that u = u' << k, v = v' << k
- k := u.abs.trailingZeroBits()
- if vk := v.abs.trailingZeroBits(); vk < k {
- k = vk
- }
- u.Rsh(u, k)
- v.Rsh(v, k)
-
- // determine t (we know that u > 0)
- t := new(Int)
- if u.abs[0]&1 != 0 {
- // u is odd
- t.Neg(v)
- } else {
- t.Set(u)
- }
-
- for len(t.abs) > 0 {
- // reduce t
- t.Rsh(t, t.abs.trailingZeroBits())
- if t.neg {
- v, t = t, v
- v.neg = len(v.abs) > 0 && !v.neg // 0 has no sign
- } else {
- u, t = t, u
- }
- t.Sub(u, v)
- }
-
- return z.Lsh(u, k)
-}
-
-// ProbablyPrime performs n Miller-Rabin tests to check whether x is prime.
-// If it returns true, x is prime with probability 1 - 1/4^n.
-// If it returns false, x is not prime.
-func (x *Int) ProbablyPrime(n int) bool {
- return !x.neg && x.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
- d.GCD(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
-}
-
-// Bit returns the value of the i'th bit of x. That is, it
-// returns (x>>i)&1. The bit index i must be >= 0.
-func (x *Int) Bit(i int) uint {
- if i == 0 {
- // optimization for common case: odd/even test of x
- if len(x.abs) > 0 {
- return uint(x.abs[0] & 1) // bit 0 is same for -x
- }
- return 0
- }
- if i < 0 {
- panic("negative bit index")
- }
- if x.neg {
- t := nat(nil).sub(x.abs, natOne)
- return t.bit(uint(i)) ^ 1
- }
-
- return x.abs.bit(uint(i))
-}
-
-// SetBit sets z to x, with x's i'th bit set to b (0 or 1).
-// That is, if b is 1 SetBit sets z = x | (1 << i);
-// if b is 0 SetBit sets z = x &^ (1 << i). If b is not 0 or 1,
-// SetBit will panic.
-func (z *Int) SetBit(x *Int, i int, b uint) *Int {
- if i < 0 {
- panic("negative bit index")
- }
- if x.neg {
- t := z.abs.sub(x.abs, natOne)
- t = t.setBit(t, uint(i), b^1)
- z.abs = t.add(t, natOne)
- z.neg = len(z.abs) > 0
- return z
- }
- z.abs = z.abs.setBit(x.abs, uint(i), b)
- 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(nil).sub(x.abs, natOne)
- y1 := nat(nil).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(nil).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(nil).sub(x.abs, natOne)
- y1 := nat(nil).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(nil).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(nil).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(nil).sub(x.abs, natOne)
- y1 := nat(nil).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(nil).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(nil).sub(x.abs, natOne)
- y1 := nat(nil).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(nil).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
-}
-
-// Gob codec version. Permits backward-compatible changes to the encoding.
-const intGobVersion byte = 1
-
-// GobEncode implements the gob.GobEncoder interface.
-func (x *Int) GobEncode() ([]byte, error) {
- if x == nil {
- return nil, nil
- }
- buf := make([]byte, 1+len(x.abs)*_S) // extra byte for version and sign bit
- i := x.abs.bytes(buf) - 1 // i >= 0
- b := intGobVersion << 1 // make space for sign bit
- if x.neg {
- b |= 1
- }
- buf[i] = b
- return buf[i:], nil
-}
-
-// GobDecode implements the gob.GobDecoder interface.
-func (z *Int) GobDecode(buf []byte) error {
- if len(buf) == 0 {
- // Other side sent a nil or default value.
- *z = Int{}
- return nil
- }
- b := buf[0]
- if b>>1 != intGobVersion {
- return errors.New(fmt.Sprintf("Int.GobDecode: encoding version %d not supported", b>>1))
- }
- z.neg = b&1 != 0
- z.abs = z.abs.setBytes(buf[1:])
- return nil
-}
-
-// MarshalJSON implements the json.Marshaler interface.
-func (z *Int) MarshalJSON() ([]byte, error) {
- // TODO(gri): get rid of the []byte/string conversions
- return []byte(z.String()), nil
-}
-
-// UnmarshalJSON implements the json.Unmarshaler interface.
-func (z *Int) UnmarshalJSON(text []byte) error {
- // TODO(gri): get rid of the []byte/string conversions
- if _, ok := z.SetString(string(text), 0); !ok {
- return fmt.Errorf("math/big: cannot unmarshal %q into a *big.Int", text)
- }
- return nil
-}
-
-// MarshalText implements the encoding.TextMarshaler interface
-func (z *Int) MarshalText() (text []byte, err error) {
- return []byte(z.String()), nil
-}
-
-// UnmarshalText implements the encoding.TextUnmarshaler interface
-func (z *Int) UnmarshalText(text []byte) error {
- if _, ok := z.SetString(string(text), 0); !ok {
- return fmt.Errorf("math/big: cannot unmarshal %q into a *big.Int", text)
- }
- return nil
-}
generated by cgit v1.2.3 (git 2.39.1) at 2025-04-29 07:09:01 +0000