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-rw-r--r--src/pkg/math/big/int.go873
1 files changed, 873 insertions, 0 deletions
diff --git a/src/pkg/math/big/int.go b/src/pkg/math/big/int.go
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+++ b/src/pkg/math/big/int.go
@@ -0,0 +1,873 @@
+// 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
+}
+
+// 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
+}
+
+// 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''.)
+//
+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.)
+//
+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 {
+ if len(x.abs) == 0 {
+ 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 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 z as a big-endian byte slice.
+func (z *Int) Bytes() []byte {
+ buf := make([]byte, len(z.abs)*_S)
+ return buf[z.abs.bytes(buf):]
+}
+
+// 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
+}
+
+// Bit returns the value of the i'th bit of z. That is, it
+// returns (z>>i)&1. The bit index i must be >= 0.
+func (z *Int) Bit(i int) uint {
+ if i < 0 {
+ panic("negative bit index")
+ }
+ if z.neg {
+ t := nat(nil).sub(z.abs, natOne)
+ return t.bit(uint(i)) ^ 1
+ }
+
+ return z.abs.bit(uint(i))
+}
+
+// SetBit sets z to x, with x's i'th bit set to b (0 or 1).
+// That is, if bit is 1 SetBit sets z = x | (1 << i);
+// if bit is 0 it sets z = x &^ (1 << i). If bit 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 (z *Int) GobEncode() ([]byte, error) {
+ buf := make([]byte, 1+len(z.abs)*_S) // extra byte for version and sign bit
+ i := z.abs.bytes(buf) - 1 // i >= 0
+ b := intGobVersion << 1 // make space for sign bit
+ if z.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 {
+ return errors.New("Int.GobDecode: no data")
+ }
+ 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
+}
generated by cgit v1.2.3 (git 2.46.0) at 2025-10-30 14:41:10 +0000