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Diffstat (limited to 'libgo/go/big/int.go')
| -rw-r--r-- | libgo/go/big/int.go | 741 |
1 files changed, 741 insertions, 0 deletions
diff --git a/libgo/go/big/int.go b/libgo/go/big/int.go new file mode 100644 index 000000000..46e008734 --- /dev/null +++ b/libgo/go/big/int.go @@ -0,0 +1,741 @@ +// 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 ( + "fmt" + "rand" +) + +// 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 { + 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.abs = z.abs.set(x.abs) + z.neg = false + return z +} + + +// Neg sets z to -x and returns z. +func (z *Int) Neg(x *Int) *Int { + z.abs = z.abs.set(x.abs) + z.neg = len(z.abs) > 0 && !x.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. +// 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. +// 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. +// 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. +// 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 { + s := "" + if x.neg { + s = "-" + } + return s + x.abs.string(10) +} + + +func fmtbase(ch int) int { + switch ch { + case 'b': + return 2 + case 'o': + return 8 + case 'd': + return 10 + case 'x': + return 16 + } + return 10 +} + + +// Format is a support routine for fmt.Formatter. It accepts +// the formats 'b' (binary), 'o' (octal), 'd' (decimal) and +// 'x' (hexadecimal). +// +func (x *Int) Format(s fmt.State, ch int) { + if x.neg { + fmt.Fprint(s, "-") + } + fmt.Fprint(s, x.abs.string(fmtbase(ch))) +} + + +// 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 { + 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 +// 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 + 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 +} |