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 // 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 "" 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, "") 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 â„¤/pâ„¤ (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 }