Documentation
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Index ¶
- func Jacobi(x, y *Int) int
- type Int
- func (z *Int) Abs(x *Int) *Int
- func (z *Int) Add(x, y *Int) *Int
- func (z *Int) And(x, y *Int) *Int
- func (z *Int) AndNot(x, y *Int) *Int
- func (z *Int) Binomial(n, k int64) *Int
- func (x *Int) Bit(i int) uint
- func (x *Int) BitLen() int
- func (x *Int) Bits() []Word
- func (x *Int) Bytes() []byte
- func (x *Int) Cmp(y *Int) (r int)
- func (x *Int) CmpAbs(y *Int) int
- func (z *Int) Div(x, y *Int) *Int
- func (z *Int) DivMod(x, y, m *Int) (*Int, *Int)
- func (z *Int) Exp(x, y, m *Int) *Int
- func (x *Int) FillBytes(buf []byte) []byte
- func (z *Int) GCD(x, y, a, b *Int) *Int
- func (x *Int) Int64() int64
- func (x *Int) IsInt64() bool
- func (x *Int) IsUint64() bool
- func (z *Int) Lsh(x *Int, n uint) *Int
- func (z *Int) Mod(x, y *Int) *Int
- func (z *Int) ModInverse(g, n *Int) *Int
- func (z *Int) ModSqrt(x, p *Int) *Int
- func (z *Int) Mul(x, y *Int) *Int
- func (z *Int) MulRange(a, b int64) *Int
- func (z *Int) Neg(x *Int) *Int
- func (z *Int) Not(x *Int) *Int
- func (z *Int) Or(x, y *Int) *Int
- func (z *Int) Quo(x, y *Int) *Int
- func (z *Int) QuoRem(x, y, r *Int) (*Int, *Int)
- func (z *Int) Rand(rnd *rand.Rand, n *Int) *Int
- func (z *Int) Rem(x, y *Int) *Int
- func (z *Int) Rsh(x *Int, n uint) *Int
- func (z *Int) Set(x *Int) *Int
- func (z *Int) SetBit(x *Int, i int, b uint) *Int
- func (z *Int) SetBits(abs []Word) *Int
- func (z *Int) SetBytes(buf []byte) *Int
- func (z *Int) SetInt64(x int64) *Int
- func (z *Int) SetString(s string, base int) (*Int, bool)
- func (z *Int) SetUint64(x uint64) *Int
- func (x *Int) Sign() int
- func (z *Int) Sqrt(x *Int) *Int
- func (x *Int) String() string
- func (z *Int) Sub(x, y *Int) *Int
- func (x *Int) TrailingZeroBits() uint
- func (x *Int) Uint64() uint64
- func (z *Int) Xor(x, y *Int) *Int
- type Word
Constants ¶
This section is empty.
Variables ¶
This section is empty.
Functions ¶
Types ¶
type Int ¶
func (*Int) Binomial ¶ added in v0.9.6
Binomial sets z to the binomial coefficient C(n, k) and returns z.
func (*Int) Bit ¶ added in v0.9.6
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 (*Int) BitLen ¶ added in v0.9.6
BitLen returns the length of the absolute value of x in bits. The bit length of 0 is 0.
func (*Int) Bits ¶ added in v0.9.6
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 (*Int) Bytes ¶ added in v0.9.6
Bytes returns the absolute value of x as a big-endian byte slice.
To use a fixed length slice, or a preallocated one, use FillBytes.
func (*Int) CmpAbs ¶
CmpAbs compares the absolute values of x and y and returns:
-1 if |x| < |y| 0 if |x| == |y| +1 if |x| > |y|
func (*Int) Div ¶ added in v0.9.6
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 (*Int) DivMod ¶ added in v0.9.6
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 < |y|
(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 (*Int) Exp ¶
Exp sets z = x**y mod |m| (i.e. the sign of m is ignored), and returns z. If m == nil or m == 0, z = x**y unless y <= 0 then z = 1. If m != 0, y < 0, and x and m are not relatively prime, z is unchanged and nil is returned.
Modular exponentiation of inputs of a particular size is not a cryptographically constant-time operation.
func (*Int) FillBytes ¶ added in v0.9.6
FillBytes sets buf to the absolute value of x, storing it as a zero-extended big-endian byte slice, and returns buf.
If the absolute value of x doesn't fit in buf, FillBytes will panic.
func (*Int) GCD ¶ added in v0.9.6
GCD sets z to the greatest common divisor of a and b and returns z. If x or y are not nil, GCD sets their value such that z = a*x + b*y.
a and b may be positive, zero or negative. (Before Go 1.14 both had to be > 0.) Regardless of the signs of a and b, z is always >= 0.
If a == b == 0, GCD sets z = x = y = 0.
If a == 0 and b != 0, GCD sets z = |b|, x = 0, y = sign(b) * 1.
If a != 0 and b == 0, GCD sets z = |a|, x = sign(a) * 1, y = 0.
func (*Int) Int64 ¶ added in v0.9.6
Int64 returns the int64 representation of x. If x cannot be represented in an int64, the result is undefined.
func (*Int) Mod ¶ added in v0.9.6
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 (*Int) ModInverse ¶ added in v0.9.6
ModInverse sets z to the multiplicative inverse of g in the ring ℤ/nℤ and returns z. If g and n are not relatively prime, g has no multiplicative inverse in the ring ℤ/nℤ. In this case, z is unchanged and the return value is nil. If n == 0, a division-by-zero run-time panic occurs.
func (*Int) ModSqrt ¶ added in v0.9.6
ModSqrt sets z to a square root of x mod p if such a square root exists, and returns z. The modulus p must be an odd prime. If x is not a square mod p, ModSqrt leaves z unchanged and returns nil. This function panics if p is not an odd integer, its behavior is undefined if p is odd but not prime.
func (*Int) MulRange ¶ added in v0.9.6
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 (*Int) Quo ¶ added in v0.9.6
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 (*Int) QuoRem ¶ added in v0.9.6
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 (*Int) Rand ¶ added in v0.9.6
Rand sets z to a pseudo-random number in [0, n) and returns z.
As this uses the math/rand package, it must not be used for security-sensitive work. Use crypto/rand.Int instead.
func (*Int) Rem ¶ added in v0.9.6
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 (*Int) SetBit ¶ added in v0.9.6
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 (*Int) SetBits ¶ added in v0.9.6
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 (*Int) SetBytes ¶ added in v0.9.6
SetBytes interprets buf as the bytes of a big-endian unsigned integer, sets z to that value, and returns z.
func (*Int) SetString ¶ added in v0.9.6
SetString sets z to the value of s, interpreted in the given base, and returns z and a boolean indicating success. The entire string (not just a prefix) must be valid for 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 between 2 and MaxBase. For base 0, the number prefix determines the actual base: A prefix of “0b” or “0B” selects base 2, “0”, “0o” or “0O” selects base 8, and “0x” or “0X” selects base 16. Otherwise, the selected base is 10 and no prefix is accepted.
For bases <= 36, lower and upper case letters are considered the same: The letters 'a' to 'z' and 'A' to 'Z' represent digit values 10 to 35. For bases > 36, the upper case letters 'A' to 'Z' represent the digit values 36 to 61.
For base 0, an underscore character “_” may appear between a base prefix and an adjacent digit, and between successive digits; such underscores do not change the value of the number. Incorrect placement of underscores is reported as an error if there are no other errors. If base != 0, underscores are not recognized and act like any other character that is not a valid digit.
func (*Int) Sqrt ¶ added in v0.9.6
Sqrt sets z to ⌊√x⌋, the largest integer such that z² ≤ x, and returns z. It panics if x is negative.
func (*Int) TrailingZeroBits ¶ added in v0.9.6
TrailingZeroBits returns the number of consecutive least significant zero bits of |x|.
Source Files