const MaxBase = 'z' - 'a' + 10 + 1 // = hexValue('z') + 1
MaxBase is the largest number base accepted for string conversions.
type Int struct {
// contains filtered or unexported fields
}
An Int represents a signed multi-precision integer. The zero value for an Int represents the value 0.
func NewInt(x int64) *Int
NewInt allocates and returns a new Int set to x.
func (z *Int) Abs(x *Int) *Int
Abs sets z to |x| (the absolute value of x) and returns z.
func (z *Int) Add(x, y *Int) *Int
Add sets z to the sum x+y and returns z.
func (z *Int) And(x, y *Int) *Int
And sets z = x & y and returns z.
func (z *Int) AndNot(x, y *Int) *Int
AndNot sets z = x &^ y and returns z.
func (z *Int) Binomial(n, k int64) *Int
Binomial sets z to the binomial coefficient of (n, k) and returns z.
func (x *Int) Bit(i int) uint
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) BitLen() int
BitLen returns the length of the absolute value of x in bits. The bit length of 0 is 0.
func (x *Int) Bits() []Word
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) Bytes() []byte
Bytes returns the absolute value of x as a big-endian byte slice.
func (x *Int) Cmp(y *Int) (r int)
Cmp compares x and y and returns:
-1 if x < y 0 if x == y +1 if x > y
func (z *Int) Div(x, y *Int) *Int
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) DivMod(x, y, m *Int) (*Int, *Int)
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) Exp(x, y, m *Int) *Int
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 (x *Int) Format(s fmt.State, ch rune)
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 (z *Int) GCD(x, y, a, b *Int) *Int
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) GobDecode(buf []byte) error
GobDecode implements the gob.GobDecoder interface.
func (x *Int) GobEncode() ([]byte, error)
GobEncode implements the gob.GobEncoder interface.
func (x *Int) Int64() int64
Int64 returns the int64 representation of x. If x cannot be represented in an int64, the result is undefined.
func (z *Int) Lsh(x *Int, n uint) *Int
Lsh sets z = x << n and returns z.
func (z *Int) MarshalJSON() ([]byte, error)
MarshalJSON implements the json.Marshaler interface.
func (z *Int) MarshalText() (text []byte, err error)
MarshalText implements the encoding.TextMarshaler interface.
func (z *Int) Mod(x, y *Int) *Int
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) ModInverse(g, n *Int) *Int
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, the result is undefined.
func (z *Int) Mul(x, y *Int) *Int
Mul sets z to the product x*y and returns z.
func (z *Int) MulRange(a, b int64) *Int
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) Neg(x *Int) *Int
Neg sets z to -x and returns z.
func (z *Int) Not(x *Int) *Int
Not sets z = ^x and returns z.
func (z *Int) Or(x, y *Int) *Int
Or sets z = x | y and returns z.
func (x *Int) ProbablyPrime(n int) bool
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 (z *Int) Quo(x, y *Int) *Int
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) QuoRem(x, y, r *Int) (*Int, *Int)
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) Rand(rnd *rand.Rand, n *Int) *Int
Rand sets z to a pseudo-random number in [0, n) and returns z.
func (z *Int) Rem(x, y *Int) *Int
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) Rsh(x *Int, n uint) *Int
Rsh sets z = x >> n and returns z.
func (z *Int) Scan(s fmt.ScanState, ch rune) error
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).
▹ Example
func (z *Int) Set(x *Int) *Int
Set sets z to x and returns z.
func (z *Int) SetBit(x *Int, i int, b uint) *Int
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) SetBits(abs []Word) *Int
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) SetBytes(buf []byte) *Int
SetBytes interprets buf as the bytes of a big-endian unsigned integer, sets z to that value, and returns z.
func (z *Int) SetInt64(x int64) *Int
SetInt64 sets z to x and returns z.
func (z *Int) SetString(s string, base int) (*Int, bool)
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.
▹ Example
func (z *Int) SetUint64(x uint64) *Int
SetUint64 sets z to x and returns z.
func (x *Int) Sign() int
Sign returns:
-1 if x < 0 0 if x == 0 +1 if x > 0
func (x *Int) String() string
func (z *Int) Sub(x, y *Int) *Int
Sub sets z to the difference x-y and returns z.
func (x *Int) Uint64() uint64
Uint64 returns the uint64 representation of x. If x cannot be represented in a uint64, the result is undefined.
func (z *Int) UnmarshalJSON(text []byte) error
UnmarshalJSON implements the json.Unmarshaler interface.
func (z *Int) UnmarshalText(text []byte) error
UnmarshalText implements the encoding.TextUnmarshaler interface.
func (z *Int) Xor(x, y *Int) *Int
Xor sets z = x ^ y and returns z.
type Rat struct {
// contains filtered or unexported fields
}
A Rat represents a quotient a/b of arbitrary precision. The zero value for a Rat represents the value 0.
func NewRat(a, b int64) *Rat
NewRat creates a new Rat with numerator a and denominator b.
func (z *Rat) Abs(x *Rat) *Rat
Abs sets z to |x| (the absolute value of x) and returns z.
func (z *Rat) Add(x, y *Rat) *Rat
Add sets z to the sum x+y and returns z.
func (x *Rat) Cmp(y *Rat) int
Cmp compares x and y and returns:
-1 if x < y 0 if x == y +1 if x > y
func (x *Rat) Denom() *Int
Denom returns the denominator of x; it is always > 0. The result is a reference to x's denominator; it may change if a new value is assigned to x, and vice versa.
func (x *Rat) Float32() (f float32, exact bool)
Float32 returns the nearest float32 value for x and a bool indicating whether f represents x exactly. If the magnitude of x is too large to be represented by a float32, f is an infinity and exact is false. The sign of f always matches the sign of x, even if f == 0.
func (x *Rat) Float64() (f float64, exact bool)
Float64 returns the nearest float64 value for x and a bool indicating whether f represents x exactly. If the magnitude of x is too large to be represented by a float64, f is an infinity and exact is false. The sign of f always matches the sign of x, even if f == 0.
func (x *Rat) FloatString(prec int) string
FloatString returns a string representation of x in decimal form with prec digits of precision after the decimal point and the last digit rounded.
func (z *Rat) GobDecode(buf []byte) error
GobDecode implements the gob.GobDecoder interface.
func (x *Rat) GobEncode() ([]byte, error)
GobEncode implements the gob.GobEncoder interface.
func (z *Rat) Inv(x *Rat) *Rat
Inv sets z to 1/x and returns z.
func (x *Rat) IsInt() bool
IsInt returns true if the denominator of x is 1.
func (r *Rat) MarshalText() (text []byte, err error)
MarshalText implements the encoding.TextMarshaler interface.
func (z *Rat) Mul(x, y *Rat) *Rat
Mul sets z to the product x*y and returns z.
func (z *Rat) Neg(x *Rat) *Rat
Neg sets z to -x and returns z.
func (x *Rat) Num() *Int
Num returns the numerator of x; it may be <= 0. The result is a reference to x's numerator; it may change if a new value is assigned to x, and vice versa. The sign of the numerator corresponds to the sign of x.
func (z *Rat) Quo(x, y *Rat) *Rat
Quo sets z to the quotient x/y and returns z. If y == 0, a division-by-zero run-time panic occurs.
func (x *Rat) RatString() string
RatString returns a string representation of x in the form "a/b" if b != 1, and in the form "a" if b == 1.
func (z *Rat) Scan(s fmt.ScanState, ch rune) error
Scan is a support routine for fmt.Scanner. It accepts the formats 'e', 'E', 'f', 'F', 'g', 'G', and 'v'. All formats are equivalent.
▹ Example
func (z *Rat) Set(x *Rat) *Rat
Set sets z to x (by making a copy of x) and returns z.
func (z *Rat) SetFloat64(f float64) *Rat
SetFloat64 sets z to exactly f and returns z. If f is not finite, SetFloat returns nil.
func (z *Rat) SetFrac(a, b *Int) *Rat
SetFrac sets z to a/b and returns z.
func (z *Rat) SetFrac64(a, b int64) *Rat
SetFrac64 sets z to a/b and returns z.
func (z *Rat) SetInt(x *Int) *Rat
SetInt sets z to x (by making a copy of x) and returns z.
func (z *Rat) SetInt64(x int64) *Rat
SetInt64 sets z to x and returns z.
func (z *Rat) SetString(s string) (*Rat, bool)
SetString sets z to the value of s and returns z and a boolean indicating success. s can be given as a fraction "a/b" or as a floating-point number optionally followed by an exponent. If the operation failed, the value of z is undefined but the returned value is nil.
▹ Example
func (x *Rat) Sign() int
Sign returns:
-1 if x < 0 0 if x == 0 +1 if x > 0
func (x *Rat) String() string
String returns a string representation of x in the form "a/b" (even if b == 1).
func (z *Rat) Sub(x, y *Rat) *Rat
Sub sets z to the difference x-y and returns z.
func (r *Rat) UnmarshalText(text []byte) error
UnmarshalText implements the encoding.TextUnmarshaler interface.
type Word uintptr
A Word represents a single digit of a multi-precision unsigned integer.