Package big
Overview ?
Overview ?
Package big implements multi-precision arithmetic (big numbers). The following numeric types are supported:
- Int signed integers - Rat rational numbers
Methods are typically of the form:
func (z *Int) Op(x, y *Int) *Int (similar for *Rat)
and implement operations z = x Op y with the result as receiver; if it is one of the operands it may be overwritten (and its memory reused). To enable chaining of operations, the result is also returned. Methods returning a result other than *Int or *Rat take one of the operands as the receiver.
Index
- Constants
- type Int
- func NewInt(x int64) *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 (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) Format(s fmt.State, ch rune)
- func (z *Int) GCD(x, y, a, b *Int) *Int
- func (z *Int) GobDecode(buf []byte) error
- func (x *Int) GobEncode() ([]byte, error)
- func (x *Int) Int64() int64
- func (z *Int) Lsh(x *Int, n uint) *Int
- func (z *Int) Mod(x, y *Int) *Int
- func (z *Int) ModInverse(g, 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 (x *Int) ProbablyPrime(n int) bool
- 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) Scan(s fmt.ScanState, ch rune) error
- 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 (x *Int) Sign() int
- func (x *Int) String() string
- func (z *Int) Sub(x, y *Int) *Int
- func (z *Int) Xor(x, y *Int) *Int
- type Rat
- func NewRat(a, b int64) *Rat
- func (z *Rat) Abs(x *Rat) *Rat
- func (z *Rat) Add(x, y *Rat) *Rat
- func (x *Rat) Cmp(y *Rat) int
- func (x *Rat) Denom() *Int
- func (x *Rat) FloatString(prec int) string
- func (z *Rat) GobDecode(buf []byte) error
- func (x *Rat) GobEncode() ([]byte, error)
- func (z *Rat) Inv(x *Rat) *Rat
- func (x *Rat) IsInt() bool
- func (z *Rat) Mul(x, y *Rat) *Rat
- func (z *Rat) Neg(x *Rat) *Rat
- func (x *Rat) Num() *Int
- func (z *Rat) Quo(x, y *Rat) *Rat
- func (x *Rat) RatString() string
- func (z *Rat) Scan(s fmt.ScanState, ch rune) error
- func (z *Rat) Set(x *Rat) *Rat
- func (z *Rat) SetFrac(a, b *Int) *Rat
- func (z *Rat) SetFrac64(a, b int64) *Rat
- func (z *Rat) SetInt(x *Int) *Rat
- func (z *Rat) SetInt64(x int64) *Rat
- func (z *Rat) SetString(s string) (*Rat, bool)
- func (x *Rat) Sign() int
- func (x *Rat) String() string
- func (z *Rat) Sub(x, y *Rat) *Rat
- type Word
Examples
Package files
arith.go arith_decl.go int.go nat.go rat.go
Constants
const MaxBase = 'z' - 'a' + 10 + 1 // = hexValue('z') + 1
MaxBase is the largest number base accepted for string conversions.
type Int
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
func NewInt(x int64) *Int
NewInt allocates and returns a new Int set to x.
func (*Int) Abs
func (z *Int) Abs(x *Int) *Int
Abs sets z to |x| (the absolute value of x) and returns z.
func (*Int) Add
func (z *Int) Add(x, y *Int) *Int
Add sets z to the sum x+y and returns z.
func (*Int) And
func (z *Int) And(x, y *Int) *Int
And sets z = x & y and returns z.
func (*Int) AndNot
func (z *Int) AndNot(x, y *Int) *Int
AndNot sets z = x &^ y and returns z.
func (*Int) Binomial
func (z *Int) Binomial(n, k int64) *Int
Binomial sets z to the binomial coefficient of (n, k) and returns z.
func (*Int) Bit
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 (*Int) BitLen
func (x *Int) BitLen() int
BitLen returns the length of the absolute value of z in bits. The bit length of 0 is 0.
func (*Int) Bits
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 (*Int) Bytes
func (x *Int) Bytes() []byte
Bytes returns the absolute value of z as a big-endian byte slice.
func (*Int) Cmp
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 (*Int) Div
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 (*Int) DivMod
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 (*Int) Exp
func (z *Int) Exp(x, y, m *Int) *Int
Exp sets z = x**y mod m and returns z. If m is nil, z = x**y. See Knuth, volume 2, section 4.6.3.
func (*Int) Format
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 (*Int) GCD
func (z *Int) GCD(x, y, a, b *Int) *Int
GCD sets z to the greatest common divisor of a and b, which must be positive numbers, 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 not positive, GCD sets z = x = y = 0.
func (*Int) GobDecode
func (z *Int) GobDecode(buf []byte) error
GobDecode implements the gob.GobDecoder interface.
func (*Int) GobEncode
func (x *Int) GobEncode() ([]byte, error)
GobEncode implements the gob.GobEncoder interface.
func (*Int) Int64
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 (*Int) Lsh
func (z *Int) Lsh(x *Int, n uint) *Int
Lsh sets z = x << n and returns z.
func (*Int) Mod
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 (*Int) ModInverse
func (z *Int) ModInverse(g, p *Int) *Int
ModInverse sets z to the multiplicative inverse of g in the group ?/p? (where p is a prime) and returns z.
func (*Int) Mul
func (z *Int) Mul(x, y *Int) *Int
Mul sets z to the product x*y and returns z.
func (*Int) MulRange
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 (*Int) Neg
func (z *Int) Neg(x *Int) *Int
Neg sets z to -x and returns z.
func (*Int) Not
func (z *Int) Not(x *Int) *Int
Not sets z = ^x and returns z.
func (*Int) Or
func (z *Int) Or(x, y *Int) *Int
Or sets z = x | y and returns z.
func (*Int) ProbablyPrime
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 (*Int) Quo
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 (*Int) QuoRem
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 (*Int) Rand
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 (*Int) Rem
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 (*Int) Rsh
func (z *Int) Rsh(x *Int, n uint) *Int
Rsh sets z = x >> n and returns z.
func (*Int) Scan
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
? Example
Code:
// The Scan function is rarely used directly; // the fmt package recognizes it as an implementation of fmt.Scanner. i := new(big.Int) _, err := fmt.Sscan("18446744073709551617", i) if err != nil { log.Println("error scanning value:", err) } else { fmt.Println(i) }
Output:
18446744073709551617
func (*Int) Set
func (z *Int) Set(x *Int) *Int
Set sets z to x and returns z.
func (*Int) SetBit
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 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 (*Int) SetBits
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 (*Int) SetBytes
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 (*Int) SetInt64
func (z *Int) SetInt64(x int64) *Int
SetInt64 sets z to x and returns z.
func (*Int) SetString
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
? Example
Code:
i := new(big.Int)
i.SetString("644", 8) // octal
fmt.Println(i)
Output:
420
func (*Int) Sign
func (x *Int) Sign() int
Sign returns:
-1 if x < 0 0 if x == 0 +1 if x > 0
func (*Int) String
func (x *Int) String() string
func (*Int) Sub
func (z *Int) Sub(x, y *Int) *Int
Sub sets z to the difference x-y and returns z.
func (*Int) Xor
func (z *Int) Xor(x, y *Int) *Int
Xor sets z = x ^ y and returns z.
type Rat
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
func NewRat(a, b int64) *Rat
NewRat creates a new Rat with numerator a and denominator b.
func (*Rat) Abs
func (z *Rat) Abs(x *Rat) *Rat
Abs sets z to |x| (the absolute value of x) and returns z.
func (*Rat) Add
func (z *Rat) Add(x, y *Rat) *Rat
Add sets z to the sum x+y and returns z.
func (*Rat) Cmp
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 (*Rat) Denom
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.
func (*Rat) FloatString
func (x *Rat) FloatString(prec int) string
FloatString returns a string representation of z in decimal form with prec digits of precision after the decimal point and the last digit rounded.
func (*Rat) GobDecode
func (z *Rat) GobDecode(buf []byte) error
GobDecode implements the gob.GobDecoder interface.
func (*Rat) GobEncode
func (x *Rat) GobEncode() ([]byte, error)
GobEncode implements the gob.GobEncoder interface.
func (*Rat) Inv
func (z *Rat) Inv(x *Rat) *Rat
Inv sets z to 1/x and returns z.
func (*Rat) IsInt
func (x *Rat) IsInt() bool
IsInt returns true if the denominator of x is 1.
func (*Rat) Mul
func (z *Rat) Mul(x, y *Rat) *Rat
Mul sets z to the product x*y and returns z.
func (*Rat) Neg
func (z *Rat) Neg(x *Rat) *Rat
Neg sets z to -x and returns z.
func (*Rat) Num
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.
func (*Rat) Quo
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 (*Rat) RatString
func (x *Rat) RatString() string
RatString returns a string representation of z in the form "a/b" if b != 1, and in the form "a" if b == 1.
func (*Rat) Scan
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
? Example
Code:
// The Scan function is rarely used directly; // the fmt package recognizes it as an implementation of fmt.Scanner. r := new(big.Rat) _, err := fmt.Sscan("1.5000", r) if err != nil { log.Println("error scanning value:", err) } else { fmt.Println(r) }
Output:
3/2
func (*Rat) Set
func (z *Rat) Set(x *Rat) *Rat
Set sets z to x (by making a copy of x) and returns z.
func (*Rat) SetFrac
func (z *Rat) SetFrac(a, b *Int) *Rat
SetFrac sets z to a/b and returns z.
func (*Rat) SetFrac64
func (z *Rat) SetFrac64(a, b int64) *Rat
SetFrac64 sets z to a/b and returns z.
func (*Rat) SetInt
func (z *Rat) SetInt(x *Int) *Rat
SetInt sets z to x (by making a copy of x) and returns z.
func (*Rat) SetInt64
func (z *Rat) SetInt64(x int64) *Rat
SetInt64 sets z to x and returns z.
func (*Rat) SetString
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
? Example
Code:
r := new(big.Rat)
r.SetString("355/113")
fmt.Println(r.FloatString(3))
Output:
3.142
func (*Rat) Sign
func (x *Rat) Sign() int
Sign returns:
-1 if x < 0 0 if x == 0 +1 if x > 0
func (*Rat) String
func (x *Rat) String() string
String returns a string representation of z in the form "a/b" (even if b == 1).
func (*Rat) Sub
func (z *Rat) Sub(x, y *Rat) *Rat
Sub sets z to the difference x-y and returns z.
type Word
type Word uintptr
A Word represents a single digit of a multi-precision unsigned integer.
Except as noted, the content of this page is licensed under the Creative Commons Attribution 3.0 License, and code is licensed under a BSD license.
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