big

package
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 Go to latest Published: Jun 9, 2011 License: BSD-3-Clause Imports: 6 Imported by: 0

Documentation

Overview

Package big implements multi-precision arithmetic (big numbers). The following numeric types are supported:

  • Int signed integers
  • Rat rational numbers

All methods on Int take the result as the 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.

Index

Constants

View Source 
const MaxBase = 'z' - 'a' + 10 + 1 // = hexValue('z') + 1

MaxBase is the largest number base accepted for string conversions.

Variables

This section is empty.

Functions

func GcdInt 

func GcdInt(d, x, y, a, b *Int)

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 ProbablyPrime 

func ProbablyPrime(z *Int, n int) bool

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.

Types

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 (z *Int) Bit(i int) uint

Bit returns the value of the i'th bit of z. That is, it returns (z>>i)&1. The bit index i must be >= 0.

func (*Int) BitLen 

func (z *Int) BitLen() int

BitLen returns the length of the absolute value of z in bits. The bit length of 0 is 0.

func (*Int) Bytes 

func (z *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. 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.)

func (*Int) Exp 

func (z *Int) Exp(x, y, m *Int) *Int

Exp sets z = x**y mod m. 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 int)

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).

func (*Int) GobDecode 

func (z *Int) GobDecode(buf []byte) os.Error

GobDecode implements the gob.GobDecoder interface.

func (*Int) GobEncode 

func (z *Int) GobEncode() ([]byte, os.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. 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 ℤ/pℤ (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) 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. 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”.)

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. 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 int) os.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).

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 the i'th bit of z to bit and returns z. 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) 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.

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 (*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, 0/0, is not a legal Rat.

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) (r int)

Cmp compares x and y and returns: 

-1 if x <  y
 0 if x == y
+1 if x >  y

func (*Rat) Denom 

func (z *Rat) Denom() *Int

Denom returns the denominator of z; it is always > 0. The result is a reference to z's denominator; it may change if a new value is assigned to z.

func (*Rat) FloatString 

func (z *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) os.Error

GobDecode implements the gob.GobDecoder interface.

func (*Rat) GobEncode 

func (z *Rat) GobEncode() ([]byte, os.Error)

GobEncode implements the gob.GobEncoder interface.

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 (by making a copy of x if necessary) and returns z.

func (*Rat) Num 

func (z *Rat) Num() *Int

Num returns the numerator of z; it may be <= 0. The result is a reference to z's numerator; it may change if a new value is assigned to z.

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 (z *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 int) os.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.

func (*Rat) Set 

func (z *Rat) Set(x *Rat) *Rat

Set sets z to x (by making a copy of x if necessary) 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.

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 (z *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

Source Files

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