big

package
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 Go to latest Published: Aug 26, 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). 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) 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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