The math big library

Overview

The big library implements arbitrary-precision arithmetic (big numbers).

Functions

Float(x float) -> Float

Constructs a Float from a float.

Float(s string) -> Float / error

Constructs a Float from a string.

Float(r Rat) -> Float

Constructs a Float from a Rat.

(x Float) + (y Float) -> Float

Adds two Float values.

(x Float) - (y Float) -> Float

Subtracts one Float value from another.

(x Float) * (y Float) -> Float

Multiplies two Float values.

(x Float) / (y Float) -> Float

Divides one Float value by another.

-(x Float) -> Float

Negates a Float value.

(x Float) < (y Float) -> bool

Compares two Float values, returning true if x < y.

(x Float) <= (y Float) -> bool

Compares two Float values, returning true if x <= y.

(x Float) > (y Float) -> bool

Compares two Float values, returning true if x > y.

(x Float) >= (y Float) -> bool

Compares two Float values, returning true if x >= y.

abs(x Float) -> Float

Returns the absolute value of a Float.

float(z Float) -> float

Converts a Float to the built-in float type.

int(z Float) -> int

Converts a Float to the built-in int type.

isInf(z Float) -> bool

Tests whether the given Float is an infinity.

isInt(z Float) -> bool

Tests whether the given Float is an integer.

sign(z Float) -> int

sign(z) returns: -1 if z < 0 0 if z == 0 1 if z > 0

sqrt(z Float) -> Float

Returns the square root of a Float.

string(z Float)

Overloads string.

text(z Float, format int, prec int) -> string

Converts the Float to a string of the given format and precision.

Int(i int) -> Int

Constructs an Int from an int.

Int(s string) -> Int / error

Constructs an Int from a string.

Int(z Float) -> Int

Constructs an Int from a Float.

(x Int) + (y Int) -> Int

Adds two Int values.

(x Int) - (y Int) -> Int

Subtracts one Int value from another.

(x Int) * (y Int) -> Int

Multiplies two Int values.

-(x Int) -> Int

Negates an Int.

(x Int) / (y Int) -> Rat

x / y returns the Rat obtained by dividing x by y.

(x Int) div (y Int) -> Int

x div y returns the Int obtained by dividing x by y.

(x Int) mod (y Int) -> Int

Returns the modulus of one Int by another.

(x Int) ^ (y Int) -> Int

Returns the exponent of on Int by another.

(x Int) < (y Int) -> bool

Compares two Int values and returns true if x < y.

(x Int) <= (y Int) -> bool

Compares two Int values and returns true if x <= y.

(x Int) > (y Int) -> bool

Compares two Int values and returns true if x > y.

(x Int) >= (y Int) -> bool

Compares two Int values and returns true if x >= y.

abs(x Int) -> Int

Returns the absolute value of an Int.

andInt(x Int, y Int) -> Int

Returns the result of a bitwise and operation on two Ints.

andNotInt(x Int, y Int) -> Int

Returns the result of a bitwise and not operation on two Ints.

binomial(n int, k int) -> Int

Returns the binomial coefficient C(n, k).

bit(z Int, i int) -> int

Returns the value of the ith bit of the Int, as 0 or 1.

bitLen(z Int) -> int

Returns the length of the absolute value of x in bits. The bit length of 0 is 0.

divMod(x any?, y any?) -> Int, Int

divMod(x, y) returns the quotient and modulus of x by y.

exp(x Int, y Int, m Int) -> Int

Returns x to the power y mod abs(m). If m == 0, z = x**y unless y <= 0, when 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.

float(z Int) -> float

Converts an Int to the built-in float type.

fromString(s string, base int) -> Int / error

Converts a string in the given base to an Int, returning an error if the string isn't well-formed.

gcd(a Int, b Int) -> Int

Returns the greatest common denominator of two Ints.

int(z Int) -> int

Converts an Int to the built-in int type.

isSmallInt(z Int) -> bool

Returns true if the given Int will fit into a built-in (64-bit) int.

lsh(x Int, n int) -> Int

Returns the result of a bitwise left shift of x by n bits.

modInverse(g Int, n Int) -> Int

Returns the inverse of g mod n.

modSqrt(x Int, p Int) -> Int

Returns a square root of x mod p.

mulRange(a int, b int) -> Int

Returns the result of multiplying the numbers in the range a::b.

notInt(x Int) -> Int

Resturns the result of performing a bitwise not on an Int.

orInt(x Int, y Int) -> Int

Returns the result of a bitwise or operation on two Ints.

probablyPrime(z Int, n int) -> bool

probablyPrime reports whether x is probably prime, applying the Miller-Rabin test with n pseudorandomly chosen bases as well as a Baillie-PSW test. If x is prime, ProbablyPrime returns true. If x is chosen randomly and not prime, probablyPrime probably returns false. The probability of returning true for a randomly chosen non-prime is at most ¼ⁿ. ProbablyPrime is 100% accurate for inputs less than 2⁶⁴. See Menezes et al., Handbook of Applied Cryptography, 1997, pp. 145-149, and FIPS 186-4 Appendix F for further discussion of the error probabilities. ProbablyPrime is not suitable for judging primes that an adversary may have crafted to fool the test.

quo(x Int, y Int) -> Int

Returns the quotient of x by y using truncated division.

quoRem(x Int, y Int) -> Int, Int

Returns the quotient and remainder of x by y using truncated division.

rem(x Int, y Int) -> Int

Returns the remainder when dividing x by y using truncated division.

rsh(x Int, n int) -> Int

Returns the result of a bitwise left shift of x by n bits.

sign(z Int) -> int

sign(z) returns: -1 if z < 0 0 if z == 0 1 if z > 0

sqrt(x Int) -> Int

Returns ⌊√x⌋, the largest integer such that z² ≤ x.

string(z Int) -> string

Overloads string.

text(z Int, base int) -> string

text returns the string representation of x in the given base. Base must be between 2 and 62, inclusive. The result uses the lower-case letters 'a' to 'z' for digit values 10 to 35, and the upper-case letters 'A' to 'Z' for digit values 36 to 61. No prefix (such as "0x") is added to the string.

trailingZeroBits(z Int) -> int

Returns the number of consecutive least significant zero bits of |x|.

xorInt(x Int, y Int) -> Int

Returns the result of a bitwise xor operation on two Ints.

Rat(i int, j int) -> Rat

Constructs a Rat from two ints.

Rat(z Float) -> Rat

Constructs a Rat from a Float.

Rat(s string) -> Rat / error

Constructs a Rat from a string.

Rat(x float) -> Rat

Converts the built-in float type to a Rat.

Rat(x Int, y Int)

Converts two Ints to the Rat which is their quotient.

Rat(x Int)

Converts an Int to its representation as a Rat.

Rat(x int)

Converts an int to its representation as a Rat.

(x Rat) + (y Rat) -> Rat

Adds two Rat values.

(x Rat) - (y Rat) -> Rat

Subtracts one Rat value from another.

(x Rat) * (y Rat) -> Rat

Multiplies two Rat values.

(x Rat) / (y Rat) -> Rat

Divides one Rat value by another.

-(x Rat) -> Rat

Negates a Rat value.

(x Rat) < (y Rat) -> bool

Compares two Rat values and returns true if x < y.

(x Rat) <= (y Rat) -> bool

Compares two Rat values and returns true if x <= y.

(x Rat) > (y Rat) -> bool

Compares two Rat values and returns true if x > y.

(x Rat) >= (y Rat) -> bool

Compares two Rat values and returns true if x >= y.

abs(z Rat)

Returns the abolute value of z.

denom(z Rat) -> Int

Returns the denominator of z.

float(z Rat)

Converts a Rat to a built-in float value.

floatString(z Rat, prec int) -> string

returns a string representation of x in decimal form with prec digits of precision after the radix point. The last digit is rounded to nearest, with halves rounded away from zero.

inv(x Rat) -> Rat

Returns the inverse of a Rat.

isInt(z Rat) -> bool

Tests whether z represents an integer.

num(z Rat) -> Int

Returns the numerator of a Rat.

ratString(z Rat) -> string

Returns a string representation of z in the form "a/b"`` if b != 1``, and in the form "a" if b == 1.

sign(z Rat) -> int

sign(z) returns: -1 if z < 0 0 if z == 0 1 if z > 0

string(z Rat)

Returns a string representation of z`` in the form "a/b" (even if `b == 1).

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