std/math/big

Index

Variables

jule

const (
	Below: Accuracy = -1
	Exact: Accuracy = 0
	Above: Accuracy = +1
)

Constants describing the [Accuracy] of a [Float].

jule

const (
	MaxBase = 10 + ('z' - 'a' + 1) + ('Z' - 'A' + 1)
)

The largest number base accepted for string conversions.

CmpFloat

jule

fn CmpFloat(&x: *float, &y: *float): int

Compares x and y and returns:

-1 if x < y;
0 if x == y (incl. -0 == 0, -Inf == -Inf, and +Inf == +Inf);
+1 if x > y.

Accuracy

jule

type Accuracy: i8

Describes the rounding error produced by the most recent operation that generated a [Float] value, relative to the exact value.

Int

jule

struct Int {
	// NOTE: contains filtered hidden or unexported fields
}

An Int represents a signed multi-precision integer. The zero value for an Int represents the value 0.

The Int type is optimized for high-performance and efficiency. Implementation focuses to reduce allocations as much as possible and suitable for stack-based use cases by default. Int instances use internal mutable slice to store data. Computations may use available capacity of the underlying slice to avoid making new allocation. So shared data needs extra attention. Any mutable operation may be reflected to shared common data. If you need to share same Int instance, using smart pointers is a best naive way. If you need to have guaranteed independent copy, use Set on a zero instance.

Note that methods may leak the Int's value through timing side-channels. Because of this and because of the scope and complexity of the implementation, Int is not well-suited to implement cryptographic operations. The standard library avoids exposing non-trivial Int methods to attacker-controlled inputs and the determination of whether a bug in the big package is considered a security vulnerability might depend on the impact on the standard library.

New

jule

fn New(x: i64): Int

Jacobi

jule

fn Jacobi(&x: *Int, &y: *Int): int

Returns the Jacobi symbol (x/y), either +1, -1, or 0. The y argument must be an odd integer.

MulRange

jule

fn MulRange(mut *self, mut a: i64, mut b: i64)

Sets self to the product of all integers in the range [a, b] inclusively. If a > b (empty range), the result is 1.

Binomial

jule

fn Binomial(mut *self, n: i64, mut k: i64)

Sets self to the binomial coefficient C(n, k).

Add

jule

fn Add(mut *self, &x: *Int, &y: *Int)

Sets self = x + y

Sub

jule

fn Sub(mut *self, &x: *Int, &y: *Int)

Sets self = x + y

Mul

jule

fn Mul(mut *self, &x: *Int, &y: *Int)

Sets self = x * y.

Sqrt

jule

fn Sqrt(mut *self, &x: *Int)

Sets self to square root |√x|. Panics if number is negative.

QuoRem

jule

fn QuoRem(mut *self, &x: *Int, &y: *Int, mut &r: *Int)

Sets self to the quotient x/y and r to the remainder x%y. If y == 0, a division-by-zero run-time panic occurs.

Implements T-division and modulus (like Jule):

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 Jule).

Quo

jule

fn Quo(mut *self, &x: *Int, &y: *Int)

Sets self to the quotient x/y for y != 0. If y == 0, a division-by-zero run-time panic occurs. Implements truncated division (like Jule); see [Int.QuoRem] for more details.

Div

jule

fn Div(mut *self, &x: *Int, &y: *Int)

Sets self to the quotient x/y for y != 0. If y == 0, a division-by-zero runtime panic occurs. Implements Euclidean division; see [Int.DivMod] for more details.

Mod

jule

fn Mod(mut *self, &x: *Int, &y: *Int)

Sets self to the modulus x%y for y != 0. If y == 0, a division-by-zero run-time panic occurs. Implements Euclidean modulus (unlike Jule); see [Int.DivMod] for more details.

DivMod

jule

fn DivMod(mut *self, mut &x: *Int, mut &y: *Int): (q: Int, m: Int)

Sets self to the quotient x div y and m to the modulus x mod y and returns the pair (q, m) for y != 0. If y == 0, a division-by-zero run-time panic occurs.

Implements Euclidean division and modulus (unlike Jule):

q = x div y  such that
m = x - y*q  with 0 <= m < |y|

(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 [Int.QuoRem] for T-division and modulus (like Jule).

Lsh

jule

fn Lsh(mut *self, &x: *Int, y: uint)

Sets self = x << y

Rsh

jule

fn Rsh(mut *self, &x: *Int, y: uint)

Sets self = x >> y

Or

jule

fn Or(mut *self, &x: *Int, &y: *Int)

Sets self = x | y

And

jule

fn And(mut *self, &x: *Int, &y: *Int)

Sets self = x & y

Xor

jule

fn Xor(mut *self, &x: *Int, &y: *Int)

Sets self = x ^ y

Set

jule

fn Set(mut *self, &x: *Int)

Sets self to copy of x.

Exp

jule

fn Exp(mut *self, &x: *Int, &y: *Int, &m: *Int)

Sets self = x**y mod |m| (i.e. the sign of m is ignored). If m == nil or m == 0, self = x**y unless y <= 0 then self = 1. If m != 0, y < 0, and x and m are not relatively prime, self is zero.

Modular exponentiation of inputs of a particular size is not a cryptographically constant-time operation.

GCD

jule

fn GCD(mut *self, mut &x: *Int, mut &y: *Int, &a: *Int, &b: *Int)

Sets self to the greatest common divisor of a and b. If x or y are not nil, GCD sets their value such that self = a*x + b*y.

a and b may be positive, zero or negative. (Before Go 1.14 both had to be > 0.) Regardless of the signs of a and b, self is always >= 0.

If a == b == 0, GCD sets self = x = y = 0.

If a == 0 and b != 0, GCD sets self = |b|, x = 0, y = sign(b) * 1.

If a != 0 and b == 0, GCD sets self = |a|, x = sign(a) * 1, y = 0.

ModInverse

jule

fn ModInverse(mut *self, &g: *Int, &n: *Int)

Sets self to the multiplicative inverse of g in the ring ℤ/nℤ. If g and n are not relatively prime, g has no multiplicative inverse in the ring ℤ/nℤ. In this case, self is zero. If n == 0, a division-by-zero run-time panic occurs.

ProbablyPrime

jule

fn ProbablyPrime(*self, n: int): bool

Reports whether self is probably prime, applying the Miller-Rabin test with n pseudorandomly chosen bases as well as a Baillie-PSW test.

If self is prime, returns true. If self is chosen randomly and not prime, probably returns false. The probability of returning true for a randomly chosen non-prime is at most ¼ⁿ.

It 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.

It is not suitable for judging primes that an adversary may have crafted to fool the test.

TrailingZeroBits

jule

fn TrailingZeroBits(*self): uint

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

BitLen

jule

fn BitLen(*self): int

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

Bit

jule

fn Bit(*self, i: int): uint

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

Abs

jule

fn Abs(mut *self, &x: *Int)

Sets self to |x| (the absolute value of x).

Not

jule

fn Not(mut *self, &x: *Int)

Sets self = ^x

Neg

jule

fn Neg(mut *self, &x: *Int)

Sets self to -x.

Odd

jule

fn Odd(*self): bool

Reports whether x(self) is odd.

Even

jule

fn Even(*self): bool

Reports whether x(self) is even.

Sign

jule

fn Sign(*self): int

Returns, x = self:

Sign() = -1 if x < 0
Sign() = 0 if x == 0
Sign() = +1 if x > 0

Cmp

jule

fn Cmp(*self, &y: *Int): (r: int)

Compares integers.

Returns +1 if self > y
Returns 0 if self == y
Returns -1 if self < y

CmpAbs

jule

fn CmpAbs(*self, &y: *Int): int

Compares absolute value.

Returns +1 if |self| > |y|
Returns 0 if |self| == |y|
Returns -1 if |self| < |y|

SetU64

jule

fn SetU64(mut *self, x: u64)

Sets self to x.

SetI64

jule

fn SetI64(mut *self, x: i64)

Sets self to x.

SetStr

jule

fn SetStr(mut *self, mut s: str, base: int): (ok: bool)

Sets self to the value of s, interpreted in the given base, and returns a boolean indicating success. The entire string (not just a prefix) must be valid for success. If SetStr fails, the value of self is undefined.

The base argument must be 0 or a value between 2 and [MaxBase]. For base 0, the number prefix determines the actual base: A prefix of “0b” or “0B” selects base 2, “0”, “0o” or “0O” selects base 8, and “0x” or “0X” selects base 16. Otherwise, the selected base is 10 and no prefix is accepted.

For bases <= 36, lower and upper case letters are considered the same: The letters 'a' to 'z' and 'A' to 'Z' represent digit values 10 to 35. For bases > 36, the upper case letters 'A' to 'Z' represent the digit values 36 to 61.

For base 0, an underscore character “_” may appear between a base prefix and an adjacent digit, and between successive digits; such underscores do not change the value of the number. Incorrect placement of underscores is reported as an error if there are no other errors. If base != 0, underscores are not recognized and act like any other character that is not a valid digit.

I64

jule

fn I64(*self): i64

Returns the i64 representation of x(self). If x cannot be represented in an i64, the result is undefined.

U64

jule

fn U64(*self): u64

Returns the u64 representation of x(self). If x cannot be represented in a u64, the result is undefined.

IsI64

jule

fn IsI64(*self): bool

Reports whether x(self) can be represented as an i64.

IsU64

jule

fn IsU64(*self): bool

Reports whether x(self) can be represented as a u64.

Str

jule

fn Str(*self): str

Returns string representation of x(self) in decimal format.

Format

jule

fn Format(*self, b: int): str

Returns the string representation of x(self) 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.

F64

jule

fn F64(*self): (f64, Accuracy)

Returns the f64 value nearest x(self), and an indication of any rounding that occurred.

Word

jule

type Word: uint

Represents a single digit of a multi-precision unsigned integer.

std/jule/constant

std/math/big ​

Index ​

Variables ​

CmpFloat ​

Accuracy ​

Int ​

New ​

Jacobi ​

MulRange ​

Binomial ​

Add ​

Sub ​

Mul ​

Sqrt ​

QuoRem ​

Quo ​

Div ​

Mod ​

DivMod ​

Lsh ​

Rsh ​

Or ​

And ​

Xor ​

Set ​

Exp ​

GCD ​

ModInverse ​

ProbablyPrime ​

TrailingZeroBits ​

BitLen ​

Bit ​

Abs ​

Not ​

Neg ​

Odd ​

Even ​

Sign ​

Cmp ​

CmpAbs ​

SetU64 ​

SetI64 ​

SetStr ​

I64 ​

U64 ​

IsI64 ​

IsU64 ​

Str ​

Format ​

F64 ​

Word ​

std/math/big

Index

Variables

CmpFloat

Accuracy

Int

New

Jacobi

MulRange

Binomial

Add

Sub

Mul

Sqrt

QuoRem

Quo

Div

Mod

DivMod

Lsh

Rsh

Or

And

Xor

Set

Exp

GCD

ModInverse

ProbablyPrime

TrailingZeroBits

BitLen

Bit

Abs

Not

Neg

Odd

Even

Sign

Cmp

CmpAbs

SetU64

SetI64

SetStr

I64

U64

IsI64

IsU64

Str

Format

F64

Word