GMP.Z

Defined in gmp-fix@0.6.0

Provides multiple-precision integer type MPZ and related functions.

Repository: https://github.com/tttmmmyyyy/fixlang-gmp

Values

namespace GMP.Z

c_SiZE_OF_MPZ

Type: Std::FFI::CInt

Size of __mpz_struct.

namespace GMP.Z::MPZ

abs

Type: GMP.Z::MPZ -> GMP.Z::MPZ

Calculates the absolute value of a MPZ value.

Parameters

num: The MPZ value to calculate the absolute value of.

addmul

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Calculates x + a * b.

Parameters

a
b
x

and

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Logical and operation on two MPZ values.

Parameters

lhs: The left-hand side value.
rhs: The right-hand side value.

bin_ui

Type: GMP.Z::MPZ -> Std::U64 -> GMP.Z::MPZ

Calculates the binomial coefficient n choose k.

Parameters

n: The total number of items.
k: The number of items to choose.

cdiv_q

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by d and returns the quotient.

"c" means "ceiling", i.e., the quotient is rounded towards positive infinity.

Parameters

d: The divisor.
n: The dividend.

cdiv_q_2exp

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by 2^b and returns the quotient.

"c" means "ceiling", i.e., the quotient is rounded towards positive infinity.

Parameters

bit: The exponent of 2.
n: The dividend.

cdiv_qr

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> (GMP.Z::MPZ, GMP.Z::MPZ)

Divides n by d and returns the quotient and remainder.

"c" means "ceiling", i.e., the quotient is rounded towards positive infinity.

Parameters

d: The divisor.
n: The dividend.

cdiv_r

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by d and returns the remainder.

"c" means "ceiling", i.e., the quotient is rounded towards positive infinity.

Parameters

d: The divisor.
n: The dividend.

cdiv_r_2exp

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by 2^b and returns the remainder.

"c" means "ceiling", i.e., the quotient is rounded towards positive infinity.

Parameters

bit: The exponent of 2.
n: The dividend.

clrbit

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Sets the specified bit in a MPZ value to 0.

Parameters

bit: The bit to clear.
n: The MPZ value to modify.

cmp

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> Std::I64

Compares two MPZ values.

Returns

a negative if lhs < rhs
zero if lhs == rhs
a positive if lhs > rhs

Parameters

lhs: The left-hand side value.
rhs: The right-hand side value.

cmp_d

Type: GMP.Z::MPZ -> Std::F64 -> Std::I64

Compares a MPZ value and an F64 value.

Returns

a negative if lhs < rhs
zero if lhs == rhs
a positive if lhs > rhs

Parameters

lhs: The left-hand side value.
rhs: The right-hand side value.

cmpabs

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> Std::I64

Compares absolute values of two MPZ values.

Returns

a negative if |lhs| < |rhs|
zero if |lhs| == |rhs|
a positive if |lhs| > |rhs|

Parameters

lhs: The left-hand side value.
rhs: The right-hand side value.

cmpabs_d

Type: GMP.Z::MPZ -> Std::F64 -> Std::I64

Compares absolute values of a MPZ value and an F64 value.

Returns

a negative if |lhs| < |rhs|
zero if |lhs| == |rhs|
a positive if |lhs| > |rhs|

Parameters

lhs: The left-hand side value.
rhs: The right-hand side value.

com

Type: GMP.Z::MPZ -> GMP.Z::MPZ

Bitwise complement operation on a MPZ value.

Parameters

n: The MPZ value to complement.

combit

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Toggles the specified bit in a MPZ value.

Parameters

bit: The bit to toggle.
n: The MPZ value to modify.

congruent_2exp_p

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ -> Std::Bool

Checks if two values a, b are congruent modulo 2^b.

Parameters

bit: The exponent of 2.
a: The first value.
b: The second value.

congruent_p

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ -> Std::Bool

Checks if two values a, b are congruent modulo m.

Parameters

m: The modulus.
a: The first value.
b: The second value.

divexact

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by d and returns the quotient.

This function assumes that n is divisible by d.

Parameters

d: The divisor.
n: The dividend.

divisible_2exp_p

Type: Std::U64 -> GMP.Z::MPZ -> Std::Bool

Checks if n is divisible by 2^b.

Parameters

bit: The exponent of 2.
n: The dividend.

divisible_p

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> Std::Bool

Checks if n is divisible by d.

Parameters

d: The divisor.
n: The dividend.

fac2_ui

Type: Std::U64 -> GMP.Z::MPZ

Calculates the double factorial of a non-negative integer n.

Parameters

n: The non-negative integer to calculate the double factorial of.

fac_ui

Type: Std::U64 -> GMP.Z::MPZ

Calculates the factorial of a non-negative integer n.

Parameters

n: The non-negative integer to calculate the factorial of.

facm_uiui

Type: Std::U64 -> Std::U64 -> GMP.Z::MPZ

Calculates the factorial of n!^(m)

Parameters

m
n: The non-negative integer to calculate the factorial of.

fdiv_q

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by d and returns the quotient.

"f" means "floored", i.e., the quotient is rounded towards negative infinity.

Parameters

d: The divisor.
n: The dividend.

fdiv_q_2exp

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by 2^b and returns the quotient.

"f" means "floored", i.e., the quotient is rounded towards negative infinity.

Parameters

bit: The exponent of 2.
n: The dividend.

fdiv_qr

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> (GMP.Z::MPZ, GMP.Z::MPZ)

Divides n by d and returns the quotient and remainder.

"f" means "floored", i.e., the quotient is rounded towards negative infinity.

Parameters

d: The divisor.
n: The dividend.

fdiv_r

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by d and returns the remainder.

"f" means "floored", i.e., the quotient is rounded towards negative infinity.

Parameters

d: The divisor.
n: The dividend.

fdiv_r_2exp

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by 2^b and returns the remainder.

"f" means "floored", i.e., the quotient is rounded towards negative infinity.

Parameters

bit: The exponent of 2.
n: The dividend.

fib2_ui

Type: Std::U64 -> (GMP.Z::MPZ, GMP.Z::MPZ)

Calculates the Fibonacci number at position n and returns both the Fibonacci number and the previous one.

Parameters

n: The position in the Fibonacci sequence.

fib_ui

Type: Std::U64 -> GMP.Z::MPZ

Calculates the Fibonacci number at position n.

Parameters

n: The position in the Fibonacci sequence.

gcd

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Calculates the greatest common divisor of two MPZ values.

Parameters

n
m

gcdext

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> (GMP.Z::MPZ, GMP.Z::MPZ, GMP.Z::MPZ)

Calculates the greatest common divisor gcd of two MPZ values and also returns coefficients s and t such that gcd = n * s + m * t.

Returns

A tuple (gcd, s, t)

Parameters

n: The first value.
m: The second value.

get_d

Type: GMP.Z::MPZ -> Std::F64

Converts a MPZ value to an F64 value.

For details, see the document of mpz_get_d in GMP.

get_d_exp

Type: GMP.Z::MPZ -> (Std::F64, Std::I64)

Converts a MPZ value to the pair (F64 value, exponent).

For details, see the document of mpz_get_d_2exp in GMP.

get_si

Type: GMP.Z::MPZ -> Std::Option Std::I64

Converts a MPZ value to an I64 value.

If the value is too large to fit in an I64, this function returns none.

get_str

Type: Std::I64 -> GMP.Z::MPZ -> Std::String

Get the string representation of a MPZ value in the given base.

Parameters

base: The base of the string representation, which must be in the range [-36, -2] or [2, 62].
num: The MPZ value to convert.

get_ui

Type: GMP.Z::MPZ -> Std::Option Std::U64

Converts a MPZ value to an U64 value.

If the value is too large to fit in an U64, this function returns none.

hamdist

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> Std::U64

Calculates the Hamming distance between two MPZ values.

For the behavior when lhs or rhs is negative, see the document of mpz_hamdist in GMP.

Parameters

lhs: The left-hand-side value.
rhs: The right-hand-side value.

init_set_d

Type: Std::F64 -> GMP.Z::MPZ

Creates a MPZ value represented by a F64 value.

Parameters

val: The F64 value to represent.

init_set_si

Type: Std::I64 -> GMP.Z::MPZ

Creates a MPZ value represented by an I64 value.

Parameters

val: The I64 value to represent.

init_set_str

Type: Std::String -> Std::I64 -> Std::Option GMP.Z::MPZ

Creates a MPZ value represented by a string in the given base.

If the string is not a valid representation of an integer in the given base, this function returns none. See document of mpz_set_str in GMP for details.

Parameters

str: The string representation of the integer.
base: The base of the string representation.

init_set_ui

Type: Std::U64 -> GMP.Z::MPZ

Creates a MPZ value represented by an U64 value.

Parameters

val: The U64 value to represent.

invert

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> Std::Option GMP.Z::MPZ

Calculates the modular inverse of n modulo m.

Parameters

m: The modulus.
n: The value to invert.

jacobi

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> Std::I64

Calculates the Jacobi symbol (a/b) for two MPZ values.

Parameters

a
b

lcm

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Calculates the least common multiple of two MPZ values.

Parameters

n: The first value.
m: The second value.

legendre

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> Std::I64

Calculates the Legendre symbol (a/p) for an MPZ value a and a prime p.

Parameters

a: The value to calculate the Legendre symbol for.
p: The prime number.

lucnum2_ui

Type: Std::U64 -> (GMP.Z::MPZ, GMP.Z::MPZ)

Calculates the Lucas number at position n and returns both the Lucas number and the previous one.

Parameters

n: The position in the Lucas sequence.

lucnum_ui

Type: Std::U64 -> GMP.Z::MPZ

Calculates the Lucas number at position n.

Parameters

n: The position in the Lucas sequence.

mod

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Calculates the remainder of n divided by d.

Parameters

d: The divisor.
n: The dividend.

mpz

Type: Std::I64 -> GMP.Z::MPZ

Create a MPZ value from an I64.

Parameters

n: The I64 value to convert.

mul_2exp

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Multiplies the MPZ value by 2^exp.

Parameters

exp: The exponent of 2.
num: The MPZ value to multiply.

nextprime

Type: GMP.Z::MPZ -> GMP.Z::MPZ

Calculates (probabilistically) the next prime number greater than x.

Parameters

x: The value to find the next prime of.

or

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Logical or operation on two MPZ values.

Parameters

lhs: The left-hand-side value.
rhs: The right-hand-side value.

perfect_power_p

Type: GMP.Z::MPZ -> Std::Bool

Checks if x is a perfect power, i.e., x = a^b for some integers a and b >= 2.

perfect_square_p

Type: GMP.Z::MPZ -> Std::Bool

Checks if x is a perfect square, i.e., x = a^2 for some integer a.

popcount

Type: GMP.Z::MPZ -> Std::U64

Counts the number of bits set to 1 in a MPZ value.

For the behavior when n is negative, see the document of mpz_popcount in GMP.

Parameters

n: The MPZ value to count bits in.

pow_ui

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Calculates b^e.

Parameters

e: The exponent.
b: The base.

powm

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Calculates b^e mod m.

Parameters

e: The exponent.
m: The modulus.
b: The base.

powm_sec

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Calculates b^e mod m.

This is a secure version of powm. For details, see the document of mpz_powm_sec in GMP.

Parameters

e: The exponent.
m: The modulus.
b: The base.

primorial_ui

Type: Std::U64 -> GMP.Z::MPZ

Calculates the primorial of a non-negative integer n, which is the product of all prime numbers less than or equal to n.

Parameters

n

probab_prime_p

Type: Std::I64 -> GMP.Z::MPZ -> Std::I64

Checks if x is a prime number.

Returns

2 if x is definitely prime, 1 if it is probably prime, and 0 if it is definitely composite.

Parameters

k: The number of iterations to perform for the probabilistic test.
x: The value to check.

remove

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> (GMP.Z::MPZ, Std::U64)

Removes the factor f from n.

Returns

A tuple (m, count) where m is the result and count is the number of times f was removed from n.

Parameters

f: The factor to remove.
n: The value to remove the factor from.

root

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Calculates the integer part of the n-th root of x.

Parameters

n: The root to calculate.
x: The value to calculate the root of.

root_rem

Type: Std::U64 -> GMP.Z::MPZ -> (GMP.Z::MPZ, GMP.Z::MPZ)

Calculates the n-th root of x and the remainder.

Returns

A pair (root, remainder) such that x = root^n + remainder.

Parameters

n: The root to calculate.
x: The value to calculate the root of.

scan0

Type: Std::U64 -> GMP.Z::MPZ -> Std::U64

Scans 0 bit in a MPZ value starting from the specified bit.

Parameters

bit: The bit to start scanning from.
n: The MPZ value to scan.

scan1

Type: Std::U64 -> GMP.Z::MPZ -> Std::U64

Scans 1 bit in a MPZ value starting from the specified bit.

Parameters

bit: The bit to start scanning from.
n: The MPZ value to scan.

set_d

Type: Std::F64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Sets the value of a MPZ to the integer part of a F64 value.

set_q

Type: GMP.Q::MPQ -> GMP.Z::MPZ -> GMP.Z::MPZ

Sets the value of a MPZ to the integer part of a MPQ value.

Parameters

q: The MPQ value to set.
x: The MPZ value to set.

set_si

Type: Std::I64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Sets the value of a MPZ to the given I64 value.

Parameters

val: The I64 value to set.
x: The MPZ value to set.

set_str

Type: Std::String -> Std::I64 -> GMP.Z::MPZ -> Std::Option GMP.Z::MPZ

Sets the value of a MPZ to the given string in the given base.

If the string is not a valid representation of an integer in the given base, this function returns none. See document of mpz_set_str in GMP for details.

Parameters

str: The string representation of the integer.
base: The base of the string representation.
num: The MPZ value to set.

set_ui

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Sets the value of a MPZ to the given U64 value.

Parameters

val: The U64 value to set.
x: The MPZ value to set.

setbit

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Sets the specified bit in a MPZ value to 1.

Parameters

bit: The bit to set.
n: The MPZ value to modify.

sgn

Type: GMP.Z::MPZ -> Std::I64

Returns the sign of a MPZ value.

Returns

-1 if n < 0
0 if n == 0
1 if n > 0

sqrt

Type: GMP.Z::MPZ -> GMP.Z::MPZ

Calculates the integer part of the root of x and the remainder.

Parameters

x: The value to calculate the root of.

sqrt_rem

Type: GMP.Z::MPZ -> (GMP.Z::MPZ, GMP.Z::MPZ)

Calculates the square root of x and the remainder.

Returns

A pair (root, remainder) such that `x = root^2 + remainder

Parameters

x: The value to calculate the square root of.

submul

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Calculates x - a * b.

Parameters

a
b
x

tdiv_q

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by d and returns the quotient.

"t" means "truncated", i.e., the quotient is rounded towards zero.

Parameters

d: The divisor.
n: The dividend.

tdiv_q_2exp

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by 2^b and returns the quotient.

"t" means "truncated", i.e., the quotient is rounded towards zero.

Parameters

bit: The exponent of 2.
n: The dividend.

tdiv_qr

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> (GMP.Z::MPZ, GMP.Z::MPZ)

Divides n by d and returns the quotient and remainder.

"t" means "truncated", i.e., the quotient is rounded towards zero.

Parameters

d: The divisor.
n: The dividend.

tdiv_r

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by d and returns the remainder.

"t" means "truncated", i.e., the quotient is rounded towards zero.

Parameters

d: The divisor.
n: The dividend.

tdiv_r_2exp

Type: Std::U64 -> GMP.Z::MPZ -> GMP.Z::MPZ

Divides n by 2^b and returns the remainder.

"t" means "truncated", i.e., the quotient is rounded towards zero.

Parameters

bit: The exponent of 2.
n: The dividend.

tstbit

Type: Std::U64 -> GMP.Z::MPZ -> Std::Bool

Checks if the specified bit in a MPZ value is set to 1.

Parameters

bit: The bit to check.
n: The MPZ value to check.

xor

Type: GMP.Z::MPZ -> GMP.Z::MPZ -> GMP.Z::MPZ

Logical xor operation on two MPZ values.

Parameters

lhs: The left-hand-side value.
rhs: The right-hand-side value.

Types and aliases

namespace GMP.Z

MPZ

Defined as: type MPZ = unbox struct { ...fields... }

Integer type with arbitrary precision.

field `_0`

Type: Std::FFI::Destructor GMP.Z::MPZHandle

MPZHandle

Defined as: type MPZHandle = Std::Ptr

A pointer to struct __mpz_struct.