Advanced Mathematical Operations

Advanced mathematical functions for arbitrary precision integers. More...

Functions
di_int	di_mod_pow (di_int base, di_int exp, di_int mod)
	Modular exponentiation: (base^exp) mod mod.
di_int	di_gcd (di_int a, di_int b)
	Greatest Common Divisor using Euclidean algorithm.
di_int	di_lcm (di_int a, di_int b)
	Least Common Multiple.
di_int	di_extended_gcd (di_int a, di_int b, di_int *x, di_int *y)
	Extended Euclidean Algorithm.
di_int	di_sqrt (di_int n)
	Integer square root using Newton's method.
di_int	di_factorial (uint32_t n)
	Calculate factorial.

Detailed Description

Advanced mathematical functions for arbitrary precision integers.

Function Documentation

di_extended_gcd()

di_int di_extended_gcd	(	di_int	a,
		di_int	b,
		di_int *	x,
		di_int *	y
	)

Extended Euclidean Algorithm.

Parameters

a	First integer (may be NULL)
b	Second integer (may be NULL)
x	Pointer to store coefficient x
y	Pointer to store coefficient y

Returns

GCD of a and b, with coefficients such that ax + by = gcd(a,b)

Since

1.0.0

Note

Sets *x and *y to coefficients satisfying the Bezout identity

Definition at line 2622 of file dynamic_int.h.

di_factorial()

di_int di_factorial

(

uint32_t

n

)

Calculate factorial.

Parameters

n	Non-negative integer

Returns

New di_int with n! (n factorial), or NULL on failure

Since

1.0.0

di_int fact5 = di_factorial(5);  // 120
di_int fact10 = di_factorial(10); // 3628800

Definition at line 2350 of file dynamic_int.h.

di_gcd()

di_int di_gcd	(	di_int	a,
		di_int	b
	)

Greatest Common Divisor using Euclidean algorithm.

Parameters

a	First integer (may be NULL)
b	Second integer (may be NULL)

Returns

New di_int with GCD of |a| and |b|, or NULL on failure

Since

1.0.0

See also

di_lcm() for Least Common Multiple

di_extended_gcd() for Extended Mathematical Operations Euclidean algorithm

Definition at line 2237 of file dynamic_int.h.

di_lcm()

di_int di_lcm	(	di_int	a,
		di_int	b
	)

Least Common Multiple.

Parameters

a	First integer (may be NULL)
b	Second integer (may be NULL)

Returns

New di_int with LCM of a and b, or NULL on failure

Since

1.0.0

Note

Uses identity: lcm(a,b) = |a*b| / gcd(a,b)

See also

di_gcd() for Greatest Common Divisor

Definition at line 2272 of file dynamic_int.h.

di_mod_pow()

di_int di_mod_pow	(	di_int	base,
		di_int	exp,
		di_int	mod
	)

Modular exponentiation: (base^exp) mod mod.

Parameters

base	Base integer (may be NULL)
exp	Exponent integer (may be NULL)
mod	Modulus integer (may be NULL)

Returns

New di_int with result of (base^exp) mod mod, or NULL on failure

Since

1.0.0

Note

Returns NULL if mod is zero or one

Uses binary exponentiation for efficiency

Definition at line 2376 of file dynamic_int.h.

di_sqrt()

di_int di_sqrt

(

di_int

n

)

Integer square root using Newton's method.

Parameters

n	Integer to find square root of (may be NULL)

Returns

New di_int with floor(sqrt(n)), or NULL on failure

Since

1.0.0

Note

Returns NULL for negative inputs

Definition at line 2301 of file dynamic_int.h.