GMP_GAP.md

GMP Function Comparison Table (not implemented)

This document records the functions of the PHP GMP extension that have not yet been implemented in the BigInt type, as a reference for future development.

Statistics

The GMP extension has 44 functions in total (excluding gmp_init and the alias gmp_div). 17 are covered, 27 are not covered.

Implemented

GMP function	BigInt method / operator	Description
gmp_init	std::bigInt()	construction
gmp_add	add() / +	addition
gmp_sub	sub() / -	subtraction
gmp_mul	mul() / *	multiplication
gmp_div_q	div() / /	division (quotient)
gmp_div_r	mod() / %	division (remainder)
gmp_div_qr	divmod()	quotient and remainder
gmp_mod	mod() / %	modulo
gmp_pow	pow()	power
gmp_powm	powmod()	modular exponentiation
gmp_neg	neg() / - (unary)	negation
gmp_abs	abs()	absolute value
gmp_sqrt	sqrt()	square root
gmp_gcd	gcd()	greatest common divisor
gmp_cmp	cmp() / <=>	comparison
gmp_and	bitAnd() / &	bitwise AND
gmp_or	bitOr() / |	bitwise OR
gmp_xor	bitXor() / ^	bitwise XOR
gmp_com	bitNot() / ~	bitwise NOT
gmp_testbit	testBit()	bit test
gmp_popcount	popCount()	population count
gmp_intval	toInt()	to int
gmp_strval	toString()	to string

Not implemented (sorted by priority)

High priority — commonly used number-theory functions

GMP function	Suggested method name	Signature	Description
gmp_sign	sign()	(): int	sign, returns -1/0/1
gmp_lcm	lcm($x)	(BigInt): BigInt	least common multiple
gmp_perfect_square	perfectSquare()	(): bool	whether it is a perfect square
gmp_perfect_power	perfectPower()	(): bool	whether it is a perfect power
gmp_prob_prime	probPrime($reps = 10)	(int): int	probabilistic primality test (Miller-Rabin)
gmp_nextprime	nextPrime()	(): BigInt	next prime
gmp_binomial	binomial($k)	(int): BigInt	binomial coefficient C(n, k)
gmp_fact	fact()	(): BigInt	factorial n!

Medium priority — advanced number-theory functions

GMP function	Suggested method name	Signature	Description
gmp_gcdext	gcdext($x)	(BigInt): array	extended GCD, returns [g, s, t] such that g = s·a + t·b
gmp_invert	invert($mod)	(BigInt): BigInt|false	modular inverse, returns false when it does not exist
gmp_sqrtrem	sqrtrem()	(): array	square root + remainder, returns [root, rem]
gmp_jacobi	jacobi($x)	(BigInt): int	Jacobi symbol
gmp_legendre	legendre($x)	(BigInt): int	Legendre symbol
gmp_kronecker	kronecker($x)	(BigInt): int	Kronecker symbol

Low priority — less commonly used

GMP function	Suggested method name	Signature	Description
gmp_divexact	divExact($x)	(BigInt): BigInt	exact division (used when divisibility is known; faster than ordinary division)
gmp_root	root($n)	(int): BigInt	n-th root (truncated)
gmp_rootrem	rootrem($n)	(int): array	n-th root + remainder
gmp_hamdist	hamDist($x)	(BigInt): int	Hamming distance

Not applicable — conflicts with the immutable design

GMP function	Reason
gmp_setbit	directly modifies the GMP object; BigInt is immutable
gmp_clrbit	directly modifies the GMP object; BigInt is immutable

To be evaluated

GMP function	Description
gmp_scan0	finds the first 0 bit from the specified position
gmp_scan1	finds the first 1 bit from the specified position
gmp_random_bits	generates a random-bit BigInt (needs a global seed; not suitable as an instance method)
gmp_random_range	random BigInt in a range (needs a global seed; not suitable as an instance method)
gmp_random_seed	sets the random seed (global state; not suitable as an instance method)
gmp_import	imports from a binary string
gmp_export	exports to a binary string

toString enhancement

Missing feature	Description
toString($base)	the current toString() only supports decimal. GMP's gmp_strval supports base 2-62 output

Update log

• 2026-05-27: initial version, compared against PHP 8.4.14 GMP extension