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Division Functions

Division is undefined if the divisor is zero. Passing a zero divisor to the division or modulo functions (including the modular powering functions mpz_powm and mpz_powm_ui), will cause an intentional division by zero. This lets a program handle arithmetic exceptions in these functions the same way as for normal C int arithmetic.

void mpz_cdiv_q (mpz_t q, mpz_t n, mpz_t d)	Function
void mpz_cdiv_r (mpz_t r, mpz_t n, mpz_t d)	Function
void mpz_cdiv_qr (mpz_t q, mpz_t r, mpz_t n, mpz_t d)	Function

unsigned long int mpz_cdiv_q_ui (mpz_t q, mpz_t n, unsigned long int d)	Function
unsigned long int mpz_cdiv_r_ui (mpz_t r, mpz_t n, unsigned long int d)	Function
unsigned long int mpz_cdiv_qr_ui (mpz_t q, mpz_t r, mpz_t n, unsigned long int d)	Function
unsigned long int mpz_cdiv_ui (mpz_t n, unsigned long int d)	Function

void mpz_cdiv_q_2exp (mpz_t q, mpz_t n, unsigned long int b)	Function
void mpz_cdiv_r_2exp (mpz_t r, mpz_t n, unsigned long int b)	Function

void mpz_fdiv_q (mpz_t q, mpz_t n, mpz_t d)	Function
void mpz_fdiv_r (mpz_t r, mpz_t n, mpz_t d)	Function
void mpz_fdiv_qr (mpz_t q, mpz_t r, mpz_t n, mpz_t d)	Function

unsigned long int mpz_fdiv_q_ui (mpz_t q, mpz_t n, unsigned long int d)	Function
unsigned long int mpz_fdiv_r_ui (mpz_t r, mpz_t n, unsigned long int d)	Function
unsigned long int mpz_fdiv_qr_ui (mpz_t q, mpz_t r, mpz_t n, unsigned long int d)	Function
unsigned long int mpz_fdiv_ui (mpz_t n, unsigned long int d)	Function

void mpz_fdiv_q_2exp (mpz_t q, mpz_t n, unsigned long int b)	Function
void mpz_fdiv_r_2exp (mpz_t r, mpz_t n, unsigned long int b)	Function

void mpz_tdiv_q (mpz_t q, mpz_t n, mpz_t d)	Function
void mpz_tdiv_r (mpz_t r, mpz_t n, mpz_t d)	Function
void mpz_tdiv_qr (mpz_t q, mpz_t r, mpz_t n, mpz_t d)	Function

unsigned long int mpz_tdiv_q_ui (mpz_t q, mpz_t n, unsigned long int d)	Function
unsigned long int mpz_tdiv_r_ui (mpz_t r, mpz_t n, unsigned long int d)	Function
unsigned long int mpz_tdiv_qr_ui (mpz_t q, mpz_t r, mpz_t n, unsigned long int d)	Function
unsigned long int mpz_tdiv_ui (mpz_t n, unsigned long int d)	Function

void mpz_tdiv_q_2exp (mpz_t q, mpz_t n, unsigned long int b)	Function
void mpz_tdiv_r_2exp (mpz_t r, mpz_t n, unsigned long int b)	Function

Divide n by d, forming a quotient q and/or remainder r. For the 2exp functions, d=2^b. The rounding is in three styles, each suiting different applications. cdiv rounds q up towards +infinity, and r will have the opposite sign to d. The c stands for "ceil". fdiv rounds q down towards -infinity, and r will have the same sign as d. The f stands for "floor". tdiv rounds q towards zero, and r will have the same sign as n. The t stands for "truncate". In all cases q and r will satisfy n=q*d+r, and r will satisfy 0<=abs(r)<abs(d). The q functions calculate only the quotient, the r functions only the remainder, and the qr functions calculate both. Note that for qr the same variable cannot be passed for both q and r, or results will be unpredictable. For the ui variants the return value is the remainder, and in fact returning the remainder is all the div_ui functions do. For tdiv and cdiv the remainder can be negative, so for those the return value is the absolute value of the remainder. The 2exp functions are right shifts and bit masks, but of course rounding the same as the other functions. For positive n both mpz_fdiv_q_2exp and mpz_tdiv_q_2exp are simple bitwise right shifts. For negative n, mpz_fdiv_q_2exp is effectively an arithmetic right shift treating n as twos complement the same as the bitwise logical functions do, whereas mpz_tdiv_q_2exp effectively treats n as sign and magnitude.

void mpz_mod (mpz_t r, mpz_t n, mpz_t d)	Function
unsigned long int mpz_mod_ui (mpz_t r, mpz_t n, unsigned long int d)	Function

Set r to n mod d. The sign of the divisor is ignored; the result is always non-negative. mpz_mod_ui is identical to mpz_fdiv_r_ui above, returning the remainder as well as setting r. See mpz_fdiv_ui above if only the return value is wanted.

void mpz_divexact (mpz_t q, mpz_t n, mpz_t d)	Function
void mpz_divexact_ui (mpz_t q, mpz_t n, unsigned long d)	Function

Set q to n/d. These functions produce correct results only when it is known in advance that d divides n. These routines are much faster than the other division functions, and are the best choice when exact division is known to occur, for example reducing a rational to lowest terms.

int mpz_divisible_p (mpz_t n, mpz_t d)	Function
int mpz_divisible_ui_p (mpz_t n, unsigned long int d)	Function
int mpz_divisible_2exp_p (mpz_t n, unsigned long int b)	Function

Return non-zero if n is exactly divisible by d, or in the case of mpz_divisible_2exp_p by 2^b.

int mpz_congruent_p (mpz_t n, mpz_t c, mpz_t d)	Function
int mpz_congruent_ui_p (mpz_t n, unsigned long int c, unsigned long int d)	Function
int mpz_congruent_2exp_p (mpz_t n, mpz_t c, unsigned long int b)	Function

Return non-zero if n is congruent to c modulo d, or in the case of mpz_congruent_2exp_p modulo 2^b.