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.
Function: void mpz_cdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
Function: void mpz_cdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
Function: void mpz_cdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
Function: unsigned long int mpz_cdiv_q_ui (mpz_t q, const mpz_t n, unsigned long int d)
Function: unsigned long int mpz_cdiv_r_ui (mpz_t r, const mpz_t n, unsigned long int d)
Function: unsigned long int mpz_cdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long int d)
Function: unsigned long int mpz_cdiv_ui (const mpz_t n, unsigned long int d)
Function: void mpz_cdiv_q_2exp (mpz_t q, const mpz_t n, mp_bitcnt_t b)
Function: void mpz_cdiv_r_2exp (mpz_t r, const mpz_t n, mp_bitcnt_t b)
Function: void mpz_fdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
Function: void mpz_fdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
Function: void mpz_fdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
Function: unsigned long int mpz_fdiv_q_ui (mpz_t q, const mpz_t n, unsigned long int d)
Function: unsigned long int mpz_fdiv_r_ui (mpz_t r, const mpz_t n, unsigned long int d)
Function: unsigned long int mpz_fdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long int d)
Function: unsigned long int mpz_fdiv_ui (const mpz_t n, unsigned long int d)
Function: void mpz_fdiv_q_2exp (mpz_t q, const mpz_t n, mp_bitcnt_t b)
Function: void mpz_fdiv_r_2exp (mpz_t r, const mpz_t n, mp_bitcnt_t b)
Function: void mpz_tdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
Function: void mpz_tdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
Function: void mpz_tdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
Function: unsigned long int mpz_tdiv_q_ui (mpz_t q, const mpz_t n, unsigned long int d)
Function: unsigned long int mpz_tdiv_r_ui (mpz_t r, const mpz_t n, unsigned long int d)
Function: unsigned long int mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long int d)
Function: unsigned long int mpz_tdiv_ui (const mpz_t n, unsigned long int d)
Function: void mpz_tdiv_q_2exp (mpz_t q, const mpz_t n, mp_bitcnt_t b)
Function: void mpz_tdiv_r_2exp (mpz_t r, const mpz_t n, mp_bitcnt_t b)
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.
For the 2exp variants the divisor is 2^b. These functions are implemented as right shifts and bit masks, but of course they round 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.
