GNU Info
(gmp.info)Integer Division
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, 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)
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.
- Function: 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)
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.
- Function: 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)
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.
- Function: 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)
Return non-zero if N is exactly divisible by D, or in the case of
`mpz_divisible_2exp_p' by 2^B.
- Function: 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)
Return non-zero if N is congruent to C modulo D, or in the case of
`mpz_congruent_2exp_p' modulo 2^B.
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