Next: Rounding-Related Functions, Previous: Formatted Output Functions, Up: MPFR Interface [Index]
Set rop to op rounded to an integer.
mpfr_rint rounds to the nearest representable integer in the
given direction rnd, and the other five functions behave in a
similar way with some fixed rounding mode:
mpfr_ceil: to the next higher or equal representable integer
(like mpfr_rint with MPFR_RNDU);
mpfr_floor to the next lower or equal representable integer
(like mpfr_rint with MPFR_RNDD);
mpfr_round to the nearest representable integer,
rounding halfway cases away from zero
(as in the roundTiesToAway mode of IEEE 754);
mpfr_roundeven to the nearest representable integer,
rounding halfway cases with the even-rounding rule
(like mpfr_rint with MPFR_RNDN);
mpfr_trunc to the next representable integer toward zero
(like mpfr_rint with MPFR_RNDZ).
When op is a zero or an infinity, set rop to the same value (with the same sign).
The return value is zero when the result is exact, positive when it is greater than the original value of op, and negative when it is smaller. More precisely, the return value is 0 when op is an integer representable in rop, 1 or −1 when op is an integer that is not representable in rop, 2 or −2 when op is not an integer.
When op is NaN, the NaN flag is set as usual. In the other cases,
the inexact flag is set when rop differs from op, following
the ISO C99 rule for the rint function. If you want the behavior to
be more like IEEE 754 / ISO TS 18661-1, i.e., the usual behavior
where the round-to-integer function is regarded as any other mathematical
function, you should use one of the mpfr_rint_* functions instead.
Note that no double rounding is performed; for instance, 10.5 (1010.1 in
binary) is rounded by mpfr_rint with rounding to nearest to 12 (1100
in binary) in 2-bit precision, because the two enclosing numbers representable
on two bits are 8 and 12, and the closest is 12.
(If one first rounded to an integer, one would round 10.5 to 10 with
even rounding, and then 10 would be rounded to 8 again with even rounding.)
Set rop to op rounded to an integer:
mpfr_rint_ceil: to the next higher or equal integer;
mpfr_rint_floor: to the next lower or equal integer;
mpfr_rint_round: to the nearest integer,
rounding halfway cases away from zero;
mpfr_rint_roundeven: to the nearest integer,
rounding halfway cases to the nearest even integer;
mpfr_rint_trunc to the next integer toward zero.
If the result is not representable, it is rounded in the direction rnd. When op is a zero or an infinity, set rop to the same value (with the same sign). The return value is the ternary value associated with the considered round-to-integer function (regarded in the same way as any other mathematical function).
Contrary to mpfr_rint, those functions do perform a double rounding:
first op is rounded to the nearest integer in the direction given by
the function name, then this nearest integer (if not representable) is
rounded in the given direction rnd. Thus these round-to-integer
functions behave more like the other mathematical functions, i.e., the
returned result is the correct rounding of the exact result of the function
in the real numbers.
For example, mpfr_rint_round with rounding to nearest and a precision
of two bits rounds 6.5 to 7 (halfway cases away from zero), then 7 is
rounded to 8 by the round-even rule, despite the fact that 6 is also
representable on two bits, and is closer to 6.5 than 8.
Set rop to the fractional part of op, having the same sign as
op, rounded in the direction rnd (unlike in mpfr_rint,
rnd affects only how the exact fractional part is rounded, not how
the fractional part is generated).
When op is an integer or an infinity, set rop to zero with
the same sign as op.
Set simultaneously iop to the integral part of op and fop to
the fractional part of op, rounded in the direction rnd with the
corresponding precision of iop and fop (equivalent to
mpfr_trunc(iop, op, rnd) and
mpfr_frac(fop, op, rnd)). The variables iop and
fop must be different. Return 0 iff both results are exact (see
mpfr_sin_cos for a more detailed description of the return value).
Set r to the value of x − ny, rounded
according to the direction rnd, where n is the integer quotient
of x divided by y, defined as follows: n is rounded
toward zero for mpfr_fmod, mpfr_fmod_ui and mpfr_fmodquo,
and to the nearest integer (ties rounded to even) for mpfr_remainder
and mpfr_remquo.
Special values are handled as described in Section F.9.7.1 of the ISO C99 standard: If x is infinite or y is zero, r is NaN. If y is infinite and x is finite, r is x rounded to the precision of r. If r is zero, it has the sign of x. The return value is the ternary value corresponding to r.
Additionally, mpfr_fmodquo and mpfr_remquo store
the low significant bits from the quotient n in *q
(more precisely the number of bits in a long int minus one),
with the sign of x divided by y
(except if those low bits are all zero, in which case zero is returned).
If the result is NaN, the value of *q is unspecified.
Note that x may be so large in magnitude relative to y that an
exact representation of the quotient is not practical.
The mpfr_remainder and mpfr_remquo functions are useful for
additive argument reduction.
Return non-zero iff op is an integer.
Next: Rounding-Related Functions, Previous: Formatted Output Functions, Up: MPFR Interface [Index]