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Set rop to op1 + op2 rounded in the direction
rnd. The IEEE 754 rules are used, in particular for signed zeros.
But for types having no signed zeros, 0 is considered unsigned
(i.e., (+0) + 0 = (+0) and (−0) + 0 = (−0)).
The mpfr_add_d function assumes that the radix of the double type
is a power of 2, with a precision at most that declared by the C implementation
(macro IEEE_DBL_MANT_DIG, and if not defined 53 bits).
Set rop to op1 − op2 rounded in the direction
rnd. The IEEE 754 rules are used, in particular for signed zeros.
But for types having no signed zeros, 0 is considered unsigned
(i.e., (+0) − 0 = (+0), (−0) − 0 = (−0),
0 − (+0) = (−0) and 0 − (−0) = (+0)).
The same restrictions as for mpfr_add_d apply to mpfr_d_sub
and mpfr_sub_d.
Set rop to op1 times op2 rounded in the
direction rnd.
When a result is zero, its sign is the product of the signs of the operands
(for types having no signed zeros, 0 is considered positive).
The same restrictions as for mpfr_add_d apply to mpfr_mul_d.
Note: when op1 and op2 are equal, use mpfr_sqr instead of
mpfr_mul for better efficiency.
Set rop to the square of op rounded in the direction rnd.
Set rop to op1 / op2 rounded in the direction rnd.
When a result is zero, its sign is the product of the signs of the operands.
For types having no signed zeros, 0 is considered positive; but note that if
op1 is non-zero and op2 is zero, the result might change from
±Inf to NaN in future MPFR versions if there is an opposite decision
on the IEEE 754 side.
The same restrictions as for mpfr_add_d apply to mpfr_d_div
and mpfr_div_d.
Set rop to the square root of op
rounded in the direction rnd. Set rop to −0 if
op is −0, to be consistent with the IEEE 754 standard
(thus this differs from mpfr_rootn_ui and mpfr_rootn_si
with n = 2).
Set rop to NaN if op is negative.
Set rop to the reciprocal square root of op
rounded in the direction rnd. Set rop to +Inf if op is
±0, +0 if op is +Inf, and NaN if op is negative.
Warning! Therefore the result on −0 is different from the one of the
rSqrt function recommended by the IEEE 754 standard (Section 9.2.1),
which is −Inf instead of +Inf. However, mpfr_rec_sqrt is
equivalent to mpfr_rootn_si with n = −2.
Set rop to the nth root (with n = 3, the cubic root,
for mpfr_cbrt) of op rounded in the direction rnd.
For n = 0, set rop to NaN.
For n odd (resp. even) and op negative (including −Inf),
set rop to a negative number (resp. NaN).
If op is zero, set rop to zero with the sign obtained by the
usual limit rules, i.e., the same sign as op if n is odd, and
positive if n is even.
These functions agree with the rootn operation of the IEEE 754 standard.
This function is the same as mpfr_rootn_ui except when op
is −0 and n is even: the result is −0 instead of +0
(the reason was to be consistent with mpfr_sqrt). Said otherwise,
if op is zero, set rop to op.
This function predates IEEE 754-2008, where rootn was introduced, and behaves differently from the IEEE 754 rootn operation. It is marked as deprecated and will be removed in a future release.
Set rop to −op and the absolute value of op respectively, rounded in the direction rnd. Just changes or adjusts the sign if rop and op are the same variable, otherwise a rounding might occur if the precision of rop is less than that of op.
The sign rule also applies to NaN in order to mimic the IEEE 754
negate and abs operations, i.e., for mpfr_neg, the
sign is reversed, and for mpfr_abs, the sign is set to positive.
But contrary to IEEE 754, the NaN flag is set as usual.
Set rop to the positive difference of op1 and op2, i.e., op1 − op2 rounded in the direction rnd if op1 > op2, +0 if op1 <= op2, and NaN if op1 or op2 is NaN.
Set rop to op1 times 2 raised to op2 rounded in the direction rnd. Just increases the exponent by op2 when rop and op1 are identical.
Set rop to op1 divided by 2 raised to op2 rounded in the direction rnd. Just decreases the exponent by op2 when rop and op1 are identical.
Set rop to the factorial of op, rounded in the direction rnd.
Set rop to (op1 times op2) + op3 (resp. (op1 times op2) − op3) rounded in the direction rnd. Concerning special values (signed zeros, infinities, NaN), these functions behave like a multiplication followed by a separate addition or subtraction. That is, the fused operation matters only for rounding.
Set rop to (op1 times op2) + (op3 times op4) (resp. (op1 times op2) − (op3 times op4)) rounded in the direction rnd. In case the computation of op1 times op2 overflows or underflows (or that of op3 times op4), the result rop is computed as if the two intermediate products were computed with rounding toward zero.
Set rop to the Euclidean norm of x and y, i.e., the square root of the sum of the squares of x and y, rounded in the direction rnd. Special values are handled as described in the ISO C99 (Section F.9.4.3) and IEEE 754 (Section 9.2.1) standards: If x or y is an infinity, then +Inf is returned in rop, even if the other number is NaN.
Set rop to the sum of all elements of tab, whose size is n,
correctly rounded in the direction rnd. Warning: for efficiency reasons,
tab is an array of pointers
to mpfr_t, not an array of mpfr_t.
If n = 0, then the result is +0, and if n = 1,
then the function is equivalent to mpfr_set.
For the special exact cases, the result is the same as the one obtained
with a succession of additions (mpfr_add) in infinite precision.
In particular, if the result is an exact zero and n >= 1:
MPFR_RNDD rounding mode, where it is −0.
Set rop to the dot product of elements of a by those of b,
whose common size is n,
correctly rounded in the direction rnd. Warning: for efficiency reasons,
a and b are arrays of pointers to mpfr_t.
This function is experimental, and does not yet handle intermediate overflows
and underflows.
For the power functions (with an integer exponent or not), see mpfr_pow in Transcendental Functions.
Next: Comparison Functions, Previous: Conversion Functions, Up: MPFR Interface [Index]