FMA(3) BSD Library Functions Manual FMA(3)NAME
fma, fmaf, fmal — fused multiply-add
Math Library (libm, -lm)
fma(double x, double y, double z);
fmaf(float x, float y, float z);
fmal(long double x, long double y, long double z);
The fma(), fmaf(), and fmal() functions return (x * y) + z, computed with
only one rounding error. Using the ordinary multiplication and addition
operators, by contrast, results in two roundings: one for the intermedi‐
ate product and one for the final result.
For instance, the expression 1.2e100 * 2.0e208 - 1.4e308 produces ∞ due
to overflow in the intermediate product, whereas fma(1.2e100, 2.0e208,
-1.4e308) returns approximately 1.0e308.
The fused multiply-add operation is often used to improve the accuracy of
calculations such as dot products. It may also be used to improve per‐
formance on machines that implement it natively. The macros FP_FAST_FMA,
FP_FAST_FMAF and FP_FAST_FMAL may be defined in <math.h> to indicate that
fma(), fmaf(), and fmal() (respectively) have comparable or faster speed
than a multiply operation followed by an add operation.
In general, these routines will behave as one would expect if x * y + z
were computed with unbounded precision and range, then rounded to the
precision of the return type. However, on some platforms, if z is NaN,
these functions may not raise an exception even when the computation of x
* y would have otherwise generated an invalid exception.
SEE ALSOfenv(3), math(3)STANDARDS
The fma(), fmaf(), and fmal() functions conform to ISO/IEC 9899:1999
(“ISO C99”). A fused multiply-add operation with virtually identical
characteristics appears in IEEE draft standard 754R.
The fma() and fmaf() routines first appeared in FreeBSD 5.4, and fmal()
appeared in FreeBSD 6.0.
BSD January 22, 2005 BSD