Updated: 2022/Sep/29

```FMA(3)                     Library Functions Manual                     FMA(3)

NAME
fma, fmaf, fmal - fused multiply-add

LIBRARY
Math Library (libm, -lm)

SYNOPSIS
#include <math.h>

double
fma(double x, double y, double z);

float
fmaf(float x, float y, float z);

long double
fmal(long double x, long double y, long double z);

DESCRIPTION
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
intermediate product and one for the final result.

For instance, the expression 1.2e100 * 2.0e208 - 1.4e308 produces
infinity 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
performance 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.

IMPLEMENTATION NOTES
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.

fenv(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.

HISTORY
The fma() and fmaf() routines first appeared in FreeBSD 5.4, and fmal()
appeared in FreeBSD 6.0.  The fma(), fmaf() and fmal() routines were
imported into NetBSD in NetBSD 7.0.

NetBSD 9.99                   September 27, 2017                   NetBSD 9.99
```