# FreeBSD Manual Pages

```FMA(3)		       FreeBSD 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 intermedi-
ate product and one for the final result.

For instance, the expression 1.2e100 * 2.0e208 - 1.4e308 produces infin-
ity 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.

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.

FreeBSD	Ports 11.2	       January 22, 2005		    FreeBSD Ports 11.2
```

NAME | LIBRARY | SYNOPSIS | DESCRIPTION | IMPLEMENTATION NOTES | SEE ALSO | STANDARDS | HISTORY

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