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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  in-
       finity	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 compara-
       ble or faster speed than	a multiply operation followed by an add	opera-
       tion.

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.

SEE ALSO
       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	14.3		       January 22, 2005				FMA(3)

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