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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.

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 5.5.

FreeBSD	6.0		       January 22, 2005			   FreeBSD 6.0

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

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