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FMA(3)                 FreeBSD Library Functions Manual                 FMA(3)

NAME
     fma, fmaf - 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);

DESCRIPTION
     The fma() and fmaf() 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 and FP_FAST_FMAF may be defined in <math.h> to indicate that
     fma() and fmaf() (respectively) have comparable or faster speed than a
     multiply operation followed by an add operation.

IMPLEMENTATION NOTES
     In general, fma() and fmaf() 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() and fmaf() 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
     These routines first appeared in FreeBSD 5.4.

FreeBSD 11.0-PRERELEASE        January 22, 2005        FreeBSD 11.0-PRERELEASE

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

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