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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 opera-
     tors, 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 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
     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 5.4		       January 22, 2005 		   FreeBSD 5.4

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