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fma, fmaf, fmal - fused multiply-add

 

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 ∞ 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 #include <math.h>
      to indicate that fma(), fmaf(), and fmal() (respectively) have comparable
      or faster speed than a multiply operation followed by an add operation.
      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.
 

Sections

Based on BSD UNIX
FreeBSD is an advanced operating system for x86 compatible (including Pentium and Athlon), amd64 compatible (including Opteron, Athlon64, and EM64T), UltraSPARC, IA-64, PC-98 and ARM architectures. It is derived from BSD, the version of UNIX developed at the University of California, Berkeley. It is developed and maintained by a large team of individuals. Additional platforms are in various stages of development.