.\" Copyright (c) 2005 David Schultz <das@FreeBSD.org> | |

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.\" $FreeBSD: src/lib/msun/man/fma.3,v 1.3 2005/11/24 09:25:10 joel Exp $ | |

.\" | |

.Dd January 22, 2005 | |

.Dt FMA 3 | |

.Os | |

.Sh NAME | |

.Nm fma , | |

.Nm fmaf , | |

.Nm fmal | |

.Nd fused multiply-add | |

.Sh LIBRARY | |

.Lb libm | |

.Sh SYNOPSIS | |

.In math.h | |

.Ft double | |

.Fn fma "double x" "double y" "double z" | |

.Ft float | |

.Fn fmaf "float x" "float y" "float z" | |

.Ft long double | |

.Fn fmal "long double x" "long double y" "long double z" | |

.Sh DESCRIPTION | |

The | |

.Fn fma , | |

.Fn fmaf , | |

and | |

.Fn fmal | |

functions return | |

.No "(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. | |

.Pp | |

For instance, the expression | |

.No "1.2e100 * 2.0e208 - 1.4e308" | |

produces \*(If due to overflow in the intermediate product, whereas | |

.No "fma(1.2e100, 2.0e208, -1.4e308)" | |

returns approximately 1.0e308. | |

.Pp | |

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 | |

.Dv FP_FAST_FMA , | |

.Dv FP_FAST_FMAF | |

and | |

.Dv FP_FAST_FMAL | |

may be defined in | |

.In math.h | |

to indicate that | |

.Fn fma , | |

.Fn fmaf , | |

and | |

.Fn fmal | |

(respectively) have comparable or faster speed than a multiply | |

operation followed by an add operation. | |

.Sh IMPLEMENTATION NOTES | |

In general, these routines will behave as one would expect if | |

.No "x * y + z" | |

were computed with unbounded precision and range, | |

then rounded to the precision of the return type. | |

However, on some platforms, if | |

.Fa z | |

is \*(Na, these functions may not raise an exception even | |

when the computation of | |

.No "x * y" | |

would have otherwise generated an invalid exception. | |

.Sh SEE ALSO | |

.Xr fenv 3 , | |

.Xr math 3 | |

.Sh STANDARDS | |

The | |

.Fn fma , | |

.Fn fmaf , | |

and | |

.Fn fmal | |

functions conform to | |

.St -isoC-99 . | |

A fused multiply-add operation with virtually identical | |

characteristics appears in IEEE draft standard 754R. | |

.Sh HISTORY | |

The | |

.Fn fma | |

and | |

.Fn fmaf | |

routines first appeared in | |

.Fx 5.4 , | |

and | |

.Fn fmal | |

appeared in | |

.Fx 6.0 . |