| .\" 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 $ |
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| .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 . |