1.\" Copyright (c) 2005 David Schultz <das@FreeBSD.org> 2.\" All rights reserved. 3.\" 4.\" Redistribution and use in source and binary forms, with or without 5.\" modification, are permitted provided that the following conditions 6.\" are met: 7.\" 1. Redistributions of source code must retain the above copyright 8.\" notice, this list of conditions and the following disclaimer. 9.\" 2. Redistributions in binary form must reproduce the above copyright 10.\" notice, this list of conditions and the following disclaimer in the 11.\" documentation and/or other materials provided with the distribution. 12.\" 13.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 14.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 15.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 16.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 17.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 18.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 19.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 20.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 21.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 22.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 23.\" SUCH DAMAGE. 24.\" 25.\" $FreeBSD$ 26.\" 27.Dd January 22, 2005 28.Dt FMA 3 29.Os 30.Sh NAME 31.Nm fma , 32.Nm fmaf , 33.Nm fmal 34.Nd fused multiply-add 35.Sh LIBRARY 36.Lb libm 37.Sh SYNOPSIS 38.In math.h 39.Ft double 40.Fn fma "double x" "double y" "double z" 41.Ft float 42.Fn fmaf "float x" "float y" "float z" 43.Ft long double 44.Fn fmal "long double x" "long double y" "long double z" 45.Sh DESCRIPTION 46The 47.Fn fma , 48.Fn fmaf , 49and 50.Fn fmal 51functions return 52.No "(x * y) + z" , 53computed with only one rounding error. 54Using the ordinary multiplication and addition operators, by contrast, 55results in two roundings: one for the intermediate product and one for 56the final result. 57.Pp 58For instance, the expression 59.No "1.2e100 * 2.0e208 - 1.4e308" 60produces \*(If due to overflow in the intermediate product, whereas 61.No "fma(1.2e100, 2.0e208, -1.4e308)" 62returns approximately 1.0e308. 63.Pp 64The fused multiply-add operation is often used to improve the 65accuracy of calculations such as dot products. 66It may also be used to improve performance on machines that implement 67it natively. 68The macros 69.Dv FP_FAST_FMA , 70.Dv FP_FAST_FMAF 71and 72.Dv FP_FAST_FMAL 73may be defined in 74.In math.h 75to indicate that 76.Fn fma , 77.Fn fmaf , 78and 79.Fn fmal 80(respectively) have comparable or faster speed than a multiply 81operation followed by an add operation. 82.Sh IMPLEMENTATION NOTES 83In general, these routines will behave as one would expect if 84.No "x * y + z" 85were computed with unbounded precision and range, 86then rounded to the precision of the return type. 87However, on some platforms, if 88.Fa z 89is \*(Na, these functions may not raise an exception even 90when the computation of 91.No "x * y" 92would have otherwise generated an invalid exception. 93.Sh SEE ALSO 94.Xr fenv 3 , 95.Xr math 3 96.Sh STANDARDS 97The 98.Fn fma , 99.Fn fmaf , 100and 101.Fn fmal 102functions conform to 103.St -isoC-99 . 104A fused multiply-add operation with virtually identical 105characteristics appears in IEEE draft standard 754R. 106.Sh HISTORY 107The 108.Fn fma 109and 110.Fn fmaf 111routines first appeared in 112.Fx 5.4 , 113and 114.Fn fmal 115appeared in 116.Fx 6.0 . 117