1.\" Copyright (c) 1985, 1991 Regents of the University of California. 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.\" 3. All advertising materials mentioning features or use of this software 13.\" must display the following acknowledgement: 14.\" This product includes software developed by the University of 15.\" California, Berkeley and its contributors. 16.\" 4. Neither the name of the University nor the names of its contributors 17.\" may be used to endorse or promote products derived from this software 18.\" without specific prior written permission. 19.\" 20.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 21.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 22.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 23.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 24.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 25.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 26.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 27.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 28.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 29.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 30.\" SUCH DAMAGE. 31.\" 32.\" from: @(#)ieee.3 6.4 (Berkeley) 5/6/91 33.\" $FreeBSD$ 34.\" 35.Dd March 24, 2005 36.Dt REMAINDER 3 37.Os 38.Sh NAME 39.Nm remainder , 40.Nm remainderf , 41.Nm remquo , 42.Nm remquof 43.Nd minimal residue functions 44.Sh LIBRARY 45.Lb libm 46.Sh SYNOPSIS 47.In math.h 48.Ft double 49.Fn remainder "double x" "double y" 50.Ft float 51.Fn remainderf "float x" "float y" 52.Ft double 53.Fn remquo "double x" "double y" "int *quo" 54.Ft float 55.Fn remquof "float x" "float y" "int *quo" 56.Sh DESCRIPTION 57.Fn remainder , 58.Fn remainderf , 59.Fn remquo , 60and 61.Fn remquof 62return the remainder 63.Fa r 64:= 65.Fa x 66\- 67.Fa n\(**y 68where 69.Fa n 70is the integer nearest the exact value of 71.Bk -words 72.Fa x Ns / Ns Fa y ; 73.Ek 74moreover if 75.Pf \\*(Ba Fa n 76\- 77.Sm off 78.Fa x No / Fa y No \\*(Ba 79.Sm on 80= 811/2 82then 83.Fa n 84is even. 85Consequently 86the remainder is computed exactly and 87.Sm off 88.Pf \\*(Ba Fa r No \\*(Ba 89.Sm on 90\*(Le 91.Sm off 92.Pf \\*(Ba Fa y No \\*(Ba/2 . 93.Sm on 94But attempting to take the remainder when 95.Fa y 96is 0 or 97.Fa x 98is \*(Pm\*(If is an invalid operation that produces a \*(Na. 99.Pp 100The 101.Fn remquo 102and 103.Fn remquof 104functions also store the last 105.Va k 106bits of 107.Fa n 108in the location pointed to by 109.Fa quo , 110provided that 111.Fa n 112exists. 113The number of bits 114.Va k 115is platform-specific, but is guaranteed to be at least 3. 116.Sh SEE ALSO 117.Xr fmod 3 , 118.Xr ieee 3 , 119.Xr math 3 120.Sh STANDARDS 121The 122.Fn remainder , 123.Fn remainderf , 124.Fn remquo , 125and 126.Fn remquof 127routines conform to 128.St -isoC-99 . 129The remainder is as defined in 130.St -ieee754 . 131.Sh HISTORY 132The 133.Fn remainder 134and 135.Fn remainderf 136functions appeared in 137.Bx 4.3 138and 139.Fx 2.0 , 140respectively. 141The 142.Fn remquo 143and 144.Fn remquof 145functions were added in 146.Fx 6.0 . 147