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.\" 4. Neither the name of the University nor the names of its contributors 13.\" may be used to endorse or promote products derived from this software 14.\" without specific prior written permission. 15.\" 16.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 17.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 20.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26.\" SUCH DAMAGE. 27.\" 28.\" from: @(#)ieee.3 6.4 (Berkeley) 5/6/91 29.\" $FreeBSD$ 30.\" 31.Dd March 30, 2008 32.Dt REMAINDER 3 33.Os 34.Sh NAME 35.Nm remainder , 36.Nm remainderf , 37.Nm remainderl , 38.Nm remquo , 39.Nm remquof , 40.Nm remquol 41.Nd minimal residue functions 42.Sh LIBRARY 43.Lb libm 44.Sh SYNOPSIS 45.In math.h 46.Ft double 47.Fn remainder "double x" "double y" 48.Ft float 49.Fn remainderf "float x" "float y" 50.Ft long double 51.Fn remainderl "long double x" "long double 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.Ft long double 57.Fn remquol "long double x" "long double y" "int *quo" 58.Sh DESCRIPTION 59.Fn remainder , 60.Fn remainderf , 61.Fn remainderl , 62.Fn remquo , 63.Fn remquof , 64and 65.Fn remquol 66return the remainder 67.Fa r 68:= 69.Fa x 70\- 71.Fa n\(**y 72where 73.Fa n 74is the integer nearest the exact value of 75.Bk -words 76.Fa x Ns / Ns Fa y ; 77.Ek 78moreover if 79.Pf \\*(Ba Fa n 80\- 81.Sm off 82.Fa x No / Fa y No \\*(Ba 83.Sm on 84= 851/2 86then 87.Fa n 88is even. 89Consequently 90the remainder is computed exactly and 91.Sm off 92.Pf \\*(Ba Fa r No \\*(Ba 93.Sm on 94\*(Le 95.Sm off 96.Pf \\*(Ba Fa y No \\*(Ba/2 . 97.Sm on 98But attempting to take the remainder when 99.Fa y 100is 0 or 101.Fa x 102is \*(Pm\*(If is an invalid operation that produces a \*(Na. 103.Pp 104The 105.Fn remquo , 106.Fn remquof , 107and 108.Fn remquol 109functions also store the last 110.Va k 111bits of 112.Fa n 113in the location pointed to by 114.Fa quo , 115provided that 116.Fa n 117exists. 118The number of bits 119.Va k 120is platform-specific, but is guaranteed to be at least 3. 121.Sh SEE ALSO 122.Xr fmod 3 , 123.Xr ieee 3 , 124.Xr math 3 125.Sh STANDARDS 126The 127.Fn remainder , 128.Fn remainderf , 129.Fn remainderl , 130.Fn remquo , 131.Fn remquof , 132and 133.Fn remquol 134routines conform to 135.St -isoC-99 . 136The remainder is as defined in 137.St -ieee754 . 138.Sh HISTORY 139The 140.Fn remainder 141and 142.Fn remainderf 143functions appeared in 144.Bx 4.3 145and 146.Fx 2.0 , 147respectively. 148The 149.Fn remquo 150and 151.Fn remquof 152functions were added in 153.Fx 6.0 , 154and 155.Fn remainderl 156and 157.Fn remquol 158were added in 159.Fx 8.0 . 160