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. 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.Dd March 30, 2008 29.Dt REMAINDER 3 30.Os 31.Sh NAME 32.Nm remainder , 33.Nm remainderf , 34.Nm remainderl , 35.Nm remquo , 36.Nm remquof , 37.Nm remquol 38.Nd minimal residue functions 39.Sh LIBRARY 40.Lb libm 41.Sh SYNOPSIS 42.In math.h 43.Ft double 44.Fn remainder "double x" "double y" 45.Ft float 46.Fn remainderf "float x" "float y" 47.Ft long double 48.Fn remainderl "long double x" "long double y" 49.Ft double 50.Fn remquo "double x" "double y" "int *quo" 51.Ft float 52.Fn remquof "float x" "float y" "int *quo" 53.Ft long double 54.Fn remquol "long double x" "long double y" "int *quo" 55.Sh DESCRIPTION 56.Fn remainder , 57.Fn remainderf , 58.Fn remainderl , 59.Fn remquo , 60.Fn remquof , 61and 62.Fn remquol 63return the remainder 64.Fa r 65:= 66.Fa x 67\- 68.Fa n\(**y 69where 70.Fa n 71is the integer nearest the exact value of 72.Bk -words 73.Fa x Ns / Ns Fa y ; 74.Ek 75moreover if 76.Pf \*(Ba Fa n 77\- 78.Sm off 79.Fa x No / Fa y No \*(Ba 80.Sm on 81= 821/2 83then 84.Fa n 85is even. 86Consequently 87the remainder is computed exactly and 88.Sm off 89.Pf \*(Ba Fa r No \*(Ba 90.Sm on 91\*(Le 92.Sm off 93.Pf \*(Ba Fa y No \*(Ba/2 . 94.Sm on 95But attempting to take the remainder when 96.Fa y 97is 0 or 98.Fa x 99is \*(Pm\*(If is an invalid operation that produces a \*(Na. 100.Pp 101The 102.Fn remquo , 103.Fn remquof , 104and 105.Fn remquol 106functions also store the last 107.Va k 108bits of 109.Fa n 110in the location pointed to by 111.Fa quo , 112provided that 113.Fa n 114exists. 115The number of bits 116.Va k 117is platform-specific, but is guaranteed to be at least 3. 118.Sh SEE ALSO 119.Xr fmod 3 , 120.Xr ieee 3 , 121.Xr math 3 122.Sh STANDARDS 123The 124.Fn remainder , 125.Fn remainderf , 126.Fn remainderl , 127.Fn remquo , 128.Fn remquof , 129and 130.Fn remquol 131routines conform to 132.St -isoC-99 . 133The remainder is as defined in 134.St -ieee754 . 135.Sh HISTORY 136The 137.Fn remainder 138and 139.Fn remainderf 140functions appeared in 141.Bx 4.3 142and 143.Fx 2.0 , 144respectively. 145The 146.Fn remquo 147and 148.Fn remquof 149functions were added in 150.Fx 6.0 , 151and 152.Fn remainderl 153and 154.Fn remquol 155were added in 156.Fx 8.0 . 157