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.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91 29.\" 30.Dd March 30, 2008 31.Dt HYPOT 3 32.Os 33.Sh NAME 34.Nm hypot , 35.Nm hypotf , 36.Nm hypotl , 37.Nm cabs , 38.Nm cabsf , 39.Nm cabsl 40.Nd Euclidean distance and complex absolute value functions 41.Sh LIBRARY 42.Lb libm 43.Sh SYNOPSIS 44.In math.h 45.Ft double 46.Fn hypot "double x" "double y" 47.Ft float 48.Fn hypotf "float x" "float y" 49.Ft "long double" 50.Fn hypotl "long double x" "long double y" 51.In complex.h 52.Ft double 53.Fn cabs "double complex z" 54.Ft float 55.Fn cabsf "float complex z" 56.Ft "long double" 57.Fn cabsl "long double complex z" 58.Sh DESCRIPTION 59The 60.Fn hypot , 61.Fn hypotf 62and 63.Fn hypotl 64functions 65compute the 66sqrt(x*x+y*y) 67in such a way that underflow will not happen, and overflow 68occurs only if the final result deserves it. 69The 70.Fn cabs , 71.Fn cabsf 72and 73.Fn cabsl 74functions compute the complex absolute value of 75.Fa z . 76.Pp 77.Fn hypot "\*(If" "v" 78= 79.Fn hypot "v" "\*(If" 80= +\*(If for all 81.Fa v , 82including \*(Na. 83.Sh ERROR (due to Roundoff, etc.) 84Below 0.97 85.Em ulps . 86Consequently 87.Fn hypot "5.0" "12.0" 88= 13.0 89exactly; 90in general, hypot and cabs return an integer whenever an 91integer might be expected. 92.Sh NOTES 93As might be expected, 94.Fn hypot "v" "\*(Na" 95and 96.Fn hypot "\*(Na" "v" 97are \*(Na for all 98.Em finite 99.Fa v . 100But programmers 101might be surprised at first to discover that 102.Fn hypot "\(+-\*(If" "\*(Na" 103= +\*(If. 104This is intentional; it happens because 105.Fn hypot "\*(If" "v" 106= +\*(If 107for 108.Em all 109.Fa v , 110finite or infinite. 111Hence 112.Fn hypot "\*(If" "v" 113is independent of 114.Fa v . 115Unlike the reserved operand fault on a 116.Tn VAX , 117the 118.Tn IEEE 119\*(Na is designed to 120disappear when it turns out to be irrelevant, as it does in 121.Fn hypot "\*(If" "\*(Na" . 122.Sh SEE ALSO 123.Xr carg 3 , 124.Xr math 3 , 125.Xr sqrt 3 126.Sh STANDARDS 127The 128.Fn hypot , 129.Fn hypotf , 130.Fn hypotl , 131.Fn cabs , 132.Fn cabsf , 133and 134.Fn cabsl 135functions conform to 136.St -isoC-99 . 137.Sh HISTORY 138Both a 139.Fn hypot 140function and a 141.Fn cabs 142function 143appeared in 144.At v7 . 145