1.\" $OpenBSD: hypot.3,v 1.24 2016/04/27 06:44:54 jmc Exp $ 2.\" Copyright (c) 1985, 1991 Regents of the University of California. 3.\" All rights reserved. 4.\" 5.\" Redistribution and use in source and binary forms, with or without 6.\" modification, are permitted provided that the following conditions 7.\" are met: 8.\" 1. Redistributions of source code must retain the above copyright 9.\" notice, this list of conditions and the following disclaimer. 10.\" 2. Redistributions in binary form must reproduce the above copyright 11.\" notice, this list of conditions and the following disclaimer in the 12.\" documentation and/or other materials provided with the distribution. 13.\" 3. Neither the name of the University nor the names of its contributors 14.\" may be used to endorse or promote products derived from this software 15.\" without specific prior written permission. 16.\" 17.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 18.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 21.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 22.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 23.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 24.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 25.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 26.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 27.\" SUCH DAMAGE. 28.\" 29.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91 30.\" 31.Dd $Mdocdate: April 27 2016 $ 32.Dt HYPOT 3 33.Os 34.Sh NAME 35.Nm hypot , 36.Nm hypotf , 37.Nm hypotl , 38.Nm cabs , 39.Nm cabsf , 40.Nm cabsl 41.Nd Euclidean distance and complex absolute value functions 42.Sh SYNOPSIS 43.In math.h 44.Ft double 45.Fn hypot "double x" "double y" 46.Ft float 47.Fn hypotf "float x" "float y" 48.Ft long double 49.Fn hypotl "long double x" "long double y" 50.In complex.h 51.Ft double 52.Fn cabs "double complex z" 53.Ft float 54.Fn cabsf "float complex z" 55.Ft long double 56.Fn cabsl "long double complex z" 57.Sh DESCRIPTION 58The 59.Fn hypot , 60.Fn hypotf 61and 62.Fn hypotl 63functions 64compute the 65sqrt(x*x+y*y) 66in such a way that underflow will not happen, and overflow 67occurs only if the final result deserves it. 68.Pp 69.Fn hypot "infinity" "v" No = Fn hypot "v" "infinity" No = +infinity 70for all 71.Ar v , 72including NaN. 73.Pp 74The 75.Fn cabs , 76.Fn cabsf 77and 78.Fn cabsl 79functions return the absolute value of the complex number 80.Fa z . 81.Sh ERRORS (due to Roundoff, etc.) 82Below 0.97 83.Em ulps . 84Consequently 85.Fn hypot "5.0" "12.0" No = 13.0 86exactly; 87in general, hypot and cabs return an integer whenever an 88integer might be expected. 89.Sh NOTES 90As might be expected, 91.Fn hypot "v" "NaN" 92and 93.Fn hypot "NaN" "v" 94are NaN for all 95.Em finite 96.Ar v . 97Programmers might be surprised at first to discover that 98.Fn hypot "\(+-infinity" "NaN" No = +infinity . 99This is intentional; it happens because 100.Fn hypot "infinity" "v" No = +infinity 101for 102.Em all 103.Ar v , 104finite or infinite. 105Hence 106.Fn hypot "infinity" "v" 107is independent of 108.Ar v . 109The IEEE NaN is designed to disappear 110when it turns out to be irrelevant, as it does in 111.Fn hypot "infinity" "NaN" . 112.Sh SEE ALSO 113.Xr fpclassify 3 , 114.Xr sqrt 3 115.Sh HISTORY 116A 117.Fn hypot 118function first appeared in 119.At v3 , 120and 121.Fn cabs 122in 123.At v7 . 124