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.\" $NetBSD: hypot.3,v 1.19 2017/09/28 05:51:26 wiz Exp $ 30.\" 31.Dd September 26, 2017 32.Dt HYPOT 3 33.Os 34.Sh NAME 35.Nm hypot , 36.Nm hypotf , 37.Nm hypotl 38.Nd Euclidean distance and complex absolute value functions 39.Sh LIBRARY 40.Lb libm 41.Sh SYNOPSIS 42.In math.h 43.Ft double 44.Fn hypot "double x" "double y" 45.Ft float 46.Fn hypotf "float x" "float y" 47.Ft long double 48.Fn hypotl "long double x" "long double y" 49.In tgmath.h 50.Ft real-floating 51.Fn hypot "real-floating" "real-floating" 52.Sh DESCRIPTION 53The 54.Fn hypot 55functions 56compute the 57sqrt(x*x+y*y) 58in such a way that underflow will not happen, and overflow 59occurs only if the final result deserves it. 60.Pp 61.Fn hypot "\*(If" "v" 62= 63.Fn hypot "v" "\*(If" 64= +\*(If for all 65.Ar v , 66including \*(Na. 67.Sh ERRORS 68Below 0.97 69.Em ulps . 70Consequently 71.Fn hypot "5.0" "12.0" 72= 13.0 73exactly; 74in general, hypot returns an integer whenever an 75integer might be expected. 76.Pp 77The same cannot be said for the shorter and faster version of hypot 78that is provided in the comments in cabs.c; its error can 79exceed 1.2 80.Em ulps . 81.Sh NOTES 82As might be expected, 83.Fn hypot "v" "\*(Na" 84and 85.Fn hypot "\*(Na" "v" 86are \*(Na for all 87.Em finite 88.Ar v ; 89with "reserved operand" in place of "\*(Na", the 90same is true on a VAX. 91But programmers on machines other than a VAX 92(it has no \*(If) 93might be surprised at first to discover that 94.Fn hypot "\(+-\*(If" "\*(Na" 95= +\*(If. 96This is intentional; it happens because 97.Fn hypot "\*(If" "v" 98= +\*(If 99for 100.Em all 101.Ar v , 102finite or infinite. 103Hence 104.Fn hypot "\*(If" "v" 105is independent of 106.Ar v . 107Unlike the reserved operand fault on a VAX, the IEEE 108\*(Na is designed to 109disappear when it turns out to be irrelevant, as it does in 110.Fn hypot "\*(If" "\*(Na" . 111.Sh SEE ALSO 112.Xr math 3 , 113.Xr sqrt 3 114.Sh HISTORY 115The 116.Fn hypot 117appeared in 118.At v7 . 119