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 1.17 2007/02/22 22:08:20 drochner Exp $ 30.\" 31.Dd February 12, 2007 32.Dt HYPOT 3 33.Os 34.Sh NAME 35.Nm hypot , 36.Nm hypotf 37.Nd Euclidean distance and complex absolute value functions 38.Sh LIBRARY 39.Lb libm 40.Sh SYNOPSIS 41.In math.h 42.Ft double 43.Fn hypot "double x" "double y" 44.Ft float 45.Fn hypotf "float x" "float y" 46.Sh DESCRIPTION 47The 48.Fn hypot 49functions 50compute the 51sqrt(x*x+y*y) 52in such a way that underflow will not happen, and overflow 53occurs only if the final result deserves it. 54.Pp 55.Fn hypot "\*(If" "v" 56= 57.Fn hypot "v" "\*(If" 58= +\*(If for all 59.Ar v , 60including \*(Na. 61.Sh ERRORS 62Below 0.97 63.Em ulps . 64Consequently 65.Fn hypot "5.0" "12.0" 66= 13.0 67exactly; 68in general, hypot returns an integer whenever an 69integer might be expected. 70.Pp 71The same cannot be said for the shorter and faster version of hypot 72that is provided in the comments in cabs.c; its error can 73exceed 1.2 74.Em ulps . 75.Sh NOTES 76As might be expected, 77.Fn hypot "v" "\*(Na" 78and 79.Fn hypot "\*(Na" "v" 80are \*(Na for all 81.Em finite 82.Ar v ; 83with "reserved operand" in place of "\*(Na", the 84same is true on a 85.Tn VAX . 86But programmers on machines other than a 87.Tn VAX 88(it has no \*(If) 89might be surprised at first to discover that 90.Fn hypot "\(+-\*(If" "\*(Na" 91= +\*(If. 92This is intentional; it happens because 93.Fn hypot "\*(If" "v" 94= +\*(If 95for 96.Em all 97.Ar v , 98finite or infinite. 99Hence 100.Fn hypot "\*(If" "v" 101is independent of 102.Ar v . 103Unlike the reserved operand fault on a 104.Tn VAX , 105the 106.Tn IEEE 107\*(Na is designed to 108disappear when it turns out to be irrelevant, as it does in 109.Fn hypot "\*(If" "\*(Na" . 110.Sh SEE ALSO 111.Xr math 3 , 112.Xr sqrt 3 113.Sh HISTORY 114Both a 115.Fn hypot 116function and a 117.Fn cabs 118function 119appeared in 120.At v7 . 121.Fn cabs 122was removed from public namespace in 123.Nx 5.0 124to avoid conflicts with the complex function in C99. 125