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 1.16 2003/11/02 11:17:16 wiz Exp $ 30.\" 31.Dd May 6, 1991 32.Dt HYPOT 3 33.Os 34.Sh NAME 35.Nm hypot , 36.Nm hypotf , 37.Nm cabs , 38.Nm cabsf 39.Nd Euclidean distance and complex absolute value functions 40.Sh LIBRARY 41.Lb libm 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 double 49.Fn cabs "struct complex { double x; double y; } z" 50.Ft float 51.Fn cabsf "struct complex { float x; float y; } z" 52.Sh DESCRIPTION 53The 54.Fn hypot 55and 56.Fn cabs 57functions 58compute the 59sqrt(x*x+y*y) 60in such a way that underflow will not happen, and overflow 61occurs only if the final result deserves it. 62.Pp 63.Fn hypot "\*(If" "v" 64= 65.Fn hypot "v" "\*(If" 66= +\*(If for all 67.Ar v , 68including \*(Na. 69.Sh ERRORS 70Below 0.97 71.Em ulps . 72Consequently 73.Fn hypot "5.0" "12.0" 74= 13.0 75exactly; 76in general, hypot and cabs return an integer whenever an 77integer might be expected. 78.Pp 79The same cannot be said for the shorter and faster version of hypot 80and cabs that is provided in the comments in cabs.c; its error can 81exceed 1.2 82.Em ulps . 83.Sh NOTES 84As might be expected, 85.Fn hypot "v" "\*(Na" 86and 87.Fn hypot "\*(Na" "v" 88are \*(Na for all 89.Em finite 90.Ar v ; 91with "reserved operand" in place of "\*(Na", the 92same is true on a 93.Tn VAX . 94But programmers on machines other than a 95.Tn VAX 96(it has no \*(If) 97might be surprised at first to discover that 98.Fn hypot "\(+-\*(If" "\*(Na" 99= +\*(If. 100This is intentional; it happens because 101.Fn hypot "\*(If" "v" 102= +\*(If 103for 104.Em all 105.Ar v , 106finite or infinite. 107Hence 108.Fn hypot "\*(If" "v" 109is independent of 110.Ar v . 111Unlike the reserved operand fault on a 112.Tn VAX , 113the 114.Tn IEEE 115\*(Na is designed to 116disappear when it turns out to be irrelevant, as it does in 117.Fn hypot "\*(If" "\*(Na" . 118.Sh SEE ALSO 119.Xr math 3 , 120.Xr sqrt 3 121.Sh HISTORY 122Both a 123.Fn hypot 124function and a 125.Fn cabs 126function 127appeared in 128.At v7 . 129.Sh BUGS 130The 131.Fn cabs 132and 133.Fn cabsf 134functions use structures that are not defined in any header and need to 135be defined by the user. 136As such they cannot be prototyped properly. 137