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. All advertising materials mentioning features or use of this software 13.\" must display the following acknowledgement: 14.\" This product includes software developed by the University of 15.\" California, Berkeley and its contributors. 16.\" 4. Neither the name of the University nor the names of its contributors 17.\" may be used to endorse or promote products derived from this software 18.\" without specific prior written permission. 19.\" 20.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 21.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 22.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 23.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 24.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 25.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 26.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 27.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 28.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 29.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 30.\" SUCH DAMAGE. 31.\" 32.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91 33.\" $NetBSD: hypot.3,v 1.6 1997/10/09 11:27:52 lukem Exp $ 34.\" 35.Dd May 6, 1991 36.Dt HYPOT 3 37.Os 38.Sh NAME 39.Nm hypot , 40.Nm cabs 41.Nd euclidean distance and complex absolute value functions 42.Sh SYNOPSIS 43.Fd #include <math.h> 44.Ft double 45.Fn hypot "double x" "double y" 46.Ft float 47.Fn hypotf "float x" "float y" 48.Fd struct {double x, y;} z; 49.Ft double 50.Fn cabs z 51.Sh DESCRIPTION 52The 53.Fn hypot 54and 55.Fn cabs 56functions 57computes the 58sqrt(x*x+y*y) 59in such a way that underflow will not happen, and overflow 60occurs only if the final result deserves it. 61.Pp 62.Fn hypot "\*(If" "v" 63= 64.Fn hypot "v" "\*(If" 65= +\*(If for all 66.Ar v , 67including \*(Na. 68.Sh ERROR (due to Roundoff, etc.) 69Below 0.97 70.Em ulps . 71Consequently 72.Fn hypot "5.0" "12.0" 73= 13.0 74exactly; 75in general, hypot and cabs return an integer whenever an 76integer might be expected. 77.Pp 78The same cannot be said for the shorter and faster version of hypot 79and cabs that is provided in the comments in cabs.c; its error can 80exceed 1.2 81.Em ulps . 82.Sh NOTES 83As might be expected, 84.Fn hypot "v" "\*(Na" 85and 86.Fn hypot "\*(Na" "v" 87are \*(Na for all 88.Em finite 89.Ar v ; 90with "reserved operand" in place of "\*(Na", the 91same is true on a 92.Tn VAX . 93But programmers on machines other than a 94.Tn VAX 95(if has no \*(If) 96might be surprised at first to discover that 97.Fn hypot "\(+-\*(If" "\*(Na" 98= +\*(If. 99This is intentional; it happens because 100.Fn hypot "\*(If" "v" 101= +\*(If 102for 103.Em all 104.Ar v , 105finite or infinite. 106Hence 107.Fn hypot "\*(If" "v" 108is independent of 109.Ar v . 110Unlike the reserved operand fault on a 111.Tn VAX , 112the 113.Tn IEEE 114\*(Na is designed to 115disappear when it turns out to be irrelevant, as it does in 116.Fn hypot "\*(If" "\*(Na" . 117.Sh SEE ALSO 118.Xr math 3 , 119.Xr sqrt 3 120.Sh HISTORY 121Both a 122.Fn hypot 123function and a 124.Fn cabs 125function 126appeared in 127.At v7 . 128