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.\" $Id: hypot.3,v 1.3 1993/08/14 13:42:48 mycroft Exp $ 34.\" 35.Dd May 6, 1991 36.Dt HYPOT 3 37.Os BSD 4 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.Fd struct {double x, y;} z; 47.Ft double 48.Fn cabs z 49.Sh DESCRIPTION 50The 51.Fn hypot 52and 53.Fn cabs 54functions 55computes the 56sqrt(x*x+y*y) 57in such a way that underflow will not happen, and overflow 58occurs only if the final result deserves it. 59.Pp 60.Fn hypot "\*(If" "v" 61= 62.Fn hypot "v" "\*(If" 63= +\*(If for all 64.Ar v , 65including \*(Na. 66.Sh ERROR (due to Roundoff, etc.) 67Below 0.97 68.Em ulps . 69Consequently 70.Fn hypot "5.0" "12.0" 71= 13.0 72exactly; 73in general, hypot and cabs return an integer whenever an 74integer might be expected. 75.Pp 76The same cannot be said for the shorter and faster version of hypot 77and cabs that is provided in the comments in cabs.c; its error can 78exceed 1.2 79.Em ulps . 80.Sh NOTES 81As might be expected, 82.Fn hypot "v" "\*(Na" 83and 84.Fn hypot "\*(Na" "v" 85are \*(Na for all 86.Em finite 87.Ar v ; 88with "reserved operand" in place of "\*(Na", the 89same is true on a 90.Tn VAX . 91But programmers on machines other than a 92.Tn VAX 93(if has no \*(If) 94might be surprised at first to discover that 95.Fn hypot "\(+-\*(If" "\*(Na" 96= +\*(If. 97This is intentional; it happens because 98.Fn hypot "\*(If" "v" 99= +\*(If 100for 101.Em all 102.Ar v , 103finite or infinite. 104Hence 105.Fn hypot "\*(If" "v" 106is independent of 107.Ar v . 108Unlike the reserved operand fault on a 109.Tn VAX , 110the 111.Tn IEEE 112\*(Na is designed to 113disappear when it turns out to be irrelevant, as it does in 114.Fn hypot "\*(If" "\*(Na" . 115.Sh SEE ALSO 116.Xr math 3 , 117.Xr sqrt 3 118.Sh HISTORY 119Both a 120.Fn hypot 121function and a 122.Fn cabs 123function 124appeared in 125.At v7 . 126