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.\" @(#)hypot.3 6.7 (Berkeley) 5/6/91 33.\" 34.Dd May 6, 1991 35.Dt HYPOT 3 36.Os BSD 4 37.Sh NAME 38.Nm hypot , 39.Nm cabs 40.Nd euclidean distance and complex absolute value functions 41.Sh SYNOPSIS 42.Fd #include <math.h> 43.Ft double 44.Fn hypot "double x" "double y" 45.Fd struct {double x, y;} z; 46.Ft double 47.Fn cabs z 48.Sh DESCRIPTION 49The 50.Fn hypot 51and 52.Fn cabs 53functions 54computes the 55sqrt(x*x+y*y) 56in such a way that underflow will not happen, and overflow 57occurs only if the final result deserves it. 58.Pp 59.Fn hypot "\*(If" "v" 60= 61.Fn hypot "v" "\*(If" 62= +\*(If for all 63.Ar v , 64including \*(Na. 65.Sh ERROR (due to Roundoff, etc.) 66Below 0.97 67.Em ulps . 68Consequently 69.Fn hypot "5.0" "12.0" 70= 13.0 71exactly; 72in general, hypot and cabs return an integer whenever an 73integer might be expected. 74.Pp 75The same cannot be said for the shorter and faster version of hypot 76and cabs that is provided in the comments in cabs.c; its error can 77exceed 1.2 78.Em ulps . 79.Sh NOTES 80As might be expected, 81.Fn hypot "v" "\*(Na" 82and 83.Fn hypot "\*(Na" "v" 84are \*(Na for all 85.Em finite 86.Ar v ; 87with "reserved operand" in place of "\*(Na", the 88same is true on a 89.Tn VAX . 90But programmers on machines other than a 91.Tn VAX 92(if 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 108.Tn VAX , 109the 110.Tn IEEE 111\*(Na is designed to 112disappear when it turns out to be irrelevant, as it does in 113.Fn hypot "\*(If" "\*(Na" . 114.Sh SEE ALSO 115.Xr math 3 , 116.Xr sqrt 3 117.Sh HISTORY 118Both a 119.Fn hypot 120function and a 121.Fn cabs 122function 123appeared in 124.At v7 . 125