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.\" $FreeBSD$ 34.\" 35.Dd May 6, 1991 36.Dt HYPOT 3 37.Os BSD 4 38.Sh NAME 39.Nm hypot , 40.Nm hypotf , 41.Nm cabs , 42.Nm cabsf 43.Nd euclidean distance and complex absolute value functions 44.Sh SYNOPSIS 45.Fd #include <math.h> 46.Ft double 47.Fn hypot "double x" "double y" 48.Ft float 49.Fn hypotf "float x" "float y" 50.Vt struct {double x, y;} z ; 51.Ft double 52.Fn cabs z 53.Vt struct {float x, y;} z ; 54.Ft float 55.Fn cabsf z 56.Sh DESCRIPTION 57The 58.Fn hypot , 59.Fn hypotf , 60.Fn cabs 61and 62.Fn cabsf 63functions 64compute the 65sqrt(x*x+y*y) 66in such a way that underflow will not happen, and overflow 67occurs only if the final result deserves it. 68.Pp 69.Fn hypot "\*(If" "v" 70= 71.Fn hypot "v" "\*(If" 72= +\*(If for all 73.Ar v , 74including \*(Na. 75.Sh ERROR (due to Roundoff, etc.) 76Below 0.97 77.Em ulps . 78Consequently 79.Fn hypot "5.0" "12.0" 80= 13.0 81exactly; 82in general, hypot and cabs return an integer whenever an 83integer might be expected. 84.Pp 85The same cannot be said for the shorter and faster version of hypot 86and cabs that is provided in the comments in cabs.c; its error can 87exceed 1.2 88.Em ulps . 89.Sh NOTES 90As might be expected, 91.Fn hypot "v" "\*(Na" 92and 93.Fn hypot "\*(Na" "v" 94are \*(Na for all 95.Em finite 96.Ar v ; 97with "reserved operand" in place of "\*(Na", the 98same is true on a 99.Tn VAX . 100But programmers on machines other than a 101.Tn VAX 102(if has no \*(If) 103might be surprised at first to discover that 104.Fn hypot "\(+-\*(If" "\*(Na" 105= +\*(If. 106This is intentional; it happens because 107.Fn hypot "\*(If" "v" 108= +\*(If 109for 110.Em all 111.Ar v , 112finite or infinite. 113Hence 114.Fn hypot "\*(If" "v" 115is independent of 116.Ar v . 117Unlike the reserved operand fault on a 118.Tn VAX , 119the 120.Tn IEEE 121\*(Na is designed to 122disappear when it turns out to be irrelevant, as it does in 123.Fn hypot "\*(If" "\*(Na" . 124.Sh SEE ALSO 125.Xr math 3 , 126.Xr sqrt 3 127.Sh HISTORY 128Both a 129.Fn hypot 130function and a 131.Fn cabs 132function 133appeared in 134.At v7 . 135