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 January 14, 2005 36.Dt HYPOT 3 37.Os 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 LIBRARY 45.Lb libm 46.Sh SYNOPSIS 47.In math.h 48.Ft double 49.Fn hypot "double x" "double y" 50.Ft float 51.Fn hypotf "float x" "float y" 52.In complex.h 53.Ft double 54.Fn cabs "double complex z" 55.Ft float 56.Fn cabsf "float complex z" 57.Sh DESCRIPTION 58The 59.Fn hypot 60and 61.Fn hypotf 62functions 63compute the 64sqrt(x*x+y*y) 65in such a way that underflow will not happen, and overflow 66occurs only if the final result deserves it. 67The 68.Fn cabs 69and 70.Fn cabsf 71functions compute the complex absolute value of 72.Fa z . 73.Pp 74.Fn hypot "\*(If" "v" 75= 76.Fn hypot "v" "\*(If" 77= +\*(If for all 78.Fa v , 79including \*(Na. 80.Sh ERROR (due to Roundoff, etc.) 81Below 0.97 82.Em ulps . 83Consequently 84.Fn hypot "5.0" "12.0" 85= 13.0 86exactly; 87in general, hypot and cabs return an integer whenever an 88integer might be expected. 89.Pp 90The same cannot be said for the shorter and faster version of hypot 91and cabs that is provided in the comments in cabs.c; its error can 92exceed 1.2 93.Em ulps . 94.Sh NOTES 95As might be expected, 96.Fn hypot "v" "\*(Na" 97and 98.Fn hypot "\*(Na" "v" 99are \*(Na for all 100.Em finite 101.Fa v . 102But programmers 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.Fa v , 112finite or infinite. 113Hence 114.Fn hypot "\*(If" "v" 115is independent of 116.Fa 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