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.\" 4. Neither the name of the University nor the names of its contributors 13.\" may be used to endorse or promote products derived from this software 14.\" without specific prior written permission. 15.\" 16.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 17.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 20.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26.\" SUCH DAMAGE. 27.\" 28.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91 29.\" $FreeBSD$ 30.\" 31.Dd December 12, 2007 32.Dt HYPOT 3 33.Os 34.Sh NAME 35.Nm hypot , 36.Nm hypotf , 37.Nm cabs , 38.Nm cabsf 39.Nd Euclidean distance and complex absolute value functions 40.Sh LIBRARY 41.Lb libm 42.Sh SYNOPSIS 43.In math.h 44.Ft double 45.Fn hypot "double x" "double y" 46.Ft float 47.Fn hypotf "float x" "float y" 48.In complex.h 49.Ft double 50.Fn cabs "double complex z" 51.Ft float 52.Fn cabsf "float complex z" 53.Sh DESCRIPTION 54The 55.Fn hypot 56and 57.Fn hypotf 58functions 59compute the 60sqrt(x*x+y*y) 61in such a way that underflow will not happen, and overflow 62occurs only if the final result deserves it. 63The 64.Fn cabs 65and 66.Fn cabsf 67functions compute the complex absolute value of 68.Fa z . 69.Pp 70.Fn hypot "\*(If" "v" 71= 72.Fn hypot "v" "\*(If" 73= +\*(If for all 74.Fa v , 75including \*(Na. 76.Sh ERROR (due to Roundoff, etc.) 77Below 0.97 78.Em ulps . 79Consequently 80.Fn hypot "5.0" "12.0" 81= 13.0 82exactly; 83in general, hypot and cabs return an integer whenever an 84integer might be expected. 85.Pp 86The same cannot be said for the shorter and faster version of hypot 87and cabs that is provided in the comments in cabs.c; its error can 88exceed 1.2 89.Em ulps . 90.Sh NOTES 91As might be expected, 92.Fn hypot "v" "\*(Na" 93and 94.Fn hypot "\*(Na" "v" 95are \*(Na for all 96.Em finite 97.Fa v . 98But programmers 99might be surprised at first to discover that 100.Fn hypot "\(+-\*(If" "\*(Na" 101= +\*(If. 102This is intentional; it happens because 103.Fn hypot "\*(If" "v" 104= +\*(If 105for 106.Em all 107.Fa v , 108finite or infinite. 109Hence 110.Fn hypot "\*(If" "v" 111is independent of 112.Fa v . 113Unlike the reserved operand fault on a 114.Tn VAX , 115the 116.Tn IEEE 117\*(Na is designed to 118disappear when it turns out to be irrelevant, as it does in 119.Fn hypot "\*(If" "\*(Na" . 120.Sh SEE ALSO 121.Xr carg 3 , 122.Xr math 3 , 123.Xr sqrt 3 124.Sh HISTORY 125Both a 126.Fn hypot 127function and a 128.Fn cabs 129function 130appeared in 131.At v7 . 132.Sh STANDARDS 133The 134.Fn hypot , 135.Fn hypotf , 136.Fn cabs , 137and 138.Fn cabsf 139functions conform to 140.St -isoC-99 . 141