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. 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 March 30, 2008 32.Dt HYPOT 3 33.Os 34.Sh NAME 35.Nm hypot , 36.Nm hypotf , 37.Nm hypotl , 38.Nm cabs , 39.Nm cabsf , 40.Nm cabsl 41.Nd Euclidean distance and complex absolute value functions 42.Sh LIBRARY 43.Lb libm 44.Sh SYNOPSIS 45.In math.h 46.Ft double 47.Fn hypot "double x" "double y" 48.Ft float 49.Fn hypotf "float x" "float y" 50.Ft "long double" 51.Fn hypotl "long double x" "long double y" 52.In complex.h 53.Ft double 54.Fn cabs "double complex z" 55.Ft float 56.Fn cabsf "float complex z" 57.Ft "long double" 58.Fn cabsl "long double complex z" 59.Sh DESCRIPTION 60The 61.Fn hypot , 62.Fn hypotf 63and 64.Fn hypotl 65functions 66compute the 67sqrt(x*x+y*y) 68in such a way that underflow will not happen, and overflow 69occurs only if the final result deserves it. 70The 71.Fn cabs , 72.Fn cabsf 73and 74.Fn cabsl 75functions compute the complex absolute value of 76.Fa z . 77.Pp 78.Fn hypot "\*(If" "v" 79= 80.Fn hypot "v" "\*(If" 81= +\*(If for all 82.Fa v , 83including \*(Na. 84.Sh ERROR (due to Roundoff, etc.) 85Below 0.97 86.Em ulps . 87Consequently 88.Fn hypot "5.0" "12.0" 89= 13.0 90exactly; 91in general, hypot and cabs return an integer whenever an 92integer might be expected. 93.Sh NOTES 94As might be expected, 95.Fn hypot "v" "\*(Na" 96and 97.Fn hypot "\*(Na" "v" 98are \*(Na for all 99.Em finite 100.Fa v . 101But programmers 102might be surprised at first to discover that 103.Fn hypot "\(+-\*(If" "\*(Na" 104= +\*(If. 105This is intentional; it happens because 106.Fn hypot "\*(If" "v" 107= +\*(If 108for 109.Em all 110.Fa v , 111finite or infinite. 112Hence 113.Fn hypot "\*(If" "v" 114is independent of 115.Fa v . 116Unlike the reserved operand fault on a 117.Tn VAX , 118the 119.Tn IEEE 120\*(Na is designed to 121disappear when it turns out to be irrelevant, as it does in 122.Fn hypot "\*(If" "\*(Na" . 123.Sh SEE ALSO 124.Xr carg 3 , 125.Xr math 3 , 126.Xr sqrt 3 127.Sh STANDARDS 128The 129.Fn hypot , 130.Fn hypotf , 131.Fn hypotl , 132.Fn cabs , 133.Fn cabsf , 134and 135.Fn cabsl 136functions conform to 137.St -isoC-99 . 138.Sh HISTORY 139Both a 140.Fn hypot 141function and a 142.Fn cabs 143function 144appeared in 145.At v7 . 146