1.\" $OpenBSD: hypot.3,v 1.21 2015/01/15 19:06:31 schwarze Exp $ 2.\" Copyright (c) 1985, 1991 Regents of the University of California. 3.\" All rights reserved. 4.\" 5.\" Redistribution and use in source and binary forms, with or without 6.\" modification, are permitted provided that the following conditions 7.\" are met: 8.\" 1. Redistributions of source code must retain the above copyright 9.\" notice, this list of conditions and the following disclaimer. 10.\" 2. Redistributions in binary form must reproduce the above copyright 11.\" notice, this list of conditions and the following disclaimer in the 12.\" documentation and/or other materials provided with the distribution. 13.\" 3. Neither the name of the University nor the names of its contributors 14.\" may be used to endorse or promote products derived from this software 15.\" without specific prior written permission. 16.\" 17.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 18.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 21.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 22.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 23.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 24.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 25.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 26.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 27.\" SUCH DAMAGE. 28.\" 29.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91 30.\" 31.Dd $Mdocdate: January 15 2015 $ 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 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.Ft long double 49.Fn hypotl "long double x" "long double y" 50.In complex.h 51.Ft double 52.Fn cabs "double complex z" 53.Ft float 54.Fn cabsf "float complex z" 55.Ft long double 56.Fn cabsl "long double complex z" 57.Sh DESCRIPTION 58The 59.Fn hypot , 60.Fn hypotf 61and 62.Fn hypotl 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.Pp 76The 77.Fn cabs , 78.Fn cabsf 79and 80.Fn cabsl 81functions return the absolute value of the complex number 82.Fa z . 83.Sh ERRORS (due to Roundoff, etc.) 84Below 0.97 85.Em ulps . 86Consequently 87.Fn hypot "5.0" "12.0" 88= 13.0 89exactly; 90in general, hypot and cabs return an integer whenever an 91integer might be expected. 92.Sh NOTES 93As might be expected, 94.Fn hypot "v" "\*(Na" 95and 96.Fn hypot "\*(Na" "v" 97are \*(Na for all 98.Em finite 99.Ar v ; 100with 101.Dq reserved operand 102in place of "\*(Na", the same is true on a VAX. 103But programmers on machines other than a VAX (it has no \*(If) 104might be surprised at first to discover that 105.Fn hypot "\(+-\*(If" "\*(Na" 106= +\*(If. 107This is intentional; it happens because 108.Fn hypot "\*(If" "v" 109= +\*(If 110for 111.Em all 112.Ar v , 113finite or infinite. 114Hence 115.Fn hypot "\*(If" "v" 116is independent of 117.Ar v . 118Unlike the reserved operand fault on a VAX, 119the IEEE \*(Na is designed to disappear 120when it turns out to be irrelevant, as it does in 121.Fn hypot "\*(If" "\*(Na" . 122.Sh SEE ALSO 123.Xr sqrt 3 124.Sh HISTORY 125A 126.Fn hypot 127function first appeared in 128.At v3 , 129and 130.Fn cabs 131in 132.At v7 . 133