1.\" $OpenBSD: hypot.3,v 1.7 2000/03/02 00:29:49 todd 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. All advertising materials mentioning features or use of this software 14.\" must display the following acknowledgement: 15.\" This product includes software developed by the University of 16.\" California, Berkeley and its contributors. 17.\" 4. Neither the name of the University nor the names of its contributors 18.\" may be used to endorse or promote products derived from this software 19.\" without specific prior written permission. 20.\" 21.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 22.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 23.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 24.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 25.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 26.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 27.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 28.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 29.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 30.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 31.\" SUCH DAMAGE. 32.\" 33.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91 34.\" 35.Dd May 6, 1991 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 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.Ft double 51.Fn cabs "struct complex { double x; double y; } z" 52.Ft float 53.Fn cabsf "struct complex { double x; double y; } z" 54.Sh DESCRIPTION 55The 56.Fn hypot 57and 58.Fn cabs 59functions 60computes the 61sqrt(x*x+y*y) 62in such a way that underflow will not happen, and overflow 63occurs only if the final result deserves it. 64.Pp 65.Fn hypot "\*(If" "v" 66= 67.Fn hypot "v" "\*(If" 68= +\*(If for all 69.Ar v , 70including \*(Na. 71.Sh ERROR (due to Roundoff, etc.) 72Below 0.97 73.Em ulps . 74Consequently 75.Fn hypot "5.0" "12.0" 76= 13.0 77exactly; 78in general, hypot and cabs return an integer whenever an 79integer might be expected. 80.Pp 81The same cannot be said for the shorter and faster version of hypot 82and cabs that is provided in the comments in cabs.c; its error can 83exceed 1.2 84.Em ulps . 85.Sh NOTES 86As might be expected, 87.Fn hypot "v" "\*(Na" 88and 89.Fn hypot "\*(Na" "v" 90are \*(Na for all 91.Em finite 92.Ar v ; 93with "reserved operand" in place of "\*(Na", the 94same is true on a 95.Tn VAX . 96But programmers on machines other than a 97.Tn VAX 98(if has no \*(If) 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.Ar v , 108finite or infinite. 109Hence 110.Fn hypot "\*(If" "v" 111is independent of 112.Ar 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 BUGS 121The 122.Fn cabs 123and 124.Fn cabsf 125functions use structures that are not defined in any header and need to 126be defined by the user. As such they cannot be prototyped properly. 127.Sh SEE ALSO 128.Xr math 3 , 129.Xr sqrt 3 130.Sh HISTORY 131Both a 132.Fn hypot 133function and a 134.Fn cabs 135function 136appeared in 137.At v7 . 138