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.\" $NetBSD: hypot.3,v 1.12 2002/10/01 19:21:30 wiz Exp $ 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 LIBRARY 45.Lb libm 46.Sh SYNOPSIS 47.Fd #include \*[Lt]math.h\*[Gt] 48.Ft double 49.Fn hypot "double x" "double y" 50.Ft float 51.Fn hypotf "float x" "float y" 52.Ft double 53.Fn cabs "struct complex { double x; double y; } z" 54.Ft float 55.Fn cabsf "struct complex { float x; float y; } z" 56.Sh DESCRIPTION 57The 58.Fn hypot 59and 60.Fn cabs 61functions 62computes the 63sqrt(x*x+y*y) 64in such a way that underflow will not happen, and overflow 65occurs only if the final result deserves it. 66.Pp 67.Fn hypot "\*(If" "v" 68= 69.Fn hypot "v" "\*(If" 70= +\*(If for all 71.Ar v , 72including \*(Na. 73.Sh ERRORS 74Below 0.97 75.Em ulps . 76Consequently 77.Fn hypot "5.0" "12.0" 78= 13.0 79exactly; 80in general, hypot and cabs return an integer whenever an 81integer might be expected. 82.Pp 83The same cannot be said for the shorter and faster version of hypot 84and cabs that is provided in the comments in cabs.c; its error can 85exceed 1.2 86.Em ulps . 87.Sh NOTES 88As might be expected, 89.Fn hypot "v" "\*(Na" 90and 91.Fn hypot "\*(Na" "v" 92are \*(Na for all 93.Em finite 94.Ar v ; 95with "reserved operand" in place of "\*(Na", the 96same is true on a 97.Tn VAX . 98But programmers on machines other than a 99.Tn VAX 100(if has no \*(If) 101might be surprised at first to discover that 102.Fn hypot "\(+-\*(If" "\*(Na" 103= +\*(If. 104This is intentional; it happens because 105.Fn hypot "\*(If" "v" 106= +\*(If 107for 108.Em all 109.Ar v , 110finite or infinite. 111Hence 112.Fn hypot "\*(If" "v" 113is independent of 114.Ar v . 115Unlike the reserved operand fault on a 116.Tn VAX , 117the 118.Tn IEEE 119\*(Na is designed to 120disappear when it turns out to be irrelevant, as it does in 121.Fn hypot "\*(If" "\*(Na" . 122.Sh SEE ALSO 123.Xr math 3 , 124.Xr sqrt 3 125.Sh HISTORY 126Both a 127.Fn hypot 128function and a 129.Fn cabs 130function 131appeared in 132.At v7 . 133.Sh BUGS 134The 135.Fn cabs 136and 137.Fn cabsf 138functions use structures that are not defined in any header and need to 139be defined by the user. 140As such they cannot be prototyped properly. 141