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.\" $FreeBSD$ 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.In math.h 48.Ft double 49.Fn hypot "double x" "double y" 50.Ft float 51.Fn hypotf "float x" "float y" 52.Vt struct {double x, y;} z ; 53.Ft double 54.Fn cabs z 55.Vt struct {float x, y;} z ; 56.Ft float 57.Fn cabsf z 58.Sh DESCRIPTION 59The 60.Fn hypot , 61.Fn hypotf , 62.Fn cabs 63and 64.Fn cabsf 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. 70.Pp 71.Fn hypot "\*(If" "v" 72= 73.Fn hypot "v" "\*(If" 74= +\*(If for all 75.Ar v , 76including \*(Na. 77.Sh ERROR (due to Roundoff, etc.) 78Below 0.97 79.Em ulps . 80Consequently 81.Fn hypot "5.0" "12.0" 82= 13.0 83exactly; 84in general, hypot and cabs return an integer whenever an 85integer might be expected. 86.Pp 87The same cannot be said for the shorter and faster version of hypot 88and cabs that is provided in the comments in cabs.c; its error can 89exceed 1.2 90.Em ulps . 91.Sh NOTES 92As might be expected, 93.Fn hypot "v" "\*(Na" 94and 95.Fn hypot "\*(Na" "v" 96are \*(Na for all 97.Em finite 98.Ar v ; 99with "reserved operand" in place of "\*(Na", the 100same is true on a 101.Tn VAX . 102But programmers on machines other than a 103.Tn VAX 104(if has no \*(If) 105might be surprised at first to discover that 106.Fn hypot "\(+-\*(If" "\*(Na" 107= +\*(If. 108This is intentional; it happens because 109.Fn hypot "\*(If" "v" 110= +\*(If 111for 112.Em all 113.Ar v , 114finite or infinite. 115Hence 116.Fn hypot "\*(If" "v" 117is independent of 118.Ar v . 119Unlike the reserved operand fault on a 120.Tn VAX , 121the 122.Tn IEEE 123\*(Na is designed to 124disappear when it turns out to be irrelevant, as it does in 125.Fn hypot "\*(If" "\*(Na" . 126.Sh SEE ALSO 127.Xr math 3 , 128.Xr sqrt 3 129.Sh HISTORY 130Both a 131.Fn hypot 132function and a 133.Fn cabs 134function 135appeared in 136.At v7 . 137