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.Dd March 30, 2008 29.Dt HYPOT 3 30.Os 31.Sh NAME 32.Nm hypot , 33.Nm hypotf , 34.Nm hypotl , 35.Nm cabs , 36.Nm cabsf , 37.Nm cabsl 38.Nd Euclidean distance and complex absolute value functions 39.Sh LIBRARY 40.Lb libm 41.Sh SYNOPSIS 42.In math.h 43.Ft double 44.Fn hypot "double x" "double y" 45.Ft float 46.Fn hypotf "float x" "float y" 47.Ft "long double" 48.Fn hypotl "long double x" "long double y" 49.In complex.h 50.Ft double 51.Fn cabs "double complex z" 52.Ft float 53.Fn cabsf "float complex z" 54.Ft "long double" 55.Fn cabsl "long double complex z" 56.Sh DESCRIPTION 57The 58.Fn hypot , 59.Fn hypotf 60and 61.Fn hypotl 62functions 63compute the 64sqrt(x*x+y*y) 65in such a way that underflow will not happen, and overflow 66occurs only if the final result deserves it. 67The 68.Fn cabs , 69.Fn cabsf 70and 71.Fn cabsl 72functions compute the complex absolute value of 73.Fa z . 74.Pp 75.Fn hypot "\*(If" "v" 76= 77.Fn hypot "v" "\*(If" 78= +\*(If for all 79.Fa v , 80including \*(Na. 81.Sh ERROR (due to Roundoff, etc.) 82Below 0.97 83.Em ulps . 84Consequently 85.Fn hypot "5.0" "12.0" 86= 13.0 87exactly; 88in general, hypot and cabs return an integer whenever an 89integer might be expected. 90.Sh NOTES 91As might be expected, 92.Fn hypot "v" "\*(Na" 93and 94.Fn hypot "\*(Na" "v" 95are \*(Na for all 96.Em finite 97.Fa v . 98But programmers 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.Fa v , 108finite or infinite. 109Hence 110.Fn hypot "\*(If" "v" 111is independent of 112.Fa 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 SEE ALSO 121.Xr carg 3 , 122.Xr math 3 , 123.Xr sqrt 3 124.Sh STANDARDS 125The 126.Fn hypot , 127.Fn hypotf , 128.Fn hypotl , 129.Fn cabs , 130.Fn cabsf , 131and 132.Fn cabsl 133functions conform to 134.St -isoC-99 . 135.Sh HISTORY 136Both a 137.Fn hypot 138function and a 139.Fn cabs 140function 141appeared in 142.At v7 . 143