1.\" Copyright (c) 2017 Steven G. Kargl <kargl@FreeBSD.org> 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.\" 13.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 14.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 15.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 16.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 17.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 18.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 19.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 20.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 21.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 22.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 23.\" SUCH DAMAGE. 24.\" 25.Dd April 1, 2017 26.Dt COSPI 3 27.Os 28.Sh NAME 29.Nm cospi , 30.Nm cospif , 31.Nm cospil 32.Nd half\(encycle cosine functions 33.Sh LIBRARY 34.Lb libm 35.Sh SYNOPSIS 36.In math.h 37.Ft double 38.Fn cospi "double x" 39.Ft float 40.Fn cospif "float x" 41.Ft long double 42.Fn cospil "long double x" 43.Sh DESCRIPTION 44The 45.Fn cospi , 46.Fn cospif , 47and 48.Fn cospil 49functions compute the cosine of 50.Fa "\(*p \(mu x" . 51and measure angles in half-cycles. 52.Sh RETURN VALUES 53The 54.Fn cospi , 55.Fn cospif , 56and 57.Fn cospil 58functions returns 59.Fn cos "\(*p \(mu x" . 60If \*(Bax\*(Ba \*(Ge 2^(p - 1) 61where p is the floating\(enpoint precision of 62.Ar x , 63then the returned value is 1 and it has no significance. 64.Sh SPECIAL VALUES 65.Bl -tag 66.It 67.Fn cospi \*(Pm0 68returns 1. 69.It 70.Fn cospi \*(Pmn/2 71returns 0 for positive integers 72.Ar n . 73.It 74.Fn cospi n 75returns 1 for even integers 76.Ar n . 77.It 78.Fn cospi n 79returns \-1 for odd integers 80.Ar n . 81.It 82.Fn cospi \*(Pm\(if 83return an \*(Na and raises an FE_INVALID exception. 84.It 85.Fn cospi \*(Na 86return an \*(Na and raises an FE_INVALID exception. 87.El 88.Sh SEE ALSO 89.Xr cos 3 , 90.Xr fenv 3 , 91.Xr math 3 , 92.Xr sin 3 , 93.Xr sinpi 3 , 94.Xr tan 3 , 95.Xr tanpi 3 96.Sh AUTHORS 97The half\(encycle trignometric functions were written by 98.An Steven G. Kargl Aq Mt kargl@FreeBSD.org . 99.Sh STANDARDS 100These functions conform to 101IEEE Std 754\(tm\(en2008 , 102\(dqIEEE Standard for Floating-Point Arithmetic\(dq 103and to 104ISO/IEC TS 18661-4 , 105\(dqInformation technology \(em Programming languages, their environments, 106and system software interfaces \(em Floating\(enpoint extensions for 107C\(dq \(em Part 4: Supplementary functions. 108 109 110