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.\" $FreeBSD$ 26.\" 27.Dd April 1, 2017 28.Dt COSPI 3 29.Os 30.Sh NAME 31.Nm cospi , 32.Nm cospif , 33.Nm cospil 34.Nd half\(encycle cosine functions 35.Sh LIBRARY 36.Lb libm 37.Sh SYNOPSIS 38.In math.h 39.Ft double 40.Fn cospi "double x" 41.Ft float 42.Fn cospif "float x" 43.Ft long double 44.Fn cospil "long double x" 45.Sh DESCRIPTION 46The 47.Fn cospi , 48.Fn cospif , 49and 50.Fn cospil 51functions compute the cosine of 52.Fa "\(*p \(mu x" . 53and measure angles in half-cycles. 54.Sh RETURN VALUES 55The 56.Fn cospi , 57.Fn cospif , 58and 59.Fn cospil 60functions returns 61.Fn cos "\(*p \(mu x" . 62If \*(Bax\*(Ba \*(Ge 2^(p - 1) 63where p is the floating\(enpoint precision of 64.Ar x , 65then the returned value is 1 and it has no significance. 66.Sh SPECIAL VALUES 67.Bl -tag 68.It 69.Fn cospi \*(Pm0 70returns 1. 71.It 72.Fn cospi \*(Pmn/2 73returns 0 for positive integers 74.Ar n . 75.It 76.Fn cospi n 77returns 1 for even integers 78.Ar n . 79.It 80.Fn cospi n 81returns \-1 for odd integers 82.Ar n . 83.It 84.Fn cospi \*(Pm\(if 85return an \*(Na and raises an FE_INVALID exception. 86.It 87.Fn cospi \*(Na 88return an \*(Na and raises an FE_INVALID exception. 89.El 90.Sh SEE ALSO 91.Xr cos 3 , 92.Xr fenv 3 , 93.Xr math 3 , 94.Xr sin 3 , 95.Xr sinpi 3 , 96.Xr tan 3 , 97.Xr tanpi 3 98.Sh AUTHORS 99The half\(encycle trignometric functions were written by 100.An Steven G. Kargl Aq Mt kargl@FreeBSD.org . 101.Sh STANDARDS 102These functions conform to 103IEEE Std 754\(tm\(en2008 , 104\(dqIEEE Standard for Floating-Point Arithmetic\(dq 105and to 106ISO/IEC TS 18661-4 , 107\(dqInformation technology \(em Programming languages, their environments, 108and system software interfaces \(em Floating\(enpoint extensions for 109C\(dq \(em Part 4: Supplementary functions. 110 111 112