1.\" Copyright (c) 2026 Steven G. Kargl. 2.\" 3.\" Redistribution and use in source and binary forms, with or without 4.\" modification, are permitted provided that the following conditions 5.\" are met: 6.\" 1. Redistributions of source code must retain the above copyright 7.\" notice, this list of conditions and the following disclaimer. 8.\" 2. Redistributions in binary form must reproduce the above copyright 9.\" notice, this list of conditions and the following disclaimer in the 10.\" documentation and/or other materials provided with the distribution. 11.\" 12.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 13.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 14.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 15.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 16.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 17.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 18.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 19.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 20.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 21.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 22.\" SUCH DAMAGE. 23.\" 24.Dd June 5, 2026 25.Dt ACOSPI 3 26.Os 27.Sh NAME 28.Nm acospi , 29.Nm acospif , 30.Nm acospil 31.Nd half-cycle arc cosine functions 32.Sh LIBRARY 33.Lb libm 34.Sh SYNOPSIS 35.In math.h 36.Ft double 37.Fn acospi "double x" 38.Ft float 39.Fn acospif "float x" 40.Ft long double 41.Fn acospil "long double x" 42.Sh DESCRIPTION 43The 44.Fn acospi , 45.Fn acospif , 46and 47.Fn acospil 48functions compute the principal value of the arc cosine of 49.Fa x , 50divided by \*(Pi, thus measuring the angle in half-cycles. 51.Sh RETURN VALUES 52The 53.Fn acospi , 54.Fn acospif , 55and 56.Fn acospil 57functions return values in the range 58.Bk -words 59.Bq -1, +1 . 60.Ek 61If 62.Pf \&| Ns Fa x Ns \&| > 1 , 63.Fn acospi x 64raise an invalid exception and returns an \*(Na. 65.Sh SEE ALSO 66.Xr asinpi 3 , 67.Xr atanpi 3 , 68.Xr acos 3 , 69.Xr cospi 3 , 70.Sh STANDARDS 71The 72.Fn acospi , 73.Fn acospif , 74and 75.Fn acospil 76functions conform to 77.St -isoC-2023 . 78