1/*- 2 * Copyright (c) 2017-2023 Steven G. Kargl 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright 9 * notice unmodified, this list of conditions, and the following 10 * disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 16 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 17 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 18 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 19 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 25 */ 26 27/* 28 * See ../src/s_cospi.c for implementation details. 29 */ 30 31#include "math.h" 32#include "math_private.h" 33 34/* 35 * pi_hi contains the leading 56 bits of a 169 bit approximation for pi. 36 */ 37static const long double 38pi_hi = 3.14159265358979322702026593105983920e+00L, 39pi_lo = 1.14423774522196636802434264184180742e-17L; 40 41#include "k_cospil.h" 42#include "k_sinpil.h" 43 44static volatile const double vzero = 0; 45 46long double 47cospil(long double x) 48{ 49 long double ai, ar, ax, c; 50 51 ax = fabsl(x); 52 53 if (ax <= 1) { 54 if (ax < 0.25) { 55 if (ax < 0x1p-60) { 56 if ((int)x == 0) 57 return (1); 58 } 59 return (__kernel_cospil(ax)); 60 } 61 62 if (ax < 0.5) 63 c = __kernel_sinpil(0.5 - ax); 64 else if (ax < 0.75) { 65 if (ax == 0.5) 66 return (0); 67 c = -__kernel_sinpil(ax - 0.5); 68 } else 69 c = -__kernel_cospil(1 - ax); 70 return (c); 71 } 72 73 if (ax < 0x1p112) { 74 /* Split ax = ai + ar with 0 <= ar < 1. */ 75 FFLOORL128(ax, ai, ar); 76 77 if (ar < 0.5) { 78 if (ar < 0.25) 79 c = ar == 0 ? 1 : __kernel_cospil(ar); 80 else 81 c = __kernel_sinpil(0.5 - ar); 82 } else { 83 if (ar < 0.75) { 84 if (ar == 0.5) 85 return (0); 86 c = -__kernel_sinpil(ar - 0.5); 87 } else 88 c = -__kernel_cospil(1 - ar); 89 } 90 return (fmodl(ai, 2.L) == 0 ? c : -c); 91 } 92 93 if (isinf(x) || isnan(x)) 94 return (vzero / vzero); 95 96 /* 97 * For |x| >= 0x1p113, it is always an even integer, so return 1. 98 */ 99 if (ax >= 0x1p113) 100 return (1); 101 /* 102 * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even 103 * or odd integer to return 1 or -1. 104 */ 105 106 return (fmodl(ax, 2.L) == 0 ? 1 : -1); 107} 108