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 "fpmath.h" 32 #include "math.h" 33 #include "math_private.h" 34 35 /* 36 * pi_hi contains the leading 56 bits of a 169 bit approximation for pi. 37 */ 38 static const long double 39 pi_hi = 3.14159265358979322702026593105983920e+00L, 40 pi_lo = 1.14423774522196636802434264184180742e-17L; 41 42 #include "k_cospil.h" 43 #include "k_sinpil.h" 44 45 volatile static const double vzero = 0; 46 47 long double 48 cospil(long double x) 49 { 50 long double ai, ar, ax, c; 51 52 ax = fabsl(x); 53 54 if (ax <= 1) { 55 if (ax < 0.25) { 56 if (ax < 0x1p-60) { 57 if ((int)x == 0) 58 return (1); 59 } 60 return (__kernel_cospil(ax)); 61 } 62 63 if (ax < 0.5) 64 c = __kernel_sinpil(0.5 - ax); 65 else if (ax < 0.75) { 66 if (ax == 0.5) 67 return (0); 68 c = -__kernel_sinpil(ax - 0.5); 69 } else 70 c = -__kernel_cospil(1 - ax); 71 return (c); 72 } 73 74 if (ax < 0x1p112) { 75 /* Split ax = ai + ar with 0 <= ar < 1. */ 76 FFLOORL128(ax, ai, ar); 77 78 if (ar < 0.5) { 79 if (ar < 0.25) 80 c = ar == 0 ? 1 : __kernel_cospil(ar); 81 else 82 c = __kernel_sinpil(0.5 - ar); 83 } else { 84 if (ar < 0.75) { 85 if (ar == 0.5) 86 return (0); 87 c = -__kernel_sinpil(ar - 0.5); 88 } else 89 c = -__kernel_cospil(1 - ar); 90 } 91 return (fmodl(ai, 2.L) == 0 ? c : -c); 92 } 93 94 if (isinf(x) || isnan(x)) 95 return (vzero / vzero); 96 97 /* 98 * For |x| >= 0x1p113, it is always an even integer, so return 1. 99 */ 100 if (ax >= 0x1p113) 101 return (1); 102 /* 103 * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even 104 * or odd integer to return 1 or -1. 105 */ 106 107 return (fmodl(ax, 2.L) == 0 ? 1 : -1); 108 } 109