1 /*- 2 * Copyright (c) 2017-2021 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 */ 37 static const long double 38 pi_hi = 3.14159265358979322702026593105983920e+00L, 39 pi_lo = 1.14423774522196636802434264184180742e-17L; 40 41 #include "k_cospil.h" 42 #include "k_sinpil.h" 43 44 volatile static const double vzero = 0; 45 46 long double 47 cospil(long double x) 48 { 49 long double ax, c, xf; 50 uint32_t ix; 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 x = n + r with 0 <= r < 1. */ 76 xf = (ax + 0x1p112L) - 0x1p112L; /* Integer part */ 77 ax -= xf; /* Remainder */ 78 if (ax < 0) { 79 ax += 1; 80 xf -= 1; 81 } 82 83 if (ax < 0.5) { 84 if (ax < 0.25) 85 c = ax == 0 ? 1 : __kernel_cospil(ax); 86 else 87 c = __kernel_sinpil(0.5 - ax); 88 } else { 89 if (ax < 0.75) { 90 if (ax == 0.5) 91 return (0); 92 c = -__kernel_sinpil(ax - 0.5); 93 } else 94 c = -__kernel_cospil(1 - ax); 95 } 96 97 if (xf > 0x1p64) 98 xf -= 0x1p64; 99 if (xf > 0x1p32) 100 xf -= 0x1p32; 101 ix = (uint32_t)xf; 102 return (ix & 1 ? -c : c); 103 } 104 105 if (isinf(x) || isnan(x)) 106 return (vzero / vzero); 107 108 /* 109 * |x| >= 0x1p112 is always an even integer, so return 1. 110 */ 111 return (1); 112 } 113