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_sinpi.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 sinpil(long double x) 49 { 50 long double ai, ar, ax, hi, lo, s, xhi, xlo; 51 52 ax = fabsl(x); 53 54 if (ax < 1) { 55 if (ax < 0.25) { 56 if (ax < 0x1p-60) { 57 if (x == 0) 58 return (x); 59 hi = (double)x; 60 hi *= 0x1p113L; 61 lo = x * 0x1p113L - hi; 62 s = (pi_lo + pi_hi) * lo + pi_lo * lo + 63 pi_hi * hi; 64 return (s * 0x1p-113L); 65 } 66 67 s = __kernel_sinpil(ax); 68 return (x < 0 ? -s : s); 69 } 70 71 if (ax < 0.5) 72 s = __kernel_cospil(0.5 - ax); 73 else if (ax < 0.75) 74 s = __kernel_cospil(ax - 0.5); 75 else 76 s = __kernel_sinpil(1 - ax); 77 return (x < 0 ? -s : s); 78 } 79 80 if (ax < 0x1p112) { 81 /* Split ax = ai + ar with 0 <= ar < 1. */ 82 FFLOORL128(ax, ai, ar); 83 84 if (ar == 0) { 85 s = 0; 86 } else { 87 if (ar < 0.5) { 88 if (ar <= 0.25) 89 s = __kernel_sinpil(ar); 90 else 91 s = __kernel_cospil(0.5 - ar); 92 } else { 93 if (ar < 0.75) 94 s = __kernel_cospil(ar - 0.5); 95 else 96 s = __kernel_sinpil(1 - ar); 97 } 98 99 s = fmodl(ai, 2.L) == 0 ? s : -s; 100 } 101 return (x < 0 ? -s : s); 102 } 103 104 if (isinf(x) || isnan(x)) 105 return (vzero / vzero); 106 107 /* 108 * |x| >= 0x1p112 is always an integer, so return +-0. 109 */ 110 return (copysignl(0, x)); 111 } 112