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 "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 47sinpil(long double x) 48{ 49 long double ai, ar, ax, hi, lo, s; 50 51 ax = fabsl(x); 52 53 if (ax < 1) { 54 if (ax < 0.25) { 55 if (ax < 0x1p-60) { 56 if (x == 0) 57 return (x); 58 hi = (double)x; 59 hi *= 0x1p113L; 60 lo = x * 0x1p113L - hi; 61 s = (pi_lo + pi_hi) * lo + pi_lo * lo + 62 pi_hi * hi; 63 return (s * 0x1p-113L); 64 } 65 66 s = __kernel_sinpil(ax); 67 return (x < 0 ? -s : s); 68 } 69 70 if (ax < 0.5) 71 s = __kernel_cospil(0.5 - ax); 72 else if (ax < 0.75) 73 s = __kernel_cospil(ax - 0.5); 74 else 75 s = __kernel_sinpil(1 - ax); 76 return (x < 0 ? -s : s); 77 } 78 79 if (ax < 0x1p112) { 80 /* Split ax = ai + ar with 0 <= ar < 1. */ 81 FFLOORL128(ax, ai, ar); 82 83 if (ar == 0) { 84 s = 0; 85 } else { 86 if (ar < 0.5) { 87 if (ar <= 0.25) 88 s = __kernel_sinpil(ar); 89 else 90 s = __kernel_cospil(0.5 - ar); 91 } else { 92 if (ar < 0.75) 93 s = __kernel_cospil(ar - 0.5); 94 else 95 s = __kernel_sinpil(1 - ar); 96 } 97 98 s = fmodl(ai, 2.L) == 0 ? s : -s; 99 } 100 return (x < 0 ? -s : s); 101 } 102 103 if (isinf(x) || isnan(x)) 104 return (vzero / vzero); 105 106 /* 107 * |x| >= 0x1p112 is always an integer, so return +-0. 108 */ 109 return (copysignl(0, x)); 110} 111