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 <stdint.h> 32 33 #include "math.h" 34 #include "math_private.h" 35 36 static const union ieee_ext_u 37 pi_hi_u = LD80C(0xc90fdaa200000000, 1, 3.14159265346825122833e+00L), 38 pi_lo_u = LD80C(0x85a308d313198a2e, -33, 1.21542010130123852029e-10L); 39 #define pi_hi (pi_hi_u.extu_ld) 40 #define pi_lo (pi_lo_u.extu_ld) 41 42 #include "k_cospil.h" 43 #include "k_sinpil.h" 44 45 static volatile const double vzero = 0; 46 47 long double 48 sinpil(long double x) 49 { 50 long double ax, hi, lo, s; 51 uint64_t lx; 52 uint32_t j0; 53 uint16_t hx, ix; 54 55 EXTRACT_LDBL80_WORDS(hx, lx, x); 56 ix = hx & 0x7fff; 57 INSERT_LDBL80_WORDS(ax, ix, lx); 58 59 ENTERI(); 60 61 if (ix < 0x3fff) { /* |x| < 1 */ 62 if (ix < 0x3ffd) { /* |x| < 0.25 */ 63 if (ix < 0x3fdd) { /* |x| < 0x1p-34 */ 64 if (x == 0) 65 RETURNI(x); 66 INSERT_LDBL80_WORDS(hi, hx, 67 lx & 0xffffffff00000000ull); 68 hi *= 0x1p63L; 69 lo = x * 0x1p63L - hi; 70 s = (pi_lo + pi_hi) * lo + pi_lo * hi + 71 pi_hi * hi; 72 RETURNI(s * 0x1p-63L); 73 } 74 s = __kernel_sinpil(ax); 75 RETURNI((hx & 0x8000) ? -s : s); 76 } 77 78 if (ix < 0x3ffe) /* |x| < 0.5 */ 79 s = __kernel_cospil(0.5 - ax); 80 else if (lx < 0xc000000000000000ull) /* |x| < 0.75 */ 81 s = __kernel_cospil(ax - 0.5); 82 else 83 s = __kernel_sinpil(1 - ax); 84 RETURNI((hx & 0x8000) ? -s : s); 85 } 86 87 if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */ 88 FFLOORL80(x, j0, ix, lx); /* Integer part of ax. */ 89 ax -= x; 90 EXTRACT_LDBL80_WORDS(ix, lx, ax); 91 92 if (ix == 0) { 93 s = 0; 94 } else { 95 if (ix < 0x3ffe) { /* |x| < 0.5 */ 96 if (ix < 0x3ffd) /* |x| < 0.25 */ 97 s = __kernel_sinpil(ax); 98 else 99 s = __kernel_cospil(0.5 - ax); 100 } else { 101 /* |x| < 0.75 */ 102 if (lx < 0xc000000000000000ull) 103 s = __kernel_cospil(ax - 0.5); 104 else 105 s = __kernel_sinpil(1 - ax); 106 } 107 108 if (j0 > 40) 109 x -= 0x1p40; 110 if (j0 > 30) 111 x -= 0x1p30; 112 j0 = (uint32_t)x; 113 if (j0 & 1) s = -s; 114 } 115 RETURNI((hx & 0x8000) ? -s : s); 116 } 117 118 /* x = +-inf or nan. */ 119 if (ix >= 0x7fff) 120 RETURNI(vzero / vzero); 121 122 /* 123 * |x| >= 0x1p63 is always an integer, so return +-0. 124 */ 125 RETURNI(copysignl(0, x)); 126 } 127