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 #ifdef __i386__ 32 #include <ieeefp.h> 33 #endif 34 #include <stdint.h> 35 36 #include "math.h" 37 #include "math_private.h" 38 39 static const union ieee_ext_u 40 pi_hi_u = LD80C(0xc90fdaa200000000, 1, 3.14159265346825122833e+00L), 41 pi_lo_u = LD80C(0x85a308d313198a2e, -33, 1.21542010130123852029e-10L); 42 #define pi_hi (pi_hi_u.extu_ld) 43 #define pi_lo (pi_lo_u.extu_ld) 44 45 #include "k_cospil.h" 46 #include "k_sinpil.h" 47 48 static volatile const double vzero = 0; 49 50 long double 51 sinpil(long double x) 52 { 53 long double ax, hi, lo, s; 54 uint64_t lx; 55 uint32_t j0; 56 uint16_t hx, ix; 57 58 EXTRACT_LDBL80_WORDS(hx, lx, x); 59 ix = hx & 0x7fff; 60 INSERT_LDBL80_WORDS(ax, ix, lx); 61 62 ENTERI(); 63 64 if (ix < 0x3fff) { /* |x| < 1 */ 65 if (ix < 0x3ffd) { /* |x| < 0.25 */ 66 if (ix < 0x3fdd) { /* |x| < 0x1p-34 */ 67 if (x == 0) 68 RETURNI(x); 69 INSERT_LDBL80_WORDS(hi, hx, 70 lx & 0xffffffff00000000ull); 71 hi *= 0x1p63L; 72 lo = x * 0x1p63L - hi; 73 s = (pi_lo + pi_hi) * lo + pi_lo * hi + 74 pi_hi * hi; 75 RETURNI(s * 0x1p-63L); 76 } 77 s = __kernel_sinpil(ax); 78 RETURNI((hx & 0x8000) ? -s : s); 79 } 80 81 if (ix < 0x3ffe) /* |x| < 0.5 */ 82 s = __kernel_cospil(0.5 - ax); 83 else if (lx < 0xc000000000000000ull) /* |x| < 0.75 */ 84 s = __kernel_cospil(ax - 0.5); 85 else 86 s = __kernel_sinpil(1 - ax); 87 RETURNI((hx & 0x8000) ? -s : s); 88 } 89 90 if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */ 91 FFLOORL80(x, j0, ix, lx); /* Integer part of ax. */ 92 ax -= x; 93 EXTRACT_LDBL80_WORDS(ix, lx, ax); 94 95 if (ix == 0) { 96 s = 0; 97 } else { 98 if (ix < 0x3ffe) { /* |x| < 0.5 */ 99 if (ix < 0x3ffd) /* |x| < 0.25 */ 100 s = __kernel_sinpil(ax); 101 else 102 s = __kernel_cospil(0.5 - ax); 103 } else { 104 /* |x| < 0.75 */ 105 if (lx < 0xc000000000000000ull) 106 s = __kernel_cospil(ax - 0.5); 107 else 108 s = __kernel_sinpil(1 - ax); 109 } 110 111 if (j0 > 40) 112 x -= 0x1p40; 113 if (j0 > 30) 114 x -= 0x1p30; 115 j0 = (uint32_t)x; 116 if (j0 & 1) s = -s; 117 } 118 RETURNI((hx & 0x8000) ? -s : s); 119 } 120 121 /* x = +-inf or nan. */ 122 if (ix >= 0x7fff) 123 RETURNI(vzero / vzero); 124 125 /* 126 * |x| >= 0x1p63 is always an integer, so return +-0. 127 */ 128 RETURNI(copysignl(0, x)); 129 } 130