1 /*- 2 * Copyright (c) 2017 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 "fpmath.h" 37 #include "math.h" 38 #include "math_private.h" 39 40 static const union IEEEl2bits 41 pi_hi_u = LD80C(0xc90fdaa200000000, 1, 3.14159265346825122833e+00L), 42 pi_lo_u = LD80C(0x85a308d313198a2e, -33, 1.21542010130123852029e-10L); 43 #define pi_hi (pi_hi_u.e) 44 #define pi_lo (pi_lo_u.e) 45 46 #include "k_cospil.h" 47 #include "k_sinpil.h" 48 49 volatile static const double vzero = 0; 50 51 long double 52 sinpil(long double x) 53 { 54 long double ax, hi, lo, s; 55 uint64_t lx, m; 56 uint32_t j0; 57 uint16_t hx, ix; 58 59 EXTRACT_LDBL80_WORDS(hx, lx, x); 60 ix = hx & 0x7fff; 61 INSERT_LDBL80_WORDS(ax, ix, lx); 62 63 ENTERI(); 64 65 if (ix < 0x3fff) { /* |x| < 1 */ 66 if (ix < 0x3ffd) { /* |x| < 0.25 */ 67 if (ix < 0x3fdd) { /* |x| < 0x1p-34 */ 68 if (x == 0) 69 RETURNI(x); 70 INSERT_LDBL80_WORDS(hi, hx, 71 lx & 0xffffffff00000000ull); 72 hi *= 0x1p63L; 73 lo = x * 0x1p63L - hi; 74 s = (pi_lo + pi_hi) * lo + pi_lo * hi + 75 pi_hi * hi; 76 RETURNI(s * 0x1p-63L); 77 } 78 s = __kernel_sinpil(ax); 79 RETURNI((hx & 0x8000) ? -s : s); 80 } 81 82 if (ix < 0x3ffe) /* |x| < 0.5 */ 83 s = __kernel_cospil(0.5 - ax); 84 else if (lx < 0xc000000000000000ull) /* |x| < 0.75 */ 85 s = __kernel_cospil(ax - 0.5); 86 else 87 s = __kernel_sinpil(1 - ax); 88 RETURNI((hx & 0x8000) ? -s : s); 89 } 90 91 if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */ 92 /* Determine integer part of ax. */ 93 j0 = ix - 0x3fff + 1; 94 if (j0 < 32) { 95 lx = (lx >> 32) << 32; 96 lx &= ~(((lx << 32)-1) >> j0); 97 } else { 98 m = (uint64_t)-1 >> (j0 + 1); 99 if (lx & m) lx &= ~m; 100 } 101 INSERT_LDBL80_WORDS(x, ix, lx); 102 103 ax -= x; 104 EXTRACT_LDBL80_WORDS(ix, lx, ax); 105 106 if (ix == 0) { 107 s = 0; 108 } else { 109 if (ix < 0x3ffe) { /* |x| < 0.5 */ 110 if (ix < 0x3ffd) /* |x| < 0.25 */ 111 s = __kernel_sinpil(ax); 112 else 113 s = __kernel_cospil(0.5 - ax); 114 } else { 115 /* |x| < 0.75 */ 116 if (lx < 0xc000000000000000ull) 117 s = __kernel_cospil(ax - 0.5); 118 else 119 s = __kernel_sinpil(1 - ax); 120 } 121 122 if (j0 > 40) 123 x -= 0x1p40; 124 if (j0 > 30) 125 x -= 0x1p30; 126 j0 = (uint32_t)x; 127 if (j0 & 1) s = -s; 128 } 129 RETURNI((hx & 0x8000) ? -s : s); 130 } 131 132 /* x = +-inf or nan. */ 133 if (ix >= 0x7fff) 134 RETURNI(vzero / vzero); 135 136 /* 137 * |x| >= 0x1p63 is always an integer, so return +-0. 138 */ 139 RETURNI(copysignl(0, x)); 140 } 141