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_cospi.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 double 41 pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */ 42 pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */ 43 44 #include "k_cospil.h" 45 #include "k_sinpil.h" 46 47 volatile static const double vzero = 0; 48 49 long double 50 cospil(long double x) 51 { 52 long double ax, c; 53 uint64_t lx, m; 54 uint32_t j0; 55 uint16_t hx, ix; 56 57 EXTRACT_LDBL80_WORDS(hx, lx, x); 58 ix = hx & 0x7fff; 59 INSERT_LDBL80_WORDS(ax, ix, lx); 60 61 ENTERI(); 62 63 if (ix < 0x3fff) { /* |x| < 1 */ 64 if (ix < 0x3ffd) { /* |x| < 0.25 */ 65 if (ix < 0x3fdd) { /* |x| < 0x1p-34 */ 66 if ((int)x == 0) 67 RETURNI(1); 68 } 69 RETURNI(__kernel_cospil(ax)); 70 } 71 72 if (ix < 0x3ffe) /* |x| < 0.5 */ 73 c = __kernel_sinpil(0.5 - ax); 74 else if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */ 75 if (ax == 0.5) 76 RETURNI(0); 77 c = -__kernel_sinpil(ax - 0.5); 78 } else 79 c = -__kernel_cospil(1 - ax); 80 RETURNI(c); 81 } 82 83 if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */ 84 FFLOORL80(x, j0, ix, lx); /* Integer part of ax. */ 85 ax -= x; 86 EXTRACT_LDBL80_WORDS(ix, lx, ax); 87 88 if (ix < 0x3ffe) { /* |x| < 0.5 */ 89 if (ix < 0x3ffd) /* |x| < 0.25 */ 90 c = ix == 0 ? 1 : __kernel_cospil(ax); 91 else 92 c = __kernel_sinpil(0.5 - ax); 93 94 } else { 95 if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */ 96 if (ax == 0.5) 97 RETURNI(0); 98 c = -__kernel_sinpil(ax - 0.5); 99 } else 100 c = -__kernel_cospil(1 - ax); 101 } 102 103 if (j0 > 40) 104 x -= 0x1p40; 105 if (j0 > 30) 106 x -= 0x1p30; 107 j0 = (uint32_t)x; 108 109 RETURNI(j0 & 1 ? -c : c); 110 } 111 112 if (ix >= 0x7fff) 113 RETURNI(vzero / vzero); 114 115 /* 116 * For 0x1p63 <= |x| < 0x1p64 need to determine if x is an even 117 * or odd integer to return t = +1 or -1. 118 * For |x| >= 0x1p64, it is always an even integer, so t = 1. 119 */ 120 RETURNI(ix >= 0x403f ? 1 : ((lx & 1) ? -1 : 1)); 121 } 122