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 #include <stdint.h> 32 33 #include "math.h" 34 #include "math_private.h" 35 36 static const double 37 pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */ 38 pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */ 39 40 #include "k_cospil.h" 41 #include "k_sinpil.h" 42 43 static volatile const double vzero = 0; 44 45 long double 46 cospil(long double x) 47 { 48 long double ax, c; 49 uint64_t lx; 50 uint32_t j0; 51 uint16_t hx, ix; 52 53 EXTRACT_LDBL80_WORDS(hx, lx, x); 54 ix = hx & 0x7fff; 55 INSERT_LDBL80_WORDS(ax, ix, lx); 56 57 ENTERI(); 58 59 if (ix < 0x3fff) { /* |x| < 1 */ 60 if (ix < 0x3ffd) { /* |x| < 0.25 */ 61 if (ix < 0x3fdd) { /* |x| < 0x1p-34 */ 62 if ((int)x == 0) 63 RETURNI(1); 64 } 65 RETURNI(__kernel_cospil(ax)); 66 } 67 68 if (ix < 0x3ffe) /* |x| < 0.5 */ 69 c = __kernel_sinpil(0.5 - ax); 70 else if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */ 71 if (ax == 0.5) 72 RETURNI(0); 73 c = -__kernel_sinpil(ax - 0.5); 74 } else 75 c = -__kernel_cospil(1 - ax); 76 RETURNI(c); 77 } 78 79 if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */ 80 FFLOORL80(x, j0, ix, lx); /* Integer part of ax. */ 81 ax -= x; 82 EXTRACT_LDBL80_WORDS(ix, lx, ax); 83 84 if (ix < 0x3ffe) { /* |x| < 0.5 */ 85 if (ix < 0x3ffd) /* |x| < 0.25 */ 86 c = ix == 0 ? 1 : __kernel_cospil(ax); 87 else 88 c = __kernel_sinpil(0.5 - ax); 89 90 } else { 91 if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */ 92 if (ax == 0.5) 93 RETURNI(0); 94 c = -__kernel_sinpil(ax - 0.5); 95 } else 96 c = -__kernel_cospil(1 - ax); 97 } 98 99 if (j0 > 40) 100 x -= 0x1p40; 101 if (j0 > 30) 102 x -= 0x1p30; 103 j0 = (uint32_t)x; 104 105 RETURNI(j0 & 1 ? -c : c); 106 } 107 108 if (ix >= 0x7fff) 109 RETURNI(vzero / vzero); 110 111 /* 112 * For 0x1p63 <= |x| < 0x1p64 need to determine if x is an even 113 * or odd integer to return t = +1 or -1. 114 * For |x| >= 0x1p64, it is always an even integer, so t = 1. 115 */ 116 RETURNI(ix >= 0x403f ? 1 : ((lx & 1) ? -1 : 1)); 117 } 118