1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD 3 * 4 * Copyright (c) 2007 Steven G. Kargl 5 * All rights reserved. 6 * 7 * Redistribution and use in source and binary forms, with or without 8 * modification, are permitted provided that the following conditions 9 * are met: 10 * 1. Redistributions of source code must retain the above copyright 11 * notice unmodified, this list of conditions, and the following 12 * disclaimer. 13 * 2. Redistributions in binary form must reproduce the above copyright 14 * notice, this list of conditions and the following disclaimer in the 15 * documentation and/or other materials provided with the distribution. 16 * 17 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 18 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 19 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 20 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 21 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 22 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 23 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 24 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 25 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 26 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 27 */ 28 29 #include <sys/cdefs.h> 30 __FBSDID("$FreeBSD$"); 31 32 /* 33 * Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows 34 * an accuracy of <= 0.7412 ULP. 35 */ 36 37 #include <float.h> 38 #ifdef __i386__ 39 #include <ieeefp.h> 40 #endif 41 42 #include "fpmath.h" 43 #include "math.h" 44 #include "math_private.h" 45 #if LDBL_MANT_DIG == 64 46 #include "../ld80/e_rem_pio2l.h" 47 static const union IEEEl2bits 48 pio4u = LD80C(0xc90fdaa22168c235, -00001, 7.85398163397448309628e-01L); 49 #define pio4 (pio4u.e) 50 #elif LDBL_MANT_DIG == 113 51 #include "../ld128/e_rem_pio2l.h" 52 long double pio4 = 7.85398163397448309615660845819875721e-1L; 53 #else 54 #error "Unsupported long double format" 55 #endif 56 57 long double 58 cosl(long double x) 59 { 60 union IEEEl2bits z; 61 int e0; 62 long double y[2]; 63 long double hi, lo; 64 65 z.e = x; 66 z.bits.sign = 0; 67 68 /* If x = +-0 or x is a subnormal number, then cos(x) = 1 */ 69 if (z.bits.exp == 0) 70 return (1.0); 71 72 /* If x = NaN or Inf, then cos(x) = NaN. */ 73 if (z.bits.exp == 32767) 74 return ((x - x) / (x - x)); 75 76 ENTERI(); 77 78 /* Optimize the case where x is already within range. */ 79 if (z.e < pio4) 80 RETURNI(__kernel_cosl(z.e, 0)); 81 82 e0 = __ieee754_rem_pio2l(x, y); 83 hi = y[0]; 84 lo = y[1]; 85 86 switch (e0 & 3) { 87 case 0: 88 hi = __kernel_cosl(hi, lo); 89 break; 90 case 1: 91 hi = - __kernel_sinl(hi, lo, 1); 92 break; 93 case 2: 94 hi = - __kernel_cosl(hi, lo); 95 break; 96 case 3: 97 hi = __kernel_sinl(hi, lo, 1); 98 break; 99 } 100 101 RETURNI(hi); 102 } 103