1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause 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 /* 30 * Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows 31 * an accuracy of <= 0.7412 ULP. 32 */ 33 34 #include <float.h> 35 #ifdef __i386__ 36 #include <ieeefp.h> 37 #endif 38 39 #include "fpmath.h" 40 #include "math.h" 41 #include "math_private.h" 42 #if LDBL_MANT_DIG == 64 43 #include "../ld80/e_rem_pio2l.h" 44 static const union IEEEl2bits 45 pio4u = LD80C(0xc90fdaa22168c235, -00001, 7.85398163397448309628e-01L); 46 #define pio4 (pio4u.e) 47 #elif LDBL_MANT_DIG == 113 48 #include "../ld128/e_rem_pio2l.h" 49 long double pio4 = 7.85398163397448309615660845819875721e-1L; 50 #else 51 #error "Unsupported long double format" 52 #endif 53 54 long double 55 cosl(long double x) 56 { 57 union IEEEl2bits z; 58 int e0; 59 long double y[2]; 60 long double hi, lo; 61 62 z.e = x; 63 z.bits.sign = 0; 64 65 /* If x = +-0 or x is a subnormal number, then cos(x) = 1 */ 66 if (z.bits.exp == 0) 67 return (1.0); 68 69 /* If x = NaN or Inf, then cos(x) = NaN. */ 70 if (z.bits.exp == 32767) 71 return ((x - x) / (x - x)); 72 73 ENTERI(); 74 75 /* Optimize the case where x is already within range. */ 76 if (z.e < pio4) 77 RETURNI(__kernel_cosl(z.e, 0)); 78 79 e0 = __ieee754_rem_pio2l(x, y); 80 hi = y[0]; 81 lo = y[1]; 82 83 switch (e0 & 3) { 84 case 0: 85 hi = __kernel_cosl(hi, lo); 86 break; 87 case 1: 88 hi = - __kernel_sinl(hi, lo, 1); 89 break; 90 case 2: 91 hi = - __kernel_cosl(hi, lo); 92 break; 93 case 3: 94 hi = __kernel_sinl(hi, lo, 1); 95 break; 96 } 97 98 RETURNI(hi); 99 } 100