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 #include <sys/cdefs.h> 30 /* 31 * Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows 32 * an accuracy of <= 0.7412 ULP. 33 */ 34 35 #include <float.h> 36 #ifdef __i386__ 37 #include <ieeefp.h> 38 #endif 39 40 #include "fpmath.h" 41 #include "math.h" 42 #include "math_private.h" 43 #if LDBL_MANT_DIG == 64 44 #include "../ld80/e_rem_pio2l.h" 45 static const union IEEEl2bits 46 pio4u = LD80C(0xc90fdaa22168c235, -00001, 7.85398163397448309628e-01L); 47 #define pio4 (pio4u.e) 48 #elif LDBL_MANT_DIG == 113 49 #include "../ld128/e_rem_pio2l.h" 50 long double pio4 = 7.85398163397448309615660845819875721e-1L; 51 #else 52 #error "Unsupported long double format" 53 #endif 54 55 long double 56 cosl(long double x) 57 { 58 union IEEEl2bits z; 59 int e0; 60 long double y[2]; 61 long double hi, lo; 62 63 z.e = x; 64 z.bits.sign = 0; 65 66 /* If x = +-0 or x is a subnormal number, then cos(x) = 1 */ 67 if (z.bits.exp == 0) 68 return (1.0); 69 70 /* If x = NaN or Inf, then cos(x) = NaN. */ 71 if (z.bits.exp == 32767) 72 return ((x - x) / (x - x)); 73 74 ENTERI(); 75 76 /* Optimize the case where x is already within range. */ 77 if (z.e < pio4) 78 RETURNI(__kernel_cosl(z.e, 0)); 79 80 e0 = __ieee754_rem_pio2l(x, y); 81 hi = y[0]; 82 lo = y[1]; 83 84 switch (e0 & 3) { 85 case 0: 86 hi = __kernel_cosl(hi, lo); 87 break; 88 case 1: 89 hi = - __kernel_sinl(hi, lo, 1); 90 break; 91 case 2: 92 hi = - __kernel_cosl(hi, lo); 93 break; 94 case 3: 95 hi = __kernel_sinl(hi, lo, 1); 96 break; 97 } 98 99 RETURNI(hi); 100 } 101