1 /*- 2 * Copyright (c) 2007 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 #include <sys/cdefs.h> 28 __FBSDID("$FreeBSD$"); 29 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 37 #include "math.h" 38 #define INLINE_REM_PIO2L 39 #include "math_private.h" 40 #if LDBL_MANT_DIG == 64 41 #include "../ld80/e_rem_pio2l.h" 42 #elif LDBL_MANT_DIG == 113 43 #include "../ld128/e_rem_pio2l.h" 44 #else 45 #error "Unsupported long double format" 46 #endif 47 48 long double 49 cosl(long double x) 50 { 51 union IEEEl2bits z; 52 int e0; 53 long double y[2]; 54 long double hi, lo; 55 56 z.e = x; 57 z.bits.sign = 0; 58 59 /* If x = +-0 or x is a subnormal number, then cos(x) = 1 */ 60 if (z.bits.exp == 0) 61 return (1.0); 62 63 /* If x = NaN or Inf, then cos(x) = NaN. */ 64 if (z.bits.exp == 32767) 65 return ((x - x) / (x - x)); 66 67 /* Optimize the case where x is already within range. */ 68 if (z.e < M_PI_4) 69 return (__kernel_cosl(z.e, 0)); 70 71 e0 = __ieee754_rem_pio2l(x, y); 72 hi = y[0]; 73 lo = y[1]; 74 75 switch (e0 & 3) { 76 case 0: 77 hi = __kernel_cosl(hi, lo); 78 break; 79 case 1: 80 hi = - __kernel_sinl(hi, lo, 1); 81 break; 82 case 2: 83 hi = - __kernel_cosl(hi, lo); 84 break; 85 case 3: 86 hi = __kernel_sinl(hi, lo, 1); 87 break; 88 } 89 90 return (hi); 91 } 92