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 * Compute cos(x) for x where x is reduced to y = x - k * pi / 2. 32 * Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows 33 * an accuracy of <= 0.7412 ULP. 34 */ 35 36 #include <float.h> 37 38 #include "math.h" 39 #include "math_private.h" 40 #include "fpmath.h" 41 42 #if LDBL_MANT_DIG == 64 43 #define NX 3 44 #define PREC 2 45 #elif LDBL_MANT_DIG == 113 46 #define NX 5 47 #define PREC 3 48 #else 49 #error "Unsupported long double format" 50 #endif 51 52 static const long double two24 = 1.67772160000000000000e+07L; 53 54 long double 55 cosl(long double x) 56 { 57 union IEEEl2bits z; 58 int i, e0; 59 double xd[NX], yd[PREC]; 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 /* Optimize the case where x is already within range. */ 74 if (z.e < M_PI_4) 75 return (__kernel_cosl(z.e, 0)); 76 77 /* Split z.e into a 24-bit representation. */ 78 e0 = ilogbl(z.e) - 23; 79 z.e = scalbnl(z.e, -e0); 80 for (i = 0; i < NX; i++) { 81 xd[i] = (double)((int32_t)z.e); 82 z.e = (z.e - xd[i]) * two24; 83 } 84 85 /* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */ 86 e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC); 87 88 #if PREC == 2 89 hi = (long double)yd[0] + yd[1]; 90 lo = yd[1] - (hi - yd[0]); 91 #else /* PREC == 3 */ 92 long double t; 93 t = (long double)yd[2] + yd[1]; 94 hi = t + yd[0]; 95 lo = yd[0] - (hi - t); 96 #endif 97 98 switch (e0 & 3) { 99 case 0: 100 hi = __kernel_cosl(hi, lo); 101 break; 102 case 1: 103 hi = - __kernel_sinl(hi, lo, 1); 104 break; 105 case 2: 106 hi = - __kernel_cosl(hi, lo); 107 break; 108 case 3: 109 hi = __kernel_sinl(hi, lo, 1); 110 break; 111 } 112 113 return (hi); 114 } 115