1 /* $OpenBSD: s_cosl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $ */ 2 /*- 3 * Copyright (c) 2007 Steven G. Kargl 4 * All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice unmodified, this list of conditions, and the following 11 * disclaimer. 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in the 14 * documentation and/or other materials provided with the distribution. 15 * 16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 17 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 18 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 19 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 20 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 21 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 22 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 23 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 24 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 25 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 26 */ 27 28 /* 29 * Compute cos(x) for x where x is reduced to y = x - k * pi / 2. 30 * Limited testing on pseudorandom numbers drawn within [-2e8:4e8] shows 31 * an accuracy of <= 0.7412 ULP. 32 */ 33 34 #include <sys/types.h> 35 #include <machine/ieee.h> 36 #include <float.h> 37 #include <math.h> 38 39 #include "math_private.h" 40 41 #if LDBL_MANT_DIG == 64 42 #define NX 3 43 #define PREC 2 44 #elif LDBL_MANT_DIG == 113 45 #define NX 5 46 #define PREC 3 47 #else 48 #error "Unsupported long double format" 49 #endif 50 51 static const long double two24 = 1.67772160000000000000e+07L; 52 53 long double 54 cosl(long double x) 55 { 56 union { 57 long double e; 58 struct ieee_ext bits; 59 } z; 60 int i, e0; 61 double xd[NX], yd[PREC]; 62 long double hi, lo; 63 64 z.e = x; 65 z.bits.ext_sign = 0; 66 67 /* If x = +-0 or x is a subnormal number, then cos(x) = 1 */ 68 if (z.bits.ext_exp == 0) 69 return (1.0); 70 71 /* If x = NaN or Inf, then cos(x) = NaN. */ 72 if (z.bits.ext_exp == 32767) 73 return ((x - x) / (x - x)); 74 75 /* Optimize the case where x is already within range. */ 76 if (z.e < M_PI_4) 77 return (__kernel_cosl(z.e, 0)); 78 79 /* Split z.e into a 24-bit representation. */ 80 e0 = ilogbl(z.e) - 23; 81 z.e = scalbnl(z.e, -e0); 82 for (i = 0; i < NX; i++) { 83 xd[i] = (double)((int32_t)z.e); 84 z.e = (z.e - xd[i]) * two24; 85 } 86 87 /* yd contains the pieces of xd rem pi/2 such that |yd| < pi/4. */ 88 e0 = __kernel_rem_pio2(xd, yd, e0, NX, PREC); 89 90 #if PREC == 2 91 hi = (long double)yd[0] + yd[1]; 92 lo = yd[1] - (hi - yd[0]); 93 #else /* PREC == 3 */ 94 long double t; 95 t = (long double)yd[2] + yd[1]; 96 hi = t + yd[0]; 97 lo = yd[0] - (hi - t); 98 #endif 99 100 switch (e0 & 3) { 101 case 0: 102 hi = __kernel_cosl(hi, lo); 103 break; 104 case 1: 105 hi = - __kernel_sinl(hi, lo, 1); 106 break; 107 case 2: 108 hi = - __kernel_cosl(hi, lo); 109 break; 110 case 3: 111 hi = __kernel_sinl(hi, lo, 1); 112 break; 113 } 114 115 return (hi); 116 } 117