usr/src/lib/libm/common/LD/sincospil.c

   1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 /*
  26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29
  30 /*
  31  * void sincospil(long double x, long double *s, long double *c)
  32  * *s = sinl(pi*x); *c = cosl(pi*x);
  33  *
  34  * Algorithm, 10/17/2002, K.C. Ng
  35  * ------------------------------
  36  * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
  37  *      1. If y == z, then x is a multiple of pi/4. Return the following values:
  38  *             ---------------------------------------------------
  39  *               n  x mod 2    sin(x*pi)    cos(x*pi)   tan(x*pi)
  40  *             ---------------------------------------------------
  41  *              000  0.00       +0 ___       +1 ___      +0
  42  *              001  0.25       +\/0.5       +\/0.5      +1
  43  *              010  0.50       +1 ___       +0 ___      +inf
  44  *              011  0.75       +\/0.5       -\/0.5      -1
  45  *              100  1.00       -0 ___       -1 ___      +0
  46  *              101  1.25       -\/0.5       -\/0.5      +1
  47  *              110  1.50       -1 ___       -0 ___      +inf
  48  *              111  1.75       -\/0.5       +\/0.5      -1
  49  *             ---------------------------------------------------
  50  *      2. Otherwise,
  51  *             ---------------------------------------------------
  52  *               n     t        sin(x*pi)    cos(x*pi)   tan(x*pi)
  53  *             ---------------------------------------------------
  54  *              000  (y-z)/4     sinpi(t)     cospi(t)    tanpi(t)
  55  *              001  (z+1-y)/4   cospi(t)     sinpi(t)    1/tanpi(t)
  56  *              010  (y-z)/4     cospi(t)    -sinpi(t)   -1/tanpi(t)
  57  *              011  (z+1-y)/4   sinpi(t)    -cospi(t)   -tanpi(t)
  58  *              100  (y-z)/4    -sinpi(t)    -cospi(t)    tanpi(t)
  59  *              101  (z+1-y)/4  -cospi(t)    -sinpi(t)    1/tanpi(t)
  60  *              110  (y-z)/4    -cospi(t)     sinpi(t)   -1/tanpi(t)
  61  *              111  (z+1-y)/4  -sinpi(t)     cospi(t)   -tanpi(t)
  62  *             ---------------------------------------------------
  63  *
  64  * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
  65  * This will return a result with error slightly more than one ulp (but less
  66  * than 2 ulp). If one wants accurate result,  one may break up pi*t in
  67  * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
  68  * instead.
  69  */
  70
  71 #include "libm.h"
  72 #include "longdouble.h"
  73
  74 #include <sys/isa_defs.h>
  75
  76 #define I(q, m) ((int *) &(q))[m]
  77 #define U(q, m) ((unsigned *) &(q))[m]
  78 #if defined(__i386) || defined(__amd64)
  79 #define LDBL_MOST_SIGNIF_I(ld)  ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15)))
  80 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0)
  81 #define PREC    64
  82 #define PRECM1  63
  83 #define PRECM2  62
  84 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L;
  85 #else
  86 #define LDBL_MOST_SIGNIF_I(ld)  I(ld, 0)
  87 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof(long double) / sizeof(int) - 1)
  88 #define PREC    113
  89 #define PRECM1  112
  90 #define PRECM2  111
  91 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L;
  92 #endif
  93
  94 static const long double
  95 zero    = 0.0L,
  96 quater  = 0.25L,
  97 one     = 1.0L,
  98 pi      = 3.141592653589793238462643383279502884197e+0000L,
  99 sqrth   = 0.707106781186547524400844362104849039284835937688474,
 100 tiny    = 1.0e-100;
 101
 102 void
 103 sincospil(long double x, long double *s, long double *c) {
 104         long double y, z, t;
 105         int hx, n, k;
 106         unsigned lx;
 107
 108         hx = LDBL_MOST_SIGNIF_I(x);
 109         lx = LDBL_LEAST_SIGNIF_U(x);
 110         k = ((hx & 0x7fff0000) >> 16) - 0x3fff;
 111         if (k >= PRECM2) {              /* |x| >= 2**(Prec-2) */
 112                 if (k >= 16384) {
 113                         *s = *c = x - x;
 114                 }
 115                 else {
 116                         if (k >= PREC) {
 117                                 *s = zero;
 118                                 *c = one;
 119                         }
 120                         else if (k == PRECM1) {
 121                                 if ((lx & 1) == 0) {
 122                                         *s = zero;
 123                                         *c = one;
 124                                 }
 125                                 else {
 126                                         *s = -zero;
 127                                         *c = -one;
 128                                 }
 129                         }
 130                         else {  /* k = Prec - 2 */
 131                                 if ((lx & 1) == 0) {
 132                                         *s = zero;
 133                                         *c = one;
 134                                 }
 135                                 else {
 136                                         *s = one;
 137                                         *c = zero;
 138                                 }
 139                                 if ((lx & 2) != 0) {
 140                                         *s = -*s;
 141                                         *c = -*c;
 142                                 }
 143                         }
 144                 }
 145         }
 146         else if (k < -2)        /* |x| < 0.25 */
 147                 *s = __k_sincosl(pi * fabsl(x), zero, c);
 148         else {
 149                 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
 150                 y = 4.0L * fabsl(x);
 151                 if (k < PRECM2) {
 152                         z = y + twoPRECM2;
 153                         n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */
 154                         t = z - twoPRECM2;
 155                         k = 0;
 156                         if (t == y)
 157                                 k = 1;
 158                         else if (t > y) {
 159                                 n -= 1;
 160                                 t = quater + (y - t) * quater;
 161                         }
 162                         else
 163                                 t = (y - t) * quater;
 164                 }
 165                 else {  /* k = Prec-3 */
 166                         n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */
 167                         k = 1;
 168                 }
 169                 if (k) {        /* x = N/4 */
 170                         if ((n & 1) != 0)
 171                                 *s = *c = sqrth + tiny;
 172                         else
 173                                 if ((n & 2) == 0) {
 174                                         *s = zero;
 175                                         *c = one;
 176                                 }
 177                                 else {
 178                                         *s = one;
 179                                         *c = zero;
 180                                 }
 181                         if ((n & 4) != 0)
 182                                 *s = -*s;
 183                         if (((n + 1) & 4) != 0)
 184                                 *c = -*c;
 185                 }
 186                 else {
 187                         if ((n & 1) != 0)
 188                                 t = quater - t;
 189                         if (((n + (n & 1)) & 2) == 0)
 190                                 *s = __k_sincosl(pi * t, zero, c);
 191                         else
 192                                 *c = __k_sincosl(pi * t, zero, s);
 193                         if ((n & 4) != 0)
 194                                 *s = -*s;
 195                         if (((n + 2) & 4) != 0)
 196                                 *c = -*c;
 197                 }
 198         }
 199         if (hx < 0)
 200                 *s = -*s;
 201 }
 202 #undef U
 203 #undef LDBL_LEAST_SIGNIF_U
 204 #undef I
 205 #undef LDBL_MOST_SIGNIF_I