usr/src/lib/libm/common/C/sincospi.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 /* INDENT OFF */
  31 /*
  32  * void sincospi(double x, double *s, double *c)
  33  * *s = sin(pi*x); *c = cos(pi*x);
  34  *
  35  * Algorithm, 10/17/2002, K.C. Ng
  36  * ------------------------------
  37  * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary).
  38  *      1. If y == z, then x is a multiple of pi/4. Return the following values:
  39  *             ---------------------------------------------------
  40  *               n  x mod 2    sin(x*pi)    cos(x*pi)   tan(x*pi)
  41  *             ---------------------------------------------------
  42  *              000  0.00       +0 ___       +1 ___      +0
  43  *              001  0.25       +\/0.5       +\/0.5      +1
  44  *              010  0.50       +1 ___       +0 ___      +inf
  45  *              011  0.75       +\/0.5       -\/0.5      -1
  46  *              100  1.00       -0 ___       -1 ___      +0
  47  *              101  1.25       -\/0.5       -\/0.5      +1
  48  *              110  1.50       -1 ___       -0 ___      +inf
  49  *              111  1.75       -\/0.5       +\/0.5      -1
  50  *             ---------------------------------------------------
  51  *      2. Otherwise,
  52  *             ---------------------------------------------------
  53  *               n     t        sin(x*pi)    cos(x*pi)   tan(x*pi)
  54  *             ---------------------------------------------------
  55  *              000  (y-z)/4     sinpi(t)     cospi(t)    tanpi(t)
  56  *              001  (z+1-y)/4   cospi(t)     sinpi(t)    1/tanpi(t)
  57  *              010  (y-z)/4     cospi(t)    -sinpi(t)   -1/tanpi(t)
  58  *              011  (z+1-y)/4   sinpi(t)    -cospi(t)   -tanpi(t)
  59  *              100  (y-z)/4    -sinpi(t)    -cospi(t)    tanpi(t)
  60  *              101  (z+1-y)/4  -cospi(t)    -sinpi(t)    1/tanpi(t)
  61  *              110  (y-z)/4    -cospi(t)     sinpi(t)   -1/tanpi(t)
  62  *              111  (z+1-y)/4  -sinpi(t)     cospi(t)   -tanpi(t)
  63  *             ---------------------------------------------------
  64  *
  65  * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0).
  66  * This will return a result with error slightly more than one ulp (but less
  67  * than 2 ulp). If one wants accurate result,  one may break up pi*t in
  68  * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo)
  69  * instead.
  70  */
  71
  72 #include "libm.h"
  73 #include "libm_protos.h"
  74 #include "libm_macros.h"
  75 #include <math.h>
  76 #if defined(__SUNPRO_C)
  77 #include <sunmath.h>
  78 #endif
  79
  80 static const double
  81         pi      = 3.14159265358979323846,       /* 400921FB,54442D18 */
  82         sqrth_h = 0.70710678118654757273731092936941422522068023681640625,
  83         sqrth_l = -4.8336466567264565185935844299127932213411660131004e-17;
  84 /* INDENT ON */
  85
  86 void
  87 sincospi(double x, double *s, double *c) {
  88         double y, z, t;
  89         int n, ix, k;
  90         int hx = ((int *) &x)[HIWORD];
  91         unsigned h, lx = ((unsigned *) &x)[LOWORD];
  92
  93         ix = hx & ~0x80000000;
  94         n = (ix >> 20) - 0x3ff;
  95         if (n >= 51) {                  /* |x| >= 2**51 */
  96                 if (n >= 1024)
  97 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
  98                         *s = *c = ix >= 0x7ff80000 ? x : x - x;
  99                         /* assumes sparc-like QNaN */
 100 #else
 101                         *s = *c = x - x;
 102 #endif
 103                 else {
 104                         if (n >= 53)  {
 105                                 *s = 0.0;
 106                                 *c = 1.0;
 107                         }
 108                         else if (n == 52)  {
 109                                 if ((lx & 1) == 0) {
 110                                         *s = 0.0;
 111                                         *c = 1.0;
 112                                 }
 113                                 else {
 114                                         *s = -0.0;
 115                                         *c = -1.0;
 116                                 }
 117                         }
 118                         else {  /* n == 51 */
 119                                 if ((lx & 1) == 0) {
 120                                         *s = 0.0;
 121                                         *c = 1.0;
 122                                 }
 123                                 else {
 124                                         *s = 1.0;
 125                                         *c = 0.0;
 126                                 }
 127                                 if ((lx & 2) != 0) {
 128                                         *s = -*s;
 129                                         *c = -*c;
 130                                 }
 131                         }
 132                 }
 133         }
 134         else if (n < -2)        /* |x| < 0.25 */
 135                 *s = __k_sincos(pi * fabs(x), 0.0, c);
 136         else {
 137                 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
 138                 if (ix < 0x41C00000) {          /* |x| < 2**29 */
 139                         y = 4.0 * fabs(x);
 140                         n = (int) y;            /* exact */
 141                         z = (double) n;
 142                         k = z == y;
 143                         t = (y - z) * 0.25;
 144                 }
 145                 else {                          /* 2**29 <= |x| < 2**51 */
 146                         y = fabs(x);
 147                         k = 50 - n;
 148                         n = lx >> k;
 149                         h = n << k;
 150                         ((unsigned *) &z)[LOWORD] = h;
 151                         ((int *) &z)[HIWORD] = ix;
 152                         k = h == lx;
 153                         t = y - z;
 154                 }
 155                 if (k) {                        /* x = N/4 */
 156                         if ((n & 1) != 0)
 157                                 *s = *c = sqrth_h + sqrth_l;
 158                         else
 159                                 if ((n & 2) == 0) {
 160                                         *s = 0.0;
 161                                         *c = 1.0;
 162                                 }
 163                                 else {
 164                                         *s = 1.0;
 165                                         *c = 0.0;
 166                                 }
 167                                 y = (n & 2) == 0 ? 0.0 : 1.0;
 168                                 if ((n & 4) != 0)
 169                                         *s = -*s;
 170                                 if (((n + 1) & 4) != 0)
 171                                         *c = -*c;
 172                 }
 173                 else {
 174                         if ((n & 1) != 0)
 175                                 t = 0.25 - t;
 176                         if (((n + (n & 1)) & 2) == 0)
 177                                 *s = __k_sincos(pi * t, 0.0, c);
 178                         else
 179                                 *c = __k_sincos(pi * t, 0.0, s);
 180                                 if ((n & 4) != 0)
 181                                         *s = -*s;
 182                                 if (((n + 2) & 4) != 0)
 183                                         *c = -*c;
 184                 }
 185         }
 186         if (hx < 0)
 187                 *s = -*s;
 188 }