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
  77 static const double
  78         pi      = 3.14159265358979323846,       /* 400921FB,54442D18 */
  79         sqrth_h = 0.70710678118654757273731092936941422522068023681640625,
  80         sqrth_l = -4.8336466567264565185935844299127932213411660131004e-17;
  81 /* INDENT ON */
  82
  83 void
  84 sincospi(double x, double *s, double *c)
  85 {
  86         double y, z, t;
  87         int n, ix, k;
  88         int hx = ((int *)&x)[HIWORD];
  89         unsigned h, lx = ((unsigned *)&x)[LOWORD];
  90
  91         ix = hx & ~0x80000000;
  92         n = (ix >> 20) - 0x3ff;
  93         if (n >= 51) {                  /* |x| >= 2**51 */
  94                 if (n >= 1024) {
  95 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
  96                         *s = *c = ix >= 0x7ff80000 ? x : x - x;
  97                         /* assumes sparc-like QNaN */
  98 #else
  99                         *s = *c = x - x;
 100 #endif
 101                 } else {
 102                         if (n >= 53) {
 103                                 *s = 0.0;
 104                                 *c = 1.0;
 105                         } else if (n == 52) {
 106                                 if ((lx & 1) == 0) {
 107                                         *s = 0.0;
 108                                         *c = 1.0;
 109                                 } else {
 110                                         *s = -0.0;
 111                                         *c = -1.0;
 112                                 }
 113                         } else {        /* n == 51 */
 114                                 if ((lx & 1) == 0) {
 115                                         *s = 0.0;
 116                                         *c = 1.0;
 117                                 } else {
 118                                         *s = 1.0;
 119                                         *c = 0.0;
 120                                 }
 121                                 if ((lx & 2) != 0) {
 122                                         *s = -*s;
 123                                         *c = -*c;
 124                                 }
 125                         }
 126                 }
 127         } else if (n < -2)      /* |x| < 0.25 */
 128                 *s = __k_sincos(pi * fabs(x), 0.0, c);
 129         else {
 130                 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */
 131                 if (ix < 0x41C00000) {          /* |x| < 2**29 */
 132                         y = 4.0 * fabs(x);
 133                         n = (int)y;             /* exact */
 134                         z = (double)n;
 135                         k = z == y;
 136                         t = (y - z) * 0.25;
 137                 } else {                        /* 2**29 <= |x| < 2**51 */
 138                         y = fabs(x);
 139                         k = 50 - n;
 140                         n = lx >> k;
 141                         h = n << k;
 142                         ((unsigned *)&z)[LOWORD] = h;
 143                         ((int *)&z)[HIWORD] = ix;
 144                         k = h == lx;
 145                         t = y - z;
 146                 }
 147                 if (k) {                        /* x = N/4 */
 148                         if ((n & 1) != 0) {
 149                                 *s = *c = sqrth_h + sqrth_l;
 150                         } else {
 151                                 if ((n & 2) == 0) {
 152                                         *s = 0.0;
 153                                         *c = 1.0;
 154                                 } else {
 155                                         *s = 1.0;
 156                                         *c = 0.0;
 157                                 }
 158                         }
 159                         if ((n & 4) != 0)
 160                                 *s = -*s;
 161                         if (((n + 1) & 4) != 0)
 162                                 *c = -*c;
 163                 } else {
 164                         if ((n & 1) != 0)
 165                                 t = 0.25 - t;
 166                         if (((n + (n & 1)) & 2) == 0)
 167                                 *s = __k_sincos(pi * t, 0.0, c);
 168                         else
 169                                 *c = __k_sincos(pi * t, 0.0, s);
 170                         if ((n & 4) != 0)
 171                                 *s = -*s;
 172                         if (((n + 2) & 4) != 0)
 173                                 *c = -*c;
 174                 }
 175         }
 176         if (hx < 0)
 177                 *s = -*s;
 178 }