usr/src/lib/libm/common/C/sin.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  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  23  */
  24 /*
  25  * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
  26  * Use is subject to license terms.
  27  */
  28
  29 #pragma weak __sin = sin
  30
  31 /* INDENT OFF */
  32 /*
  33  * sin(x)
  34  * Accurate Table look-up algorithm by K.C. Ng, May, 1995.
  35  *
  36  * Algorithm: see sincos.c
  37  */
  38
  39 #include "libm.h"
  40
  41 static const double sc[] = {
  42 /* ONE  = */  1.0,
  43 /* NONE = */ -1.0,
  44 /*
  45  * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008
  46  */
  47 /* PP1  = */ -0.166666666666316558867252052378889521480627858683055567,
  48 /* PP2  = */   .008333315652997472323564894248466758248475374977974017927,
  49 /*
  50  * |(sin(x) - (x+p1*x^3+...+p4*x^9)|
  51  * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125
  52  * |                 x             |
  53  */
  54 /* P1   = */ -1.666666666666629669805215138920301589656e-0001,
  55 /* P2   = */  8.333333332390951295683993455280336376663e-0003,
  56 /* P3   = */ -1.984126237997976692791551778230098403960e-0004,
  57 /* P4   = */  2.753403624854277237649987622848330351110e-0006,
  58 /*
  59  * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d)
  60  */
  61 /* QQ1  = */ -0.4999999999975492381842911981948418542742729,
  62 /* QQ2  = */  0.041666542904352059294545209158357640398771740,
  63 /* PI_H = */  3.1415926535897931159979634685,
  64 /* PI_L    = */  1.22464679914735317722606593227425e-16,
  65 /* PI_L0   = */  1.22464679914558443311283879205095e-16,
  66 /* PI_L1   = */  1.768744113227140223300005233735517376e-28,
  67 /* PI2_H   = */  6.2831853071795862319959269370,
  68 /* PI2_L   = */  2.44929359829470635445213186454850e-16,
  69 /* PI2_L0  = */  2.44929359829116886622567758410190e-16,
  70 /* PI2_L1  = */  3.537488226454280446600010467471034752e-28,
  71 };
  72 /* INDENT ON */
  73
  74 #define ONEA    sc
  75 #define ONE     sc[0]
  76 #define NONE    sc[1]
  77 #define PP1     sc[2]
  78 #define PP2     sc[3]
  79 #define P1      sc[4]
  80 #define P2      sc[5]
  81 #define P3      sc[6]
  82 #define P4      sc[7]
  83 #define QQ1     sc[8]
  84 #define QQ2     sc[9]
  85 #define PI_H    sc[10]
  86 #define PI_L    sc[11]
  87 #define PI_L0   sc[12]
  88 #define PI_L1   sc[13]
  89 #define PI2_H   sc[14]
  90 #define PI2_L   sc[15]
  91 #define PI2_L0  sc[16]
  92 #define PI2_L1  sc[17]
  93
  94 extern const double  _TBL_sincos[], _TBL_sincosx[];
  95
  96 double
  97 sin(double x) {
  98         double  z, y[2], w, s, v, p, q;
  99         int     i, j, n, hx, ix, lx;
 100
 101         hx = ((int *)&x)[HIWORD];
 102         lx = ((int *)&x)[LOWORD];
 103         ix = hx & ~0x80000000;
 104
 105         if (ix <= 0x3fc50000) { /* |x| < .1640625 */
 106                 if (ix < 0x3e400000)    /* |x| < 2**-27 */
 107                         if ((int)x == 0)
 108                                 return (x);
 109                 z = x * x;
 110                 if (ix < 0x3f800000)    /* |x| < 2**-8 */
 111                         w = (z * x) * (PP1 + z * PP2);
 112                 else
 113                         w = (x * z) * ((P1 + z * P2) + (z * z) * (P3 + z * P4));
 114                 return (x + w);
 115         }
 116
 117         /* for .1640625 < x < M, */
 118         n = ix >> 20;
 119         if (n < 0x402) {        /* x < 8 */
 120                 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
 121                 j = i - 10;
 122                 x = fabs(x);
 123                 v = x - _TBL_sincosx[j];
 124                 if (((j - 181) ^ (j - 201)) < 0) {
 125                         /* near pi, sin(x) = sin(pi-x) */
 126                         p = PI_H - x;
 127                         i = ix - 0x400921fb;
 128                         x = p + PI_L;
 129                         if ((i | ((lx - 0x54442D00) & 0xffffff00)) == 0) {
 130                                 /* very close to pi */
 131                                 x = p + PI_L0;
 132                                 return ((hx >= 0)? x + PI_L1 : -(x + PI_L1));
 133                         }
 134                         z = x * x;
 135                         if (((ix - 0x40092000) >> 11) == 0) {
 136                                 /* |pi-x|<2**-8 */
 137                                 w = PI_L + (z * x) * (PP1 + z * PP2);
 138                         } else {
 139                                 w = PI_L + (z * x) * ((P1 + z * P2) +
 140                                     (z * z) * (P3 + z * P4));
 141                         }
 142                         return ((hx >= 0)? p + w : -p - w);
 143                 }
 144                 s = v * v;
 145                 if (((j - 382) ^ (j - 402)) < 0) {
 146                         /* near 2pi, sin(x) = sin(x-2pi) */
 147                         p = x - PI2_H;
 148                         i = ix - 0x401921fb;
 149                         x = p - PI2_L;
 150                         if ((i | ((lx - 0x54442D00) & 0xffffff00)) == 0) {
 151                                 /* very close to 2pi */
 152                                 x = p - PI2_L0;
 153                                 return ((hx >= 0)? x - PI2_L1 : -(x - PI2_L1));
 154                         }
 155                         z = x * x;
 156                         if (((ix - 0x40192000) >> 10) == 0) {
 157                                 /* |x-2pi|<2**-8 */
 158                                 w = (z * x) * (PP1 + z * PP2) - PI2_L;
 159                         } else {
 160                                 w = (z * x) * ((P1 + z * P2) +
 161                                     (z * z) * (P3 + z * P4)) - PI2_L;
 162                         }
 163                         return ((hx >= 0)? p + w : -p - w);
 164                 }
 165                 j <<= 1;
 166                 w = _TBL_sincos[j+1];
 167                 z = _TBL_sincos[j];
 168                 p = v + (v * s) * (PP1 + s * PP2);
 169                 q = s * (QQ1 + s * QQ2);
 170                 v = w * p + z * q;
 171                 return ((hx >= 0)? z + v : -z - v);
 172         }
 173
 174         if (ix >= 0x7ff00000)   /* sin(Inf or NaN) is NaN */
 175                 return (x / x);
 176
 177         /* argument reduction needed */
 178         n = __rem_pio2(x, y);
 179         switch (n & 3) {
 180         case 0:
 181                 return (__k_sin(y[0], y[1]));
 182         case 1:
 183                 return (__k_cos(y[0], y[1]));
 184         case 2:
 185                 return (-__k_sin(y[0], y[1]));
 186         default:
 187                 return (-__k_cos(y[0], y[1]));
 188         }
 189 }