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 /* INDENT OFF */
  30 /*
  31  * __k_sin( double x;  double y )
  32  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.785398164
  33  * Input x is assumed to be bounded by ~pi/4 in magnitude.
  34  * Input y is the tail of x.
  35  *
  36  * Accurate Table look-up algorithm by K.C. Ng, May, 1995.
  37  *
  38  * Algorithm: see __sincos.c
  39  */
  40
  41 #include "libm.h"
  42
  43 static const double sc[] = {
  44 /* ONE  = */  1.0,
  45 /* NONE = */ -1.0,
  46 /*
  47  * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008
  48  */
  49 /* PP1  = */ -0.166666666666316558867252052378889521480627858683055567,
  50 /* PP2  = */   .008333315652997472323564894248466758248475374977974017927,
  51 /*
  52  * |(sin(x) - (x+p1*x^3+...+p4*x^9)|
  53  * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125
  54  * |                 x             |
  55  */
  56 /* P1   = */ -1.666666666666629669805215138920301589656e-0001,
  57 /* P2   = */  8.333333332390951295683993455280336376663e-0003,
  58 /* P3   = */ -1.984126237997976692791551778230098403960e-0004,
  59 /* P4   = */  2.753403624854277237649987622848330351110e-0006,
  60 /*
  61  * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d)
  62  */
  63 /* QQ1  = */ -0.4999999999975492381842911981948418542742729,
  64 /* QQ2  = */  0.041666542904352059294545209158357640398771740,
  65 /*
  66  * |cos(x) - (1+q1*x^2+...+q4*x^8)| <= 2^-55.86 for |x| <= 0.1640625 (10.5/64)
  67  */
  68 /* Q1   = */ -0.5,
  69 /* Q2   = */  4.166666666500350703680945520860748617445e-0002,
  70 /* Q3   = */ -1.388888596436972210694266290577848696006e-0003,
  71 /* Q4   = */  2.478563078858589473679519517892953492192e-0005,
  72 };
  73 /* INDENT ON */
  74
  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 Q1      sc[10]
  86 #define Q2      sc[11]
  87 #define Q3      sc[12]
  88 #define Q4      sc[13]
  89
  90 extern const double _TBL_sincos[], _TBL_sincosx[];
  91
  92 double
  93 __k_sin(double x, double y) {
  94         double  z, w, s, v, p, q;
  95         int     i, j, n, hx, ix;
  96
  97         hx = ((int *)&x)[HIWORD];
  98         ix = hx & ~0x80000000;
  99
 100         if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */
 101                 if (ix < 0x3e400000)    /* |x| < 2**-27 */
 102                         if ((int)x == 0)
 103                                 return (x + y);
 104                 z = x * x;
 105                 if (ix < 0x3f800000)    /* |x| < 0.008  */
 106                         p = (x * z) * (PP1 + z * PP2) + y;
 107                 else
 108                         p = (x * z) * ((P1 + z * P2) + (z * z) * (P3 +
 109                             z * P4)) + y;
 110                 return (x + p);
 111         } else {                /* 0.164062500 < |x| < ~pi/4 */
 112                 n = ix >> 20;
 113                 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n);
 114                 j = i - 10;
 115                 if (hx < 0)
 116                         v = -y - (_TBL_sincosx[j] + x);
 117                 else
 118                         v = y - (_TBL_sincosx[j] - x);
 119                 s = v * v;
 120                 j <<= 1;
 121                 w = _TBL_sincos[j];
 122                 z = _TBL_sincos[j+1];
 123                 p = s * (PP1 + s * PP2);
 124                 q = s * (QQ1 + s * QQ2);
 125                 p = v + v * p;
 126                 s = w * q + z * p;
 127                 return ((hx >= 0)? w + s : -(w + s));
 128         }
 129 }