js/src/fdlibm/k_cos.c

   1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
   2  *
   3  * ***** BEGIN LICENSE BLOCK *****
   4  * Version: MPL 1.1/GPL 2.0/LGPL 2.1
   5  *
   6  * The contents of this file are subject to the Mozilla Public License Version
   7  * 1.1 (the "License"); you may not use this file except in compliance with
   8  * the License. You may obtain a copy of the License at
   9  * http://www.mozilla.org/MPL/
  10  *
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  12  * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
  13  * for the specific language governing rights and limitations under the
  14  * License.
  15  *
  16  * The Original Code is Mozilla Communicator client code, released
  17  * March 31, 1998.
  18  *
  19  * The Initial Developer of the Original Code is
  20  * Sun Microsystems, Inc.
  21  * Portions created by the Initial Developer are Copyright (C) 1998
  22  * the Initial Developer. All Rights Reserved.
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  26  * Alternatively, the contents of this file may be used under the terms of
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  38  * ***** END LICENSE BLOCK ***** */
  39
  40 /* @(#)k_cos.c 1.3 95/01/18 */
  41 /*
  42  * ====================================================
  43  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  44  *
  45  * Developed at SunSoft, a Sun Microsystems, Inc. business.
  46  * Permission to use, copy, modify, and distribute this
  47  * software is freely granted, provided that this notice
  48  * is preserved.
  49  * ====================================================
  50  */
  51
  52 /*
  53  * __kernel_cos( x,  y )
  54  * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
  55  * Input x is assumed to be bounded by ~pi/4 in magnitude.
  56  * Input y is the tail of x.
  57  *
  58  * Algorithm
  59  *      1. Since cos(-x) = cos(x), we need only to consider positive x.
  60  *      2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
  61  *      3. cos(x) is approximated by a polynomial of degree 14 on
  62  *         [0,pi/4]
  63  *                                       4            14
  64  *              cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
  65  *         where the remez error is
  66  *
  67  *      |              2     4     6     8     10    12     14 |     -58
  68  *      |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
  69  *      |                                                      |
  70  *
  71  *                     4     6     8     10    12     14
  72  *      4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
  73  *             cos(x) = 1 - x*x/2 + r
  74  *         since cos(x+y) ~ cos(x) - sin(x)*y
  75  *                        ~ cos(x) - x*y,
  76  *         a correction term is necessary in cos(x) and hence
  77  *              cos(x+y) = 1 - (x*x/2 - (r - x*y))
  78  *         For better accuracy when x > 0.3, let qx = |x|/4 with
  79  *         the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
  80  *         Then
  81  *              cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
  82  *         Note that 1-qx and (x*x/2-qx) is EXACT here, and the
  83  *         magnitude of the latter is at least a quarter of x*x/2,
  84  *         thus, reducing the rounding error in the subtraction.
  85  */
  86
  87 #include "fdlibm.h"
  88
  89 #ifdef __STDC__
  90 static const double
  91 #else
  92 static double
  93 #endif
  94 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  95 C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
  96 C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
  97 C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
  98 C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
  99 C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
 100 C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
 101
 102 #ifdef __STDC__
 103         double __kernel_cos(double x, double y)
 104 #else
 105         double __kernel_cos(x, y)
 106         double x,y;
 107 #endif
 108 {
 109         fd_twoints u;
 110         double qx = 0;
 111         double a,hz,z,r;
 112         int ix;
 113         u.d = x;
 114         ix = __HI(u)&0x7fffffff;        /* ix = |x|'s high word*/
 115         if(ix<0x3e400000) {                     /* if x < 2**27 */
 116             if(((int)x)==0) return one;         /* generate inexact */
 117         }
 118         z  = x*x;
 119         r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
 120         if(ix < 0x3FD33333)                     /* if |x| < 0.3 */
 121             return one - (0.5*z - (z*r - x*y));
 122         else {
 123             if(ix > 0x3fe90000) {               /* x > 0.78125 */
 124                 qx = 0.28125;
 125             } else {
 126                 u.d = qx;
 127                 __HI(u) = ix-0x00200000;        /* x/4 */
 128                 __LO(u) = 0;
 129                 qx = u.d;
 130             }
 131             hz = 0.5*z-qx;
 132             a  = one-qx;
 133             return a - (hz - (z*r-x*y));
 134         }
 135 }