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lightning-sunbird  0.9+nobinonly
k_sin.c
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00001 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
00002  *
00003  * ***** BEGIN LICENSE BLOCK *****
00004  * Version: MPL 1.1/GPL 2.0/LGPL 2.1
00005  *
00006  * The contents of this file are subject to the Mozilla Public License Version
00007  * 1.1 (the "License"); you may not use this file except in compliance with
00008  * the License. You may obtain a copy of the License at
00009  * http://www.mozilla.org/MPL/
00010  *
00011  * Software distributed under the License is distributed on an "AS IS" basis,
00012  * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
00013  * for the specific language governing rights and limitations under the
00014  * License.
00015  *
00016  * The Original Code is Mozilla Communicator client code, released
00017  * March 31, 1998.
00018  *
00019  * The Initial Developer of the Original Code is
00020  * Sun Microsystems, Inc.
00021  * Portions created by the Initial Developer are Copyright (C) 1998
00022  * the Initial Developer. All Rights Reserved.
00023  *
00024  * Contributor(s):
00025  *
00026  * Alternatively, the contents of this file may be used under the terms of
00027  * either of the GNU General Public License Version 2 or later (the "GPL"),
00028  * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
00029  * in which case the provisions of the GPL or the LGPL are applicable instead
00030  * of those above. If you wish to allow use of your version of this file only
00031  * under the terms of either the GPL or the LGPL, and not to allow others to
00032  * use your version of this file under the terms of the MPL, indicate your
00033  * decision by deleting the provisions above and replace them with the notice
00034  * and other provisions required by the GPL or the LGPL. If you do not delete
00035  * the provisions above, a recipient may use your version of this file under
00036  * the terms of any one of the MPL, the GPL or the LGPL.
00037  *
00038  * ***** END LICENSE BLOCK ***** */
00039 
00040 /* @(#)k_sin.c 1.3 95/01/18 */
00041 /*
00042  * ====================================================
00043  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00044  *
00045  * Developed at SunSoft, a Sun Microsystems, Inc. business.
00046  * Permission to use, copy, modify, and distribute this
00047  * software is freely granted, provided that this notice 
00048  * is preserved.
00049  * ====================================================
00050  */
00051 
00052 /* __kernel_sin( x, y, iy)
00053  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
00054  * Input x is assumed to be bounded by ~pi/4 in magnitude.
00055  * Input y is the tail of x.
00056  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 
00057  *
00058  * Algorithm
00059  *     1. Since sin(-x) = -sin(x), we need only to consider positive x. 
00060  *     2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
00061  *     3. sin(x) is approximated by a polynomial of degree 13 on
00062  *        [0,pi/4]
00063  *                            3            13
00064  *            sin(x) ~ x + S1*x + ... + S6*x
00065  *        where
00066  *     
00067  *     |sin(x)         2     4     6     8     10     12  |     -58
00068  *     |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
00069  *     |  x                                          | 
00070  * 
00071  *     4. sin(x+y) = sin(x) + sin'(x')*y
00072  *                ~ sin(x) + (1-x*x/2)*y
00073  *        For better accuracy, let 
00074  *                 3      2      2      2      2
00075  *            r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
00076  *        then                   3    2
00077  *            sin(x) = x + (S1*x + (x *(r-y/2)+y))
00078  */
00079 
00080 #include "fdlibm.h"
00081 
00082 #ifdef __STDC__
00083 static const double 
00084 #else
00085 static double 
00086 #endif
00087 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
00088 S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
00089 S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
00090 S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
00091 S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
00092 S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
00093 S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
00094 
00095 #ifdef __STDC__
00096        double __kernel_sin(double x, double y, int iy)
00097 #else
00098        double __kernel_sin(x, y, iy)
00099        double x,y; int iy;         /* iy=0 if y is zero */
00100 #endif
00101 {
00102         fd_twoints u;
00103        double z,r,v;
00104        int ix;
00105         u.d = x;
00106        ix = __HI(u)&0x7fffffff;    /* high word of x */
00107        if(ix<0x3e400000)                  /* |x| < 2**-27 */
00108           {if((int)x==0) return x;}              /* generate inexact */
00109        z      =  x*x;
00110        v      =  z*x;
00111        r      =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
00112        if(iy==0) return x+v*(S1+z*r);
00113        else      return x-((z*(half*y-v*r)-y)-v*S1);
00114 }