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/* * Mode: C; tabwidth: 8; indenttabsmode: nil; cbasicoffset: 4 * 
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* 
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* ***** BEGIN LICENSE BLOCK ***** 
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* Version: MPL 1.1/GPL 2.0/LGPL 2.1 
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* 
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* The contents of this file are subject to the Mozilla Public License Version 
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* 1.1 (the "License"); you may not use this file except in compliance with 
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* the License. You may obtain a copy of the License at 
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* http://www.mozilla.org/MPL/ 
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* 
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* Software distributed under the License is distributed on an "AS IS" basis, 
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* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License 
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* for the specific language governing rights and limitations under the 
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* License. 
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* 
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* The Original Code is Mozilla Communicator client code, released 
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* March 31, 1998. 
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* 
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* The Initial Developer of the Original Code is 
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* Sun Microsystems, Inc. 
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* Portions created by the Initial Developer are Copyright (C) 1998 
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* the Initial Developer. All Rights Reserved. 
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* 
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* Contributor(s): 
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* 
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* Alternatively, the contents of this file may be used under the terms of 
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* either of the GNU General Public License Version 2 or later (the "GPL"), 
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* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), 
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* in which case the provisions of the GPL or the LGPL are applicable instead 
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* of those above. If you wish to allow use of your version of this file only 
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* under the terms of either the GPL or the LGPL, and not to allow others to 
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* use your version of this file under the terms of the MPL, indicate your 
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* decision by deleting the provisions above and replace them with the notice 
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* and other provisions required by the GPL or the LGPL. If you do not delete 
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* the provisions above, a recipient may use your version of this file under 
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* the terms of any one of the MPL, the GPL or the LGPL. 
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* 
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* ***** END LICENSE BLOCK ***** */ 
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/* @(#)k_cos.c 1.3 95/01/18 */ 
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/* 
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* ==================================================== 
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 
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* 
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* Developed at SunSoft, a Sun Microsystems, Inc. business. 
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* Permission to use, copy, modify, and distribute this 
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* software is freely granted, provided that this notice 
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* is preserved. 
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* ==================================================== 
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*/ 
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/* 
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* __kernel_cos( x, y ) 
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* kernel cos function on [pi/4, pi/4], pi/4 ~ 0.785398164 
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* Input x is assumed to be bounded by ~pi/4 in magnitude. 
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* Input y is the tail of x. 
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* 
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* Algorithm 
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* 1. Since cos(x) = cos(x), we need only to consider positive x. 
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* 2. if x < 2^27 (hx<0x3e400000 0), return 1 with inexact if x!=0. 
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* 3. cos(x) is approximated by a polynomial of degree 14 on 
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* [0,pi/4] 
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* 4 14 
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* cos(x) ~ 1  x*x/2 + C1*x + ... + C6*x 
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* where the remez error is 
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* 
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*  2 4 6 8 10 12 14  58 
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* cos(x)(1.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x ) <= 2 
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*   
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* 
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* 4 6 8 10 12 14 
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* 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then 
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* cos(x) = 1  x*x/2 + r 
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* since cos(x+y) ~ cos(x)  sin(x)*y 
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* ~ cos(x)  x*y, 
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* a correction term is necessary in cos(x) and hence 
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* cos(x+y) = 1  (x*x/2  (r  x*y)) 
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* For better accuracy when x > 0.3, let qx = x/4 with 
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* the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. 
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* Then 
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* cos(x+y) = (1qx)  ((x*x/2qx)  (rx*y)). 
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* Note that 1qx and (x*x/2qx) is EXACT here, and the 
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* magnitude of the latter is at least a quarter of x*x/2, 
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* thus, reducing the rounding error in the subtraction. 
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*/ 
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#include "fdlibm.h" 
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#ifdef __STDC__ 
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static const double 
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#else 
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static double 
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#endif 
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 
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C1 = 4.16666666666666019037e02, /* 0x3FA55555, 0x5555554C */ 
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C2 = 1.38888888888741095749e03, /* 0xBF56C16C, 0x16C15177 */ 
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C3 = 2.48015872894767294178e05, /* 0x3EFA01A0, 0x19CB1590 */ 
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C4 = 2.75573143513906633035e07, /* 0xBE927E4F, 0x809C52AD */ 
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C5 = 2.08757232129817482790e09, /* 0x3E21EE9E, 0xBDB4B1C4 */ 
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C6 = 1.13596475577881948265e11; /* 0xBDA8FAE9, 0xBE8838D4 */ 
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#ifdef __STDC__ 
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double __kernel_cos(double x, double y) 
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#else 
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double __kernel_cos(x, y) 
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double x,y; 
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#endif 
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{ 
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fd_twoints u; 
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double qx = 0; 
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double a,hz,z,r; 
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int ix; 
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u.d = x; 
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ix = __HI(u)&0x7fffffff; /* ix = x's high word*/ 
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if(ix<0x3e400000) { /* if x < 2**27 */ 
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if(((int)x)==0) return one; /* generate inexact */ 
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} 
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z = x*x; 
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r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); 
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if(ix < 0x3FD33333) /* if x < 0.3 */ 
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return one  (0.5*z  (z*r  x*y)); 
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else { 
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if(ix > 0x3fe90000) { /* x > 0.78125 */ 
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qx = 0.28125; 
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} else { 
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u.d = qx; 
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__HI(u) = ix0x00200000; /* x/4 */ 
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__LO(u) = 0; 
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qx = u.d; 
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} 
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hz = 0.5*zqx; 
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a = oneqx; 
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return a  (hz  (z*rx*y)); 
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} 
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} 