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/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 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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|
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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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/* |
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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) = (1-qx) - ((x*x/2-qx) - (r-x*y)). |
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* Note that 1-qx and (x*x/2-qx) 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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|
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#include "fdlibm.h" |
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|
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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 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ |
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C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ |
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C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ |
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C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ |
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C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ |
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C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ |
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|
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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) = ix-0x00200000; /* 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*z-qx; |
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a = one-qx; |
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return a - (hz - (z*r-x*y)); |
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} |
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} |
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