125 lines
5.2 KiB
C
125 lines
5.2 KiB
C
/****************************************************************************
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* libc/math/__cos.c
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*
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* Ported to NuttX from FreeBSD by Alan Carvalho de Assis:
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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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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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* 3. Neither the name NuttX nor the names of its contributors may be
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* used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
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* OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
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* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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*
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****************************************************************************/
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/* __cos( x, y )
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*
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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, rearrange to
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* cos(x+y) ~ w + (tmp + (r-x*y))
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* where w = 1 - x*x/2 and tmp is a tiny correction term
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* (1 - x*x/2 == w + tmp exactly in infinite precision).
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* The exactness of w + tmp in infinite precision depends on w
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* and tmp having the same precision as x. If they have extra
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* precision due to compiler bugs, then the extra precision is
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* only good provided it is retained in all terms of the final
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* expression for cos(). Retention happens in all cases tested
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* under FreeBSD, so don't pessimize things by forcibly clipping
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* any extra precision in w.
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*/
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/****************************************************************************
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* Included Files
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****************************************************************************/
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#include <nuttx/config.h>
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#include <nuttx/compiler.h>
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#include <sys/types.h>
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#include <math.h>
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#ifdef CONFIG_HAVE_DOUBLE
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/****************************************************************************
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* Private Data
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****************************************************************************/
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static const double g_c1 = 4.16666666666666019037e-02; /* 0x3fa55555, 0x5555554c */
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static const double g_c2 = -1.38888888888741095749e-03; /* 0xbf56C16c, 0x16c15177 */
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static const double g_c3 = 2.48015872894767294178e-05; /* 0x3efa01a0, 0x19cb1590 */
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static const double g_c4 = -2.75573143513906633035e-07; /* 0xbe927e4e, 0x809c52ad */
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static const double g_c5 = 2.08757232129817482790e-09; /* 0x3e21ee9E, 0xbdb4b1c4 */
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static const double g_c6 = -1.13596475577881948265e-11; /* 0xbda8fae9, 0xbe8838d4 */
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/****************************************************************************
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* Public Functions
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****************************************************************************/
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double __cos(double x, double y)
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{
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double hz;
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double z;
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double r;
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double w;
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z = x * x;
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w = z * z;
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r =
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z * (g_c1 + z * (g_c2 + z * g_c3)) + w * w * (g_c4 + z * (g_c5 + z * g_c6));
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hz = 0.5 * z;
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w = 1.0 - hz;
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return w + (((1.0 - w) - hz) + (z * r - x * y));
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}
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#endif
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