122 lines
4.7 KiB
C
122 lines
4.7 KiB
C
/****************************************************************************
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* libs/libc/math/__sin.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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/* __sin( x, y, iy)
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*
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* kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
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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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* Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
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*
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* Algorithm
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* 1. Since sin(-x) = -sin(x), we need only to consider positive x.
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* 2. Callers must return sin(-0) = -0 without calling here since our
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* odd polynomial is not evaluated in a way that preserves -0.
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* Callers may do the optimization sin(x) ~ x for tiny x.
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* 3. sin(x) is approximated by a polynomial of degree 13 on
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* [0,pi/4]
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* 3 13
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* sin(x) ~ x + S1*x + ... + S6*x
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* where
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*
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* |sin(x) 2 4 6 8 10 12 | -58
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* |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
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* | x |
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*
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* 4. sin(x+y) = sin(x) + sin'(x')*y
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* ~ sin(x) + (1-x*x/2)*y
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* For better accuracy, let
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* 3 2 2 2 2
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* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
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* then 3 2
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* sin(x) = x + (S1*x + (x *(r-y/2)+y))
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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_s1 = -1.66666666666666324348e-01; /* 0xbfc55555, 0x55555549 */
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static const double g_s2 = 8.33333333332248946124e-03; /* 0x3f811111, 0x1110f8a6 */
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static const double g_s3 = -1.98412698298579493134e-04; /* 0xbf2a01a0, 0x19c161d5 */
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static const double g_s4 = 2.75573137070700676789e-06; /* 0x3ec71de3, 0x57b1fe7d */
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static const double g_s5 = -2.50507602534068634195e-08; /* 0xbe5ae5e6, 0x8a2b9ceb */
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static const double g_s6 = 1.58969099521155010221e-10; /* 0x3de5d93a, 0x5acfd57c */
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/****************************************************************************
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* Public Functions
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****************************************************************************/
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double __sin(double x, double y, int iy)
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{
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double z;
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double r;
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double v;
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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 = g_s2 + z * (g_s3 + z * g_s4) + z * w * (g_s5 + z * g_s6);
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v = z * x;
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if (iy == 0)
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{
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return x + v * (g_s1 + z * r);
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}
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else
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{
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return x - ((z * (0.5 * y - v * r) - y) - v * g_s1);
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}
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}
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#endif
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