106 lines
3.0 KiB
C
106 lines
3.0 KiB
C
/****************************************************************************
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* libs/libc/math/lib_asin.c
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*
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* This file is a part of NuttX:
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*
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* Copyright (C) 2012, 2015-2016 Gregory Nutt. All rights reserved.
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* Ported by: Darcy Gong
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*
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* It derives from the Rhombus OS math library by Nick Johnson which has
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* a compatibile, MIT-style license:
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*
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* Copyright (C) 2009-2011 Nick Johnson <nickbjohnson4224 at gmail.com>
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*
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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 <math.h>
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#include <float.h>
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#ifdef CONFIG_HAVE_DOUBLE
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/****************************************************************************
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* Pre-processor Definitions
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****************************************************************************/
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#undef DBL_EPSILON
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#define DBL_EPSILON 1e-12
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/****************************************************************************
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* Private Functions
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****************************************************************************/
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/* This lib uses Newton's method to approximate asin(x). Newton's Method
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* converges very slowly for x close to 1. We can accelerate convergence
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* with the following identy: asin(x)=Sign(x)*(Pi/2-asin(sqrt(1-x^2)))
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*/
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static double asin_aux(double x)
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{
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long double y;
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double y_cos;
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double y_sin;
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y = 0.0;
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y_sin = 0.0;
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while (fabs(y_sin - x) > DBL_EPSILON)
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{
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y_cos = cos(y);
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y -= ((long double)y_sin - (long double)x) / (long double)y_cos;
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y_sin = sin(y);
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}
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return y;
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}
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/****************************************************************************
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* Public Functions
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****************************************************************************/
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double asin(double x)
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{
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double y;
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/* Verify that the input value is in the domain of the function */
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if (x < -1.0 || x > 1.0 || isnan(x))
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{
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return NAN;
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}
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/* if x is > sqrt(2), use identity for faster convergence */
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if (fabs(x) > 0.71)
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{
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y = M_PI_2 - asin_aux(sqrt(1.0 - x * x));
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y = copysign(y, x);
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}
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else
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{
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y = asin_aux(x);
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}
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return y;
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}
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#endif /* CONFIG_HAVE_DOUBLE */
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