nuttx/libc/math/lib_asin.c

105 lines
3.0 KiB
C

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