/*							asin.c
 *
 *	Inverse circular sine
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, asin();
 *
 * y = asin( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns radian angle between -pi/2 and +pi/2 whose sine is x.
 *
 * A rational function of the form x + x**3 P(x**2)/Q(x**2)
 * is used for |x| in the interval [0, 0.5].  If |x| > 0.5 it is
 * transformed by the identity
 *
 *    asin(x) = pi/2 - 2 asin( sqrt( (1-x)/2 ) ).
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC      -1, 1        40000       2.6e-17     7.1e-18
 *    IEEE     -1, 1        10^6        1.9e-16     5.4e-17
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * asin domain        |x| > 1           NAN
 *
 */
/*							acos()
 *
 *	Inverse circular cosine
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, acos();
 *
 * y = acos( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns radian angle between 0 and pi whose cosine
 * is x.
 *
 * Analytically, acos(x) = pi/2 - asin(x).  However if |x| is
 * near 1, there is cancellation error in subtracting asin(x)
 * from pi/2.  Hence if x < -0.5,
 *
 *    acos(x) =	 pi - 2.0 * asin( sqrt((1+x)/2) );
 *
 * or if x > +0.5,
 *
 *    acos(x) =	 2.0 * asin(  sqrt((1-x)/2) ).
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    DEC       -1, 1       50000       3.3e-17     8.2e-18
 *    IEEE      -1, 1       10^6        2.2e-16     6.5e-17
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * asin domain        |x| > 1           NAN
 */

/*							asin.c	*/

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice,
   this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions and the following disclaimer in the
   documentation and/or other materials provided with the distribution.
3. Neither the name of the <ORGANIZATION> nor the names of its
   contributors may be used to endorse or promote products derived from
   this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
*/

#include "mconf.h"

/* arcsin(x)  =  x + x^3 P(x^2)/Q(x^2)
   0 <= x <= 0.625
   Peak relative error = 1.2e-18  */
#if UNK
static double P[6] = {
 4.253011369004428248960E-3,
-6.019598008014123785661E-1,
 5.444622390564711410273E0,
-1.626247967210700244449E1,
 1.956261983317594739197E1,
-8.198089802484824371615E0,
};
static double Q[5] = {
/* 1.000000000000000000000E0, */
-1.474091372988853791896E1,
 7.049610280856842141659E1,
-1.471791292232726029859E2,
 1.395105614657485689735E2,
-4.918853881490881290097E1,
};
#endif
#if DEC
static short P[24] = {
0036213,0056330,0057244,0053234,
0140032,0015011,0114762,0160255,
0040656,0035130,0136121,0067313,
0141202,0014616,0170474,0101731,
0041234,0100076,0151674,0111310,
0141003,0025540,0033165,0077246,
};
static short Q[20] = {
/* 0040200,0000000,0000000,0000000, */
0141153,0155310,0055360,0072530,
0041614,0177001,0027764,0101237,
0142023,0026733,0064653,0133266,
0042013,0101264,0023775,0176351,
0141504,0140420,0050660,0036543,
};
#endif
#if IBMPC
static short P[24] = {
0x8ad3,0x0bd4,0x6b9b,0x3f71,
0x5c16,0x333e,0x4341,0xbfe3,
0x2dd9,0x178a,0xc74b,0x4015,
0x907b,0xde27,0x4331,0xc030,
0x9259,0xda77,0x9007,0x4033,
0xafd5,0x06ce,0x656c,0xc020,
};
static short Q[20] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0x0eab,0x0b5e,0x7b59,0xc02d,
0x9054,0x25fe,0x9fc0,0x4051,
0x76d7,0x6d35,0x65bb,0xc062,
0xbf9d,0x84ff,0x7056,0x4061,
0x07ac,0x0a36,0x9822,0xc048,
};
#endif
#if MIEEE
static short P[24] = {
0x3f71,0x6b9b,0x0bd4,0x8ad3,
0xbfe3,0x4341,0x333e,0x5c16,
0x4015,0xc74b,0x178a,0x2dd9,
0xc030,0x4331,0xde27,0x907b,
0x4033,0x9007,0xda77,0x9259,
0xc020,0x656c,0x06ce,0xafd5,
};
static short Q[20] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0xc02d,0x7b59,0x0b5e,0x0eab,
0x4051,0x9fc0,0x25fe,0x9054,
0xc062,0x65bb,0x6d35,0x76d7,
0x4061,0x7056,0x84ff,0xbf9d,
0xc048,0x9822,0x0a36,0x07ac,
};
#endif

/* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x))
   0 <= x <= 0.5
   Peak relative error = 4.2e-18  */
#if UNK
static double R[5] = {
 2.967721961301243206100E-3,
-5.634242780008963776856E-1,
 6.968710824104713396794E0,
-2.556901049652824852289E1,
 2.853665548261061424989E1,
};
static double S[4] = {
/* 1.000000000000000000000E0, */
-2.194779531642920639778E1,
 1.470656354026814941758E2,
-3.838770957603691357202E2,
 3.424398657913078477438E2,
};
#endif
#if DEC
static short R[20] = {
0036102,0077034,0142164,0174103,
0140020,0036222,0147711,0044173,
0040736,0177655,0153631,0171523,
0141314,0106525,0060015,0055474,
0041344,0045422,0003630,0040344,
};
static short S[16] = {
/* 0040200,0000000,0000000,0000000, */
0141257,0112425,0132772,0166136,
0042023,0010315,0075523,0175020,
0142277,0170104,0126203,0017563,
0042253,0034115,0102662,0022757,
};
#endif
#if IBMPC
static short R[20] = {
0x9f08,0x988e,0x4fc3,0x3f68,
0x290f,0x59f9,0x0792,0xbfe2,
0x3e6a,0xbaf3,0xdff5,0x401b,
0xab68,0xac01,0x91aa,0xc039,
0x081d,0x40f3,0x8962,0x403c,
};
static short S[16] = {
/* 0x0000,0x0000,0x0000,0x3ff0, */
0x5d8c,0xb6bf,0xf2a2,0xc035,
0x7f42,0xaf6a,0x6219,0x4062,
0x63ee,0x9590,0xfe08,0xc077,
0x44be,0xb0b6,0x6709,0x4075,
};
#endif
#if MIEEE
static short R[20] = {
0x3f68,0x4fc3,0x988e,0x9f08,
0xbfe2,0x0792,0x59f9,0x290f,
0x401b,0xdff5,0xbaf3,0x3e6a,
0xc039,0x91aa,0xac01,0xab68,
0x403c,0x8962,0x40f3,0x081d,
};
static short S[16] = {
/* 0x3ff0,0x0000,0x0000,0x0000, */
0xc035,0xf2a2,0xb6bf,0x5d8c,
0x4062,0x6219,0xaf6a,0x7f42,
0xc077,0xfe08,0x9590,0x63ee,
0x4075,0x6709,0xb0b6,0x44be,
};
#endif

/* pi/2 = PIO2 + MOREBITS.  */
#ifdef DEC
#define MOREBITS 5.721188726109831840122E-18
#else
#define MOREBITS 6.123233995736765886130E-17
#endif

#ifdef ANSIPROT
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern double c_sqrt ( double );
double c_asin ( double );
#else
double c_sqrt(), polevl(), p1evl();
double c_asin();
#endif
extern double PIO2, PIO4, NAN;

double c_asin(double x)
{
double a, p, z, zz;
short sign;

if( x > 0 )
	{
	sign = 1;
	a = x;
	}
else
	{
	sign = -1;
	a = -x;
	}

if( a > 1.0 )
	{
	mtherr( "asin", DOMAIN );
	return( NAN );
	}

if( a > 0.625 )
	{
	/* arcsin(1-x) = pi/2 - sqrt(2x)(1+R(x))  */
	zz = 1.0 - a;
	p = zz * polevl( zz, R, 4)/p1evl( zz, S, 4);
	zz = c_sqrt(zz+zz);
	z = PIO4 - zz;
	zz = zz * p - MOREBITS;
	z = z - zz;
	z = z + PIO4;
	}
else
	{
	if( a < 1.0e-8 )
		{
		return(x);
		}
	zz = a * a;
	z = zz * polevl( zz, P, 5)/p1evl( zz, Q, 5);
	z = a * z + a;
	}
if( sign < 0 )
	z = -z;
return(z);
}



double c_acos(double x)
{
if( (x < -1.0) || (x > 1.0) )
	{
	mtherr( "acos", DOMAIN );
	return( NAN );
	}
	return PIO2 - c_asin(x) + MOREBITS;
}
