Output of file : ASIN.C contained in archive : CEPHES22.ZIP
/* 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 20000 5.7e-17 1.2e-17
* IEEE -1, 1 30000 4.8e-16 8.4e-17
*
*
* ERROR MESSAGES:
*
* message condition value returned
* asin domain |x| > 1 0.0
*
*/
/* acos()
*
* Inverse circular cosine
*
*
*
* SYNOPSIS:
*
* double x, y, acos();
*
* y = acos( x );
*
*
*
* DESCRIPTION:
*
* Returns radian angle between -pi/2 and +pi/2 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 13000 3.2e-17 7.8e-18
* IEEE -1, 1 30000 2.7e-16 7.1e-17
*
*
* ERROR MESSAGES:
*
* message condition value returned
* asin domain |x| > 1 0.0
*/

/* asin.c */

/*
Cephes Math Library Release 2.0: April, 1987
Copyright 1984, 1987 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/

#include "mconf.h"

#ifdef UNK
static double P[] = {
-6.96822599948686174217E-1,
1.01598286089872099722E1,
-3.97340771391578757294E1,
5.72912144709846496134E1,
-2.74148200465925708020E1
};
static double Q[] = {
/* 1.00000000000000000000E0,*/
-2.38368245005177488242E1,
1.51095072703128995631E2,
-3.82340216045978957023E2,
4.17767300951716199422E2,
-1.64488920279555473283E2
};
#endif

#ifdef DEC
static short P[] = {
0140062,0061367,0042744,0127464,
0041042,0107250,0070611,0005470,
0141436,0167661,0165345,0131200,
0041545,0025064,0020124,0000411,
0141333,0050615,0026056,0134351
};
static short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0141276,0130721,0005461,0134336,
0042027,0014126,0127506,0127155,
0142277,0025614,0031413,0103353,
0042320,0161066,0165346,0163707,
0142044,0076451,0160443,0005274
};
#endif

#ifdef IBMPC
static short P[] = {
0x95e7,0xe8bc,0x4c5e,0xbfe6,
0x2167,0x0e31,0x51d5,0x4024,
0xb650,0x3d5c,0xddf6,0xc043,
0x8021,0x840a,0xa546,0x404c,
0xd71d,0xa585,0x6a31,0xc03b
};
static short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x371c,0x2166,0xd63a,0xc037,
0xd5ce,0xd5e8,0xe30a,0x4062,
0x70dd,0x8661,0xe571,0xc077,
0xdcf9,0xdd5c,0x1c46,0x407a,
0x6158,0x3c24,0x8fa5,0xc064
};
#endif

#ifdef MIEEE
static short P[] = {
0xbfe6,0x4c5e,0xe8bc,0x95e7,
0x4024,0x51d5,0x0e31,0x2167,
0xc043,0xddf6,0x3d5c,0xb650,
0x404c,0xa546,0x840a,0x8021,
0xc03b,0x6a31,0xa585,0xd71d
};
static short Q[] = {
0xc037,0xd63a,0x2166,0x371c,
0x4062,0xe30a,0xd5e8,0xd5ce,
0xc077,0xe571,0x8661,0x70dd,
0x407a,0x1c46,0xdd5c,0xdcf9,
0xc064,0x8fa5,0x3c24,0x6158
};
#endif

double asin(x)
double x;
{
double a, p, z, zz;
double sqrt(), polevl(), p1evl();
short sign, flag;
extern double PIO2;

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

if( a > 1.0 )
{
mtherr( "asin", DOMAIN );
return( 0.0 );
}

if( a < 1.0e-7 )
{
z = a;
goto done;
}

if( a > 0.5 )
{
zz = 0.5 -a;
zz = (zz + 0.5)/2.0;
z = sqrt( zz );
flag = 1;
}
else
{
z = a;
zz = z * z;
flag = 0;
}

p = zz * polevl( zz, P, 4)/p1evl( zz, Q, 5);
z = z * p + z;
if( flag != 0 )
{
z = z + z;
z = PIO2 - z;
}
done:
if( sign < 0 )
z = -z;
return(z);
}

extern double PIO2, PI;

double acos(x)
double x;
{
double asin(), sqrt();

if( x < -1.0 )
goto domerr;

if( x < -0.5)
return( PI - 2.0 * asin( sqrt(0.5*(1.0+x)) ) );

if( x > 1.0 )
{
domerr: mtherr( "acos", DOMAIN );
return( 0.0 );
}

if( x > 0.5 )
return( 2.0 * asin( sqrt(0.5*(1.0-x) ) ) );

return( PIO2 - asin(x) );
}

### 3 Responses to “Category : C Source CodeArchive   : CEPHES22.ZIPFilename : ASIN.C”

1. Very nice! Thank you for this wonderful archive. I wonder why I found it only now. Long live the BBS file archives!

2. This is so awesome! 😀 I’d be cool if you could download an entire archive of this at once, though.

3. But one thing that puzzles me is the “mtswslnkmcjklsdlsbdmMICROSOFT” string. There is an article about it here. It is definitely worth a read: http://www.os2museum.com/wp/mtswslnk/