/*							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, 2000Copyright 1984, 1995, 2000 by Stephen L. Moshier*/#include <math.h>/* arcsin(x)  =  x + x^3 P(x^2)/Q(x^2)   0 <= x <= 0.625   Peak relative error = 1.2e-18  */#if UNKstatic 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 DECstatic 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 IBMPCstatic 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 MIEEEstatic 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 UNKstatic 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 DECstatic 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 IBMPCstatic 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 MIEEEstatic 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 ANSIPROTextern double polevl ( double, void *, int );extern double p1evl ( double, void *, int );extern double sqrt ( double );double asin ( double );#elsedouble sqrt(), polevl(), p1evl();double asin();#endifextern double PIO2, PIO4, NAN;double asin(x)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 = 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 acos(x)double x;{double z;if( (x < -1.0) || (x > 1.0) )	{	mtherr( "acos", DOMAIN );	return( NAN );	}if( x > 0.5 )	{	return( 2.0 * asin(  sqrt(0.5 - 0.5*x) ) );	}z = PIO4 - asin(x);z = z + MOREBITS;z = z + PIO4;return( z );}