/* asinf.c * * Inverse circular sine * * * * SYNOPSIS: * * float x, y, asinf(); * * y = asinf( x ); * * * * DESCRIPTION: * * Returns radian angle between -pi/2 and +pi/2 whose sine is x. * * A polynomial of the form x + x**3 P(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 * IEEE -1, 1 100000 2.5e-7 5.0e-8 * * * ERROR MESSAGES: * * message condition value returned * asinf domain |x| > 1 0.0 * */ /* acosf() * * Inverse circular cosine * * * * SYNOPSIS: * * float x, y, acosf(); * * y = acosf( 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 * IEEE -1, 1 100000 1.4e-7 4.2e-8 * * * ERROR MESSAGES: * * message condition value returned * acosf domain |x| > 1 0.0 */ /* asin.c */ /* Cephes Math Library Release 2.2: June, 1992 Copyright 1984, 1987, 1992 by Stephen L. Moshier Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */ /* Single precision circular arcsine * test interval: [-0.5, +0.5] * trials: 10000 * peak relative error: 6.7e-8 * rms relative error: 2.5e-8 */ #include <math.h> extern float PIF, PIO2F; float sqrtf( float ); float asinf( float xx ) { float a, x, z; int sign, flag; x = xx; if( x > 0 ) { sign = 1; a = x; } else { sign = -1; a = -x; } if( a > 1.0 ) { mtherr( "asinf", DOMAIN ); return( 0.0 ); } if( a < 1.0e-4 ) { z = a; goto done; } if( a > 0.5 ) { z = 0.5 * (1.0 - a); x = sqrtf( z ); flag = 1; } else { x = a; z = x * x; flag = 0; } z = (((( 4.2163199048E-2 * z + 2.4181311049E-2) * z + 4.5470025998E-2) * z + 7.4953002686E-2) * z + 1.6666752422E-1) * z * x + x; if( flag != 0 ) { z = z + z; z = PIO2F - z; } done: if( sign < 0 ) z = -z; return( z ); } float acosf( float x ) { if( x < -1.0 ) goto domerr; if( x < -0.5) return( PIF - 2.0 * asinf( sqrtf(0.5*(1.0+x)) ) ); if( x > 1.0 ) { domerr: mtherr( "acosf", DOMAIN ); return( 0.0 ); } if( x > 0.5 ) return( 2.0 * asinf( sqrtf(0.5*(1.0-x) ) ) ); return( PIO2F - asinf(x) ); }