/* atanf.c * * Inverse circular tangent * (arctangent) * * * * SYNOPSIS: * * float x, y, atanf(); * * y = atanf( x ); * * * * DESCRIPTION: * * Returns radian angle between -pi/2 and +pi/2 whose tangent * is x. * * Range reduction is from four intervals into the interval * from zero to tan( pi/8 ). A polynomial approximates * the function in this basic interval. * * * * ACCURACY: * * Relative error: * arithmetic domain # trials peak rms * IEEE -10, 10 100000 1.9e-7 4.1e-8 * */ /* atan2f() * * Quadrant correct inverse circular tangent * * * * SYNOPSIS: * * float x, y, z, atan2f(); * * z = atan2f( y, x ); * * * * DESCRIPTION: * * Returns radian angle whose tangent is y/x. * Define compile time symbol ANSIC = 1 for ANSI standard, * range -PI < z <= +PI, args (y,x); else ANSIC = 0 for range * 0 to 2PI, args (x,y). * * * * ACCURACY: * * Relative error: * arithmetic domain # trials peak rms * IEEE -10, 10 100000 1.9e-7 4.1e-8 * See atan.c. * */ /* atan.c */ /* Cephes Math Library Release 2.2: June, 1992 Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */ /* Single precision circular arcsine * test interval: [-tan(pi/8), +tan(pi/8)] * trials: 10000 * peak relative error: 7.7e-8 * rms relative error: 2.9e-8 */ #include extern float PIF, PIO2F, PIO4F; float atanf( float xx ) { float x, y, z; int sign; x = xx; /* make argument positive and save the sign */ if( xx < 0.0 ) { sign = -1; x = -xx; } else { sign = 1; x = xx; } /* range reduction */ if( x > 2.414213562373095 ) /* tan 3pi/8 */ { y = PIO2F; x = -( 1.0/x ); } else if( x > 0.4142135623730950 ) /* tan pi/8 */ { y = PIO4F; x = (x-1.0)/(x+1.0); } else y = 0.0; z = x * x; y += ((( 8.05374449538e-2 * z - 1.38776856032E-1) * z + 1.99777106478E-1) * z - 3.33329491539E-1) * z * x + x; if( sign < 0 ) y = -y; return( y ); } float atan2f( float y, float x ) { float z, w; int code; code = 0; if( x < 0.0 ) code = 2; if( y < 0.0 ) code |= 1; if( x == 0.0 ) { if( code & 1 ) { #if ANSIC return( -PIO2F ); #else return( 3.0*PIO2F ); #endif } if( y == 0.0 ) return( 0.0 ); return( PIO2F ); } if( y == 0.0 ) { if( code & 2 ) return( PIF ); return( 0.0 ); } switch( code ) { default: #if ANSIC case 0: case 1: w = 0.0; break; case 2: w = PIF; break; case 3: w = -PIF; break; #else case 0: w = 0.0; break; case 1: w = 2.0 * PIF; break; case 2: case 3: w = PIF; break; #endif } z = atanf( y/x ); return( w + z ); }