#include #include FT_TRIGONOMETRY_H /* the following is 0.2715717684432231 * 2^30 */ #define FT_TRIG_COSCALE 0x11616E8E /* 291597966 = 0.2715717684432241 * 2^30, valid for j>13 */ /* this table was generated for FT_PI = 180L << 16, i.e. degrees */ #define FT_TRIG_MAX_ITERS 23 static const FT_Fixed ft_trig_arctan_table[ 24 ] = { 4157273, 2949120, 1740967, 919879, 466945, 234379, 117304, 58666, 29335, 14668, 7334, 3667, 1833, 917, 458, 229, 115, 57, 29, 14, 7, 4, 2, 1 }; /* the Cordic shrink factor, multiplied by 2^32 */ #define FT_TRIG_SCALE 1166391785 /* 0x4585BA38U */ #ifdef FT_CONFIG_HAS_INT64 /* multiply a given value by the CORDIC shrink factor */ static FT_Fixed ft_trig_downscale( FT_Fixed val ) { FT_Fixed s; FT_Int64 v; s = val; val = (val >= 0) ? val : -val; v = (val * (FT_Int64)FT_TRIG_SCALE) + 0x100000000L; val = (FT_Fixed)(v >> 32); return ( s >= 0 ) ? val : -val; } #else /* !FT_CONFIG_HAS_INT64 */ /* multiply a given value by the CORDIC shrink factor */ static FT_Fixed ft_trig_downscale( FT_Fixed val ) { FT_Fixed s; FT_UInt32 v1, v2, k1, k2, hi, lo1, lo2, lo3; s = val; val = ( val >= 0 ) ? val : -val; v1 = (FT_UInt32)val >> 16; v2 = (FT_UInt32)val & 0xFFFF; k1 = FT_TRIG_SCALE >> 16; /* constant */ k2 = FT_TRIG_SCALE & 0xFFFF; /* constant */ hi = k1*v1; lo1 = k1*v2 + k2*v1; /* can't overflow */ lo2 = k2*v2 >> 16; lo3 = ( lo1 >= lo2 ) ? lo1 : lo2; lo1 += lo2; hi += lo1 >> 16; if (lo1 < lo3) hi += 0x10000U; val = (FT_Fixed)hi; return ( s >= 0 ) ? val : -val; } #endif /* !FT_CONFIG_HAS_INT64 */ static FT_Int ft_trig_prenorm( FT_Vector* vec ) { FT_Fixed x, y, z; FT_Int shift; x = vec->x; y = vec->y; z = (( x >= 0 ) ? x : - x) | ((y >= 0) ? y : -y); shift = 0; if ( z < (1L << 27) ) { do { shift++; z <<= 1; } while ( z < (1L << 27) ); vec->x = (x << shift); vec->y = (y << shift); } else if ( z > (1L << 28 ) ) { do { shift++; z >>= 1; } while ( z > (1L << 28) ); vec->x = (x >> shift); vec->y = (y >> shift); shift = -shift; } return shift; } static void ft_trig_pseudo_rotate( FT_Vector* vec, FT_Angle theta ) { FT_Int i; FT_Fixed x, y, xtemp; const FT_Fixed *arctanptr; x = vec->x; y = vec->y; /* Get angle between -90 and 90 degrees */ while (theta <= -FT_ANGLE_PI2) { x = -x; y = -y; theta += FT_ANGLE_PI; } while (theta > FT_ANGLE_PI2) { x = -x; y = -y; theta -= FT_ANGLE_PI; } /* Initial pseudorotation, with left shift */ arctanptr = ft_trig_arctan_table; if (theta < 0) { xtemp = x + (y << 1); y = y - (x << 1); x = xtemp; theta += *arctanptr++; } else { xtemp = x - (y << 1); y = y + (x << 1); x = xtemp; theta -= *arctanptr++; } /* Subsequent pseudorotations, with right shifts */ i = 0; do { if (theta < 0) { xtemp = x + (y >> i); y = y - (x >> i); x = xtemp; theta += *arctanptr++; } else { xtemp = x - (y >> i); y = y + (x >> i); x = xtemp; theta -= *arctanptr++; } } while ( ++i < FT_TRIG_MAX_ITERS ); vec->x = x; vec->y = y; } static void ft_trig_pseudo_polarize( FT_Vector* vec ) { FT_Fixed theta; FT_Fixed yi, i; FT_Fixed x, y; const FT_Fixed *arctanptr; x = vec->x; y = vec->y; /* Get the vector into the right half plane */ theta = 0; if (x < 0) { x = -x; y = -y; theta = 2 * FT_ANGLE_PI2; } if (y > 0) theta = - theta; arctanptr = ft_trig_arctan_table; if (y < 0) { /* Rotate positive */ yi = y + (x << 1); x = x - (y << 1); y = yi; theta -= *arctanptr++; /* Subtract angle */ } else { /* Rotate negative */ yi = y - (x << 1); x = x + (y << 1); y = yi; theta += *arctanptr++; /* Add angle */ } i = 0; do { if (y < 0) { /* Rotate positive */ yi = y + (x >> i); x = x - (y >> i); y = yi; theta -= *arctanptr++; } else { /* Rotate negative */ yi = y - (x >> i); x = x + (y >> i); y = yi; theta += *arctanptr++; } } while (++i < FT_TRIG_MAX_ITERS); /* round theta */ if ( theta >= 0 ) theta = ( theta + 16 ) & -32; else theta = - (( -theta + 16 ) & -32); vec->x = x; vec->y = theta; } FT_EXPORT_DEF(FT_Fixed) FT_Cos( FT_Angle angle ) { FT_Vector v; v.x = FT_TRIG_COSCALE >> 2; v.y = 0; ft_trig_pseudo_rotate( &v, angle ); return v.x >> 12; } FT_EXPORT_DEF(FT_Fixed) FT_Sin( FT_Angle angle ) { return FT_Cos( FT_ANGLE_PI2-angle ); } FT_EXPORT_DEF(FT_Fixed) FT_Tan( FT_Angle angle ) { FT_Vector v; v.x = FT_TRIG_COSCALE >> 2; v.y = 0; ft_trig_pseudo_rotate( &v, angle ); return FT_DivFix( v.y, v.x ); } FT_EXPORT_DEF(FT_Angle) FT_Atan2( FT_Fixed dx, FT_Fixed dy ) { FT_Vector v; if ( dx == 0 && dy == 0 ) return 0; v.x = dx; v.y = dy; ft_trig_prenorm( &v ); ft_trig_pseudo_polarize( &v ); return v.y; } FT_EXPORT_DEF(void) FT_Vector_Unit( FT_Vector* vec, FT_Angle angle ) { vec->x = FT_TRIG_COSCALE >> 2; vec->y = 0; ft_trig_pseudo_rotate( vec, angle ); vec->x >>= 12; vec->y >>= 12; } FT_EXPORT_DEF(void) FT_Vector_Rotate( FT_Vector* vec, FT_Angle angle ) { FT_Int shift; FT_Vector v; v.x = vec->x; v.y = vec->y; if ( angle && ( v.x != 0 || v.y != 0 ) ) { shift = ft_trig_prenorm( &v ); ft_trig_pseudo_rotate( &v, angle ); v.x = ft_trig_downscale( v.x ); v.y = ft_trig_downscale( v.y ); if ( shift >= 0 ) { vec->x = v.x >> shift; vec->y = v.y >> shift; } else { shift = -shift; vec->x = v.x << shift; vec->y = v.y << shift; } } } FT_EXPORT_DEF(FT_Fixed) FT_Vector_Length( FT_Vector* vec ) { FT_Int shift; FT_Vector v; v = *vec; /* handle trivial cases */ if ( v.x == 0 ) { return ( v.y >= 0 ) ? v.y : -v.y; } else if ( v.y == 0 ) { return ( v.x >= 0 ) ? v.x : -v.x; } /* general case */ shift = ft_trig_prenorm( &v ); ft_trig_pseudo_polarize( &v ); v.x = ft_trig_downscale( v.x ); return ( shift >= 0 ) ? (v.x >> shift) : (v.x << -shift); } FT_EXPORT_DEF(void) FT_Vector_Polarize( FT_Vector* vec, FT_Fixed *length, FT_Angle *angle ) { FT_Int shift; FT_Vector v; v = *vec; if ( v.x == 0 && v.y == 0 ) return; shift = ft_trig_prenorm( &v ); ft_trig_pseudo_polarize( &v ); v.x = ft_trig_downscale( v.x ); *length = ( shift >= 0 ) ? (v.x >> shift) : (v.x << -shift); *angle = v.y; }