ref: 89a529f3176fc68415cc5e3ab50f89629fb269cd
dir: /src/base/fttrigon.c/
/***************************************************************************/ /* */ /* fttrigon.c */ /* */ /* FreeType trigonometric functions (body). */ /* */ /* Copyright 2001-2005, 2012-2013 by */ /* David Turner, Robert Wilhelm, and Werner Lemberg. */ /* */ /* This file is part of the FreeType project, and may only be used, */ /* modified, and distributed under the terms of the FreeType project */ /* license, LICENSE.TXT. By continuing to use, modify, or distribute */ /* this file you indicate that you have read the license and */ /* understand and accept it fully. */ /* */ /***************************************************************************/ /*************************************************************************/ /* */ /* This is a fixed-point CORDIC implementation of trigonometric */ /* functions as well as transformations between Cartesian and polar */ /* coordinates. The angles are represented as 16.16 fixed-point values */ /* in degrees, i.e., the angular resolution is 2^-16 degrees. Note that */ /* only vectors longer than 2^16*180/pi (or at least 22 bits) on a */ /* discrete Cartesian grid can have the same or better angular */ /* resolution. Therefore, to maintain this precision, some functions */ /* require an interim upscaling of the vectors, whereas others operate */ /* with 24-bit long vectors directly. */ /* */ /*************************************************************************/ #include <ft2build.h> #include FT_INTERNAL_OBJECTS_H #include FT_INTERNAL_CALC_H #include FT_TRIGONOMETRY_H /* the Cordic shrink factor 0.858785336480436 * 2^32 */ #define FT_TRIG_SCALE 0xDBD95B16UL /* the highest bit in overflow-safe vector components, */ /* MSB of 0.858785336480436 * sqrt(0.5) * 2^30 */ #define FT_TRIG_SAFE_MSB 29 /* 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[] = { 1740967L, 919879L, 466945L, 234379L, 117304L, 58666L, 29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L, 57L, 29L, 14L, 7L, 4L, 2L, 1L }; #ifdef FT_LONG64 /* 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 = FT_ABS( val ); v = ( val * (FT_Int64)FT_TRIG_SCALE ) + 0x100000000UL; val = (FT_Fixed)( v >> 32 ); return ( s >= 0 ) ? val : -val; } #else /* !FT_LONG64 */ /* 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 = FT_ABS( val ); v1 = (FT_UInt32)val >> 16; v2 = (FT_UInt32)( val & 0xFFFFL ); k1 = (FT_UInt32)FT_TRIG_SCALE >> 16; /* constant */ k2 = (FT_UInt32)( FT_TRIG_SCALE & 0xFFFFL ); /* constant */ hi = k1 * v1; lo1 = k1 * v2 + k2 * v1; /* can't overflow */ lo2 = ( k2 * v2 ) >> 16; lo3 = FT_MAX( lo1, lo2 ); lo1 += lo2; hi += lo1 >> 16; if ( lo1 < lo3 ) hi += (FT_UInt32)0x10000UL; val = (FT_Fixed)hi; return ( s >= 0 ) ? val : -val; } #endif /* !FT_LONG64 */ static FT_Int ft_trig_prenorm( FT_Vector* vec ) { FT_Pos x, y; FT_Int shift; x = vec->x; y = vec->y; shift = FT_MSB( FT_ABS( x ) | FT_ABS( y ) ); if ( shift <= FT_TRIG_SAFE_MSB ) { shift = FT_TRIG_SAFE_MSB - shift; vec->x = (FT_Pos)( (FT_ULong)x << shift ); vec->y = (FT_Pos)( (FT_ULong)y << shift ); } else { shift -= FT_TRIG_SAFE_MSB; 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, b; const FT_Fixed *arctanptr; x = vec->x; y = vec->y; /* Rotate inside [-PI/4,PI/4] sector */ while ( theta < -FT_ANGLE_PI4 ) { xtemp = y; y = -x; x = xtemp; theta += FT_ANGLE_PI2; } while ( theta > FT_ANGLE_PI4 ) { xtemp = -y; y = x; x = xtemp; theta -= FT_ANGLE_PI2; } arctanptr = ft_trig_arctan_table; /* Pseudorotations, with right shifts */ for ( i = 1, b = 1; i < FT_TRIG_MAX_ITERS; b <<= 1, i++ ) { if ( theta < 0 ) { xtemp = x + ( ( y + b ) >> i ); y = y - ( ( x + b ) >> i ); x = xtemp; theta += *arctanptr++; } else { xtemp = x - ( ( y + b ) >> i ); y = y + ( ( x + b ) >> i ); x = xtemp; theta -= *arctanptr++; } } vec->x = x; vec->y = y; } static void ft_trig_pseudo_polarize( FT_Vector* vec ) { FT_Angle theta; FT_Int i; FT_Fixed x, y, xtemp, b; const FT_Fixed *arctanptr; x = vec->x; y = vec->y; /* Get the vector into [-PI/4,PI/4] sector */ if ( y > x ) { if ( y > -x ) { theta = FT_ANGLE_PI2; xtemp = y; y = -x; x = xtemp; } else { theta = y > 0 ? FT_ANGLE_PI : -FT_ANGLE_PI; x = -x; y = -y; } } else { if ( y < -x ) { theta = -FT_ANGLE_PI2; xtemp = -y; y = x; x = xtemp; } else { theta = 0; } } arctanptr = ft_trig_arctan_table; /* Pseudorotations, with right shifts */ for ( i = 1, b = 1; i < FT_TRIG_MAX_ITERS; b <<= 1, i++ ) { if ( y > 0 ) { xtemp = x + ( ( y + b ) >> i ); y = y - ( ( x + b ) >> i ); x = xtemp; theta += *arctanptr++; } else { xtemp = x - ( ( y + b ) >> i ); y = y + ( ( x + b ) >> i ); x = xtemp; theta -= *arctanptr++; } } /* round theta */ if ( theta >= 0 ) theta = FT_PAD_ROUND( theta, 32 ); else theta = -FT_PAD_ROUND( -theta, 32 ); vec->x = x; vec->y = theta; } /* documentation is in fttrigon.h */ FT_EXPORT_DEF( FT_Fixed ) FT_Cos( FT_Angle angle ) { FT_Vector v; v.x = FT_TRIG_SCALE >> 8; v.y = 0; ft_trig_pseudo_rotate( &v, angle ); return ( v.x + 0x80L ) >> 8; } /* documentation is in fttrigon.h */ FT_EXPORT_DEF( FT_Fixed ) FT_Sin( FT_Angle angle ) { return FT_Cos( FT_ANGLE_PI2 - angle ); } /* documentation is in fttrigon.h */ FT_EXPORT_DEF( FT_Fixed ) FT_Tan( FT_Angle angle ) { FT_Vector v; v.x = FT_TRIG_SCALE >> 8; v.y = 0; ft_trig_pseudo_rotate( &v, angle ); return FT_DivFix( v.y, v.x ); } /* documentation is in fttrigon.h */ 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; } /* documentation is in fttrigon.h */ FT_EXPORT_DEF( void ) FT_Vector_Unit( FT_Vector* vec, FT_Angle angle ) { vec->x = FT_TRIG_SCALE >> 8; vec->y = 0; ft_trig_pseudo_rotate( vec, angle ); vec->x = ( vec->x + 0x80L ) >> 8; vec->y = ( vec->y + 0x80L ) >> 8; } /* these macros return 0 for positive numbers, and -1 for negative ones */ #define FT_SIGN_LONG( x ) ( (x) >> ( FT_SIZEOF_LONG * 8 - 1 ) ) #define FT_SIGN_INT( x ) ( (x) >> ( FT_SIZEOF_INT * 8 - 1 ) ) #define FT_SIGN_INT32( x ) ( (x) >> 31 ) #define FT_SIGN_INT16( x ) ( (x) >> 15 ) /* documentation is in fttrigon.h */ 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 ) { FT_Int32 half = (FT_Int32)1L << ( shift - 1 ); vec->x = ( v.x + half + FT_SIGN_LONG( v.x ) ) >> shift; vec->y = ( v.y + half + FT_SIGN_LONG( v.y ) ) >> shift; } else { shift = -shift; vec->x = (FT_Pos)( (FT_ULong)v.x << shift ); vec->y = (FT_Pos)( (FT_ULong)v.y << shift ); } } } /* documentation is in fttrigon.h */ 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 FT_ABS( v.y ); } else if ( v.y == 0 ) { return FT_ABS( v.x ); } /* general case */ shift = ft_trig_prenorm( &v ); ft_trig_pseudo_polarize( &v ); v.x = ft_trig_downscale( v.x ); if ( shift > 0 ) return ( v.x + ( 1 << ( shift - 1 ) ) ) >> shift; return (FT_Fixed)( (FT_UInt32)v.x << -shift ); } /* documentation is in fttrigon.h */ 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 ) : (FT_Fixed)( (FT_UInt32)v.x << -shift ); *angle = v.y; } /* documentation is in fttrigon.h */ FT_EXPORT_DEF( void ) FT_Vector_From_Polar( FT_Vector* vec, FT_Fixed length, FT_Angle angle ) { vec->x = length; vec->y = 0; FT_Vector_Rotate( vec, angle ); } /* documentation is in fttrigon.h */ FT_EXPORT_DEF( FT_Angle ) FT_Angle_Diff( FT_Angle angle1, FT_Angle angle2 ) { FT_Angle delta = angle2 - angle1; delta %= FT_ANGLE_2PI; if ( delta < 0 ) delta += FT_ANGLE_2PI; if ( delta > FT_ANGLE_PI ) delta -= FT_ANGLE_2PI; return delta; } /* END */