diff -r f9283dc4860d -r 88f2e05288ba misc/libfreetype/src/base/fttrigon.c --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/misc/libfreetype/src/base/fttrigon.c Mon Apr 25 01:46:54 2011 +0200 @@ -0,0 +1,546 @@ +/***************************************************************************/ +/* */ +/* fttrigon.c */ +/* */ +/* FreeType trigonometric functions (body). */ +/* */ +/* Copyright 2001, 2002, 2003, 2004, 2005 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. */ +/* */ +/***************************************************************************/ + + +#include +#include FT_INTERNAL_OBJECTS_H +#include FT_TRIGONOMETRY_H + + + /* the following is 0.2715717684432231 * 2^30 */ +#define FT_TRIG_COSCALE 0x11616E8EUL + + /* 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] = + { + 4157273L, 2949120L, 1740967L, 919879L, 466945L, 234379L, 117304L, + 58666L, 29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L, + 57L, 29L, 14L, 7L, 4L, 2L, 1L + }; + + /* the Cordic shrink factor, multiplied by 2^32 */ +#define FT_TRIG_SCALE 1166391785UL /* 0x4585BA38UL */ + + +#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 ) + 0x100000000UL; + 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 & 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 = ( lo1 >= lo2 ) ? 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_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 1 + /* determine msb bit index in `shift' */ + if ( z >= ( 1L << 16 ) ) + { + z >>= 16; + shift += 16; + } + if ( z >= ( 1L << 8 ) ) + { + z >>= 8; + shift += 8; + } + if ( z >= ( 1L << 4 ) ) + { + z >>= 4; + shift += 4; + } + if ( z >= ( 1L << 2 ) ) + { + z >>= 2; + shift += 2; + } + if ( z >= ( 1L << 1 ) ) + { + z >>= 1; + shift += 1; + } + + if ( shift <= 27 ) + { + shift = 27 - shift; + vec->x = x << shift; + vec->y = y << shift; + } + else + { + shift -= 27; + vec->x = x >> shift; + vec->y = y >> shift; + shift = -shift; + } + +#else /* 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; + } + +#endif /* 0 */ + + 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 = 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_COSCALE >> 2; + v.y = 0; + ft_trig_pseudo_rotate( &v, angle ); + + return v.x / ( 1 << 12 ); + } + + + /* 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_COSCALE >> 2; + 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_COSCALE >> 2; + vec->y = 0; + ft_trig_pseudo_rotate( vec, angle ); + vec->x >>= 12; + vec->y >>= 12; + } + + + /* 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 = v.x << shift; + vec->y = 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 ( 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 ); + + if ( shift > 0 ) + return ( v.x + ( 1 << ( shift - 1 ) ) ) >> shift; + + return 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 ) : ( 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 */