diff -r f3840de881bd -r 915436ff64ab misc/libfreetype/src/base/fttrigon.c --- a/misc/libfreetype/src/base/fttrigon.c Thu Jul 25 23:16:06 2013 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,546 +0,0 @@ -/***************************************************************************/ -/* */ -/* 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 */