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Diffstat (limited to 'third_party/freetype/src/base/fttrigon.c')
-rw-r--r-- | third_party/freetype/src/base/fttrigon.c | 526 |
1 files changed, 0 insertions, 526 deletions
diff --git a/third_party/freetype/src/base/fttrigon.c b/third_party/freetype/src/base/fttrigon.c deleted file mode 100644 index 7a4d17c829..0000000000 --- a/third_party/freetype/src/base/fttrigon.c +++ /dev/null @@ -1,526 +0,0 @@ -/***************************************************************************/ -/* */ -/* fttrigon.c */ -/* */ -/* FreeType trigonometric functions (body). */ -/* */ -/* Copyright 2001-2017 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_Angle - 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_Int s = 1; - - - if ( val < 0 ) - { - val = -val; - s = -1; - } - - /* 0x40000000 comes from regression analysis between true */ - /* and CORDIC hypotenuse, so it minimizes the error */ - val = (FT_Fixed)( - ( (FT_UInt64)val * FT_TRIG_SCALE + 0x40000000UL ) >> 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_Int s = 1; - FT_UInt32 lo1, hi1, lo2, hi2, lo, hi, i1, i2; - - - if ( val < 0 ) - { - val = -val; - s = -1; - } - - lo1 = (FT_UInt32)val & 0x0000FFFFU; - hi1 = (FT_UInt32)val >> 16; - lo2 = FT_TRIG_SCALE & 0x0000FFFFU; - hi2 = FT_TRIG_SCALE >> 16; - - lo = lo1 * lo2; - i1 = lo1 * hi2; - i2 = lo2 * hi1; - hi = hi1 * hi2; - - /* Check carry overflow of i1 + i2 */ - i1 += i2; - hi += (FT_UInt32)( i1 < i2 ) << 16; - - hi += i1 >> 16; - i1 = i1 << 16; - - /* Check carry overflow of i1 + lo */ - lo += i1; - hi += ( lo < i1 ); - - /* 0x40000000 comes from regression analysis between true */ - /* and CORDIC hypotenuse, so it minimizes the error */ - - /* Check carry overflow of lo + 0x40000000 */ - lo += 0x40000000UL; - hi += ( lo < 0x40000000UL ); - - val = (FT_Fixed)hi; - - return s < 0 ? -val : val; - } - -#endif /* !FT_LONG64 */ - - - /* undefined and never called for zero vector */ - 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_UInt32)( 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_Angle *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_Angle *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 to acknowledge its error that mostly comes */ - /* from accumulated rounding errors in the arctan table */ - if ( theta >= 0 ) - theta = FT_PAD_ROUND( theta, 16 ); - else - theta = -FT_PAD_ROUND( -theta, 16 ); - - vec->x = x; - vec->y = theta; - } - - - /* documentation is in fttrigon.h */ - - FT_EXPORT_DEF( FT_Fixed ) - FT_Cos( FT_Angle angle ) - { - FT_Vector v; - - - FT_Vector_Unit( &v, angle ); - - return v.x; - } - - - /* documentation is in fttrigon.h */ - - FT_EXPORT_DEF( FT_Fixed ) - FT_Sin( FT_Angle angle ) - { - FT_Vector v; - - - FT_Vector_Unit( &v, angle ); - - return v.y; - } - - - /* documentation is in fttrigon.h */ - - FT_EXPORT_DEF( FT_Fixed ) - FT_Tan( FT_Angle angle ) - { - FT_Vector v; - - - FT_Vector_Unit( &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 ) - { - if ( !vec ) - return; - - 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; - - - if ( !vec || !angle ) - return; - - v = *vec; - - if ( v.x == 0 && v.y == 0 ) - return; - - 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; - - - if ( !vec ) - return 0; - - 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 + ( 1L << ( 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; - - - if ( !vec || !length || !angle ) - return; - - 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 ) - { - if ( !vec ) - return; - - 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; - - - while ( delta <= -FT_ANGLE_PI ) - delta += FT_ANGLE_2PI; - - while ( delta > FT_ANGLE_PI ) - delta -= FT_ANGLE_2PI; - - return delta; - } - - -/* END */ |