diff options
Diffstat (limited to 'src/base/fttrigon.c')
-rw-r--r-- | src/base/fttrigon.c | 286 |
1 files changed, 116 insertions, 170 deletions
diff --git a/src/base/fttrigon.c b/src/base/fttrigon.c index fdf433a..4ffdcb7 100644 --- a/src/base/fttrigon.c +++ b/src/base/fttrigon.c @@ -4,7 +4,7 @@ /* */ /* FreeType trigonometric functions (body). */ /* */ -/* Copyright 2001, 2002, 2003, 2004, 2005 by */ +/* 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, */ @@ -15,31 +15,46 @@ /* */ /***************************************************************************/ + /*************************************************************************/ + /* */ + /* 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 following is 0.2715717684432231 * 2^30 */ -#define FT_TRIG_COSCALE 0x11616E8EUL + /* 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[24] = + ft_trig_arctan_table[] = { - 4157273L, 2949120L, 1740967L, 919879L, 466945L, 234379L, 117304L, - 58666L, 29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L, + 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 +#ifdef FT_LONG64 /* multiply a given value by the CORDIC shrink factor */ static FT_Fixed @@ -50,7 +65,7 @@ s = val; - val = ( val >= 0 ) ? val : -val; + val = FT_ABS( val ); v = ( val * (FT_Int64)FT_TRIG_SCALE ) + 0x100000000UL; val = (FT_Fixed)( v >> 32 ); @@ -58,7 +73,7 @@ return ( s >= 0 ) ? val : -val; } -#else /* !FT_CONFIG_HAS_INT64 */ +#else /* !FT_LONG64 */ /* multiply a given value by the CORDIC shrink factor */ static FT_Fixed @@ -69,19 +84,19 @@ s = val; - val = ( val >= 0 ) ? val : -val; + val = FT_ABS( val ); v1 = (FT_UInt32)val >> 16; - v2 = (FT_UInt32)(val & 0xFFFFL); + v2 = (FT_UInt32)( val & 0xFFFFL ); - k1 = (FT_UInt32)FT_TRIG_SCALE >> 16; /* constant */ - k2 = (FT_UInt32)(FT_TRIG_SCALE & 0xFFFFL); /* constant */ + 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; + lo3 = FT_MAX( lo1, lo2 ); lo1 += lo2; hi += lo1 >> 16; @@ -93,91 +108,35 @@ return ( s >= 0 ) ? val : -val; } -#endif /* !FT_CONFIG_HAS_INT64 */ +#endif /* !FT_LONG64 */ static FT_Int ft_trig_prenorm( FT_Vector* vec ) { - FT_Fixed x, y, z; - FT_Int shift; + FT_Pos x, y; + FT_Int shift; x = vec->x; y = vec->y; - z = ( ( x >= 0 ) ? x : - x ) | ( (y >= 0) ? y : -y ); - shift = 0; + shift = FT_MSB( FT_ABS( x ) | FT_ABS( y ) ); -#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 ) ) + if ( shift <= FT_TRIG_SAFE_MSB ) { - 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; + shift = FT_TRIG_SAFE_MSB - shift; + vec->x = (FT_Pos)( (FT_ULong)x << shift ); + vec->y = (FT_Pos)( (FT_ULong)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 ) ); - + shift -= FT_TRIG_SAFE_MSB; vec->x = x >> shift; vec->y = y >> shift; shift = -shift; } -#endif /* 0 */ - return shift; } @@ -187,65 +146,50 @@ FT_Angle theta ) { FT_Int i; - FT_Fixed x, y, xtemp; + FT_Fixed x, y, xtemp, b; const FT_Fixed *arctanptr; x = vec->x; y = vec->y; - /* Get angle between -90 and 90 degrees */ - while ( theta <= -FT_ANGLE_PI2 ) + /* Rotate inside [-PI/4,PI/4] sector */ + while ( theta < -FT_ANGLE_PI4 ) { - x = -x; - y = -y; - theta += FT_ANGLE_PI; + xtemp = y; + y = -x; + x = xtemp; + theta += FT_ANGLE_PI2; } - while ( theta > FT_ANGLE_PI2 ) + while ( theta > FT_ANGLE_PI4 ) { - x = -x; - y = -y; - theta -= FT_ANGLE_PI; + xtemp = -y; + y = x; + x = xtemp; + theta -= FT_ANGLE_PI2; } - /* 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 + /* Pseudorotations, with right shifts */ + for ( i = 1, b = 1; i < FT_TRIG_MAX_ITERS; b <<= 1, i++ ) { if ( theta < 0 ) { - xtemp = x + ( y >> i ); - y = y - ( x >> i ); + xtemp = x + ( ( y + b ) >> i ); + y = y - ( ( x + b ) >> i ); x = xtemp; theta += *arctanptr++; } else { - xtemp = x - ( y >> i ); - y = y + ( x >> i ); + xtemp = x - ( ( y + b ) >> i ); + y = y + ( ( x + b ) >> i ); x = xtemp; theta -= *arctanptr++; } - } while ( ++i < FT_TRIG_MAX_ITERS ); + } vec->x = x; vec->y = y; @@ -255,66 +199,67 @@ static void ft_trig_pseudo_polarize( FT_Vector* vec ) { - FT_Fixed theta; - FT_Fixed yi, i; - FT_Fixed x, y; + 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 the right half plane */ - theta = 0; - if ( x < 0 ) + /* Get the vector into [-PI/4,PI/4] sector */ + if ( y > x ) { - 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 */ + 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 { - /* Rotate negative */ - yi = y - ( x << 1 ); - x = x + ( y << 1 ); - y = yi; - theta += *arctanptr++; /* Add angle */ + if ( y < -x ) + { + theta = -FT_ANGLE_PI2; + xtemp = -y; + y = x; + x = xtemp; + } + else + { + theta = 0; + } } - i = 0; - do + 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 ) + if ( y > 0 ) { - /* Rotate positive */ - yi = y + ( x >> i ); - x = x - ( y >> i ); - y = yi; - theta -= *arctanptr++; + xtemp = x + ( ( y + b ) >> i ); + y = y - ( ( x + b ) >> i ); + x = xtemp; + theta += *arctanptr++; } else { - /* Rotate negative */ - yi = y - ( x >> i ); - x = x + ( y >> i ); - y = yi; - theta += *arctanptr++; + xtemp = x - ( ( y + b ) >> i ); + y = y + ( ( x + b ) >> i ); + x = xtemp; + theta -= *arctanptr++; } - } while ( ++i < FT_TRIG_MAX_ITERS ); + } /* round theta */ if ( theta >= 0 ) @@ -335,11 +280,11 @@ FT_Vector v; - v.x = FT_TRIG_COSCALE >> 2; + v.x = FT_TRIG_SCALE >> 8; v.y = 0; ft_trig_pseudo_rotate( &v, angle ); - return v.x / ( 1 << 12 ); + return ( v.x + 0x80L ) >> 8; } @@ -360,7 +305,7 @@ FT_Vector v; - v.x = FT_TRIG_COSCALE >> 2; + v.x = FT_TRIG_SCALE >> 8; v.y = 0; ft_trig_pseudo_rotate( &v, angle ); @@ -395,11 +340,11 @@ FT_Vector_Unit( FT_Vector* vec, FT_Angle angle ) { - vec->x = FT_TRIG_COSCALE >> 2; + vec->x = FT_TRIG_SCALE >> 8; vec->y = 0; ft_trig_pseudo_rotate( vec, angle ); - vec->x >>= 12; - vec->y >>= 12; + vec->x = ( vec->x + 0x80L ) >> 8; + vec->y = ( vec->y + 0x80L ) >> 8; } @@ -442,8 +387,8 @@ else { shift = -shift; - vec->x = v.x << shift; - vec->y = v.y << shift; + vec->x = (FT_Pos)( (FT_ULong)v.x << shift ); + vec->y = (FT_Pos)( (FT_ULong)v.y << shift ); } } } @@ -463,11 +408,11 @@ /* handle trivial cases */ if ( v.x == 0 ) { - return ( v.y >= 0 ) ? v.y : -v.y; + return FT_ABS( v.y ); } else if ( v.y == 0 ) { - return ( v.x >= 0 ) ? v.x : -v.x; + return FT_ABS( v.x ); } /* general case */ @@ -479,7 +424,7 @@ if ( shift > 0 ) return ( v.x + ( 1 << ( shift - 1 ) ) ) >> shift; - return v.x << -shift; + return (FT_Fixed)( (FT_UInt32)v.x << -shift ); } @@ -504,7 +449,8 @@ v.x = ft_trig_downscale( v.x ); - *length = ( shift >= 0 ) ? ( v.x >> shift ) : ( v.x << -shift ); + *length = ( shift >= 0 ) ? ( v.x >> shift ) + : (FT_Fixed)( (FT_UInt32)v.x << -shift ); *angle = v.y; } |