diff options
Diffstat (limited to 'src/base/fttrigon.c')
| -rw-r--r-- | src/base/fttrigon.c | 167 |
1 files changed, 100 insertions, 67 deletions
diff --git a/src/base/fttrigon.c b/src/base/fttrigon.c index 4ffdcb7..5b24304 100644 --- a/src/base/fttrigon.c +++ b/src/base/fttrigon.c @@ -4,7 +4,7 @@ /* */ /* FreeType trigonometric functions (body). */ /* */ -/* Copyright 2001-2005, 2012-2013 by */ +/* Copyright 2001-2015 by */ /* David Turner, Robert Wilhelm, and Werner Lemberg. */ /* */ /* This file is part of the FreeType project, and may only be used, */ @@ -45,7 +45,7 @@ /* this table was generated for FT_PI = 180L << 16, i.e. degrees */ #define FT_TRIG_MAX_ITERS 23 - static const FT_Fixed + static const FT_Angle ft_trig_arctan_table[] = { 1740967L, 919879L, 466945L, 234379L, 117304L, 58666L, 29335L, @@ -60,17 +60,20 @@ static FT_Fixed ft_trig_downscale( FT_Fixed val ) { - FT_Fixed s; - FT_Int64 v; + FT_Int s = 1; - s = val; - val = FT_ABS( val ); + if ( val < 0 ) + { + val = -val; + s = -1; + } - v = ( val * (FT_Int64)FT_TRIG_SCALE ) + 0x100000000UL; - val = (FT_Fixed)( v >> 32 ); + /* 0x40000000 comes from regression analysis between true */ + /* and CORDIC hypotenuse, so it minimizes the error */ + val = (FT_Fixed)( ( (FT_Int64)val * FT_TRIG_SCALE + 0x40000000UL ) >> 32 ); - return ( s >= 0 ) ? val : -val; + return s < 0 ? -val : val; } #else /* !FT_LONG64 */ @@ -79,38 +82,53 @@ static FT_Fixed ft_trig_downscale( FT_Fixed val ) { - FT_Fixed s; - FT_UInt32 v1, v2, k1, k2, hi, lo1, lo2, lo3; + 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; - s = val; - val = FT_ABS( val ); + lo = lo1 * lo2; + i1 = lo1 * hi2; + i2 = lo2 * hi1; + hi = hi1 * hi2; - v1 = (FT_UInt32)val >> 16; - v2 = (FT_UInt32)( val & 0xFFFFL ); + /* Check carry overflow of i1 + i2 */ + i1 += i2; + hi += (FT_UInt32)( i1 < i2 ) << 16; - k1 = (FT_UInt32)FT_TRIG_SCALE >> 16; /* constant */ - k2 = (FT_UInt32)( FT_TRIG_SCALE & 0xFFFFL ); /* constant */ + hi += i1 >> 16; + i1 = i1 << 16; - hi = k1 * v1; - lo1 = k1 * v2 + k2 * v1; /* can't overflow */ + /* Check carry overflow of i1 + lo */ + lo += i1; + hi += ( lo < i1 ); - lo2 = ( k2 * v2 ) >> 16; - lo3 = FT_MAX( lo1, lo2 ); - lo1 += lo2; + /* 0x40000000 comes from regression analysis between true */ + /* and CORDIC hypotenuse, so it minimizes the error */ - hi += lo1 >> 16; - if ( lo1 < lo3 ) - hi += (FT_UInt32)0x10000UL; + /* Check carry overflow of lo + 0x40000000 */ + lo += 0x40000000UL; + hi += ( lo < 0x40000000UL ); - val = (FT_Fixed)hi; + val = (FT_Fixed)hi; - return ( s >= 0 ) ? val : -val; + return s < 0 ? -val : val; } #endif /* !FT_LONG64 */ + /* undefined and never called for zero vector */ static FT_Int ft_trig_prenorm( FT_Vector* vec ) { @@ -121,7 +139,7 @@ x = vec->x; y = vec->y; - shift = FT_MSB( FT_ABS( x ) | FT_ABS( y ) ); + shift = FT_MSB( (FT_UInt32)( FT_ABS( x ) | FT_ABS( y ) ) ); if ( shift <= FT_TRIG_SAFE_MSB ) { @@ -147,7 +165,7 @@ { FT_Int i; FT_Fixed x, y, xtemp, b; - const FT_Fixed *arctanptr; + const FT_Angle *arctanptr; x = vec->x; @@ -202,7 +220,7 @@ FT_Angle theta; FT_Int i; FT_Fixed x, y, xtemp, b; - const FT_Fixed *arctanptr; + const FT_Angle *arctanptr; x = vec->x; @@ -261,11 +279,12 @@ } } - /* round theta */ + /* 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, 32 ); + theta = FT_PAD_ROUND( theta, 16 ); else - theta = -FT_PAD_ROUND( -theta, 32 ); + theta = -FT_PAD_ROUND( -theta, 16 ); vec->x = x; vec->y = theta; @@ -280,11 +299,9 @@ FT_Vector v; - v.x = FT_TRIG_SCALE >> 8; - v.y = 0; - ft_trig_pseudo_rotate( &v, angle ); + FT_Vector_Unit( &v, angle ); - return ( v.x + 0x80L ) >> 8; + return v.x; } @@ -293,7 +310,12 @@ FT_EXPORT_DEF( FT_Fixed ) FT_Sin( FT_Angle angle ) { - return FT_Cos( FT_ANGLE_PI2 - angle ); + FT_Vector v; + + + FT_Vector_Unit( &v, angle ); + + return v.y; } @@ -305,9 +327,7 @@ FT_Vector v; - v.x = FT_TRIG_SCALE >> 8; - v.y = 0; - ft_trig_pseudo_rotate( &v, angle ); + FT_Vector_Unit( &v, angle ); return FT_DivFix( v.y, v.x ); } @@ -340,6 +360,9 @@ 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 ); @@ -366,30 +389,32 @@ FT_Vector v; - v.x = vec->x; - v.y = vec->y; + if ( !vec || !angle ) + return; - 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 ); + v = *vec; - if ( shift > 0 ) - { - FT_Int32 half = (FT_Int32)1L << ( shift - 1 ); + 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 ); - 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 ); - } + 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 ); } } @@ -403,6 +428,9 @@ FT_Vector v; + if ( !vec ) + return 0; + v = *vec; /* handle trivial cases */ @@ -422,7 +450,7 @@ v.x = ft_trig_downscale( v.x ); if ( shift > 0 ) - return ( v.x + ( 1 << ( shift - 1 ) ) ) >> shift; + return ( v.x + ( 1L << ( shift - 1 ) ) ) >> shift; return (FT_Fixed)( (FT_UInt32)v.x << -shift ); } @@ -439,6 +467,9 @@ FT_Vector v; + if ( !vec || !length || !angle ) + return; + v = *vec; if ( v.x == 0 && v.y == 0 ) @@ -449,8 +480,8 @@ v.x = ft_trig_downscale( v.x ); - *length = ( shift >= 0 ) ? ( v.x >> shift ) - : (FT_Fixed)( (FT_UInt32)v.x << -shift ); + *length = shift >= 0 ? ( v.x >> shift ) + : (FT_Fixed)( (FT_UInt32)v.x << -shift ); *angle = v.y; } @@ -462,6 +493,9 @@ FT_Fixed length, FT_Angle angle ) { + if ( !vec ) + return; + vec->x = length; vec->y = 0; @@ -478,11 +512,10 @@ FT_Angle delta = angle2 - angle1; - delta %= FT_ANGLE_2PI; - if ( delta < 0 ) + while ( delta <= -FT_ANGLE_PI ) delta += FT_ANGLE_2PI; - if ( delta > FT_ANGLE_PI ) + while ( delta > FT_ANGLE_PI ) delta -= FT_ANGLE_2PI; return delta; |