diff options
Diffstat (limited to 'src/base/ftcalc.c')
| -rw-r--r-- | src/base/ftcalc.c | 201 |
1 files changed, 126 insertions, 75 deletions
diff --git a/src/base/ftcalc.c b/src/base/ftcalc.c index dca0e1d..619a08b 100644 --- a/src/base/ftcalc.c +++ b/src/base/ftcalc.c @@ -86,8 +86,7 @@ FT_EXPORT_DEF( FT_Fixed ) FT_RoundFix( FT_Fixed a ) { - return a >= 0 ? ( a + 0x8000L ) & ~0xFFFFL - : -((-a + 0x8000L ) & ~0xFFFFL ); + return ( a + 0x8000L - ( a < 0 ) ) & ~0xFFFFL; } @@ -96,8 +95,7 @@ FT_EXPORT_DEF( FT_Fixed ) FT_CeilFix( FT_Fixed a ) { - return a >= 0 ? ( a + 0xFFFFL ) & ~0xFFFFL - : -((-a + 0xFFFFL ) & ~0xFFFFL ); + return ( a + 0xFFFFL ) & ~0xFFFFL; } @@ -106,8 +104,7 @@ FT_EXPORT_DEF( FT_Fixed ) FT_FloorFix( FT_Fixed a ) { - return a >= 0 ? a & ~0xFFFFL - : -((-a) & ~0xFFFFL ); + return a & ~0xFFFFL; } #ifndef FT_MSB @@ -240,22 +237,10 @@ #else - FT_Int s = 1; - FT_UInt64 a, b, c; - FT_Long c_; - + FT_Int64 ab = (FT_Int64)a_ * (FT_Int64)b_; - FT_MOVE_SIGN( a_, s ); - FT_MOVE_SIGN( b_, s ); - - a = (FT_UInt64)a_; - b = (FT_UInt64)b_; - - c = ( a * b + 0x8000UL ) >> 16; - - c_ = (FT_Long)c; - - return s < 0 ? -c_ : c_; + /* this requires arithmetic right shift of signed numbers */ + return (FT_Long)( ( ab + 0x8000L - ( ab < 0 ) ) >> 16 ); #endif /* FT_MULFIX_ASSEMBLER */ } @@ -437,9 +422,6 @@ /* XXX: this function does not allow 64-bit arguments */ - if ( a_ == 0 || b_ == c_ ) - return a_; - FT_MOVE_SIGN( a_, s ); FT_MOVE_SIGN( b_, s ); FT_MOVE_SIGN( c_, s ); @@ -488,9 +470,6 @@ /* XXX: this function does not allow 64-bit arguments */ - if ( a_ == 0 || b_ == c_ ) - return a_; - FT_MOVE_SIGN( a_, s ); FT_MOVE_SIGN( b_, s ); FT_MOVE_SIGN( c_, s ); @@ -546,9 +525,6 @@ FT_UInt32 a, b; - if ( a_ == 0 || b_ == 0x10000L ) - return a_; - /* * This is a clever way of converting a signed number `a' into its * absolute value (stored back into `a') and its sign. The sign is @@ -599,9 +575,6 @@ /* XXX: this function does not allow 64-bit arguments */ - if ( a_ == 0 || b_ == 0x10000L ) - return a_; - FT_MOVE_SIGN( a_, s ); FT_MOVE_SIGN( b_, s ); @@ -785,6 +758,102 @@ } + /* documentation is in ftcalc.h */ + + FT_BASE_DEF( FT_UInt32 ) + FT_Vector_NormLen( FT_Vector* vector ) + { + FT_Int32 x_ = vector->x; + FT_Int32 y_ = vector->y; + FT_Int32 b, z; + FT_UInt32 x, y, u, v, l; + FT_Int sx = 1, sy = 1, shift; + + + FT_MOVE_SIGN( x_, sx ); + FT_MOVE_SIGN( y_, sy ); + + x = (FT_UInt32)x_; + y = (FT_UInt32)y_; + + /* trivial cases */ + if ( x == 0 ) + { + if ( y > 0 ) + vector->y = sy * 0x10000; + return y; + } + else if ( y == 0 ) + { + if ( x > 0 ) + vector->x = sx * 0x10000; + return x; + } + + /* Estimate length and prenormalize by shifting so that */ + /* the new approximate length is between 2/3 and 4/3. */ + /* The magic constant 0xAAAAAAAAUL (2/3 of 2^32) helps */ + /* achieve this in 16.16 fixed-point representation. */ + l = x > y ? x + ( y >> 1 ) + : y + ( x >> 1 ); + + shift = 31 - FT_MSB( l ); + shift -= 15 + ( l >= ( 0xAAAAAAAAUL >> shift ) ); + + if ( shift > 0 ) + { + x <<= shift; + y <<= shift; + + /* re-estimate length for tiny vectors */ + l = x > y ? x + ( y >> 1 ) + : y + ( x >> 1 ); + } + else + { + x >>= -shift; + y >>= -shift; + l >>= -shift; + } + + /* lower linear approximation for reciprocal length minus one */ + b = 0x10000 - (FT_Int32)l; + + x_ = (FT_Int32)x; + y_ = (FT_Int32)y; + + /* Newton's iterations */ + do + { + u = (FT_UInt32)( x_ + ( x_ * b >> 16 ) ); + v = (FT_UInt32)( y_ + ( y_ * b >> 16 ) ); + + /* Normalized squared length in the parentheses approaches 2^32. */ + /* On two's complement systems, converting to signed gives the */ + /* difference with 2^32 even if the expression wraps around. */ + z = -(FT_Int32)( u * u + v * v ) / 0x200; + z = z * ( ( 0x10000 + b ) >> 8 ) / 0x10000; + + b += z; + + } while ( z > 0 ); + + vector->x = sx < 0 ? -(FT_Pos)u : (FT_Pos)u; + vector->y = sy < 0 ? -(FT_Pos)v : (FT_Pos)v; + + /* Conversion to signed helps to recover from likely wrap around */ + /* in calculating the prenormalized length, because it gives the */ + /* correct difference with 2^32 on two's complement systems. */ + l = (FT_UInt32)( 0x10000 + (FT_Int32)( u * x + v * y ) / 0x10000 ); + if ( shift > 0 ) + l = ( l + ( 1 << ( shift - 1 ) ) ) >> shift; + else + l <<= -shift; + + return l; + } + + #if 0 /* documentation is in ftcalc.h */ @@ -832,52 +901,34 @@ FT_Pos out_x, FT_Pos out_y ) { - FT_Long result; /* avoid overflow on 16-bit system */ - - - /* deal with the trivial cases quickly */ - if ( in_y == 0 ) - { - if ( in_x >= 0 ) - result = out_y; - else - result = -out_y; - } - else if ( in_x == 0 ) - { - if ( in_y >= 0 ) - result = -out_x; - else - result = out_x; - } - else if ( out_y == 0 ) - { - if ( out_x >= 0 ) - result = in_y; - else - result = -in_y; - } - else if ( out_x == 0 ) - { - if ( out_y >= 0 ) - result = -in_x; - else - result = in_x; - } - else /* general case */ - { #ifdef FT_LONG64 - FT_Int64 delta = (FT_Int64)in_x * out_y - (FT_Int64)in_y * out_x; + FT_Int64 delta = (FT_Int64)in_x * out_y - (FT_Int64)in_y * out_x; - if ( delta == 0 ) - result = 0; - else - result = 1 - 2 * ( delta < 0 ); + return ( delta > 0 ) - ( delta < 0 ); #else + FT_Int result; + + + if ( (FT_ULong)FT_ABS( in_x ) + (FT_ULong)FT_ABS( out_y ) <= 131071UL && + (FT_ULong)FT_ABS( in_y ) + (FT_ULong)FT_ABS( out_x ) <= 131071UL ) + { + FT_Long z1 = in_x * out_y; + FT_Long z2 = in_y * out_x; + + + if ( z1 > z2 ) + result = +1; + else if ( z1 < z2 ) + result = -1; + else + result = 0; + } + else /* products might overflow 32 bits */ + { FT_Int64 z1, z2; @@ -895,12 +946,12 @@ result = -1; else result = 0; - -#endif } /* XXX: only the sign of return value, +1/0/-1 must be used */ - return (FT_Int)result; + return result; + +#endif } |