| /***************************************************************************/ |
| /* */ |
| /* ftcalc.c */ |
| /* */ |
| /* Arithmetic computations (body). */ |
| /* */ |
| /* Copyright 1996-2015 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. */ |
| /* */ |
| /***************************************************************************/ |
| |
| /*************************************************************************/ |
| /* */ |
| /* Support for 1-complement arithmetic has been totally dropped in this */ |
| /* release. You can still write your own code if you need it. */ |
| /* */ |
| /*************************************************************************/ |
| |
| /*************************************************************************/ |
| /* */ |
| /* Implementing basic computation routines. */ |
| /* */ |
| /* FT_MulDiv(), FT_MulFix(), FT_DivFix(), FT_RoundFix(), FT_CeilFix(), */ |
| /* and FT_FloorFix() are declared in freetype.h. */ |
| /* */ |
| /*************************************************************************/ |
| |
| |
| #include <ft2build.h> |
| #include FT_GLYPH_H |
| #include FT_TRIGONOMETRY_H |
| #include FT_INTERNAL_CALC_H |
| #include FT_INTERNAL_DEBUG_H |
| #include FT_INTERNAL_OBJECTS_H |
| |
| |
| #ifdef FT_MULFIX_ASSEMBLER |
| #undef FT_MulFix |
| #endif |
| |
| /* we need to emulate a 64-bit data type if a real one isn't available */ |
| |
| #ifndef FT_LONG64 |
| |
| typedef struct FT_Int64_ |
| { |
| FT_UInt32 lo; |
| FT_UInt32 hi; |
| |
| } FT_Int64; |
| |
| #endif /* !FT_LONG64 */ |
| |
| |
| /*************************************************************************/ |
| /* */ |
| /* The macro FT_COMPONENT is used in trace mode. It is an implicit */ |
| /* parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log */ |
| /* messages during execution. */ |
| /* */ |
| #undef FT_COMPONENT |
| #define FT_COMPONENT trace_calc |
| |
| |
| /* transfer sign leaving a positive number */ |
| #define FT_MOVE_SIGN( x, s ) \ |
| FT_BEGIN_STMNT \ |
| if ( x < 0 ) \ |
| { \ |
| x = -x; \ |
| s = -s; \ |
| } \ |
| FT_END_STMNT |
| |
| /* The following three functions are available regardless of whether */ |
| /* FT_LONG64 is defined. */ |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Fixed ) |
| FT_RoundFix( FT_Fixed a ) |
| { |
| return a >= 0 ? ( a + 0x8000L ) & ~0xFFFFL |
| : -((-a + 0x8000L ) & ~0xFFFFL ); |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Fixed ) |
| FT_CeilFix( FT_Fixed a ) |
| { |
| return a >= 0 ? ( a + 0xFFFFL ) & ~0xFFFFL |
| : -((-a + 0xFFFFL ) & ~0xFFFFL ); |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Fixed ) |
| FT_FloorFix( FT_Fixed a ) |
| { |
| return a >= 0 ? a & ~0xFFFFL |
| : -((-a) & ~0xFFFFL ); |
| } |
| |
| #ifndef FT_MSB |
| |
| FT_BASE_DEF ( FT_Int ) |
| FT_MSB( FT_UInt32 z ) |
| { |
| FT_Int shift = 0; |
| |
| |
| /* determine msb bit index in `shift' */ |
| if ( z & 0xFFFF0000UL ) |
| { |
| z >>= 16; |
| shift += 16; |
| } |
| if ( z & 0x0000FF00UL ) |
| { |
| z >>= 8; |
| shift += 8; |
| } |
| if ( z & 0x000000F0UL ) |
| { |
| z >>= 4; |
| shift += 4; |
| } |
| if ( z & 0x0000000CUL ) |
| { |
| z >>= 2; |
| shift += 2; |
| } |
| if ( z & 0x00000002UL ) |
| { |
| /* z >>= 1; */ |
| shift += 1; |
| } |
| |
| return shift; |
| } |
| |
| #endif /* !FT_MSB */ |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_BASE_DEF( FT_Fixed ) |
| FT_Hypot( FT_Fixed x, |
| FT_Fixed y ) |
| { |
| FT_Vector v; |
| |
| |
| v.x = x; |
| v.y = y; |
| |
| return FT_Vector_Length( &v ); |
| } |
| |
| |
| #ifdef FT_LONG64 |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Long ) |
| FT_MulDiv( FT_Long a_, |
| FT_Long b_, |
| FT_Long c_ ) |
| { |
| FT_Int s = 1; |
| FT_UInt64 a, b, c, d; |
| FT_Long d_; |
| |
| |
| FT_MOVE_SIGN( a_, s ); |
| FT_MOVE_SIGN( b_, s ); |
| FT_MOVE_SIGN( c_, s ); |
| |
| a = (FT_UInt64)a_; |
| b = (FT_UInt64)b_; |
| c = (FT_UInt64)c_; |
| |
| d = c > 0 ? ( a * b + ( c >> 1 ) ) / c |
| : 0x7FFFFFFFUL; |
| |
| d_ = (FT_Long)d; |
| |
| return s < 0 ? -d_ : d_; |
| } |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_BASE_DEF( FT_Long ) |
| FT_MulDiv_No_Round( FT_Long a_, |
| FT_Long b_, |
| FT_Long c_ ) |
| { |
| FT_Int s = 1; |
| FT_UInt64 a, b, c, d; |
| FT_Long d_; |
| |
| |
| FT_MOVE_SIGN( a_, s ); |
| FT_MOVE_SIGN( b_, s ); |
| FT_MOVE_SIGN( c_, s ); |
| |
| a = (FT_UInt64)a_; |
| b = (FT_UInt64)b_; |
| c = (FT_UInt64)c_; |
| |
| d = c > 0 ? a * b / c |
| : 0x7FFFFFFFUL; |
| |
| d_ = (FT_Long)d; |
| |
| return s < 0 ? -d_ : d_; |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Long ) |
| FT_MulFix( FT_Long a_, |
| FT_Long b_ ) |
| { |
| #ifdef FT_MULFIX_ASSEMBLER |
| |
| return FT_MULFIX_ASSEMBLER( a_, b_ ); |
| |
| #else |
| |
| FT_Int s = 1; |
| FT_UInt64 a, b, c; |
| FT_Long c_; |
| |
| |
| 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_; |
| |
| #endif /* FT_MULFIX_ASSEMBLER */ |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Long ) |
| FT_DivFix( FT_Long a_, |
| FT_Long b_ ) |
| { |
| FT_Int s = 1; |
| FT_UInt64 a, b, q; |
| FT_Long q_; |
| |
| |
| FT_MOVE_SIGN( a_, s ); |
| FT_MOVE_SIGN( b_, s ); |
| |
| a = (FT_UInt64)a_; |
| b = (FT_UInt64)b_; |
| |
| q = b > 0 ? ( ( a << 16 ) + ( b >> 1 ) ) / b |
| : 0x7FFFFFFFUL; |
| |
| q_ = (FT_Long)q; |
| |
| return s < 0 ? -q_ : q_; |
| } |
| |
| |
| #else /* !FT_LONG64 */ |
| |
| |
| static void |
| ft_multo64( FT_UInt32 x, |
| FT_UInt32 y, |
| FT_Int64 *z ) |
| { |
| FT_UInt32 lo1, hi1, lo2, hi2, lo, hi, i1, i2; |
| |
| |
| lo1 = x & 0x0000FFFFU; hi1 = x >> 16; |
| lo2 = y & 0x0000FFFFU; hi2 = y >> 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 ); |
| |
| z->lo = lo; |
| z->hi = hi; |
| } |
| |
| |
| static FT_UInt32 |
| ft_div64by32( FT_UInt32 hi, |
| FT_UInt32 lo, |
| FT_UInt32 y ) |
| { |
| FT_UInt32 r, q; |
| FT_Int i; |
| |
| |
| if ( hi >= y ) |
| return (FT_UInt32)0x7FFFFFFFL; |
| |
| /* We shift as many bits as we can into the high register, perform */ |
| /* 32-bit division with modulo there, then work through the remaining */ |
| /* bits with long division. This optimization is especially noticeable */ |
| /* for smaller dividends that barely use the high register. */ |
| |
| i = 31 - FT_MSB( hi ); |
| r = ( hi << i ) | ( lo >> ( 32 - i ) ); lo <<= i; /* left 64-bit shift */ |
| q = r / y; |
| r -= q * y; /* remainder */ |
| |
| i = 32 - i; /* bits remaining in low register */ |
| do |
| { |
| q <<= 1; |
| r = ( r << 1 ) | ( lo >> 31 ); lo <<= 1; |
| |
| if ( r >= y ) |
| { |
| r -= y; |
| q |= 1; |
| } |
| } while ( --i ); |
| |
| return q; |
| } |
| |
| |
| static void |
| FT_Add64( FT_Int64* x, |
| FT_Int64* y, |
| FT_Int64 *z ) |
| { |
| FT_UInt32 lo, hi; |
| |
| |
| lo = x->lo + y->lo; |
| hi = x->hi + y->hi + ( lo < x->lo ); |
| |
| z->lo = lo; |
| z->hi = hi; |
| } |
| |
| |
| /* The FT_MulDiv function has been optimized thanks to ideas from */ |
| /* Graham Asher and Alexei Podtelezhnikov. The trick is to optimize */ |
| /* a rather common case when everything fits within 32-bits. */ |
| /* */ |
| /* We compute 'a*b+c/2', then divide it by 'c' (all positive values). */ |
| /* */ |
| /* The product of two positive numbers never exceeds the square of */ |
| /* its mean values. Therefore, we always avoid the overflow by */ |
| /* imposing */ |
| /* */ |
| /* (a + b) / 2 <= sqrt(X - c/2) , */ |
| /* */ |
| /* where X = 2^32 - 1, the maximum unsigned 32-bit value, and using */ |
| /* unsigned arithmetic. Now we replace `sqrt' with a linear function */ |
| /* that is smaller or equal for all values of c in the interval */ |
| /* [0;X/2]; it should be equal to sqrt(X) and sqrt(3X/4) at the */ |
| /* endpoints. Substituting the linear solution and explicit numbers */ |
| /* we get */ |
| /* */ |
| /* a + b <= 131071.99 - c / 122291.84 . */ |
| /* */ |
| /* In practice, we should use a faster and even stronger inequality */ |
| /* */ |
| /* a + b <= 131071 - (c >> 16) */ |
| /* */ |
| /* or, alternatively, */ |
| /* */ |
| /* a + b <= 129894 - (c >> 17) . */ |
| /* */ |
| /* FT_MulFix, on the other hand, is optimized for a small value of */ |
| /* the first argument, when the second argument can be much larger. */ |
| /* This can be achieved by scaling the second argument and the limit */ |
| /* in the above inequalities. For example, */ |
| /* */ |
| /* a + (b >> 8) <= (131071 >> 4) */ |
| /* */ |
| /* covers the practical range of use. The actual test below is a bit */ |
| /* tighter to avoid the border case overflows. */ |
| /* */ |
| /* In the case of FT_DivFix, the exact overflow check */ |
| /* */ |
| /* a << 16 <= X - c/2 */ |
| /* */ |
| /* is scaled down by 2^16 and we use */ |
| /* */ |
| /* a <= 65535 - (c >> 17) . */ |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Long ) |
| FT_MulDiv( FT_Long a_, |
| FT_Long b_, |
| FT_Long c_ ) |
| { |
| FT_Int s = 1; |
| FT_UInt32 a, b, c; |
| |
| |
| /* 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 ); |
| |
| a = (FT_UInt32)a_; |
| b = (FT_UInt32)b_; |
| c = (FT_UInt32)c_; |
| |
| if ( c == 0 ) |
| a = 0x7FFFFFFFUL; |
| |
| else if ( a + b <= 129894UL - ( c >> 17 ) ) |
| a = ( a * b + ( c >> 1 ) ) / c; |
| |
| else |
| { |
| FT_Int64 temp, temp2; |
| |
| |
| ft_multo64( a, b, &temp ); |
| |
| temp2.hi = 0; |
| temp2.lo = c >> 1; |
| |
| FT_Add64( &temp, &temp2, &temp ); |
| |
| /* last attempt to ditch long division */ |
| a = temp.hi == 0 ? temp.lo / c |
| : ft_div64by32( temp.hi, temp.lo, c ); |
| } |
| |
| a_ = (FT_Long)a; |
| |
| return s < 0 ? -a_ : a_; |
| } |
| |
| |
| FT_BASE_DEF( FT_Long ) |
| FT_MulDiv_No_Round( FT_Long a_, |
| FT_Long b_, |
| FT_Long c_ ) |
| { |
| FT_Int s = 1; |
| FT_UInt32 a, b, c; |
| |
| |
| /* 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 ); |
| |
| a = (FT_UInt32)a_; |
| b = (FT_UInt32)b_; |
| c = (FT_UInt32)c_; |
| |
| if ( c == 0 ) |
| a = 0x7FFFFFFFUL; |
| |
| else if ( a + b <= 131071UL ) |
| a = a * b / c; |
| |
| else |
| { |
| FT_Int64 temp; |
| |
| |
| ft_multo64( a, b, &temp ); |
| |
| /* last attempt to ditch long division */ |
| a = temp.hi == 0 ? temp.lo / c |
| : ft_div64by32( temp.hi, temp.lo, c ); |
| } |
| |
| a_ = (FT_Long)a; |
| |
| return s < 0 ? -a_ : a_; |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Long ) |
| FT_MulFix( FT_Long a_, |
| FT_Long b_ ) |
| { |
| #ifdef FT_MULFIX_ASSEMBLER |
| |
| return FT_MULFIX_ASSEMBLER( a_, b_ ); |
| |
| #elif 0 |
| |
| /* |
| * This code is nonportable. See comment below. |
| * |
| * However, on a platform where right-shift of a signed quantity fills |
| * the leftmost bits by copying the sign bit, it might be faster. |
| */ |
| |
| FT_Long sa, sb; |
| 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 |
| * stored in `sa'; 0 means `a' was positive or zero, and -1 means `a' |
| * was negative. (Similarly for `b' and `sb'). |
| * |
| * Unfortunately, it doesn't work (at least not portably). |
| * |
| * It makes the assumption that right-shift on a negative signed value |
| * fills the leftmost bits by copying the sign bit. This is wrong. |
| * According to K&R 2nd ed, section `A7.8 Shift Operators' on page 206, |
| * the result of right-shift of a negative signed value is |
| * implementation-defined. At least one implementation fills the |
| * leftmost bits with 0s (i.e., it is exactly the same as an unsigned |
| * right shift). This means that when `a' is negative, `sa' ends up |
| * with the value 1 rather than -1. After that, everything else goes |
| * wrong. |
| */ |
| sa = ( a_ >> ( sizeof ( a_ ) * 8 - 1 ) ); |
| a = ( a_ ^ sa ) - sa; |
| sb = ( b_ >> ( sizeof ( b_ ) * 8 - 1 ) ); |
| b = ( b_ ^ sb ) - sb; |
| |
| a = (FT_UInt32)a_; |
| b = (FT_UInt32)b_; |
| |
| if ( a + ( b >> 8 ) <= 8190UL ) |
| a = ( a * b + 0x8000U ) >> 16; |
| else |
| { |
| FT_UInt32 al = a & 0xFFFFUL; |
| |
| |
| a = ( a >> 16 ) * b + al * ( b >> 16 ) + |
| ( ( al * ( b & 0xFFFFUL ) + 0x8000UL ) >> 16 ); |
| } |
| |
| sa ^= sb; |
| a = ( a ^ sa ) - sa; |
| |
| return (FT_Long)a; |
| |
| #else /* 0 */ |
| |
| FT_Int s = 1; |
| FT_UInt32 a, b; |
| |
| |
| /* 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 ); |
| |
| a = (FT_UInt32)a_; |
| b = (FT_UInt32)b_; |
| |
| if ( a + ( b >> 8 ) <= 8190UL ) |
| a = ( a * b + 0x8000UL ) >> 16; |
| else |
| { |
| FT_UInt32 al = a & 0xFFFFUL; |
| |
| |
| a = ( a >> 16 ) * b + al * ( b >> 16 ) + |
| ( ( al * ( b & 0xFFFFUL ) + 0x8000UL ) >> 16 ); |
| } |
| |
| a_ = (FT_Long)a; |
| |
| return s < 0 ? -a_ : a_; |
| |
| #endif /* 0 */ |
| |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Long ) |
| FT_DivFix( FT_Long a_, |
| FT_Long b_ ) |
| { |
| FT_Int s = 1; |
| FT_UInt32 a, b, q; |
| FT_Long q_; |
| |
| |
| /* XXX: this function does not allow 64-bit arguments */ |
| |
| FT_MOVE_SIGN( a_, s ); |
| FT_MOVE_SIGN( b_, s ); |
| |
| a = (FT_UInt32)a_; |
| b = (FT_UInt32)b_; |
| |
| if ( b == 0 ) |
| { |
| /* check for division by 0 */ |
| q = 0x7FFFFFFFUL; |
| } |
| else if ( a <= 65535UL - ( b >> 17 ) ) |
| { |
| /* compute result directly */ |
| q = ( ( a << 16 ) + ( b >> 1 ) ) / b; |
| } |
| else |
| { |
| /* we need more bits; we have to do it by hand */ |
| FT_Int64 temp, temp2; |
| |
| |
| temp.hi = a >> 16; |
| temp.lo = a << 16; |
| temp2.hi = 0; |
| temp2.lo = b >> 1; |
| |
| FT_Add64( &temp, &temp2, &temp ); |
| q = ft_div64by32( temp.hi, temp.lo, b ); |
| } |
| |
| q_ = (FT_Long)q; |
| |
| return s < 0 ? -q_ : q_; |
| } |
| |
| |
| #endif /* !FT_LONG64 */ |
| |
| |
| /* documentation is in ftglyph.h */ |
| |
| FT_EXPORT_DEF( void ) |
| FT_Matrix_Multiply( const FT_Matrix* a, |
| FT_Matrix *b ) |
| { |
| FT_Fixed xx, xy, yx, yy; |
| |
| |
| if ( !a || !b ) |
| return; |
| |
| xx = FT_MulFix( a->xx, b->xx ) + FT_MulFix( a->xy, b->yx ); |
| xy = FT_MulFix( a->xx, b->xy ) + FT_MulFix( a->xy, b->yy ); |
| yx = FT_MulFix( a->yx, b->xx ) + FT_MulFix( a->yy, b->yx ); |
| yy = FT_MulFix( a->yx, b->xy ) + FT_MulFix( a->yy, b->yy ); |
| |
| b->xx = xx; b->xy = xy; |
| b->yx = yx; b->yy = yy; |
| } |
| |
| |
| /* documentation is in ftglyph.h */ |
| |
| FT_EXPORT_DEF( FT_Error ) |
| FT_Matrix_Invert( FT_Matrix* matrix ) |
| { |
| FT_Pos delta, xx, yy; |
| |
| |
| if ( !matrix ) |
| return FT_THROW( Invalid_Argument ); |
| |
| /* compute discriminant */ |
| delta = FT_MulFix( matrix->xx, matrix->yy ) - |
| FT_MulFix( matrix->xy, matrix->yx ); |
| |
| if ( !delta ) |
| return FT_THROW( Invalid_Argument ); /* matrix can't be inverted */ |
| |
| matrix->xy = - FT_DivFix( matrix->xy, delta ); |
| matrix->yx = - FT_DivFix( matrix->yx, delta ); |
| |
| xx = matrix->xx; |
| yy = matrix->yy; |
| |
| matrix->xx = FT_DivFix( yy, delta ); |
| matrix->yy = FT_DivFix( xx, delta ); |
| |
| return FT_Err_Ok; |
| } |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_BASE_DEF( void ) |
| FT_Matrix_Multiply_Scaled( const FT_Matrix* a, |
| FT_Matrix *b, |
| FT_Long scaling ) |
| { |
| FT_Fixed xx, xy, yx, yy; |
| |
| FT_Long val = 0x10000L * scaling; |
| |
| |
| if ( !a || !b ) |
| return; |
| |
| xx = FT_MulDiv( a->xx, b->xx, val ) + FT_MulDiv( a->xy, b->yx, val ); |
| xy = FT_MulDiv( a->xx, b->xy, val ) + FT_MulDiv( a->xy, b->yy, val ); |
| yx = FT_MulDiv( a->yx, b->xx, val ) + FT_MulDiv( a->yy, b->yx, val ); |
| yy = FT_MulDiv( a->yx, b->xy, val ) + FT_MulDiv( a->yy, b->yy, val ); |
| |
| b->xx = xx; b->xy = xy; |
| b->yx = yx; b->yy = yy; |
| } |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_BASE_DEF( void ) |
| FT_Vector_Transform_Scaled( FT_Vector* vector, |
| const FT_Matrix* matrix, |
| FT_Long scaling ) |
| { |
| FT_Pos xz, yz; |
| |
| FT_Long val = 0x10000L * scaling; |
| |
| |
| if ( !vector || !matrix ) |
| return; |
| |
| xz = FT_MulDiv( vector->x, matrix->xx, val ) + |
| FT_MulDiv( vector->y, matrix->xy, val ); |
| |
| yz = FT_MulDiv( vector->x, matrix->yx, val ) + |
| FT_MulDiv( vector->y, matrix->yy, val ); |
| |
| vector->x = xz; |
| vector->y = yz; |
| } |
| |
| |
| #if 0 |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_BASE_DEF( FT_Int32 ) |
| FT_SqrtFixed( FT_Int32 x ) |
| { |
| FT_UInt32 root, rem_hi, rem_lo, test_div; |
| FT_Int count; |
| |
| |
| root = 0; |
| |
| if ( x > 0 ) |
| { |
| rem_hi = 0; |
| rem_lo = (FT_UInt32)x; |
| count = 24; |
| do |
| { |
| rem_hi = ( rem_hi << 2 ) | ( rem_lo >> 30 ); |
| rem_lo <<= 2; |
| root <<= 1; |
| test_div = ( root << 1 ) + 1; |
| |
| if ( rem_hi >= test_div ) |
| { |
| rem_hi -= test_div; |
| root += 1; |
| } |
| } while ( --count ); |
| } |
| |
| return (FT_Int32)root; |
| } |
| |
| #endif /* 0 */ |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_BASE_DEF( FT_Int ) |
| ft_corner_orientation( FT_Pos in_x, |
| FT_Pos in_y, |
| 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; |
| |
| |
| if ( delta == 0 ) |
| result = 0; |
| else |
| result = 1 - 2 * ( delta < 0 ); |
| |
| #else |
| |
| FT_Int64 z1, z2; |
| |
| |
| /* XXX: this function does not allow 64-bit arguments */ |
| ft_multo64( (FT_UInt32)in_x, (FT_UInt32)out_y, &z1 ); |
| ft_multo64( (FT_UInt32)in_y, (FT_UInt32)out_x, &z2 ); |
| |
| if ( z1.hi > z2.hi ) |
| result = +1; |
| else if ( z1.hi < z2.hi ) |
| result = -1; |
| else if ( z1.lo > z2.lo ) |
| result = +1; |
| else if ( z1.lo < z2.lo ) |
| result = -1; |
| else |
| result = 0; |
| |
| #endif |
| } |
| |
| /* XXX: only the sign of return value, +1/0/-1 must be used */ |
| return (FT_Int)result; |
| } |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_BASE_DEF( FT_Int ) |
| ft_corner_is_flat( FT_Pos in_x, |
| FT_Pos in_y, |
| FT_Pos out_x, |
| FT_Pos out_y ) |
| { |
| FT_Pos ax = in_x + out_x; |
| FT_Pos ay = in_y + out_y; |
| |
| FT_Pos d_in, d_out, d_hypot; |
| |
| |
| /* The idea of this function is to compare the length of the */ |
| /* hypotenuse with the `in' and `out' length. The `corner' */ |
| /* represented by `in' and `out' is flat if the hypotenuse's */ |
| /* length isn't too large. */ |
| /* */ |
| /* This approach has the advantage that the angle between */ |
| /* `in' and `out' is not checked. In case one of the two */ |
| /* vectors is `dominant', this is, much larger than the */ |
| /* other vector, we thus always have a flat corner. */ |
| /* */ |
| /* hypotenuse */ |
| /* x---------------------------x */ |
| /* \ / */ |
| /* \ / */ |
| /* in \ / out */ |
| /* \ / */ |
| /* o */ |
| /* Point */ |
| |
| d_in = FT_HYPOT( in_x, in_y ); |
| d_out = FT_HYPOT( out_x, out_y ); |
| d_hypot = FT_HYPOT( ax, ay ); |
| |
| /* now do a simple length comparison: */ |
| /* */ |
| /* d_in + d_out < 17/16 d_hypot */ |
| |
| return ( d_in + d_out - d_hypot ) < ( d_hypot >> 4 ); |
| } |
| |
| |
| /* END */ |
