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Diffstat (limited to 'src/freetype/ftcalc.c')
| -rw-r--r-- | src/freetype/ftcalc.c | 972 |
1 files changed, 972 insertions, 0 deletions
diff --git a/src/freetype/ftcalc.c b/src/freetype/ftcalc.c new file mode 100644 index 0000000..7e41ec0 --- /dev/null +++ b/src/freetype/ftcalc.c @@ -0,0 +1,972 @@ +/***************************************************************************/ +/* */ +/* ftcalc.c */ +/* */ +/* Arithmetic computations (body). */ +/* */ +/* Copyright 1996-2018 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() */ + /* 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; */ + /* we need an unsigned value to safely negate INT_MIN (or LONG_MIN) */ +#define FT_MOVE_SIGN( x, x_unsigned, s ) \ + FT_BEGIN_STMNT \ + if ( x < 0 ) \ + { \ + x_unsigned = 0U - (x_unsigned); \ + 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 ( ADD_LONG( a, 0x8000L - ( a < 0 ) ) ) & ~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_; + + + a = (FT_UInt64)a_; + b = (FT_UInt64)b_; + c = (FT_UInt64)c_; + + FT_MOVE_SIGN( a_, a, s ); + FT_MOVE_SIGN( b_, b, s ); + FT_MOVE_SIGN( c_, c, s ); + + d = c > 0 ? ( a * b + ( c >> 1 ) ) / c + : 0x7FFFFFFFUL; + + d_ = (FT_Long)d; + + return s < 0 ? NEG_LONG( 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_; + + + a = (FT_UInt64)a_; + b = (FT_UInt64)b_; + c = (FT_UInt64)c_; + + FT_MOVE_SIGN( a_, a, s ); + FT_MOVE_SIGN( b_, b, s ); + FT_MOVE_SIGN( c_, c, s ); + + d = c > 0 ? a * b / c + : 0x7FFFFFFFUL; + + d_ = (FT_Long)d; + + return s < 0 ? NEG_LONG( 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( (FT_Int32)a_, (FT_Int32)b_ ); + +#else + + FT_Int64 ab = (FT_Int64)a_ * (FT_Int64)b_; + + /* this requires arithmetic right shift of signed numbers */ + return (FT_Long)( ( ab + 0x8000L - ( ab < 0 ) ) >> 16 ); + +#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_; + + + a = (FT_UInt64)a_; + b = (FT_UInt64)b_; + + FT_MOVE_SIGN( a_, a, s ); + FT_MOVE_SIGN( b_, b, s ); + + q = b > 0 ? ( ( a << 16 ) + ( b >> 1 ) ) / b + : 0x7FFFFFFFUL; + + q_ = (FT_Long)q; + + return s < 0 ? NEG_LONG( 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 */ + + a = (FT_UInt32)a_; + b = (FT_UInt32)b_; + c = (FT_UInt32)c_; + + FT_MOVE_SIGN( a_, a, s ); + FT_MOVE_SIGN( b_, b, s ); + FT_MOVE_SIGN( c_, c, s ); + + 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 ? NEG_LONG( 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 */ + + a = (FT_UInt32)a_; + b = (FT_UInt32)b_; + c = (FT_UInt32)c_; + + FT_MOVE_SIGN( a_, a, s ); + FT_MOVE_SIGN( b_, b, s ); + FT_MOVE_SIGN( c_, c, s ); + + 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 ? NEG_LONG( 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; + + + /* + * 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 */ + + a = (FT_UInt32)a_; + b = (FT_UInt32)b_; + + FT_MOVE_SIGN( a_, a, s ); + FT_MOVE_SIGN( b_, b, s ); + + 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 ? NEG_LONG( 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 */ + + a = (FT_UInt32)a_; + b = (FT_UInt32)b_; + + FT_MOVE_SIGN( a_, a, s ); + FT_MOVE_SIGN( b_, b, s ); + + 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 ? NEG_LONG( q_ ) : q_; + } + + +#endif /* !FT_LONG64 */ + + + /* 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 = ADD_LONG( FT_MulDiv( a->xx, b->xx, val ), + FT_MulDiv( a->xy, b->yx, val ) ); + xy = ADD_LONG( FT_MulDiv( a->xx, b->xy, val ), + FT_MulDiv( a->xy, b->yy, val ) ); + yx = ADD_LONG( FT_MulDiv( a->yx, b->xx, val ), + FT_MulDiv( a->yy, b->yx, val ) ); + yy = ADD_LONG( 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 = ADD_LONG( FT_MulDiv( vector->x, matrix->xx, val ), + FT_MulDiv( vector->y, matrix->xy, val ) ); + yz = ADD_LONG( FT_MulDiv( vector->x, matrix->yx, val ), + FT_MulDiv( vector->y, matrix->yy, val ) ); + + vector->x = xz; + vector->y = yz; + } + + + /* 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; + + + x = (FT_UInt32)x_; + y = (FT_UInt32)y_; + + FT_MOVE_SIGN( x_, x, sx ); + FT_MOVE_SIGN( y_, y, sy ); + + /* 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 */ + + 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 ) + { +#ifdef FT_LONG64 + + FT_Int64 delta = (FT_Int64)in_x * out_y - (FT_Int64)in_y * out_x; + + + return ( delta > 0 ) - ( delta < 0 ); + +#else + + FT_Int result; + + + /* we silently ignore overflow errors, since such large values */ + /* lead to even more (harmless) rendering errors later on */ + if ( ADD_LONG( FT_ABS( in_x ), FT_ABS( out_y ) ) <= 131071L && + ADD_LONG( FT_ABS( in_y ), FT_ABS( out_x ) ) <= 131071L ) + { + FT_Long z1 = MUL_LONG( in_x, out_y ); + FT_Long z2 = MUL_LONG( 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; + + + /* 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; + } + + /* XXX: only the sign of return value, +1/0/-1 must be used */ + return result; + +#endif + } + + + /* 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 */ |