Edit
kc3-lang/freetype/src/base/ftcalc.c
Werner Lemberg
- src/base/ftcalc.c
-
/**************************************************************************** * * ftcalc.c * * Arithmetic computations (body). * * Copyright (C) 1996-2024 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 <freetype/ftglyph.h> #include <freetype/fttrigon.h> #include <freetype/internal/ftcalc.h> #include <freetype/internal/ftdebug.h> #include <freetype/internal/ftobjs.h> /* cancel inlining macro from internal/ftcalc.h */ #ifdef FT_MulFix #undef FT_MulFix #endif /************************************************************************** * * 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 calc /* transfer sign, leaving a positive number; */ /* we need an unsigned value to safely negate INT_MIN (or LONG_MIN) */ #define FT_MOVE_SIGN( utype, x, x_unsigned, s ) \ FT_BEGIN_STMNT \ if ( x < 0 ) \ { \ x_unsigned = 0U - (utype)x; \ s = -s; \ } \ else \ x_unsigned = (utype)x; \ FT_END_STMNT /* The following three functions are available regardless of whether */ /* FT_INT64 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; } /* documentation is in freetype.h */ FT_EXPORT_DEF( FT_Fixed ) FT_CeilFix( FT_Fixed a ) { return ADD_LONG( a, 0xFFFFL ) & ~0xFFFFL; } /* documentation is in freetype.h */ FT_EXPORT_DEF( FT_Fixed ) FT_FloorFix( FT_Fixed a ) { return 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_INT64 /* 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( FT_UInt64, a_, a, s ); FT_MOVE_SIGN( FT_UInt64, b_, b, s ); FT_MOVE_SIGN( FT_UInt64, 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_; FT_MOVE_SIGN( FT_UInt64, a_, a, s ); FT_MOVE_SIGN( FT_UInt64, b_, b, s ); FT_MOVE_SIGN( FT_UInt64, 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_CONFIG_OPTION_INLINE_MULFIX return FT_MulFix_64( a_, b_ ); #else FT_Int64 ab = MUL_INT64( a_, b_ ); /* this requires arithmetic right shift of signed numbers */ return (FT_Long)( ( ab + 0x8000L + ( ab >> 63 ) ) >> 16 ); #endif /* FT_CONFIG_OPTION_INLINE_MULFIX */ } /* 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( FT_UInt64, a_, a, s ); FT_MOVE_SIGN( FT_UInt64, 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_INT64 */ 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 */ FT_MOVE_SIGN( FT_UInt32, a_, a, s ); FT_MOVE_SIGN( FT_UInt32, b_, b, s ); FT_MOVE_SIGN( FT_UInt32, 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 */ FT_MOVE_SIGN( FT_UInt32, a_, a, s ); FT_MOVE_SIGN( FT_UInt32, b_, b, s ); FT_MOVE_SIGN( FT_UInt32, 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 */ FT_MOVE_SIGN( FT_UInt32, a_, a, s ); FT_MOVE_SIGN( FT_UInt32, 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 */ FT_MOVE_SIGN( FT_UInt32, a_, a, s ); FT_MOVE_SIGN( FT_UInt32, 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_INT64 */ /* 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 = ADD_LONG( FT_MulFix( a->xx, b->xx ), FT_MulFix( a->xy, b->yx ) ); xy = ADD_LONG( FT_MulFix( a->xx, b->xy ), FT_MulFix( a->xy, b->yy ) ); yx = ADD_LONG( FT_MulFix( a->yx, b->xx ), FT_MulFix( a->yy, b->yx ) ); yy = ADD_LONG( 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 = 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( FT_Bool ) FT_Matrix_Check( const FT_Matrix* matrix ) { FT_Fixed xx, xy, yx, yy; FT_Fixed val; FT_Int shift; FT_ULong temp1, temp2; if ( !matrix ) return 0; xx = matrix->xx; xy = matrix->xy; yx = matrix->yx; yy = matrix->yy; val = FT_ABS( xx ) | FT_ABS( xy ) | FT_ABS( yx ) | FT_ABS( yy ); /* we only handle non-zero 32-bit values */ if ( !val || val > 0x7FFFFFFFL ) return 0; /* Scale matrix to avoid the temp1 overflow, which is */ /* more stringent than avoiding the temp2 overflow. */ shift = FT_MSB( val ) - 12; if ( shift > 0 ) { xx >>= shift; xy >>= shift; yx >>= shift; yy >>= shift; } temp1 = 32U * (FT_ULong)FT_ABS( xx * yy - xy * yx ); temp2 = (FT_ULong)( xx * xx ) + (FT_ULong)( xy * xy ) + (FT_ULong)( yx * yx ) + (FT_ULong)( yy * yy ); if ( temp1 <= temp2 ) return 0; return 1; } /* 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; FT_MOVE_SIGN( FT_UInt32, x_, x, sx ); FT_MOVE_SIGN( FT_UInt32, 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; } /* documentation is in ftcalc.h */ FT_BASE_DEF( FT_UInt32 ) FT_SqrtFixed( FT_UInt32 v ) { if ( v == 0 ) return 0; #ifndef FT_INT64 /* Algorithm by Christophe Meessen (1993) with overflow fixed and */ /* rounding added. Any unsigned fixed 16.16 argument is acceptable. */ /* However, this algorithm is slower than the Babylonian method with */ /* a good initial guess. We only use it for large 32-bit values when */ /* 64-bit computations are not desirable. */ else if ( v > 0x10000U ) { FT_UInt32 r = v >> 1; FT_UInt32 q = ( v & 1 ) << 15; FT_UInt32 b = 0x20000000; FT_UInt32 t; do { t = q + b; if ( r >= t ) { r -= t; q = t + b; /* equivalent to q += 2*b */ } r <<= 1; b >>= 1; } while ( b > 0x10 ); /* exactly 25 cycles */ return ( q + 0x40 ) >> 7; } else { FT_UInt32 r = ( v << 16 ) - 1; #else /* FT_INT64 */ else { FT_UInt64 r = ( (FT_UInt64)v << 16 ) - 1; #endif /* FT_INT64 */ FT_UInt32 q = 1 << ( ( 17 + FT_MSB( v ) ) >> 1 ); FT_UInt32 t; /* Babylonian method with rounded-up division */ do { t = q; q = ( t + (FT_UInt32)( r / t ) + 1 ) >> 1; } while ( q != t ); /* less than 6 cycles */ return q; } } /* 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 ) { /* we silently ignore overflow errors since such large values */ /* lead to even more (harmless) rendering errors later on */ #ifdef FT_INT64 FT_Int64 delta = SUB_INT64( MUL_INT64( in_x, out_y ), MUL_INT64( in_y, out_x ) ); return ( delta > 0 ) - ( delta < 0 ); #else FT_Int64 z1, z2; FT_Int result; if ( (FT_ULong)FT_ABS( in_x ) + (FT_ULong)FT_ABS( out_y ) <= 92681UL ) { z1.lo = (FT_UInt32)in_x * (FT_UInt32)out_y; z1.hi = (FT_UInt32)( (FT_Int32)z1.lo >> 31 ); /* sign-expansion */ } else ft_multo64( (FT_UInt32)in_x, (FT_UInt32)out_y, &z1 ); if ( (FT_ULong)FT_ABS( in_y ) + (FT_ULong)FT_ABS( out_x ) <= 92681UL ) { z2.lo = (FT_UInt32)in_y * (FT_UInt32)out_x; z2.hi = (FT_UInt32)( (FT_Int32)z2.lo >> 31 ); /* sign-expansion */ } else ft_multo64( (FT_UInt32)in_y, (FT_UInt32)out_x, &z2 ); if ( (FT_Int32)z1.hi > (FT_Int32)z2.hi ) result = +1; else if ( (FT_Int32)z1.hi < (FT_Int32)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', that 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 */