diff -r f9283dc4860d -r 88f2e05288ba misc/libfreetype/src/base/ftcalc.c --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/misc/libfreetype/src/base/ftcalc.c Mon Apr 25 01:46:54 2011 +0200 @@ -0,0 +1,957 @@ +/***************************************************************************/ +/* */ +/* ftcalc.c */ +/* */ +/* Arithmetic computations (body). */ +/* */ +/* Copyright 1996-2001, 2002, 2003, 2004, 2005, 2006, 2008 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 +#include FT_GLYPH_H +#include FT_INTERNAL_CALC_H +#include FT_INTERNAL_DEBUG_H +#include FT_INTERNAL_OBJECTS_H + +#ifdef FT_MULFIX_INLINED +#undef FT_MulFix +#endif + +/* we need to define a 64-bits data type here */ + +#ifdef FT_LONG64 + + typedef FT_INT64 FT_Int64; + +#else + + 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 + + + /* 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 ); + } + + +#ifdef FT_CONFIG_OPTION_OLD_INTERNALS + + /* documentation is in ftcalc.h */ + + FT_EXPORT_DEF( FT_Int32 ) + FT_Sqrt32( FT_Int32 x ) + { + FT_UInt32 val, root, newroot, mask; + + + root = 0; + mask = (FT_UInt32)0x40000000UL; + val = (FT_UInt32)x; + + do + { + newroot = root + mask; + if ( newroot <= val ) + { + val -= newroot; + root = newroot + mask; + } + + root >>= 1; + mask >>= 2; + + } while ( mask != 0 ); + + return root; + } + +#endif /* FT_CONFIG_OPTION_OLD_INTERNALS */ + + +#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; + FT_Long d; + + + s = 1; + if ( a < 0 ) { a = -a; s = -1; } + if ( b < 0 ) { b = -b; s = -s; } + if ( c < 0 ) { c = -c; s = -s; } + + d = (FT_Long)( c > 0 ? ( (FT_Int64)a * b + ( c >> 1 ) ) / c + : 0x7FFFFFFFL ); + + return ( s > 0 ) ? d : -d; + } + + +#ifdef TT_USE_BYTECODE_INTERPRETER + + /* 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; + FT_Long d; + + + s = 1; + if ( a < 0 ) { a = -a; s = -1; } + if ( b < 0 ) { b = -b; s = -s; } + if ( c < 0 ) { c = -c; s = -s; } + + d = (FT_Long)( c > 0 ? (FT_Int64)a * b / c + : 0x7FFFFFFFL ); + + return ( s > 0 ) ? d : -d; + } + +#endif /* TT_USE_BYTECODE_INTERPRETER */ + + + /* 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_Long c; + + + if ( a < 0 ) + { + a = -a; + s = -1; + } + + if ( b < 0 ) + { + b = -b; + s = -s; + } + + c = (FT_Long)( ( (FT_Int64)a * b + 0x8000L ) >> 16 ); + + 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_Int32 s; + FT_UInt32 q; + + s = 1; + if ( a < 0 ) { a = -a; s = -1; } + if ( b < 0 ) { b = -b; s = -s; } + + if ( b == 0 ) + /* check for division by 0 */ + q = 0x7FFFFFFFL; + else + /* compute result directly */ + q = (FT_UInt32)( ( ( (FT_Int64)a << 16 ) + ( b >> 1 ) ) / b ); + + return ( s < 0 ? -(FT_Long)q : (FT_Long)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; + + + q = 0; + r = hi; + + if ( r >= y ) + return (FT_UInt32)0x7FFFFFFFL; + + i = 32; + do + { + r <<= 1; + q <<= 1; + r |= lo >> 31; + + if ( r >= (FT_UInt32)y ) + { + r -= y; + q |= 1; + } + lo <<= 1; + } while ( --i ); + + return q; + } + + + static void + FT_Add64( FT_Int64* x, + FT_Int64* y, + FT_Int64 *z ) + { + register FT_UInt32 lo, hi; + + + lo = x->lo + y->lo; + hi = x->hi + y->hi + ( lo < x->lo ); + + z->lo = lo; + z->hi = hi; + } + + + /* documentation is in freetype.h */ + + /* The FT_MulDiv function has been optimized thanks to ideas from */ + /* Graham Asher. The trick is to optimize computation when everything */ + /* fits within 32-bits (a rather common case). */ + /* */ + /* we compute 'a*b+c/2', then divide it by 'c'. (positive values) */ + /* */ + /* 46340 is FLOOR(SQRT(2^31-1)). */ + /* */ + /* if ( a <= 46340 && b <= 46340 ) then ( a*b <= 0x7FFEA810 ) */ + /* */ + /* 0x7FFFFFFF - 0x7FFEA810 = 0x157F0 */ + /* */ + /* if ( c < 0x157F0*2 ) then ( a*b+c/2 <= 0x7FFFFFFF ) */ + /* */ + /* and 2*0x157F0 = 176096 */ + /* */ + + FT_EXPORT_DEF( FT_Long ) + FT_MulDiv( FT_Long a, + FT_Long b, + FT_Long c ) + { + long s; + + + /* XXX: this function does not allow 64-bit arguments */ + if ( a == 0 || b == c ) + return a; + + s = a; a = FT_ABS( a ); + s ^= b; b = FT_ABS( b ); + s ^= c; c = FT_ABS( c ); + + if ( a <= 46340L && b <= 46340L && c <= 176095L && c > 0 ) + a = ( a * b + ( c >> 1 ) ) / c; + + else if ( c > 0 ) + { + FT_Int64 temp, temp2; + + + ft_multo64( (FT_Int32)a, (FT_Int32)b, &temp ); + + temp2.hi = 0; + temp2.lo = (FT_UInt32)(c >> 1); + FT_Add64( &temp, &temp2, &temp ); + a = ft_div64by32( temp.hi, temp.lo, (FT_Int32)c ); + } + else + a = 0x7FFFFFFFL; + + return ( s < 0 ? -a : a ); + } + + +#ifdef TT_USE_BYTECODE_INTERPRETER + + FT_BASE_DEF( FT_Long ) + FT_MulDiv_No_Round( FT_Long a, + FT_Long b, + FT_Long c ) + { + long s; + + + if ( a == 0 || b == c ) + return a; + + s = a; a = FT_ABS( a ); + s ^= b; b = FT_ABS( b ); + s ^= c; c = FT_ABS( c ); + + if ( a <= 46340L && b <= 46340L && c > 0 ) + a = a * b / c; + + else if ( c > 0 ) + { + FT_Int64 temp; + + + ft_multo64( (FT_Int32)a, (FT_Int32)b, &temp ); + a = ft_div64by32( temp.hi, temp.lo, (FT_Int32)c ); + } + else + a = 0x7FFFFFFFL; + + return ( s < 0 ? -a : a ); + } + +#endif /* TT_USE_BYTECODE_INTERPRETER */ + + + /* 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_ULong ua, ub; + + + 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; + + ua = (FT_ULong)a; + ub = (FT_ULong)b; + + if ( ua <= 2048 && ub <= 1048576L ) + ua = ( ua * ub + 0x8000U ) >> 16; + else + { + FT_ULong al = ua & 0xFFFFU; + + + ua = ( ua >> 16 ) * ub + al * ( ub >> 16 ) + + ( ( al * ( ub & 0xFFFFU ) + 0x8000U ) >> 16 ); + } + + sa ^= sb, + ua = (FT_ULong)(( ua ^ sa ) - sa); + + return (FT_Long)ua; + +#else /* 0 */ + + FT_Long s; + FT_ULong ua, ub; + + + if ( a == 0 || b == 0x10000L ) + return a; + + s = a; a = FT_ABS( a ); + s ^= b; b = FT_ABS( b ); + + ua = (FT_ULong)a; + ub = (FT_ULong)b; + + if ( ua <= 2048 && ub <= 1048576L ) + ua = ( ua * ub + 0x8000UL ) >> 16; + else + { + FT_ULong al = ua & 0xFFFFUL; + + + ua = ( ua >> 16 ) * ub + al * ( ub >> 16 ) + + ( ( al * ( ub & 0xFFFFUL ) + 0x8000UL ) >> 16 ); + } + + return ( s < 0 ? -(FT_Long)ua : (FT_Long)ua ); + +#endif /* 0 */ + + } + + + /* documentation is in freetype.h */ + + FT_EXPORT_DEF( FT_Long ) + FT_DivFix( FT_Long a, + FT_Long b ) + { + FT_Int32 s; + FT_UInt32 q; + + + /* XXX: this function does not allow 64-bit arguments */ + s = (FT_Int32)a; a = FT_ABS( a ); + s ^= (FT_Int32)b; b = FT_ABS( b ); + + if ( b == 0 ) + { + /* check for division by 0 */ + q = (FT_UInt32)0x7FFFFFFFL; + } + else if ( ( a >> 16 ) == 0 ) + { + /* compute result directly */ + q = (FT_UInt32)( (a << 16) + (b >> 1) ) / (FT_UInt32)b; + } + else + { + /* we need more bits; we have to do it by hand */ + FT_Int64 temp, temp2; + + temp.hi = (FT_Int32) (a >> 16); + temp.lo = (FT_UInt32)(a << 16); + temp2.hi = 0; + temp2.lo = (FT_UInt32)( b >> 1 ); + FT_Add64( &temp, &temp2, &temp ); + q = ft_div64by32( temp.hi, temp.lo, (FT_Int32)b ); + } + + return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); + } + + +#if 0 + + /* documentation is in ftcalc.h */ + + FT_EXPORT_DEF( void ) + FT_MulTo64( FT_Int32 x, + FT_Int32 y, + FT_Int64 *z ) + { + FT_Int32 s; + + + s = x; x = FT_ABS( x ); + s ^= y; y = FT_ABS( y ); + + ft_multo64( x, y, z ); + + if ( s < 0 ) + { + z->lo = (FT_UInt32)-(FT_Int32)z->lo; + z->hi = ~z->hi + !( z->lo ); + } + } + + + /* apparently, the second version of this code is not compiled correctly */ + /* on Mac machines with the MPW C compiler.. tsk, tsk, tsk... */ + +#if 1 + + FT_EXPORT_DEF( FT_Int32 ) + FT_Div64by32( FT_Int64* x, + FT_Int32 y ) + { + FT_Int32 s; + FT_UInt32 q, r, i, lo; + + + s = x->hi; + if ( s < 0 ) + { + x->lo = (FT_UInt32)-(FT_Int32)x->lo; + x->hi = ~x->hi + !x->lo; + } + s ^= y; y = FT_ABS( y ); + + /* Shortcut */ + if ( x->hi == 0 ) + { + if ( y > 0 ) + q = x->lo / y; + else + q = 0x7FFFFFFFL; + + return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); + } + + r = x->hi; + lo = x->lo; + + if ( r >= (FT_UInt32)y ) /* we know y is to be treated as unsigned here */ + return ( s < 0 ? 0x80000001UL : 0x7FFFFFFFUL ); + /* Return Max/Min Int32 if division overflow. */ + /* This includes division by zero! */ + q = 0; + for ( i = 0; i < 32; i++ ) + { + r <<= 1; + q <<= 1; + r |= lo >> 31; + + if ( r >= (FT_UInt32)y ) + { + r -= y; + q |= 1; + } + lo <<= 1; + } + + return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); + } + +#else /* 0 */ + + FT_EXPORT_DEF( FT_Int32 ) + FT_Div64by32( FT_Int64* x, + FT_Int32 y ) + { + FT_Int32 s; + FT_UInt32 q; + + + s = x->hi; + if ( s < 0 ) + { + x->lo = (FT_UInt32)-(FT_Int32)x->lo; + x->hi = ~x->hi + !x->lo; + } + s ^= y; y = FT_ABS( y ); + + /* Shortcut */ + if ( x->hi == 0 ) + { + if ( y > 0 ) + q = ( x->lo + ( y >> 1 ) ) / y; + else + q = 0x7FFFFFFFL; + + return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); + } + + q = ft_div64by32( x->hi, x->lo, y ); + + return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); + } + +#endif /* 0 */ + +#endif /* 0 */ + + +#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_Err_Invalid_Argument; + + /* compute discriminant */ + delta = FT_MulFix( matrix->xx, matrix->yy ) - + FT_MulFix( matrix->xy, matrix->yx ); + + if ( !delta ) + return FT_Err_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; + } + + + /* 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 = 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; + } + + + /* 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_Int32)in_x, (FT_Int32)out_y, &z1 ); + ft_multo64( (FT_Int32)in_y, (FT_Int32)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; + FT_Pos ay = in_y; + + FT_Pos d_in, d_out, d_corner; + + + if ( ax < 0 ) + ax = -ax; + if ( ay < 0 ) + ay = -ay; + d_in = ax + ay; + + ax = out_x; + if ( ax < 0 ) + ax = -ax; + ay = out_y; + if ( ay < 0 ) + ay = -ay; + d_out = ax + ay; + + ax = out_x + in_x; + if ( ax < 0 ) + ax = -ax; + ay = out_y + in_y; + if ( ay < 0 ) + ay = -ay; + d_corner = ax + ay; + + return ( d_in + d_out - d_corner ) < ( d_corner >> 4 ); + } + + +/* END */