Edit
kc3-lang/freetype/src/base/ftcalc.c
Alexei Podtelezhnikov
- src/base/ftcalc.c
-
/***************************************************************************/ /* */ /* ftcalc.c */ /* */ /* Arithmetic computations (body). */ /* */ /* Copyright 1996-2006, 2008, 2012-2014 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 & 0xFFFF0000U ) { z >>= 16; shift += 16; } if ( z & 0x0000FF00U ) { z >>= 8; shift += 8; } if ( z & 0x000000F0U ) { z >>= 4; shift += 4; } if ( z & 0x0000000CU ) { z >>= 2; shift += 2; } if ( z & 0x00000002U ) { /* 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_Long d; FT_MOVE_SIGN( a, s ); FT_MOVE_SIGN( b, s ); FT_MOVE_SIGN( c, s ); d = (FT_Long)( c > 0 ? ( (FT_Int64)a * b + ( c >> 1 ) ) / c : 0x7FFFFFFFL ); 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_Long d; FT_MOVE_SIGN( a, s ); FT_MOVE_SIGN( b, s ); FT_MOVE_SIGN( c, s ); d = (FT_Long)( c > 0 ? (FT_Int64)a * b / c : 0x7FFFFFFFL ); 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_Long c; FT_MOVE_SIGN( a, s ); FT_MOVE_SIGN( b, 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_Int s = 1; FT_Long q; FT_MOVE_SIGN( a, s ); FT_MOVE_SIGN( b, s ); q = (FT_Long)( b > 0 ? ( ( (FT_UInt64)a << 16 ) + ( b >> 1 ) ) / b : 0x7FFFFFFFL ); 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; /* 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 ); if ( c == 0 ) a = 0x7FFFFFFFL; else if ( (FT_ULong)a + b <= 129894UL - ( c >> 17 ) ) a = ( (FT_ULong)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 ); } 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; if ( a == 0 || b == c ) return a; FT_MOVE_SIGN( a, s ); FT_MOVE_SIGN( b, s ); FT_MOVE_SIGN( c, s ); if ( c == 0 ) a = 0x7FFFFFFFL; else if ( (FT_ULong)a + b <= 131071UL ) a = (FT_ULong)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 ); } 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_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 + ( ub >> 8 ) <= 8190UL ) 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_Int s = 1; FT_ULong ua, ub; if ( a == 0 || b == 0x10000L ) return a; FT_MOVE_SIGN( a, s ); FT_MOVE_SIGN( b, s ); ua = (FT_ULong)a; ub = (FT_ULong)b; if ( ua + ( ub >> 8 ) <= 8190UL ) 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_Int s = 1; FT_Long q; /* XXX: this function does not allow 64-bit arguments */ FT_MOVE_SIGN( a, s ); FT_MOVE_SIGN( b, s ); if ( b == 0 ) { /* check for division by 0 */ q = 0x7FFFFFFFL; } else if ( a <= 65535L - ( b >> 17 ) ) { /* compute result directly */ q = (FT_Long)( ( ( (FT_ULong)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_Long)ft_div64by32( temp.hi, temp.lo, b ); } 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 = 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_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 + 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 */