kc3-lang/freetype/src/base/ftcalc.c
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Hash : 78575dc0
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Date : 2000-06-12T19:36:41
A lot of formatting. Added more tracing levels. More Makefile fixes. Minor other changes.
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src/base/ftcalc.c
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/***************************************************************************/ /* */ /* ftcalc.c */ /* */ /* Arithmetic computations (body). */ /* */ /* Copyright 1996-2000 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() and FT_MulFix() are declared in freetype.h. */ /* */ /*************************************************************************/ #include <freetype/internal/ftcalc.h> #include <freetype/internal/ftdebug.h> #include <freetype/internal/ftobjs.h> /* for ABS() */ /*************************************************************************/ /* */ /* 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 #ifdef FT_CONFIG_OPTION_OLD_CALCS static const FT_Long ft_square_roots[63] = { 1, 1, 2, 3, 4, 5, 8, 11, 16, 22, 32, 45, 64, 90, 128, 181, 256, 362, 512, 724, 1024, 1448, 2048, 2896, 4096, 5892, 8192, 11585, 16384, 23170, 32768, 46340, 65536, 92681, 131072, 185363, 262144, 370727, 524288, 741455, 1048576, 1482910, 2097152, 2965820, 4194304, 5931641, 8388608, 11863283, 16777216, 23726566, 33554432, 47453132, 67108864, 94906265, 134217728, 189812531, 268435456, 379625062, 536870912, 759250125, 1073741824, 1518500250, 2147483647 }; #else /*************************************************************************/ /* */ /* <Function> */ /* FT_Sqrt32 */ /* */ /* <Description> */ /* Computes the square root of an Int32 integer (which will be */ /* handled as an unsigned long value). */ /* */ /* <Input> */ /* x :: The value to compute the root for. */ /* */ /* <Return> */ /* The result of `sqrt(x)'. */ /* */ FT_EXPORT_FUNC( FT_Int32 ) FT_Sqrt32( FT_Int32 x ) { FT_ULong val, root, newroot, mask; root = 0; mask = 0x40000000L; val = (FT_ULong)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_CALCS */ #ifdef LONG64 /*************************************************************************/ /* */ /* <Function> */ /* FT_MulDiv */ /* */ /* <Description> */ /* A very simple function used to perform the computation `(a*b)/c' */ /* with maximal accuracy (it uses a 64-bit intermediate integer */ /* whenever necessary). */ /* */ /* This function isn't necessarily as fast as some processor specific */ /* operations, but is at least completely portable. */ /* */ /* <Input> */ /* a :: The first multiplier. */ /* b :: The second multiplier. */ /* c :: The divisor. */ /* */ /* <Return> */ /* The result of `(a*b)/c'. This function never traps when trying to */ /* divide by zero; it simply returns `MaxInt' or `MinInt' depending */ /* on the signs of `a' and `b'. */ /* */ FT_EXPORT_FUNC( FT_Long ) FT_MulDiv( FT_Long a, FT_Long b, FT_Long c ) { FT_Int s; s = 1; if ( a < 0 ) { a = -a; s = -s; } if ( b < 0 ) { b = -b; s = -s; } if ( c < 0 ) { c = -c; s = -s; } return s * ( c > 0 ? ( (FT_Int64)a * b + ( c >> 1 ) ) / c : 0x7FFFFFFFL ); } /*************************************************************************/ /* */ /* <Function> */ /* FT_MulFix */ /* */ /* <Description> */ /* A very simple function used to perform the computation */ /* `(a*b)/0x10000' with maximal accuracy. Most of the time this is */ /* used to multiply a given value by a 16.16 fixed float factor. */ /* */ /* <Input> */ /* a :: The first multiplier. */ /* b :: The second multiplier. Use a 16.16 factor here whenever */ /* possible (see note below). */ /* */ /* <Return> */ /* The result of `(a*b)/0x10000'. */ /* */ /* <Note> */ /* This function has been optimized for the case where the absolute */ /* value of `a' is less than 2048, and `b' is a 16.16 scaling factor. */ /* As this happens mainly when scaling from notional units to */ /* fractional pixels in FreeType, it resulted in noticeable speed */ /* improvements between versions 2.x and 1.x. */ /* */ /* As a conclusion, always try to place a 16.16 factor as the */ /* _second_ argument of this function; this can make a great */ /* difference. */ /* */ FT_EXPORT_FUNC( FT_Long ) FT_MulFix( FT_Long a, FT_Long b ) { FT_Int s; s = 1; if ( a < 0 ) { a = -a; s = -s; } if ( b < 0 ) { b = -b; s = -s; } return s * (FT_Long)( ( (FT_Int64)a * b + 0x8000 ) >> 16 ); } /*************************************************************************/ /* */ /* <Function> */ /* FT_DivFix */ /* */ /* <Description> */ /* A very simple function used to perform the computation */ /* `(a*0x10000)/b' with maximal accuracy. Most of the time, this is */ /* used to divide a given value by a 16.16 fixed float factor. */ /* */ /* <Input> */ /* a :: The first multiplier. */ /* b :: The second multiplier. Use a 16.16 factor here whenever */ /* possible (see note below). */ /* */ /* <Return> */ /* The result of `(a*0x10000)/b'. */ /* */ /* <Note> */ /* The optimization for FT_DivFix() is simple: If (a << 16) fits in */ /* 32 bits, then the division is computed directly. Otherwise, we */ /* use a specialized version of the old FT_MulDiv64(). */ /* */ FT_EXPORT_FUNC( FT_Long ) FT_DivFix( FT_Long a, FT_Long b ) { FT_Int32 s; FT_Word32 q; s = a; a = ABS(a); s ^= b; b = ABS(b); if ( b == 0 ) /* check for division by 0 */ q = 0x7FFFFFFFL; else /* compute result directly */ q = ( (FT_Int64)a << 16 ) / b; return (FT_Int32)( s < 0 ? -q : q ); } #ifdef FT_CONFIG_OPTION_OLD_CALCS /* a helper function for FT_Sqrt64() */ static int ft_order64( FT_Int64 z ) { int j = 0; while ( z ) { z = (unsigned INT64)z >> 1; j++; } return j - 1; } /*************************************************************************/ /* */ /* <Function> */ /* FT_Sqrt64 */ /* */ /* <Description> */ /* Computes the square root of a 64-bit value. That sounds stupid, */ /* but it is needed to obtain maximal accuracy in the TrueType */ /* bytecode interpreter. */ /* */ /* <Input> */ /* l :: A 64-bit integer. */ /* */ /* <Return> */ /* The 32-bit square-root. */ /* */ FT_EXPORT_FUNC( FT_Int32 ) FT_Sqrt64( FT_Int64 l ) { FT_Int64 r, s; if ( l <= 0 ) return 0; if ( l == 1 ) return 1; r = ft_square_roots[ft_order64( l )]; do { s = r; r = ( r + l / r ) >> 1; } while ( r > s || r * r > l ); return r; } #endif /* FT_CONFIG_OPTION_OLD_CALCS */ #else /* LONG64 */ /*************************************************************************/ /* */ /* <Function> */ /* FT_MulDiv */ /* */ /* <Description> */ /* A very simple function used to perform the computation `(a*b)/c' */ /* with maximal accuracy (it uses a 64-bit intermediate integer */ /* whenever necessary). */ /* */ /* This function isn't necessarily as fast as some processor specific */ /* operations, but is at least completely portable. */ /* */ /* <Input> */ /* a :: The first multiplier. */ /* b :: The second multiplier. */ /* c :: The divisor. */ /* */ /* <Return> */ /* The result of `(a*b)/c'. This function never traps when trying to */ /* divide by zero; it simply returns `MaxInt' or `MinInt' depending */ /* on the signs of `a' and `b'. */ /* */ /* <Note> */ /* The FT_MulDiv() function has been optimized thanks to ideas from */ /* Graham Asher. The trick is to optimize computation if 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_FUNC( FT_Long ) FT_MulDiv( FT_Long a, FT_Long b, FT_Long c ) { long s; if ( a == 0 || b == c ) return a; s = a; a = ABS( a ); s ^= b; b = ABS( b ); s ^= c; c = ABS( c ); if ( a <= 46340 && b <= 46340 && c <= 176095L && c > 0 ) { a = ( a * b + ( c >> 1 ) ) / c; } else if ( c > 0 ) { FT_Int64 temp, temp2; FT_MulTo64( a, b, &temp ); temp2.hi = (FT_Int32)( c >> 31 ); temp2.lo = (FT_Word32)( c / 2 ); FT_Add64( &temp, &temp2, &temp ); a = FT_Div64by32( &temp, c ); } else a = 0x7FFFFFFFL; return ( s < 0 ? -a : a ); } /*************************************************************************/ /* */ /* <Function> */ /* FT_MulFix */ /* */ /* <Description> */ /* A very simple function used to perform the computation */ /* `(a*b)/0x10000' with maximal accuracy. Most of the time, this is */ /* used to multiply a given value by a 16.16 fixed float factor. */ /* */ /* <Input> */ /* a :: The first multiplier. */ /* b :: The second multiplier. Use a 16.16 factor here whenever */ /* possible (see note below). */ /* */ /* <Return> */ /* The result of `(a*b)/0x10000'. */ /* */ /* <Note> */ /* The optimization for FT_MulFix() is different. We could simply be */ /* happy by applying the same principles as with FT_MulDiv(), because */ /* */ /* c = 0x10000 < 176096 */ /* */ /* However, in most cases, we have a `b' with a value around 0x10000 */ /* which is greater than 46340. */ /* */ /* According to some testing, most cases have `a' < 2048, so a good */ /* idea is to use bounds like 2048 and 1048576 (=floor((2^31-1)/2048) */ /* for `a' and `b', respectively. */ /* */ FT_EXPORT_FUNC( FT_Long ) FT_MulFix( FT_Long a, FT_Long b ) { FT_Long s; FT_ULong ua, ub; if ( a == 0 || b == 0x10000L ) return a; s = a; a = ABS(a); s ^= b; b = ABS(b); ua = (FT_ULong)a; ub = (FT_ULong)b; if ( ua <= 2048 && ub <= 1048576L ) { ua = ( ua * ub + 0x8000 ) >> 16; } else { FT_ULong al = ua & 0xFFFF; ua = ( ua >> 16 ) * ub + al * ( ub >> 16 ) + ( al * ( ub & 0xFFFF ) >> 16 ); } return ( s < 0 ? -(FT_Long)ua : ua ); } /*************************************************************************/ /* */ /* <Function> */ /* FT_DivFix */ /* */ /* <Description> */ /* A very simple function used to perform the computation */ /* `(a*0x10000)/b' with maximal accuracy. Most of the time, this is */ /* used to divide a given value by a 16.16 fixed float factor. */ /* */ /* <Input> */ /* a :: The first multiplier. */ /* b :: The second multiplier. Use a 16.16 factor here whenever */ /* possible (see note below). */ /* */ /* <Return> */ /* The result of `(a*0x10000)/b'. */ /* */ /* <Note> */ /* The optimization for FT_DivFix() is simple: If (a << 16) fits into */ /* 32 bits, then the division is computed directly. Otherwise, we */ /* use a specialized version of the old FT_MulDiv64(). */ /* */ FT_EXPORT_FUNC( FT_Long ) FT_DivFix( FT_Long a, FT_Long b ) { FT_Int32 s; FT_Word32 q; s = a; a = ABS(a); s ^= b; b = ABS(b); if ( b == 0 ) { /* check for division by 0 */ q = 0x7FFFFFFFL; } else if ( ( a >> 16 ) == 0 ) { /* compute result directly */ q = (FT_Word32)( a << 16 ) / (FT_Word32)b; } else { /* we need more bits, we'll have to do it by hand */ FT_Word32 c; q = ( a / b ) << 16; c = a % b; /* we must compute C*0x10000/B; we simply shift C and B so */ /* C becomes smaller than 16 bits */ while ( c >> 16 ) { c >>= 1; b <<= 1; } q += ( c << 16 ) / b; } return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); } /*************************************************************************/ /* */ /* <Function> */ /* FT_Add64 */ /* */ /* <Description> */ /* Add two Int64 values. */ /* */ /* <Input> */ /* x :: A pointer to the first value to be added. */ /* y :: A pointer to the second value to be added. */ /* */ /* <Output> */ /* z :: A pointer to the result of `x + y'. */ /* */ /* <Note> */ /* Will be wrapped by the ADD_64() macro. */ /* */ FT_EXPORT_FUNC( void ) FT_Add64( FT_Int64* x, FT_Int64* y, FT_Int64* z ) { register FT_Word32 lo, hi; lo = x->lo + y->lo; hi = x->hi + y->hi + ( lo < x->lo ); z->lo = lo; z->hi = hi; } /*************************************************************************/ /* */ /* <Function> */ /* FT_MulTo64 */ /* */ /* <Description> */ /* Multiplies two Int32 integers. Returns an Int64 integer. */ /* */ /* <Input> */ /* x :: The first multiplier. */ /* y :: The second multiplier. */ /* */ /* <Output> */ /* z :: A pointer to the result of `x * y'. */ /* */ /* <Note> */ /* Will be wrapped by the MUL_64() macro. */ /* */ FT_EXPORT_FUNC( void ) FT_MulTo64( FT_Int32 x, FT_Int32 y, FT_Int64* z ) { FT_Int32 s; s = x; x = ABS( x ); s ^= y; y = ABS( y ); { FT_Word32 lo1, hi1, lo2, hi2, lo, hi, i1, i2; lo1 = x & 0x0000FFFF; hi1 = x >> 16; lo2 = y & 0x0000FFFF; hi2 = y >> 16; lo = lo1 * lo2; i1 = lo1 * hi2; i2 = lo2 * hi1; hi = hi1 * hi2; /* Check carry overflow of i1 + i2 */ i1 += i2; if ( i1 < i2 ) hi += 1L << 16; hi += i1 >> 16; i1 = i1 << 16; /* Check carry overflow of i1 + lo */ lo += i1; hi += ( lo < i1 ); z->lo = lo; z->hi = hi; } if ( s < 0 ) { z->lo = (FT_Word32)-(FT_Int32)z->lo; z->hi = ~z->hi + !(z->lo); } } /*************************************************************************/ /* */ /* <Function> */ /* FT_Div64by32 */ /* */ /* <Description> */ /* Divides an Int64 value by an Int32 value. Returns an Int32 */ /* integer. */ /* */ /* <Input> */ /* x :: A pointer to the dividend. */ /* y :: The divisor. */ /* */ /* <Return> */ /* The result of `x / y'. */ /* */ /* <Note> */ /* Will be wrapped by the DIV_64() macro. */ /* */ FT_EXPORT_FUNC( FT_Int32 ) FT_Div64by32( FT_Int64* x, FT_Int32 y ) { FT_Int32 s; FT_Word32 q, r, i, lo; s = x->hi; if ( s < 0 ) { x->lo = (FT_Word32)-(FT_Int32)x->lo; x->hi = ~x->hi + !(x->lo); } s ^= y; y = 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_Word32)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_Word32)y ) { r -= y; q |= 1; } lo <<= 1; } return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); } #ifdef FT_CONFIG_OPTION_OLD_CALCS /* two helper functions for FT_Sqrt64() */ static void FT_Sub64( FT_Int64* x, FT_Int64* y, FT_Int64* z ) { register FT_Word32 lo, hi; lo = x->lo - y->lo; hi = x->hi - y->hi - ( (FT_Int32)lo < 0 ); z->lo = lo; z->hi = hi; } static int ft_order64( FT_Int64* z ) { FT_Word32 i; int j; i = z->lo; j = 0; if ( z->hi ) { i = z->hi; j = 32; } while ( i > 0 ) { i >>= 1; j++; } return j - 1; } /*************************************************************************/ /* */ /* <Function> */ /* FT_Sqrt64 */ /* */ /* <Description> */ /* Computes the square root of a 64-bits value. That sounds stupid, */ /* but it is needed to obtain maximal accuracy in the TrueType */ /* bytecode interpreter. */ /* */ /* <Input> */ /* z :: A pointer to a 64-bit integer. */ /* */ /* <Return> */ /* The 32-bit square-root. */ /* */ FT_EXPORT_FUNC( FT_Int32 ) FT_Sqrt64( FT_Int64* l ) { FT_Int64 l2; FT_Int32 r, s; if ( (FT_Int32)l->hi < 0 || ( l->hi == 0 && l->lo == 0 ) ) return 0; s = ft_order64( l ); if ( s == 0 ) return 1; r = ft_square_roots[s]; do { s = r; r = ( r + FT_Div64by32( l, r ) ) >> 1; FT_MulTo64( r, r, &l2 ); FT_Sub64 ( l, &l2, &l2 ); } while ( r > s || (FT_Int32)l2.hi < 0 ); return r; } #endif /* FT_CONFIG_OPTION_OLD_CALCS */ #endif /* LONG64 */ /* END */