kc3-lang/freetype/src/base/ftcalc.c
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Hash : f993b6a0
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Date : 2000-01-08T17:10:33
demos/config/x11/rules.mk: support for multiple X11R6 entries in $(PATH) added. ftxbbox.c, ftcalc.c, ftdebug.c, ftdriver.h: doc fixes. ftdebug.c: formatting. ftdebug.h: making makros `;'-safe (i.e., they can now be used within if-else clauses without side effects resp. don't produce a single `;').
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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 <ftcalc.h> #include <ftdebug.h> #include <ftobjs.h> /* for ABS() */ /*************************************************************************/ /* */ /* <Function> */ /* FT_Sqrt32 */ /* */ /* <Description> */ /* Computes the square root of an Int32 integer (which will be */ /* as an unsigned long value). */ /* */ /* <Input> */ /* x :: The value to compute the root for. */ /* */ /* <Return> */ /* The result of `sqrt(x)'. */ /* */ BASE_FUNC FT_Int32 FT_Sqrt32( FT_Int32 x ) { FT_ULong val, root, newroot, mask; root = 0; mask = 0x40000000; 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; } #ifdef LONG64 /*************************************************************************/ /* */ /* <Function> */ /* FT_MulDiv */ /* */ /* <Description> */ /* A very simple function used to perform the computation `(a*b)/c' */ /* with maximum 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'. */ /* */ 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 * ( ( (FT_Int64)a * b + ( c >> 1 ) ) / c ); } /*************************************************************************/ /* */ /* <Function> */ /* FT_MulFix */ /* */ /* <Description> */ /* A very simple function used to perform the computation */ /* `(a*b)/0x10000' with maximum 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. */ /* */ 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 maximum 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(). */ /* */ EXPORT_FUNC FT_Int32 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 divide by 0 */ q = 0x7FFFFFFF; else /* compute result directly */ q = ((FT_Int64)a << 16) / b; return (FT_Int32)( s < 0 ? -q : q ); } #else /* LONG64 */ /*************************************************************************/ /* */ /* <Function> */ /* FT_MulDiv */ /* */ /* <Description> */ /* A very simple function used to perform the computation `(a*b)/c' */ /* with maximum 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. */ /* */ 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 ) { a = ( a*b + (c >> 1) ) / c; } else { 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 ); } return ( s < 0 ) ? -a : a; } /*************************************************************************/ /* */ /* <Function> */ /* FT_MulFix */ /* */ /* <Description> */ /* A very simple function used to perform the computation */ /* `(a*b)/0x10000' with maximum 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. */ /* */ EXPORT_FUNC FT_Long FT_MulFix( FT_Long a, FT_Long b ) { FT_Long s; if ( a == 0 || b == 0x10000L ) return a; s = a; a = ABS(a); s ^= b; b = ABS(b); if ( a <= 2048 && b <= 1048576L ) { a = ( a*b + 0x8000 ) >> 16; } else { FT_Long al = a & 0xFFFF; a = (a >> 16)*b + al*(b >> 16) + ( al*(b & 0xFFFF) >> 16 ); } return ( s < 0 ? -a : a ); } /*************************************************************************/ /* */ /* <Function> */ /* FT_DivFix */ /* */ /* <Description> */ /* A very simple function used to perform the computation */ /* `(a*0x10000)/b' with maximum 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(). */ /* */ 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 divide by 0 */ q = 0x7FFFFFFF; 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. */ /* */ BASE_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 a 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. */ /* */ BASE_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. */ /* */ BASE_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 ) { q = x->lo / y; 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 ) ? 0x80000001L : 0x7FFFFFFFL; /* Return Max/Min Int32 if divide 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; } #endif /* LONG64 */ /* END */