| /***************************************************************************/ |
| /* */ |
| /* 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 */ |
