| /***************************************************************************/ |
| /* */ |
| /* ftcalc.c */ |
| /* */ |
| /* Arithmetic computations (body). */ |
| /* */ |
| /* Copyright 1996-2001 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_INTERNAL_CALC_H |
| #include FT_INTERNAL_DEBUG_H |
| #include FT_INTERNAL_OBJECTS_H |
| |
| |
| /* we need to define a 64-bits data type here */ |
| #ifndef FT_CONFIG_OPTION_OLD_CALCS |
| |
| #ifdef FT_LONG64 |
| |
| typedef FT_INT64 FT_Int64; |
| |
| #else |
| |
| typedef struct FT_Int64_ |
| { |
| FT_UInt32 lo; |
| FT_UInt32 hi; |
| |
| } FT_Int64; |
| |
| #endif /* FT_LONG64 */ |
| |
| #endif /* !FT_CONFIG_OPTION_OLD_CALCS */ |
| |
| |
| /*************************************************************************/ |
| /* */ |
| /* 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 or FT_CONFIG_OPTION_OLD_CALCS is defined. */ |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Fixed ) |
| FT_RoundFix( FT_Fixed a ) |
| { |
| return ( a >= 0 ) ? ( a + 0x8000L ) & -0x10000L |
| : -((-a + 0x8000L ) & -0x10000L ); |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Fixed ) |
| FT_CeilFix( FT_Fixed a ) |
| { |
| return ( a >= 0 ) ? ( a + 0xFFFFL ) & -0x10000L |
| : -((-a + 0xFFFFL ) & -0x10000L ); |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Fixed ) |
| FT_FloorFix( FT_Fixed a ) |
| { |
| return ( a >= 0 ) ? a & -0x10000L |
| : -((-a) & -0x10000L ); |
| } |
| |
| |
| #ifdef FT_CONFIG_OPTION_OLD_CALCS |
| |
| static const FT_Long ft_square_roots[63] = |
| { |
| 1L, 1L, 2L, 3L, 4L, 5L, 8L, 11L, |
| 16L, 22L, 32L, 45L, 64L, 90L, 128L, 181L, |
| 256L, 362L, 512L, 724L, 1024L, 1448L, 2048L, 2896L, |
| 4096L, 5892L, 8192L, 11585L, 16384L, 23170L, 32768L, 46340L, |
| |
| 65536L, 92681L, 131072L, 185363L, 262144L, 370727L, |
| 524288L, 741455L, 1048576L, 1482910L, 2097152L, 2965820L, |
| 4194304L, 5931641L, 8388608L, 11863283L, 16777216L, 23726566L, |
| |
| 33554432L, 47453132L, 67108864L, 94906265L, |
| 134217728L, 189812531L, 268435456L, 379625062L, |
| 536870912L, 759250125L, 1073741824L, 1518500250L, |
| 2147483647L |
| }; |
| |
| #else |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_EXPORT_DEF( 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 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; |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Long ) |
| FT_MulFix( FT_Long a, |
| FT_Long b ) |
| { |
| 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 + 0x8000 ) >> 16 ); |
| return ( s > 0 ) ? c : -c ; |
| } |
| |
| |
| /* 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 ); |
| } |
| |
| |
| #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 FT_INT64)z >> 1; |
| j++; |
| } |
| return j - 1; |
| } |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_EXPORT_DEF( 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 (FT_Int32)r; |
| } |
| |
| #endif /* FT_CONFIG_OPTION_OLD_CALCS */ |
| |
| |
| #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; |
| } |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_EXPORT_DEF( void ) |
| FT_Add64( FT_Int64* x, |
| FT_Int64* y, |
| FT_Int64 *z ) |
| { |
| register FT_UInt32 lo, hi, max; |
| |
| |
| max = x->lo > y->lo ? x->lo : y->lo; |
| lo = x->lo + y->lo; |
| hi = x->hi + y->hi + ( lo < max ); |
| |
| z->lo = lo; |
| z->hi = hi; |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( 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 <= 46340L && b <= 46340L && 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 = 0; |
| temp2.lo = (FT_UInt32)(c >> 1); |
| FT_Add64( &temp, &temp2, &temp ); |
| a = ft_div64by32( temp.hi, temp.lo, c ); |
| } |
| else |
| a = 0x7FFFFFFFL; |
| |
| return ( s < 0 ? -a : a ); |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( 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 ) + 0x8000 ) >> 16 ); |
| } |
| |
| return ( s < 0 ? -(FT_Long)ua : ua ); |
| } |
| |
| |
| /* 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 = 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_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, b ); |
| } |
| |
| return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q ); |
| } |
| |
| |
| /* 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 = ABS( x ); |
| s ^= y; y = ABS( y ); |
| |
| ft_multo64( x, y, z ); |
| |
| if ( s < 0 ) |
| { |
| z->lo = (FT_UInt32)-(FT_Int32)z->lo; |
| z->hi = ~z->hi + !( z->lo ); |
| } |
| } |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| /* apparently, the second version of this code is not compiled correctly */ |
| /* on Mac machines with the MPW C compiler.. tsss, tsss, tss... */ |
| #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 = 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 |
| 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 = 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 |
| |
| |
| #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_UInt32 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_UInt32 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; |
| } |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_EXPORT_DEF( 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 /* FT_LONG64 */ |
| |
| |
| /* a not-so-fast but working 16.16 fixed point square root function */ |
| |
| FT_EXPORT_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; |
| } |
| |
| |
| /* END */ |
