| /***************************************************************************/ |
| /* */ |
| /* ftcalc.c */ |
| /* */ |
| /* Arithmetic computations (body). */ |
| /* */ |
| /* Copyright 1996-2001, 2002, 2003, 2004, 2005, 2006 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 */ |
| |
| #ifdef FT_LONG64 |
| |
| typedef FT_INT64 FT_Int64; |
| |
| #else |
| |
| 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 |
| |
| |
| /* 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 ); |
| } |
| |
| |
| #ifdef FT_CONFIG_OPTION_OLD_INTERNALS |
| |
| /* 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_INTERNALS */ |
| |
| |
| #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; |
| } |
| |
| |
| #ifdef TT_USE_BYTECODE_INTERPRETER |
| |
| /* 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; |
| 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 |
| : 0x7FFFFFFFL ); |
| |
| return ( s > 0 ) ? d : -d; |
| } |
| |
| #endif /* TT_USE_BYTECODE_INTERPRETER */ |
| |
| |
| /* 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 + 0x8000L ) >> 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 ); |
| } |
| |
| |
| #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; |
| } |
| |
| |
| static void |
| FT_Add64( FT_Int64* x, |
| FT_Int64* y, |
| FT_Int64 *z ) |
| { |
| register FT_UInt32 lo, hi; |
| |
| |
| lo = x->lo + y->lo; |
| hi = x->hi + y->hi + ( lo < x->lo ); |
| |
| z->lo = lo; |
| z->hi = hi; |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| /* The FT_MulDiv function has been optimized thanks to ideas from */ |
| /* Graham Asher. The trick is to optimize computation when 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_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 = FT_ABS( a ); |
| s ^= b; b = FT_ABS( b ); |
| s ^= c; c = FT_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 ); |
| } |
| |
| |
| #ifdef TT_USE_BYTECODE_INTERPRETER |
| |
| FT_BASE_DEF( FT_Long ) |
| FT_MulDiv_No_Round( FT_Long a, |
| FT_Long b, |
| FT_Long c ) |
| { |
| long s; |
| |
| |
| if ( a == 0 || b == c ) |
| return a; |
| |
| s = a; a = FT_ABS( a ); |
| s ^= b; b = FT_ABS( b ); |
| s ^= c; c = FT_ABS( c ); |
| |
| if ( a <= 46340L && b <= 46340L && c > 0 ) |
| a = a * b / c; |
| |
| else if ( c > 0 ) |
| { |
| FT_Int64 temp; |
| |
| |
| ft_multo64( a, b, &temp ); |
| a = ft_div64by32( temp.hi, temp.lo, c ); |
| } |
| else |
| a = 0x7FFFFFFFL; |
| |
| return ( s < 0 ? -a : a ); |
| } |
| |
| #endif /* TT_USE_BYTECODE_INTERPRETER */ |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Long ) |
| FT_MulFix( FT_Long a, |
| FT_Long b ) |
| { |
| /* use inline assembly to speed up things a bit */ |
| |
| #if defined( __GNUC__ ) && defined( i386 ) |
| |
| FT_Long result; |
| |
| |
| __asm__ __volatile__ ( |
| "imul %%edx\n" |
| "movl %%edx, %%ecx\n" |
| "sarl $31, %%ecx\n" |
| "addl $0x8000, %%ecx\n" |
| "addl %%ecx, %%eax\n" |
| "adcl $0, %%edx\n" |
| "shrl $16, %%eax\n" |
| "shll $16, %%edx\n" |
| "addl %%edx, %%eax\n" |
| "mov %%eax, %0\n" |
| : "=r"(result) |
| : "a"(a), "d"(b) |
| : "%ecx" |
| ); |
| return result; |
| |
| #elif 1 |
| |
| FT_Long sa, sb; |
| FT_ULong ua, ub; |
| |
| |
| if ( a == 0 || b == 0x10000L ) |
| return a; |
| |
| 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 <= 2048 && ub <= 1048576L ) |
| 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_Long s; |
| FT_ULong ua, ub; |
| |
| |
| if ( a == 0 || b == 0x10000L ) |
| return a; |
| |
| s = a; a = FT_ABS( a ); |
| s ^= b; b = FT_ABS( b ); |
| |
| ua = (FT_ULong)a; |
| ub = (FT_ULong)b; |
| |
| if ( ua <= 2048 && ub <= 1048576L ) |
| 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_Int32 s; |
| FT_UInt32 q; |
| |
| |
| s = a; a = FT_ABS(a); |
| s ^= b; b = FT_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 ); |
| } |
| |
| |
| #if 0 |
| |
| /* 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 = FT_ABS( x ); |
| s ^= y; y = FT_ABS( y ); |
| |
| ft_multo64( x, y, z ); |
| |
| if ( s < 0 ) |
| { |
| z->lo = (FT_UInt32)-(FT_Int32)z->lo; |
| z->hi = ~z->hi + !( z->lo ); |
| } |
| } |
| |
| |
| /* apparently, the second version of this code is not compiled correctly */ |
| /* on Mac machines with the MPW C compiler.. tsk, tsk, tsk... */ |
| |
| #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 = FT_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 /* 0 */ |
| |
| 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 = FT_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 /* 0 */ |
| |
| #endif /* 0 */ |
| |
| |
| #endif /* FT_LONG64 */ |
| |
| |
| /* 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; |
| } |
| |
| |
| /* 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_Int result; |
| |
| |
| /* 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; |
| |
| |
| ft_multo64( in_x, out_y, &z1 ); |
| ft_multo64( in_y, 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 |
| } |
| |
| return 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; |
| FT_Pos ay = in_y; |
| |
| FT_Pos d_in, d_out, d_corner; |
| |
| |
| if ( ax < 0 ) |
| ax = -ax; |
| if ( ay < 0 ) |
| ay = -ay; |
| d_in = ax + ay; |
| |
| ax = out_x; |
| if ( ax < 0 ) |
| ax = -ax; |
| ay = out_y; |
| if ( ay < 0 ) |
| ay = -ay; |
| d_out = ax + ay; |
| |
| ax = out_x + in_x; |
| if ( ax < 0 ) |
| ax = -ax; |
| ay = out_y + in_y; |
| if ( ay < 0 ) |
| ay = -ay; |
| d_corner = ax + ay; |
| |
| return ( d_in + d_out - d_corner ) < ( d_corner >> 4 ); |
| } |
| |
| |
| /* END */ |
