Edit
kc3-lang/freetype/src/base/ftcalc.c
David Turner
- src/base/ftcalc.c
-
/***************************************************************************/ /* */ /* 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 */