+++ /dev/null
-/***************************************************************************/
-/* */
-/* 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 */
-
- 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 );
- }
-
-
-#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 */
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