ref: 8636c29ae87b7147d8ab61cc7b3d6a19a8a7e392
dir: /src/base/ftcalc.c/
/***************************************************************************/
/* */
/* 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 */