404 lines
8.7 KiB
C
404 lines
8.7 KiB
C
/*******************************************************************
|
|
*
|
|
* ttcalc.c
|
|
*
|
|
* Arithmetic Computations (body).
|
|
*
|
|
* Copyright 1996-1999 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.
|
|
*
|
|
******************************************************************/
|
|
|
|
#include "ttcalc.h"
|
|
#include "ttdebug.h"
|
|
#include "tttables.h"
|
|
|
|
/* required by the tracing mode */
|
|
#undef TT_COMPONENT
|
|
#define TT_COMPONENT trace_calc
|
|
|
|
|
|
/* Support for 1-complement arithmetic has been totally dropped in this */
|
|
/* release. You can still write your own code if you need it... */
|
|
|
|
static const Long Roots[63] =
|
|
{
|
|
1, 1, 2, 3, 4, 5, 8, 11,
|
|
16, 22, 32, 45, 64, 90, 128, 181,
|
|
256, 362, 512, 724, 1024, 1448, 2048, 2896,
|
|
4096, 5892, 8192, 11585, 16384, 23170, 32768, 46340,
|
|
|
|
65536, 92681, 131072, 185363, 262144, 370727,
|
|
524288, 741455, 1048576, 1482910, 2097152, 2965820,
|
|
4194304, 5931641, 8388608, 11863283, 16777216, 23726566,
|
|
|
|
33554432, 47453132, 67108864, 94906265,
|
|
134217728, 189812531, 268435456, 379625062,
|
|
536870912, 759250125, 1073741824, 1518500250,
|
|
2147483647
|
|
};
|
|
|
|
|
|
#ifdef LONG64
|
|
|
|
EXPORT_FUNC
|
|
TT_Long TT_MulDiv( TT_Long a, TT_Long b, TT_Long c )
|
|
{
|
|
Long s;
|
|
|
|
|
|
s = a; a = ABS( a );
|
|
s ^= b; b = ABS( b );
|
|
s ^= c; c = ABS( c );
|
|
|
|
a = ((TT_Int64)a * b + c/2) / c;
|
|
return ( s < 0 ) ? -a : a;
|
|
}
|
|
|
|
|
|
EXPORT_FUNC
|
|
TT_Long TT_MulFix( TT_Long a, TT_Long b )
|
|
{
|
|
Long s;
|
|
|
|
|
|
s = a; a = ABS( a );
|
|
s ^= b; b = ABS( b );
|
|
|
|
a = ((TT_Int64)a * b + 0x8000) / 0x10000;
|
|
return ( s < 0 ) ? -a : a;
|
|
}
|
|
|
|
|
|
LOCAL_FUNC
|
|
Int Order64( TT_Int64 z )
|
|
{
|
|
Int j = 0;
|
|
|
|
|
|
while ( z )
|
|
{
|
|
z = (unsigned INT64)z >> 1;
|
|
j++;
|
|
}
|
|
return j - 1;
|
|
}
|
|
|
|
|
|
LOCAL_FUNC
|
|
TT_Int32 Sqrt64( TT_Int64 l )
|
|
{
|
|
TT_Int64 r, s;
|
|
|
|
|
|
if ( l <= 0 ) return 0;
|
|
if ( l == 1 ) return 1;
|
|
|
|
r = Roots[Order64( l )];
|
|
|
|
do
|
|
{
|
|
s = r;
|
|
r = ( r + l/r ) >> 1;
|
|
}
|
|
while ( r > s || r*r > l );
|
|
|
|
return r;
|
|
}
|
|
|
|
#else /* LONG64 */
|
|
|
|
|
|
/* The TT_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 */
|
|
/* */
|
|
|
|
EXPORT_FUNC
|
|
TT_Long TT_MulDiv( TT_Long a, TT_Long b, TT_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 <= 46340 && b <= 46340 && c <= 176095 )
|
|
{
|
|
a = ( a*b + c/2 )/c;
|
|
}
|
|
else
|
|
{
|
|
TT_Int64 temp, temp2;
|
|
|
|
MulTo64( a, b, &temp );
|
|
temp2.hi = (TT_Int32)(c >> 31);
|
|
temp2.lo = (TT_Word32)(c / 2);
|
|
Add64( &temp, &temp2, &temp );
|
|
a = Div64by32( &temp, c );
|
|
}
|
|
|
|
return ( s < 0 ) ? -a : a;
|
|
}
|
|
|
|
/* The optimization for TT_MulFix is different. We could simply be */
|
|
/* happy by applying the same principles than with TT_MulDiv, because */
|
|
/* */
|
|
/* c = 0x10000 < 176096 */
|
|
/* */
|
|
/* however, in most cases, we have a 'b' with a value around 0x10000 */
|
|
/* which is greater than 46340. */
|
|
/* */
|
|
/* According to Graham's testing, most cases have 'a' < 100, so a good */
|
|
/* idea is to use bounds like 1024 and 2097151 (= floor(2^31-1)/1024 ) */
|
|
/* for 'a' and 'b' respectively.. */
|
|
/* */
|
|
|
|
EXPORT_FUNC
|
|
TT_Long TT_MulFix( TT_Long a, TT_Long b )
|
|
{
|
|
long s;
|
|
|
|
if ( a == 0 || b == 0x10000 )
|
|
return a;
|
|
|
|
s = a; a = ABS( a );
|
|
s ^= b; b = ABS( b );
|
|
|
|
if ( a <= 1024 && b <= 2097151 )
|
|
{
|
|
a = ( a*b + 0x8000 ) >> 16;
|
|
}
|
|
else
|
|
{
|
|
TT_Int64 temp, temp2;
|
|
|
|
MulTo64( a, b, &temp );
|
|
temp2.hi = 0;
|
|
temp2.lo = 0x8000;
|
|
Add64( &temp, &temp2, &temp );
|
|
a = Div64by32( &temp, 0x10000 );
|
|
}
|
|
|
|
return ( s < 0 ) ? -a : a;
|
|
}
|
|
|
|
|
|
LOCAL_FUNC
|
|
void Neg64( TT_Int64* x )
|
|
{
|
|
/* Remember that -(0x80000000) == 0x80000000 with 2-complement! */
|
|
/* We take care of that here. */
|
|
|
|
x->hi ^= 0xFFFFFFFFUL;
|
|
x->lo ^= 0xFFFFFFFFUL;
|
|
x->lo++;
|
|
|
|
if ( !x->lo )
|
|
{
|
|
x->hi++;
|
|
if ( x->hi == 0x80000000UL ) /* Check -MaxInt32 - 1 */
|
|
{
|
|
x->lo--;
|
|
x->hi--; /* We return 0x7FFFFFFF! */
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
LOCAL_FUNC
|
|
void Add64( TT_Int64* x, TT_Int64* y, TT_Int64* z )
|
|
{
|
|
register TT_Word32 lo, hi;
|
|
|
|
|
|
lo = x->lo + y->lo;
|
|
hi = x->hi + y->hi + ( lo < x->lo );
|
|
|
|
z->lo = lo;
|
|
z->hi = hi;
|
|
}
|
|
|
|
|
|
LOCAL_FUNC
|
|
void Sub64( TT_Int64* x, TT_Int64* y, TT_Int64* z )
|
|
{
|
|
register TT_Word32 lo, hi;
|
|
|
|
|
|
lo = x->lo - y->lo;
|
|
hi = x->hi - y->hi - ( (TT_Int32)lo < 0 );
|
|
|
|
z->lo = lo;
|
|
z->hi = hi;
|
|
}
|
|
|
|
|
|
LOCAL_FUNC
|
|
void MulTo64( TT_Int32 x, TT_Int32 y, TT_Int64* z )
|
|
{
|
|
TT_Int32 s;
|
|
TT_Word32 lo1, hi1, lo2, hi2, lo, hi, i1, i2;
|
|
|
|
|
|
s = x; x = ABS( x );
|
|
s ^= y; y = ABS( y );
|
|
|
|
lo1 = x & 0x0000FFFF; hi1 = x >> 16;
|
|
lo2 = y & 0x0000FFFF; hi2 = y >> 16;
|
|
|
|
lo = lo1*lo2;
|
|
i1 = lo1*hi2;
|
|
i2 = lo2*hi1;
|
|
hi = hi1*hi2;
|
|
|
|
/* Check carry overflow of i1 + i2 */
|
|
|
|
if ( i2 )
|
|
{
|
|
if ( i1 >= (TT_Word32)-(TT_Int32)i2 ) hi += 1L << 16;
|
|
i1 += i2;
|
|
}
|
|
|
|
i2 = i1 >> 16;
|
|
i1 = i1 << 16;
|
|
|
|
/* Check carry overflow of i1 + lo */
|
|
if ( i1 )
|
|
{
|
|
if ( lo >= (TT_Word32)-(TT_Int32)i1 ) hi++;
|
|
lo += i1;
|
|
}
|
|
|
|
hi += i2;
|
|
|
|
z->lo = lo;
|
|
z->hi = hi;
|
|
|
|
if ( s < 0 ) Neg64( z );
|
|
}
|
|
|
|
|
|
LOCAL_FUNC
|
|
TT_Int32 Div64by32( TT_Int64* x, TT_Int32 y )
|
|
{
|
|
TT_Int32 s;
|
|
TT_Word32 q, r, i, lo;
|
|
|
|
|
|
s = x->hi; if ( s < 0 ) Neg64( x );
|
|
s ^= y; y = ABS( y );
|
|
|
|
/* Shortcut */
|
|
if ( x->hi == 0 )
|
|
{
|
|
q = x->lo / y;
|
|
return ( s < 0 ) ? -(TT_Int32)q : (TT_Int32)q;
|
|
}
|
|
|
|
r = x->hi;
|
|
lo = x->lo;
|
|
|
|
if ( r >= (TT_Word32)y ) /* we know y is to be treated as unsigned here */
|
|
return ( s < 0 ) ? 0x80000001UL : 0x7FFFFFFFUL;
|
|
/* Return Max/Min Int32 if divide overflow */
|
|
/* This includes division by zero! */
|
|
q = 0;
|
|
for ( i = 0; i < 32; i++ )
|
|
{
|
|
r <<= 1;
|
|
q <<= 1;
|
|
r |= lo >> 31;
|
|
|
|
if ( r >= (TT_Word32)y )
|
|
{
|
|
r -= y;
|
|
q |= 1;
|
|
}
|
|
lo <<= 1;
|
|
}
|
|
|
|
return ( s < 0 ) ? -(TT_Int32)q : (TT_Int32)q;
|
|
}
|
|
|
|
|
|
LOCAL_FUNC
|
|
Int Order64( TT_Int64* z )
|
|
{
|
|
TT_Word32 i;
|
|
Int j;
|
|
|
|
|
|
if ( z->hi )
|
|
{
|
|
i = z->hi;
|
|
j = 32;
|
|
}
|
|
else
|
|
{
|
|
i = z->lo;
|
|
j = 0;
|
|
}
|
|
|
|
while ( i > 0 )
|
|
{
|
|
i >>= 1;
|
|
j++;
|
|
}
|
|
return j-1;
|
|
}
|
|
|
|
|
|
LOCAL_FUNC
|
|
TT_Int32 Sqrt64( TT_Int64* l )
|
|
{
|
|
TT_Int64 l2;
|
|
TT_Int32 r, s;
|
|
|
|
|
|
if ( (TT_Int32)l->hi < 0 ||
|
|
(l->hi == 0 && l->lo == 0) ) return 0;
|
|
|
|
s = Order64( l );
|
|
if ( s == 0 ) return 1;
|
|
|
|
r = Roots[s];
|
|
do
|
|
{
|
|
s = r;
|
|
r = ( r + Div64by32(l,r) ) >> 1;
|
|
MulTo64( r, r, &l2 );
|
|
Sub64 ( l, &l2, &l2 );
|
|
}
|
|
while ( r > s || (TT_Int32)l2.hi < 0 );
|
|
|
|
return r;
|
|
}
|
|
|
|
#endif /* LONG64 */
|
|
|
|
|
|
/* END */
|