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authorKarl Berry <karl@freefriends.org>2006-01-16 00:09:26 +0000
committerKarl Berry <karl@freefriends.org>2006-01-16 00:09:26 +0000
commit6c0eafbb1395d426a72a74538e0b2a95e8344ca6 (patch)
tree2a5f80b80fc76086a2602b812c2a182d00f961b7 /Build/source/libs/libttf/ttcalc.c
parent70f7efeb5c9965a63a4143ad1c1f473585dc364c (diff)
libs 1
git-svn-id: svn://tug.org/texlive/trunk@1483 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Build/source/libs/libttf/ttcalc.c')
-rw-r--r--Build/source/libs/libttf/ttcalc.c403
1 files changed, 403 insertions, 0 deletions
diff --git a/Build/source/libs/libttf/ttcalc.c b/Build/source/libs/libttf/ttcalc.c
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+/*******************************************************************
+ *
+ * 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 */