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-rw-r--r--src/base/ftcalc.c885
1 files changed, 298 insertions, 587 deletions
diff --git a/src/base/ftcalc.c b/src/base/ftcalc.c
index 4db43e0..dca0e1d 100644
--- a/src/base/ftcalc.c
+++ b/src/base/ftcalc.c
@@ -4,7 +4,7 @@
/* */
/* Arithmetic computations (body). */
/* */
-/* Copyright 1996-2006, 2008, 2012-2014 by */
+/* Copyright 1996-2015 by */
/* David Turner, Robert Wilhelm, and Werner Lemberg. */
/* */
/* This file is part of the FreeType project, and may only be used, */
@@ -40,235 +40,7 @@
#include FT_INTERNAL_OBJECTS_H
-#ifndef FT_CONFIG_OPTION_NO_ASSEMBLER
- /* Provide assembler fragments for performance-critical functions. */
- /* These must be defined `static __inline__' with GCC. */
-
-#if defined( __CC_ARM ) || defined( __ARMCC__ ) /* RVCT */
-
-#define FT_MULFIX_ASSEMBLER FT_MulFix_arm
-
- /* documentation is in freetype.h */
-
- static __inline FT_Int32
- FT_MulFix_arm( FT_Int32 a,
- FT_Int32 b )
- {
- register FT_Int32 t, t2;
-
-
- __asm
- {
- smull t2, t, b, a /* (lo=t2,hi=t) = a*b */
- mov a, t, asr #31 /* a = (hi >> 31) */
- add a, a, #0x8000 /* a += 0x8000 */
- adds t2, t2, a /* t2 += a */
- adc t, t, #0 /* t += carry */
- mov a, t2, lsr #16 /* a = t2 >> 16 */
- orr a, a, t, lsl #16 /* a |= t << 16 */
- }
- return a;
- }
-
-#endif /* __CC_ARM || __ARMCC__ */
-
-
-#ifdef __GNUC__
-
-#if defined( __arm__ ) && \
- ( !defined( __thumb__ ) || defined( __thumb2__ ) ) && \
- !( defined( __CC_ARM ) || defined( __ARMCC__ ) )
-
-#define FT_MULFIX_ASSEMBLER FT_MulFix_arm
-
- /* documentation is in freetype.h */
-
- static __inline__ FT_Int32
- FT_MulFix_arm( FT_Int32 a,
- FT_Int32 b )
- {
- register FT_Int32 t, t2;
-
-
- __asm__ __volatile__ (
- "smull %1, %2, %4, %3\n\t" /* (lo=%1,hi=%2) = a*b */
- "mov %0, %2, asr #31\n\t" /* %0 = (hi >> 31) */
-#if defined( __clang__ ) && defined( __thumb2__ )
- "add.w %0, %0, #0x8000\n\t" /* %0 += 0x8000 */
-#else
- "add %0, %0, #0x8000\n\t" /* %0 += 0x8000 */
-#endif
- "adds %1, %1, %0\n\t" /* %1 += %0 */
- "adc %2, %2, #0\n\t" /* %2 += carry */
- "mov %0, %1, lsr #16\n\t" /* %0 = %1 >> 16 */
- "orr %0, %0, %2, lsl #16\n\t" /* %0 |= %2 << 16 */
- : "=r"(a), "=&r"(t2), "=&r"(t)
- : "r"(a), "r"(b)
- : "cc" );
- return a;
- }
-
-#endif /* __arm__ && */
- /* ( __thumb2__ || !__thumb__ ) && */
- /* !( __CC_ARM || __ARMCC__ ) */
-
-
-#if defined( __i386__ )
-
-#define FT_MULFIX_ASSEMBLER FT_MulFix_i386
-
- /* documentation is in freetype.h */
-
- static __inline__ FT_Int32
- FT_MulFix_i386( FT_Int32 a,
- FT_Int32 b )
- {
- register FT_Int32 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"
- : "=a"(result), "=d"(b)
- : "a"(a), "d"(b)
- : "%ecx", "cc" );
- return result;
- }
-
-#endif /* i386 */
-
-#endif /* __GNUC__ */
-
-
-#ifdef _MSC_VER /* Visual C++ */
-
-#ifdef _M_IX86
-
-#define FT_MULFIX_ASSEMBLER FT_MulFix_i386
-
- /* documentation is in freetype.h */
-
- static __inline FT_Int32
- FT_MulFix_i386( FT_Int32 a,
- FT_Int32 b )
- {
- register FT_Int32 result;
-
- __asm
- {
- mov eax, a
- mov edx, b
- imul edx
- mov ecx, edx
- sar ecx, 31
- add ecx, 8000h
- add eax, ecx
- adc edx, 0
- shr eax, 16
- shl edx, 16
- add eax, edx
- mov result, eax
- }
- return result;
- }
-
-#endif /* _M_IX86 */
-
-#endif /* _MSC_VER */
-
-
-#if defined( __GNUC__ ) && defined( __x86_64__ )
-
-#define FT_MULFIX_ASSEMBLER FT_MulFix_x86_64
-
- static __inline__ FT_Int32
- FT_MulFix_x86_64( FT_Int32 a,
- FT_Int32 b )
- {
- /* Temporarily disable the warning that C90 doesn't support */
- /* `long long'. */
-#if ( __GNUC__ > 4 ) || ( ( __GNUC__ == 4 ) && ( __GNUC_MINOR__ >= 6 ) )
-#pragma GCC diagnostic push
-#pragma GCC diagnostic ignored "-Wlong-long"
-#endif
-
-#if 1
- /* Technically not an assembly fragment, but GCC does a really good */
- /* job at inlining it and generating good machine code for it. */
- long long ret, tmp;
-
-
- ret = (long long)a * b;
- tmp = ret >> 63;
- ret += 0x8000 + tmp;
-
- return (FT_Int32)( ret >> 16 );
-#else
-
- /* For some reason, GCC 4.6 on Ubuntu 12.04 generates invalid machine */
- /* code from the lines below. The main issue is that `wide_a' is not */
- /* properly initialized by sign-extending `a'. Instead, the generated */
- /* machine code assumes that the register that contains `a' on input */
- /* can be used directly as a 64-bit value, which is wrong most of the */
- /* time. */
- long long wide_a = (long long)a;
- long long wide_b = (long long)b;
- long long result;
-
-
- __asm__ __volatile__ (
- "imul %2, %1\n"
- "mov %1, %0\n"
- "sar $63, %0\n"
- "lea 0x8000(%1, %0), %0\n"
- "sar $16, %0\n"
- : "=&r"(result), "=&r"(wide_a)
- : "r"(wide_b)
- : "cc" );
-
- return (FT_Int32)result;
-#endif
-
-#if ( __GNUC__ > 4 ) || ( ( __GNUC__ == 4 ) && ( __GNUC_MINOR__ >= 6 ) )
-#pragma GCC diagnostic pop
-#endif
- }
-
-#endif /* __GNUC__ && __x86_64__ */
-
-#if defined( __GNUC__ )
-#if ( __GNUC__ > 3 ) || ( ( __GNUC__ == 3 ) && ( __GNUC_MINOR__ >= 4 ) )
-
-#if FT_SIZEOF_INT == 4
-
-#define FT_MSB_BUILTIN( x ) ( 31 - __builtin_clz( x ) )
-
-#elif FT_SIZEOF_LONG == 4
-
-#define FT_MSB_BUILTIN( x ) ( 31 - __builtin_clzl( x ) )
-
-#endif
-
-#endif
-#endif /* __GNUC__ */
-
-#endif /* !FT_CONFIG_OPTION_NO_ASSEMBLER */
-
-
-#ifdef FT_CONFIG_OPTION_INLINE_MULFIX
#ifdef FT_MULFIX_ASSEMBLER
-#define FT_MULFIX_INLINED FT_MULFIX_ASSEMBLER
-#endif
-#endif
-
-#ifdef FT_MULFIX_INLINED
#undef FT_MulFix
#endif
@@ -296,6 +68,16 @@
#define FT_COMPONENT trace_calc
+ /* transfer sign leaving a positive number */
+#define FT_MOVE_SIGN( x, s ) \
+ FT_BEGIN_STMNT \
+ if ( x < 0 ) \
+ { \
+ x = -x; \
+ s = -s; \
+ } \
+ FT_END_STMNT
+
/* The following three functions are available regardless of whether */
/* FT_LONG64 is defined. */
@@ -304,8 +86,8 @@
FT_EXPORT_DEF( FT_Fixed )
FT_RoundFix( FT_Fixed a )
{
- return ( a >= 0 ) ? ( a + 0x8000L ) & ~0xFFFFL
- : -((-a + 0x8000L ) & ~0xFFFFL );
+ return a >= 0 ? ( a + 0x8000L ) & ~0xFFFFL
+ : -((-a + 0x8000L ) & ~0xFFFFL );
}
@@ -314,8 +96,8 @@
FT_EXPORT_DEF( FT_Fixed )
FT_CeilFix( FT_Fixed a )
{
- return ( a >= 0 ) ? ( a + 0xFFFFL ) & ~0xFFFFL
- : -((-a + 0xFFFFL ) & ~0xFFFFL );
+ return a >= 0 ? ( a + 0xFFFFL ) & ~0xFFFFL
+ : -((-a + 0xFFFFL ) & ~0xFFFFL );
}
@@ -324,54 +106,50 @@
FT_EXPORT_DEF( FT_Fixed )
FT_FloorFix( FT_Fixed a )
{
- return ( a >= 0 ) ? a & ~0xFFFFL
- : -((-a) & ~0xFFFFL );
+ return a >= 0 ? a & ~0xFFFFL
+ : -((-a) & ~0xFFFFL );
}
+#ifndef FT_MSB
FT_BASE_DEF ( FT_Int )
FT_MSB( FT_UInt32 z )
{
-#ifdef FT_MSB_BUILTIN
-
- return FT_MSB_BUILTIN( z );
+ FT_Int shift = 0;
-#else
-
- FT_Int shift = 0;
/* determine msb bit index in `shift' */
- if ( z >= ( 1L << 16 ) )
+ if ( z & 0xFFFF0000UL )
{
z >>= 16;
shift += 16;
}
- if ( z >= ( 1L << 8 ) )
+ if ( z & 0x0000FF00UL )
{
z >>= 8;
shift += 8;
}
- if ( z >= ( 1L << 4 ) )
+ if ( z & 0x000000F0UL )
{
z >>= 4;
shift += 4;
}
- if ( z >= ( 1L << 2 ) )
+ if ( z & 0x0000000CUL )
{
z >>= 2;
shift += 2;
}
- if ( z >= ( 1L << 1 ) )
+ if ( z & 0x00000002UL )
{
/* z >>= 1; */
shift += 1;
}
return shift;
-
-#endif /* FT_MSB_BUILTIN */
}
+#endif /* !FT_MSB */
+
/* documentation is in ftcalc.h */
@@ -395,80 +173,89 @@
/* documentation is in freetype.h */
FT_EXPORT_DEF( FT_Long )
- FT_MulDiv( FT_Long a,
- FT_Long b,
- FT_Long c )
+ FT_MulDiv( FT_Long a_,
+ FT_Long b_,
+ FT_Long c_ )
{
- FT_Int s;
- FT_Long d;
+ FT_Int s = 1;
+ FT_UInt64 a, b, c, d;
+ 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; }
+ FT_MOVE_SIGN( a_, s );
+ FT_MOVE_SIGN( b_, s );
+ FT_MOVE_SIGN( c_, s );
- d = (FT_Long)( c > 0 ? ( (FT_Int64)a * b + ( c >> 1 ) ) / c
- : 0x7FFFFFFFL );
+ a = (FT_UInt64)a_;
+ b = (FT_UInt64)b_;
+ c = (FT_UInt64)c_;
- return ( s > 0 ) ? d : -d;
+ d = c > 0 ? ( a * b + ( c >> 1 ) ) / c
+ : 0x7FFFFFFFUL;
+
+ d_ = (FT_Long)d;
+
+ return s < 0 ? -d_ : d_;
}
/* documentation is in ftcalc.h */
FT_BASE_DEF( FT_Long )
- FT_MulDiv_No_Round( FT_Long a,
- FT_Long b,
- FT_Long c )
+ FT_MulDiv_No_Round( FT_Long a_,
+ FT_Long b_,
+ FT_Long c_ )
{
- FT_Int s;
- FT_Long d;
+ FT_Int s = 1;
+ FT_UInt64 a, b, c, d;
+ FT_Long d_;
+
+ FT_MOVE_SIGN( a_, s );
+ FT_MOVE_SIGN( b_, s );
+ FT_MOVE_SIGN( c_, s );
- s = 1;
- if ( a < 0 ) { a = -a; s = -1; }
- if ( b < 0 ) { b = -b; s = -s; }
- if ( c < 0 ) { c = -c; s = -s; }
+ a = (FT_UInt64)a_;
+ b = (FT_UInt64)b_;
+ c = (FT_UInt64)c_;
- d = (FT_Long)( c > 0 ? (FT_Int64)a * b / c
- : 0x7FFFFFFFL );
+ d = c > 0 ? a * b / c
+ : 0x7FFFFFFFUL;
- return ( s > 0 ) ? d : -d;
+ d_ = (FT_Long)d;
+
+ return s < 0 ? -d_ : d_;
}
/* documentation is in freetype.h */
FT_EXPORT_DEF( FT_Long )
- FT_MulFix( FT_Long a,
- FT_Long b )
+ FT_MulFix( FT_Long a_,
+ FT_Long b_ )
{
#ifdef FT_MULFIX_ASSEMBLER
- return FT_MULFIX_ASSEMBLER( a, b );
+ return FT_MULFIX_ASSEMBLER( a_, b_ );
#else
- FT_Int s = 1;
- FT_Long c;
+ FT_Int s = 1;
+ FT_UInt64 a, b, c;
+ FT_Long c_;
- if ( a < 0 )
- {
- a = -a;
- s = -1;
- }
+ FT_MOVE_SIGN( a_, s );
+ FT_MOVE_SIGN( b_, s );
- if ( b < 0 )
- {
- b = -b;
- s = -s;
- }
+ a = (FT_UInt64)a_;
+ b = (FT_UInt64)b_;
+
+ c = ( a * b + 0x8000UL ) >> 16;
- c = (FT_Long)( ( (FT_Int64)a * b + 0x8000L ) >> 16 );
+ c_ = (FT_Long)c;
- return ( s > 0 ) ? c : -c;
+ return s < 0 ? -c_ : c_;
#endif /* FT_MULFIX_ASSEMBLER */
}
@@ -477,33 +264,26 @@
/* documentation is in freetype.h */
FT_EXPORT_DEF( FT_Long )
- FT_DivFix( FT_Long a,
- FT_Long b )
+ FT_DivFix( FT_Long a_,
+ FT_Long b_ )
{
- FT_Int32 s;
- FT_UInt32 q;
+ FT_Int s = 1;
+ FT_UInt64 a, b, q;
+ FT_Long q_;
- s = 1;
- if ( a < 0 )
- {
- a = -a;
- s = -1;
- }
- if ( b < 0 )
- {
- b = -b;
- s = -s;
- }
+ FT_MOVE_SIGN( a_, s );
+ FT_MOVE_SIGN( b_, s );
- if ( b == 0 )
- /* check for division by 0 */
- q = 0x7FFFFFFFL;
- else
- /* compute result directly */
- q = (FT_UInt32)( ( ( (FT_UInt64)a << 16 ) + ( b >> 1 ) ) / b );
+ a = (FT_UInt64)a_;
+ b = (FT_UInt64)b_;
+
+ q = b > 0 ? ( ( a << 16 ) + ( b >> 1 ) ) / b
+ : 0x7FFFFFFFUL;
- return ( s < 0 ? -(FT_Long)q : (FT_Long)q );
+ q_ = (FT_Long)q;
+
+ return s < 0 ? -q_ : q_;
}
@@ -551,25 +331,30 @@
FT_Int i;
- q = 0;
- r = hi;
-
- if ( r >= y )
+ if ( hi >= y )
return (FT_UInt32)0x7FFFFFFFL;
- i = 32;
+ /* We shift as many bits as we can into the high register, perform */
+ /* 32-bit division with modulo there, then work through the remaining */
+ /* bits with long division. This optimization is especially noticeable */
+ /* for smaller dividends that barely use the high register. */
+
+ i = 31 - FT_MSB( hi );
+ r = ( hi << i ) | ( lo >> ( 32 - i ) ); lo <<= i; /* left 64-bit shift */
+ q = r / y;
+ r -= q * y; /* remainder */
+
+ i = 32 - i; /* bits remaining in low register */
do
{
- r <<= 1;
q <<= 1;
- r |= lo >> 31;
+ r = ( r << 1 ) | ( lo >> 31 ); lo <<= 1;
if ( r >= y )
{
r -= y;
q |= 1;
}
- lo <<= 1;
} while ( --i );
return q;
@@ -581,7 +366,7 @@
FT_Int64* y,
FT_Int64 *z )
{
- register FT_UInt32 lo, hi;
+ FT_UInt32 lo, hi;
lo = x->lo + y->lo;
@@ -592,111 +377,161 @@
}
- /* documentation is in freetype.h */
-
- /* The FT_MulDiv function has been optimized thanks to ideas from */
- /* Graham Asher and Alexei Podtelezhnikov. The trick is to optimize */
- /* a rather common case when everything fits within 32-bits. */
+ /* The FT_MulDiv function has been optimized thanks to ideas from */
+ /* Graham Asher and Alexei Podtelezhnikov. The trick is to optimize */
+ /* a rather common case when everything fits within 32-bits. */
/* */
- /* We compute 'a*b+c/2', then divide it by 'c'. (positive values) */
+ /* We compute 'a*b+c/2', then divide it by 'c' (all positive values). */
/* */
/* The product of two positive numbers never exceeds the square of */
- /* their mean. Therefore, we always avoid the overflow by imposing */
+ /* its mean values. Therefore, we always avoid the overflow by */
+ /* imposing */
+ /* */
+ /* (a + b) / 2 <= sqrt(X - c/2) , */
+ /* */
+ /* where X = 2^32 - 1, the maximum unsigned 32-bit value, and using */
+ /* unsigned arithmetic. Now we replace `sqrt' with a linear function */
+ /* that is smaller or equal for all values of c in the interval */
+ /* [0;X/2]; it should be equal to sqrt(X) and sqrt(3X/4) at the */
+ /* endpoints. Substituting the linear solution and explicit numbers */
+ /* we get */
+ /* */
+ /* a + b <= 131071.99 - c / 122291.84 . */
+ /* */
+ /* In practice, we should use a faster and even stronger inequality */
+ /* */
+ /* a + b <= 131071 - (c >> 16) */
/* */
- /* ( a + b ) / 2 <= sqrt( X - c/2 ) */
+ /* or, alternatively, */
/* */
- /* where X = 2^31 - 1. Now we replace sqrt with a linear function */
- /* that is smaller or equal in the entire range of c from 0 to X; */
- /* it should be equal to sqrt(X) and sqrt(X/2) at the range termini. */
- /* Substituting the linear solution and explicit numbers we get */
+ /* a + b <= 129894 - (c >> 17) . */
/* */
- /* a + b <= 92681.9 - c / 79108.95 */
+ /* FT_MulFix, on the other hand, is optimized for a small value of */
+ /* the first argument, when the second argument can be much larger. */
+ /* This can be achieved by scaling the second argument and the limit */
+ /* in the above inequalities. For example, */
/* */
- /* In practice we use a faster and even stronger inequality */
+ /* a + (b >> 8) <= (131071 >> 4) */
/* */
- /* a + b <= 92681 - (c >> 16) */
+ /* covers the practical range of use. The actual test below is a bit */
+ /* tighter to avoid the border case overflows. */
/* */
+ /* In the case of FT_DivFix, the exact overflow check */
+ /* */
+ /* a << 16 <= X - c/2 */
+ /* */
+ /* is scaled down by 2^16 and we use */
+ /* */
+ /* a <= 65535 - (c >> 17) . */
+
+ /* documentation is in freetype.h */
FT_EXPORT_DEF( FT_Long )
- FT_MulDiv( FT_Long a,
- FT_Long b,
- FT_Long c )
+ FT_MulDiv( FT_Long a_,
+ FT_Long b_,
+ FT_Long c_ )
{
- long s;
+ FT_Int s = 1;
+ FT_UInt32 a, b, c;
/* XXX: this function does not allow 64-bit arguments */
- 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_ == 0 || b_ == c_ )
+ return a_;
+
+ FT_MOVE_SIGN( a_, s );
+ FT_MOVE_SIGN( b_, s );
+ FT_MOVE_SIGN( c_, s );
+
+ a = (FT_UInt32)a_;
+ b = (FT_UInt32)b_;
+ c = (FT_UInt32)c_;
- if ( (FT_ULong)a + (FT_ULong)b <= 92681UL - ( c >> 16 ) && c > 0 )
+ if ( c == 0 )
+ a = 0x7FFFFFFFUL;
+
+ else if ( a + b <= 129894UL - ( c >> 17 ) )
a = ( a * b + ( c >> 1 ) ) / c;
- else if ( (FT_Int32)c > 0 )
+ else
{
FT_Int64 temp, temp2;
- ft_multo64( (FT_Int32)a, (FT_Int32)b, &temp );
+ ft_multo64( a, b, &temp );
temp2.hi = 0;
- temp2.lo = (FT_UInt32)(c >> 1);
+ temp2.lo = c >> 1;
+
FT_Add64( &temp, &temp2, &temp );
- a = ft_div64by32( temp.hi, temp.lo, (FT_Int32)c );
+
+ /* last attempt to ditch long division */
+ a = temp.hi == 0 ? temp.lo / c
+ : ft_div64by32( temp.hi, temp.lo, c );
}
- else
- a = 0x7FFFFFFFL;
- return ( s < 0 ? -a : a );
+ a_ = (FT_Long)a;
+
+ return s < 0 ? -a_ : a_;
}
FT_BASE_DEF( FT_Long )
- FT_MulDiv_No_Round( FT_Long a,
- FT_Long b,
- FT_Long c )
+ FT_MulDiv_No_Round( FT_Long a_,
+ FT_Long b_,
+ FT_Long c_ )
{
- long s;
+ FT_Int s = 1;
+ FT_UInt32 a, b, c;
- if ( a == 0 || b == c )
- return a;
+ /* XXX: this function does not allow 64-bit arguments */
+
+ if ( a_ == 0 || b_ == c_ )
+ return a_;
+
+ FT_MOVE_SIGN( a_, s );
+ FT_MOVE_SIGN( b_, s );
+ FT_MOVE_SIGN( c_, s );
+
+ a = (FT_UInt32)a_;
+ b = (FT_UInt32)b_;
+ c = (FT_UInt32)c_;
- s = a; a = FT_ABS( a );
- s ^= b; b = FT_ABS( b );
- s ^= c; c = FT_ABS( c );
+ if ( c == 0 )
+ a = 0x7FFFFFFFUL;
- if ( (FT_ULong)a + (FT_ULong)b <= 92681UL && c > 0 )
+ else if ( a + b <= 131071UL )
a = a * b / c;
- else if ( (FT_Int32)c > 0 )
+ else
{
FT_Int64 temp;
- ft_multo64( (FT_Int32)a, (FT_Int32)b, &temp );
- a = ft_div64by32( temp.hi, temp.lo, (FT_Int32)c );
+ ft_multo64( a, b, &temp );
+
+ /* last attempt to ditch long division */
+ a = temp.hi == 0 ? temp.lo / c
+ : ft_div64by32( temp.hi, temp.lo, c );
}
- else
- a = 0x7FFFFFFFL;
- return ( s < 0 ? -a : a );
+ a_ = (FT_Long)a;
+
+ return s < 0 ? -a_ : a_;
}
/* documentation is in freetype.h */
FT_EXPORT_DEF( FT_Long )
- FT_MulFix( FT_Long a,
- FT_Long b )
+ FT_MulFix( FT_Long a_,
+ FT_Long b_ )
{
#ifdef FT_MULFIX_ASSEMBLER
- return FT_MULFIX_ASSEMBLER( a, b );
+ return FT_MULFIX_ASSEMBLER( a_, b_ );
#elif 0
@@ -707,12 +542,12 @@
* the leftmost bits by copying the sign bit, it might be faster.
*/
- FT_Long sa, sb;
- FT_ULong ua, ub;
+ FT_Long sa, sb;
+ FT_UInt32 a, b;
- if ( a == 0 || b == 0x10000L )
- return a;
+ if ( a_ == 0 || b_ == 0x10000L )
+ return a_;
/*
* This is a clever way of converting a signed number `a' into its
@@ -732,57 +567,61 @@
* with the value 1 rather than -1. After that, everything else goes
* wrong.
*/
- sa = ( a >> ( sizeof ( a ) * 8 - 1 ) );
- a = ( a ^ sa ) - sa;
- sb = ( b >> ( sizeof ( b ) * 8 - 1 ) );
- b = ( b ^ sb ) - sb;
+ 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;
+ a = (FT_UInt32)a_;
+ b = (FT_UInt32)b_;
- if ( ua <= 2048 && ub <= 1048576L )
- ua = ( ua * ub + 0x8000U ) >> 16;
+ if ( a + ( b >> 8 ) <= 8190UL )
+ a = ( a * b + 0x8000U ) >> 16;
else
{
- FT_ULong al = ua & 0xFFFFU;
+ FT_UInt32 al = a & 0xFFFFUL;
- ua = ( ua >> 16 ) * ub + al * ( ub >> 16 ) +
- ( ( al * ( ub & 0xFFFFU ) + 0x8000U ) >> 16 );
+ a = ( a >> 16 ) * b + al * ( b >> 16 ) +
+ ( ( al * ( b & 0xFFFFUL ) + 0x8000UL ) >> 16 );
}
- sa ^= sb,
- ua = (FT_ULong)(( ua ^ sa ) - sa);
+ sa ^= sb;
+ a = ( a ^ sa ) - sa;
- return (FT_Long)ua;
+ return (FT_Long)a;
#else /* 0 */
- FT_Long s;
- FT_ULong ua, ub;
+ FT_Int s = 1;
+ FT_UInt32 a, b;
+
+ /* XXX: this function does not allow 64-bit arguments */
- if ( a == 0 || b == 0x10000L )
- return a;
+ if ( a_ == 0 || b_ == 0x10000L )
+ return a_;
- s = a; a = FT_ABS( a );
- s ^= b; b = FT_ABS( b );
+ FT_MOVE_SIGN( a_, s );
+ FT_MOVE_SIGN( b_, s );
- ua = (FT_ULong)a;
- ub = (FT_ULong)b;
+ a = (FT_UInt32)a_;
+ b = (FT_UInt32)b_;
- if ( ua <= 2048 && ub <= 1048576L )
- ua = ( ua * ub + 0x8000UL ) >> 16;
+ if ( a + ( b >> 8 ) <= 8190UL )
+ a = ( a * b + 0x8000UL ) >> 16;
else
{
- FT_ULong al = ua & 0xFFFFUL;
+ FT_UInt32 al = a & 0xFFFFUL;
- ua = ( ua >> 16 ) * ub + al * ( ub >> 16 ) +
- ( ( al * ( ub & 0xFFFFUL ) + 0x8000UL ) >> 16 );
+ a = ( a >> 16 ) * b + al * ( b >> 16 ) +
+ ( ( al * ( b & 0xFFFFUL ) + 0x8000UL ) >> 16 );
}
- return ( s < 0 ? -(FT_Long)ua : (FT_Long)ua );
+ a_ = (FT_Long)a;
+
+ return s < 0 ? -a_ : a_;
#endif /* 0 */
@@ -792,26 +631,31 @@
/* documentation is in freetype.h */
FT_EXPORT_DEF( FT_Long )
- FT_DivFix( FT_Long a,
- FT_Long b )
+ FT_DivFix( FT_Long a_,
+ FT_Long b_ )
{
- FT_Int32 s;
- FT_UInt32 q;
+ FT_Int s = 1;
+ FT_UInt32 a, b, q;
+ FT_Long q_;
/* XXX: this function does not allow 64-bit arguments */
- s = (FT_Int32)a; a = FT_ABS( a );
- s ^= (FT_Int32)b; b = FT_ABS( b );
- if ( (FT_UInt32)b == 0 )
+ FT_MOVE_SIGN( a_, s );
+ FT_MOVE_SIGN( b_, s );
+
+ a = (FT_UInt32)a_;
+ b = (FT_UInt32)b_;
+
+ if ( b == 0 )
{
/* check for division by 0 */
- q = (FT_UInt32)0x7FFFFFFFL;
+ q = 0x7FFFFFFFUL;
}
- else if ( ( a >> 16 ) == 0 )
+ else if ( a <= 65535UL - ( b >> 17 ) )
{
/* compute result directly */
- q = (FT_UInt32)( ( (FT_ULong)a << 16 ) + ( b >> 1 ) ) / (FT_UInt32)b;
+ q = ( ( a << 16 ) + ( b >> 1 ) ) / b;
}
else
{
@@ -819,140 +663,22 @@
FT_Int64 temp, temp2;
- temp.hi = (FT_Int32)( a >> 16 );
- temp.lo = (FT_UInt32)a << 16;
+ temp.hi = a >> 16;
+ temp.lo = a << 16;
temp2.hi = 0;
- temp2.lo = (FT_UInt32)( b >> 1 );
- FT_Add64( &temp, &temp2, &temp );
- q = ft_div64by32( temp.hi, temp.lo, (FT_Int32)b );
- }
+ temp2.lo = b >> 1;
- 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 );
+ FT_Add64( &temp, &temp2, &temp );
+ q = ft_div64by32( temp.hi, temp.lo, b );
}
- q = ft_div64by32( x->hi, x->lo, y );
+ q_ = (FT_Long)q;
- return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
+ return s < 0 ? -q_ : q_;
}
-#endif /* 0 */
-
-#endif /* 0 */
-
-#endif /* FT_LONG64 */
+#endif /* !FT_LONG64 */
/* documentation is in ftglyph.h */
@@ -1075,7 +801,7 @@
if ( x > 0 )
{
rem_hi = 0;
- rem_lo = x;
+ rem_lo = (FT_UInt32)x;
count = 24;
do
{
@@ -1156,8 +882,8 @@
/* XXX: this function does not allow 64-bit arguments */
- ft_multo64( (FT_Int32)in_x, (FT_Int32)out_y, &z1 );
- ft_multo64( (FT_Int32)in_y, (FT_Int32)out_x, &z2 );
+ ft_multo64( (FT_UInt32)in_x, (FT_UInt32)out_y, &z1 );
+ ft_multo64( (FT_UInt32)in_y, (FT_UInt32)out_x, &z2 );
if ( z1.hi > z2.hi )
result = +1;
@@ -1186,55 +912,40 @@
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;
-
-
- /* We approximate the Euclidean metric (sqrt(x^2 + y^2)) with */
- /* the Taxicab metric (|x| + |y|), which can be computed much */
- /* faster. If one of the two vectors is much longer than the */
- /* other one, the direction of the shorter vector doesn't */
- /* influence the result any more. */
- /* */
- /* corner */
- /* x---------------------------x */
- /* \ / */
- /* \ / */
- /* in \ / out */
- /* \ / */
- /* o */
- /* Point */
- /* */
-
- if ( ax < 0 )
- ax = -ax;
- if ( ay < 0 )
- ay = -ay;
- d_in = ax + ay; /* d_in = || in || */
-
- ax = out_x;
- if ( ax < 0 )
- ax = -ax;
- ay = out_y;
- if ( ay < 0 )
- ay = -ay;
- d_out = ax + ay; /* d_out = || out || */
-
- ax = out_x + in_x;
- if ( ax < 0 )
- ax = -ax;
- ay = out_y + in_y;
- if ( ay < 0 )
- ay = -ay;
- d_corner = ax + ay; /* d_corner = || in + out || */
+ FT_Pos ax = in_x + out_x;
+ FT_Pos ay = in_y + out_y;
+
+ FT_Pos d_in, d_out, d_hypot;
+
+
+ /* The idea of this function is to compare the length of the */
+ /* hypotenuse with the `in' and `out' length. The `corner' */
+ /* represented by `in' and `out' is flat if the hypotenuse's */
+ /* length isn't too large. */
+ /* */
+ /* This approach has the advantage that the angle between */
+ /* `in' and `out' is not checked. In case one of the two */
+ /* vectors is `dominant', this is, much larger than the */
+ /* other vector, we thus always have a flat corner. */
+ /* */
+ /* hypotenuse */
+ /* x---------------------------x */
+ /* \ / */
+ /* \ / */
+ /* in \ / out */
+ /* \ / */
+ /* o */
+ /* Point */
+
+ d_in = FT_HYPOT( in_x, in_y );
+ d_out = FT_HYPOT( out_x, out_y );
+ d_hypot = FT_HYPOT( ax, ay );
/* now do a simple length comparison: */
/* */
- /* d_in + d_out < 17/16 d_corner */
+ /* d_in + d_out < 17/16 d_hypot */
- return ( d_in + d_out - d_corner ) < ( d_corner >> 4 );
+ return ( d_in + d_out - d_hypot ) < ( d_hypot >> 4 );
}
generated by cgit v1.2.3 (git 2.25.1) at 2024-04-24 06:04:40 +0000