| /***************************************************************************/ |
| /* */ |
| /* ftcalc.c */ |
| /* */ |
| /* Arithmetic computations (body). */ |
| /* */ |
| /* Copyright 1996-2006, 2008, 2012-2014 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_GLYPH_H |
| #include FT_TRIGONOMETRY_H |
| #include FT_INTERNAL_CALC_H |
| #include FT_INTERNAL_DEBUG_H |
| #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 |
| |
| /* we need to emulate a 64-bit data type if a real one isn't available */ |
| |
| #ifndef FT_LONG64 |
| |
| 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 ); |
| } |
| |
| |
| FT_BASE_DEF ( FT_Int ) |
| FT_MSB( FT_UInt32 z ) |
| { |
| #ifdef FT_MSB_BUILTIN |
| |
| return FT_MSB_BUILTIN( z ); |
| |
| #else |
| |
| FT_Int shift = 0; |
| |
| /* determine msb bit index in `shift' */ |
| if ( z >= ( 1L << 16 ) ) |
| { |
| z >>= 16; |
| shift += 16; |
| } |
| if ( z >= ( 1L << 8 ) ) |
| { |
| z >>= 8; |
| shift += 8; |
| } |
| if ( z >= ( 1L << 4 ) ) |
| { |
| z >>= 4; |
| shift += 4; |
| } |
| if ( z >= ( 1L << 2 ) ) |
| { |
| z >>= 2; |
| shift += 2; |
| } |
| if ( z >= ( 1L << 1 ) ) |
| { |
| /* z >>= 1; */ |
| shift += 1; |
| } |
| |
| return shift; |
| |
| #endif /* FT_MSB_BUILTIN */ |
| } |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_BASE_DEF( FT_Fixed ) |
| FT_Hypot( FT_Fixed x, |
| FT_Fixed y ) |
| { |
| FT_Vector v; |
| |
| |
| v.x = x; |
| v.y = y; |
| |
| return FT_Vector_Length( &v ); |
| } |
| |
| |
| #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 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; |
| } |
| |
| |
| /* documentation is in freetype.h */ |
| |
| FT_EXPORT_DEF( FT_Long ) |
| FT_MulFix( FT_Long a, |
| FT_Long b ) |
| { |
| #ifdef FT_MULFIX_ASSEMBLER |
| |
| return FT_MULFIX_ASSEMBLER( a, b ); |
| |
| #else |
| |
| 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; |
| |
| #endif /* FT_MULFIX_ASSEMBLER */ |
| } |
| |
| |
| /* 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_UInt64)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 >= 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 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) */ |
| /* */ |
| /* The product of two positive numbers never exceeds the square of */ |
| /* their mean. Therefore, we always avoid the overflow by imposing */ |
| /* */ |
| /* ( a + b ) / 2 <= sqrt( X - c/2 ) */ |
| /* */ |
| /* 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 <= 92681.9 - c / 79108.95 */ |
| /* */ |
| /* In practice we use a faster and even stronger inequality */ |
| /* */ |
| /* a + b <= 92681 - (c >> 16) */ |
| /* */ |
| |
| FT_EXPORT_DEF( FT_Long ) |
| FT_MulDiv( FT_Long a, |
| FT_Long b, |
| FT_Long c ) |
| { |
| long s; |
| |
| |
| /* 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 ( (FT_ULong)a + (FT_ULong)b <= 92681UL - ( c >> 16 ) && c > 0 ) |
| a = ( a * b + ( c >> 1 ) ) / c; |
| |
| else if ( (FT_Int32)c > 0 ) |
| { |
| FT_Int64 temp, temp2; |
| |
| |
| ft_multo64( (FT_Int32)a, (FT_Int32)b, &temp ); |
| |
| temp2.hi = 0; |
| temp2.lo = (FT_UInt32)(c >> 1); |
| FT_Add64( &temp, &temp2, &temp ); |
| a = ft_div64by32( temp.hi, temp.lo, (FT_Int32)c ); |
| } |
| else |
| a = 0x7FFFFFFFL; |
| |
| return ( s < 0 ? -a : a ); |
| } |
| |
| |
| 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 ( (FT_ULong)a + (FT_ULong)b <= 92681UL && c > 0 ) |
| a = a * b / c; |
| |
| else if ( (FT_Int32)c > 0 ) |
| { |
| FT_Int64 temp; |
| |
| |
| ft_multo64( (FT_Int32)a, (FT_Int32)b, &temp ); |
| a = ft_div64by32( temp.hi, temp.lo, (FT_Int32)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 ) |
| { |
| #ifdef FT_MULFIX_ASSEMBLER |
| |
| return FT_MULFIX_ASSEMBLER( a, b ); |
| |
| #elif 0 |
| |
| /* |
| * This code is nonportable. See comment below. |
| * |
| * However, on a platform where right-shift of a signed quantity fills |
| * the leftmost bits by copying the sign bit, it might be faster. |
| */ |
| |
| FT_Long sa, sb; |
| FT_ULong ua, ub; |
| |
| |
| if ( a == 0 || b == 0x10000L ) |
| return a; |
| |
| /* |
| * This is a clever way of converting a signed number `a' into its |
| * absolute value (stored back into `a') and its sign. The sign is |
| * stored in `sa'; 0 means `a' was positive or zero, and -1 means `a' |
| * was negative. (Similarly for `b' and `sb'). |
| * |
| * Unfortunately, it doesn't work (at least not portably). |
| * |
| * It makes the assumption that right-shift on a negative signed value |
| * fills the leftmost bits by copying the sign bit. This is wrong. |
| * According to K&R 2nd ed, section `A7.8 Shift Operators' on page 206, |
| * the result of right-shift of a negative signed value is |
| * implementation-defined. At least one implementation fills the |
| * leftmost bits with 0s (i.e., it is exactly the same as an unsigned |
| * right shift). This means that when `a' is negative, `sa' ends up |
| * 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; |
| |
| 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; |
| |
| |
| /* 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 ) |
| { |
| /* check for division by 0 */ |
| q = (FT_UInt32)0x7FFFFFFFL; |
| } |
| else if ( ( a >> 16 ) == 0 ) |
| { |
| /* compute result directly */ |
| q = (FT_UInt32)( ( (FT_ULong)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, (FT_Int32)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 ftglyph.h */ |
| |
| FT_EXPORT_DEF( void ) |
| FT_Matrix_Multiply( const FT_Matrix* a, |
| FT_Matrix *b ) |
| { |
| FT_Fixed xx, xy, yx, yy; |
| |
| |
| if ( !a || !b ) |
| return; |
| |
| xx = FT_MulFix( a->xx, b->xx ) + FT_MulFix( a->xy, b->yx ); |
| xy = FT_MulFix( a->xx, b->xy ) + FT_MulFix( a->xy, b->yy ); |
| yx = FT_MulFix( a->yx, b->xx ) + FT_MulFix( a->yy, b->yx ); |
| yy = FT_MulFix( a->yx, b->xy ) + FT_MulFix( a->yy, b->yy ); |
| |
| b->xx = xx; b->xy = xy; |
| b->yx = yx; b->yy = yy; |
| } |
| |
| |
| /* documentation is in ftglyph.h */ |
| |
| FT_EXPORT_DEF( FT_Error ) |
| FT_Matrix_Invert( FT_Matrix* matrix ) |
| { |
| FT_Pos delta, xx, yy; |
| |
| |
| if ( !matrix ) |
| return FT_THROW( Invalid_Argument ); |
| |
| /* compute discriminant */ |
| delta = FT_MulFix( matrix->xx, matrix->yy ) - |
| FT_MulFix( matrix->xy, matrix->yx ); |
| |
| if ( !delta ) |
| return FT_THROW( Invalid_Argument ); /* matrix can't be inverted */ |
| |
| matrix->xy = - FT_DivFix( matrix->xy, delta ); |
| matrix->yx = - FT_DivFix( matrix->yx, delta ); |
| |
| xx = matrix->xx; |
| yy = matrix->yy; |
| |
| matrix->xx = FT_DivFix( yy, delta ); |
| matrix->yy = FT_DivFix( xx, delta ); |
| |
| return FT_Err_Ok; |
| } |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_BASE_DEF( void ) |
| FT_Matrix_Multiply_Scaled( const FT_Matrix* a, |
| FT_Matrix *b, |
| FT_Long scaling ) |
| { |
| FT_Fixed xx, xy, yx, yy; |
| |
| FT_Long val = 0x10000L * scaling; |
| |
| |
| if ( !a || !b ) |
| return; |
| |
| xx = FT_MulDiv( a->xx, b->xx, val ) + FT_MulDiv( a->xy, b->yx, val ); |
| xy = FT_MulDiv( a->xx, b->xy, val ) + FT_MulDiv( a->xy, b->yy, val ); |
| yx = FT_MulDiv( a->yx, b->xx, val ) + FT_MulDiv( a->yy, b->yx, val ); |
| yy = FT_MulDiv( a->yx, b->xy, val ) + FT_MulDiv( a->yy, b->yy, val ); |
| |
| b->xx = xx; b->xy = xy; |
| b->yx = yx; b->yy = yy; |
| } |
| |
| |
| /* documentation is in ftcalc.h */ |
| |
| FT_BASE_DEF( void ) |
| FT_Vector_Transform_Scaled( FT_Vector* vector, |
| const FT_Matrix* matrix, |
| FT_Long scaling ) |
| { |
| FT_Pos xz, yz; |
| |
| FT_Long val = 0x10000L * scaling; |
| |
| |
| if ( !vector || !matrix ) |
| return; |
| |
| xz = FT_MulDiv( vector->x, matrix->xx, val ) + |
| FT_MulDiv( vector->y, matrix->xy, val ); |
| |
| yz = FT_MulDiv( vector->x, matrix->yx, val ) + |
| FT_MulDiv( vector->y, matrix->yy, val ); |
| |
| vector->x = xz; |
| vector->y = yz; |
| } |
| |
| |
| #if 0 |
| |
| /* 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; |
| } |
| |
| #endif /* 0 */ |
| |
| |
| /* 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_Long result; /* avoid overflow on 16-bit system */ |
| |
| |
| /* 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; |
| |
| |
| /* 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 ); |
| |
| 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 |
| } |
| |
| /* XXX: only the sign of return value, +1/0/-1 must be used */ |
| return (FT_Int)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; |
| |
| |
| /* 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 || */ |
| |
| /* now do a simple length comparison: */ |
| /* */ |
| /* d_in + d_out < 17/16 d_corner */ |
| |
| return ( d_in + d_out - d_corner ) < ( d_corner >> 4 ); |
| } |
| |
| |
| /* END */ |
