/***************************************************************************/ | |
/* */ | |
/* ftcalc.c */ | |
/* */ | |
/* Arithmetic computations (body). */ | |
/* */ | |
/* Copyright 1996-2015 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 | |
#ifdef FT_MULFIX_ASSEMBLER | |
#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 | |
/* 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. */ | |
/* documentation is in freetype.h */ | |
FT_EXPORT_DEF( FT_Fixed ) | |
FT_RoundFix( FT_Fixed a ) | |
{ | |
return ( a + 0x8000L - ( a < 0 ) ) & ~0xFFFFL; | |
} | |
/* documentation is in freetype.h */ | |
FT_EXPORT_DEF( FT_Fixed ) | |
FT_CeilFix( FT_Fixed a ) | |
{ | |
return ( a + 0xFFFFL ) & ~0xFFFFL; | |
} | |
/* documentation is in freetype.h */ | |
FT_EXPORT_DEF( FT_Fixed ) | |
FT_FloorFix( FT_Fixed a ) | |
{ | |
return a & ~0xFFFFL; | |
} | |
#ifndef FT_MSB | |
FT_BASE_DEF ( FT_Int ) | |
FT_MSB( FT_UInt32 z ) | |
{ | |
FT_Int shift = 0; | |
/* determine msb bit index in `shift' */ | |
if ( z & 0xFFFF0000UL ) | |
{ | |
z >>= 16; | |
shift += 16; | |
} | |
if ( z & 0x0000FF00UL ) | |
{ | |
z >>= 8; | |
shift += 8; | |
} | |
if ( z & 0x000000F0UL ) | |
{ | |
z >>= 4; | |
shift += 4; | |
} | |
if ( z & 0x0000000CUL ) | |
{ | |
z >>= 2; | |
shift += 2; | |
} | |
if ( z & 0x00000002UL ) | |
{ | |
/* z >>= 1; */ | |
shift += 1; | |
} | |
return shift; | |
} | |
#endif /* !FT_MSB */ | |
/* 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 = 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 ); | |
a = (FT_UInt64)a_; | |
b = (FT_UInt64)b_; | |
c = (FT_UInt64)c_; | |
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_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 ); | |
a = (FT_UInt64)a_; | |
b = (FT_UInt64)b_; | |
c = (FT_UInt64)c_; | |
d = c > 0 ? a * b / c | |
: 0x7FFFFFFFUL; | |
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_ ) | |
{ | |
#ifdef FT_MULFIX_ASSEMBLER | |
return FT_MULFIX_ASSEMBLER( a_, b_ ); | |
#else | |
FT_Int64 ab = (FT_Int64)a_ * (FT_Int64)b_; | |
/* this requires arithmetic right shift of signed numbers */ | |
return (FT_Long)( ( ab + 0x8000L - ( ab < 0 ) ) >> 16 ); | |
#endif /* FT_MULFIX_ASSEMBLER */ | |
} | |
/* documentation is in freetype.h */ | |
FT_EXPORT_DEF( FT_Long ) | |
FT_DivFix( FT_Long a_, | |
FT_Long b_ ) | |
{ | |
FT_Int s = 1; | |
FT_UInt64 a, b, q; | |
FT_Long q_; | |
FT_MOVE_SIGN( a_, s ); | |
FT_MOVE_SIGN( b_, s ); | |
a = (FT_UInt64)a_; | |
b = (FT_UInt64)b_; | |
q = b > 0 ? ( ( a << 16 ) + ( b >> 1 ) ) / b | |
: 0x7FFFFFFFUL; | |
q_ = (FT_Long)q; | |
return s < 0 ? -q_ : 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; | |
if ( hi >= y ) | |
return (FT_UInt32)0x7FFFFFFFL; | |
/* 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 | |
{ | |
q <<= 1; | |
r = ( r << 1 ) | ( lo >> 31 ); lo <<= 1; | |
if ( r >= y ) | |
{ | |
r -= y; | |
q |= 1; | |
} | |
} while ( --i ); | |
return q; | |
} | |
static void | |
FT_Add64( FT_Int64* x, | |
FT_Int64* y, | |
FT_Int64 *z ) | |
{ | |
FT_UInt32 lo, hi; | |
lo = x->lo + y->lo; | |
hi = x->hi + y->hi + ( lo < x->lo ); | |
z->lo = lo; | |
z->hi = hi; | |
} | |
/* 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' (all positive values). */ | |
/* */ | |
/* The product of two positive numbers never exceeds the square of */ | |
/* 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) */ | |
/* */ | |
/* or, alternatively, */ | |
/* */ | |
/* a + b <= 129894 - (c >> 17) . */ | |
/* */ | |
/* 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, */ | |
/* */ | |
/* a + (b >> 8) <= (131071 >> 4) */ | |
/* */ | |
/* 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_Int s = 1; | |
FT_UInt32 a, b, c; | |
/* XXX: this function does not allow 64-bit arguments */ | |
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 ( c == 0 ) | |
a = 0x7FFFFFFFUL; | |
else if ( a + b <= 129894UL - ( c >> 17 ) ) | |
a = ( a * b + ( c >> 1 ) ) / c; | |
else | |
{ | |
FT_Int64 temp, temp2; | |
ft_multo64( a, b, &temp ); | |
temp2.hi = 0; | |
temp2.lo = c >> 1; | |
FT_Add64( &temp, &temp2, &temp ); | |
/* last attempt to ditch long division */ | |
a = temp.hi == 0 ? temp.lo / c | |
: ft_div64by32( temp.hi, temp.lo, c ); | |
} | |
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_Int s = 1; | |
FT_UInt32 a, b, c; | |
/* XXX: this function does not allow 64-bit arguments */ | |
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 ( c == 0 ) | |
a = 0x7FFFFFFFUL; | |
else if ( a + b <= 131071UL ) | |
a = a * b / c; | |
else | |
{ | |
FT_Int64 temp; | |
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 ); | |
} | |
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_ ) | |
{ | |
#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_UInt32 a, b; | |
/* | |
* 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; | |
a = (FT_UInt32)a_; | |
b = (FT_UInt32)b_; | |
if ( a + ( b >> 8 ) <= 8190UL ) | |
a = ( a * b + 0x8000U ) >> 16; | |
else | |
{ | |
FT_UInt32 al = a & 0xFFFFUL; | |
a = ( a >> 16 ) * b + al * ( b >> 16 ) + | |
( ( al * ( b & 0xFFFFUL ) + 0x8000UL ) >> 16 ); | |
} | |
sa ^= sb; | |
a = ( a ^ sa ) - sa; | |
return (FT_Long)a; | |
#else /* 0 */ | |
FT_Int s = 1; | |
FT_UInt32 a, b; | |
/* XXX: this function does not allow 64-bit arguments */ | |
FT_MOVE_SIGN( a_, s ); | |
FT_MOVE_SIGN( b_, s ); | |
a = (FT_UInt32)a_; | |
b = (FT_UInt32)b_; | |
if ( a + ( b >> 8 ) <= 8190UL ) | |
a = ( a * b + 0x8000UL ) >> 16; | |
else | |
{ | |
FT_UInt32 al = a & 0xFFFFUL; | |
a = ( a >> 16 ) * b + al * ( b >> 16 ) + | |
( ( al * ( b & 0xFFFFUL ) + 0x8000UL ) >> 16 ); | |
} | |
a_ = (FT_Long)a; | |
return s < 0 ? -a_ : a_; | |
#endif /* 0 */ | |
} | |
/* documentation is in freetype.h */ | |
FT_EXPORT_DEF( FT_Long ) | |
FT_DivFix( FT_Long a_, | |
FT_Long b_ ) | |
{ | |
FT_Int s = 1; | |
FT_UInt32 a, b, q; | |
FT_Long q_; | |
/* XXX: this function does not allow 64-bit arguments */ | |
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 = 0x7FFFFFFFUL; | |
} | |
else if ( a <= 65535UL - ( b >> 17 ) ) | |
{ | |
/* compute result directly */ | |
q = ( ( a << 16 ) + ( b >> 1 ) ) / b; | |
} | |
else | |
{ | |
/* we need more bits; we have to do it by hand */ | |
FT_Int64 temp, temp2; | |
temp.hi = a >> 16; | |
temp.lo = a << 16; | |
temp2.hi = 0; | |
temp2.lo = b >> 1; | |
FT_Add64( &temp, &temp2, &temp ); | |
q = ft_div64by32( temp.hi, temp.lo, b ); | |
} | |
q_ = (FT_Long)q; | |
return s < 0 ? -q_ : q_; | |
} | |
#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; | |
} | |
/* documentation is in ftcalc.h */ | |
FT_BASE_DEF( FT_UInt32 ) | |
FT_Vector_NormLen( FT_Vector* vector ) | |
{ | |
FT_Int32 x_ = vector->x; | |
FT_Int32 y_ = vector->y; | |
FT_Int32 b, z; | |
FT_UInt32 x, y, u, v, l; | |
FT_Int sx = 1, sy = 1, shift; | |
FT_MOVE_SIGN( x_, sx ); | |
FT_MOVE_SIGN( y_, sy ); | |
x = (FT_UInt32)x_; | |
y = (FT_UInt32)y_; | |
/* trivial cases */ | |
if ( x == 0 ) | |
{ | |
if ( y > 0 ) | |
vector->y = sy * 0x10000; | |
return y; | |
} | |
else if ( y == 0 ) | |
{ | |
if ( x > 0 ) | |
vector->x = sx * 0x10000; | |
return x; | |
} | |
/* Estimate length and prenormalize by shifting so that */ | |
/* the new approximate length is between 2/3 and 4/3. */ | |
/* The magic constant 0xAAAAAAAAUL (2/3 of 2^32) helps */ | |
/* achieve this in 16.16 fixed-point representation. */ | |
l = x > y ? x + ( y >> 1 ) | |
: y + ( x >> 1 ); | |
shift = 31 - FT_MSB( l ); | |
shift -= 15 + ( l >= ( 0xAAAAAAAAUL >> shift ) ); | |
if ( shift > 0 ) | |
{ | |
x <<= shift; | |
y <<= shift; | |
/* re-estimate length for tiny vectors */ | |
l = x > y ? x + ( y >> 1 ) | |
: y + ( x >> 1 ); | |
} | |
else | |
{ | |
x >>= -shift; | |
y >>= -shift; | |
l >>= -shift; | |
} | |
/* lower linear approximation for reciprocal length minus one */ | |
b = 0x10000 - (FT_Int32)l; | |
x_ = (FT_Int32)x; | |
y_ = (FT_Int32)y; | |
/* Newton's iterations */ | |
do | |
{ | |
u = (FT_UInt32)( x_ + ( x_ * b >> 16 ) ); | |
v = (FT_UInt32)( y_ + ( y_ * b >> 16 ) ); | |
/* Normalized squared length in the parentheses approaches 2^32. */ | |
/* On two's complement systems, converting to signed gives the */ | |
/* difference with 2^32 even if the expression wraps around. */ | |
z = -(FT_Int32)( u * u + v * v ) / 0x200; | |
z = z * ( ( 0x10000 + b ) >> 8 ) / 0x10000; | |
b += z; | |
} while ( z > 0 ); | |
vector->x = sx < 0 ? -(FT_Pos)u : (FT_Pos)u; | |
vector->y = sy < 0 ? -(FT_Pos)v : (FT_Pos)v; | |
/* Conversion to signed helps to recover from likely wrap around */ | |
/* in calculating the prenormalized length, because it gives the */ | |
/* correct difference with 2^32 on two's complement systems. */ | |
l = (FT_UInt32)( 0x10000 + (FT_Int32)( u * x + v * y ) / 0x10000 ); | |
if ( shift > 0 ) | |
l = ( l + ( 1 << ( shift - 1 ) ) ) >> shift; | |
else | |
l <<= -shift; | |
return l; | |
} | |
#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 = (FT_UInt32)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 ) | |
{ | |
#ifdef FT_LONG64 | |
FT_Int64 delta = (FT_Int64)in_x * out_y - (FT_Int64)in_y * out_x; | |
return ( delta > 0 ) - ( delta < 0 ); | |
#else | |
FT_Int result; | |
if ( (FT_ULong)FT_ABS( in_x ) + (FT_ULong)FT_ABS( out_y ) <= 131071UL && | |
(FT_ULong)FT_ABS( in_y ) + (FT_ULong)FT_ABS( out_x ) <= 131071UL ) | |
{ | |
FT_Long z1 = in_x * out_y; | |
FT_Long z2 = in_y * out_x; | |
if ( z1 > z2 ) | |
result = +1; | |
else if ( z1 < z2 ) | |
result = -1; | |
else | |
result = 0; | |
} | |
else /* products might overflow 32 bits */ | |
{ | |
FT_Int64 z1, z2; | |
/* XXX: this function does not allow 64-bit arguments */ | |
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; | |
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; | |
} | |
/* XXX: only the sign of return value, +1/0/-1 must be used */ | |
return result; | |
#endif | |
} | |
/* 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 + 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_hypot */ | |
return ( d_in + d_out - d_hypot ) < ( d_hypot >> 4 ); | |
} | |
/* END */ |