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diff --git a/third_party/freetype/src/base/ftcalc.c b/third_party/freetype/src/base/ftcalc.c
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-/***************************************************************************/
-/* */
-/* ftcalc.c */
-/* */
-/* Arithmetic computations (body). */
-/* */
-/* Copyright 1996-2017 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( (FT_Int32)a_, (FT_Int32)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 */
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