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+/***************************************************************************/
+/* */
+/* ftcalc.h */
+/* */
+/* Arithmetic computations (specification). */
+/* */
+/* Copyright 1996-2001, 2002, 2003, 2004, 2005, 2006, 2008 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. */
+/* */
+/***************************************************************************/
+
+
+#ifndef __FTCALC_H__
+#define __FTCALC_H__
+
+
+#include <ft2build.h>
+#include FT_FREETYPE_H
+
+
+FT_BEGIN_HEADER
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* FT_FixedSqrt */
+ /* */
+ /* <Description> */
+ /* Computes the square root of a 16.16 fixed point value. */
+ /* */
+ /* <Input> */
+ /* x :: The value to compute the root for. */
+ /* */
+ /* <Return> */
+ /* The result of `sqrt(x)'. */
+ /* */
+ /* <Note> */
+ /* This function is not very fast. */
+ /* */
+ FT_BASE( FT_Int32 )
+ FT_SqrtFixed( FT_Int32 x );
+
+
+#ifdef FT_CONFIG_OPTION_OLD_INTERNALS
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* FT_Sqrt32 */
+ /* */
+ /* <Description> */
+ /* Computes the square root of an Int32 integer (which will be */
+ /* handled as an unsigned long value). */
+ /* */
+ /* <Input> */
+ /* x :: The value to compute the root for. */
+ /* */
+ /* <Return> */
+ /* The result of `sqrt(x)'. */
+ /* */
+ FT_EXPORT( FT_Int32 )
+ FT_Sqrt32( FT_Int32 x );
+
+#endif /* FT_CONFIG_OPTION_OLD_INTERNALS */
+
+
+ /*************************************************************************/
+ /* */
+ /* FT_MulDiv() and FT_MulFix() are declared in freetype.h. */
+ /* */
+ /*************************************************************************/
+
+
+#ifdef TT_USE_BYTECODE_INTERPRETER
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* FT_MulDiv_No_Round */
+ /* */
+ /* <Description> */
+ /* A very simple function used to perform the computation `(a*b)/c' */
+ /* (without rounding) with maximal accuracy (it uses a 64-bit */
+ /* intermediate integer whenever necessary). */
+ /* */
+ /* This function isn't necessarily as fast as some processor specific */
+ /* operations, but is at least completely portable. */
+ /* */
+ /* <Input> */
+ /* a :: The first multiplier. */
+ /* b :: The second multiplier. */
+ /* c :: The divisor. */
+ /* */
+ /* <Return> */
+ /* The result of `(a*b)/c'. This function never traps when trying to */
+ /* divide by zero; it simply returns `MaxInt' or `MinInt' depending */
+ /* on the signs of `a' and `b'. */
+ /* */
+ FT_BASE( FT_Long )
+ FT_MulDiv_No_Round( FT_Long a,
+ FT_Long b,
+ FT_Long c );
+
+#endif /* TT_USE_BYTECODE_INTERPRETER */
+
+
+ /*
+ * A variant of FT_Matrix_Multiply which scales its result afterwards.
+ * The idea is that both `a' and `b' are scaled by factors of 10 so that
+ * the values are as precise as possible to get a correct result during
+ * the 64bit multiplication. Let `sa' and `sb' be the scaling factors of
+ * `a' and `b', respectively, then the scaling factor of the result is
+ * `sa*sb'.
+ */
+ FT_BASE( void )
+ FT_Matrix_Multiply_Scaled( const FT_Matrix* a,
+ FT_Matrix *b,
+ FT_Long scaling );
+
+
+ /*
+ * A variant of FT_Vector_Transform. See comments for
+ * FT_Matrix_Multiply_Scaled.
+ */
+
+ FT_BASE( void )
+ FT_Vector_Transform_Scaled( FT_Vector* vector,
+ const FT_Matrix* matrix,
+ FT_Long scaling );
+
+
+ /*
+ * Return -1, 0, or +1, depending on the orientation of a given corner.
+ * We use the Cartesian coordinate system, with positive vertical values
+ * going upwards. The function returns +1 if the corner turns to the
+ * left, -1 to the right, and 0 for undecidable cases.
+ */
+ FT_BASE( FT_Int )
+ ft_corner_orientation( FT_Pos in_x,
+ FT_Pos in_y,
+ FT_Pos out_x,
+ FT_Pos out_y );
+
+ /*
+ * Return TRUE if a corner is flat or nearly flat. This is equivalent to
+ * saying that the angle difference between the `in' and `out' vectors is
+ * very small.
+ */
+ FT_BASE( FT_Int )
+ ft_corner_is_flat( FT_Pos in_x,
+ FT_Pos in_y,
+ FT_Pos out_x,
+ FT_Pos out_y );
+
+
+#define INT_TO_F26DOT6( x ) ( (FT_Long)(x) << 6 )
+#define INT_TO_F2DOT14( x ) ( (FT_Long)(x) << 14 )
+#define INT_TO_FIXED( x ) ( (FT_Long)(x) << 16 )
+#define F2DOT14_TO_FIXED( x ) ( (FT_Long)(x) << 2 )
+#define FLOAT_TO_FIXED( x ) ( (FT_Long)( x * 65536.0 ) )
+
+#define ROUND_F26DOT6( x ) ( x >= 0 ? ( ( (x) + 32 ) & -64 ) \
+ : ( -( ( 32 - (x) ) & -64 ) ) )
+
+
+FT_END_HEADER
+
+#endif /* __FTCALC_H__ */
+
+
+/* END */