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+/***************************************************************************/
+/* */
+/* ftcalc.h */
+/* */
+/* Arithmetic computations (specification). */
+/* */
+/* Copyright 1996-2018 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
+
+
+ /*************************************************************************/
+ /* */
+ /* FT_MulDiv() and FT_MulFix() are declared in freetype.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 )
+ {
+ 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 )
+ {
+ 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 )
+ {
+ 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 )
+ {
+ 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__ */
+
+#endif /* !FT_CONFIG_OPTION_NO_ASSEMBLER */
+
+
+#ifdef FT_CONFIG_OPTION_INLINE_MULFIX
+#ifdef FT_MULFIX_ASSEMBLER
+#define FT_MulFix( a, b ) FT_MULFIX_ASSEMBLER( (FT_Int32)(a), (FT_Int32)(b) )
+#endif
+#endif
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* FT_MulDiv_No_Round */
+ /* */
+ /* <Description> */
+ /* A very simple function used to perform the computation `(a*b)/c' */
+ /* (without rounding) with maximum 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 );
+
+
+ /*
+ * 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 );
+
+
+ /*
+ * This function normalizes a vector and returns its original length.
+ * The normalized vector is a 16.16 fixed-point unit vector with length
+ * close to 0x10000. The accuracy of the returned length is limited to
+ * 16 bits also. The function utilizes quick inverse square root
+ * approximation without divisions and square roots relying on Newton's
+ * iterations instead.
+ */
+ FT_BASE( FT_UInt32 )
+ FT_Vector_NormLen( FT_Vector* vector );
+
+
+ /*
+ * 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 corner point is close to its neighbors, or inside an
+ * ellipse defined by the neighbor focal points to be more precise.
+ */
+ FT_BASE( FT_Int )
+ ft_corner_is_flat( FT_Pos in_x,
+ FT_Pos in_y,
+ FT_Pos out_x,
+ FT_Pos out_y );
+
+
+ /*
+ * Return the most significant bit index.
+ */
+
+#ifndef FT_CONFIG_OPTION_NO_ASSEMBLER
+#if defined( __GNUC__ ) && \
+ ( __GNUC__ > 3 || ( __GNUC__ == 3 && __GNUC_MINOR__ >= 4 ) )
+
+#if FT_SIZEOF_INT == 4
+
+#define FT_MSB( x ) ( 31 - __builtin_clz( x ) )
+
+#elif FT_SIZEOF_LONG == 4
+
+#define FT_MSB( x ) ( 31 - __builtin_clzl( x ) )
+
+#endif
+
+#endif /* __GNUC__ */
+#endif /* !FT_CONFIG_OPTION_NO_ASSEMBLER */
+
+#ifndef FT_MSB
+
+ FT_BASE( FT_Int )
+ FT_MSB( FT_UInt32 z );
+
+#endif
+
+
+ /*
+ * Return sqrt(x*x+y*y), which is the same as `FT_Vector_Length' but uses
+ * two fixed-point arguments instead.
+ */
+ FT_BASE( FT_Fixed )
+ FT_Hypot( FT_Fixed x,
+ FT_Fixed y );
+
+
+#if 0
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* FT_SqrtFixed */
+ /* */
+ /* <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 );
+
+#endif /* 0 */
+
+
+#define INT_TO_F26DOT6( x ) ( (FT_Long)(x) * 64 ) /* << 6 */
+#define INT_TO_F2DOT14( x ) ( (FT_Long)(x) * 16384 ) /* << 14 */
+#define INT_TO_FIXED( x ) ( (FT_Long)(x) * 65536 ) /* << 16 */
+#define F2DOT14_TO_FIXED( x ) ( (FT_Long)(x) * 4 ) /* << 2 */
+#define FIXED_TO_INT( x ) ( FT_RoundFix( x ) >> 16 )
+
+#define ROUND_F26DOT6( x ) ( x >= 0 ? ( ( (x) + 32 ) & -64 ) \
+ : ( -( ( 32 - (x) ) & -64 ) ) )
+
+ /*
+ * The following macros have two purposes.
+ *
+ * . Tag places where overflow is expected and harmless.
+ *
+ * . Avoid run-time sanitizer errors.
+ *
+ * Use with care!
+ */
+#define ADD_LONG( a, b ) \
+ (FT_Long)( (FT_ULong)(a) + (FT_ULong)(b) )
+#define SUB_LONG( a, b ) \
+ (FT_Long)( (FT_ULong)(a) - (FT_ULong)(b) )
+#define MUL_LONG( a, b ) \
+ (FT_Long)( (FT_ULong)(a) * (FT_ULong)(b) )
+#define NEG_LONG( a ) \
+ (FT_Long)( (FT_ULong)0 - (FT_ULong)(a) )
+
+#define ADD_INT32( a, b ) \
+ (FT_Int32)( (FT_UInt32)(a) + (FT_UInt32)(b) )
+#define SUB_INT32( a, b ) \
+ (FT_Int32)( (FT_UInt32)(a) - (FT_UInt32)(b) )
+#define MUL_INT32( a, b ) \
+ (FT_Int32)( (FT_UInt32)(a) * (FT_UInt32)(b) )
+#define NEG_INT32( a ) \
+ (FT_Int32)( (FT_UInt32)0 - (FT_UInt32)(a) )
+
+
+FT_END_HEADER
+
+#endif /* FTCALC_H_ */
+
+
+/* END */
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