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ftcalc.h
/****************************************************************************
*
* ftcalc.h
*
* Arithmetic computations (specification).
*
* Copyright (C) 1996-2019 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 );
/*
* Check a matrix. If the transformation would lead to extreme shear or
* extreme scaling, for example, return 0. If everything is OK, return 1.
*
* Based on geometric considerations we use the following inequality to
* identify a degenerate matrix.
*
* 50 * abs(xx*yy - xy*yx) < xx^2 + xy^2 + yx^2 + yy^2
*
* Value 50 is heuristic.
*/
FT_BASE( FT_Bool )
FT_Matrix_Check( const FT_Matrix* matrix );
/*
* 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 /* __GNUC__ */
#elif defined( _MSC_VER ) && ( _MSC_VER >= 1400 )
#if FT_SIZEOF_INT == 4
#include <intrin.h>
#pragma intrinsic( _BitScanReverse )
static __inline FT_Int32
FT_MSB_i386( FT_UInt32 x )
{
unsigned long where;
_BitScanReverse( &where, x );
return (FT_Int32)where;
}
#define FT_MSB( x ) ( FT_MSB_i386( x ) )
#endif
#endif /* _MSC_VER */
#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_INT( a, b ) \
(FT_Int)( (FT_UInt)(a) + (FT_UInt)(b) )
#define SUB_INT( a, b ) \
(FT_Int)( (FT_UInt)(a) - (FT_UInt)(b) )
#define MUL_INT( a, b ) \
(FT_Int)( (FT_UInt)(a) * (FT_UInt)(b) )
#define NEG_INT( a ) \
(FT_Int)( (FT_UInt)0 - (FT_UInt)(a) )
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