/***************************************************************************/
/* */
/* ftcalc.h */
/* */
/* Arithmetic computations (specification). */
/* */
/* Copyright 1996-2016 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) << 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 FIXED_TO_INT( x ) ( FT_RoundFix( x ) >> 16 )
#define ROUND_F26DOT6( x ) ( x >= 0 ? ( ( (x) + 32 ) & -64 ) \
: ( -( ( 32 - (x) ) & -64 ) ) )
FT_END_HEADER
#endif /* FTCALC_H_ */
/* END */
|
