| /**************************************************************************** |
| * |
| * 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> |
| |
| static __inline FT_Int32 |
| FT_MSB_i386( FT_UInt32 x ) |
| { |
| unsigned long where; |
| |
| |
| /* not available in older VC versions */ |
| _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) ) |
| |
| #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) ) |
| |
| #ifdef FT_LONG64 |
| |
| #define ADD_INT64( a, b ) \ |
| (FT_Int64)( (FT_UInt64)(a) + (FT_UInt64)(b) ) |
| #define SUB_INT64( a, b ) \ |
| (FT_Int64)( (FT_UInt64)(a) - (FT_UInt64)(b) ) |
| #define MUL_INT64( a, b ) \ |
| (FT_Int64)( (FT_UInt64)(a) * (FT_UInt64)(b) ) |
| #define NEG_INT64( a ) \ |
| (FT_Int64)( (FT_UInt64)0 - (FT_UInt64)(a) ) |
| |
| #endif /* FT_LONG64 */ |
| |
| |
| FT_END_HEADER |
| |
| #endif /* FTCALC_H_ */ |
| |
| |
| /* END */ |
