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 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 ``` ``````/***************************************************************************/ /* */ /* ftcalc.h */ /* */ /* Arithmetic computations (specification). */ /* */ /* Copyright 1996-2015 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 #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 ) { register 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 ) { register 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 ) { register 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 ) { register 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 /*************************************************************************/ /* */ /* */ /* FT_MulDiv_No_Round */ /* */ /* */ /* 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. */ /* */ /* */ /* a :: The first multiplier. */ /* b :: The second multiplier. */ /* c :: The divisor. */ /* */ /* */ /* 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 /*************************************************************************/ /* */ /* */ /* FT_SqrtFixed */ /* */ /* */ /* Computes the square root of a 16.16 fixed-point value. */ /* */ /* */ /* x :: The value to compute the root for. */ /* */ /* */ /* The result of `sqrt(x)'. */ /* */ /* */ /* 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 */ ``````