| OLD | NEW |
|---|
| (Empty) |
| 1 /***************************************************************************/ | |
| 2 /* */ | |
| 3 /* fttrigon.c */ | |
| 4 /* */ | |
| 5 /* FreeType trigonometric functions (body). */ | |
| 6 /* */ | |
| 7 /* Copyright 2001-2005, 2012-2013 by */ | |
| 8 /* David Turner, Robert Wilhelm, and Werner Lemberg. */ | |
| 9 /* */ | |
| 10 /* This file is part of the FreeType project, and may only be used, */ | |
| 11 /* modified, and distributed under the terms of the FreeType project */ | |
| 12 /* license, LICENSE.TXT. By continuing to use, modify, or distribute */ | |
| 13 /* this file you indicate that you have read the license and */ | |
| 14 /* understand and accept it fully. */ | |
| 15 /* */ | |
| 16 /***************************************************************************/ | |
| 17 | |
| 18 /*************************************************************************/ | |
| 19 /* */ | |
| 20 /* This is a fixed-point CORDIC implementation of trigonometric */ | |
| 21 /* functions as well as transformations between Cartesian and polar */ | |
| 22 /* coordinates. The angles are represented as 16.16 fixed-point values */ | |
| 23 /* in degrees, i.e., the angular resolution is 2^-16 degrees. Note that */ | |
| 24 /* only vectors longer than 2^16*180/pi (or at least 22 bits) on a */ | |
| 25 /* discrete Cartesian grid can have the same or better angular */ | |
| 26 /* resolution. Therefore, to maintain this precision, some functions */ | |
| 27 /* require an interim upscaling of the vectors, whereas others operate */ | |
| 28 /* with 24-bit long vectors directly. */ | |
| 29 /* */ | |
| 30 /*************************************************************************/ | |
| 31 | |
| 32 #include "../../include/ft2build.h" | |
| 33 #include "../../include/freetype/internal/ftobjs.h" | |
| 34 #include "../../include/freetype/internal/ftcalc.h" | |
| 35 #include "../../include/freetype/fttrigon.h" | |
| 36 | |
| 37 | |
| 38 /* the Cordic shrink factor 0.858785336480436 * 2^32 */ | |
| 39 #define FT_TRIG_SCALE 0xDBD95B16UL | |
| 40 | |
| 41 /* the highest bit in overflow-safe vector components, */ | |
| 42 /* MSB of 0.858785336480436 * sqrt(0.5) * 2^30 */ | |
| 43 #define FT_TRIG_SAFE_MSB 29 | |
| 44 | |
| 45 /* this table was generated for FT_PI = 180L << 16, i.e. degrees */ | |
| 46 #define FT_TRIG_MAX_ITERS 23 | |
| 47 | |
| 48 static const FT_Fixed | |
| 49 ft_trig_arctan_table[] = | |
| 50 { | |
| 51 1740967L, 919879L, 466945L, 234379L, 117304L, 58666L, 29335L, | |
| 52 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L, | |
| 53 57L, 29L, 14L, 7L, 4L, 2L, 1L | |
| 54 }; | |
| 55 | |
| 56 | |
| 57 #ifdef FT_LONG64 | |
| 58 | |
| 59 /* multiply a given value by the CORDIC shrink factor */ | |
| 60 static FT_Fixed | |
| 61 ft_trig_downscale( FT_Fixed val ) | |
| 62 { | |
| 63 FT_Fixed s; | |
| 64 FT_Int64 v; | |
| 65 | |
| 66 | |
| 67 s = val; | |
| 68 val = FT_ABS( val ); | |
| 69 | |
| 70 v = ( val * (FT_Int64)FT_TRIG_SCALE ) + 0x100000000UL; | |
| 71 val = (FT_Fixed)( v >> 32 ); | |
| 72 | |
| 73 return ( s >= 0 ) ? val : -val; | |
| 74 } | |
| 75 | |
| 76 #else /* !FT_LONG64 */ | |
| 77 | |
| 78 /* multiply a given value by the CORDIC shrink factor */ | |
| 79 static FT_Fixed | |
| 80 ft_trig_downscale( FT_Fixed val ) | |
| 81 { | |
| 82 FT_Fixed s; | |
| 83 FT_UInt32 v1, v2, k1, k2, hi, lo1, lo2, lo3; | |
| 84 | |
| 85 | |
| 86 s = val; | |
| 87 val = FT_ABS( val ); | |
| 88 | |
| 89 v1 = (FT_UInt32)val >> 16; | |
| 90 v2 = (FT_UInt32)( val & 0xFFFFL ); | |
| 91 | |
| 92 k1 = (FT_UInt32)FT_TRIG_SCALE >> 16; /* constant */ | |
| 93 k2 = (FT_UInt32)( FT_TRIG_SCALE & 0xFFFFL ); /* constant */ | |
| 94 | |
| 95 hi = k1 * v1; | |
| 96 lo1 = k1 * v2 + k2 * v1; /* can't overflow */ | |
| 97 | |
| 98 lo2 = ( k2 * v2 ) >> 16; | |
| 99 lo3 = FT_MAX( lo1, lo2 ); | |
| 100 lo1 += lo2; | |
| 101 | |
| 102 hi += lo1 >> 16; | |
| 103 if ( lo1 < lo3 ) | |
| 104 hi += (FT_UInt32)0x10000UL; | |
| 105 | |
| 106 val = (FT_Fixed)hi; | |
| 107 | |
| 108 return ( s >= 0 ) ? val : -val; | |
| 109 } | |
| 110 | |
| 111 #endif /* !FT_LONG64 */ | |
| 112 | |
| 113 | |
| 114 static FT_Int | |
| 115 ft_trig_prenorm( FT_Vector* vec ) | |
| 116 { | |
| 117 FT_Pos x, y; | |
| 118 FT_Int shift; | |
| 119 | |
| 120 | |
| 121 x = vec->x; | |
| 122 y = vec->y; | |
| 123 | |
| 124 shift = FT_MSB( FT_ABS( x ) | FT_ABS( y ) ); | |
| 125 | |
| 126 if ( shift <= FT_TRIG_SAFE_MSB ) | |
| 127 { | |
| 128 shift = FT_TRIG_SAFE_MSB - shift; | |
| 129 vec->x = (FT_Pos)( (FT_ULong)x << shift ); | |
| 130 vec->y = (FT_Pos)( (FT_ULong)y << shift ); | |
| 131 } | |
| 132 else | |
| 133 { | |
| 134 shift -= FT_TRIG_SAFE_MSB; | |
| 135 vec->x = x >> shift; | |
| 136 vec->y = y >> shift; | |
| 137 shift = -shift; | |
| 138 } | |
| 139 | |
| 140 return shift; | |
| 141 } | |
| 142 | |
| 143 | |
| 144 static void | |
| 145 ft_trig_pseudo_rotate( FT_Vector* vec, | |
| 146 FT_Angle theta ) | |
| 147 { | |
| 148 FT_Int i; | |
| 149 FT_Fixed x, y, xtemp, b; | |
| 150 const FT_Fixed *arctanptr; | |
| 151 | |
| 152 | |
| 153 x = vec->x; | |
| 154 y = vec->y; | |
| 155 | |
| 156 /* Rotate inside [-PI/4,PI/4] sector */ | |
| 157 while ( theta < -FT_ANGLE_PI4 ) | |
| 158 { | |
| 159 xtemp = y; | |
| 160 y = -x; | |
| 161 x = xtemp; | |
| 162 theta += FT_ANGLE_PI2; | |
| 163 } | |
| 164 | |
| 165 while ( theta > FT_ANGLE_PI4 ) | |
| 166 { | |
| 167 xtemp = -y; | |
| 168 y = x; | |
| 169 x = xtemp; | |
| 170 theta -= FT_ANGLE_PI2; | |
| 171 } | |
| 172 | |
| 173 arctanptr = ft_trig_arctan_table; | |
| 174 | |
| 175 /* Pseudorotations, with right shifts */ | |
| 176 for ( i = 1, b = 1; i < FT_TRIG_MAX_ITERS; b <<= 1, i++ ) | |
| 177 { | |
| 178 if ( theta < 0 ) | |
| 179 { | |
| 180 xtemp = x + ( ( y + b ) >> i ); | |
| 181 y = y - ( ( x + b ) >> i ); | |
| 182 x = xtemp; | |
| 183 theta += *arctanptr++; | |
| 184 } | |
| 185 else | |
| 186 { | |
| 187 xtemp = x - ( ( y + b ) >> i ); | |
| 188 y = y + ( ( x + b ) >> i ); | |
| 189 x = xtemp; | |
| 190 theta -= *arctanptr++; | |
| 191 } | |
| 192 } | |
| 193 | |
| 194 vec->x = x; | |
| 195 vec->y = y; | |
| 196 } | |
| 197 | |
| 198 | |
| 199 static void | |
| 200 ft_trig_pseudo_polarize( FT_Vector* vec ) | |
| 201 { | |
| 202 FT_Angle theta; | |
| 203 FT_Int i; | |
| 204 FT_Fixed x, y, xtemp, b; | |
| 205 const FT_Fixed *arctanptr; | |
| 206 | |
| 207 | |
| 208 x = vec->x; | |
| 209 y = vec->y; | |
| 210 | |
| 211 /* Get the vector into [-PI/4,PI/4] sector */ | |
| 212 if ( y > x ) | |
| 213 { | |
| 214 if ( y > -x ) | |
| 215 { | |
| 216 theta = FT_ANGLE_PI2; | |
| 217 xtemp = y; | |
| 218 y = -x; | |
| 219 x = xtemp; | |
| 220 } | |
| 221 else | |
| 222 { | |
| 223 theta = y > 0 ? FT_ANGLE_PI : -FT_ANGLE_PI; | |
| 224 x = -x; | |
| 225 y = -y; | |
| 226 } | |
| 227 } | |
| 228 else | |
| 229 { | |
| 230 if ( y < -x ) | |
| 231 { | |
| 232 theta = -FT_ANGLE_PI2; | |
| 233 xtemp = -y; | |
| 234 y = x; | |
| 235 x = xtemp; | |
| 236 } | |
| 237 else | |
| 238 { | |
| 239 theta = 0; | |
| 240 } | |
| 241 } | |
| 242 | |
| 243 arctanptr = ft_trig_arctan_table; | |
| 244 | |
| 245 /* Pseudorotations, with right shifts */ | |
| 246 for ( i = 1, b = 1; i < FT_TRIG_MAX_ITERS; b <<= 1, i++ ) | |
| 247 { | |
| 248 if ( y > 0 ) | |
| 249 { | |
| 250 xtemp = x + ( ( y + b ) >> i ); | |
| 251 y = y - ( ( x + b ) >> i ); | |
| 252 x = xtemp; | |
| 253 theta += *arctanptr++; | |
| 254 } | |
| 255 else | |
| 256 { | |
| 257 xtemp = x - ( ( y + b ) >> i ); | |
| 258 y = y + ( ( x + b ) >> i ); | |
| 259 x = xtemp; | |
| 260 theta -= *arctanptr++; | |
| 261 } | |
| 262 } | |
| 263 | |
| 264 /* round theta */ | |
| 265 if ( theta >= 0 ) | |
| 266 theta = FT_PAD_ROUND( theta, 32 ); | |
| 267 else | |
| 268 theta = -FT_PAD_ROUND( -theta, 32 ); | |
| 269 | |
| 270 vec->x = x; | |
| 271 vec->y = theta; | |
| 272 } | |
| 273 | |
| 274 | |
| 275 /* documentation is in fttrigon.h */ | |
| 276 | |
| 277 FT_EXPORT_DEF( FT_Fixed ) | |
| 278 FT_Cos( FT_Angle angle ) | |
| 279 { | |
| 280 FT_Vector v; | |
| 281 | |
| 282 | |
| 283 v.x = FT_TRIG_SCALE >> 8; | |
| 284 v.y = 0; | |
| 285 ft_trig_pseudo_rotate( &v, angle ); | |
| 286 | |
| 287 return ( v.x + 0x80L ) >> 8; | |
| 288 } | |
| 289 | |
| 290 | |
| 291 /* documentation is in fttrigon.h */ | |
| 292 | |
| 293 FT_EXPORT_DEF( FT_Fixed ) | |
| 294 FT_Sin( FT_Angle angle ) | |
| 295 { | |
| 296 return FT_Cos( FT_ANGLE_PI2 - angle ); | |
| 297 } | |
| 298 | |
| 299 | |
| 300 /* documentation is in fttrigon.h */ | |
| 301 | |
| 302 FT_EXPORT_DEF( FT_Fixed ) | |
| 303 FT_Tan( FT_Angle angle ) | |
| 304 { | |
| 305 FT_Vector v; | |
| 306 | |
| 307 | |
| 308 v.x = FT_TRIG_SCALE >> 8; | |
| 309 v.y = 0; | |
| 310 ft_trig_pseudo_rotate( &v, angle ); | |
| 311 | |
| 312 return FT_DivFix( v.y, v.x ); | |
| 313 } | |
| 314 | |
| 315 | |
| 316 /* documentation is in fttrigon.h */ | |
| 317 | |
| 318 FT_EXPORT_DEF( FT_Angle ) | |
| 319 FT_Atan2( FT_Fixed dx, | |
| 320 FT_Fixed dy ) | |
| 321 { | |
| 322 FT_Vector v; | |
| 323 | |
| 324 | |
| 325 if ( dx == 0 && dy == 0 ) | |
| 326 return 0; | |
| 327 | |
| 328 v.x = dx; | |
| 329 v.y = dy; | |
| 330 ft_trig_prenorm( &v ); | |
| 331 ft_trig_pseudo_polarize( &v ); | |
| 332 | |
| 333 return v.y; | |
| 334 } | |
| 335 | |
| 336 | |
| 337 /* documentation is in fttrigon.h */ | |
| 338 | |
| 339 FT_EXPORT_DEF( void ) | |
| 340 FT_Vector_Unit( FT_Vector* vec, | |
| 341 FT_Angle angle ) | |
| 342 { | |
| 343 vec->x = FT_TRIG_SCALE >> 8; | |
| 344 vec->y = 0; | |
| 345 ft_trig_pseudo_rotate( vec, angle ); | |
| 346 vec->x = ( vec->x + 0x80L ) >> 8; | |
| 347 vec->y = ( vec->y + 0x80L ) >> 8; | |
| 348 } | |
| 349 | |
| 350 | |
| 351 /* these macros return 0 for positive numbers, | |
| 352 and -1 for negative ones */ | |
| 353 #define FT_SIGN_LONG( x ) ( (x) >> ( FT_SIZEOF_LONG * 8 - 1 ) ) | |
| 354 #define FT_SIGN_INT( x ) ( (x) >> ( FT_SIZEOF_INT * 8 - 1 ) ) | |
| 355 #define FT_SIGN_INT32( x ) ( (x) >> 31 ) | |
| 356 #define FT_SIGN_INT16( x ) ( (x) >> 15 ) | |
| 357 | |
| 358 | |
| 359 /* documentation is in fttrigon.h */ | |
| 360 | |
| 361 FT_EXPORT_DEF( void ) | |
| 362 FT_Vector_Rotate( FT_Vector* vec, | |
| 363 FT_Angle angle ) | |
| 364 { | |
| 365 FT_Int shift; | |
| 366 FT_Vector v; | |
| 367 | |
| 368 | |
| 369 v.x = vec->x; | |
| 370 v.y = vec->y; | |
| 371 | |
| 372 if ( angle && ( v.x != 0 || v.y != 0 ) ) | |
| 373 { | |
| 374 shift = ft_trig_prenorm( &v ); | |
| 375 ft_trig_pseudo_rotate( &v, angle ); | |
| 376 v.x = ft_trig_downscale( v.x ); | |
| 377 v.y = ft_trig_downscale( v.y ); | |
| 378 | |
| 379 if ( shift > 0 ) | |
| 380 { | |
| 381 FT_Int32 half = (FT_Int32)1L << ( shift - 1 ); | |
| 382 | |
| 383 | |
| 384 vec->x = ( v.x + half + FT_SIGN_LONG( v.x ) ) >> shift; | |
| 385 vec->y = ( v.y + half + FT_SIGN_LONG( v.y ) ) >> shift; | |
| 386 } | |
| 387 else | |
| 388 { | |
| 389 shift = -shift; | |
| 390 vec->x = (FT_Pos)( (FT_ULong)v.x << shift ); | |
| 391 vec->y = (FT_Pos)( (FT_ULong)v.y << shift ); | |
| 392 } | |
| 393 } | |
| 394 } | |
| 395 | |
| 396 | |
| 397 /* documentation is in fttrigon.h */ | |
| 398 | |
| 399 FT_EXPORT_DEF( FT_Fixed ) | |
| 400 FT_Vector_Length( FT_Vector* vec ) | |
| 401 { | |
| 402 FT_Int shift; | |
| 403 FT_Vector v; | |
| 404 | |
| 405 | |
| 406 v = *vec; | |
| 407 | |
| 408 /* handle trivial cases */ | |
| 409 if ( v.x == 0 ) | |
| 410 { | |
| 411 return FT_ABS( v.y ); | |
| 412 } | |
| 413 else if ( v.y == 0 ) | |
| 414 { | |
| 415 return FT_ABS( v.x ); | |
| 416 } | |
| 417 | |
| 418 /* general case */ | |
| 419 shift = ft_trig_prenorm( &v ); | |
| 420 ft_trig_pseudo_polarize( &v ); | |
| 421 | |
| 422 v.x = ft_trig_downscale( v.x ); | |
| 423 | |
| 424 if ( shift > 0 ) | |
| 425 return ( v.x + ( 1 << ( shift - 1 ) ) ) >> shift; | |
| 426 | |
| 427 return (FT_Fixed)( (FT_UInt32)v.x << -shift ); | |
| 428 } | |
| 429 | |
| 430 | |
| 431 /* documentation is in fttrigon.h */ | |
| 432 | |
| 433 FT_EXPORT_DEF( void ) | |
| 434 FT_Vector_Polarize( FT_Vector* vec, | |
| 435 FT_Fixed *length, | |
| 436 FT_Angle *angle ) | |
| 437 { | |
| 438 FT_Int shift; | |
| 439 FT_Vector v; | |
| 440 | |
| 441 | |
| 442 v = *vec; | |
| 443 | |
| 444 if ( v.x == 0 && v.y == 0 ) | |
| 445 return; | |
| 446 | |
| 447 shift = ft_trig_prenorm( &v ); | |
| 448 ft_trig_pseudo_polarize( &v ); | |
| 449 | |
| 450 v.x = ft_trig_downscale( v.x ); | |
| 451 | |
| 452 *length = ( shift >= 0 ) ? ( v.x >> shift ) | |
| 453 : (FT_Fixed)( (FT_UInt32)v.x << -shift ); | |
| 454 *angle = v.y; | |
| 455 } | |
| 456 | |
| 457 | |
| 458 /* documentation is in fttrigon.h */ | |
| 459 | |
| 460 FT_EXPORT_DEF( void ) | |
| 461 FT_Vector_From_Polar( FT_Vector* vec, | |
| 462 FT_Fixed length, | |
| 463 FT_Angle angle ) | |
| 464 { | |
| 465 vec->x = length; | |
| 466 vec->y = 0; | |
| 467 | |
| 468 FT_Vector_Rotate( vec, angle ); | |
| 469 } | |
| 470 | |
| 471 | |
| 472 /* documentation is in fttrigon.h */ | |
| 473 | |
| 474 FT_EXPORT_DEF( FT_Angle ) | |
| 475 FT_Angle_Diff( FT_Angle angle1, | |
| 476 FT_Angle angle2 ) | |
| 477 { | |
| 478 FT_Angle delta = angle2 - angle1; | |
| 479 | |
| 480 | |
| 481 delta %= FT_ANGLE_2PI; | |
| 482 if ( delta < 0 ) | |
| 483 delta += FT_ANGLE_2PI; | |
| 484 | |
| 485 if ( delta > FT_ANGLE_PI ) | |
| 486 delta -= FT_ANGLE_2PI; | |
| 487 | |
| 488 return delta; | |
| 489 } | |
| 490 | |
| 491 | |
| 492 /* END */ | |
| OLD | NEW |
|---|
Chromium Code Reviews
Issue 815103002:
Update freetype to 2.5.4. (Closed)
Base URL: https://pdfium.googlesource.com/pdfium.git@master