1 /* 2 * Copyright (C) 2006-2008 The Android Open Source Project 3 * 4 * Licensed under the Apache License, Version 2.0 (the "License"); 5 * you may not use this file except in compliance with the License. 6 * You may obtain a copy of the License at 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 10 * Unless required by applicable law or agreed to in writing, software 11 * distributed under the License is distributed on an "AS IS" BASIS, 12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13 * See the License for the specific language governing permissions and 14 * limitations under the License. 15 */ 16 17 #include "SkMath.h" 18 #include "SkCordic.h" 19 #include "SkFloatBits.h" 20 #include "SkFloatingPoint.h" 21 #include "Sk64.h" 22 #include "SkScalar.h" 23 24 #ifdef SK_SCALAR_IS_FLOAT 25 const uint32_t gIEEENotANumber = 0x7FFFFFFF; 26 const uint32_t gIEEEInfinity = 0x7F800000; 27 #endif 28 29 #define sub_shift(zeros, x, n) \ 30 zeros -= n; \ 31 x >>= n 32 33 int SkCLZ_portable(uint32_t x) { 34 if (x == 0) { 35 return 32; 36 } 37 38 #ifdef SK_CPU_HAS_CONDITIONAL_INSTR 39 int zeros = 31; 40 if (x & 0xFFFF0000) { 41 sub_shift(zeros, x, 16); 42 } 43 if (x & 0xFF00) { 44 sub_shift(zeros, x, 8); 45 } 46 if (x & 0xF0) { 47 sub_shift(zeros, x, 4); 48 } 49 if (x & 0xC) { 50 sub_shift(zeros, x, 2); 51 } 52 if (x & 0x2) { 53 sub_shift(zeros, x, 1); 54 } 55 #else 56 int zeros = ((x >> 16) - 1) >> 31 << 4; 57 x <<= zeros; 58 59 int nonzero = ((x >> 24) - 1) >> 31 << 3; 60 zeros += nonzero; 61 x <<= nonzero; 62 63 nonzero = ((x >> 28) - 1) >> 31 << 2; 64 zeros += nonzero; 65 x <<= nonzero; 66 67 nonzero = ((x >> 30) - 1) >> 31 << 1; 68 zeros += nonzero; 69 x <<= nonzero; 70 71 zeros += (~x) >> 31; 72 #endif 73 74 return zeros; 75 } 76 77 int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom) { 78 SkASSERT(denom); 79 80 Sk64 tmp; 81 tmp.setMul(numer1, numer2); 82 tmp.div(denom, Sk64::kTrunc_DivOption); 83 return tmp.get32(); 84 } 85 86 int32_t SkMulShift(int32_t a, int32_t b, unsigned shift) { 87 int sign = SkExtractSign(a ^ b); 88 89 if (shift > 63) { 90 return sign; 91 } 92 93 a = SkAbs32(a); 94 b = SkAbs32(b); 95 96 uint32_t ah = a >> 16; 97 uint32_t al = a & 0xFFFF; 98 uint32_t bh = b >> 16; 99 uint32_t bl = b & 0xFFFF; 100 101 uint32_t A = ah * bh; 102 uint32_t B = ah * bl + al * bh; 103 uint32_t C = al * bl; 104 105 /* [ A ] 106 [ B ] 107 [ C ] 108 */ 109 uint32_t lo = C + (B << 16); 110 int32_t hi = A + (B >> 16) + (lo < C); 111 112 if (sign < 0) { 113 hi = -hi - Sk32ToBool(lo); 114 lo = 0 - lo; 115 } 116 117 if (shift == 0) { 118 #ifdef SK_DEBUGx 119 SkASSERT(((int32_t)lo >> 31) == hi); 120 #endif 121 return lo; 122 } else if (shift >= 32) { 123 return hi >> (shift - 32); 124 } else { 125 #ifdef SK_DEBUGx 126 int32_t tmp = hi >> shift; 127 SkASSERT(tmp == 0 || tmp == -1); 128 #endif 129 // we want (hi << (32 - shift)) | (lo >> shift) but rounded 130 int roundBit = (lo >> (shift - 1)) & 1; 131 return ((hi << (32 - shift)) | (lo >> shift)) + roundBit; 132 } 133 } 134 135 SkFixed SkFixedMul_portable(SkFixed a, SkFixed b) { 136 #if 0 137 Sk64 tmp; 138 139 tmp.setMul(a, b); 140 tmp.shiftRight(16); 141 return tmp.fLo; 142 #elif defined(SkLONGLONG) 143 return static_cast<SkFixed>((SkLONGLONG)a * b >> 16); 144 #else 145 int sa = SkExtractSign(a); 146 int sb = SkExtractSign(b); 147 // now make them positive 148 a = SkApplySign(a, sa); 149 b = SkApplySign(b, sb); 150 151 uint32_t ah = a >> 16; 152 uint32_t al = a & 0xFFFF; 153 uint32_t bh = b >> 16; 154 uint32_t bl = b & 0xFFFF; 155 156 uint32_t R = ah * b + al * bh + (al * bl >> 16); 157 158 return SkApplySign(R, sa ^ sb); 159 #endif 160 } 161 162 SkFract SkFractMul_portable(SkFract a, SkFract b) { 163 #if 0 164 Sk64 tmp; 165 tmp.setMul(a, b); 166 return tmp.getFract(); 167 #elif defined(SkLONGLONG) 168 return static_cast<SkFract>((SkLONGLONG)a * b >> 30); 169 #else 170 int sa = SkExtractSign(a); 171 int sb = SkExtractSign(b); 172 // now make them positive 173 a = SkApplySign(a, sa); 174 b = SkApplySign(b, sb); 175 176 uint32_t ah = a >> 16; 177 uint32_t al = a & 0xFFFF; 178 uint32_t bh = b >> 16; 179 uint32_t bl = b & 0xFFFF; 180 181 uint32_t A = ah * bh; 182 uint32_t B = ah * bl + al * bh; 183 uint32_t C = al * bl; 184 185 /* [ A ] 186 [ B ] 187 [ C ] 188 */ 189 uint32_t Lo = C + (B << 16); 190 uint32_t Hi = A + (B >>16) + (Lo < C); 191 192 SkASSERT((Hi >> 29) == 0); // else overflow 193 194 int32_t R = (Hi << 2) + (Lo >> 30); 195 196 return SkApplySign(R, sa ^ sb); 197 #endif 198 } 199 200 int SkFixedMulCommon(SkFixed a, int b, int bias) { 201 // this function only works if b is 16bits 202 SkASSERT(b == (int16_t)b); 203 SkASSERT(b >= 0); 204 205 int sa = SkExtractSign(a); 206 a = SkApplySign(a, sa); 207 uint32_t ah = a >> 16; 208 uint32_t al = a & 0xFFFF; 209 uint32_t R = ah * b + ((al * b + bias) >> 16); 210 return SkApplySign(R, sa); 211 } 212 213 #ifdef SK_DEBUGx 214 #define TEST_FASTINVERT 215 #endif 216 217 SkFixed SkFixedFastInvert(SkFixed x) { 218 /* Adapted (stolen) from gglRecip() 219 */ 220 221 if (x == SK_Fixed1) { 222 return SK_Fixed1; 223 } 224 225 int sign = SkExtractSign(x); 226 uint32_t a = SkApplySign(x, sign); 227 228 if (a <= 2) { 229 return SkApplySign(SK_MaxS32, sign); 230 } 231 232 #ifdef TEST_FASTINVERT 233 SkFixed orig = a; 234 uint32_t slow = SkFixedDiv(SK_Fixed1, a); 235 #endif 236 237 // normalize a 238 int lz = SkCLZ(a); 239 a = a << lz >> 16; 240 241 // compute 1/a approximation (0.5 <= a < 1.0) 242 uint32_t r = 0x17400 - a; // (2.90625 (~2.914) - 2*a) >> 1 243 244 // Newton-Raphson iteration: 245 // x = r*(2 - a*r) = ((r/2)*(1 - a*r/2))*4 246 r = ( (0x10000 - ((a*r)>>16)) * r ) >> 15; 247 r = ( (0x10000 - ((a*r)>>16)) * r ) >> (30 - lz); 248 249 #ifdef TEST_FASTINVERT 250 SkDebugf("SkFixedFastInvert(%x %g) = %x %g Slow[%x %g]\n", 251 orig, orig/65536., 252 r, r/65536., 253 slow, slow/65536.); 254 #endif 255 256 return SkApplySign(r, sign); 257 } 258 259 /////////////////////////////////////////////////////////////////////////////// 260 261 #define DIVBITS_ITER(n) \ 262 case n: \ 263 if ((numer = (numer << 1) - denom) >= 0) \ 264 result |= 1 << (n - 1); else numer += denom 265 266 int32_t SkDivBits(int32_t numer, int32_t denom, int shift_bias) { 267 SkASSERT(denom != 0); 268 if (numer == 0) { 269 return 0; 270 } 271 272 // make numer and denom positive, and sign hold the resulting sign 273 int32_t sign = SkExtractSign(numer ^ denom); 274 numer = SkAbs32(numer); 275 denom = SkAbs32(denom); 276 277 int nbits = SkCLZ(numer) - 1; 278 int dbits = SkCLZ(denom) - 1; 279 int bits = shift_bias - nbits + dbits; 280 281 if (bits < 0) { // answer will underflow 282 return 0; 283 } 284 if (bits > 31) { // answer will overflow 285 return SkApplySign(SK_MaxS32, sign); 286 } 287 288 denom <<= dbits; 289 numer <<= nbits; 290 291 SkFixed result = 0; 292 293 // do the first one 294 if ((numer -= denom) >= 0) { 295 result = 1; 296 } else { 297 numer += denom; 298 } 299 300 // Now fall into our switch statement if there are more bits to compute 301 if (bits > 0) { 302 // make room for the rest of the answer bits 303 result <<= bits; 304 switch (bits) { 305 DIVBITS_ITER(31); DIVBITS_ITER(30); DIVBITS_ITER(29); 306 DIVBITS_ITER(28); DIVBITS_ITER(27); DIVBITS_ITER(26); 307 DIVBITS_ITER(25); DIVBITS_ITER(24); DIVBITS_ITER(23); 308 DIVBITS_ITER(22); DIVBITS_ITER(21); DIVBITS_ITER(20); 309 DIVBITS_ITER(19); DIVBITS_ITER(18); DIVBITS_ITER(17); 310 DIVBITS_ITER(16); DIVBITS_ITER(15); DIVBITS_ITER(14); 311 DIVBITS_ITER(13); DIVBITS_ITER(12); DIVBITS_ITER(11); 312 DIVBITS_ITER(10); DIVBITS_ITER( 9); DIVBITS_ITER( 8); 313 DIVBITS_ITER( 7); DIVBITS_ITER( 6); DIVBITS_ITER( 5); 314 DIVBITS_ITER( 4); DIVBITS_ITER( 3); DIVBITS_ITER( 2); 315 // we merge these last two together, makes GCC make better ARM 316 default: 317 DIVBITS_ITER( 1); 318 } 319 } 320 321 if (result < 0) { 322 result = SK_MaxS32; 323 } 324 return SkApplySign(result, sign); 325 } 326 327 /* mod(float numer, float denom) seems to always return the sign 328 of the numer, so that's what we do too 329 */ 330 SkFixed SkFixedMod(SkFixed numer, SkFixed denom) { 331 int sn = SkExtractSign(numer); 332 int sd = SkExtractSign(denom); 333 334 numer = SkApplySign(numer, sn); 335 denom = SkApplySign(denom, sd); 336 337 if (numer < denom) { 338 return SkApplySign(numer, sn); 339 } else if (numer == denom) { 340 return 0; 341 } else { 342 SkFixed div = SkFixedDiv(numer, denom); 343 return SkApplySign(SkFixedMul(denom, div & 0xFFFF), sn); 344 } 345 } 346 347 /* www.worldserver.com/turk/computergraphics/FixedSqrt.pdf 348 */ 349 int32_t SkSqrtBits(int32_t x, int count) { 350 SkASSERT(x >= 0 && count > 0 && (unsigned)count <= 30); 351 352 uint32_t root = 0; 353 uint32_t remHi = 0; 354 uint32_t remLo = x; 355 356 do { 357 root <<= 1; 358 359 remHi = (remHi<<2) | (remLo>>30); 360 remLo <<= 2; 361 362 uint32_t testDiv = (root << 1) + 1; 363 if (remHi >= testDiv) { 364 remHi -= testDiv; 365 root++; 366 } 367 } while (--count >= 0); 368 369 return root; 370 } 371 372 int32_t SkCubeRootBits(int32_t value, int bits) { 373 SkASSERT(bits > 0); 374 375 int sign = SkExtractSign(value); 376 value = SkApplySign(value, sign); 377 378 uint32_t root = 0; 379 uint32_t curr = (uint32_t)value >> 30; 380 value <<= 2; 381 382 do { 383 root <<= 1; 384 uint32_t guess = root * root + root; 385 guess = (guess << 1) + guess; // guess *= 3 386 if (guess < curr) { 387 curr -= guess + 1; 388 root |= 1; 389 } 390 curr = (curr << 3) | ((uint32_t)value >> 29); 391 value <<= 3; 392 } while (--bits); 393 394 return SkApplySign(root, sign); 395 } 396 397 SkFixed SkFixedMean(SkFixed a, SkFixed b) { 398 Sk64 tmp; 399 400 tmp.setMul(a, b); 401 return tmp.getSqrt(); 402 } 403 404 /////////////////////////////////////////////////////////////////////////////// 405 406 #ifdef SK_SCALAR_IS_FLOAT 407 float SkScalarSinCos(float radians, float* cosValue) { 408 float sinValue = sk_float_sin(radians); 409 410 if (cosValue) { 411 *cosValue = sk_float_cos(radians); 412 if (SkScalarNearlyZero(*cosValue)) { 413 *cosValue = 0; 414 } 415 } 416 417 if (SkScalarNearlyZero(sinValue)) { 418 sinValue = 0; 419 } 420 return sinValue; 421 } 422 #endif 423 424 #define INTERP_SINTABLE 425 #define BUILD_TABLE_AT_RUNTIMEx 426 427 #define kTableSize 256 428 429 #ifdef BUILD_TABLE_AT_RUNTIME 430 static uint16_t gSkSinTable[kTableSize]; 431 432 static void build_sintable(uint16_t table[]) { 433 for (int i = 0; i < kTableSize; i++) { 434 double rad = i * 3.141592653589793 / (2*kTableSize); 435 double val = sin(rad); 436 int ival = (int)(val * SK_Fixed1); 437 table[i] = SkToU16(ival); 438 } 439 } 440 #else 441 #include "SkSinTable.h" 442 #endif 443 444 #define SK_Fract1024SizeOver2PI 0x28BE60 /* floatToFract(1024 / 2PI) */ 445 446 #ifdef INTERP_SINTABLE 447 static SkFixed interp_table(const uint16_t table[], int index, int partial255) { 448 SkASSERT((unsigned)index < kTableSize); 449 SkASSERT((unsigned)partial255 <= 255); 450 451 SkFixed lower = table[index]; 452 SkFixed upper = (index == kTableSize - 1) ? SK_Fixed1 : table[index + 1]; 453 454 SkASSERT(lower < upper); 455 SkASSERT(lower >= 0); 456 SkASSERT(upper <= SK_Fixed1); 457 458 partial255 += (partial255 >> 7); 459 return lower + ((upper - lower) * partial255 >> 8); 460 } 461 #endif 462 463 SkFixed SkFixedSinCos(SkFixed radians, SkFixed* cosValuePtr) { 464 SkASSERT(SK_ARRAY_COUNT(gSkSinTable) == kTableSize); 465 466 #ifdef BUILD_TABLE_AT_RUNTIME 467 static bool gFirstTime = true; 468 if (gFirstTime) { 469 build_sintable(gSinTable); 470 gFirstTime = false; 471 } 472 #endif 473 474 // make radians positive 475 SkFixed sinValue, cosValue; 476 int32_t cosSign = 0; 477 int32_t sinSign = SkExtractSign(radians); 478 radians = SkApplySign(radians, sinSign); 479 // scale it to 0...1023 ... 480 481 #ifdef INTERP_SINTABLE 482 radians = SkMulDiv(radians, 2 * kTableSize * 256, SK_FixedPI); 483 int findex = radians & (kTableSize * 256 - 1); 484 int index = findex >> 8; 485 int partial = findex & 255; 486 sinValue = interp_table(gSkSinTable, index, partial); 487 488 findex = kTableSize * 256 - findex - 1; 489 index = findex >> 8; 490 partial = findex & 255; 491 cosValue = interp_table(gSkSinTable, index, partial); 492 493 int quad = ((unsigned)radians / (kTableSize * 256)) & 3; 494 #else 495 radians = SkMulDiv(radians, 2 * kTableSize, SK_FixedPI); 496 int index = radians & (kTableSize - 1); 497 498 if (index == 0) { 499 sinValue = 0; 500 cosValue = SK_Fixed1; 501 } else { 502 sinValue = gSkSinTable[index]; 503 cosValue = gSkSinTable[kTableSize - index]; 504 } 505 int quad = ((unsigned)radians / kTableSize) & 3; 506 #endif 507 508 if (quad & 1) { 509 SkTSwap<SkFixed>(sinValue, cosValue); 510 } 511 if (quad & 2) { 512 sinSign = ~sinSign; 513 } 514 if (((quad - 1) & 2) == 0) { 515 cosSign = ~cosSign; 516 } 517 518 // restore the sign for negative angles 519 sinValue = SkApplySign(sinValue, sinSign); 520 cosValue = SkApplySign(cosValue, cosSign); 521 522 #ifdef SK_DEBUG 523 if (1) { 524 SkFixed sin2 = SkFixedMul(sinValue, sinValue); 525 SkFixed cos2 = SkFixedMul(cosValue, cosValue); 526 int diff = cos2 + sin2 - SK_Fixed1; 527 SkASSERT(SkAbs32(diff) <= 7); 528 } 529 #endif 530 531 if (cosValuePtr) { 532 *cosValuePtr = cosValue; 533 } 534 return sinValue; 535 } 536 537 /////////////////////////////////////////////////////////////////////////////// 538 539 SkFixed SkFixedTan(SkFixed radians) { return SkCordicTan(radians); } 540 SkFixed SkFixedASin(SkFixed x) { return SkCordicASin(x); } 541 SkFixed SkFixedACos(SkFixed x) { return SkCordicACos(x); } 542 SkFixed SkFixedATan2(SkFixed y, SkFixed x) { return SkCordicATan2(y, x); } 543 SkFixed SkFixedExp(SkFixed x) { return SkCordicExp(x); } 544 SkFixed SkFixedLog(SkFixed x) { return SkCordicLog(x); } 545 546
