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| 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 (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 (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 /////////////////////////////////////////////////////////////////////////////// | |
| 547 /////////////////////////////////////////////////////////////////////////////// | |
| 548 | |
| 549 #ifdef SK_DEBUG | |
| 550 | |
| 551 #include "SkRandom.h" | |
| 552 | |
| 553 #ifdef SkLONGLONG | |
| 554 static int symmetric_fixmul(int a, int b) { | |
| 555 int sa = SkExtractSign(a); | |
| 556 int sb = SkExtractSign(b); | |
| 557 | |
| 558 a = SkApplySign(a, sa); | |
| 559 b = SkApplySign(b, sb); | |
| 560 | |
| 561 #if 1 | |
| 562 int c = (int)(((SkLONGLONG)a * b) >> 16); | |
| 563 | |
| 564 return SkApplySign(c, sa ^ sb); | |
| 565 #else | |
| 566 SkLONGLONG ab = (SkLONGLONG)a * b; | |
| 567 if (sa ^ sb) { | |
| 568 ab = -ab; | |
| 569 } | |
| 570 return ab >> 16; | |
| 571 #endif | |
| 572 } | |
| 573 #endif | |
| 574 | |
| 575 #include "SkPoint.h" | |
| 576 | |
| 577 #ifdef SK_SUPPORT_UNITTEST | |
| 578 static void check_length(const SkPoint& p, SkScalar targetLen) { | |
| 579 float x = SkScalarToFloat(p.fX); | |
| 580 float y = SkScalarToFloat(p.fY); | |
| 581 float len = sk_float_sqrt(x*x + y*y); | |
| 582 | |
| 583 len /= SkScalarToFloat(targetLen); | |
| 584 | |
| 585 SkASSERT(len > 0.999f && len < 1.001f); | |
| 586 } | |
| 587 #endif | |
| 588 | |
| 589 #ifdef SK_CAN_USE_FLOAT | |
| 590 | |
| 591 static float nextFloat(SkRandom& rand) { | |
| 592 SkFloatIntUnion data; | |
| 593 data.fSignBitInt = rand.nextU(); | |
| 594 return data.fFloat; | |
| 595 } | |
| 596 | |
| 597 /* returns true if a == b as resulting from (int)x. Since it is undefined | |
| 598 what to do if the float exceeds 2^32-1, we check for that explicitly. | |
| 599 */ | |
| 600 static bool equal_float_native_skia(float x, uint32_t ni, uint32_t si) { | |
| 601 if (!(x == x)) { // NAN | |
| 602 return si == SK_MaxS32 || si == SK_MinS32; | |
| 603 } | |
| 604 // for out of range, C is undefined, but skia always should return NaN32 | |
| 605 if (x > SK_MaxS32) { | |
| 606 return si == SK_MaxS32; | |
| 607 } | |
| 608 if (x < -SK_MaxS32) { | |
| 609 return si == SK_MinS32; | |
| 610 } | |
| 611 return si == ni; | |
| 612 } | |
| 613 | |
| 614 static void assert_float_equal(const char op[], float x, uint32_t ni, | |
| 615 uint32_t si) { | |
| 616 if (!equal_float_native_skia(x, ni, si)) { | |
| 617 SkDebugf("-- %s float %g bits %x native %x skia %x\n", op, x, ni, si); | |
| 618 SkASSERT(!"oops"); | |
| 619 } | |
| 620 } | |
| 621 | |
| 622 static void test_float_cast(float x) { | |
| 623 int ix = (int)x; | |
| 624 int iix = SkFloatToIntCast(x); | |
| 625 assert_float_equal("cast", x, ix, iix); | |
| 626 } | |
| 627 | |
| 628 static void test_float_floor(float x) { | |
| 629 int ix = (int)floor(x); | |
| 630 int iix = SkFloatToIntFloor(x); | |
| 631 assert_float_equal("floor", x, ix, iix); | |
| 632 } | |
| 633 | |
| 634 static void test_float_round(float x) { | |
| 635 double xx = x + 0.5; // need intermediate double to avoid temp loss | |
| 636 int ix = (int)floor(xx); | |
| 637 int iix = SkFloatToIntRound(x); | |
| 638 assert_float_equal("round", x, ix, iix); | |
| 639 } | |
| 640 | |
| 641 static void test_float_ceil(float x) { | |
| 642 int ix = (int)ceil(x); | |
| 643 int iix = SkFloatToIntCeil(x); | |
| 644 assert_float_equal("ceil", x, ix, iix); | |
| 645 } | |
| 646 | |
| 647 static void test_float_conversions(float x) { | |
| 648 test_float_cast(x); | |
| 649 test_float_floor(x); | |
| 650 test_float_round(x); | |
| 651 test_float_ceil(x); | |
| 652 } | |
| 653 | |
| 654 static void test_int2float(int ival) { | |
| 655 float x0 = (float)ival; | |
| 656 float x1 = SkIntToFloatCast(ival); | |
| 657 float x2 = SkIntToFloatCast_NoOverflowCheck(ival); | |
| 658 SkASSERT(x0 == x1); | |
| 659 SkASSERT(x0 == x2); | |
| 660 } | |
| 661 | |
| 662 static void unittest_fastfloat() { | |
| 663 SkRandom rand; | |
| 664 size_t i; | |
| 665 | |
| 666 static const float gFloats[] = { | |
| 667 0.f, 1.f, 0.5f, 0.499999f, 0.5000001f, 1.f/3, | |
| 668 0.000000001f, 1000000000.f, // doesn't overflow | |
| 669 0.0000000001f, 10000000000.f // does overflow | |
| 670 }; | |
| 671 for (i = 0; i < SK_ARRAY_COUNT(gFloats); i++) { | |
| 672 // SkDebugf("---- test floats %g %d\n", gFloats[i], (int)gFloats[i]); | |
| 673 test_float_conversions(gFloats[i]); | |
| 674 test_float_conversions(-gFloats[i]); | |
| 675 } | |
| 676 | |
| 677 for (int outer = 0; outer < 100; outer++) { | |
| 678 rand.setSeed(outer); | |
| 679 for (i = 0; i < 100000; i++) { | |
| 680 float x = nextFloat(rand); | |
| 681 test_float_conversions(x); | |
| 682 } | |
| 683 | |
| 684 test_int2float(0); | |
| 685 test_int2float(1); | |
| 686 test_int2float(-1); | |
| 687 for (i = 0; i < 100000; i++) { | |
| 688 // for now only test ints that are 24bits or less, since we don't | |
| 689 // round (down) large ints the same as IEEE... | |
| 690 int ival = rand.nextU() & 0xFFFFFF; | |
| 691 test_int2float(ival); | |
| 692 test_int2float(-ival); | |
| 693 } | |
| 694 } | |
| 695 } | |
| 696 | |
| 697 #endif | |
| 698 | |
| 699 static void test_muldiv255() { | |
| 700 for (int a = 0; a <= 255; a++) { | |
| 701 for (int b = 0; b <= 255; b++) { | |
| 702 int ab = a * b; | |
| 703 float s = ab / 255.0f; | |
| 704 int round = (int)floorf(s + 0.5f); | |
| 705 int trunc = (int)floorf(s); | |
| 706 | |
| 707 int iround = SkMulDiv255Round(a, b); | |
| 708 int itrunc = SkMulDiv255Trunc(a, b); | |
| 709 | |
| 710 SkASSERT(iround == round); | |
| 711 SkASSERT(itrunc == trunc); | |
| 712 | |
| 713 SkASSERT(itrunc <= iround); | |
| 714 SkASSERT(iround <= a); | |
| 715 SkASSERT(iround <= b); | |
| 716 } | |
| 717 } | |
| 718 } | |
| 719 | |
| 720 void SkMath::UnitTest() { | |
| 721 #ifdef SK_SUPPORT_UNITTEST | |
| 722 int i; | |
| 723 int32_t x; | |
| 724 SkRandom rand; | |
| 725 | |
| 726 SkToS8(127); SkToS8(-128); SkToU8(255); | |
| 727 SkToS16(32767); SkToS16(-32768); SkToU16(65535); | |
| 728 SkToS32(2*1024*1024); SkToS32(-2*1024*1024); SkToU32(4*1024*1024); | |
| 729 | |
| 730 SkCordic_UnitTest(); | |
| 731 | |
| 732 // these should assert | |
| 733 #if 0 | |
| 734 SkToS8(128); | |
| 735 SkToS8(-129); | |
| 736 SkToU8(256); | |
| 737 SkToU8(-5); | |
| 738 | |
| 739 SkToS16(32768); | |
| 740 SkToS16(-32769); | |
| 741 SkToU16(65536); | |
| 742 SkToU16(-5); | |
| 743 | |
| 744 if (sizeof(size_t) > 4) { | |
| 745 SkToS32(4*1024*1024); | |
| 746 SkToS32(-4*1024*1024); | |
| 747 SkToU32(5*1024*1024); | |
| 748 SkToU32(-5); | |
| 749 } | |
| 750 #endif | |
| 751 | |
| 752 test_muldiv255(); | |
| 753 | |
| 754 #ifdef SK_DEBUG | |
| 755 { | |
| 756 SkScalar x = SK_ScalarNaN; | |
| 757 SkASSERT(SkScalarIsNaN(x)); | |
| 758 } | |
| 759 #endif | |
| 760 | |
| 761 for (i = 1; i <= 10; i++) { | |
| 762 x = SkCubeRootBits(i*i*i, 11); | |
| 763 SkASSERT(x == i); | |
| 764 } | |
| 765 | |
| 766 x = SkFixedSqrt(SK_Fixed1); | |
| 767 SkASSERT(x == SK_Fixed1); | |
| 768 x = SkFixedSqrt(SK_Fixed1/4); | |
| 769 SkASSERT(x == SK_Fixed1/2); | |
| 770 x = SkFixedSqrt(SK_Fixed1*4); | |
| 771 SkASSERT(x == SK_Fixed1*2); | |
| 772 | |
| 773 x = SkFractSqrt(SK_Fract1); | |
| 774 SkASSERT(x == SK_Fract1); | |
| 775 x = SkFractSqrt(SK_Fract1/4); | |
| 776 SkASSERT(x == SK_Fract1/2); | |
| 777 x = SkFractSqrt(SK_Fract1/16); | |
| 778 SkASSERT(x == SK_Fract1/4); | |
| 779 | |
| 780 for (i = 1; i < 100; i++) { | |
| 781 x = SkFixedSqrt(SK_Fixed1 * i * i); | |
| 782 SkASSERT(x == SK_Fixed1 * i); | |
| 783 } | |
| 784 | |
| 785 for (i = 0; i < 1000; i++) { | |
| 786 int value = rand.nextS16(); | |
| 787 int max = rand.nextU16(); | |
| 788 | |
| 789 int clamp = SkClampMax(value, max); | |
| 790 int clamp2 = value < 0 ? 0 : (value > max ? max : value); | |
| 791 SkASSERT(clamp == clamp2); | |
| 792 } | |
| 793 | |
| 794 for (i = 0; i < 100000; i++) { | |
| 795 SkPoint p; | |
| 796 | |
| 797 p.setLength(rand.nextS(), rand.nextS(), SK_Scalar1); | |
| 798 check_length(p, SK_Scalar1); | |
| 799 p.setLength(rand.nextS() >> 13, rand.nextS() >> 13, SK_Scalar1); | |
| 800 check_length(p, SK_Scalar1); | |
| 801 } | |
| 802 | |
| 803 { | |
| 804 SkFixed result = SkFixedDiv(100, 100); | |
| 805 SkASSERT(result == SK_Fixed1); | |
| 806 result = SkFixedDiv(1, SK_Fixed1); | |
| 807 SkASSERT(result == 1); | |
| 808 } | |
| 809 | |
| 810 #ifdef SK_CAN_USE_FLOAT | |
| 811 unittest_fastfloat(); | |
| 812 #endif | |
| 813 | |
| 814 #ifdef SkLONGLONG | |
| 815 for (i = 0; i < 100000; i++) { | |
| 816 SkFixed numer = rand.nextS(); | |
| 817 SkFixed denom = rand.nextS(); | |
| 818 SkFixed result = SkFixedDiv(numer, denom); | |
| 819 SkLONGLONG check = ((SkLONGLONG)numer << 16) / denom; | |
| 820 | |
| 821 (void)SkCLZ(numer); | |
| 822 (void)SkCLZ(denom); | |
| 823 | |
| 824 SkASSERT(result != (SkFixed)SK_NaN32); | |
| 825 if (check > SK_MaxS32) { | |
| 826 check = SK_MaxS32; | |
| 827 } else if (check < -SK_MaxS32) { | |
| 828 check = SK_MinS32; | |
| 829 } | |
| 830 SkASSERT(result == (int32_t)check); | |
| 831 | |
| 832 result = SkFractDiv(numer, denom); | |
| 833 check = ((SkLONGLONG)numer << 30) / denom; | |
| 834 | |
| 835 SkASSERT(result != (SkFixed)SK_NaN32); | |
| 836 if (check > SK_MaxS32) { | |
| 837 check = SK_MaxS32; | |
| 838 } else if (check < -SK_MaxS32) { | |
| 839 check = SK_MinS32; | |
| 840 } | |
| 841 SkASSERT(result == (int32_t)check); | |
| 842 | |
| 843 // make them <= 2^24, so we don't overflow in fixmul | |
| 844 numer = numer << 8 >> 8; | |
| 845 denom = denom << 8 >> 8; | |
| 846 | |
| 847 result = SkFixedMul(numer, denom); | |
| 848 SkFixed r2 = symmetric_fixmul(numer, denom); | |
| 849 // SkASSERT(result == r2); | |
| 850 | |
| 851 result = SkFixedMul(numer, numer); | |
| 852 r2 = SkFixedSquare(numer); | |
| 853 SkASSERT(result == r2); | |
| 854 | |
| 855 #ifdef SK_CAN_USE_FLOAT | |
| 856 if (numer >= 0 && denom >= 0) { | |
| 857 SkFixed mean = SkFixedMean(numer, denom); | |
| 858 float fm = sk_float_sqrt(sk_float_abs(SkFixedToFloat(numer) * SkFixe
dToFloat(denom))); | |
| 859 SkFixed mean2 = SkFloatToFixed(fm); | |
| 860 int diff = SkAbs32(mean - mean2); | |
| 861 SkASSERT(diff <= 1); | |
| 862 } | |
| 863 | |
| 864 { | |
| 865 SkFixed mod = SkFixedMod(numer, denom); | |
| 866 float n = SkFixedToFloat(numer); | |
| 867 float d = SkFixedToFloat(denom); | |
| 868 float m = sk_float_mod(n, d); | |
| 869 #if 0 | |
| 870 SkDebugf("%g mod %g = %g [%g]\n", | |
| 871 SkFixedToFloat(numer), SkFixedToFloat(denom), | |
| 872 SkFixedToFloat(mod), m); | |
| 873 #endif | |
| 874 SkASSERT(mod == 0 || (mod < 0) == (m < 0)); // ensure the same sign | |
| 875 int diff = SkAbs32(mod - SkFloatToFixed(m)); | |
| 876 SkASSERT((diff >> 7) == 0); | |
| 877 } | |
| 878 #endif | |
| 879 } | |
| 880 #endif | |
| 881 | |
| 882 #ifdef SK_CAN_USE_FLOAT | |
| 883 for (i = 0; i < 100000; i++) { | |
| 884 SkFract x = rand.nextU() >> 1; | |
| 885 double xx = (double)x / SK_Fract1; | |
| 886 SkFract xr = SkFractSqrt(x); | |
| 887 SkFract check = SkFloatToFract(sqrt(xx)); | |
| 888 SkASSERT(xr == check || xr == check-1 || xr == check+1); | |
| 889 | |
| 890 xr = SkFixedSqrt(x); | |
| 891 xx = (double)x / SK_Fixed1; | |
| 892 check = SkFloatToFixed(sqrt(xx)); | |
| 893 SkASSERT(xr == check || xr == check-1); | |
| 894 | |
| 895 xr = SkSqrt32(x); | |
| 896 xx = (double)x; | |
| 897 check = (int32_t)sqrt(xx); | |
| 898 SkASSERT(xr == check || xr == check-1); | |
| 899 } | |
| 900 #endif | |
| 901 | |
| 902 #if !defined(SK_SCALAR_IS_FLOAT) && defined(SK_CAN_USE_FLOAT) | |
| 903 { | |
| 904 SkFixed s, c; | |
| 905 s = SkFixedSinCos(0, &c); | |
| 906 SkASSERT(s == 0); | |
| 907 SkASSERT(c == SK_Fixed1); | |
| 908 } | |
| 909 | |
| 910 int maxDiff = 0; | |
| 911 for (i = 0; i < 10000; i++) { | |
| 912 SkFixed rads = rand.nextS() >> 10; | |
| 913 double frads = SkFixedToFloat(rads); | |
| 914 | |
| 915 SkFixed s, c; | |
| 916 s = SkScalarSinCos(rads, &c); | |
| 917 | |
| 918 double fs = sin(frads); | |
| 919 double fc = cos(frads); | |
| 920 | |
| 921 SkFixed is = SkFloatToFixed(fs); | |
| 922 SkFixed ic = SkFloatToFixed(fc); | |
| 923 | |
| 924 maxDiff = SkMax32(maxDiff, SkAbs32(is - s)); | |
| 925 maxDiff = SkMax32(maxDiff, SkAbs32(ic - c)); | |
| 926 } | |
| 927 SkDebugf("SinCos: maximum error = %d\n", maxDiff); | |
| 928 #endif | |
| 929 #endif | |
| 930 } | |
| 931 | |
| 932 #endif | |
| OLD | NEW |
|---|
Chromium Code Reviews
Issue 113827:
Remove the remainder of the skia source code from the Chromium repo.... (Closed)
Base URL: svn://chrome-svn/chrome/trunk/src/