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| 1 /* | 1 /* |
| 2 * Copyright 2008 The Android Open Source Project | 2 * Copyright 2008 The Android Open Source Project |
| 3 * | 3 * |
| 4 * Use of this source code is governed by a BSD-style license that can be | 4 * Use of this source code is governed by a BSD-style license that can be |
| 5 * found in the LICENSE file. | 5 * found in the LICENSE file. |
| 6 */ | 6 */ |
| 7 | 7 |
| 8 #include "SkMathPriv.h" | 8 #include "SkMathPriv.h" |
| 9 #include "SkCordic.h" | |
| 10 #include "SkFloatBits.h" | 9 #include "SkFloatBits.h" |
| 11 #include "SkFloatingPoint.h" | 10 #include "SkFloatingPoint.h" |
| 12 #include "Sk64.h" | 11 #include "Sk64.h" |
| 13 #include "SkScalar.h" | 12 #include "SkScalar.h" |
| 14 | 13 |
| 15 const uint32_t gIEEENotANumber = 0x7FFFFFFF; | 14 const uint32_t gIEEENotANumber = 0x7FFFFFFF; |
| 16 const uint32_t gIEEEInfinity = 0x7F800000; | 15 const uint32_t gIEEEInfinity = 0x7F800000; |
| 17 const uint32_t gIEEENegativeInfinity = 0xFF800000; | 16 const uint32_t gIEEENegativeInfinity = 0xFF800000; |
| 18 | 17 |
| 19 #define sub_shift(zeros, x, n) \ | 18 #define sub_shift(zeros, x, n) \ |
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| 47 | 46 |
| 48 int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom) { | 47 int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom) { |
| 49 SkASSERT(denom); | 48 SkASSERT(denom); |
| 50 | 49 |
| 51 Sk64 tmp; | 50 Sk64 tmp; |
| 52 tmp.setMul(numer1, numer2); | 51 tmp.setMul(numer1, numer2); |
| 53 tmp.div(denom, Sk64::kTrunc_DivOption); | 52 tmp.div(denom, Sk64::kTrunc_DivOption); |
| 54 return tmp.get32(); | 53 return tmp.get32(); |
| 55 } | 54 } |
| 56 | 55 |
| 57 int32_t SkMulShift(int32_t a, int32_t b, unsigned shift) { | |
| 58 int sign = SkExtractSign(a ^ b); | |
| 59 | |
| 60 if (shift > 63) { | |
| 61 return sign; | |
| 62 } | |
| 63 | |
| 64 a = SkAbs32(a); | |
| 65 b = SkAbs32(b); | |
| 66 | |
| 67 uint32_t ah = a >> 16; | |
| 68 uint32_t al = a & 0xFFFF; | |
| 69 uint32_t bh = b >> 16; | |
| 70 uint32_t bl = b & 0xFFFF; | |
| 71 | |
| 72 uint32_t A = ah * bh; | |
| 73 uint32_t B = ah * bl + al * bh; | |
| 74 uint32_t C = al * bl; | |
| 75 | |
| 76 /* [ A ] | |
| 77 [ B ] | |
| 78 [ C ] | |
| 79 */ | |
| 80 uint32_t lo = C + (B << 16); | |
| 81 int32_t hi = A + (B >> 16) + (lo < C); | |
| 82 | |
| 83 if (sign < 0) { | |
| 84 hi = -hi - Sk32ToBool(lo); | |
| 85 lo = 0 - lo; | |
| 86 } | |
| 87 | |
| 88 if (shift == 0) { | |
| 89 #ifdef SK_DEBUGx | |
| 90 SkASSERT(((int32_t)lo >> 31) == hi); | |
| 91 #endif | |
| 92 return lo; | |
| 93 } else if (shift >= 32) { | |
| 94 return hi >> (shift - 32); | |
| 95 } else { | |
| 96 #ifdef SK_DEBUGx | |
| 97 int32_t tmp = hi >> shift; | |
| 98 SkASSERT(tmp == 0 || tmp == -1); | |
| 99 #endif | |
| 100 // we want (hi << (32 - shift)) | (lo >> shift) but rounded | |
| 101 int roundBit = (lo >> (shift - 1)) & 1; | |
| 102 return ((hi << (32 - shift)) | (lo >> shift)) + roundBit; | |
| 103 } | |
| 104 } | |
| 105 | |
| 106 SkFixed SkFixedMul_portable(SkFixed a, SkFixed b) { | 56 SkFixed SkFixedMul_portable(SkFixed a, SkFixed b) { |
| 107 #if 0 | 57 #if defined(SkLONGLONG) |
| 108 Sk64 tmp; | |
| 109 | |
| 110 tmp.setMul(a, b); | |
| 111 tmp.shiftRight(16); | |
| 112 return tmp.fLo; | |
| 113 #elif defined(SkLONGLONG) | |
| 114 return static_cast<SkFixed>((SkLONGLONG)a * b >> 16); | 58 return static_cast<SkFixed>((SkLONGLONG)a * b >> 16); |
| 115 #else | 59 #else |
| 116 int sa = SkExtractSign(a); | 60 int sa = SkExtractSign(a); |
| 117 int sb = SkExtractSign(b); | 61 int sb = SkExtractSign(b); |
| 118 // now make them positive | 62 // now make them positive |
| 119 a = SkApplySign(a, sa); | 63 a = SkApplySign(a, sa); |
| 120 b = SkApplySign(b, sb); | 64 b = SkApplySign(b, sb); |
| 121 | 65 |
| 122 uint32_t ah = a >> 16; | 66 uint32_t ah = a >> 16; |
| 123 uint32_t al = a & 0xFFFF; | 67 uint32_t al = a & 0xFFFF; |
| 124 uint32_t bh = b >> 16; | 68 uint32_t bh = b >> 16; |
| 125 uint32_t bl = b & 0xFFFF; | 69 uint32_t bl = b & 0xFFFF; |
| 126 | 70 |
| 127 uint32_t R = ah * b + al * bh + (al * bl >> 16); | 71 uint32_t R = ah * b + al * bh + (al * bl >> 16); |
| 128 | 72 |
| 129 return SkApplySign(R, sa ^ sb); | 73 return SkApplySign(R, sa ^ sb); |
| 130 #endif | 74 #endif |
| 131 } | 75 } |
| 132 | 76 |
| 133 SkFract SkFractMul_portable(SkFract a, SkFract b) { | |
| 134 #if 0 | |
| 135 Sk64 tmp; | |
| 136 tmp.setMul(a, b); | |
| 137 return tmp.getFract(); | |
| 138 #elif defined(SkLONGLONG) | |
| 139 return static_cast<SkFract>((SkLONGLONG)a * b >> 30); | |
| 140 #else | |
| 141 int sa = SkExtractSign(a); | |
| 142 int sb = SkExtractSign(b); | |
| 143 // now make them positive | |
| 144 a = SkApplySign(a, sa); | |
| 145 b = SkApplySign(b, sb); | |
| 146 | |
| 147 uint32_t ah = a >> 16; | |
| 148 uint32_t al = a & 0xFFFF; | |
| 149 uint32_t bh = b >> 16; | |
| 150 uint32_t bl = b & 0xFFFF; | |
| 151 | |
| 152 uint32_t A = ah * bh; | |
| 153 uint32_t B = ah * bl + al * bh; | |
| 154 uint32_t C = al * bl; | |
| 155 | |
| 156 /* [ A ] | |
| 157 [ B ] | |
| 158 [ C ] | |
| 159 */ | |
| 160 uint32_t Lo = C + (B << 16); | |
| 161 uint32_t Hi = A + (B >>16) + (Lo < C); | |
| 162 | |
| 163 SkASSERT((Hi >> 29) == 0); // else overflow | |
| 164 | |
| 165 int32_t R = (Hi << 2) + (Lo >> 30); | |
| 166 | |
| 167 return SkApplySign(R, sa ^ sb); | |
| 168 #endif | |
| 169 } | |
| 170 | |
| 171 int SkFixedMulCommon(SkFixed a, int b, int bias) { | |
| 172 // this function only works if b is 16bits | |
| 173 SkASSERT(b == (int16_t)b); | |
| 174 SkASSERT(b >= 0); | |
| 175 | |
| 176 int sa = SkExtractSign(a); | |
| 177 a = SkApplySign(a, sa); | |
| 178 uint32_t ah = a >> 16; | |
| 179 uint32_t al = a & 0xFFFF; | |
| 180 uint32_t R = ah * b + ((al * b + bias) >> 16); | |
| 181 return SkApplySign(R, sa); | |
| 182 } | |
| 183 | |
| 184 #ifdef SK_DEBUGx | |
| 185 #define TEST_FASTINVERT | |
| 186 #endif | |
| 187 | |
| 188 SkFixed SkFixedFastInvert(SkFixed x) { | |
| 189 /* Adapted (stolen) from gglRecip() | |
| 190 */ | |
| 191 | |
| 192 if (x == SK_Fixed1) { | |
| 193 return SK_Fixed1; | |
| 194 } | |
| 195 | |
| 196 int sign = SkExtractSign(x); | |
| 197 uint32_t a = SkApplySign(x, sign); | |
| 198 | |
| 199 if (a <= 2) { | |
| 200 return SkApplySign(SK_MaxS32, sign); | |
| 201 } | |
| 202 | |
| 203 #ifdef TEST_FASTINVERT | |
| 204 SkFixed orig = a; | |
| 205 uint32_t slow = SkFixedDiv(SK_Fixed1, a); | |
| 206 #endif | |
| 207 | |
| 208 // normalize a | |
| 209 int lz = SkCLZ(a); | |
| 210 a = a << lz >> 16; | |
| 211 | |
| 212 // compute 1/a approximation (0.5 <= a < 1.0) | |
| 213 uint32_t r = 0x17400 - a; // (2.90625 (~2.914) - 2*a) >> 1 | |
| 214 | |
| 215 // Newton-Raphson iteration: | |
| 216 // x = r*(2 - a*r) = ((r/2)*(1 - a*r/2))*4 | |
| 217 r = ( (0x10000 - ((a*r)>>16)) * r ) >> 15; | |
| 218 r = ( (0x10000 - ((a*r)>>16)) * r ) >> (30 - lz); | |
| 219 | |
| 220 #ifdef TEST_FASTINVERT | |
| 221 SkDebugf("SkFixedFastInvert(%x %g) = %x %g Slow[%x %g]\n", | |
| 222 orig, orig/65536., | |
| 223 r, r/65536., | |
| 224 slow, slow/65536.); | |
| 225 #endif | |
| 226 | |
| 227 return SkApplySign(r, sign); | |
| 228 } | |
| 229 | |
| 230 /////////////////////////////////////////////////////////////////////////////// | 77 /////////////////////////////////////////////////////////////////////////////// |
| 231 | 78 |
| 232 #define DIVBITS_ITER(n) \ | 79 #define DIVBITS_ITER(n) \ |
| 233 case n: \ | 80 case n: \ |
| 234 if ((numer = (numer << 1) - denom) >= 0) \ | 81 if ((numer = (numer << 1) - denom) >= 0) \ |
| 235 result |= 1 << (n - 1); else numer += denom | 82 result |= 1 << (n - 1); else numer += denom |
| 236 | 83 |
| 237 int32_t SkDivBits(int32_t numer, int32_t denom, int shift_bias) { | 84 int32_t SkDivBits(int32_t numer, int32_t denom, int shift_bias) { |
| 238 SkASSERT(denom != 0); | 85 SkASSERT(denom != 0); |
| 239 if (numer == 0) { | 86 if (numer == 0) { |
| (...skipping 48 matching lines...) Expand 10 before | Expand all | Expand 10 after Loading... |
| 288 DIVBITS_ITER( 1); | 135 DIVBITS_ITER( 1); |
| 289 } | 136 } |
| 290 } | 137 } |
| 291 | 138 |
| 292 if (result < 0) { | 139 if (result < 0) { |
| 293 result = SK_MaxS32; | 140 result = SK_MaxS32; |
| 294 } | 141 } |
| 295 return SkApplySign(result, sign); | 142 return SkApplySign(result, sign); |
| 296 } | 143 } |
| 297 | 144 |
| 298 /* mod(float numer, float denom) seems to always return the sign | |
| 299 of the numer, so that's what we do too | |
| 300 */ | |
| 301 SkFixed SkFixedMod(SkFixed numer, SkFixed denom) { | |
| 302 int sn = SkExtractSign(numer); | |
| 303 int sd = SkExtractSign(denom); | |
| 304 | |
| 305 numer = SkApplySign(numer, sn); | |
| 306 denom = SkApplySign(denom, sd); | |
| 307 | |
| 308 if (numer < denom) { | |
| 309 return SkApplySign(numer, sn); | |
| 310 } else if (numer == denom) { | |
| 311 return 0; | |
| 312 } else { | |
| 313 SkFixed div = SkFixedDiv(numer, denom); | |
| 314 return SkApplySign(SkFixedMul(denom, div & 0xFFFF), sn); | |
| 315 } | |
| 316 } | |
| 317 | |
| 318 /* www.worldserver.com/turk/computergraphics/FixedSqrt.pdf | 145 /* www.worldserver.com/turk/computergraphics/FixedSqrt.pdf |
| 319 */ | 146 */ |
| 320 int32_t SkSqrtBits(int32_t x, int count) { | 147 int32_t SkSqrtBits(int32_t x, int count) { |
| 321 SkASSERT(x >= 0 && count > 0 && (unsigned)count <= 30); | 148 SkASSERT(x >= 0 && count > 0 && (unsigned)count <= 30); |
| 322 | 149 |
| 323 uint32_t root = 0; | 150 uint32_t root = 0; |
| 324 uint32_t remHi = 0; | 151 uint32_t remHi = 0; |
| 325 uint32_t remLo = x; | 152 uint32_t remLo = x; |
| 326 | 153 |
| 327 do { | 154 do { |
| 328 root <<= 1; | 155 root <<= 1; |
| 329 | 156 |
| 330 remHi = (remHi<<2) | (remLo>>30); | 157 remHi = (remHi<<2) | (remLo>>30); |
| 331 remLo <<= 2; | 158 remLo <<= 2; |
| 332 | 159 |
| 333 uint32_t testDiv = (root << 1) + 1; | 160 uint32_t testDiv = (root << 1) + 1; |
| 334 if (remHi >= testDiv) { | 161 if (remHi >= testDiv) { |
| 335 remHi -= testDiv; | 162 remHi -= testDiv; |
| 336 root++; | 163 root++; |
| 337 } | 164 } |
| 338 } while (--count >= 0); | 165 } while (--count >= 0); |
| 339 | 166 |
| 340 return root; | 167 return root; |
| 341 } | 168 } |
| 342 | 169 |
| 343 int32_t SkCubeRootBits(int32_t value, int bits) { | |
| 344 SkASSERT(bits > 0); | |
| 345 | |
| 346 int sign = SkExtractSign(value); | |
| 347 value = SkApplySign(value, sign); | |
| 348 | |
| 349 uint32_t root = 0; | |
| 350 uint32_t curr = (uint32_t)value >> 30; | |
| 351 value <<= 2; | |
| 352 | |
| 353 do { | |
| 354 root <<= 1; | |
| 355 uint32_t guess = root * root + root; | |
| 356 guess = (guess << 1) + guess; // guess *= 3 | |
| 357 if (guess < curr) { | |
| 358 curr -= guess + 1; | |
| 359 root |= 1; | |
| 360 } | |
| 361 curr = (curr << 3) | ((uint32_t)value >> 29); | |
| 362 value <<= 3; | |
| 363 } while (--bits); | |
| 364 | |
| 365 return SkApplySign(root, sign); | |
| 366 } | |
| 367 | |
| 368 SkFixed SkFixedMean(SkFixed a, SkFixed b) { | |
| 369 Sk64 tmp; | |
| 370 | |
| 371 tmp.setMul(a, b); | |
| 372 return tmp.getSqrt(); | |
| 373 } | |
| 374 | |
| 375 /////////////////////////////////////////////////////////////////////////////// | 170 /////////////////////////////////////////////////////////////////////////////// |
| 376 | 171 |
| 377 float SkScalarSinCos(float radians, float* cosValue) { | 172 float SkScalarSinCos(float radians, float* cosValue) { |
| 378 float sinValue = sk_float_sin(radians); | 173 float sinValue = sk_float_sin(radians); |
| 379 | 174 |
| 380 if (cosValue) { | 175 if (cosValue) { |
| 381 *cosValue = sk_float_cos(radians); | 176 *cosValue = sk_float_cos(radians); |
| 382 if (SkScalarNearlyZero(*cosValue)) { | 177 if (SkScalarNearlyZero(*cosValue)) { |
| 383 *cosValue = 0; | 178 *cosValue = 0; |
| 384 } | 179 } |
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| 496 SkASSERT(SkAbs32(diff) <= 7); | 291 SkASSERT(SkAbs32(diff) <= 7); |
| 497 } | 292 } |
| 498 #endif | 293 #endif |
| 499 | 294 |
| 500 if (cosValuePtr) { | 295 if (cosValuePtr) { |
| 501 *cosValuePtr = cosValue; | 296 *cosValuePtr = cosValue; |
| 502 } | 297 } |
| 503 return sinValue; | 298 return sinValue; |
| 504 } | 299 } |
| 505 | 300 |
| 506 /////////////////////////////////////////////////////////////////////////////// | |
| 507 | |
| 508 SkFixed SkFixedTan(SkFixed radians) { return SkCordicTan(radians); } | |
| 509 SkFixed SkFixedASin(SkFixed x) { return SkCordicASin(x); } | |
| 510 SkFixed SkFixedACos(SkFixed x) { return SkCordicACos(x); } | |
| 511 SkFixed SkFixedATan2(SkFixed y, SkFixed x) { return SkCordicATan2(y, x); } | |
| 512 SkFixed SkFixedExp(SkFixed x) { return SkCordicExp(x); } | |
| 513 SkFixed SkFixedLog(SkFixed x) { return SkCordicLog(x); } | |
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