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| 1 // Copyright 2012 the V8 project authors. All rights reserved. |
| 2 // Redistribution and use in source and binary forms, with or without |
| 3 // modification, are permitted provided that the following conditions are |
| 4 // met: |
| 5 // |
| 6 // * Redistributions of source code must retain the above copyright |
| 7 // notice, this list of conditions and the following disclaimer. |
| 8 // * Redistributions in binary form must reproduce the above |
| 9 // copyright notice, this list of conditions and the following |
| 10 // disclaimer in the documentation and/or other materials provided |
| 11 // with the distribution. |
| 12 // * Neither the name of Google Inc. nor the names of its |
| 13 // contributors may be used to endorse or promote products derived |
| 14 // from this software without specific prior written permission. |
| 15 // |
| 16 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| 17 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| 18 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| 19 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
| 20 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| 21 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
| 22 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
| 23 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
| 24 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| 25 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
| 26 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| 27 |
| 28 #ifndef DOUBLE_CONVERSION_DOUBLE_H_ |
| 29 #define DOUBLE_CONVERSION_DOUBLE_H_ |
| 30 |
| 31 #include "diy-fp.h" |
| 32 |
| 33 namespace double_conversion { |
| 34 |
| 35 // We assume that doubles and uint64_t have the same endianness. |
| 36 static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); } |
| 37 static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); } |
| 38 static uint32_t float_to_uint32(float f) { return BitCast<uint32_t>(f); } |
| 39 static float uint32_to_float(uint32_t d32) { return BitCast<float>(d32); } |
| 40 |
| 41 // Helper functions for doubles. |
| 42 class Double { |
| 43 public: |
| 44 static const uint64_t kSignMask = UINT64_2PART_C(0x80000000, 00000000); |
| 45 static const uint64_t kExponentMask = UINT64_2PART_C(0x7FF00000, 00000000); |
| 46 static const uint64_t kSignificandMask = UINT64_2PART_C(0x000FFFFF, FFFFFFFF); |
| 47 static const uint64_t kHiddenBit = UINT64_2PART_C(0x00100000, 00000000); |
| 48 static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit. |
| 49 static const int kSignificandSize = 53; |
| 50 |
| 51 Double() : d64_(0) {} |
| 52 explicit Double(double d) : d64_(double_to_uint64(d)) {} |
| 53 explicit Double(uint64_t d64) : d64_(d64) {} |
| 54 explicit Double(DiyFp diy_fp) |
| 55 : d64_(DiyFpToUint64(diy_fp)) {} |
| 56 |
| 57 // The value encoded by this Double must be greater or equal to +0.0. |
| 58 // It must not be special (infinity, or NaN). |
| 59 DiyFp AsDiyFp() const { |
| 60 ASSERT(Sign() > 0); |
| 61 ASSERT(!IsSpecial()); |
| 62 return DiyFp(Significand(), Exponent()); |
| 63 } |
| 64 |
| 65 // The value encoded by this Double must be strictly greater than 0. |
| 66 DiyFp AsNormalizedDiyFp() const { |
| 67 ASSERT(value() > 0.0); |
| 68 uint64_t f = Significand(); |
| 69 int e = Exponent(); |
| 70 |
| 71 // The current double could be a denormal. |
| 72 while ((f & kHiddenBit) == 0) { |
| 73 f <<= 1; |
| 74 e--; |
| 75 } |
| 76 // Do the final shifts in one go. |
| 77 f <<= DiyFp::kSignificandSize - kSignificandSize; |
| 78 e -= DiyFp::kSignificandSize - kSignificandSize; |
| 79 return DiyFp(f, e); |
| 80 } |
| 81 |
| 82 // Returns the double's bit as uint64. |
| 83 uint64_t AsUint64() const { |
| 84 return d64_; |
| 85 } |
| 86 |
| 87 // Returns the next greater double. Returns +infinity on input +infinity. |
| 88 double NextDouble() const { |
| 89 if (d64_ == kInfinity) return Double(kInfinity).value(); |
| 90 if (Sign() < 0 && Significand() == 0) { |
| 91 // -0.0 |
| 92 return 0.0; |
| 93 } |
| 94 if (Sign() < 0) { |
| 95 return Double(d64_ - 1).value(); |
| 96 } else { |
| 97 return Double(d64_ + 1).value(); |
| 98 } |
| 99 } |
| 100 |
| 101 double PreviousDouble() const { |
| 102 if (d64_ == (kInfinity | kSignMask)) return -Double::Infinity(); |
| 103 if (Sign() < 0) { |
| 104 return Double(d64_ + 1).value(); |
| 105 } else { |
| 106 if (Significand() == 0) return -0.0; |
| 107 return Double(d64_ - 1).value(); |
| 108 } |
| 109 } |
| 110 |
| 111 int Exponent() const { |
| 112 if (IsDenormal()) return kDenormalExponent; |
| 113 |
| 114 uint64_t d64 = AsUint64(); |
| 115 int biased_e = |
| 116 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); |
| 117 return biased_e - kExponentBias; |
| 118 } |
| 119 |
| 120 uint64_t Significand() const { |
| 121 uint64_t d64 = AsUint64(); |
| 122 uint64_t significand = d64 & kSignificandMask; |
| 123 if (!IsDenormal()) { |
| 124 return significand + kHiddenBit; |
| 125 } else { |
| 126 return significand; |
| 127 } |
| 128 } |
| 129 |
| 130 // Returns true if the double is a denormal. |
| 131 bool IsDenormal() const { |
| 132 uint64_t d64 = AsUint64(); |
| 133 return (d64 & kExponentMask) == 0; |
| 134 } |
| 135 |
| 136 // We consider denormals not to be special. |
| 137 // Hence only Infinity and NaN are special. |
| 138 bool IsSpecial() const { |
| 139 uint64_t d64 = AsUint64(); |
| 140 return (d64 & kExponentMask) == kExponentMask; |
| 141 } |
| 142 |
| 143 bool IsNan() const { |
| 144 uint64_t d64 = AsUint64(); |
| 145 return ((d64 & kExponentMask) == kExponentMask) && |
| 146 ((d64 & kSignificandMask) != 0); |
| 147 } |
| 148 |
| 149 bool IsInfinite() const { |
| 150 uint64_t d64 = AsUint64(); |
| 151 return ((d64 & kExponentMask) == kExponentMask) && |
| 152 ((d64 & kSignificandMask) == 0); |
| 153 } |
| 154 |
| 155 int Sign() const { |
| 156 uint64_t d64 = AsUint64(); |
| 157 return (d64 & kSignMask) == 0? 1: -1; |
| 158 } |
| 159 |
| 160 // Precondition: the value encoded by this Double must be greater or equal |
| 161 // than +0.0. |
| 162 DiyFp UpperBoundary() const { |
| 163 ASSERT(Sign() > 0); |
| 164 return DiyFp(Significand() * 2 + 1, Exponent() - 1); |
| 165 } |
| 166 |
| 167 // Computes the two boundaries of this. |
| 168 // The bigger boundary (m_plus) is normalized. The lower boundary has the same |
| 169 // exponent as m_plus. |
| 170 // Precondition: the value encoded by this Double must be greater than 0. |
| 171 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { |
| 172 ASSERT(value() > 0.0); |
| 173 DiyFp v = this->AsDiyFp(); |
| 174 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); |
| 175 DiyFp m_minus; |
| 176 if (LowerBoundaryIsCloser()) { |
| 177 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); |
| 178 } else { |
| 179 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); |
| 180 } |
| 181 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); |
| 182 m_minus.set_e(m_plus.e()); |
| 183 *out_m_plus = m_plus; |
| 184 *out_m_minus = m_minus; |
| 185 } |
| 186 |
| 187 bool LowerBoundaryIsCloser() const { |
| 188 // The boundary is closer if the significand is of the form f == 2^p-1 then |
| 189 // the lower boundary is closer. |
| 190 // Think of v = 1000e10 and v- = 9999e9. |
| 191 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but |
| 192 // at a distance of 1e8. |
| 193 // The only exception is for the smallest normal: the largest denormal is |
| 194 // at the same distance as its successor. |
| 195 // Note: denormals have the same exponent as the smallest normals. |
| 196 bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0); |
| 197 return physical_significand_is_zero && (Exponent() != kDenormalExponent); |
| 198 } |
| 199 |
| 200 double value() const { return uint64_to_double(d64_); } |
| 201 |
| 202 // Returns the significand size for a given order of magnitude. |
| 203 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude. |
| 204 // This function returns the number of significant binary digits v will have |
| 205 // once it's encoded into a double. In almost all cases this is equal to |
| 206 // kSignificandSize. The only exceptions are denormals. They start with |
| 207 // leading zeroes and their effective significand-size is hence smaller. |
| 208 static int SignificandSizeForOrderOfMagnitude(int order) { |
| 209 if (order >= (kDenormalExponent + kSignificandSize)) { |
| 210 return kSignificandSize; |
| 211 } |
| 212 if (order <= kDenormalExponent) return 0; |
| 213 return order - kDenormalExponent; |
| 214 } |
| 215 |
| 216 static double Infinity() { |
| 217 return Double(kInfinity).value(); |
| 218 } |
| 219 |
| 220 static double NaN() { |
| 221 return Double(kNaN).value(); |
| 222 } |
| 223 |
| 224 private: |
| 225 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; |
| 226 static const int kDenormalExponent = -kExponentBias + 1; |
| 227 static const int kMaxExponent = 0x7FF - kExponentBias; |
| 228 static const uint64_t kInfinity = UINT64_2PART_C(0x7FF00000, 00000000); |
| 229 static const uint64_t kNaN = UINT64_2PART_C(0x7FF80000, 00000000); |
| 230 |
| 231 const uint64_t d64_; |
| 232 |
| 233 static uint64_t DiyFpToUint64(DiyFp diy_fp) { |
| 234 uint64_t significand = diy_fp.f(); |
| 235 int exponent = diy_fp.e(); |
| 236 while (significand > kHiddenBit + kSignificandMask) { |
| 237 significand >>= 1; |
| 238 exponent++; |
| 239 } |
| 240 if (exponent >= kMaxExponent) { |
| 241 return kInfinity; |
| 242 } |
| 243 if (exponent < kDenormalExponent) { |
| 244 return 0; |
| 245 } |
| 246 while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) { |
| 247 significand <<= 1; |
| 248 exponent--; |
| 249 } |
| 250 uint64_t biased_exponent; |
| 251 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) { |
| 252 biased_exponent = 0; |
| 253 } else { |
| 254 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias); |
| 255 } |
| 256 return (significand & kSignificandMask) | |
| 257 (biased_exponent << kPhysicalSignificandSize); |
| 258 } |
| 259 |
| 260 DISALLOW_COPY_AND_ASSIGN(Double); |
| 261 }; |
| 262 |
| 263 class Single { |
| 264 public: |
| 265 static const uint32_t kSignMask = 0x80000000; |
| 266 static const uint32_t kExponentMask = 0x7F800000; |
| 267 static const uint32_t kSignificandMask = 0x007FFFFF; |
| 268 static const uint32_t kHiddenBit = 0x00800000; |
| 269 static const int kPhysicalSignificandSize = 23; // Excludes the hidden bit. |
| 270 static const int kSignificandSize = 24; |
| 271 |
| 272 Single() : d32_(0) {} |
| 273 explicit Single(float f) : d32_(float_to_uint32(f)) {} |
| 274 explicit Single(uint32_t d32) : d32_(d32) {} |
| 275 |
| 276 // The value encoded by this Single must be greater or equal to +0.0. |
| 277 // It must not be special (infinity, or NaN). |
| 278 DiyFp AsDiyFp() const { |
| 279 ASSERT(Sign() > 0); |
| 280 ASSERT(!IsSpecial()); |
| 281 return DiyFp(Significand(), Exponent()); |
| 282 } |
| 283 |
| 284 // Returns the single's bit as uint64. |
| 285 uint32_t AsUint32() const { |
| 286 return d32_; |
| 287 } |
| 288 |
| 289 int Exponent() const { |
| 290 if (IsDenormal()) return kDenormalExponent; |
| 291 |
| 292 uint32_t d32 = AsUint32(); |
| 293 int biased_e = |
| 294 static_cast<int>((d32 & kExponentMask) >> kPhysicalSignificandSize); |
| 295 return biased_e - kExponentBias; |
| 296 } |
| 297 |
| 298 uint32_t Significand() const { |
| 299 uint32_t d32 = AsUint32(); |
| 300 uint32_t significand = d32 & kSignificandMask; |
| 301 if (!IsDenormal()) { |
| 302 return significand + kHiddenBit; |
| 303 } else { |
| 304 return significand; |
| 305 } |
| 306 } |
| 307 |
| 308 // Returns true if the single is a denormal. |
| 309 bool IsDenormal() const { |
| 310 uint32_t d32 = AsUint32(); |
| 311 return (d32 & kExponentMask) == 0; |
| 312 } |
| 313 |
| 314 // We consider denormals not to be special. |
| 315 // Hence only Infinity and NaN are special. |
| 316 bool IsSpecial() const { |
| 317 uint32_t d32 = AsUint32(); |
| 318 return (d32 & kExponentMask) == kExponentMask; |
| 319 } |
| 320 |
| 321 bool IsNan() const { |
| 322 uint32_t d32 = AsUint32(); |
| 323 return ((d32 & kExponentMask) == kExponentMask) && |
| 324 ((d32 & kSignificandMask) != 0); |
| 325 } |
| 326 |
| 327 bool IsInfinite() const { |
| 328 uint32_t d32 = AsUint32(); |
| 329 return ((d32 & kExponentMask) == kExponentMask) && |
| 330 ((d32 & kSignificandMask) == 0); |
| 331 } |
| 332 |
| 333 int Sign() const { |
| 334 uint32_t d32 = AsUint32(); |
| 335 return (d32 & kSignMask) == 0? 1: -1; |
| 336 } |
| 337 |
| 338 // Computes the two boundaries of this. |
| 339 // The bigger boundary (m_plus) is normalized. The lower boundary has the same |
| 340 // exponent as m_plus. |
| 341 // Precondition: the value encoded by this Single must be greater than 0. |
| 342 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { |
| 343 ASSERT(value() > 0.0); |
| 344 DiyFp v = this->AsDiyFp(); |
| 345 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); |
| 346 DiyFp m_minus; |
| 347 if (LowerBoundaryIsCloser()) { |
| 348 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); |
| 349 } else { |
| 350 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); |
| 351 } |
| 352 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); |
| 353 m_minus.set_e(m_plus.e()); |
| 354 *out_m_plus = m_plus; |
| 355 *out_m_minus = m_minus; |
| 356 } |
| 357 |
| 358 // Precondition: the value encoded by this Single must be greater or equal |
| 359 // than +0.0. |
| 360 DiyFp UpperBoundary() const { |
| 361 ASSERT(Sign() > 0); |
| 362 return DiyFp(Significand() * 2 + 1, Exponent() - 1); |
| 363 } |
| 364 |
| 365 bool LowerBoundaryIsCloser() const { |
| 366 // The boundary is closer if the significand is of the form f == 2^p-1 then |
| 367 // the lower boundary is closer. |
| 368 // Think of v = 1000e10 and v- = 9999e9. |
| 369 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but |
| 370 // at a distance of 1e8. |
| 371 // The only exception is for the smallest normal: the largest denormal is |
| 372 // at the same distance as its successor. |
| 373 // Note: denormals have the same exponent as the smallest normals. |
| 374 bool physical_significand_is_zero = ((AsUint32() & kSignificandMask) == 0); |
| 375 return physical_significand_is_zero && (Exponent() != kDenormalExponent); |
| 376 } |
| 377 |
| 378 float value() const { return uint32_to_float(d32_); } |
| 379 |
| 380 static float Infinity() { |
| 381 return Single(kInfinity).value(); |
| 382 } |
| 383 |
| 384 static float NaN() { |
| 385 return Single(kNaN).value(); |
| 386 } |
| 387 |
| 388 private: |
| 389 static const int kExponentBias = 0x7F + kPhysicalSignificandSize; |
| 390 static const int kDenormalExponent = -kExponentBias + 1; |
| 391 static const int kMaxExponent = 0xFF - kExponentBias; |
| 392 static const uint32_t kInfinity = 0x7F800000; |
| 393 static const uint32_t kNaN = 0x7FC00000; |
| 394 |
| 395 const uint32_t d32_; |
| 396 |
| 397 DISALLOW_COPY_AND_ASSIGN(Single); |
| 398 }; |
| 399 |
| 400 } // namespace double_conversion |
| 401 |
| 402 #endif // DOUBLE_CONVERSION_DOUBLE_H_ |
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