Victor Chang | 7322950 | 2020-09-17 13:39:19 +0100 | [diff] [blame] | 1 | // © 2018 and later: Unicode, Inc. and others. |
| 2 | // License & terms of use: http://www.unicode.org/copyright.html |
| 3 | // |
| 4 | // From the double-conversion library. Original license: |
| 5 | // |
| 6 | // Copyright 2012 the V8 project authors. All rights reserved. |
| 7 | // Redistribution and use in source and binary forms, with or without |
| 8 | // modification, are permitted provided that the following conditions are |
| 9 | // met: |
| 10 | // |
| 11 | // * Redistributions of source code must retain the above copyright |
| 12 | // notice, this list of conditions and the following disclaimer. |
| 13 | // * Redistributions in binary form must reproduce the above |
| 14 | // copyright notice, this list of conditions and the following |
| 15 | // disclaimer in the documentation and/or other materials provided |
| 16 | // with the distribution. |
| 17 | // * Neither the name of Google Inc. nor the names of its |
| 18 | // contributors may be used to endorse or promote products derived |
| 19 | // from this software without specific prior written permission. |
| 20 | // |
| 21 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| 22 | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| 23 | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| 24 | // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
| 25 | // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| 26 | // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
| 27 | // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
| 28 | // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
| 29 | // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| 30 | // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
| 31 | // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| 32 | |
| 33 | // ICU PATCH: ifdef around UCONFIG_NO_FORMATTING |
| 34 | #include "unicode/utypes.h" |
| 35 | #if !UCONFIG_NO_FORMATTING |
| 36 | |
| 37 | #ifndef DOUBLE_CONVERSION_DOUBLE_H_ |
| 38 | #define DOUBLE_CONVERSION_DOUBLE_H_ |
| 39 | |
| 40 | // ICU PATCH: Customize header file paths for ICU. |
| 41 | |
| 42 | #include "double-conversion-diy-fp.h" |
| 43 | |
| 44 | // ICU PATCH: Wrap in ICU namespace |
| 45 | U_NAMESPACE_BEGIN |
| 46 | |
| 47 | namespace double_conversion { |
| 48 | |
| 49 | // We assume that doubles and uint64_t have the same endianness. |
| 50 | static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); } |
| 51 | static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); } |
| 52 | static uint32_t float_to_uint32(float f) { return BitCast<uint32_t>(f); } |
| 53 | static float uint32_to_float(uint32_t d32) { return BitCast<float>(d32); } |
| 54 | |
| 55 | // Helper functions for doubles. |
| 56 | class Double { |
| 57 | public: |
| 58 | static const uint64_t kSignMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x80000000, 00000000); |
| 59 | static const uint64_t kExponentMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF00000, 00000000); |
| 60 | static const uint64_t kSignificandMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x000FFFFF, FFFFFFFF); |
| 61 | static const uint64_t kHiddenBit = DOUBLE_CONVERSION_UINT64_2PART_C(0x00100000, 00000000); |
Victor Chang | d8aa9d5 | 2021-01-05 23:49:57 +0000 | [diff] [blame] | 62 | static const uint64_t kQuietNanBit = DOUBLE_CONVERSION_UINT64_2PART_C(0x00080000, 00000000); |
Victor Chang | 7322950 | 2020-09-17 13:39:19 +0100 | [diff] [blame] | 63 | static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit. |
| 64 | static const int kSignificandSize = 53; |
| 65 | static const int kExponentBias = 0x3FF + kPhysicalSignificandSize; |
| 66 | static const int kMaxExponent = 0x7FF - kExponentBias; |
| 67 | |
| 68 | Double() : d64_(0) {} |
| 69 | explicit Double(double d) : d64_(double_to_uint64(d)) {} |
| 70 | explicit Double(uint64_t d64) : d64_(d64) {} |
| 71 | explicit Double(DiyFp diy_fp) |
| 72 | : d64_(DiyFpToUint64(diy_fp)) {} |
| 73 | |
| 74 | // The value encoded by this Double must be greater or equal to +0.0. |
| 75 | // It must not be special (infinity, or NaN). |
| 76 | DiyFp AsDiyFp() const { |
| 77 | DOUBLE_CONVERSION_ASSERT(Sign() > 0); |
| 78 | DOUBLE_CONVERSION_ASSERT(!IsSpecial()); |
| 79 | return DiyFp(Significand(), Exponent()); |
| 80 | } |
| 81 | |
| 82 | // The value encoded by this Double must be strictly greater than 0. |
| 83 | DiyFp AsNormalizedDiyFp() const { |
| 84 | DOUBLE_CONVERSION_ASSERT(value() > 0.0); |
| 85 | uint64_t f = Significand(); |
| 86 | int e = Exponent(); |
| 87 | |
| 88 | // The current double could be a denormal. |
| 89 | while ((f & kHiddenBit) == 0) { |
| 90 | f <<= 1; |
| 91 | e--; |
| 92 | } |
| 93 | // Do the final shifts in one go. |
| 94 | f <<= DiyFp::kSignificandSize - kSignificandSize; |
| 95 | e -= DiyFp::kSignificandSize - kSignificandSize; |
| 96 | return DiyFp(f, e); |
| 97 | } |
| 98 | |
| 99 | // Returns the double's bit as uint64. |
| 100 | uint64_t AsUint64() const { |
| 101 | return d64_; |
| 102 | } |
| 103 | |
| 104 | // Returns the next greater double. Returns +infinity on input +infinity. |
| 105 | double NextDouble() const { |
| 106 | if (d64_ == kInfinity) return Double(kInfinity).value(); |
| 107 | if (Sign() < 0 && Significand() == 0) { |
| 108 | // -0.0 |
| 109 | return 0.0; |
| 110 | } |
| 111 | if (Sign() < 0) { |
| 112 | return Double(d64_ - 1).value(); |
| 113 | } else { |
| 114 | return Double(d64_ + 1).value(); |
| 115 | } |
| 116 | } |
| 117 | |
| 118 | double PreviousDouble() const { |
| 119 | if (d64_ == (kInfinity | kSignMask)) return -Infinity(); |
| 120 | if (Sign() < 0) { |
| 121 | return Double(d64_ + 1).value(); |
| 122 | } else { |
| 123 | if (Significand() == 0) return -0.0; |
| 124 | return Double(d64_ - 1).value(); |
| 125 | } |
| 126 | } |
| 127 | |
| 128 | int Exponent() const { |
| 129 | if (IsDenormal()) return kDenormalExponent; |
| 130 | |
| 131 | uint64_t d64 = AsUint64(); |
| 132 | int biased_e = |
| 133 | static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize); |
| 134 | return biased_e - kExponentBias; |
| 135 | } |
| 136 | |
| 137 | uint64_t Significand() const { |
| 138 | uint64_t d64 = AsUint64(); |
| 139 | uint64_t significand = d64 & kSignificandMask; |
| 140 | if (!IsDenormal()) { |
| 141 | return significand + kHiddenBit; |
| 142 | } else { |
| 143 | return significand; |
| 144 | } |
| 145 | } |
| 146 | |
| 147 | // Returns true if the double is a denormal. |
| 148 | bool IsDenormal() const { |
| 149 | uint64_t d64 = AsUint64(); |
| 150 | return (d64 & kExponentMask) == 0; |
| 151 | } |
| 152 | |
| 153 | // We consider denormals not to be special. |
| 154 | // Hence only Infinity and NaN are special. |
| 155 | bool IsSpecial() const { |
| 156 | uint64_t d64 = AsUint64(); |
| 157 | return (d64 & kExponentMask) == kExponentMask; |
| 158 | } |
| 159 | |
| 160 | bool IsNan() const { |
| 161 | uint64_t d64 = AsUint64(); |
| 162 | return ((d64 & kExponentMask) == kExponentMask) && |
| 163 | ((d64 & kSignificandMask) != 0); |
| 164 | } |
| 165 | |
Victor Chang | d8aa9d5 | 2021-01-05 23:49:57 +0000 | [diff] [blame] | 166 | bool IsQuietNan() const { |
| 167 | return IsNan() && ((AsUint64() & kQuietNanBit) != 0); |
| 168 | } |
| 169 | |
| 170 | bool IsSignalingNan() const { |
| 171 | return IsNan() && ((AsUint64() & kQuietNanBit) == 0); |
| 172 | } |
| 173 | |
| 174 | |
Victor Chang | 7322950 | 2020-09-17 13:39:19 +0100 | [diff] [blame] | 175 | bool IsInfinite() const { |
| 176 | uint64_t d64 = AsUint64(); |
| 177 | return ((d64 & kExponentMask) == kExponentMask) && |
| 178 | ((d64 & kSignificandMask) == 0); |
| 179 | } |
| 180 | |
| 181 | int Sign() const { |
| 182 | uint64_t d64 = AsUint64(); |
| 183 | return (d64 & kSignMask) == 0? 1: -1; |
| 184 | } |
| 185 | |
| 186 | // Precondition: the value encoded by this Double must be greater or equal |
| 187 | // than +0.0. |
| 188 | DiyFp UpperBoundary() const { |
| 189 | DOUBLE_CONVERSION_ASSERT(Sign() > 0); |
| 190 | return DiyFp(Significand() * 2 + 1, Exponent() - 1); |
| 191 | } |
| 192 | |
| 193 | // Computes the two boundaries of this. |
| 194 | // The bigger boundary (m_plus) is normalized. The lower boundary has the same |
| 195 | // exponent as m_plus. |
| 196 | // Precondition: the value encoded by this Double must be greater than 0. |
| 197 | void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { |
| 198 | DOUBLE_CONVERSION_ASSERT(value() > 0.0); |
| 199 | DiyFp v = this->AsDiyFp(); |
| 200 | DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); |
| 201 | DiyFp m_minus; |
| 202 | if (LowerBoundaryIsCloser()) { |
| 203 | m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); |
| 204 | } else { |
| 205 | m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); |
| 206 | } |
| 207 | m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); |
| 208 | m_minus.set_e(m_plus.e()); |
| 209 | *out_m_plus = m_plus; |
| 210 | *out_m_minus = m_minus; |
| 211 | } |
| 212 | |
| 213 | bool LowerBoundaryIsCloser() const { |
| 214 | // The boundary is closer if the significand is of the form f == 2^p-1 then |
| 215 | // the lower boundary is closer. |
| 216 | // Think of v = 1000e10 and v- = 9999e9. |
| 217 | // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but |
| 218 | // at a distance of 1e8. |
| 219 | // The only exception is for the smallest normal: the largest denormal is |
| 220 | // at the same distance as its successor. |
| 221 | // Note: denormals have the same exponent as the smallest normals. |
| 222 | bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0); |
| 223 | return physical_significand_is_zero && (Exponent() != kDenormalExponent); |
| 224 | } |
| 225 | |
| 226 | double value() const { return uint64_to_double(d64_); } |
| 227 | |
| 228 | // Returns the significand size for a given order of magnitude. |
| 229 | // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude. |
| 230 | // This function returns the number of significant binary digits v will have |
| 231 | // once it's encoded into a double. In almost all cases this is equal to |
| 232 | // kSignificandSize. The only exceptions are denormals. They start with |
| 233 | // leading zeroes and their effective significand-size is hence smaller. |
| 234 | static int SignificandSizeForOrderOfMagnitude(int order) { |
| 235 | if (order >= (kDenormalExponent + kSignificandSize)) { |
| 236 | return kSignificandSize; |
| 237 | } |
| 238 | if (order <= kDenormalExponent) return 0; |
| 239 | return order - kDenormalExponent; |
| 240 | } |
| 241 | |
| 242 | static double Infinity() { |
| 243 | return Double(kInfinity).value(); |
| 244 | } |
| 245 | |
| 246 | static double NaN() { |
| 247 | return Double(kNaN).value(); |
| 248 | } |
| 249 | |
| 250 | private: |
| 251 | static const int kDenormalExponent = -kExponentBias + 1; |
| 252 | static const uint64_t kInfinity = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF00000, 00000000); |
| 253 | static const uint64_t kNaN = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF80000, 00000000); |
| 254 | |
| 255 | const uint64_t d64_; |
| 256 | |
| 257 | static uint64_t DiyFpToUint64(DiyFp diy_fp) { |
| 258 | uint64_t significand = diy_fp.f(); |
| 259 | int exponent = diy_fp.e(); |
| 260 | while (significand > kHiddenBit + kSignificandMask) { |
| 261 | significand >>= 1; |
| 262 | exponent++; |
| 263 | } |
| 264 | if (exponent >= kMaxExponent) { |
| 265 | return kInfinity; |
| 266 | } |
| 267 | if (exponent < kDenormalExponent) { |
| 268 | return 0; |
| 269 | } |
| 270 | while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) { |
| 271 | significand <<= 1; |
| 272 | exponent--; |
| 273 | } |
| 274 | uint64_t biased_exponent; |
| 275 | if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) { |
| 276 | biased_exponent = 0; |
| 277 | } else { |
| 278 | biased_exponent = static_cast<uint64_t>(exponent + kExponentBias); |
| 279 | } |
| 280 | return (significand & kSignificandMask) | |
| 281 | (biased_exponent << kPhysicalSignificandSize); |
| 282 | } |
| 283 | |
| 284 | DOUBLE_CONVERSION_DISALLOW_COPY_AND_ASSIGN(Double); |
| 285 | }; |
| 286 | |
| 287 | class Single { |
| 288 | public: |
| 289 | static const uint32_t kSignMask = 0x80000000; |
| 290 | static const uint32_t kExponentMask = 0x7F800000; |
| 291 | static const uint32_t kSignificandMask = 0x007FFFFF; |
| 292 | static const uint32_t kHiddenBit = 0x00800000; |
Victor Chang | d8aa9d5 | 2021-01-05 23:49:57 +0000 | [diff] [blame] | 293 | static const uint32_t kQuietNanBit = 0x00400000; |
Victor Chang | 7322950 | 2020-09-17 13:39:19 +0100 | [diff] [blame] | 294 | static const int kPhysicalSignificandSize = 23; // Excludes the hidden bit. |
| 295 | static const int kSignificandSize = 24; |
| 296 | |
| 297 | Single() : d32_(0) {} |
| 298 | explicit Single(float f) : d32_(float_to_uint32(f)) {} |
| 299 | explicit Single(uint32_t d32) : d32_(d32) {} |
| 300 | |
| 301 | // The value encoded by this Single must be greater or equal to +0.0. |
| 302 | // It must not be special (infinity, or NaN). |
| 303 | DiyFp AsDiyFp() const { |
| 304 | DOUBLE_CONVERSION_ASSERT(Sign() > 0); |
| 305 | DOUBLE_CONVERSION_ASSERT(!IsSpecial()); |
| 306 | return DiyFp(Significand(), Exponent()); |
| 307 | } |
| 308 | |
| 309 | // Returns the single's bit as uint64. |
| 310 | uint32_t AsUint32() const { |
| 311 | return d32_; |
| 312 | } |
| 313 | |
| 314 | int Exponent() const { |
| 315 | if (IsDenormal()) return kDenormalExponent; |
| 316 | |
| 317 | uint32_t d32 = AsUint32(); |
| 318 | int biased_e = |
| 319 | static_cast<int>((d32 & kExponentMask) >> kPhysicalSignificandSize); |
| 320 | return biased_e - kExponentBias; |
| 321 | } |
| 322 | |
| 323 | uint32_t Significand() const { |
| 324 | uint32_t d32 = AsUint32(); |
| 325 | uint32_t significand = d32 & kSignificandMask; |
| 326 | if (!IsDenormal()) { |
| 327 | return significand + kHiddenBit; |
| 328 | } else { |
| 329 | return significand; |
| 330 | } |
| 331 | } |
| 332 | |
| 333 | // Returns true if the single is a denormal. |
| 334 | bool IsDenormal() const { |
| 335 | uint32_t d32 = AsUint32(); |
| 336 | return (d32 & kExponentMask) == 0; |
| 337 | } |
| 338 | |
| 339 | // We consider denormals not to be special. |
| 340 | // Hence only Infinity and NaN are special. |
| 341 | bool IsSpecial() const { |
| 342 | uint32_t d32 = AsUint32(); |
| 343 | return (d32 & kExponentMask) == kExponentMask; |
| 344 | } |
| 345 | |
| 346 | bool IsNan() const { |
| 347 | uint32_t d32 = AsUint32(); |
| 348 | return ((d32 & kExponentMask) == kExponentMask) && |
| 349 | ((d32 & kSignificandMask) != 0); |
| 350 | } |
| 351 | |
Victor Chang | d8aa9d5 | 2021-01-05 23:49:57 +0000 | [diff] [blame] | 352 | bool IsQuietNan() const { |
| 353 | return IsNan() && ((AsUint32() & kQuietNanBit) != 0); |
| 354 | } |
| 355 | |
| 356 | bool IsSignalingNan() const { |
| 357 | return IsNan() && ((AsUint32() & kQuietNanBit) == 0); |
| 358 | } |
| 359 | |
| 360 | |
Victor Chang | 7322950 | 2020-09-17 13:39:19 +0100 | [diff] [blame] | 361 | bool IsInfinite() const { |
| 362 | uint32_t d32 = AsUint32(); |
| 363 | return ((d32 & kExponentMask) == kExponentMask) && |
| 364 | ((d32 & kSignificandMask) == 0); |
| 365 | } |
| 366 | |
| 367 | int Sign() const { |
| 368 | uint32_t d32 = AsUint32(); |
| 369 | return (d32 & kSignMask) == 0? 1: -1; |
| 370 | } |
| 371 | |
| 372 | // Computes the two boundaries of this. |
| 373 | // The bigger boundary (m_plus) is normalized. The lower boundary has the same |
| 374 | // exponent as m_plus. |
| 375 | // Precondition: the value encoded by this Single must be greater than 0. |
| 376 | void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const { |
| 377 | DOUBLE_CONVERSION_ASSERT(value() > 0.0); |
| 378 | DiyFp v = this->AsDiyFp(); |
| 379 | DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1)); |
| 380 | DiyFp m_minus; |
| 381 | if (LowerBoundaryIsCloser()) { |
| 382 | m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2); |
| 383 | } else { |
| 384 | m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1); |
| 385 | } |
| 386 | m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e())); |
| 387 | m_minus.set_e(m_plus.e()); |
| 388 | *out_m_plus = m_plus; |
| 389 | *out_m_minus = m_minus; |
| 390 | } |
| 391 | |
| 392 | // Precondition: the value encoded by this Single must be greater or equal |
| 393 | // than +0.0. |
| 394 | DiyFp UpperBoundary() const { |
| 395 | DOUBLE_CONVERSION_ASSERT(Sign() > 0); |
| 396 | return DiyFp(Significand() * 2 + 1, Exponent() - 1); |
| 397 | } |
| 398 | |
| 399 | bool LowerBoundaryIsCloser() const { |
| 400 | // The boundary is closer if the significand is of the form f == 2^p-1 then |
| 401 | // the lower boundary is closer. |
| 402 | // Think of v = 1000e10 and v- = 9999e9. |
| 403 | // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but |
| 404 | // at a distance of 1e8. |
| 405 | // The only exception is for the smallest normal: the largest denormal is |
| 406 | // at the same distance as its successor. |
| 407 | // Note: denormals have the same exponent as the smallest normals. |
| 408 | bool physical_significand_is_zero = ((AsUint32() & kSignificandMask) == 0); |
| 409 | return physical_significand_is_zero && (Exponent() != kDenormalExponent); |
| 410 | } |
| 411 | |
| 412 | float value() const { return uint32_to_float(d32_); } |
| 413 | |
| 414 | static float Infinity() { |
| 415 | return Single(kInfinity).value(); |
| 416 | } |
| 417 | |
| 418 | static float NaN() { |
| 419 | return Single(kNaN).value(); |
| 420 | } |
| 421 | |
| 422 | private: |
| 423 | static const int kExponentBias = 0x7F + kPhysicalSignificandSize; |
| 424 | static const int kDenormalExponent = -kExponentBias + 1; |
| 425 | static const int kMaxExponent = 0xFF - kExponentBias; |
| 426 | static const uint32_t kInfinity = 0x7F800000; |
| 427 | static const uint32_t kNaN = 0x7FC00000; |
| 428 | |
| 429 | const uint32_t d32_; |
| 430 | |
| 431 | DOUBLE_CONVERSION_DISALLOW_COPY_AND_ASSIGN(Single); |
| 432 | }; |
| 433 | |
| 434 | } // namespace double_conversion |
| 435 | |
| 436 | // ICU PATCH: Close ICU namespace |
| 437 | U_NAMESPACE_END |
| 438 | |
| 439 | #endif // DOUBLE_CONVERSION_DOUBLE_H_ |
| 440 | #endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING |