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| 1 // Copyright 2010 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 #include <math.h> | |
| 29 | |
| 30 #include "v8.h" | |
| 31 | |
| 32 #include "double.h" | |
| 33 #include "fixed-dtoa.h" | |
| 34 | |
| 35 namespace v8 { | |
| 36 namespace internal { | |
| 37 | |
| 38 // Represents a 128bit type. This class should be replaced by a native type on | |
| 39 // platforms that support 128bit integers. | |
| 40 class UInt128 { | |
| 41 public: | |
| 42 UInt128() : high_bits_(0), low_bits_(0) { } | |
| 43 UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { } | |
| 44 | |
| 45 void Multiply(uint32_t multiplicand) { | |
| 46 uint64_t accumulator; | |
| 47 | |
| 48 accumulator = (low_bits_ & kMask32) * multiplicand; | |
| 49 uint32_t part = static_cast<uint32_t>(accumulator & kMask32); | |
| 50 accumulator >>= 32; | |
| 51 accumulator = accumulator + (low_bits_ >> 32) * multiplicand; | |
| 52 low_bits_ = (accumulator << 32) + part; | |
| 53 accumulator >>= 32; | |
| 54 accumulator = accumulator + (high_bits_ & kMask32) * multiplicand; | |
| 55 part = static_cast<uint32_t>(accumulator & kMask32); | |
| 56 accumulator >>= 32; | |
| 57 accumulator = accumulator + (high_bits_ >> 32) * multiplicand; | |
| 58 high_bits_ = (accumulator << 32) + part; | |
| 59 ASSERT((accumulator >> 32) == 0); | |
| 60 } | |
| 61 | |
| 62 void Shift(int shift_amount) { | |
| 63 ASSERT(-64 <= shift_amount && shift_amount <= 64); | |
| 64 if (shift_amount == 0) { | |
| 65 return; | |
| 66 } else if (shift_amount == -64) { | |
| 67 high_bits_ = low_bits_; | |
| 68 low_bits_ = 0; | |
| 69 } else if (shift_amount == 64) { | |
| 70 low_bits_ = high_bits_; | |
| 71 high_bits_ = 0; | |
| 72 } else if (shift_amount <= 0) { | |
| 73 high_bits_ <<= -shift_amount; | |
| 74 high_bits_ += low_bits_ >> (64 + shift_amount); | |
| 75 low_bits_ <<= -shift_amount; | |
| 76 } else { | |
| 77 low_bits_ >>= shift_amount; | |
| 78 low_bits_ += high_bits_ << (64 - shift_amount); | |
| 79 high_bits_ >>= shift_amount; | |
| 80 } | |
| 81 } | |
| 82 | |
| 83 // Modifies *this to *this MOD (2^power). | |
| 84 // Returns *this DIV (2^power). | |
| 85 int DivModPowerOf2(int power) { | |
| 86 if (power >= 64) { | |
| 87 int result = static_cast<int>(high_bits_ >> (power - 64)); | |
| 88 high_bits_ -= static_cast<uint64_t>(result) << (power - 64); | |
| 89 return result; | |
| 90 } else { | |
| 91 uint64_t part_low = low_bits_ >> power; | |
| 92 uint64_t part_high = high_bits_ << (64 - power); | |
| 93 int result = static_cast<int>(part_low + part_high); | |
| 94 high_bits_ = 0; | |
| 95 low_bits_ -= part_low << power; | |
| 96 return result; | |
| 97 } | |
| 98 } | |
| 99 | |
| 100 bool IsZero() const { | |
| 101 return high_bits_ == 0 && low_bits_ == 0; | |
| 102 } | |
| 103 | |
| 104 int BitAt(int position) { | |
| 105 if (position >= 64) { | |
| 106 return (high_bits_ >> (position - 64)) & 1; | |
| 107 } else { | |
| 108 return (low_bits_ >> position) & 1; | |
| 109 } | |
| 110 } | |
| 111 | |
| 112 private: | |
| 113 static const uint64_t kMask32 = 0xFFFFFFFF; | |
| 114 // Value == (high_bits_ << 64) + low_bits_ | |
| 115 uint64_t high_bits_; | |
| 116 uint64_t low_bits_; | |
| 117 }; | |
| 118 | |
| 119 | |
| 120 static const int kDoubleSignificandSize = 53; // Includes the hidden bit. | |
| 121 | |
| 122 | |
| 123 static void FillDigits32FixedLength(uint32_t number, int requested_length, | |
| 124 Vector<char> buffer, int* length) { | |
| 125 for (int i = requested_length - 1; i >= 0; --i) { | |
| 126 buffer[(*length) + i] = '0' + number % 10; | |
| 127 number /= 10; | |
| 128 } | |
| 129 *length += requested_length; | |
| 130 } | |
| 131 | |
| 132 | |
| 133 static void FillDigits32(uint32_t number, Vector<char> buffer, int* length) { | |
| 134 int number_length = 0; | |
| 135 // We fill the digits in reverse order and exchange them afterwards. | |
| 136 while (number != 0) { | |
| 137 int digit = number % 10; | |
| 138 number /= 10; | |
| 139 buffer[(*length) + number_length] = '0' + digit; | |
| 140 number_length++; | |
| 141 } | |
| 142 // Exchange the digits. | |
| 143 int i = *length; | |
| 144 int j = *length + number_length - 1; | |
| 145 while (i < j) { | |
| 146 char tmp = buffer[i]; | |
| 147 buffer[i] = buffer[j]; | |
| 148 buffer[j] = tmp; | |
| 149 i++; j--; | |
| 150 } | |
| 151 *length += number_length; | |
| 152 } | |
| 153 | |
| 154 | |
| 155 static void FillDigits64FixedLength(uint64_t number, int requested_length, | |
| 156 Vector<char> buffer, int* length) { | |
| 157 const uint32_t kTen7 = 10000000; | |
| 158 // For efficiency cut the number into 3 uint32_t parts, and print those. | |
| 159 uint32_t part2 = number % kTen7; | |
| 160 number /= kTen7; | |
| 161 uint32_t part1 = number % kTen7; | |
| 162 uint32_t part0 = number / kTen7; | |
| 163 | |
| 164 FillDigits32FixedLength(part0, 3, buffer, length); | |
| 165 FillDigits32FixedLength(part1, 7, buffer, length); | |
| 166 FillDigits32FixedLength(part2, 7, buffer, length); | |
| 167 } | |
| 168 | |
| 169 | |
| 170 static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) { | |
| 171 const uint32_t kTen7 = 10000000; | |
| 172 // For efficiency cut the number into 3 uint32_t parts, and print those. | |
| 173 uint32_t part2 = number % kTen7; | |
| 174 number /= kTen7; | |
| 175 uint32_t part1 = number % kTen7; | |
| 176 uint32_t part0 = number / kTen7; | |
| 177 | |
| 178 if (part0 != 0) { | |
| 179 FillDigits32(part0, buffer, length); | |
| 180 FillDigits32FixedLength(part1, 7, buffer, length); | |
| 181 FillDigits32FixedLength(part2, 7, buffer, length); | |
| 182 } else if (part1 != 0) { | |
| 183 FillDigits32(part1, buffer, length); | |
| 184 FillDigits32FixedLength(part2, 7, buffer, length); | |
| 185 } else { | |
| 186 FillDigits32(part2, buffer, length); | |
| 187 } | |
| 188 } | |
| 189 | |
| 190 | |
| 191 static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) { | |
| 192 // An empty buffer represents 0. | |
| 193 if (*length == 0) { | |
| 194 buffer[0] = '1'; | |
| 195 *decimal_point = 1; | |
| 196 *length = 1; | |
| 197 return; | |
| 198 } | |
| 199 // Round the last digit until we either have a digit that was not '9' or until | |
| 200 // we reached the first digit. | |
| 201 buffer[(*length) - 1]++; | |
| 202 for (int i = (*length) - 1; i > 0; --i) { | |
| 203 if (buffer[i] != '0' + 10) { | |
| 204 return; | |
| 205 } | |
| 206 buffer[i] = '0'; | |
| 207 buffer[i - 1]++; | |
| 208 } | |
| 209 // If the first digit is now '0' + 10, we would need to set it to '0' and add | |
| 210 // a '1' in front. However we reach the first digit only if all following | |
| 211 // digits had been '9' before rounding up. Now all trailing digits are '0' and | |
| 212 // we simply switch the first digit to '1' and update the decimal-point | |
| 213 // (indicating that the point is now one digit to the right). | |
| 214 if (buffer[0] == '0' + 10) { | |
| 215 buffer[0] = '1'; | |
| 216 (*decimal_point)++; | |
| 217 } | |
| 218 } | |
| 219 | |
| 220 | |
| 221 // The given fractionals number represents a fixed-point number with binary | |
| 222 // point at bit (-exponent). | |
| 223 // Preconditions: | |
| 224 // -128 <= exponent <= 0. | |
| 225 // 0 <= fractionals * 2^exponent < 1 | |
| 226 // The buffer holds the result. | |
| 227 // The function will round its result. During the rounding-process digits not | |
| 228 // generated by this function might be updated, and the decimal-point variable | |
| 229 // might be updated. If this function generates the digits 99 and the buffer | |
| 230 // already contained "199" (thus yielding a buffer of "19999") then a | |
| 231 // rounding-up will change the contents of the buffer to "20000". | |
| 232 static void FillFractionals(uint64_t fractionals, int exponent, | |
| 233 int fractional_count, Vector<char> buffer, | |
| 234 int* length, int* decimal_point) { | |
| 235 ASSERT(-128 <= exponent && exponent <= 0); | |
| 236 // 'fractionals' is a fixed-point number, with binary point at bit | |
| 237 // (-exponent). Inside the function the non-converted remainder of fractionals | |
| 238 // is a fixed-point number, with binary point at bit 'point'. | |
| 239 if (-exponent <= 64) { | |
| 240 // One 64 bit number is sufficient. | |
| 241 ASSERT(fractionals >> 56 == 0); | |
| 242 int point = -exponent; | |
| 243 for (int i = 0; i < fractional_count; ++i) { | |
| 244 if (fractionals == 0) break; | |
| 245 // Instead of multiplying by 10 we multiply by 5 and adjust the point | |
| 246 // location. This way the fractionals variable will not overflow. | |
| 247 // Invariant at the beginning of the loop: fractionals < 2^point. | |
| 248 // Initially we have: point <= 64 and fractionals < 2^56 | |
| 249 // After each iteration the point is decremented by one. | |
| 250 // Note that 5^3 = 125 < 128 = 2^7. | |
| 251 // Therefore three iterations of this loop will not overflow fractionals | |
| 252 // (even without the subtraction at the end of the loop body). At this tim
e | |
| 253 // point will satisfy point <= 61 and therefore fractionals < 2^point and | |
| 254 // any further multiplication of fractionals by 5 will not overflow. | |
| 255 fractionals *= 5; | |
| 256 point--; | |
| 257 int digit = static_cast<int>(fractionals >> point); | |
| 258 buffer[*length] = '0' + digit; | |
| 259 (*length)++; | |
| 260 fractionals -= static_cast<uint64_t>(digit) << point; | |
| 261 } | |
| 262 // If the first bit after the point is set we have to round up. | |
| 263 if (((fractionals >> (point - 1)) & 1) == 1) { | |
| 264 RoundUp(buffer, length, decimal_point); | |
| 265 } | |
| 266 } else { // We need 128 bits. | |
| 267 ASSERT(64 < -exponent && -exponent <= 128); | |
| 268 UInt128 fractionals128 = UInt128(fractionals, 0); | |
| 269 fractionals128.Shift(-exponent - 64); | |
| 270 int point = 128; | |
| 271 for (int i = 0; i < fractional_count; ++i) { | |
| 272 if (fractionals128.IsZero()) break; | |
| 273 // As before: instead of multiplying by 10 we multiply by 5 and adjust the | |
| 274 // point location. | |
| 275 // This multiplication will not overflow for the same reasons as before. | |
| 276 fractionals128.Multiply(5); | |
| 277 point--; | |
| 278 int digit = fractionals128.DivModPowerOf2(point); | |
| 279 buffer[*length] = '0' + digit; | |
| 280 (*length)++; | |
| 281 } | |
| 282 if (fractionals128.BitAt(point - 1) == 1) { | |
| 283 RoundUp(buffer, length, decimal_point); | |
| 284 } | |
| 285 } | |
| 286 } | |
| 287 | |
| 288 | |
| 289 // Removes leading and trailing zeros. | |
| 290 // If leading zeros are removed then the decimal point position is adjusted. | |
| 291 static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) { | |
| 292 while (*length > 0 && buffer[(*length) - 1] == '0') { | |
| 293 (*length)--; | |
| 294 } | |
| 295 int first_non_zero = 0; | |
| 296 while (first_non_zero < *length && buffer[first_non_zero] == '0') { | |
| 297 first_non_zero++; | |
| 298 } | |
| 299 if (first_non_zero != 0) { | |
| 300 for (int i = first_non_zero; i < *length; ++i) { | |
| 301 buffer[i - first_non_zero] = buffer[i]; | |
| 302 } | |
| 303 *length -= first_non_zero; | |
| 304 *decimal_point -= first_non_zero; | |
| 305 } | |
| 306 } | |
| 307 | |
| 308 | |
| 309 bool FastFixedDtoa(double v, | |
| 310 int fractional_count, | |
| 311 Vector<char> buffer, | |
| 312 int* length, | |
| 313 int* decimal_point) { | |
| 314 const uint32_t kMaxUInt32 = 0xFFFFFFFF; | |
| 315 uint64_t significand = Double(v).Significand(); | |
| 316 int exponent = Double(v).Exponent(); | |
| 317 // v = significand * 2^exponent (with significand a 53bit integer). | |
| 318 // If the exponent is larger than 20 (i.e. we may have a 73bit number) then we | |
| 319 // don't know how to compute the representation. 2^73 ~= 9.5*10^21. | |
| 320 // If necessary this limit could probably be increased, but we don't need | |
| 321 // more. | |
| 322 if (exponent > 20) return false; | |
| 323 if (fractional_count > 20) return false; | |
| 324 *length = 0; | |
| 325 // At most kDoubleSignificandSize bits of the significand are non-zero. | |
| 326 // Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero | |
| 327 // bits: 0..11*..0xxx..53*..xx | |
| 328 if (exponent + kDoubleSignificandSize > 64) { | |
| 329 // The exponent must be > 11. | |
| 330 // | |
| 331 // We know that v = significand * 2^exponent. | |
| 332 // And the exponent > 11. | |
| 333 // We simplify the task by dividing v by 10^17. | |
| 334 // The quotient delivers the first digits, and the remainder fits into a 64 | |
| 335 // bit number. | |
| 336 // Dividing by 10^17 is equivalent to dividing by 5^17*2^17. | |
| 337 const uint64_t kFive17 = V8_2PART_UINT64_C(0xB1, A2BC2EC5); // 5^17 | |
| 338 uint64_t divisor = kFive17; | |
| 339 int divisor_power = 17; | |
| 340 uint64_t dividend = significand; | |
| 341 uint64_t quotient; | |
| 342 uint64_t remainder; | |
| 343 // Let v = f * 2^e with f == significand and e == exponent. | |
| 344 // Then need q (quotient) and r (remainder) as follows: | |
| 345 // v = q * 10^17 + r | |
| 346 // f * 2^e = q * 10^17 + r | |
| 347 // f * 2^e = q * 5^17 * 2^17 + r | |
| 348 // If e > 17 then | |
| 349 // f * 2^(e-17) = q * 5^17 + r/2^17 | |
| 350 // else | |
| 351 // f = q * 5^17 * 2^(17-e) + r/2^e | |
| 352 if (exponent > divisor_power) { | |
| 353 // We only allow exponents of up to 20 and therefore (17 - e) <= 3 | |
| 354 dividend <<= exponent - divisor_power; | |
| 355 quotient = dividend / divisor; | |
| 356 remainder = (dividend % divisor) << divisor_power; | |
| 357 } else { | |
| 358 divisor <<= divisor_power - exponent; | |
| 359 quotient = dividend / divisor; | |
| 360 remainder = (dividend % divisor) << exponent; | |
| 361 } | |
| 362 FillDigits32(quotient, buffer, length); | |
| 363 FillDigits64FixedLength(remainder, divisor_power, buffer, length); | |
| 364 *decimal_point = *length; | |
| 365 } else if (exponent >= 0) { | |
| 366 // 0 <= exponent <= 11 | |
| 367 significand <<= exponent; | |
| 368 FillDigits64(significand, buffer, length); | |
| 369 *decimal_point = *length; | |
| 370 } else if (exponent > -kDoubleSignificandSize) { | |
| 371 // We have to cut the number. | |
| 372 uint64_t integrals = significand >> -exponent; | |
| 373 uint64_t fractionals = significand - (integrals << -exponent); | |
| 374 if (integrals > kMaxUInt32) { | |
| 375 FillDigits64(integrals, buffer, length); | |
| 376 } else { | |
| 377 FillDigits32(static_cast<uint32_t>(integrals), buffer, length); | |
| 378 } | |
| 379 *decimal_point = *length; | |
| 380 FillFractionals(fractionals, exponent, fractional_count, | |
| 381 buffer, length, decimal_point); | |
| 382 } else if (exponent < -128) { | |
| 383 // This configuration (with at most 20 digits) means that all digits must be | |
| 384 // 0. | |
| 385 ASSERT(fractional_count <= 20); | |
| 386 buffer[0] = '\0'; | |
| 387 *length = 0; | |
| 388 *decimal_point = -fractional_count; | |
| 389 } else { | |
| 390 *decimal_point = 0; | |
| 391 FillFractionals(significand, exponent, fractional_count, | |
| 392 buffer, length, decimal_point); | |
| 393 } | |
| 394 TrimZeros(buffer, length, decimal_point); | |
| 395 buffer[*length] = '\0'; | |
| 396 if ((*length) == 0) { | |
| 397 // The string is empty and the decimal_point thus has no importance. Mimick | |
| 398 // Gay's dtoa and and set it to -fractional_count. | |
| 399 *decimal_point = -fractional_count; | |
| 400 } | |
| 401 return true; | |
| 402 } | |
| 403 | |
| 404 } } // namespace v8::internal | |
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