Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 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 <stdarg.h> |
| 29 | #include <limits.h> |
| 30 | |
| 31 | #include "v8.h" |
| 32 | |
| 33 | #include "strtod.h" |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 34 | #include "cached-powers.h" |
| 35 | #include "double.h" |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 36 | |
| 37 | namespace v8 { |
| 38 | namespace internal { |
| 39 | |
| 40 | // 2^53 = 9007199254740992. |
| 41 | // Any integer with at most 15 decimal digits will hence fit into a double |
| 42 | // (which has a 53bit significand) without loss of precision. |
| 43 | static const int kMaxExactDoubleIntegerDecimalDigits = 15; |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 44 | // 2^64 = 18446744073709551616 > 10^19 |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 45 | static const int kMaxUint64DecimalDigits = 19; |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 46 | |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 47 | // Max double: 1.7976931348623157 x 10^308 |
| 48 | // Min non-zero double: 4.9406564584124654 x 10^-324 |
| 49 | // Any x >= 10^309 is interpreted as +infinity. |
| 50 | // Any x <= 10^-324 is interpreted as 0. |
| 51 | // Note that 2.5e-324 (despite being smaller than the min double) will be read |
| 52 | // as non-zero (equal to the min non-zero double). |
| 53 | static const int kMaxDecimalPower = 309; |
| 54 | static const int kMinDecimalPower = -324; |
| 55 | |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 56 | // 2^64 = 18446744073709551616 |
| 57 | static const uint64_t kMaxUint64 = V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF); |
| 58 | |
| 59 | |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 60 | static const double exact_powers_of_ten[] = { |
| 61 | 1.0, // 10^0 |
| 62 | 10.0, |
| 63 | 100.0, |
| 64 | 1000.0, |
| 65 | 10000.0, |
| 66 | 100000.0, |
| 67 | 1000000.0, |
| 68 | 10000000.0, |
| 69 | 100000000.0, |
| 70 | 1000000000.0, |
| 71 | 10000000000.0, // 10^10 |
| 72 | 100000000000.0, |
| 73 | 1000000000000.0, |
| 74 | 10000000000000.0, |
| 75 | 100000000000000.0, |
| 76 | 1000000000000000.0, |
| 77 | 10000000000000000.0, |
| 78 | 100000000000000000.0, |
| 79 | 1000000000000000000.0, |
| 80 | 10000000000000000000.0, |
| 81 | 100000000000000000000.0, // 10^20 |
| 82 | 1000000000000000000000.0, |
| 83 | // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22 |
| 84 | 10000000000000000000000.0 |
| 85 | }; |
| 86 | |
| 87 | static const int kExactPowersOfTenSize = ARRAY_SIZE(exact_powers_of_ten); |
| 88 | |
| 89 | |
| 90 | extern "C" double gay_strtod(const char* s00, const char** se); |
| 91 | |
| 92 | static double old_strtod(Vector<const char> buffer, int exponent) { |
| 93 | // gay_strtod is broken on Linux,x86. For numbers with few decimal digits |
| 94 | // the computation is done using floating-point operations which (on Linux) |
| 95 | // are prone to double-rounding errors. |
| 96 | // By adding several zeroes to the buffer gay_strtod falls back to a slower |
| 97 | // (but correct) algorithm. |
| 98 | const int kInsertedZeroesCount = 20; |
| 99 | char gay_buffer[1024]; |
| 100 | Vector<char> gay_buffer_vector(gay_buffer, sizeof(gay_buffer)); |
| 101 | int pos = 0; |
| 102 | for (int i = 0; i < buffer.length(); ++i) { |
| 103 | gay_buffer_vector[pos++] = buffer[i]; |
| 104 | } |
| 105 | for (int i = 0; i < kInsertedZeroesCount; ++i) { |
| 106 | gay_buffer_vector[pos++] = '0'; |
| 107 | } |
| 108 | exponent -= kInsertedZeroesCount; |
| 109 | gay_buffer_vector[pos++] = 'e'; |
| 110 | if (exponent < 0) { |
| 111 | gay_buffer_vector[pos++] = '-'; |
| 112 | exponent = -exponent; |
| 113 | } |
| 114 | const int kNumberOfExponentDigits = 5; |
| 115 | for (int i = kNumberOfExponentDigits - 1; i >= 0; i--) { |
| 116 | gay_buffer_vector[pos + i] = exponent % 10 + '0'; |
| 117 | exponent /= 10; |
| 118 | } |
| 119 | pos += kNumberOfExponentDigits; |
| 120 | gay_buffer_vector[pos] = '\0'; |
| 121 | return gay_strtod(gay_buffer, NULL); |
| 122 | } |
| 123 | |
| 124 | |
| 125 | static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) { |
| 126 | for (int i = 0; i < buffer.length(); i++) { |
| 127 | if (buffer[i] != '0') { |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 128 | return buffer.SubVector(i, buffer.length()); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 129 | } |
| 130 | } |
| 131 | return Vector<const char>(buffer.start(), 0); |
| 132 | } |
| 133 | |
| 134 | |
| 135 | static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) { |
| 136 | for (int i = buffer.length() - 1; i >= 0; --i) { |
| 137 | if (buffer[i] != '0') { |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 138 | return buffer.SubVector(0, i + 1); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 139 | } |
| 140 | } |
| 141 | return Vector<const char>(buffer.start(), 0); |
| 142 | } |
| 143 | |
| 144 | |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 145 | // Reads digits from the buffer and converts them to a uint64. |
| 146 | // Reads in as many digits as fit into a uint64. |
| 147 | // When the string starts with "1844674407370955161" no further digit is read. |
| 148 | // Since 2^64 = 18446744073709551616 it would still be possible read another |
| 149 | // digit if it was less or equal than 6, but this would complicate the code. |
| 150 | static uint64_t ReadUint64(Vector<const char> buffer, |
| 151 | int* number_of_read_digits) { |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 152 | uint64_t result = 0; |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 153 | int i = 0; |
| 154 | while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) { |
| 155 | int digit = buffer[i++] - '0'; |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 156 | ASSERT(0 <= digit && digit <= 9); |
| 157 | result = 10 * result + digit; |
| 158 | } |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 159 | *number_of_read_digits = i; |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 160 | return result; |
| 161 | } |
| 162 | |
| 163 | |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 164 | // Reads a DiyFp from the buffer. |
| 165 | // The returned DiyFp is not necessarily normalized. |
| 166 | // If remaining_decimals is zero then the returned DiyFp is accurate. |
| 167 | // Otherwise it has been rounded and has error of at most 1/2 ulp. |
| 168 | static void ReadDiyFp(Vector<const char> buffer, |
| 169 | DiyFp* result, |
| 170 | int* remaining_decimals) { |
| 171 | int read_digits; |
| 172 | uint64_t significand = ReadUint64(buffer, &read_digits); |
| 173 | if (buffer.length() == read_digits) { |
| 174 | *result = DiyFp(significand, 0); |
| 175 | *remaining_decimals = 0; |
| 176 | } else { |
| 177 | // Round the significand. |
| 178 | if (buffer[read_digits] >= '5') { |
| 179 | significand++; |
| 180 | } |
| 181 | // Compute the binary exponent. |
| 182 | int exponent = 0; |
| 183 | *result = DiyFp(significand, exponent); |
| 184 | *remaining_decimals = buffer.length() - read_digits; |
| 185 | } |
| 186 | } |
| 187 | |
| 188 | |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 189 | static bool DoubleStrtod(Vector<const char> trimmed, |
| 190 | int exponent, |
| 191 | double* result) { |
| 192 | #if (defined(V8_TARGET_ARCH_IA32) || defined(USE_SIMULATOR)) && !defined(WIN32) |
| 193 | // On x86 the floating-point stack can be 64 or 80 bits wide. If it is |
| 194 | // 80 bits wide (as is the case on Linux) then double-rounding occurs and the |
| 195 | // result is not accurate. |
| 196 | // We know that Windows32 uses 64 bits and is therefore accurate. |
| 197 | // Note that the ARM simulator is compiled for 32bits. It therefore exhibits |
| 198 | // the same problem. |
| 199 | return false; |
| 200 | #endif |
| 201 | if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) { |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 202 | int read_digits; |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 203 | // The trimmed input fits into a double. |
| 204 | // If the 10^exponent (resp. 10^-exponent) fits into a double too then we |
| 205 | // can compute the result-double simply by multiplying (resp. dividing) the |
| 206 | // two numbers. |
| 207 | // This is possible because IEEE guarantees that floating-point operations |
| 208 | // return the best possible approximation. |
| 209 | if (exponent < 0 && -exponent < kExactPowersOfTenSize) { |
| 210 | // 10^-exponent fits into a double. |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 211 | *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); |
| 212 | ASSERT(read_digits == trimmed.length()); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 213 | *result /= exact_powers_of_ten[-exponent]; |
| 214 | return true; |
| 215 | } |
| 216 | if (0 <= exponent && exponent < kExactPowersOfTenSize) { |
| 217 | // 10^exponent fits into a double. |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 218 | *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); |
| 219 | ASSERT(read_digits == trimmed.length()); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 220 | *result *= exact_powers_of_ten[exponent]; |
| 221 | return true; |
| 222 | } |
| 223 | int remaining_digits = |
| 224 | kMaxExactDoubleIntegerDecimalDigits - trimmed.length(); |
| 225 | if ((0 <= exponent) && |
| 226 | (exponent - remaining_digits < kExactPowersOfTenSize)) { |
| 227 | // The trimmed string was short and we can multiply it with |
| 228 | // 10^remaining_digits. As a result the remaining exponent now fits |
| 229 | // into a double too. |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 230 | *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); |
| 231 | ASSERT(read_digits == trimmed.length()); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 232 | *result *= exact_powers_of_ten[remaining_digits]; |
| 233 | *result *= exact_powers_of_ten[exponent - remaining_digits]; |
| 234 | return true; |
| 235 | } |
| 236 | } |
| 237 | return false; |
| 238 | } |
| 239 | |
| 240 | |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 241 | // Returns 10^exponent as an exact DiyFp. |
| 242 | // The given exponent must be in the range [1; kDecimalExponentDistance[. |
| 243 | static DiyFp AdjustmentPowerOfTen(int exponent) { |
| 244 | ASSERT(0 < exponent); |
| 245 | ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance); |
| 246 | // Simply hardcode the remaining powers for the given decimal exponent |
| 247 | // distance. |
| 248 | ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8); |
| 249 | switch (exponent) { |
| 250 | case 1: return DiyFp(V8_2PART_UINT64_C(0xa0000000, 00000000), -60); |
| 251 | case 2: return DiyFp(V8_2PART_UINT64_C(0xc8000000, 00000000), -57); |
| 252 | case 3: return DiyFp(V8_2PART_UINT64_C(0xfa000000, 00000000), -54); |
| 253 | case 4: return DiyFp(V8_2PART_UINT64_C(0x9c400000, 00000000), -50); |
| 254 | case 5: return DiyFp(V8_2PART_UINT64_C(0xc3500000, 00000000), -47); |
| 255 | case 6: return DiyFp(V8_2PART_UINT64_C(0xf4240000, 00000000), -44); |
| 256 | case 7: return DiyFp(V8_2PART_UINT64_C(0x98968000, 00000000), -40); |
| 257 | default: |
| 258 | UNREACHABLE(); |
| 259 | return DiyFp(0, 0); |
| 260 | } |
| 261 | } |
| 262 | |
| 263 | |
| 264 | // If the function returns true then the result is the correct double. |
| 265 | // Otherwise it is either the correct double or the double that is just below |
| 266 | // the correct double. |
| 267 | static bool DiyFpStrtod(Vector<const char> buffer, |
| 268 | int exponent, |
| 269 | double* result) { |
| 270 | DiyFp input; |
| 271 | int remaining_decimals; |
| 272 | ReadDiyFp(buffer, &input, &remaining_decimals); |
| 273 | // Since we may have dropped some digits the input is not accurate. |
| 274 | // If remaining_decimals is different than 0 than the error is at most |
| 275 | // .5 ulp (unit in the last place). |
| 276 | // We don't want to deal with fractions and therefore keep a common |
| 277 | // denominator. |
| 278 | const int kDenominatorLog = 3; |
| 279 | const int kDenominator = 1 << kDenominatorLog; |
| 280 | // Move the remaining decimals into the exponent. |
| 281 | exponent += remaining_decimals; |
| 282 | int error = (remaining_decimals == 0 ? 0 : kDenominator / 2); |
| 283 | |
| 284 | int old_e = input.e(); |
| 285 | input.Normalize(); |
| 286 | error <<= old_e - input.e(); |
| 287 | |
| 288 | ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent); |
| 289 | if (exponent < PowersOfTenCache::kMinDecimalExponent) { |
| 290 | *result = 0.0; |
| 291 | return true; |
| 292 | } |
| 293 | DiyFp cached_power; |
| 294 | int cached_decimal_exponent; |
| 295 | PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent, |
| 296 | &cached_power, |
| 297 | &cached_decimal_exponent); |
| 298 | |
| 299 | if (cached_decimal_exponent != exponent) { |
| 300 | int adjustment_exponent = exponent - cached_decimal_exponent; |
| 301 | DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent); |
| 302 | input.Multiply(adjustment_power); |
| 303 | if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) { |
| 304 | // The product of input with the adjustment power fits into a 64 bit |
| 305 | // integer. |
| 306 | ASSERT(DiyFp::kSignificandSize == 64); |
| 307 | } else { |
| 308 | // The adjustment power is exact. There is hence only an error of 0.5. |
| 309 | error += kDenominator / 2; |
| 310 | } |
| 311 | } |
| 312 | |
| 313 | input.Multiply(cached_power); |
| 314 | // The error introduced by a multiplication of a*b equals |
| 315 | // error_a + error_b + error_a*error_b/2^64 + 0.5 |
| 316 | // Substituting a with 'input' and b with 'cached_power' we have |
| 317 | // error_b = 0.5 (all cached powers have an error of less than 0.5 ulp), |
| 318 | // error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64 |
| 319 | int error_b = kDenominator / 2; |
| 320 | int error_ab = (error == 0 ? 0 : 1); // We round up to 1. |
| 321 | int fixed_error = kDenominator / 2; |
| 322 | error += error_b + error_ab + fixed_error; |
| 323 | |
| 324 | old_e = input.e(); |
| 325 | input.Normalize(); |
| 326 | error <<= old_e - input.e(); |
| 327 | |
| 328 | // See if the double's significand changes if we add/subtract the error. |
| 329 | int order_of_magnitude = DiyFp::kSignificandSize + input.e(); |
| 330 | int effective_significand_size = |
| 331 | Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude); |
| 332 | int precision_digits_count = |
| 333 | DiyFp::kSignificandSize - effective_significand_size; |
| 334 | if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) { |
| 335 | // This can only happen for very small denormals. In this case the |
| 336 | // half-way multiplied by the denominator exceeds the range of an uint64. |
| 337 | // Simply shift everything to the right. |
| 338 | int shift_amount = (precision_digits_count + kDenominatorLog) - |
| 339 | DiyFp::kSignificandSize + 1; |
| 340 | input.set_f(input.f() >> shift_amount); |
| 341 | input.set_e(input.e() + shift_amount); |
| 342 | // We add 1 for the lost precision of error, and kDenominator for |
| 343 | // the lost precision of input.f(). |
| 344 | error = (error >> shift_amount) + 1 + kDenominator; |
| 345 | precision_digits_count -= shift_amount; |
| 346 | } |
| 347 | // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too. |
| 348 | ASSERT(DiyFp::kSignificandSize == 64); |
| 349 | ASSERT(precision_digits_count < 64); |
| 350 | uint64_t one64 = 1; |
| 351 | uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1; |
| 352 | uint64_t precision_bits = input.f() & precision_bits_mask; |
| 353 | uint64_t half_way = one64 << (precision_digits_count - 1); |
| 354 | precision_bits *= kDenominator; |
| 355 | half_way *= kDenominator; |
| 356 | DiyFp rounded_input(input.f() >> precision_digits_count, |
| 357 | input.e() + precision_digits_count); |
| 358 | if (precision_bits >= half_way + error) { |
| 359 | rounded_input.set_f(rounded_input.f() + 1); |
| 360 | } |
| 361 | // If the last_bits are too close to the half-way case than we are too |
| 362 | // inaccurate and round down. In this case we return false so that we can |
| 363 | // fall back to a more precise algorithm. |
| 364 | |
| 365 | *result = Double(rounded_input).value(); |
| 366 | if (half_way - error < precision_bits && precision_bits < half_way + error) { |
| 367 | // Too imprecise. The caller will have to fall back to a slower version. |
| 368 | // However the returned number is guaranteed to be either the correct |
| 369 | // double, or the next-lower double. |
| 370 | return false; |
| 371 | } else { |
| 372 | return true; |
| 373 | } |
| 374 | } |
| 375 | |
| 376 | |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 377 | double Strtod(Vector<const char> buffer, int exponent) { |
| 378 | Vector<const char> left_trimmed = TrimLeadingZeros(buffer); |
| 379 | Vector<const char> trimmed = TrimTrailingZeros(left_trimmed); |
| 380 | exponent += left_trimmed.length() - trimmed.length(); |
| 381 | if (trimmed.length() == 0) return 0.0; |
| 382 | if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) return V8_INFINITY; |
| 383 | if (exponent + trimmed.length() <= kMinDecimalPower) return 0.0; |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 384 | |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 385 | double result; |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame^] | 386 | if (DoubleStrtod(trimmed, exponent, &result) || |
| 387 | DiyFpStrtod(trimmed, exponent, &result)) { |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 388 | return result; |
| 389 | } |
| 390 | return old_strtod(trimmed, exponent); |
| 391 | } |
| 392 | |
| 393 | } } // namespace v8::internal |