Ben Murdoch | 3ef787d | 2012-04-12 10:51:47 +0100 | [diff] [blame] | 1 | // Copyright 2012 the V8 project authors. All rights reserved. |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 2 | // Use of this source code is governed by a BSD-style license that can be |
| 3 | // found in the LICENSE file. |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 4 | |
| 5 | #include <stdarg.h> |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 6 | #include <cmath> |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 7 | |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 8 | #include "src/v8.h" |
| 9 | |
| 10 | #include "src/bignum.h" |
| 11 | #include "src/cached-powers.h" |
| 12 | #include "src/double.h" |
| 13 | #include "src/globals.h" |
| 14 | #include "src/strtod.h" |
| 15 | #include "src/utils.h" |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 16 | |
| 17 | namespace v8 { |
| 18 | namespace internal { |
| 19 | |
| 20 | // 2^53 = 9007199254740992. |
| 21 | // Any integer with at most 15 decimal digits will hence fit into a double |
| 22 | // (which has a 53bit significand) without loss of precision. |
| 23 | static const int kMaxExactDoubleIntegerDecimalDigits = 15; |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 24 | // 2^64 = 18446744073709551616 > 10^19 |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 25 | static const int kMaxUint64DecimalDigits = 19; |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 26 | |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 27 | // Max double: 1.7976931348623157 x 10^308 |
| 28 | // Min non-zero double: 4.9406564584124654 x 10^-324 |
| 29 | // Any x >= 10^309 is interpreted as +infinity. |
| 30 | // Any x <= 10^-324 is interpreted as 0. |
| 31 | // Note that 2.5e-324 (despite being smaller than the min double) will be read |
| 32 | // as non-zero (equal to the min non-zero double). |
| 33 | static const int kMaxDecimalPower = 309; |
| 34 | static const int kMinDecimalPower = -324; |
| 35 | |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 36 | // 2^64 = 18446744073709551616 |
| 37 | static const uint64_t kMaxUint64 = V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF); |
| 38 | |
| 39 | |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 40 | static const double exact_powers_of_ten[] = { |
| 41 | 1.0, // 10^0 |
| 42 | 10.0, |
| 43 | 100.0, |
| 44 | 1000.0, |
| 45 | 10000.0, |
| 46 | 100000.0, |
| 47 | 1000000.0, |
| 48 | 10000000.0, |
| 49 | 100000000.0, |
| 50 | 1000000000.0, |
| 51 | 10000000000.0, // 10^10 |
| 52 | 100000000000.0, |
| 53 | 1000000000000.0, |
| 54 | 10000000000000.0, |
| 55 | 100000000000000.0, |
| 56 | 1000000000000000.0, |
| 57 | 10000000000000000.0, |
| 58 | 100000000000000000.0, |
| 59 | 1000000000000000000.0, |
| 60 | 10000000000000000000.0, |
| 61 | 100000000000000000000.0, // 10^20 |
| 62 | 1000000000000000000000.0, |
| 63 | // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22 |
| 64 | 10000000000000000000000.0 |
| 65 | }; |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 66 | static const int kExactPowersOfTenSize = arraysize(exact_powers_of_ten); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 67 | |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 68 | // Maximum number of significant digits in the decimal representation. |
| 69 | // In fact the value is 772 (see conversions.cc), but to give us some margin |
| 70 | // we round up to 780. |
| 71 | static const int kMaxSignificantDecimalDigits = 780; |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 72 | |
| 73 | static Vector<const char> TrimLeadingZeros(Vector<const char> buffer) { |
| 74 | for (int i = 0; i < buffer.length(); i++) { |
| 75 | if (buffer[i] != '0') { |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 76 | return buffer.SubVector(i, buffer.length()); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 77 | } |
| 78 | } |
| 79 | return Vector<const char>(buffer.start(), 0); |
| 80 | } |
| 81 | |
| 82 | |
| 83 | static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) { |
| 84 | for (int i = buffer.length() - 1; i >= 0; --i) { |
| 85 | if (buffer[i] != '0') { |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 86 | return buffer.SubVector(0, i + 1); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 87 | } |
| 88 | } |
| 89 | return Vector<const char>(buffer.start(), 0); |
| 90 | } |
| 91 | |
| 92 | |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 93 | static void TrimToMaxSignificantDigits(Vector<const char> buffer, |
| 94 | int exponent, |
| 95 | char* significant_buffer, |
| 96 | int* significant_exponent) { |
| 97 | for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) { |
| 98 | significant_buffer[i] = buffer[i]; |
| 99 | } |
| 100 | // The input buffer has been trimmed. Therefore the last digit must be |
| 101 | // different from '0'. |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 102 | DCHECK(buffer[buffer.length() - 1] != '0'); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 103 | // Set the last digit to be non-zero. This is sufficient to guarantee |
| 104 | // correct rounding. |
| 105 | significant_buffer[kMaxSignificantDecimalDigits - 1] = '1'; |
| 106 | *significant_exponent = |
| 107 | exponent + (buffer.length() - kMaxSignificantDecimalDigits); |
| 108 | } |
| 109 | |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 110 | |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 111 | // Reads digits from the buffer and converts them to a uint64. |
| 112 | // Reads in as many digits as fit into a uint64. |
| 113 | // When the string starts with "1844674407370955161" no further digit is read. |
| 114 | // Since 2^64 = 18446744073709551616 it would still be possible read another |
| 115 | // digit if it was less or equal than 6, but this would complicate the code. |
| 116 | static uint64_t ReadUint64(Vector<const char> buffer, |
| 117 | int* number_of_read_digits) { |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 118 | uint64_t result = 0; |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 119 | int i = 0; |
| 120 | while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) { |
| 121 | int digit = buffer[i++] - '0'; |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 122 | DCHECK(0 <= digit && digit <= 9); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 123 | result = 10 * result + digit; |
| 124 | } |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 125 | *number_of_read_digits = i; |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 126 | return result; |
| 127 | } |
| 128 | |
| 129 | |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 130 | // Reads a DiyFp from the buffer. |
| 131 | // The returned DiyFp is not necessarily normalized. |
| 132 | // If remaining_decimals is zero then the returned DiyFp is accurate. |
| 133 | // Otherwise it has been rounded and has error of at most 1/2 ulp. |
| 134 | static void ReadDiyFp(Vector<const char> buffer, |
| 135 | DiyFp* result, |
| 136 | int* remaining_decimals) { |
| 137 | int read_digits; |
| 138 | uint64_t significand = ReadUint64(buffer, &read_digits); |
| 139 | if (buffer.length() == read_digits) { |
| 140 | *result = DiyFp(significand, 0); |
| 141 | *remaining_decimals = 0; |
| 142 | } else { |
| 143 | // Round the significand. |
| 144 | if (buffer[read_digits] >= '5') { |
| 145 | significand++; |
| 146 | } |
| 147 | // Compute the binary exponent. |
| 148 | int exponent = 0; |
| 149 | *result = DiyFp(significand, exponent); |
| 150 | *remaining_decimals = buffer.length() - read_digits; |
| 151 | } |
| 152 | } |
| 153 | |
| 154 | |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 155 | static bool DoubleStrtod(Vector<const char> trimmed, |
| 156 | int exponent, |
| 157 | double* result) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 158 | #if (V8_TARGET_ARCH_IA32 || V8_TARGET_ARCH_X87 || defined(USE_SIMULATOR)) && \ |
| 159 | !defined(_MSC_VER) |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 160 | // On x86 the floating-point stack can be 64 or 80 bits wide. If it is |
| 161 | // 80 bits wide (as is the case on Linux) then double-rounding occurs and the |
| 162 | // result is not accurate. |
Ben Murdoch | 3ef787d | 2012-04-12 10:51:47 +0100 | [diff] [blame] | 163 | // We know that Windows32 with MSVC, unlike with MinGW32, uses 64 bits and is |
| 164 | // therefore accurate. |
| 165 | // Note that the ARM and MIPS simulators are compiled for 32bits. They |
| 166 | // therefore exhibit the same problem. |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 167 | return false; |
| 168 | #endif |
| 169 | if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) { |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 170 | int read_digits; |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 171 | // The trimmed input fits into a double. |
| 172 | // If the 10^exponent (resp. 10^-exponent) fits into a double too then we |
| 173 | // can compute the result-double simply by multiplying (resp. dividing) the |
| 174 | // two numbers. |
| 175 | // This is possible because IEEE guarantees that floating-point operations |
| 176 | // return the best possible approximation. |
| 177 | if (exponent < 0 && -exponent < kExactPowersOfTenSize) { |
| 178 | // 10^-exponent fits into a double. |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 179 | *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 180 | DCHECK(read_digits == trimmed.length()); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 181 | *result /= exact_powers_of_ten[-exponent]; |
| 182 | return true; |
| 183 | } |
| 184 | if (0 <= exponent && exponent < kExactPowersOfTenSize) { |
| 185 | // 10^exponent fits into a double. |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 186 | *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 187 | DCHECK(read_digits == trimmed.length()); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 188 | *result *= exact_powers_of_ten[exponent]; |
| 189 | return true; |
| 190 | } |
| 191 | int remaining_digits = |
| 192 | kMaxExactDoubleIntegerDecimalDigits - trimmed.length(); |
| 193 | if ((0 <= exponent) && |
| 194 | (exponent - remaining_digits < kExactPowersOfTenSize)) { |
| 195 | // The trimmed string was short and we can multiply it with |
| 196 | // 10^remaining_digits. As a result the remaining exponent now fits |
| 197 | // into a double too. |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 198 | *result = static_cast<double>(ReadUint64(trimmed, &read_digits)); |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 199 | DCHECK(read_digits == trimmed.length()); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 200 | *result *= exact_powers_of_ten[remaining_digits]; |
| 201 | *result *= exact_powers_of_ten[exponent - remaining_digits]; |
| 202 | return true; |
| 203 | } |
| 204 | } |
| 205 | return false; |
| 206 | } |
| 207 | |
| 208 | |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 209 | // Returns 10^exponent as an exact DiyFp. |
| 210 | // The given exponent must be in the range [1; kDecimalExponentDistance[. |
| 211 | static DiyFp AdjustmentPowerOfTen(int exponent) { |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 212 | DCHECK(0 < exponent); |
| 213 | DCHECK(exponent < PowersOfTenCache::kDecimalExponentDistance); |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 214 | // Simply hardcode the remaining powers for the given decimal exponent |
| 215 | // distance. |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 216 | DCHECK(PowersOfTenCache::kDecimalExponentDistance == 8); |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 217 | switch (exponent) { |
| 218 | case 1: return DiyFp(V8_2PART_UINT64_C(0xa0000000, 00000000), -60); |
| 219 | case 2: return DiyFp(V8_2PART_UINT64_C(0xc8000000, 00000000), -57); |
| 220 | case 3: return DiyFp(V8_2PART_UINT64_C(0xfa000000, 00000000), -54); |
| 221 | case 4: return DiyFp(V8_2PART_UINT64_C(0x9c400000, 00000000), -50); |
| 222 | case 5: return DiyFp(V8_2PART_UINT64_C(0xc3500000, 00000000), -47); |
| 223 | case 6: return DiyFp(V8_2PART_UINT64_C(0xf4240000, 00000000), -44); |
| 224 | case 7: return DiyFp(V8_2PART_UINT64_C(0x98968000, 00000000), -40); |
| 225 | default: |
| 226 | UNREACHABLE(); |
| 227 | return DiyFp(0, 0); |
| 228 | } |
| 229 | } |
| 230 | |
| 231 | |
| 232 | // If the function returns true then the result is the correct double. |
| 233 | // Otherwise it is either the correct double or the double that is just below |
| 234 | // the correct double. |
| 235 | static bool DiyFpStrtod(Vector<const char> buffer, |
| 236 | int exponent, |
| 237 | double* result) { |
| 238 | DiyFp input; |
| 239 | int remaining_decimals; |
| 240 | ReadDiyFp(buffer, &input, &remaining_decimals); |
| 241 | // Since we may have dropped some digits the input is not accurate. |
| 242 | // If remaining_decimals is different than 0 than the error is at most |
| 243 | // .5 ulp (unit in the last place). |
| 244 | // We don't want to deal with fractions and therefore keep a common |
| 245 | // denominator. |
| 246 | const int kDenominatorLog = 3; |
| 247 | const int kDenominator = 1 << kDenominatorLog; |
| 248 | // Move the remaining decimals into the exponent. |
| 249 | exponent += remaining_decimals; |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 250 | int64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2); |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 251 | |
| 252 | int old_e = input.e(); |
| 253 | input.Normalize(); |
| 254 | error <<= old_e - input.e(); |
| 255 | |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 256 | DCHECK(exponent <= PowersOfTenCache::kMaxDecimalExponent); |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 257 | if (exponent < PowersOfTenCache::kMinDecimalExponent) { |
| 258 | *result = 0.0; |
| 259 | return true; |
| 260 | } |
| 261 | DiyFp cached_power; |
| 262 | int cached_decimal_exponent; |
| 263 | PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent, |
| 264 | &cached_power, |
| 265 | &cached_decimal_exponent); |
| 266 | |
| 267 | if (cached_decimal_exponent != exponent) { |
| 268 | int adjustment_exponent = exponent - cached_decimal_exponent; |
| 269 | DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent); |
| 270 | input.Multiply(adjustment_power); |
| 271 | if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) { |
| 272 | // The product of input with the adjustment power fits into a 64 bit |
| 273 | // integer. |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 274 | DCHECK(DiyFp::kSignificandSize == 64); |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 275 | } else { |
| 276 | // The adjustment power is exact. There is hence only an error of 0.5. |
| 277 | error += kDenominator / 2; |
| 278 | } |
| 279 | } |
| 280 | |
| 281 | input.Multiply(cached_power); |
| 282 | // The error introduced by a multiplication of a*b equals |
| 283 | // error_a + error_b + error_a*error_b/2^64 + 0.5 |
| 284 | // Substituting a with 'input' and b with 'cached_power' we have |
| 285 | // error_b = 0.5 (all cached powers have an error of less than 0.5 ulp), |
| 286 | // error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64 |
| 287 | int error_b = kDenominator / 2; |
| 288 | int error_ab = (error == 0 ? 0 : 1); // We round up to 1. |
| 289 | int fixed_error = kDenominator / 2; |
| 290 | error += error_b + error_ab + fixed_error; |
| 291 | |
| 292 | old_e = input.e(); |
| 293 | input.Normalize(); |
| 294 | error <<= old_e - input.e(); |
| 295 | |
| 296 | // See if the double's significand changes if we add/subtract the error. |
| 297 | int order_of_magnitude = DiyFp::kSignificandSize + input.e(); |
| 298 | int effective_significand_size = |
| 299 | Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude); |
| 300 | int precision_digits_count = |
| 301 | DiyFp::kSignificandSize - effective_significand_size; |
| 302 | if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) { |
| 303 | // This can only happen for very small denormals. In this case the |
| 304 | // half-way multiplied by the denominator exceeds the range of an uint64. |
| 305 | // Simply shift everything to the right. |
| 306 | int shift_amount = (precision_digits_count + kDenominatorLog) - |
| 307 | DiyFp::kSignificandSize + 1; |
| 308 | input.set_f(input.f() >> shift_amount); |
| 309 | input.set_e(input.e() + shift_amount); |
| 310 | // We add 1 for the lost precision of error, and kDenominator for |
| 311 | // the lost precision of input.f(). |
| 312 | error = (error >> shift_amount) + 1 + kDenominator; |
| 313 | precision_digits_count -= shift_amount; |
| 314 | } |
| 315 | // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too. |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 316 | DCHECK(DiyFp::kSignificandSize == 64); |
| 317 | DCHECK(precision_digits_count < 64); |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 318 | uint64_t one64 = 1; |
| 319 | uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1; |
| 320 | uint64_t precision_bits = input.f() & precision_bits_mask; |
| 321 | uint64_t half_way = one64 << (precision_digits_count - 1); |
| 322 | precision_bits *= kDenominator; |
| 323 | half_way *= kDenominator; |
| 324 | DiyFp rounded_input(input.f() >> precision_digits_count, |
| 325 | input.e() + precision_digits_count); |
| 326 | if (precision_bits >= half_way + error) { |
| 327 | rounded_input.set_f(rounded_input.f() + 1); |
| 328 | } |
| 329 | // If the last_bits are too close to the half-way case than we are too |
| 330 | // inaccurate and round down. In this case we return false so that we can |
| 331 | // fall back to a more precise algorithm. |
| 332 | |
| 333 | *result = Double(rounded_input).value(); |
| 334 | if (half_way - error < precision_bits && precision_bits < half_way + error) { |
| 335 | // Too imprecise. The caller will have to fall back to a slower version. |
| 336 | // However the returned number is guaranteed to be either the correct |
| 337 | // double, or the next-lower double. |
| 338 | return false; |
| 339 | } else { |
| 340 | return true; |
| 341 | } |
| 342 | } |
| 343 | |
| 344 | |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 345 | // Returns the correct double for the buffer*10^exponent. |
| 346 | // The variable guess should be a close guess that is either the correct double |
| 347 | // or its lower neighbor (the nearest double less than the correct one). |
| 348 | // Preconditions: |
| 349 | // buffer.length() + exponent <= kMaxDecimalPower + 1 |
| 350 | // buffer.length() + exponent > kMinDecimalPower |
| 351 | // buffer.length() <= kMaxDecimalSignificantDigits |
| 352 | static double BignumStrtod(Vector<const char> buffer, |
| 353 | int exponent, |
| 354 | double guess) { |
| 355 | if (guess == V8_INFINITY) { |
| 356 | return guess; |
| 357 | } |
| 358 | |
| 359 | DiyFp upper_boundary = Double(guess).UpperBoundary(); |
| 360 | |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 361 | DCHECK(buffer.length() + exponent <= kMaxDecimalPower + 1); |
| 362 | DCHECK(buffer.length() + exponent > kMinDecimalPower); |
| 363 | DCHECK(buffer.length() <= kMaxSignificantDecimalDigits); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 364 | // Make sure that the Bignum will be able to hold all our numbers. |
| 365 | // Our Bignum implementation has a separate field for exponents. Shifts will |
| 366 | // consume at most one bigit (< 64 bits). |
| 367 | // ln(10) == 3.3219... |
Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame] | 368 | DCHECK(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 369 | Bignum input; |
| 370 | Bignum boundary; |
| 371 | input.AssignDecimalString(buffer); |
| 372 | boundary.AssignUInt64(upper_boundary.f()); |
| 373 | if (exponent >= 0) { |
| 374 | input.MultiplyByPowerOfTen(exponent); |
| 375 | } else { |
| 376 | boundary.MultiplyByPowerOfTen(-exponent); |
| 377 | } |
| 378 | if (upper_boundary.e() > 0) { |
| 379 | boundary.ShiftLeft(upper_boundary.e()); |
| 380 | } else { |
| 381 | input.ShiftLeft(-upper_boundary.e()); |
| 382 | } |
| 383 | int comparison = Bignum::Compare(input, boundary); |
| 384 | if (comparison < 0) { |
| 385 | return guess; |
| 386 | } else if (comparison > 0) { |
| 387 | return Double(guess).NextDouble(); |
| 388 | } else if ((Double(guess).Significand() & 1) == 0) { |
| 389 | // Round towards even. |
| 390 | return guess; |
| 391 | } else { |
| 392 | return Double(guess).NextDouble(); |
| 393 | } |
| 394 | } |
| 395 | |
| 396 | |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 397 | double Strtod(Vector<const char> buffer, int exponent) { |
| 398 | Vector<const char> left_trimmed = TrimLeadingZeros(buffer); |
| 399 | Vector<const char> trimmed = TrimTrailingZeros(left_trimmed); |
| 400 | exponent += left_trimmed.length() - trimmed.length(); |
| 401 | if (trimmed.length() == 0) return 0.0; |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 402 | if (trimmed.length() > kMaxSignificantDecimalDigits) { |
| 403 | char significant_buffer[kMaxSignificantDecimalDigits]; |
| 404 | int significant_exponent; |
| 405 | TrimToMaxSignificantDigits(trimmed, exponent, |
| 406 | significant_buffer, &significant_exponent); |
Shimeng (Simon) Wang | 8a31eba | 2010-12-06 19:01:33 -0800 | [diff] [blame] | 407 | return Strtod(Vector<const char>(significant_buffer, |
| 408 | kMaxSignificantDecimalDigits), |
| 409 | significant_exponent); |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 410 | } |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 411 | if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) return V8_INFINITY; |
| 412 | if (exponent + trimmed.length() <= kMinDecimalPower) return 0.0; |
John Reck | 5913587 | 2010-11-02 12:39:01 -0700 | [diff] [blame] | 413 | |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 414 | double guess; |
| 415 | if (DoubleStrtod(trimmed, exponent, &guess) || |
| 416 | DiyFpStrtod(trimmed, exponent, &guess)) { |
| 417 | return guess; |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 418 | } |
Russell Brenner | 90bac25 | 2010-11-18 13:33:46 -0800 | [diff] [blame] | 419 | return BignumStrtod(trimmed, exponent, guess); |
Ben Murdoch | f87a203 | 2010-10-22 12:50:53 +0100 | [diff] [blame] | 420 | } |
| 421 | |
| 422 | } } // namespace v8::internal |