// Copyright 2010 the V8 project authors. All rights reserved. // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are // met: // // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above // copyright notice, this list of conditions and the following // disclaimer in the documentation and/or other materials provided // with the distribution. // * Neither the name of Google Inc. nor the names of its // contributors may be used to endorse or promote products derived // from this software without specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. #include #include #include "v8.h" #include "strtod.h" // #include "cached-powers.h" namespace v8 { namespace internal { // 2^53 = 9007199254740992. // Any integer with at most 15 decimal digits will hence fit into a double // (which has a 53bit significand) without loss of precision. static const int kMaxExactDoubleIntegerDecimalDigits = 15; // 2^64 = 18446744073709551616 // Any integer with at most 19 digits will hence fit into a 64bit datatype. static const int kMaxUint64DecimalDigits = 19; // Max double: 1.7976931348623157 x 10^308 // Min non-zero double: 4.9406564584124654 x 10^-324 // Any x >= 10^309 is interpreted as +infinity. // Any x <= 10^-324 is interpreted as 0. // Note that 2.5e-324 (despite being smaller than the min double) will be read // as non-zero (equal to the min non-zero double). static const int kMaxDecimalPower = 309; static const int kMinDecimalPower = -324; static const double exact_powers_of_ten[] = { 1.0, // 10^0 10.0, 100.0, 1000.0, 10000.0, 100000.0, 1000000.0, 10000000.0, 100000000.0, 1000000000.0, 10000000000.0, // 10^10 100000000000.0, 1000000000000.0, 10000000000000.0, 100000000000000.0, 1000000000000000.0, 10000000000000000.0, 100000000000000000.0, 1000000000000000000.0, 10000000000000000000.0, 100000000000000000000.0, // 10^20 1000000000000000000000.0, // 10^22 = 0x21e19e0c9bab2400000 = 0x878678326eac9 * 2^22 10000000000000000000000.0 }; static const int kExactPowersOfTenSize = ARRAY_SIZE(exact_powers_of_ten); extern "C" double gay_strtod(const char* s00, const char** se); static double old_strtod(Vector buffer, int exponent) { // gay_strtod is broken on Linux,x86. For numbers with few decimal digits // the computation is done using floating-point operations which (on Linux) // are prone to double-rounding errors. // By adding several zeroes to the buffer gay_strtod falls back to a slower // (but correct) algorithm. const int kInsertedZeroesCount = 20; char gay_buffer[1024]; Vector gay_buffer_vector(gay_buffer, sizeof(gay_buffer)); int pos = 0; for (int i = 0; i < buffer.length(); ++i) { gay_buffer_vector[pos++] = buffer[i]; } for (int i = 0; i < kInsertedZeroesCount; ++i) { gay_buffer_vector[pos++] = '0'; } exponent -= kInsertedZeroesCount; gay_buffer_vector[pos++] = 'e'; if (exponent < 0) { gay_buffer_vector[pos++] = '-'; exponent = -exponent; } const int kNumberOfExponentDigits = 5; for (int i = kNumberOfExponentDigits - 1; i >= 0; i--) { gay_buffer_vector[pos + i] = exponent % 10 + '0'; exponent /= 10; } pos += kNumberOfExponentDigits; gay_buffer_vector[pos] = '\0'; return gay_strtod(gay_buffer, NULL); } static Vector TrimLeadingZeros(Vector buffer) { for (int i = 0; i < buffer.length(); i++) { if (buffer[i] != '0') { return Vector(buffer.start() + i, buffer.length() - i); } } return Vector(buffer.start(), 0); } static Vector TrimTrailingZeros(Vector buffer) { for (int i = buffer.length() - 1; i >= 0; --i) { if (buffer[i] != '0') { return Vector(buffer.start(), i + 1); } } return Vector(buffer.start(), 0); } uint64_t ReadUint64(Vector buffer) { ASSERT(buffer.length() <= kMaxUint64DecimalDigits); uint64_t result = 0; for (int i = 0; i < buffer.length(); ++i) { int digit = buffer[i] - '0'; ASSERT(0 <= digit && digit <= 9); result = 10 * result + digit; } return result; } static bool DoubleStrtod(Vector trimmed, int exponent, double* result) { #if defined(V8_TARGET_ARCH_IA32) && !defined(WIN32) // On x86 the floating-point stack can be 64 or 80 bits wide. If it is // 80 bits wide (as is the case on Linux) then double-rounding occurs and the // result is not accurate. // We know that Windows32 uses 64 bits and is therefore accurate. return false; #endif if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) { // The trimmed input fits into a double. // If the 10^exponent (resp. 10^-exponent) fits into a double too then we // can compute the result-double simply by multiplying (resp. dividing) the // two numbers. // This is possible because IEEE guarantees that floating-point operations // return the best possible approximation. if (exponent < 0 && -exponent < kExactPowersOfTenSize) { // 10^-exponent fits into a double. *result = static_cast(ReadUint64(trimmed)); *result /= exact_powers_of_ten[-exponent]; return true; } if (0 <= exponent && exponent < kExactPowersOfTenSize) { // 10^exponent fits into a double. *result = static_cast(ReadUint64(trimmed)); *result *= exact_powers_of_ten[exponent]; return true; } int remaining_digits = kMaxExactDoubleIntegerDecimalDigits - trimmed.length(); if ((0 <= exponent) && (exponent - remaining_digits < kExactPowersOfTenSize)) { // The trimmed string was short and we can multiply it with // 10^remaining_digits. As a result the remaining exponent now fits // into a double too. *result = static_cast(ReadUint64(trimmed)); *result *= exact_powers_of_ten[remaining_digits]; *result *= exact_powers_of_ten[exponent - remaining_digits]; return true; } } return false; } double Strtod(Vector buffer, int exponent) { Vector left_trimmed = TrimLeadingZeros(buffer); Vector trimmed = TrimTrailingZeros(left_trimmed); exponent += left_trimmed.length() - trimmed.length(); if (trimmed.length() == 0) return 0.0; if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) return V8_INFINITY; if (exponent + trimmed.length() <= kMinDecimalPower) return 0.0; double result; if (DoubleStrtod(trimmed, exponent, &result)) { return result; } return old_strtod(trimmed, exponent); } } } // namespace v8::internal