// © 2018 and later: Unicode, Inc. and others. // License & terms of use: http://www.unicode.org/copyright.html // // From the double-conversion library. Original license: // // 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. // ICU PATCH: ifdef around UCONFIG_NO_FORMATTING #include "unicode/utypes.h" #if !UCONFIG_NO_FORMATTING #include #include // ICU PATCH: Customize header file paths for ICU. #include "double-conversion-bignum.h" #include "double-conversion-cached-powers.h" #include "double-conversion-ieee.h" #include "double-conversion-strtod.h" // ICU PATCH: Wrap in ICU namespace U_NAMESPACE_BEGIN namespace double_conversion { #if defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS) // 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; #endif // #if defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS) // 2^64 = 18446744073709551616 > 10^19 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; // 2^64 = 18446744073709551616 static const uint64_t kMaxUint64 = DOUBLE_CONVERSION_UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF); #if defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS) 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 = DOUBLE_CONVERSION_ARRAY_SIZE(exact_powers_of_ten); #endif // #if defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS) // Maximum number of significant digits in the decimal representation. // In fact the value is 772 (see conversions.cc), but to give us some margin // we round up to 780. static const int kMaxSignificantDecimalDigits = 780; static Vector TrimLeadingZeros(Vector buffer) { for (int i = 0; i < buffer.length(); i++) { if (buffer[i] != '0') { return buffer.SubVector(i, buffer.length()); } } return Vector(buffer.start(), 0); } static Vector TrimTrailingZeros(Vector buffer) { for (int i = buffer.length() - 1; i >= 0; --i) { if (buffer[i] != '0') { return buffer.SubVector(0, i + 1); } } return Vector(buffer.start(), 0); } static void CutToMaxSignificantDigits(Vector buffer, int exponent, char* significant_buffer, int* significant_exponent) { for (int i = 0; i < kMaxSignificantDecimalDigits - 1; ++i) { significant_buffer[i] = buffer[i]; } // The input buffer has been trimmed. Therefore the last digit must be // different from '0'. DOUBLE_CONVERSION_ASSERT(buffer[buffer.length() - 1] != '0'); // Set the last digit to be non-zero. This is sufficient to guarantee // correct rounding. significant_buffer[kMaxSignificantDecimalDigits - 1] = '1'; *significant_exponent = exponent + (buffer.length() - kMaxSignificantDecimalDigits); } // Trims the buffer and cuts it to at most kMaxSignificantDecimalDigits. // If possible the input-buffer is reused, but if the buffer needs to be // modified (due to cutting), then the input needs to be copied into the // buffer_copy_space. static void TrimAndCut(Vector buffer, int exponent, char* buffer_copy_space, int space_size, Vector* trimmed, int* updated_exponent) { Vector left_trimmed = TrimLeadingZeros(buffer); Vector right_trimmed = TrimTrailingZeros(left_trimmed); exponent += left_trimmed.length() - right_trimmed.length(); if (right_trimmed.length() > kMaxSignificantDecimalDigits) { (void) space_size; // Mark variable as used. DOUBLE_CONVERSION_ASSERT(space_size >= kMaxSignificantDecimalDigits); CutToMaxSignificantDigits(right_trimmed, exponent, buffer_copy_space, updated_exponent); *trimmed = Vector(buffer_copy_space, kMaxSignificantDecimalDigits); } else { *trimmed = right_trimmed; *updated_exponent = exponent; } } // Reads digits from the buffer and converts them to a uint64. // Reads in as many digits as fit into a uint64. // When the string starts with "1844674407370955161" no further digit is read. // Since 2^64 = 18446744073709551616 it would still be possible read another // digit if it was less or equal than 6, but this would complicate the code. static uint64_t ReadUint64(Vector buffer, int* number_of_read_digits) { uint64_t result = 0; int i = 0; while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) { int digit = buffer[i++] - '0'; DOUBLE_CONVERSION_ASSERT(0 <= digit && digit <= 9); result = 10 * result + digit; } *number_of_read_digits = i; return result; } // Reads a DiyFp from the buffer. // The returned DiyFp is not necessarily normalized. // If remaining_decimals is zero then the returned DiyFp is accurate. // Otherwise it has been rounded and has error of at most 1/2 ulp. static void ReadDiyFp(Vector buffer, DiyFp* result, int* remaining_decimals) { int read_digits; uint64_t significand = ReadUint64(buffer, &read_digits); if (buffer.length() == read_digits) { *result = DiyFp(significand, 0); *remaining_decimals = 0; } else { // Round the significand. if (buffer[read_digits] >= '5') { significand++; } // Compute the binary exponent. int exponent = 0; *result = DiyFp(significand, exponent); *remaining_decimals = buffer.length() - read_digits; } } static bool DoubleStrtod(Vector trimmed, int exponent, double* result) { #if !defined(DOUBLE_CONVERSION_CORRECT_DOUBLE_OPERATIONS) // 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. // Note that the ARM simulator is compiled for 32bits. It therefore exhibits // the same problem. return false; #else if (trimmed.length() <= kMaxExactDoubleIntegerDecimalDigits) { int read_digits; // 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, &read_digits)); DOUBLE_CONVERSION_ASSERT(read_digits == trimmed.length()); *result /= exact_powers_of_ten[-exponent]; return true; } if (0 <= exponent && exponent < kExactPowersOfTenSize) { // 10^exponent fits into a double. *result = static_cast(ReadUint64(trimmed, &read_digits)); DOUBLE_CONVERSION_ASSERT(read_digits == trimmed.length()); *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, &read_digits)); DOUBLE_CONVERSION_ASSERT(read_digits == trimmed.length()); *result *= exact_powers_of_ten[remaining_digits]; *result *= exact_powers_of_ten[exponent - remaining_digits]; return true; } } return false; #endif } // Returns 10^exponent as an exact DiyFp. // The given exponent must be in the range [1; kDecimalExponentDistance[. static DiyFp AdjustmentPowerOfTen(int exponent) { DOUBLE_CONVERSION_ASSERT(0 < exponent); DOUBLE_CONVERSION_ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance); // Simply hardcode the remaining powers for the given decimal exponent // distance. DOUBLE_CONVERSION_ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8); switch (exponent) { case 1: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xa0000000, 00000000), -60); case 2: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xc8000000, 00000000), -57); case 3: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xfa000000, 00000000), -54); case 4: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0x9c400000, 00000000), -50); case 5: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xc3500000, 00000000), -47); case 6: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0xf4240000, 00000000), -44); case 7: return DiyFp(DOUBLE_CONVERSION_UINT64_2PART_C(0x98968000, 00000000), -40); default: DOUBLE_CONVERSION_UNREACHABLE(); } } // If the function returns true then the result is the correct double. // Otherwise it is either the correct double or the double that is just below // the correct double. static bool DiyFpStrtod(Vector buffer, int exponent, double* result) { DiyFp input; int remaining_decimals; ReadDiyFp(buffer, &input, &remaining_decimals); // Since we may have dropped some digits the input is not accurate. // If remaining_decimals is different than 0 than the error is at most // .5 ulp (unit in the last place). // We don't want to deal with fractions and therefore keep a common // denominator. const int kDenominatorLog = 3; const int kDenominator = 1 << kDenominatorLog; // Move the remaining decimals into the exponent. exponent += remaining_decimals; uint64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2); int old_e = input.e(); input.Normalize(); error <<= old_e - input.e(); DOUBLE_CONVERSION_ASSERT(exponent <= PowersOfTenCache::kMaxDecimalExponent); if (exponent < PowersOfTenCache::kMinDecimalExponent) { *result = 0.0; return true; } DiyFp cached_power; int cached_decimal_exponent; PowersOfTenCache::GetCachedPowerForDecimalExponent(exponent, &cached_power, &cached_decimal_exponent); if (cached_decimal_exponent != exponent) { int adjustment_exponent = exponent - cached_decimal_exponent; DiyFp adjustment_power = AdjustmentPowerOfTen(adjustment_exponent); input.Multiply(adjustment_power); if (kMaxUint64DecimalDigits - buffer.length() >= adjustment_exponent) { // The product of input with the adjustment power fits into a 64 bit // integer. DOUBLE_CONVERSION_ASSERT(DiyFp::kSignificandSize == 64); } else { // The adjustment power is exact. There is hence only an error of 0.5. error += kDenominator / 2; } } input.Multiply(cached_power); // The error introduced by a multiplication of a*b equals // error_a + error_b + error_a*error_b/2^64 + 0.5 // Substituting a with 'input' and b with 'cached_power' we have // error_b = 0.5 (all cached powers have an error of less than 0.5 ulp), // error_ab = 0 or 1 / kDenominator > error_a*error_b/ 2^64 int error_b = kDenominator / 2; int error_ab = (error == 0 ? 0 : 1); // We round up to 1. int fixed_error = kDenominator / 2; error += error_b + error_ab + fixed_error; old_e = input.e(); input.Normalize(); error <<= old_e - input.e(); // See if the double's significand changes if we add/subtract the error. int order_of_magnitude = DiyFp::kSignificandSize + input.e(); int effective_significand_size = Double::SignificandSizeForOrderOfMagnitude(order_of_magnitude); int precision_digits_count = DiyFp::kSignificandSize - effective_significand_size; if (precision_digits_count + kDenominatorLog >= DiyFp::kSignificandSize) { // This can only happen for very small denormals. In this case the // half-way multiplied by the denominator exceeds the range of an uint64. // Simply shift everything to the right. int shift_amount = (precision_digits_count + kDenominatorLog) - DiyFp::kSignificandSize + 1; input.set_f(input.f() >> shift_amount); input.set_e(input.e() + shift_amount); // We add 1 for the lost precision of error, and kDenominator for // the lost precision of input.f(). error = (error >> shift_amount) + 1 + kDenominator; precision_digits_count -= shift_amount; } // We use uint64_ts now. This only works if the DiyFp uses uint64_ts too. DOUBLE_CONVERSION_ASSERT(DiyFp::kSignificandSize == 64); DOUBLE_CONVERSION_ASSERT(precision_digits_count < 64); uint64_t one64 = 1; uint64_t precision_bits_mask = (one64 << precision_digits_count) - 1; uint64_t precision_bits = input.f() & precision_bits_mask; uint64_t half_way = one64 << (precision_digits_count - 1); precision_bits *= kDenominator; half_way *= kDenominator; DiyFp rounded_input(input.f() >> precision_digits_count, input.e() + precision_digits_count); if (precision_bits >= half_way + error) { rounded_input.set_f(rounded_input.f() + 1); } // If the last_bits are too close to the half-way case than we are too // inaccurate and round down. In this case we return false so that we can // fall back to a more precise algorithm. *result = Double(rounded_input).value(); if (half_way - error < precision_bits && precision_bits < half_way + error) { // Too imprecise. The caller will have to fall back to a slower version. // However the returned number is guaranteed to be either the correct // double, or the next-lower double. return false; } else { return true; } } // Returns // - -1 if buffer*10^exponent < diy_fp. // - 0 if buffer*10^exponent == diy_fp. // - +1 if buffer*10^exponent > diy_fp. // Preconditions: // buffer.length() + exponent <= kMaxDecimalPower + 1 // buffer.length() + exponent > kMinDecimalPower // buffer.length() <= kMaxDecimalSignificantDigits static int CompareBufferWithDiyFp(Vector buffer, int exponent, DiyFp diy_fp) { DOUBLE_CONVERSION_ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1); DOUBLE_CONVERSION_ASSERT(buffer.length() + exponent > kMinDecimalPower); DOUBLE_CONVERSION_ASSERT(buffer.length() <= kMaxSignificantDecimalDigits); // Make sure that the Bignum will be able to hold all our numbers. // Our Bignum implementation has a separate field for exponents. Shifts will // consume at most one bigit (< 64 bits). // ln(10) == 3.3219... DOUBLE_CONVERSION_ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits); Bignum buffer_bignum; Bignum diy_fp_bignum; buffer_bignum.AssignDecimalString(buffer); diy_fp_bignum.AssignUInt64(diy_fp.f()); if (exponent >= 0) { buffer_bignum.MultiplyByPowerOfTen(exponent); } else { diy_fp_bignum.MultiplyByPowerOfTen(-exponent); } if (diy_fp.e() > 0) { diy_fp_bignum.ShiftLeft(diy_fp.e()); } else { buffer_bignum.ShiftLeft(-diy_fp.e()); } return Bignum::Compare(buffer_bignum, diy_fp_bignum); } // Returns true if the guess is the correct double. // Returns false, when guess is either correct or the next-lower double. static bool ComputeGuess(Vector trimmed, int exponent, double* guess) { if (trimmed.length() == 0) { *guess = 0.0; return true; } if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) { *guess = Double::Infinity(); return true; } if (exponent + trimmed.length() <= kMinDecimalPower) { *guess = 0.0; return true; } if (DoubleStrtod(trimmed, exponent, guess) || DiyFpStrtod(trimmed, exponent, guess)) { return true; } if (*guess == Double::Infinity()) { return true; } return false; } #if U_DEBUG // needed for ICU only in debug mode static bool IsDigit(const char d) { return ('0' <= d) && (d <= '9'); } static bool IsNonZeroDigit(const char d) { return ('1' <= d) && (d <= '9'); } static bool AssertTrimmedDigits(const Vector& buffer) { for(int i = 0; i < buffer.length(); ++i) { if(!IsDigit(buffer[i])) { return false; } } return (buffer.length() == 0) || (IsNonZeroDigit(buffer[0]) && IsNonZeroDigit(buffer[buffer.length()-1])); } #endif // needed for ICU only in debug mode double StrtodTrimmed(Vector trimmed, int exponent) { DOUBLE_CONVERSION_ASSERT(trimmed.length() <= kMaxSignificantDecimalDigits); DOUBLE_CONVERSION_ASSERT(AssertTrimmedDigits(trimmed)); double guess; const bool is_correct = ComputeGuess(trimmed, exponent, &guess); if (is_correct) { return guess; } DiyFp upper_boundary = Double(guess).UpperBoundary(); int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary); if (comparison < 0) { return guess; } else if (comparison > 0) { return Double(guess).NextDouble(); } else if ((Double(guess).Significand() & 1) == 0) { // Round towards even. return guess; } else { return Double(guess).NextDouble(); } } double Strtod(Vector buffer, int exponent) { char copy_buffer[kMaxSignificantDecimalDigits]; Vector trimmed; int updated_exponent; TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits, &trimmed, &updated_exponent); return StrtodTrimmed(trimmed, updated_exponent); } static float SanitizedDoubletof(double d) { DOUBLE_CONVERSION_ASSERT(d >= 0.0); // ASAN has a sanitize check that disallows casting doubles to floats if // they are too big. // https://clang.llvm.org/docs/UndefinedBehaviorSanitizer.html#available-checks // The behavior should be covered by IEEE 754, but some projects use this // flag, so work around it. float max_finite = 3.4028234663852885981170418348451692544e+38; // The half-way point between the max-finite and infinity value. // Since infinity has an even significand everything equal or greater than // this value should become infinity. double half_max_finite_infinity = 3.40282356779733661637539395458142568448e+38; if (d >= max_finite) { if (d >= half_max_finite_infinity) { return Single::Infinity(); } else { return max_finite; } } else { return static_cast(d); } } float Strtof(Vector buffer, int exponent) { char copy_buffer[kMaxSignificantDecimalDigits]; Vector trimmed; int updated_exponent; TrimAndCut(buffer, exponent, copy_buffer, kMaxSignificantDecimalDigits, &trimmed, &updated_exponent); exponent = updated_exponent; double double_guess; bool is_correct = ComputeGuess(trimmed, exponent, &double_guess); float float_guess = SanitizedDoubletof(double_guess); if (float_guess == double_guess) { // This shortcut triggers for integer values. return float_guess; } // We must catch double-rounding. Say the double has been rounded up, and is // now a boundary of a float, and rounds up again. This is why we have to // look at previous too. // Example (in decimal numbers): // input: 12349 // high-precision (4 digits): 1235 // low-precision (3 digits): // when read from input: 123 // when rounded from high precision: 124. // To do this we simply look at the neigbors of the correct result and see // if they would round to the same float. If the guess is not correct we have // to look at four values (since two different doubles could be the correct // double). double double_next = Double(double_guess).NextDouble(); double double_previous = Double(double_guess).PreviousDouble(); float f1 = SanitizedDoubletof(double_previous); float f2 = float_guess; float f3 = SanitizedDoubletof(double_next); float f4; if (is_correct) { f4 = f3; } else { double double_next2 = Double(double_next).NextDouble(); f4 = SanitizedDoubletof(double_next2); } (void) f2; // Mark variable as used. DOUBLE_CONVERSION_ASSERT(f1 <= f2 && f2 <= f3 && f3 <= f4); // If the guess doesn't lie near a single-precision boundary we can simply // return its float-value. if (f1 == f4) { return float_guess; } DOUBLE_CONVERSION_ASSERT((f1 != f2 && f2 == f3 && f3 == f4) || (f1 == f2 && f2 != f3 && f3 == f4) || (f1 == f2 && f2 == f3 && f3 != f4)); // guess and next are the two possible candidates (in the same way that // double_guess was the lower candidate for a double-precision guess). float guess = f1; float next = f4; DiyFp upper_boundary; if (guess == 0.0f) { float min_float = 1e-45f; upper_boundary = Double(static_cast(min_float) / 2).AsDiyFp(); } else { upper_boundary = Single(guess).UpperBoundary(); } int comparison = CompareBufferWithDiyFp(trimmed, exponent, upper_boundary); if (comparison < 0) { return guess; } else if (comparison > 0) { return next; } else if ((Single(guess).Significand() & 1) == 0) { // Round towards even. return guess; } else { return next; } } } // namespace double_conversion // ICU PATCH: Close ICU namespace U_NAMESPACE_END #endif // ICU PATCH: close #if !UCONFIG_NO_FORMATTING