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Unified Diff: third_party/WebKit/Source/wtf/dtoa/strtod.cc

Issue 2700123003: DO NOT COMMIT: Results of running old (current) clang-format on Blink (Closed)
Patch Set: Created 3 years, 10 months ago
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Index: third_party/WebKit/Source/wtf/dtoa/strtod.cc
diff --git a/third_party/WebKit/Source/wtf/dtoa/strtod.cc b/third_party/WebKit/Source/wtf/dtoa/strtod.cc
index 998a0c4e912bcb9ab9bce844343c445685271378..0de14e94fc07ecd00eb1d5d27fd141dd4ba25d8b 100644
--- a/third_party/WebKit/Source/wtf/dtoa/strtod.cc
+++ b/third_party/WebKit/Source/wtf/dtoa/strtod.cc
@@ -27,419 +27,403 @@
#include "strtod.h"
+#include <limits.h>
+#include <stdarg.h>
#include "bignum.h"
#include "cached-powers.h"
#include "double.h"
-#include <stdarg.h>
-#include <limits.h>
namespace WTF {
namespace double_conversion {
- // 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 > 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 = UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF);
-
-
- 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);
-
- // 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<const char> TrimLeadingZeros(Vector<const char> buffer) {
- for (int i = 0; i < buffer.length(); i++) {
- if (buffer[i] != '0') {
- return buffer.SubVector(i, buffer.length());
- }
- }
- return Vector<const char>(buffer.start(), 0);
+// 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 > 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 = UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF);
+
+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);
+
+// 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<const char> TrimLeadingZeros(Vector<const char> buffer) {
+ for (int i = 0; i < buffer.length(); i++) {
+ if (buffer[i] != '0') {
+ return buffer.SubVector(i, buffer.length());
}
-
-
- static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {
- for (int i = buffer.length() - 1; i >= 0; --i) {
- if (buffer[i] != '0') {
- return buffer.SubVector(0, i + 1);
- }
- }
- return Vector<const char>(buffer.start(), 0);
- }
-
-
- static void TrimToMaxSignificantDigits(Vector<const char> 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'.
- 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);
+ }
+ return Vector<const char>(buffer.start(), 0);
+}
+
+static Vector<const char> TrimTrailingZeros(Vector<const char> buffer) {
+ for (int i = buffer.length() - 1; i >= 0; --i) {
+ if (buffer[i] != '0') {
+ return buffer.SubVector(0, i + 1);
}
-
- // 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<const char> 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';
- ASSERT(0 <= digit && digit <= 9);
- result = 10 * result + digit;
- }
- *number_of_read_digits = i;
- return result;
+ }
+ return Vector<const char>(buffer.start(), 0);
+}
+
+static void TrimToMaxSignificantDigits(Vector<const char> 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'.
+ 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);
+}
+
+// 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<const char> 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';
+ 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<const char> 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++;
}
-
-
- // 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<const char> 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<const char> trimmed,
- int exponent,
- double* result) {
+ // Compute the binary exponent.
+ int exponent = 0;
+ *result = DiyFp(significand, exponent);
+ *remaining_decimals = buffer.length() - read_digits;
+ }
+}
+
+static bool DoubleStrtod(Vector<const char> 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;
+ // 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;
#endif
- 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<double>(ReadUint64(trimmed, &read_digits));
- 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<double>(ReadUint64(trimmed, &read_digits));
- 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<double>(ReadUint64(trimmed, &read_digits));
- ASSERT(read_digits == trimmed.length());
- *result *= exact_powers_of_ten[remaining_digits];
- *result *= exact_powers_of_ten[exponent - remaining_digits];
- return true;
- }
- }
- return false;
+ 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<double>(ReadUint64(trimmed, &read_digits));
+ ASSERT(read_digits == trimmed.length());
+ *result /= exact_powers_of_ten[-exponent];
+ return true;
}
-
-
- // Returns 10^exponent as an exact DiyFp.
- // The given exponent must be in the range [1; kDecimalExponentDistance[.
- static DiyFp AdjustmentPowerOfTen(int exponent) {
- ASSERT(0 < exponent);
- ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);
- // Simply hardcode the remaining powers for the given decimal exponent
- // distance.
- ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);
- switch (exponent) {
- case 1: return DiyFp(UINT64_2PART_C(0xa0000000, 00000000), -60);
- case 2: return DiyFp(UINT64_2PART_C(0xc8000000, 00000000), -57);
- case 3: return DiyFp(UINT64_2PART_C(0xfa000000, 00000000), -54);
- case 4: return DiyFp(UINT64_2PART_C(0x9c400000, 00000000), -50);
- case 5: return DiyFp(UINT64_2PART_C(0xc3500000, 00000000), -47);
- case 6: return DiyFp(UINT64_2PART_C(0xf4240000, 00000000), -44);
- case 7: return DiyFp(UINT64_2PART_C(0x98968000, 00000000), -40);
- default:
- UNREACHABLE();
- return DiyFp(0, 0);
- }
- }
-
-
- // 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<const char> 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;
- int64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2);
-
- int old_e = input.e();
- input.Normalize();
- error <<= old_e - input.e();
-
- 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.
- 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.
- ASSERT(DiyFp::kSignificandSize == 64);
- 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;
- }
+ if (0 <= exponent && exponent < kExactPowersOfTenSize) {
+ // 10^exponent fits into a double.
+ *result = static_cast<double>(ReadUint64(trimmed, &read_digits));
+ ASSERT(read_digits == trimmed.length());
+ *result *= exact_powers_of_ten[exponent];
+ return true;
}
-
-
- // Returns the correct double for the buffer*10^exponent.
- // The variable guess should be a close guess that is either the correct double
- // or its lower neighbor (the nearest double less than the correct one).
- // Preconditions:
- // buffer.length() + exponent <= kMaxDecimalPower + 1
- // buffer.length() + exponent > kMinDecimalPower
- // buffer.length() <= kMaxDecimalSignificantDigits
- static double BignumStrtod(Vector<const char> buffer,
- int exponent,
- double guess) {
- if (guess == Double::Infinity()) {
- return guess;
- }
-
- DiyFp upper_boundary = Double(guess).UpperBoundary();
-
- ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);
- ASSERT(buffer.length() + exponent > kMinDecimalPower);
- 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...
- ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits);
- Bignum input;
- Bignum boundary;
- input.AssignDecimalString(buffer);
- boundary.AssignUInt64(upper_boundary.f());
- if (exponent >= 0) {
- input.MultiplyByPowerOfTen(exponent);
- } else {
- boundary.MultiplyByPowerOfTen(-exponent);
- }
- if (upper_boundary.e() > 0) {
- boundary.ShiftLeft(upper_boundary.e());
- } else {
- input.ShiftLeft(-upper_boundary.e());
- }
- int comparison = Bignum::Compare(input, 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();
- }
+ 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<double>(ReadUint64(trimmed, &read_digits));
+ ASSERT(read_digits == trimmed.length());
+ *result *= exact_powers_of_ten[remaining_digits];
+ *result *= exact_powers_of_ten[exponent - remaining_digits];
+ return true;
}
-
-
- double Strtod(Vector<const char> buffer, int exponent) {
- Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
- Vector<const char> trimmed = TrimTrailingZeros(left_trimmed);
- exponent += left_trimmed.length() - trimmed.length();
- if (trimmed.length() == 0) return 0.0;
- if (trimmed.length() > kMaxSignificantDecimalDigits) {
- char significant_buffer[kMaxSignificantDecimalDigits];
- int significant_exponent;
- TrimToMaxSignificantDigits(trimmed, exponent,
- significant_buffer, &significant_exponent);
- return Strtod(Vector<const char>(significant_buffer,
- kMaxSignificantDecimalDigits),
- significant_exponent);
- }
- if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) {
- return Double::Infinity();
- }
- if (exponent + trimmed.length() <= kMinDecimalPower) {
- return 0.0;
- }
-
- double guess;
- if (DoubleStrtod(trimmed, exponent, &guess) ||
- DiyFpStrtod(trimmed, exponent, &guess)) {
- return guess;
- }
- return BignumStrtod(trimmed, exponent, guess);
+ }
+ return false;
+}
+
+// Returns 10^exponent as an exact DiyFp.
+// The given exponent must be in the range [1; kDecimalExponentDistance[.
+static DiyFp AdjustmentPowerOfTen(int exponent) {
+ ASSERT(0 < exponent);
+ ASSERT(exponent < PowersOfTenCache::kDecimalExponentDistance);
+ // Simply hardcode the remaining powers for the given decimal exponent
+ // distance.
+ ASSERT(PowersOfTenCache::kDecimalExponentDistance == 8);
+ switch (exponent) {
+ case 1:
+ return DiyFp(UINT64_2PART_C(0xa0000000, 00000000), -60);
+ case 2:
+ return DiyFp(UINT64_2PART_C(0xc8000000, 00000000), -57);
+ case 3:
+ return DiyFp(UINT64_2PART_C(0xfa000000, 00000000), -54);
+ case 4:
+ return DiyFp(UINT64_2PART_C(0x9c400000, 00000000), -50);
+ case 5:
+ return DiyFp(UINT64_2PART_C(0xc3500000, 00000000), -47);
+ case 6:
+ return DiyFp(UINT64_2PART_C(0xf4240000, 00000000), -44);
+ case 7:
+ return DiyFp(UINT64_2PART_C(0x98968000, 00000000), -40);
+ default:
+ UNREACHABLE();
+ return DiyFp(0, 0);
+ }
+}
+
+// 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<const char> 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;
+ int64_t error = (remaining_decimals == 0 ? 0 : kDenominator / 2);
+
+ int old_e = input.e();
+ input.Normalize();
+ error <<= old_e - input.e();
+
+ 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.
+ 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.
+ ASSERT(DiyFp::kSignificandSize == 64);
+ 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 the correct double for the buffer*10^exponent.
+// The variable guess should be a close guess that is either the correct double
+// or its lower neighbor (the nearest double less than the correct one).
+// Preconditions:
+// buffer.length() + exponent <= kMaxDecimalPower + 1
+// buffer.length() + exponent > kMinDecimalPower
+// buffer.length() <= kMaxDecimalSignificantDigits
+static double BignumStrtod(Vector<const char> buffer,
+ int exponent,
+ double guess) {
+ if (guess == Double::Infinity()) {
+ return guess;
+ }
+
+ DiyFp upper_boundary = Double(guess).UpperBoundary();
+
+ ASSERT(buffer.length() + exponent <= kMaxDecimalPower + 1);
+ ASSERT(buffer.length() + exponent > kMinDecimalPower);
+ 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...
+ ASSERT(((kMaxDecimalPower + 1) * 333 / 100) < Bignum::kMaxSignificantBits);
+ Bignum input;
+ Bignum boundary;
+ input.AssignDecimalString(buffer);
+ boundary.AssignUInt64(upper_boundary.f());
+ if (exponent >= 0) {
+ input.MultiplyByPowerOfTen(exponent);
+ } else {
+ boundary.MultiplyByPowerOfTen(-exponent);
+ }
+ if (upper_boundary.e() > 0) {
+ boundary.ShiftLeft(upper_boundary.e());
+ } else {
+ input.ShiftLeft(-upper_boundary.e());
+ }
+ int comparison = Bignum::Compare(input, 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<const char> buffer, int exponent) {
+ Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
+ Vector<const char> trimmed = TrimTrailingZeros(left_trimmed);
+ exponent += left_trimmed.length() - trimmed.length();
+ if (trimmed.length() == 0)
+ return 0.0;
+ if (trimmed.length() > kMaxSignificantDecimalDigits) {
+ char significant_buffer[kMaxSignificantDecimalDigits];
+ int significant_exponent;
+ TrimToMaxSignificantDigits(trimmed, exponent, significant_buffer,
+ &significant_exponent);
+ return Strtod(
+ Vector<const char>(significant_buffer, kMaxSignificantDecimalDigits),
+ significant_exponent);
+ }
+ if (exponent + trimmed.length() - 1 >= kMaxDecimalPower) {
+ return Double::Infinity();
+ }
+ if (exponent + trimmed.length() <= kMinDecimalPower) {
+ return 0.0;
+ }
+
+ double guess;
+ if (DoubleStrtod(trimmed, exponent, &guess) ||
+ DiyFpStrtod(trimmed, exponent, &guess)) {
+ return guess;
+ }
+ return BignumStrtod(trimmed, exponent, guess);
+}
} // namespace double_conversion
-} // namespace WTF
+} // namespace WTF
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