};
static const CachedPower kCachedPowers[] = {
- {V8_2PART_UINT64_C(0xfa8fd5a0, 081c0288), -1220, -348},
- {V8_2PART_UINT64_C(0xbaaee17f, a23ebf76), -1193, -340},
- {V8_2PART_UINT64_C(0x8b16fb20, 3055ac76), -1166, -332},
- {V8_2PART_UINT64_C(0xcf42894a, 5dce35ea), -1140, -324},
- {V8_2PART_UINT64_C(0x9a6bb0aa, 55653b2d), -1113, -316},
{V8_2PART_UINT64_C(0xe61acf03, 3d1a45df), -1087, -308},
{V8_2PART_UINT64_C(0xab70fe17, c79ac6ca), -1060, -300},
{V8_2PART_UINT64_C(0xff77b1fc, bebcdc4f), -1034, -292},
static const int kCachedPowersLength = ARRAY_SIZE(kCachedPowers);
static const int kCachedPowersOffset = -kCachedPowers[0].decimal_exponent;
static const double kD_1_LOG2_10 = 0.30102999566398114; // 1 / lg(10)
-const int PowersOfTenCache::kDecimalExponentDistance =
+static const int kCachedPowersDecimalDistance =
kCachedPowers[1].decimal_exponent - kCachedPowers[0].decimal_exponent;
-const int PowersOfTenCache::kMinDecimalExponent =
- kCachedPowers[0].decimal_exponent;
-const int PowersOfTenCache::kMaxDecimalExponent =
- kCachedPowers[kCachedPowersLength - 1].decimal_exponent;
-void PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
- int min_exponent,
- int max_exponent,
- DiyFp* power,
- int* decimal_exponent) {
- int kQ = DiyFp::kSignificandSize;
- double k = ceiling((min_exponent + kQ - 1) * kD_1_LOG2_10);
- int foo = kCachedPowersOffset;
- int index =
- (foo + static_cast<int>(k) - 1) / kDecimalExponentDistance + 1;
- ASSERT(0 <= index && index < kCachedPowersLength);
- CachedPower cached_power = kCachedPowers[index];
- ASSERT(min_exponent <= cached_power.binary_exponent);
- ASSERT(cached_power.binary_exponent <= max_exponent);
- *decimal_exponent = cached_power.decimal_exponent;
- *power = DiyFp(cached_power.significand, cached_power.binary_exponent);
-}
-
-
-void PowersOfTenCache::GetCachedPowerForDecimalExponent(int requested_exponent,
- DiyFp* power,
- int* found_exponent) {
- ASSERT(kMinDecimalExponent <= requested_exponent);
- ASSERT(requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance);
- int index =
- (requested_exponent + kCachedPowersOffset) / kDecimalExponentDistance;
- CachedPower cached_power = kCachedPowers[index];
- *power = DiyFp(cached_power.significand, cached_power.binary_exponent);
- *found_exponent = cached_power.decimal_exponent;
- ASSERT(*found_exponent <= requested_exponent);
- ASSERT(requested_exponent < *found_exponent + kDecimalExponentDistance);
+void GetCachedPowerForBinaryExponentRange(int min_exponent,
+ int max_exponent,
+ DiyFp* power,
+ int* decimal_exponent) {
+ int kQ = DiyFp::kSignificandSize;
+ double k = ceiling((min_exponent + kQ - 1) * kD_1_LOG2_10);
+ int foo = kCachedPowersOffset;
+ int index =
+ (foo + static_cast<int>(k) - 1) / kCachedPowersDecimalDistance + 1;
+ ASSERT(0 <= index && index < kCachedPowersLength);
+ CachedPower cached_power = kCachedPowers[index];
+ ASSERT(min_exponent <= cached_power.binary_exponent);
+ ASSERT(cached_power.binary_exponent <= max_exponent);
+ *decimal_exponent = cached_power.decimal_exponent;
+ *power = DiyFp(cached_power.significand, cached_power.binary_exponent);
}
} } // namespace v8::internal
namespace v8 {
namespace internal {
-class PowersOfTenCache {
- public:
-
- // Not all powers of ten are cached. The decimal exponent of two neighboring
- // cached numbers will differ by kDecimalExponentDistance.
- static const int kDecimalExponentDistance;
-
- static const int kMinDecimalExponent;
- static const int kMaxDecimalExponent;
-
- // Returns a cached power-of-ten with a binary exponent in the range
- // [min_exponent; max_exponent] (boundaries included).
- static void GetCachedPowerForBinaryExponentRange(int min_exponent,
- int max_exponent,
- DiyFp* power,
- int* decimal_exponent);
-
- // Returns a cached power of ten x ~= 10^k such that
- // k <= decimal_exponent < k + kCachedPowersDecimalDistance.
- // The given decimal_exponent must satisfy
- // kMinDecimalExponent <= requested_exponent, and
- // requested_exponent < kMaxDecimalExponent + kDecimalExponentDistance.
- static void GetCachedPowerForDecimalExponent(int requested_exponent,
- DiyFp* power,
- int* found_exponent);
-};
+void GetCachedPowerForBinaryExponentRange(int min_exponent,
+ int max_exponent,
+ DiyFp* power,
+ int* decimal_exponent);
} } // namespace v8::internal
static const uint64_t kSignificandMask =
V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF);
static const uint64_t kHiddenBit = V8_2PART_UINT64_C(0x00100000, 00000000);
- static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit.
- static const int kSignificandSize = 53;
Double() : d64_(0) {}
explicit Double(double d) : d64_(double_to_uint64(d)) {}
explicit Double(uint64_t d64) : d64_(d64) {}
- Double(uint64_t significand, int exponent)
- : d64_(SignificandExponentToUint64(significand, exponent)) {}
DiyFp AsDiyFp() const {
ASSERT(!IsSpecial());
f <<= 1;
e--;
}
- // Do the final shifts in one go.
- f <<= DiyFp::kSignificandSize - kSignificandSize;
- e -= DiyFp::kSignificandSize - kSignificandSize;
+ // Do the final shifts in one go. Don't forget the hidden bit (the '-1').
+ f <<= DiyFp::kSignificandSize - kSignificandSize - 1;
+ e -= DiyFp::kSignificandSize - kSignificandSize - 1;
return DiyFp(f, e);
}
if (IsDenormal()) return kDenormalExponent;
uint64_t d64 = AsUint64();
- int biased_e =
- static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
+ int biased_e = static_cast<int>((d64 & kExponentMask) >> kSignificandSize);
return biased_e - kExponentBias;
}
double value() const { return uint64_to_double(d64_); }
- // Returns the significand size for a given order of magnitude.
- // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
- // This function returns the number of significant binary digits v will have
- // once its encoded into a double. In almost all cases this is equal to
- // kSignificandSize. The only exception are denormals. They start with leading
- // zeroes and their effective significand-size is hence smaller.
- static int SignificandSizeForOrderOfMagnitude(int order) {
- if (order >= (kDenormalExponent + kSignificandSize)) {
- return kSignificandSize;
- }
- if (order <= kDenormalExponent) return 0;
- return order - kDenormalExponent;
- }
-
private:
- static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
+ static const int kSignificandSize = 52; // Excludes the hidden bit.
+ static const int kExponentBias = 0x3FF + kSignificandSize;
static const int kDenormalExponent = -kExponentBias + 1;
- static const int kMaxExponent = 0x7FF - kExponentBias;
- static const uint64_t kInfinity = V8_2PART_UINT64_C(0x7FF00000, 00000000);
-
- const uint64_t d64_;
-
- static uint64_t SignificandExponentToUint64(uint64_t significand,
- int exponent) {
- ASSERT(significand <= kSignificandMask + kHiddenBit);
- ASSERT(((significand & kHiddenBit) != 0) || exponent <= kDenormalExponent);
- // Clamp.
- if (exponent < kDenormalExponent) {
- return 0;
- }
- if (exponent >= kMaxExponent) {
- return kInfinity;
- }
- uint64_t biased_exponent;
- if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
- biased_exponent = 0;
- } else {
- biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
- }
- return (significand & kSignificandMask) |
- (biased_exponent << kPhysicalSignificandSize);
- }
+
+ uint64_t d64_;
};
} } // namespace v8::internal
kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize);
int ten_mk_maximal_binary_exponent =
kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize);
- PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
- ten_mk_minimal_binary_exponent,
- ten_mk_maximal_binary_exponent,
- &ten_mk, &mk);
+ GetCachedPowerForBinaryExponentRange(ten_mk_minimal_binary_exponent,
+ ten_mk_maximal_binary_exponent,
+ &ten_mk, &mk);
ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
DiyFp::kSignificandSize) &&
(kMaximalTargetExponent >= w.e() + ten_mk.e() +
kMinimalTargetExponent - (w.e() + DiyFp::kSignificandSize);
int ten_mk_maximal_binary_exponent =
kMaximalTargetExponent - (w.e() + DiyFp::kSignificandSize);
- PowersOfTenCache::GetCachedPowerForBinaryExponentRange(
- ten_mk_minimal_binary_exponent,
- ten_mk_maximal_binary_exponent,
- &ten_mk, &mk);
+ GetCachedPowerForBinaryExponentRange(ten_mk_minimal_binary_exponent,
+ ten_mk_maximal_binary_exponent,
+ &ten_mk, &mk);
ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
DiyFp::kSignificandSize) &&
(kMaximalTargetExponent >= w.e() + ten_mk.e() +
#include "v8.h"
#include "strtod.h"
-#include "cached-powers.h"
-#include "double.h"
+// #include "cached-powers.h"
namespace v8 {
namespace internal {
// 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
+// 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.
static const int kMaxDecimalPower = 309;
static const int kMinDecimalPower = -324;
-// 2^64 = 18446744073709551616
-static const uint64_t kMaxUint64 = V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF);
-
-
static const double exact_powers_of_ten[] = {
1.0, // 10^0
10.0,
}
-// 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 ReadUint64(Vector<const char> buffer) {
+ ASSERT(buffer.length() <= kMaxUint64DecimalDigits);
uint64_t result = 0;
- int i = 0;
- while (i < buffer.length() && result <= (kMaxUint64 / 10 - 1)) {
- int digit = buffer[i++] - '0';
+ for (int i = 0; i < buffer.length(); ++i) {
+ 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++;
- }
- // 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) {
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
// 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 = static_cast<double>(ReadUint64(trimmed));
*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 = static_cast<double>(ReadUint64(trimmed));
*result *= exact_powers_of_ten[exponent];
return true;
}
// 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 = static_cast<double>(ReadUint64(trimmed));
*result *= exact_powers_of_ten[remaining_digits];
*result *= exact_powers_of_ten[exponent - remaining_digits];
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(V8_2PART_UINT64_C(0xa0000000, 00000000), -60);
- case 2: return DiyFp(V8_2PART_UINT64_C(0xc8000000, 00000000), -57);
- case 3: return DiyFp(V8_2PART_UINT64_C(0xfa000000, 00000000), -54);
- case 4: return DiyFp(V8_2PART_UINT64_C(0x9c400000, 00000000), -50);
- case 5: return DiyFp(V8_2PART_UINT64_C(0xc3500000, 00000000), -47);
- case 6: return DiyFp(V8_2PART_UINT64_C(0xf4240000, 00000000), -44);
- case 7: return DiyFp(V8_2PART_UINT64_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;
- int 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;
- // 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.
- uint64_t significand = input.f();
- if (precision_bits >= half_way + error) {
- significand = (significand >> precision_digits_count) + 1;
- exponent = input.e() + precision_digits_count;
- } else {
- significand = (significand >> precision_digits_count);
- exponent = input.e() + precision_digits_count;
- }
- Double d = Double(significand, exponent);
- *result = d.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;
- }
-}
-
-
double Strtod(Vector<const char> buffer, int exponent) {
Vector<const char> left_trimmed = TrimLeadingZeros(buffer);
Vector<const char> trimmed = TrimTrailingZeros(left_trimmed);
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) ||
- DiyFpStrtod(trimmed, exponent, &result)) {
+ if (DoubleStrtod(trimmed, exponent, &result)) {
return result;
}
return old_strtod(trimmed, exponent);
// the floating-point stack is set to 80bits and the double-rounding
// introduces an error.
CHECK_EQ(89255e-22, StrtodChar("89255", -22));
- CHECK_EQ(104110013277974872254e-225,
- StrtodChar("104110013277974872254", -225));
-
- CHECK_EQ(123456789e108, StrtodChar("123456789", 108));
- CHECK_EQ(123456789e109, StrtodChar("123456789", 109));
- CHECK_EQ(123456789e110, StrtodChar("123456789", 110));
- CHECK_EQ(123456789e111, StrtodChar("123456789", 111));
- CHECK_EQ(123456789e112, StrtodChar("123456789", 112));
- CHECK_EQ(123456789e113, StrtodChar("123456789", 113));
- CHECK_EQ(123456789e114, StrtodChar("123456789", 114));
- CHECK_EQ(123456789e115, StrtodChar("123456789", 115));
-
- CHECK_EQ(1234567890123456789012345e108,
- StrtodChar("1234567890123456789012345", 108));
- CHECK_EQ(1234567890123456789012345e109,
- StrtodChar("1234567890123456789012345", 109));
- CHECK_EQ(1234567890123456789012345e110,
- StrtodChar("1234567890123456789012345", 110));
- CHECK_EQ(1234567890123456789012345e111,
- StrtodChar("1234567890123456789012345", 111));
- CHECK_EQ(1234567890123456789012345e112,
- StrtodChar("1234567890123456789012345", 112));
- CHECK_EQ(1234567890123456789012345e113,
- StrtodChar("1234567890123456789012345", 113));
- CHECK_EQ(1234567890123456789012345e114,
- StrtodChar("1234567890123456789012345", 114));
- CHECK_EQ(1234567890123456789012345e115,
- StrtodChar("1234567890123456789012345", 115));
-
- CHECK_EQ(1234567890123456789052345e108,
- StrtodChar("1234567890123456789052345", 108));
- CHECK_EQ(1234567890123456789052345e109,
- StrtodChar("1234567890123456789052345", 109));
- CHECK_EQ(1234567890123456789052345e110,
- StrtodChar("1234567890123456789052345", 110));
- CHECK_EQ(1234567890123456789052345e111,
- StrtodChar("1234567890123456789052345", 111));
- CHECK_EQ(1234567890123456789052345e112,
- StrtodChar("1234567890123456789052345", 112));
- CHECK_EQ(1234567890123456789052345e113,
- StrtodChar("1234567890123456789052345", 113));
- CHECK_EQ(1234567890123456789052345e114,
- StrtodChar("1234567890123456789052345", 114));
- CHECK_EQ(1234567890123456789052345e115,
- StrtodChar("1234567890123456789052345", 115));
}
projects / platform / upstream / v8.git / commitdiff