update V8 to r5532 as required by WebKit r68651
Change-Id: I5f75eeffbf64b30dd5080348528d277f293490ad
diff --git a/src/fast-dtoa.cc b/src/fast-dtoa.cc
index b4b7be0..d2a00cc 100644
--- a/src/fast-dtoa.cc
+++ b/src/fast-dtoa.cc
@@ -42,8 +42,8 @@
//
// A different range might be chosen on a different platform, to optimize digit
// generation, but a smaller range requires more powers of ten to be cached.
-static const int minimal_target_exponent = -60;
-static const int maximal_target_exponent = -32;
+static const int kMinimalTargetExponent = -60;
+static const int kMaximalTargetExponent = -32;
// Adjusts the last digit of the generated number, and screens out generated
@@ -61,13 +61,13 @@
// Output: returns true if the buffer is guaranteed to contain the closest
// representable number to the input.
// Modifies the generated digits in the buffer to approach (round towards) w.
-bool RoundWeed(Vector<char> buffer,
- int length,
- uint64_t distance_too_high_w,
- uint64_t unsafe_interval,
- uint64_t rest,
- uint64_t ten_kappa,
- uint64_t unit) {
+static bool RoundWeed(Vector<char> buffer,
+ int length,
+ uint64_t distance_too_high_w,
+ uint64_t unsafe_interval,
+ uint64_t rest,
+ uint64_t ten_kappa,
+ uint64_t unit) {
uint64_t small_distance = distance_too_high_w - unit;
uint64_t big_distance = distance_too_high_w + unit;
// Let w_low = too_high - big_distance, and
@@ -75,7 +75,7 @@
// Note: w_low < w < w_high
//
// The real w (* unit) must lie somewhere inside the interval
- // ]w_low; w_low[ (often written as "(w_low; w_low)")
+ // ]w_low; w_high[ (often written as "(w_low; w_high)")
// Basically the buffer currently contains a number in the unsafe interval
// ]too_low; too_high[ with too_low < w < too_high
@@ -122,10 +122,10 @@
// inside the safe interval then we simply do not know and bail out (returning
// false).
//
- // Similarly we have to take into account the imprecision of 'w' when rounding
- // the buffer. If we have two potential representations we need to make sure
- // that the chosen one is closer to w_low and w_high since v can be anywhere
- // between them.
+ // Similarly we have to take into account the imprecision of 'w' when finding
+ // the closest representation of 'w'. If we have two potential
+ // representations, and one is closer to both w_low and w_high, then we know
+ // it is closer to the actual value v.
//
// By generating the digits of too_high we got the largest (closest to
// too_high) buffer that is still in the unsafe interval. In the case where
@@ -139,6 +139,9 @@
// (buffer{-1} < w_high) && w_high - buffer{-1} > buffer - w_high
// Instead of using the buffer directly we use its distance to too_high.
// Conceptually rest ~= too_high - buffer
+ // We need to do the following tests in this order to avoid over- and
+ // underflows.
+ ASSERT(rest <= unsafe_interval);
while (rest < small_distance && // Negated condition 1
unsafe_interval - rest >= ten_kappa && // Negated condition 2
(rest + ten_kappa < small_distance || // buffer{-1} > w_high
@@ -166,6 +169,62 @@
}
+// Rounds the buffer upwards if the result is closer to v by possibly adding
+// 1 to the buffer. If the precision of the calculation is not sufficient to
+// round correctly, return false.
+// The rounding might shift the whole buffer in which case the kappa is
+// adjusted. For example "99", kappa = 3 might become "10", kappa = 4.
+//
+// If 2*rest > ten_kappa then the buffer needs to be round up.
+// rest can have an error of +/- 1 unit. This function accounts for the
+// imprecision and returns false, if the rounding direction cannot be
+// unambiguously determined.
+//
+// Precondition: rest < ten_kappa.
+static bool RoundWeedCounted(Vector<char> buffer,
+ int length,
+ uint64_t rest,
+ uint64_t ten_kappa,
+ uint64_t unit,
+ int* kappa) {
+ ASSERT(rest < ten_kappa);
+ // The following tests are done in a specific order to avoid overflows. They
+ // will work correctly with any uint64 values of rest < ten_kappa and unit.
+ //
+ // If the unit is too big, then we don't know which way to round. For example
+ // a unit of 50 means that the real number lies within rest +/- 50. If
+ // 10^kappa == 40 then there is no way to tell which way to round.
+ if (unit >= ten_kappa) return false;
+ // Even if unit is just half the size of 10^kappa we are already completely
+ // lost. (And after the previous test we know that the expression will not
+ // over/underflow.)
+ if (ten_kappa - unit <= unit) return false;
+ // If 2 * (rest + unit) <= 10^kappa we can safely round down.
+ if ((ten_kappa - rest > rest) && (ten_kappa - 2 * rest >= 2 * unit)) {
+ return true;
+ }
+ // If 2 * (rest - unit) >= 10^kappa, then we can safely round up.
+ if ((rest > unit) && (ten_kappa - (rest - unit) <= (rest - unit))) {
+ // Increment the last digit recursively until we find a non '9' digit.
+ buffer[length - 1]++;
+ for (int i = length - 1; i > 0; --i) {
+ if (buffer[i] != '0' + 10) break;
+ buffer[i] = '0';
+ buffer[i - 1]++;
+ }
+ // If the first digit is now '0'+ 10 we had a buffer with all '9's. With the
+ // exception of the first digit all digits are now '0'. Simply switch the
+ // first digit to '1' and adjust the kappa. Example: "99" becomes "10" and
+ // the power (the kappa) is increased.
+ if (buffer[0] == '0' + 10) {
+ buffer[0] = '1';
+ (*kappa) += 1;
+ }
+ return true;
+ }
+ return false;
+}
+
static const uint32_t kTen4 = 10000;
static const uint32_t kTen5 = 100000;
@@ -178,7 +237,7 @@
// number. We furthermore receive the maximum number of bits 'number' has.
// If number_bits == 0 then 0^-1 is returned
// The number of bits must be <= 32.
-// Precondition: (1 << number_bits) <= number < (1 << (number_bits + 1)).
+// Precondition: number < (1 << (number_bits + 1)).
static void BiggestPowerTen(uint32_t number,
int number_bits,
uint32_t* power,
@@ -281,18 +340,18 @@
// Generates the digits of input number w.
// w is a floating-point number (DiyFp), consisting of a significand and an
-// exponent. Its exponent is bounded by minimal_target_exponent and
-// maximal_target_exponent.
+// exponent. Its exponent is bounded by kMinimalTargetExponent and
+// kMaximalTargetExponent.
// Hence -60 <= w.e() <= -32.
//
// Returns false if it fails, in which case the generated digits in the buffer
// should not be used.
// Preconditions:
// * low, w and high are correct up to 1 ulp (unit in the last place). That
-// is, their error must be less that a unit of their last digits.
+// is, their error must be less than a unit of their last digits.
// * low.e() == w.e() == high.e()
// * low < w < high, and taking into account their error: low~ <= high~
-// * minimal_target_exponent <= w.e() <= maximal_target_exponent
+// * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
// Postconditions: returns false if procedure fails.
// otherwise:
// * buffer is not null-terminated, but len contains the number of digits.
@@ -321,15 +380,15 @@
// represent 'w' we can stop. Everything inside the interval low - high
// represents w. However we have to pay attention to low, high and w's
// imprecision.
-bool DigitGen(DiyFp low,
- DiyFp w,
- DiyFp high,
- Vector<char> buffer,
- int* length,
- int* kappa) {
+static bool DigitGen(DiyFp low,
+ DiyFp w,
+ DiyFp high,
+ Vector<char> buffer,
+ int* length,
+ int* kappa) {
ASSERT(low.e() == w.e() && w.e() == high.e());
ASSERT(low.f() + 1 <= high.f() - 1);
- ASSERT(minimal_target_exponent <= w.e() && w.e() <= maximal_target_exponent);
+ ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
// low, w and high are imprecise, but by less than one ulp (unit in the last
// place).
// If we remove (resp. add) 1 ulp from low (resp. high) we are certain that
@@ -359,23 +418,23 @@
uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e());
// Modulo by one is an and.
uint64_t fractionals = too_high.f() & (one.f() - 1);
- uint32_t divider;
- int divider_exponent;
+ uint32_t divisor;
+ int divisor_exponent;
BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
- ÷r, ÷r_exponent);
- *kappa = divider_exponent + 1;
+ &divisor, &divisor_exponent);
+ *kappa = divisor_exponent + 1;
*length = 0;
// Loop invariant: buffer = too_high / 10^kappa (integer division)
// The invariant holds for the first iteration: kappa has been initialized
- // with the divider exponent + 1. And the divider is the biggest power of ten
+ // with the divisor exponent + 1. And the divisor is the biggest power of ten
// that is smaller than integrals.
while (*kappa > 0) {
- int digit = integrals / divider;
+ int digit = integrals / divisor;
buffer[*length] = '0' + digit;
(*length)++;
- integrals %= divider;
+ integrals %= divisor;
(*kappa)--;
- // Note that kappa now equals the exponent of the divider and that the
+ // Note that kappa now equals the exponent of the divisor and that the
// invariant thus holds again.
uint64_t rest =
(static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
@@ -386,32 +445,24 @@
// that lies within the unsafe interval.
return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f(),
unsafe_interval.f(), rest,
- static_cast<uint64_t>(divider) << -one.e(), unit);
+ static_cast<uint64_t>(divisor) << -one.e(), unit);
}
- divider /= 10;
+ divisor /= 10;
}
// The integrals have been generated. We are at the point of the decimal
// separator. In the following loop we simply multiply the remaining digits by
// 10 and divide by one. We just need to pay attention to multiply associated
// data (like the interval or 'unit'), too.
- // Instead of multiplying by 10 we multiply by 5 (cheaper operation) and
- // increase its (imaginary) exponent. At the same time we decrease the
- // divider's (one's) exponent and shift its significand.
- // Basically, if fractionals was a DiyFp (with fractionals.e == one.e):
- // fractionals.f *= 10;
- // fractionals.f >>= 1; fractionals.e++; // value remains unchanged.
- // one.f >>= 1; one.e++; // value remains unchanged.
- // and we have again fractionals.e == one.e which allows us to divide
- // fractionals.f() by one.f()
- // We simply combine the *= 10 and the >>= 1.
+ // Note that the multiplication by 10 does not overflow, because w.e >= -60
+ // and thus one.e >= -60.
+ ASSERT(one.e() >= -60);
+ ASSERT(fractionals < one.f());
+ ASSERT(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
while (true) {
- fractionals *= 5;
- unit *= 5;
- unsafe_interval.set_f(unsafe_interval.f() * 5);
- unsafe_interval.set_e(unsafe_interval.e() + 1); // Will be optimized out.
- one.set_f(one.f() >> 1);
- one.set_e(one.e() + 1);
+ fractionals *= 10;
+ unit *= 10;
+ unsafe_interval.set_f(unsafe_interval.f() * 10);
// Integer division by one.
int digit = static_cast<int>(fractionals >> -one.e());
buffer[*length] = '0' + digit;
@@ -426,6 +477,113 @@
}
+
+// Generates (at most) requested_digits of input number w.
+// w is a floating-point number (DiyFp), consisting of a significand and an
+// exponent. Its exponent is bounded by kMinimalTargetExponent and
+// kMaximalTargetExponent.
+// Hence -60 <= w.e() <= -32.
+//
+// Returns false if it fails, in which case the generated digits in the buffer
+// should not be used.
+// Preconditions:
+// * w is correct up to 1 ulp (unit in the last place). That
+// is, its error must be strictly less than a unit of its last digit.
+// * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
+//
+// Postconditions: returns false if procedure fails.
+// otherwise:
+// * buffer is not null-terminated, but length contains the number of
+// digits.
+// * the representation in buffer is the most precise representation of
+// requested_digits digits.
+// * buffer contains at most requested_digits digits of w. If there are less
+// than requested_digits digits then some trailing '0's have been removed.
+// * kappa is such that
+// w = buffer * 10^kappa + eps with |eps| < 10^kappa / 2.
+//
+// Remark: This procedure takes into account the imprecision of its input
+// numbers. If the precision is not enough to guarantee all the postconditions
+// then false is returned. This usually happens rarely, but the failure-rate
+// increases with higher requested_digits.
+static bool DigitGenCounted(DiyFp w,
+ int requested_digits,
+ Vector<char> buffer,
+ int* length,
+ int* kappa) {
+ ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
+ ASSERT(kMinimalTargetExponent >= -60);
+ ASSERT(kMaximalTargetExponent <= -32);
+ // w is assumed to have an error less than 1 unit. Whenever w is scaled we
+ // also scale its error.
+ uint64_t w_error = 1;
+ // We cut the input number into two parts: the integral digits and the
+ // fractional digits. We don't emit any decimal separator, but adapt kappa
+ // instead. Example: instead of writing "1.2" we put "12" into the buffer and
+ // increase kappa by 1.
+ DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
+ // Division by one is a shift.
+ uint32_t integrals = static_cast<uint32_t>(w.f() >> -one.e());
+ // Modulo by one is an and.
+ uint64_t fractionals = w.f() & (one.f() - 1);
+ uint32_t divisor;
+ int divisor_exponent;
+ BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
+ &divisor, &divisor_exponent);
+ *kappa = divisor_exponent + 1;
+ *length = 0;
+
+ // Loop invariant: buffer = w / 10^kappa (integer division)
+ // The invariant holds for the first iteration: kappa has been initialized
+ // with the divisor exponent + 1. And the divisor is the biggest power of ten
+ // that is smaller than 'integrals'.
+ while (*kappa > 0) {
+ int digit = integrals / divisor;
+ buffer[*length] = '0' + digit;
+ (*length)++;
+ requested_digits--;
+ integrals %= divisor;
+ (*kappa)--;
+ // Note that kappa now equals the exponent of the divisor and that the
+ // invariant thus holds again.
+ if (requested_digits == 0) break;
+ divisor /= 10;
+ }
+
+ if (requested_digits == 0) {
+ uint64_t rest =
+ (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
+ return RoundWeedCounted(buffer, *length, rest,
+ static_cast<uint64_t>(divisor) << -one.e(), w_error,
+ kappa);
+ }
+
+ // The integrals have been generated. We are at the point of the decimal
+ // separator. In the following loop we simply multiply the remaining digits by
+ // 10 and divide by one. We just need to pay attention to multiply associated
+ // data (the 'unit'), too.
+ // Note that the multiplication by 10 does not overflow, because w.e >= -60
+ // and thus one.e >= -60.
+ ASSERT(one.e() >= -60);
+ ASSERT(fractionals < one.f());
+ ASSERT(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
+ while (requested_digits > 0 && fractionals > w_error) {
+ fractionals *= 10;
+ w_error *= 10;
+ // Integer division by one.
+ int digit = static_cast<int>(fractionals >> -one.e());
+ buffer[*length] = '0' + digit;
+ (*length)++;
+ requested_digits--;
+ fractionals &= one.f() - 1; // Modulo by one.
+ (*kappa)--;
+ }
+ if (requested_digits != 0) return false;
+ return RoundWeedCounted(buffer, *length, fractionals, one.f(), w_error,
+ kappa);
+}
+
+
// Provides a decimal representation of v.
// Returns true if it succeeds, otherwise the result cannot be trusted.
// There will be *length digits inside the buffer (not null-terminated).
@@ -437,7 +595,10 @@
// The last digit will be closest to the actual v. That is, even if several
// digits might correctly yield 'v' when read again, the closest will be
// computed.
-bool grisu3(double v, Vector<char> buffer, int* length, int* decimal_exponent) {
+static bool Grisu3(double v,
+ Vector<char> buffer,
+ int* length,
+ int* decimal_exponent) {
DiyFp w = Double(v).AsNormalizedDiyFp();
// boundary_minus and boundary_plus are the boundaries between v and its
// closest floating-point neighbors. Any number strictly between
@@ -448,12 +609,12 @@
ASSERT(boundary_plus.e() == w.e());
DiyFp ten_mk; // Cached power of ten: 10^-k
int mk; // -k
- GetCachedPower(w.e() + DiyFp::kSignificandSize, minimal_target_exponent,
- maximal_target_exponent, &mk, &ten_mk);
- ASSERT(minimal_target_exponent <= w.e() + ten_mk.e() +
- DiyFp::kSignificandSize &&
- maximal_target_exponent >= w.e() + ten_mk.e() +
- DiyFp::kSignificandSize);
+ GetCachedPower(w.e() + DiyFp::kSignificandSize, kMinimalTargetExponent,
+ kMaximalTargetExponent, &mk, &ten_mk);
+ ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
+ DiyFp::kSignificandSize) &&
+ (kMaximalTargetExponent >= w.e() + ten_mk.e() +
+ DiyFp::kSignificandSize));
// Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
// 64 bit significand and ten_mk is thus only precise up to 64 bits.
@@ -488,17 +649,75 @@
}
+// The "counted" version of grisu3 (see above) only generates requested_digits
+// number of digits. This version does not generate the shortest representation,
+// and with enough requested digits 0.1 will at some point print as 0.9999999...
+// Grisu3 is too imprecise for real halfway cases (1.5 will not work) and
+// therefore the rounding strategy for halfway cases is irrelevant.
+static bool Grisu3Counted(double v,
+ int requested_digits,
+ Vector<char> buffer,
+ int* length,
+ int* decimal_exponent) {
+ DiyFp w = Double(v).AsNormalizedDiyFp();
+ DiyFp ten_mk; // Cached power of ten: 10^-k
+ int mk; // -k
+ GetCachedPower(w.e() + DiyFp::kSignificandSize, kMinimalTargetExponent,
+ kMaximalTargetExponent, &mk, &ten_mk);
+ ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
+ DiyFp::kSignificandSize) &&
+ (kMaximalTargetExponent >= w.e() + ten_mk.e() +
+ DiyFp::kSignificandSize));
+ // Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
+ // 64 bit significand and ten_mk is thus only precise up to 64 bits.
+
+ // The DiyFp::Times procedure rounds its result, and ten_mk is approximated
+ // too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
+ // off by a small amount.
+ // In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
+ // In other words: let f = scaled_w.f() and e = scaled_w.e(), then
+ // (f-1) * 2^e < w*10^k < (f+1) * 2^e
+ DiyFp scaled_w = DiyFp::Times(w, ten_mk);
+
+ // We now have (double) (scaled_w * 10^-mk).
+ // DigitGen will generate the first requested_digits digits of scaled_w and
+ // return together with a kappa such that scaled_w ~= buffer * 10^kappa. (It
+ // will not always be exactly the same since DigitGenCounted only produces a
+ // limited number of digits.)
+ int kappa;
+ bool result = DigitGenCounted(scaled_w, requested_digits,
+ buffer, length, &kappa);
+ *decimal_exponent = -mk + kappa;
+ return result;
+}
+
+
bool FastDtoa(double v,
+ FastDtoaMode mode,
+ int requested_digits,
Vector<char> buffer,
int* length,
- int* point) {
+ int* decimal_point) {
ASSERT(v > 0);
ASSERT(!Double(v).IsSpecial());
- int decimal_exponent;
- bool result = grisu3(v, buffer, length, &decimal_exponent);
- *point = *length + decimal_exponent;
- buffer[*length] = '\0';
+ bool result = false;
+ int decimal_exponent = 0;
+ switch (mode) {
+ case FAST_DTOA_SHORTEST:
+ result = Grisu3(v, buffer, length, &decimal_exponent);
+ break;
+ case FAST_DTOA_PRECISION:
+ result = Grisu3Counted(v, requested_digits,
+ buffer, length, &decimal_exponent);
+ break;
+ default:
+ UNREACHABLE();
+ }
+ if (result) {
+ *decimal_point = *length + decimal_exponent;
+ buffer[*length] = '\0';
+ }
return result;
}