DO NOT COMMIT: Results of running old (current) clang-format on Blink

third_party/WebKit/Source/wtf/dtoa/fast-dtoa.cc

Index: third_party/WebKit/Source/wtf/dtoa/fast-dtoa.cc
diff --git a/third_party/WebKit/Source/wtf/dtoa/fast-dtoa.cc b/third_party/WebKit/Source/wtf/dtoa/fast-dtoa.cc
index 44ecae68f6e8e0280833fd74f83e4efa56b75f44..6670fa293d02626eaa3cc486e19458d529377121 100644
--- a/third_party/WebKit/Source/wtf/dtoa/fast-dtoa.cc
+++ b/third_party/WebKit/Source/wtf/dtoa/fast-dtoa.cc
@@ -35,705 +35,698 @@ namespace WTF {
 
 namespace double_conversion {
 
-    // The minimal and maximal target exponent define the range of w's binary
-    // exponent, where 'w' is the result of multiplying the input by a cached power
-    // of ten.
-    //
-    // 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 kMinimalTargetExponent = -60;
-    static const int kMaximalTargetExponent = -32;
-
-
-    // Adjusts the last digit of the generated number, and screens out generated
-    // solutions that may be inaccurate. A solution may be inaccurate if it is
-    // outside the safe interval, or if we cannot prove that it is closer to the
-    // input than a neighboring representation of the same length.
-    //
-    // Input: * buffer containing the digits of too_high / 10^kappa
-    //        * the buffer's length
-    //        * distance_too_high_w == (too_high - w).f() * unit
-    //        * unsafe_interval == (too_high - too_low).f() * unit
-    //        * rest = (too_high - buffer * 10^kappa).f() * unit
-    //        * ten_kappa = 10^kappa * unit
-    //        * unit = the common multiplier
-    // 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.
-    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
-        //     w_high = too_high - small_distance.
-        // Note: w_low < w < w_high
-        //
-        // The real w (* unit) must lie somewhere inside the interval
-        // ]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
-        //
-        //  too_high - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-        //                     ^v 1 unit            ^      ^                 ^      ^
-        //  boundary_high ---------------------     .      .                 .      .
-        //                     ^v 1 unit            .      .                 .      .
-        //   - - - - - - - - - - - - - - - - - - -  +  - - + - - - - - -     .      .
-        //                                          .      .         ^       .      .
-        //                                          .  big_distance  .       .      .
-        //                                          .      .         .       .    rest
-        //                              small_distance     .         .       .      .
-        //                                          v      .         .       .      .
-        //  w_high - - - - - - - - - - - - - - - - - -     .         .       .      .
-        //                     ^v 1 unit                   .         .       .      .
-        //  w ----------------------------------------     .         .       .      .
-        //                     ^v 1 unit                   v         .       .      .
-        //  w_low  - - - - - - - - - - - - - - - - - - - - -         .       .      .
-        //                                                           .       .      v
-        //  buffer --------------------------------------------------+-------+--------
-        //                                                           .       .
-        //                                                  safe_interval    .
-        //                                                           v       .
-        //   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -     .
-        //                     ^v 1 unit                                     .
-        //  boundary_low -------------------------                     unsafe_interval
-        //                     ^v 1 unit                                     v
-        //  too_low  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-        //
-        //
-        // Note that the value of buffer could lie anywhere inside the range too_low
-        // to too_high.
-        //
-        // boundary_low, boundary_high and w are approximations of the real boundaries
-        // and v (the input number). They are guaranteed to be precise up to one unit.
-        // In fact the error is guaranteed to be strictly less than one unit.
-        //
-        // Anything that lies outside the unsafe interval is guaranteed not to round
-        // to v when read again.
-        // Anything that lies inside the safe interval is guaranteed to round to v
-        // when read again.
-        // If the number inside the buffer lies inside the unsafe interval but not
-        // 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 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
-        // w_high < buffer < too_high we try to decrement the buffer.
-        // This way the buffer approaches (rounds towards) w.
-        // There are 3 conditions that stop the decrementation process:
-        //   1) the buffer is already below w_high
-        //   2) decrementing the buffer would make it leave the unsafe interval
-        //   3) decrementing the buffer would yield a number below w_high and farther
-        //      away than the current number. In other words:
-        //              (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
-                small_distance - rest >= rest + ten_kappa - small_distance)) {
-                   buffer[length - 1]--;
-                   rest += ten_kappa;
-               }
-
-        // We have approached w+ as much as possible. We now test if approaching w-
-        // would require changing the buffer. If yes, then we have two possible
-        // representations close to w, but we cannot decide which one is closer.
-        if (rest < big_distance &&
-            unsafe_interval - rest >= ten_kappa &&
-            (rest + ten_kappa < big_distance ||
-             big_distance - rest > rest + ten_kappa - big_distance)) {
-                return false;
-            }
-
-        // Weeding test.
-        //   The safe interval is [too_low + 2 ulp; too_high - 2 ulp]
-        //   Since too_low = too_high - unsafe_interval this is equivalent to
-        //      [too_high - unsafe_interval + 4 ulp; too_high - 2 ulp]
-        //   Conceptually we have: rest ~= too_high - buffer
-        return (2 * unit <= rest) && (rest <= unsafe_interval - 4 * unit);
-    }
-
-
-    // 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;
-    static const uint32_t kTen6 = 1000000;
-    static const uint32_t kTen7 = 10000000;
-    static const uint32_t kTen8 = 100000000;
-    static const uint32_t kTen9 = 1000000000;
-
-    // Returns the biggest power of ten that is less than or equal to the given
-    // 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: number < (1 << (number_bits + 1)).
-    static void BiggestPowerTen(uint32_t number,
-                                int number_bits,
-                                uint32_t* power,
-                                int* exponent) {
-        ASSERT(number < (uint32_t)(1 << (number_bits + 1)));
-
-        switch (number_bits) {
-            case 32:
-            case 31:
-            case 30:
-                if (kTen9 <= number) {
-                    *power = kTen9;
-                    *exponent = 9;
-                    break;
-                }  // else fallthrough
-            case 29:
-            case 28:
-            case 27:
-                if (kTen8 <= number) {
-                    *power = kTen8;
-                    *exponent = 8;
-                    break;
-                }  // else fallthrough
-            case 26:
-            case 25:
-            case 24:
-                if (kTen7 <= number) {
-                    *power = kTen7;
-                    *exponent = 7;
-                    break;
-                }  // else fallthrough
-            case 23:
-            case 22:
-            case 21:
-            case 20:
-                if (kTen6 <= number) {
-                    *power = kTen6;
-                    *exponent = 6;
-                    break;
-                }  // else fallthrough
-            case 19:
-            case 18:
-            case 17:
-                if (kTen5 <= number) {
-                    *power = kTen5;
-                    *exponent = 5;
-                    break;
-                }  // else fallthrough
-            case 16:
-            case 15:
-            case 14:
-                if (kTen4 <= number) {
-                    *power = kTen4;
-                    *exponent = 4;
-                    break;
-                }  // else fallthrough
-            case 13:
-            case 12:
-            case 11:
-            case 10:
-                if (1000 <= number) {
-                    *power = 1000;
-                    *exponent = 3;
-                    break;
-                }  // else fallthrough
-            case 9:
-            case 8:
-            case 7:
-                if (100 <= number) {
-                    *power = 100;
-                    *exponent = 2;
-                    break;
-                }  // else fallthrough
-            case 6:
-            case 5:
-            case 4:
-                if (10 <= number) {
-                    *power = 10;
-                    *exponent = 1;
-                    break;
-                }  // else fallthrough
-            case 3:
-            case 2:
-            case 1:
-                if (1 <= number) {
-                    *power = 1;
-                    *exponent = 0;
-                    break;
-                }  // else fallthrough
-            case 0:
-                *power = 0;
-                *exponent = -1;
-                break;
-            default:
-                // Following assignments are here to silence compiler warnings.
-                *power = 0;
-                *exponent = 0;
-                UNREACHABLE();
-        }
-    }
-
-
-    // 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 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 than a unit of their last digits.
-    //  * low.e() == w.e() == high.e()
-    //  * low < w < high, and taking into account their error: low~ <= high~
-    //  * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
-    // Postconditions: returns false if procedure fails.
-    //   otherwise:
-    //     * buffer is not null-terminated, but len contains the number of digits.
-    //     * buffer contains the shortest possible decimal digit-sequence
-    //       such that LOW < buffer * 10^kappa < HIGH, where LOW and HIGH are the
-    //       correct values of low and high (without their error).
-    //     * if more than one decimal representation gives the minimal number of
-    //       decimal digits then the one closest to W (where W is the correct value
-    //       of w) is chosen.
-    // 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 (~0.5%).
-    //
-    // Say, for the sake of example, that
-    //   w.e() == -48, and w.f() == 0x1234567890abcdef
-    // w's value can be computed by w.f() * 2^w.e()
-    // We can obtain w's integral digits by simply shifting w.f() by -w.e().
-    //  -> w's integral part is 0x1234
-    //  w's fractional part is therefore 0x567890abcdef.
-    // Printing w's integral part is easy (simply print 0x1234 in decimal).
-    // In order to print its fraction we repeatedly multiply the fraction by 10 and
-    // get each digit. Example the first digit after the point would be computed by
-    //   (0x567890abcdef * 10) >> 48. -> 3
-    // The whole thing becomes slightly more complicated because we want to stop
-    // once we have enough digits. That is, once the digits inside the buffer
-    // 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.
-    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(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
-        // the new numbers are outside of the interval we want the final
-        // representation to lie in.
-        // Inversely adding (resp. removing) 1 ulp from low (resp. high) would yield
-        // numbers that are certain to lie in the interval. We will use this fact
-        // later on.
-        // We will now start by generating the digits within the uncertain
-        // interval. Later we will weed out representations that lie outside the safe
-        // interval and thus _might_ lie outside the correct interval.
-        uint64_t unit = 1;
-        DiyFp too_low = DiyFp(low.f() - unit, low.e());
-        DiyFp too_high = DiyFp(high.f() + unit, high.e());
-        // too_low and too_high are guaranteed to lie outside the interval we want the
-        // generated number in.
-        DiyFp unsafe_interval = DiyFp::Minus(too_high, too_low);
-        // We now cut the input number into two parts: the integral digits and the
-        // fractionals. We will not write any decimal separator though, but adapt
-        // kappa instead.
-        // Reminder: we are currently computing the digits (stored inside the buffer)
-        // such that:   too_low < buffer * 10^kappa < too_high
-        // We use too_high for the digit_generation and stop as soon as possible.
-        // If we stop early we effectively round down.
-        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>(too_high.f() >> -one.e());
-        // Modulo by one is an and.
-        uint64_t fractionals = too_high.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 = too_high / 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) {
-            char digit = static_cast<char>(integrals / divisor);
-            buffer[*length] = '0' + digit;
-            (*length)++;
-            integrals %= divisor;
-            (*kappa)--;
-            // 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;
-            // Invariant: too_high = buffer * 10^kappa + DiyFp(rest, one.e())
-            // Reminder: unsafe_interval.e() == one.e()
-            if (rest < unsafe_interval.f()) {
-                // Rounding down (by not emitting the remaining digits) yields a number
-                // that lies within the unsafe interval.
-                return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f(),
-                                 unsafe_interval.f(), rest,
-                                 static_cast<uint64_t>(divisor) << -one.e(), unit);
-            }
-            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.
-        // 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(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
-        while (true) {
-            fractionals *= 10;
-            unit *= 10;
-            unsafe_interval.set_f(unsafe_interval.f() * 10);
-            // Integer division by one.
-            char digit = static_cast<char>(fractionals >> -one.e());
-            buffer[*length] = '0' + digit;
-            (*length)++;
-            fractionals &= one.f() - 1;  // Modulo by one.
-            (*kappa)--;
-            if (fractionals < unsafe_interval.f()) {
-                return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f() * unit,
-                                 unsafe_interval.f(), fractionals, one.f(), unit);
-            }
-        }
-    }
-
-
-
-    // Generates (at most) requested_digits 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) {
-            char digit = static_cast<char>(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(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
-        while (requested_digits > 0 && fractionals > w_error) {
-            fractionals *= 10;
-            w_error *= 10;
-            // Integer division by one.
-            char digit = static_cast<char>(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);
+// The minimal and maximal target exponent define the range of w's binary
+// exponent, where 'w' is the result of multiplying the input by a cached power
+// of ten.
+//
+// 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 kMinimalTargetExponent = -60;
+static const int kMaximalTargetExponent = -32;
+
+// Adjusts the last digit of the generated number, and screens out generated
+// solutions that may be inaccurate. A solution may be inaccurate if it is
+// outside the safe interval, or if we cannot prove that it is closer to the
+// input than a neighboring representation of the same length.
+//
+// Input: * buffer containing the digits of too_high / 10^kappa
+//        * the buffer's length
+//        * distance_too_high_w == (too_high - w).f() * unit
+//        * unsafe_interval == (too_high - too_low).f() * unit
+//        * rest = (too_high - buffer * 10^kappa).f() * unit
+//        * ten_kappa = 10^kappa * unit
+//        * unit = the common multiplier
+// 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.
+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
+  //     w_high = too_high - small_distance.
+  // Note: w_low < w < w_high
+  //
+  // The real w (* unit) must lie somewhere inside the interval
+  // ]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
+  //
+  //  too_high - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+  //                     ^v 1 unit            ^      ^                 ^      ^
+  //  boundary_high ---------------------     .      .                 .      .
+  //                     ^v 1 unit            .      .                 .      .
+  //   - - - - - - - - - - - - - - - - - - -  +  - - + - - - - - -     .      .
+  //                                          .      .         ^       .      .
+  //                                          .  big_distance  .       .      .
+  //                                          .      .         .       .    rest
+  //                              small_distance     .         .       .      .
+  //                                          v      .         .       .      .
+  //  w_high - - - - - - - - - - - - - - - - - -     .         .       .      .
+  //                     ^v 1 unit                   .         .       .      .
+  //  w ----------------------------------------     .         .       .      .
+  //                     ^v 1 unit                   v         .       .      .
+  //  w_low  - - - - - - - - - - - - - - - - - - - - -         .       .      .
+  //                                                           .       .      v
+  //  buffer --------------------------------------------------+-------+--------
+  //                                                           .       .
+  //                                                  safe_interval    .
+  //                                                           v       .
+  //   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -     .
+  //                     ^v 1 unit                                     .
+  //  boundary_low -------------------------                     unsafe_interval
+  //                     ^v 1 unit                                     v
+  //  too_low  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
+  //
+  //
+  // Note that the value of buffer could lie anywhere inside the range too_low
+  // to too_high.
+  //
+  // boundary_low, boundary_high and w are approximations of the real boundaries
+  // and v (the input number). They are guaranteed to be precise up to one unit.
+  // In fact the error is guaranteed to be strictly less than one unit.
+  //
+  // Anything that lies outside the unsafe interval is guaranteed not to round
+  // to v when read again.
+  // Anything that lies inside the safe interval is guaranteed to round to v
+  // when read again.
+  // If the number inside the buffer lies inside the unsafe interval but not
+  // 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 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
+  // w_high < buffer < too_high we try to decrement the buffer.
+  // This way the buffer approaches (rounds towards) w.
+  // There are 3 conditions that stop the decrementation process:
+  //   1) the buffer is already below w_high
+  //   2) decrementing the buffer would make it leave the unsafe interval
+  //   3) decrementing the buffer would yield a number below w_high and farther
+  //      away than the current number. In other words:
+  //              (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
+          small_distance - rest >= rest + ten_kappa - small_distance)) {
+    buffer[length - 1]--;
+    rest += ten_kappa;
+  }
+
+  // We have approached w+ as much as possible. We now test if approaching w-
+  // would require changing the buffer. If yes, then we have two possible
+  // representations close to w, but we cannot decide which one is closer.
+  if (rest < big_distance && unsafe_interval - rest >= ten_kappa &&
+      (rest + ten_kappa < big_distance ||
+       big_distance - rest > rest + ten_kappa - big_distance)) {
+    return false;
+  }
+
+  // Weeding test.
+  //   The safe interval is [too_low + 2 ulp; too_high - 2 ulp]
+  //   Since too_low = too_high - unsafe_interval this is equivalent to
+  //      [too_high - unsafe_interval + 4 ulp; too_high - 2 ulp]
+  //   Conceptually we have: rest ~= too_high - buffer
+  return (2 * unit <= rest) && (rest <= unsafe_interval - 4 * unit);
+}
+
+// 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]++;
     }
-
-
-    // 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).
-    // If the function returns true then
-    //        v == (double) (buffer * 10^decimal_exponent).
-    // The digits in the buffer are the shortest representation possible: no
-    // 0.09999999999999999 instead of 0.1. The shorter representation will even be
-    // chosen even if the longer one would be closer to v.
-    // 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.
-    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
-        // boundary_minus and boundary_plus will round to v when convert to a double.
-        // Grisu3 will never output representations that lie exactly on a boundary.
-        DiyFp boundary_minus, boundary_plus;
-        Double(v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
-        ASSERT(boundary_plus.e() == w.e());
-        DiyFp ten_mk;  // Cached power of ten: 10^-k
-        int mk;        // -k
-        int ten_mk_minimal_binary_exponent =
-        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);
-        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);
-        ASSERT(scaled_w.e() ==
-               boundary_plus.e() + ten_mk.e() + DiyFp::kSignificandSize);
-        // In theory it would be possible to avoid some recomputations by computing
-        // the difference between w and boundary_minus/plus (a power of 2) and to
-        // compute scaled_boundary_minus/plus by subtracting/adding from
-        // scaled_w. However the code becomes much less readable and the speed
-        // enhancements are not terriffic.
-        DiyFp scaled_boundary_minus = DiyFp::Times(boundary_minus, ten_mk);
-        DiyFp scaled_boundary_plus  = DiyFp::Times(boundary_plus,  ten_mk);
-
-        // DigitGen will generate the digits of scaled_w. Therefore we have
-        // v == (double) (scaled_w * 10^-mk).
-        // Set decimal_exponent == -mk and pass it to DigitGen. If scaled_w is not an
-        // integer than it will be updated. For instance if scaled_w == 1.23 then
-        // the buffer will be filled with "123" und the decimal_exponent will be
-        // decreased by 2.
-        int kappa;
-        bool result = DigitGen(scaled_boundary_minus, scaled_w, scaled_boundary_plus,
-                               buffer, length, &kappa);
-        *decimal_exponent = -mk + kappa;
-        return result;
+    // 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;
     }
-
-
-    // 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
-        int ten_mk_minimal_binary_exponent =
-        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);
-        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;
+    return true;
+  }
+  return false;
+}
+
+static const uint32_t kTen4 = 10000;
+static const uint32_t kTen5 = 100000;
+static const uint32_t kTen6 = 1000000;
+static const uint32_t kTen7 = 10000000;
+static const uint32_t kTen8 = 100000000;
+static const uint32_t kTen9 = 1000000000;
+
+// Returns the biggest power of ten that is less than or equal to the given
+// 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: number < (1 << (number_bits + 1)).
+static void BiggestPowerTen(uint32_t number,
+                            int number_bits,
+                            uint32_t* power,
+                            int* exponent) {
+  ASSERT(number < (uint32_t)(1 << (number_bits + 1)));
+
+  switch (number_bits) {
+    case 32:
+    case 31:
+    case 30:
+      if (kTen9 <= number) {
+        *power = kTen9;
+        *exponent = 9;
+        break;
+      }  // else fallthrough
+    case 29:
+    case 28:
+    case 27:
+      if (kTen8 <= number) {
+        *power = kTen8;
+        *exponent = 8;
+        break;
+      }  // else fallthrough
+    case 26:
+    case 25:
+    case 24:
+      if (kTen7 <= number) {
+        *power = kTen7;
+        *exponent = 7;
+        break;
+      }  // else fallthrough
+    case 23:
+    case 22:
+    case 21:
+    case 20:
+      if (kTen6 <= number) {
+        *power = kTen6;
+        *exponent = 6;
+        break;
+      }  // else fallthrough
+    case 19:
+    case 18:
+    case 17:
+      if (kTen5 <= number) {
+        *power = kTen5;
+        *exponent = 5;
+        break;
+      }  // else fallthrough
+    case 16:
+    case 15:
+    case 14:
+      if (kTen4 <= number) {
+        *power = kTen4;
+        *exponent = 4;
+        break;
+      }  // else fallthrough
+    case 13:
+    case 12:
+    case 11:
+    case 10:
+      if (1000 <= number) {
+        *power = 1000;
+        *exponent = 3;
+        break;
+      }  // else fallthrough
+    case 9:
+    case 8:
+    case 7:
+      if (100 <= number) {
+        *power = 100;
+        *exponent = 2;
+        break;
+      }  // else fallthrough
+    case 6:
+    case 5:
+    case 4:
+      if (10 <= number) {
+        *power = 10;
+        *exponent = 1;
+        break;
+      }  // else fallthrough
+    case 3:
+    case 2:
+    case 1:
+      if (1 <= number) {
+        *power = 1;
+        *exponent = 0;
+        break;
+      }  // else fallthrough
+    case 0:
+      *power = 0;
+      *exponent = -1;
+      break;
+    default:
+      // Following assignments are here to silence compiler warnings.
+      *power = 0;
+      *exponent = 0;
+      UNREACHABLE();
+  }
+}
+
+// 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 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 than a unit of their last digits.
+//  * low.e() == w.e() == high.e()
+//  * low < w < high, and taking into account their error: low~ <= high~
+//  * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
+// Postconditions: returns false if procedure fails.
+//   otherwise:
+//     * buffer is not null-terminated, but len contains the number of digits.
+//     * buffer contains the shortest possible decimal digit-sequence
+//       such that LOW < buffer * 10^kappa < HIGH, where LOW and HIGH are the
+//       correct values of low and high (without their error).
+//     * if more than one decimal representation gives the minimal number of
+//       decimal digits then the one closest to W (where W is the correct value
+//       of w) is chosen.
+// 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 (~0.5%).
+//
+// Say, for the sake of example, that
+//   w.e() == -48, and w.f() == 0x1234567890abcdef
+// w's value can be computed by w.f() * 2^w.e()
+// We can obtain w's integral digits by simply shifting w.f() by -w.e().
+//  -> w's integral part is 0x1234
+//  w's fractional part is therefore 0x567890abcdef.
+// Printing w's integral part is easy (simply print 0x1234 in decimal).
+// In order to print its fraction we repeatedly multiply the fraction by 10 and
+// get each digit. Example the first digit after the point would be computed by
+//   (0x567890abcdef * 10) >> 48. -> 3
+// The whole thing becomes slightly more complicated because we want to stop
+// once we have enough digits. That is, once the digits inside the buffer
+// 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.
+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(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
+  // the new numbers are outside of the interval we want the final
+  // representation to lie in.
+  // Inversely adding (resp. removing) 1 ulp from low (resp. high) would yield
+  // numbers that are certain to lie in the interval. We will use this fact
+  // later on.
+  // We will now start by generating the digits within the uncertain
+  // interval. Later we will weed out representations that lie outside the safe
+  // interval and thus _might_ lie outside the correct interval.
+  uint64_t unit = 1;
+  DiyFp too_low = DiyFp(low.f() - unit, low.e());
+  DiyFp too_high = DiyFp(high.f() + unit, high.e());
+  // too_low and too_high are guaranteed to lie outside the interval we want the
+  // generated number in.
+  DiyFp unsafe_interval = DiyFp::Minus(too_high, too_low);
+  // We now cut the input number into two parts: the integral digits and the
+  // fractionals. We will not write any decimal separator though, but adapt
+  // kappa instead.
+  // Reminder: we are currently computing the digits (stored inside the buffer)
+  // such that:   too_low < buffer * 10^kappa < too_high
+  // We use too_high for the digit_generation and stop as soon as possible.
+  // If we stop early we effectively round down.
+  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>(too_high.f() >> -one.e());
+  // Modulo by one is an and.
+  uint64_t fractionals = too_high.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 = too_high / 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) {
+    char digit = static_cast<char>(integrals / divisor);
+    buffer[*length] = '0' + digit;
+    (*length)++;
+    integrals %= divisor;
+    (*kappa)--;
+    // 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;
+    // Invariant: too_high = buffer * 10^kappa + DiyFp(rest, one.e())
+    // Reminder: unsafe_interval.e() == one.e()
+    if (rest < unsafe_interval.f()) {
+      // Rounding down (by not emitting the remaining digits) yields a number
+      // that lies within the unsafe interval.
+      return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f(),
+                       unsafe_interval.f(), rest,
+                       static_cast<uint64_t>(divisor) << -one.e(), unit);
     }
-
-
-    bool FastDtoa(double v,
-                  FastDtoaMode mode,
-                  int requested_digits,
-                  Vector<char> buffer,
-                  int* length,
-                  int* decimal_point) {
-        ASSERT(v > 0);
-        ASSERT(!Double(v).IsSpecial());
-
-        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;
+    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.
+  // 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(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
+  while (true) {
+    fractionals *= 10;
+    unit *= 10;
+    unsafe_interval.set_f(unsafe_interval.f() * 10);
+    // Integer division by one.
+    char digit = static_cast<char>(fractionals >> -one.e());
+    buffer[*length] = '0' + digit;
+    (*length)++;
+    fractionals &= one.f() - 1;  // Modulo by one.
+    (*kappa)--;
+    if (fractionals < unsafe_interval.f()) {
+      return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f() * unit,
+                       unsafe_interval.f(), fractionals, one.f(), unit);
     }
+  }
+}
+
+// Generates (at most) requested_digits 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) {
+    char digit = static_cast<char>(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(UINT64_2PART_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
+  while (requested_digits > 0 && fractionals > w_error) {
+    fractionals *= 10;
+    w_error *= 10;
+    // Integer division by one.
+    char digit = static_cast<char>(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).
+// If the function returns true then
+//        v == (double) (buffer * 10^decimal_exponent).
+// The digits in the buffer are the shortest representation possible: no
+// 0.09999999999999999 instead of 0.1. The shorter representation will even be
+// chosen even if the longer one would be closer to v.
+// 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.
+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
+  // boundary_minus and boundary_plus will round to v when convert to a double.
+  // Grisu3 will never output representations that lie exactly on a boundary.
+  DiyFp boundary_minus, boundary_plus;
+  Double(v).NormalizedBoundaries(&boundary_minus, &boundary_plus);
+  ASSERT(boundary_plus.e() == w.e());
+  DiyFp ten_mk;  // Cached power of ten: 10^-k
+  int mk;        // -k
+  int ten_mk_minimal_binary_exponent =
+      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);
+  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);
+  ASSERT(scaled_w.e() ==
+         boundary_plus.e() + ten_mk.e() + DiyFp::kSignificandSize);
+  // In theory it would be possible to avoid some recomputations by computing
+  // the difference between w and boundary_minus/plus (a power of 2) and to
+  // compute scaled_boundary_minus/plus by subtracting/adding from
+  // scaled_w. However the code becomes much less readable and the speed
+  // enhancements are not terriffic.
+  DiyFp scaled_boundary_minus = DiyFp::Times(boundary_minus, ten_mk);
+  DiyFp scaled_boundary_plus = DiyFp::Times(boundary_plus, ten_mk);
+
+  // DigitGen will generate the digits of scaled_w. Therefore we have
+  // v == (double) (scaled_w * 10^-mk).
+  // Set decimal_exponent == -mk and pass it to DigitGen. If scaled_w is not an
+  // integer than it will be updated. For instance if scaled_w == 1.23 then
+  // the buffer will be filled with "123" und the decimal_exponent will be
+  // decreased by 2.
+  int kappa;
+  bool result = DigitGen(scaled_boundary_minus, scaled_w, scaled_boundary_plus,
+                         buffer, length, &kappa);
+  *decimal_exponent = -mk + kappa;
+  return result;
+}
+
+// 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
+  int ten_mk_minimal_binary_exponent =
+      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);
+  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* decimal_point) {
+  ASSERT(v > 0);
+  ASSERT(!Double(v).IsSpecial());
+
+  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;
+}
 
 }  // namespace double_conversion
 
-} // namespace WTF
+}  // namespace WTF