Rename grisu to fast_dtoa. Get rid of template.

src/fast-dtoa.cc

 // Copyright 2010 the V8 project authors. All rights reserved.
 // Redistribution and use in source and binary forms, with or without
 // modification, are permitted provided that the following conditions are
 // met:
 //
 //     * Redistributions of source code must retain the above copyright
 //       notice, this list of conditions and the following disclaimer.
 //     * Redistributions in binary form must reproduce the above
 //       copyright notice, this list of conditions and the following
 //       disclaimer in the documentation and/or other materials provided
 //       with the distribution.
 //     * Neither the name of Google Inc. nor the names of its
 //       contributors may be used to endorse or promote products derived
 //       from this software without specific prior written permission.
 //
 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
 #include "v8.h"
 
-#include "grisu3.h"
+#include "fast-dtoa.h"
 
 #include "cached_powers.h"
 #include "diy_fp.h"
 #include "double.h"
 
 namespace v8 {
 namespace internal {
 
-template <int alpha = -60, int gamma = -32>
-class Grisu3 {
- public:
-  // Provides a decimal representation of v.
-  // Returns true if it succeeds, otherwise the result can not 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
-  // 0.099999999999 instead of 0.1.
-  // 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,
-                     char* buffer, int* length, int* decimal_exponent);
-
- private:
-  // Rounds the buffer according to the rest.
-  // If there is too much imprecision to round then false is returned.
-  // Similarily false is returned when the buffer is not within Delta.
-  static bool RoundWeed(char* buffer, int len, uint64_t wp_W, uint64_t Delta,
-                        uint64_t rest, uint64_t ten_kappa, uint64_t ulp);
-  // Dispatches to the a specialized digit-generation routine. The chosen
-  // routine depends on w.e (which in turn depends on alpha and gamma).
-  // Currently there is only one digit-generation routine, but it would be easy
-  // to add others.
-  static bool DigitGen(DiyFp low, DiyFp w, DiyFp high,
-                       char* buffer, int* len, int* kappa);
-  // Generates w's digits. The result is the shortest in the interval low-high.
-  // All DiyFp are assumed to be imprecise and this function takes this
-  // imprecision into account. If the function cannot compute the best
-  // representation (due to the imprecision) then false is returned.
-  static bool DigitGen_m60_m32(DiyFp low, DiyFp w, DiyFp high,
-                               char* buffer, int* length, int* 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 minimal_target_exponent = -60;
+static const int maximal_target_exponent = -32;
 
 
-template<int alpha, int gamma>
-bool Grisu3<alpha, gamma>::grisu3(double v,
-                                  char* buffer,
-                                  int* length,
-                                  int* decimal_exponent) {
-  DiyFp w = Double(v).AsNormalizedDiyFp();
-  // boundary_minus and boundary_plus are the boundaries between v and its
-  // neighbors. Any number strictly between boundary_minus and boundary_plus
-  // will round to v when read as 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
-  GetCachedPower(w.e() + DiyFp::kSignificandSize, alpha, gamma, &mk, &ten_mk);
-  ASSERT(alpha <= w.e() + ten_mk.e() + DiyFp::kSignificandSize &&
-         gamma >= 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.
+// 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 ctannot 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.
+bool RoundWeed(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_low[ (often written as "(w_low; w_low)")
 
-  // 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);
+  // 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 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.
+  //
+  // 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
+  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;
+  }
 
-  // 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;
+  // 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);
 }
 
-// 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 alpha and gamma. Typically alpha >= -63
-// and gamma <= 3.
-// 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.
-//  * low.e() == w.e() == high.e()
-//  * low < w < high, and taking into account their error: low~ <= high~
-//  * alpha <= w.e() <= gamma
-// 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%).
-template<int alpha, int gamma>
-bool Grisu3<alpha, gamma>::DigitGen(DiyFp low,
-                                    DiyFp w,
-                                    DiyFp high,
-                                    char* buffer,
-                                    int* len,
-                                    int* kappa) {
-  ASSERT(low.e() == w.e() && w.e() == high.e());
-  ASSERT(low.f() + 1 <= high.f() - 1);
-  ASSERT(alpha <= w.e() && w.e() <= gamma);
-  // The following tests use alpha and gamma to avoid unnecessary dynamic tests.
-  if ((alpha >= -60 && gamma <= -32) ||  // -60 <= w.e() <= -32
-      (alpha <= -32 && gamma >= -60 &&   // Alpha/gamma overlaps -60/-32 region.
-       -60 <= w.e() && w.e() <= -32)) {
-    return DigitGen_m60_m32(low, w, high, buffer, len, kappa);
-  } else {
-    // A simple adaption of the special case -60/-32 would allow greater ranges
-    // of alpha/gamma and thus reduce the number of precomputed cached powers of
-    // ten.
-    UNIMPLEMENTED();
-    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 <= than the given number. We
-// furthermore receive the maximum number of bits 'number' has.
+// Returns the biggest power of ten that is less than or equal than 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: (1 << number_bits) <= number < (1 << (number_bits + 1)).
 static void BiggestPowerTen(uint32_t number,
                             int number_bits,
                             uint32_t* power,
                             int* exponent) {
   switch (number_bits) {
     case 32:
     case 31:
     case 30:
       if (kTen9 <= number) {
         *power = kTen9;
@@ skipping 80 matching lines @@
       break;
     default:
       // Following assignments are here to silence compiler warnings.
       *power = 0;
       *exponent = 0;
       UNREACHABLE();
   }
 }
 
 
-// Same comments as for DigitGen but with additional precondition:
-//    -60 <= w.e() <= -32
+// 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.
+//       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.
+//  * 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
+// 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 comma 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.
-template<int alpha, int gamma>
-bool Grisu3<alpha, gamma>::DigitGen_m60_m32(DiyFp low,
-                                            DiyFp w,
-                                            DiyFp high,
-                                            char* buffer,
-                                            int* length,
-                                            int* kappa) {
+bool DigitGen(DiyFp low,
+              DiyFp w,
+              DiyFp high,
+              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);
   // 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
@@ skipping 76 matching lines @@
     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);
     }
   }
 }
 
 
-// Rounds the given generated digits in the buffer and weeds out generated
-// digits that are not in the safe interval, or where we cannot find a rounded
-// representation.
-// 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 on success.
-//    Modifies the generated digits in the buffer to approach (round towards) w.
-template<int alpha, int gamma>
-bool Grisu3<alpha, gamma>::RoundWeed(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- = too_high - big_distance, and
-  //     w+ = too_high - small_distance.
-  // Note: w- < w < w+
-  //
-  // The real w (* unit) must lie somewhere inside the interval
-  // ]w-; w+[ (often written as "(w-; w+)")
+// 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.
+bool grisu3(double v, 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
+  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);
+  // 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.
 
-  // Basically the buffer currently contains a number in the unsafe interval
-  // ]too_low; too_high[ with too_low < w < too_high
-  //
-  // By generating the digits of too_high we got the biggest last digit.
-  // In the case that w+ < 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+
-  //   2) decrementing the buffer would make it leave the unsafe interval
-  //   3) decrementing the buffer would yield a number below w+ and farther away
-  //      than the current number. In other words:
-  //                       (buffer{-1} < w+) && w+ - buffer{-1} > buffer - w+
-  // Instead of using the buffer directly we use its distance to too_high.
-  // Conceptually rest ~= too_high - buffer
-  while (rest < small_distance &&  // Negated condition 1
-         unsafe_interval - rest >= ten_kappa &&  // Negated condition 2
-         (rest + ten_kappa < small_distance ||  // buffer{-1} > w+
-          small_distance - rest >= rest + ten_kappa - small_distance)) {
-    buffer[length - 1]--;
-    rest += ten_kappa;
-  }
+  // 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);
 
-  // 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 too
-  //      [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);
+  // 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;
 }
 
 
-bool grisu3(double v, char* buffer, int* sign, int* length, int* point) {
+bool FastDtoa(double v, char* buffer, int* sign, int* length, int* point) {
   ASSERT(v != 0);
   ASSERT(!Double(v).IsSpecial());
 
   if (v < 0) {
     v = -v;
     *sign = 1;
   } else {
     *sign = 0;
   }
   int decimal_exponent;
-  bool result = Grisu3<-60, -32>::grisu3(v, buffer, length, &decimal_exponent);
+  bool result = grisu3(v, buffer, length, &decimal_exponent);
   *point = *length + decimal_exponent;
   buffer[*length] = '\0';
   return result;
 }
 
 } }  // namespace v8::internal