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

Index: third_party/WebKit/Source/wtf/dtoa/bignum-dtoa.cc
diff --git a/third_party/WebKit/Source/wtf/dtoa/bignum-dtoa.cc b/third_party/WebKit/Source/wtf/dtoa/bignum-dtoa.cc
index 0d79df4c3daf7febd5b87bce000a45261cd234ca..bf37b6d7894a2f238928dcafa20e1478e01f5fd6 100644
--- a/third_party/WebKit/Source/wtf/dtoa/bignum-dtoa.cc
+++ b/third_party/WebKit/Source/wtf/dtoa/bignum-dtoa.cc
@@ -27,630 +27,653 @@
 
 #include "bignum-dtoa.h"
 
+#include <math.h>
 #include "bignum.h"
 #include "double.h"
-#include <math.h>
 
 namespace WTF {
 
 namespace double_conversion {
 
-    static int NormalizedExponent(uint64_t significand, int exponent) {
-        ASSERT(significand != 0);
-        while ((significand & Double::kHiddenBit) == 0) {
-            significand = significand << 1;
-            exponent = exponent - 1;
-        }
-        return exponent;
-    }
-
-
-    // Forward declarations:
-    // Returns an estimation of k such that 10^(k-1) <= v < 10^k.
-    static int EstimatePower(int exponent);
-    // Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
-    // and denominator.
-    static void InitialScaledStartValues(double v,
-                                         int estimated_power,
-                                         bool need_boundary_deltas,
-                                         Bignum* numerator,
-                                         Bignum* denominator,
-                                         Bignum* delta_minus,
-                                         Bignum* delta_plus);
-    // Multiplies numerator/denominator so that its values lies in the range 1-10.
-    // Returns decimal_point s.t.
-    //  v = numerator'/denominator' * 10^(decimal_point-1)
-    //     where numerator' and denominator' are the values of numerator and
-    //     denominator after the call to this function.
-    static void FixupMultiply10(int estimated_power, bool is_even,
-                                int* decimal_point,
-                                Bignum* numerator, Bignum* denominator,
-                                Bignum* delta_minus, Bignum* delta_plus);
-    // Generates digits from the left to the right and stops when the generated
-    // digits yield the shortest decimal representation of v.
-    static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
-                                       Bignum* delta_minus, Bignum* delta_plus,
-                                       bool is_even,
-                                       Vector<char> buffer, int* length);
-    // Generates 'requested_digits' after the decimal point.
-    static void BignumToFixed(int requested_digits, int* decimal_point,
-                              Bignum* numerator, Bignum* denominator,
-                              Vector<char>(buffer), int* length);
-    // Generates 'count' digits of numerator/denominator.
-    // Once 'count' digits have been produced rounds the result depending on the
-    // remainder (remainders of exactly .5 round upwards). Might update the
-    // decimal_point when rounding up (for example for 0.9999).
-    static void GenerateCountedDigits(int count, int* decimal_point,
-                                      Bignum* numerator, Bignum* denominator,
-                                      Vector<char>(buffer), int* length);
-
-
-    void BignumDtoa(double v, BignumDtoaMode mode, int requested_digits,
-                    Vector<char> buffer, int* length, int* decimal_point) {
-        ASSERT(v > 0);
-        ASSERT(!Double(v).IsSpecial());
-        uint64_t significand = Double(v).Significand();
-        bool is_even = (significand & 1) == 0;
-        int exponent = Double(v).Exponent();
-        int normalized_exponent = NormalizedExponent(significand, exponent);
-        // estimated_power might be too low by 1.
-        int estimated_power = EstimatePower(normalized_exponent);
-
-        // Shortcut for Fixed.
-        // The requested digits correspond to the digits after the point. If the
-        // number is much too small, then there is no need in trying to get any
-        // digits.
-        if (mode == BIGNUM_DTOA_FIXED && -estimated_power - 1 > requested_digits) {
-            buffer[0] = '\0';
-            *length = 0;
-            // Set decimal-point to -requested_digits. This is what Gay does.
-            // Note that it should not have any effect anyways since the string is
-            // empty.
-            *decimal_point = -requested_digits;
-            return;
-        }
-
-        Bignum numerator;
-        Bignum denominator;
-        Bignum delta_minus;
-        Bignum delta_plus;
-        // Make sure the bignum can grow large enough. The smallest double equals
-        // 4e-324. In this case the denominator needs fewer than 324*4 binary digits.
-        // The maximum double is 1.7976931348623157e308 which needs fewer than
-        // 308*4 binary digits.
-        ASSERT(Bignum::kMaxSignificantBits >= 324*4);
-        bool need_boundary_deltas = (mode == BIGNUM_DTOA_SHORTEST);
-        InitialScaledStartValues(v, estimated_power, need_boundary_deltas,
-                                 &numerator, &denominator,
-                                 &delta_minus, &delta_plus);
-        // We now have v = (numerator / denominator) * 10^estimated_power.
-        FixupMultiply10(estimated_power, is_even, decimal_point,
-                        &numerator, &denominator,
-                        &delta_minus, &delta_plus);
-        // We now have v = (numerator / denominator) * 10^(decimal_point-1), and
-        //  1 <= (numerator + delta_plus) / denominator < 10
-        switch (mode) {
-            case BIGNUM_DTOA_SHORTEST:
-                GenerateShortestDigits(&numerator, &denominator,
-                                       &delta_minus, &delta_plus,
-                                       is_even, buffer, length);
-                break;
-            case BIGNUM_DTOA_FIXED:
-                BignumToFixed(requested_digits, decimal_point,
-                              &numerator, &denominator,
-                              buffer, length);
-                break;
-            case BIGNUM_DTOA_PRECISION:
-                GenerateCountedDigits(requested_digits, decimal_point,
-                                      &numerator, &denominator,
-                                      buffer, length);
-                break;
-            default:
-                UNREACHABLE();
-        }
-        buffer[*length] = '\0';
-    }
-
-
-    // The procedure starts generating digits from the left to the right and stops
-    // when the generated digits yield the shortest decimal representation of v. A
-    // decimal representation of v is a number lying closer to v than to any other
-    // double, so it converts to v when read.
-    //
-    // This is true if d, the decimal representation, is between m- and m+, the
-    // upper and lower boundaries. d must be strictly between them if !is_even.
-    //           m- := (numerator - delta_minus) / denominator
-    //           m+ := (numerator + delta_plus) / denominator
-    //
-    // Precondition: 0 <= (numerator+delta_plus) / denominator < 10.
-    //   If 1 <= (numerator+delta_plus) / denominator < 10 then no leading 0 digit
-    //   will be produced. This should be the standard precondition.
-    static void GenerateShortestDigits(Bignum* numerator, Bignum* denominator,
-                                       Bignum* delta_minus, Bignum* delta_plus,
-                                       bool is_even,
-                                       Vector<char> buffer, int* length) {
-        // Small optimization: if delta_minus and delta_plus are the same just reuse
-        // one of the two bignums.
-        if (Bignum::Equal(*delta_minus, *delta_plus)) {
-            delta_plus = delta_minus;
-        }
-        *length = 0;
-        while (true) {
-            uint16_t digit;
-            digit = numerator->DivideModuloIntBignum(*denominator);
-            ASSERT(digit <= 9);  // digit is a uint16_t and therefore always positive.
-            // digit = numerator / denominator (integer division).
-            // numerator = numerator % denominator.
-            buffer[(*length)++] = static_cast<char>(digit + '0');
-
-            // Can we stop already?
-            // If the remainder of the division is less than the distance to the lower
-            // boundary we can stop. In this case we simply round down (discarding the
-            // remainder).
-            // Similarly we test if we can round up (using the upper boundary).
-            bool in_delta_room_minus;
-            bool in_delta_room_plus;
-            if (is_even) {
-                in_delta_room_minus = Bignum::LessEqual(*numerator, *delta_minus);
-            } else {
-                in_delta_room_minus = Bignum::Less(*numerator, *delta_minus);
-            }
-            if (is_even) {
-                in_delta_room_plus =
-                Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
-            } else {
-                in_delta_room_plus =
-                Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
-            }
-            if (!in_delta_room_minus && !in_delta_room_plus) {
-                // Prepare for next iteration.
-                numerator->Times10();
-                delta_minus->Times10();
-                // We optimized delta_plus to be equal to delta_minus (if they share the
-                // same value). So don't multiply delta_plus if they point to the same
-                // object.
-                if (delta_minus != delta_plus) {
-                    delta_plus->Times10();
-                }
-            } else if (in_delta_room_minus && in_delta_room_plus) {
-                // Let's see if 2*numerator < denominator.
-                // If yes, then the next digit would be < 5 and we can round down.
-                int compare = Bignum::PlusCompare(*numerator, *numerator, *denominator);
-                if (compare < 0) {
-                    // Remaining digits are less than .5. -> Round down (== do nothing).
-                } else if (compare > 0) {
-                    // Remaining digits are more than .5 of denominator. -> Round up.
-                    // Note that the last digit could not be a '9' as otherwise the whole
-                    // loop would have stopped earlier.
-                    // We still have an assert here in case the preconditions were not
-                    // satisfied.
-                    ASSERT(buffer[(*length) - 1] != '9');
-                    buffer[(*length) - 1]++;
-                } else {
-                    // Halfway case.
-                    // TODO(floitsch): need a way to solve half-way cases.
-                    //   For now let's round towards even (since this is what Gay seems to
-                    //   do).
-
-                    if ((buffer[(*length) - 1] - '0') % 2 == 0) {
-                        // Round down => Do nothing.
-                    } else {
-                        ASSERT(buffer[(*length) - 1] != '9');
-                        buffer[(*length) - 1]++;
-                    }
-                }
-                return;
-            } else if (in_delta_room_minus) {
-                // Round down (== do nothing).
-                return;
-            } else {  // in_delta_room_plus
-                // Round up.
-                // Note again that the last digit could not be '9' since this would have
-                // stopped the loop earlier.
-                // We still have an ASSERT here, in case the preconditions were not
-                // satisfied.
-                ASSERT(buffer[(*length) -1] != '9');
-                buffer[(*length) - 1]++;
-                return;
-            }
-        }
+static int NormalizedExponent(uint64_t significand, int exponent) {
+  ASSERT(significand != 0);
+  while ((significand & Double::kHiddenBit) == 0) {
+    significand = significand << 1;
+    exponent = exponent - 1;
+  }
+  return exponent;
+}
+
+// Forward declarations:
+// Returns an estimation of k such that 10^(k-1) <= v < 10^k.
+static int EstimatePower(int exponent);
+// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
+// and denominator.
+static void InitialScaledStartValues(double v,
+                                     int estimated_power,
+                                     bool need_boundary_deltas,
+                                     Bignum* numerator,
+                                     Bignum* denominator,
+                                     Bignum* delta_minus,
+                                     Bignum* delta_plus);
+// Multiplies numerator/denominator so that its values lies in the range 1-10.
+// Returns decimal_point s.t.
+//  v = numerator'/denominator' * 10^(decimal_point-1)
+//     where numerator' and denominator' are the values of numerator and
+//     denominator after the call to this function.
+static void FixupMultiply10(int estimated_power,
+                            bool is_even,
+                            int* decimal_point,
+                            Bignum* numerator,
+                            Bignum* denominator,
+                            Bignum* delta_minus,
+                            Bignum* delta_plus);
+// Generates digits from the left to the right and stops when the generated
+// digits yield the shortest decimal representation of v.
+static void GenerateShortestDigits(Bignum* numerator,
+                                   Bignum* denominator,
+                                   Bignum* delta_minus,
+                                   Bignum* delta_plus,
+                                   bool is_even,
+                                   Vector<char> buffer,
+                                   int* length);
+// Generates 'requested_digits' after the decimal point.
+static void BignumToFixed(int requested_digits,
+                          int* decimal_point,
+                          Bignum* numerator,
+                          Bignum* denominator,
+                          Vector<char>(buffer),
+                          int* length);
+// Generates 'count' digits of numerator/denominator.
+// Once 'count' digits have been produced rounds the result depending on the
+// remainder (remainders of exactly .5 round upwards). Might update the
+// decimal_point when rounding up (for example for 0.9999).
+static void GenerateCountedDigits(int count,
+                                  int* decimal_point,
+                                  Bignum* numerator,
+                                  Bignum* denominator,
+                                  Vector<char>(buffer),
+                                  int* length);
+
+void BignumDtoa(double v,
+                BignumDtoaMode mode,
+                int requested_digits,
+                Vector<char> buffer,
+                int* length,
+                int* decimal_point) {
+  ASSERT(v > 0);
+  ASSERT(!Double(v).IsSpecial());
+  uint64_t significand = Double(v).Significand();
+  bool is_even = (significand & 1) == 0;
+  int exponent = Double(v).Exponent();
+  int normalized_exponent = NormalizedExponent(significand, exponent);
+  // estimated_power might be too low by 1.
+  int estimated_power = EstimatePower(normalized_exponent);
+
+  // Shortcut for Fixed.
+  // The requested digits correspond to the digits after the point. If the
+  // number is much too small, then there is no need in trying to get any
+  // digits.
+  if (mode == BIGNUM_DTOA_FIXED && -estimated_power - 1 > requested_digits) {
+    buffer[0] = '\0';
+    *length = 0;
+    // Set decimal-point to -requested_digits. This is what Gay does.
+    // Note that it should not have any effect anyways since the string is
+    // empty.
+    *decimal_point = -requested_digits;
+    return;
+  }
+
+  Bignum numerator;
+  Bignum denominator;
+  Bignum delta_minus;
+  Bignum delta_plus;
+  // Make sure the bignum can grow large enough. The smallest double equals
+  // 4e-324. In this case the denominator needs fewer than 324*4 binary digits.
+  // The maximum double is 1.7976931348623157e308 which needs fewer than
+  // 308*4 binary digits.
+  ASSERT(Bignum::kMaxSignificantBits >= 324 * 4);
+  bool need_boundary_deltas = (mode == BIGNUM_DTOA_SHORTEST);
+  InitialScaledStartValues(v, estimated_power, need_boundary_deltas, &numerator,
+                           &denominator, &delta_minus, &delta_plus);
+  // We now have v = (numerator / denominator) * 10^estimated_power.
+  FixupMultiply10(estimated_power, is_even, decimal_point, &numerator,
+                  &denominator, &delta_minus, &delta_plus);
+  // We now have v = (numerator / denominator) * 10^(decimal_point-1), and
+  //  1 <= (numerator + delta_plus) / denominator < 10
+  switch (mode) {
+    case BIGNUM_DTOA_SHORTEST:
+      GenerateShortestDigits(&numerator, &denominator, &delta_minus,
+                             &delta_plus, is_even, buffer, length);
+      break;
+    case BIGNUM_DTOA_FIXED:
+      BignumToFixed(requested_digits, decimal_point, &numerator, &denominator,
+                    buffer, length);
+      break;
+    case BIGNUM_DTOA_PRECISION:
+      GenerateCountedDigits(requested_digits, decimal_point, &numerator,
+                            &denominator, buffer, length);
+      break;
+    default:
+      UNREACHABLE();
+  }
+  buffer[*length] = '\0';
+}
+
+// The procedure starts generating digits from the left to the right and stops
+// when the generated digits yield the shortest decimal representation of v. A
+// decimal representation of v is a number lying closer to v than to any other
+// double, so it converts to v when read.
+//
+// This is true if d, the decimal representation, is between m- and m+, the
+// upper and lower boundaries. d must be strictly between them if !is_even.
+//           m- := (numerator - delta_minus) / denominator
+//           m+ := (numerator + delta_plus) / denominator
+//
+// Precondition: 0 <= (numerator+delta_plus) / denominator < 10.
+//   If 1 <= (numerator+delta_plus) / denominator < 10 then no leading 0 digit
+//   will be produced. This should be the standard precondition.
+static void GenerateShortestDigits(Bignum* numerator,
+                                   Bignum* denominator,
+                                   Bignum* delta_minus,
+                                   Bignum* delta_plus,
+                                   bool is_even,
+                                   Vector<char> buffer,
+                                   int* length) {
+  // Small optimization: if delta_minus and delta_plus are the same just reuse
+  // one of the two bignums.
+  if (Bignum::Equal(*delta_minus, *delta_plus)) {
+    delta_plus = delta_minus;
+  }
+  *length = 0;
+  while (true) {
+    uint16_t digit;
+    digit = numerator->DivideModuloIntBignum(*denominator);
+    ASSERT(digit <= 9);  // digit is a uint16_t and therefore always positive.
+    // digit = numerator / denominator (integer division).
+    // numerator = numerator % denominator.
+    buffer[(*length)++] = static_cast<char>(digit + '0');
+
+    // Can we stop already?
+    // If the remainder of the division is less than the distance to the lower
+    // boundary we can stop. In this case we simply round down (discarding the
+    // remainder).
+    // Similarly we test if we can round up (using the upper boundary).
+    bool in_delta_room_minus;
+    bool in_delta_room_plus;
+    if (is_even) {
+      in_delta_room_minus = Bignum::LessEqual(*numerator, *delta_minus);
+    } else {
+      in_delta_room_minus = Bignum::Less(*numerator, *delta_minus);
     }
-
-
-    // Let v = numerator / denominator < 10.
-    // Then we generate 'count' digits of d = x.xxxxx... (without the decimal point)
-    // from left to right. Once 'count' digits have been produced we decide wether
-    // to round up or down. Remainders of exactly .5 round upwards. Numbers such
-    // as 9.999999 propagate a carry all the way, and change the
-    // exponent (decimal_point), when rounding upwards.
-    static void GenerateCountedDigits(int count, int* decimal_point,
-                                      Bignum* numerator, Bignum* denominator,
-                                      Vector<char>(buffer), int* length) {
-        ASSERT(count >= 0);
-        for (int i = 0; i < count - 1; ++i) {
-            uint16_t digit;
-            digit = numerator->DivideModuloIntBignum(*denominator);
-            ASSERT(digit <= 9);  // digit is a uint16_t and therefore always positive.
-            // digit = numerator / denominator (integer division).
-            // numerator = numerator % denominator.
-            buffer[i] = static_cast<char>(digit + '0');
-            // Prepare for next iteration.
-            numerator->Times10();
-        }
-        // Generate the last digit.
-        uint16_t digit;
-        digit = numerator->DivideModuloIntBignum(*denominator);
-        if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
-            digit++;
-        }
-        buffer[count - 1] = static_cast<char>(digit + '0');
-        // Correct bad digits (in case we had a sequence of '9's). Propagate the
-        // carry until we hat a non-'9' or til we reach the first digit.
-        for (int i = count - 1; i > 0; --i) {
-            if (buffer[i] != '0' + 10) break;
-            buffer[i] = '0';
-            buffer[i - 1]++;
-        }
-        if (buffer[0] == '0' + 10) {
-            // Propagate a carry past the top place.
-            buffer[0] = '1';
-            (*decimal_point)++;
-        }
-        *length = count;
+    if (is_even) {
+      in_delta_room_plus =
+          Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
+    } else {
+      in_delta_room_plus =
+          Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
     }
-
-
-    // Generates 'requested_digits' after the decimal point. It might omit
-    // trailing '0's. If the input number is too small then no digits at all are
-    // generated (ex.: 2 fixed digits for 0.00001).
-    //
-    // Input verifies:  1 <= (numerator + delta) / denominator < 10.
-    static void BignumToFixed(int requested_digits, int* decimal_point,
-                              Bignum* numerator, Bignum* denominator,
-                              Vector<char>(buffer), int* length) {
-        // Note that we have to look at more than just the requested_digits, since
-        // a number could be rounded up. Example: v=0.5 with requested_digits=0.
-        // Even though the power of v equals 0 we can't just stop here.
-        if (-(*decimal_point) > requested_digits) {
-            // The number is definitively too small.
-            // Ex: 0.001 with requested_digits == 1.
-            // Set decimal-point to -requested_digits. This is what Gay does.
-            // Note that it should not have any effect anyways since the string is
-            // empty.
-            *decimal_point = -requested_digits;
-            *length = 0;
-            return;
-        } else if (-(*decimal_point) == requested_digits) {
-            // We only need to verify if the number rounds down or up.
-            // Ex: 0.04 and 0.06 with requested_digits == 1.
-            ASSERT(*decimal_point == -requested_digits);
-            // Initially the fraction lies in range (1, 10]. Multiply the denominator
-            // by 10 so that we can compare more easily.
-            denominator->Times10();
-            if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
-                // If the fraction is >= 0.5 then we have to include the rounded
-                // digit.
-                buffer[0] = '1';
-                *length = 1;
-                (*decimal_point)++;
-            } else {
-                // Note that we caught most of similar cases earlier.
-                *length = 0;
-            }
-            return;
+    if (!in_delta_room_minus && !in_delta_room_plus) {
+      // Prepare for next iteration.
+      numerator->Times10();
+      delta_minus->Times10();
+      // We optimized delta_plus to be equal to delta_minus (if they share the
+      // same value). So don't multiply delta_plus if they point to the same
+      // object.
+      if (delta_minus != delta_plus) {
+        delta_plus->Times10();
+      }
+    } else if (in_delta_room_minus && in_delta_room_plus) {
+      // Let's see if 2*numerator < denominator.
+      // If yes, then the next digit would be < 5 and we can round down.
+      int compare = Bignum::PlusCompare(*numerator, *numerator, *denominator);
+      if (compare < 0) {
+        // Remaining digits are less than .5. -> Round down (== do nothing).
+      } else if (compare > 0) {
+        // Remaining digits are more than .5 of denominator. -> Round up.
+        // Note that the last digit could not be a '9' as otherwise the whole
+        // loop would have stopped earlier.
+        // We still have an assert here in case the preconditions were not
+        // satisfied.
+        ASSERT(buffer[(*length) - 1] != '9');
+        buffer[(*length) - 1]++;
+      } else {
+        // Halfway case.
+        // TODO(floitsch): need a way to solve half-way cases.
+        //   For now let's round towards even (since this is what Gay seems to
+        //   do).
+
+        if ((buffer[(*length) - 1] - '0') % 2 == 0) {
+          // Round down => Do nothing.
         } else {
-            // The requested digits correspond to the digits after the point.
-            // The variable 'needed_digits' includes the digits before the point.
-            int needed_digits = (*decimal_point) + requested_digits;
-            GenerateCountedDigits(needed_digits, decimal_point,
-                                  numerator, denominator,
-                                  buffer, length);
+          ASSERT(buffer[(*length) - 1] != '9');
+          buffer[(*length) - 1]++;
         }
+      }
+      return;
+    } else if (in_delta_room_minus) {
+      // Round down (== do nothing).
+      return;
+    } else {  // in_delta_room_plus
+      // Round up.
+      // Note again that the last digit could not be '9' since this would have
+      // stopped the loop earlier.
+      // We still have an ASSERT here, in case the preconditions were not
+      // satisfied.
+      ASSERT(buffer[(*length) - 1] != '9');
+      buffer[(*length) - 1]++;
+      return;
     }
-
-
-    // Returns an estimation of k such that 10^(k-1) <= v < 10^k where
-    // v = f * 2^exponent and 2^52 <= f < 2^53.
-    // v is hence a normalized double with the given exponent. The output is an
-    // approximation for the exponent of the decimal approimation .digits * 10^k.
-    //
-    // The result might undershoot by 1 in which case 10^k <= v < 10^k+1.
-    // Note: this property holds for v's upper boundary m+ too.
-    //    10^k <= m+ < 10^k+1.
-    //   (see explanation below).
-    //
-    // Examples:
-    //  EstimatePower(0)   => 16
-    //  EstimatePower(-52) => 0
-    //
-    // Note: e >= 0 => EstimatedPower(e) > 0. No similar claim can be made for e<0.
-    static int EstimatePower(int exponent) {
-        // This function estimates log10 of v where v = f*2^e (with e == exponent).
-        // Note that 10^floor(log10(v)) <= v, but v <= 10^ceil(log10(v)).
-        // Note that f is bounded by its container size. Let p = 53 (the double's
-        // significand size). Then 2^(p-1) <= f < 2^p.
-        //
-        // Given that log10(v) == log2(v)/log2(10) and e+(len(f)-1) is quite close
-        // to log2(v) the function is simplified to (e+(len(f)-1)/log2(10)).
-        // The computed number undershoots by less than 0.631 (when we compute log3
-        // and not log10).
-        //
-        // Optimization: since we only need an approximated result this computation
-        // can be performed on 64 bit integers. On x86/x64 architecture the speedup is
-        // not really measurable, though.
-        //
-        // Since we want to avoid overshooting we decrement by 1e10 so that
-        // floating-point imprecisions don't affect us.
-        //
-        // Explanation for v's boundary m+: the computation takes advantage of
-        // the fact that 2^(p-1) <= f < 2^p. Boundaries still satisfy this requirement
-        // (even for denormals where the delta can be much more important).
-
-        const double k1Log10 = 0.30102999566398114;  // 1/lg(10)
-
-        // For doubles len(f) == 53 (don't forget the hidden bit).
-        const int kSignificandSize = 53;
-        double estimate = ceil((exponent + kSignificandSize - 1) * k1Log10 - 1e-10);
-        return static_cast<int>(estimate);
-    }
-
-
-    // See comments for InitialScaledStartValues.
-    static void InitialScaledStartValuesPositiveExponent(
-                                                         double v, int estimated_power, bool need_boundary_deltas,
-                                                         Bignum* numerator, Bignum* denominator,
-                                                         Bignum* delta_minus, Bignum* delta_plus) {
-        // A positive exponent implies a positive power.
-        ASSERT(estimated_power >= 0);
-        // Since the estimated_power is positive we simply multiply the denominator
-        // by 10^estimated_power.
-
-        // numerator = v.
-        numerator->AssignUInt64(Double(v).Significand());
-        numerator->ShiftLeft(Double(v).Exponent());
-        // denominator = 10^estimated_power.
-        denominator->AssignPowerUInt16(10, estimated_power);
-
-        if (need_boundary_deltas) {
-            // Introduce a common denominator so that the deltas to the boundaries are
-            // integers.
-            denominator->ShiftLeft(1);
-            numerator->ShiftLeft(1);
-            // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
-            // denominator (of 2) delta_plus equals 2^e.
-            delta_plus->AssignUInt16(1);
-            delta_plus->ShiftLeft(Double(v).Exponent());
-            // Same for delta_minus (with adjustments below if f == 2^p-1).
-            delta_minus->AssignUInt16(1);
-            delta_minus->ShiftLeft(Double(v).Exponent());
-
-            // If the significand (without the hidden bit) is 0, then the lower
-            // boundary is closer than just half a ulp (unit in the last place).
-            // There is only one exception: if the next lower number is a denormal then
-            // the distance is 1 ulp. This cannot be the case for exponent >= 0 (but we
-            // have to test it in the other function where exponent < 0).
-            uint64_t v_bits = Double(v).AsUint64();
-            if ((v_bits & Double::kSignificandMask) == 0) {
-                // The lower boundary is closer at half the distance of "normal" numbers.
-                // Increase the common denominator and adapt all but the delta_minus.
-                denominator->ShiftLeft(1);  // *2
-                numerator->ShiftLeft(1);    // *2
-                delta_plus->ShiftLeft(1);   // *2
-            }
-        }
+  }
+}
+
+// Let v = numerator / denominator < 10.
+// Then we generate 'count' digits of d = x.xxxxx... (without the decimal point)
+// from left to right. Once 'count' digits have been produced we decide wether
+// to round up or down. Remainders of exactly .5 round upwards. Numbers such
+// as 9.999999 propagate a carry all the way, and change the
+// exponent (decimal_point), when rounding upwards.
+static void GenerateCountedDigits(int count,
+                                  int* decimal_point,
+                                  Bignum* numerator,
+                                  Bignum* denominator,
+                                  Vector<char>(buffer),
+                                  int* length) {
+  ASSERT(count >= 0);
+  for (int i = 0; i < count - 1; ++i) {
+    uint16_t digit;
+    digit = numerator->DivideModuloIntBignum(*denominator);
+    ASSERT(digit <= 9);  // digit is a uint16_t and therefore always positive.
+    // digit = numerator / denominator (integer division).
+    // numerator = numerator % denominator.
+    buffer[i] = static_cast<char>(digit + '0');
+    // Prepare for next iteration.
+    numerator->Times10();
+  }
+  // Generate the last digit.
+  uint16_t digit;
+  digit = numerator->DivideModuloIntBignum(*denominator);
+  if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
+    digit++;
+  }
+  buffer[count - 1] = static_cast<char>(digit + '0');
+  // Correct bad digits (in case we had a sequence of '9's). Propagate the
+  // carry until we hat a non-'9' or til we reach the first digit.
+  for (int i = count - 1; i > 0; --i) {
+    if (buffer[i] != '0' + 10)
+      break;
+    buffer[i] = '0';
+    buffer[i - 1]++;
+  }
+  if (buffer[0] == '0' + 10) {
+    // Propagate a carry past the top place.
+    buffer[0] = '1';
+    (*decimal_point)++;
+  }
+  *length = count;
+}
+
+// Generates 'requested_digits' after the decimal point. It might omit
+// trailing '0's. If the input number is too small then no digits at all are
+// generated (ex.: 2 fixed digits for 0.00001).
+//
+// Input verifies:  1 <= (numerator + delta) / denominator < 10.
+static void BignumToFixed(int requested_digits,
+                          int* decimal_point,
+                          Bignum* numerator,
+                          Bignum* denominator,
+                          Vector<char>(buffer),
+                          int* length) {
+  // Note that we have to look at more than just the requested_digits, since
+  // a number could be rounded up. Example: v=0.5 with requested_digits=0.
+  // Even though the power of v equals 0 we can't just stop here.
+  if (-(*decimal_point) > requested_digits) {
+    // The number is definitively too small.
+    // Ex: 0.001 with requested_digits == 1.
+    // Set decimal-point to -requested_digits. This is what Gay does.
+    // Note that it should not have any effect anyways since the string is
+    // empty.
+    *decimal_point = -requested_digits;
+    *length = 0;
+    return;
+  } else if (-(*decimal_point) == requested_digits) {
+    // We only need to verify if the number rounds down or up.
+    // Ex: 0.04 and 0.06 with requested_digits == 1.
+    ASSERT(*decimal_point == -requested_digits);
+    // Initially the fraction lies in range (1, 10]. Multiply the denominator
+    // by 10 so that we can compare more easily.
+    denominator->Times10();
+    if (Bignum::PlusCompare(*numerator, *numerator, *denominator) >= 0) {
+      // If the fraction is >= 0.5 then we have to include the rounded
+      // digit.
+      buffer[0] = '1';
+      *length = 1;
+      (*decimal_point)++;
+    } else {
+      // Note that we caught most of similar cases earlier.
+      *length = 0;
     }
-
-
-    // See comments for InitialScaledStartValues
-    static void InitialScaledStartValuesNegativeExponentPositivePower(
-                                                                      double v, int estimated_power, bool need_boundary_deltas,
-                                                                      Bignum* numerator, Bignum* denominator,
-                                                                      Bignum* delta_minus, Bignum* delta_plus) {
-        uint64_t significand = Double(v).Significand();
-        int exponent = Double(v).Exponent();
-        // v = f * 2^e with e < 0, and with estimated_power >= 0.
-        // This means that e is close to 0 (have a look at how estimated_power is
-        // computed).
-
-        // numerator = significand
-        //  since v = significand * 2^exponent this is equivalent to
-        //  numerator = v * / 2^-exponent
-        numerator->AssignUInt64(significand);
-        // denominator = 10^estimated_power * 2^-exponent (with exponent < 0)
-        denominator->AssignPowerUInt16(10, estimated_power);
-        denominator->ShiftLeft(-exponent);
-
-        if (need_boundary_deltas) {
-            // Introduce a common denominator so that the deltas to the boundaries are
-            // integers.
-            denominator->ShiftLeft(1);
-            numerator->ShiftLeft(1);
-            // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
-            // denominator (of 2) delta_plus equals 2^e.
-            // Given that the denominator already includes v's exponent the distance
-            // to the boundaries is simply 1.
-            delta_plus->AssignUInt16(1);
-            // Same for delta_minus (with adjustments below if f == 2^p-1).
-            delta_minus->AssignUInt16(1);
-
-            // If the significand (without the hidden bit) is 0, then the lower
-            // boundary is closer than just one ulp (unit in the last place).
-            // There is only one exception: if the next lower number is a denormal
-            // then the distance is 1 ulp. Since the exponent is close to zero
-            // (otherwise estimated_power would have been negative) this cannot happen
-            // here either.
-            uint64_t v_bits = Double(v).AsUint64();
-            if ((v_bits & Double::kSignificandMask) == 0) {
-                // The lower boundary is closer at half the distance of "normal" numbers.
-                // Increase the denominator and adapt all but the delta_minus.
-                denominator->ShiftLeft(1);  // *2
-                numerator->ShiftLeft(1);    // *2
-                delta_plus->ShiftLeft(1);   // *2
-            }
-        }
+    return;
+  } else {
+    // The requested digits correspond to the digits after the point.
+    // The variable 'needed_digits' includes the digits before the point.
+    int needed_digits = (*decimal_point) + requested_digits;
+    GenerateCountedDigits(needed_digits, decimal_point, numerator, denominator,
+                          buffer, length);
+  }
+}
+
+// Returns an estimation of k such that 10^(k-1) <= v < 10^k where
+// v = f * 2^exponent and 2^52 <= f < 2^53.
+// v is hence a normalized double with the given exponent. The output is an
+// approximation for the exponent of the decimal approimation .digits * 10^k.
+//
+// The result might undershoot by 1 in which case 10^k <= v < 10^k+1.
+// Note: this property holds for v's upper boundary m+ too.
+//    10^k <= m+ < 10^k+1.
+//   (see explanation below).
+//
+// Examples:
+//  EstimatePower(0)   => 16
+//  EstimatePower(-52) => 0
+//
+// Note: e >= 0 => EstimatedPower(e) > 0. No similar claim can be made for e<0.
+static int EstimatePower(int exponent) {
+  // This function estimates log10 of v where v = f*2^e (with e == exponent).
+  // Note that 10^floor(log10(v)) <= v, but v <= 10^ceil(log10(v)).
+  // Note that f is bounded by its container size. Let p = 53 (the double's
+  // significand size). Then 2^(p-1) <= f < 2^p.
+  //
+  // Given that log10(v) == log2(v)/log2(10) and e+(len(f)-1) is quite close
+  // to log2(v) the function is simplified to (e+(len(f)-1)/log2(10)).
+  // The computed number undershoots by less than 0.631 (when we compute log3
+  // and not log10).
+  //
+  // Optimization: since we only need an approximated result this computation
+  // can be performed on 64 bit integers. On x86/x64 architecture the speedup is
+  // not really measurable, though.
+  //
+  // Since we want to avoid overshooting we decrement by 1e10 so that
+  // floating-point imprecisions don't affect us.
+  //
+  // Explanation for v's boundary m+: the computation takes advantage of
+  // the fact that 2^(p-1) <= f < 2^p. Boundaries still satisfy this requirement
+  // (even for denormals where the delta can be much more important).
+
+  const double k1Log10 = 0.30102999566398114;  // 1/lg(10)
+
+  // For doubles len(f) == 53 (don't forget the hidden bit).
+  const int kSignificandSize = 53;
+  double estimate = ceil((exponent + kSignificandSize - 1) * k1Log10 - 1e-10);
+  return static_cast<int>(estimate);
+}
+
+// See comments for InitialScaledStartValues.
+static void InitialScaledStartValuesPositiveExponent(double v,
+                                                     int estimated_power,
+                                                     bool need_boundary_deltas,
+                                                     Bignum* numerator,
+                                                     Bignum* denominator,
+                                                     Bignum* delta_minus,
+                                                     Bignum* delta_plus) {
+  // A positive exponent implies a positive power.
+  ASSERT(estimated_power >= 0);
+  // Since the estimated_power is positive we simply multiply the denominator
+  // by 10^estimated_power.
+
+  // numerator = v.
+  numerator->AssignUInt64(Double(v).Significand());
+  numerator->ShiftLeft(Double(v).Exponent());
+  // denominator = 10^estimated_power.
+  denominator->AssignPowerUInt16(10, estimated_power);
+
+  if (need_boundary_deltas) {
+    // Introduce a common denominator so that the deltas to the boundaries are
+    // integers.
+    denominator->ShiftLeft(1);
+    numerator->ShiftLeft(1);
+    // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
+    // denominator (of 2) delta_plus equals 2^e.
+    delta_plus->AssignUInt16(1);
+    delta_plus->ShiftLeft(Double(v).Exponent());
+    // Same for delta_minus (with adjustments below if f == 2^p-1).
+    delta_minus->AssignUInt16(1);
+    delta_minus->ShiftLeft(Double(v).Exponent());
+
+    // If the significand (without the hidden bit) is 0, then the lower
+    // boundary is closer than just half a ulp (unit in the last place).
+    // There is only one exception: if the next lower number is a denormal then
+    // the distance is 1 ulp. This cannot be the case for exponent >= 0 (but we
+    // have to test it in the other function where exponent < 0).
+    uint64_t v_bits = Double(v).AsUint64();
+    if ((v_bits & Double::kSignificandMask) == 0) {
+      // The lower boundary is closer at half the distance of "normal" numbers.
+      // Increase the common denominator and adapt all but the delta_minus.
+      denominator->ShiftLeft(1);  // *2
+      numerator->ShiftLeft(1);    // *2
+      delta_plus->ShiftLeft(1);   // *2
     }
-
-
-    // See comments for InitialScaledStartValues
-    static void InitialScaledStartValuesNegativeExponentNegativePower(
-                                                                      double v, int estimated_power, bool need_boundary_deltas,
-                                                                      Bignum* numerator, Bignum* denominator,
-                                                                      Bignum* delta_minus, Bignum* delta_plus) {
-        const uint64_t kMinimalNormalizedExponent =
-        UINT64_2PART_C(0x00100000, 00000000);
-        uint64_t significand = Double(v).Significand();
-        int exponent = Double(v).Exponent();
-        // Instead of multiplying the denominator with 10^estimated_power we
-        // multiply all values (numerator and deltas) by 10^-estimated_power.
-
-        // Use numerator as temporary container for power_ten.
-        Bignum* power_ten = numerator;
-        power_ten->AssignPowerUInt16(10, -estimated_power);
-
-        if (need_boundary_deltas) {
-            // Since power_ten == numerator we must make a copy of 10^estimated_power
-            // before we complete the computation of the numerator.
-            // delta_plus = delta_minus = 10^estimated_power
-            delta_plus->AssignBignum(*power_ten);
-            delta_minus->AssignBignum(*power_ten);
-        }
-
-        // numerator = significand * 2 * 10^-estimated_power
-        //  since v = significand * 2^exponent this is equivalent to
-        // numerator = v * 10^-estimated_power * 2 * 2^-exponent.
-        // Remember: numerator has been abused as power_ten. So no need to assign it
-        //  to itself.
-        ASSERT(numerator == power_ten);
-        numerator->MultiplyByUInt64(significand);
-
-        // denominator = 2 * 2^-exponent with exponent < 0.
-        denominator->AssignUInt16(1);
-        denominator->ShiftLeft(-exponent);
-
-        if (need_boundary_deltas) {
-            // Introduce a common denominator so that the deltas to the boundaries are
-            // integers.
-            numerator->ShiftLeft(1);
-            denominator->ShiftLeft(1);
-            // With this shift the boundaries have their correct value, since
-            // delta_plus = 10^-estimated_power, and
-            // delta_minus = 10^-estimated_power.
-            // These assignments have been done earlier.
-
-            // The special case where the lower boundary is twice as close.
-            // This time we have to look out for the exception too.
-            uint64_t v_bits = Double(v).AsUint64();
-            if ((v_bits & Double::kSignificandMask) == 0 &&
-                // The only exception where a significand == 0 has its boundaries at
-                // "normal" distances:
-                (v_bits & Double::kExponentMask) != kMinimalNormalizedExponent) {
-                numerator->ShiftLeft(1);    // *2
-                denominator->ShiftLeft(1);  // *2
-                delta_plus->ShiftLeft(1);   // *2
-            }
-        }
+  }
+}
+
+// See comments for InitialScaledStartValues
+static void InitialScaledStartValuesNegativeExponentPositivePower(
+    double v,
+    int estimated_power,
+    bool need_boundary_deltas,
+    Bignum* numerator,
+    Bignum* denominator,
+    Bignum* delta_minus,
+    Bignum* delta_plus) {
+  uint64_t significand = Double(v).Significand();
+  int exponent = Double(v).Exponent();
+  // v = f * 2^e with e < 0, and with estimated_power >= 0.
+  // This means that e is close to 0 (have a look at how estimated_power is
+  // computed).
+
+  // numerator = significand
+  //  since v = significand * 2^exponent this is equivalent to
+  //  numerator = v * / 2^-exponent
+  numerator->AssignUInt64(significand);
+  // denominator = 10^estimated_power * 2^-exponent (with exponent < 0)
+  denominator->AssignPowerUInt16(10, estimated_power);
+  denominator->ShiftLeft(-exponent);
+
+  if (need_boundary_deltas) {
+    // Introduce a common denominator so that the deltas to the boundaries are
+    // integers.
+    denominator->ShiftLeft(1);
+    numerator->ShiftLeft(1);
+    // Let v = f * 2^e, then m+ - v = 1/2 * 2^e; With the common
+    // denominator (of 2) delta_plus equals 2^e.
+    // Given that the denominator already includes v's exponent the distance
+    // to the boundaries is simply 1.
+    delta_plus->AssignUInt16(1);
+    // Same for delta_minus (with adjustments below if f == 2^p-1).
+    delta_minus->AssignUInt16(1);
+
+    // If the significand (without the hidden bit) is 0, then the lower
+    // boundary is closer than just one ulp (unit in the last place).
+    // There is only one exception: if the next lower number is a denormal
+    // then the distance is 1 ulp. Since the exponent is close to zero
+    // (otherwise estimated_power would have been negative) this cannot happen
+    // here either.
+    uint64_t v_bits = Double(v).AsUint64();
+    if ((v_bits & Double::kSignificandMask) == 0) {
+      // The lower boundary is closer at half the distance of "normal" numbers.
+      // Increase the denominator and adapt all but the delta_minus.
+      denominator->ShiftLeft(1);  // *2
+      numerator->ShiftLeft(1);    // *2
+      delta_plus->ShiftLeft(1);   // *2
     }
-
-
-    // Let v = significand * 2^exponent.
-    // Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
-    // and denominator. The functions GenerateShortestDigits and
-    // GenerateCountedDigits will then convert this ratio to its decimal
-    // representation d, with the required accuracy.
-    // Then d * 10^estimated_power is the representation of v.
-    // (Note: the fraction and the estimated_power might get adjusted before
-    // generating the decimal representation.)
-    //
-    // The initial start values consist of:
-    //  - a scaled numerator: s.t. numerator/denominator == v / 10^estimated_power.
-    //  - a scaled (common) denominator.
-    //  optionally (used by GenerateShortestDigits to decide if it has the shortest
-    //  decimal converting back to v):
-    //  - v - m-: the distance to the lower boundary.
-    //  - m+ - v: the distance to the upper boundary.
-    //
-    // v, m+, m-, and therefore v - m- and m+ - v all share the same denominator.
-    //
-    // Let ep == estimated_power, then the returned values will satisfy:
-    //  v / 10^ep = numerator / denominator.
-    //  v's boundarys m- and m+:
-    //    m- / 10^ep == v / 10^ep - delta_minus / denominator
-    //    m+ / 10^ep == v / 10^ep + delta_plus / denominator
-    //  Or in other words:
-    //    m- == v - delta_minus * 10^ep / denominator;
-    //    m+ == v + delta_plus * 10^ep / denominator;
-    //
-    // Since 10^(k-1) <= v < 10^k    (with k == estimated_power)
-    //  or       10^k <= v < 10^(k+1)
-    //  we then have 0.1 <= numerator/denominator < 1
-    //           or    1 <= numerator/denominator < 10
-    //
-    // It is then easy to kickstart the digit-generation routine.
-    //
-    // The boundary-deltas are only filled if need_boundary_deltas is set.
-    static void InitialScaledStartValues(double v,
-                                         int estimated_power,
-                                         bool need_boundary_deltas,
-                                         Bignum* numerator,
-                                         Bignum* denominator,
-                                         Bignum* delta_minus,
-                                         Bignum* delta_plus) {
-        if (Double(v).Exponent() >= 0) {
-            InitialScaledStartValuesPositiveExponent(
-                                                     v, estimated_power, need_boundary_deltas,
-                                                     numerator, denominator, delta_minus, delta_plus);
-        } else if (estimated_power >= 0) {
-            InitialScaledStartValuesNegativeExponentPositivePower(
-                                                                  v, estimated_power, need_boundary_deltas,
-                                                                  numerator, denominator, delta_minus, delta_plus);
-        } else {
-            InitialScaledStartValuesNegativeExponentNegativePower(
-                                                                  v, estimated_power, need_boundary_deltas,
-                                                                  numerator, denominator, delta_minus, delta_plus);
-        }
+  }
+}
+
+// See comments for InitialScaledStartValues
+static void InitialScaledStartValuesNegativeExponentNegativePower(
+    double v,
+    int estimated_power,
+    bool need_boundary_deltas,
+    Bignum* numerator,
+    Bignum* denominator,
+    Bignum* delta_minus,
+    Bignum* delta_plus) {
+  const uint64_t kMinimalNormalizedExponent =
+      UINT64_2PART_C(0x00100000, 00000000);
+  uint64_t significand = Double(v).Significand();
+  int exponent = Double(v).Exponent();
+  // Instead of multiplying the denominator with 10^estimated_power we
+  // multiply all values (numerator and deltas) by 10^-estimated_power.
+
+  // Use numerator as temporary container for power_ten.
+  Bignum* power_ten = numerator;
+  power_ten->AssignPowerUInt16(10, -estimated_power);
+
+  if (need_boundary_deltas) {
+    // Since power_ten == numerator we must make a copy of 10^estimated_power
+    // before we complete the computation of the numerator.
+    // delta_plus = delta_minus = 10^estimated_power
+    delta_plus->AssignBignum(*power_ten);
+    delta_minus->AssignBignum(*power_ten);
+  }
+
+  // numerator = significand * 2 * 10^-estimated_power
+  //  since v = significand * 2^exponent this is equivalent to
+  // numerator = v * 10^-estimated_power * 2 * 2^-exponent.
+  // Remember: numerator has been abused as power_ten. So no need to assign it
+  //  to itself.
+  ASSERT(numerator == power_ten);
+  numerator->MultiplyByUInt64(significand);
+
+  // denominator = 2 * 2^-exponent with exponent < 0.
+  denominator->AssignUInt16(1);
+  denominator->ShiftLeft(-exponent);
+
+  if (need_boundary_deltas) {
+    // Introduce a common denominator so that the deltas to the boundaries are
+    // integers.
+    numerator->ShiftLeft(1);
+    denominator->ShiftLeft(1);
+    // With this shift the boundaries have their correct value, since
+    // delta_plus = 10^-estimated_power, and
+    // delta_minus = 10^-estimated_power.
+    // These assignments have been done earlier.
+
+    // The special case where the lower boundary is twice as close.
+    // This time we have to look out for the exception too.
+    uint64_t v_bits = Double(v).AsUint64();
+    if ((v_bits & Double::kSignificandMask) == 0 &&
+        // The only exception where a significand == 0 has its boundaries at
+        // "normal" distances:
+        (v_bits & Double::kExponentMask) != kMinimalNormalizedExponent) {
+      numerator->ShiftLeft(1);    // *2
+      denominator->ShiftLeft(1);  // *2
+      delta_plus->ShiftLeft(1);   // *2
     }
-
-
-    // This routine multiplies numerator/denominator so that its values lies in the
-    // range 1-10. That is after a call to this function we have:
-    //    1 <= (numerator + delta_plus) /denominator < 10.
-    // Let numerator the input before modification and numerator' the argument
-    // after modification, then the output-parameter decimal_point is such that
-    //  numerator / denominator * 10^estimated_power ==
-    //    numerator' / denominator' * 10^(decimal_point - 1)
-    // In some cases estimated_power was too low, and this is already the case. We
-    // then simply adjust the power so that 10^(k-1) <= v < 10^k (with k ==
-    // estimated_power) but do not touch the numerator or denominator.
-    // Otherwise the routine multiplies the numerator and the deltas by 10.
-    static void FixupMultiply10(int estimated_power, bool is_even,
-                                int* decimal_point,
-                                Bignum* numerator, Bignum* denominator,
-                                Bignum* delta_minus, Bignum* delta_plus) {
-        bool in_range;
-        if (is_even) {
-            // For IEEE doubles half-way cases (in decimal system numbers ending with 5)
-            // are rounded to the closest floating-point number with even significand.
-            in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
-        } else {
-            in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
-        }
-        if (in_range) {
-            // Since numerator + delta_plus >= denominator we already have
-            // 1 <= numerator/denominator < 10. Simply update the estimated_power.
-            *decimal_point = estimated_power + 1;
-        } else {
-            *decimal_point = estimated_power;
-            numerator->Times10();
-            if (Bignum::Equal(*delta_minus, *delta_plus)) {
-                delta_minus->Times10();
-                delta_plus->AssignBignum(*delta_minus);
-            } else {
-                delta_minus->Times10();
-                delta_plus->Times10();
-            }
-        }
+  }
+}
+
+// Let v = significand * 2^exponent.
+// Computes v / 10^estimated_power exactly, as a ratio of two bignums, numerator
+// and denominator. The functions GenerateShortestDigits and
+// GenerateCountedDigits will then convert this ratio to its decimal
+// representation d, with the required accuracy.
+// Then d * 10^estimated_power is the representation of v.
+// (Note: the fraction and the estimated_power might get adjusted before
+// generating the decimal representation.)
+//
+// The initial start values consist of:
+//  - a scaled numerator: s.t. numerator/denominator == v / 10^estimated_power.
+//  - a scaled (common) denominator.
+//  optionally (used by GenerateShortestDigits to decide if it has the shortest
+//  decimal converting back to v):
+//  - v - m-: the distance to the lower boundary.
+//  - m+ - v: the distance to the upper boundary.
+//
+// v, m+, m-, and therefore v - m- and m+ - v all share the same denominator.
+//
+// Let ep == estimated_power, then the returned values will satisfy:
+//  v / 10^ep = numerator / denominator.
+//  v's boundarys m- and m+:
+//    m- / 10^ep == v / 10^ep - delta_minus / denominator
+//    m+ / 10^ep == v / 10^ep + delta_plus / denominator
+//  Or in other words:
+//    m- == v - delta_minus * 10^ep / denominator;
+//    m+ == v + delta_plus * 10^ep / denominator;
+//
+// Since 10^(k-1) <= v < 10^k    (with k == estimated_power)
+//  or       10^k <= v < 10^(k+1)
+//  we then have 0.1 <= numerator/denominator < 1
+//           or    1 <= numerator/denominator < 10
+//
+// It is then easy to kickstart the digit-generation routine.
+//
+// The boundary-deltas are only filled if need_boundary_deltas is set.
+static void InitialScaledStartValues(double v,
+                                     int estimated_power,
+                                     bool need_boundary_deltas,
+                                     Bignum* numerator,
+                                     Bignum* denominator,
+                                     Bignum* delta_minus,
+                                     Bignum* delta_plus) {
+  if (Double(v).Exponent() >= 0) {
+    InitialScaledStartValuesPositiveExponent(
+        v, estimated_power, need_boundary_deltas, numerator, denominator,
+        delta_minus, delta_plus);
+  } else if (estimated_power >= 0) {
+    InitialScaledStartValuesNegativeExponentPositivePower(
+        v, estimated_power, need_boundary_deltas, numerator, denominator,
+        delta_minus, delta_plus);
+  } else {
+    InitialScaledStartValuesNegativeExponentNegativePower(
+        v, estimated_power, need_boundary_deltas, numerator, denominator,
+        delta_minus, delta_plus);
+  }
+}
+
+// This routine multiplies numerator/denominator so that its values lies in the
+// range 1-10. That is after a call to this function we have:
+//    1 <= (numerator + delta_plus) /denominator < 10.
+// Let numerator the input before modification and numerator' the argument
+// after modification, then the output-parameter decimal_point is such that
+//  numerator / denominator * 10^estimated_power ==
+//    numerator' / denominator' * 10^(decimal_point - 1)
+// In some cases estimated_power was too low, and this is already the case. We
+// then simply adjust the power so that 10^(k-1) <= v < 10^k (with k ==
+// estimated_power) but do not touch the numerator or denominator.
+// Otherwise the routine multiplies the numerator and the deltas by 10.
+static void FixupMultiply10(int estimated_power,
+                            bool is_even,
+                            int* decimal_point,
+                            Bignum* numerator,
+                            Bignum* denominator,
+                            Bignum* delta_minus,
+                            Bignum* delta_plus) {
+  bool in_range;
+  if (is_even) {
+    // For IEEE doubles half-way cases (in decimal system numbers ending with 5)
+    // are rounded to the closest floating-point number with even significand.
+    in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) >= 0;
+  } else {
+    in_range = Bignum::PlusCompare(*numerator, *delta_plus, *denominator) > 0;
+  }
+  if (in_range) {
+    // Since numerator + delta_plus >= denominator we already have
+    // 1 <= numerator/denominator < 10. Simply update the estimated_power.
+    *decimal_point = estimated_power + 1;
+  } else {
+    *decimal_point = estimated_power;
+    numerator->Times10();
+    if (Bignum::Equal(*delta_minus, *delta_plus)) {
+      delta_minus->Times10();
+      delta_plus->AssignBignum(*delta_minus);
+    } else {
+      delta_minus->Times10();
+      delta_plus->Times10();
     }
+  }
+}
 
 }  // namespace double_conversion
 
-} // namespace WTF
+}  // namespace WTF