Added precision mode to fast-dtoa.

Review URL: http://codereview.chromium.org/2000004

git-svn-id: http://v8.googlecode.com/svn/branches/bleeding_edge@5491 ce2b1a6d-e550-0410-aec6-3dcde31c8c00

src/conversions.cc

@@ -956,8 +956,9 @@ static char* CreateExponentialRepresentation(char* decimal_rep,
 
 
 char* DoubleToExponentialCString(double value, int f) {
+  const int kMaxDigitsAfterPoint = 20;
   // f might be -1 to signal that f was undefined in JavaScript.
-  ASSERT(f >= -1 && f <= 20);
+  ASSERT(f >= -1 && f <= kMaxDigitsAfterPoint);
 
   bool negative = false;
   if (value < 0) {
@@ -969,29 +970,60 @@ char* DoubleToExponentialCString(double value, int f) {
   int decimal_point;
   int sign;
   char* decimal_rep = NULL;
+  bool used_gay_dtoa = false;
+  // f corresponds to the digits after the point. There is always one digit
+  // before the point. The number of requested_digits equals hence f + 1.
+  // And we have to add one character for the null-terminator.
+  const int kV8DtoaBufferCapacity = kMaxDigitsAfterPoint + 1 + 1;
+  // Make sure that the buffer is big enough, even if we fall back to the
+  // shortest representation (which happens when f equals -1).
+  ASSERT(kBase10MaximalLength <= kMaxDigitsAfterPoint + 1);
+  char v8_dtoa_buffer[kV8DtoaBufferCapacity];
+  int decimal_rep_length;
+
   if (f == -1) {
+    if (DoubleToAscii(value, DTOA_SHORTEST, 0,
+                      Vector<char>(v8_dtoa_buffer, kV8DtoaBufferCapacity),
+                      &sign, &decimal_rep_length, &decimal_point)) {
+      f = decimal_rep_length - 1;
+      decimal_rep = v8_dtoa_buffer;
+    } else {
       decimal_rep = dtoa(value, 0, 0, &decimal_point, &sign, NULL);
-    f = StrLength(decimal_rep) - 1;
+      decimal_rep_length = StrLength(decimal_rep);
+      f = decimal_rep_length - 1;
+      used_gay_dtoa = true;
+    }
+  } else {
+    if (DoubleToAscii(value, DTOA_PRECISION, f + 1,
+                      Vector<char>(v8_dtoa_buffer, kV8DtoaBufferCapacity),
+                      &sign, &decimal_rep_length, &decimal_point)) {
+      decimal_rep = v8_dtoa_buffer;
     } else {
       decimal_rep = dtoa(value, 2, f + 1, &decimal_point, &sign, NULL);
+      decimal_rep_length = StrLength(decimal_rep);
+      used_gay_dtoa = true;
+    }
   }
-  int decimal_rep_length = StrLength(decimal_rep);
   ASSERT(decimal_rep_length > 0);
   ASSERT(decimal_rep_length <= f + 1);
-  USE(decimal_rep_length);
 
   int exponent = decimal_point - 1;
   char* result =
       CreateExponentialRepresentation(decimal_rep, exponent, negative, f+1);
 
+  if (used_gay_dtoa) {
     freedtoa(decimal_rep);
+  }
 
   return result;
 }
 
 
 char* DoubleToPrecisionCString(double value, int p) {
-  ASSERT(p >= 1 && p <= 21);
+  const int kMinimalDigits = 1;
+  const int kMaximalDigits = 21;
+  ASSERT(p >= kMinimalDigits && p <= kMaximalDigits);
+  USE(kMinimalDigits);
 
   bool negative = false;
   if (value < 0) {
@@ -1002,8 +1034,22 @@ char* DoubleToPrecisionCString(double value, int p) {
   // Find a sufficiently precise decimal representation of n.
   int decimal_point;
   int sign;
-  char* decimal_rep = dtoa(value, 2, p, &decimal_point, &sign, NULL);
+  char* decimal_rep = NULL;
-  int decimal_rep_length = StrLength(decimal_rep);
+  bool used_gay_dtoa = false;
+  // Add one for the terminating null character.
+  const int kV8DtoaBufferCapacity = kMaximalDigits + 1;
+  char v8_dtoa_buffer[kV8DtoaBufferCapacity];
+  int decimal_rep_length;
+
+  if (DoubleToAscii(value, DTOA_PRECISION, p,
+                    Vector<char>(v8_dtoa_buffer, kV8DtoaBufferCapacity),
+                    &sign, &decimal_rep_length, &decimal_point)) {
+    decimal_rep = v8_dtoa_buffer;
+  } else {
+    decimal_rep = dtoa(value, 2, p, &decimal_point, &sign, NULL);
+    decimal_rep_length = StrLength(decimal_rep);
+    used_gay_dtoa = true;
+  }
   ASSERT(decimal_rep_length <= p);
 
   int exponent = decimal_point - 1;
@@ -1047,7 +1093,9 @@ char* DoubleToPrecisionCString(double value, int p) {
     result = builder.Finalize();
   }
 
+  if (used_gay_dtoa) {
     freedtoa(decimal_rep);
+  }
   return result;
 }
 

src/dtoa.cc

@@ -65,11 +65,12 @@ bool DoubleToAscii(double v, DtoaMode mode, int requested_digits,
 
   switch (mode) {
     case DTOA_SHORTEST:
-      return FastDtoa(v, buffer, length, point);
+      return FastDtoa(v, FAST_DTOA_SHORTEST, 0, buffer, length, point);
     case DTOA_FIXED:
       return FastFixedDtoa(v, requested_digits, buffer, length, point);
-    default:
+    case DTOA_PRECISION:
-      break;
+      return FastDtoa(v, FAST_DTOA_PRECISION, requested_digits,
+                      buffer, length, point);
   }
   return false;
 }

src/fast-dtoa.cc

@@ -42,8 +42,8 @@ namespace internal {
 //
 // 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 kMinimalTargetExponent = -60;
-static const int maximal_target_exponent = -32;
+static const int kMaximalTargetExponent = -32;
 
 
 // Adjusts the last digit of the generated number, and screens out generated
@@ -61,7 +61,7 @@ static const int maximal_target_exponent = -32;
 // Output: returns true if the buffer is guaranteed to contain the closest
 //    representable number to the input.
 //  Modifies the generated digits in the buffer to approach (round towards) w.
-bool RoundWeed(Vector<char> buffer,
+static bool RoundWeed(Vector<char> buffer,
                       int length,
                       uint64_t distance_too_high_w,
                       uint64_t unsafe_interval,
@@ -75,7 +75,7 @@ bool RoundWeed(Vector<char> buffer,
   // Note: w_low < w < w_high
   //
   // The real w (* unit) must lie somewhere inside the interval
-  // ]w_low; w_low[ (often written as "(w_low; w_low)")
+  // ]w_low; w_high[ (often written as "(w_low; w_high)")
 
   // Basically the buffer currently contains a number in the unsafe interval
   // ]too_low; too_high[ with too_low < w < too_high
@@ -122,10 +122,10 @@ bool RoundWeed(Vector<char> buffer,
   // 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
+  // Similarly we have to take into account the imprecision of 'w' when finding
-  // the buffer. If we have two potential representations we need to make sure
+  // the closest representation of 'w'. If we have two potential
-  // that the chosen one is closer to w_low and w_high since v can be anywhere
+  // representations, and one is closer to both w_low and w_high, then we know
-  // between them.
+  // it is closer to the actual value v.
   //
   // By generating the digits of too_high we got the largest (closest to
   // too_high) buffer that is still in the unsafe interval. In the case where
@@ -139,6 +139,9 @@ bool RoundWeed(Vector<char> buffer,
   //              (buffer{-1} < w_high) && w_high - buffer{-1} > buffer - w_high
   // Instead of using the buffer directly we use its distance to too_high.
   // Conceptually rest ~= too_high - buffer
+  // We need to do the following tests in this order to avoid over- and
+  // underflows.
+  ASSERT(rest <= unsafe_interval);
   while (rest < small_distance &&  // Negated condition 1
          unsafe_interval - rest >= ten_kappa &&  // Negated condition 2
          (rest + ten_kappa < small_distance ||  // buffer{-1} > w_high
@@ -166,6 +169,62 @@ bool RoundWeed(Vector<char> buffer,
 }
 
 
+// Rounds the buffer upwards if the result is closer to v by possibly adding
+// 1 to the buffer. If the precision of the calculation is not sufficient to
+// round correctly, return false.
+// The rounding might shift the whole buffer in which case the kappa is
+// adjusted. For example "99", kappa = 3 might become "10", kappa = 4.
+//
+// If 2*rest > ten_kappa then the buffer needs to be round up.
+// rest can have an error of +/- 1 unit. This function accounts for the
+// imprecision and returns false, if the rounding direction cannot be
+// unambiguously determined.
+//
+// Precondition: rest < ten_kappa.
+static bool RoundWeedCounted(Vector<char> buffer,
+                             int length,
+                             uint64_t rest,
+                             uint64_t ten_kappa,
+                             uint64_t unit,
+                             int* kappa) {
+  ASSERT(rest < ten_kappa);
+  // The following tests are done in a specific order to avoid overflows. They
+  // will work correctly with any uint64 values of rest < ten_kappa and unit.
+  //
+  // If the unit is too big, then we don't know which way to round. For example
+  // a unit of 50 means that the real number lies within rest +/- 50. If
+  // 10^kappa == 40 then there is no way to tell which way to round.
+  if (unit >= ten_kappa) return false;
+  // Even if unit is just half the size of 10^kappa we are already completely
+  // lost. (And after the previous test we know that the expression will not
+  // over/underflow.)
+  if (ten_kappa - unit <= unit) return false;
+  // If 2 * (rest + unit) <= 10^kappa we can safely round down.
+  if ((ten_kappa - rest > rest) && (ten_kappa - 2 * rest >= 2 * unit)) {
+    return true;
+  }
+  // If 2 * (rest - unit) >= 10^kappa, then we can safely round up.
+  if ((rest > unit) && (ten_kappa - (rest - unit) <= (rest - unit))) {
+    // Increment the last digit recursively until we find a non '9' digit.
+    buffer[length - 1]++;
+    for (int i = length - 1; i > 0; --i) {
+      if (buffer[i] != '0' + 10) break;
+      buffer[i] = '0';
+      buffer[i - 1]++;
+    }
+    // If the first digit is now '0'+ 10 we had a buffer with all '9's. With the
+    // exception of the first digit all digits are now '0'. Simply switch the
+    // first digit to '1' and adjust the kappa. Example: "99" becomes "10" and
+    // the power (the kappa) is increased.
+    if (buffer[0] == '0' + 10) {
+      buffer[0] = '1';
+      (*kappa) += 1;
+    }
+    return true;
+  }
+  return false;
+}
+
 
 static const uint32_t kTen4 = 10000;
 static const uint32_t kTen5 = 100000;
@@ -178,7 +237,7 @@ static const uint32_t kTen9 = 1000000000;
 // number. We furthermore receive the maximum number of bits 'number' has.
 // If number_bits == 0 then 0^-1 is returned
 // The number of bits must be <= 32.
-// Precondition: (1 << number_bits) <= number < (1 << (number_bits + 1)).
+// Precondition: number < (1 << (number_bits + 1)).
 static void BiggestPowerTen(uint32_t number,
                             int number_bits,
                             uint32_t* power,
@@ -281,18 +340,18 @@ static void BiggestPowerTen(uint32_t number,
 
 // 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
+// exponent. Its exponent is bounded by kMinimalTargetExponent and
-// maximal_target_exponent.
+// kMaximalTargetExponent.
 //       Hence -60 <= w.e() <= -32.
 //
 // Returns false if it fails, in which case the generated digits in the buffer
 // should not be used.
 // Preconditions:
 //  * low, w and high are correct up to 1 ulp (unit in the last place). That
-//    is, their error must be less that a unit of their last digits.
+//    is, their error must be less than a unit of their last digits.
 //  * low.e() == w.e() == high.e()
 //  * low < w < high, and taking into account their error: low~ <= high~
-//  * minimal_target_exponent <= w.e() <= maximal_target_exponent
+//  * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
 // Postconditions: returns false if procedure fails.
 //   otherwise:
 //     * buffer is not null-terminated, but len contains the number of digits.
@@ -321,7 +380,7 @@ static void BiggestPowerTen(uint32_t number,
 // represent 'w' we can stop. Everything inside the interval low - high
 // represents w. However we have to pay attention to low, high and w's
 // imprecision.
-bool DigitGen(DiyFp low,
+static bool DigitGen(DiyFp low,
                      DiyFp w,
                      DiyFp high,
                      Vector<char> buffer,
@@ -329,7 +388,7 @@ bool DigitGen(DiyFp low,
                      int* kappa) {
   ASSERT(low.e() == w.e() && w.e() == high.e());
   ASSERT(low.f() + 1 <= high.f() - 1);
-  ASSERT(minimal_target_exponent <= w.e() && w.e() <= maximal_target_exponent);
+  ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
   // low, w and high are imprecise, but by less than one ulp (unit in the last
   // place).
   // If we remove (resp. add) 1 ulp from low (resp. high) we are certain that
@@ -359,23 +418,23 @@ bool DigitGen(DiyFp low,
   uint32_t integrals = static_cast<uint32_t>(too_high.f() >> -one.e());
   // Modulo by one is an and.
   uint64_t fractionals = too_high.f() & (one.f() - 1);
-  uint32_t divider;
+  uint32_t divisor;
-  int divider_exponent;
+  int divisor_exponent;
   BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
-                  &divider, &divider_exponent);
+                  &divisor, &divisor_exponent);
-  *kappa = divider_exponent + 1;
+  *kappa = divisor_exponent + 1;
   *length = 0;
   // Loop invariant: buffer = too_high / 10^kappa  (integer division)
   // The invariant holds for the first iteration: kappa has been initialized
-  // with the divider exponent + 1. And the divider is the biggest power of ten
+  // with the divisor exponent + 1. And the divisor is the biggest power of ten
   // that is smaller than integrals.
   while (*kappa > 0) {
-    int digit = integrals / divider;
+    int digit = integrals / divisor;
     buffer[*length] = '0' + digit;
     (*length)++;
-    integrals %= divider;
+    integrals %= divisor;
     (*kappa)--;
-    // Note that kappa now equals the exponent of the divider and that the
+    // Note that kappa now equals the exponent of the divisor and that the
     // invariant thus holds again.
     uint64_t rest =
         (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
@@ -386,32 +445,24 @@ bool DigitGen(DiyFp low,
       // that lies within the unsafe interval.
       return RoundWeed(buffer, *length, DiyFp::Minus(too_high, w).f(),
                        unsafe_interval.f(), rest,
-                       static_cast<uint64_t>(divider) << -one.e(), unit);
+                       static_cast<uint64_t>(divisor) << -one.e(), unit);
     }
-    divider /= 10;
+    divisor /= 10;
   }
 
   // The integrals have been generated. We are at the point of the decimal
   // separator. In the following loop we simply multiply the remaining digits by
   // 10 and divide by one. We just need to pay attention to multiply associated
   // data (like the interval or 'unit'), too.
-  // Instead of multiplying by 10 we multiply by 5 (cheaper operation) and
+  // Note that the multiplication by 10 does not overflow, because w.e >= -60
-  // increase its (imaginary) exponent. At the same time we decrease the
+  // and thus one.e >= -60.
-  // divider's (one's) exponent and shift its significand.
+  ASSERT(one.e() >= -60);
-  // Basically, if fractionals was a DiyFp (with fractionals.e == one.e):
+  ASSERT(fractionals < one.f());
-  //      fractionals.f *= 10;
+  ASSERT(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
-  //      fractionals.f >>= 1; fractionals.e++; // value remains unchanged.
-  //      one.f >>= 1; one.e++;                 // value remains unchanged.
-  //      and we have again fractionals.e == one.e which allows us to divide
-  //           fractionals.f() by one.f()
-  // We simply combine the *= 10 and the >>= 1.
   while (true) {
-    fractionals *= 5;
+    fractionals *= 10;
-    unit *= 5;
+    unit *= 10;
-    unsafe_interval.set_f(unsafe_interval.f() * 5);
+    unsafe_interval.set_f(unsafe_interval.f() * 10);
-    unsafe_interval.set_e(unsafe_interval.e() + 1);  // Will be optimized out.
-    one.set_f(one.f() >> 1);
-    one.set_e(one.e() + 1);
     // Integer division by one.
     int digit = static_cast<int>(fractionals >> -one.e());
     buffer[*length] = '0' + digit;
@@ -426,6 +477,113 @@ bool DigitGen(DiyFp low,
 }
 
 
+
+// Generates (at most) requested_digits of input number w.
+// w is a floating-point number (DiyFp), consisting of a significand and an
+// exponent. Its exponent is bounded by kMinimalTargetExponent and
+// kMaximalTargetExponent.
+//       Hence -60 <= w.e() <= -32.
+//
+// Returns false if it fails, in which case the generated digits in the buffer
+// should not be used.
+// Preconditions:
+//  * w is correct up to 1 ulp (unit in the last place). That
+//    is, its error must be strictly less than a unit of its last digit.
+//  * kMinimalTargetExponent <= w.e() <= kMaximalTargetExponent
+//
+// Postconditions: returns false if procedure fails.
+//   otherwise:
+//     * buffer is not null-terminated, but length contains the number of
+//       digits.
+//     * the representation in buffer is the most precise representation of
+//       requested_digits digits.
+//     * buffer contains at most requested_digits digits of w. If there are less
+//       than requested_digits digits then some trailing '0's have been removed.
+//     * kappa is such that
+//            w = buffer * 10^kappa + eps with |eps| < 10^kappa / 2.
+//
+// Remark: This procedure takes into account the imprecision of its input
+//   numbers. If the precision is not enough to guarantee all the postconditions
+//   then false is returned. This usually happens rarely, but the failure-rate
+//   increases with higher requested_digits.
+static bool DigitGenCounted(DiyFp w,
+                            int requested_digits,
+                            Vector<char> buffer,
+                            int* length,
+                            int* kappa) {
+  ASSERT(kMinimalTargetExponent <= w.e() && w.e() <= kMaximalTargetExponent);
+  ASSERT(kMinimalTargetExponent >= -60);
+  ASSERT(kMaximalTargetExponent <= -32);
+  // w is assumed to have an error less than 1 unit. Whenever w is scaled we
+  // also scale its error.
+  uint64_t w_error = 1;
+  // We cut the input number into two parts: the integral digits and the
+  // fractional digits. We don't emit any decimal separator, but adapt kappa
+  // instead. Example: instead of writing "1.2" we put "12" into the buffer and
+  // increase kappa by 1.
+  DiyFp one = DiyFp(static_cast<uint64_t>(1) << -w.e(), w.e());
+  // Division by one is a shift.
+  uint32_t integrals = static_cast<uint32_t>(w.f() >> -one.e());
+  // Modulo by one is an and.
+  uint64_t fractionals = w.f() & (one.f() - 1);
+  uint32_t divisor;
+  int divisor_exponent;
+  BiggestPowerTen(integrals, DiyFp::kSignificandSize - (-one.e()),
+                  &divisor, &divisor_exponent);
+  *kappa = divisor_exponent + 1;
+  *length = 0;
+
+  // Loop invariant: buffer = w / 10^kappa  (integer division)
+  // The invariant holds for the first iteration: kappa has been initialized
+  // with the divisor exponent + 1. And the divisor is the biggest power of ten
+  // that is smaller than 'integrals'.
+  while (*kappa > 0) {
+    int digit = integrals / divisor;
+    buffer[*length] = '0' + digit;
+    (*length)++;
+    requested_digits--;
+    integrals %= divisor;
+    (*kappa)--;
+    // Note that kappa now equals the exponent of the divisor and that the
+    // invariant thus holds again.
+    if (requested_digits == 0) break;
+    divisor /= 10;
+  }
+
+  if (requested_digits == 0) {
+    uint64_t rest =
+        (static_cast<uint64_t>(integrals) << -one.e()) + fractionals;
+    return RoundWeedCounted(buffer, *length, rest,
+                            static_cast<uint64_t>(divisor) << -one.e(), w_error,
+                            kappa);
+  }
+
+  // The integrals have been generated. We are at the point of the decimal
+  // separator. In the following loop we simply multiply the remaining digits by
+  // 10 and divide by one. We just need to pay attention to multiply associated
+  // data (the 'unit'), too.
+  // Note that the multiplication by 10 does not overflow, because w.e >= -60
+  // and thus one.e >= -60.
+  ASSERT(one.e() >= -60);
+  ASSERT(fractionals < one.f());
+  ASSERT(V8_2PART_UINT64_C(0xFFFFFFFF, FFFFFFFF) / 10 >= one.f());
+  while (requested_digits > 0 && fractionals > w_error) {
+    fractionals *= 10;
+    w_error *= 10;
+    // Integer division by one.
+    int digit = static_cast<int>(fractionals >> -one.e());
+    buffer[*length] = '0' + digit;
+    (*length)++;
+    requested_digits--;
+    fractionals &= one.f() - 1;  // Modulo by one.
+    (*kappa)--;
+  }
+  if (requested_digits != 0) return false;
+  return RoundWeedCounted(buffer, *length, fractionals, one.f(), w_error,
+                          kappa);
+}
+
+
 // Provides a decimal representation of v.
 // Returns true if it succeeds, otherwise the result cannot be trusted.
 // There will be *length digits inside the buffer (not null-terminated).
@@ -437,7 +595,10 @@ bool DigitGen(DiyFp low,
 // The last digit will be closest to the actual v. That is, even if several
 // digits might correctly yield 'v' when read again, the closest will be
 // computed.
-bool grisu3(double v, Vector<char> buffer, int* length, int* decimal_exponent) {
+static bool Grisu3(double v,
+                   Vector<char> buffer,
+                   int* length,
+                   int* decimal_exponent) {
   DiyFp w = Double(v).AsNormalizedDiyFp();
   // boundary_minus and boundary_plus are the boundaries between v and its
   // closest floating-point neighbors. Any number strictly between
@@ -448,12 +609,12 @@ bool grisu3(double v, Vector<char> buffer, int* length, int* decimal_exponent) {
   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,
+  GetCachedPower(w.e() + DiyFp::kSignificandSize, kMinimalTargetExponent,
-                 maximal_target_exponent, &mk, &ten_mk);
+                 kMaximalTargetExponent, &mk, &ten_mk);
-  ASSERT(minimal_target_exponent <= w.e() + ten_mk.e() +
+  ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
-         DiyFp::kSignificandSize &&
+          DiyFp::kSignificandSize) &&
-         maximal_target_exponent >= w.e() + ten_mk.e() +
+         (kMaximalTargetExponent >= w.e() + ten_mk.e() +
-         DiyFp::kSignificandSize);
+          DiyFp::kSignificandSize));
   // Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
   // 64 bit significand and ten_mk is thus only precise up to 64 bits.
 
@@ -488,17 +649,73 @@ bool grisu3(double v, Vector<char> buffer, int* length, int* decimal_exponent) {
 }
 
 
-bool FastDtoa(double v,
+// 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* point) {
+                          int* decimal_exponent) {
+  DiyFp w = Double(v).AsNormalizedDiyFp();
+  DiyFp ten_mk;  // Cached power of ten: 10^-k
+  int mk;        // -k
+  GetCachedPower(w.e() + DiyFp::kSignificandSize, kMinimalTargetExponent,
+                 kMaximalTargetExponent, &mk, &ten_mk);
+  ASSERT((kMinimalTargetExponent <= w.e() + ten_mk.e() +
+          DiyFp::kSignificandSize) &&
+         (kMaximalTargetExponent >= w.e() + ten_mk.e() +
+          DiyFp::kSignificandSize));
+  // Note that ten_mk is only an approximation of 10^-k. A DiyFp only contains a
+  // 64 bit significand and ten_mk is thus only precise up to 64 bits.
+
+  // The DiyFp::Times procedure rounds its result, and ten_mk is approximated
+  // too. The variable scaled_w (as well as scaled_boundary_minus/plus) are now
+  // off by a small amount.
+  // In fact: scaled_w - w*10^k < 1ulp (unit in the last place) of scaled_w.
+  // In other words: let f = scaled_w.f() and e = scaled_w.e(), then
+  //           (f-1) * 2^e < w*10^k < (f+1) * 2^e
+  DiyFp scaled_w = DiyFp::Times(w, ten_mk);
+
+  // We now have (double) (scaled_w * 10^-mk).
+  // DigitGen will generate the first requested_digits digits of scaled_w and
+  // return together with a kappa such that scaled_w ~= buffer * 10^kappa. (It
+  // will not always be exactly the same since DigitGenCounted only produces a
+  // limited number of digits.)
+  int kappa;
+  bool result = DigitGenCounted(scaled_w, requested_digits,
+                                buffer, length, &kappa);
+  *decimal_exponent = -mk + kappa;
+  return result;
+}
+
+
+bool FastDtoa(double v,
+              FastDtoaMode mode,
+              int requested_digits,
+              Vector<char> buffer,
+              int* length,
+              int* decimal_point) {
   ASSERT(v > 0);
   ASSERT(!Double(v).IsSpecial());
 
+  bool result = false;
   int decimal_exponent;
-  bool result = grisu3(v, buffer, length, &decimal_exponent);
+  switch (mode) {
-  *point = *length + decimal_exponent;
+    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;
+  }
+  if (result) {
+    *decimal_point = *length + decimal_exponent;
     buffer[*length] = '\0';
+  }
   return result;
 }
 

src/fast-dtoa.h

@@ -31,27 +31,52 @@
 namespace v8 {
 namespace internal {
 
+enum FastDtoaMode {
+  // Computes the shortest representation of the given input. The returned
+  // result will be the most accurate number of this length. Longer
+  // representations might be more accurate.
+  FAST_DTOA_SHORTEST,
+  // Computes a representation where the precision (number of digits) is
+  // given as input. The precision is independent of the decimal point.
+  FAST_DTOA_PRECISION
+};
+
 // FastDtoa will produce at most kFastDtoaMaximalLength digits. This does not
 // include the terminating '\0' character.
 static const int kFastDtoaMaximalLength = 17;
 
 // Provides a decimal representation of v.
-// v must be a strictly positive finite double.
+// The result should be interpreted as buffer * 10^(point - length).
+//
+// Precondition:
+//   * v must be a strictly positive finite double.
+//
 // Returns true if it succeeds, otherwise the result can not be trusted.
 // There will be *length digits inside the buffer followed by a null terminator.
-// If the function returns true then
+// If the function returns true and mode equals
+//   - FAST_DTOA_SHORTEST, then
+//     the parameter requested_digits is ignored.
+//     The result satisfies
 //         v == (double) (buffer * 10^(point - length)).
-// The digits in the buffer are the shortest representation possible: no
+//     The digits in the buffer are the shortest representation possible. E.g.
-// 0.099999999999 instead of 0.1.
+//     if 0.099999999999 and 0.1 represent the same double then "1" is returned
+//     with point = 0.
 //     The last digit will be closest to the actual v. That is, even if several
-// digits might correctly yield 'v' when read again, the buffer will contain the
+//     digits might correctly yield 'v' when read again, the buffer will contain
-// one closest to v.
+//     the one closest to v.
-// The variable 'sign' will be '0' if the given number is positive, and '1'
+//   - FAST_DTOA_PRECISION, then
-//   otherwise.
+//     the buffer contains requested_digits digits.
+//     the difference v - (buffer * 10^(point-length)) is closest to zero for
+//     all possible representations of requested_digits digits.
+//     If there are two values that are equally close, then FastDtoa returns
+//     false.
+// For both modes the buffer must be large enough to hold the result.
 bool FastDtoa(double d,
+              FastDtoaMode mode,
+              int requested_digits,
               Vector<char> buffer,
               int* length,
-              int* point);
+              int* decimal_point);
 
 } }  // namespace v8::internal
 

test/cctest/SConscript

@@ -35,6 +35,7 @@ Import('context object_files')
 SOURCES = {
   'all': [
     'gay-fixed.cc',
+    'gay-precision.cc',
     'gay-shortest.cc',
     'test-accessors.cc',
     'test-alloc.cc',

test/cctest/gay-precision.h

@@ -0,0 +1,47 @@
+// Copyright 2006-2008 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.
+
+#ifndef GAY_PRECISION_H_
+#define GAY_PRECISION_H_
+
+namespace v8 {
+namespace internal {
+
+struct PrecomputedPrecision {
+  double v;
+  int number_digits;
+  const char* representation;
+  int decimal_point;
+};
+
+// Returns precomputed values of dtoa. The strings have been generated using
+// Gay's dtoa in mode "precision".
+Vector<const PrecomputedPrecision> PrecomputedPrecisionRepresentations();
+
+} }  // namespace v8::internal
+
+#endif  // GAY_PRECISION_H_

test/cctest/test-fast-dtoa.cc

@@ -9,13 +9,26 @@
 #include "diy-fp.h"
 #include "double.h"
 #include "fast-dtoa.h"
+#include "gay-precision.h"
 #include "gay-shortest.h"
 
 using namespace v8::internal;
 
 static const int kBufferSize = 100;
 
-TEST(FastDtoaVariousDoubles) {
+
+// Removes trailing '0' digits.
+static void TrimRepresentation(Vector<char> representation) {
+  int len = strlen(representation.start());
+  int i;
+  for (i = len - 1; i >= 0; --i) {
+    if (representation[i] != '0') break;
+  }
+  representation[i + 1] = '\0';
+}
+
+
+TEST(FastDtoaShortestVariousDoubles) {
   char buffer_container[kBufferSize];
   Vector<char> buffer(buffer_container, kBufferSize);
   int length;
@@ -23,38 +36,45 @@ TEST(FastDtoaVariousDoubles) {
   int status;
 
   double min_double = 5e-324;
-  status = FastDtoa(min_double, buffer, &length, &point);
+  status = FastDtoa(min_double, FAST_DTOA_SHORTEST, 0,
+                    buffer, &length, &point);
   CHECK(status);
   CHECK_EQ("5", buffer.start());
   CHECK_EQ(-323, point);
 
   double max_double = 1.7976931348623157e308;
-  status = FastDtoa(max_double, buffer, &length, &point);
+  status = FastDtoa(max_double, FAST_DTOA_SHORTEST, 0,
+                    buffer, &length, &point);
   CHECK(status);
   CHECK_EQ("17976931348623157", buffer.start());
   CHECK_EQ(309, point);
 
-  status = FastDtoa(4294967272.0, buffer, &length, &point);
+  status = FastDtoa(4294967272.0, FAST_DTOA_SHORTEST, 0,
+                    buffer, &length, &point);
   CHECK(status);
   CHECK_EQ("4294967272", buffer.start());
   CHECK_EQ(10, point);
 
-  status = FastDtoa(4.1855804968213567e298, buffer, &length, &point);
+  status = FastDtoa(4.1855804968213567e298, FAST_DTOA_SHORTEST, 0,
+                    buffer, &length, &point);
   CHECK(status);
   CHECK_EQ("4185580496821357", buffer.start());
   CHECK_EQ(299, point);
 
-  status = FastDtoa(5.5626846462680035e-309, buffer, &length, &point);
+  status = FastDtoa(5.5626846462680035e-309, FAST_DTOA_SHORTEST, 0,
+                    buffer, &length, &point);
   CHECK(status);
   CHECK_EQ("5562684646268003", buffer.start());
   CHECK_EQ(-308, point);
 
-  status = FastDtoa(2147483648.0, buffer, &length, &point);
+  status = FastDtoa(2147483648.0, FAST_DTOA_SHORTEST, 0,
+                    buffer, &length, &point);
   CHECK(status);
   CHECK_EQ("2147483648", buffer.start());
   CHECK_EQ(10, point);
 
-  status = FastDtoa(3.5844466002796428e+298, buffer, &length, &point);
+  status = FastDtoa(3.5844466002796428e+298, FAST_DTOA_SHORTEST, 0,
+                    buffer, &length, &point);
   if (status) {  // Not all FastDtoa variants manage to compute this number.
     CHECK_EQ("35844466002796428", buffer.start());
     CHECK_EQ(299, point);
@@ -62,7 +82,7 @@ TEST(FastDtoaVariousDoubles) {
 
   uint64_t smallest_normal64 = V8_2PART_UINT64_C(0x00100000, 00000000);
   double v = Double(smallest_normal64).value();
-  status = FastDtoa(v, buffer, &length, &point);
+  status = FastDtoa(v, FAST_DTOA_SHORTEST, 0, buffer, &length, &point);
   if (status) {
     CHECK_EQ("22250738585072014", buffer.start());
     CHECK_EQ(-307, point);
@@ -70,7 +90,7 @@ TEST(FastDtoaVariousDoubles) {
 
   uint64_t largest_denormal64 = V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF);
   v = Double(largest_denormal64).value();
-  status = FastDtoa(v, buffer, &length, &point);
+  status = FastDtoa(v, FAST_DTOA_SHORTEST, 0, buffer, &length, &point);
   if (status) {
     CHECK_EQ("2225073858507201", buffer.start());
     CHECK_EQ(-307, point);
@@ -78,6 +98,107 @@ TEST(FastDtoaVariousDoubles) {
 }
 
 
+TEST(FastDtoaPrecisionVariousDoubles) {
+  char buffer_container[kBufferSize];
+  Vector<char> buffer(buffer_container, kBufferSize);
+  int length;
+  int point;
+  int status;
+
+  status = FastDtoa(1.0, FAST_DTOA_PRECISION, 3, buffer, &length, &point);
+  CHECK(status);
+  CHECK_GE(3, length);
+  TrimRepresentation(buffer);
+  CHECK_EQ("1", buffer.start());
+  CHECK_EQ(1, point);
+
+  status = FastDtoa(1.5, FAST_DTOA_PRECISION, 10, buffer, &length, &point);
+  if (status) {
+    CHECK_GE(10, length);
+    TrimRepresentation(buffer);
+    CHECK_EQ("15", buffer.start());
+    CHECK_EQ(1, point);
+  }
+
+  double min_double = 5e-324;
+  status = FastDtoa(min_double, FAST_DTOA_PRECISION, 5,
+                    buffer, &length, &point);
+  CHECK(status);
+  CHECK_EQ("49407", buffer.start());
+  CHECK_EQ(-323, point);
+
+  double max_double = 1.7976931348623157e308;
+  status = FastDtoa(max_double, FAST_DTOA_PRECISION, 7,
+                    buffer, &length, &point);
+  CHECK(status);
+  CHECK_EQ("1797693", buffer.start());
+  CHECK_EQ(309, point);
+
+  status = FastDtoa(4294967272.0, FAST_DTOA_PRECISION, 14,
+                    buffer, &length, &point);
+  if (status) {
+    CHECK_GE(14, length);
+    TrimRepresentation(buffer);
+    CHECK_EQ("4294967272", buffer.start());
+    CHECK_EQ(10, point);
+  }
+
+  status = FastDtoa(4.1855804968213567e298, FAST_DTOA_PRECISION, 17,
+                    buffer, &length, &point);
+  CHECK(status);
+  CHECK_EQ("41855804968213567", buffer.start());
+  CHECK_EQ(299, point);
+
+  status = FastDtoa(5.5626846462680035e-309, FAST_DTOA_PRECISION, 1,
+                    buffer, &length, &point);
+  CHECK(status);
+  CHECK_EQ("6", buffer.start());
+  CHECK_EQ(-308, point);
+
+  status = FastDtoa(2147483648.0, FAST_DTOA_PRECISION, 5,
+                    buffer, &length, &point);
+  CHECK(status);
+  CHECK_EQ("21475", buffer.start());
+  CHECK_EQ(10, point);
+
+  status = FastDtoa(3.5844466002796428e+298, FAST_DTOA_PRECISION, 10,
+                    buffer, &length, &point);
+  CHECK(status);
+  CHECK_GE(10, length);
+  TrimRepresentation(buffer);
+  CHECK_EQ("35844466", buffer.start());
+  CHECK_EQ(299, point);
+
+  uint64_t smallest_normal64 = V8_2PART_UINT64_C(0x00100000, 00000000);
+  double v = Double(smallest_normal64).value();
+  status = FastDtoa(v, FAST_DTOA_PRECISION, 17, buffer, &length, &point);
+  CHECK(status);
+  CHECK_EQ("22250738585072014", buffer.start());
+  CHECK_EQ(-307, point);
+
+  uint64_t largest_denormal64 = V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF);
+  v = Double(largest_denormal64).value();
+  status = FastDtoa(v, FAST_DTOA_PRECISION, 17, buffer, &length, &point);
+  CHECK(status);
+  CHECK_GE(20, length);
+  TrimRepresentation(buffer);
+  CHECK_EQ("22250738585072009", buffer.start());
+  CHECK_EQ(-307, point);
+
+  v = 3.3161339052167390562200598e-237;
+  status = FastDtoa(v, FAST_DTOA_PRECISION, 18, buffer, &length, &point);
+  CHECK(status);
+  CHECK_EQ("331613390521673906", buffer.start());
+  CHECK_EQ(-236, point);
+
+  v = 7.9885183916008099497815232e+191;
+  status = FastDtoa(v, FAST_DTOA_PRECISION, 4, buffer, &length, &point);
+  CHECK(status);
+  CHECK_EQ("7989", buffer.start());
+  CHECK_EQ(192, point);
+}
+
+
 TEST(FastDtoaGayShortest) {
   char buffer_container[kBufferSize];
   Vector<char> buffer(buffer_container, kBufferSize);
@@ -94,7 +215,7 @@ TEST(FastDtoaGayShortest) {
     const PrecomputedShortest current_test = precomputed[i];
     total++;
     double v = current_test.v;
-    status = FastDtoa(v, buffer, &length, &point);
+    status = FastDtoa(v, FAST_DTOA_SHORTEST, 0, buffer, &length, &point);
     CHECK_GE(kFastDtoaMaximalLength, length);
     if (!status) continue;
     if (length == kFastDtoaMaximalLength) needed_max_length = true;
@@ -105,3 +226,43 @@ TEST(FastDtoaGayShortest) {
   CHECK_GT(succeeded*1.0/total, 0.99);
   CHECK(needed_max_length);
 }
+
+
+TEST(FastDtoaGayPrecision) {
+  char buffer_container[kBufferSize];
+  Vector<char> buffer(buffer_container, kBufferSize);
+  bool status;
+  int length;
+  int point;
+  int succeeded = 0;
+  int total = 0;
+  // Count separately for entries with less than 15 requested digits.
+  int succeeded_15 = 0;
+  int total_15 = 0;
+
+  Vector<const PrecomputedPrecision> precomputed =
+      PrecomputedPrecisionRepresentations();
+  for (int i = 0; i < precomputed.length(); ++i) {
+    const PrecomputedPrecision current_test = precomputed[i];
+    double v = current_test.v;
+    int number_digits = current_test.number_digits;
+    total++;
+    if (number_digits <= 15) total_15++;
+    status = FastDtoa(v, FAST_DTOA_PRECISION, number_digits,
+                      buffer, &length, &point);
+    CHECK_GE(number_digits, length);
+    if (!status) continue;
+    succeeded++;
+    if (number_digits <= 15) succeeded_15++;
+    TrimRepresentation(buffer);
+    CHECK_EQ(current_test.decimal_point, point);
+    CHECK_EQ(current_test.representation, buffer.start());
+  }
+  // The precomputed numbers contain many entries with many requested
+  // digits. These have a high failure rate and we therefore expect a lower
+  // success rate than for the shortest representation.
+  CHECK_GT(succeeded*1.0/total, 0.85);
+  // However with less than 15 digits almost the algorithm should almost always
+  // succeed.
+  CHECK_GT(succeeded_15*1.0/total_15, 0.9999);
+}