Provide (non Gay) dtoa for fixed notation.

src/fixed-dtoa.cc

+// Copyright 2010 the V8 project authors. All rights reserved.
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//     * Redistributions of source code must retain the above copyright
+//       notice, this list of conditions and the following disclaimer.
+//     * Redistributions in binary form must reproduce the above
+//       copyright notice, this list of conditions and the following
+//       disclaimer in the documentation and/or other materials provided
+//       with the distribution.
+//     * Neither the name of Google Inc. nor the names of its
+//       contributors may be used to endorse or promote products derived
+//       from this software without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+#include <math.h>
+
+#include "v8.h"
+
+#include "double.h"
+#include "fixed-dtoa.h"
+
+namespace v8 {
+namespace internal {
+
+// Represents a 128bit type. This class should be replaced by a native type on
+// platforms that support 128bit integers.
+class UInt128 {
+ public:
+  UInt128() : high_bits_(0), low_bits_(0) { }
+  UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { }
+
+  void Multiply(uint32_t multiplicand) {
+    uint64_t accumulator;
+
+    accumulator = (low_bits_ & kMask32) * multiplicand;
+    uint32_t part = static_cast<uint32_t>(accumulator & kMask32);
+    accumulator >>= 32;
+    accumulator = accumulator + (low_bits_ >> 32) * multiplicand;
+    low_bits_ = (accumulator << 32) + part;
+    accumulator >>= 32;
+    accumulator = accumulator + (high_bits_ & kMask32) * multiplicand;
+    part = static_cast<uint32_t>(accumulator & kMask32);
+    accumulator >>= 32;
+    accumulator = accumulator + (high_bits_ >> 32) * multiplicand;
+    high_bits_ = (accumulator << 32) + part;
+    ASSERT((accumulator >> 32) == 0);
+  }
+
+  void Shift(int shift_amount) {
+    ASSERT(-64 <= shift_amount && shift_amount <= 64);
+    if (shift_amount == 0) {
+      return;
+    } else if (shift_amount == -64) {
+      high_bits_ = low_bits_;
+      low_bits_ = 0;
+    } else if (shift_amount == 64) {
+      low_bits_ = high_bits_;
+      high_bits_ = 0;
+    } else if (shift_amount <= 0) {
+      high_bits_ <<= -shift_amount;
+      high_bits_ += low_bits_ >> (64 + shift_amount);
+      low_bits_ <<= -shift_amount;
+    } else {
+      low_bits_ >>= shift_amount;
+      low_bits_ += high_bits_ << (64 - shift_amount);
+      high_bits_ >>= shift_amount;
+    }
+  }
+
+  // Modifies *this to *this MOD (2^power).
+  // Returns *this DIV (2^power).
+  int DivModPowerOf2(int power) {
+    if (power >= 64) {
+      int result = static_cast<int>(high_bits_ >> (power - 64));
+      high_bits_ -= static_cast<uint64_t>(result) << (power - 64);
+      return result;
+    } else {
+      uint64_t part_low = low_bits_ >> power;
+      uint64_t part_high = high_bits_ << (64 - power);
+      int result = static_cast<int>(part_low + part_high);
+      high_bits_ = 0;
+      low_bits_ -= part_low << power;
+      return result;
+    }
+  }
+
+  bool IsZero() const {
+    return high_bits_ == 0 && low_bits_ == 0;
+  }
+
+  int BitAt(int position) {
+    if (position >= 64) {
+      return (high_bits_ >> (position - 64)) & 1;
+    } else {
+      return (low_bits_ >> position) & 1;
+    }
+  }
+
+ private:
+  static const uint64_t kMask32 = 0xFFFFFFFF;
+  // Value == (high_bits_ << 64) + low_bits_
+  uint64_t high_bits_;
+  uint64_t low_bits_;
+};
+
+
+static const int kDoubleSignificandSize = 53;  // Includes the hidden bit.
+
+
+static void FillDigits32FixedLength(uint32_t number, int requested_length,
+                                    Vector<char> buffer, int* length) {
+  for (int i = requested_length - 1; i >= 0; --i) {
+    buffer[(*length) + i] = '0' + number % 10;
+    number /= 10;
+  }
+  *length += requested_length;
+}
+
+
+static void FillDigits32(uint32_t number, Vector<char> buffer, int* length) {
+  int number_length = 0;
+  // We fill the digits in reverse order and exchange them afterwards.
+  while (number != 0) {
+    int digit = number % 10;
+    number /= 10;
+    buffer[(*length) + number_length] = '0' + digit;
+    number_length++;
+  }
+  // Exchange the digits.
+  for (int i = 0, j = number_length - 1; i < j; ++i, --j) {
+    char digit_i = buffer[(*length) + i];
+    char digit_j = buffer[(*length) + j];
+    buffer[(*length) + i] = digit_j;
+    buffer[(*length) + j] = digit_i;
+  }
+  *length += number_length;
+}
+
+
+static void FillDigits64FixedLength(uint64_t number, int requested_length,
+                                    Vector<char> buffer, int* length) {
+  const uint32_t kTen7 = 10000000;
+  // For efficiency cut the number into 3 uint32_t parts, and print those.
+  uint32_t part2 = number % kTen7;
+  number /= kTen7;
+  uint32_t part1 = number % kTen7;
+  uint32_t part0 = number / kTen7;
+
+  FillDigits32FixedLength(part0, 3, buffer, length);
+  FillDigits32FixedLength(part1, 7, buffer, length);
+  FillDigits32FixedLength(part2, 7, buffer, length);
+}
+
+
+static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) {
+  const uint32_t kTen7 = 10000000;
+  // For efficiency cut the number into 3 uint32_t parts, and print those.
+  uint32_t part2 = number % kTen7;
+  number /= kTen7;
+  uint32_t part1 = number % kTen7;
+  uint32_t part0 = number / kTen7;
+
+  if (part0 != 0) {
+    FillDigits32(part0, buffer, length);
+    FillDigits32FixedLength(part1, 7, buffer, length);
+    FillDigits32FixedLength(part2, 7, buffer, length);
+  } else if (part1 != 0) {
+    FillDigits32(part1, buffer, length);
+    FillDigits32FixedLength(part2, 7, buffer, length);
+  } else {
+    FillDigits32(part2, buffer, length);
+  }
+}
+
+
+static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) {
+  // An empty buffer represents 0.
+  if (*length == 0) {
+    buffer[0] = '1';
+    *decimal_point = 1;
+    *length = 1;
+    return;
+  }
+  // Round the last digit until we either have a digit that was not '9' or until
+  // we reached the first digit.
+  buffer[(*length) - 1]++;
+  for (int i = (*length) - 1; i > 0; --i) {
+    if (buffer[i] != '0' + 10) {
+      return;
+    }
+    buffer[i] = '0';
+    buffer[i - 1]++;
+  }
+  // If the first digit is now '0' + 10, we would need to set it to '0' and add
+  // a '1' in front. However we reach the first digit only if all following
+  // digits had been '9' before rounding up. Now all trailing digits are '0' and
+  // we simply switch the first digit to '1' and update the decimal-point
+  // (indicating that the point is now one digit to the right).
+  if (buffer[0] == '0' + 10) {
+    buffer[0] = '1';
+    (*decimal_point)++;
+  }
+}
+
+
+// The given fractionals number represents a fixed-point number with binary
+// point at bit (-exponent).
+// Preconditions:
+//   -128 <= exponent <= 0.
+//   0 <= fractionals * 2^exponent < 1
+//   The buffer holds the result.
+// The function will round its result. During the rounding-process digits not
+// generated by this function might be updated, and the decimal-point variable
+// might be updated. If this function generates the digits 99 and the buffer
+// already contained "199" (thus yielding a buffer of "19999") then a
+// rounding-up will change the contents of the buffer to "20000".
+static void FillFractionals(uint64_t fractionals, int exponent,
+                            int fractional_count, Vector<char> buffer,
+                            int* length, int* decimal_point) {
+  ASSERT(-128 <= exponent && exponent <= 0);
+  // 'fractionals' is a fixed-point number, with binary point at bit
+  // (-exponent). Inside the function the non-converted remainder of fractionals
+  // is a fixed-point number, with binary point at bit 'point'.
+  if (-exponent <= 64) {
+    // One 64 bit number is sufficient.
+    ASSERT(fractionals >> 56 == 0);
+    int point = -exponent;
+    for (int i = 0; i < fractional_count; ++i) {
+      if (fractionals == 0) break;
+      // Instead of multiplying by 10 we multiply by 5 and adjust the point
+      // location. This way the fractionals variable will not overflow.
+      // Invariant at the beginning of the loop: fractionals < 2^point.
+      // Initially we have: point <= 64 and fractionals < 2^56
+      // After each iteration the point is decremented by one.
+      // Note that 5^3 = 125 < 128 = 2^7.
+      // Therefore three iterations of this loop will not overflow fractionals
+      // (even without the subtraction at the end of the loop body). At this time
+      // point will satisfy point <= 61 and therefore fractionals < 2^point and
+      // any further multiplication of fractionals by 5 will not overflow.
+      fractionals *= 5;
+      point--;
+      int digit = static_cast<int>(fractionals >> point);
+      buffer[*length] = '0' + digit;
+      (*length)++;
+      fractionals -= static_cast<uint64_t>(digit) << point;
+    }
+    // If the first bit after the point is set we have to round up.
+    if (((fractionals >> (point - 1)) & 1) == 1) {
+      RoundUp(buffer, length, decimal_point);
+    }
+  } else {  // We need 128 bits.
+    ASSERT(64 < -exponent && -exponent <= 128);
+    UInt128 fractionals128 = UInt128(fractionals, 0);
+    fractionals128.Shift(-exponent - 64);
+    int point = 128;
+    for (int i = 0; i < fractional_count; ++i) {
+      if (fractionals128.IsZero()) break;
+      // As before: instead of multiplying by 10 we multiply by 5 and adjust the
+      // point location.
+      // This multiplication will not overflow for the same reasons as before.
+      fractionals128.Multiply(5);
+      point--;
+      int digit = fractionals128.DivModPowerOf2(point);
+      buffer[*length] = '0' + digit;
+      (*length)++;
+    }
+    if (fractionals128.BitAt(point - 1) == 1) {
+      RoundUp(buffer, length, decimal_point);
+    }
+  }
+}
+
+
+// Removes leading and trailing zeros.
+// If leading zeros are removed then the decimal point position is adjusted.
+static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) {
+  while (*length > 0 && buffer[(*length) - 1] == '0') {
+    (*length)--;
+  }
+  int first_non_zero = 0;
+  while (first_non_zero < *length && buffer[first_non_zero] == '0') {
+    first_non_zero++;
+  }
+  if (first_non_zero != 0) {
+    for (int i = first_non_zero; i < *length; ++i) {
+      buffer[i - first_non_zero] = buffer[i];
+    }
+    *length -= first_non_zero;
+    *decimal_point -= first_non_zero;
+  }
+}
+
+
+bool FastFixedDtoa(double v,
+                   int fractional_count,
+                   Vector<char> buffer,
+                   int* length,
+                   int* decimal_point) {
+  const uint32_t kMaxUInt32 = 0xFFFFFFFF;
+  uint64_t significand = Double(v).Significand();
+  int exponent = Double(v).Exponent();
+  // v = significand * 2^exponent (with significand a 53bit integer).
+  // If the exponent is larger than 20 (i.e. we may have a 73bit number) then we
+  // don't know how to compute the representation. 2^73 ~= 9.5*10^21.
+  // If necessary this limit could probably be increased, but we don't need
+  // more.
+  if (exponent > 20) return false;
+  if (fractional_count > 20) return false;
+  *length = 0;
+  // At most kDoubleSignificandSize bits of the significand are non-zero.
+  // Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero
+  // bits:  0..11*..0xxx..53*..xx
+  if (exponent + kDoubleSignificandSize > 64) {
+    // The exponent must be > 11.
+    //
+    // We know that v = significand * 2^exponent.
+    // And the exponent > 11.
+    // We simplify the task by dividing v by 10^17.
+    // The quotient delivers the first digits, and the remainder fits into a 64
+    // bit number.
+    // Dividing by 10^17 is equivalent to dividing by 5^17*2^17.
+    const uint64_t kFive17 = V8_2PART_UINT64_C(0xB1, A2BC2EC5);  // 5^17
+    uint64_t divisor = kFive17;
+    int divisor_power = 17;
+    uint64_t dividend = significand;
+    uint64_t quotient;
+    uint64_t remainder;
+    // Let v = f * 2^e with f == significand and e == exponent.
+    // Then need q (quotient) and r (remainder) as follows:
+    //   v            = q * 10^17       + r
+    //   f * 2^e      = q * 10^17       + r
+    //   f * 2^e      = q * 5^17 * 2^17 + r
+    // If e > 17 then
+    //   f * 2^(e-17) = q * 5^17        + r/2^17
+    // else
+    //   f  = q * 5^17 * 2^(17-e) + r/2^e
+    if (exponent > divisor_power) {
+      // We only allow exponents of up to 20 and therefore (17 - e) <= 3
+      dividend <<= exponent - divisor_power;
+      quotient = dividend / divisor;
+      remainder = (dividend % divisor) << divisor_power;
+    } else {
+      divisor <<= divisor_power - exponent;
+      quotient = dividend / divisor;
+      remainder = (dividend % divisor) << exponent;
+    }
+    FillDigits32(quotient, buffer, length);
+    FillDigits64FixedLength(remainder, divisor_power, buffer, length);
+    *decimal_point = *length;
+  } else if (exponent >= 0) {
+    // 0 <= exponent <= 11
+    significand <<= exponent;
+    FillDigits64(significand, buffer, length);
+    *decimal_point = *length;
+  } else if (exponent > -kDoubleSignificandSize) {
+    // We have to cut the number.
+    uint64_t integrals = significand >> -exponent;
+    uint64_t fractionals = significand - (integrals << -exponent);
+    if (integrals > kMaxUInt32) {
+      FillDigits64(integrals, buffer, length);
+    } else {
+      FillDigits32(static_cast<uint32_t>(integrals), buffer, length);
+    }
+    *decimal_point = *length;
+    FillFractionals(fractionals, exponent, fractional_count,
+                    buffer, length, decimal_point);
+  } else if (exponent < -128) {
+    // This configuration (with at most 20 digits) means that all digits must be
+    // 0.
+    ASSERT(fractional_count <= 20);
+    buffer[0] = '\0';
+    *length = 0;
+    *decimal_point = -fractional_count;
+  } else {
+    *decimal_point = 0;
+    FillFractionals(significand, exponent, fractional_count,
+                    buffer, length, decimal_point);
+  }
+  TrimZeros(buffer, length, decimal_point);
+  buffer[*length] = '\0';
+  if ((*length) == 0) {
+    // The string is empty and the decimal_point thus has no importance. Mimick
+    // Gay's dtoa and and set it to -fractional_count.
+    *decimal_point = -fractional_count;
+  }
+  return true;
+}
+
+} }  // namespace v8::internal