mfbt/double-conversion/fixed-dtoa.cc

changeset 0
6474c204b198
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/mfbt/double-conversion/fixed-dtoa.cc	Wed Dec 31 06:09:35 2014 +0100
     1.3 @@ -0,0 +1,402 @@
     1.4 +// Copyright 2010 the V8 project authors. All rights reserved.
     1.5 +// Redistribution and use in source and binary forms, with or without
     1.6 +// modification, are permitted provided that the following conditions are
     1.7 +// met:
     1.8 +//
     1.9 +//     * Redistributions of source code must retain the above copyright
    1.10 +//       notice, this list of conditions and the following disclaimer.
    1.11 +//     * Redistributions in binary form must reproduce the above
    1.12 +//       copyright notice, this list of conditions and the following
    1.13 +//       disclaimer in the documentation and/or other materials provided
    1.14 +//       with the distribution.
    1.15 +//     * Neither the name of Google Inc. nor the names of its
    1.16 +//       contributors may be used to endorse or promote products derived
    1.17 +//       from this software without specific prior written permission.
    1.18 +//
    1.19 +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
    1.20 +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
    1.21 +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
    1.22 +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
    1.23 +// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
    1.24 +// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
    1.25 +// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
    1.26 +// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
    1.27 +// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
    1.28 +// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
    1.29 +// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
    1.30 +
    1.31 +#include <math.h>
    1.32 +
    1.33 +#include "fixed-dtoa.h"
    1.34 +#include "ieee.h"
    1.35 +
    1.36 +namespace double_conversion {
    1.37 +
    1.38 +// Represents a 128bit type. This class should be replaced by a native type on
    1.39 +// platforms that support 128bit integers.
    1.40 +class UInt128 {
    1.41 + public:
    1.42 +  UInt128() : high_bits_(0), low_bits_(0) { }
    1.43 +  UInt128(uint64_t high, uint64_t low) : high_bits_(high), low_bits_(low) { }
    1.44 +
    1.45 +  void Multiply(uint32_t multiplicand) {
    1.46 +    uint64_t accumulator;
    1.47 +
    1.48 +    accumulator = (low_bits_ & kMask32) * multiplicand;
    1.49 +    uint32_t part = static_cast<uint32_t>(accumulator & kMask32);
    1.50 +    accumulator >>= 32;
    1.51 +    accumulator = accumulator + (low_bits_ >> 32) * multiplicand;
    1.52 +    low_bits_ = (accumulator << 32) + part;
    1.53 +    accumulator >>= 32;
    1.54 +    accumulator = accumulator + (high_bits_ & kMask32) * multiplicand;
    1.55 +    part = static_cast<uint32_t>(accumulator & kMask32);
    1.56 +    accumulator >>= 32;
    1.57 +    accumulator = accumulator + (high_bits_ >> 32) * multiplicand;
    1.58 +    high_bits_ = (accumulator << 32) + part;
    1.59 +    ASSERT((accumulator >> 32) == 0);
    1.60 +  }
    1.61 +
    1.62 +  void Shift(int shift_amount) {
    1.63 +    ASSERT(-64 <= shift_amount && shift_amount <= 64);
    1.64 +    if (shift_amount == 0) {
    1.65 +      return;
    1.66 +    } else if (shift_amount == -64) {
    1.67 +      high_bits_ = low_bits_;
    1.68 +      low_bits_ = 0;
    1.69 +    } else if (shift_amount == 64) {
    1.70 +      low_bits_ = high_bits_;
    1.71 +      high_bits_ = 0;
    1.72 +    } else if (shift_amount <= 0) {
    1.73 +      high_bits_ <<= -shift_amount;
    1.74 +      high_bits_ += low_bits_ >> (64 + shift_amount);
    1.75 +      low_bits_ <<= -shift_amount;
    1.76 +    } else {
    1.77 +      low_bits_ >>= shift_amount;
    1.78 +      low_bits_ += high_bits_ << (64 - shift_amount);
    1.79 +      high_bits_ >>= shift_amount;
    1.80 +    }
    1.81 +  }
    1.82 +
    1.83 +  // Modifies *this to *this MOD (2^power).
    1.84 +  // Returns *this DIV (2^power).
    1.85 +  int DivModPowerOf2(int power) {
    1.86 +    if (power >= 64) {
    1.87 +      int result = static_cast<int>(high_bits_ >> (power - 64));
    1.88 +      high_bits_ -= static_cast<uint64_t>(result) << (power - 64);
    1.89 +      return result;
    1.90 +    } else {
    1.91 +      uint64_t part_low = low_bits_ >> power;
    1.92 +      uint64_t part_high = high_bits_ << (64 - power);
    1.93 +      int result = static_cast<int>(part_low + part_high);
    1.94 +      high_bits_ = 0;
    1.95 +      low_bits_ -= part_low << power;
    1.96 +      return result;
    1.97 +    }
    1.98 +  }
    1.99 +
   1.100 +  bool IsZero() const {
   1.101 +    return high_bits_ == 0 && low_bits_ == 0;
   1.102 +  }
   1.103 +
   1.104 +  int BitAt(int position) {
   1.105 +    if (position >= 64) {
   1.106 +      return static_cast<int>(high_bits_ >> (position - 64)) & 1;
   1.107 +    } else {
   1.108 +      return static_cast<int>(low_bits_ >> position) & 1;
   1.109 +    }
   1.110 +  }
   1.111 +
   1.112 + private:
   1.113 +  static const uint64_t kMask32 = 0xFFFFFFFF;
   1.114 +  // Value == (high_bits_ << 64) + low_bits_
   1.115 +  uint64_t high_bits_;
   1.116 +  uint64_t low_bits_;
   1.117 +};
   1.118 +
   1.119 +
   1.120 +static const int kDoubleSignificandSize = 53;  // Includes the hidden bit.
   1.121 +
   1.122 +
   1.123 +static void FillDigits32FixedLength(uint32_t number, int requested_length,
   1.124 +                                    Vector<char> buffer, int* length) {
   1.125 +  for (int i = requested_length - 1; i >= 0; --i) {
   1.126 +    buffer[(*length) + i] = '0' + number % 10;
   1.127 +    number /= 10;
   1.128 +  }
   1.129 +  *length += requested_length;
   1.130 +}
   1.131 +
   1.132 +
   1.133 +static void FillDigits32(uint32_t number, Vector<char> buffer, int* length) {
   1.134 +  int number_length = 0;
   1.135 +  // We fill the digits in reverse order and exchange them afterwards.
   1.136 +  while (number != 0) {
   1.137 +    int digit = number % 10;
   1.138 +    number /= 10;
   1.139 +    buffer[(*length) + number_length] = '0' + digit;
   1.140 +    number_length++;
   1.141 +  }
   1.142 +  // Exchange the digits.
   1.143 +  int i = *length;
   1.144 +  int j = *length + number_length - 1;
   1.145 +  while (i < j) {
   1.146 +    char tmp = buffer[i];
   1.147 +    buffer[i] = buffer[j];
   1.148 +    buffer[j] = tmp;
   1.149 +    i++;
   1.150 +    j--;
   1.151 +  }
   1.152 +  *length += number_length;
   1.153 +}
   1.154 +
   1.155 +
   1.156 +static void FillDigits64FixedLength(uint64_t number, int requested_length,
   1.157 +                                    Vector<char> buffer, int* length) {
   1.158 +  const uint32_t kTen7 = 10000000;
   1.159 +  // For efficiency cut the number into 3 uint32_t parts, and print those.
   1.160 +  uint32_t part2 = static_cast<uint32_t>(number % kTen7);
   1.161 +  number /= kTen7;
   1.162 +  uint32_t part1 = static_cast<uint32_t>(number % kTen7);
   1.163 +  uint32_t part0 = static_cast<uint32_t>(number / kTen7);
   1.164 +
   1.165 +  FillDigits32FixedLength(part0, 3, buffer, length);
   1.166 +  FillDigits32FixedLength(part1, 7, buffer, length);
   1.167 +  FillDigits32FixedLength(part2, 7, buffer, length);
   1.168 +}
   1.169 +
   1.170 +
   1.171 +static void FillDigits64(uint64_t number, Vector<char> buffer, int* length) {
   1.172 +  const uint32_t kTen7 = 10000000;
   1.173 +  // For efficiency cut the number into 3 uint32_t parts, and print those.
   1.174 +  uint32_t part2 = static_cast<uint32_t>(number % kTen7);
   1.175 +  number /= kTen7;
   1.176 +  uint32_t part1 = static_cast<uint32_t>(number % kTen7);
   1.177 +  uint32_t part0 = static_cast<uint32_t>(number / kTen7);
   1.178 +
   1.179 +  if (part0 != 0) {
   1.180 +    FillDigits32(part0, buffer, length);
   1.181 +    FillDigits32FixedLength(part1, 7, buffer, length);
   1.182 +    FillDigits32FixedLength(part2, 7, buffer, length);
   1.183 +  } else if (part1 != 0) {
   1.184 +    FillDigits32(part1, buffer, length);
   1.185 +    FillDigits32FixedLength(part2, 7, buffer, length);
   1.186 +  } else {
   1.187 +    FillDigits32(part2, buffer, length);
   1.188 +  }
   1.189 +}
   1.190 +
   1.191 +
   1.192 +static void RoundUp(Vector<char> buffer, int* length, int* decimal_point) {
   1.193 +  // An empty buffer represents 0.
   1.194 +  if (*length == 0) {
   1.195 +    buffer[0] = '1';
   1.196 +    *decimal_point = 1;
   1.197 +    *length = 1;
   1.198 +    return;
   1.199 +  }
   1.200 +  // Round the last digit until we either have a digit that was not '9' or until
   1.201 +  // we reached the first digit.
   1.202 +  buffer[(*length) - 1]++;
   1.203 +  for (int i = (*length) - 1; i > 0; --i) {
   1.204 +    if (buffer[i] != '0' + 10) {
   1.205 +      return;
   1.206 +    }
   1.207 +    buffer[i] = '0';
   1.208 +    buffer[i - 1]++;
   1.209 +  }
   1.210 +  // If the first digit is now '0' + 10, we would need to set it to '0' and add
   1.211 +  // a '1' in front. However we reach the first digit only if all following
   1.212 +  // digits had been '9' before rounding up. Now all trailing digits are '0' and
   1.213 +  // we simply switch the first digit to '1' and update the decimal-point
   1.214 +  // (indicating that the point is now one digit to the right).
   1.215 +  if (buffer[0] == '0' + 10) {
   1.216 +    buffer[0] = '1';
   1.217 +    (*decimal_point)++;
   1.218 +  }
   1.219 +}
   1.220 +
   1.221 +
   1.222 +// The given fractionals number represents a fixed-point number with binary
   1.223 +// point at bit (-exponent).
   1.224 +// Preconditions:
   1.225 +//   -128 <= exponent <= 0.
   1.226 +//   0 <= fractionals * 2^exponent < 1
   1.227 +//   The buffer holds the result.
   1.228 +// The function will round its result. During the rounding-process digits not
   1.229 +// generated by this function might be updated, and the decimal-point variable
   1.230 +// might be updated. If this function generates the digits 99 and the buffer
   1.231 +// already contained "199" (thus yielding a buffer of "19999") then a
   1.232 +// rounding-up will change the contents of the buffer to "20000".
   1.233 +static void FillFractionals(uint64_t fractionals, int exponent,
   1.234 +                            int fractional_count, Vector<char> buffer,
   1.235 +                            int* length, int* decimal_point) {
   1.236 +  ASSERT(-128 <= exponent && exponent <= 0);
   1.237 +  // 'fractionals' is a fixed-point number, with binary point at bit
   1.238 +  // (-exponent). Inside the function the non-converted remainder of fractionals
   1.239 +  // is a fixed-point number, with binary point at bit 'point'.
   1.240 +  if (-exponent <= 64) {
   1.241 +    // One 64 bit number is sufficient.
   1.242 +    ASSERT(fractionals >> 56 == 0);
   1.243 +    int point = -exponent;
   1.244 +    for (int i = 0; i < fractional_count; ++i) {
   1.245 +      if (fractionals == 0) break;
   1.246 +      // Instead of multiplying by 10 we multiply by 5 and adjust the point
   1.247 +      // location. This way the fractionals variable will not overflow.
   1.248 +      // Invariant at the beginning of the loop: fractionals < 2^point.
   1.249 +      // Initially we have: point <= 64 and fractionals < 2^56
   1.250 +      // After each iteration the point is decremented by one.
   1.251 +      // Note that 5^3 = 125 < 128 = 2^7.
   1.252 +      // Therefore three iterations of this loop will not overflow fractionals
   1.253 +      // (even without the subtraction at the end of the loop body). At this
   1.254 +      // time point will satisfy point <= 61 and therefore fractionals < 2^point
   1.255 +      // and any further multiplication of fractionals by 5 will not overflow.
   1.256 +      fractionals *= 5;
   1.257 +      point--;
   1.258 +      int digit = static_cast<int>(fractionals >> point);
   1.259 +      buffer[*length] = '0' + digit;
   1.260 +      (*length)++;
   1.261 +      fractionals -= static_cast<uint64_t>(digit) << point;
   1.262 +    }
   1.263 +    // If the first bit after the point is set we have to round up.
   1.264 +    if (((fractionals >> (point - 1)) & 1) == 1) {
   1.265 +      RoundUp(buffer, length, decimal_point);
   1.266 +    }
   1.267 +  } else {  // We need 128 bits.
   1.268 +    ASSERT(64 < -exponent && -exponent <= 128);
   1.269 +    UInt128 fractionals128 = UInt128(fractionals, 0);
   1.270 +    fractionals128.Shift(-exponent - 64);
   1.271 +    int point = 128;
   1.272 +    for (int i = 0; i < fractional_count; ++i) {
   1.273 +      if (fractionals128.IsZero()) break;
   1.274 +      // As before: instead of multiplying by 10 we multiply by 5 and adjust the
   1.275 +      // point location.
   1.276 +      // This multiplication will not overflow for the same reasons as before.
   1.277 +      fractionals128.Multiply(5);
   1.278 +      point--;
   1.279 +      int digit = fractionals128.DivModPowerOf2(point);
   1.280 +      buffer[*length] = '0' + digit;
   1.281 +      (*length)++;
   1.282 +    }
   1.283 +    if (fractionals128.BitAt(point - 1) == 1) {
   1.284 +      RoundUp(buffer, length, decimal_point);
   1.285 +    }
   1.286 +  }
   1.287 +}
   1.288 +
   1.289 +
   1.290 +// Removes leading and trailing zeros.
   1.291 +// If leading zeros are removed then the decimal point position is adjusted.
   1.292 +static void TrimZeros(Vector<char> buffer, int* length, int* decimal_point) {
   1.293 +  while (*length > 0 && buffer[(*length) - 1] == '0') {
   1.294 +    (*length)--;
   1.295 +  }
   1.296 +  int first_non_zero = 0;
   1.297 +  while (first_non_zero < *length && buffer[first_non_zero] == '0') {
   1.298 +    first_non_zero++;
   1.299 +  }
   1.300 +  if (first_non_zero != 0) {
   1.301 +    for (int i = first_non_zero; i < *length; ++i) {
   1.302 +      buffer[i - first_non_zero] = buffer[i];
   1.303 +    }
   1.304 +    *length -= first_non_zero;
   1.305 +    *decimal_point -= first_non_zero;
   1.306 +  }
   1.307 +}
   1.308 +
   1.309 +
   1.310 +bool FastFixedDtoa(double v,
   1.311 +                   int fractional_count,
   1.312 +                   Vector<char> buffer,
   1.313 +                   int* length,
   1.314 +                   int* decimal_point) {
   1.315 +  const uint32_t kMaxUInt32 = 0xFFFFFFFF;
   1.316 +  uint64_t significand = Double(v).Significand();
   1.317 +  int exponent = Double(v).Exponent();
   1.318 +  // v = significand * 2^exponent (with significand a 53bit integer).
   1.319 +  // If the exponent is larger than 20 (i.e. we may have a 73bit number) then we
   1.320 +  // don't know how to compute the representation. 2^73 ~= 9.5*10^21.
   1.321 +  // If necessary this limit could probably be increased, but we don't need
   1.322 +  // more.
   1.323 +  if (exponent > 20) return false;
   1.324 +  if (fractional_count > 20) return false;
   1.325 +  *length = 0;
   1.326 +  // At most kDoubleSignificandSize bits of the significand are non-zero.
   1.327 +  // Given a 64 bit integer we have 11 0s followed by 53 potentially non-zero
   1.328 +  // bits:  0..11*..0xxx..53*..xx
   1.329 +  if (exponent + kDoubleSignificandSize > 64) {
   1.330 +    // The exponent must be > 11.
   1.331 +    //
   1.332 +    // We know that v = significand * 2^exponent.
   1.333 +    // And the exponent > 11.
   1.334 +    // We simplify the task by dividing v by 10^17.
   1.335 +    // The quotient delivers the first digits, and the remainder fits into a 64
   1.336 +    // bit number.
   1.337 +    // Dividing by 10^17 is equivalent to dividing by 5^17*2^17.
   1.338 +    const uint64_t kFive17 = UINT64_2PART_C(0xB1, A2BC2EC5);  // 5^17
   1.339 +    uint64_t divisor = kFive17;
   1.340 +    int divisor_power = 17;
   1.341 +    uint64_t dividend = significand;
   1.342 +    uint32_t quotient;
   1.343 +    uint64_t remainder;
   1.344 +    // Let v = f * 2^e with f == significand and e == exponent.
   1.345 +    // Then need q (quotient) and r (remainder) as follows:
   1.346 +    //   v            = q * 10^17       + r
   1.347 +    //   f * 2^e      = q * 10^17       + r
   1.348 +    //   f * 2^e      = q * 5^17 * 2^17 + r
   1.349 +    // If e > 17 then
   1.350 +    //   f * 2^(e-17) = q * 5^17        + r/2^17
   1.351 +    // else
   1.352 +    //   f  = q * 5^17 * 2^(17-e) + r/2^e
   1.353 +    if (exponent > divisor_power) {
   1.354 +      // We only allow exponents of up to 20 and therefore (17 - e) <= 3
   1.355 +      dividend <<= exponent - divisor_power;
   1.356 +      quotient = static_cast<uint32_t>(dividend / divisor);
   1.357 +      remainder = (dividend % divisor) << divisor_power;
   1.358 +    } else {
   1.359 +      divisor <<= divisor_power - exponent;
   1.360 +      quotient = static_cast<uint32_t>(dividend / divisor);
   1.361 +      remainder = (dividend % divisor) << exponent;
   1.362 +    }
   1.363 +    FillDigits32(quotient, buffer, length);
   1.364 +    FillDigits64FixedLength(remainder, divisor_power, buffer, length);
   1.365 +    *decimal_point = *length;
   1.366 +  } else if (exponent >= 0) {
   1.367 +    // 0 <= exponent <= 11
   1.368 +    significand <<= exponent;
   1.369 +    FillDigits64(significand, buffer, length);
   1.370 +    *decimal_point = *length;
   1.371 +  } else if (exponent > -kDoubleSignificandSize) {
   1.372 +    // We have to cut the number.
   1.373 +    uint64_t integrals = significand >> -exponent;
   1.374 +    uint64_t fractionals = significand - (integrals << -exponent);
   1.375 +    if (integrals > kMaxUInt32) {
   1.376 +      FillDigits64(integrals, buffer, length);
   1.377 +    } else {
   1.378 +      FillDigits32(static_cast<uint32_t>(integrals), buffer, length);
   1.379 +    }
   1.380 +    *decimal_point = *length;
   1.381 +    FillFractionals(fractionals, exponent, fractional_count,
   1.382 +                    buffer, length, decimal_point);
   1.383 +  } else if (exponent < -128) {
   1.384 +    // This configuration (with at most 20 digits) means that all digits must be
   1.385 +    // 0.
   1.386 +    ASSERT(fractional_count <= 20);
   1.387 +    buffer[0] = '\0';
   1.388 +    *length = 0;
   1.389 +    *decimal_point = -fractional_count;
   1.390 +  } else {
   1.391 +    *decimal_point = 0;
   1.392 +    FillFractionals(significand, exponent, fractional_count,
   1.393 +                    buffer, length, decimal_point);
   1.394 +  }
   1.395 +  TrimZeros(buffer, length, decimal_point);
   1.396 +  buffer[*length] = '\0';
   1.397 +  if ((*length) == 0) {
   1.398 +    // The string is empty and the decimal_point thus has no importance. Mimick
   1.399 +    // Gay's dtoa and and set it to -fractional_count.
   1.400 +    *decimal_point = -fractional_count;
   1.401 +  }
   1.402 +  return true;
   1.403 +}
   1.404 +
   1.405 +}  // namespace double_conversion

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