// Copyright (c) 2012, the Dart project authors.  Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.

part of fixnum;

/**
 * An immutable 64-bit signed integer, in the range [-2^63, 2^63 - 1].
 * Arithmetic operations may overflow in order to maintain this range.
 */
class Int64 implements IntX {

  // A 64-bit integer is represented internally as three non-negative
  // integers, storing the 22 low, 22 middle, and 20 high bits of the
  // 64-bit value.  _l (low) and _m (middle) are in the range
  // [0, 2^22 - 1] and _h (high) is in the range [0, 2^20 - 1].
  int _l, _m, _h;

  // Note: instances of [Int64] are immutable outside of this library,
  // therefore we may return a reference to an existing instance.
  // We take care to perform mutation only on internally-generated
  // instances before they are exposed to external code.

  // Note: several functions require _BITS == 22 -- do not change this value.
  static const int _BITS = 22;
  static const int _BITS01 = 44; // 2 * _BITS
  static const int _BITS2 = 20; // 64 - _BITS01
  static const int _MASK = 4194303; // (1 << _BITS) - 1
  static const int _MASK2 = 1048575; // (1 << _BITS2) - 1
  static const int _SIGN_BIT = 19; // _BITS2 - 1
  static const int _SIGN_BIT_MASK = 524288; // 1 << _SIGN_BIT

  // Cached constants
  static Int64 _MAX_VALUE;
  static Int64 _MIN_VALUE;
  static Int64 _ZERO;
  static Int64 _ONE;
  static Int64 _TWO;

  // The remainder of the last divide operation.
  static Int64 _remainder;

  /**
   * The maximum positive value attainable by an [Int64], namely
   * 9,223,372,036,854,775,807.
   */
  static Int64 get MAX_VALUE {
    if (_MAX_VALUE == null) {
      _MAX_VALUE = new Int64._bits(_MASK, _MASK, _MASK2 >> 1);
    }
    return _MAX_VALUE;
  }

  /**
   * The minimum positive value attainable by an [Int64], namely
   * -9,223,372,036,854,775,808.
   */
  static Int64 get MIN_VALUE {
    if (_MIN_VALUE == null) {
      _MIN_VALUE = new Int64._bits(0, 0, _SIGN_BIT_MASK);
    }
    return _MIN_VALUE;
  }

  /**
   * An [Int64] constant equal to 0.
   */
  static Int64 get ZERO {
    if (_ZERO == null) {
      _ZERO = new Int64();
    }
    return _ZERO;
  }

  /**
   * An [Int64] constant equal to 1.
   */
  static Int64 get ONE {
    if (_ONE == null) {
      _ONE = new Int64._bits(1, 0, 0);
    }
    return _ONE;
  }

  /**
   * An [Int64] constant equal to 2.
   */
  static Int64 get TWO {
    if (_TWO == null) {
      _TWO = new Int64._bits(2, 0, 0);
    }
    return _TWO;
  }

  /**
   * Parses a [String] in a given [radix] between 2 and 36 and returns an
   * [Int64].
   */
  static Int64 parseRadix(String s, int radix) {
    if ((radix <= 1) || (radix > 36)) {
      throw new ArgumentError("Bad radix: $radix");
    }
    return _parseRadix(s, radix);
  }

  static Int64 _parseRadix(String s, int radix) {
    int i = 0;
    bool negative = false;
    if (s[0] == '-') {
      negative = true;
      i++;
    }
    int d0 = 0, d1 = 0, d2 = 0;  //  low, middle, high components.
    for (; i < s.length; i++) {
      int c = s.codeUnitAt(i);
      int digit = Int32._decodeDigit(c);
      if (digit < 0 || digit >= radix) {
        throw new Exception("Non-radix char code: $c");
      }

      // [radix] and [digit] are at most 6 bits, component is 22, so we can
      // multiply and add within 30 bit temporary values.
      d0 = d0 * radix + digit;
      int carry = d0 >> _BITS;
      d0 &= _MASK;

      d1 = d1 * radix + carry;
      carry = d1 >> _BITS;
      d1 &= _MASK;

      d2 = d2 * radix + carry;
      d2 &= _MASK2;
    }

    if (negative) {
      d0 = 0 - d0;
      int borrow = (d0 >> _BITS) & 1;
      d0 &= _MASK;
      d1 = 0 - d1 - borrow;
      borrow = (d1 >> _BITS) & 1;
      d1 &= _MASK;
      d2 = 0 - d2 - borrow;
      d2 &= _MASK2;
    }
    return new Int64._bits(d0, d1, d2);
  }

  /**
   * Parses a decimal [String] and returns an [Int64].
   */
  static Int64 parseInt(String s) => _parseRadix(s, 10);

  /**
   * Parses a hexadecimal [String] and returns an [Int64].
   */
  static Int64 parseHex(String s) => _parseRadix(s, 16);

  //
  // Public constructors
  //

  /**
   * Constructs an [Int64] equal to 0.
   */
  Int64() : _l = 0, _m = 0, _h = 0;

  /**
   * Constructs an [Int64] with a given [int] value.
   */
  Int64.fromInt(int value) {
    bool negative = false;
    if (value < 0) {
      negative = true;
      value = -value - 1;
    }
    if (_haveBigInts) {
      _l = value & _MASK;
      _m = (value >> _BITS) & _MASK;
      _h = (value >> _BITS01) & _MASK2;
    } else {
      // Avoid using bitwise operations that coerce their input to 32 bits.
      _h = value ~/ 17592186044416; // 2^44
      value -= _h * 17592186044416;
      _m = value ~/ 4194304; // 2^22
      value -= _m * 4194304;
      _l = value;
    }

    if (negative) {
      _l = ~_l & _MASK;
      _m = ~_m & _MASK;
      _h = ~_h & _MASK2;
    }
  }

  factory Int64.fromBytes(List<int> bytes) {
    int top = bytes[7] & 0xff;
    top <<= 8;
    top |= bytes[6] & 0xff;
    top <<= 8;
    top |= bytes[5] & 0xff;
    top <<= 8;
    top |= bytes[4] & 0xff;

    int bottom = bytes[3] & 0xff;
    bottom <<= 8;
    bottom |= bytes[2] & 0xff;
    bottom <<= 8;
    bottom |= bytes[1] & 0xff;
    bottom <<= 8;
    bottom |= bytes[0] & 0xff;

    return new Int64.fromInts(top, bottom);
  }

  factory Int64.fromBytesBigEndian(List<int> bytes) {
    int top = bytes[0] & 0xff;
    top <<= 8;
    top |= bytes[1] & 0xff;
    top <<= 8;
    top |= bytes[2] & 0xff;
    top <<= 8;
    top |= bytes[3] & 0xff;

    int bottom = bytes[4] & 0xff;
    bottom <<= 8;
    bottom |= bytes[5] & 0xff;
    bottom <<= 8;
    bottom |= bytes[6] & 0xff;
    bottom <<= 8;
    bottom |= bytes[7] & 0xff;

    return new Int64.fromInts(top, bottom);
 }

  /**
   * Constructs an [Int64] from a pair of 32-bit integers having the value
   * [:((top & 0xffffffff) << 32) | (bottom & 0xffffffff):].
   */
  factory Int64.fromInts(int top, int bottom) {
    top &= 0xffffffff;
    bottom &= 0xffffffff;
    int d0 = bottom & _MASK;
    int d1 = ((top & 0xfff) << 10) | ((bottom >> _BITS) & 0x3ff);
    int d2 = (top >> 12) & _MASK2;
    return new Int64._bits(d0, d1, d2);
  }

  // Returns the [Int64] representation of the specified value. Throws
  // [ArgumentError] for non-integer arguments.
  Int64 _promote(val) {
    if (val is Int64) {
      return val;
    } else if (val is int) {
      return new Int64.fromInt(val);
    } else if (val is Int32) {
      return val.toInt64();
    }
    throw new ArgumentError(val);
  }

  Int64 operator +(other) {
    Int64 o = _promote(other);
    int sum0 = _l + o._l;
    int sum1 = _m + o._m + _shiftRight(sum0, _BITS);
    int sum2 = _h + o._h + _shiftRight(sum1, _BITS);

    Int64 result = new Int64._bits(sum0 & _MASK, sum1 & _MASK, sum2 & _MASK2);
    return result;
  }

  Int64 operator -(other) {
    Int64 o = _promote(other);
    int sum0 = _l - o._l;
    int sum1 = _m - o._m + _shiftRight(sum0, _BITS);
    int sum2 = _h - o._h + _shiftRight(sum1, _BITS);

    Int64 result = new Int64._bits(sum0 & _MASK, sum1 & _MASK, sum2 & _MASK2);
    return result;
  }

  Int64 operator -() {
    // Like 0 - this.
    int sum0 = -_l;
    int sum1 = -_m + _shiftRight(sum0, _BITS);
    int sum2 = -_h + _shiftRight(sum1, _BITS);

    return new Int64._bits(sum0 & _MASK, sum1 & _MASK, sum2 & _MASK2);
  }

  Int64 operator *(other) {
    Int64 o = _promote(other);

    // Grab 13-bit chunks.
    int a0 = _l & 0x1fff;
    int a1 = (_l >> 13) | ((_m & 0xf) << 9);
    int a2 = (_m >> 4) & 0x1fff;
    int a3 = (_m >> 17) | ((_h & 0xff) << 5);
    int a4 = (_h & 0xfff00) >> 8;

    int b0 = o._l & 0x1fff;
    int b1 = (o._l >> 13) | ((o._m & 0xf) << 9);
    int b2 = (o._m >> 4) & 0x1fff;
    int b3 = (o._m >> 17) | ((o._h & 0xff) << 5);
    int b4 = (o._h & 0xfff00) >> 8;

    // Compute partial products.
    // Optimization: if b is small, avoid multiplying by parts that are 0.
    int p0 = a0 * b0; // << 0
    int p1 = a1 * b0; // << 13
    int p2 = a2 * b0; // << 26
    int p3 = a3 * b0; // << 39
    int p4 = a4 * b0; // << 52

    if (b1 != 0) {
      p1 += a0 * b1;
      p2 += a1 * b1;
      p3 += a2 * b1;
      p4 += a3 * b1;
    }
    if (b2 != 0) {
      p2 += a0 * b2;
      p3 += a1 * b2;
      p4 += a2 * b2;
    }
    if (b3 != 0) {
      p3 += a0 * b3;
      p4 += a1 * b3;
    }
    if (b4 != 0) {
      p4 += a0 * b4;
    }

    // Accumulate into 22-bit chunks:
    // .........................................c10|...................c00|
    // |....................|..................xxxx|xxxxxxxxxxxxxxxxxxxxxx| p0
    // |....................|......................|......................|
    // |....................|...................c11|......c01.............|
    // |....................|....xxxxxxxxxxxxxxxxxx|xxxxxxxxx.............| p1
    // |....................|......................|......................|
    // |.................c22|...............c12....|......................|
    // |..........xxxxxxxxxx|xxxxxxxxxxxxxxxxxx....|......................| p2
    // |....................|......................|......................|
    // |.................c23|..c13.................|......................|
    // |xxxxxxxxxxxxxxxxxxxx|xxxxx.................|......................| p3
    // |....................|......................|......................|
    // |.........c24........|......................|......................|
    // |xxxxxxxxxxxx........|......................|......................| p4

    int c00 = p0 & 0x3fffff;
    int c01 = (p1 & 0x1ff) << 13;
    int c0 = c00 + c01;

    int c10 = p0 >> 22;
    int c11 = p1 >> 9;
    int c12 = (p2 & 0x3ffff) << 4;
    int c13 = (p3 & 0x1f) << 17;
    int c1 = c10 + c11 + c12 + c13;

    int c22 = p2 >> 18;
    int c23 = p3 >> 5;
    int c24 = (p4 & 0xfff) << 8;
    int c2 = c22 + c23 + c24;

    // Propagate high bits from c0 -> c1, c1 -> c2.
    c1 += c0 >> _BITS;
    c0 &= _MASK;
    c2 += c1 >> _BITS;
    c1 &= _MASK;
    c2 &= _MASK2;

    return new Int64._bits(c0, c1, c2);
  }

  Int64 operator %(other) {
    if (other.isZero) {
      throw new IntegerDivisionByZeroException();
    }
    if (this.isZero) {
      return ZERO;
    }
    Int64 o = _promote(other).abs();
    _divMod(this, o, true);
    return _remainder < 0 ? (_remainder + o) : _remainder;
  }

  Int64 operator ~/(other) => _divMod(this, _promote(other), false);

  // Int64 remainder(other) => this - (this ~/ other) * other;
  Int64 remainder(other) {
    if (other.isZero) {
      throw new IntegerDivisionByZeroException();
    }
    Int64 o = _promote(other).abs();
    _divMod(this, o, true);
    return _remainder;
  }

  Int64 operator &(other) {
    Int64 o = _promote(other);
    int a0 = _l & o._l;
    int a1 = _m & o._m;
    int a2 = _h & o._h;
    return new Int64._bits(a0, a1, a2);
  }

  Int64 operator |(other) {
    Int64 o = _promote(other);
    int a0 = _l | o._l;
    int a1 = _m | o._m;
    int a2 = _h | o._h;
    return new Int64._bits(a0, a1, a2);
  }

  Int64 operator ^(other) {
    Int64 o = _promote(other);
    int a0 = _l ^ o._l;
    int a1 = _m ^ o._m;
    int a2 = _h ^ o._h;
    return new Int64._bits(a0, a1, a2);
  }

  Int64 operator ~() {
    var result = new Int64._bits((~_l) & _MASK, (~_m) & _MASK, (~_h) & _MASK2);
    return result;
  }

  Int64 operator <<(int n) {
    if (n < 0) {
      throw new ArgumentError(n);
    }
    n &= 63;

    int res0, res1, res2;
    if (n < _BITS) {
      res0 = _l << n;
      res1 = (_m << n) | (_l >> (_BITS - n));
      res2 = (_h << n) | (_m >> (_BITS - n));
    } else if (n < _BITS01) {
      res0 = 0;
      res1 = _l << (n - _BITS);
      res2 = (_m << (n - _BITS)) | (_l >> (_BITS01 - n));
    } else {
      res0 = 0;
      res1 = 0;
      res2 = _l << (n - _BITS01);
    }

    return new Int64._bits(res0 & _MASK, res1 & _MASK, res2 & _MASK2);
  }

  Int64 operator >>(int n) {
    if (n < 0) {
      throw new ArgumentError(n);
    }
    n &= 63;

    int res0, res1, res2;

    // Sign extend h(a).
    int a2 = _h;
    bool negative = (a2 & _SIGN_BIT_MASK) != 0;
    if (negative) {
      a2 += 0x3 << _BITS2; // add extra one bits on the left
    }

    if (n < _BITS) {
      res2 = _shiftRight(a2, n);
      if (negative) {
        res2 |= _MASK2 & ~(_MASK2 >> n);
      }
      res1 = _shiftRight(_m, n) | (a2 << (_BITS - n));
      res0 = _shiftRight(_l, n) | (_m << (_BITS - n));
    } else if (n < _BITS01) {
      res2 = negative ? _MASK2 : 0;
      res1 = _shiftRight(a2, n - _BITS);
      if (negative) {
        res1 |= _MASK & ~(_MASK >> (n - _BITS));
      }
      res0 = _shiftRight(_m, n - _BITS) | (a2 << (_BITS01 - n));
    } else {
      res2 = negative ? _MASK2 : 0;
      res1 = negative ? _MASK : 0;
      res0 = _shiftRight(a2, n - _BITS01);
      if (negative) {
        res0 |= _MASK & ~(_MASK >> (n - _BITS01));
      }
    }

    return new Int64._bits(res0 & _MASK, res1 & _MASK, res2 & _MASK2);
  }

  Int64 shiftRightUnsigned(int n) {
    if (n < 0) {
      throw new ArgumentError(n);
    }
    n &= 63;

    int res0, res1, res2;
    int a2 = _h & _MASK2; // Ensure a2 is positive.
    if (n < _BITS) {
      res2 = a2 >> n;
      res1 = (_m >> n) | (a2 << (_BITS - n));
      res0 = (_l >> n) | (_m << (_BITS - n));
    } else if (n < _BITS01) {
      res2 = 0;
      res1 = a2 >> (n - _BITS);
      res0 = (_m >> (n - _BITS)) | (_h << (_BITS01 - n));
    } else {
      res2 = 0;
      res1 = 0;
      res0 = a2 >> (n - _BITS01);
    }

    return new Int64._bits(res0 & _MASK, res1 & _MASK, res2 & _MASK2);
  }

  /**
   * Returns [true] if this [Int64] has the same numeric value as the
   * given object.  The argument may be an [int] or an [IntX].
   */
  bool operator ==(other) {
    Int64 o;
    if (other is Int64) {
      o = other;
    } else if (other is int) {
      o = new Int64.fromInt(other);
    } else if (other is Int32) {
      o = other.toInt64();
    }
    if (o != null) {
      return _l == o._l && _m == o._m && _h == o._h;
    }
    return false;
  }

  int compareTo(Comparable other) {
    Int64 o = _promote(other);
    int signa = _h >> (_BITS2 - 1);
    int signb = o._h >> (_BITS2 - 1);
    if (signa != signb) {
      return signa == 0 ? 1 : -1;
    }
    if (_h > o._h) {
      return 1;
    } else if (_h < o._h) {
      return -1;
    }
    if (_m > o._m) {
      return 1;
    } else if (_m < o._m) {
      return -1;
    }
    if (_l > o._l) {
      return 1;
    } else if (_l < o._l) {
      return -1;
    }
    return 0;
  }

  bool operator <(other) {
    return this.compareTo(other) < 0;
  }

  bool operator <=(other) {
    return this.compareTo(other) <= 0;
  }

  bool operator >(other) {
    return this.compareTo(other) > 0;
  }

  bool operator >=(other) {
    return this.compareTo(other) >= 0;
  }

  bool get isEven => (_l & 0x1) == 0;
  bool get isMaxValue => (_h == _MASK2 >> 1) && _m == _MASK && _l == _MASK;
  bool get isMinValue => _h == _SIGN_BIT_MASK && _m == 0 && _l == 0;
  bool get isNegative => (_h >> (_BITS2 - 1)) != 0;
  bool get isOdd => (_l & 0x1) == 1;
  bool get isZero => _h == 0 && _m == 0 && _l == 0;

  /**
   * Returns a hash code based on all the bits of this [Int64].
   */
  int get hashCode {
    int bottom = ((_m & 0x3ff) << _BITS) | _l;
    int top = (_h << 12) | ((_m >> 10) & 0xfff);
    return bottom ^ top;
  }

  Int64 abs() {
    return this < 0 ? -this : this;
  }

  /**
   * Returns the number of leading zeros in this [Int64] as an [int]
   * between 0 and 64.
   */
  int numberOfLeadingZeros() {
    int b2 = Int32._numberOfLeadingZeros(_h);
    if (b2 == 32) {
      int b1 = Int32._numberOfLeadingZeros(_m);
      if (b1 == 32) {
        return Int32._numberOfLeadingZeros(_l) + 32;
      } else {
        return b1 + _BITS2 - (32 - _BITS);
      }
    } else {
      return b2 - (32 - _BITS2);
    }
  }

  /**
   * Returns the number of trailing zeros in this [Int64] as an [int]
   * between 0 and 64.
   */
  int numberOfTrailingZeros() {
    int zeros = Int32._numberOfTrailingZeros(_l);
    if (zeros < 32) {
      return zeros;
    }

    zeros = Int32._numberOfTrailingZeros(_m);
    if (zeros < 32) {
      return _BITS + zeros;
    }

    zeros = Int32._numberOfTrailingZeros(_h);
    if (zeros < 32) {
      return _BITS01 + zeros;
    }
    // All zeros
    return 64;
  }

  List<int> toBytes() {
    List<int> result = new List<int>(8);
    result[0] = _l & 0xff;
    result[1] = (_l >> 8) & 0xff;
    result[2] = ((_m << 6) & 0xfc) | ((_l >> 16) & 0x3f);
    result[3] = (_m >> 2) & 0xff;
    result[4] = (_m >> 10) & 0xff;
    result[5] = ((_h << 4) & 0xf0) | ((_m >> 18) & 0xf);
    result[6] = (_h >> 4) & 0xff;
    result[7] = (_h >> 12) & 0xff;
    return result;
  }

  int toInt() {
    int l = _l;
    int m = _m;
    int h = _h;
    bool negative = false;
    if ((_h & _SIGN_BIT_MASK) != 0) {
      l = ~_l & _MASK;
      m = ~_m & _MASK;
      h = ~_h & _MASK2;
      negative = true;
    }

    int result;
    if (_haveBigInts) {
      result = (h << _BITS01) | (m << _BITS) | l;
    } else {
      result = (h * 17592186044416) + (m * 4194304) + l;
    }
    return negative ? -result - 1 : result;
  }

  /**
   * Returns an [Int32] containing the low 32 bits of this [Int64].
   */
  Int32 toInt32() {
    return new Int32.fromInt(((_m & 0x3ff) << _BITS) | _l);
  }

  /**
   * Returns [this].
   */
  Int64 toInt64() => this;

  /**
   * Returns the value of this [Int64] as a decimal [String].
   */
  String toString() => _toRadixString(10);

  // TODO(rice) - Make this faster by avoiding arithmetic.
  String toHexString() {
    Int64 x = new Int64._copy(this);
    if (isZero) {
      return "0";
    }
    String hexStr = "";
    Int64 digit_f = new Int64.fromInt(0xf);
    while (!x.isZero) {
      int digit = x._l & 0xf;
      hexStr = "${_hexDigit(digit)}$hexStr";
      x = x.shiftRightUnsigned(4);
    }
    return hexStr;
  }

  String toRadixString(int radix) {
    if ((radix <= 1) || (radix > 36)) {
      throw new ArgumentError("Bad radix: $radix");
    }
    return _toRadixString(radix);
  }

  String _toRadixString(int radix) {
    int d0 = _l;
    int d1 = _m;
    int d2 = _h;

    if (d0 == 0 && d1 == 0 && d2 == 0) return '0';

    String sign = '';
    if ((d2 & _SIGN_BIT_MASK) != 0) {
      sign = '-';

      // Negate in-place.
      d0 = 0 - d0;
      int borrow = (d0 >> _BITS) & 1;
      d0 &= _MASK;
      d1 = 0 - d1 - borrow;
      borrow = (d1 >> _BITS) & 1;
      d1 &= _MASK;
      d2 = 0 - d2 - borrow;
      d2 &= _MASK2;
      // d2, d1, d0 now are an unsigned 64 bit integer for MIN_VALUE and an
      // unsigned 63 bit integer for other values.
    }

    // Rearrange components into five components where all but the most
    // significant are 10 bits wide.
    //
    //     d4, d3, d4, d1, d0:  24 + 10 + 10 + 10 + 10 bits
    //
    // The choice of 10 bits allows a remainder of 20 bits to be scaled by 10
    // bits and added during division while keeping all intermediate values
    // within 30 bits (unsigned small integer range for 32 bit implementations
    // of Dart VM and V8).
    //
    //     6  6         5         4         3         2         1
    //     3210987654321098765432109876543210987654321098765432109876543210
    //     [--------d2--------][---------d1---------][---------d0---------]
    //  -->
    //     [----------d4----------][---d3---][---d2---][---d1---][---d0---]


    int d4 = (d2 << 4) | (d1 >> 18);
    int d3 = (d1 >> 8) & 0x3ff;
    d2 = ((d1 << 2) | (d0 >> 20)) & 0x3ff;
    d1 = (d0 >> 10) & 0x3ff;
    d0 = d0 & 0x3ff;

    int fatRadix = _fatRadixTable[radix];

    // Generate chunks of digits.  In radix 10, generate 6 digits per chunk.
    //
    // This loop generates at most 3 chunks, so we store the chunks in locals
    // rather than a list.  We are trying to generate digits 20 bits at a time
    // until we have only 30 bits left.  20 + 20 + 30 > 64 would imply that we
    // need only two chunks, but radix values 17-19 and 33-36 generate only 15
    // or 16 bits per iteration, so sometimes the third chunk is needed.

    String chunk1 = "", chunk2 = "", chunk3 = "";

    while (!(d4 == 0 && d3 == 0)) {
      int q = d4 ~/ fatRadix;
      int r = d4 - q * fatRadix;
      d4 = q;
      d3 += r << 10;

      q = d3 ~/ fatRadix;
      r = d3 - q * fatRadix;
      d3 = q;
      d2 += r << 10;

      q = d2 ~/ fatRadix;
      r = d2 - q * fatRadix;
      d2 = q;
      d1 += r << 10;

      q = d1 ~/ fatRadix;
      r = d1 - q * fatRadix;
      d1 = q;
      d0 += r << 10;

      q = d0 ~/ fatRadix;
      r = d0 - q * fatRadix;
      d0 = q;

      assert(chunk3 == "");
      chunk3 = chunk2;
      chunk2 = chunk1;
      // Adding [fatRadix] Forces an extra digit which we discard to get a fixed
      // width.  E.g.  (1000000 + 123) -> "1000123" -> "000123".  An alternative
      // would be to pad to the left with zeroes.
      chunk1 = (fatRadix + r).toRadixString(radix).substring(1);
    }
    int residue = (d2 << 20) + (d1 << 10) + d0;
    String leadingDigits = residue == 0 ? '' : residue.toRadixString(radix);
    return '$sign$leadingDigits$chunk1$chunk2$chunk3';
  }

  // Table of 'fat' radix values.  Each entry for index `i` is the largest power
  // of `i` whose remainder fits in 20 bits.
  static const _fatRadixTable = const <int>[
      0,
      0,
      2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
        * 2,
      3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3,
      4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4,
      5 * 5 * 5 * 5 * 5 * 5 * 5 * 5,
      6 * 6 * 6 * 6 * 6 * 6 * 6,
      7 * 7 * 7 * 7 * 7 * 7 * 7,
      8 * 8 * 8 * 8 * 8 * 8,
      9 * 9 * 9 * 9 * 9 * 9,
      10 * 10 * 10 * 10 * 10 * 10,
      11 * 11 * 11 * 11 * 11,
      12 * 12 * 12 * 12 * 12,
      13 * 13 * 13 * 13 * 13,
      14 * 14 * 14 * 14 * 14,
      15 * 15 * 15 * 15 * 15,
      16 * 16 * 16 * 16 * 16,
      17 * 17 * 17 * 17,
      18 * 18 * 18 * 18,
      19 * 19 * 19 * 19,
      20 * 20 * 20 * 20,
      21 * 21 * 21 * 21,
      22 * 22 * 22 * 22,
      23 * 23 * 23 * 23,
      24 * 24 * 24 * 24,
      25 * 25 * 25 * 25,
      26 * 26 * 26 * 26,
      27 * 27 * 27 * 27,
      28 * 28 * 28 * 28,
      29 * 29 * 29 * 29,
      30 * 30 * 30 * 30,
      31 * 31 * 31 * 31,
      32 * 32 * 32 * 32,
      33 * 33 * 33,
      34 * 34 * 34,
      35 * 35 * 35,
      36 * 36 * 36
  ];

  String toDebugString() {
    return "Int64[_l=$_l, _m=$_m, _h=$_h]";
  }

  /**
   * Constructs an [Int64] with a given bitwise representation.  No validation
   * is performed.
   */
  Int64._bits(int this._l, int this._m, int this._h);

  /**
   * Constructs an [Int64] with the same value as an existing [Int64].
   */
  Int64._copy(Int64 other)
      : _l = other._l,
        _m = other._m,
        _h = other._h;

  // Determine whether the platform supports ints greater than 2^53
  // without loss of precision.
  static bool _haveBigIntsCached = null;

  static bool get _haveBigInts {
    if (_haveBigIntsCached == null) {
      var x = 9007199254740992;
      // Defeat compile-time constant folding.
      if (2 + 2 != 4) {
        x = 0;
      }
      var y = x + 1;
      var same = y == x;
      _haveBigIntsCached = !same;
    }
    return _haveBigIntsCached;
  }

  String _hexDigit(int digit) => "0123456789ABCDEF"[digit];

  // Implementation of '~/' and '%'.

  // Note: mutates [this].
  void _negate() {
    int neg0 = (~_l + 1) & _MASK;
    int neg1 = (~_m + (neg0 == 0 ? 1 : 0)) & _MASK;
    int neg2 = (~_h + ((neg0 == 0 && neg1 == 0) ? 1 : 0)) & _MASK2;

    _l = neg0;
    _m = neg1;
    _h = neg2;
  }

  // Note: mutates [this].
  void _setBit(int bit) {
    if (bit < _BITS) {
      _l |= 0x1 << bit;
    } else if (bit < _BITS01) {
      _m |= 0x1 << (bit - _BITS);
    } else {
      _h |= 0x1 << (bit - _BITS01);
    }
  }

  // Note: mutates [this].
  void _toShru1() {
    int a2 = _h;
    int a1 = _m;
    int a0 = _l;

    _h = a2 >> 1;
    _m = (a1 >> 1) | ((a2 & 0x1) << (_BITS - 1));
    _l = (a0 >> 1) | ((a1 & 0x1) << (_BITS - 1));
  }

  // Work around dart2js bugs with negative arguments to '>>' operator.
  static int _shiftRight(int x, int n) {
    if (x >= 0) {
      return x >> n;
    } else {
      int shifted = x >> n;
      if (shifted >= 0x80000000) {
        shifted -= 4294967296;
      }
      return shifted;
    }
  }

  /**
   * Attempt to subtract b from a if a >= b:
   *
   * if (a >= b) {
   *   a -= b;
   *   return true;
   * } else {
   *   return false;
   * }
   */
  // Note: mutates [a].
  static bool _trialSubtract(Int64 a, Int64 b) {
    // Early exit.
    int sum2 = a._h - b._h;
    if (sum2 < 0) {
      return false;
    }

    int sum0 = a._l - b._l;
    int sum1 = a._m - b._m + _shiftRight(sum0, _BITS);
    sum2 += _shiftRight(sum1, _BITS);

    if (sum2 < 0) {
      return false;
    }

    a._l = sum0 & _MASK;
    a._m = sum1 & _MASK;
    a._h = sum2 & _MASK2;

    return true;
  }

  // Note: mutates [a] via _trialSubtract.
  static Int64 _divModHelper(Int64 a, Int64 b,
      bool negative, bool aIsNegative, bool aIsMinValue,
      bool computeRemainder) {
    // Align the leading one bits of a and b by shifting b left.
    int shift = b.numberOfLeadingZeros() - a.numberOfLeadingZeros();
    Int64 bshift = b << shift;

    // Quotient must be a new instance since we mutate it.
    Int64 quotient = new Int64();
    while (shift >= 0) {
      bool gte = _trialSubtract(a, bshift);
      if (gte) {
        quotient._setBit(shift);
        if (a.isZero) {
          break;
        }
      }

      bshift._toShru1();
      shift--;
    }

    if (negative) {
      quotient._negate();
    }

    if (computeRemainder) {
      if (aIsNegative) {
        _remainder = -a;
        if (aIsMinValue) {
          _remainder = _remainder - ONE;
        }
      } else {
        _remainder = a;
      }
    }

    return quotient;
  }

  Int64 _divModByMinValue(bool computeRemainder) {
    // MIN_VALUE / MIN_VALUE == 1, remainder = 0
    // (x != MIN_VALUE) / MIN_VALUE == 0, remainder == x
    if (isMinValue) {
      if (computeRemainder) {
        _remainder = ZERO;
      }
      return ONE;
    }
    if (computeRemainder) {
      _remainder = this;
    }
    return ZERO;
  }

  /**
   * this &= ((1L << bits) - 1)
   */
  // Note: mutates [this].
  Int64 _maskRight(int bits) {
    int b0, b1, b2;
    if (bits <= _BITS) {
      b0 = _l & ((1 << bits) - 1);
      b1 = b2 = 0;
    } else if (bits <= _BITS01) {
      b0 = _l;
      b1 = _m & ((1 << (bits - _BITS)) - 1);
      b2 = 0;
    } else {
      b0 = _l;
      b1 = _m;
      b2 = _h & ((1 << (bits - _BITS01)) - 1);
    }

    _l = b0;
    _m = b1;
    _h = b2;
  }

  static Int64 _divModByShift(Int64 a, int bpower, bool negative, bool aIsCopy,
      bool aIsNegative, bool computeRemainder) {
    Int64 c = a >> bpower;
    if (negative) {
      c._negate();
    }

    if (computeRemainder) {
      if (!aIsCopy) {
        a = new Int64._copy(a);
      }
      a._maskRight(bpower);
      if (aIsNegative) {
        a._negate();
      }
      _remainder = a;
    }
    return c;
  }

  /**
   * Return the exact log base 2 of this, or -1 if this is not a power of two.
   */
  int _powerOfTwo() {
    // Power of two or 0.
    int l = _l;
    if ((l & (l - 1)) != 0) {
      return -1;
    }
    int m = _m;
    if ((m & (m - 1)) != 0) {
      return -1;
    }
    int h = _h;
    if ((h & (h - 1)) != 0) {
      return -1;
    }
    if (h == 0 && m == 0 && l == 0) {
      return -1;
    }
    if (h == 0 && m == 0 && l != 0) {
      return Int32._numberOfTrailingZeros(l);
    }
    if (h == 0 && m != 0 && l == 0) {
      return Int32._numberOfTrailingZeros(m) + _BITS;
    }
    if (h != 0 && m == 0 && l == 0) {
      return Int32._numberOfTrailingZeros(h) + _BITS01;
    }

    return -1;
  }

  static Int64 _divMod(Int64 a, Int64 b, bool computeRemainder) {
    if (b.isZero) {
      throw new IntegerDivisionByZeroException();
    }
    if (a.isZero) {
      if (computeRemainder) {
        _remainder = ZERO;
      }
      return ZERO;
    }
    // MIN_VALUE / MIN_VALUE = 1, anything other a / MIN_VALUE is 0.
    if (b.isMinValue) {
      return a._divModByMinValue(computeRemainder);
    }
    // Normalize b to abs(b), keeping track of the parity in 'negative'.
    // We can do this because we have already ensured that b != MIN_VALUE.
    bool negative = false;
    if (b.isNegative) {
      b = -b;
      negative = !negative;
    }
    // If b == 2^n, bpower will be n, otherwise it will be -1.
    int bpower = b._powerOfTwo();

    // True if the original value of a is negative.
    bool aIsNegative = false;
    // True if the original value of a is Int64.MIN_VALUE.
    bool aIsMinValue = false;

    /*
     * Normalize a to a positive value, keeping track of the sign change in
     * 'negative' (which tracks the sign of both a and b and is used to
     * determine the sign of the quotient) and 'aIsNegative' (which is used to
     * determine the sign of the remainder).
     *
     * For all values of a except MIN_VALUE, we can just negate a and modify
     * negative and aIsNegative appropriately. When a == MIN_VALUE, negation is
     * not possible without overflowing 64 bits, so instead of computing
     * abs(MIN_VALUE) / abs(b) we compute (abs(MIN_VALUE) - 1) / abs(b). The
     * only circumstance under which these quotients differ is when b is a power
     * of two, which will divide abs(MIN_VALUE) == 2^64 exactly. In this case,
     * we can get the proper result by shifting MIN_VALUE in unsigned fashion.
     *
     * We make a single copy of a before the first operation that needs to
     * modify its value.
     */
    bool aIsCopy = false;
    if (a.isMinValue) {
      aIsMinValue = true;
      aIsNegative = true;
      // If b is not a power of two, treat -a as MAX_VALUE (instead of the
      // actual value (MAX_VALUE + 1)).
      if (bpower == -1) {
        a = new Int64._copy(MAX_VALUE);
        aIsCopy = true;
        negative = !negative;
      } else {
        // Signed shift of MIN_VALUE produces the right answer.
        Int64 c = a >> bpower;
        if (negative) {
          c._negate();
        }
        if (computeRemainder) {
          _remainder = ZERO;
        }
        return c;
      }
    } else if (a.isNegative) {
      aIsNegative = true;
      a = -a;
      aIsCopy = true;
      negative = !negative;
    }

    // Now both a and b are non-negative.
    // If b is a power of two, just shift.
    if (bpower != -1) {
      return _divModByShift(a, bpower, negative, aIsCopy, aIsNegative,
        computeRemainder);
    }

    // If a < b, the quotient is 0 and the remainder is a.
    if (a < b) {
      if (computeRemainder) {
        if (aIsNegative) {
          _remainder = -a;
        } else {
          _remainder = aIsCopy ? a : new Int64._copy(a);
        }
      }
      return ZERO;
    }

    // Generate the quotient using bit-at-a-time long division.
    return _divModHelper(aIsCopy ? a : new Int64._copy(a), b, negative,
        aIsNegative, aIsMinValue, computeRemainder);
  }
}