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 final int _BITS = 22;
 static final int _BITS01 = 44; // 2 * _BITS
 static final int _BITS2 = 20; // 64 - _BITS01
 static final int _MASK = 4194303; // (1 << _BITS) - 1
 static final int _MASK_2 = 1048575; // (1 << _BITS2) - 1
 static final int _SIGN_BIT = 19; // _BITS2 - 1
 static final int _SIGN_BIT_VALUE = 524288; // 1 << _SIGN_BIT

 // Cached constants
 static int64 _MAX_VALUE;
 static int64 _MIN_VALUE;
 static int64 _ZERO;
 static int64 _ONE;
 static int64 _TWO;

 // Precompute the radix strings for MIN_VALUE to avoid the problem
 // of overflow of -MIN_VALUE.
 static List<String> _minValues = const <String>[
     null, null,
     "-1000000000000000000000000000000000000000000000000000000000000000", // 2
     "-2021110011022210012102010021220101220222", // base 3
     "-20000000000000000000000000000000", // base 4
     "-1104332401304422434310311213", // base 5
     "-1540241003031030222122212", // base 6
     "-22341010611245052052301", // base 7
     "-1000000000000000000000", // base 8
     "-67404283172107811828", // base 9
     "-9223372036854775808", // base 10
     "-1728002635214590698", // base 11
     "-41A792678515120368", // base 12
     "-10B269549075433C38", // base 13
     "-4340724C6C71DC7A8", // base 14
     "-160E2AD3246366808", // base 15
     "-8000000000000000" // base 16
 ];

 // 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, _MASK_2 >> 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_VALUE);
   }
   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 16 and returns an
  * [int64].
  */
 // TODO(rice) - make this faster by converting several digits at once.
 static int64 parseRadix(String s, int radix) {
   if ((radix <= 1) || (radix > 16)) {
     throw "Bad radix: $radix";
   }
   int64 x = ZERO;
   int i = 0;
   bool negative = false;
   if (s[0] == '-') {
     negative = true;
     i++;
   }
   for (; i < s.length; i++) {
     int c = s.codeUnitAt(i);
     int digit = int32._decodeHex(c);
     if (digit < 0 || digit >= radix) {
       throw new Exception("Non-radix char code: $c");
     }
     x = (x * radix) + digit;
   }
   return negative ? -x : x;
 }

 /**
  * 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) & _MASK_2;
   } 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 & _MASK_2;
   }
 }

 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):].
  */
 int64.fromInts(int top, int bottom) {
   top &= 0xffffffff;
   bottom &= 0xffffffff;
   _l = bottom & _MASK;
   _m = ((top & 0xfff) << 10) | ((bottom >> _BITS) & 0x3ff);
   _h = (top >> 12) & _MASK_2;
 }

 int64 _promote(other) {
   if (other == null) {
     throw new ArgumentError("null");
   } else if (other is intx) {
     other = other.toInt64();
   } else if (other is int) {
     other = new int64.fromInt(other);
   }
   if (other is !int64) {
     throw new Exception("Can't promote $other to int64");
   }
   return other;
 }

 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 & _MASK_2);
   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 & _MASK_2);
   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 & _MASK_2);
 }

 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 &= _MASK_2;

   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) & _MASK_2);
   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 & _MASK_2);
 }

 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_VALUE) != 0;
   if (negative) {
     a2 += 0x3 << _BITS2; // add extra one bits on the left
   }

   if (n < _BITS) {
     res2 = _shiftRight(a2, n);
     if (negative) {
       res2 |= _MASK_2 & ~(_MASK_2 >> n);
     }
     res1 = _shiftRight(_m, n) | (a2 << (_BITS - n));
     res0 = _shiftRight(_l, n) | (_m << (_BITS - n));
   } else if (n < _BITS01) {
     res2 = negative ? _MASK_2 : 0;
     res1 = _shiftRight(a2, n - _BITS);
     if (negative) {
       res1 |= _MASK & ~(_MASK >> (n - _BITS));
     }
     res0 = _shiftRight(_m, n - _BITS) | (a2 << (_BITS01 - n));
   } else {
     res2 = negative ? _MASK_2 : 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 & _MASK_2);
 }

 int64 shiftRightUnsigned(int n) {
   if (n < 0) {
     throw new ArgumentError("$n");
   }
   n &= 63;

   int res0, res1, res2;
   int a2 = _h & _MASK_2; // 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 & _MASK_2);
 }

 /**
  * 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) {
   if (other == null) {
     return false;
   }
   int64 o = _promote(other);
   return _l == o._l && _m == o._m && _h == o._h;
 }

 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 isEven() => (_l & 0x1) == 0;
 bool isMaxValue() => (_h == _MASK_2 >> 1) && _m == _MASK && _l == _MASK;
 bool isMinValue() => _h == _SIGN_BIT_VALUE && _m == 0 && _l == 0;
 bool isNegative() => (_h >> (_BITS2 - 1)) != 0;
 bool isOdd() => (_l & 0x1) == 1;
 bool 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_VALUE) != 0) {
     l = ~_l & _MASK;
     m = ~_m & _MASK;
     h = ~_h & _MASK_2;
     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].
  */
 // TODO(rice) - Make this faster by converting several digits at once.
 String toString() {
   int64 a = this;
   if (a.isZero()) {
     return "0";
   }
   if (a.isMinValue()) {
     return "-9223372036854775808";
   }

   String result = "";
   bool negative = false;
   if (a.isNegative()) {
     negative = true;
     a = -a;
   }

   int64 ten = new int64._bits(10, 0, 0);
   while (!a.isZero()) {
     a = _divMod(a, ten, true);
     result = "${_remainder._l}$result";
   }
   if (negative) {
     result = "-$result";
   }
   return result;
 }

 // 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 > 16)) {
     throw "Bad radix: $radix";
   }
   int64 a = this;
   if (a.isZero()) {
     return "0";
   }
   if (a.isMinValue()) {
     return _minValues[radix];
   }

   String result = "";
   bool negative = false;
   if (a.isNegative()) {
     negative = true;
     a = -a;
   }

   int64 r = new int64._bits(radix, 0, 0);
   while (!a.isZero()) {
     a = _divMod(a, r, true);
     result = "${_hexDigit(_remainder._l)}$result";
   }
   return negative ? "-$result" : result;
 }

 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)) & _MASK_2;

   _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 & _MASK_2;

   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;
 }

 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;
 }

 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);
 }
}