public override string ToString()
{
if (IsZero(this))
{
return("0");
}
if (Equals(this, MIN_VALUE))
{
// Special-case MIN_VALUE because neg(MIN_VALUE)==MIN_VALUE
return("-9223372036854775808");
}
if (IsNegative(this))
{
return("-" + (-this).ToString());
}
Long rem = this;
String res = "";
while (!IsZero(rem))
{
// Do several digits each time through the loop, so as to
// minimize the calls to the very expensive emulated div.
int tenPowerZeroes = 9;
int tenPower = 1000000000;
Long tenPowerLong = tenPower;
Long remDivTenPower = (rem / tenPowerLong);
String digits = "" + (int)((rem - (remDivTenPower * tenPowerLong)));
rem = remDivTenPower;
if (!IsZero(rem))
{
int zeroesNeeded = tenPowerZeroes - digits.Length;
for (; zeroesNeeded > 0; zeroesNeeded--)
{
digits = "0" + digits;
}
}
res = digits + res;
}
return(res);
}
public static Long ShiftRight(Long a, int n)
{
n &= 63;
double shiftFact = Pow(n);
double newHigh = Math.Floor(a.high / shiftFact);
double newLow = Math.Floor(a.low / shiftFact);
/*
* Doing the above floors separately on each component is safe. If n<32,
* a.high/shiftFact is guaranteed to be an integer already. For n>32,
* a.high/shiftFact will have fractional bits, but we need to discard them
* as they shift away. We will end up discarding all of a.low in this case,
* as it divides out to entirely fractional.
*/
return(create(newLow, newHigh));
}
public static Long ShiftLeft(Long a, int n)
{
n &= 63;
if (Equals(a, MIN_VALUE))
{
if (n == 0)
{
return(a);
}
else
{
return(ZERO);
}
}
if (IsNegative(a))
{
return(-ShiftLeft((-a), n));
}
double twoToN = Pow(n);
double newHigh = a.high * twoToN % TWO_PWR_64_DBL;
double newLow = a.low * twoToN;
double diff = newLow - (newLow % TWO_PWR_32_DBL);
newHigh += diff;
newLow -= diff;
if (newHigh >= TWO_PWR_63_DBL)
{
newHigh -= TWO_PWR_64_DBL;
}
return(new Long(newLow, newHigh));
}
public bool Equals(Long other)
{
return(Equals(this, other));
}
public static Long operator /(Long a, Long b)
{
if (IsZero(b))
{
throw new DivideByZeroException();
}
if (IsZero(a))
{
return(ZERO);
}
if (a.Equals(MIN_VALUE))
{
// handle a==MIN_VALUE carefully because of overflow issues
if (b.Equals(ONE) || b.Equals(NEG_ONE))
{
// this strange exception is described in JLS3 17.17.2
return(MIN_VALUE);
}
// at this point, abs(b) >= 2, so |a/b| < -MIN_VALUE
Long halfa = ShiftRight(a, 1);
Long approx = ShiftLeft((halfa / b), 1);
Long rem = (a - (b * approx));
Assert((rem > MIN_VALUE));
return(approx + (rem / b));
}
if (Equals(b, MIN_VALUE))
{
Assert(!Equals(a, MIN_VALUE));
return(ZERO);
}
// To keep the implementation compact, make a and be
// both be positive and swap the sign of the result
// if necessary.
if (IsNegative(a))
{
if (IsNegative(b))
{
return((-a) / (-b));
}
else
{
return(-((-a) / b));
}
}
Assert(!IsNegative(a));
if (IsNegative(b))
{
return(-(a / (-b)));
}
Assert(!IsNegative(b));
// Use float division to approximate the answer.
// Repeat until the remainder is less than b.
Long result = ZERO;
Long remainder = a;
while (remainder > b)
{
// approximate using float division
Long deltaResult = (Long)(Math.Floor(ToDoubleRoundDown(remainder)
/ ToDoubleRoundUp(b)));
if (IsZero(deltaResult))
{
deltaResult = ONE;
}
Long deltaRem = (deltaResult * b);
//Assert(deltaResult > ONE);
//Assert(deltaRem < remainder);
result = result + deltaResult;
remainder = remainder - deltaRem;
}
return(result);
}
public static Long operator *(Long a, Long b)
{
if (IsZero(a))
{
return(ZERO);
}
if (IsZero(b))
{
return(ZERO);
}
// handle MIN_VALUE carefully, because neg(MIN_VALUE)==MIN_VALUE
if (Equals(a, MIN_VALUE))
{
return(multByMinValue(b));
}
if (Equals(b, MIN_VALUE))
{
return(multByMinValue(a));
}
// If either argument is negative, change it to positive, multiply,
// and then negate the result.
if (IsNegative(a))
{
if (IsNegative(b))
{
return((-a) * (-b));
}
else
{
return(-((-a) * b));
}
}
Assert(!IsNegative(a));
if (IsNegative(b))
{
return(-(a * (-b)));
}
Assert(!IsNegative(b));
// If both numbers are small, use float multiplication
if ((a < TWO_PWR_24) && (b < TWO_PWR_24))
{
return(create(((double)a) * ((double)b), 0.0));
}
// Divide each number into 4 chunks of 16 bits, and then add
// up 4x4 multiplies. Skip the six multiplies where the result
// mod 2^64 would be 0.
double a3 = a.high % TWO_PWR_48_DBL;
double a4 = a.high - a3;
double a1 = a.low % TWO_PWR_16_DBL;
double a2 = a.low - a1;
double b3 = b.high % TWO_PWR_48_DBL;
double b4 = b.high - b3;
double b1 = b.low % TWO_PWR_16_DBL;
double b2 = b.low - b1;
Long res = ZERO;
res = AddTimes(res, a4, b1);
res = AddTimes(res, a3, b2);
res = AddTimes(res, a3, b1);
res = AddTimes(res, a2, b3);
res = AddTimes(res, a2, b2);
res = AddTimes(res, a2, b1);
res = AddTimes(res, a1, b4);
res = AddTimes(res, a1, b3);
res = AddTimes(res, a1, b2);
res = AddTimes(res, a1, b1);
return(res);
}
private static Long multByMinValue(Long value)
{
if (IsOdd(value))
{
return MIN_VALUE;
}
else
{
return ZERO;
}
}
private static bool IsZero(Long value)
{
return(value.low == 0.0 && value.high == 0.0);
}
private static int LowBits(Long value)
{
if (value.low >= TWO_PWR_31_DBL)
{
return (int)(value.low - TWO_PWR_32_DBL);
}
else
{
return (int)value.low;
}
}
private static double ToDoubleRoundUp(Long a)
{
int magnitute = (int)(Math.Log(a.high) / LN_2);
if (magnitute <= PRECISION_BITS)
{
return (double)a;
}
else
{
int diff = magnitute - PRECISION_BITS;
int toAdd = (1 << diff) - 1;
return a.high + (a.low + toAdd);
}
}
private static bool IsOdd(Long value)
{
return (LowBits(value) & 1) == 1;
}
private static bool IsZero(Long value)
{
return value.low == 0.0 && value.high == 0.0;
}
private static bool IsNegative(Long value)
{
return value.high < 0;
}
public static bool Equals(Long left, Long right)
{
return ((left.low == right.low) && (left.high == right.high));
}
public bool Equals(Long other)
{
return Equals(this, other);
}
public static bool Equals(Long left, Long right)
{
return((left.low == right.low) && (left.high == right.high));
}
private static bool IsNegative(Long value)
{
return(value.high < 0);
}
public static Long ShiftLeft(Long a, int n)
{
n &= 63;
if (Equals(a, MIN_VALUE))
{
if (n == 0)
{
return a;
}
else
{
return ZERO;
}
}
if (IsNegative(a))
{
return (-ShiftLeft((-a), n));
}
double twoToN = Pow(n);
double newHigh = a.high * twoToN % TWO_PWR_64_DBL;
double newLow = a.low * twoToN;
double diff = newLow - (newLow % TWO_PWR_32_DBL);
newHigh += diff;
newLow -= diff;
if (newHigh >= TWO_PWR_63_DBL)
{
newHigh -= TWO_PWR_64_DBL;
}
return new Long(newLow, newHigh);
}
private static bool IsOdd(Long value)
{
return((LowBits(value) & 1) == 1);
}
public static Long ShiftRight(Long a, int n)
{
n &= 63;
double shiftFact = Pow(n);
double newHigh = Math.Floor(a.high / shiftFact);
double newLow = Math.Floor(a.low / shiftFact);
/*
* Doing the above floors separately on each component is safe. If n<32,
* a.high/shiftFact is guaranteed to be an integer already. For n>32,
* a.high/shiftFact will have fractional bits, but we need to discard them
* as they shift away. We will end up discarding all of a.low in this case,
* as it divides out to entirely fractional.
*/
return create(newLow, newHigh);
}
/**
* Logical right shift. It does not preserve the sign of the input.
*/
private static Long shru(Long a, int n)
{
n &= 63;
Long sr = ShiftRight(a, n);
if (IsNegative(a))
{
// the following changes the high bits to 0, using
// a formula from JLS3 section 15.19
sr = sr + ShiftLeft(TWO, 63 - n);
}
return sr;
}
private static Long AddTimes(Long accum, double a, double b)
{
if (a == 0.0)
{
return accum;
}
if (b == 0.0)
{
return accum;
}
return (accum + create(a * b, 0.0));
}