public Binary64 NextRepresentableValue(Binary64InsignificantBits insignificantBits)
{
ulong lsb = (ulong)1 << insignificantBits;
ulong mask = lsb - 1;
ulong maxMask = BITS_MAX_POSITIVE ^ mask;
// Only keep the significant bits, drop the sign.
ulong nextBits = _bits & maxMask;
if (Sign.IsNegative)
{
if (nextBits != 0)
{
// Some negative number getting smaller.
nextBits -= lsb;
nextBits |= BITS_SIGN;
}
}
else
{
if (nextBits == maxMask)
{
throw new InvalidOperationException();
}
// Some positive number getting larger.
nextBits += lsb;
}
return(new Binary64(nextBits));
}
public Binary64 Round(Binary64InsignificantBits insignificantBits)
{
// Don't round special values...
if (IsNan || IsInfinite)
{
return(new Binary64(_bits));
}
ulong lsb = (ulong)1 << insignificantBits;
ulong mask = lsb - 1;
ulong maxMask = BITS_MAX_POSITIVE ^ mask;
// Only keep the significant bits, drop the sign.
ulong bits = _bits & maxMask;
// Imlpement rounding by adding half of the maximum value that can
// be represented by the insignificant bits, and then truncating.
bits += mask / 2;
// It is possible that the significand just overflowed. If so, we
// just rounded up to one of the special values (Infinity or Nan).
// Simply return +/- infinite.
if (bits > BITS_MAX_NORMAL)
{
if (Sign.IsNegative)
{
// NegativeInfinity
bits = BITS_SIGN | BITS_EXPONENT;
}
else
{
// PositiveInfinity
bits = BITS_EXPONENT;
}
}
else
{
// Restore the sign. We never round from negative to positive.
if (Sign.IsNegative)
{
bits |= BITS_SIGN;
}
}
return(new Binary64(bits));
}
public Binary64 PreviousRepresentableValue(Binary64InsignificantBits insignificantBits)
{
ulong lsb = (ulong)1 << (int)insignificantBits;
ulong mask = lsb - 1;
ulong maxMask = BITS_MAX_POSITIVE ^ mask;
// Only keep the significant bits, drop the sign.
ulong prevBits = _bits & maxMask;
if (Sign.IsPositive)
{
if (prevBits != 0)
{
// Some positive number getting smaller
prevBits -= lsb;
}
else
{
// Positive 0 will turn into negative 0.
prevBits |= BITS_SIGN;
}
}
else
{
if (prevBits == maxMask)
{
throw new InvalidOperationException();
}
// Some negative number getting larger.
prevBits -= lsb;
prevBits |= BITS_SIGN;
}
return(new Binary64(prevBits));
}
public static double RoundInsignificantBits(this double value, Binary64InsignificantBits insignificantBits)
{
return(((Binary64)value).Round(insignificantBits));
}
public static double GetPreviousRepresentableValue(this double value, Binary64InsignificantBits insignificantBits)
{
return(((Binary64)value).PreviousRepresentableValue(insignificantBits));
}
public Binary64 Round(Binary64InsignificantBits insignificantBits)
{
// Don't round special values...
if (IsNan || IsInfinite)
{
return new Binary64(this._bits);
}
ulong lsb = (ulong)1 << (int)insignificantBits;
ulong mask = lsb - 1;
ulong maxMask = BITS_MAX_POSITIVE ^ mask;
// Only keep the significant bits, drop the sign.
ulong bits = _bits & maxMask;
// Imlpement rounding by adding half of the maximum value that can
// be represented by the insignificant bits, and then truncating.
bits += (mask / 2);
// It is possible that the significand just overflowed. If so, we
// just rounded up to one of the special values (Infinity or Nan).
// Simply return +/- infinite.
if (bits > BITS_MAX_NORMAL)
{
if (Sign.IsNegative)
{
// NegativeInfinity
bits = BITS_SIGN | BITS_EXPONENT;
}
else
{
// PositiveInfinity
bits = BITS_EXPONENT;
}
}
else
{
// Restore the sign. We never round from negative to positive.
if (Sign.IsNegative)
{
bits |= BITS_SIGN;
}
}
return new Binary64(bits);
}
public Binary64 PreviousRepresentableValue(Binary64InsignificantBits insignificantBits)
{
ulong lsb = (ulong)1 << (int)insignificantBits;
ulong mask = lsb - 1;
ulong maxMask = BITS_MAX_POSITIVE ^ mask;
// Only keep the significant bits, drop the sign.
ulong prevBits = _bits & maxMask;
if (Sign.IsPositive)
{
if (prevBits != 0)
{
// Some positive number getting smaller
prevBits -= lsb;
}
else
{
// Positive 0 will turn into negative 0.
prevBits |= BITS_SIGN;
}
}
else
{
if (prevBits == maxMask)
{
throw new InvalidOperationException();
}
// Some negative number getting larger.
prevBits -= lsb;
prevBits |= BITS_SIGN;
}
return new Binary64(prevBits);
}
public static double RoundInsignificantBits(this double value, Binary64InsignificantBits insignificantBits)
{
return ((Binary64)value).Round(insignificantBits);
}
public static double GetPreviousRepresentableValue(this double value, Binary64InsignificantBits insignificantBits)
{
return ((Binary64)value).PreviousRepresentableValue(insignificantBits);
}