/// <summary>
/// Computes the quotient of two double double numbers.
/// </summary>
/// <param name="a">The dividend.</param>
/// <param name="b">The divisor.</param>
/// <returns>The value of <paramref name="a"/> / <paramref name="b"/>.</returns>
public static DoubleDouble operator /(DoubleDouble a, DoubleDouble b)
{
double q1 = a.hi / b.hi;
DoubleDouble r = a - q1 * b;
double q2 = r.hi / b.hi;
r = r - q2 * b;
double q3 = r.hi / b.hi;
double qHi, qLo;
double t1, t2, t3;
ExtendedMath.TwoSum(q1, q2, out t1, out t2);
ExtendedMath.TwoSum(q3, t1, out qHi, out t3);
ExtendedMath.TwoSum(t2, t3, out qLo, out t1);
return(new DoubleDouble(qHi, qLo));
/*
* // Compute an initial approximation by dividing hi parts.
* double qHi = a.hi / b.hi;
*
* // Compute the product of qHi and bHi to full precision.
* // Ideally this would be exactly aHi but it won't be.
* double uHi, uLo;
* ExtendedMath.TwoProduct(qHi, b.hi, out uHi, out uLo);
*
* // Now compute the correction and but it in qLo.
* double qLo = ((((a.hi - uHi) - uLo) + a.lo) - qHi * b.lo) / b.hi;
*
* return new DoubleDouble(qHi, qLo);
*/
}
public static void ThreeSum(double a, double b, double c, out double sum, out double err)
{
double t1, t2, t3;
ExtendedMath.TwoSum(a, b, out t1, out t2);
ExtendedMath.TwoSum(c, t1, out sum, out t3);
ExtendedMath.TwoSum(t2, t3, out err, out t1);
}
/// <summary>
/// Computes the sum of two double double numbers.
/// </summary>
/// <param name="x">The first number.</param>
/// <param name="y">The second number.</param>
/// <returns>The value of <paramref name="x"/> + <paramref name="y"/>.</returns>
public static DoubleDouble operator +(DoubleDouble x, DoubleDouble y)
{
// Add high components
ExtendedMath.TwoSum(x.hi, y.hi, out double sHi, out double sLo);
if (ExtendedMath.IsNotFinite(sHi))
{
return((DoubleDouble)sHi);
}
// Add low components
ExtendedMath.TwoSum(x.lo, y.lo, out double tHi, out double tLo);
ExtendedMath.TwoSum(sHi, sLo + tHi, out double vHi, out double vLo);
ExtendedMath.FastTwoSum(vHi, tLo + vLo, out double zHi, out double zLo);
return(new DoubleDouble(zHi, zLo));
}
/// <summary>
/// Computes the quotient of two double double numbers.
/// </summary>
/// <param name="x">The dividend.</param>
/// <param name="y">The divisor.</param>
/// <returns>The value of <paramref name="x"/> / <paramref name="y"/>.</returns>
public static DoubleDouble operator /(DoubleDouble x, DoubleDouble y)
{
double q1 = x.hi / y.hi;
// If leading order result is NaN or infinity or zero, we are done.
// To continue would introduce NaNs even if result is infinite, so this early return is necessary.
if (q1 == 0.0 || ExtendedMath.IsNotFinite(q1))
{
return((DoubleDouble)q1);
}
DoubleDouble r = x - q1 * y;
double q2 = r.hi / y.hi;
r = r - q2 * y;
double q3 = r.hi / y.hi;
double qHi, qLo;
double t1, t2, t3;
ExtendedMath.TwoSum(q1, q2, out t1, out t2);
ExtendedMath.TwoSum(q3, t1, out qHi, out t3);
ExtendedMath.TwoSum(t2, t3, out qLo, out t1);
return(new DoubleDouble(qHi, qLo));
/*
* // Compute an initial approximation by dividing hi parts.
* double qHi = a.hi / b.hi;
*
* // Compute the product of qHi and bHi to full precision.
* // Ideally this would be exactly aHi but it won't be.
* double uHi, uLo;
* ExtendedMath.TwoProduct(qHi, b.hi, out uHi, out uLo);
*
* // Now compute the correction and but it in qLo.
* double qLo = ((((a.hi - uHi) - uLo) + a.lo) - qHi * b.lo) / b.hi;
*
* return new DoubleDouble(qHi, qLo);
*/
}
/// <summary>
/// Computes the sum of two double double numbers.
/// </summary>
/// <param name="a">The first number.</param>
/// <param name="b">The second number.</param>
/// <returns>The value of <paramref name="a"/> + <paramref name="b"/>.</returns>
public static DoubleDouble operator +(DoubleDouble a, DoubleDouble b)
{
// Add high components
double sHi, sLo;
ExtendedMath.TwoSum(a.hi, b.hi, out sHi, out sLo);
// Add low components
double tHi, tLo;
ExtendedMath.TwoSum(a.lo, b.lo, out tHi, out tLo);
double vHi, vLo;
ExtendedMath.TwoSum(sHi, sLo + tHi, out vHi, out vLo);
double zHi, zLo;
ExtendedMath.FastTwoSum(vHi, tLo + vLo, out zHi, out zLo);
return(new DoubleDouble(zHi, zLo));
}
