/// <summary>
/// Calculates Sin(x):
/// This takes a little longer and is less accurate if the input is out of the range (-pi, pi].
/// </summary>
public void Sin()
{
if (IsSpecialValue)
{
//Sin(x) has no limit as x->inf
if (SpecialValue == SpecialValueType.INF_MINUS || SpecialValue == SpecialValueType.INF_PLUS)
{
SetNaN();
}
return;
}
//Convert to positive range (0 <= x < inf)
bool sign = mantissa.Sign;
mantissa.Sign = false;
if (pi == null || pi.mantissa.Precision.NumBits != mantissa.Precision.NumBits)
{
CalculatePi(mantissa.Precision.NumBits);
}
if (inverseFactorialCache == null || invFactorialCutoff != mantissa.Precision.NumBits)
{
CalculateFactorials(mantissa.Precision.NumBits);
}
//Rescale into 0 <= x < 2*pi
if (GreaterThan(twoPi))
{
//There will be an inherent loss of precision doing this.
BigFloat newAngle = new BigFloat(this);
newAngle.Mul(twoPiRecip);
newAngle.FPart();
newAngle.Mul(twoPi);
Assign(newAngle);
}
//Rescale into range 0 <= x < pi
if (GreaterThan(pi))
{
//sin(pi + a) = sin(pi)cos(a) + sin(a)cos(pi) = 0 - sin(a) = -sin(a)
Sub(pi);
sign = !sign;
}
BigFloat temp = new BigFloat(mantissa.Precision);
//Rescale into range 0 <= x < pi/2
if (GreaterThan(piBy2))
{
temp.Assign(this);
Assign(pi);
Sub(temp);
}
//Rescale into range 0 <= x < pi/6 to accelerate convergence.
//This is done using sin(3x) = 3sin(x) - 4sin^3(x)
Mul(threeRecip);
if (mantissa.IsZero())
{
exponent = 0;
return;
}
BigFloat term = new BigFloat(this);
BigFloat square = new BigFloat(this);
square.Mul(term);
BigFloat sum = new BigFloat(this);
bool termSign = true;
int length = inverseFactorialCache.Length;
int numBits = mantissa.Precision.NumBits;
for (int i = 3; i < length; i += 2)
{
term.Mul(square);
temp.Assign(inverseFactorialCache[i]);
temp.Mul(term);
temp.mantissa.Sign = termSign;
termSign = !termSign;
if (temp.exponent < -numBits) break;
sum.Add(temp);
}
//Restore the triple-angle: sin(3x) = 3sin(x) - 4sin^3(x)
Assign(sum);
sum.Mul(this);
sum.Mul(this);
Mul(new BigFloat(3, mantissa.Precision));
sum.exponent += 2;
Sub(sum);
//Restore the sign
mantissa.Sign = sign;
}
/// <summary>
/// Returns the fractional (non-integer component of the input)
/// </summary>
/// <param name="n1">The input number</param>
public static BigFloat FPart(BigFloat n1)
{
BigFloat res = new BigFloat(n1);
n1.FPart();
return n1;
}
/// <summary>
/// Calculates tan(x)
/// </summary>
public void Tan()
{
if (IsSpecialValue)
{
//Tan(x) has no limit as x->inf
if (SpecialValue == SpecialValueType.INF_MINUS || SpecialValue == SpecialValueType.INF_PLUS)
{
SetNaN();
}
else if (SpecialValue == SpecialValueType.ZERO)
{
SetZero();
}
return;
}
if (pi == null || pi.mantissa.Precision.NumBits != mantissa.Precision.NumBits)
{
CalculatePi(mantissa.Precision.NumBits);
}
//Work out the sign change (involves replicating some rescaling).
bool sign = mantissa.Sign;
mantissa.Sign = false;
if (mantissa.IsZero())
{
return;
}
//Rescale into 0 <= x < pi
if (GreaterThan(pi))
{
//There will be an inherent loss of precision doing this.
BigFloat newAngle = new BigFloat(this);
newAngle.Mul(piRecip);
newAngle.FPart();
newAngle.Mul(pi);
Assign(newAngle);
}
//Rescale to -pi/2 <= x < pi/2
if (!LessThan(piBy2))
{
Sub(pi);
}
//Now the sign of the sin determines the sign of the tan.
//tan(x) = sin(x) / sqrt(1 - sin^2(x))
Sin();
BigFloat denom = new BigFloat(this);
denom.Mul(this);
denom.Sub(new BigFloat(1, mantissa.Precision));
denom.mantissa.Sign = !denom.mantissa.Sign;
if (denom.mantissa.Sign)
{
denom.SetZero();
}
denom.Sqrt();
Div(denom);
if (sign) mantissa.Sign = !mantissa.Sign;
}