A number
The context settings to use.
Calculates the natural logarithm (to the base \( e \)) of a given number with rounding according to the given context settings.
Method:
For larger values of \( x \)(\( > 1 \)), the range can be adjusted such that \[ x = 2^k(1 + f) \]
where \( k \) is such that \( |f| < 1 \). Therefore, \[ \ln x = k \ln 2 + \ln (1 + f) \]
For faster convergence we can write \( \ln (1+f) \) as
\[ \ln (1+f) = \ln (1+s) - \ln (1-s) \]
This gives us \( s = \frac{x}{2+x} \) and
\[ \ln (1+f) = 2 \sum_{n=0}^{\infty} \frac{s^{2n+1}}{2n+1} \]
Finally, we can write \[ \ln x = k \ln 2 + 2 \sum_{n=0}^{\infty} \frac{s^{2n+1}}{2n+1} \]
A number.
The context settings to use.
Raises base to the power of ex using the rounding according to the
given context settings.
Method:
\[ a^b = e^{b \ln a} \]
A number.
The context settings object to use.
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Calculates the exponential of a given number with rounding according to the given context settings.
Method:
Find the values \( k \) such that \[ x = k\ln 2 + r \] where \( \lvert r \rvert \leqslant \frac{\ln 2}{2} \).
Therefore, \[ \exp{x} = 2^k e^{r} \]