Gamma special function #625
Conversation
jvdp1
left a comment
jvdp1
left a comment
There was a problem hiding this comment.
Thank you. It looks already good to me, while I am not a user of such functions. A main question is why not all functions support all kinds of reals.
|
|
||
| ### Description | ||
|
|
||
| Due to the different branch cut structures and a different principal branch, natural logarithm of gamma function log_gamma(z) with complex argument is different from the ln(Gamma(z)). The two have the same real part but different imaginary part. |
There was a problem hiding this comment.
Explain first the aim of this function.
There was a problem hiding this comment.
I would suggest to move these sentences to the section Returned value.
Co-authored-by: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Co-authored-by: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Co-authored-by: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Very good question. Short answer is limits of precision. Detailed answer is as follows. During the calculation of most special functions such as Gamma, Bessel functions, there are no finite analytical formulae to exactly calculate the function values. Those functions have to be approximated by using various techniques, which introducing truncation error and rounding error. These errors are more pronouncing during complex value multiplication and division arithmetic of the special functions. Because of the propagation of these errors, the calculated results will have much less significant digits or even incorrect value if the same precision as calculated result is used during calculation. By using higher precision during calculation, the desired precision digits are guaranteed to be correct. So single precision uses double precision for calculation, double precision uses quadruple precision for calculation. Extended precision calculation may need higher precision a little over quadruple, while quadruple precision calculation need much higher precision not available right now. If there is a package for arbitrary precision, all kinds of reals can be supported. |
Co-authored-by: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Co-authored-by: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Co-authored-by: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
Co-authored-by: Jeremie Vandenplas <jeremie.vandenplas@gmail.com>
jvdp1
left a comment
jvdp1
left a comment
There was a problem hiding this comment.
LGTM (only a minor comment). Thank you.
3 participants
During implementing the gamma probability distribution(#278), I realized there is a need for gamma function and log_gamma with complex argument as well as incomplete gamma functions. So here is the PR for gamma special function. The gamma and log_gamma functions with complex argument was coded for single and double precision. All implemented functions were tested against available multi-precision package version with satisfactory results. This PR includes the following:
Please test it and provide any comment and suggestion.