This program is intended for use with HP49/50G calculators.
Need HPTools, then just run make
.
The pre-built binary for the library is EFLIB
, copy it to the HP
calculator the way you usually do, and attach the library.
There are seven functions of type % --> %
provided, they are ERF
function, Q function, and their inverse implemented using numerical
approximation methods. Internally they are all computed using extended
float.
Implementation of error function and its inverse using method from Sergei Winitzki's paper.
Implementation of inverse error function using method from Mike Giles' paper.
Implementation of Q function and its inverse using ERF
and IERF
.
Note the UPTN
function actually gives a more acurrate result for
Q function, but the inverse Q function is much faster than
computing the inverse of Q using numerical solver, while
the accuracy of both methods are approximately the same.
A slightly better Q function approximation from [Dao Ngoc Phong et al].
If you ask me the result is still not as good as UPTN
.
This function from Pingyi Fan's paper gives decent approximation to
inverse Q function when the input is small enough, and can compute the
inverse when IQNORM
gives infinity error.
[Sergei Winitzki] A handy approximation for the error function and its inverse, February 6, 2008.
[Dao Ngoc Phong, Nguyen Xuan Hoai, R.I. (Bob) McKay] Evolving the Best Known Approximation to the Q Function.
[Mike Giles] Approximating the erfinv function.
[Pingyi Fan] New inequalities of Mill's ratio and Its Application to The Inverse Q-function Approximation