ldbeth / eflib

Error Function Library in SysRPL

SysRPL implementation of Error function and Q function.

This program is intended for use with HP49/50G calculators.

Build

Need HPTools, then just run make.

Install

The pre-built binary for the library is EFLIB, copy it to the HP calculator the way you usually do, and attach the library.

Usage

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.

ERF, IERF

Implementation of error function and its inverse using method from Sergei Winitzki's paper.

ERFIV

Implementation of inverse error function using method from Mike Giles' paper.

QNORM, IQNORM

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.

QBEST

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.

IQSML

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.

Reference

[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