[NUMBERS-172] Update the Erf function to use the Boost rational function approximtion

• Type: Improvement
• Status: Closed
• Priority: Major
• Resolution: Implemented
• Affects Version/s: 1.0
• Fix Version/s: 1.1
• Component/s: gamma
• Assignee: Unassigned
• Reporter: Alex Herbert
• Created: 18/Oct/21 20:12
• Updated: 01/Nov/22 11:00
• Resolved: 21/Oct/21 08:42

Description

The error function (erf) and complementary error function (erfc) are implemented using the continued fraction evaluation performed in the regularized gamma P and Q implementation. This is a generic function called with a fixed argument of 0.5:

erf(x)  = gammap(0.5, x*x)
erfc(x) = gammaq(0.5, x*x)

These functions have an implementation in the Boost c++ library using a rational function approximation.

NUMBERS-171 ported the inverse erf functions from Boost with an improvement in accuracy and speed. Investigate the use of the corresponding forward erf and erfc functions from Boost as replacements for the use of the regularized gamma function to evaluate the error function.

Issue Links

• is related to: NUMBERS-171 Update the InverseErfc function to support the full range of x in [0, 2]
• relates to: NUMBERS-174 Update Gamma functions using the Boost implementation