|Re: Error function 35s vs. 32SII|
Message #5 Posted by Les Wright on 31 July 2007, 12:48 p.m.,
in response to message #4 by Les Wright
Thomas, here is my offering. The reference is formula 7.1.6 of Abramowitz and Stegun, whereas you seem to use 7.1.5. The idea of each term being a recursion on the prior term I get from the Numerical Recipes code for the series computation of the incomplete gamma function.
(E001) LBL E
(E009) STO O
5 XEQ E ENTER returns 1.00000000002 in a few seconds (certainly no more than 10), whereas the actual 12-digit result should be 9.99999999998e-1. This should come as no surprise--rounding error is bound to crop up. For input greater than about 1.8, one should compute erfc by the continued fraction and get erf as the complement (erf(z) = 1 - erfc(z))
But for smaller arguments, the above does very well--erf(1) is computed swiftly as 0.84270079295, which is completely accurate. erf(0.1) is even faster, giving 1.12462916019e-1 (the last digit should be an 8).
I guess what caught my attention is that I knew one could compute these series faster on the 33S and 32sii than what you were reporting. I must confess that the comparative sluggishness of the 35S (though still much faster than the 41 series, the 11C, the 15C, the Spice series, and even the 42S) is a disappointment. I love the speed of the 33S, despite its foibles, and really hoped this would port to the 35s intact. Alas, that hasn't happened.
I may port my continued fraction code for the incomplete gamma function, modified for the special case of erfc, and post it later if anyone is interested.
Edited: 31 July 2007, 12:49 p.m.