|Re: Algorithm used to find Q and Q^-1 on HP32E|
Message #8 Posted by hugh steers on 18 Nov 2005, 8:37 a.m.,
in response to message #3 by bernhard
for sure, the 32e doesnt use the Abramowitz and Stegun "Hastings" approximation. at least not the standard one, although i understand there are other hasting approxes. the polynomial you mention is the one use by most programmable libraries include those of casio.
however, it is not 10 digit accurate, but the 32e is. also for inversion (ie inv Q). my guess is that it is, in fact, an iteration, as this would be less storage than the bigger polynomials needed for 10 digit accuracy. Q, erf and gamma are all related and normally require two iterative algorithms, one that converges over 0-1 and the other for x>1.
a while back, i ran some tests on this, here,
in other news....
the lygea 12c emulator has added N(z) and z. which are exactly Q and inv Q. this is a huge plus for black-scholes on the 12 and why hp couldnt have done this for the 12cp, who knows. AFAIK, the lygea 12c is a true emulator and not a simulator, which means they've suceeded in adding functions to the original code (or bolted them on somehow). so this proves its possible to revise functionality.
it alsp appears to be 10 digit accurate.