Algorithms in the 21S


I am wondering if anybody here knows which algorithms are used to calculate the inverses of upper tails in the 21s, this is nearly as fast as the 49g+ so I believe the results are not done by a solver.
I know such algorithms exist as I tried to use them when I rewrote STAT48 for the 48G, however it was from a Russian book and I could not figure them out completely.
The 21S manual refers to D. Knuth, Seminumerical Algorihms, Vol. 2, London: Addison Wesley, 1981 for the random number generator test. There may be something in there?

If anyone knows of fast algorithms to get the inverse of upper tails (other than normal distribution which I already have), I would be very interested.




the 32e could also invert upper tails, but it looks like it has an internal solver for its own upper tail function (called Q).

Q is fast and i did some tests to find it is full 10 digit accurate. this is interesting since all versions in program libraries use a polynomial approximation which is less accurate (about 7 digits). whether the 32e simply had a more accurate internal polynomial or not i don’t know. but there are no clues and the inverse is not too slow for such an old machine.


If you get a plynomial approximation to 7 digits, it is quite easy for a solver to quickly get the next 3 digits from this starting point.
The polynomial in here works for the normal distribution. But the 21s also does student, F and x2 with a good speed. I would really be interested to know how they really do.

Now I have to find a 32e


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