Dividing factorials on 15C CE

[David Hayden]

(01-09-2024 01:23 AM)Thomas Klemm Wrote:  This avoids rounding errors:

P(50, 45) = 1 * 50 * 49 * 48 * 47 * 46
C(50, 45) = 1 * 50/1 * 49/2 * 48/3 * 47/4 * 46/5

Th really cool think about computing combinations this way is that the divisions always result in an integer.

Computing combinations was discussed in great detail in PPC journal. I don't have a reference handy, but I recall one final trick to prevent overflow in the multiplication: you start with 1E-99 (or whatever the smallest exponent is) as your result, run the algorithm, and then multiply the result by 1E99.