(50g) Normal Distribution

[John Keith]

(12-05-2018 03:02 PM)Albert Chan Wrote:  For x = 16.4285 714286 (~ 115/7), Z(x) errors is much worse.

x²/2 suffered from double roundings, 134.948 979592 30612 ... => 134.948 979593

2 Exp method got Z(x) correctly = 9.84720 298683 e-60
Direct method shorted 687 ULP -> 9.84720 297996 e-60

Edit: above assumed calculator do half-round-up.
With halfway-to-even, direct method got 9.84720 298986 e-60, error = +303 ULP

I have compared your 2 EXP method and Dieter's original 3 Exp method and the 3 Exp version is actually faster on the HP 50. Exp is pretty fast on the HP 50 and the 3 Exp program is shorter, which helps because of RPL system overhead. Both methods give results accurate to +/- 1 ULP for all cases stated above.

The one problem I am having, due to my rusty algebra skills, is factoring in the variance. I would like the program to take the same arguments as the UTPN function, mean on level 3, variance on level 2, and x on level 1, as my attempt in the first post did. However, if I divide by 2v instead of by 2, I get the wrong answer. Any helpful hints would be appreciated.