(50g) Normal Distribution

[Albert Chan]

(12-04-2018 09:48 PM)Dieter Wrote:  ... try a larger value with more digits, say 61/3 = 20,3333333333.
The exact PDF for this (12-digit rounded) input is 6,64644887122 E-91.

You really pick a hard one ...
x²/2 = 206.722 222221 544444 444445 ~ 206.722 222222, almost a half-way case

Doing everything with Casio FX-115MS, which have 12 digits precision

Direct method, with k = √(2 Pi):

Z(x) = exp(-x²/2) ÷ k = 6.64644 886816e-91, error = -306 ULP

3 Exp method, I = INT(x) = 20, F = FRAC(x) = 0.33333 33333:

Z(x) = exp(-I²/2) exp(-I F) exp(-F²/2) ÷ k = 6.64644 887123e-91, error = +1ULP

2 Exp method: B = INT(x²)/2 = 413/2 = 206.5

Z(x) = exp(-B) exp(B - I²/2 - I F - F²/2) ÷ k = 6.64644 887123e-91, error = +1 ULP

I think direct method is good enough (9 digits precision, even with extreme case)