(11C) Random Prime Number Generator

[Albert Chan]

(10-21-2018 04:41 PM)Dieter Wrote:  There is another point where the program may not work as intended. The random number can be as large as 0,99999 99999. Multiplying this by 300 with 10-digit precision returns 300 exactly.

It seems about 50% of the time, N * RAN# = N rounding bug will not occur.

Example: 501 * 0.99999 99999 = 501 - 501/10^10 = 500.9999999 (501 - 1 decimal ULP)

Just like the binary case (post 10), error term slightly bigger than 1/2 decimal ULP, thus rounded-up.

--> If N mantissa fraction M = N/10^ceil(log10(N)), error term = M decimal ULP
--> If M > 1/2, max(N * RAN#) = N - 1 decimal ULP < N

So, a simulated dice = INT(6 * RAN#) + 1 is correct.

But, coin flipping INT(2 * RAN#) may be wrong. (Unless 2 = standing on edge)
Instead, it should remove precision a bit: INT(2 * FRAC(RAN# + 1))

Edit: because of the minus sign in front of error term, rounding rule is half-round-down.
Example: 500 * 0.99999 99999 = 500 - 500/10^10 = 500 - 0 = 500