HHC 2015 - Savage benchmark curiosity

[Dieter]

(10-09-2015 12:53 PM)Claudio L. Wrote:  This is a lot less magical than it appeared at the beginning (at least to me). All numbers between 1074 and 3790 in the last 4 digits will produce the same result.
(...)
I think the mystery is solved...

So finally there is an answer. ;-)

But, maybe more important for you:

(10-07-2015 03:18 PM)Claudio L. Wrote:  Old HP's consistently returned 2499.99948647, while newRPL returned 2499.99942402.

This is great news for newRPL users. Because it is the perfect result for a 12-digit machine. I did the Savage benchmark in a 34-digit environment (WP34s) with n-digit rounding after every single operation. For n=12 this is exactly the "perfect" result that should appear if every single intermediate result was correctly rounded to 12 digits.

So...

(10-09-2015 12:53 PM)Claudio L. Wrote:  Intrigued by this, and assuming there had to be a bug in newRPL somewhere ...

...the bug is seems to be not in newRPL, but in the "classic" (Saturn based) implementation.

For comparison, here are the results for some other cases:

Code:

n=8     2508,9828
n=10    2499,970323
n=12    2499,99942402
n=15    2499,99999975044
n=16    2500,000000006490

This implies the 34s runs in rounding mode RM 0 (round to closest value, exactly 0,500000... rounds to next even digit). Classic HPs rounded 0.5 always up, which is RM 1 on the 34s. However, the results will only differ if there is an intermediate result where the n+1st digit is 5 and all following ones are zero. ;-)

Dieter