Let's vote for suggestions and bugs

[CyberAngel]

(09-23-2018 05:39 AM)sasa Wrote:  

(09-23-2018 01:24 AM)Joe Horn Wrote:  As its documentation states, the 'dec' program returns the exact DECIMAL equivalent of 48-bit CAS reals. So, yes, dec(pi) returns a number which is the closest 48-bit approximation less than pi. But that's precisely its stated purpose. There only other way to see exactly what you have is to use the CAS command 'format' to see the number in hex, like this: format(pi,"a12").

The claim that program shows 44 exact digits of PI with only available 48-bit mantissa obviously made a confusion...

If mantissa is limited to 48-bits, it is rather correct to show no more than 15 digits, i.e. 14 significant digits +1, where last extra digit can indicate to user how to correctly round it with desired decimal places. Or more precisely, to automatically correctly round it itself to 14 digits, since other digits are out of interest for exact decimal representation of the number stored with in binary representation limited to 48-bits mantissa.

Simply based on fact: Num. of sign. dig. = [bits of mantissa] * log10(2)
In case of 48-bits mantissa, that is approx. 14.4 digits.

Emphasis mine.
Joe insists that all the dec digits represents the pi approximation exactly.
The problem is that that after those 14.4 digits the number is wrong.
No reason whatsoever for 50 digits yet along 1000 digits.
(The algorithm works, though - but it's misused)
<sigh>
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