Re: ver 1.9.4 use more decimal digits

[John Machin <sjmachin lexicon net>]

On 2/03/2009 2:32 PM, bill lam wrote:
> On Sun, 01 Mar 2009, Morten Welinder wrote:
> > Correct.  We need 17 digits for "double":
>
> iirc ieee double (8 byte) use 53 bit (including the implied bit) for
> mantissa so that it has
>
> log10(2^53)=15.95459 significant digits
>
> 16 digit is already enough. the 17 digits used by new gnumeric does
> not add more accuracy or precision assuming that ieee standard has
> been taken for granted.

Hi Bill,

The question is: What is the smallest integer N such that, for each 
possible IEEE 754 64-bit number, when you round it to N decimal digits 
of precision for storage/transmission purposes and then convert it back 
to the IEEE form, you get the original number?

The answer is: 17

See this: http://www.validlab.com/goldberg/paper.pdf
page 236, "Binary to Decimal Conversion", where it proves that 9 digits 
(not 8) are required for single precision, and states that likewise 17 
are needed for double precision.


HTH,
John