Re: Aw: Re: deco-Math project, step 00_a: exact bin and dec 'ranges' (in gnumeric). follow up.

[John Denker <jsd av8n com>]

On 7/8/21 4:34 PM, newbie nullzwei wrote:

> works, did similar for testing which algorithm could work, your sheet is a 
> little off as 2^53 is not represented as 0,5*2^54 but 1,0*2^53, the mantissa has 
> to be normalized to [1 .. 2[ thus 0,5 is wrong, and once you do further 
> calculations with erroneous log / int results in col. B, C you run into wrong 
> exponent, wrong mantissa, both together seemingly correct result, but wrong in 
> the details ... but it is on the right track ...

I have no idea what you're talking about.
Here's a quote from the frexp() manpage:

        These  functions  return the normalized fraction.
        If the argument x is not zero, the normalized fraction
        is x times a power of two, and its absolute value is
        always in the range 1/2 (inclusive) to 1 (exclusive), that is, [0.5,1).

So a mantissa of 0.5 is not wrong.
A mantissa of 1.0 would be wrong.
The spreadsheet does not make this mistake.
Column I makes a specific check for this, so it couldn't go unnoticed.

Columns B and C are preliminary intermediate results.
The final results are in columns G and H.
I was hoping you would notice the red boldface column headers.