Dear TCL math enthusiasts,

I have programs to weight a minimum quantity using a scale.
Up to now, I used double math:

The scale has a certain resolution and returns a string like
"8.24 g". It always has 2 fractional digits ("24" in this example).

The minimum quantity is calculated from many factors and displayed to
the users.

What I did so far:
set weightIs "8.24 g"
set plan 6.8;set efficiency 1.2; set remainder 0.081
set weightShould [expr {$plan * $efficiency - $remainder}]
# the upper formular is arbitrary. It is just a calculation of multiple
factors
set weightIs [scan $weightIs "%f g"]
set weightShouldDisplay [format %.2f $weightShould]

if {$weightShould <= $weightIs} {#Ok}

The last comparision is the issue. If the user sees:
Minimum: 8.24
it really starts at something like: 8.235
So a remainder of 0.081 gives ok, but 0.078 gives not ok while
displaying the same number.

I also have an issue in documentation. The systems are validated and
should be consistent.

I also fear, that two doubles may have the same text representation. I
am not sure, if this may happen. Kevin Kenny has worked a lot on the
roundtrip, e.g. double->text->double gives the same result.

But is it true, that two doubles created from strings with same number
of digits are equal, if the strings are equal ?
set t1 [format %02f $d1]
set t2 [format %02f $d2]
set dt1 [scan $t1 %f]
set dt2 [scan $t2 %f]
if {$dt1 == $dt2} then $t1 eq $t2

So, I thought to use exact decimal quotational math. Each number is
represented by an entier and a fractional count

8.24 -> 824 2

(This is the q notation I know from embedded systems, but in decimal not
binary)

Limited math like multiplication, addition and comparison are possible.

Is this a good idea?
Is there already a library for this type of math?
I suppose, a custom TCL type may be defined, that would be weired ;-).

I know, something like this is used in accounting.
The rounding of operations is well defined in this case.
Banks are forced to take 3 fractional decimal digits for any operation.

Any idea welcome !

Thank you and take care,
Harald

Harald Oehlmann <wortkarg3@yahoo.com> wrote:
> So, I thought to use exact decimal quotational math. Each number is
> represented by an entier and a fractional count
>
> 8.24 -> 824 2

> Is there already a library for this type of math?

Yes, Tcllib math::decimal
https://core.tcl-lang.org/tcllib/doc/tcllib-1-18/embedded/www/tcllib/files/modules/math/decimal.html

Am 01.03.2024 um 23:42 schrieb Rich:
> Harald Oehlmann <wortkarg3@yahoo.com> wrote:
>> So, I thought to use exact decimal quotational math. Each number is
>> represented by an entier and a fractional count
>>
>> 8.24 -> 824 2
>
>> Is there already a library for this type of math?
>
> Yes, Tcllib math::decimal
> https://core.tcl-lang.org/tcllib/doc/tcllib-1-18/embedded/www/tcllib/files/modules/math/decimal.html
>

Thanks, Rich, that was exactly what I was looking for!
Great that you know all those details over many years!

Take care,
Harald