Re: Fixed vs float and precision and conversions

[Niklas Holsti <niklas.holsti@tidorum.invalid>]

On 2020-07-08 22:39, Björn Lundin wrote:
> Den 2020-07-08 kl. 20:21, skrev Niklas Holsti:
>> On 2020-07-08 21:10, Björn Lundin wrote:
>>> Den 2020-07-08 kl. 20:08, skrev Björn Lundin:
>>>
>>> The main reason for asking was to see if I got the whole concept
>>> of fixed types wrong or not.
>>> I did expect
>>> 'You should do this or that one-liner' as Niklas proposed.
>>> I did not get that to work though
>>
>> Oh. What happened when you tried? How did it fail?
>>
> 
> I did a test routine like below,
> but realized that Float(5.10) - which was converted to Fixed_Type(5.099)
> is a valid fixed_type of course.


No, see below. You are confusing decimal (base-10) reals with binary 
(base-2) floats.


> so
>        Fix1 := Fixed_Type(Flt);
> or
>        Fix2 := Fixed_Type'Round(Flt);
> 
> does not really matter, since both may return 5.099
> when given 5.10


Wrong. The point is that Float'(5.10) is not exactly 5.10, because 
base-2 floats cannot represent decimal fractions exactly. Since the 
result, as you showed in your first post, of converting (with 
truncation) Float'(5.10) to Fixed_Type is 5.099, the actual (binary) 
value of Float'(5.10) is a little less than 5.10, so the truncation 
gives 5.099 instead of 5.100.

But Fixed_Type'Round (Float'(5.10)) will always give 5.100.


> It is at least not certain that the number expressed in fixed_type is 
> one of them in the array below.
> And that is my real problem - I think.


That is certainly true -- if you don't know anything about the Float 
number, then you won't know much about the result of Fixed_Type'Round on 
that Float number. If you want to be sure that the result is one of the 
numbers in your table, you have to check.


>    ------------------------------
>    type Fixed_Type is delta 0.001 digits 18;
>    Bad_odds : exception;
>    type Tics_Type is new integer range 1 .. 350;
> 
>    ---------------------------
>    Global_Odds_Table : array(Tics_Type'Range) of Fixed_Type :=
>    (
>              1.01,   1.02,   1.03,   1.04,
>      1.05,   1.06,   1.07,   1.08,   1.09,


    [snip]


>   950.00, 960.00, 970.00, 980.00, 990.00,
>   1000.00);


If your Float numbers are as high as that (1000), you are approaching 
the limit of Float precision (about 7 decimal digits) compared to the 
delta of 0.001 for the Fixed_Type. That is, the Float representation of 
a Fixed_Type value close to 1000.0 might just be off by more than 
0.0005, in which case Fixed_Type'Round would give the corresponding (but 
wrong) value.

However, I tried Fixed_Type'Round on Float values of 999.998, 999.999, 
1000.001 and 1000.002, and got the corresponding Fixed_Type values, so 
it may be ok.

But the values in the Global_Odds table are all given with two decimals, 
not three, so why not define Fixed_Type with delta 0.01, which avoids 
this possible Float precision problem, as well as being more apt?

-- 
Niklas Holsti
niklas holsti tidorum fi
       .      @       .