Floating numbers issue

[MrCreatoR]

$i = 2

While $i < 3
    $i += 0.01
    
    If $i == 2.23 Then
        ConsoleWrite($i + 0.01 & @CRLF)
        ConsoleWrite(2.23 + 0.01 & @CRLF)
    EndIf
WEnd

Is it normal?

Edited January 26, 2021 by MrCreatoR

[Melba23]

MrCreatoR,

Quote

Is it normal?

Absolutely - exactly what one would expect with floating number arithmetic.

M23

[Nine]

1 hour ago, MrCreatoR said:

If $i == 2.23 Then

And using case-sensitive strings operator is not going to help either 

[Musashi]

1 hour ago, MrCreatoR said:

Is it normal?

I am sure you are looking for an explanation, not a solution . However (for other readers) :

$i = 2
While $i < 3
    $i = Round($i + 0.01, 2)
    If $i = 2.23 Then
        ConsoleWrite($i + 0.01 & @CRLF)
        ConsoleWrite(2.23 + 0.01 & @CRLF)
    EndIf
WEnd

 

Edited January 26, 2021 by Musashi

[argumentum]

4 hours ago, MrCreatoR said:

Is it normal?

the ^$$@#$^ floating points
In 2 decimal ( money ) stuff, I move everything to integer. Do the whatever calculations, and then move it back to decimal.   

[MrCreatoR]

4 hours ago, Melba23 said:

Absolutely

Then how you explain the fact that this happens starting from 2.23 and not earlier?

Check this:

$i = 2

While $i < 3
    $i += 0.01
    ConsoleWrite($i & @CRLF)
WEnd

and then this:

$i = 1

While $i < 2
    $i += 0.01
    ConsoleWrite($i & @CRLF)
WEnd

with the second example this behavior not occurred.

 

3 hours ago, Musashi said:

I am sure you are looking for an explanation, not a solution . However (for other readers) :

Another solution(s)...

$i = 2

While $i < 3
    $i = String($i) + 0.01
    
    If $i = 2.23 Then
        ConsoleWrite($i + 0.01 & @CRLF)
        ConsoleWrite(2.23 + 0.01 & @CRLF)
    EndIf
WEnd

 

Edited January 27, 2021 by MrCreatoR

[AspirinJunkie]

5 hours ago, MrCreatoR said:

Then how you explain the fact that this happens starting from 2.23 and not earlier?

It is not started at 2.23 it already starts before.
You just don't see it because of the internal rounding rules for the string presentation of the numbers:

$i = 1
While $i < 3
    $i += 0.01
    ConsoleWrite(StringFormat("%16s\t%.17f\n", $i, $i))
WEnd

 

So you have several ways to keep the effect of the round-off-error as small as possible.
One solution is to avoid ther error sum up by recalculating every time:

$i = 1
For $x = 1 To 300
    ConsoleWrite(StringFormat("%16s\t%.16f\n", 1 + 0.01 * $x, 1 + 0.01 * $x))
Next

Another one is (as @argumentum already stated) to calculate in a number expression without rounding error (e.g. integer) as long as possible:

$i = 100
While $i < 300
    $i += 1
    ConsoleWrite(StringFormat("%16s\t%.16f\n", $i / 100, $i / 100))
WEnd

 

Edited January 27, 2021 by AspirinJunkie

[Musashi]

@MrCreatoR :

As  @Melba23 , @argumentum and @AspirinJunkie have pointed out, this is not an internal problem of AutoIt.

For a deeper understanding, the following treatise may be helpful :

This is an edited reprint of the paper "What Every Computer Scientist Should Know About Floating-Point Arithmetic", by David Goldberg, published in the March, 1991 issue of Computing Surveys. Copyright 1991, Association for Computing Machinery, Inc. :

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

Not necessarily light fare , but often referenced in discussions regarding 'Floating-Point Arithmetic'.

Edited January 27, 2021 by Musashi
typo

[jchd]

A more low-level illustration of what's under the hood:

$n = 0.01 is represented internally by the exact value
+0.0099840000000000002078337502098293043673038482666015625

After performing this loop:

Local $n = 2
For $i = 1 To 23
    $n += 0.01
Next

$n has the exact internal representation
+2.2299999999999950972551232553087174892425537109375

while the value 2.23 is exactly represented internally as
+2.229999999999999982236431605997495353221893310546875
which shows that equality can't be achieved.

Each value shown above results from exactly computing and composing the components (sign, scale, mantissa) of the low-level FP representation.