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I found some inconsistencies in storing/using numbers in variables end in expressions.

Here is the test script:

Global $var 
For $i = 0 To 1024 Step 2 
;~         Local $var = Number(3 + 2 ^ $i) 
        $var = Number(3 + 2 ^ $i) 
        ConsoleWrite($i & "/VarGetType(" & VarGetType($var) & ")/Binary(" & Binary($var) & ")/IsFloat(" & IsFloat($var) & ")/String(" & String($var) & ")") 
        ConsoleWrite(@CRLF) 
Next

It can be seen in the output that for $i = 50, VarGetType is (Double) and IsFloat (0).
In addition, INT64 is enough for 2 ^ 50 + 3, but this is the double actually.
Similarly for $i = 0 (3 + 2 ^ 0 = 4).

It can also be seen from the output of the Binary function,
that the internal type of $var is INT64 for $i = 1 to 48 and Double otherwise.
Therefore, I conclude that the result of the VarGetType function is OK.
The IsFloat function is incorrect for $ i = 50 to 62 and also for 0.

I understand that the expression produces a double instead of an INT64 even where it is not needed.

Changing the variable from Global to Local does not change anything.

I don't know if these are AutoItScript errors or mine.

My environment:

>"C:\Program Files (x86)\AutoIt3\SciTE\..\AutoIt3.exe" "C:\Program Files (x86)\AutoIt3\SciTE\AutoIt3Wrapper\AutoIt3Wrapper.au3" /run /prod /ErrorStdOut /in "R:\P\sort\testPoradi.au3" /UserParams     
+>16:50:38 Starting AutoIt3Wrapper (19.1127.1402.26) from:SciTE.exe (4.2.0.0)  Keyboard:00010405  OS:WIN_10/1909  CPU:X64 OS:X64  Environment(Language:0405)  CodePage:0  utf8.auto.check:4 
+>         SciTEDir => C:\Program Files (x86)\AutoIt3\SciTE   UserDir => C:\Users\du\AppData\Local\AutoIt v3\SciTE\AutoIt3Wrapper   SCITE_USERHOME => C:\Users\du\AppData\Local\AutoIt v3\SciTE 
>Running AU3Check (3.3.14.5)  from:C:\Program Files (x86)\AutoIt3  input:R:\P\sort\testPoradi.au3 
+>16:50:39 AU3Check ended.rc:0 
>Running:(3.3.14.5):C:\Program Files (x86)\AutoIt3\autoit3.exe "R:\P\sort\testPoradi.au3"

 

Edited by Krsta
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There is no error, strictly speaking.

A double stores a value, integral or not, which is what IsFloat tells you. IsFloat() doesn't tell you about the variable datatype, just that it holds an integral value or not.

And yes, the returned datatype for $i = 0 is an anomaly, which isn't an error since the result is mathematically correct.

Now why the datatype change around 2^50 is a mystery as well, but still not a bug (the result is always correct).

My version:

Global $var
For $i = 0 To 1024
    $var = 3 + 2 ^ $i
    ConsoleWrite($i & @TAB & VarGetType($var) & @TAB & Binary($var) & @TAB  & (IsFloat($var) ? "Fractional" : "Integral") & @TAB & '"' & String($var) & '"' & @LF)
    If $i = 4 Then
        $i = 45
        ConsoleWrite("..." & @LF)
    EndIf
    If $i = 51 Then
        $i = 59
        ConsoleWrite("..." & @LF)
    EndIf
    If $i = 65 Then
        $i = 1020
        ConsoleWrite("..." & @LF)
    EndIf
Next

 

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jchd,

Quote

why the datatype change around 2^50 is a mystery

I imagine it is because the value of 2 ^ $i becomes too big to store in an Int64 and so needs a Double - see this extract from the output of my slightly amended script:

48/VarGetType(Int64)/Binary(0x0300000000000100)/IsFloat(0)/String(281474976710659)
2^48 = 281474976710656
50/VarGetType(Double)/Binary(0x0C00000000001043)/IsFloat(0)/String(1.12589990684263e+15)
2^50 = 1.12589990684262e+15

M23

Public_Domain.png.2d871819fcb9957cf44f4514551a2935.png Any of my own code posted anywhere on the forum is available for use by others without any restriction of any kind

Open spoiler to see my UDFs:

Spoiler

ArrayMultiColSort ---- Sort arrays on multiple columns
ChooseFileFolder ---- Single and multiple selections from specified path treeview listing
Date_Time_Convert -- Easily convert date/time formats, including the language used
ExtMsgBox --------- A highly customisable replacement for MsgBox
GUIExtender -------- Extend and retract multiple sections within a GUI
GUIFrame ---------- Subdivide GUIs into many adjustable frames
GUIListViewEx ------- Insert, delete, move, drag, sort, edit and colour ListView items
GUITreeViewEx ------ Check/clear parent and child checkboxes in a TreeView
Marquee ----------- Scrolling tickertape GUIs
NoFocusLines ------- Remove the dotted focus lines from buttons, sliders, radios and checkboxes
Notify ------------- Small notifications on the edge of the display
Scrollbars ----------Automatically sized scrollbars with a single command
StringSize ---------- Automatically size controls to fit text
Toast -------------- Small GUIs which pop out of the notification area

 

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3 minutes ago, Melba23 said:

I imagine it is because the value of 2 ^ $i becomes too big to store in an Int64 and so needs a Double

No, because an int64 can store up to 2^63-1.

Local $n = 33554432 ; that is 2^25
Local $p = $n * $n  ; 2^50
ConsoleWrite($p & @TAB & VarGetType($p) & @LF)

$n = 1073741824 ; that is 2^30
Local $p = $n * $n  ; 2^60
ConsoleWrite($p & @TAB & VarGetType($p) & @LF)

 

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@jchd You mean Uint64 as int64 is signed. 

But in any case there is still that "bug" :

#AutoIt3Wrapper_UseX64=y
#include <Constants.au3>
#include <Array.au3>

For $i = 46 to 50
  $num = 2^$i
  ConsoleWrite ($i & " = " & Hex($num) & @CRLF)
Next

where it breaks at 49.

Edited by Nine
nvm misread your post
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No I really meant 2^63-1 for an INT64. Count up to 2^64-1 for an UINT64 (which AutoIt doesn't have).

This wonderful site allows debugging and testing regular expressions (many flavors available). An absolute must have in your bookmarks.
Another excellent RegExp tutorial. Don't forget downloading your copy of up-to-date pcretest.exe and pcregrep.exe here
RegExp tutorial: enough to get started
PCRE v8.33 regexp documentation latest available release and currently implemented in AutoIt beta.

SQLitespeed is another feature-rich premier SQLite manager (includes import/export). Well worth a try.
SQLite Expert (freeware Personal Edition or payware Pro version) is a very useful SQLite database manager.
An excellent eBook covering almost every aspect of SQLite3: a must-read for anyone doing serious work.
SQL tutorial (covers "generic" SQL, but most of it applies to SQLite as well)
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jchd,

Well, something happens when we reach 2^50 as can be seen by change to expressing the value in scientific notation - perhaps an internal AutoIt limit?

M23

Public_Domain.png.2d871819fcb9957cf44f4514551a2935.png Any of my own code posted anywhere on the forum is available for use by others without any restriction of any kind

Open spoiler to see my UDFs:

Spoiler

ArrayMultiColSort ---- Sort arrays on multiple columns
ChooseFileFolder ---- Single and multiple selections from specified path treeview listing
Date_Time_Convert -- Easily convert date/time formats, including the language used
ExtMsgBox --------- A highly customisable replacement for MsgBox
GUIExtender -------- Extend and retract multiple sections within a GUI
GUIFrame ---------- Subdivide GUIs into many adjustable frames
GUIListViewEx ------- Insert, delete, move, drag, sort, edit and colour ListView items
GUITreeViewEx ------ Check/clear parent and child checkboxes in a TreeView
Marquee ----------- Scrolling tickertape GUIs
NoFocusLines ------- Remove the dotted focus lines from buttons, sliders, radios and checkboxes
Notify ------------- Small notifications on the edge of the display
Scrollbars ----------Automatically sized scrollbars with a single command
StringSize ---------- Automatically size controls to fit text
Toast -------------- Small GUIs which pop out of the notification area

 

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One approach: Let's assume that internally the calculation is always done with float/double, no matter if the operands are integers or not. Many libraries do not offer an integer power function.
Only at the end the result is cast to integer.
However, crazy casting problems occur, which show up only from 2^49:

ConsoleWrite(StringFormat("%19s : %s (%s)\n", "2 ^ 49",              2^49,              VarGetType(2^49)))
ConsoleWrite(StringFormat("%19s : %s (%s)\n", "2.0 ^ 49",            2.0^49,            VarGetType(2.0^49)))
ConsoleWrite(StringFormat("%19s : %s (%s)\n", "Int(2.0 ^ 49)",       Int(2.0^49),       VarGetType(Int(2.0^49))))
ConsoleWrite(StringFormat("%19s : %s (%s)\n", "Number(2.0 ^ 49, 2)", Number(2.0^49, 2), VarGetType(Number(2.0^49, 2))))

;problem in short:
ConsoleWrite(Int(562949953421312) & @CRLF & Int(562949953421312.0) & @CRLF)

Therefore one has probably drawn in this hard limit for the casting in integer so that these "rounding errors" cannot occur.
However, it is an absolute mystery to me how this comes about, since 2^49 can be represented exactly in IEEE 754 Double.
So there should be no binary rounding problem or something equivalent in question.

If you really want to use an integer power, you can of course also use AutoIt:

For $i = 46 to 50
  $num = 2^Int($i)
  ConsoleWrite($i & @TAB & $num & @TAB & VarGetType($num) & @CRLF)
Next
ConsoleWrite("---------------------" & @CRLF)

For $i = 46 to 50
  $num = pow(2, $i)
  ConsoleWrite($i & @TAB & $num & @TAB & VarGetType($num) & @CRLF)
Next

Func pow($iE, $iP)
    If $iP = 0 Then Return 1
    If $iP = 1 Then Return $iE

    Local $iT = pow($iE, BitShift($iP, 1))
    If Mod($iP, 2) = 0 Then Return $iT * $iT

    Return $iE * $iT * $iT
EndFunc

 

Edited by AspirinJunkie
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It's more mystery of the number 49 not 50.

If we change script slightly (Step 1):

Global $var
For $i = 0 To 102 Step 1
;~         Local $var = Number(3 + 2 ^ $i)
        $var = Number(3 + 2 ^ $i)
        ConsoleWrite($i & "/VarGetType(" & VarGetType($var) & ")/Binary(" & Binary($var) & ")/IsFloat(" & IsFloat($var) & ")/String(" & String($var) & ")")
        ConsoleWrite(@CRLF)
Next

we can see, that change from INT64 to Double is for $i = 49.

But it is still mystery...

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There is a version without "^":

Global $var, $prod = 1
For $i = 1 To 102 Step 1
    $prod = $prod * 2
    $var = Number(3 + $prod)
    ConsoleWrite($i & "/VarGetType(" & VarGetType($var) & ")/Binary(" & Binary($var) & ")/IsFloat(" & IsFloat($var) & ")/String(" & String($var) & ")")
    ConsoleWrite(@CRLF)
Next

No 49 mystery.

But for $i = 63 there is another problem. $var should be Double, but instead is negative INT64.

And more: $var = 3 for $i > 63

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17 minutes ago, Krsta said:

But for $i = 63 there is another problem. $var should be Double, but instead is negative INT64.

And more: $var = 3 for $i > 63

That is integer overflow because you operate on integers. Very few languages have guards against that.

It doesn't occur with ^ since (I believe) the operation in this case is first done with the FP unit before being cast to Int.

You can get a similar integer overflow with addition:

Local $n = 9223372036854775807  ; max positive int64
ConsoleWrite($n & @TAB & VarGetType($n) & @LF)
$n += 1
ConsoleWrite($n & @TAB & VarGetType($n) & @LF)

As usual: know the data you operate on.

Edited by jchd

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SQL tutorial (covers "generic" SQL, but most of it applies to SQLite as well)
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;just for fun

ConsoleWrite(_pow(2,49)&@CRLF)
ConsoleWrite(_pow(2,50)&@CRLF)
ConsoleWrite(_pow(2,62)&@CRLF)

ConsoleWrite(_pow(2.0,63));<~~cuts off the end of the number 


Func _pow($a,$b)
    if $a=0 or $b<0 then return 0
    if $b=0 or $a=1 then return 1
    if $a<0 then $a= -$a
    
    Local $result=$a

    While $b>1
        $result*=$a
        $b-=1
    WEnd
    Return $result

EndFunc

I was kinda interested in this so I been playing around with it for a bit.  I knew when I started that the pow function in c++ takes doubles as params and returns a double.  That and the difference between 2^49 = 15 digits and 2^50=16 digits.  Apparently a double can only be 15 digits long so once the return value of the pow is greater than 15 digits then some precision is lost.  As you can see from the picture 2^50 = 1,125,899,906,842,624 the return value of  pow(2,50) = 1.12589990684262e+15.  The 4 gets cut off and I'm assuming that nothing can be done about that unless you write a custom function.  Then you can see when I cast to an int it rounds up to 1,125......625 for some reason.  IDK just my 2 cents.

 

pow.png

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53 minutes ago, markyrocks said:

Apparently a double can only be 15 digits long so once the return value of the pow is greater than 15 digits then some precision is lost.  As you can see from the picture 2^50 = 1,125,899,906,842,624 the return value of  pow(2,50) = 1.12589990684262e+15.  The 4 gets cut off and I'm assuming that nothing can be done about that unless you write a custom function.

This is only due to the implicit string conversion because of the presentation in the messagebox.
You can force to print the number completely instead of the scientific notation with StringFormat:

$i = 2.0^50
MsgBox(0,"", StringFormat("%30f", $i))

 

58 minutes ago, markyrocks said:

Then you can see when I cast to an int it rounds up to 1,125......625 for some reason.

That's the whole point.
As I wrote above, this problem does not affect 2^50 but already 2^49 where 562,949,953,421,312.0 is cast to 562,949,953,421,313
So the real problem is the conversion to integer and probably that's why they refrained from casting to integer above 2^48.

The question is where exactly is the problem with the internal type conversion as it is obviously also used in Int(). The problematic numbers can all be mapped completely and without rounding errors in IEEE754 double precision. Therefore, no problems with the conversion are actually to be expected.

C/C++ (where AutoIt was written) does not show the same behavior:

#include <iostream>

using namespace std;

int main()
{
    double f = 562949953421312.0;
    long long iInt1 = (long long)f;
    long long iInt2 = static_cast<long long>(f);
    
    cout<<iInt1<<"\n"<<iInt2;
}

 

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After closer look, the behavior is correct. The double format has 52 bit of mantissa (while I wrongly seemed to recall it has a few more). The bit sign is separate, hence the mantissa represents the absolute value (after scaling). Since zero has a separate (fractional) representation the 52 bit of mantissa can represent one more than 52 bits of integral types.

As a consequence integral values in [-(2^53), 2^53] can be stored exactly as integers in the mantissa. Any integral value outside that interval will be stored as fractional. EDIT: except integral powers of 2 in [2^54, 2^1023], where the mantissa is exactly 1.

Here's a breakout of values around the limit. You can see that 9007199254740993 can't be represented exactly.

ULPs(0)
ULPs(2^53-1)
ULPs(2^53)
ULPs(2^53+1)

Result:

Input value = 0
FP (binary) = 0x0000000000000000
Sign        = +
Exponent    = -1023
Scaling     = 2^-1023 = 1/89884656743115795386465259539451236680898848947115328636715040578866337902750481566354238661203768010560056939935696678829394884407208311246423715319737062188883946712432742638151109800623047059726541476042502884419075341171231440736956555270413618581675255342293149119973622969239858152417678164812112068608
Mantissa    = 1

Nearby exact values (computed from FP bits)
PrePrevious    = +0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011
Previous       = +0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011
Value          = +0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011
Next           = +0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011
NextNext       = +0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011

==================================

Input value = 9.00719925474099e+15
FP (binary) = 0x433FFFFFFFFFFFFF
Sign        = +
Exponent    = 52
Scaling     = 2^52 = 4503599627370496
Mantissa    = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024 + 1/2048 + 1/4096 + 1/8192 + 1/16384 + 1/32768 + 1/65536 + 1/131072 + 1/262144 + 1/524288 + 1/1048576 + 1/2097152 + 1/4194304 + 1/8388608 + 1/16777216 + 1/33554432 + 1/67108864 + 1/134217728 + 1/268435456 + 1/536870912 + 1/1073741824 + 1/2147483648 + 1/4294967296 + 1/8589934592 + 1/17179869184 + 1/34359738368 + 1/68719476736 + 1/137438953472 + 1/274877906944 + 1/549755813888 + 1/1099511627776 + 1/2199023255552 + 1/4398046511104 + 1/8796093022208 + 1/17592186044416 + 1/35184372088832 + 1/70368744177664 + 1/140737488355328 + 1/281474976710656 + 1/562949953421312 + 1/1125899906842624 + 1/2251799813685248 + 1/4503599627370496

Nearby exact values (computed from FP bits)
PrePrevious    = +9007199254740989
Previous       = +9007199254740990
Value          = +9007199254740991
Next           = +9007199254740992
NextNext       = +9007199254740994

==================================

Input value = 9.00719925474099e+15
FP (binary) = 0x4340000000000000
Sign        = +
Exponent    = 53
Scaling     = 2^53 = 9007199254740992
Mantissa    = 1

Nearby exact values (computed from FP bits)
PrePrevious    = +9007199254740990
Previous       = +9007199254740991
Value          = +9007199254740992
Next           = +9007199254740994
NextNext       = +9007199254740996

==================================

Input value = 9.00719925474099e+15
FP (binary) = 0x4340000000000000
Sign        = +
Exponent    = 53
Scaling     = 2^53 = 9007199254740992
Mantissa    = 1

Nearby exact values (computed from FP bits)
PrePrevious    = +9007199254740990
Previous       = +9007199254740991
Value          = +9007199254740992
Next           = +9007199254740994
NextNext       = +9007199254740996

 

Edited by jchd

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6 minutes ago, jchd said:

After closer look, the behavior is correct.
[...]
As a consequence integral values in [-(2^53), 2^53] can be stored exactly as integers in the mantissa.

The behavior occurs already at 2^49 and not only at 2^53.
Also the conversion problem of Int().

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Ha yes, that.

You're correct that the conversion from FP to Int64 goes wrong above 2^48, didn't notice that before. And it actually is a bug.

Local $n
For $i = 47 To 54
    $n = 2^$i
    ConsoleWrite($i & @TAB & StringFormat("%20s", Int($n)) & @TAB & StringFormat("%20.1f", $n) & @TAB & (IsFloat($n) ? "Fractional" : "Integral") & @TAB & VarGetType($n) & @LF)
Next

Shows that Int(2^49) and beyond yields an odd result, trivially wrong.

47       140737488355328       140737488355328.0    Integral    Int64
48       281474976710656       281474976710656.0    Integral    Int64
49       562949953421313       562949953421312.0    Integral    Double
50      1125899906842625      1125899906842624.0    Integral    Double
51      2251799813685249      2251799813685248.0    Integral    Double
52      4503599627370497      4503599627370496.0    Integral    Double
53      9007199254740993      9007199254740992.0    Integral    Double
54     18014398509481985     18014398509481984.0    Integral    Double

 

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Thanks for the ticket.

My advice when one has clues that values can get unusually large: use the BigNum UDF.

It isn't a full-fledged arbitrary precision library but reveals much more stable in most use cases than FP when at least one value gets quite large, e.g. 3^157 + 43 or when you really have to deal with many decimals.

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SQLitespeed is another feature-rich premier SQLite manager (includes import/export). Well worth a try.
SQLite Expert (freeware Personal Edition or payware Pro version) is a very useful SQLite database manager.
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SQL tutorial (covers "generic" SQL, but most of it applies to SQLite as well)
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12 hours ago, AspirinJunkie said:

This is only due to the implicit string conversion because of the presentation in the messagebox.

 

 

Good to know.  For some reason I thought that some data had been lost after a double became so big due to some memory limitation or etc.  I did find it odd that the int cast rounded to 5  so I had a feeling the data was there bc it would have been a zero otherwise but just kinda fell through the cracks in my thought process.   

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