Iterators
The overload Operators For, Next, and Step, allowing to construct User-Defined Types Iterators (instead of only intrinsic scalar types iterators) for a For...Next loop
Syntax (declaration)
{ Type | Class | Union } typename
' `For...Next`' statement with implicit step (1st version of operators)
Declare Operator For ( )
Declare Operator Next ( [ ByRef | ByVal ] cond As typename ) As Integer
Declare Operator Step ( )
' `For...Next`' statement with explicit step (2nd version of operators)
Declare Operator For ( [ ByRef | ByVal ] stp As typename )
Declare Operator Next ( [ ByRef | ByVal ] cond As typename, [ ByRef | ByVal ] stp As typename ) As Integer
Declare Operator Step ( [ ByRef | ByVal ] stp As typename )
End { Type | Class | Union }
Usage
For iterator [ As typename ] = start_value To end_value [ Step step_value ]
[ ...statements... ]
Next
The first version of operators is used if no `step_value` is given in the `For...Next` statement.
If a `step_value` is given, the second version is used and a step object (initialized with `step-value`) is passed through the `stp` parameter:
- to `Operator For` because eventual additional initialization may use it,
- to `Operator Next` because testing for iterating end may depend on it,
- to `Operator Step` to increment the iterator object.
Both versions of the operators can coexist (thanks to member overloading) in the same user-defined type (to be able to both use and not use the explicit increment in `For...Next` statements of the user code).
Parameters
`(including arguments)`
`typename`
name of the `Type`, `Class`, or `Union`
`stp`, `step_value`
a `typename` object used as an incremental value
`iterator`
a `typename` object used as an iterator
`cond`, `end_value`
a `typename` object used as a loop-terminating value
`start_value`
a `typename` object used to copy construct or assign to the iterator initially
Description
`Operator For`, `Operator Next` and `Operator Step` can be overloaded in user-defined type definitions to allow objects of that type to be used as iterators and step values in `For...Next` loops (instead of the pre-defined for intrinsic scalar types).
As all non-static member procedures, the 3 operators have passed a hidden `This` parameter that allows to access by reference to the iterator object (initialized to the `start_value` argument value from the `For...Next` statement).
The `cond` parameter of the `Operator Next` allows to access the `end_value` argument value from the `For...Next` statement.
If a `step_value` is given (as argument) in the `For...Next` statement, the `stp` parameter allows to access this value in the 3 operators.
Note: If no `step_value` is given in the `For...Next` statement (implicit step), the user-defined type must have a default constructor (implicit or explicit) or a conversion constructor. It is a bug at the moment because if the user defines a default constructor, the compiler does not even use it when initializing the `For...Next` loop!
Operator For
`Operator For` is called once immediately after copy constructing or assigning to the iterator object (with the `start_value`), constructing the end object (with the `end_value`), and constructing the step object (with `step_value` if defined in the `For...Next` statement).
`Operator For` allows to perform any additional initialization needed in preparation for the loop.
Operator Next
`Operator Next` is called every time the iterator object needs to be checked against the end value. This happens immediately after the call to the `Operator For`, and then immediately after any calls to the `Operator Step`.
`Operator Next` should return zero (0) if the loop should be terminated, or non-zero if the loop should continue iterating.
The first time `Operator Next` is called, no statements in the `For...Next` body have been executed yet.
`Operator Next` also allows to perform some processing before the execution of all statements in the `For...Next` body.
Operator Step
`Operator Step` is called to increment the iterator object immediately after all statements in the `For...Next` body are executed.
Advanced usage
The above description seems to imply that the 3 arguments `start_value`, `end_value`, and `step_value` must be of the same type as the `iterator` (this is the more obvious use), but it is not quite true:
- The `start_value`, `end_value`, and `step_value` arguments can be of any type (of different types among themselves and also of different types from the one of the `iterator`).
- The only constraint is that the `iterator` could be constructed (in case of local `iterator`) or assigned (in case of global `iterator`) from the `start_value` argument (because the `iterator` is implicitly constructed or assigned under the hood).
- Similarly the other arguments `end_value`, and `step_value` must be able to be converted into objects of the same type as the `iterator`.
Algorithm
`For...Next` loop algorithm around the 3 overload operators:

    '                       FOR...NEXT loop
    '                              V
    '                              |
    '            constructing/assigning iterator object
    '       (This = start_value from For...Next statement)
    '                              |
    '                   constructing end object
    '       (cond = end_value from For...Next statement)
    '                              |
    '                   if step_value is defined >---------------------.
    '                            else                                  :
    '                              v                                   v
    '                              :                        constructing step object
    '                              :               (stp = step_value from For...Next statement)
    '                              :                                   :
    '                              :<----------------------------------'
    '                              |
    '                    calling Operator For
    '                              |
    '     .----------------------->|
    '     |                        |
    '     |              calling Operator Next
    '     |     (if end-condition verified: =0 returned) >-------------.
    '     |               (else: <>0 returned)                         |
    '     |                        v                                   |
    '     |                        |                                   |
    '     |            executing For...Next body                       |
    '     |                        |                                   |
    '     |              calling Operator Step                         |
    '     |                        |                                   |
    '     '------------------------'                                   |
    '                                                                  |
    '                                                                  V

Example
Type for iterating through screen resolutions, with implicit step-value:
`
Type screenResolution
' user interface
Declare Constructor (ByVal colorBit As Long)
Declare Property colorDepth () As Long
Declare Property screenWidth () As Long
Declare Property screenHeigth () As Long
' overload iteration operators when Step is not defined in For...Next statement
Declare Operator For ()
Declare Operator Next (ByRef iterateCondition As screenResolution) As Integer
Declare Operator Step ()
' internal variables
Dim As Long colorBit, resolutionWH
End Type
Constructor screenResolution (ByVal colorBit As Long)
This.colorBit = colorBit
End Constructor
Property screenResolution.colorDepth () As Long
Return This.colorBit
End Property
Property screenResolution.screenWidth () As Long
Return HiWord(This.resolutionWH)
End Property
Property screenResolution.screenHeigth () As Long
Return LoWord(This.resolutionWH)
End Property
Operator screenResolution.For ()
This.resolutionWH = ScreenList(This.colorBit)
End Operator
Operator screenResolution.Next (ByRef iterateCondition As screenResolution) As Integer
While This.resolutionWH = 0
If This.colorBit < iterateCondition.colorBit Then
This.colorBit += 1
This.resolutionWH = ScreenList(This.colorBit)
Else
Exit While
End If
Wend
Return (This.resolutionWH <> iterateCondition.resolutionWH)
End Operator
Operator screenResolution.Step ()
This.resolutionWH = ScreenList()
End Operator
Print "Screen resolutions supported within [1 bpp , 64 bpp]:"
For iterator As screenResolution = screenResolution(1) To screenResolution(64)
Print " " & iterator.colorDepth & " bpp ",
Print ":" & iterator.screenWidth & "x" & iterator.screenHeigth
Next iterator
Print "End of supported screen resolutions"
Sleep
`
Output example:

    Screen resolutions supported within [1 bpp , 64 bpp]:
    	24 bpp    :320x200
    	24 bpp    :320x240
    	24 bpp    :400x300
    	24 bpp    :512x384
    	24 bpp    :640x400
    	24 bpp    :640x480
    	24 bpp    :800x600
    	24 bpp    :1024x768
    	24 bpp    :1152x864
    	24 bpp    :1280x600
    	24 bpp    :1280x720
    	24 bpp    :1280x768
    	24 bpp    :1280x800
    	24 bpp    :1280x960
    	24 bpp    :1280x1024
    	24 bpp    :1360x768
    	24 bpp    :1366x768
    	24 bpp    :1400x1050
    	24 bpp    :1440x900
    	24 bpp    :1600x900
    	24 bpp    :1680x1050
    	24 bpp    :1920x1080
    	32 bpp    :320x200
    	32 bpp    :320x240
    	32 bpp    :400x300
    	32 bpp    :512x384
    	32 bpp    :640x400
    	32 bpp    :640x480
    	32 bpp    :800x600
    	32 bpp    :1024x768
    	32 bpp    :1152x864
    	32 bpp    :1280x600
    	32 bpp    :1280x720
    	32 bpp    :1280x768
    	32 bpp    :1280x800
    	32 bpp    :1280x960
    	32 bpp    :1280x1024
    	32 bpp    :1360x768
    	32 bpp    :1366x768
    	32 bpp    :1400x1050
    	32 bpp    :1440x900
    	32 bpp    :1600x900
    	32 bpp    :1680x1050
    	32 bpp    :1920x1080
    End of supported screen resolutions

Type for iterating through fractions, with explicit step-value used in the 3 operators:
(improved example compared to the one of `Operator Step` page)
`
Type fraction
' user interface
Declare Constructor (ByVal n As Integer, ByVal d As Integer)
Declare Operator Cast () As String
' overload iteration operators when Step is defined in For...Next statement
Declare Operator For (ByRef iterateStep As fraction)
Declare Operator Next (ByRef iterateCondition As fraction, ByRef iterateStep As fraction) As Integer
Declare Operator Step (ByRef step_var As fraction)
' internal variables and cast operator
As Integer num, den
Declare Operator Cast () As Double
End Type
Constructor fraction (ByVal n As Integer, ByVal d As Integer)
this.num = n
this.den = d
End Constructor
Operator fraction.Cast () As String
' search for the highest common factor (a) between numerator and denominator
Dim As Integer a = Abs(This.num), b = Abs(This.den)
If a <> 0 Then
While a <> b
If a > b Then
a -= b
Else
b -= a
End If
Wend
Else
a = 1
End If
' reduce the fraction
Return num \ a & "/" & den \ a
End Operator
Operator fraction.Cast () As Double
Return This.num / This.den
End Operator
Operator fraction.For (ByRef iterateStep As fraction)
' search for the least common multiple (a) between the two denominators
Dim As Integer a = Abs(This.den), b = Abs(iterateStep.den), c = a, d = b
While a <> b
If a > b Then
b += d
Else
a += c
End If
Wend
' align at the same denominator the 2 fractions
This.num *= a \ This.den
This.den = a
iterateStep.num *= a \ iterateStep.den
iterateStep.den = a
End Operator
Operator fraction.Next (ByRef iterateCondition As fraction, ByRef iterateStep As fraction) As Integer
If iterateStep.num < 0 Or iterateStep.den < 0 Then
Return This >= iterateCondition
Else
Return This <= iterateCondition
End If
End Operator
Operator fraction.Step (ByRef iterateStep As fraction)
This.num += iterateStep.num
End Operator
Print "iteration from 1/8 to 1/2 by step of 1/12:"
For iterator As fraction = fraction(1, 8) To fraction(1, 2) Step fraction(1, 12)
Print " " & iterator;
Next
Print
Print
Print "iteration from 7/10 to -8/5 by step of -8/15:"
For iterator As fraction = fraction(7, 10) To fraction(-8, 5) Step fraction(-8, 15)
Print " " & iterator;
Next
Print
Sleep
`
Output:

    iteration from 1/8 to 1/2 by step of 1/12:
    	1/8    5/24    7/24    3/8    11/24

    iteration from 7/10 to -8/5 by step of -8/15:
    	7/10    1/6    -11/30    -9/10    -43/30

See also

- `For...Next`
- `Operator`