VBA number :: min to max


VBA numbers - integer to floating-point


VBA and Excel specifications state the limits of numbers used in the application environment.


This module provides formulas written in VBA code, to return the minimum and maximum values (positive and negative) of:

as specified in Excel VBA. The values for double precision floating point numbers are also applicable to formulas in Excel.


All formulas are binary (base 2) as depicted in code 1.



Code 1: VBA number :: minimum, maximum value demonstrator.

Sub DemoVBAnumbers()

Dim iMin As Integer
Dim iMax As Integer

Dim lMin As Long
Dim lMax As Long

Dim lPtrMin As LongPtr
Dim lPtrMax As LongPtr

Dim sPositiveMin As Single, sPositiveMax As Single
Dim sNegativeMin As Single, sNegativeMax As Single

Dim dPositiveMin As Double, dPositiveMax As Double
Dim dNegativeMin As Double, dNegativeMax As Double

    Debug.Print vbNewLine & "==============================="
    Debug.Print "Time: " & Format(Time, "hh:mm:ss am/pm")
' Integer (2 bytes)
        Debug.Print "Integer ==="
    iMin = -2 ^ 15
        Debug.Print vbTab & "iMin:: [-2 ^ 15] = " & iMin & vbTab & "  (" & Format(iMin, "#,##0") & ")"
    iMax = 2 ^ 15 - 1
        Debug.Print vbTab & "iMax:: [2 ^ 15 - 1] = " & iMax & vbTab & vbTab & "  (" & Format(iMax, "#,##0") & ")"

' Long (4 bytes)
        Debug.Print vbNewLine & "Long ==="
    lMin = -2 ^ 31
        Debug.Print vbTab & "lMin:: [-2 ^ 31] = " & lMin & vbTab & "  (" & Format(lMin, "#,##0") & ")"
    lMax = 2 ^ 31 - 1
        Debug.Print vbTab & "lMax:: [2 ^ 31 - 1] = " & lMax & vbTab & "  (" & Format(lMax, "#,##0") & ")"

' LongPtr
        Debug.Print vbNewLine & "LongPtr (in a 64 bit environment) ==="
        ' Long integer on 32-bit systems
        ' LongLong integer on 64-bit systems
    lPtrMin = -2 ^ 63
        Debug.Print vbTab & "lPtrMin:: [-2 ^ 63] = " & lPtrMin & vbTab & "  (" & Format(lPtrMin, "#,##0") & ")"
    lPtrMax = 2 ^ 63 - 1
        Debug.Print vbTab & "lPtrMax:: [2 ^ 63 - 1] = " & lPtrMax & vbTab & "  (" & Format(lPtrMax, "#,##0") & ")"

' Single precision floating point (4 bytes, 32 bits)
        Debug.Print vbNewLine & "Single ==="
    sPositiveMin = 2 ^ -149
        Debug.Print vbTab & "sPositiveMin:: [2 ^ -149] = " & sPositiveMin
    sPositiveMax = (1 - 2 ^ -24) * 2 ^ 128
        Debug.Print vbTab & "sPositiveMax:: [(1 - 2 ^ -24) * 2 ^ 128] = " & sPositiveMax

        Debug.Print vbNewLine
    sNegativeMin = -(1 - 2 ^ -24) * 2 ^ 128
        Debug.Print vbTab & "sNegativeMin:: [-(1 - 2 ^ -24) * 2 ^ 128] = " & sNegativeMin
    sNegativeMax = -2 ^ -149
        Debug.Print vbTab & "sNegativeMax:: [-2 ^ -149] = " & sNegativeMax

' Double precision floating point (8 bytes, 64 bits)
        Debug.Print vbNewLine & "Double ==="
    dPositiveMin = 2 ^ -1074
        Debug.Print vbTab & "dPositiveMin:: [2 ^ -1074] = " & dPositiveMin
    dPositiveMax = (1 + (1 - 2 ^ -52)) * 2 ^ 1023
        Debug.Print vbTab & "dPositiveMax:: [(1 + (1 - 2 ^ -52)) * 2 ^ 1023] = " & dPositiveMax

        Debug.Print vbNewLine
    dNegativeMin = -(1 + (1 - 2 ^ -52)) * 2 ^ 1023
        Debug.Print vbTab & "dNegativeMin:: [-(1 + (1 - 2 ^ -52)) * 2 ^ 1023] = " & dNegativeMin
    dNegativeMax = -2 ^ -1074
        Debug.Print vbTab & "dNegativeMax:: [-2 ^ -1074] = " & dNegativeMax

Stop    ' halt code to view Locals Window

End Sub


The output from code 1 is sent to the Immediate Window, see figure 1, and the Locals Window in figure 2.


xlf-vba-number-immediate
Fig 1: Immediate Window showing the limit values for VBA number types: integer, long, longptr (longlong), single, and double

Single precision floating point numbers occupy 32 bits (4 bytes) of computer memory. The sign occupies 1 bit, the exponent 8 bits, and the fraction 23 bits. The fraction component has a maximum of 7 digits.


Double precision floating point numbers occupy 64 bits (8 bytes) of computer memory. The sign occupies 1 bit, the exponent 11 bits, and the fraction 52 bits. The fraction component has a maximum of 15 digits.


xlf-vba-number-locals
Fig 2: Locals Window showing the limit values for VBA number types: integer, long, longptr, single, and double


All numbers in Excel, as distinct from VBA, are double precision floating point, and the Excel specifications state that the:


Fig 3: Excel Web App #1 - worksheet estimation of number limits

References


IEEE, IEEE 754: Standard for Binary Floating-Point Arithmetic Accessed: 26 April 2017

Microsoft - support, Excel specifications and limits Accessed: 26 April 2017

Microsoft - msdn, VBA data type summary Accessed: 26 April 2017

O'Connor I, (2011), VBA data types pdf [19KB]. Accessed 22 July 2917