Rnd Function

Returns a Single containing a pseudo-random number.

Syntax

Rnd[(number)]

Parameters

• number - Optional. Single or any valid numeric expression.

Return Value

Returns a Single value greater than or equal to 0 and less than 1.

The behavior depends on the number argument:

Remarks

The Rnd function returns a pseudo-random number from a deterministic sequence. It is used for generating random values in games, simulations, testing, and sampling.

Each new number is the product of the previous number times a constant (a) plus another constant (c). The result is kept modulo a third number (m), which is invariably the width of its ‘long’ integer size (or fraction thereof). Standard examples are m=2^64, 2^48 or 2^32. Mathematically, this is represented as: r(i+1)=r(i)*a+c (mod m), where r(0) is the ‘seed’ value.

Although the algorithm in use can be obtained from analyzing a string of outputs from the generator and deducing the values of a, c and M. Microsoft has published their constants on their web site and it turns out that they use an LCPRNG with:

```a = 16598013, c = 2820163 and m=2^24 = 16777216

[Reference](http://www.noesis.net.au/main/Resources/Resources/prng_files/vba_prng.html)

**Important Notes**:
- Returns values in range [0, 1) - includes 0, excludes 1
- Same seed produces same sequence (deterministic)
- Use `Randomize` statement to initialize random number generator with time-based seed
- Without `Randomize`, same sequence is generated each program run
- Passing negative number sets seed for reproducible sequences
- Passing 0 returns last generated number (useful for debugging)

**Common Usage Pattern**:

vb Randomize ' Initialize with time-based seed x = Rnd ' Get random number 0 <= x < 1

**Generating Random Integers**:

vb ' Random integer from min to max (inclusive) randomInt = Int((max - min + 1) * Rnd + min)

**Seeding for Reproducibility**:

vb Rnd -1 ' Reset to use seed Randomize seed ' Set specific seed x = Rnd ' Get first number in sequence

## Typical Uses

1. **Games**: Generate random positions, events, or outcomes
2. **Simulations**: Create random data for Monte Carlo simulations
3. **Testing**: Generate random test data
4. **Sampling**: Random selection from datasets
5. **Shuffling**: Randomize order of items
6. **Password Generation**: Create random character sequences
7. **Animation**: Random movement or effects
8. **Data Masking**: Generate random replacement values

## Basic Examples

### Example 1: Simple Random Number

vb ' Generate random number between 0 and 1 Randomize Dim randomValue As Single randomValue = Rnd() ' e.g., 0.7234567

### Example 2: Random Integer in Range

vb ' Generate random integer from 1 to 100 Randomize Dim randomInt As Integer randomInt = Int(Rnd * 100) + 1

### Example 3: Random Dice Roll

vb ' Simulate rolling a six-sided die Randomize Dim diceRoll As Integer diceRoll = Int(Rnd * 6) + 1 ' Returns 1-6

### Example 4: Random Selection

vb ' Select random item from array Randomize Dim items(5) As String Dim randomIndex As Integer

items(0) = "Apple" items(1) = "Banana" items(2) = "Cherry" items(3) = "Date" items(4) = "Elderberry"

randomIndex = Int(Rnd * 5) MsgBox "Selected: " & items(randomIndex)

## Common Patterns

### Pattern 1: `RandomInteger`

vb Function RandomInteger(minValue As Long, maxValue As Long) As Long ' Generate random integer in range [minValue, maxValue] RandomInteger = Int((maxValue - minValue + 1) * Rnd + minValue) End Function

### Pattern 2: `RandomDouble`

vb Function RandomDouble(minValue As Double, maxValue As Double) As Double ' Generate random double in range [minValue, maxValue) RandomDouble = (maxValue - minValue) * Rnd + minValue End Function

### Pattern 3: `RandomBoolean`

vb Function RandomBoolean() As Boolean ' Generate random True/False RandomBoolean = (Rnd >= 0.5) End Function

### Pattern 4: `RandomChoice`

vb Function RandomChoice(items As Variant) As Variant ' Select random item from array Dim index As Integer

If Not IsArray(items) Then Err.Raise 5, , "Parameter must be an array" End If

index = Int(Rnd * (UBound(items) - LBound(items) + 1)) + LBound(items) RandomChoice = items(index) End Function

### Pattern 5: `ShuffleArray`

vb Sub ShuffleArray(arr As Variant) ' Randomly shuffle array elements (Fisher-Yates algorithm) Dim i As Integer Dim j As Integer Dim temp As Variant

For i = UBound(arr) To LBound(arr) + 1 Step -1 j = Int(Rnd * (i - LBound(arr) + 1)) + LBound(arr)

temp = arr(i) arr(i) = arr(j) arr(j) = temp Next i End Sub

### Pattern 6: `RandomString`

vb Function RandomString(length As Integer, _ Optional chars As String = "ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789") As String ' Generate random string of specified length Dim i As Integer Dim result As String Dim index As Integer

result = ""

For i = 1 To length index = Int(Rnd * Len(chars)) + 1 result = result & Mid(chars, index, 1) Next i

RandomString = result End Function

### Pattern 7: `RandomColor`

vb Function RandomColor() As Long ' Generate random RGB color Dim r As Integer Dim g As Integer Dim b As Integer

r = Int(Rnd * 256) g = Int(Rnd * 256) b = Int(Rnd * 256)

RandomColor = RGB(r, g, b) End Function

### Pattern 8: `RandomPercentage`

vb Function RandomPercentage(probability As Double) As Boolean ' Return True with specified probability (0.0 to 1.0) RandomPercentage = (Rnd < probability) End Function

### Pattern 9: `RandomDate`

vb Function RandomDate(startDate As Date, endDate As Date) As Date ' Generate random date between start and end dates Dim daysDiff As Long Dim randomDays As Long

daysDiff = DateDiff("d", startDate, endDate) randomDays = Int(Rnd * (daysDiff + 1))

RandomDate = DateAdd("d", randomDays, startDate) End Function

### Pattern 10: `WeightedRandom`

vb Function WeightedRandom(weights() As Double) As Integer ' Select index based on weighted probabilities Dim total As Double Dim i As Integer Dim randomValue As Double Dim cumulative As Double

' Calculate total weight total = 0 For i = LBound(weights) To UBound(weights) total = total + weights(i) Next i

' Generate random value randomValue = Rnd * total

' Find corresponding index cumulative = 0 For i = LBound(weights) To UBound(weights) cumulative = cumulative + weights(i) If randomValue < cumulative Then WeightedRandom = i Exit Function End If Next i

WeightedRandom = UBound(weights) End Function

## Advanced Usage

### Example 1: Random Number Generator Class

vb ' Comprehensive random number generator with multiple distributions Class RandomGenerator Private m_seed As Long Private m_seeded As Boolean

Public Sub Initialize(Optional seed As Long = 0) If seed <> 0 Then m_seed = seed Rnd -1 Randomize seed m_seeded = True Else Randomize m_seeded = False End If End Sub

Public Function NextDouble() As Double ' Get next random double [0, 1) NextDouble = Rnd End Function

Public Function NextInteger(minValue As Long, maxValue As Long) As Long ' Get random integer [minValue, maxValue] If minValue > maxValue Then Err.Raise 5, , "minValue must be <= maxValue" End If

NextInteger = Int((maxValue - minValue + 1) * Rnd + minValue) End Function

Public Function NextBoolean() As Boolean ' Get random boolean NextBoolean = (Rnd >= 0.5) End Function

Public Function NextGaussian(Optional mean As Double = 0, _ Optional stdDev As Double = 1) As Double ' Generate Gaussian (normal) distribution using Box-Muller transform Dim u1 As Double, u2 As Double Dim z0 As Double

u1 = Rnd u2 = Rnd

' Box-Muller transform z0 = Sqr(-2 * Log(u1)) * Cos(2 * 3.14159265358979 * u2)

NextGaussian = mean + stdDev * z0 End Function

Public Function NextBytes(count As Long) As Byte() ' Generate array of random bytes Dim bytes() As Byte Dim i As Long

ReDim bytes(0 To count - 1)

For i = 0 To count - 1 bytes(i) = Int(Rnd * 256) Next i

NextBytes = bytes End Function

Public Sub Reset() ' Reset to original seed if seeded If m_seeded Then Rnd -1 Randomize m_seed Else Randomize End If End Sub

Public Function GetSeed() As Long GetSeed = m_seed End Function End Class

### Example 2: Monte Carlo Simulator

vb ' Monte Carlo simulation for estimating probabilities Module MonteCarloSimulator Public Function EstimatePi(iterations As Long) As Double ' Estimate Pi using Monte Carlo method Dim insideCircle As Long Dim i As Long Dim x As Double, y As Double

Randomize insideCircle = 0

For i = 1 To iterations x = Rnd y = Rnd

If (x * x + y * y) < 1 Then insideCircle = insideCircle + 1 End If Next i

EstimatePi = 4 * (insideCircle / iterations) End Function

Public Function SimulateDiceRolls(numDice As Integer, _ numRolls As Long) As Long() ' Simulate rolling multiple dice and return frequency distribution Dim results() As Long Dim minSum As Integer, maxSum As Integer Dim i As Long, j As Integer Dim sum As Integer

minSum = numDice maxSum = numDice * 6

ReDim results(minSum To maxSum)

Randomize

For i = 1 To numRolls sum = 0 For j = 1 To numDice sum = sum + Int(Rnd * 6) + 1 Next j results(sum) = results(sum) + 1 Next i

SimulateDiceRolls = results End Function

Public Function SimulateStockPrice(startPrice As Double, _ days As Long, _ volatility As Double, _ drift As Double) As Double() ' Simulate stock price using geometric Brownian motion Dim prices() As Double Dim i As Long Dim randomShock As Double

ReDim prices(0 To days) prices(0) = startPrice

Randomize

For i = 1 To days randomShock = (Rnd - 0.5) * 2 ' -1 to 1 prices(i) = prices(i - 1) * (1 + drift + volatility * randomShock) Next i

SimulateStockPrice = prices End Function End Module

### Example 3: Random Data Generator

vb ' Generate random test data for various purposes Class RandomDataGenerator Private m_firstNames() As String Private m_lastNames() As String Private m_emailDomains() As String

Public Sub Initialize() Randomize

m_firstNames = Array("John", "Jane", "Michael", "Sarah", "David", _ "Emily", "James", "Emma", "Robert", "Lisa") m_lastNames = Array("Smith", "Johnson", "Williams", "Brown", "Jones", _ "Garcia", "Miller", "Davis", "Rodriguez", "Martinez") m_emailDomains = Array("gmail.com", "yahoo.com", "hotmail.com", _ "outlook.com", "example.com") End Sub

Public Function GenerateName() As String ' Generate random full name Dim firstName As String Dim lastName As String

firstName = m_firstNames(Int(Rnd * (UBound(m_firstNames) + 1))) lastName = m_lastNames(Int(Rnd * (UBound(m_lastNames) + 1)))

GenerateName = firstName & " " & lastName End Function

Public Function GenerateEmail(Optional name As String = "") As String ' Generate random email address Dim localPart As String Dim domain As String

If name = "" Then localPart = "user" & Int(Rnd * 10000) Else localPart = LCase(Replace(name, " ", ".")) End If

domain = m_emailDomains(Int(Rnd * (UBound(m_emailDomains) + 1)))

GenerateEmail = localPart & "@" & domain End Function

Public Function GeneratePhoneNumber() As String ' Generate random US phone number Dim areaCode As String Dim exchange As String Dim number As String

areaCode = Format(Int(Rnd * 900) + 100, "000") exchange = Format(Int(Rnd * 900) + 100, "000") number = Format(Int(Rnd * 10000), "0000")

GeneratePhoneNumber = "(" & areaCode & ") " & exchange & "-" & number End Function

Public Function GenerateAddress() As String ' Generate random street address Dim streetNumber As String Dim streetNames() As String Dim streetName As String Dim streetTypes() As String Dim streetType As String

streetNames = Array("Main", "Oak", "Maple", "Cedar", "Elm", _ "Washington", "Park", "Lake", "Hill", "Pine") streetTypes = Array("St", "Ave", "Blvd", "Rd", "Ln", "Dr")

streetNumber = Int(Rnd * 9900) + 100 streetName = streetNames(Int(Rnd * (UBound(streetNames) + 1))) streetType = streetTypes(Int(Rnd * (UBound(streetTypes) + 1)))

GenerateAddress = streetNumber & " " & streetName & " " & streetType End Function

Public Function GeneratePassword(length As Integer) As String ' Generate random password with mixed characters Dim chars As String Dim i As Integer Dim result As String Dim index As Integer

chars = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789!@#$%^&*" result = ""

For i = 1 To length index = Int(Rnd * Len(chars)) + 1 result = result & Mid(chars, index, 1) Next i

GeneratePassword = result End Function End Class

### Example 4: Card Deck Shuffler

vb ' Simulate a deck of cards with shuffling Class CardDeck Private Type Card Suit As String Rank As String Value As Integer End Type

Private m_cards() As Card Private m_currentCard As Integer

Public Sub Initialize() Dim suits() As String Dim ranks() As String Dim i As Integer, j As Integer Dim cardIndex As Integer

suits = Array("Hearts", "Diamonds", "Clubs", "Spades") ranks = Array("2", "3", "4", "5", "6", "7", "8", "9", "10", _ "Jack", "Queen", "King", "Ace")

ReDim m_cards(0 To 51) cardIndex = 0

For i = 0 To 3 For j = 0 To 12 m_cards(cardIndex).Suit = suits(i) m_cards(cardIndex).Rank = ranks(j) m_cards(cardIndex).Value = j + 2 cardIndex = cardIndex + 1 Next j Next i

m_currentCard = 0 End Sub

Public Sub Shuffle() ' Shuffle deck using Fisher-Yates algorithm Dim i As Integer Dim j As Integer Dim temp As Card

Randomize

For i = 51 To 1 Step -1 j = Int(Rnd * (i + 1))

temp = m_cards(i) m_cards(i) = m_cards(j) m_cards(j) = temp Next i

m_currentCard = 0 End Sub

Public Function DrawCard() As String ' Draw next card from deck Dim card As Card

If m_currentCard > 51 Then DrawCard = "No cards left" Exit Function End If

card = m_cards(m_currentCard) m_currentCard = m_currentCard + 1

DrawCard = card.Rank & " of " & card.Suit End Function

Public Function CardsRemaining() As Integer CardsRemaining = 52 - m_currentCard End Function

Public Sub Reset() m_currentCard = 0 End Sub End Class

## Error Handling

The `Rnd` function rarely generates errors, but there are some considerations:

**Type Mismatch (Error 13)**:
- Occurs if the optional number parameter cannot be converted to numeric type

Example error handling:

vb On Error Resume Next Dim randomValue As Single randomValue = Rnd(userInput) If Err.Number <> 0 Then MsgBox "Invalid seed value" randomValue = Rnd ' Use default behavior End If On Error GoTo 0 ```

Performance Considerations

• Rnd is very fast - can generate millions of numbers per second
• Not cryptographically secure - don't use for security purposes
• Same seed produces same sequence (deterministic)
• For better randomness, call Randomize at program start
• Calling Randomize frequently can reduce randomness quality
• Consider caching random values if generating many at once

Best Practices

1. Always Randomize: Call Randomize once at program start for non-deterministic behavior
2. Use Seed for Testing: Use fixed seed (negative number) for reproducible test cases
3. Validate Ranges: Check min/max values when generating random integers
4. Avoid Modulo Bias: Use Int(Rnd * n) not Rnd Mod n for uniform distribution
5. Don't Use for Security: Not suitable for passwords, encryption keys, or security tokens
6. Cache Rnd Values: If generating many values, avoid repeated function calls overhead
7. Document Seed Usage: Clearly document when using fixed seeds for reproducibility
8. Test Edge Cases: Verify behavior at range boundaries (min, max values)
9. Use Helper Functions: Wrap Rnd in helper functions for cleaner code
10. Consider Distribution: Understand that Rnd provides uniform distribution

Comparison with Related Functions

Platform and Version Notes

• Available in all versions of VB6 and VBA
• Uses linear congruential generator (LCG) algorithm
• Not cryptographically secure
• Sequence repeats after approximately 16 million numbers
• In VB.NET, replaced by System.Random class
• Randomize uses Timer function by default if no seed provided

Limitations

• Not cryptographically secure (predictable sequence)
• Limited period (sequence repeats after ~16M values)
• No built-in support for other distributions (normal, exponential, etc.)
• Cannot generate random integers directly (requires Int/Floor conversion)
• Thread safety not guaranteed in multi-threaded scenarios
• Quality lower than modern RNGs (Mersenne Twister, etc.)

Related Functions

• Randomize: Initializes the random number generator with a seed
• Int: Returns the integer portion of a number (used to convert Rnd to integer range)
• Timer: Returns seconds since midnight (often used with Randomize)