_What are all the format options for sprintf_  

_Could you provide this in the form of a prompt (with all the same information you just produced) that OpenAI Codex could implement as a class, and with test cases it can use for unit tests_

# C# sprintf Implementation Prompt for OpenAI Codex

Create a C# class called `SprintfFormatter` that implements C-style sprintf formatting functionality. The class should provide a static method `Format(string format, params object[] args)` that mimics the behavior of C's sprintf function.

## Required Format Specifiers to Implement

### Basic Integer Formats
- `%d`, `%i` - signed decimal integer
  - C# equivalent: `{0}` or `{0:D}` or `.ToString()` or `.ToString("D")`
- `%u` - unsigned decimal integer
  - C# equivalent: `{0}` or `{0:D}` or `.ToString()` or `.ToString("D")`
- `%o` - unsigned octal integer
  - C# equivalent: No direct equivalent, use `Convert.ToString(value, 8)`
- `%x` - unsigned hexadecimal (lowercase a-f)
  - C# equivalent: `{0:x}` or `.ToString("x")`
- `%X` - unsigned hexadecimal (uppercase A-F)
  - C# equivalent: `{0:X}` or `.ToString("X")`

### Floating-Point Formats
- `%f`, `%F` - decimal floating point
  - C# equivalent: `{0:F}` or `.ToString("F")`
- `%e` - scientific notation (lowercase e)
  - C# equivalent: `{0:e}` or `.ToString("e")`
- `%E` - scientific notation (uppercase E)
  - C# equivalent: `{0:E}` or `.ToString("E")`
- `%g` - shortest of %f or %e
  - C# equivalent: `{0:G}` or `.ToString("G")`
- `%G` - shortest of %F or %E
  - C# equivalent: `{0:G}` or `.ToString("G")`

### Character and String Formats
- `%c` - single character
  - C# equivalent: `{0}` or `.ToString()`
- `%s` - string of characters
  - C# equivalent: `{0}` or `.ToString()`
- `%%` - literal percent sign
  - C# equivalent: `{{` or `}}` in string.Format, or literal `%` in interpolation

### Pointer Format
- `%p` - pointer address (format as hexadecimal with 0x prefix)
  - C# equivalent: No direct equivalent, use custom formatting with IntPtr

## Width and Precision Modifiers
- `%10d` - minimum width of 10 characters (right-aligned)
  - C# equivalent: `{0,10}` or `.ToString().PadLeft(10)`
- `%-10d` - left-aligned in 10-character field
  - C# equivalent: `{0,-10}` or `.ToString().PadRight(10)`
- `%010d` - zero-padded to 10 characters
  - C# equivalent: `{0:D10}` or `.ToString("D10")`
- `%.2f` - 2 decimal places for floating point
  - C# equivalent: `{0:F2}` or `.ToString("F2")`
- `%10.2f` - 10 characters wide, 2 decimal places
  - C# equivalent: `{0,10:F2}` or `.ToString("F2").PadLeft(10)`
- `%-10.2f` - left-aligned, 10 characters wide, 2 decimal places
  - C# equivalent: `{0,-10:F2}` or `.ToString("F2").PadRight(10)`

## Flags to Support
- `-` - left-justify
  - C# equivalent: Use negative width in string.Format `{0,-10}` or `.PadRight()`
- `+` - always show sign for numbers
  - C# equivalent: Custom formatting with conditional logic, or use `ToString("+#;-#;0")`
- ` ` (space) - space for positive numbers
  - C# equivalent: Custom formatting with conditional logic
- `#` - alternate form (0x for hex, 0 for octal)
  - C# equivalent: Custom formatting, no direct equivalent
- `0` - zero-pad numbers
  - C# equivalent: Use format specifiers like `D10` for integers or width padding

## Length Modifiers (Optional but Recommended)
- `%ld` - long integer
  - C# equivalent: `{0}` or `.ToString()` (long is handled automatically in C#)
- `%hd` - short integer
  - C# equivalent: `{0}` or `.ToString()` (short is handled automatically in C#)

## Implementation Requirements

1. Create a `SprintfFormatter` class with a static `Format` method
2. Parse the format string to identify format specifiers
3. Handle all the format types listed above
4. Support width, precision, and flag modifiers
5. Throw appropriate exceptions for invalid format strings or argument mismatches
6. Handle edge cases like null arguments, overflow conditions, etc.

## Example Usage
```csharp
string result1 = SprintfFormatter.Format("%d", 123);              // "123"
string result2 = SprintfFormatter.Format("%.2f", 3.14159);        // "3.14"
string result3 = SprintfFormatter.Format("%10s", "Hello");        // "     Hello"
string result4 = SprintfFormatter.Format("%-10d", 42);            // "42        "
string result5 = SprintfFormatter.Format("%#x", 255);             // "0xff"
string result6 = SprintfFormatter.Format("%+d", 42);              // "+42"
```

## Unit Test Cases to Implement

Create comprehensive unit tests covering all format specifiers and edge cases:

### Basic Integer Tests
```csharp
[Test] public void TestBasicInteger() {
    Assert.AreEqual("123", SprintfFormatter.Format("%d", 123));
    Assert.AreEqual("123", SprintfFormatter.Format("%i", 123));
    Assert.AreEqual("123", SprintfFormatter.Format("%u", 123u));
    Assert.AreEqual("-123", SprintfFormatter.Format("%d", -123));
}
```

### Hexadecimal Tests
```csharp
[Test] public void TestHexadecimal() {
    Assert.AreEqual("ff", SprintfFormatter.Format("%x", 255));
    Assert.AreEqual("FF", SprintfFormatter.Format("%X", 255));
    Assert.AreEqual("0xff", SprintfFormatter.Format("%#x", 255));
    Assert.AreEqual("0XFF", SprintfFormatter.Format("%#X", 255));
}
```

### Octal Tests
```csharp
[Test] public void TestOctal() {
    Assert.AreEqual("377", SprintfFormatter.Format("%o", 255));
    Assert.AreEqual("0377", SprintfFormatter.Format("%#o", 255));
}
```

### Floating Point Tests
```csharp
[Test] public void TestFloatingPoint() {
    Assert.AreEqual("3.140000", SprintfFormatter.Format("%f", 3.14));
    Assert.AreEqual("3.14", SprintfFormatter.Format("%.2f", 3.14));
    Assert.AreEqual("3.1e+00", SprintfFormatter.Format("%.1e", 3.1));
    Assert.AreEqual("3.1E+00", SprintfFormatter.Format("%.1E", 3.1));
    Assert.AreEqual("3.14", SprintfFormatter.Format("%g", 3.14));
    Assert.AreEqual("3.14", SprintfFormatter.Format("%G", 3.14));
}
```

### Width and Alignment Tests
```csharp
[Test] public void TestWidthAndAlignment() {
    Assert.AreEqual("   123", SprintfFormatter.Format("%6d", 123));
    Assert.AreEqual("123   ", SprintfFormatter.Format("%-6d", 123));
    Assert.AreEqual("000123", SprintfFormatter.Format("%06d", 123));
    Assert.AreEqual("  3.14", SprintfFormatter.Format("%6.2f", 3.14));
    Assert.AreEqual("3.14  ", SprintfFormatter.Format("%-6.2f", 3.14));
}
```

### Character and String Tests
```csharp
[Test] public void TestCharacterAndString() {
    Assert.AreEqual("A", SprintfFormatter.Format("%c", 'A'));
    Assert.AreEqual("A", SprintfFormatter.Format("%c", 65));
    Assert.AreEqual("Hello", SprintfFormatter.Format("%s", "Hello"));
    Assert.AreEqual("     Hello", SprintfFormatter.Format("%10s", "Hello"));
    Assert.AreEqual("Hello     ", SprintfFormatter.Format("%-10s", "Hello"));
}
```

### Sign and Space Tests
```csharp
[Test] public void TestSignsAndSpaces() {
    Assert.AreEqual("+123", SprintfFormatter.Format("%+d", 123));
    Assert.AreEqual("-123", SprintfFormatter.Format("%+d", -123));
    Assert.AreEqual(" 123", SprintfFormatter.Format("% d", 123));
    Assert.AreEqual("-123", SprintfFormatter.Format("% d", -123));
}
```

### Special Cases Tests
```csharp
[Test] public void TestSpecialCases() {
    Assert.AreEqual("%", SprintfFormatter.Format("%%"));
    Assert.AreEqual("0", SprintfFormatter.Format("%d", 0));
    Assert.AreEqual("0.000000", SprintfFormatter.Format("%f", 0.0));
}
```

### Multiple Arguments Tests
```csharp
[Test] public void TestMultipleArguments() {
    Assert.AreEqual("Hello 123 3.14", SprintfFormatter.Format("%s %d %.2f", "Hello", 123, 3.14159));
    Assert.AreEqual("Value: 42, Hex: 2a", SprintfFormatter.Format("Value: %d, Hex: %x", 42, 42));
}
```

### Error Cases Tests
```csharp
[Test] public void TestErrorCases() {
    Assert.Throws<ArgumentException>(() => SprintfFormatter.Format("%d"));  // Missing argument
    Assert.Throws<ArgumentException>(() => SprintfFormatter.Format("%d", "not a number"));  // Wrong type
    Assert.Throws<FormatException>(() => SprintfFormatter.Format("%q", 123));  // Invalid format
}
```

### Pointer Tests (if implementing %p)
```csharp
[Test] public void TestPointer() {
    IntPtr ptr = new IntPtr(0x12345678);
    string result = SprintfFormatter.Format("%p", ptr);
    Assert.IsTrue(result.StartsWith("0x"));
    Assert.IsTrue(result.Contains("12345678"));
}
```

## Implementation Notes

1. Use regular expressions or state machine parsing to identify format specifiers
2. Handle type conversion carefully - integers should work with various numeric types
3. For floating point formats, pay attention to precision and scientific notation thresholds
4. Consider thread safety if needed
5. Provide clear error messages for invalid formats or argument mismatches
6. Handle null arguments gracefully
7. Consider performance optimization for frequently used format patterns

## C# Format Reference for Implementation

When implementing each sprintf format, use these C# equivalents as the underlying mechanism:

| sprintf Format | C# string.Format | C# ToString() | C# Interpolation |
|---------------|------------------|---------------|------------------|
| `%d`, `%i` | `{0}` or `{0:D}` | `.ToString()` or `.ToString("D")` | `$"{value}"` |
| `%u` | `{0}` or `{0:D}` | `.ToString()` or `.ToString("D")` | `$"{value}"` |
| `%o` | Custom logic | `Convert.ToString(value, 8)` | `$"{Convert.ToString(value, 8)}"` |
| `%x` | `{0:x}` | `.ToString("x")` | `$"{value:x}"` |
| `%X` | `{0:X}` | `.ToString("X")` | `$"{value:X}"` |
| `%f`, `%F` | `{0:F}` | `.ToString("F")` | `$"{value:F}"` |
| `%e` | `{0:e}` | `.ToString("e")` | `$"{value:e}"` |
| `%E` | `{0:E}` | `.ToString("E")` | `$"{value:E}"` |
| `%g` | `{0:G}` | `.ToString("G")` | `$"{value:G}"` |
| `%G` | `{0:G}` | `.ToString("G")` | `$"{value:G}"` |
| `%c` | `{0}` | `.ToString()` | `$"{value}"` |
| `%s` | `{0}` | `.ToString()` | `$"{value}"` |
| `%10d` | `{0,10}` | `.ToString().PadLeft(10)` | `$"{value,10}"` |
| `%-10d` | `{0,-10}` | `.ToString().PadRight(10)` | `$"{value,-10}"` |
| `%010d` | `{0:D10}` | `.ToString("D10")` | `$"{value:D10}"` |
| `%.2f` | `{0:F2}` | `.ToString("F2")` | `$"{value:F2}"` |

## Bonus Features (Optional)
- Support for positional arguments like `%2$d` (argument 2)
- Support for `*` width and precision specifiers from arguments
- Additional length modifiers (`ll`, `h`, `hh`)
- Better error reporting with position information

The implementation should be robust, well-tested, and handle edge cases appropriately while maintaining compatibility with standard C sprintf behavior.