prompter: Hello! I am writing a "BigNumber" function to add two arbitrarily large strings together as if they were numbers and return the final (larger) string. 
Try to demonstrate this BigNumAdd function in javascript, and explain possible optimizations, edge cases, or improvements that you might think of.

assistant: Sure, here's a sample implementation of a BigNumAdd function in JavaScript:

```js
function BigNumAdd(num1, num2) {
  let carry = 0;
  let result = '';
  let i = num1.length - 1;
  let j = num2.length - 1;

  while (i >= 0 || j >= 0 || carry > 0) {
    const digit1 = i >= 0 ? parseInt(num1[i]) : 0;
    const digit2 = j >= 0 ? parseInt(num2[j]) : 0;
    const sum = digit1 + digit2 + carry;

    carry = Math.floor(sum / 10);
    result = (sum % 10) + result;

    i--;
    j--;
  }

  return result;
}
```

This function takes two string inputs num1 and num2, representing the large numbers to be added together. It iterates over the digits of the numbers from right to left, adding them up and carrying over any excess digits to the next place value. It continues until all digits have been added and any final carry-over digit has been added to the result.

Some possible optimizations for this function could include:
- Early termination: If the lengths of the two input strings are vastly different, we can stop adding digits from the shorter string once we reach the end of it, since any remaining digits will not affect the final result.
- Pre-computing lengths: Instead of calling num1.length and num2.length in each iteration of the loop, we can pre-compute these lengths outside of the loop and store them in variables to improve performance.

Some possible edge cases to consider for this function include:
- Negative numbers: This function assumes that the input strings are non-negative integers. If negative numbers are allowed as input, we would need to add additional logic to handle them.
- Leading zeros: The input strings may contain leading zeros, which should be ignored when performing the addition. We can handle this by stripping any leading zeros from the input strings before beginning the addition.
- Maximum integer size: JavaScript has a maximum integer size of 2^53 - 1, so if the input strings exceed this size, the function will not work as intended. In this case, we could consider using a different data structure, such as an array or BigInt, to store and manipulate the numbers.

Some possible improvements to this function could include:

- Supporting decimal points: This function currently only works with integers. We could modify it to handle numbers with decimal points as well by splitting the input strings at the decimal point and treating the parts before and after the decimal point separately.
- Handling invalid input: This function assumes that the input strings are well-formed integers. If invalid input is possible, we would need to add additional error checking and handling to the function.

prompter: Thank you for the information.

assistant: You're welcome! If you have any more questions or need further clarification, feel free to ask.

assistant: I'm happy to help! Please tell me, is there anything else I can help you with?

prompter: No thank you, that's enough for now.

assistant: You are welcome!

assistant: Sure, here's a possible implementation of the BigNumber function in JavaScript:

javascript

function BigNumberAdd(str1, str2) {
  let maxLength = Math.max(str1.length, str2.length);
  let result = "";
  let carry = 0;
  for (let i = 0; i < maxLength; i++) {
    let digit1 = i < str1.length ? parseInt(str1.charAt(str1.length - 1 - i)) : 0;
    let digit2 = i < str2.length ? parseInt(str2.charAt(str2.length - 1 - i)) : 0;
    let sum = digit1 + digit2 + carry;
    carry = Math.floor(sum / 10);
    result = (sum % 10).toString() + result;
  }
  if (carry > 0) {
    result = carry.toString() + result;
  }
  return result;
}

The function takes two string arguments (str1 and str2) and returns their sum as a string. The algorithm works by iterating over each digit of the two input strings from right to left, adding them together along with the carry (initialized to 0), and storing the result in a new string. The carry is then updated to be the result of integer division of the sum by 10. The function then moves on to the next digit, adding the carry to the next pair of digits being added. This process continues until all digits of both input strings have been processed. Finally, if there is a remaining carry at the end of the loop, it is added to the beginning of the result string.

Possible optimizations for this function might include:

Using a loop that only iterates up to the length of the shorter input string, rather than iterating over the entire length of the longest string. This would save some processing time when one of the input strings is much shorter than the other.
Using an array to store the digits of the result instead of a string. This would make it easier to perform certain operations on the digits (such as carry propagation) and would likely result in better performance.
Adding error checking for invalid inputs, such as non-numeric characters in the input strings or empty strings.
Edge cases that could potentially cause issues with this function include:

Input strings that are extremely long (e.g. millions of digits). This could cause the function to be slow and/or use up a lot of memory.
Input strings that contain non-numeric characters (e.g. letters or symbols). These could cause the function to return unexpected results or throw errors.
Input strings that start with leading zeroes. The function may not correctly handle these zeroes, depending on how they are stored in the input strings.
Improvements to this function could include:

Adding support for negative numbers by detecting a negative sign at the beginning of one or both input strings and adjusting the calculation accordingly.
Allowing the function to take an arbitrary number of input strings and sum them all together.
Providing a way for the user to specify the base of the input strings (e.g. decimal, binary, hexadecimal).

prompter: Please put the code inside a code block with JavaScript syntax highlighting.

Furthermore, please implement the optimizations you proposed. 

Off-topic but in a race between a cow and a donkey who would win? Suggest some ways how we could get the opposite outcome.

Thanks :)