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).
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