Implement precise string-based decimal addition

Given two non-empty strings representing decimal numbers (e.g., "123.456" and "6234.42432"), implement a function that returns their exact sum as a string without using floating-point arithmetic or big-number libraries and without precision loss. Inputs may be very large (up to 1e5 total digits) and may contain leading/trailing zeros and decimal points but no scientific notation. Describe how you align fractional parts, propagate carries across the decimal point, and normalize the output (e.g., removing unnecessary leading/trailing zeros while preserving a fractional zero when needed). State time and space complexity and provide tests for edge cases such as different fractional lengths, one operand lacking a fractional part, all-zero values, and very large inputs.