Fast Number Parsing Without Fallback

In recent work, Lemire (2021) presented a fast algorithm to convert number strings into binary floating-point numbers. The algorithm has been adopted by several important systems: e.g., it is part of the runtime libraries of GCC 12, Rust 1.55, and Go 1.16. The algorithm parses any number string with a significand containing no more than 19 digits into an IEEE floating-point number. However, there is a check leading to a fallback function to ensure correctness. This fallback function is never called in practice. We prove that the fallback is unnecessary. Thus we can slightly simplify the algorithm and its implementation.