  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.
