Fixed precision floating point arithmetic is useful when you work over a large range of numbers and care about relative accuracy. That makes them also useful wh

Fixed precision floating point arithmetic is useful when you work over a large range of numbers and care about relative accuracy. That makes them also useful when the range is not known. However, the range is not irrelevant. Violating the allowed range can lead to bad accuracy, and shifting the numbers via a factor into the limitations can improve accuracy. From what you say, this happened in your case; the numbers got too small and you shifted them into the supported range, which is 2^(−126) to (1 − 2^(−24)) × 2^128 for IEEE 754-2008 32 bit numbers.