[Python-Dev] Expert floats (original) (raw)

Shane Hathaway shane at zope.com
Tue Mar 30 17:05:30 EST 2004

Tim Peters wrote:

Suppose you had a binary float format with 3 bits of precision, and the result of a computation on that box is .001 binary = 1/8 = 0.125 decimal. The "shortest-possible reproducing decimal representation" on that box is 0.1. Is it more accurate to move that result to a wider machine via the string "0.1" or via the string "0.125"? The former is off by 25%, but the latter is exactly right. repr() on the former machine has no way to guess whether the 1/8 it's fed is the result of the user typing in "0.1" or the result of dividing 1.0 by 8.0. By taking the bits at face value, and striving to communicate that as faithfully as possible, it's explainable, predictable, and indeed as faithful as possible. "Looks pretty too" isn't a requirement for serious floating-point work.

It seems like most people who write '1.1' don't really want to dive into serious floating-point work. I wonder if literals like 1.1 should generate decimal objects as described by PEP 327, rather than floats. Operations on decimals that have no finite decimal representation (like 1.1 / 3) should use floating-point arithmetic internally, but they should store in decimal rather than floating-point format.

Shane

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