[Greg Ewing <greg.ew...@canterbury.ac.nz>]
> So can you elaborate on how you use variable precision?
Numeric programmers frequently want this. An extreme example is in
function `collision_stats()` in your Python distribution's
Lib/test/support/__init__.py. This needs to compute the variance of a
distribution for which we only have a mathematical derivation. That's
exact "in theory", but the expression suffers massive cancellation in
native floating point. In context, it would deliver 100% gibberish
results.
The comments note that it's easy to use rationals (fractions.Fraction)
instead - but doing so in context would require multi-million bit
integer arithmetic and be unbearably slow (voice of experience there -
that's how I wrote it at first, and wondered why test_tuple never
finished).
`decimal` to the rescue! It's fast and highly accurate now. It just
sets the context to use a number of decimal digits twice the number of
bits in the crucial input. There's still utterly massive cancellation,
but it doesn't matter: there are enough "extra" decimal digits that
losing mounds of the leading digits to cancellation doesn't matter to
the result.
Base 10 is irrelevant to this - base 2 would work fine too. It's the
ability to greatly boost precision that matters.
BTW, like any sane isolated code that messes with the context, it does
so locally:
with decimal.localcontext() as ctx:
bits = n.bit_length() * 2 # bits in n**2
# At least that many bits will likely cancel out.
# Use that many decimal digits instead.
ctx.prec = max(bits, 30)
I know of no other way to get this done with sane effort in core
Python; and, e.g., we can't reasonably require installing the `mpmath`
extension just to run Python's standard test suite.
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