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certivl

Exact rational and certified interval arithmetic. A float comparison tells you what the hardware thought; an enclosure tells you what is true, because the answer is bracketed and the bracket is carried through every operation.

0.2.0 · pip install certivl · MIT · exact rational and interval

What it does

Exact rational and certified interval arithmetic. A float comparison tells you what the hardware thought; an enclosure tells you what is true, because the answer is bracketed and the bracket is carried through every operation.

pip install certivl

Why an interval rather than a number

A computed inequality is only evidence until the rounding is accounted for. An enclosure that stays strictly on one side of zero settles the question; one that straddles zero says the computation did not decide it. The second answer is the useful one, and floating point never gives it to you — it gives you a number and no idea how much of it is real.

Where it is used

Behind the certified bounds in the discrete-geometry papers: covering, packing and opacity results where a machine-checked upper bound has to survive someone re-running it on different hardware.

How it works

  1. Install itpip install certivl.
  2. Compute inside an enclosureEvery operation carries the bracket forward rather than collapsing to a number that has lost its error.
  3. Read the verdict, including 'undecided'An enclosure strictly on one side of zero settles the inequality. One that straddles zero says the computation did not decide it — which is the answer floating point never gives you.

What it gives you

Exact rational arithmeticNo rounding at all where the numbers allow it.
Certified intervalsWhere they do not, an enclosure whose width is the honest uncertainty.
An honest 'I do not know'The most useful result and the one a float cannot produce.
Machine-checkable boundsA result that survives somebody re-running it on different hardware.
Behind the geometry papersCovering, packing and opacity bounds in the deposited work.
MITRead it, use it, ship it.

Specifications

Installpip install certivl
Version0.2.0
LicenceMIT
ArithmeticExact rational, certified interval
Sourcevince-gonzalez/certivl

Questions

Why not just use floats carefully?
Carefully is not a property you can check. An enclosure is.
Is it slow?
Slower than a float and faster than being wrong in a published bound.
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