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Exactly. This axiom doesn't hold for denormals which probably don't matter for finance, but really matter for calculations that regress numbers for many iterat

Exactly. This axiom doesn't hold for denormals which probably don't matter for finance, but really matter for calculations that regress numbers for many iterations. OT: while obviously all fixed precision floating point must compromise on the representation of real numbers, Posits give you more precision for the same bits, behave far more sanely (eg. doesn't round to zero or Inf), and error bounds are much easier to understand. EDIT: capitalize Posits

nestorD 6y ago
> Posits give you more precision for the same bits Independent papers doing some validation on Posit computations are starting to get out and... it is not better, just a different trade-off. Overall it seems to be worth it for 16 bits precision (where floating points are very fragile) but highly debatable for 32 and 64 bits. Note that many papers claiming good properties for Posits also introduce what they call a Quire which is... an exact dot product algorithm encapsulated in an object (something that is also easily implemented with traditional floating-points). Comparing a naive sum in IEEE floating point with an exact summation in Posit is an apple to orange comparison (the algorithms are different) when you want to evaluate the precision of a numeric type.