Added exponentation operator for numerical types. #1084
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An exponentation operation `x ^ n` is added for `x : ty` implementing `Num ty` and `k : Nat`. The operator `(^)` is right-associative, following mathematical conventions, and is of precedence level `10`. The implementation is based on the repeated-squaring algorithm and is reasonably fast.
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I have an implementation for arbitrary monoids in #1063 |
Ah, my bad, I didn't see that! |
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An exponentation operation
x ^ nis added for all types implementingNumand natural numbersn. In particular, this fixes issue #592.Remarks regarding the implementation
The operator
(^)is right-associative, following mathematicalconventions, with precedence level
10.It is implemented using repeating squaring. This is reasonably fast, e.g. computing
2 ^ 2 ^ 2 ^ 2 ^ 2takes under 10 seconds.Justification for the draft PR
Currently, there is no exponentation operator defined (for any of the numerical types), even though there is a power function for natural numbers. This power function is very slow however.
Problems with this draft
Even though this operator makes sense for any numerical type, it is defined in the module
Data.Nat.Views, which seems a rather odd place. However, I couldn't place it inPrelude.Numbecause it uses the recursive half-view for natural numbers, and even if it wasn't, it would still result in a circular module dependency asPrelude.Numis imported inPrelude.Types(whereNatis defined).I therefore welcome any suggestions for a better placement.