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This definition of "the real math" is quite arguable. Doing a lot of computations efficiently is a realm of modeling and statistics; that does not clarify the very nature of computation, the inner laws of formal systems. Haskell is much more about "what computation is" than about "how to do computations".

Besides that, from mathematician's point of view, "efficient numerical computation" is a necessary and useful practically, but very ugly thing. Speaking of C-like types `int`/`long`/`uint32_t`: they are only a crude approximation of natural numbers, they are a ring modulo 2n, which we pretend to use as natural/integer numbers, silently failing when this range wraps up.

And that is not the end of the story: for integer numbers we can at least specify what mathematical model describes them (a ring modulo some power of two), for floating point numbers it is impossible: set of possible IEEE 754 values is a very weird and irregular finite set of values (NaN, +Inf, -Inf, +0, -0, exponential distribution of points density with min/max bounds) with complex modes of failure. Associative law, distributive law, commutative law? The very equality check? Forget about it, floating point numbers have none of that.




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