Reductions with defaulted identity value

[jdgarciauc3m]

Reductions with defaulted identity value

[jdgarciauc3m]

@droccom has raised in comments at issue #290 if we should provide reduce either with an identity value or an initial value. Rationale is being aligned with std::reduce

We need to discuss this in detail to make a decision.

[mdrocco]

If the target is strict consistency with std::reduce, there should be no way to both avoiding the initial value and using a custom binary operator (only std::plus<> is supported).

I think this case is very specific, so I suggest to either:
a. avoid adding it to the GrPPI API;
b. extend it to support generic binary operators (relaxing consistency with std::reduce)

[jdgarciauc3m]

New proposed resolution:

Do not take initial value or identity for reduction operations and apply the following semantics:

• reduce(ex, b, e, binop) -> if (distance(b,e) = 1) return *b
• reduce(ex, b, e, binop) -> Apply reduction over range [b,e)
• reduce(ex, b, e, binop) -> if (distance(b,e) <1) return default constructed value

Requirements:

• value type must be default constructible
• The result is indeterminate if either binop is not associative or not commutative.

[mdrocco]

This solution makes great sense to me.

[jdgarciauc3m]

We keep the requirement of having to provide identity_value.

Rationale: This is in-line with new reduction objects of parallelism TS in C++. Fastflow also requires an identity value.