math.Complex: genericize arithmetics with reals, replace mulbyi with comptime-generic i-shifted arithmetic

[expikr]

uses anytype to enable binary arithmetic operations (add/sub/mul/div) with real arguments

also added iadd, isub, imul, and idiv, and removed mulbyi which can be achieved with z.imul(1) that lowers to the equivalent data shuffle ops at comptime.

[andrewrk]

provide alternate functions for operating on scalars rather than abusing anytype

[expikr]

provide alternate functions for operating on scalars rather than abusing anytype

Disagree. This is in preparation for #16278 according what this link says wrt C99 spec:

Standard arithmetic operators +, -, *, / can be used with real, complex, and imaginary types in any combination.

Until #16278 is implemented, the arithmetic methods serve as stand-ins for the arithmetic operators.

I can make them more strict with additional comptime type constraints, but the anytype argument is the entire premise.

c.c. @Snektron

[Snektron]

I feel that Andrew is right here. Maybe an alternative solution would be to add a constructor that initializes a Complex from just a real value? Together with #9938, this would form a relatively concise way to write complex operations on reals:

var a: Complex = .init(1, 2);
var b = a.mul(.real(3));
...

[expikr]

But this way they don't get lowered to scalar operations at compile time though?

The intent is to generalize permutation operations like mulbyi, divbyi, or neg into comptime-known algebraic expressions,
i.e. z.imul(1), z.imul(-1), z.mul(-1) which turns them into permutation ops without any extra arithmetic

And they are not just for operations with scalars. Consider expressions like $z + is$ where both z and are complex, being able to write z.iadd(s) is significantly more concise.

[expikr]

closed in favor of #20346