prod for tuples uses *

[yurivish]

julia> prod([Int8(100), Int8(100)])
10000

julia> prod((Int8(100), Int8(100)))
16

julia> versioninfo()
Julia Version 1.5.3
Commit 788b2c77c1 (2020-11-09 13:37 UTC)
Platform Info:
  OS: macOS (x86_64-apple-darwin18.7.0)
  CPU: Intel(R) Core(TM) i9-9980HK CPU @ 2.40GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-9.0.1 (ORCJIT, skylake)

Ref. #39182, which is the same issue but for sum and +

The is a todo in the code that says this function definition is inconsistent with regular prod:

julia/base/tuple.jl

Lines 399 to 400 in 788b2c7

	# TODO: this is inconsistent with the regular prod in cases where the arguments
	# require size promotion to system size.

[yurivish]

I just noticed that the sum and prod definitions are right next to each other in the code with the same comment on both, so it might not be worth having a separate issue. Would the fix be the same in both cases?

[NHDaly]

👍 according to the docstring, this is definitely a bug, yeah:

help?> prod([Int8(100), Int8(100)])
  prod(itr)

  Returns the product of all elements of a collection.

  The return type is Int for signed integers of less than system word size, and UInt for unsigned integers of less than system word size. For all other
  arguments, a common return type is found to which all arguments are promoted.

  Examples
  ≡≡≡≡≡≡≡≡≡≡

  julia> prod(1:20)
  2432902008176640000

[NHDaly]

Closed in #41510.