@fastmath and literal_pow not compatible

[KlausC]

While @fastmath claims to mimic the compiler:

julia/base/fastmath.jl

Lines 104 to 107 in 9145571

	elseif expr.head === :call && expr.args[1] === :^ && expr.args[3] isa Integer
	# mimic Julia's literal_pow lowering of literal integer powers
	return Expr(:call, :(Base.FastMath.pow_fast), make_fastmath(expr.args[2]), Val{expr.args[3]}())
	end

in reality there are some corner cases, where that fails. The condition in the first line seems incorrect. See also #53713.
Examples:

julia> @fastmath 2^-2305843009213693953
0.0

julia> 2^-2305843009213693953
ERROR: DomainError with -2305843009213693953:
Cannot raise an integer x to a negative power -2305843009213693953.

and

julia> foo(a) = a^0x2 
foo (generic function with 1 method)

julia> foofast(a) = @fastmath a^0x2
foofast (generic function with 1 method) 

julia> @code_typed debuginfo=:source foo(2)
CodeInfo(
    @ REPL[58]:1 within `foo`
   ┌ @ intfuncs.jl:349 within `^`
1 ─│ %1 = Base.power_by_squaring::typeof(Base.power_by_squaring)
│  │┌ @ intfuncs.jl:313 within `power_by_squaring`
│  ││ %2 = invoke Base.:(var"#power_by_squaring#522")(Base.:*::typeof(*), %1::typeof(Base.power_by_squaring), a::Int64, 0x02::UInt8)::Int64
└──││      return %2
   └└
) => Int64

julia> @code_typed debuginfo=:source foofast(2)
CodeInfo(
    @ REPL[61]:1 within `foofast`
   ┌ @ fastmath.jl:284 within `pow_fast`
   │┌ @ intfuncs.jl:389 within `literal_pow`
   ││┌ @ intfuncs.jl:349 within `^`
1 ─│││ %1 = Base.power_by_squaring::typeof(Base.power_by_squaring)
│  │││┌ @ intfuncs.jl:313 within `power_by_squaring`
│  ││││ %2 = invoke Base.:(var"#power_by_squaring#522")(Base.:*::typeof(*), %1::typeof(Base.power_by_squaring), a::Int64, 0x02::UInt8)::Int64
└──││││      return %2
   └└└└
) => Int64

[KlausC]

Example in error case:

julia> ^(2)
ERROR: MethodError: no method matching ^(::Int64)
The function `^` exists, but no method is defined for this combination of argument types.
  ...

julia> @fastmath ^(2)
ERROR: LoadError: BoundsError: attempt to access 2-element Vector{Any} at index [3]
 ...
 [3] make_fastmath(expr::Expr)
   @ Base.FastMath ./fastmath.jl:104