Exponentiation of negative single and half precision fails on nightly

[palday]

julia> versioninfo()
Julia Version 1.7.0-DEV.1011
Commit 4e176ac965* (2021-04-26 08:26 UTC)
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: Intel(R) Xeon(R) E-2288G CPU @ 3.70GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-11.0.1 (ORCJIT, skylake)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 8

julia> Float64(-2)^5
-32.0

julia> Float32(-2)^5
ERROR: DomainError with -2.0:
log2 will only return a complex result if called with a complex argument. Try log2(Complex(x)).
Stacktrace:
 [1] throw_complex_domainerror(f::Symbol, x::Float64)
   @ Base.Math ./math.jl:33
 [2] _log(x::Float64, base::Val{2}, func::Symbol)
   @ Base.Math ./special/log.jl:304
 [3] log2
   @ ./special/log.jl:268 [inlined]
 [4] ^
   @ ./math.jl:914 [inlined]
 [5] ^
   @ ./math.jl:942 [inlined]
 [6] literal_pow(#unused#::typeof(^), x::Float32, #unused#::Val{5})
   @ Base ./intfuncs.jl:315
 [7] top-level scope
   @ REPL[34]:1

julia> Float16(-2)^5
ERROR: DomainError with -2.0:
log2 will only return a complex result if called with a complex argument. Try log2(Complex(x)).
Stacktrace:
 [1] throw_complex_domainerror(f::Symbol, x::Float64)
   @ Base.Math ./math.jl:33
 [2] _log(x::Float64, base::Val{2}, func::Symbol)
   @ Base.Math ./special/log.jl:304
 [3] log2
   @ ./special/log.jl:268 [inlined]
 [4] ^
   @ ./math.jl:914 [inlined]
 [5] ^
   @ ./math.jl:942 [inlined]
 [6] ^
   @ ./math.jl:944 [inlined]
 [7] literal_pow(#unused#::typeof(^), x::Float16, #unused#::Val{5})
   @ Base ./intfuncs.jl:315
 [8] top-level scope
   @ REPL[40]:1

[palday]

@oscardssmith

This comes from #40236 -- there is a relatively obvious problem with taking the logarithm of the base without checking its sign. This could be fixed by taking the absolute value first and then computing what the sign of the final result should be, but I'm not sure would preserve the speed gain. The fix should definitely include a test with negative bases.

[fredrikekre]

Let's add the relevant tests before closing this.