make @fastmath mirror how lowering applies literal_pow (#53819)

The expressions `a^x` and `@fastmath a^x` are now producing equivalent
results (apart from floating point accuracy) in the case of literal
integer `x`.
The logic in the `fastmath` macro, trying to mimic the behaviour of the
compiler is fixed.

Fixes #53817

---------

Co-authored-by: Oscar Smith <oscardssmith@gmail.com>

Author: KlausC

base/fastmath.jl

@@ -101,9 +101,12 @@ const rewrite_op =
 function make_fastmath(expr::Expr)
     if expr.head === :quote
         return expr
-    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]}())
+    elseif expr.head === :call && expr.args[1] === :^
+        ea = expr.args
+        if length(ea) >= 3 && isa(ea[3], Int)
+            # mimic Julia's literal_pow lowering of literal integer powers
+            return Expr(:call, :(Base.FastMath.pow_fast), make_fastmath(ea[2]), Val(ea[3]))
+        end
     end
     op = get(rewrite_op, expr.head, :nothing)
     if op !== :nothing
@@ -364,6 +367,10 @@ for f in (:^, :atan, :hypot, :log)
         # fall-back implementation that applies after promotion
         $f_fast(x::T, y::T) where {T<:Number} = $f(x, y)
     end
+    # Issue 53886 - avoid promotion of Int128 etc to be consistent with non-fastmath
+    if f === :^
+        @eval $f_fast(x::Number, y::Integer) = $f(x, y)
+    end
 end
 
 # Reductions

test/fastmath.jl

@@ -256,6 +256,22 @@ end
 
 @testset "literal powers" begin
     @test @fastmath(2^-2) == @fastmath(2.0^-2) == 0.25
+    # Issue #53817
+    # Note that exponent -2^63 fails testing because of issue #53881
+    # Therefore we test with -(2^63-1). For Int == Int32 there is an analogue restriction.
+    # See also PR #53860.
+    if Int == Int64
+        @test @fastmath(2^-9223372036854775807) === 0.0
+        @test_throws DomainError @fastmath(2^-9223372036854775809)
+        @test @fastmath(1^-9223372036854775807) isa Float64
+        @test @fastmath(1^-9223372036854775809) isa Int
+    elseif Int == Int32
+        @test @fastmath(2^-2147483647) === 0.0
+        @test_throws DomainError @fastmath(2^-2147483649)
+        @test @fastmath(1^-2147483647) isa Float64
+        @test @fastmath(1^-2147483649) isa Int
+    end
+    @test_throws MethodError @fastmath(^(2))
 end
 
 @testset "sincos fall-backs" begin