fix Float32/Float16 power for giant integer exponents (#57829)

alternative to #57488

---------

Co-authored-by: Lilith Orion Hafner <[email protected]>

Author: oscardssmith

base/math.jl

@@ -1173,6 +1173,8 @@ end
     return @inline Base.Math.exp_impl(hi, xylo-(hi-xyhi), Val(:ℯ))
 end
 
+# @constprop aggressive to help the compiler see the switch between the integer and float
+# variants for callers with constant `y`
 @constprop :aggressive function ^(x::T, y::T) where T <: Union{Float16, Float32}
     x == 1 && return one(T)
     # Exponents greater than this will always overflow or underflow.
@@ -1183,17 +1185,31 @@ end
         y = sign(y)*max_exp
     end
     yint = unsafe_trunc(Int32, y) # This is actually safe since julia freezes the result
-    y == yint && return x^yint
-    x < 0 && throw_exp_domainerror(x)
-    !isfinite(x) && return x*(y>0 || isnan(x))
-    x==0 && return abs(y)*T(Inf)*(!(y>0))
-    return pow_body(x, y)
+    yisint = y == yint
+    if yisint
+        yint == 0 && return one(T)
+        use_power_by_squaring(yint) && return pow_body(x, yint)
+    end
+    s = 1
+    if x < 0
+        !yisint && throw_exp_domainerror(x) # y isn't an integer
+        s = ifelse(isodd(yint), -1, 1)
+    end
+    !isfinite(x) && return copysign(x,s)*(y>0 || isnan(x)) # x is inf or NaN
+    return copysign(pow_body(abs(x), y), s)
 end
 
-@inline function pow_body(x::T, y::T) where T <: Union{Float16, Float32}
+@inline function pow_body(x::T, y) where T <: Union{Float16, Float32}
     return T(exp2(log2(abs(widen(x))) * y))
 end
 
+@inline function pow_body(x::Union{Float16, Float32}, n::Int32)
+    n == -2 && return (i=inv(x); i*i)
+    n == 3 && return x*x*x #keep compatibility with literal_pow
+    n < 0 && return oftype(x, Base.power_by_squaring(inv(widen(x)), -n))
+    return oftype(x, Base.power_by_squaring(widen(x), n))
+end
+
 @constprop :aggressive @inline function ^(x::Float64, n::Integer)
     n = clamp(n, Int64)
     n == 0 && return one(x)
@@ -1242,11 +1258,17 @@ end
     return ifelse(isfinite(x) & isfinite(err), muladd(x, y, err), x*y)
 end
 
-function ^(x::Union{Float16,Float32}, n::Integer)
-    n == -2 && return (i=inv(x); i*i)
-    n == 3 && return x*x*x #keep compatibility with literal_pow
-    n < 0 && return oftype(x, Base.power_by_squaring(inv(widen(x)),-n))
-    oftype(x, Base.power_by_squaring(widen(x),n))
+# @constprop aggressive to help the compiler see the switch between the integer and float
+# variants for callers with constant `y`
+@constprop :aggressive @inline function ^(x::T, n::Integer) where T <: Union{Float16, Float32}
+    n = clamp(n, Int32)
+    # Exponents greater than this will always overflow or underflow.
+    # Note that NaN can pass through this, but that will end up fine.
+    n == 0 && return one(x)
+    use_power_by_squaring(n) && return pow_body(x, n)
+    s = ifelse(x < 0 && isodd(n), -one(T), one(T))
+    x = abs(x)
+    return pow_body(x, widen(T)(n))
 end
 
 ## rem2pi-related calculations ##

test/math.jl

@@ -1443,6 +1443,7 @@ end
                     Float32=>[.51, .51, .51, 2.0, 1.5],
                     Float64=>[.55, 0.8, 1.5, 2.0, 1.5])
     for T in (Float16, Float32, Float64)
+        @inferred T T(1.1)^T(1.1) #test that we always return the right type
         for x in (0.0, -0.0, 1.0, 10.0, 2.0, Inf, NaN, -Inf, -NaN)
             for y in (0.0, -0.0, 1.0, -3.0,-10.0 , Inf, NaN, -Inf, -NaN)
                 got, expected = T(x)^T(y), T(big(x)^T(y))
@@ -1547,6 +1548,33 @@ end
         @test EvenInteger(16) === @inferred EvenInteger(2)^Int(4)  # avoid `literal_pow`
         @test EvenInteger(16) === @inferred EvenInteger(2)^EvenInteger(4)
     end
+
+    # issue #57464
+    @test Float32(1.1)^typemin(Int) == Float32(0.0)
+    @test Float16(1.1)^typemin(Int) == Float16(0.0)
+    @test Float32(1.1)^unsigned(0) === Float32(1.0)
+    @test Float32(1.1)^big(0) === Float32(1.0)
+
+    # By using a limited-precision integer (3 bits) we can trigger issue 57464
+    # for a case where the answer isn't zero.
+    struct Int3 <: Integer
+        x::Int8
+        function Int3(x::Integer)
+            if x < -4 || x > 3
+                Core.throw_inexacterror(:Int3, Int3, x)
+            end
+            return new(x)
+        end
+    end
+    Base.typemin(::Type{Int3}) = Int3(-4)
+    Base.promote_rule(::Type{Int3}, ::Type{T}) where {T<:Integer} = T
+    Base.convert(::Type{T}, x::Int3) where {T<:Integer} = convert(T, x.x)
+    Base.:-(x::Int3) = x.x == -4 ? x : Int3(-x.x)
+    Base.trailing_zeros(x::Int3) = trailing_zeros(x.x)
+    Base.:>>(x::Int3, n::UInt64) = Int3(x.x>>n)
+
+    @test 1.001f0^-3 == 1.001f0^Int3(-3)
+    @test 1.001f0^-4 == 1.001f0^typemin(Int3)
 end
 
 @testset "special function `::Real` fallback shouldn't recur without bound, issue #57789" begin