fix nextpow, prevpow for types without typemax (#49669)

Without this change `prevpow` and `nextpow` fail for, e.g., `BigInt`;
incorrectly throwing a `MethodError`. For example, calls like
`prevpow(3, big"10")` or `nextpow(3, big"10")` fail.

The issue is that the code incorrectly assumes the existence of a
`typemax` method.

Another issue was a missing promote for the arguments of a
`mul_with_overflow` call.

Fixes #57906

Author: nsajko

base/intfuncs.jl

@@ -570,7 +570,8 @@ function nextpow(a::Real, x::Real)
     n = ceil(Integer,log(a, x))
     # round-off error of log can go either direction, so need some checks
     p = a^(n-1)
-    x > typemax(p) && throw(DomainError(x,"argument is beyond the range of type of the base"))
+    hastypemax(typeof(p)) && x > typemax(p) &&
+        throw(DomainError(x,"argument is beyond the range of type of the base"))
     p >= x && return p
     wp = a^n
     wp > p || throw(OverflowError("result is beyond the range of type of the base"))
@@ -611,9 +612,10 @@ function prevpow(a::T, x::Real) where T <: Real
     n = floor(Integer,log(a, x))
     # round-off error of log can go either direction, so need some checks
     p = a^n
-    x > typemax(p) && throw(DomainError(x,"argument is beyond the range of type of the base"))
+    hastypemax(typeof(p)) && x > typemax(p) &&
+        throw(DomainError(x,"argument is beyond the range of type of the base"))
     if a isa Integer
-        wp, overflow = mul_with_overflow(a, p)
+        wp, overflow = mul_with_overflow(promote(a, p)...)
         wp <= x && !overflow && return wp
     else
         wp = a^(n+1)

test/intfuncs.jl

@@ -326,6 +326,14 @@ end
 end
 
 @testset "nextpow/prevpow" begin
+    fs = (prevpow, nextpow)
+    types = (Int8, BigInt, BigFloat)
+    for f ∈ fs, P ∈ types, R ∈ types, p ∈ 1:20, r ∈ 2:5
+        q = P(p)
+        n = R(r)
+        @test f(r, p) == f(n, q)
+    end
+
     @test nextpow(2, 3) == 4
     @test nextpow(2, 4) == 4
     @test nextpow(2, 7) == 8
@@ -339,7 +347,14 @@ end
     @test prevpow(10, 101.0) === 100
     @test prevpow(10.0, 101) === 100.0
     @test_throws DomainError prevpow(0, 3)
-    @test_throws DomainError prevpow(0, 3)
+    @test_throws DomainError prevpow(3, 0)
+
+    # "argument is beyond the range of type of the base"
+    @test_throws DomainError prevpow(Int8(3), 243)
+    @test_throws DomainError nextpow(Int8(3), 243)
+
+    # "result is beyond the range of type of the base"
+    @test_throws OverflowError nextpow(Int8(3), 82)
 end
 
 @testset "ndigits/ndigits0z" begin