diff --git a/base/gmp.jl b/base/gmp.jl
index b5edee0436f5a..004ec803a48e9 100644
--- a/base/gmp.jl
+++ b/base/gmp.jl
@@ -520,12 +520,12 @@ end
 
 function ndigits0z(x::BigInt, b::Integer=10)
     b < 2 && throw(DomainError())
-    if ispow2(b)
-        Int(ccall((:__gmpz_sizeinbase,:libgmp), Culong, (Ptr{BigInt}, Int32), &x, b))
+    if ispow2(b) && 2 <= b <= 62 # GMP assumes b is in this range
+        Int(ccall((:__gmpz_sizeinbase,:libgmp), Csize_t, (Ptr{BigInt}, Cint), &x, b))
     else
         # non-base 2 mpz_sizeinbase might return an answer 1 too big
         # use property that log(b, x) < ndigits(x, b) <= log(b, x) + 1
-        n = Int(ccall((:__gmpz_sizeinbase,:libgmp), Culong, (Ptr{BigInt}, Int32), &x, 2))
+        n = Int(ccall((:__gmpz_sizeinbase,:libgmp), Csize_t, (Ptr{BigInt}, Cint), &x, 2))
         lb = log2(b) # assumed accurate to <1ulp (true for openlibm)
         q,r = divrem(n,lb)
         iq = Int(q)
diff --git a/test/bigint.jl b/test/bigint.jl
index 90a318926ed2a..e2946d575d259 100644
--- a/test/bigint.jl
+++ b/test/bigint.jl
@@ -280,6 +280,12 @@ ndigits_mismatch(n) = ndigits(n) != ndigits(BigInt(n))
 @test !any(ndigits_mismatch, 512:999)
 @test !any(ndigits_mismatch, 8192:9999)
 
+# The following should not crash (#16579)
+ndigits(rand(big(-999:999)), rand(63:typemax(Int)))
+ndigits(rand(big(-999:999)), big(2)^rand(2:999))
+
+@test_throws DomainError ndigits(rand(big(-999:999)), rand(typemin(Int):1))
+
 # conversion from float
 @test BigInt(2.0) == BigInt(2.0f0) == BigInt(big(2.0)) == 2
 @test_throws InexactError convert(BigInt, 2.1)