Add tests and docs for divisors

Author: adrsm108

docs/src/api.md

@@ -34,4 +34,5 @@ Primes.primesmask
 ```@docs
 Primes.radical
 Primes.totient
+Primes.divisors
 ```

test/runtests.jl

@@ -313,6 +313,29 @@ end
     end
 end
 
+# brute-force way to get divisors. Same elements as divisors(n), but order may differ.
+divisors_brute_force(n) = [d for d in one(n):n if iszero(n % d)]
+
+@testset "divisors(::$T)" for T in [Int16, Int32, Int64, BigInt]
+    # 1 and 0 are handled specially
+    @test divisors(one(T)) == divisors(-one(T)) == T[one(T)]
+    @test_throws ArgumentError @inferred(divisors(T(0)))
+
+    for n in 2:1000
+        ds = divisors(T(n))
+        @test ds == divisors(-T(n)) 
+        @test sort!(ds) == divisors_brute_force(T(n))
+    end
+end
+
+@testset "divisors(::Factorization)" begin
+    # divisors(n) calls divisors(factor(abs(n))), so the previous testset covers most cases.
+    # We just need to verify that the following cases are also handled correctly:
+    @test divisors(factor(1)) == divisors(factor(-1)) == [1] # factorizations of 1 and -1
+    @test divisors(factor(-56)) == divisors(factor(56)) == [1, 2, 4, 8, 7, 14, 28, 56] # factorizations of negative numbers
+    @test_throws ArgumentError @inferred(divisors(factor(0))) # factorizations of 0
+end
+
 # check copy property for big primes relied upon in nextprime/prevprime
 for n = rand(big(-10):big(10), 10)
     @test n+0 !== n