TST more combinatorics tests

(cherry picked from commit ff0470c)
ref PR #9620

Conflicts:
	test/combinatorics.jl

TST intfuncs more coverage

(cherry picked from commit 3d376d1)
(leave out ndigits tests that rely on #8266 which was not backported)
Conflicts:
	test/intfuncs.jl

TST fix 32bit bits test, add comment to interesting binomial result

(cherry picked from commit 93f6ccb)

test/combinatorics.jl

@@ -1,20 +1,37 @@
-@test factorial(7) == 5040
-@test factorial(7,3) == 7*6*5*4
 @test binomial(5,-1) == 0
 @test binomial(5,10) == 0
 @test binomial(5,3) == 10
+@test binomial(2,1) == 2
+@test binomial(1,2) == 0
+@test binomial(-2,1) == -2 # let's agree
+@test binomial(2,-1) == 0
+
+#Issue 6154
+@test binomial(int32(34), int32(15)) == binomial(BigInt(34), BigInt(15)) == 1855967520
+@test binomial(int64(67), int64(29)) == binomial(BigInt(67), BigInt(29)) == 7886597962249166160
+@test binomial(int128(131), int128(62)) == binomial(BigInt(131), BigInt(62)) == 157311720980559117816198361912717812000
+@test_throws InexactError binomial(int64(67), int64(30))
+
 p = shuffle([1:1000])
 @test isperm(p)
 @test all(invperm(invperm(p)) .== p)
+
 push!(p, 1)
 @test !isperm(p)
+
 a = randcycle(10)
 @test ipermute!(permute!([1:10], a),a) == [1:10]
+
+@test collect(combinations("abc",3)) == ["abc"]
 @test collect(combinations("abc",2)) == ["ab","ac","bc"]
+@test collect(combinations("abc",1)) == ["a","b","c"]
+@test collect(combinations("abc",0)) == [""]
 @test collect(permutations("abc")) == ["abc","acb","bac","bca","cab","cba"]
+
 @test collect(filter(x->(iseven(x[1])),permutations([1,2,3]))) == {[2,1,3],[2,3,1]}
 @test collect(filter(x->(iseven(x[3])),permutations([1,2,3]))) == {[1,3,2],[3,1,2]}
 @test collect(filter(x->(iseven(x[1])),combinations([1,2,3],2))) == {[2,3]}
+
 @test collect(partitions(4)) == {[4], [3,1], [2,2], [2,1,1], [1,1,1,1]}
 @test collect(partitions(8,3)) == {[6,1,1], [5,2,1], [4,3,1], [4,2,2], [3,3,2]}
 @test collect(partitions(8, 1)) == {[8]}
@@ -35,18 +52,16 @@ for n = 0:7, k = 1:factorial(n)
  @test nthperm(p) == k
 end
 
-#Issue 6154
-@test binomial(int32(34), int32(15)) == binomial(BigInt(34), BigInt(15)) == 1855967520
-@test binomial(int64(67), int64(29)) == binomial(BigInt(67), BigInt(29)) == 7886597962249166160
-@test binomial(int128(131), int128(62)) == binomial(BigInt(131), BigInt(62)) == 157311720980559117816198361912717812000
-
-# issue #6579
+@test factorial(7) == 5040
+@test factorial(7,3) == 7*6*5*4
 @test factorial(0) == 1
+@test_throws DomainError factorial(-1)
+
 @test factorial(int64(20)) == 2432902008176640000
+# issue #6579
 @test_throws OverflowError factorial(int64(21))
-@test_throws DomainError factorial(-1)
 @test typeof(factorial(int8(2))) == typeof(factorial(int8(1)))
 if Int === Int32
-@test factorial(int32(12)) === int32(479001600)
-@test_throws OverflowError factorial(int32(13))
+ @test factorial(int32(12)) === int32(479001600)
+ @test_throws OverflowError factorial(int32(13))
 end

test/intfuncs.jl

@@ -0,0 +1,73 @@
+@test gcd(3, 5) == 1
+@test gcd(3, 15) == 3
+@test gcd(0, 15) == 15
+@test gcd(3, -15) == 3
+@test gcd(-3, -15) == 3
+@test gcd(0, 0) == 0
+
+@test gcd(2, 4, 6) == 2
+
+@test typeof(gcd(int32(3), int32(15))) == Int32
+
+@test lcm(2, 3) == 6
+@test lcm(4, 6) == 12
+@test lcm(3, 0) == 0
+@test lcm(0, 0) == 0
+@test lcm(4, -6) == 12
+@test lcm(-4, -6) == 12
+
+@test lcm(2, 4, 6) == 12
+
+@test typeof(lcm(int32(2), int32(3))) == Int32
+
+@test gcdx(5, 12) == (1, 5, -2)
+@test gcdx(5, -12) == (1, 5, 2)
+@test gcdx(-25, -4) == (1, -1, 6)
+
+@test invmod(6, 31) == 26
+@test invmod(-1, 3) == 2
+@test invmod(-1, -3) == 2
+@test_throws ErrorException invmod(0, 3)
+
+@test powermod(2, 3, 5) == 3
+@test powermod(2, 3, -5) == -2
+@test_throws DomainError powermod(2, -3, 5)
+
+@test nextpow2(3) == 4
+@test nextpow(2, 3) == 4
+@test nextpow(2, 4) == 4
+@test nextpow(2, 7) == 8
+@test_throws DomainError nextpow(0, 3)
+@test_throws DomainError nextpow(3, 0)
+
+@test prevpow2(3) == 2
+@test prevpow(2, 4) == 4
+@test prevpow(2, 5) == 4
+@test_throws DomainError prevpow(0, 3)
+@test_throws DomainError prevpow(0, 3)
+
+@test bin(3) == "11"
+@test bin(3, 2) == "11"
+@test bin(3, 3) == "011"
+@test bin(-3) == "-11"
+@test bin(-3, 3) == "-011"
+
+@test oct(9) == "11"
+@test oct(-9) == "-11"
+
+@test dec(121) == "121"
+
+@test hex(12) == "c"
+@test hex(-12, 3) == "-00c"
+@test num2hex(1243) == (Int == Int32 ? "000004db" : "00000000000004db")
+
+@test base(2, 5, 7) == "0000101"
+
+@test bits(1035) == (Int == Int32 ? "00000000000000000000010000001011" :
+ "0000000000000000000000000000000000000000000000000000010000001011")
+
+@test digits(4, 2) == [0, 0, 1]
+@test digits(5, 3) == [2, 1]
+
+@test isqrt(4) == 2
+@test isqrt(5) == 2