2 files changed, 105 insertions, 0 deletions
diff --git a/factors/property_test.go b/factors/property_test.go
new file mode 100644
index 0000000..7072050
--- /dev/null
+++ b/factors/property_test.go
@@ -0,0 +1,105 @@
+package factors
+
+import (
+	"fmt"
+	"math/rand"
+	"testing"
+)
+
+// TestFactorsDivisible ensures that every number returned by
+// Factors is actually a factor of the argument.
+func TestFactorsDivisible(t *testing.T) {
+	for r := uint(1); r < (1 << 16); r++ {
+		t.Run(fmt.Sprintf("%d", r), func(t *testing.T) {
+			testFactorsDivisibleOnce(t, r)
+		})
+	}
+}
+
+// One execution of TestFactorsDivisible
+func testFactorsDivisibleOnce(t *testing.T, r uint) {
+	t.Parallel()
+	factors := Factors(r)
+	for _, factor := range factors {
+		if r%factor != 0 {
+			t.Errorf("%d reported as factor of %d, but not divisible", factor, r)
+		}
+	}
+}
+
+// TestTotatives ensures that every number returned by
+// TotativeDigits is actually a totative of the argument.
+// It also tests that len(TotativeDigits(r)) = Totient(r).
+func TestTotatives(t *testing.T) {
+	for r := uint32(0); r < (1 << 12); r++ {
+		t.Run(fmt.Sprintf("%d", r), func(t *testing.T) {
+			testTotativesOnce(t, r)
+		})
+	}
+}
+
+// TestTotativesRandom is like TestTotatives,
+// except it randomly chooses radices.
+func TestTotativesRandom(t *testing.T) {
+	for testRun := 0; testRun < 144; testRun++ {
+		r := uint32(rand.Int31n(1 << 16))
+		t.Run(fmt.Sprintf("%d", r), func(t *testing.T) {
+			testTotativesOnce(t, r)
+		})
+	}
+}
+
+// One execution of TestTotatives
+func testTotativesOnce(t *testing.T, r uint32) {
+	t.Parallel()
+	totatives := TotativeDigits(r)
+	for _, totative := range totatives {
+		if gcd(totative, r) != 1 {
+			t.Errorf("%d reported as totative of %d, but gcd(%d, %d) = %d",
+				totative, r, totative, r, gcd(totative, r))
+		}
+	}
+
+	totient := Totient(uint(r))
+	if uint(len(totatives)) != totient {
+		t.Errorf(
+			"len(TotativeDigits(%d)) = %d, Totient(%d) = %d, should be equal",
+			r, len(totatives), r, totient)
+	}
+}
+
+// TestSplitProperties tests Split(digit, radix) to ensure
+// totative is a totative and regular * totative = digit.
+func TestSplitProperties(t *testing.T) {
+	for radix := uint(1); radix < 1<<7; radix++ {
+		for digit := uint(1); digit < 1<<8; digit++ {
+			t.Run(fmt.Sprintf("radix=%d,digit=%d", radix, digit),
+				func(t *testing.T) { testSplitOnce(t, digit, radix) })
+		}
+	}
+}
+
+// TestSplitRandom is like TestSplitProperties,
+// but with randomly chosen values.
+func TestSplitRandom(t *testing.T) {
+	for i := 0; i < 1728; i++ {
+		radix := uint(rand.Int31n((1<<15)-1)) + 1
+		digit := uint(rand.Int31n((1<<16)-1)) + 1
+		t.Run(fmt.Sprintf("radix=%d,digit=%d", radix, digit),
+			func(t *testing.T) { testSplitOnce(t, digit, radix) })
+	}
+}
+
+// One execution of TestSplitProperties
+func testSplitOnce(t *testing.T, digit, radix uint) {
+	t.Parallel()
+	regular, totative := Split(digit, radix)
+	if gcd(uint32(totative), uint32(radix)) != 1 {
+		t.Errorf("Split(%d, %d) = %d, %d; %d not coprime to %d.",
+			digit, radix, regular, totative, totative, radix)
+	}
+	if regular*totative != digit {
+		t.Errorf("Split(%d, %d) = %d, %d; %d * %d ≠ %d.",
+			digit, radix, regular, totative, regular, totative, digit)
+	}
+}
diff --git a/factors/factors_test.go b/factors/table_test.go
index ab06aba..ab06aba 100644
--- a/factors/factors_test.go
+++ b/factors/table_test.go