merge: Consolidate Primality Algorithm testing into single suite (The…

…Algorithms#504)

* chore: add testing interface

* chore: add benchmark helper

* chore: remove individual tests (1)

* chore: remove individual tests (2)

* chore: add miller rabin test suite

* refactor: trial division primality tests

* chore: add trial division test suite

* refactor: trial division tests now accept `int64`

* chore: remove `error` return from `primalityTest`

* fix: remove redundant identifier

* chore: add function names for debug

* chore: fix typo

* chore: add explicit type conversions

* fix: index out of range in tests

* fix: random witness generation

math/prime/millerrabinprimalitytest.go → math/prime/millerrabintest.go

@@ -75,7 +75,7 @@ func MillerTest(num, witness int64) (bool, error) {
 // miller rabin primality test for better probabilitic chances of
 // receiving the correct result with random witnesses.
 func MillerRandomTest(num int64) (bool, error) {
-	random := rand.Int63n(num-1) + 2
+	random := rand.Int63n(num-2) + 2
 	return MillerTest(num, random)
 }
 

math/prime/prime_test.go

@@ -0,0 +1,95 @@
+package prime
+
+import (
+	"fmt"
+	"testing"
+)
+
+var primeList = []int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127}
+var testLimit = 127
+
+type primalityTest func(int64) bool
+
+func primalityTestTestingHelper(t *testing.T, name string, f primalityTest) {
+	arrayIndex := 0
+	for i := 1; i <= testLimit; i++ {
+		isPrime := i == primeList[arrayIndex]
+
+		testName := fmt.Sprintf("%s(%d)", name, i)
+		t.Run(testName, func(t *testing.T) {
+			result := f(int64(i))
+
+			if isPrime {
+				arrayIndex++
+			}
+
+			if result != isPrime {
+				t.Errorf("%d: %s function returned %v\n", i, name, result)
+			}
+		})
+	}
+}
+
+func primalityTestBenchmarkHelper(b *testing.B, f primalityTest) {
+	for i := 0; i < b.N; i++ {
+		f(104729)
+	}
+}
+
+// Miller-Rabin Probabilistic test
+
+func millerRabinProbabilisticTester(n int64) bool {
+	result, err := MillerRabinProbabilistic(n, 40)
+	if err != nil {
+		panic(err)
+	}
+
+	return result
+}
+
+func TestMillerRabinProbabilistic(t *testing.T) {
+	primalityTestTestingHelper(t, "Miller-Rabin Probabilistic", millerRabinProbabilisticTester)
+}
+
+func BenchmarkMillerRabinProbabilistic(b *testing.B) {
+	primalityTestBenchmarkHelper(b, millerRabinProbabilisticTester)
+}
+
+// Miller-Rabin deterministic test
+
+func millerRabinDeterministicTester(n int64) bool {
+	result, err := MillerRabinDeterministic(n)
+	if err != nil {
+		panic(err)
+	}
+
+	return result
+}
+
+func TestMillerRabinDeterministic(t *testing.T) {
+	primalityTestTestingHelper(t, "Miller-Rabin Deterministic", millerRabinDeterministicTester)
+}
+
+func BenchmarkMillerRabinDeterministic(b *testing.B) {
+	primalityTestBenchmarkHelper(b, millerRabinDeterministicTester)
+}
+
+// Trial Division test
+
+func TestTrialDivision(t *testing.T) {
+	primalityTestTestingHelper(t, "Trial Division", TrialDivision)
+}
+
+func BenchmarkTrialDivision(b *testing.B) {
+	primalityTestBenchmarkHelper(b, TrialDivision)
+}
+
+// Trial Division (optimized)
+
+func TestOptimizedTrialDivision(t *testing.T) {
+	primalityTestTestingHelper(t, "Trial Division (optimized)", OptimizedTrialDivision)
+}
+
+func BenchmarkOptimizedTrialDivision(b *testing.B) {
+	primalityTestBenchmarkHelper(b, OptimizedTrialDivision)
+}

math/prime/primecheck.go

@@ -1,15 +1,17 @@
 package prime
 
-// A primality test is an algorithm for determining whether an input number is prime.Among other fields of mathematics, it is used for cryptography.
-//Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not.
-//Source - Wikipedia https://en.wikipedia.org/wiki/Primality_test
+// A primality test is an algorithm for determining whether an input number is prime. Among other
+// fields of mathematics, it is used for cryptography. Unlike integer factorization, primality
+// tests do not generally give prime factors, only stating whether the input number is prime or not.
+// Source - Wikipedia https://en.wikipedia.org/wiki/Primality_test
 
-// NaiveApproach checks if an integer is prime or not. Returns a bool.
-func NaiveApproach(n int) bool {
+// TrialDivision tests whether a number is prime by trying to divide it by the numbers less than it.
+func TrialDivision(n int64) bool {
 	if n < 2 {
 		return false
 	}
-	for i := 2; i < n; i++ {
+
+	for i := int64(2); i < n; i++ {
 
 		if n%i == 0 {
 			return false
@@ -18,12 +20,26 @@ func NaiveApproach(n int) bool {
 	return true
 }
 
-// PairApproach checks primality of an integer and returns a bool. More efficient than the naive approach as number of iterations are less.
-func PairApproach(n int) bool {
+// OptimizedTrialDivision checks primality of an integer using an optimized trial division method.
+// The optimizations include not checking divisibility by the even numbers and only checking up to
+// the square root of the given number.
+func OptimizedTrialDivision(n int64) bool {
+	// 0 and 1 are not prime
 	if n < 2 {
 		return false
 	}
-	for i := 2; i*i <= n; i++ {
+
+	// 2 and 3 are prime
+	if n < 4 {
+		return true
+	}
+
+	// all numbers divisible by 2 except 2 are not prime
+	if n%2 == 0 {
+		return false
+	}
+
+	for i := int64(3); i*i <= n; i += 2 {
 		if n%i == 0 {
 			return false
 		}