Math updates

Author: williamfiset

README.md

@@ -243,7 +243,6 @@ $ java -cp classes com.williamfiset.algorithms.search.BinarySearch
 - [Prime number sieve (sieve of Eratosthenes)](src/main/java/com/williamfiset/algorithms/math/SieveOfEratosthenes.java) **- O(nlog(log(n)))**
 - [Prime number sieve (sieve of Eratosthenes, compressed)](src/main/java/com/williamfiset/algorithms/math/CompressedPrimeSieve.java) **- O(nlog(log(n)))**
 - [Totient function (phi function, relatively prime number count)](src/main/java/com/williamfiset/algorithms/math/EulerTotientFunction.java) **- O(√n)**
-- [Totient function using sieve (phi function, relatively prime number count)](src/main/java/com/williamfiset/algorithms/math/EulerTotientFunctionWithSieve.java) **- O(nlog(log(n)))**
 - [Extended euclidean algorithm](src/main/java/com/williamfiset/algorithms/math/ExtendedEuclideanAlgorithm.java) **- ~O(log(a + b))**
 - [Greatest Common Divisor (GCD)](src/main/java/com/williamfiset/algorithms/math/Gcd.java) **- ~O(log(a + b))**
 - [Fast Fourier transform (quick polynomial multiplication)](src/main/java/com/williamfiset/algorithms/math/FastFourierTransform.java) **- O(nlog(n))**

src/main/java/com/williamfiset/algorithms/math/BUILD

@@ -21,13 +21,6 @@ java_binary(
     runtime_deps = [":math"],
 )
 
-# bazel run //src/main/java/com/williamfiset/algorithms/math:EulerTotientFunctionWithSieve
-java_binary(
-    name = "EulerTotientFunctionWithSieve",
-    main_class = "com.williamfiset.algorithms.math.EulerTotientFunctionWithSieve",
-    runtime_deps = [":math"],
-)
-
 # bazel run //src/main/java/com/williamfiset/algorithms/math:FastFourierTransform
 java_binary(
     name = "FastFourierTransform",

src/main/java/com/williamfiset/algorithms/math/EulerTotientFunctionWithSieve.java

@@ -55,18 +55,13 @@ public static boolean isPrimeWheel30(long n) {
       return true;
     if (n % 2 == 0 || n % 3 == 0 || n % 5 == 0)
       return false;
+    // Gaps between consecutive residues coprime to 30: 7,11,13,17,19,23,29,31 (i.e. +4,+2,+4,+2,+4,+6,+2,+6).
+    int[] gaps = {4, 2, 4, 2, 4, 6, 2, 6};
     long limit = (long) Math.sqrt(n);
-    int[] offsets = {1, 7, 11, 13, 17, 19, 23, 29};
-    for (long base = 0; base <= limit; base += 30)
-      for (int offset : offsets) {
-        long d = base + offset;
-        if (d < 7)
-          continue;
-        if (d > limit)
-          break;
-        if (n % d == 0)
-          return false;
-      }
+    int gi = 0;
+    for (long d = 7; d <= limit; d += gaps[gi++ % 8])
+      if (n % d == 0)
+        return false;
     return true;
   }