Data update

Task/Arithmetic-derivative/EasyLang/arithmetic-derivative.easy

@@ -0,0 +1,20 @@
+func lagarias n .
+   if n < 0
+      return -lagarias -n
+   .
+   if n = 0 or n = 1
+      return 0
+   .
+   f = 2
+   while n mod f <> 0
+      f += 1
+   .
+   q = n / f
+   if q = 1
+      return 1
+   .
+   return q * lagarias f + f * lagarias q
+.
+for n = -99 to 100
+   write lagarias n & " "
+.

Task/Arithmetic-derivative/Scala/arithmetic-derivative.scala

@@ -0,0 +1,37 @@
+import java.math.BigInteger
+
+object ArithmeticDerivative extends App {
+
+  println("Arithmetic derivatives for -99 to 100 inclusive:")
+  for {
+    n <- -99 to 100
+    column = n + 100
+  } print(f"${derivative(BigInteger.valueOf(n))}%4d${if (column % 10 == 0) "\n" else " "}")
+
+  println()
+
+  val seven = BigInteger.valueOf(7)
+  for (power <- 1 to 20) {
+    println(f"D(10^$power%d) / 7 = ${derivative(BigInteger.TEN.pow(power)).divide(seven)}")
+  }
+
+  def derivative(aNumber: BigInteger): BigInteger = {
+    if (aNumber.signum == -1) {
+      return derivative(aNumber.negate()).negate()
+    }
+    if (aNumber == BigInteger.ZERO || aNumber == BigInteger.ONE) {
+      return BigInteger.ZERO
+    }
+
+    var divisor = BigInteger.TWO
+    while (divisor.multiply(divisor).compareTo(aNumber) <= 0) {
+      if (aNumber.mod(divisor).signum == 0) {
+        val quotient = aNumber.divide(divisor)
+        return quotient.multiply(derivative(divisor)).add(divisor.multiply(derivative(quotient)))
+      }
+      divisor = divisor.add(BigInteger.ONE)
+    }
+    BigInteger.ONE
+  }
+
+}

Task/Arithmetic-derivative/XPL0/arithmetic-derivative.xpl0

@@ -0,0 +1,28 @@
+function integer Lagarias (N); \Lagarias arithmetic derivative
+integer N;
+integer F, Q;
+
+        function integer SmallPF (J, K); \Smallest prime factor
+        integer J, K;
+        return if rem(J/K) = 0 then K else SmallPF(J, K+1);
+
+begin
+if N < 0
+then return -Lagarias (-N)
+else if N = 0 or N = 1
+then return 0
+else    begin
+        F := SmallPF (N, 2);  Q := N / F;
+        return if Q = 1
+        then 1
+        else Q * Lagarias (F)  +  F * Lagarias (Q)
+        end;
+end \Lagarias\ ;
+
+integer N;
+begin
+    for N:= -99 to 100 do begin
+        IntOut(0, Lagarias(N) );
+        if rem(N/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);
+    end;
+end