Data commit

Task/Metallic-ratios/Zkl/metallic-ratios-1.zkl

@@ -0,0 +1,22 @@
+var [const] BI=Import("zklBigNum");  // libGMP
+fcn lucasSeq(b){
+   Walker.zero().tweak('wrap(xs){
+      xm2,xm1 := xs;	// x[n-2], x[n-1]
+      xn:=xm1*b + xm2;
+      xs.append(xn).del(0);
+      xn
+   }.fp(L(BI(1),BI(1)))).push(1,1)  // xn can get big so use BigInts
+}
+fcn metallicRatio(lucasSeq,digits=32,roundup=True){ #-->(String,num iterations)
+   bige:=BI("1e"+(digits+1));  # x[n-1]*bige*b / x[n-2] to get our digits from Ints
+   a,b,mr := lucasSeq.next(), lucasSeq.next(), (bige*b).div(a);
+   do(20_000){	// limit iterations
+      c,mr2 := lucasSeq.next(), (bige*c).div(b);
+      if(mr==mr2){
+	 mr=mr2.add(5*roundup).div(10).toString();
+	 return(String(mr[0],".",mr.del(0)),
+	    lucasSeq.idx); // idx ignores push(), ie first 2 terms
+      }
+      b,mr = c,mr2;
+   }
+}

Task/Metallic-ratios/Zkl/metallic-ratios-2.zkl

@@ -0,0 +1,7 @@
+metals:="Platinum Golden Silver Bronze Copper Nickel Aluminum Iron Tin Lead";
+foreach metal in (metals.split(" ")){ n:=__metalWalker.idx;
+   println("\nLucas sequence for %s ratio; where b = %d:".fmt(metal,n));
+   println("First 15 elements: ",lucasSeq(n).walk(15).concat(" "));
+   mr,i := metallicRatio(lucasSeq(n));
+   println("Approximated value: %s - Reached after ~%d iterations.".fmt(mr,i));
+}

Task/Metallic-ratios/Zkl/metallic-ratios-3.zkl

@@ -0,0 +1,3 @@
+println("Golden ratio (B==1) to 256 digits:");
+mr,i := metallicRatio(lucasSeq(1),256);
+println("Approximated value: %s\nReached after ~%d iterations.".fmt(mr,i));