Metallic ratios: Difference between revisions

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@@ Line 345: / Line 345: @@
 printlucas(b, len=15) = (for i in take(Lucas(b), len) print(i, ", ") end; println("..."))
+function lucasratios(b, len)
+	iter = BigFloat.(collect(take(Lucas(b), len + 1)))
+	return map(i -> iter[i + 1] / iter[i], 1:length(iter)-1)
+end
 function metallic(b, dplaces=32)
     setprecision(dplaces * 5)
-    estimate, err, x1, iter = big"0.0", BigFloat(10)^(-dplaces), big"1", Lucas(b)
+    ratios, err = lucasratios(b, dplaces * 50), BigFloat(10)^(-dplaces)
+    errors = map(i -> abs(ratios[i + 1] - ratios[i]), 1:length(ratios)-1)
-    next = iterate(iter); (_, state) = next; next = iterate(iter, state)  # iterate past first 1 in sequence
+    iternum = findfirst(x -> x < err, errors)
-    for iterations in 1:dplaces*100
+    println("After $(iternum + 1) iterations, the value of ",
-        (x2, state) = next
+		format(ratios[iternum + 1], precision=dplaces),
-        newestimate = BigFloat(x2) / BigFloat(x1)
+		" is stable to $dplaces decimal places.\n")
-        if abs(newestimate - estimate) < err
-            println("After $iterations iterations, the value of ",
-                format(newestimate, precision=dplaces),
-                " is stable to $dplaces decimal places.\n")
-            break
-        end
-        x1, estimate, next = x2, newestimate, iterate(iter, state)
-    end
 end