tasks a-s

Task/Nth-root/CoffeeScript/nth-root-1.coffeescript

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+nth_root = (A, n, precision=0.0000000000001) ->
+  x = 1
+  while true
+    x_new = (1 / n) * ((n - 1) * x + A / Math.pow(x, n - 1))
+    return x_new if Math.abs(x_new - x) < precision
+    x = x_new
+
+# tests
+do ->
+  tests = [
+    [8, 3]
+    [16, 4]
+    [32, 5]
+    [343, 3]
+    [1024, 10]
+    [1000000000, 3]
+    [1000000000, 9]
+    [100, 2]
+    [100, 3]
+    [100, 5]
+    [100, 10]
+  ]
+  for test in tests
+    [x, n] = test
+    root = nth_root x, n
+    console.log "#{x} root #{n} = #{root} (root^#{n} = #{Math.pow root, n})"

Task/Nth-root/CoffeeScript/nth-root-2.coffeescript

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+> coffee nth_root.coffee
+8 root 3 = 2 (root^3 = 8)
+16 root 4 = 2 (root^4 = 16)
+32 root 5 = 2 (root^5 = 32)
+343 root 3 = 7 (root^3 = 343)
+1024 root 10 = 2 (root^10 = 1024)
+1000000000 root 3 = 1000 (root^3 = 1000000000)
+1000000000 root 9 = 10 (root^9 = 1000000000)
+100 root 2 = 10 (root^2 = 100)
+100 root 3 = 4.641588833612778 (root^3 = 99.99999999999997)
+100 root 5 = 2.5118864315095806 (root^5 = 100.0000000000001)
+100 root 10 = 1.5848931924611134 (root^10 = 99.99999999999993)