Convert decimal number to rational: Difference between revisions

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@@ Line 1,409: / Line 1,409: @@
 Deriving an approximation within a specified tolerance:
 <syntaxhighlight lang="javascript">(() => {
-    'use strict';
+    "use strict";
+    // ---------------- APPROXIMATE RATIO ----------------
+    // approxRatio :: Real -> Real -> Ratio
+    const approxRatio = epsilon =>
+        n => {
+            const
+                c = gcdApprox(
+< epsilon
+                        ? epsilon
+                        : (1 / 10000)
+                )(1, n);
+            return Ratio(
+                Math.floor(n / c),
+                Math.floor(1 / c)
+            );
+        };
+    // gcdApprox :: Real -> (Real, Real) -> Real
+    const gcdApprox = epsilon =>
+        (x, y) => {
+            const _gcd = (a, b) =>
+                b < epsilon
+                    ? a
+                    : _gcd(b, a % b);
+            return _gcd(Math.abs(x), Math.abs(y));
+        };
+    // ---------------------- TEST -----------------------
+    // main :: IO ()
     const main = () =>
-        showJSON(
+        // Using a tolerance of 1/10000
+        [0.9054054, 0.518518, 0.75]
-            map( // Using a tolerance epsilon of 1/10000
+        .map(
-                n => showRatio(approxRatio(0.0001)(n)),
-                [0.9054054, 0.518518, 0.75]
+            compose(
+                showRatio,
+                approxRatio(0.0001)
             )
-        );
+        )
+        .join("\n");
-    // Epsilon -> Real -> Ratio
+    // ---------------- GENERIC FUNCTIONS ----------------
-    // approxRatio :: Real -> Real -> Ratio
-    const approxRatio = eps => n => {
+    // compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
-        const
-            gcde = (e, x, y) => {
+    const compose = (...fs) =>
+    // A function defined by the right-to-left
-                const _gcd = (a, b) => (b < e ? a : _gcd(b, a % b));
+    // composition of all the functions in fs.
-                return _gcd(Math.abs(x), Math.abs(y));
-            },
+        fs.reduce(
-            c = gcde(Boolean(eps) ? eps : (1 / 10000), 1, n);
+            (f, g) => x => f(g(x)),
-        return Ratio(
+            x => x
-            Math.floor(n / c), // numerator
-            Math.floor(1 / c) // denominator
         );
-    };
-    // GENERIC FUNCTIONS ----------------------------------
     // Ratio :: Int -> Int -> Ratio
     const Ratio = (n, d) => ({
-        type: 'Ratio',
+        type: "Ratio",
-        'n': n, // numerator
+        n,
-        'd': d // denominator
+        d
     });
-    // map :: (a -> b) -> [a] -> [b]
-    const map = (f, xs) => xs.map(f);
-    // showJSON :: a -> String
-    const showJSON = x => JSON.stringify(x, null, 2);
     // showRatio :: Ratio -> String
     const showRatio = nd =>
-        nd.n.toString() + '/' + nd.d.toString();
+        `${nd.n.toString()}/${nd.d.toString()}`;
     // MAIN ---
@@ Line 1,458: / Line 1,485: @@
 })();</syntaxhighlight>
 {{Out}}
-<pre>[
+<pre>67/74
+/27
-  "67/74",
+/4</pre>
-  "14/27",
-  "3/4"
-]</pre>
 =={{header|jq}}==