From: Scott Worley <scottworley@scottworley.com>
Date: Thu, 23 May 2019 20:12:56 +0000 (-0700)
Subject: invert
X-Git-Tag: v1.0~18
X-Git-Url: http://git.scottworley.com/inverse-tax/commitdiff_plain/53d6ad337ca89bb5ee82e1ce28fdcf18aec00568

invert
---

diff --git a/tax.js b/tax.js
index 2319d21..0d94200 100644
--- a/tax.js
+++ b/tax.js
@@ -47,3 +47,42 @@ function merge_tax_tables(t1, t2) {
   }
   return merge_tax_tables(t2, t1);
 }
+
+function invert(table) {
+  // Here we solve
+  //   net = m * gross + b
+  // for gross:
+  //   net - b = m * gross
+  //   (net - b) / m = gross
+  // and the calculate the inverse's bounds
+
+  const ms = table.map(([start, end, rate]) => 1 - rate);
+  const full_brackets = [[0]].concat(table.map(([start, end, rate]) => (end - start) * rate)).slice(0, table.length);
+  function sum_lower_brackets(remaining_brackets, acc = 0) {
+    if (remaining_brackets.length == 0) return [];
+    return [acc + remaining_brackets[0]].concat(sum_lower_brackets(remaining_brackets.slice(1), acc + remaining_brackets[0]));
+  }
+  const bs = sum_lower_brackets(full_brackets).map((lower_brackets, i) => {
+    const [start, end, rate] = table[i];
+    // Finding b:
+    //   net = gross - lower_brackets - rate * (gross - start)
+    //   net = gross - lower_brackets - rate * gross + rate * start
+    //   net = gross - rate * gross - lower_brackets + rate * start
+    //   net = (1 - rate) * gross - lower_brackets + rate * start
+    //   net = m * gross - lower_brackets + rate * start
+    //                   \_____________________________/  - here is b
+    return rate * start - lower_brackets;
+  });
+  const inverse_table = table.map(([start, end, rate], i) => {
+    const m = ms[i];
+    const b = bs[i];
+    return [(start - b) / m, (end - b) / m, m, b];
+  });
+  return function(net) {
+    for (const [start, end, m, b] of inverse_table) {
+      if (start < net && net < end) {
+        return (net - b) / m;
+      }
+    }
+  };
+}
diff --git a/tax.test.js b/tax.test.js
index 067ca91..479323b 100644
--- a/tax.test.js
+++ b/tax.test.js
@@ -43,3 +43,9 @@ test("merge tax tables", () => {
     }
   }
 });
+
+test("invert", () => {
+  assert.strictEqual(invert([[ 0, Infinity, .1]])( 9), 10);
+  assert.strictEqual(invert([[10, Infinity, .1]])(19), 20);
+  assert.strictEqual(invert([[0, 100, .1], [100, Infinity, .2]])(170), 200);
+});