Calculate inverse bounds correctly

[inverse-tax] / tax.js

diff --git a/tax.js b/tax.js
index 2b5bd4a1a820a0299683a68fd2aba9d0cbbb8add..cd0027a1475930802935b28e34cba14597ea5fa5 100644 (file)
--- a/tax.js
+++ b/tax.js
@@ -7,11 +7,15 @@ function parse_table(as_text) {
   return as_text.trim().split('\n').map(parse_line);
 }
 
-function parse_tax_table(as_text) {
-  return parse_table(as_text).map(([start, rate], i, table) =>
+function tax_table_from_table(table) {
+  return table.map(([start, rate], i, table) =>
     [start, i < table.length - 1 ? table[i+1][0] : Infinity, rate / 100.0]);
 }
 
+function parse_tax_table(as_text) {
+  return tax_table_from_table(parse_table(as_text));
+}
+
 function sum(nums) {
   return nums.reduce((total, num) => total + num, 0);
 }
@@ -28,8 +32,8 @@ function apply_deductible(table, deductible) {
 function merge_tax_tables(t1, t2) {
   if (t1.length == 0) return t2;
   if (t2.length == 0) return t1;
-  [start1, end1, rate1] = t1[0];
-  [start2, end2, rate2] = t2[0];
+  const [start1, end1, rate1] = t1[0];
+  const [start2, end2, rate2] = t2[0];
   if (start1 == start2) {
     if (end1 == end2) {
       return [[start1, end1, rate1 + rate2]].concat(merge_tax_tables(t1.slice(1), t2.slice(1)));
@@ -47,3 +51,43 @@ 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 [m * start + b, m * end + b, m, b];
+  });
+  return function(net) {
+    for (const [start, end, m, b] of inverse_table) {
+      if (start < net && net < end) {
+        return (net - b) / m;
+      }
+    }
+    return net;
+  };
+}