git.scottworley.com Git - inverse-tax/blob - tax.js

   1 "use strict";
   2
   3 function parse_table(as_text) {
   4   function parse_line(line) {
   5     return line.trim().split(' ').filter(x => x !== '').map(x => parseFloat(x));
   6   }
   7   return as_text.trim().split('\n').map(parse_line);
   8 }
   9
  10 function tax_table_from_table(table) {
  11   return table.map(([start, rate], i, table) =>
  12     [start, i < table.length - 1 ? table[i+1][0] : Infinity, rate / 100.0]);
  13 }
  14
  15 function parse_tax_table(as_text) {
  16   return tax_table_from_table(parse_table(as_text));
  17 }
  18
  19 function sum(nums) {
  20   return nums.reduce((total, num) => total + num, 0);
  21 }
  22
  23 function tax(table, income) {
  24   return sum(table.map(([start, end, rate]) =>
  25     Math.max(0, Math.min(income, end) - start) * rate));
  26 }
  27
  28 function apply_deductible(table, deductible) {
  29   return table.map(([start, end, rate]) => [start + deductible, end + deductible, rate]);
  30 }
  31
  32 function merge_tax_tables(t1, t2) {
  33   if (t1.length == 0) return t2;
  34   if (t2.length == 0) return t1;
  35   const [start1, end1, rate1] = t1[0];
  36   const [start2, end2, rate2] = t2[0];
  37   if (start1 == start2) {
  38     if (end1 == end2) {
  39       return [[start1, end1, rate1 + rate2]].concat(merge_tax_tables(t1.slice(1), t2.slice(1)));
  40     }
  41     if (end1 < end2) {
  42       return [[start1, end1, rate1 + rate2]].concat(merge_tax_tables(t1.slice(1), [[end1, end2, rate2]].concat(t2.slice(1))));
  43     }
  44     return merge_tax_tables(t2, t1);
  45   }
  46   if (start1 < start2) {
  47     if (end1 <= start2) {
  48       return [t1[0]].concat(merge_tax_tables(t1.slice(1), t2));
  49     }
  50     return [[start1, start2, rate1]].concat(merge_tax_tables([[start2, end1, rate1]].concat(t1.slice(1)), t2));
  51   }
  52   return merge_tax_tables(t2, t1);
  53 }
  54
  55 function invert(table) {
  56   if (table.length == 0) return x => x;
  57
  58   // Here we solve
  59   //   net = m * gross + b
  60   // for gross:
  61   //   net - b = m * gross
  62   //   (net - b) / m = gross
  63   // and the calculate the inverse's bounds
  64
  65   const ms = table.map(([start, end, rate]) => 1 - rate);
  66   const full_brackets = [[0]].concat(table.map(([start, end, rate]) => (end - start) * rate)).slice(0, table.length);
  67   function sum_lower_brackets(remaining_brackets, acc = 0) {
  68     if (remaining_brackets.length == 0) return [];
  69     return [acc + remaining_brackets[0]].concat(sum_lower_brackets(remaining_brackets.slice(1), acc + remaining_brackets[0]));
  70   }
  71   const bs = sum_lower_brackets(full_brackets).map((lower_brackets, i) => {
  72     const [start, end, rate] = table[i];
  73     // Finding b:
  74     //   net = gross - lower_brackets - rate * (gross - start)
  75     //   net = gross - lower_brackets - rate * gross + rate * start
  76     //   net = gross - rate * gross - lower_brackets + rate * start
  77     //   net = (1 - rate) * gross - lower_brackets + rate * start
  78     //   net = m * gross - lower_brackets + rate * start
  79     //                   \_____________________________/  - here is b
  80     return rate * start - lower_brackets;
  81   });
  82   const inverse_table = table.map(([start, end, rate], i) => {
  83     const m = ms[i];
  84     const b = bs[i];
  85     return [(start - b) / m, (end - b) / m, m, b];
  86   });
  87   return function(net) {
  88     for (const [start, end, m, b] of inverse_table) {
  89       if (start < net && net < end) {
  90         return (net - b) / m;
  91       }
  92     }
  93   };
  94 }