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[inverse-tax] / 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 }