From: Scott Worley 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); +});