improve accuracy of Math.{ asinh, cbrt, log1p } polyfills with big and small values

CHANGELOG.md

@@ -4,7 +4,7 @@
 - Fixed possible early error in `get-iterator-method` helper
 - Added missed `MAX_SAFE_INTEGER` excess check in `Array.from` and `{ Map, Object }.groupBy` polyfills
 - Improved the way of inner iterators cleaning in iterator helpers
-- Improved accuracy of `Math.asinh` polyfill
+- Improved accuracy of `Math.{ asinh, cbrt, log1p }` polyfills with big and small values
 - Improved performance of `Uint8Array` base64 methods
 - Improved performance of `es.escape`
 - Slight performance improvement for engines with native `Array#fill` on `ArrayBuffer` constructor and `%TypedArray%#fill`

packages/core-js/internals/math-log1p.js

@@ -6,5 +6,7 @@ var log = Math.log;
 // eslint-disable-next-line es/no-math-log1p -- safe
 module.exports = Math.log1p || function log1p(x) {
   var n = +x;
-  return n > -1e-8 && n < 1e-8 ? n - n * n / 2 : log(1 + n);
+  if (n > -1e-8 && n < 1e-8) return n - n * n / 2;
+  var u = 1 + n;
+  return u === 1 ? n : n === u - 1 ? log(u) : n * log(u) / (u - 1);
 };

packages/core-js/modules/es.math.asinh.js

@@ -1,5 +1,6 @@
 'use strict';
 var $ = require('../internals/export');
+var log1p = require('../internals/math-log1p');
 
 // eslint-disable-next-line es/no-math-asinh -- required for testing
 var $asinh = Math.asinh;
@@ -11,7 +12,8 @@ var SQRT_2_POW_53 = 94906265.62425156;
 
 function asinh(x) {
   var n = +x;
-  return !isFinite(n) || n === 0 ? n : n < 0 ? -asinh(-n) : n > SQRT_2_POW_53 ? log(n) + LN2 : n < 1e-8 ? n : log(n + sqrt(n * n + 1));
+  return !isFinite(n) || n === 0 ? n : n < 0 ? -asinh(-n) : n > SQRT_2_POW_53 ? log(n) + LN2
+    : n < 1e-8 ? n : log1p(n + n * n / (1 + sqrt(n * n + 1)));
 }
 
 var FORCED = !($asinh && 1 / $asinh(0) > 0);

packages/core-js/modules/es.math.cbrt.js

@@ -10,6 +10,8 @@ var pow = Math.pow;
 $({ target: 'Math', stat: true }, {
   cbrt: function cbrt(x) {
     var n = +x;
-    return sign(n) * pow(abs(n), 1 / 3);
+    var y = sign(n) * pow(abs(n), 1 / 3);
+    // Newton-Raphson refinement for better precision
+    return n !== 0 && isFinite(n) ? (2 * y + n / (y * y)) / 3 : y;
   }
 });

tests/unit-global/es.math.asinh.js

@@ -24,6 +24,10 @@ QUnit.test('Math.asinh', assert => {
   assert.closeTo(asinh(1e-16), 1e-16, 1e-30, 'small value 1e-16');
   assert.closeTo(asinh(1e-20), 1e-20, 1e-34, 'small value 1e-20');
   assert.closeTo(asinh(-1e-16), -1e-16, 1e-30, 'small negative value -1e-16');
+  assert.closeTo(asinh(1e-8), 1e-8, 1e-16, 'precision at 1e-8');
+  assert.closeTo(asinh(1e-5), 9.999999999833334e-6, 1e-16, 'precision at 1e-5');
+  assert.closeTo(asinh(0.01), 0.009999833340832886, 1e-14, 'precision at 0.01');
+  assert.closeTo(asinh(0.1), 0.09983407889920758, 1e-14, 'precision at 0.1');
 
   const checker = createConversionChecker(1234);
   assert.closeTo(asinh(checker), 7.811163549201245, 1e-11);

tests/unit-global/es.math.cbrt.js

@@ -16,6 +16,12 @@ QUnit.test('Math.cbrt', assert => {
   assert.same(cbrt(8), 2);
   assert.closeTo(cbrt(-1000), -10, 1e-11);
   assert.closeTo(cbrt(1000), 10, 1e-11);
+  assert.same(cbrt(27), 3, 'exact cube root of 27');
+  assert.same(cbrt(64), 4, 'exact cube root of 64');
+  assert.same(cbrt(125), 5, 'exact cube root of 125');
+  assert.same(cbrt(-27), -3, 'exact cube root of -27');
+  assert.closeTo(cbrt(1e-300), 1e-100, 1e-114, 'extreme small value');
+  assert.closeTo(cbrt(1e300), 1e100, 1e86, 'extreme large value');
 
   const checker = createConversionChecker(1000);
   assert.closeTo(cbrt(checker), 10, 1e-11);

tests/unit-global/es.math.log1p.js

@@ -16,6 +16,8 @@ QUnit.test('Math.log1p', assert => {
   assert.same(log1p(Infinity), Infinity);
   assert.closeTo(log1p(5), 1.791759469228055, 1e-11);
   assert.closeTo(log1p(50), 3.9318256327243257, 1e-11);
+  assert.closeTo(log1p(0.01), 0.00995033085317, 1e-14, 'small value 0.01');
+  assert.closeTo(log1p(0.1), 0.0953101798043, 1e-13, 'small value 0.1');
 
   const checker = createConversionChecker(5);
   assert.closeTo(log1p(checker), 1.791759469228055, 1e-11);

tests/unit-pure/es.math.asinh.js

@@ -23,6 +23,10 @@ QUnit.test('Math.asinh', assert => {
   assert.closeTo(asinh(1e-16), 1e-16, 1e-30, 'small value 1e-16');
   assert.closeTo(asinh(1e-20), 1e-20, 1e-34, 'small value 1e-20');
   assert.closeTo(asinh(-1e-16), -1e-16, 1e-30, 'small negative value -1e-16');
+  assert.closeTo(asinh(1e-8), 1e-8, 1e-16, 'precision at 1e-8');
+  assert.closeTo(asinh(1e-5), 9.999999999833334e-6, 1e-16, 'precision at 1e-5');
+  assert.closeTo(asinh(0.01), 0.009999833340832886, 1e-14, 'precision at 0.01');
+  assert.closeTo(asinh(0.1), 0.09983407889920758, 1e-14, 'precision at 0.1');
 
   const checker = createConversionChecker(1234);
   assert.closeTo(asinh(checker), 7.811163549201245, 1e-11);

tests/unit-pure/es.math.cbrt.js

@@ -15,6 +15,12 @@ QUnit.test('Math.cbrt', assert => {
   assert.same(cbrt(8), 2);
   assert.closeTo(cbrt(-1000), -10, 1e-11);
   assert.closeTo(cbrt(1000), 10, 1e-11);
+  assert.same(cbrt(27), 3, 'exact cube root of 27');
+  assert.same(cbrt(64), 4, 'exact cube root of 64');
+  assert.same(cbrt(125), 5, 'exact cube root of 125');
+  assert.same(cbrt(-27), -3, 'exact cube root of -27');
+  assert.closeTo(cbrt(1e-300), 1e-100, 1e-114, 'extreme small value');
+  assert.closeTo(cbrt(1e300), 1e100, 1e86, 'extreme large value');
 
   const checker = createConversionChecker(1000);
   assert.closeTo(cbrt(checker), 10, 1e-11);

tests/unit-pure/es.math.log1p.js

@@ -15,6 +15,8 @@ QUnit.test('Math.log1p', assert => {
   assert.same(log1p(Infinity), Infinity);
   assert.closeTo(log1p(5), 1.791759469228055, 1e-11);
   assert.closeTo(log1p(50), 3.9318256327243257, 1e-11);
+  assert.closeTo(log1p(0.01), 0.00995033085317, 1e-14, 'small value 0.01');
+  assert.closeTo(log1p(0.1), 0.0953101798043, 1e-13, 'small value 0.1');
 
   const checker = createConversionChecker(5);
   assert.closeTo(log1p(checker), 1.791759469228055, 1e-11);