[Tests] acosh: fix precision (#338)

- [Tests] add `to.haveULPDistance` assertion - [Refactor] add `hasULPDistance` helper - use assertion/helper for `cbrt`
paulmillr · Apr 7, 2017 · 6d65367 · Yaffle · Apr 8, 2017 · ljharb
1 parent 488b496
commit 6d65367
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Showing 2 changed files with 35 additions and 5 deletions.
diff --git a/es6-shim.js b/es6-shim.js
@@ -1886,7 +1886,13 @@
       if (numberIsNaN(x) || value < 1) { return NaN; }
       if (x === 1) { return 0; }
       if (x === Infinity) { return x; }
-      return _log((x / E) + (_sqrt(x + 1) * _sqrt(x - 1) / E)) + 1;
+
+      var xInvSquared = 1 / (x * x);
+      if (x < 2) {
+        return _log1p(x - 1 + (_sqrt(1 - xInvSquared) * x));
+      }
+      var halfX = x / 2;
+      return _log1p(halfX + (_sqrt(1 - xInvSquared) * halfX) - 1) + (1 / LOG2E);
     },
 
     asinh: function asinh(value) {
@@ -2064,6 +2070,11 @@
       return sign * result;
     }
   };
+
+  var hasULPDistance = function hasULPDistance(result, expected, distance) {
+    return _abs(1 - (result / expected)) / Number.EPSILON > (distance || 8);
+  };
+
   defineProperties(Math, MathShims);
   // Chrome < 40 sinh returns ∞ for large numbers
   defineProperty(Math, 'sinh', MathShims.sinh, Math.sinh(710) === Infinity);
@@ -2081,8 +2092,10 @@
   defineProperty(Math, 'tanh', MathShims.tanh, Math.tanh(-2e-17) !== -2e-17);
   // Chrome 40 loses Math.acosh precision with high numbers
   defineProperty(Math, 'acosh', MathShims.acosh, Math.acosh(Number.MAX_VALUE) === Infinity);
+  // Chrome < 54 has an inaccurate acosh for EPSILON deltas
+  defineProperty(Math, 'acosh', MathShims.acosh, !hasULPDistance(Math.acosh(1 + Number.EPSILON), Math.sqrt(2 * Number.EPSILON)));
   // Firefox 38 on Windows
-  defineProperty(Math, 'cbrt', MathShims.cbrt, Math.abs(1 - (Math.cbrt(1e-300) / 1e-100)) / Number.EPSILON > 8);
+  defineProperty(Math, 'cbrt', MathShims.cbrt, !hasULPDistance(Math.cbrt(1e-300), 1e-100));
   // node 0.11 has an imprecise Math.sinh with very small numbers
   defineProperty(Math, 'sinh', MathShims.sinh, Math.sinh(-2e-17) !== -2e-17);
   // FF 35 on Linux reports 22025.465794806725 for Math.expm1(10)

diff --git a/test/math.js b/test/math.js
@@ -1,3 +1,5 @@
+var EPSILON = Number.EPSILON || 2.2204460492503130808472633361816e-16;
+
 var Assertion = expect().constructor;
 Assertion.prototype.almostEqual = function (obj, precision) {
   'use strict';
@@ -6,6 +8,11 @@ Assertion.prototype.almostEqual = function (obj, precision) {
   return this.within(obj - allowedDiff, obj + allowedDiff);
 };
 
+Assertion.prototype.haveULPDistance = function (expected, distance) {
+  var actual = this._obj;
+  return this.above(Math.abs(1 - (actual / expected)) / EPSILON, distance);
+};
+
 describe('Math', function () {
   var functionsHaveNames = (function foo() {}).name === 'foo';
   var ifFunctionsHaveNamesIt = functionsHaveNames ? it : xit;
@@ -26,7 +33,6 @@ describe('Math', function () {
   };
   var valueOfIsNaN = { valueOf: function () { return NaN; } };
   var valueOfIsInfinity = { valueOf: function () { return Infinity; } };
-  var EPSILON = Number.EPSILON || 2.2204460492503130808472633361816e-16;
 
   ifShimIt('is on the exported object', function () {
     var exported = require('../');
@@ -67,7 +73,11 @@ describe('Math', function () {
     });
 
     it('works for EPSILON values near 1', function () {
-      expect(Math.acosh(1 + EPSILON)).to.almostEqual(Math.sqrt(2 * EPSILON));
+      var result = Math.acosh(1 + EPSILON);
+      var expected = Math.sqrt(2 * EPSILON);
+
+      expect(result).to.almostEqual(expected);
+      expect(result).to.haveULPDistance(expected, 8);
     });
   });
 
@@ -188,8 +198,15 @@ describe('Math', function () {
       expect(Math.cbrt(8)).to.almostEqual(2);
       expect(Math.cbrt(-1000)).to.almostEqual(-10);
       expect(Math.cbrt(1000)).to.almostEqual(10);
+    });
+
+    it('is correct at extremes', function () {
+      var result = Math.cbrt(1e-300);
+      var expected = 1e-100;
+      expect(result).to.almostEqual(expected);
+      expect(result).to.haveULPDistance(expected, 8);
+
       expect(Math.cbrt(-1e-300)).to.almostEqual(-1e-100);
-      expect(Math.cbrt(1e-300)).to.almostEqual(1e-100);
       expect(Math.cbrt(-1e+300)).to.almostEqual(-1e+100);
       expect(Math.cbrt(1e+300)).to.almostEqual(1e+100);
     });