improve accuracy of Number.prototype.toExponential polyfills with big and small values

Author: zloirock

CHANGELOG.md

@@ -5,6 +5,7 @@
   - Throw a `RangeError` on `NaN` `start` / `end` / `step`
   - Allow `null` as `optionOrStep`
 - Improved accuracy of `Math.{ asinh, atanh }` polyfills with big and small values
+- Improved accuracy of `Number.prototype.toExponential` polyfills with big and small values
 - Wrap `Symbol.for` in `Symbol.prototype.description` polyfill for correct handling of empty string descriptions
 - Fixed one more case (`Iterator.prototype.take`) of a V8 ~ Chromium < 126 [bug](https://issues.chromium.org/issues/336839115)
 - Forced replacement of `Iterator.{ concat, zip, zipKeyed }` in the pure version for ensuring proper wrapped `Iterator` instances as the result

packages/core-js/modules/es.number.to-exponential.js

@@ -18,6 +18,8 @@ var nativeToExponential = uncurryThis(1.1.toExponential);
 var repeat = uncurryThis($repeat);
 var stringSlice = uncurryThis(''.slice);
 
+var POW_10_308 = pow(10, 308);
+
 // Edge 17-
 var ROUNDS_PROPERLY = nativeToExponential(-6.9e-11, 4) === '-6.9000e-11'
   // IE11- && Edge 14-
@@ -58,7 +60,7 @@ $({ target: 'Number', proto: true, forced: FORCED }, {
     if (f < 0 || f > 20) throw new $RangeError('Incorrect fraction digits');
     if (ROUNDS_PROPERLY) return nativeToExponential(x, f);
     var s = '';
-    var m, e, c, d;
+    var m, e, c, d, l, n, xScaled;
     if (x < 0) {
       s = '-';
       x = -x;
@@ -67,13 +69,20 @@ $({ target: 'Number', proto: true, forced: FORCED }, {
       e = 0;
       m = repeat('0', f + 1);
     } else {
-      // this block is based on https://gist.github.com/SheetJSDev/1100ad56b9f856c95299ed0e068eea08
       // TODO: improve accuracy with big fraction digits
-      var l = log10(x);
+      l = log10(x);
       e = floor(l);
-      var w = pow(10, e - f);
-      var n = round(x / w);
-      if (2 * x >= (2 * n + 1) * w) {
+      // compute x / pow(10, e - f) and round, avoiding underflow/overflow
+      if (f - e >= 308) {
+        // pow(10, e - f) would underflow to a subnormal or zero; split computation
+        xScaled = x * POW_10_308 * pow(10, f - e - 308);
+      } else {
+        xScaled = x / pow(10, e - f);
+      }
+      n = round(xScaled);
+      // correct tie-breaking: round half up
+      // avoids `2 * x` overflow for values near MAX_VALUE
+      if (xScaled - n >= 0.5) {
         n += 1;
       }
       if (n >= pow(10, f + 1)) {

tests/unit-global/es.number.to-exponential.js

@@ -126,6 +126,15 @@ QUnit.test('Number#toExponential', assert => {
   assert.same(toExponential.call(-0, 7), '0.0000000e+0', '-0 and 7');
   assert.same(toExponential.call(-0, 20), '0.00000000000000000000e+0', '-0 and 20');
 
+  // overflow / underflow edge cases
+  assert.same(toExponential.call(9e307, 0), '9e+307', '9e307, 0');
+  assert.same(toExponential.call(-9e307, 0), '-9e+307', '-9e307, 0');
+  assert.same(toExponential.call(Number.MAX_VALUE, 0), '2e+308', 'MAX_VALUE, 0');
+  assert.same(toExponential.call(Number.MAX_VALUE, 5), '1.79769e+308', 'MAX_VALUE, 5');
+  assert.same(toExponential.call(Number.MIN_VALUE, 0), '5e-324', 'MIN_VALUE, 0');
+  assert.same(toExponential.call(Number.MIN_VALUE, 1), '4.9e-324', 'MIN_VALUE, 1');
+  assert.same(toExponential.call(1e-323, 0), '1e-323', '1e-323, 0');
+
   assert.same(toExponential.call(NaN, 1000), 'NaN', 'NaN check before fractionDigits check');
   assert.same(toExponential.call(Infinity, 1000), 'Infinity', 'Infinity check before fractionDigits check');
   assert.notThrows(() => toExponential.call(new Number(1e21), -0.1) === '1e+21');

tests/unit-pure/es.number.to-exponential.js

@@ -122,6 +122,15 @@ QUnit.test('Number#toExponential', assert => {
   assert.same(toExponential.call(-0, 7), '0.0000000e+0', '-0 and 7');
   assert.same(toExponential.call(-0, 20), '0.00000000000000000000e+0', '-0 and 20');
 
+  // overflow / underflow edge cases
+  assert.same(toExponential.call(9e307, 0), '9e+307', '9e307, 0');
+  assert.same(toExponential.call(-9e307, 0), '-9e+307', '-9e307, 0');
+  assert.same(toExponential.call(Number.MAX_VALUE, 0), '2e+308', 'MAX_VALUE, 0');
+  assert.same(toExponential.call(Number.MAX_VALUE, 5), '1.79769e+308', 'MAX_VALUE, 5');
+  assert.same(toExponential.call(Number.MIN_VALUE, 0), '5e-324', 'MIN_VALUE, 0');
+  assert.same(toExponential.call(Number.MIN_VALUE, 1), '4.9e-324', 'MIN_VALUE, 1');
+  assert.same(toExponential.call(1e-323, 0), '1e-323', '1e-323, 0');
+
   assert.same(toExponential.call(NaN, 1000), 'NaN', 'NaN check before fractionDigits check');
   assert.same(toExponential.call(Infinity, 1000), 'Infinity', 'Infinity check before fractionDigits check');
   assert.notThrows(() => toExponential.call(new Number(1e21), -0.1) === '1e+21');