Harmony: implement Math.cbrt, Math.expm1 and Math.log1p.

test/mjsunit/harmony/math-expm1.js

+// Copyright 2014 the V8 project authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// Flags: --harmony-maths --no-fast-math
+
+assertTrue(isNaN(Math.expm1(NaN)));
+assertTrue(isNaN(Math.expm1(function() {})));
+assertTrue(isNaN(Math.expm1({ toString: function() { return NaN; } })));
+assertTrue(isNaN(Math.expm1({ valueOf: function() { return "abc"; } })));
+assertEquals("Infinity", String(1/Math.expm1(0)));
+assertEquals("-Infinity", String(1/Math.expm1(-0)));
+assertEquals("Infinity", String(Math.expm1(Infinity)));
+assertEquals(-1, Math.expm1(-Infinity));
+
+for (var x = 0.1; x < 700; x += 0.1) {
+  var expected = Math.exp(x) - 1;
+  assertEqualsDelta(expected, Math.expm1(x), expected * 1E-14);
+  expected = Math.exp(-x) - 1;
+  assertEqualsDelta(expected, Math.expm1(-x), -expected * 1E-14);
+}
+
+// Values close to 0:
+// Use six terms of Taylor expansion at 0 for exp(x) as test expectation:
+// exp(x) - 1 == exp(0) + exp(0) * x + x * x / 2 + ... - 1
+//            == x + x * x / 2 + x * x * x / 6 + ...
+function expm1(x) {
+  return x * (1 + x * (1/2 + x * (
+              1/6 + x * (1/24 + x * (
+              1/120 + x * (1/720 + x * (
+              1/5040 + x * (1/40320 + x*(
+              1/362880 + x * (1/3628800))))))))));
+}
+
+for (var x = 1E-1; x > 1E-300; x *= 0.8) {
+  var expected = expm1(x);
+  assertEqualsDelta(expected, Math.expm1(x), expected * 1E-14);
+}