// 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: --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, 1/Math.expm1(0)); assertEquals(-Infinity, 1/Math.expm1(-0)); assertEquals(Infinity, Math.expm1(Infinity)); assertEquals(-1, Math.expm1(-Infinity)); // Sanity check: // Math.expm1(x) stays reasonably close to Math.exp(x) - 1 for large values. for (var x = 1; x < 700; x += 0.25) { var expected = Math.exp(x) - 1; assertEqualsDelta(expected, Math.expm1(x), expected * 1E-15); expected = Math.exp(-x) - 1; assertEqualsDelta(expected, Math.expm1(-x), -expected * 1E-15); } // Approximation for 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)))))))))); } // Sanity check: // Math.expm1(x) stays reasonabliy close to the Taylor series for small values. for (var x = 1E-1; x > 1E-300; x *= 0.8) { var expected = expm1(x); assertEqualsDelta(expected, Math.expm1(x), expected * 1E-15); } // Tests related to the fdlibm implementation. // Test overflow. assertEquals(Infinity, Math.expm1(709.8)); // Test largest double value. assertEquals(Infinity, Math.exp(1.7976931348623157e308)); // Cover various code paths. assertEquals(-1, Math.expm1(-56 * Math.LN2)); assertEquals(-1, Math.expm1(-50)); // Test most negative double value. assertEquals(-1, Math.expm1(-1.7976931348623157e308)); // Test argument reduction. // Cases for 0.5*log(2) < |x| < 1.5*log(2). assertEquals(Math.E - 1, Math.expm1(1)); assertEquals(1/Math.E - 1, Math.expm1(-1)); // Cases for 1.5*log(2) < |x|. assertEquals(6.38905609893065, Math.expm1(2)); assertEquals(-0.8646647167633873, Math.expm1(-2)); // Cases where Math.expm1(x) = x. assertEquals(0, Math.expm1(0)); assertEquals(Math.pow(2,-55), Math.expm1(Math.pow(2,-55))); // Tests for the case where argument reduction has x in the primary range. // Test branch for k = 0. assertEquals(0.18920711500272105, Math.expm1(0.25 * Math.LN2)); // Test branch for k = -1. assertEquals(-0.5, Math.expm1(-Math.LN2)); // Test branch for k = 1. assertEquals(1, Math.expm1(Math.LN2)); // Test branch for k <= -2 || k > 56. k = -3. assertEquals(1.4411518807585582e17, Math.expm1(57 * Math.LN2)); // Test last branch for k < 20, k = 19. assertEquals(524286.99999999994, Math.expm1(19 * Math.LN2)); // Test the else branch, k = 20. assertEquals(1048575, Math.expm1(20 * Math.LN2));