Ben Murdoch | b8a8cc1 | 2014-11-26 15:28:44 +0000 | [diff] [blame^] | 1 | // Copyright 2014 the V8 project authors. All rights reserved. |
| 2 | // Use of this source code is governed by a BSD-style license that can be |
| 3 | // found in the LICENSE file. |
| 4 | |
| 5 | // Flags: --no-fast-math |
| 6 | |
| 7 | assertTrue(isNaN(Math.expm1(NaN))); |
| 8 | assertTrue(isNaN(Math.expm1(function() {}))); |
| 9 | assertTrue(isNaN(Math.expm1({ toString: function() { return NaN; } }))); |
| 10 | assertTrue(isNaN(Math.expm1({ valueOf: function() { return "abc"; } }))); |
| 11 | assertEquals(Infinity, 1/Math.expm1(0)); |
| 12 | assertEquals(-Infinity, 1/Math.expm1(-0)); |
| 13 | assertEquals(Infinity, Math.expm1(Infinity)); |
| 14 | assertEquals(-1, Math.expm1(-Infinity)); |
| 15 | |
| 16 | |
| 17 | // Sanity check: |
| 18 | // Math.expm1(x) stays reasonably close to Math.exp(x) - 1 for large values. |
| 19 | for (var x = 1; x < 700; x += 0.25) { |
| 20 | var expected = Math.exp(x) - 1; |
| 21 | assertEqualsDelta(expected, Math.expm1(x), expected * 1E-15); |
| 22 | expected = Math.exp(-x) - 1; |
| 23 | assertEqualsDelta(expected, Math.expm1(-x), -expected * 1E-15); |
| 24 | } |
| 25 | |
| 26 | // Approximation for values close to 0: |
| 27 | // Use six terms of Taylor expansion at 0 for exp(x) as test expectation: |
| 28 | // exp(x) - 1 == exp(0) + exp(0) * x + x * x / 2 + ... - 1 |
| 29 | // == x + x * x / 2 + x * x * x / 6 + ... |
| 30 | function expm1(x) { |
| 31 | return x * (1 + x * (1/2 + x * ( |
| 32 | 1/6 + x * (1/24 + x * ( |
| 33 | 1/120 + x * (1/720 + x * ( |
| 34 | 1/5040 + x * (1/40320 + x*( |
| 35 | 1/362880 + x * (1/3628800)))))))))); |
| 36 | } |
| 37 | |
| 38 | // Sanity check: |
| 39 | // Math.expm1(x) stays reasonabliy close to the Taylor series for small values. |
| 40 | for (var x = 1E-1; x > 1E-300; x *= 0.8) { |
| 41 | var expected = expm1(x); |
| 42 | assertEqualsDelta(expected, Math.expm1(x), expected * 1E-15); |
| 43 | } |
| 44 | |
| 45 | |
| 46 | // Tests related to the fdlibm implementation. |
| 47 | // Test overflow. |
| 48 | assertEquals(Infinity, Math.expm1(709.8)); |
| 49 | // Test largest double value. |
| 50 | assertEquals(Infinity, Math.exp(1.7976931348623157e308)); |
| 51 | // Cover various code paths. |
| 52 | assertEquals(-1, Math.expm1(-56 * Math.LN2)); |
| 53 | assertEquals(-1, Math.expm1(-50)); |
| 54 | // Test most negative double value. |
| 55 | assertEquals(-1, Math.expm1(-1.7976931348623157e308)); |
| 56 | // Test argument reduction. |
| 57 | // Cases for 0.5*log(2) < |x| < 1.5*log(2). |
| 58 | assertEquals(Math.E - 1, Math.expm1(1)); |
| 59 | assertEquals(1/Math.E - 1, Math.expm1(-1)); |
| 60 | // Cases for 1.5*log(2) < |x|. |
| 61 | assertEquals(6.38905609893065, Math.expm1(2)); |
| 62 | assertEquals(-0.8646647167633873, Math.expm1(-2)); |
| 63 | // Cases where Math.expm1(x) = x. |
| 64 | assertEquals(0, Math.expm1(0)); |
| 65 | assertEquals(Math.pow(2,-55), Math.expm1(Math.pow(2,-55))); |
| 66 | // Tests for the case where argument reduction has x in the primary range. |
| 67 | // Test branch for k = 0. |
| 68 | assertEquals(0.18920711500272105, Math.expm1(0.25 * Math.LN2)); |
| 69 | // Test branch for k = -1. |
| 70 | assertEquals(-0.5, Math.expm1(-Math.LN2)); |
| 71 | // Test branch for k = 1. |
| 72 | assertEquals(1, Math.expm1(Math.LN2)); |
| 73 | // Test branch for k <= -2 || k > 56. k = -3. |
| 74 | assertEquals(1.4411518807585582e17, Math.expm1(57 * Math.LN2)); |
| 75 | // Test last branch for k < 20, k = 19. |
| 76 | assertEquals(524286.99999999994, Math.expm1(19 * Math.LN2)); |
| 77 | // Test the else branch, k = 20. |
| 78 | assertEquals(1048575, Math.expm1(20 * Math.LN2)); |