OLD | NEW |
1 // Copyright 2011 the V8 project authors. All rights reserved. | 1 // Copyright 2011 the V8 project authors. All rights reserved. |
2 // Redistribution and use in source and binary forms, with or without | 2 // Redistribution and use in source and binary forms, with or without |
3 // modification, are permitted provided that the following conditions are | 3 // modification, are permitted provided that the following conditions are |
4 // met: | 4 // met: |
5 // | 5 // |
6 // * Redistributions of source code must retain the above copyright | 6 // * Redistributions of source code must retain the above copyright |
7 // notice, this list of conditions and the following disclaimer. | 7 // notice, this list of conditions and the following disclaimer. |
8 // * Redistributions in binary form must reproduce the above | 8 // * Redistributions in binary form must reproduce the above |
9 // copyright notice, this list of conditions and the following | 9 // copyright notice, this list of conditions and the following |
10 // disclaimer in the documentation and/or other materials provided | 10 // disclaimer in the documentation and/or other materials provided |
(...skipping 24 matching lines...) Expand all Loading... |
35 function cosTest() { | 35 function cosTest() { |
36 assertEquals(1, Math.cos(0)); | 36 assertEquals(1, Math.cos(0)); |
37 assertEquals(-1, Math.cos(Math.PI)); | 37 assertEquals(-1, Math.cos(Math.PI)); |
38 } | 38 } |
39 | 39 |
40 sinTest(); | 40 sinTest(); |
41 cosTest(); | 41 cosTest(); |
42 | 42 |
43 // By accident, the slow case for sine and cosine were both sine at | 43 // By accident, the slow case for sine and cosine were both sine at |
44 // some point. This is a regression test for that issue. | 44 // some point. This is a regression test for that issue. |
45 var x = Math.pow(2, 70); | 45 var x = Math.pow(2, 30); |
46 assertTrue(Math.sin(x) != Math.cos(x)); | 46 assertTrue(Math.sin(x) != Math.cos(x)); |
47 | 47 |
48 // Ensure that sine and log are not the same. | 48 // Ensure that sine and log are not the same. |
49 x = 0.5; | 49 x = 0.5; |
50 assertTrue(Math.sin(x) != Math.log(x)); | 50 assertTrue(Math.sin(x) != Math.log(x)); |
| 51 |
| 52 // Test against approximation by series. |
| 53 var factorial = [1]; |
| 54 var accuracy = 50; |
| 55 for (var i = 1; i < accuracy; i++) { |
| 56 factorial[i] = factorial[i-1] * i; |
| 57 } |
| 58 |
| 59 // We sum up in the reverse order for higher precision, as we expect the terms |
| 60 // to grow smaller for x reasonably close to 0. |
| 61 function precision_sum(array) { |
| 62 var result = 0; |
| 63 while (array.length > 0) { |
| 64 result += array.pop(); |
| 65 } |
| 66 return result; |
| 67 } |
| 68 |
| 69 function sin(x) { |
| 70 var sign = 1; |
| 71 var x2 = x*x; |
| 72 var terms = []; |
| 73 for (var i = 1; i < accuracy; i += 2) { |
| 74 terms.push(sign * x / factorial[i]); |
| 75 x *= x2; |
| 76 sign *= -1; |
| 77 } |
| 78 return precision_sum(terms); |
| 79 } |
| 80 |
| 81 function cos(x) { |
| 82 var sign = -1; |
| 83 var x2 = x*x; |
| 84 x = x2; |
| 85 var terms = [1]; |
| 86 for (var i = 2; i < accuracy; i += 2) { |
| 87 terms.push(sign * x / factorial[i]); |
| 88 x *= x2; |
| 89 sign *= -1; |
| 90 } |
| 91 return precision_sum(terms); |
| 92 } |
| 93 |
| 94 function abs_error(fun, ref, x) { |
| 95 return Math.abs(ref(x) - fun(x)); |
| 96 } |
| 97 |
| 98 var test_inputs = []; |
| 99 for (var i = -10000; i < 10000; i += 177) test_inputs.push(i/1257); |
| 100 var epsilon = 0.000001; |
| 101 |
| 102 test_inputs.push(0); |
| 103 test_inputs.push(0 + epsilon); |
| 104 test_inputs.push(0 - epsilon); |
| 105 test_inputs.push(Math.PI/2); |
| 106 test_inputs.push(Math.PI/2 + epsilon); |
| 107 test_inputs.push(Math.PI/2 - epsilon); |
| 108 test_inputs.push(Math.PI); |
| 109 test_inputs.push(Math.PI + epsilon); |
| 110 test_inputs.push(Math.PI - epsilon); |
| 111 test_inputs.push(- 2*Math.PI); |
| 112 test_inputs.push(- 2*Math.PI + epsilon); |
| 113 test_inputs.push(- 2*Math.PI - epsilon); |
| 114 |
| 115 var squares = []; |
| 116 for (var i = 0; i < test_inputs.length; i++) { |
| 117 var x = test_inputs[i]; |
| 118 var err_sin = abs_error(Math.sin, sin, x); |
| 119 var err_cos = abs_error(Math.cos, cos, x) |
| 120 assertTrue(err_sin < 1E-13); |
| 121 assertTrue(err_cos < 1E-13); |
| 122 squares.push(err_sin*err_sin + err_cos*err_cos); |
| 123 } |
| 124 |
| 125 // Sum squares up by adding them pairwise, to avoid losing precision. |
| 126 while (squares.length > 1) { |
| 127 var reduced = []; |
| 128 if (squares.length % 2 == 1) reduced.push(squares.pop()); |
| 129 // Remaining number of elements is even. |
| 130 while(squares.length > 1) reduced.push(squares.pop() + squares.pop()); |
| 131 squares = reduced; |
| 132 } |
| 133 |
| 134 var err_rms = Math.sqrt(squares[0] / test_inputs.length / 2); |
| 135 assertTrue(err_rms < 1E-14); |
| 136 |
| 137 assertEquals(-1, Math.cos({ valueOf: function() { return Math.PI; } })); |
| 138 assertEquals(0, Math.sin("0x00000")); |
| 139 assertTrue(isNaN(Math.sin(Infinity))); |
| 140 assertTrue(isNaN(Math.cos("-Infinity"))); |
| 141 assertEquals("Infinity", String(Math.tan(Math.PI/2))); |
| 142 assertEquals("-Infinity", String(Math.tan(-Math.PI/2))); |
OLD | NEW |