// Copyright 2011 the V8 project authors. All rights reserved. // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are // met: // // * Redistributions of source code must retain the above copyright // notice, this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above // copyright notice, this list of conditions and the following // disclaimer in the documentation and/or other materials provided // with the distribution. // * Neither the name of Google Inc. nor the names of its // contributors may be used to endorse or promote products derived // from this software without specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. // Test Math.sin and Math.cos. // Flags: --allow-natives-syntax assertEquals("-Infinity", String(1/Math.sin(-0))); assertEquals(1, Math.cos(-0)); assertEquals("-Infinity", String(1/Math.tan(-0))); // Assert that minus zero does not cause deopt. function no_deopt_on_minus_zero(x) { return Math.sin(x) + Math.cos(x) + Math.tan(x); } no_deopt_on_minus_zero(1); no_deopt_on_minus_zero(1); %OptimizeFunctionOnNextCall(no_deopt_on_minus_zero); no_deopt_on_minus_zero(-0); assertOptimized(no_deopt_on_minus_zero); function sinTest() { assertEquals(0, Math.sin(0)); assertEquals(1, Math.sin(Math.PI / 2)); } function cosTest() { assertEquals(1, Math.cos(0)); assertEquals(-1, Math.cos(Math.PI)); } sinTest(); cosTest(); // By accident, the slow case for sine and cosine were both sine at // some point. This is a regression test for that issue. var x = Math.pow(2, 30); assertTrue(Math.sin(x) != Math.cos(x)); // Ensure that sine and log are not the same. x = 0.5; assertTrue(Math.sin(x) != Math.log(x)); // Test against approximation by series. var factorial = [1]; var accuracy = 50; for (var i = 1; i < accuracy; i++) { factorial[i] = factorial[i-1] * i; } // We sum up in the reverse order for higher precision, as we expect the terms // to grow smaller for x reasonably close to 0. function precision_sum(array) { var result = 0; while (array.length > 0) { result += array.pop(); } return result; } function sin(x) { var sign = 1; var x2 = x*x; var terms = []; for (var i = 1; i < accuracy; i += 2) { terms.push(sign * x / factorial[i]); x *= x2; sign *= -1; } return precision_sum(terms); } function cos(x) { var sign = -1; var x2 = x*x; x = x2; var terms = [1]; for (var i = 2; i < accuracy; i += 2) { terms.push(sign * x / factorial[i]); x *= x2; sign *= -1; } return precision_sum(terms); } function abs_error(fun, ref, x) { return Math.abs(ref(x) - fun(x)); } var test_inputs = []; for (var i = -10000; i < 10000; i += 177) test_inputs.push(i/1257); var epsilon = 0.0000001; test_inputs.push(0); test_inputs.push(0 + epsilon); test_inputs.push(0 - epsilon); test_inputs.push(Math.PI/2); test_inputs.push(Math.PI/2 + epsilon); test_inputs.push(Math.PI/2 - epsilon); test_inputs.push(Math.PI); test_inputs.push(Math.PI + epsilon); test_inputs.push(Math.PI - epsilon); test_inputs.push(- 2*Math.PI); test_inputs.push(- 2*Math.PI + epsilon); test_inputs.push(- 2*Math.PI - epsilon); var squares = []; for (var i = 0; i < test_inputs.length; i++) { var x = test_inputs[i]; var err_sin = abs_error(Math.sin, sin, x); var err_cos = abs_error(Math.cos, cos, x) assertEqualsDelta(0, err_sin, 1E-13); assertEqualsDelta(0, err_cos, 1E-13); squares.push(err_sin*err_sin + err_cos*err_cos); } // Sum squares up by adding them pairwise, to avoid losing precision. while (squares.length > 1) { var reduced = []; if (squares.length % 2 == 1) reduced.push(squares.pop()); // Remaining number of elements is even. while(squares.length > 1) reduced.push(squares.pop() + squares.pop()); squares = reduced; } var err_rms = Math.sqrt(squares[0] / test_inputs.length / 2); assertEqualsDelta(0, err_rms, 1E-14); assertEquals(-1, Math.cos({ valueOf: function() { return Math.PI; } })); assertEquals(0, Math.sin("0x00000")); assertEquals(1, Math.cos("0x00000")); assertTrue(isNaN(Math.sin(Infinity))); assertTrue(isNaN(Math.cos("-Infinity"))); assertEquals("Infinity", String(Math.tan(Math.PI/2))); assertEquals("-Infinity", String(Math.tan(-Math.PI/2))); assertEquals("-Infinity", String(1/Math.sin("-0"))); // Assert that the remainder after division by pi is reasonably precise. function assertError(expected, x, epsilon) { assertTrue(Math.abs(x - expected) < epsilon); } assertEqualsDelta(0.9367521275331447, Math.cos(1e06), 1e-15); assertEqualsDelta(0.8731196226768560, Math.cos(1e10), 1e-08); assertEqualsDelta(0.9367521275331447, Math.cos(-1e06), 1e-15); assertEqualsDelta(0.8731196226768560, Math.cos(-1e10), 1e-08); assertEqualsDelta(-0.3499935021712929, Math.sin(1e06), 1e-15); assertEqualsDelta(-0.4875060250875106, Math.sin(1e10), 1e-08); assertEqualsDelta(0.3499935021712929, Math.sin(-1e06), 1e-15); assertEqualsDelta(0.4875060250875106, Math.sin(-1e10), 1e-08); assertEqualsDelta(0.7796880066069787, Math.sin(1e16), 1e-05); assertEqualsDelta(-0.6261681981330861, Math.cos(1e16), 1e-05); // Assert that remainder calculation terminates. for (var i = -1024; i < 1024; i++) { assertFalse(isNaN(Math.sin(Math.pow(2, i)))); } assertFalse(isNaN(Math.cos(1.57079632679489700))); assertFalse(isNaN(Math.cos(-1e-100))); assertFalse(isNaN(Math.cos(-1e-323)));