Upgrade to 3.29
Update V8 to 3.29.88.17 and update makefiles to support building on
all the relevant platforms.
Bug: 17370214
Change-Id: Ia3407c157fd8d72a93e23d8318ccaf6ecf77fa4e
diff --git a/test/mjsunit/sin-cos.js b/test/mjsunit/sin-cos.js
index e38dfdf..fb6f858 100644
--- a/test/mjsunit/sin-cos.js
+++ b/test/mjsunit/sin-cos.js
@@ -27,6 +27,24 @@
// 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));
@@ -42,9 +60,223 @@
// 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, 70);
+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")));
+assertTrue(Math.tan(Math.PI/2) > 1e16);
+assertTrue(Math.tan(-Math.PI/2) < -1e16);
+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)));
+
+// Tests for specific values expected from the fdlibm implementation.
+
+var two_32 = Math.pow(2, -32);
+var two_28 = Math.pow(2, -28);
+
+// Tests for Math.sin for |x| < pi/4
+assertEquals(Infinity, 1/Math.sin(+0.0));
+assertEquals(-Infinity, 1/Math.sin(-0.0));
+// sin(x) = x for x < 2^-27
+assertEquals(two_32, Math.sin(two_32));
+assertEquals(-two_32, Math.sin(-two_32));
+// sin(pi/8) = sqrt(sqrt(2)-1)/2^(3/4)
+assertEquals(0.3826834323650898, Math.sin(Math.PI/8));
+assertEquals(-0.3826834323650898, -Math.sin(Math.PI/8));
+
+// Tests for Math.cos for |x| < pi/4
+// cos(x) = 1 for |x| < 2^-27
+assertEquals(1, Math.cos(two_32));
+assertEquals(1, Math.cos(-two_32));
+// Test KERNELCOS for |x| < 0.3.
+// cos(pi/20) = sqrt(sqrt(2)*sqrt(sqrt(5)+5)+4)/2^(3/2)
+assertEquals(0.9876883405951378, Math.cos(Math.PI/20));
+// Test KERNELCOS for x ~= 0.78125
+assertEquals(0.7100335477927638, Math.cos(0.7812504768371582));
+assertEquals(0.7100338835660797, Math.cos(0.78125));
+// Test KERNELCOS for |x| > 0.3.
+// cos(pi/8) = sqrt(sqrt(2)+1)/2^(3/4)
+assertEquals(0.9238795325112867, Math.cos(Math.PI/8));
+// Test KERNELTAN for |x| < 0.67434.
+assertEquals(0.9238795325112867, Math.cos(-Math.PI/8));
+
+// Tests for Math.tan for |x| < pi/4
+assertEquals(Infinity, 1/Math.tan(0.0));
+assertEquals(-Infinity, 1/Math.tan(-0.0));
+// tan(x) = x for |x| < 2^-28
+assertEquals(two_32, Math.tan(two_32));
+assertEquals(-two_32, Math.tan(-two_32));
+// Test KERNELTAN for |x| > 0.67434.
+assertEquals(0.8211418015898941, Math.tan(11/16));
+assertEquals(-0.8211418015898941, Math.tan(-11/16));
+assertEquals(0.41421356237309503, Math.tan(Math.PI / 8));
+// crbug/427468
+assertEquals(0.7993357819992383, Math.tan(0.6743358));
+
+// Tests for Math.sin.
+assertEquals(0.479425538604203, Math.sin(0.5));
+assertEquals(-0.479425538604203, Math.sin(-0.5));
+assertEquals(1, Math.sin(Math.PI/2));
+assertEquals(-1, Math.sin(-Math.PI/2));
+// Test that Math.sin(Math.PI) != 0 since Math.PI is not exact.
+assertEquals(1.2246467991473532e-16, Math.sin(Math.PI));
+assertEquals(-7.047032979958965e-14, Math.sin(2200*Math.PI));
+// Test Math.sin for various phases.
+assertEquals(-0.7071067811865477, Math.sin(7/4 * Math.PI));
+assertEquals(0.7071067811865474, Math.sin(9/4 * Math.PI));
+assertEquals(0.7071067811865483, Math.sin(11/4 * Math.PI));
+assertEquals(-0.7071067811865479, Math.sin(13/4 * Math.PI));
+assertEquals(-3.2103381051568376e-11, Math.sin(1048576/4 * Math.PI));
+
+// Tests for Math.cos.
+assertEquals(1, Math.cos(two_28));
+// Cover different code paths in KERNELCOS.
+assertEquals(0.9689124217106447, Math.cos(0.25));
+assertEquals(0.8775825618903728, Math.cos(0.5));
+assertEquals(0.7073882691671998, Math.cos(0.785));
+// Test that Math.cos(Math.PI/2) != 0 since Math.PI is not exact.
+assertEquals(6.123233995736766e-17, Math.cos(Math.PI/2));
+// Test Math.cos for various phases.
+assertEquals(0.7071067811865474, Math.cos(7/4 * Math.PI));
+assertEquals(0.7071067811865477, Math.cos(9/4 * Math.PI));
+assertEquals(-0.7071067811865467, Math.cos(11/4 * Math.PI));
+assertEquals(-0.7071067811865471, Math.cos(13/4 * Math.PI));
+assertEquals(0.9367521275331447, Math.cos(1000000));
+assertEquals(-3.435757038074824e-12, Math.cos(1048575/2 * Math.PI));
+
+// Tests for Math.tan.
+assertEquals(two_28, Math.tan(two_28));
+// Test that Math.tan(Math.PI/2) != Infinity since Math.PI is not exact.
+assertEquals(1.633123935319537e16, Math.tan(Math.PI/2));
+// Cover different code paths in KERNELTAN (tangent and cotangent)
+assertEquals(0.5463024898437905, Math.tan(0.5));
+assertEquals(2.0000000000000027, Math.tan(1.107148717794091));
+assertEquals(-1.0000000000000004, Math.tan(7/4*Math.PI));
+assertEquals(0.9999999999999994, Math.tan(9/4*Math.PI));
+assertEquals(-6.420676210313675e-11, Math.tan(1048576/2*Math.PI));
+assertEquals(2.910566692924059e11, Math.tan(1048575/2*Math.PI));
+
+// Test Hayne-Panek reduction.
+assertEquals(0.377820109360752e0, Math.sin(Math.pow(2, 120)));
+assertEquals(-0.9258790228548379e0, Math.cos(Math.pow(2, 120)));
+assertEquals(-0.40806638884180424e0, Math.tan(Math.pow(2, 120)));
+assertEquals(-0.377820109360752e0, Math.sin(-Math.pow(2, 120)));
+assertEquals(-0.9258790228548379e0, Math.cos(-Math.pow(2, 120)));
+assertEquals(0.40806638884180424e0, Math.tan(-Math.pow(2, 120)));