Implement Math.sin, cos and tan using table lookup and spline interpolation.

test/mjsunit/sin-cos.js

Index: test/mjsunit/sin-cos.js
diff --git a/test/mjsunit/sin-cos.js b/test/mjsunit/sin-cos.js
index e38dfdf814e18c7013b288a4d0c460a7a5355096..5d7b5aa6812cee57942c1f02aa627959fef66ee4 100644
--- a/test/mjsunit/sin-cos.js
+++ b/test/mjsunit/sin-cos.js
@@ -42,9 +42,97 @@ 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, 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;
+}
+
+function 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 = [];

[Jakob Kummerow, 2013/10/29 17:17:53]

Might wanna add a comment here that the reason for the "needless" allocation is
that we sum up the terms in reverse order for increased precision.

+  for (var i = 1; i < accuracy; i += 2) {
+    terms.push(sign * x / factorial[i]);
+    x *= x2;
+    sign *= -1;
+  }
+  return 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 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 = 0.000001;
+
+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)
+  assertTrue(err_sin < 1E-13);
+  assertTrue(err_cos < 1E-13);
+  squares.push(err_sin*err_sin + err_cos*err_cos);
+}
+
+// Sum squares up by adding them pairwise, to avoid not losing precision.

[Jakob Kummerow, 2013/10/29 17:17:53]

s/not // ;-)

+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);
+assertTrue(err_rms < 1E-14);
+
+assertEquals(-1, Math.cos({ valueOf: function() { return Math.PI; } }));
+assertEquals(0, Math.sin("0x00000"));
+assertTrue(isNaN(Math.sin(Infinity)));
+assertTrue(isNaN(Math.cos("-Infinity")));