Further improve Math.sin/cos.

src/math.js

Index: src/math.js
diff --git a/src/math.js b/src/math.js
index 529033ebd82ccad43fd949f39cfdfd89d65c519b..2097ed429b1edf3e5914635bfb766a3f269566bd 100644
--- a/src/math.js
+++ b/src/math.js
@@ -217,14 +217,8 @@ var InitTrigonometricFunctions;
 // Also define the initialization function that populates the lookup table
 // and then wires up the function definitions.
 function SetupTrigonometricFunctions() {
-  var samples = 1800;  // Table size.
-  var pi = 3.1415926535897932;
-  var pi_half = pi / 2;
-  var inverse_pi_half = 2 / pi;
-  var two_pi = 2 * pi;
-  var four_pi = 4 * pi;
-  var interval = pi_half / samples;
-  var inverse_interval = samples / pi_half;
+  var samples = 1620;  // Table size.  Do not change arbitrarily.
+  var inverse_pi_half = 0.63661977236758134;
   var table_sin;
   var table_cos_interval;
 
@@ -240,7 +234,7 @@ function SetupTrigonometricFunctions() {
   // 7) Negate the result if x was in the 3rd or 4th quadrant.
   // 8) Get rid of -0 by adding 0.
   var Interpolation = function(x) {
-    var double_index = x * inverse_interval;
+    var double_index = x * samples;
     var index = double_index | 0;
     var t1 = double_index - index;
     var t2 = 1 - t1;
@@ -253,21 +247,19 @@ function SetupTrigonometricFunctions() {
   }
 
   var MathSinInterpolation = function(x) {
-    // This is to make Sunspider's result verification happy.
-    if (x > four_pi) x -= four_pi;
-    var multiple = MathFloor(x * inverse_pi_half);
-    if (%_IsMinusZero(multiple)) return multiple;
-    x = (multiple & 1) * pi_half +
-        (1 - ((multiple & 1) << 1)) * (x - multiple * pi_half);
+    x = x * inverse_pi_half;
+    var multiple = MathFloor(x);
+    if (%_IsMinusZero(multiple)) return -0;

[Jakob Kummerow, 2013/11/18 13:53:46]

Why this change? "return multiple" might be (ever so slightly) faster.

+    x = (multiple & 1) + (1 - ((multiple & 1) << 1)) * (x - multiple);
     return Interpolation(x) * (1 - (multiple & 2)) + 0;
   }
 
   // Cosine is sine with a phase offset of pi/2.
   var MathCosInterpolation = function(x) {
-    var multiple = MathFloor(x * inverse_pi_half);
+    x = x * inverse_pi_half;
+    var multiple = MathFloor(x);
     var phase = multiple + 1;
-    x = (phase & 1) * pi_half +
-        (1 - ((phase & 1) << 1)) * (x - multiple * pi_half);
+    x = (phase & 1) + (1 - ((phase & 1) << 1)) * (x - multiple);
     return Interpolation(x) * (1 - (phase & 2)) + 0;
   };