Sin/Cos Opts

common/api/src/main/java/com/dfsek/terra/api/util/MathUtil.java

@@ -18,41 +18,51 @@ public final class MathUtil {
      * Epsilon for fuzzy floating point comparisons.
      */
     public static final double EPSILON = 1.0E-5;
-    private static final int SIN_BITS, SIN_MASK, SIN_COUNT;
+    private static final int lookupBits = 14;
-    private static final double radFull, radToIndex;
+
-    private static final double degFull, degToIndex;
+    static final int lookupTableSize = 1 << lookupBits;
-    private static final double[] sin, cos;
+
+    private static final int lookupTableSizeWithMargin = lookupTableSize + 1;
+    private static final double tauOverLookupSize = TrigonometryConstants.TAU / lookupTableSize;
+    static final double radianToIndex = (~(-1 << lookupBits) + 1) / TrigonometryConstants.TAU;
+    private static final long[] sinTable;
+
     static {
-        SIN_BITS = 12;
+        sinTable = new long[lookupTableSizeWithMargin];
-        SIN_MASK = ~(-1 << SIN_BITS);
+        for (int i = 0; i < lookupTableSizeWithMargin; i++) {
-        SIN_COUNT = SIN_MASK + 1;
+            double d = i * tauOverLookupSize;
-
+            sinTable[i] = Double.doubleToRawLongBits(StrictMath.sin(d));
-        radFull = Math.PI * 2.0;
-        degFull = 360.0;
-        radToIndex = SIN_COUNT / radFull;
-        degToIndex = SIN_COUNT / degFull;
-
-        sin = new double[SIN_COUNT];
-        cos = new double[SIN_COUNT];
-
-        for(int i = 0; i < SIN_COUNT; i++) {
-            sin[i] = Math.sin((i + 0.5f) / SIN_COUNT * radFull);
-            cos[i] = Math.cos((i + 0.5f) / SIN_COUNT * radFull);
         }
+    }
 
-        // Four cardinal directions (credits: Nate)
+    static double sinLookup(long index) {
-        for(int i = 0; i < 360; i += 90) {
+        // Trigonometric identity: sin(-x) = -sin(x)
-            sin[(int) (i * degToIndex) & SIN_MASK] = Math.sin(i * Math.PI / 180.0);
+        // Given a domain of 0 <= x <= 2*pi, just negate the value if x > pi.
-            cos[(int) (i * degToIndex) & SIN_MASK] = Math.cos(i * Math.PI / 180.0);
+        // This allows the sin table size to be halved.
-        }
+        long neg = (index & 0x8000000000000000L) << 32;
+
+        // All bits set if (pi/2 <= x), none set otherwise
+        // Extracts the 31st bit from 'half'
+        long mask = (index << 33) >> 63;
+
+        // Trigonometric identity: sin(x) = sin(pi/2 - x)
+        long pos = (0x8000000000000001L & mask) + (index ^ mask);
+
+        // Wrap the position in the table. Moving this down to immediately before the array access
+        // seems to help the Hotspot compiler optimize the bit math better.
+        pos &= 0x7fffffffffffffffL;
+
+        // Fetch the corresponding value from the LUT and invert the sign bit as needed
+        // This directly manipulate the sign bit on the double bits to simplify logic
+        return Double.longBitsToDouble(sinTable[(int) pos] ^ neg);
     }
 
     public static double sin(double rad) {
-        return sin[(int) (rad * radToIndex) & SIN_MASK];
+        return sinLookup((long) (rad * radianToIndex) & 0xFFFFFFFFL);
     }
 
     public static double cos(double rad) {
-        return cos[(int) (rad * radToIndex) & SIN_MASK];
+        return sinLookup((long) (rad * radianToIndex + lookupTableSize) & 0xFFFFFFFFL);
     }
 
     public static double tan(double rad) {