Add javadocs for BBQ dot product method (#129419)

Author: thecoop

libs/simdvec/src/main/java/org/elasticsearch/simdvec/internal/vectorization/DefaultESVectorUtilSupport.java

@@ -204,19 +204,58 @@ static float ipFloatBitImpl(float[] q, byte[] d, int start) {
         return acc0 + acc1 + acc2 + acc3;
     }
 
+    /**
+     * Returns the inner product (aka dot product) between the query vector {@code q}, and the data vector {@code d}.
+     * <p>
+     * The query vector should be {@link #B_QUERY}-bit quantized and striped, so that the first {@code n} bits
+     * of the array are the initial bits of each of the {@code n} vector dimensions; the next {@code n}
+     * bits are the second bits of each of the {@code n} vector dimensions, and so on
+     * (this algorithm is only valid for vectors with dimensions a multiple of 8).
+     * The striping is usually done by {@code BQSpaceUtils.transposeHalfByte}.
+     * <p>
+     * The data vector should be single-bit quantized.
+     *
+     * <h4>Dot products with bit quantization</h4>
+     *
+     * The dot product of any vector with a bit vector is a simple selector - each query vector dimension is multiplied
+     * by the 0 or 1 in the corresponding data vector dimension; the result is that each dimension value
+     * is either kept or ignored, with the dimensions that are kept then summed together.
+     *
+     * <h4>The algorithm</h4>
+     *
+     * The transposition already applied to the query vector ensures there's a 1-to-1 correspondence
+     * between the data vector bits and query vector bits (see {@code BQSpaceUtils.transposeHalfByte)};
+     * this means we can use a bitwise {@code &} to keep only the bits of the vector elements we want to sum.
+     * Essentially, the data vector is used as a selector for each of the striped bits of each vector dimension
+     * as stored, concatenated together, in {@code q}.
+     * <p>
+     * The final dot product result can be obtained by observing that the sum of each stripe of {@code n} bits
+     * can be computed using the bit count of that stripe. Similar to
+     * <a href="https://en.wikipedia.org/wiki/Multiplication_algorithm#Long_multiplication">long multiplication</a>,
+     * the result of each stripe of {@code n} bits can be added together by shifting the value {@code s} bits to the left,
+     * where {@code s} is the stripe number (0-3), then adding to the overall result. Any carry is handled by the add operation.
+     *
+     * @param q query vector, {@link #B_QUERY}-bit quantized and striped (see {@code BQSpaceUtils.transposeHalfByte})
+     * @param d data vector, 1-bit quantized
+     * @return  inner product result
+     */
     public static long ipByteBinByteImpl(byte[] q, byte[] d) {
         long ret = 0;
         int size = d.length;
-        for (int i = 0; i < B_QUERY; i++) {
+        for (int s = 0; s < B_QUERY; s++) { // for each stripe of B_QUERY-bit quantization in q...
             int r = 0;
-            long subRet = 0;
+            long stripeRet = 0;
+            // bitwise & the query and data vectors together, 32-bits at a time, and counting up the bits still set
             for (final int upperBound = d.length & -Integer.BYTES; r < upperBound; r += Integer.BYTES) {
-                subRet += Integer.bitCount((int) BitUtil.VH_NATIVE_INT.get(q, i * size + r) & (int) BitUtil.VH_NATIVE_INT.get(d, r));
+                stripeRet += Integer.bitCount((int) BitUtil.VH_NATIVE_INT.get(q, s * size + r) & (int) BitUtil.VH_NATIVE_INT.get(d, r));
             }
+            // handle any tail
+            // Java operations on bytes automatically extend to int, so we need to mask back down again in case it sign-extends the int
             for (; r < d.length; r++) {
-                subRet += Integer.bitCount((q[i * size + r] & d[r]) & 0xFF);
+                stripeRet += Integer.bitCount((q[s * size + r] & d[r]) & 0xFF);
             }
-            ret += subRet << i;
+            // shift the result of the s'th stripe s to the left and add to the result
+            ret += stripeRet << s;
         }
         return ret;
     }

libs/simdvec/src/main/java/org/elasticsearch/simdvec/internal/vectorization/ESVectorUtilSupport.java

@@ -11,8 +11,16 @@
 
 public interface ESVectorUtilSupport {
 
+    /**
+     * The number of bits in bit-quantized query vectors
+     */
     short B_QUERY = 4;
 
+    /**
+     * Compute dot product between {@code q} and {@code d}
+     * @param q query vector, {@link #B_QUERY}-bit quantized and striped (see {@code BQSpaceUtils.transposeHalfByte})
+     * @param d data vector, 1-bit quantized
+     */
     long ipByteBinByte(byte[] q, byte[] d);
 
     int ipByteBit(byte[] q, byte[] d);