Improve: Faster serial Jaccard with SWAR

Author: ashvardanian

include/simsimd/binary.h

@@ -6,10 +6,10 @@
  *
  *  Contains following similarity measures:
  *
- *  - Bit-level Hamming distance → @c u32 counter
- *  - Bit-level Jaccard distance (Tanimoto coefficient) → @c f32 ratio
- *  - Jaccard distance for @c u32 integral MinHash vectors from StringZilla → @c f32 ratio
- *  - TODO: Weighted Jaccard distance for @c u32 integral Count-Min-Sketch vectors → @c f32 ratio
+ *  - Bit-level Hamming distance → `u32` counter
+ *  - Bit-level Jaccard distance (Tanimoto coefficient) → `f32` ratio
+ *  - Jaccard distance for `u32` integral MinHash vectors from StringZilla → `f32` ratio
+ *  - TODO: Weighted Jaccard distance for `u32` integral Count-Min-Sketch vectors → `f32` ratio
  *
  *  For hardware architectures:
  *
@@ -343,26 +343,10 @@ SIMSIMD_INTERNAL void simsimd_jaccard_b128_init_serial(simsimd_jaccard_b128_stat
 
 SIMSIMD_INTERNAL void simsimd_jaccard_b128_update_serial(simsimd_jaccard_b128_state_serial_t *state,
                                                          simsimd_b128_vec_t a, simsimd_b128_vec_t b) {
-    simsimd_u64_t intersection_lo = a.u64s[0] & b.u64s[0];
-    simsimd_u64_t intersection_hi = a.u64s[1] & b.u64s[1];
-
-    // Unrolled lookup table popcount for portability
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_lo));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_lo >> 8));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_lo >> 16));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_lo >> 24));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_lo >> 32));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_lo >> 40));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_lo >> 48));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_lo >> 56));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_hi));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_hi >> 8));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_hi >> 16));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_hi >> 24));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_hi >> 32));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_hi >> 40));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_hi >> 48));
-    state->intersection_count += simsimd_popcount_b8((simsimd_b8_t)(intersection_hi >> 56));
+    simsimd_u64_t intersection_low = a.u64s[0] & b.u64s[0];
+    simsimd_u64_t intersection_high = a.u64s[1] & b.u64s[1];
+    state->intersection_count += _simsimd_u64_popcount(intersection_low);
+    state->intersection_count += _simsimd_u64_popcount(intersection_high);
 }
 
 SIMSIMD_INTERNAL void simsimd_jaccard_b128_finalize_serial(

include/simsimd/types.h

@@ -1401,6 +1401,24 @@ SIMSIMD_INTERNAL void _simsimd_u64_smul(simsimd_u64_t const *a, simsimd_u64_t co
     else { *r = (hi_lo << 32) + (lo_hi << 32) + lo_lo; } // Combine parts if no overflow
 }
 
+/**
+ *  @brief  SWAR population count for 64-bit integers.
+ *
+ *  Classic algorithm from Hacker's Delight using parallel bit summation:
+ *  - Step 1: Count bits in pairs (2-bit sums)
+ *  - Step 2: Count bits in nibbles (4-bit sums)
+ *  - Step 3: Count bits in bytes (8-bit sums)
+ *  - Step 4: Horizontal sum via multiply - each byte contributes to bits 56-63
+ *
+ *  Cost: ~12 ALU ops, zero memory access (vs 8 table lookups for byte-wise).
+ */
+SIMSIMD_INTERNAL simsimd_u64_t _simsimd_u64_popcount(simsimd_u64_t x) {
+    x = x - ((x >> 1) & 0x5555555555555555ull);
+    x = (x & 0x3333333333333333ull) + ((x >> 2) & 0x3333333333333333ull);
+    x = (x + (x >> 4)) & 0x0F0F0F0F0F0F0F0Full;
+    return (x * 0x0101010101010101ull) >> 56;
+}
+
 SIMSIMD_INTERNAL void _simsimd_i8_smul(simsimd_i8_t const *a, simsimd_i8_t const *b, simsimd_i8_t *r) {
     simsimd_i16_t result = (simsimd_i16_t)(*a) * (simsimd_i16_t)(*b);
     *r = (result > 127) ? 127 : (result < -128 ? -128 : (simsimd_i8_t)result);