fix: rearrange bitwise operations while transform

While optimized transform function holds same results, operations in
each assignments are not the same number. So we reduce and rearrange
some operators back to original positions. Improved performance is still
valid.

Fix #120

src/pow_avx.c

@@ -31,10 +31,9 @@ static void transform256(__m256i *lmid, __m256i *hmid)
 
             alpha = lfrom[t1];
             beta = hfrom[t1];
-            delta = _mm256_xor_si256(lfrom[t2], beta); /* lfrom[t2] ^ beta */
-
-            lto[j] = _mm256_andnot_si256(_mm256_and_si256(delta, alpha),
-                                         one); /* ~(delta & alpha) */
+            delta = _mm256_and_si256( alpha, _mm256_xor_si256(lfrom[t2], beta));
+                    /* alpha & (lfrom[t2] ^ beta) */
+            lto[j] = _mm256_andnot_si256(delta, one); /* ~delta */
             hto[j] = _mm256_or_si256(_mm256_xor_si256(alpha, hfrom[t2]),
                                      delta); /* (alpha ^ hfrom[t2]) | delta */
         }
@@ -49,10 +48,9 @@ static void transform256(__m256i *lmid, __m256i *hmid)
         t2 = indices[j + 1];
         alpha = lfrom[t1];
         beta = hfrom[t1];
-        delta = _mm256_xor_si256(lfrom[t2], beta); /* lfrom[t2] ^ beta */
-
-        lto[j] = _mm256_andnot_si256(_mm256_and_si256(delta, alpha),
-                                     one); /* ~(delta & alpha) */
+        delta = _mm256_and_si256( alpha, _mm256_xor_si256(lfrom[t2], beta));
+                /* alpha & (lfrom[t2] ^ beta) */
+        lto[j] = _mm256_andnot_si256(delta, one); /* ~delta */
         hto[j] = _mm256_or_si256(_mm256_xor_si256(alpha, hfrom[t2]),
                                  delta); /* (alpha ^ hfrom[t2]) | delta */
     }
@@ -223,10 +221,9 @@ static void transform256(__m256d *lmid, __m256d *hmid)
 
             alpha = lfrom[t1];
             beta = hfrom[t1];
-            delta = _mm256_xor_pd(lfrom[t2], beta); /* lfrom[t2] ^ beta */
-
-            lto[j] = _mm256_andnot_pd(_mm256_and_pd(delta, alpha),
-                                      one); /* ~(delta & alpha) */
+            delta = _mm256_and_pd(alpha, _mm256_xor_pd(lfrom[t2], beta));
+                    /* alpha & (lfrom[t2] ^ beta) */
+            lto[j] = _mm256_andnot_pd(delta, one); /* ~delta */
             hto[j] = _mm256_or_pd(_mm256_xor_pd(alpha, hfrom[t2]),
                                   delta); /* (alpha ^ hfrom[t2]) | delta */
         }
@@ -242,10 +239,9 @@ static void transform256(__m256d *lmid, __m256d *hmid)
 
         alpha = lfrom[t1];
         beta = hfrom[t1];
-        delta = _mm256_xor_pd(lfrom[t2], beta); /* lfrom[t2] ^ beta */
-
-        lto[j] = _mm256_andnot_pd(_mm256_and_pd(delta, alpha),
-                                  one); /* ~(delta & alpha) */
+        delta = _mm256_and_pd(alpha, _mm256_xor_pd(lfrom[t2], beta));
+                /* alpha & (lfrom[t2] ^ beta) */
+        lto[j] = _mm256_andnot_pd(delta, one); /* ~delta */
         hto[j] = _mm256_or_pd(_mm256_xor_pd(alpha, hfrom[t2]),
                               delta); /* (alpha ^ hfrom[t2]) | delta */
     }

src/pow_c.c

@@ -27,9 +27,9 @@ static void transform64(uint64_t *lmid, uint64_t *hmid)
             int t2 = indices[j + 1];
             alpha = lfrom[t1];
             beta = hfrom[t1];
-            delta = beta ^ lfrom[t2];
-            lto[j] = ~(delta & alpha);
-            hto[j] = delta | (alpha ^ hfrom[t2]);
+            delta = alpha & (lfrom[t2] ^ beta);
+            lto[j] = ~delta;
+            hto[j] = (alpha ^ hfrom[t2]) | delta;
         }
         uint64_t *lswap = lfrom, *hswap = hfrom;
         lfrom = lto;
@@ -43,9 +43,9 @@ static void transform64(uint64_t *lmid, uint64_t *hmid)
         int t2 = indices[j + 1];
         alpha = lfrom[t1];
         beta = hfrom[t1];
-        delta = beta ^ lfrom[t2];
-        lto[j] = ~(delta & alpha);
-        hto[j] = delta | (alpha ^ hfrom[t2]);
+        delta = alpha & (lfrom[t2] ^ beta);
+        lto[j] = ~delta;
+        hto[j] = (alpha ^ hfrom[t2]) | delta;
     }
 }
 

src/pow_kernel.cl

@@ -134,9 +134,9 @@ void transform(__global bc_trit_t* state_low, __global bc_trit_t* state_high,
       k = j+1;
       alpha = state_low[INDEX[j]];
       beta = state_high[INDEX[j]];
-      delta = beta ^ state_low[INDEX[k]];
-      sp_low[i] = ~(delta & alpha);
-      sp_high[i] = delta | (alpha ^ state_high[INDEX[k]]);
+      delta = alpha & (beta ^ state_low[INDEX[k]]);
+      sp_low[i] = ~delta;
+      sp_high[i] = (alpha ^ state_high[INDEX[k]]) | delta;
     }
     barrier(CLK_LOCAL_MEM_FENCE);
     for (i = 0; i < n_trits; i++) {

src/pow_sse.c

@@ -29,9 +29,9 @@ static void transform128(__m128i *lmid, __m128i *hmid)
             t2 = indices[j + 1];
             alpha = lfrom[t1];
             beta = hfrom[t1];
-            delta = beta ^ lfrom[t2];
-            lto[j] = ~(delta & alpha);
-            hto[j] = delta | (alpha ^ hfrom[t2]);
+            delta = alpha & (beta ^ lfrom[t2]);
+            lto[j] = ~delta;
+            hto[j] = (alpha ^ hfrom[t2]) | delta;
         }
         __m128i *lswap = lfrom, *hswap = hfrom;
         lfrom = lto;
@@ -44,9 +44,9 @@ static void transform128(__m128i *lmid, __m128i *hmid)
         t2 = indices[j + 1];
         alpha = lfrom[t1];
         beta = hfrom[t1];
-        delta = beta ^ lfrom[t2];
-        lto[j] = ~(delta & alpha);
-        hto[j] = delta | (alpha ^ hfrom[t2]);
+        delta = alpha & (beta ^ lfrom[t2]);
+        lto[j] = ~delta;
+        hto[j] = (alpha ^ hfrom[t2]) | delta;
     }
 }