factor: 25% faster sieving

function                                             old     new   delta
factorize                                            287     260     -27

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>

1 files changed, 48 insertions, 19 deletions

diff --git a/coreutils/factor.c b/coreutils/factor.c
index aa2f63089..4a131813b 100644
--- a/coreutils/factor.c
+++ b/coreutils/factor.c
@@ -96,9 +96,27 @@ static NOINLINE void factorize(wide_t N)
 {
         half_t factor;
         half_t max_factor;
-        unsigned count3;
-        unsigned count5;
-        unsigned count7;
+        // unsigned count3;
+        // unsigned count5;
+        // unsigned count7;
+        // ^^^^^^^^^^^^^^^ commented-out simple siving code (easier to grasp).
+        // Faster sieving, using one word for potentially up to 6 counters:
+        // count upwards in each mask, counter "triggers" when it sets its mask to "100[0]..."
+        // 10987654321098765432109876543210 - bits 31-0 in 32-bit word
+        //    17777713333311111777775555333 - bit masks for counters for primes 3,5,7,11,13,17
+        //         100000100001000010001001 - value for adding 1 to each mask
+        //    10000010000010000100001000100 - value for checking that any mask reached msb
+        enum {
+                SHIFT_3 = 1 << 0,
+                SHIFT_5 = 1 << 3,
+                SHIFT_7 = 1 << 7,
+                INCREMENT_EACH = SHIFT_3 | SHIFT_5 | SHIFT_7,
+                MULTIPLE_OF_3 = 1 << 2,
+                MULTIPLE_OF_5 = 1 << 6,
+                MULTIPLE_OF_7 = 1 << 11,
+                MULTIPLE_3_5_7 = MULTIPLE_OF_3 | MULTIPLE_OF_5 | MULTIPLE_OF_7,
+        };
+        unsigned sieve_word;
 
         if (N < 4)
                 goto end;
@@ -119,9 +137,14 @@ static NOINLINE void factorize(wide_t N)
          * 589959129 - about 100 million iterations.
          */
         max_factor = isqrt_odd(N);
-        count3 = 3;
-        count5 = 6;
-        count7 = 9;
+        // count3 = 3;
+        // count5 = 6;
+        // count7 = 9;
+        sieve_word = 0
+                + (MULTIPLE_OF_3 - 3 * SHIFT_3)
+                + (MULTIPLE_OF_5 - 6 * SHIFT_5)
+                + (MULTIPLE_OF_7 - 9 * SHIFT_7)
+        ;
         factor = 3;
         for (;;) {
                 /* The division is the most costly part of the loop.
@@ -143,10 +166,13 @@ static NOINLINE void factorize(wide_t N)
                  * (^ = primes, _ = would-be-primes-if-not-divisible-by-5)
                  * The numbers with space under them are excluded by sieve 3.
                  */
-                count7--;
-                count5--;
-                count3--;
-                if (count3 && count5 && count7)
+                // count7--;
+                // count5--;
+                // count3--;
+                // if (count3 && count5 && count7)
+                //      continue;
+                sieve_word += INCREMENT_EACH;
+                if (!(sieve_word & MULTIPLE_3_5_7))
                         continue;
                 /*
                  * "factor" is multiple of 3 33% of the time (count3 reached 0),
@@ -154,15 +180,18 @@ static NOINLINE void factorize(wide_t N)
                  * else, multiple of 7 7.6% of the time.
                  * Cumulatively, with 3,5,7 sieving we are here 54.3% of the time.
                  */
-                if (count3 == 0) {
-                        count3 = 3;
-                }
-                if (count5 == 0) {
-                        count5 = 5;
-                }
-                if (count7 == 0) {
-                        count7 = 7;
-                }
+                // if (count3 == 0)
+                //      count3 = 3;
+                if (sieve_word & MULTIPLE_OF_3)
+                        sieve_word -= SHIFT_3 * 3;
+                // if (count5 == 0)
+                //      count5 = 5;
+                if (sieve_word & MULTIPLE_OF_5)
+                        sieve_word -= SHIFT_5 * 5;
+                // if (count7 == 0)
+                //      count7 = 7;
+                if (sieve_word & MULTIPLE_OF_7)
+                        sieve_word -= SHIFT_7 * 7;
                 goto next_factor;
         }
  end: