factor: better comments, slightl more clever conversion even->odd

function                                             old     new   delta
isqrt_odd                                            114     111      -3

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

1 files changed, 26 insertions, 5 deletions

diff --git a/coreutils/factor.c b/coreutils/factor.c
index 5c4d124a8..aa2f63089 100644
--- a/coreutils/factor.c
+++ b/coreutils/factor.c
@@ -86,8 +86,9 @@ static inline half_t isqrt(wide_t N)
 static NOINLINE half_t isqrt_odd(wide_t N)
 {
         half_t s = isqrt(N);
-        if (s && !(s & 1)) /* even? */
-                s--;
+        /* Subtract 1 from even s, odd s won't change: */
+        /* (doesnt work for zero, but we know that s != 0 here) */
+        s = (s - 1) | 1;
         return s;
 }
 
@@ -107,6 +108,16 @@ static NOINLINE void factorize(wide_t N)
                 N >>= 1;
         }
 
+        /* The code needs to be optimized for the case where
+         * there are large prime factors. For example,
+         * this is not hard:
+         * 8262075252869367027 = 3 7 17 23 47 101 113 127 131 137 823
+         * (the largest factor to test is only ~sqrt(823) = 28)
+         * but this is:
+         * 18446744073709551601 = 53 348051774975651917
+         * the last factor requires testing up to
+         * 589959129 - about 100 million iterations.
+         */
         max_factor = isqrt_odd(N);
         count3 = 3;
         count5 = 6;
@@ -130,18 +141,28 @@ static NOINLINE void factorize(wide_t N)
                  * 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47...
                  * ^ ^   ^  ^     ^  ^     ^  _     ^  ^     _  ^     ^  ^     ^
                  * (^ = 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)
                         continue;
-                if (count3 == 0)
+                /*
+                 * "factor" is multiple of 3 33% of the time (count3 reached 0),
+                 * else, multiple of 5 13% of the time,
+                 * 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)
+                }
+                if (count5 == 0) {
                         count5 = 5;
-                if (count7 == 0)
+                }
+                if (count7 == 0) {
                         count7 = 7;
+                }
                 goto next_factor;
         }
  end: