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

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function                                             old     new   delta
isqrt_odd                                            114     111      -3

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>
This commit is contained in:
Denys Vlasenko 2017-04-10 11:47:48 +02:00
parent f428f1dc6c
commit 4908c79a01
1 changed files with 26 additions and 5 deletions
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31
coreutils/factor.c
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@ -86,8 +86,9 @@ static inline half_t isqrt(wide_t N)
static NOINLINE half_t isqrt_odd(wide_t N) static NOINLINE half_t isqrt_odd(wide_t N)
{ {
half_t s = isqrt(N); half_t s = isqrt(N);
if (s && !(s & 1)) /* even? */ /* Subtract 1 from even s, odd s won't change: */
s--; /* (doesnt work for zero, but we know that s != 0 here) */
s = (s - 1) | 1;
return s; return s;
} }
@ -107,6 +108,16 @@ static NOINLINE void factorize(wide_t N)
N >>= 1; 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); max_factor = isqrt_odd(N);
count3 = 3; count3 = 3;
count5 = 6; 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... * 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) * (^ = primes, _ = would-be-primes-if-not-divisible-by-5)
* The numbers with space under them are excluded by sieve 3.
*/ */
count7--; count7--;
count5--; count5--;
count3--; count3--;
if (count3 && count5 && count7) if (count3 && count5 && count7)
continue; 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; count3 = 3;
if (count5 == 0) }
if (count5 == 0) {
count5 = 5; count5 = 5;
if (count7 == 0) }
if (count7 == 0) {
count7 = 7; count7 = 7;
}
goto next_factor; goto next_factor;
} }
end: end: