emo/busybox
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

factor: 25% faster sieving

Browse Source 
function                                             old     new   delta
factorize                                            287     260     -27

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>
This commit is contained in:
Denys Vlasenko 2017-04-10 12:10:46 +02:00
parent 4908c79a01
commit dd3a395053
1 changed files with 48 additions and 19 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

67
coreutils/factor.c
View File

@ -96,9 +96,27 @@ static NOINLINE void factorize(wide_t N)
{ {
half_t factor; half_t factor;
half_t max_factor; half_t max_factor;
unsigned count3; // unsigned count3;
unsigned count5; // unsigned count5;
unsigned count7; // 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) if (N < 4)
goto end; goto end;
@ -119,9 +137,14 @@ static NOINLINE void factorize(wide_t N)
* 589959129 - about 100 million iterations. * 589959129 - about 100 million iterations.
*/ */
max_factor = isqrt_odd(N); max_factor = isqrt_odd(N);
count3 = 3; // count3 = 3;
count5 = 6; // count5 = 6;
count7 = 9; // 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; factor = 3;
for (;;) { for (;;) {
/* The division is the most costly part of the loop. /* 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) * (^ = primes, _ = would-be-primes-if-not-divisible-by-5)
* The numbers with space under them are excluded by sieve 3. * 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;
sieve_word += INCREMENT_EACH;
if (!(sieve_word & MULTIPLE_3_5_7))
continue; continue;
/* /*
* "factor" is multiple of 3 33% of the time (count3 reached 0), * "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. * else, multiple of 7 7.6% of the time.
* Cumulatively, with 3,5,7 sieving we are here 54.3% of the time. * Cumulatively, with 3,5,7 sieving we are here 54.3% of the time.
*/ */
if (count3 == 0) { // if (count3 == 0)
count3 = 3; // count3 = 3;
} if (sieve_word & MULTIPLE_OF_3)
if (count5 == 0) { sieve_word -= SHIFT_3 * 3;
count5 = 5; // if (count5 == 0)
} // count5 = 5;
if (count7 == 0) { if (sieve_word & MULTIPLE_OF_5)
count7 = 7; sieve_word -= SHIFT_5 * 5;
} // if (count7 == 0)
// count7 = 7;
if (sieve_word & MULTIPLE_OF_7)
sieve_word -= SHIFT_7 * 7;
goto next_factor; goto next_factor;
} }
end: end: