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factor: 25% faster sieving

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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
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67
coreutils/factor.c
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@@ -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: