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authorGravatar Denys Vlasenko <vda.linux@googlemail.com>2020-12-22 20:08:40 +0100
committerGravatar Denys Vlasenko <vda.linux@googlemail.com>2020-12-22 20:24:30 +0100
commit6452c300366cf0e322227ad39991ec2fdfd6beed (patch)
treed2086c915ebeddea5775aa66e0dc07dae41addc2
parent96717d9fb4560ad98a737108f83c7b247ef04674 (diff)
downloadbusybox-6452c300366cf0e322227ad39991ec2fdfd6beed.tar.gz
busybox-6452c300366cf0e322227ad39991ec2fdfd6beed.tar.bz2
factor: detect squares
If we have a square, the speedup can be extremely large (in best case example below, it's ~40000 times faster): $ time ./busybox_old factor 18446743988964486098 18446743988964486098: 2 3037000493 3037000493 real 0m4.246s $ time ./busybox factor 18446743988964486098 18446743988964486098: 2 3037000493 3037000493 real 0m0.000s function old new delta isqrt_odd - 57 +57 print_w - 36 +36 factorize 218 236 +18 print_h - 7 +7 factorize_numstr 65 72 +7 ------------------------------------------------------------------------------ (add/remove: 3/0 grow/shrink: 2/0 up/down: 125/0) Total: 125 bytes Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>
-rw-r--r--coreutils/factor.c42
-rwxr-xr-xtestsuite/factor.tests23
2 files changed, 62 insertions, 3 deletions
diff --git a/coreutils/factor.c b/coreutils/factor.c
index 27f26fe3f..729bd36a0 100644
--- a/coreutils/factor.c
+++ b/coreutils/factor.c
@@ -85,7 +85,8 @@ static const uint64_t packed_wheel[] = {
#undef R
#define WHEEL_START 5
#define WHEEL_SIZE (5 + 24 * 20)
-#define wheel_tab ((uint8_t*)&bb_common_bufsiz1)
+#define square_count (((uint8_t*)&bb_common_bufsiz1)[0])
+#define wheel_tab (((uint8_t*)&bb_common_bufsiz1) + 1)
/*
* Why, you ask?
* plain byte array:
@@ -119,9 +120,39 @@ static void unpack_wheel(void)
}
}
+/* Prevent inlining, factorize() needs all help it can get with reducing register pressure */
+static NOINLINE void print_w(wide_t n)
+{
+ unsigned rep = square_count;
+ do
+ printf(" %llu", n);
+ while (--rep != 0);
+}
+static NOINLINE void print_h(half_t n)
+{
+ print_w(n);
+}
+
+static void factorize(wide_t N);
+
static half_t isqrt_odd(wide_t N)
{
half_t s = isqrt(N);
+ /* s^2 is <= N, (s+1)^2 > N */
+
+ /* If s^2 in fact is EQUAL to N, it's very lucky.
+ * Examples:
+ * factor 18446743988964486098 = 2 * 3037000493 * 3037000493
+ * factor 18446743902517389507 = 3 * 2479700513 * 2479700513
+ */
+ if ((wide_t)s * s == N) {
+ /* factorize sqrt(N), printing each factor twice */
+ square_count *= 2;
+ factorize(s);
+ /* Let caller know we recursed */
+ return 0;
+ }
+
/* 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;
@@ -152,6 +183,8 @@ static NOINLINE void factorize(wide_t N)
* factor 18446744073709551557 (0xffffffffffffffc5).
*/
max_factor = isqrt_odd(N);
+ if (!max_factor)
+ return; /* square was detected and recursively factored */
factor = 2;
w = 0;
for (;;) {
@@ -162,8 +195,10 @@ static NOINLINE void factorize(wide_t N)
*/
while ((N % factor) == 0) { /* not likely */
N = N / factor;
- printf(" %"HALF_FMT"u", factor);
+ print_h(factor);
max_factor = isqrt_odd(N);
+ if (!max_factor)
+ return; /* square was detected */
}
if (factor >= max_factor)
break;
@@ -178,7 +213,7 @@ static NOINLINE void factorize(wide_t N)
}
end:
if (N > 1)
- printf(" %llu", N);
+ print_w(N);
bb_putchar('\n');
}
@@ -193,6 +228,7 @@ static void factorize_numstr(const char *numstr)
if (errno)
bb_show_usage();
printf("%llu:", N);
+ square_count = 1;
factorize(N);
}
diff --git a/testsuite/factor.tests b/testsuite/factor.tests
index 2cf4a54ce..e404e29c1 100755
--- a/testsuite/factor.tests
+++ b/testsuite/factor.tests
@@ -45,4 +45,27 @@ testing "factor \$((2*3*5*7*11*13*17*19*23*29*31*37*41*43*47))" \
"614889782588491410: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47\n" \
"" ""
+# Test that square-detection code is not buggy
+testing "factor 2 * 3037000493 * 3037000493" \
+ "factor 18446743988964486098" \
+ "18446743988964486098: 2 3037000493 3037000493\n" \
+ "" ""
+testing "factor 3 * 2479700513 * 2479700513" \
+ "factor 18446743902517389507" \
+ "18446743902517389507: 3 2479700513 2479700513\n" \
+ "" ""
+# including square-of-square cases:
+testing "factor 3 * 37831 * 37831 * 37831 * 37831" \
+ "factor 6144867742934288163" \
+ "6144867742934288163: 3 37831 37831 37831 37831\n" \
+ "" ""
+testing "factor 3 * 13^16" \
+ "factor 1996249827549539523" \
+ "1996249827549539523: 3 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13\n" \
+ "" ""
+testing "factor 13^16" \
+ "factor 665416609183179841" \
+ "665416609183179841: 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13\n" \
+ "" ""
+
exit $FAILCOUNT