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-rw-r--r--coreutils/factor.c42
1 files changed, 39 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);
}