factor: 30% faster code (estimate max possible factor just once)

function                                             old     new   delta
factorize                                              -     161    +161
isqrt_odd                                              -     102    +102
factor_main                                          281     110    -171
------------------------------------------------------------------------------
(add/remove: 2/0 grow/shrink: 0/1 up/down: 263/-171)           Total: 92 bytes

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>

1 files changed, 82 insertions, 24 deletions

diff --git a/coreutils/factor.c b/coreutils/factor.c
index 0f838a735..e01190150 100644
--- a/coreutils/factor.c
+++ b/coreutils/factor.c
@@ -20,65 +20,111 @@
 
 #include "libbb.h"
 
+#if 0
+# define dbg(...) bb_error_msg(__VA_ARGS__)
+#else
+# define dbg(...) ((void)0)
+#endif
+
+typedef unsigned long long wide_t;
+#define WIDE_BITS (unsigned)(sizeof(wide_t)*8)
+#define TOPMOST_WIDE_BIT ((wide_t)1 << (WIDE_BITS-1))
+
 #if ULLONG_MAX == (UINT_MAX * UINT_MAX + 2 * UINT_MAX)
 /* "unsigned" is half as wide as ullong */
 typedef unsigned half_t;
+#define HALF_MAX UINT_MAX
 #define HALF_FMT ""
 #elif ULLONG_MAX == (ULONG_MAX * ULONG_MAX + 2 * ULONG_MAX)
 /* long is half as wide as ullong */
 typedef unsigned long half_t;
+#define HALF_MAX ULONG_MAX
 #define HALF_FMT "l"
 #else
 #error Cant find an integer type which is half as wide as ullong
 #endif
 
-static void factorize(const char *numstr)
+/* Returns such x that x+1 > sqrt(N) */
+static inline half_t isqrt(wide_t N)
 {
-        unsigned long long N, factor2;
-        half_t factor;
-        unsigned count3;
+        wide_t x;
+        unsigned c;
+
+// Never called with N < 1
+//      if (N == 0)
+//              return 0;
+//
+        /* Count leading zeros */
+        c = 0;
+        while (!(N & TOPMOST_WIDE_BIT)) {
+                c++;
+                N <<= 1;
+        }
+        N >>= c;
 
-        /* Coreutils compat */
-        numstr = skip_whitespace(numstr);
-        if (*numstr == '+')
-                numstr++;
+        /* Make x > sqrt(n) */
+        x = (wide_t)1 << ((WIDE_BITS + 1 - c) / 2);
+        dbg("x:%llx", x);
+        for (;;) {
+                wide_t y = (x + N/x) / 2;
+                dbg("y:%llx y^2:%llx (y+1)^2:%llx]", y, y*y, (y+1)*(y+1));
+                if (y >= x) {
+                        /* Handle degenerate case N = 0xffffffffff...fffffff */
+                        if (y == (wide_t)HALF_MAX + 1)
+                                y--;
+                        dbg("isqrt(%llx)=%llx"HALF_FMT, N, y);
+                        return y;
+                }
+                x = y;
+        }
+}
 
-        N = bb_strtoull(numstr, NULL, 10);
-        if (errno)
-                bb_show_usage();
+static NOINLINE half_t isqrt_odd(wide_t N)
+{
+        half_t s = isqrt(N);
+        if (s && !(s & 1)) /* even? */
+                s--;
+        return s;
+}
 
-        printf("%llu:", N);
+static NOINLINE void factorize(wide_t N)
+{
+        wide_t factor2;
+        half_t factor;
+        half_t max_factor;
+        unsigned count3;
 
         if (N < 4)
                 goto end;
+
         while (!(N & 1)) {
                 printf(" 2");
                 N >>= 1;
         }
 
+        max_factor = isqrt_odd(N);
         count3 = 3;
         factor = 3;
         factor2 = 3 * 3;
         for (;;) {
-                unsigned long long nfactor2;
-
                 while ((N % factor) == 0) {
                         N = N / factor;
                         printf(" %u"HALF_FMT"", factor);
+                        max_factor = isqrt_odd(N);
                 }
  next_factor:
-                /* (f + 2)^2 = f^2 + 4*f + 4 = f^2 + 4*(f+1) */
-                nfactor2 = factor2 + 4 * (factor + 1);
-                if (nfactor2 < factor2) /* overflow? */
-                        break;
-                factor2 = nfactor2;
-                if (factor2 > N)
+                if (factor >= max_factor)
                         break;
+                /* (f + 2)^2 = f^2 + 4*f + 4 = f^2 + 4*(f+1) */
+                factor2 = factor2 + 4 * (factor + 1);
+                /* overflow is impossible due to max_factor check */
+                /* (factor2 > N) is impossible due to max_factor check */
                 factor += 2;
                 /* Rudimentary wheel sieving: skip multiples of 3:
                  * Every third odd number is divisible by three and thus isn't a prime:
-                 * 5  7  9  11  13  15  17 19 21 23 25 27 29 31 33 35 37...
-                 * ^  ^     ^   ^       ^  ^     ^  _     ^  ^     _  ^ (^primes)
+                 * 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37...
+                 * ^ ^   ^  ^     ^  ^     ^  _     ^  ^     _  ^
+                 * (^ = primes, _ = would-be-primes-if-not-divisible-by-5)
                  */
                 --count3;
                 if (count3 == 0) {
@@ -105,8 +151,20 @@ int factor_main(int argc UNUSED_PARAM, char **argv)
                 bb_show_usage();
 
         do {
-                factorize(*argv);
+                wide_t N;
+                const char *numstr;
+
+                /* Coreutils compat */
+                numstr = skip_whitespace(*argv);
+                if (*numstr == '+')
+                        numstr++;
+
+                N = bb_strtoull(numstr, NULL, 10);
+                if (errno)
+                        bb_show_usage();
+                printf("%llu:", N);
+                factorize(N);
         } while (*++argv);
 
-        fflush_stdout_and_exit(EXIT_SUCCESS);
+        return EXIT_SUCCESS;
 }