factor: much faster, and very slightly larger isqrt()

function                                             old     new   delta
isqrt_odd                                             70      88     +18

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

1 files changed, 10 insertions, 34 deletions

diff --git a/coreutils/factor.c b/coreutils/factor.c
index 11097c12d..f910fdb44 100644
--- a/coreutils/factor.c
+++ b/coreutils/factor.c
@@ -48,41 +48,17 @@ typedef unsigned long half_t;
 static inline half_t isqrt(wide_t N)
 {
         half_t x;
+        unsigned shift;
 
-        // Never called with N < 1
-        //if (N == 0)
-        //      return 0;
-
-        x = HALF_MAX;
-        /* First approximation of x+1 > sqrt(N) - all-ones, half as many bits:
-         * 1xxxxx -> 111 (six bits to three)
-         * 01xxxx -> 111
-         * 001xxx -> 011
-         * 0001xx -> 011 and so on.
-         */
-        // It is actually not performance-critical at all.
-        // Can simply start Newton loop with very conservative x=0xffffffff.
-        //wide_t mask_2bits;
-        //mask_2bits = TOPMOST_WIDE_BIT | (TOPMOST_WIDE_BIT >> 1);
-        //while (!(N & mask_2bits)) {
-        //      x >>= 1;
-        //      mask_2bits >>= 2;
-        //}
-        dbg("x:%"HALF_FMT"x", x);
-
-        for (;;) {
-                half_t y = (x + N/x) / 2;
-                dbg("y:%x y^2:%llx", y, (wide_t)y * y);
-                /*
-                 * "real" y may be one bit wider: 0x100000000 and get truncated to 0.
-                 * In this case, "real" y is > x. The first check below is for this case:
-                 */
-                if (y == 0 || y >= x) {
-                        dbg("isqrt(%llx)=%"HALF_FMT"x", N, x);
-                        return x;
-                }
-                x = y;
-        }
+        shift = WIDE_BITS - 2;
+        x = 0;
+        do {
+                x = (x << 1) + 1;
+                if ((wide_t)x * x > (N >> shift))
+                        x--; /* whoops, that +1 was too much */
+                shift -= 2;
+        } while ((int)shift >= 0);
+        return x;
 }
 
 static NOINLINE half_t isqrt_odd(wide_t N)