Original patch from: perfpow.c.diff

-= BEGIN original header =-
Copyright 1998, 1999, 2000, 2001, 2005, 2008 Free Software Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.

-= END original header =-

diff -durN gmp-4.2.4.orig/mpz/perfpow.c gmp-4.2.4/mpz/perfpow.c
--- gmp-4.2.4.orig/mpz/perfpow.c	2007-08-30 20:31:41.000000000 +0200
+++ gmp-4.2.4/mpz/perfpow.c	2009-03-08 18:36:16.000000000 +0100
@@ -1,7 +1,7 @@
 /* mpz_perfect_power_p(arg) -- Return non-zero if ARG is a perfect power,
    zero otherwise.
 
-Copyright 1998, 1999, 2000, 2001, 2005 Free Software Foundation, Inc.
+Copyright 1998, 1999, 2000, 2001, 2005, 2008 Free Software Foundation, Inc.
 
 This file is part of the GNU MP Library.
 
@@ -59,6 +59,8 @@
 #define SMALLEST_OMITTED_PRIME 1009
 
 
+#define POW2P(a) (((a) & ((a) - 1)) == 0)
+
 int
 mpz_perfect_power_p (mpz_srcptr u)
 {
@@ -72,16 +74,13 @@
   mp_size_t usize = SIZ (u);
   TMP_DECL;
 
-  if (usize == 0)
-    return 1;			/* consider 0 a perfect power */
+  if (mpz_cmpabs_ui (u, 1) <= 0)
+    return 1;			/* -1, 0, and +1 are perfect powers */
 
   n2 = mpz_scan1 (u, 0);
   if (n2 == 1)
     return 0;			/* 2 divides exactly once.  */
 
-  if (n2 != 0 && (n2 & 1) == 0 && usize < 0)
-    return 0;			/* 2 has even multiplicity with negative U */
-
   TMP_MARK;
 
   uns = ABS (usize) - n2 / BITS_PER_MP_LIMB;
@@ -89,6 +88,14 @@
   MPZ_TMP_INIT (u2, uns);
 
   mpz_tdiv_q_2exp (u2, u, n2);
+  mpz_abs (u2, u2);
+
+  if (mpz_cmp_ui (u2, 1) == 0)
+    {
+      TMP_FREE;
+      /* factoring completed; consistent power */
+      return ! (usize < 0 && POW2P(n2));
+    }
 
   if (isprime (n2))
     goto n2prime;
@@ -97,6 +104,9 @@
     {
       prime = primes[i];
 
+      if (mpz_cmp_ui (u2, prime) < 0)
+	break;
+
       if (mpz_divisible_ui_p (u2, prime))	/* divisible by this prime? */
 	{
 	  rem = mpz_tdiv_q_ui (q, u2, prime * prime);
@@ -115,12 +125,6 @@
 	      n++;
 	    }
 
-	  if ((n & 1) == 0 && usize < 0)
-	    {
-	      TMP_FREE;
-	      return 0;		/* even multiplicity with negative U, reject */
-	    }
-
 	  n2 = gcd (n2, n);
 	  if (n2 == 1)
 	    {
@@ -128,10 +132,11 @@
 	      return 0;		/* we have multiplicity 1 of some factor */
 	    }
 
-	  if (mpz_cmpabs_ui (u2, 1) == 0)
+	  if (mpz_cmp_ui (u2, 1) == 0)
 	    {
 	      TMP_FREE;
-	      return 1;		/* factoring completed; consistent power */
+	      /* factoring completed; consistent power */
+	      return ! (usize < 0 && POW2P(n2));
 	    }
 
 	  /* As soon as n2 becomes a prime number, stop factoring.
@@ -169,6 +174,10 @@
   else
     {
       unsigned long int nth;
+
+      if (usize < 0 && POW2P(n2))
+	return 0;
+
       /* We found some factors above.  We just need to consider values of n
 	 that divides n2.  */
       for (nth = 2; nth <= n2; nth++)
@@ -184,8 +193,11 @@
 	    exact = mpz_root (q, u2, nth);
 	  if (exact)
 	    {
-	      TMP_FREE;
-	      return 1;
+	      if (! (usize < 0 && POW2P(nth)))
+		{
+		  TMP_FREE;
+		  return 1;
+		}
 	    }
 	  if (mpz_cmp_ui (q, SMALLEST_OMITTED_PRIME) < 0)
 	    {
@@ -199,6 +211,9 @@
     }
 
 n2prime:
+  if (usize < 0 && POW2P(n2))
+    return 0;
+
   exact = mpz_root (NULL, u2, n2);
   TMP_FREE;
   return exact;