diff --git a/lib/mini-gmp.c b/lib/mini-gmp.c
index 9168d98667..8d79019df6 100644
--- a/lib/mini-gmp.c
+++ b/lib/mini-gmp.c
@@ -4285,8 +4285,39 @@ mpz_sizeinbase (const mpz_t u, int base)
       return (bits + 3) / 4;
     case 32:
       return (bits + 4) / 5;
-      /* FIXME: Do something more clever for the common case of base
-	 10. */
+    }
+
+  if (GMP_LIMB_BITS >= 32 && bits <= (1UL << 30))
+    {
+      /* ceil (2^32 / log2 (base)) (rounded up),
+         for bases 3 through 62.  */
+      static const unsigned long log2_inverse[] = {
+        2709822658,  /*done*/0, 1849741733, 1661520156,
+        1529898220,  /*done*/0, 1354911329, 1292913987,
+        1241523976, 1198050830, 1160664036, 1128071164,
+        1099331346,  /*done*/0, 1050766078, 1029986702,
+        1011073585,  993761859,  977836273,  963119892,
+         949465784,  936750802,  924870867,  913737343,
+         903274220,  893415895,  884105414,  875293063,
+         866935226,  /*done*/0,  851433730,  844225783,
+         837342624,  830760078,  824456425,  818412085,
+         812609357,  807032192,  801666002,  796497491,
+         791514512,  786705943,  782061578,  777572033,
+         773228661,  769023480,  764949110,  760998713,
+         757165946,  753444911,  749830123,  746316465,
+         742899164,  739573757,  736336068,  733182184,
+         730108433,  727111368,  724187745,  721334514,
+      };
+      mp_limb_t hi, lo;
+      int shift = (int) GMP_LIMB_BITS - 32;
+
+      /* With bits <= 2^30, coefficient rounding adds less than 1/4
+         digit.  The bit-length estimate adds at most 1/log2(3),
+         and 1/4 + 1/log2(3) < 1, ensuring at most one extra digit.  */
+      gmp_umul_ppmm (hi, lo, (mp_limb_t) bits,
+                    (mp_limb_t) log2_inverse[base - 3] << shift);
+      (void) lo;
+      return 1 + hi;
     }
 
   tp = gmp_alloc_limbs (un);