without:
  printf "%x\n" $((0x8000000000000000>>1))
  c000000000000000

with:
  $ printf "%x\n" $((0x8000000000000000>>1))
  4000000000000000

without, bash behavior is compiler dependent.
The default bash behavior should be to support portable scripts.
Also signed shift is just not useful from shell scripts.

--- expr.arithmetic_shift.c	2008-10-06 07:35:09.000000000 +0000
+++ expr.c	2008-10-06 07:11:44.000000000 +0000
@@ -452,7 +452,7 @@
 	      lvalue <<= value;
 	      break;
 	    case RSH:
-	      lvalue >>= value;
+	      lvalue = ((uintmax_t)lvalue) >> value;
 	      break;
 	    case BAND:
 	      lvalue &= value;
@@ -703,7 +703,7 @@
       if (op == LSH)
 	val1 = val1 << val2;
       else
-	val1 = val1 >> val2;
+	val1 = ((uintmax_t)val1) >> val2;
     }
 
   return (val1);