Index: longobject.c
===================================================================
--- longobject.c	(revision 66590)
+++ longobject.c	(working copy)
@@ -2495,18 +2495,94 @@
 		}
 	}
 	else {	/* a is not the same as b -- gradeschool long mult */
-		for (i = 0; i < size_a; ++i) {
-			twodigits carry = 0;
-			twodigits f = a->ob_digit[i];
+             /* To reduce the number of shift and mask operations
+              * collect terms in the following way
+              *     (a[0] + a[1]*BASE + a[2]*BASE**2 + ...) *
+              *     (b[0] + b[1]*BASE + b[2]*BASE**2 + ...) =
+              *     a[0]*b[0] + (a[0]*b[1] + a[1]*b[0])*BASE +
+              *     (a[0]*b[2] + a[1]*b[1])*BASE**2 + ...
+              */
+		for (i = 0; i < size_a - 1; i += 2) {
+			twodigits f0 = a->ob_digit[i];
+			twodigits f1 = a->ob_digit[i+1];
 			digit *pz = z->ob_digit + i;
 			digit *pb = b->ob_digit;
+			twodigits carry = *pz + pb[0] * f0;
+			*pz++ = (digit)(carry & PyLong_MASK);
+			/* carry <= MASK*(MASK+1) = BASE**2 - BASE */
+			carry >>= PyLong_SHIFT;
+			/* carry <= BASE - 2 = MASK - 1 */ 
+			SIGCHECK({
+				Py_DECREF(z);
+				return NULL;
+			})
+			int j;
+			/* Bounds on carry in the loop to guarantee
+                        *  that it does not overflow: 
+			*  For j = 0:
+			*  carry += *pz + pb[j+1] * f0 + pb[j] * f1;  
+			*  carry <= MASK-1 + MASK + 2*MASK**2
+                        *         = 2*MASK**2 + 2*MASK - 1
+			*         = 2*BASE**2 - 2*BASE - 1
+			*  carry >>= PyLong_SHIFT;
+			*  carry <= BASE - 3 = 2*MASK - 1
+			*  For j = 1:
+			*  carry += *pz + pb[j+1] * f0 + pb[j] * f1;
+			*  carry <= 2*MASK-1 + MASK + 2*MASK**2 = 
+			*         = 2*MASK**2 + 3*MASK - 1 =
+			*         = 2*BASE**2 - BASE - 2
+			*  carry >>= PyLong_SHIFT;
+			*  carry <= 2*BASE - 2 = 2*MASK
+			*  For j = 2:
+			*  carry += *pz + pb[j+1] * f0 + pb[j] * f1;
+			*  carry <= 2*MASK + MASK + 2*MASK**2 =
+			*         = 2*MASK**2 + 3*MASK 
+			*         = 2*BASE**2 - BASE - 1
+			*  carry >>= PyLong_SHIFT;
+			*  carry <= 2*BASE - 2 = 2*MASK; 
+			*  as in the case j=1, so that the bounds remain
+			*  the same for the rest of the loop; therefore
+			*  in this loop one has always
+			*  carry <= 2*MASK**2 + 3*MASK
+			*  which fits in a twodigits, see longintrepr.h
+			*  
+			*/
+			for(j=0; j < size_b-1; j++) {
+				carry += *pz + pb[j+1] * f0 + pb[j] * f1;
+				*pz++ = (digit)(carry & PyLong_MASK);
+				carry >>= PyLong_SHIFT;
+				assert(carry <= 2*PyLong_MASK);
+			}
+			carry += *pz + pb[size_b-1] * f1;
+			/* carry  <= 2*MASK + MASK + MASK**2 =
+			 *         = MASK**2 + 3*MASK = BASE**2 + BASE - 2
+			 */
+			*pz++ = (digit)(carry & PyLong_MASK);
+			carry >>= PyLong_SHIFT;
+			/* carry <= BASE  */
+			if (carry)
+				*pz += (digit)(carry & PyLong_MASK);
+			/* according to the above bound one has
+			 * (carry >> PyLong_SHIFT) <= 1
+			 * However it must be strictly
+                         * (carry >> PyLong_SHIFT) == 0
+			 * otherwise z would exceed size_a + size_b, which
+			 * is impossible.
+			 */
+			assert((carry >> PyLong_SHIFT) == 0);
+		}
+		if (size_a&1) {
+			twodigits carry = 0;
+			twodigits f = a->ob_digit[size_a - 1];
+			digit *pz = z->ob_digit + size_a - 1;
+			digit *pb = b->ob_digit;
 			digit *pbend = b->ob_digit + size_b;
-
+        
 			SIGCHECK({
 				Py_DECREF(z);
 				return NULL;
 			})
-
+        
 			while (pb < pbend) {
 				carry += *pz + *pb++ * f;
 				*pz++ = (digit)(carry & PyLong_MASK);