gh-100687: Reduce frequency of overallocation in long_add

Misc/NEWS.d/next/Core and Builtins/2023-01-02-14-54-12.gh-issue-100688.yenIag.rst

@@ -0,0 +1,2 @@
+Reduce frequency of overallocation in some cases of multidigit integer
+additions and subtractions.

Objects/longobject.c

@@ -3387,16 +3387,29 @@ x_add(PyLongObject *a, PyLongObject *b)
     Py_ssize_t i;
     digit carry = 0;
 
+    /* There are fast paths for cases where a and b both have at most a single
+       digit, so if we end up here then at least one of them is multi-digit. */
+    assert(size_a >= 2 || size_b >= 2);
+
     /* Ensure a is the larger of the two: */
     if (size_a < size_b) {
         { PyLongObject *temp = a; a = b; b = temp; }
         { Py_ssize_t size_temp = size_a;
             size_a = size_b;
             size_b = size_temp; }
     }
-    z = _PyLong_New(size_a+1);
+
+    /* Allocate sufficient space for the result. In the majority of cases
+       we allocate exactly the right number of digits, but in the (relatively
+       rare) case where the sum of the topmost digits is exactly PyLong_MASK,
+       we'll sometimes end up overallocating by a single digit. */
+    digit top_sum = a->ob_digit[size_a-1]
+        + (size_b == size_a ? b->ob_digit[size_b-1] : (digit)0);
+    int extra_digit = top_sum >= PyLong_MASK;
+    z = _PyLong_New(size_a+extra_digit);
     if (z == NULL)
         return NULL;
+
     for (i = 0; i < size_b; ++i) {
         carry += a->ob_digit[i] + b->ob_digit[i];
         z->ob_digit[i] = carry & PyLong_MASK;
@@ -3407,8 +3420,16 @@ x_add(PyLongObject *a, PyLongObject *b)
         z->ob_digit[i] = carry & PyLong_MASK;
         carry >>= PyLong_SHIFT;
     }
-    z->ob_digit[i] = carry;
-    return long_normalize(z);
+    if (extra_digit) {
+        if (carry) {
+            z->ob_digit[i] = carry;
+        }
+        else {
+            /* rare case: we didn't need the extra digit after all */
+            Py_SET_SIZE(z, size_a);
+        }
+    }
+    return z;
 }
 
 /* Subtract the absolute values of two integers. */