py/mpz: Fix bug with overflowing C-shift in division routine.

When DIG_SIZE=32, a uint32_t is used to store limbs, and no normalisation
is needed because the MSB is already set, then there will be left and
right shifts (in C) by 32 of a 32-bit variable, leading to undefined
behaviour.  This patch fixes this bug.

py/mpz.c

@@ -491,7 +491,7 @@ STATIC void mpn_div(mpz_dig_t *num_dig, mp_uint_t *num_len, mpz_dig_t *den_dig,
     for (mpz_dig_t *den = den_dig, carry = 0; den < den_dig + den_len; ++den) {
         mpz_dig_t d = *den;
         *den = ((d << norm_shift) | carry) & DIG_MASK;
-        carry = d >> (DIG_SIZE - norm_shift);
+        carry = (mpz_dbl_dig_t)d >> (DIG_SIZE - norm_shift);
     }
 
     // now need to shift numerator by same amount as denominator
@@ -501,7 +501,7 @@ STATIC void mpn_div(mpz_dig_t *num_dig, mp_uint_t *num_len, mpz_dig_t *den_dig,
     for (mpz_dig_t *num = num_dig, carry = 0; num < num_dig + *num_len; ++num) {
         mpz_dig_t n = *num;
         *num = ((n << norm_shift) | carry) & DIG_MASK;
-        carry = n >> (DIG_SIZE - norm_shift);
+        carry = (mpz_dbl_dig_t)n >> (DIG_SIZE - norm_shift);
     }
 
     // cache the leading digit of the denominator
@@ -618,14 +618,14 @@ STATIC void mpn_div(mpz_dig_t *num_dig, mp_uint_t *num_len, mpz_dig_t *den_dig,
     for (mpz_dig_t *den = den_dig + den_len - 1, carry = 0; den >= den_dig; --den) {
         mpz_dig_t d = *den;
         *den = ((d >> norm_shift) | carry) & DIG_MASK;
-        carry = d << (DIG_SIZE - norm_shift);
+        carry = (mpz_dbl_dig_t)d << (DIG_SIZE - norm_shift);
     }
 
     // unnormalise numerator (remainder now)
     for (mpz_dig_t *num = orig_num_dig + *num_len - 1, carry = 0; num >= orig_num_dig; --num) {
         mpz_dig_t n = *num;
         *num = ((n >> norm_shift) | carry) & DIG_MASK;
-        carry = n << (DIG_SIZE - norm_shift);
+        carry = (mpz_dbl_dig_t)n << (DIG_SIZE - norm_shift);
     }
 
     // strip trailing zeros

tests/basics/int_big_div.py

@@ -1,3 +1,10 @@
 for lhs in (1000000000000000000000000, 10000000000100000000000000, 10012003400000000000000007, 12349083434598210349871029923874109871234789):
     for rhs in range(1, 555):
         print(lhs // rhs)
+
+# these check an edge case on 64-bit machines where two mpz limbs
+# are used and the most significant one has the MSB set
+x = 0x8000000000000000
+print((x + 1) // x)
+x = 0x86c60128feff5330
+print((x + 1) // x)

tests/basics/int_big_mod.py

@@ -8,3 +8,10 @@ for i in range(11):
         y = delta * (j)# - 5) # TODO reinstate negative number test when % is working with sign correctly
         if y != 0:
             print(x % y)
+
+# these check an edge case on 64-bit machines where two mpz limbs
+# are used and the most significant one has the MSB set
+x = 0x8000000000000000
+print((x + 1) % x)
+x = 0x86c60128feff5330
+print((x + 1) % x)