py/mpz: Fix bugs with bitwise of -0 by ensuring all 0's are positive.

This commit makes sure that the value zero is always encoded in an mpz_t as
neg=0 and len=0 (previously it was just len=0).

This invariant is needed for some of the bitwise operations that operate on
negative numbers, because they cannot handle -0.  For example
(-((1<<100)-(1<<100)))|1 was being computed as -65535, instead of 1.

Fixes issue #8042.

Signed-off-by: Damien George <damien@micropython.org>

py/mpz.c

@@ -713,6 +713,7 @@ void mpz_set(mpz_t *dest, const mpz_t *src) {
 
 void mpz_set_from_int(mpz_t *z, mp_int_t val) {
     if (val == 0) {
+        z->neg = 0;
         z->len = 0;
         return;
     }
@@ -899,10 +900,6 @@ bool mpz_is_even(const mpz_t *z) {
 #endif
 
 int mpz_cmp(const mpz_t *z1, const mpz_t *z2) {
-    // to catch comparison of -0 with +0
-    if (z1->len == 0 && z2->len == 0) {
-        return 0;
-    }
     int cmp = (int)z2->neg - (int)z1->neg;
     if (cmp != 0) {
         return cmp;
@@ -1052,7 +1049,9 @@ void mpz_neg_inpl(mpz_t *dest, const mpz_t *z) {
     if (dest != z) {
         mpz_set(dest, z);
     }
+    if (dest->len) {
         dest->neg = 1 - dest->neg;
+    }
 }
 
 /* computes dest = ~z (= -z - 1)
@@ -1148,7 +1147,7 @@ void mpz_add_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs) {
         dest->len = mpn_sub(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
     }
 
-    dest->neg = lhs->neg;
+    dest->neg = lhs->neg & !!dest->len;
 }
 
 /* computes dest = lhs - rhs
@@ -1172,7 +1171,9 @@ void mpz_sub_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs) {
         dest->len = mpn_sub(dest->dig, lhs->dig, lhs->len, rhs->dig, rhs->len);
     }
 
-    if (neg) {
+    if (dest->len == 0) {
+        dest->neg = 0;
+    } else if (neg) {
         dest->neg = 1 - lhs->neg;
     } else {
         dest->neg = lhs->neg;
@@ -1484,14 +1485,16 @@ void mpz_divmod_inpl(mpz_t *dest_quo, mpz_t *dest_rem, const mpz_t *lhs, const m
 
     mpz_need_dig(dest_quo, lhs->len + 1); // +1 necessary?
     memset(dest_quo->dig, 0, (lhs->len + 1) * sizeof(mpz_dig_t));
+    dest_quo->neg = 0;
     dest_quo->len = 0;
     mpz_need_dig(dest_rem, lhs->len + 1); // +1 necessary?
     mpz_set(dest_rem, lhs);
     mpn_div(dest_rem->dig, &dest_rem->len, rhs->dig, rhs->len, dest_quo->dig, &dest_quo->len);
+    dest_rem->neg &= !!dest_rem->len;
 
     // check signs and do Python style modulo
     if (lhs->neg != rhs->neg) {
-        dest_quo->neg = 1;
+        dest_quo->neg = !!dest_quo->len;
         if (!mpz_is_zero(dest_rem)) {
             mpz_t mpzone;
             mpz_init_from_int(&mpzone, -1);

py/mpz.h

@@ -91,6 +91,7 @@ typedef int8_t mpz_dbl_dig_signed_t;
 #define MPZ_NUM_DIG_FOR_LL ((sizeof(long long) * 8 + MPZ_DIG_SIZE - 1) / MPZ_DIG_SIZE)
 
 typedef struct _mpz_t {
+    // Zero has neg=0, len=0.  Negative zero is not allowed.
     size_t neg : 1;
     size_t fixed_dig : 1;
     size_t alloc : (8 * sizeof(size_t) - 2);
@@ -119,7 +120,7 @@ static inline bool mpz_is_zero(const mpz_t *z) {
     return z->len == 0;
 }
 static inline bool mpz_is_neg(const mpz_t *z) {
-    return z->len != 0 && z->neg != 0;
+    return z->neg != 0;
 }
 int mpz_cmp(const mpz_t *lhs, const mpz_t *rhs);
 

tests/basics/int_big_zeroone.py

@@ -1,4 +1,4 @@
-# test [0,-0,1,-1] edge cases of bignum
+# test [0,1,-1] edge cases of bignum
 
 long_zero = (2**64) >> 65
 long_neg_zero = -long_zero
@@ -13,7 +13,7 @@ print([~c for c in cases])
 print([c >> 1 for c in cases])
 print([c << 1 for c in cases])
 
-# comparison of 0/-0/+0
+# comparison of 0
 print(long_zero == 0)
 print(long_neg_zero == 0)
 print(long_one - 1 == 0)
@@ -26,3 +26,40 @@ print(long_neg_zero < 1)
 print(long_neg_zero < -1)
 print(long_neg_zero > 1)
 print(long_neg_zero > -1)
+
+# generate zeros that involve negative numbers
+large = 1 << 70
+large_plus_one = large + 1
+zeros = (
+    large - large,
+    -large + large,
+    large + -large,
+    -(large - large),
+    large - large_plus_one + 1,
+    -large & (large - large),
+    -large ^ -large,
+    -large * (large - large),
+    (large - large) // -large,
+    -large // -large_plus_one,
+    -(large + large) % large,
+    (large + large) % -large,
+    -(large + large) % -large,
+)
+print(zeros)
+
+# compute arithmetic operations that may have problems with -0
+# (this checks that -0 is never generated in the zeros tuple)
+cases = (0, 1, -1) + zeros
+for lhs in cases:
+    print("-{} = {}".format(lhs, -lhs))
+    print("~{} = {}".format(lhs, ~lhs))
+    print("{} >> 1 = {}".format(lhs, lhs >> 1))
+    print("{} << 1 = {}".format(lhs, lhs << 1))
+    for rhs in cases:
+        print("{} == {} = {}".format(lhs, rhs, lhs == rhs))
+        print("{} + {} = {}".format(lhs, rhs, lhs + rhs))
+        print("{} - {} = {}".format(lhs, rhs, lhs - rhs))
+        print("{} * {} = {}".format(lhs, rhs, lhs * rhs))
+        print("{} | {} = {}".format(lhs, rhs, lhs | rhs))
+        print("{} & {} = {}".format(lhs, rhs, lhs & rhs))
+        print("{} ^ {} = {}".format(lhs, rhs, lhs ^ rhs))