Test demonstrating discrepancy in sqr output

src/tests.c

@@ -312,6 +312,29 @@ void run_field_inv_all_var() {
     }
 }
 
+void run_sqr() {
+    secp256k1_fe_t x, s;
+
+#if defined(USE_FIELD_5X52)
+    // Known issue with reduction part of sqr. For simplicity, we trigger the problem here
+    // with "negative" powers of 2, but the problem exists for large ranges of values.
+    {
+        secp256k1_fe_set_int(&x, 1);
+        secp256k1_fe_negate(&x, &x, 1);
+
+        for (int i=1; i<=512; ++i) {
+            secp256k1_fe_mul_int(&x, 2);
+            secp256k1_fe_normalize(&x);
+            secp256k1_fe_sqr(&s, &x);
+            if (!secp256k1_fe_verify(&s)) {
+                printf("%4i: %016llx %016llx %016llx %016llx %016llx\n",
+                    i, s.n[4], s.n[3], s.n[2], s.n[1], s.n[0]);
+            }
+        }
+    }
+#endif
+}
+
 void test_sqrt(const secp256k1_fe_t *a, const secp256k1_fe_t *k) {
     secp256k1_fe_t r1, r2;
     int v = secp256k1_fe_sqrt(&r1, a);
@@ -609,6 +632,7 @@ int main(int argc, char **argv) {
     run_field_inv_var();
     run_field_inv_all();
     run_field_inv_all_var();
+    run_sqr();
     run_sqrt();
 
     // ecmult tests