lp: add dio_calls_period_decrease parameter

Introduce the lp.dio_calls_period_decrease parameter (default 2) that
controls how fast dio_calls_period is decreased on each final_check()
call where the Diophantine handler is not triggered, gradually
re-enabling dio solving after it was backed off (its period doubled).

Replaces the previous placeholder that left the recovery amount
unparameterized.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

src/math/lp/int_solver.cpp

@@ -239,8 +239,11 @@ namespace lp {
 
         bool should_solve_dioph_eq() {
             bool ret = lia.settings().dio() && hit_period(settings().dio_calls_period());
-            if (!ret && lia.settings().dio_calls_period() > m_initial_dio_calls_period)
+            if (!ret && lia.settings().dio_calls_period() > m_initial_dio_calls_period) {
-                lia.settings().dio_calls_period() --;
+                unsigned dec = settings().dio_calls_period_decrease();
+                unsigned& period = lia.settings().dio_calls_period();
+                period = period > m_initial_dio_calls_period + dec ? period - dec : m_initial_dio_calls_period;
+            }
             return ret;
         }
 

src/math/lp/lp_params_helper.pyg

@@ -8,6 +8,7 @@ def_module_params(module_name='lp',
                           ('dio_cuts_enable_hnf', BOOL, True, 'enable hnf cuts together with Diophantine cuts, only relevant when dioph_eq is true'),
                           ('dio_ignore_big_nums', BOOL, True, 'Ignore the terms with big numbers in the Diophantine handler, only relevant when dioph_eq is true'),
                           ('dio_calls_period', UINT, 1, 'Period of calling the Diophantine handler in the final_check()'),
+                          ('dio_calls_period_decrease', UINT, 2, 'Amount by which dio_calls_period is decreased on each final_check() call where the Diophantine handler is not triggered, until it returns to its initial value'),
                           ('dio_run_gcd', BOOL, False, 'Run the GCD heuristic if dio is on, if dio is disabled the option is not used'),
                           ('lcube', BOOL, True, 'use the largest cube test for integer feasibility'),
                           ('lcube_flips', UINT, 16, 'maximal number of coordinate flips when repairing the rounded largest cube center, only relevant when lcube is true'),

src/math/lp/lp_settings.cpp

@@ -42,6 +42,7 @@ void lp::lp_settings::updt_params(params_ref const& _p) {
     m_dump_bound_lemmas = p.arith_dump_bound_lemmas();
     m_dio_ignore_big_nums = lp_p.dio_ignore_big_nums();
     m_dio_calls_period = lp_p.dio_calls_period();
+    m_dio_calls_period_decrease = lp_p.dio_calls_period_decrease();
     m_dio_run_gcd = lp_p.dio_run_gcd();
     m_random_hammers = lp_p.random_hammers();
     m_lcube = lp_p.lcube();

src/math/lp/lp_settings.h

@@ -263,6 +263,7 @@ private:
     bool             m_dump_bound_lemmas = false;
     bool             m_dio_ignore_big_nums = false;
     unsigned         m_dio_calls_period = 4;
+    unsigned         m_dio_calls_period_decrease = 2;
     bool             m_dio_run_gcd = true;
     bool             m_random_hammers = true;
     bool             m_lcube = true;
@@ -272,6 +273,8 @@ public:
     unsigned lcube_flips() const { return m_lcube_flips; }
     unsigned dio_calls_period() const { return m_dio_calls_period; }
     unsigned & dio_calls_period() { return m_dio_calls_period; }
+    unsigned dio_calls_period_decrease() const { return m_dio_calls_period_decrease; }
+    unsigned & dio_calls_period_decrease() { return m_dio_calls_period_decrease; }
     bool random_hammers() const { return m_random_hammers; }
     bool & random_hammers() { return m_random_hammers; }
     bool print_external_var_name() const { return m_print_external_var_name; }