From 98c7069f75b19df1aed92087cc4fef34a76c38b7 Mon Sep 17 00:00:00 2001
From: Nikolaj Bjorner <nbjorner@microsoft.com>
Date: Mon, 18 Apr 2022 14:29:16 +0200
Subject: [PATCH] add rewrite for hoisting multipliers over modular inverses

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
---
 src/ast/rewriter/arith_rewriter.cpp | 23 +++++++++++++++++++++++
 src/ast/rewriter/arith_rewriter.h   |  4 +++-
 2 files changed, 26 insertions(+), 1 deletion(-)

diff --git a/src/ast/rewriter/arith_rewriter.cpp b/src/ast/rewriter/arith_rewriter.cpp
index 857ae0755..1b52e335d 100644
--- a/src/ast/rewriter/arith_rewriter.cpp
+++ b/src/ast/rewriter/arith_rewriter.cpp
@@ -700,9 +700,32 @@ br_status arith_rewriter::mk_eq_core(expr * arg1, expr * arg2, expr_ref & result
     else if (m_arith_lhs || is_arith_term(arg1) || is_arith_term(arg2)) {
         st = mk_le_ge_eq_core(arg1, arg2, EQ, result);
     }
+
+    if (st == BR_FAILED && mk_eq_mod(arg1, arg2, result)) 
+        st = BR_REWRITE2;
     return st;
 }
 
+bool arith_rewriter::mk_eq_mod(expr* arg1, expr* arg2, expr_ref& result) {
+    expr* x = nullptr, *y = nullptr, *z = nullptr, *u = nullptr;
+    rational p, k, l;
+    // match k*u mod p = l, where k, p, l are integers
+    if (m_util.is_mod(arg1, x, y) && m_util.is_numeral(y, p) &&
+        m_util.is_mul(x, z, u) && m_util.is_numeral(z, k) &&
+        m_util.is_numeral(arg2, l) && 0 <= l && l < p) {
+        // a*p + k*b = g
+        rational a, b;
+        rational g = gcd(p, k, a, b);
+        if (g == 1) {
+            expr_ref nb(m_util.mk_numeral(b, true), m());
+            result = m().mk_eq(m_util.mk_mod(u, y),
+                               m_util.mk_mod(m_util.mk_mul(nb, arg2), y));
+            return true;            
+        }
+    }
+    return false;
+}
+
 expr_ref arith_rewriter::neg_monomial(expr* e) const {
     expr_ref_vector args(m());
     rational a1;
diff --git a/src/ast/rewriter/arith_rewriter.h b/src/ast/rewriter/arith_rewriter.h
index d64896d3d..19a8363a0 100644
--- a/src/ast/rewriter/arith_rewriter.h
+++ b/src/ast/rewriter/arith_rewriter.h
@@ -104,7 +104,9 @@ class arith_rewriter : public poly_rewriter<arith_rewriter_core> {
     bool divides(expr* d, expr* n, expr_ref& result);
     expr_ref remove_divisor(expr* arg, expr* num, expr* den); 
     void flat_mul(expr* e, ptr_buffer<expr>& args); 
-    void remove_divisor(expr* d, ptr_buffer<expr>& args); 
+    void remove_divisor(expr* d, ptr_buffer<expr>& args);
+
+    bool mk_eq_mod(expr* arg1, expr* arg2, expr_ref& result);
 public:
     arith_rewriter(ast_manager & m, params_ref const & p = params_ref()):
         poly_rewriter<arith_rewriter_core>(m, p) {