diff --git a/src/compiler/nir/meson.build b/src/compiler/nir/meson.build
index de19f600ab1..cd588303672 100644
--- a/src/compiler/nir/meson.build
+++ b/src/compiler/nir/meson.build
@@ -519,4 +519,17 @@ if with_tests
     ),
     suite : ['compiler', 'nir'],
   )
+
+  test(
+    'algebraic',
+    executable(
+      'algebraic',
+      files('tests/algebraic_tests.cpp'),
+      c_args : [c_msvc_compat_args, no_override_init_args],
+      gnu_symbol_visibility : 'hidden',
+      include_directories : [inc_include, inc_src, inc_mapi, inc_mesa, inc_gallium, inc_gallium_aux],
+      dependencies : [dep_thread, idep_gtest, idep_nir, idep_mesautil],
+    ),
+    suite : ['compiler', 'nir'],
+  )
 endif
diff --git a/src/compiler/nir/tests/algebraic_tests.cpp b/src/compiler/nir/tests/algebraic_tests.cpp
new file mode 100644
index 00000000000..2cadb3927f8
--- /dev/null
+++ b/src/compiler/nir/tests/algebraic_tests.cpp
@@ -0,0 +1,186 @@
+/*
+ * Copyright © 2018 Intel Corporation
+ * Copyright © 2021 Valve Corporation
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice (including the next
+ * paragraph) shall be included in all copies or substantial portions of the
+ * Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
+ * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+ * DEALINGS IN THE SOFTWARE.
+ */
+
+#include <gtest/gtest.h>
+
+#include "nir.h"
+#include "nir_builder.h"
+
+namespace {
+
+class algebraic_test_base : public ::testing::Test {
+protected:
+   algebraic_test_base();
+   ~algebraic_test_base();
+
+   virtual void run_pass()=0;
+
+   void test_op(nir_op op, nir_ssa_def *src0, nir_ssa_def *src1, nir_ssa_def *src2,
+                nir_ssa_def *src3, const char *desc);
+
+   void test_2src_op(nir_op op, int64_t src0, int64_t src1);
+
+   nir_variable *res_var;
+   nir_builder *b, _b;
+};
+
+algebraic_test_base::algebraic_test_base()
+{
+   glsl_type_singleton_init_or_ref();
+
+   static const nir_shader_compiler_options options = { };
+   _b = nir_builder_init_simple_shader(MESA_SHADER_COMPUTE, &options, "opt_algebraic test");
+   b = &_b;
+
+   res_var = nir_local_variable_create(b->impl, glsl_int_type(), "res");
+}
+
+algebraic_test_base::~algebraic_test_base()
+{
+   ralloc_free(b->shader);
+
+   glsl_type_singleton_decref();
+}
+
+void algebraic_test_base::test_op(nir_op op, nir_ssa_def *src0, nir_ssa_def *src1,
+                                     nir_ssa_def *src2, nir_ssa_def *src3, const char *desc)
+{
+   nir_ssa_def *res_deref = &nir_build_deref_var(b, res_var)->dest.ssa;
+
+   /* create optimized expression */
+   nir_intrinsic_instr *optimized_instr = nir_build_store_deref(
+      b, res_deref, nir_build_alu(b, op, src0, src1, src2, src3), 0x1);
+
+   run_pass();
+   b->cursor = nir_after_cf_list(&b->impl->body);
+
+   /* create reference expression */
+   nir_intrinsic_instr *ref_instr = nir_build_store_deref(
+      b, res_deref, nir_build_alu(b, op, src0, src1, src2, src3), 0x1);
+
+   /* test equality */
+   nir_opt_constant_folding(b->shader);
+
+   ASSERT_TRUE(nir_src_is_const(ref_instr->src[1]));
+   ASSERT_TRUE(nir_src_is_const(optimized_instr->src[1]));
+
+   int32_t ref = nir_src_as_int(ref_instr->src[1]);
+   int32_t optimized = nir_src_as_int(optimized_instr->src[1]);
+
+   EXPECT_EQ(ref, optimized) << "Test input: " << desc;
+
+   /* reset shader */
+   exec_list_make_empty(&nir_start_block(b->impl)->instr_list);
+   b->cursor = nir_after_cf_list(&b->impl->body);
+}
+
+void algebraic_test_base::test_2src_op(nir_op op, int64_t src0, int64_t src1)
+{
+   char desc[128];
+   snprintf(desc, sizeof(desc), "%s(%" PRId64 ", %" PRId64 ")", nir_op_infos[op].name, src0, src1);
+   test_op(op, nir_imm_int(b, src0), nir_imm_int(b, src1), NULL, NULL, desc);
+}
+
+class nir_opt_algebraic_test : public algebraic_test_base {
+protected:
+   virtual void run_pass() {
+      nir_opt_algebraic(b->shader);
+   }
+};
+
+class nir_opt_idiv_const_test : public algebraic_test_base {
+protected:
+   virtual void run_pass() {
+      nir_opt_idiv_const(b->shader, 8);
+   }
+};
+
+TEST_F(nir_opt_algebraic_test, umod_pow2_src2)
+{
+   for (int i = 0; i <= 9; i++)
+      test_2src_op(nir_op_umod, i, 4);
+   test_2src_op(nir_op_umod, UINT32_MAX, 4);
+}
+
+TEST_F(nir_opt_algebraic_test, imod_pow2_src2)
+{
+   for (int i = -9; i <= 9; i++) {
+      test_2src_op(nir_op_imod, i, 4);
+      test_2src_op(nir_op_imod, i, -4);
+      test_2src_op(nir_op_imod, i, INT32_MIN);
+   }
+   test_2src_op(nir_op_imod, INT32_MAX, 4);
+   test_2src_op(nir_op_imod, INT32_MAX, -4);
+   test_2src_op(nir_op_imod, INT32_MIN, 4);
+   test_2src_op(nir_op_imod, INT32_MIN, -4);
+   test_2src_op(nir_op_imod, INT32_MIN, INT32_MIN);
+}
+
+TEST_F(nir_opt_algebraic_test, irem_pow2_src2)
+{
+   for (int i = -9; i <= 9; i++) {
+      test_2src_op(nir_op_irem, i, 4);
+      test_2src_op(nir_op_irem, i, -4);
+   }
+   test_2src_op(nir_op_irem, INT32_MAX, 4);
+   test_2src_op(nir_op_irem, INT32_MAX, -4);
+   test_2src_op(nir_op_irem, INT32_MIN, 4);
+   test_2src_op(nir_op_irem, INT32_MIN, -4);
+}
+
+TEST_F(nir_opt_idiv_const_test, umod)
+{
+   for (uint32_t d : {16u, 17u, 0u, UINT32_MAX}) {
+      for (int i = 0; i <= 40; i++)
+         test_2src_op(nir_op_umod, i, d);
+      for (int i = 0; i < 20; i++)
+         test_2src_op(nir_op_umod, UINT32_MAX - i, d);
+   }
+}
+
+TEST_F(nir_opt_idiv_const_test, imod)
+{
+   for (int32_t d : {16, -16, 17, -17, 0, INT32_MIN, INT32_MAX}) {
+      for (int i = -40; i <= 40; i++)
+         test_2src_op(nir_op_imod, i, d);
+      for (int i = 0; i < 20; i++)
+         test_2src_op(nir_op_imod, INT32_MIN + i, d);
+      for (int i = 0; i < 20; i++)
+         test_2src_op(nir_op_imod, INT32_MAX - i, d);
+   }
+}
+
+TEST_F(nir_opt_idiv_const_test, irem)
+{
+   for (int32_t d : {16, -16, 17, -17, 0, INT32_MIN, INT32_MAX}) {
+      for (int i = -40; i <= 40; i++)
+         test_2src_op(nir_op_irem, i, d);
+      for (int i = 0; i < 20; i++)
+         test_2src_op(nir_op_irem, INT32_MIN + i, d);
+      for (int i = 0; i < 20; i++)
+         test_2src_op(nir_op_irem, INT32_MAX - i, d);
+   }
+}
+
+}