From 5fad8b946887d0ac37d6c379e04ba8bfe0c9f16b Mon Sep 17 00:00:00 2001
From: Xiretza <xiretza@xiretza.xyz>
Date: Sat, 11 Apr 2020 13:32:18 +0200
Subject: Add formal tests for mod/rem

---
 testsuite/formal/gates/test_mod_rem.sby | 13 +++++
 testsuite/formal/gates/test_mod_rem.vhd | 99 +++++++++++++++++++++++++++++++++
 testsuite/formal/gates/testsuite.sh     |  2 +-
 3 files changed, 113 insertions(+), 1 deletion(-)
 create mode 100644 testsuite/formal/gates/test_mod_rem.sby
 create mode 100644 testsuite/formal/gates/test_mod_rem.vhd

(limited to 'testsuite')

diff --git a/testsuite/formal/gates/test_mod_rem.sby b/testsuite/formal/gates/test_mod_rem.sby
new file mode 100644
index 0000000..ee47e96
--- /dev/null
+++ b/testsuite/formal/gates/test_mod_rem.sby
@@ -0,0 +1,13 @@
+[options]
+mode prove
+depth 3
+
+[engines]
+smtbmc z3
+
+[script]
+ghdl --std=08 test_mod_rem.vhd -e ent
+prep -top ent
+
+[files]
+test_mod_rem.vhd
diff --git a/testsuite/formal/gates/test_mod_rem.vhd b/testsuite/formal/gates/test_mod_rem.vhd
new file mode 100644
index 0000000..5995ef7
--- /dev/null
+++ b/testsuite/formal/gates/test_mod_rem.vhd
@@ -0,0 +1,99 @@
+library ieee;
+use ieee.std_logic_1164.all;
+use ieee.numeric_std.all;
+
+entity ent is
+	port (
+		clk : in std_logic;
+		a : in std_logic_vector(7 downto 0);
+		b : in std_logic_vector(7 downto 0);
+		rem_sgn : out signed(7 downto 0);
+		mod_sgn : out signed(7 downto 0);
+		rem_uns : out unsigned(7 downto 0);
+		mod_uns : out unsigned(7 downto 0)
+	);
+end;
+
+architecture a of ent is
+begin
+	process(clk)
+	begin
+		if rising_edge(clk) then
+			rem_sgn <= signed(a) rem signed(b);
+			mod_sgn <= signed(a) mod signed(b);
+
+			rem_uns <= unsigned(a) rem unsigned(b);
+			mod_uns <= unsigned(a) mod unsigned(b);
+		end if;
+	end process;
+
+	formal: block
+		signal prev_a : std_logic_vector(7 downto 0);
+		signal prev_b : std_logic_vector(7 downto 0);
+		signal has_run : std_logic := '0';
+
+		function same_sign(x, y : signed) return boolean is
+		begin
+			return x = 0 or y = 0 or (x > 0) = (y > 0);
+		end function;
+
+		function longer(x : signed) return signed is
+		begin
+			return resize(x, x'length+1);
+		end function;
+
+		-- artificial flooring integer division, constructed from native
+		-- truncating integer division operator (/)
+		function floordiv(x, y : signed) return signed is
+		begin
+			-- same signs on inputs will give positive result - rounded in same
+			-- direction as truncating division
+			if same_sign(x, y) then
+				return x / y;
+			-- otherwise, increase the absolute value of x by abs(y)-1
+			elsif x < 0 then
+				-- x is negative, y is positive
+				return (x - (y - 1)) / y;
+			else
+				-- x is positive, y is negative
+				return (x - (y + 1)) / y;
+			end if;
+		end function;
+	begin
+		process(clk)
+		begin
+			if rising_edge(clk) then
+				has_run <= '1';
+				prev_a <= a;
+				prev_b <= b;
+			end if;
+		end process;
+
+		default clock is rising_edge(clk);
+
+		mod_sgn_sign: assert always has_run -> same_sign(signed(prev_b), mod_sgn);
+		mod_sgn_correct: assert always has_run ->
+			floordiv(
+				longer(signed(prev_a)),
+				longer(signed(prev_b))
+			)
+			* signed(prev_b)
+			+ mod_sgn = signed(prev_a);
+
+		rem_sgn_sign: assert always has_run -> same_sign(signed(prev_a), rem_sgn);
+		rem_sgn_correct: assert always has_run ->
+			longer(signed(prev_a)) / longer(signed(prev_b))
+			* signed(prev_b)
+			+ rem_sgn = signed(prev_a);
+
+		-- calculating modulo from remainder
+		assert always has_run ->
+			(rem_sgn = 0 and mod_sgn = rem_sgn) or
+			(same_sign(signed(prev_a), signed(prev_b)) and mod_sgn = rem_sgn) or
+			mod_sgn = rem_sgn + signed(prev_b);
+
+		uns_mod_correct: assert always has_run ->
+			unsigned(prev_a) / unsigned(prev_b) * unsigned(prev_b) + mod_uns = unsigned(prev_a);
+		unsigned_equal: assert always has_run -> mod_uns = rem_uns;
+	end block;
+end;
diff --git a/testsuite/formal/gates/testsuite.sh b/testsuite/formal/gates/testsuite.sh
index e74df99..9274618 100755
--- a/testsuite/formal/gates/testsuite.sh
+++ b/testsuite/formal/gates/testsuite.sh
@@ -3,7 +3,7 @@
 topdir=../..
 . $topdir/testenv.sh
 
-for f in abs minmax pmux lsl lsr asr; do
+for f in abs minmax pmux lsl lsr asr mod_rem; do
   formal "test_${f}"
 done
 
-- 
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