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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;
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