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---------------------------------------------------------------------------- ---- ---- ---- File : cordic_iterative_int.vhd ---- ---- Project : YAC (Yet Another CORDIC Core) ---- ---- Creation : Feb. 2014 ---- ---- Limitations : ---- ---- Synthesizer : ---- ---- Target : ---- ---- ---- ---- Author(s): : Christian Haettich ---- ---- Email : feddischson@opencores.org ---- ---- ---- ---- ---- ----- ----- ---- ---- ---- Description ---- ---- VHDL implementation of YAC ---- ---- ---- ---- ---- ---- ---- ----- ----- ---- ---- ---- TODO ---- ---- Some documentation and function description ---- ---- Optimization ---- ---- ---- ---- ---- ---- ---- ---------------------------------------------------------------------------- ---- ---- ---- Copyright Notice ---- ---- ---- ---- This file is part of YAC - Yet Another CORDIC Core ---- ---- Copyright (c) 2014, Author(s), All rights reserved. ---- ---- ---- ---- YAC is free software; you can redistribute it and/or ---- ---- modify it under the terms of the GNU Lesser General Public ---- ---- License as published by the Free Software Foundation; either ---- ---- version 3.0 of the License, or (at your option) any later version. ---- ---- ---- ---- YAC is distributed in the hope that it will be useful, ---- ---- but WITHOUT ANY WARRANTY; without even the implied warranty of ---- ---- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ---- ---- Lesser General Public License for more details. ---- ---- ---- ---- You should have received a copy of the GNU Lesser General Public ---- ---- License along with this library. If not, download it from ---- ---- http://www.gnu.org/licenses/lgpl ---- ---- ---- ---------------------------------------------------------------------------- library ieee; library std; use std.textio.all; use ieee.std_logic_1164.ALL; use ieee.numeric_std.ALL; use ieee.std_logic_textio.all; -- I/O for logic types use work.cordic_pkg.ALL; use ieee.math_real.ALL; entity cordic_iterative_int is generic( XY_WIDTH : natural := 12; A_WIDTH : natural := 12; GUARD_BITS : natural := 2; RM_GAIN : natural := 4 ); port( clk, rst : in std_logic; en : in std_logic; start : in std_logic; done : out std_logic; mode_i : in std_logic_vector( 4-1 downto 0 ); x_i : in std_logic_vector( XY_WIDTH-1 downto 0 ); y_i : in std_logic_vector( XY_WIDTH-1 downto 0 ); a_i : in std_logic_vector( A_WIDTH+2-1 downto 0 ); x_o : out std_logic_vector( XY_WIDTH+GUARD_BITS-1 downto 0 ); y_o : out std_logic_vector( XY_WIDTH+GUARD_BITS-1 downto 0 ); a_o : out std_logic_vector( A_WIDTH+2-1 downto 0 ) ); end entity cordic_iterative_int; architecture BEHAVIORAL of cordic_iterative_int is -- log2( max-iteration ) constant L2_MAX_I : natural := 8; constant MAX_A_WIDTH : natural := 34; -- Internal angle width constant A_WIDTH_I : natural := A_WIDTH+2; constant SQRT2_REAL : real := 1.4142135623730951454746218587388284504413604; constant PI_REAL : real := 3.1415926535897931159979634685441851615905762; constant PI : integer := natural( round( PI_REAL * real( 2**( A_WIDTH-1 ) ) ) ); constant PI_H : integer := natural( round( PI_REAL * real( 2**( A_WIDTH-2 ) ) ) ); constant SQRT2 : integer := natural( round( SQRT2_REAL * real( 2**( XY_WIDTH-1 ) ) ) ); constant XY_MAX : integer := natural( 2**( XY_WIDTH-1)-1); constant XY_WIDTH_G : natural := XY_WIDTH + GUARD_BITS; type state_st is( ST_IDLE, ST_INIT, ST_ROTATE, ST_RM_GAIN, ST_DONE ); type state_t is record st : state_st; mode : std_logic_vector( mode_i'range ); x : signed( XY_WIDTH_G -1 downto 0 ); y : signed( XY_WIDTH_G -1 downto 0 ); x_sh : signed( XY_WIDTH_G -1 downto 0 ); y_sh : signed( XY_WIDTH_G -1 downto 0 ); x_sum : signed( XY_WIDTH_G -1 downto 0 ); y_sum : signed( XY_WIDTH_G -1 downto 0 ); a : signed( A_WIDTH_I -1 downto 0 ); a_tmp : signed( A_WIDTH_I -1 downto 0 ); ylst : signed( XY_WIDTH_G -1 downto 0 ); alst : signed( A_WIDTH_I -1 downto 0 ); i : signed( L2_MAX_I -1 downto 0 ); do_shift : std_logic; repeate : std_logic; end record state_t; signal state : state_t; --------------------------------------- -- Auto-generated function -- by matlab (see c_octave/cordic_iterative_code.m) function angular_lut( n : integer; mode : std_logic_vector; ANG_WIDTH : natural ) return signed is variable result : signed( ANG_WIDTH-1 downto 0 ); variable temp : signed( MAX_A_WIDTH-1 downto 0 ); begin if mode = VAL_MODE_CIR then case n is when 0 => temp := "0110010010000111111011010101000100"; -- -1843415740 when 1 => temp := "0011101101011000110011100000101011"; -- -312264661 when 2 => temp := "0001111101011011011101011111100100"; -- 2104350692 when 3 => temp := "0000111111101010110111010100110101"; -- 1068201269 when 4 => temp := "0000011111111101010101101110110111"; -- 536173495 when 5 => temp := "0000001111111111101010101011011101"; -- 268348125 when 6 => temp := "0000000111111111111101010101010110"; -- 134206806 when 7 => temp := "0000000011111111111111101010101010"; -- 67107498 when 8 => temp := "0000000001111111111111111101010101"; -- 33554261 when 9 => temp := "0000000000111111111111111111101010"; -- 16777194 when 10 => temp := "0000000000011111111111111111111101"; -- 8388605 when others => temp := to_signed( 2**(MAX_A_WIDTH-1-n), MAX_A_WIDTH ); end case; elsif mode = VAL_MODE_HYP then case n is when 1 => temp := "0100011001001111101010011110101010"; -- 423536554 when 2 => temp := "0010000010110001010111011111010100"; -- -2100987948 when 3 => temp := "0001000000010101100010010001110010"; -- 1079387250 when 4 => temp := "0000100000000010101011000100010101"; -- 537571605 when 5 => temp := "0000010000000000010101010110001000"; -- 268522888 when 6 => temp := "0000001000000000000010101010101100"; -- 134228652 when 7 => temp := "0000000100000000000000010101010101"; -- 67110229 when 8 => temp := "0000000010000000000000000010101010"; -- 33554602 when 9 => temp := "0000000001000000000000000000010101"; -- 16777237 when 10 => temp := "0000000000100000000000000000000010"; -- 8388610 when others => temp := to_signed( 2**(MAX_A_WIDTH-1-n), MAX_A_WIDTH ); end case; elsif mode = VAL_MODE_LIN then temp := ( others => '0' ); temp( temp'high-1-n downto 0 ) := ( others => '1' ); end if; result := temp( temp'high downto temp'high-result'length+1 ); return result; end function angular_lut; --------------------------------------- function repeat_hyperbolic_it( i : integer ) return boolean is variable res : boolean; begin case i is when 5 => res := true; when 14 => res := true; when 41 => res := true; when 122 => res := true; when others => res := false; end case; return res; end; begin ST : process( clk, rst ) variable sign : std_logic; begin if clk'event and clk = '1' then if rst = '1' then state <= ( st => ST_IDLE, x => ( others => '0' ), y => ( others => '0' ), x_sh => ( others => '0' ), y_sh => ( others => '0' ), x_sum => ( others => '0' ), y_sum => ( others => '0' ), a => ( others => '0' ), a_tmp => ( others => '0' ), ylst => ( others => '0' ), alst => ( others => '0' ), mode => ( others => '0' ), i => ( others => '0' ), do_shift => '0', repeate => '0' ); elsif en = '1' then if state.st = ST_IDLE and start = '1' then state.st <= ST_INIT; state.mode <= mode_i; state.x <= resize( signed( x_i ), state.x'length ); state.y <= resize( signed( y_i ), state.y'length ); state.a <= resize( signed( a_i ), state.a'length ); state.i <= ( others => '0' ); state.alst <= ( others => '0' ); state.ylst <= ( others => '0' ); elsif state.st = ST_INIT then -- -- initialization state -- -> do initial rotation (alignment) -- -> check special situations / miss-configurations (TODO) -- state.st <= ST_ROTATE; state.do_shift <= '1'; if state.mode( 1 downto 0 ) = VAL_MODE_HYP then -- if we do a hyperbolic rotation, we start with 1 state.i(0) <= '1'; end if; if state.mode( I_FLAG_VEC_ROT ) = '1' and state.y = 0 then -- zero-input state.x_sum <= state.x; state.y_sum <= state.y; state.a <= ( others => '0' ); state.st <= ST_DONE; elsif state.mode( I_FLAG_VEC_ROT ) = '0' and state.a = 0 then -- nothing to do, a is zero state.x_sum <= state.x; state.y_sum <= state.y; state.st <= ST_DONE; elsif state.mode( I_FLAG_VEC_ROT ) = '0' and state.mode( 1 downto 0 ) = VAL_MODE_CIR then -- circular vector mode if state.a < - PI_H then -- move from third quadrant to first state.a <= state.a + PI; state.x <= - state.x; state.y <= - state.y; elsif state.a > PI_H then -- move from second quadrant to fourth state.a <= state.a - PI; state.x <= - state.x; state.y <= - state.y; end if; elsif state.mode( I_FLAG_VEC_ROT ) = '1' and state.mode( 1 downto 0 ) = VAL_MODE_CIR then -- circular rotation mode if state.y = 0 then -- zero-input state.x_sum <= state.x; state.y_sum <= state.y; state.a <= ( others => '0' ); state.st <= ST_DONE; elsif state.x = XY_MAX and state.y = XY_MAX then -- all-max 1 state.x_sum <= to_signed( SQRT2, state.x'length ); state.y_sum <= (others => '0' ); state.a <= resize( angular_lut( 0, state.mode( 1 downto 0 ), A_WIDTH ), A_WIDTH_I ); state.st <= ST_DONE; elsif state.x = -XY_MAX and state.y = -XY_MAX then -- all-max 2 state.x_sum <= to_signed( SQRT2, state.x'length ); state.y_sum <= (others => '0' ); state.a <= resize( angular_lut( 0, state.mode( 1 downto 0 ), A_WIDTH ), A_WIDTH_I ) - PI; state.st <= ST_DONE; elsif state.x = XY_MAX and state.y = -XY_MAX then -- all-max 3 state.x_sum <= to_signed( SQRT2, state.x'length ); state.y_sum <= (others => '0' ); state.a <= resize( -angular_lut( 0, state.mode( 1 downto 0 ), A_WIDTH ), A_WIDTH_I ); state.st <= ST_DONE; elsif state.x = -XY_MAX and state.y = XY_MAX then -- all-max 4 state.x_sum <= to_signed( SQRT2, state.x'length ); state.y_sum <= (others => '0' ); state.a <= PI- resize( angular_lut( 0, state.mode( 1 downto 0 ), A_WIDTH ), A_WIDTH_I ); state.st <= ST_DONE; elsif state.x = 0 and state.y > 0 then -- fixed rotation of pi/2 state.x_sum <= state.y; state.y_sum <= ( others => '0' ); state.a <= to_signed( PI_H, state.a'length ); state.st <= ST_DONE; elsif state.x = 0 and state.y < 0 then -- fixed rotation of -pi/2 state.x_sum <= -state.y; state.y_sum <= ( others => '0' ); state.a <= to_signed( -PI_H, state.a'length ); state.st <= ST_DONE; elsif state.x < 0 and state.y >= 0 then -- move from second quadrant to fourth state.x <= - state.x; state.y <= - state.y; state.a <= to_signed( PI, state.a'length ); elsif state.x < 0 and state.y < 0 then -- move from third quadrant to first state.x <= - state.x; state.y <= - state.y; state.a <= to_signed( -PI, state.a'length ); else state.a <= ( others => '0' ); end if; elsif state.mode( I_FLAG_VEC_ROT ) = '1' and state.mode( 1 downto 0 ) = VAL_MODE_LIN then -- linear rotation mode if state.x < 0 then state.x <= - state.x; state.y <= - state.y; end if; state.a <= to_signed( 0, state.a'length ); end if; -- -- rotation state -- -- Each rotation takes -- two steps: in the first step, the shifting is -- done, in the second step, the -- shift-result is added/subtracted -- -- -- elsif state.st = ST_ROTATE then -- get the sign if state.mode( I_FLAG_VEC_ROT ) = '0' then if state.a < 0 then sign := '0'; else sign := '1'; end if; else if state.y < 0 then sign := '1'; else sign := '0'; end if; end if; if state.do_shift = '1' then state.do_shift <= '0'; -- get the angle, do the shifting and set the correct angle if sign = '1' then -- circular case if state.mode( 1 downto 0 ) = VAL_MODE_CIR then state.a_tmp <= resize( - angular_lut( to_integer( state.i ), state.mode( 1 downto 0 ), A_WIDTH), A_WIDTH_I ); state.y_sh <= - SHIFT_RIGHT( state.y, to_integer( state.i ) ); -- hyperbolic case elsif state.mode( 1 downto 0 ) = VAL_MODE_HYP then state.a_tmp <= resize( - angular_lut( to_integer( state.i ), state.mode( 1 downto 0 ), A_WIDTH), A_WIDTH_I ); state.y_sh <= SHIFT_RIGHT( state.y, to_integer( state.i ) ); -- linear case else state.a_tmp <= resize( - angular_lut( to_integer( state.i ), state.mode( 1 downto 0 ), A_WIDTH ), A_WIDTH_I ) ; state.y_sh <= ( others => '0' ); end if; state.x_sh <= SHIFT_RIGHT( state.x, to_integer( state.i ) ); else -- circular case if state.mode( 1 downto 0 ) = VAL_MODE_CIR then state.a_tmp <= resize( angular_lut( to_integer( state.i ), state.mode( 1 downto 0 ), A_WIDTH ), A_WIDTH_I ); state.y_sh <= SHIFT_RIGHT( state.y, to_integer( state.i ) ); -- hyperbolic case elsif state.mode( 1 downto 0 ) = VAL_MODE_HYP then state.a_tmp <= resize( angular_lut( to_integer( state.i ), state.mode( 1 downto 0 ), A_WIDTH ), A_WIDTH_I ); state.y_sh <= - SHIFT_RIGHT( state.y, to_integer( state.i ) ); -- linear case else state.a_tmp <= resize( angular_lut( to_integer( state.i ), state.mode( 1 downto 0 ), A_WIDTH ), A_WIDTH_I ) ; state.y_sh <= ( others => '0' ); end if; state.x_sh <= - SHIFT_RIGHT( state.x, to_integer( state.i ) ); end if; -- abort condition if( state.mode( I_FLAG_VEC_ROT ) = '0' and state.a = 0 ) then state.st <= ST_RM_GAIN; state.i <= ( others => '0' ); elsif( state.mode( I_FLAG_VEC_ROT ) = '0' and state.a = state.alst ) then state.st <= ST_RM_GAIN; state.i <= ( others => '0' ); elsif( state.mode( I_FLAG_VEC_ROT ) = '1' and state.y = 0 ) then state.st <= ST_RM_GAIN; state.i <= ( others => '0' ); elsif( state.mode( I_FLAG_VEC_ROT ) = '1' and ( state.y = state.ylst ) ) then state.st <= ST_RM_GAIN; state.i <= ( others => '0' ); end if; state.ylst <= state.y; state.alst <= state.a; else state.x <= state.x + state.y_sh; state.y <= state.y + state.x_sh; state.a <= state.a + state.a_tmp; if VAL_MODE_HYP = state.mode( 1 downto 0 ) and state.repeate = '0' and repeat_hyperbolic_it( to_integer( state.i ) ) then state.repeate <= '1'; else state.repeate <= '0'; state.i <= state.i+1; end if; state.do_shift <= '1'; end if; -- -- removal of the cordic gain -- elsif state.st = ST_RM_GAIN then -- we need RM_GAIN+1 cycles to -- calculate the RM_GAIN steps if state.i = (RM_GAIN) then state.st <= ST_DONE; state.i <= ( others => '0' ); else state.i <= state.i + 1; end if; if state.mode( 1 downto 0 ) = VAL_MODE_CIR then mult_0_61( state.x, state.x_sh, state.x_sum, to_integer( state.i ), RM_GAIN ); mult_0_61( state.y, state.y_sh, state.y_sum, to_integer( state.i ), RM_GAIN ); elsif state.mode( 1 downto 0 ) = VAL_MODE_HYP then mult_0_21( state.x, state.x_sh, state.x_sum, to_integer( state.i ), RM_GAIN ); mult_0_21( state.y, state.y_sh, state.y_sum, to_integer( state.i ), RM_GAIN ); else state.st <= ST_DONE; state.x_sum <= state.x; state.y_sum <= state.y; end if; elsif state.st = ST_DONE then state.st <= ST_IDLE; end if; -- end states end if; -- end ena end if; -- end clk end process; done <= '1' when state.st = ST_DONE else '0'; x_o <= std_logic_vector( state.x_sum ); y_o <= std_logic_vector( state.y_sum ); a_o <= std_logic_vector( state.a ); end architecture BEHAVIORAL;