afkt.vhd

-- test 2, ISE 14.7 

---A.Kurka, 13.05.21, 

--afkt mit neue Formel, mit 10 clk und 5 componenten

--    P(X) = P0 + X*(P1 + X*P2), ausgewertet von innen nach außen

--    Q(X) = Q0 + X*(Q1 + X*Q2), ausgewertet von innen nach außen

--    a(X) = P(X) / Q(X)

--========================================================== 

library IEEE;

use IEEE.STD_LOGIC_1164.ALL;

use IEEE.STD_LOGIC_ARITH.ALL;

use IEEE.STD_LOGIC_UNSIGNED.ALL;

--X"3f7ffffd",--P0  +0.99999984852024669   index 0

--X"be8c8cb6",--P1  -0.27451104135987186

--X"00000000",--P2   +0.0              index 2

--X"00000000"             

----------------------------------

--X"3f800000",--Q0  +1.0               index 0

--X"beb73881",--Q1  -0.35785296234245088

--X"3c36a182",--Q2  +0.011146905255803363   indesx 2

--X"00000000"

entity afkt is

  generic(  P0:std_logic_vector(31 downto 0):=X"00000000";

        P1:std_logic_vector(31 downto 0):=X"00000000";

        P2:std_logic_vector(31 downto 0):=X"00000000";

        Q0:std_logic_vector(31 downto 0):=X"00000000";

        Q1:std_logic_vector(31 downto 0):=X"00000000";

        Q2:std_logic_vector(31 downto 0):=X"00000000"

        );    

  port(  nrst  : in std_logic;

      clk    : in std_logic;

      ceafkt  : in std_logic; -- startimpuls afkt

      Xinp  : in std_logic_vector(31 downto 0); -- Input in [0, 0.5] in FP-Format

      aout  : OUT std_logic_vector(31 downto 0) -- Output in [1, 1.047197+] in FP-Format, 1.047197=2*asin(0.5)

      );

end afkt;

architecture Behavioral of afkt is

----------------------------------------------------

COMPONENT mulFP IS

  port (

  a: IN std_logic_VECTOR(31 downto 0);

  b: IN std_logic_VECTOR(31 downto 0);

  clk: IN std_logic;

  ce: IN std_logic;

  result: OUT std_logic_VECTOR(31 downto 0));

END COMPONENT;

---------------------------------------------

COMPONENT addFP IS

  port (

  a: IN std_logic_VECTOR(31 downto 0);

  b: IN std_logic_VECTOR(31 downto 0);

  clk: IN std_logic;

  ce: IN std_logic;

  result: OUT std_logic_VECTOR(31 downto 0));

END COMPONENT;

------------------------------------------------------------

COMPONENT divFP IS

  port (

  a: IN std_logic_VECTOR(31 downto 0);

  b: IN std_logic_VECTOR(31 downto 0);

  clk: IN std_logic;

  ce: IN std_logic;

  result: OUT std_logic_VECTOR(31 downto 0)

  );

END COMPONENT;

-----------------------------------------------------

TYPE T_PQTab IS ARRAY(0 TO 3) OF std_logic_vector(31 DOWNTO 0); -- Koeff Tabelle für Polynom mit Grad <= 3.

--==========================================================================

CONSTANT Cnan : std_logic_vector(31 DOWNTO 0) := X"FFC00000"; -- silent NaN (Not-a-Number) in FP IEEE single (32bit)

CONSTANT C0  :std_logic_vector(31 DOWNTO 0) := X"FFC00000";--Null im FP Format

------------------------------------------------------------------------

-- Koeffizienten-Tabellen für P / Q, MiniMax Approximation, X in [0, 1/2].

-- a(x) = p(x) / q(x) = asin(sqrt(x/2)) / sqrt(x/2)

-- p(x) = 2.2395545700203E+01 + x * (-9.2247557732604 + x * 4.9573581589364E-01)

-- q(x) = 2.2395545641439E+01 + x * (-1.1091046068928E+01 + x)

-- |rel. Fehler| < 1.63e-9 (5e-7 mit IEEE single).

--

--CONSTANT PTab : T_PQTab :=

--(

--  X"41b32a14", -- P0  +2.2395545700203E+01

--  X"c113989a", -- P1  -9.2247557732604

--  X"3efdd116", -- P2  +4.9573581589364E-01

--  X"00000000"  -- unused

--);

--CONSTANT QTab : T_PQTab :=

--(

--  X"41b32a14", -- Q0  +2.2395545641439E+01

--  X"c13174ed", -- Q1  -1.1091046068928E+01

--  X"3f800000", -- Q2  +1.0

--  X"00000000"  -- unused

--);

-- koeffizienten Tabellen für P , MinMax Approximation

CONSTANT PTab :T_PQTab:= -- alle werte in FP

(

P0,------------------X"3f7ffffd",--P0  +0.99999984852024669   index 0

P1,-------------------X"be8c8cb6",--P1  -0.27451104135987186

P2,--------------------X"00000000",--P2   +0.0              index 2

X"00000000"             

);

--------------------------------

CONSTANT QTab :T_PQTab:= -- alle werte in FP

(

Q0,--------------X"3f800000",--Q0  +1.0               index 0

Q1,----------X"beb73881",--Q1  -0.35785296234245088

Q2,-----------X"3c36a182",--Q2  +0.011146905255803363   indesx 2

X"00000000"

);  

--==================== Signale für afkt ==================================

SIGNAL stateafkt  :integer range 0 to 7:= 0;

--SIGNAL ceafkt   :std_logic:='0';-- Startimpuls afkt, extern

SIGNAL ce1      :std_logic:='0';-- Start Pmul = Xinp*Pinp;   Qmul = Xinp*Qinp

SIGNAL ce2      :std_logic:='0';-- Start Padd = Pmul+PKoeff; Qadd = Qmul+QKoeff

SIGNAL ce3      :std_logic:='0';-- Start aout = Pplus/Qplus

SIGNAL ce4      :std_logic:='0';-- Start aout = Padd/Qadd

SIGNAL RDYdiv    :std_logic:='0';-- Div Result Ready 

SIGNAL Pinp      :std_logic_vector(31 DOWNTO 0):=X"00000000";-- 2. Input cPmul

SIGNAL Qinp      :std_logic_vector(31 DOWNTO 0):=X"00000000";-- 2. input cQmul

SIGNAL Pmul      :std_logic_vector(31 DOWNTO 0):=X"00000000";-- Resultat cPmul

SIGNAL Qmul      :std_logic_vector(31 DOWNTO 0):=X"00000000";-- Resultat cQmul

SIGNAL Pplus    :std_logic_vector(31 DOWNTO 0):=X"00000000";-- Resultat cPmul

SIGNAL Qplus    :std_logic_vector(31 DOWNTO 0):=X"00000000";-- Resultat cQmul

SIGNAL Pa      :std_logic_vector(31 DOWNTO 0):=X"00000000";-- Resultat cPadd

SIGNAL Qa      :std_logic_vector(31 DOWNTO 0):=X"00000000";-- Resultat cPadd

SIGNAL Padd      :std_logic_vector(31 DOWNTO 0):=X"00000000";-- Resultat cPadd, Ergebnis Auswertung P()

SIGNAL Qadd      :std_logic_vector(31 DOWNTO 0):=X"00000000";-- Resultat cQadd, Ergebnis Auswertung Q()

SIGNAL PKoeff    :std_logic_vector(31 DOWNTO 0):=X"00000000";-- Koeff von P()

SIGNAL QKoeff    :std_logic_vector(31 DOWNTO 0):=X"00000000";-- Koeff von Q()

--================================================================

begin

--=========== a(x) ==============================================

-- a(X) = (P0 + P1*X + P2*X^2) / (Q0 + Q1*X + Q2*X^2)

-- Berechnungsformel:

--    P(X) = P0 + X*(P1 + X*P2), ausgewertet von innen nach außen

--    Q(X) = Q0 + X*(Q1 + X*Q2), ausgewertet von innen nach außen

--    a(X) = P(X) / Q(X)

--************************************************************************ 

pafkt:PROCESS(clk) -- Process für a(Xinp), vorläufig 8(?) clk.

-- als Index in PTab und QTab.

VARIABLE TabIdx : INTEGER RANGE 0 TO 3 := 0;

VARIABLE count :INTEGER RANGE 0 TO 7:= 0;

BEGIN

  IF rising_edge(clk) THEN  

    IF nrst = '0' THEN 

      TabIdx := 0; -- Init Inx Pointer

      PKoeff <= C0; 

      QKoeff <= C0; 

      Pinp   <= C0;

      Qinp   <= C0; 

      ce1 <= '0';

      ce2 <= '0';

      ce4 <= '0';

      stateafkt <= 0;

    ELSE

      CASE stateafkt IS

      WHEN 0 => -- Start afkt

        IF ceafkt = '1' THEN

          TabIdx := 2; -- Init Index in Tabellen (1 = max. Polynomgrad - 1)--****************.

          Pinp <= PTab(2); -- Init Pinp = PTab(2), (2 = max. Polynomgrad)

          Qinp <= QTab(2); -- Init Qinp = QTab(2), (2 = max. Polynomgrad)

          ce1 <= '1';--starten mul

          ce2 <= '0';

          ce3 <= '0';

          ce4 <= '0';

          stateafkt <= 1;-- Dann Auswertung gestartet

        ELSE

          Padd <= X"00000000";

          Qadd <= X"00000000";

          stateafkt <= 0;

        END IF;

        ---------------------------------

      WHEN 1 => -- ausführen  mul : Xinp * Ptab(2),Xinp * Qtab(2),   

          ce1 <= '0'; -- reset

          -- Pmul,Qmul sind bereit

            -- Decrement Tab-Index

          TabIdx := TabIdx - 1;

          PKoeff <= PTab(TabIdx);

          QKoeff <= QTab(TabIdx);

          stateafkt <= 2;

      WHEN 2 =>

          Pplus <= Pmul;

          Qplus <= Qmul;

          ce2 <= '1';

          stateafkt <= 3;

      When 3 =>

          ce2 <= '0';

          stateafkt <= 4;

      When 4 =>

          Padd <= Pa;

          Qadd <= Qa;

          IF TabIdx = 0 THEN

            Pplus <= X"00000000";

            Qplus <= X"00000000";

            ce3 <= '1';-- start div

            count := 1;

            stateafkt <= 5; -- und div

          ELSE

            Pinp <= Pa;

            Qinp <= Qa;

            ce1 <= '1';  -- start für Pmul,Qmul    

            stateafkt <= 1; -- und wiederholen

          END IF;

      WHEN 5 =>  -- div fertig

        IF count > 0 THEN

          count := count - 1;

          ce3 <= '0';

          stateafkt <= 5;

        ELSE

            stateafkt <= 0;--un warten auf neustart

        END IF;

      WHEN OTHERS =>

          stateafkt <= 0;

      END CASE; -- stateafkt

    END IF; -- nrst

  END IF; --clk

END PROCESS; --end pafkt

--=========Components Implementation====================================

-- ce1

cPmul:    mulFP port map(a=>Xinp, b=>Pinp, clk=>clk, ce=>ce1, result=>Pmul);

cQmul:    mulFP port map(a=>Xinp, b=>Qinp, clk=>clk, ce=>ce1, result=>Qmul);

-- ce2

cPadd:     addFP port map(a=>Pplus, b=>PKoeff, clk=>clk, ce=>ce2, result=>Pa);--

cQadd:     addFP port map(a=>Qplus, b=>QKoeff, clk=>clk, ce=>ce2, result=>Qa);--

-- ce3

cPQdiv:    divFP port map(a=>Padd, b=>Qadd,clk=>clk, ce=>ce3,result=>aout);

--===============================================================================00

end Behavioral;