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djah |
library ieee;
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use ieee.std_logic_1164.all;
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use ieee.numeric_std.all;
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entity square_root is
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generic(
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WIDTH : positive := 32
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);
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port(
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clk : in std_logic;
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res : in std_logic;
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ARG : in unsigned (WIDTH - 1 downto 0);
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Z : out unsigned (WIDTH - 1 downto 0)
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);
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end entity square_root;
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architecture rtl of square_root is
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constant SQRT_LUT_K : positive := 8;
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constant SQRT_LUT_N : positive := 128; --2^(K-1)
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constant SQRT_ITER : positive := 3;
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type sqrt_table is array (natural range <>) of unsigned (WIDTH-1 downto 0);
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type pipe is array (natural range <>) of unsigned (WIDTH - 1 downto 0);
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constant SQRT_TABLE_1 : sqrt_table(0 to SQRT_LUT_N -1) := (
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x"B504F334", x"B44F9363", x"B39C5088", x"B2EB2034",
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x"B23BF845", x"B18ECED9", x"B0E39A54", x"B03A5158",
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x"AF92EAC8", x"AEED5DC0", x"AE49A198", x"ADA7ADE2",
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x"AD077A62", x"AC68FF15", x"ABCC3428", x"AB3111FD",
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x"AA979122", x"A9FFAA55", x"A9695681", x"A8D48EBE",
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x"A8414C4B", x"A7AF8892", x"A71F3D24", x"A69063BA",
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x"A602F631", x"A576EE88", x"A4EC46E7", x"A462F992",
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x"A3DB00F1", x"A354578E", x"A2CEF80E", x"A24ADD38",
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x"A1C801EF", x"A1466132", x"A0C5F61D", x"A046BBE7",
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x"9FC8ADE0", x"9F4BC775", x"9ED00428", x"9E555F96",
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x"9DDBD571", x"9D636184", x"9CEBFFB1", x"9C75ABED",
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x"9C006245", x"9B8C1ED8", x"9B18DDDC", x"9AA69B99",
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x"9A355468", x"99C504B9", x"9955A90B", x"98E73DF0",
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x"9879C009", x"980D2C0B", x"97A17EB9", x"9736B4E7",
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x"96CCCB78", x"9663BF5F", x"95FB8D9D", x"95943342",
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x"952DAD6B", x"94C7F945", x"94631407", x"93FEFAF9",
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x"939BAB6C", x"933922C1", x"92D75E64", x"92765BCB",
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x"9216187A", x"91B69200", x"9157C5F6", x"90F9B200",
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x"909C53CF", x"903FA91C", x"8FE3AFAB", x"8F886548",
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x"8F2DC7CC", x"8ED3D518", x"8E7A8B16", x"8E21E7B8",
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x"8DC9E8FC", x"8D728CE5", x"8D1BD182", x"8CC5B4E8",
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x"8C703534", x"8C1B508D", x"8BC70521", x"8B735123",
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x"8B2032D2", x"8ACDA871", x"8A7BB04A", x"8A2A48B2",
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x"89D97000", x"89892494", x"893964D5", x"88EA2F2F",
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x"889B8216", x"884D5C04", x"87FFBB77", x"87B29EF6",
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x"8766050B", x"8719EC47", x"86CE5342", x"86833897",
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x"86389AE8", x"85EE78DC", x"85A4D11E", x"855BA261",
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x"8512EB59", x"84CAAAC3", x"8482DF5D", x"843B87ED",
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x"83F4A33B", x"83AE3016", x"83682D4F", x"832299BD",
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x"82DD743A", x"8298BBA6", x"82546EE5", x"82108CDC",
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x"81CD1478", x"818A04A6", x"81475C5C", x"81051A8E",
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x"80C33E38", x"8081C657", x"8040B1ED", x"80000000"
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);
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constant SQRT_TABLE_2 : sqrt_table(0 to SQRT_LUT_N -1) := (
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x"FFFFFFFF", x"FE000000", x"FC07F020", x"FA17A17A",
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x"F82EE698", x"F64D9365", x"F4737D1D", x"F2A07A45",
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x"F0D4629B", x"EF0F0F0F", x"ED5059B2", x"EB981DAE",
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x"E9E63740", x"E83A83A8", x"E694E122", x"E4F52EE0",
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x"E35B4CFB", x"E1C71C72", x"E0387F1E", x"DEAF57AC",
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x"DD2B8994", x"DBACF915", x"DA338B2B", x"D8BF258C",
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x"D74FAE9F", x"D5E50D79", x"D47F29D4", x"D31DEC0D",
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x"D1C13D1C", x"D0690690", x"CF15328C", x"CDC5ABBF",
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x"CC7A5D62", x"CB333333", x"C9F01971", x"C8B0FCD7",
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x"C775CA9A", x"C63E7064", x"C50ADC51", x"C3DAFCEA",
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x"C2AEC126", x"C1861862", x"C060F25E", x"BF3F3F3F",
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x"BE20EF88", x"BD05F418", x"BBEE3E26", x"BAD9BF44",
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x"B9C86953", x"B8BA2E8C", x"B7AF0172", x"B6A6D4DB",
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x"B5A19BE3", x"B49F49F5", x"B39FD2BE", x"B2A32A33",
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x"B1A9448C", x"B0B21643", x"AFBD9411", x"AECBB2ED",
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x"ADDC680B", x"ACEFA8DA", x"AC056B01", x"AB1DA461",
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x"AA384B0F", x"A9555555", x"A874B9B3", x"A7966ED8",
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x"A6BA6BA7", x"A5E0A72F", x"A50918B1", x"A433B799",
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x"A3607B7F", x"A28F5C29", x"A1C05183", x"A0F353A5",
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x"A0285ACC", x"9F5F5F5F", x"9E9859EA", x"9DD3431B",
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x"9D1013CA", x"9C4EC4EC", x"9B8F4F9E", x"9AD1AD1B",
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x"9A15D6C0", x"995BC60A", x"98A37495", x"97ECDC1D",
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x"9737F679", x"9684BDA1", x"95D32BA6", x"95233AB7",
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x"9474E51D", x"93C8253D", x"931CF593", x"927350B9",
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x"91CB315D", x"91249249", x"907F6E5D", x"8FDBC091",
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x"8F3983F2", x"8E98B3A6", x"8DF94AE6", x"8D5B4502",
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x"8CBE9D5E", x"8C234F73", x"8B8956CC", x"8AF0AF0B",
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x"8A5953E1", x"89C34116", x"892E727F", x"889AE409",
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x"880891AC", x"87777777", x"86E79187", x"8658DC08",
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x"85CB533A", x"853EF369", x"84B3B8F2", x"8429A043",
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x"83A0A5D4", x"8318C632", x"8291FDF2", x"820C49BA",
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x"8187A63F", x"81041041", x"8081848E", x"80000000"
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);
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constant one_and_half : unsigned(WIDTH-1 downto 0) := x"C0000000";--"11000000000000000000000000000000";
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signal n : pipe(0 to SQRT_ITER);
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signal n_next : pipe(0 to SQRT_ITER);
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signal d : pipe(0 to SQRT_ITER);
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signal d_next : pipe(0 to SQRT_ITER);
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signal r : pipe(0 to SQRT_ITER);
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signal r_next : pipe(0 to SQRT_ITER);
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signal rsqr : pipe(0 to SQRT_ITER);
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signal rsqr_next : pipe(0 to SQRT_ITER);
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begin
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-- pipe stages
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process(clk) is
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begin
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if rising_edge(clk) then
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for i in 0 to SQRT_ITER loop
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if (res = '0') then
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n(i) <= (others => '0');
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d(i) <= (others => '0');
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r(i) <= (others => '0');
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rsqr(i) <= (others => '0');
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else
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n(i) <= n_next(i);
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d(i) <= d_next(i);
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r(i) <= r_next(i);
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rsqr(i) <= rsqr_next(i);
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end if;
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end loop;
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end if;
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end process;
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-- process inputs for the next stage
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process(d,r,rsqr,n,ARG) is
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variable n_extended : unsigned(2*WIDTH-1 downto 0);
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variable d_extended : unsigned(2*WIDTH-1 downto 0);
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variable r_next_tmp : unsigned(WIDTH-1 downto 0);
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variable d_shift : unsigned(WIDTH-1 downto 0);
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variable rsqr_extended : unsigned(2*WIDTH-1 downto 0);
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variable index_vec : unsigned(SQRT_LUT_K-2 downto 0);
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variable index : integer;
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begin
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n_next(0) <= ARG;
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d_next(0) <= ARG;
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index_vec := ARG(WIDTH - 3 downto WIDTH - SQRT_LUT_K - 1);
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index := to_integer(index_vec);
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r_next(0) <= SQRT_TABLE_1(index);
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rsqr_next(0)<= SQRT_TABLE_2(index);
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for i in 1 to SQRT_ITER loop
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--operations
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n_extended := n(i-1) * r(i-1);
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d_extended := d(i-1) * rsqr(i-1);
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d_shift := "0" & d_extended(2*WIDTH -2 downto WIDTH);
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r_next_tmp := one_and_half - d_shift;
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rsqr_extended := r_next_tmp * r_next_tmp;
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--assignments
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n_next(i) <= n_extended(2*WIDTH-2 downto WIDTH-1);
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d_next(i) <= d_extended(2*WIDTH-2 downto WIDTH-1);
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rsqr_next(i) <= rsqr_extended(2*WIDTH-2 downto WIDTH-1);
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r_next(i) <= r_next_tmp;
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end loop;
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end process;
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-- assign output
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Z <= n(SQRT_ITER);
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end rtl;
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