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/trunk/dds_sine_pack.vhd
0,0 → 1,20783
--------------------------------------------------------------------------
-- Package of Direct Digital Synthesizer (DDS) sinewave generator components
--
-- NOTE: These components are for producing digital samples of sinewaves
-- by using sinewave lookup tables. For modules which produce
-- single bit pulses of known frequency and/or duty cycle, please
-- refer to "dds_pack.vhd"
--
 
library ieee;
use ieee.std_logic_1164.all;
use ieee.numeric_std.all;
 
package dds_sine_pack is
 
component quadrature_oscillator
generic(
AMPL_BITS : natural;
AMPL_VALUE : natural; -- Set to some value below full scale. There is no saturation!
SAMPLES_PER_CYCLE : natural
);
port(
clk_i : in std_logic; -- System clock
rst_n_i : in std_logic; -- Low asserted reset
clk_en_i : in std_logic; -- clock enable, determines sample rate
 
-- Sine and Cosine outputs
sin_o : out signed(AMPL_BITS-1 downto 0);
cos_o : out signed(AMPL_BITS-1 downto 0)
);
end component;
 
component sine_generator_dds
generic(
PHI_BITS : natural; -- Bits in phase accumulator, must be >= PHASE_BITS
AMPL_BITS : natural;
PHASE_BITS : natural
);
port(
clk_i : in std_logic;
rst_n_i : in std_logic;
clk_en_i : in std_logic;
 
-- Frequency Tuning Word input
ftw_i : in unsigned(PHI_BITS-1 downto 0);
 
-- Outputs
accum_o : out unsigned(PHI_BITS-1 downto 0);
sine_o : out signed(AMPL_BITS-1 downto 0)
);
end component;
 
component dds_sine
generic(
PHI_BITS : natural; -- Bits in phase accumulator, must be >= PHASE_BITS
AMPL_BITS : natural;
PHASE_BITS : natural
);
port(
clk_i : in std_logic;
rst_n_i : in std_logic;
clk_en_i : in std_logic;
 
-- Look Up Table interface
lut_adr_o : out unsigned(PHASE_BITS-3 downto 0); -- Quarter wave LUT
lut_dat_i : in unsigned(AMPL_BITS-1 downto 0);
 
-- Frequency Tuning Word input
ftw_i : in unsigned(PHI_BITS-1 downto 0);
 
-- Outputs
accum_o : out unsigned(PHI_BITS-1 downto 0);
sine_o : out signed(AMPL_BITS-1 downto 0)
);
end component;
 
component dds_sine_non_power_of_two
generic(
PHI_BITS : natural; -- Bits in phase accumulator, must be >= PHASE_BITS
AMPL_BITS : natural;
PHASE_LENGTH : natural;
PHASE_BITS : natural
);
port(
clk_i : in std_logic;
rst_n_i : in std_logic;
clk_en_i : in std_logic;
 
-- Look Up Table interface
lut_adr_o : out unsigned(PHASE_BITS-3 downto 0); -- Quarter wave LUT
lut_dat_i : in unsigned(AMPL_BITS-1 downto 0);
 
-- Frequency Tuning Word input
ftw_i : in unsigned(PHI_BITS-1 downto 0);
 
-- Outputs
accum_o : out unsigned(PHI_BITS-1 downto 0);
sine_o : out signed(AMPL_BITS-1 downto 0)
);
end component;
 
component dds_arb
generic(
PHI_BITS : natural; -- Bits in phase accumulator, must be >= PHASE_BITS
AMPL_BITS : natural;
PHASE_BITS : natural
);
port(
clk_i : in std_logic;
rst_n_i : in std_logic;
clk_en_i : in std_logic;
 
-- Look Up Table interface
lut_adr_o : out unsigned(PHASE_BITS-1 downto 0); -- Full Wave LUT
lut_dat_i : in unsigned(AMPL_BITS-1 downto 0);
 
-- Frequency Tuning Word input
ftw_i : in unsigned(PHI_BITS-1 downto 0);
 
-- Outputs
accum_o : out unsigned(PHI_BITS-1 downto 0);
arb_o : out signed(AMPL_BITS-1 downto 0)
);
end component;
 
-- Quarter sine lookup table
type lut_5000_x_16_type is array(0 to 1249) of unsigned(15 downto 0);
constant sine_lut_5000_x_16 : lut_5000_x_16_type := (
to_unsigned(0,16),
to_unsigned(41,16),
to_unsigned(82,16),
to_unsigned(124,16),
to_unsigned(165,16),
to_unsigned(206,16),
to_unsigned(247,16),
to_unsigned(288,16),
to_unsigned(329,16),
to_unsigned(371,16),
to_unsigned(412,16),
to_unsigned(453,16),
to_unsigned(494,16),
to_unsigned(535,16),
to_unsigned(576,16),
to_unsigned(618,16),
to_unsigned(659,16),
to_unsigned(700,16),
to_unsigned(741,16),
to_unsigned(782,16),
to_unsigned(823,16),
to_unsigned(865,16),
to_unsigned(906,16),
to_unsigned(947,16),
to_unsigned(988,16),
to_unsigned(1029,16),
to_unsigned(1070,16),
to_unsigned(1112,16),
to_unsigned(1153,16),
to_unsigned(1194,16),
to_unsigned(1235,16),
to_unsigned(1276,16),
to_unsigned(1317,16),
to_unsigned(1358,16),
to_unsigned(1400,16),
to_unsigned(1441,16),
to_unsigned(1482,16),
to_unsigned(1523,16),
to_unsigned(1564,16),
to_unsigned(1605,16),
to_unsigned(1646,16),
to_unsigned(1687,16),
to_unsigned(1729,16),
to_unsigned(1770,16),
to_unsigned(1811,16),
to_unsigned(1852,16),
to_unsigned(1893,16),
to_unsigned(1934,16),
to_unsigned(1975,16),
to_unsigned(2016,16),
to_unsigned(2057,16),
to_unsigned(2099,16),
to_unsigned(2140,16),
to_unsigned(2181,16),
to_unsigned(2222,16),
to_unsigned(2263,16),
to_unsigned(2304,16),
to_unsigned(2345,16),
to_unsigned(2386,16),
to_unsigned(2427,16),
to_unsigned(2468,16),
to_unsigned(2509,16),
to_unsigned(2550,16),
to_unsigned(2591,16),
to_unsigned(2632,16),
to_unsigned(2673,16),
to_unsigned(2715,16),
to_unsigned(2756,16),
to_unsigned(2797,16),
to_unsigned(2838,16),
to_unsigned(2879,16),
to_unsigned(2920,16),
to_unsigned(2961,16),
to_unsigned(3002,16),
to_unsigned(3043,16),
to_unsigned(3084,16),
to_unsigned(3125,16),
to_unsigned(3166,16),
to_unsigned(3207,16),
to_unsigned(3248,16),
to_unsigned(3289,16),
to_unsigned(3330,16),
to_unsigned(3370,16),
to_unsigned(3411,16),
to_unsigned(3452,16),
to_unsigned(3493,16),
to_unsigned(3534,16),
to_unsigned(3575,16),
to_unsigned(3616,16),
to_unsigned(3657,16),
to_unsigned(3698,16),
to_unsigned(3739,16),
to_unsigned(3780,16),
to_unsigned(3821,16),
to_unsigned(3862,16),
to_unsigned(3902,16),
to_unsigned(3943,16),
to_unsigned(3984,16),
to_unsigned(4025,16),
to_unsigned(4066,16),
to_unsigned(4107,16),
to_unsigned(4148,16),
to_unsigned(4188,16),
to_unsigned(4229,16),
to_unsigned(4270,16),
to_unsigned(4311,16),
to_unsigned(4352,16),
to_unsigned(4393,16),
to_unsigned(4433,16),
to_unsigned(4474,16),
to_unsigned(4515,16),
to_unsigned(4556,16),
to_unsigned(4597,16),
to_unsigned(4637,16),
to_unsigned(4678,16),
to_unsigned(4719,16),
to_unsigned(4760,16),
to_unsigned(4800,16),
to_unsigned(4841,16),
to_unsigned(4882,16),
to_unsigned(4922,16),
to_unsigned(4963,16),
to_unsigned(5004,16),
to_unsigned(5045,16),
to_unsigned(5085,16),
to_unsigned(5126,16),
to_unsigned(5167,16),
to_unsigned(5207,16),
to_unsigned(5248,16),
to_unsigned(5288,16),
to_unsigned(5329,16),
to_unsigned(5370,16),
to_unsigned(5410,16),
to_unsigned(5451,16),
to_unsigned(5492,16),
to_unsigned(5532,16),
to_unsigned(5573,16),
to_unsigned(5613,16),
to_unsigned(5654,16),
to_unsigned(5694,16),
to_unsigned(5735,16),
to_unsigned(5776,16),
to_unsigned(5816,16),
to_unsigned(5857,16),
to_unsigned(5897,16),
to_unsigned(5938,16),
to_unsigned(5978,16),
to_unsigned(6019,16),
to_unsigned(6059,16),
to_unsigned(6099,16),
to_unsigned(6140,16),
to_unsigned(6180,16),
to_unsigned(6221,16),
to_unsigned(6261,16),
to_unsigned(6302,16),
to_unsigned(6342,16),
to_unsigned(6382,16),
to_unsigned(6423,16),
to_unsigned(6463,16),
to_unsigned(6504,16),
to_unsigned(6544,16),
to_unsigned(6584,16),
to_unsigned(6625,16),
to_unsigned(6665,16),
to_unsigned(6705,16),
to_unsigned(6746,16),
to_unsigned(6786,16),
to_unsigned(6826,16),
to_unsigned(6866,16),
to_unsigned(6907,16),
to_unsigned(6947,16),
to_unsigned(6987,16),
to_unsigned(7027,16),
to_unsigned(7068,16),
to_unsigned(7108,16),
to_unsigned(7148,16),
to_unsigned(7188,16),
to_unsigned(7228,16),
to_unsigned(7268,16),
to_unsigned(7309,16),
to_unsigned(7349,16),
to_unsigned(7389,16),
to_unsigned(7429,16),
to_unsigned(7469,16),
to_unsigned(7509,16),
to_unsigned(7549,16),
to_unsigned(7589,16),
to_unsigned(7629,16),
to_unsigned(7669,16),
to_unsigned(7709,16),
to_unsigned(7749,16),
to_unsigned(7789,16),
to_unsigned(7829,16),
to_unsigned(7869,16),
to_unsigned(7909,16),
to_unsigned(7949,16),
to_unsigned(7989,16),
to_unsigned(8029,16),
to_unsigned(8069,16),
to_unsigned(8109,16),
to_unsigned(8149,16),
to_unsigned(8189,16),
to_unsigned(8229,16),
to_unsigned(8268,16),
to_unsigned(8308,16),
to_unsigned(8348,16),
to_unsigned(8388,16),
to_unsigned(8428,16),
to_unsigned(8467,16),
to_unsigned(8507,16),
to_unsigned(8547,16),
to_unsigned(8587,16),
to_unsigned(8626,16),
to_unsigned(8666,16),
to_unsigned(8706,16),
to_unsigned(8746,16),
to_unsigned(8785,16),
to_unsigned(8825,16),
to_unsigned(8865,16),
to_unsigned(8904,16),
to_unsigned(8944,16),
to_unsigned(8983,16),
to_unsigned(9023,16),
to_unsigned(9063,16),
to_unsigned(9102,16),
to_unsigned(9142,16),
to_unsigned(9181,16),
to_unsigned(9221,16),
to_unsigned(9260,16),
to_unsigned(9300,16),
to_unsigned(9339,16),
to_unsigned(9379,16),
to_unsigned(9418,16),
to_unsigned(9458,16),
to_unsigned(9497,16),
to_unsigned(9536,16),
to_unsigned(9576,16),
to_unsigned(9615,16),
to_unsigned(9654,16),
to_unsigned(9694,16),
to_unsigned(9733,16),
to_unsigned(9772,16),
to_unsigned(9812,16),
to_unsigned(9851,16),
to_unsigned(9890,16),
to_unsigned(9930,16),
to_unsigned(9969,16),
to_unsigned(10008,16),
to_unsigned(10047,16),
to_unsigned(10086,16),
to_unsigned(10126,16),
to_unsigned(10165,16),
to_unsigned(10204,16),
to_unsigned(10243,16),
to_unsigned(10282,16),
to_unsigned(10321,16),
to_unsigned(10360,16),
to_unsigned(10399,16),
to_unsigned(10438,16),
to_unsigned(10477,16),
to_unsigned(10516,16),
to_unsigned(10555,16),
to_unsigned(10594,16),
to_unsigned(10633,16),
to_unsigned(10672,16),
to_unsigned(10711,16),
to_unsigned(10750,16),
to_unsigned(10789,16),
to_unsigned(10828,16),
to_unsigned(10867,16),
to_unsigned(10905,16),
to_unsigned(10944,16),
to_unsigned(10983,16),
to_unsigned(11022,16),
to_unsigned(11061,16),
to_unsigned(11099,16),
to_unsigned(11138,16),
to_unsigned(11177,16),
to_unsigned(11216,16),
to_unsigned(11254,16),
to_unsigned(11293,16),
to_unsigned(11332,16),
to_unsigned(11370,16),
to_unsigned(11409,16),
to_unsigned(11447,16),
to_unsigned(11486,16),
to_unsigned(11525,16),
to_unsigned(11563,16),
to_unsigned(11602,16),
to_unsigned(11640,16),
to_unsigned(11679,16),
to_unsigned(11717,16),
to_unsigned(11755,16),
to_unsigned(11794,16),
to_unsigned(11832,16),
to_unsigned(11871,16),
to_unsigned(11909,16),
to_unsigned(11947,16),
to_unsigned(11986,16),
to_unsigned(12024,16),
to_unsigned(12062,16),
to_unsigned(12101,16),
to_unsigned(12139,16),
to_unsigned(12177,16),
to_unsigned(12215,16),
to_unsigned(12254,16),
to_unsigned(12292,16),
to_unsigned(12330,16),
to_unsigned(12368,16),
to_unsigned(12406,16),
to_unsigned(12444,16),
to_unsigned(12482,16),
to_unsigned(12520,16),
to_unsigned(12558,16),
to_unsigned(12596,16),
to_unsigned(12634,16),
to_unsigned(12672,16),
to_unsigned(12710,16),
to_unsigned(12748,16),
to_unsigned(12786,16),
to_unsigned(12824,16),
to_unsigned(12862,16),
to_unsigned(12900,16),
to_unsigned(12938,16),
to_unsigned(12976,16),
to_unsigned(13013,16),
to_unsigned(13051,16),
to_unsigned(13089,16),
to_unsigned(13127,16),
to_unsigned(13164,16),
to_unsigned(13202,16),
to_unsigned(13240,16),
to_unsigned(13277,16),
to_unsigned(13315,16),
to_unsigned(13353,16),
to_unsigned(13390,16),
to_unsigned(13428,16),
to_unsigned(13465,16),
to_unsigned(13503,16),
to_unsigned(13540,16),
to_unsigned(13578,16),
to_unsigned(13615,16),
to_unsigned(13653,16),
to_unsigned(13690,16),
to_unsigned(13728,16),
to_unsigned(13765,16),
to_unsigned(13802,16),
to_unsigned(13840,16),
to_unsigned(13877,16),
to_unsigned(13914,16),
to_unsigned(13952,16),
to_unsigned(13989,16),
to_unsigned(14026,16),
to_unsigned(14063,16),
to_unsigned(14100,16),
to_unsigned(14138,16),
to_unsigned(14175,16),
to_unsigned(14212,16),
to_unsigned(14249,16),
to_unsigned(14286,16),
to_unsigned(14323,16),
to_unsigned(14360,16),
to_unsigned(14397,16),
to_unsigned(14434,16),
to_unsigned(14471,16),
to_unsigned(14508,16),
to_unsigned(14545,16),
to_unsigned(14582,16),
to_unsigned(14619,16),
to_unsigned(14655,16),
to_unsigned(14692,16),
to_unsigned(14729,16),
to_unsigned(14766,16),
to_unsigned(14802,16),
to_unsigned(14839,16),
to_unsigned(14876,16),
to_unsigned(14913,16),
to_unsigned(14949,16),
to_unsigned(14986,16),
to_unsigned(15022,16),
to_unsigned(15059,16),
to_unsigned(15096,16),
to_unsigned(15132,16),
to_unsigned(15169,16),
to_unsigned(15205,16),
to_unsigned(15242,16),
to_unsigned(15278,16),
to_unsigned(15314,16),
to_unsigned(15351,16),
to_unsigned(15387,16),
to_unsigned(15424,16),
to_unsigned(15460,16),
to_unsigned(15496,16),
to_unsigned(15532,16),
to_unsigned(15569,16),
to_unsigned(15605,16),
to_unsigned(15641,16),
to_unsigned(15677,16),
to_unsigned(15713,16),
to_unsigned(15750,16),
to_unsigned(15786,16),
to_unsigned(15822,16),
to_unsigned(15858,16),
to_unsigned(15894,16),
to_unsigned(15930,16),
to_unsigned(15966,16),
to_unsigned(16002,16),
to_unsigned(16038,16),
to_unsigned(16073,16),
to_unsigned(16109,16),
to_unsigned(16145,16),
to_unsigned(16181,16),
to_unsigned(16217,16),
to_unsigned(16253,16),
to_unsigned(16288,16),
to_unsigned(16324,16),
to_unsigned(16360,16),
to_unsigned(16395,16),
to_unsigned(16431,16),
to_unsigned(16467,16),
to_unsigned(16502,16),
to_unsigned(16538,16),
to_unsigned(16573,16),
to_unsigned(16609,16),
to_unsigned(16644,16),
to_unsigned(16680,16),
to_unsigned(16715,16),
to_unsigned(16751,16),
to_unsigned(16786,16),
to_unsigned(16821,16),
to_unsigned(16857,16),
to_unsigned(16892,16),
to_unsigned(16927,16),
to_unsigned(16962,16),
to_unsigned(16998,16),
to_unsigned(17033,16),
to_unsigned(17068,16),
to_unsigned(17103,16),
to_unsigned(17138,16),
to_unsigned(17173,16),
to_unsigned(17208,16),
to_unsigned(17243,16),
to_unsigned(17278,16),
to_unsigned(17313,16),
to_unsigned(17348,16),
to_unsigned(17383,16),
to_unsigned(17418,16),
to_unsigned(17453,16),
to_unsigned(17488,16),
to_unsigned(17523,16),
to_unsigned(17557,16),
to_unsigned(17592,16),
to_unsigned(17627,16),
to_unsigned(17662,16),
to_unsigned(17696,16),
to_unsigned(17731,16),
to_unsigned(17766,16),
to_unsigned(17800,16),
to_unsigned(17835,16),
to_unsigned(17869,16),
to_unsigned(17904,16),
to_unsigned(17938,16),
to_unsigned(17973,16),
to_unsigned(18007,16),
to_unsigned(18041,16),
to_unsigned(18076,16),
to_unsigned(18110,16),
to_unsigned(18144,16),
to_unsigned(18179,16),
to_unsigned(18213,16),
to_unsigned(18247,16),
to_unsigned(18281,16),
to_unsigned(18315,16),
to_unsigned(18350,16),
to_unsigned(18384,16),
to_unsigned(18418,16),
to_unsigned(18452,16),
to_unsigned(18486,16),
to_unsigned(18520,16),
to_unsigned(18554,16),
to_unsigned(18588,16),
to_unsigned(18622,16),
to_unsigned(18655,16),
to_unsigned(18689,16),
to_unsigned(18723,16),
to_unsigned(18757,16),
to_unsigned(18791,16),
to_unsigned(18824,16),
to_unsigned(18858,16),
to_unsigned(18892,16),
to_unsigned(18925,16),
to_unsigned(18959,16),
to_unsigned(18992,16),
to_unsigned(19026,16),
to_unsigned(19060,16),
to_unsigned(19093,16),
to_unsigned(19126,16),
to_unsigned(19160,16),
to_unsigned(19193,16),
to_unsigned(19227,16),
to_unsigned(19260,16),
to_unsigned(19293,16),
to_unsigned(19327,16),
to_unsigned(19360,16),
to_unsigned(19393,16),
to_unsigned(19426,16),
to_unsigned(19459,16),
to_unsigned(19492,16),
to_unsigned(19525,16),
to_unsigned(19559,16),
to_unsigned(19592,16),
to_unsigned(19625,16),
to_unsigned(19658,16),
to_unsigned(19690,16),
to_unsigned(19723,16),
to_unsigned(19756,16),
to_unsigned(19789,16),
to_unsigned(19822,16),
to_unsigned(19855,16),
to_unsigned(19887,16),
to_unsigned(19920,16),
to_unsigned(19953,16),
to_unsigned(19985,16),
to_unsigned(20018,16),
to_unsigned(20051,16),
to_unsigned(20083,16),
to_unsigned(20116,16),
to_unsigned(20148,16),
to_unsigned(20181,16),
to_unsigned(20213,16),
to_unsigned(20245,16),
to_unsigned(20278,16),
to_unsigned(20310,16),
to_unsigned(20342,16),
to_unsigned(20375,16),
to_unsigned(20407,16),
to_unsigned(20439,16),
to_unsigned(20471,16),
to_unsigned(20503,16),
to_unsigned(20535,16),
to_unsigned(20568,16),
to_unsigned(20600,16),
to_unsigned(20632,16),
to_unsigned(20664,16),
to_unsigned(20696,16),
to_unsigned(20727,16),
to_unsigned(20759,16),
to_unsigned(20791,16),
to_unsigned(20823,16),
to_unsigned(20855,16),
to_unsigned(20886,16),
to_unsigned(20918,16),
to_unsigned(20950,16),
to_unsigned(20982,16),
to_unsigned(21013,16),
to_unsigned(21045,16),
to_unsigned(21076,16),
to_unsigned(21108,16),
to_unsigned(21139,16),
to_unsigned(21171,16),
to_unsigned(21202,16),
to_unsigned(21233,16),
to_unsigned(21265,16),
to_unsigned(21296,16),
to_unsigned(21327,16),
to_unsigned(21359,16),
to_unsigned(21390,16),
to_unsigned(21421,16),
to_unsigned(21452,16),
to_unsigned(21483,16),
to_unsigned(21514,16),
to_unsigned(21545,16),
to_unsigned(21576,16),
to_unsigned(21607,16),
to_unsigned(21638,16),
to_unsigned(21669,16),
to_unsigned(21700,16),
to_unsigned(21731,16),
to_unsigned(21762,16),
to_unsigned(21792,16),
to_unsigned(21823,16),
to_unsigned(21854,16),
to_unsigned(21885,16),
to_unsigned(21915,16),
to_unsigned(21946,16),
to_unsigned(21976,16),
to_unsigned(22007,16),
to_unsigned(22037,16),
to_unsigned(22068,16),
to_unsigned(22098,16),
to_unsigned(22129,16),
to_unsigned(22159,16),
to_unsigned(22189,16),
to_unsigned(22220,16),
to_unsigned(22250,16),
to_unsigned(22280,16),
to_unsigned(22310,16),
to_unsigned(22340,16),
to_unsigned(22370,16),
to_unsigned(22401,16),
to_unsigned(22431,16),
to_unsigned(22461,16),
to_unsigned(22491,16),
to_unsigned(22520,16),
to_unsigned(22550,16),
to_unsigned(22580,16),
to_unsigned(22610,16),
to_unsigned(22640,16),
to_unsigned(22670,16),
to_unsigned(22699,16),
to_unsigned(22729,16),
to_unsigned(22759,16),
to_unsigned(22788,16),
to_unsigned(22818,16),
to_unsigned(22847,16),
to_unsigned(22877,16),
to_unsigned(22906,16),
to_unsigned(22936,16),
to_unsigned(22965,16),
to_unsigned(22994,16),
to_unsigned(23024,16),
to_unsigned(23053,16),
to_unsigned(23082,16),
to_unsigned(23111,16),
to_unsigned(23141,16),
to_unsigned(23170,16),
to_unsigned(23199,16),
to_unsigned(23228,16),
to_unsigned(23257,16),
to_unsigned(23286,16),
to_unsigned(23315,16),
to_unsigned(23344,16),
to_unsigned(23373,16),
to_unsigned(23402,16),
to_unsigned(23430,16),
to_unsigned(23459,16),
to_unsigned(23488,16),
to_unsigned(23517,16),
to_unsigned(23545,16),
to_unsigned(23574,16),
to_unsigned(23602,16),
to_unsigned(23631,16),
to_unsigned(23659,16),
to_unsigned(23688,16),
to_unsigned(23716,16),
to_unsigned(23745,16),
to_unsigned(23773,16),
to_unsigned(23801,16),
to_unsigned(23830,16),
to_unsigned(23858,16),
to_unsigned(23886,16),
to_unsigned(23914,16),
to_unsigned(23942,16),
to_unsigned(23971,16),
to_unsigned(23999,16),
to_unsigned(24027,16),
to_unsigned(24055,16),
to_unsigned(24082,16),
to_unsigned(24110,16),
to_unsigned(24138,16),
to_unsigned(24166,16),
to_unsigned(24194,16),
to_unsigned(24222,16),
to_unsigned(24249,16),
to_unsigned(24277,16),
to_unsigned(24305,16),
to_unsigned(24332,16),
to_unsigned(24360,16),
to_unsigned(24387,16),
to_unsigned(24415,16),
to_unsigned(24442,16),
to_unsigned(24470,16),
to_unsigned(24497,16),
to_unsigned(24524,16),
to_unsigned(24552,16),
to_unsigned(24579,16),
to_unsigned(24606,16),
to_unsigned(24633,16),
to_unsigned(24660,16),
to_unsigned(24687,16),
to_unsigned(24715,16),
to_unsigned(24742,16),
to_unsigned(24769,16),
to_unsigned(24795,16),
to_unsigned(24822,16),
to_unsigned(24849,16),
to_unsigned(24876,16),
to_unsigned(24903,16),
to_unsigned(24930,16),
to_unsigned(24956,16),
to_unsigned(24983,16),
to_unsigned(25010,16),
to_unsigned(25036,16),
to_unsigned(25063,16),
to_unsigned(25089,16),
to_unsigned(25116,16),
to_unsigned(25142,16),
to_unsigned(25168,16),
to_unsigned(25195,16),
to_unsigned(25221,16),
to_unsigned(25247,16),
to_unsigned(25274,16),
to_unsigned(25300,16),
to_unsigned(25326,16),
to_unsigned(25352,16),
to_unsigned(25378,16),
to_unsigned(25404,16),
to_unsigned(25430,16),
to_unsigned(25456,16),
to_unsigned(25482,16),
to_unsigned(25508,16),
to_unsigned(25534,16),
to_unsigned(25559,16),
to_unsigned(25585,16),
to_unsigned(25611,16),
to_unsigned(25637,16),
to_unsigned(25662,16),
to_unsigned(25688,16),
to_unsigned(25713,16),
to_unsigned(25739,16),
to_unsigned(25764,16),
to_unsigned(25790,16),
to_unsigned(25815,16),
to_unsigned(25840,16),
to_unsigned(25866,16),
to_unsigned(25891,16),
to_unsigned(25916,16),
to_unsigned(25941,16),
to_unsigned(25967,16),
to_unsigned(25992,16),
to_unsigned(26017,16),
to_unsigned(26042,16),
to_unsigned(26067,16),
to_unsigned(26092,16),
to_unsigned(26116,16),
to_unsigned(26141,16),
to_unsigned(26166,16),
to_unsigned(26191,16),
to_unsigned(26216,16),
to_unsigned(26240,16),
to_unsigned(26265,16),
to_unsigned(26290,16),
to_unsigned(26314,16),
to_unsigned(26339,16),
to_unsigned(26363,16),
to_unsigned(26388,16),
to_unsigned(26412,16),
to_unsigned(26436,16),
to_unsigned(26461,16),
to_unsigned(26485,16),
to_unsigned(26509,16),
to_unsigned(26533,16),
to_unsigned(26557,16),
to_unsigned(26581,16),
to_unsigned(26606,16),
to_unsigned(26630,16),
to_unsigned(26654,16),
to_unsigned(26677,16),
to_unsigned(26701,16),
to_unsigned(26725,16),
to_unsigned(26749,16),
to_unsigned(26773,16),
to_unsigned(26796,16),
to_unsigned(26820,16),
to_unsigned(26844,16),
to_unsigned(26867,16),
to_unsigned(26891,16),
to_unsigned(26914,16),
to_unsigned(26938,16),
to_unsigned(26961,16),
to_unsigned(26985,16),
to_unsigned(27008,16),
to_unsigned(27031,16),
to_unsigned(27055,16),
to_unsigned(27078,16),
to_unsigned(27101,16),
to_unsigned(27124,16),
to_unsigned(27147,16),
to_unsigned(27170,16),
to_unsigned(27193,16),
to_unsigned(27216,16),
to_unsigned(27239,16),
to_unsigned(27262,16),
to_unsigned(27285,16),
to_unsigned(27308,16),
to_unsigned(27330,16),
to_unsigned(27353,16),
to_unsigned(27376,16),
to_unsigned(27398,16),
to_unsigned(27421,16),
to_unsigned(27443,16),
to_unsigned(27466,16),
to_unsigned(27488,16),
to_unsigned(27511,16),
to_unsigned(27533,16),
to_unsigned(27555,16),
to_unsigned(27577,16),
to_unsigned(27600,16),
to_unsigned(27622,16),
to_unsigned(27644,16),
to_unsigned(27666,16),
to_unsigned(27688,16),
to_unsigned(27710,16),
to_unsigned(27732,16),
to_unsigned(27754,16),
to_unsigned(27776,16),
to_unsigned(27798,16),
to_unsigned(27819,16),
to_unsigned(27841,16),
to_unsigned(27863,16),
to_unsigned(27885,16),
to_unsigned(27906,16),
to_unsigned(27928,16),
to_unsigned(27949,16),
to_unsigned(27971,16),
to_unsigned(27992,16),
to_unsigned(28013,16),
to_unsigned(28035,16),
to_unsigned(28056,16),
to_unsigned(28077,16),
to_unsigned(28099,16),
to_unsigned(28120,16),
to_unsigned(28141,16),
to_unsigned(28162,16),
to_unsigned(28183,16),
to_unsigned(28204,16),
to_unsigned(28225,16),
to_unsigned(28246,16),
to_unsigned(28267,16),
to_unsigned(28287,16),
to_unsigned(28308,16),
to_unsigned(28329,16),
to_unsigned(28350,16),
to_unsigned(28370,16),
to_unsigned(28391,16),
to_unsigned(28411,16),
to_unsigned(28432,16),
to_unsigned(28452,16),
to_unsigned(28473,16),
to_unsigned(28493,16),
to_unsigned(28513,16),
to_unsigned(28534,16),
to_unsigned(28554,16),
to_unsigned(28574,16),
to_unsigned(28594,16),
to_unsigned(28614,16),
to_unsigned(28634,16),
to_unsigned(28654,16),
to_unsigned(28674,16),
to_unsigned(28694,16),
to_unsigned(28714,16),
to_unsigned(28734,16),
to_unsigned(28754,16),
to_unsigned(28773,16),
to_unsigned(28793,16),
to_unsigned(28813,16),
to_unsigned(28832,16),
to_unsigned(28852,16),
to_unsigned(28871,16),
to_unsigned(28891,16),
to_unsigned(28910,16),
to_unsigned(28929,16),
to_unsigned(28949,16),
to_unsigned(28968,16),
to_unsigned(28987,16),
to_unsigned(29006,16),
to_unsigned(29026,16),
to_unsigned(29045,16),
to_unsigned(29064,16),
to_unsigned(29083,16),
to_unsigned(29102,16),
to_unsigned(29120,16),
to_unsigned(29139,16),
to_unsigned(29158,16),
to_unsigned(29177,16),
to_unsigned(29196,16),
to_unsigned(29214,16),
to_unsigned(29233,16),
to_unsigned(29251,16),
to_unsigned(29270,16),
to_unsigned(29289,16),
to_unsigned(29307,16),
to_unsigned(29325,16),
to_unsigned(29344,16),
to_unsigned(29362,16),
to_unsigned(29380,16),
to_unsigned(29398,16),
to_unsigned(29417,16),
to_unsigned(29435,16),
to_unsigned(29453,16),
to_unsigned(29471,16),
to_unsigned(29489,16),
to_unsigned(29507,16),
to_unsigned(29525,16),
to_unsigned(29542,16),
to_unsigned(29560,16),
to_unsigned(29578,16),
to_unsigned(29596,16),
to_unsigned(29613,16),
to_unsigned(29631,16),
to_unsigned(29648,16),
to_unsigned(29666,16),
to_unsigned(29683,16),
to_unsigned(29701,16),
to_unsigned(29718,16),
to_unsigned(29736,16),
to_unsigned(29753,16),
to_unsigned(29770,16),
to_unsigned(29787,16),
to_unsigned(29804,16),
to_unsigned(29821,16),
to_unsigned(29838,16),
to_unsigned(29855,16),
to_unsigned(29872,16),
to_unsigned(29889,16),
to_unsigned(29906,16),
to_unsigned(29923,16),
to_unsigned(29940,16),
to_unsigned(29956,16),
to_unsigned(29973,16),
to_unsigned(29990,16),
to_unsigned(30006,16),
to_unsigned(30023,16),
to_unsigned(30039,16),
to_unsigned(30056,16),
to_unsigned(30072,16),
to_unsigned(30088,16),
to_unsigned(30105,16),
to_unsigned(30121,16),
to_unsigned(30137,16),
to_unsigned(30153,16),
to_unsigned(30169,16),
to_unsigned(30185,16),
to_unsigned(30201,16),
to_unsigned(30217,16),
to_unsigned(30233,16),
to_unsigned(30249,16),
to_unsigned(30265,16),
to_unsigned(30281,16),
to_unsigned(30296,16),
to_unsigned(30312,16),
to_unsigned(30328,16),
to_unsigned(30343,16),
to_unsigned(30359,16),
to_unsigned(30374,16),
to_unsigned(30390,16),
to_unsigned(30405,16),
to_unsigned(30420,16),
to_unsigned(30436,16),
to_unsigned(30451,16),
to_unsigned(30466,16),
to_unsigned(30481,16),
to_unsigned(30496,16),
to_unsigned(30511,16),
to_unsigned(30526,16),
to_unsigned(30541,16),
to_unsigned(30556,16),
to_unsigned(30571,16),
to_unsigned(30586,16),
to_unsigned(30600,16),
to_unsigned(30615,16),
to_unsigned(30630,16),
to_unsigned(30644,16),
to_unsigned(30659,16),
to_unsigned(30673,16),
to_unsigned(30688,16),
to_unsigned(30702,16),
to_unsigned(30717,16),
to_unsigned(30731,16),
to_unsigned(30745,16),
to_unsigned(30759,16),
to_unsigned(30774,16),
to_unsigned(30788,16),
to_unsigned(30802,16),
to_unsigned(30816,16),
to_unsigned(30830,16),
to_unsigned(30844,16),
to_unsigned(30858,16),
to_unsigned(30871,16),
to_unsigned(30885,16),
to_unsigned(30899,16),
to_unsigned(30913,16),
to_unsigned(30926,16),
to_unsigned(30940,16),
to_unsigned(30953,16),
to_unsigned(30967,16),
to_unsigned(30980,16),
to_unsigned(30994,16),
to_unsigned(31007,16),
to_unsigned(31020,16),
to_unsigned(31034,16),
to_unsigned(31047,16),
to_unsigned(31060,16),
to_unsigned(31073,16),
to_unsigned(31086,16),
to_unsigned(31099,16),
to_unsigned(31112,16),
to_unsigned(31125,16),
to_unsigned(31138,16),
to_unsigned(31151,16),
to_unsigned(31163,16),
to_unsigned(31176,16),
to_unsigned(31189,16),
to_unsigned(31201,16),
to_unsigned(31214,16),
to_unsigned(31226,16),
to_unsigned(31239,16),
to_unsigned(31251,16),
to_unsigned(31263,16),
to_unsigned(31276,16),
to_unsigned(31288,16),
to_unsigned(31300,16),
to_unsigned(31312,16),
to_unsigned(31325,16),
to_unsigned(31337,16),
to_unsigned(31349,16),
to_unsigned(31361,16),
to_unsigned(31372,16),
to_unsigned(31384,16),
to_unsigned(31396,16),
to_unsigned(31408,16),
to_unsigned(31420,16),
to_unsigned(31431,16),
to_unsigned(31443,16),
to_unsigned(31454,16),
to_unsigned(31466,16),
to_unsigned(31477,16),
to_unsigned(31489,16),
to_unsigned(31500,16),
to_unsigned(31511,16),
to_unsigned(31523,16),
to_unsigned(31534,16),
to_unsigned(31545,16),
to_unsigned(31556,16),
to_unsigned(31567,16),
to_unsigned(31578,16),
to_unsigned(31589,16),
to_unsigned(31600,16),
to_unsigned(31611,16),
to_unsigned(31622,16),
to_unsigned(31633,16),
to_unsigned(31643,16),
to_unsigned(31654,16),
to_unsigned(31665,16),
to_unsigned(31675,16),
to_unsigned(31686,16),
to_unsigned(31696,16),
to_unsigned(31707,16),
to_unsigned(31717,16),
to_unsigned(31727,16),
to_unsigned(31738,16),
to_unsigned(31748,16),
to_unsigned(31758,16),
to_unsigned(31768,16),
to_unsigned(31778,16),
to_unsigned(31788,16),
to_unsigned(31798,16),
to_unsigned(31808,16),
to_unsigned(31818,16),
to_unsigned(31828,16),
to_unsigned(31837,16),
to_unsigned(31847,16),
to_unsigned(31857,16),
to_unsigned(31866,16),
to_unsigned(31876,16),
to_unsigned(31886,16),
to_unsigned(31895,16),
to_unsigned(31904,16),
to_unsigned(31914,16),
to_unsigned(31923,16),
to_unsigned(31932,16),
to_unsigned(31942,16),
to_unsigned(31951,16),
to_unsigned(31960,16),
to_unsigned(31969,16),
to_unsigned(31978,16),
to_unsigned(31987,16),
to_unsigned(31996,16),
to_unsigned(32005,16),
to_unsigned(32013,16),
to_unsigned(32022,16),
to_unsigned(32031,16),
to_unsigned(32040,16),
to_unsigned(32048,16),
to_unsigned(32057,16),
to_unsigned(32065,16),
to_unsigned(32074,16),
to_unsigned(32082,16),
to_unsigned(32090,16),
to_unsigned(32099,16),
to_unsigned(32107,16),
to_unsigned(32115,16),
to_unsigned(32123,16),
to_unsigned(32131,16),
to_unsigned(32139,16),
to_unsigned(32147,16),
to_unsigned(32155,16),
to_unsigned(32163,16),
to_unsigned(32171,16),
to_unsigned(32179,16),
to_unsigned(32187,16),
to_unsigned(32194,16),
to_unsigned(32202,16),
to_unsigned(32210,16),
to_unsigned(32217,16),
to_unsigned(32225,16),
to_unsigned(32232,16),
to_unsigned(32239,16),
to_unsigned(32247,16),
to_unsigned(32254,16),
to_unsigned(32261,16),
to_unsigned(32268,16),
to_unsigned(32276,16),
to_unsigned(32283,16),
to_unsigned(32290,16),
to_unsigned(32297,16),
to_unsigned(32304,16),
to_unsigned(32310,16),
to_unsigned(32317,16),
to_unsigned(32324,16),
to_unsigned(32331,16),
to_unsigned(32337,16),
to_unsigned(32344,16),
to_unsigned(32351,16),
to_unsigned(32357,16),
to_unsigned(32364,16),
to_unsigned(32370,16),
to_unsigned(32376,16),
to_unsigned(32383,16),
to_unsigned(32389,16),
to_unsigned(32395,16),
to_unsigned(32401,16),
to_unsigned(32407,16),
to_unsigned(32413,16),
to_unsigned(32419,16),
to_unsigned(32425,16),
to_unsigned(32431,16),
to_unsigned(32437,16),
to_unsigned(32443,16),
to_unsigned(32449,16),
to_unsigned(32454,16),
to_unsigned(32460,16),
to_unsigned(32466,16),
to_unsigned(32471,16),
to_unsigned(32477,16),
to_unsigned(32482,16),
to_unsigned(32488,16),
to_unsigned(32493,16),
to_unsigned(32498,16),
to_unsigned(32503,16),
to_unsigned(32509,16),
to_unsigned(32514,16),
to_unsigned(32519,16),
to_unsigned(32524,16),
to_unsigned(32529,16),
to_unsigned(32534,16),
to_unsigned(32539,16),
to_unsigned(32543,16),
to_unsigned(32548,16),
to_unsigned(32553,16),
to_unsigned(32558,16),
to_unsigned(32562,16),
to_unsigned(32567,16),
to_unsigned(32571,16),
to_unsigned(32576,16),
to_unsigned(32580,16),
to_unsigned(32585,16),
to_unsigned(32589,16),
to_unsigned(32593,16),
to_unsigned(32597,16),
to_unsigned(32602,16),
to_unsigned(32606,16),
to_unsigned(32610,16),
to_unsigned(32614,16),
to_unsigned(32618,16),
to_unsigned(32622,16),
to_unsigned(32625,16),
to_unsigned(32629,16),
to_unsigned(32633,16),
to_unsigned(32637,16),
to_unsigned(32640,16),
to_unsigned(32644,16),
to_unsigned(32647,16),
to_unsigned(32651,16),
to_unsigned(32654,16),
to_unsigned(32658,16),
to_unsigned(32661,16),
to_unsigned(32664,16),
to_unsigned(32668,16),
to_unsigned(32671,16),
to_unsigned(32674,16),
to_unsigned(32677,16),
to_unsigned(32680,16),
to_unsigned(32683,16),
to_unsigned(32686,16),
to_unsigned(32689,16),
to_unsigned(32692,16),
to_unsigned(32694,16),
to_unsigned(32697,16),
to_unsigned(32700,16),
to_unsigned(32702,16),
to_unsigned(32705,16),
to_unsigned(32707,16),
to_unsigned(32710,16),
to_unsigned(32712,16),
to_unsigned(32715,16),
to_unsigned(32717,16),
to_unsigned(32719,16),
to_unsigned(32721,16),
to_unsigned(32724,16),
to_unsigned(32726,16),
to_unsigned(32728,16),
to_unsigned(32730,16),
to_unsigned(32732,16),
to_unsigned(32733,16),
to_unsigned(32735,16),
to_unsigned(32737,16),
to_unsigned(32739,16),
to_unsigned(32741,16),
to_unsigned(32742,16),
to_unsigned(32744,16),
to_unsigned(32745,16),
to_unsigned(32747,16),
to_unsigned(32748,16),
to_unsigned(32750,16),
to_unsigned(32751,16),
to_unsigned(32752,16),
to_unsigned(32753,16),
to_unsigned(32754,16),
to_unsigned(32756,16),
to_unsigned(32757,16),
to_unsigned(32758,16),
to_unsigned(32759,16),
to_unsigned(32760,16),
to_unsigned(32760,16),
to_unsigned(32761,16),
to_unsigned(32762,16),
to_unsigned(32763,16),
to_unsigned(32763,16),
to_unsigned(32764,16),
to_unsigned(32764,16),
to_unsigned(32765,16),
to_unsigned(32765,16),
to_unsigned(32766,16),
to_unsigned(32766,16),
to_unsigned(32766,16),
to_unsigned(32767,16),
to_unsigned(32767,16),
to_unsigned(32767,16),
to_unsigned(32767,16)
);
 
-- Quarter sine lookup table
type lut_10000_type is array(0 to 2499) of unsigned(15 downto 0);
constant sine_lut_10000_x_16 : lut_10000_type := (
to_unsigned(0,16),
to_unsigned(21,16),
to_unsigned(41,16),
to_unsigned(62,16),
to_unsigned(82,16),
to_unsigned(103,16),
to_unsigned(124,16),
to_unsigned(144,16),
to_unsigned(165,16),
to_unsigned(185,16),
to_unsigned(206,16),
to_unsigned(226,16),
to_unsigned(247,16),
to_unsigned(268,16),
to_unsigned(288,16),
to_unsigned(309,16),
to_unsigned(329,16),
to_unsigned(350,16),
to_unsigned(371,16),
to_unsigned(391,16),
to_unsigned(412,16),
to_unsigned(432,16),
to_unsigned(453,16),
to_unsigned(474,16),
to_unsigned(494,16),
to_unsigned(515,16),
to_unsigned(535,16),
to_unsigned(556,16),
to_unsigned(576,16),
to_unsigned(597,16),
to_unsigned(618,16),
to_unsigned(638,16),
to_unsigned(659,16),
to_unsigned(679,16),
to_unsigned(700,16),
to_unsigned(721,16),
to_unsigned(741,16),
to_unsigned(762,16),
to_unsigned(782,16),
to_unsigned(803,16),
to_unsigned(823,16),
to_unsigned(844,16),
to_unsigned(865,16),
to_unsigned(885,16),
to_unsigned(906,16),
to_unsigned(926,16),
to_unsigned(947,16),
to_unsigned(968,16),
to_unsigned(988,16),
to_unsigned(1009,16),
to_unsigned(1029,16),
to_unsigned(1050,16),
to_unsigned(1070,16),
to_unsigned(1091,16),
to_unsigned(1112,16),
to_unsigned(1132,16),
to_unsigned(1153,16),
to_unsigned(1173,16),
to_unsigned(1194,16),
to_unsigned(1214,16),
to_unsigned(1235,16),
to_unsigned(1256,16),
to_unsigned(1276,16),
to_unsigned(1297,16),
to_unsigned(1317,16),
to_unsigned(1338,16),
to_unsigned(1358,16),
to_unsigned(1379,16),
to_unsigned(1400,16),
to_unsigned(1420,16),
to_unsigned(1441,16),
to_unsigned(1461,16),
to_unsigned(1482,16),
to_unsigned(1502,16),
to_unsigned(1523,16),
to_unsigned(1544,16),
to_unsigned(1564,16),
to_unsigned(1585,16),
to_unsigned(1605,16),
to_unsigned(1626,16),
to_unsigned(1646,16),
to_unsigned(1667,16),
to_unsigned(1687,16),
to_unsigned(1708,16),
to_unsigned(1729,16),
to_unsigned(1749,16),
to_unsigned(1770,16),
to_unsigned(1790,16),
to_unsigned(1811,16),
to_unsigned(1831,16),
to_unsigned(1852,16),
to_unsigned(1872,16),
to_unsigned(1893,16),
to_unsigned(1914,16),
to_unsigned(1934,16),
to_unsigned(1955,16),
to_unsigned(1975,16),
to_unsigned(1996,16),
to_unsigned(2016,16),
to_unsigned(2037,16),
to_unsigned(2057,16),
to_unsigned(2078,16),
to_unsigned(2099,16),
to_unsigned(2119,16),
to_unsigned(2140,16),
to_unsigned(2160,16),
to_unsigned(2181,16),
to_unsigned(2201,16),
to_unsigned(2222,16),
to_unsigned(2242,16),
to_unsigned(2263,16),
to_unsigned(2283,16),
to_unsigned(2304,16),
to_unsigned(2325,16),
to_unsigned(2345,16),
to_unsigned(2366,16),
to_unsigned(2386,16),
to_unsigned(2407,16),
to_unsigned(2427,16),
to_unsigned(2448,16),
to_unsigned(2468,16),
to_unsigned(2489,16),
to_unsigned(2509,16),
to_unsigned(2530,16),
to_unsigned(2550,16),
to_unsigned(2571,16),
to_unsigned(2591,16),
to_unsigned(2612,16),
to_unsigned(2632,16),
to_unsigned(2653,16),
to_unsigned(2673,16),
to_unsigned(2694,16),
to_unsigned(2715,16),
to_unsigned(2735,16),
to_unsigned(2756,16),
to_unsigned(2776,16),
to_unsigned(2797,16),
to_unsigned(2817,16),
to_unsigned(2838,16),
to_unsigned(2858,16),
to_unsigned(2879,16),
to_unsigned(2899,16),
to_unsigned(2920,16),
to_unsigned(2940,16),
to_unsigned(2961,16),
to_unsigned(2981,16),
to_unsigned(3002,16),
to_unsigned(3022,16),
to_unsigned(3043,16),
to_unsigned(3063,16),
to_unsigned(3084,16),
to_unsigned(3104,16),
to_unsigned(3125,16),
to_unsigned(3145,16),
to_unsigned(3166,16),
to_unsigned(3186,16),
to_unsigned(3207,16),
to_unsigned(3227,16),
to_unsigned(3248,16),
to_unsigned(3268,16),
to_unsigned(3289,16),
to_unsigned(3309,16),
to_unsigned(3330,16),
to_unsigned(3350,16),
to_unsigned(3370,16),
to_unsigned(3391,16),
to_unsigned(3411,16),
to_unsigned(3432,16),
to_unsigned(3452,16),
to_unsigned(3473,16),
to_unsigned(3493,16),
to_unsigned(3514,16),
to_unsigned(3534,16),
to_unsigned(3555,16),
to_unsigned(3575,16),
to_unsigned(3596,16),
to_unsigned(3616,16),
to_unsigned(3637,16),
to_unsigned(3657,16),
to_unsigned(3678,16),
to_unsigned(3698,16),
to_unsigned(3718,16),
to_unsigned(3739,16),
to_unsigned(3759,16),
to_unsigned(3780,16),
to_unsigned(3800,16),
to_unsigned(3821,16),
to_unsigned(3841,16),
to_unsigned(3862,16),
to_unsigned(3882,16),
to_unsigned(3902,16),
to_unsigned(3923,16),
to_unsigned(3943,16),
to_unsigned(3964,16),
to_unsigned(3984,16),
to_unsigned(4005,16),
to_unsigned(4025,16),
to_unsigned(4046,16),
to_unsigned(4066,16),
to_unsigned(4086,16),
to_unsigned(4107,16),
to_unsigned(4127,16),
to_unsigned(4148,16),
to_unsigned(4168,16),
to_unsigned(4188,16),
to_unsigned(4209,16),
to_unsigned(4229,16),
to_unsigned(4250,16),
to_unsigned(4270,16),
to_unsigned(4291,16),
to_unsigned(4311,16),
to_unsigned(4331,16),
to_unsigned(4352,16),
to_unsigned(4372,16),
to_unsigned(4393,16),
to_unsigned(4413,16),
to_unsigned(4433,16),
to_unsigned(4454,16),
to_unsigned(4474,16),
to_unsigned(4495,16),
to_unsigned(4515,16),
to_unsigned(4535,16),
to_unsigned(4556,16),
to_unsigned(4576,16),
to_unsigned(4597,16),
to_unsigned(4617,16),
to_unsigned(4637,16),
to_unsigned(4658,16),
to_unsigned(4678,16),
to_unsigned(4698,16),
to_unsigned(4719,16),
to_unsigned(4739,16),
to_unsigned(4760,16),
to_unsigned(4780,16),
to_unsigned(4800,16),
to_unsigned(4821,16),
to_unsigned(4841,16),
to_unsigned(4861,16),
to_unsigned(4882,16),
to_unsigned(4902,16),
to_unsigned(4922,16),
to_unsigned(4943,16),
to_unsigned(4963,16),
to_unsigned(4983,16),
to_unsigned(5004,16),
to_unsigned(5024,16),
to_unsigned(5045,16),
to_unsigned(5065,16),
to_unsigned(5085,16),
to_unsigned(5106,16),
to_unsigned(5126,16),
to_unsigned(5146,16),
to_unsigned(5167,16),
to_unsigned(5187,16),
to_unsigned(5207,16),
to_unsigned(5228,16),
to_unsigned(5248,16),
to_unsigned(5268,16),
to_unsigned(5288,16),
to_unsigned(5309,16),
to_unsigned(5329,16),
to_unsigned(5349,16),
to_unsigned(5370,16),
to_unsigned(5390,16),
to_unsigned(5410,16),
to_unsigned(5431,16),
to_unsigned(5451,16),
to_unsigned(5471,16),
to_unsigned(5492,16),
to_unsigned(5512,16),
to_unsigned(5532,16),
to_unsigned(5552,16),
to_unsigned(5573,16),
to_unsigned(5593,16),
to_unsigned(5613,16),
to_unsigned(5634,16),
to_unsigned(5654,16),
to_unsigned(5674,16),
to_unsigned(5694,16),
to_unsigned(5715,16),
to_unsigned(5735,16),
to_unsigned(5755,16),
to_unsigned(5776,16),
to_unsigned(5796,16),
to_unsigned(5816,16),
to_unsigned(5836,16),
to_unsigned(5857,16),
to_unsigned(5877,16),
to_unsigned(5897,16),
to_unsigned(5917,16),
to_unsigned(5938,16),
to_unsigned(5958,16),
to_unsigned(5978,16),
to_unsigned(5998,16),
to_unsigned(6019,16),
to_unsigned(6039,16),
to_unsigned(6059,16),
to_unsigned(6079,16),
to_unsigned(6099,16),
to_unsigned(6120,16),
to_unsigned(6140,16),
to_unsigned(6160,16),
to_unsigned(6180,16),
to_unsigned(6201,16),
to_unsigned(6221,16),
to_unsigned(6241,16),
to_unsigned(6261,16),
to_unsigned(6281,16),
to_unsigned(6302,16),
to_unsigned(6322,16),
to_unsigned(6342,16),
to_unsigned(6362,16),
to_unsigned(6382,16),
to_unsigned(6403,16),
to_unsigned(6423,16),
to_unsigned(6443,16),
to_unsigned(6463,16),
to_unsigned(6483,16),
to_unsigned(6504,16),
to_unsigned(6524,16),
to_unsigned(6544,16),
to_unsigned(6564,16),
to_unsigned(6584,16),
to_unsigned(6604,16),
to_unsigned(6625,16),
to_unsigned(6645,16),
to_unsigned(6665,16),
to_unsigned(6685,16),
to_unsigned(6705,16),
to_unsigned(6725,16),
to_unsigned(6746,16),
to_unsigned(6766,16),
to_unsigned(6786,16),
to_unsigned(6806,16),
to_unsigned(6826,16),
to_unsigned(6846,16),
to_unsigned(6866,16),
to_unsigned(6886,16),
to_unsigned(6907,16),
to_unsigned(6927,16),
to_unsigned(6947,16),
to_unsigned(6967,16),
to_unsigned(6987,16),
to_unsigned(7007,16),
to_unsigned(7027,16),
to_unsigned(7047,16),
to_unsigned(7068,16),
to_unsigned(7088,16),
to_unsigned(7108,16),
to_unsigned(7128,16),
to_unsigned(7148,16),
to_unsigned(7168,16),
to_unsigned(7188,16),
to_unsigned(7208,16),
to_unsigned(7228,16),
to_unsigned(7248,16),
to_unsigned(7268,16),
to_unsigned(7288,16),
to_unsigned(7309,16),
to_unsigned(7329,16),
to_unsigned(7349,16),
to_unsigned(7369,16),
to_unsigned(7389,16),
to_unsigned(7409,16),
to_unsigned(7429,16),
to_unsigned(7449,16),
to_unsigned(7469,16),
to_unsigned(7489,16),
to_unsigned(7509,16),
to_unsigned(7529,16),
to_unsigned(7549,16),
to_unsigned(7569,16),
to_unsigned(7589,16),
to_unsigned(7609,16),
to_unsigned(7629,16),
to_unsigned(7649,16),
to_unsigned(7669,16),
to_unsigned(7689,16),
to_unsigned(7709,16),
to_unsigned(7729,16),
to_unsigned(7749,16),
to_unsigned(7769,16),
to_unsigned(7789,16),
to_unsigned(7809,16),
to_unsigned(7829,16),
to_unsigned(7849,16),
to_unsigned(7869,16),
to_unsigned(7889,16),
to_unsigned(7909,16),
to_unsigned(7929,16),
to_unsigned(7949,16),
to_unsigned(7969,16),
to_unsigned(7989,16),
to_unsigned(8009,16),
to_unsigned(8029,16),
to_unsigned(8049,16),
to_unsigned(8069,16),
to_unsigned(8089,16),
to_unsigned(8109,16),
to_unsigned(8129,16),
to_unsigned(8149,16),
to_unsigned(8169,16),
to_unsigned(8189,16),
to_unsigned(8209,16),
to_unsigned(8229,16),
to_unsigned(8248,16),
to_unsigned(8268,16),
to_unsigned(8288,16),
to_unsigned(8308,16),
to_unsigned(8328,16),
to_unsigned(8348,16),
to_unsigned(8368,16),
to_unsigned(8388,16),
to_unsigned(8408,16),
to_unsigned(8428,16),
to_unsigned(8448,16),
to_unsigned(8467,16),
to_unsigned(8487,16),
to_unsigned(8507,16),
to_unsigned(8527,16),
to_unsigned(8547,16),
to_unsigned(8567,16),
to_unsigned(8587,16),
to_unsigned(8607,16),
to_unsigned(8626,16),
to_unsigned(8646,16),
to_unsigned(8666,16),
to_unsigned(8686,16),
to_unsigned(8706,16),
to_unsigned(8726,16),
to_unsigned(8746,16),
to_unsigned(8765,16),
to_unsigned(8785,16),
to_unsigned(8805,16),
to_unsigned(8825,16),
to_unsigned(8845,16),
to_unsigned(8865,16),
to_unsigned(8884,16),
to_unsigned(8904,16),
to_unsigned(8924,16),
to_unsigned(8944,16),
to_unsigned(8964,16),
to_unsigned(8983,16),
to_unsigned(9003,16),
to_unsigned(9023,16),
to_unsigned(9043,16),
to_unsigned(9063,16),
to_unsigned(9082,16),
to_unsigned(9102,16),
to_unsigned(9122,16),
to_unsigned(9142,16),
to_unsigned(9161,16),
to_unsigned(9181,16),
to_unsigned(9201,16),
to_unsigned(9221,16),
to_unsigned(9241,16),
to_unsigned(9260,16),
to_unsigned(9280,16),
to_unsigned(9300,16),
to_unsigned(9319,16),
to_unsigned(9339,16),
to_unsigned(9359,16),
to_unsigned(9379,16),
to_unsigned(9398,16),
to_unsigned(9418,16),
to_unsigned(9438,16),
to_unsigned(9458,16),
to_unsigned(9477,16),
to_unsigned(9497,16),
to_unsigned(9517,16),
to_unsigned(9536,16),
to_unsigned(9556,16),
to_unsigned(9576,16),
to_unsigned(9595,16),
to_unsigned(9615,16),
to_unsigned(9635,16),
to_unsigned(9654,16),
to_unsigned(9674,16),
to_unsigned(9694,16),
to_unsigned(9714,16),
to_unsigned(9733,16),
to_unsigned(9753,16),
to_unsigned(9772,16),
to_unsigned(9792,16),
to_unsigned(9812,16),
to_unsigned(9831,16),
to_unsigned(9851,16),
to_unsigned(9871,16),
to_unsigned(9890,16),
to_unsigned(9910,16),
to_unsigned(9930,16),
to_unsigned(9949,16),
to_unsigned(9969,16),
to_unsigned(9988,16),
to_unsigned(10008,16),
to_unsigned(10028,16),
to_unsigned(10047,16),
to_unsigned(10067,16),
to_unsigned(10086,16),
to_unsigned(10106,16),
to_unsigned(10126,16),
to_unsigned(10145,16),
to_unsigned(10165,16),
to_unsigned(10184,16),
to_unsigned(10204,16),
to_unsigned(10223,16),
to_unsigned(10243,16),
to_unsigned(10263,16),
to_unsigned(10282,16),
to_unsigned(10302,16),
to_unsigned(10321,16),
to_unsigned(10341,16),
to_unsigned(10360,16),
to_unsigned(10380,16),
to_unsigned(10399,16),
to_unsigned(10419,16),
to_unsigned(10438,16),
to_unsigned(10458,16),
to_unsigned(10477,16),
to_unsigned(10497,16),
to_unsigned(10516,16),
to_unsigned(10536,16),
to_unsigned(10555,16),
to_unsigned(10575,16),
to_unsigned(10594,16),
to_unsigned(10614,16),
to_unsigned(10633,16),
to_unsigned(10653,16),
to_unsigned(10672,16),
to_unsigned(10692,16),
to_unsigned(10711,16),
to_unsigned(10731,16),
to_unsigned(10750,16),
to_unsigned(10769,16),
to_unsigned(10789,16),
to_unsigned(10808,16),
to_unsigned(10828,16),
to_unsigned(10847,16),
to_unsigned(10867,16),
to_unsigned(10886,16),
to_unsigned(10905,16),
to_unsigned(10925,16),
to_unsigned(10944,16),
to_unsigned(10964,16),
to_unsigned(10983,16),
to_unsigned(11003,16),
to_unsigned(11022,16),
to_unsigned(11041,16),
to_unsigned(11061,16),
to_unsigned(11080,16),
to_unsigned(11099,16),
to_unsigned(11119,16),
to_unsigned(11138,16),
to_unsigned(11158,16),
to_unsigned(11177,16),
to_unsigned(11196,16),
to_unsigned(11216,16),
to_unsigned(11235,16),
to_unsigned(11254,16),
to_unsigned(11274,16),
to_unsigned(11293,16),
to_unsigned(11312,16),
to_unsigned(11332,16),
to_unsigned(11351,16),
to_unsigned(11370,16),
to_unsigned(11389,16),
to_unsigned(11409,16),
to_unsigned(11428,16),
to_unsigned(11447,16),
to_unsigned(11467,16),
to_unsigned(11486,16),
to_unsigned(11505,16),
to_unsigned(11525,16),
to_unsigned(11544,16),
to_unsigned(11563,16),
to_unsigned(11582,16),
to_unsigned(11602,16),
to_unsigned(11621,16),
to_unsigned(11640,16),
to_unsigned(11659,16),
to_unsigned(11679,16),
to_unsigned(11698,16),
to_unsigned(11717,16),
to_unsigned(11736,16),
to_unsigned(11755,16),
to_unsigned(11775,16),
to_unsigned(11794,16),
to_unsigned(11813,16),
to_unsigned(11832,16),
to_unsigned(11851,16),
to_unsigned(11871,16),
to_unsigned(11890,16),
to_unsigned(11909,16),
to_unsigned(11928,16),
to_unsigned(11947,16),
to_unsigned(11967,16),
to_unsigned(11986,16),
to_unsigned(12005,16),
to_unsigned(12024,16),
to_unsigned(12043,16),
to_unsigned(12062,16),
to_unsigned(12081,16),
to_unsigned(12101,16),
to_unsigned(12120,16),
to_unsigned(12139,16),
to_unsigned(12158,16),
to_unsigned(12177,16),
to_unsigned(12196,16),
to_unsigned(12215,16),
to_unsigned(12234,16),
to_unsigned(12254,16),
to_unsigned(12273,16),
to_unsigned(12292,16),
to_unsigned(12311,16),
to_unsigned(12330,16),
to_unsigned(12349,16),
to_unsigned(12368,16),
to_unsigned(12387,16),
to_unsigned(12406,16),
to_unsigned(12425,16),
to_unsigned(12444,16),
to_unsigned(12463,16),
to_unsigned(12482,16),
to_unsigned(12501,16),
to_unsigned(12520,16),
to_unsigned(12539,16),
to_unsigned(12558,16),
to_unsigned(12577,16),
to_unsigned(12596,16),
to_unsigned(12615,16),
to_unsigned(12634,16),
to_unsigned(12653,16),
to_unsigned(12672,16),
to_unsigned(12691,16),
to_unsigned(12710,16),
to_unsigned(12729,16),
to_unsigned(12748,16),
to_unsigned(12767,16),
to_unsigned(12786,16),
to_unsigned(12805,16),
to_unsigned(12824,16),
to_unsigned(12843,16),
to_unsigned(12862,16),
to_unsigned(12881,16),
to_unsigned(12900,16),
to_unsigned(12919,16),
to_unsigned(12938,16),
to_unsigned(12957,16),
to_unsigned(12976,16),
to_unsigned(12994,16),
to_unsigned(13013,16),
to_unsigned(13032,16),
to_unsigned(13051,16),
to_unsigned(13070,16),
to_unsigned(13089,16),
to_unsigned(13108,16),
to_unsigned(13127,16),
to_unsigned(13145,16),
to_unsigned(13164,16),
to_unsigned(13183,16),
to_unsigned(13202,16),
to_unsigned(13221,16),
to_unsigned(13240,16),
to_unsigned(13259,16),
to_unsigned(13277,16),
to_unsigned(13296,16),
to_unsigned(13315,16),
to_unsigned(13334,16),
to_unsigned(13353,16),
to_unsigned(13371,16),
to_unsigned(13390,16),
to_unsigned(13409,16),
to_unsigned(13428,16),
to_unsigned(13447,16),
to_unsigned(13465,16),
to_unsigned(13484,16),
to_unsigned(13503,16),
to_unsigned(13522,16),
to_unsigned(13540,16),
to_unsigned(13559,16),
to_unsigned(13578,16),
to_unsigned(13597,16),
to_unsigned(13615,16),
to_unsigned(13634,16),
to_unsigned(13653,16),
to_unsigned(13671,16),
to_unsigned(13690,16),
to_unsigned(13709,16),
to_unsigned(13728,16),
to_unsigned(13746,16),
to_unsigned(13765,16),
to_unsigned(13784,16),
to_unsigned(13802,16),
to_unsigned(13821,16),
to_unsigned(13840,16),
to_unsigned(13858,16),
to_unsigned(13877,16),
to_unsigned(13896,16),
to_unsigned(13914,16),
to_unsigned(13933,16),
to_unsigned(13952,16),
to_unsigned(13970,16),
to_unsigned(13989,16),
to_unsigned(14007,16),
to_unsigned(14026,16),
to_unsigned(14045,16),
to_unsigned(14063,16),
to_unsigned(14082,16),
to_unsigned(14100,16),
to_unsigned(14119,16),
to_unsigned(14138,16),
to_unsigned(14156,16),
to_unsigned(14175,16),
to_unsigned(14193,16),
to_unsigned(14212,16),
to_unsigned(14230,16),
to_unsigned(14249,16),
to_unsigned(14267,16),
to_unsigned(14286,16),
to_unsigned(14304,16),
to_unsigned(14323,16),
to_unsigned(14341,16),
to_unsigned(14360,16),
to_unsigned(14378,16),
to_unsigned(14397,16),
to_unsigned(14415,16),
to_unsigned(14434,16),
to_unsigned(14452,16),
to_unsigned(14471,16),
to_unsigned(14489,16),
to_unsigned(14508,16),
to_unsigned(14526,16),
to_unsigned(14545,16),
to_unsigned(14563,16),
to_unsigned(14582,16),
to_unsigned(14600,16),
to_unsigned(14619,16),
to_unsigned(14637,16),
to_unsigned(14655,16),
to_unsigned(14674,16),
to_unsigned(14692,16),
to_unsigned(14711,16),
to_unsigned(14729,16),
to_unsigned(14747,16),
to_unsigned(14766,16),
to_unsigned(14784,16),
to_unsigned(14802,16),
to_unsigned(14821,16),
to_unsigned(14839,16),
to_unsigned(14858,16),
to_unsigned(14876,16),
to_unsigned(14894,16),
to_unsigned(14913,16),
to_unsigned(14931,16),
to_unsigned(14949,16),
to_unsigned(14968,16),
to_unsigned(14986,16),
to_unsigned(15004,16),
to_unsigned(15022,16),
to_unsigned(15041,16),
to_unsigned(15059,16),
to_unsigned(15077,16),
to_unsigned(15096,16),
to_unsigned(15114,16),
to_unsigned(15132,16),
to_unsigned(15150,16),
to_unsigned(15169,16),
to_unsigned(15187,16),
to_unsigned(15205,16),
to_unsigned(15223,16),
to_unsigned(15242,16),
to_unsigned(15260,16),
to_unsigned(15278,16),
to_unsigned(15296,16),
to_unsigned(15314,16),
to_unsigned(15333,16),
to_unsigned(15351,16),
to_unsigned(15369,16),
to_unsigned(15387,16),
to_unsigned(15405,16),
to_unsigned(15424,16),
to_unsigned(15442,16),
to_unsigned(15460,16),
to_unsigned(15478,16),
to_unsigned(15496,16),
to_unsigned(15514,16),
to_unsigned(15532,16),
to_unsigned(15551,16),
to_unsigned(15569,16),
to_unsigned(15587,16),
to_unsigned(15605,16),
to_unsigned(15623,16),
to_unsigned(15641,16),
to_unsigned(15659,16),
to_unsigned(15677,16),
to_unsigned(15695,16),
to_unsigned(15713,16),
to_unsigned(15731,16),
to_unsigned(15750,16),
to_unsigned(15768,16),
to_unsigned(15786,16),
to_unsigned(15804,16),
to_unsigned(15822,16),
to_unsigned(15840,16),
to_unsigned(15858,16),
to_unsigned(15876,16),
to_unsigned(15894,16),
to_unsigned(15912,16),
to_unsigned(15930,16),
to_unsigned(15948,16),
to_unsigned(15966,16),
to_unsigned(15984,16),
to_unsigned(16002,16),
to_unsigned(16020,16),
to_unsigned(16038,16),
to_unsigned(16056,16),
to_unsigned(16073,16),
to_unsigned(16091,16),
to_unsigned(16109,16),
to_unsigned(16127,16),
to_unsigned(16145,16),
to_unsigned(16163,16),
to_unsigned(16181,16),
to_unsigned(16199,16),
to_unsigned(16217,16),
to_unsigned(16235,16),
to_unsigned(16253,16),
to_unsigned(16270,16),
to_unsigned(16288,16),
to_unsigned(16306,16),
to_unsigned(16324,16),
to_unsigned(16342,16),
to_unsigned(16360,16),
to_unsigned(16378,16),
to_unsigned(16395,16),
to_unsigned(16413,16),
to_unsigned(16431,16),
to_unsigned(16449,16),
to_unsigned(16467,16),
to_unsigned(16484,16),
to_unsigned(16502,16),
to_unsigned(16520,16),
to_unsigned(16538,16),
to_unsigned(16556,16),
to_unsigned(16573,16),
to_unsigned(16591,16),
to_unsigned(16609,16),
to_unsigned(16627,16),
to_unsigned(16644,16),
to_unsigned(16662,16),
to_unsigned(16680,16),
to_unsigned(16697,16),
to_unsigned(16715,16),
to_unsigned(16733,16),
to_unsigned(16751,16),
to_unsigned(16768,16),
to_unsigned(16786,16),
to_unsigned(16804,16),
to_unsigned(16821,16),
to_unsigned(16839,16),
to_unsigned(16857,16),
to_unsigned(16874,16),
to_unsigned(16892,16),
to_unsigned(16910,16),
to_unsigned(16927,16),
to_unsigned(16945,16),
to_unsigned(16962,16),
to_unsigned(16980,16),
to_unsigned(16998,16),
to_unsigned(17015,16),
to_unsigned(17033,16),
to_unsigned(17050,16),
to_unsigned(17068,16),
to_unsigned(17086,16),
to_unsigned(17103,16),
to_unsigned(17121,16),
to_unsigned(17138,16),
to_unsigned(17156,16),
to_unsigned(17173,16),
to_unsigned(17191,16),
to_unsigned(17208,16),
to_unsigned(17226,16),
to_unsigned(17243,16),
to_unsigned(17261,16),
to_unsigned(17278,16),
to_unsigned(17296,16),
to_unsigned(17313,16),
to_unsigned(17331,16),
to_unsigned(17348,16),
to_unsigned(17366,16),
to_unsigned(17383,16),
to_unsigned(17401,16),
to_unsigned(17418,16),
to_unsigned(17436,16),
to_unsigned(17453,16),
to_unsigned(17470,16),
to_unsigned(17488,16),
to_unsigned(17505,16),
to_unsigned(17523,16),
to_unsigned(17540,16),
to_unsigned(17557,16),
to_unsigned(17575,16),
to_unsigned(17592,16),
to_unsigned(17610,16),
to_unsigned(17627,16),
to_unsigned(17644,16),
to_unsigned(17662,16),
to_unsigned(17679,16),
to_unsigned(17696,16),
to_unsigned(17714,16),
to_unsigned(17731,16),
to_unsigned(17748,16),
to_unsigned(17766,16),
to_unsigned(17783,16),
to_unsigned(17800,16),
to_unsigned(17817,16),
to_unsigned(17835,16),
to_unsigned(17852,16),
to_unsigned(17869,16),
to_unsigned(17886,16),
to_unsigned(17904,16),
to_unsigned(17921,16),
to_unsigned(17938,16),
to_unsigned(17955,16),
to_unsigned(17973,16),
to_unsigned(17990,16),
to_unsigned(18007,16),
to_unsigned(18024,16),
to_unsigned(18041,16),
to_unsigned(18059,16),
to_unsigned(18076,16),
to_unsigned(18093,16),
to_unsigned(18110,16),
to_unsigned(18127,16),
to_unsigned(18144,16),
to_unsigned(18162,16),
to_unsigned(18179,16),
to_unsigned(18196,16),
to_unsigned(18213,16),
to_unsigned(18230,16),
to_unsigned(18247,16),
to_unsigned(18264,16),
to_unsigned(18281,16),
to_unsigned(18298,16),
to_unsigned(18315,16),
to_unsigned(18333,16),
to_unsigned(18350,16),
to_unsigned(18367,16),
to_unsigned(18384,16),
to_unsigned(18401,16),
to_unsigned(18418,16),
to_unsigned(18435,16),
to_unsigned(18452,16),
to_unsigned(18469,16),
to_unsigned(18486,16),
to_unsigned(18503,16),
to_unsigned(18520,16),
to_unsigned(18537,16),
to_unsigned(18554,16),
to_unsigned(18571,16),
to_unsigned(18588,16),
to_unsigned(18605,16),
to_unsigned(18622,16),
to_unsigned(18639,16),
to_unsigned(18655,16),
to_unsigned(18672,16),
to_unsigned(18689,16),
to_unsigned(18706,16),
to_unsigned(18723,16),
to_unsigned(18740,16),
to_unsigned(18757,16),
to_unsigned(18774,16),
to_unsigned(18791,16),
to_unsigned(18807,16),
to_unsigned(18824,16),
to_unsigned(18841,16),
to_unsigned(18858,16),
to_unsigned(18875,16),
to_unsigned(18892,16),
to_unsigned(18909,16),
to_unsigned(18925,16),
to_unsigned(18942,16),
to_unsigned(18959,16),
to_unsigned(18976,16),
to_unsigned(18992,16),
to_unsigned(19009,16),
to_unsigned(19026,16),
to_unsigned(19043,16),
to_unsigned(19060,16),
to_unsigned(19076,16),
to_unsigned(19093,16),
to_unsigned(19110,16),
to_unsigned(19126,16),
to_unsigned(19143,16),
to_unsigned(19160,16),
to_unsigned(19177,16),
to_unsigned(19193,16),
to_unsigned(19210,16),
to_unsigned(19227,16),
to_unsigned(19243,16),
to_unsigned(19260,16),
to_unsigned(19277,16),
to_unsigned(19293,16),
to_unsigned(19310,16),
to_unsigned(19327,16),
to_unsigned(19343,16),
to_unsigned(19360,16),
to_unsigned(19376,16),
to_unsigned(19393,16),
to_unsigned(19410,16),
to_unsigned(19426,16),
to_unsigned(19443,16),
to_unsigned(19459,16),
to_unsigned(19476,16),
to_unsigned(19492,16),
to_unsigned(19509,16),
to_unsigned(19525,16),
to_unsigned(19542,16),
to_unsigned(19559,16),
to_unsigned(19575,16),
to_unsigned(19592,16),
to_unsigned(19608,16),
to_unsigned(19625,16),
to_unsigned(19641,16),
to_unsigned(19658,16),
to_unsigned(19674,16),
to_unsigned(19690,16),
to_unsigned(19707,16),
to_unsigned(19723,16),
to_unsigned(19740,16),
to_unsigned(19756,16),
to_unsigned(19773,16),
to_unsigned(19789,16),
to_unsigned(19805,16),
to_unsigned(19822,16),
to_unsigned(19838,16),
to_unsigned(19855,16),
to_unsigned(19871,16),
to_unsigned(19887,16),
to_unsigned(19904,16),
to_unsigned(19920,16),
to_unsigned(19936,16),
to_unsigned(19953,16),
to_unsigned(19969,16),
to_unsigned(19985,16),
to_unsigned(20002,16),
to_unsigned(20018,16),
to_unsigned(20034,16),
to_unsigned(20051,16),
to_unsigned(20067,16),
to_unsigned(20083,16),
to_unsigned(20099,16),
to_unsigned(20116,16),
to_unsigned(20132,16),
to_unsigned(20148,16),
to_unsigned(20164,16),
to_unsigned(20181,16),
to_unsigned(20197,16),
to_unsigned(20213,16),
to_unsigned(20229,16),
to_unsigned(20245,16),
to_unsigned(20262,16),
to_unsigned(20278,16),
to_unsigned(20294,16),
to_unsigned(20310,16),
to_unsigned(20326,16),
to_unsigned(20342,16),
to_unsigned(20359,16),
to_unsigned(20375,16),
to_unsigned(20391,16),
to_unsigned(20407,16),
to_unsigned(20423,16),
to_unsigned(20439,16),
to_unsigned(20455,16),
to_unsigned(20471,16),
to_unsigned(20487,16),
to_unsigned(20503,16),
to_unsigned(20519,16),
to_unsigned(20535,16),
to_unsigned(20552,16),
to_unsigned(20568,16),
to_unsigned(20584,16),
to_unsigned(20600,16),
to_unsigned(20616,16),
to_unsigned(20632,16),
to_unsigned(20648,16),
to_unsigned(20664,16),
to_unsigned(20680,16),
to_unsigned(20696,16),
to_unsigned(20711,16),
to_unsigned(20727,16),
to_unsigned(20743,16),
to_unsigned(20759,16),
to_unsigned(20775,16),
to_unsigned(20791,16),
to_unsigned(20807,16),
to_unsigned(20823,16),
to_unsigned(20839,16),
to_unsigned(20855,16),
to_unsigned(20871,16),
to_unsigned(20886,16),
to_unsigned(20902,16),
to_unsigned(20918,16),
to_unsigned(20934,16),
to_unsigned(20950,16),
to_unsigned(20966,16),
to_unsigned(20982,16),
to_unsigned(20997,16),
to_unsigned(21013,16),
to_unsigned(21029,16),
to_unsigned(21045,16),
to_unsigned(21060,16),
to_unsigned(21076,16),
to_unsigned(21092,16),
to_unsigned(21108,16),
to_unsigned(21123,16),
to_unsigned(21139,16),
to_unsigned(21155,16),
to_unsigned(21171,16),
to_unsigned(21186,16),
to_unsigned(21202,16),
to_unsigned(21218,16),
to_unsigned(21233,16),
to_unsigned(21249,16),
to_unsigned(21265,16),
to_unsigned(21280,16),
to_unsigned(21296,16),
to_unsigned(21312,16),
to_unsigned(21327,16),
to_unsigned(21343,16),
to_unsigned(21359,16),
to_unsigned(21374,16),
to_unsigned(21390,16),
to_unsigned(21405,16),
to_unsigned(21421,16),
to_unsigned(21437,16),
to_unsigned(21452,16),
to_unsigned(21468,16),
to_unsigned(21483,16),
to_unsigned(21499,16),
to_unsigned(21514,16),
to_unsigned(21530,16),
to_unsigned(21545,16),
to_unsigned(21561,16),
to_unsigned(21576,16),
to_unsigned(21592,16),
to_unsigned(21607,16),
to_unsigned(21623,16),
to_unsigned(21638,16),
to_unsigned(21654,16),
to_unsigned(21669,16),
to_unsigned(21685,16),
to_unsigned(21700,16),
to_unsigned(21715,16),
to_unsigned(21731,16),
to_unsigned(21746,16),
to_unsigned(21762,16),
to_unsigned(21777,16),
to_unsigned(21792,16),
to_unsigned(21808,16),
to_unsigned(21823,16),
to_unsigned(21839,16),
to_unsigned(21854,16),
to_unsigned(21869,16),
to_unsigned(21885,16),
to_unsigned(21900,16),
to_unsigned(21915,16),
to_unsigned(21931,16),
to_unsigned(21946,16),
to_unsigned(21961,16),
to_unsigned(21976,16),
to_unsigned(21992,16),
to_unsigned(22007,16),
to_unsigned(22022,16),
to_unsigned(22037,16),
to_unsigned(22053,16),
to_unsigned(22068,16),
to_unsigned(22083,16),
to_unsigned(22098,16),
to_unsigned(22113,16),
to_unsigned(22129,16),
to_unsigned(22144,16),
to_unsigned(22159,16),
to_unsigned(22174,16),
to_unsigned(22189,16),
to_unsigned(22204,16),
to_unsigned(22220,16),
to_unsigned(22235,16),
to_unsigned(22250,16),
to_unsigned(22265,16),
to_unsigned(22280,16),
to_unsigned(22295,16),
to_unsigned(22310,16),
to_unsigned(22325,16),
to_unsigned(22340,16),
to_unsigned(22355,16),
to_unsigned(22370,16),
to_unsigned(22385,16),
to_unsigned(22401,16),
to_unsigned(22416,16),
to_unsigned(22431,16),
to_unsigned(22446,16),
to_unsigned(22461,16),
to_unsigned(22476,16),
to_unsigned(22491,16),
to_unsigned(22505,16),
to_unsigned(22520,16),
to_unsigned(22535,16),
to_unsigned(22550,16),
to_unsigned(22565,16),
to_unsigned(22580,16),
to_unsigned(22595,16),
to_unsigned(22610,16),
to_unsigned(22625,16),
to_unsigned(22640,16),
to_unsigned(22655,16),
to_unsigned(22670,16),
to_unsigned(22684,16),
to_unsigned(22699,16),
to_unsigned(22714,16),
to_unsigned(22729,16),
to_unsigned(22744,16),
to_unsigned(22759,16),
to_unsigned(22773,16),
to_unsigned(22788,16),
to_unsigned(22803,16),
to_unsigned(22818,16),
to_unsigned(22833,16),
to_unsigned(22847,16),
to_unsigned(22862,16),
to_unsigned(22877,16),
to_unsigned(22892,16),
to_unsigned(22906,16),
to_unsigned(22921,16),
to_unsigned(22936,16),
to_unsigned(22950,16),
to_unsigned(22965,16),
to_unsigned(22980,16),
to_unsigned(22994,16),
to_unsigned(23009,16),
to_unsigned(23024,16),
to_unsigned(23038,16),
to_unsigned(23053,16),
to_unsigned(23068,16),
to_unsigned(23082,16),
to_unsigned(23097,16),
to_unsigned(23111,16),
to_unsigned(23126,16),
to_unsigned(23141,16),
to_unsigned(23155,16),
to_unsigned(23170,16),
to_unsigned(23184,16),
to_unsigned(23199,16),
to_unsigned(23213,16),
to_unsigned(23228,16),
to_unsigned(23242,16),
to_unsigned(23257,16),
to_unsigned(23271,16),
to_unsigned(23286,16),
to_unsigned(23300,16),
to_unsigned(23315,16),
to_unsigned(23329,16),
to_unsigned(23344,16),
to_unsigned(23358,16),
to_unsigned(23373,16),
to_unsigned(23387,16),
to_unsigned(23402,16),
to_unsigned(23416,16),
to_unsigned(23430,16),
to_unsigned(23445,16),
to_unsigned(23459,16),
to_unsigned(23473,16),
to_unsigned(23488,16),
to_unsigned(23502,16),
to_unsigned(23517,16),
to_unsigned(23531,16),
to_unsigned(23545,16),
to_unsigned(23559,16),
to_unsigned(23574,16),
to_unsigned(23588,16),
to_unsigned(23602,16),
to_unsigned(23617,16),
to_unsigned(23631,16),
to_unsigned(23645,16),
to_unsigned(23659,16),
to_unsigned(23674,16),
to_unsigned(23688,16),
to_unsigned(23702,16),
to_unsigned(23716,16),
to_unsigned(23731,16),
to_unsigned(23745,16),
to_unsigned(23759,16),
to_unsigned(23773,16),
to_unsigned(23787,16),
to_unsigned(23801,16),
to_unsigned(23816,16),
to_unsigned(23830,16),
to_unsigned(23844,16),
to_unsigned(23858,16),
to_unsigned(23872,16),
to_unsigned(23886,16),
to_unsigned(23900,16),
to_unsigned(23914,16),
to_unsigned(23928,16),
to_unsigned(23942,16),
to_unsigned(23956,16),
to_unsigned(23971,16),
to_unsigned(23985,16),
to_unsigned(23999,16),
to_unsigned(24013,16),
to_unsigned(24027,16),
to_unsigned(24041,16),
to_unsigned(24055,16),
to_unsigned(24069,16),
to_unsigned(24082,16),
to_unsigned(24096,16),
to_unsigned(24110,16),
to_unsigned(24124,16),
to_unsigned(24138,16),
to_unsigned(24152,16),
to_unsigned(24166,16),
to_unsigned(24180,16),
to_unsigned(24194,16),
to_unsigned(24208,16),
to_unsigned(24222,16),
to_unsigned(24235,16),
to_unsigned(24249,16),
to_unsigned(24263,16),
to_unsigned(24277,16),
to_unsigned(24291,16),
to_unsigned(24305,16),
to_unsigned(24318,16),
to_unsigned(24332,16),
to_unsigned(24346,16),
to_unsigned(24360,16),
to_unsigned(24374,16),
to_unsigned(24387,16),
to_unsigned(24401,16),
to_unsigned(24415,16),
to_unsigned(24429,16),
to_unsigned(24442,16),
to_unsigned(24456,16),
to_unsigned(24470,16),
to_unsigned(24483,16),
to_unsigned(24497,16),
to_unsigned(24511,16),
to_unsigned(24524,16),
to_unsigned(24538,16),
to_unsigned(24552,16),
to_unsigned(24565,16),
to_unsigned(24579,16),
to_unsigned(24592,16),
to_unsigned(24606,16),
to_unsigned(24620,16),
to_unsigned(24633,16),
to_unsigned(24647,16),
to_unsigned(24660,16),
to_unsigned(24674,16),
to_unsigned(24687,16),
to_unsigned(24701,16),
to_unsigned(24715,16),
to_unsigned(24728,16),
to_unsigned(24742,16),
to_unsigned(24755,16),
to_unsigned(24769,16),
to_unsigned(24782,16),
to_unsigned(24795,16),
to_unsigned(24809,16),
to_unsigned(24822,16),
to_unsigned(24836,16),
to_unsigned(24849,16),
to_unsigned(24863,16),
to_unsigned(24876,16),
to_unsigned(24889,16),
to_unsigned(24903,16),
to_unsigned(24916,16),
to_unsigned(24930,16),
to_unsigned(24943,16),
to_unsigned(24956,16),
to_unsigned(24970,16),
to_unsigned(24983,16),
to_unsigned(24996,16),
to_unsigned(25010,16),
to_unsigned(25023,16),
to_unsigned(25036,16),
to_unsigned(25049,16),
to_unsigned(25063,16),
to_unsigned(25076,16),
to_unsigned(25089,16),
to_unsigned(25102,16),
to_unsigned(25116,16),
to_unsigned(25129,16),
to_unsigned(25142,16),
to_unsigned(25155,16),
to_unsigned(25168,16),
to_unsigned(25182,16),
to_unsigned(25195,16),
to_unsigned(25208,16),
to_unsigned(25221,16),
to_unsigned(25234,16),
to_unsigned(25247,16),
to_unsigned(25261,16),
to_unsigned(25274,16),
to_unsigned(25287,16),
to_unsigned(25300,16),
to_unsigned(25313,16),
to_unsigned(25326,16),
to_unsigned(25339,16),
to_unsigned(25352,16),
to_unsigned(25365,16),
to_unsigned(25378,16),
to_unsigned(25391,16),
to_unsigned(25404,16),
to_unsigned(25417,16),
to_unsigned(25430,16),
to_unsigned(25443,16),
to_unsigned(25456,16),
to_unsigned(25469,16),
to_unsigned(25482,16),
to_unsigned(25495,16),
to_unsigned(25508,16),
to_unsigned(25521,16),
to_unsigned(25534,16),
to_unsigned(25547,16),
to_unsigned(25559,16),
to_unsigned(25572,16),
to_unsigned(25585,16),
to_unsigned(25598,16),
to_unsigned(25611,16),
to_unsigned(25624,16),
to_unsigned(25637,16),
to_unsigned(25649,16),
to_unsigned(25662,16),
to_unsigned(25675,16),
to_unsigned(25688,16),
to_unsigned(25701,16),
to_unsigned(25713,16),
to_unsigned(25726,16),
to_unsigned(25739,16),
to_unsigned(25752,16),
to_unsigned(25764,16),
to_unsigned(25777,16),
to_unsigned(25790,16),
to_unsigned(25802,16),
to_unsigned(25815,16),
to_unsigned(25828,16),
to_unsigned(25840,16),
to_unsigned(25853,16),
to_unsigned(25866,16),
to_unsigned(25878,16),
to_unsigned(25891,16),
to_unsigned(25904,16),
to_unsigned(25916,16),
to_unsigned(25929,16),
to_unsigned(25941,16),
to_unsigned(25954,16),
to_unsigned(25967,16),
to_unsigned(25979,16),
to_unsigned(25992,16),
to_unsigned(26004,16),
to_unsigned(26017,16),
to_unsigned(26029,16),
to_unsigned(26042,16),
to_unsigned(26054,16),
to_unsigned(26067,16),
to_unsigned(26079,16),
to_unsigned(26092,16),
to_unsigned(26104,16),
to_unsigned(26116,16),
to_unsigned(26129,16),
to_unsigned(26141,16),
to_unsigned(26154,16),
to_unsigned(26166,16),
to_unsigned(26179,16),
to_unsigned(26191,16),
to_unsigned(26203,16),
to_unsigned(26216,16),
to_unsigned(26228,16),
to_unsigned(26240,16),
to_unsigned(26253,16),
to_unsigned(26265,16),
to_unsigned(26277,16),
to_unsigned(26290,16),
to_unsigned(26302,16),
to_unsigned(26314,16),
to_unsigned(26326,16),
to_unsigned(26339,16),
to_unsigned(26351,16),
to_unsigned(26363,16),
to_unsigned(26375,16),
to_unsigned(26388,16),
to_unsigned(26400,16),
to_unsigned(26412,16),
to_unsigned(26424,16),
to_unsigned(26436,16),
to_unsigned(26448,16),
to_unsigned(26461,16),
to_unsigned(26473,16),
to_unsigned(26485,16),
to_unsigned(26497,16),
to_unsigned(26509,16),
to_unsigned(26521,16),
to_unsigned(26533,16),
to_unsigned(26545,16),
to_unsigned(26557,16),
to_unsigned(26569,16),
to_unsigned(26581,16),
to_unsigned(26594,16),
to_unsigned(26606,16),
to_unsigned(26618,16),
to_unsigned(26630,16),
to_unsigned(26642,16),
to_unsigned(26654,16),
to_unsigned(26665,16),
to_unsigned(26677,16),
to_unsigned(26689,16),
to_unsigned(26701,16),
to_unsigned(26713,16),
to_unsigned(26725,16),
to_unsigned(26737,16),
to_unsigned(26749,16),
to_unsigned(26761,16),
to_unsigned(26773,16),
to_unsigned(26785,16),
to_unsigned(26796,16),
to_unsigned(26808,16),
to_unsigned(26820,16),
to_unsigned(26832,16),
to_unsigned(26844,16),
to_unsigned(26856,16),
to_unsigned(26867,16),
to_unsigned(26879,16),
to_unsigned(26891,16),
to_unsigned(26903,16),
to_unsigned(26914,16),
to_unsigned(26926,16),
to_unsigned(26938,16),
to_unsigned(26950,16),
to_unsigned(26961,16),
to_unsigned(26973,16),
to_unsigned(26985,16),
to_unsigned(26996,16),
to_unsigned(27008,16),
to_unsigned(27020,16),
to_unsigned(27031,16),
to_unsigned(27043,16),
to_unsigned(27055,16),
to_unsigned(27066,16),
to_unsigned(27078,16),
to_unsigned(27089,16),
to_unsigned(27101,16),
to_unsigned(27113,16),
to_unsigned(27124,16),
to_unsigned(27136,16),
to_unsigned(27147,16),
to_unsigned(27159,16),
to_unsigned(27170,16),
to_unsigned(27182,16),
to_unsigned(27193,16),
to_unsigned(27205,16),
to_unsigned(27216,16),
to_unsigned(27228,16),
to_unsigned(27239,16),
to_unsigned(27250,16),
to_unsigned(27262,16),
to_unsigned(27273,16),
to_unsigned(27285,16),
to_unsigned(27296,16),
to_unsigned(27308,16),
to_unsigned(27319,16),
to_unsigned(27330,16),
to_unsigned(27342,16),
to_unsigned(27353,16),
to_unsigned(27364,16),
to_unsigned(27376,16),
to_unsigned(27387,16),
to_unsigned(27398,16),
to_unsigned(27409,16),
to_unsigned(27421,16),
to_unsigned(27432,16),
to_unsigned(27443,16),
to_unsigned(27455,16),
to_unsigned(27466,16),
to_unsigned(27477,16),
to_unsigned(27488,16),
to_unsigned(27499,16),
to_unsigned(27511,16),
to_unsigned(27522,16),
to_unsigned(27533,16),
to_unsigned(27544,16),
to_unsigned(27555,16),
to_unsigned(27566,16),
to_unsigned(27577,16),
to_unsigned(27589,16),
to_unsigned(27600,16),
to_unsigned(27611,16),
to_unsigned(27622,16),
to_unsigned(27633,16),
to_unsigned(27644,16),
to_unsigned(27655,16),
to_unsigned(27666,16),
to_unsigned(27677,16),
to_unsigned(27688,16),
to_unsigned(27699,16),
to_unsigned(27710,16),
to_unsigned(27721,16),
to_unsigned(27732,16),
to_unsigned(27743,16),
to_unsigned(27754,16),
to_unsigned(27765,16),
to_unsigned(27776,16),
to_unsigned(27787,16),
to_unsigned(27798,16),
to_unsigned(27809,16),
to_unsigned(27819,16),
to_unsigned(27830,16),
to_unsigned(27841,16),
to_unsigned(27852,16),
to_unsigned(27863,16),
to_unsigned(27874,16),
to_unsigned(27885,16),
to_unsigned(27895,16),
to_unsigned(27906,16),
to_unsigned(27917,16),
to_unsigned(27928,16),
to_unsigned(27938,16),
to_unsigned(27949,16),
to_unsigned(27960,16),
to_unsigned(27971,16),
to_unsigned(27981,16),
to_unsigned(27992,16),
to_unsigned(28003,16),
to_unsigned(28013,16),
to_unsigned(28024,16),
to_unsigned(28035,16),
to_unsigned(28045,16),
to_unsigned(28056,16),
to_unsigned(28067,16),
to_unsigned(28077,16),
to_unsigned(28088,16),
to_unsigned(28099,16),
to_unsigned(28109,16),
to_unsigned(28120,16),
to_unsigned(28130,16),
to_unsigned(28141,16),
to_unsigned(28151,16),
to_unsigned(28162,16),
to_unsigned(28172,16),
to_unsigned(28183,16),
to_unsigned(28193,16),
to_unsigned(28204,16),
to_unsigned(28214,16),
to_unsigned(28225,16),
to_unsigned(28235,16),
to_unsigned(28246,16),
to_unsigned(28256,16),
to_unsigned(28267,16),
to_unsigned(28277,16),
to_unsigned(28287,16),
to_unsigned(28298,16),
to_unsigned(28308,16),
to_unsigned(28319,16),
to_unsigned(28329,16),
to_unsigned(28339,16),
to_unsigned(28350,16),
to_unsigned(28360,16),
to_unsigned(28370,16),
to_unsigned(28380,16),
to_unsigned(28391,16),
to_unsigned(28401,16),
to_unsigned(28411,16),
to_unsigned(28422,16),
to_unsigned(28432,16),
to_unsigned(28442,16),
to_unsigned(28452,16),
to_unsigned(28462,16),
to_unsigned(28473,16),
to_unsigned(28483,16),
to_unsigned(28493,16),
to_unsigned(28503,16),
to_unsigned(28513,16),
to_unsigned(28523,16),
to_unsigned(28534,16),
to_unsigned(28544,16),
to_unsigned(28554,16),
to_unsigned(28564,16),
to_unsigned(28574,16),
to_unsigned(28584,16),
to_unsigned(28594,16),
to_unsigned(28604,16),
to_unsigned(28614,16),
to_unsigned(28624,16),
to_unsigned(28634,16),
to_unsigned(28644,16),
to_unsigned(28654,16),
to_unsigned(28664,16),
to_unsigned(28674,16),
to_unsigned(28684,16),
to_unsigned(28694,16),
to_unsigned(28704,16),
to_unsigned(28714,16),
to_unsigned(28724,16),
to_unsigned(28734,16),
to_unsigned(28744,16),
to_unsigned(28754,16),
to_unsigned(28763,16),
to_unsigned(28773,16),
to_unsigned(28783,16),
to_unsigned(28793,16),
to_unsigned(28803,16),
to_unsigned(28813,16),
to_unsigned(28822,16),
to_unsigned(28832,16),
to_unsigned(28842,16),
to_unsigned(28852,16),
to_unsigned(28861,16),
to_unsigned(28871,16),
to_unsigned(28881,16),
to_unsigned(28891,16),
to_unsigned(28900,16),
to_unsigned(28910,16),
to_unsigned(28920,16),
to_unsigned(28929,16),
to_unsigned(28939,16),
to_unsigned(28949,16),
to_unsigned(28958,16),
to_unsigned(28968,16),
to_unsigned(28978,16),
to_unsigned(28987,16),
to_unsigned(28997,16),
to_unsigned(29006,16),
to_unsigned(29016,16),
to_unsigned(29026,16),
to_unsigned(29035,16),
to_unsigned(29045,16),
to_unsigned(29054,16),
to_unsigned(29064,16),
to_unsigned(29073,16),
to_unsigned(29083,16),
to_unsigned(29092,16),
to_unsigned(29102,16),
to_unsigned(29111,16),
to_unsigned(29120,16),
to_unsigned(29130,16),
to_unsigned(29139,16),
to_unsigned(29149,16),
to_unsigned(29158,16),
to_unsigned(29168,16),
to_unsigned(29177,16),
to_unsigned(29186,16),
to_unsigned(29196,16),
to_unsigned(29205,16),
to_unsigned(29214,16),
to_unsigned(29224,16),
to_unsigned(29233,16),
to_unsigned(29242,16),
to_unsigned(29251,16),
to_unsigned(29261,16),
to_unsigned(29270,16),
to_unsigned(29279,16),
to_unsigned(29289,16),
to_unsigned(29298,16),
to_unsigned(29307,16),
to_unsigned(29316,16),
to_unsigned(29325,16),
to_unsigned(29335,16),
to_unsigned(29344,16),
to_unsigned(29353,16),
to_unsigned(29362,16),
to_unsigned(29371,16),
to_unsigned(29380,16),
to_unsigned(29389,16),
to_unsigned(29398,16),
to_unsigned(29408,16),
to_unsigned(29417,16),
to_unsigned(29426,16),
to_unsigned(29435,16),
to_unsigned(29444,16),
to_unsigned(29453,16),
to_unsigned(29462,16),
to_unsigned(29471,16),
to_unsigned(29480,16),
to_unsigned(29489,16),
to_unsigned(29498,16),
to_unsigned(29507,16),
to_unsigned(29516,16),
to_unsigned(29525,16),
to_unsigned(29534,16),
to_unsigned(29542,16),
to_unsigned(29551,16),
to_unsigned(29560,16),
to_unsigned(29569,16),
to_unsigned(29578,16),
to_unsigned(29587,16),
to_unsigned(29596,16),
to_unsigned(29604,16),
to_unsigned(29613,16),
to_unsigned(29622,16),
to_unsigned(29631,16),
to_unsigned(29640,16),
to_unsigned(29648,16),
to_unsigned(29657,16),
to_unsigned(29666,16),
to_unsigned(29675,16),
to_unsigned(29683,16),
to_unsigned(29692,16),
to_unsigned(29701,16),
to_unsigned(29710,16),
to_unsigned(29718,16),
to_unsigned(29727,16),
to_unsigned(29736,16),
to_unsigned(29744,16),
to_unsigned(29753,16),
to_unsigned(29761,16),
to_unsigned(29770,16),
to_unsigned(29779,16),
to_unsigned(29787,16),
to_unsigned(29796,16),
to_unsigned(29804,16),
to_unsigned(29813,16),
to_unsigned(29821,16),
to_unsigned(29830,16),
to_unsigned(29838,16),
to_unsigned(29847,16),
to_unsigned(29855,16),
to_unsigned(29864,16),
to_unsigned(29872,16),
to_unsigned(29881,16),
to_unsigned(29889,16),
to_unsigned(29898,16),
to_unsigned(29906,16),
to_unsigned(29915,16),
to_unsigned(29923,16),
to_unsigned(29931,16),
to_unsigned(29940,16),
to_unsigned(29948,16),
to_unsigned(29956,16),
to_unsigned(29965,16),
to_unsigned(29973,16),
to_unsigned(29981,16),
to_unsigned(29990,16),
to_unsigned(29998,16),
to_unsigned(30006,16),
to_unsigned(30015,16),
to_unsigned(30023,16),
to_unsigned(30031,16),
to_unsigned(30039,16),
to_unsigned(30047,16),
to_unsigned(30056,16),
to_unsigned(30064,16),
to_unsigned(30072,16),
to_unsigned(30080,16),
to_unsigned(30088,16),
to_unsigned(30097,16),
to_unsigned(30105,16),
to_unsigned(30113,16),
to_unsigned(30121,16),
to_unsigned(30129,16),
to_unsigned(30137,16),
to_unsigned(30145,16),
to_unsigned(30153,16),
to_unsigned(30161,16),
to_unsigned(30169,16),
to_unsigned(30177,16),
to_unsigned(30185,16),
to_unsigned(30193,16),
to_unsigned(30201,16),
to_unsigned(30209,16),
to_unsigned(30217,16),
to_unsigned(30225,16),
to_unsigned(30233,16),
to_unsigned(30241,16),
to_unsigned(30249,16),
to_unsigned(30257,16),
to_unsigned(30265,16),
to_unsigned(30273,16),
to_unsigned(30281,16),
to_unsigned(30288,16),
to_unsigned(30296,16),
to_unsigned(30304,16),
to_unsigned(30312,16),
to_unsigned(30320,16),
to_unsigned(30328,16),
to_unsigned(30335,16),
to_unsigned(30343,16),
to_unsigned(30351,16),
to_unsigned(30359,16),
to_unsigned(30366,16),
to_unsigned(30374,16),
to_unsigned(30382,16),
to_unsigned(30390,16),
to_unsigned(30397,16),
to_unsigned(30405,16),
to_unsigned(30413,16),
to_unsigned(30420,16),
to_unsigned(30428,16),
to_unsigned(30436,16),
to_unsigned(30443,16),
to_unsigned(30451,16),
to_unsigned(30458,16),
to_unsigned(30466,16),
to_unsigned(30474,16),
to_unsigned(30481,16),
to_unsigned(30489,16),
to_unsigned(30496,16),
to_unsigned(30504,16),
to_unsigned(30511,16),
to_unsigned(30519,16),
to_unsigned(30526,16),
to_unsigned(30534,16),
to_unsigned(30541,16),
to_unsigned(30549,16),
to_unsigned(30556,16),
to_unsigned(30563,16),
to_unsigned(30571,16),
to_unsigned(30578,16),
to_unsigned(30586,16),
to_unsigned(30593,16),
to_unsigned(30600,16),
to_unsigned(30608,16),
to_unsigned(30615,16),
to_unsigned(30622,16),
to_unsigned(30630,16),
to_unsigned(30637,16),
to_unsigned(30644,16),
to_unsigned(30652,16),
to_unsigned(30659,16),
to_unsigned(30666,16),
to_unsigned(30673,16),
to_unsigned(30681,16),
to_unsigned(30688,16),
to_unsigned(30695,16),
to_unsigned(30702,16),
to_unsigned(30710,16),
to_unsigned(30717,16),
to_unsigned(30724,16),
to_unsigned(30731,16),
to_unsigned(30738,16),
to_unsigned(30745,16),
to_unsigned(30752,16),
to_unsigned(30759,16),
to_unsigned(30767,16),
to_unsigned(30774,16),
to_unsigned(30781,16),
to_unsigned(30788,16),
to_unsigned(30795,16),
to_unsigned(30802,16),
to_unsigned(30809,16),
to_unsigned(30816,16),
to_unsigned(30823,16),
to_unsigned(30830,16),
to_unsigned(30837,16),
to_unsigned(30844,16),
to_unsigned(30851,16),
to_unsigned(30858,16),
to_unsigned(30865,16),
to_unsigned(30871,16),
to_unsigned(30878,16),
to_unsigned(30885,16),
to_unsigned(30892,16),
to_unsigned(30899,16),
to_unsigned(30906,16),
to_unsigned(30913,16),
to_unsigned(30919,16),
to_unsigned(30926,16),
to_unsigned(30933,16),
to_unsigned(30940,16),
to_unsigned(30947,16),
to_unsigned(30953,16),
to_unsigned(30960,16),
to_unsigned(30967,16),
to_unsigned(30974,16),
to_unsigned(30980,16),
to_unsigned(30987,16),
to_unsigned(30994,16),
to_unsigned(31000,16),
to_unsigned(31007,16),
to_unsigned(31014,16),
to_unsigned(31020,16),
to_unsigned(31027,16),
to_unsigned(31034,16),
to_unsigned(31040,16),
to_unsigned(31047,16),
to_unsigned(31053,16),
to_unsigned(31060,16),
to_unsigned(31066,16),
to_unsigned(31073,16),
to_unsigned(31080,16),
to_unsigned(31086,16),
to_unsigned(31093,16),
to_unsigned(31099,16),
to_unsigned(31106,16),
to_unsigned(31112,16),
to_unsigned(31118,16),
to_unsigned(31125,16),
to_unsigned(31131,16),
to_unsigned(31138,16),
to_unsigned(31144,16),
to_unsigned(31151,16),
to_unsigned(31157,16),
to_unsigned(31163,16),
to_unsigned(31170,16),
to_unsigned(31176,16),
to_unsigned(31182,16),
to_unsigned(31189,16),
to_unsigned(31195,16),
to_unsigned(31201,16),
to_unsigned(31208,16),
to_unsigned(31214,16),
to_unsigned(31220,16),
to_unsigned(31226,16),
to_unsigned(31233,16),
to_unsigned(31239,16),
to_unsigned(31245,16),
to_unsigned(31251,16),
to_unsigned(31257,16),
to_unsigned(31263,16),
to_unsigned(31270,16),
to_unsigned(31276,16),
to_unsigned(31282,16),
to_unsigned(31288,16),
to_unsigned(31294,16),
to_unsigned(31300,16),
to_unsigned(31306,16),
to_unsigned(31312,16),
to_unsigned(31318,16),
to_unsigned(31325,16),
to_unsigned(31331,16),
to_unsigned(31337,16),
to_unsigned(31343,16),
to_unsigned(31349,16),
to_unsigned(31355,16),
to_unsigned(31361,16),
to_unsigned(31367,16),
to_unsigned(31372,16),
to_unsigned(31378,16),
to_unsigned(31384,16),
to_unsigned(31390,16),
to_unsigned(31396,16),
to_unsigned(31402,16),
to_unsigned(31408,16),
to_unsigned(31414,16),
to_unsigned(31420,16),
to_unsigned(31425,16),
to_unsigned(31431,16),
to_unsigned(31437,16),
to_unsigned(31443,16),
to_unsigned(31449,16),
to_unsigned(31454,16),
to_unsigned(31460,16),
to_unsigned(31466,16),
to_unsigned(31472,16),
to_unsigned(31477,16),
to_unsigned(31483,16),
to_unsigned(31489,16),
to_unsigned(31495,16),
to_unsigned(31500,16),
to_unsigned(31506,16),
to_unsigned(31511,16),
to_unsigned(31517,16),
to_unsigned(31523,16),
to_unsigned(31528,16),
to_unsigned(31534,16),
to_unsigned(31540,16),
to_unsigned(31545,16),
to_unsigned(31551,16),
to_unsigned(31556,16),
to_unsigned(31562,16),
to_unsigned(31567,16),
to_unsigned(31573,16),
to_unsigned(31578,16),
to_unsigned(31584,16),
to_unsigned(31589,16),
to_unsigned(31595,16),
to_unsigned(31600,16),
to_unsigned(31606,16),
to_unsigned(31611,16),
to_unsigned(31616,16),
to_unsigned(31622,16),
to_unsigned(31627,16),
to_unsigned(31633,16),
to_unsigned(31638,16),
to_unsigned(31643,16),
to_unsigned(31649,16),
to_unsigned(31654,16),
to_unsigned(31659,16),
to_unsigned(31665,16),
to_unsigned(31670,16),
to_unsigned(31675,16),
to_unsigned(31680,16),
to_unsigned(31686,16),
to_unsigned(31691,16),
to_unsigned(31696,16),
to_unsigned(31701,16),
to_unsigned(31707,16),
to_unsigned(31712,16),
to_unsigned(31717,16),
to_unsigned(31722,16),
to_unsigned(31727,16),
to_unsigned(31732,16),
to_unsigned(31738,16),
to_unsigned(31743,16),
to_unsigned(31748,16),
to_unsigned(31753,16),
to_unsigned(31758,16),
to_unsigned(31763,16),
to_unsigned(31768,16),
to_unsigned(31773,16),
to_unsigned(31778,16),
to_unsigned(31783,16),
to_unsigned(31788,16),
to_unsigned(31793,16),
to_unsigned(31798,16),
to_unsigned(31803,16),
to_unsigned(31808,16),
to_unsigned(31813,16),
to_unsigned(31818,16),
to_unsigned(31823,16),
to_unsigned(31828,16),
to_unsigned(31833,16),
to_unsigned(31837,16),
to_unsigned(31842,16),
to_unsigned(31847,16),
to_unsigned(31852,16),
to_unsigned(31857,16),
to_unsigned(31862,16),
to_unsigned(31866,16),
to_unsigned(31871,16),
to_unsigned(31876,16),
to_unsigned(31881,16),
to_unsigned(31886,16),
to_unsigned(31890,16),
to_unsigned(31895,16),
to_unsigned(31900,16),
to_unsigned(31904,16),
to_unsigned(31909,16),
to_unsigned(31914,16),
to_unsigned(31918,16),
to_unsigned(31923,16),
to_unsigned(31928,16),
to_unsigned(31932,16),
to_unsigned(31937,16),
to_unsigned(31942,16),
to_unsigned(31946,16),
to_unsigned(31951,16),
to_unsigned(31955,16),
to_unsigned(31960,16),
to_unsigned(31964,16),
to_unsigned(31969,16),
to_unsigned(31973,16),
to_unsigned(31978,16),
to_unsigned(31982,16),
to_unsigned(31987,16),
to_unsigned(31991,16),
to_unsigned(31996,16),
to_unsigned(32000,16),
to_unsigned(32005,16),
to_unsigned(32009,16),
to_unsigned(32013,16),
to_unsigned(32018,16),
to_unsigned(32022,16),
to_unsigned(32027,16),
to_unsigned(32031,16),
to_unsigned(32035,16),
to_unsigned(32040,16),
to_unsigned(32044,16),
to_unsigned(32048,16),
to_unsigned(32052,16),
to_unsigned(32057,16),
to_unsigned(32061,16),
to_unsigned(32065,16),
to_unsigned(32069,16),
to_unsigned(32074,16),
to_unsigned(32078,16),
to_unsigned(32082,16),
to_unsigned(32086,16),
to_unsigned(32090,16),
to_unsigned(32095,16),
to_unsigned(32099,16),
to_unsigned(32103,16),
to_unsigned(32107,16),
to_unsigned(32111,16),
to_unsigned(32115,16),
to_unsigned(32119,16),
to_unsigned(32123,16),
to_unsigned(32127,16),
to_unsigned(32131,16),
to_unsigned(32135,16),
to_unsigned(32139,16),
to_unsigned(32143,16),
to_unsigned(32147,16),
to_unsigned(32151,16),
to_unsigned(32155,16),
to_unsigned(32159,16),
to_unsigned(32163,16),
to_unsigned(32167,16),
to_unsigned(32171,16),
to_unsigned(32175,16),
to_unsigned(32179,16),
to_unsigned(32183,16),
to_unsigned(32187,16),
to_unsigned(32190,16),
to_unsigned(32194,16),
to_unsigned(32198,16),
to_unsigned(32202,16),
to_unsigned(32206,16),
to_unsigned(32210,16),
to_unsigned(32213,16),
to_unsigned(32217,16),
to_unsigned(32221,16),
to_unsigned(32225,16),
to_unsigned(32228,16),
to_unsigned(32232,16),
to_unsigned(32236,16),
to_unsigned(32239,16),
to_unsigned(32243,16),
to_unsigned(32247,16),
to_unsigned(32250,16),
to_unsigned(32254,16),
to_unsigned(32258,16),
to_unsigned(32261,16),
to_unsigned(32265,16),
to_unsigned(32268,16),
to_unsigned(32272,16),
to_unsigned(32276,16),
to_unsigned(32279,16),
to_unsigned(32283,16),
to_unsigned(32286,16),
to_unsigned(32290,16),
to_unsigned(32293,16),
to_unsigned(32297,16),
to_unsigned(32300,16),
to_unsigned(32304,16),
to_unsigned(32307,16),
to_unsigned(32310,16),
to_unsigned(32314,16),
to_unsigned(32317,16),
to_unsigned(32321,16),
to_unsigned(32324,16),
to_unsigned(32327,16),
to_unsigned(32331,16),
to_unsigned(32334,16),
to_unsigned(32337,16),
to_unsigned(32341,16),
to_unsigned(32344,16),
to_unsigned(32347,16),
to_unsigned(32351,16),
to_unsigned(32354,16),
to_unsigned(32357,16),
to_unsigned(32360,16),
to_unsigned(32364,16),
to_unsigned(32367,16),
to_unsigned(32370,16),
to_unsigned(32373,16),
to_unsigned(32376,16),
to_unsigned(32380,16),
to_unsigned(32383,16),
to_unsigned(32386,16),
to_unsigned(32389,16),
to_unsigned(32392,16),
to_unsigned(32395,16),
to_unsigned(32398,16),
to_unsigned(32401,16),
to_unsigned(32404,16),
to_unsigned(32407,16),
to_unsigned(32410,16),
to_unsigned(32413,16),
to_unsigned(32416,16),
to_unsigned(32419,16),
to_unsigned(32422,16),
to_unsigned(32425,16),
to_unsigned(32428,16),
to_unsigned(32431,16),
to_unsigned(32434,16),
to_unsigned(32437,16),
to_unsigned(32440,16),
to_unsigned(32443,16),
to_unsigned(32446,16),
to_unsigned(32449,16),
to_unsigned(32452,16),
to_unsigned(32454,16),
to_unsigned(32457,16),
to_unsigned(32460,16),
to_unsigned(32463,16),
to_unsigned(32466,16),
to_unsigned(32468,16),
to_unsigned(32471,16),
to_unsigned(32474,16),
to_unsigned(32477,16),
to_unsigned(32479,16),
to_unsigned(32482,16),
to_unsigned(32485,16),
to_unsigned(32488,16),
to_unsigned(32490,16),
to_unsigned(32493,16),
to_unsigned(32496,16),
to_unsigned(32498,16),
to_unsigned(32501,16),
to_unsigned(32503,16),
to_unsigned(32506,16),
to_unsigned(32509,16),
to_unsigned(32511,16),
to_unsigned(32514,16),
to_unsigned(32516,16),
to_unsigned(32519,16),
to_unsigned(32521,16),
to_unsigned(32524,16),
to_unsigned(32526,16),
to_unsigned(32529,16),
to_unsigned(32531,16),
to_unsigned(32534,16),
to_unsigned(32536,16),
to_unsigned(32539,16),
to_unsigned(32541,16),
to_unsigned(32543,16),
to_unsigned(32546,16),
to_unsigned(32548,16),
to_unsigned(32551,16),
to_unsigned(32553,16),
to_unsigned(32555,16),
to_unsigned(32558,16),
to_unsigned(32560,16),
to_unsigned(32562,16),
to_unsigned(32565,16),
to_unsigned(32567,16),
to_unsigned(32569,16),
to_unsigned(32571,16),
to_unsigned(32574,16),
to_unsigned(32576,16),
to_unsigned(32578,16),
to_unsigned(32580,16),
to_unsigned(32582,16),
to_unsigned(32585,16),
to_unsigned(32587,16),
to_unsigned(32589,16),
to_unsigned(32591,16),
to_unsigned(32593,16),
to_unsigned(32595,16),
to_unsigned(32597,16),
to_unsigned(32599,16),
to_unsigned(32602,16),
to_unsigned(32604,16),
to_unsigned(32606,16),
to_unsigned(32608,16),
to_unsigned(32610,16),
to_unsigned(32612,16),
to_unsigned(32614,16),
to_unsigned(32616,16),
to_unsigned(32618,16),
to_unsigned(32620,16),
to_unsigned(32622,16),
to_unsigned(32624,16),
to_unsigned(32625,16),
to_unsigned(32627,16),
to_unsigned(32629,16),
to_unsigned(32631,16),
to_unsigned(32633,16),
to_unsigned(32635,16),
to_unsigned(32637,16),
to_unsigned(32638,16),
to_unsigned(32640,16),
to_unsigned(32642,16),
to_unsigned(32644,16),
to_unsigned(32646,16),
to_unsigned(32647,16),
to_unsigned(32649,16),
to_unsigned(32651,16),
to_unsigned(32653,16),
to_unsigned(32654,16),
to_unsigned(32656,16),
to_unsigned(32658,16),
to_unsigned(32659,16),
to_unsigned(32661,16),
to_unsigned(32663,16),
to_unsigned(32664,16),
to_unsigned(32666,16),
to_unsigned(32668,16),
to_unsigned(32669,16),
to_unsigned(32671,16),
to_unsigned(32672,16),
to_unsigned(32674,16),
to_unsigned(32675,16),
to_unsigned(32677,16),
to_unsigned(32679,16),
to_unsigned(32680,16),
to_unsigned(32681,16),
to_unsigned(32683,16),
to_unsigned(32684,16),
to_unsigned(32686,16),
to_unsigned(32687,16),
to_unsigned(32689,16),
to_unsigned(32690,16),
to_unsigned(32692,16),
to_unsigned(32693,16),
to_unsigned(32694,16),
to_unsigned(32696,16),
to_unsigned(32697,16),
to_unsigned(32698,16),
to_unsigned(32700,16),
to_unsigned(32701,16),
to_unsigned(32702,16),
to_unsigned(32704,16),
to_unsigned(32705,16),
to_unsigned(32706,16),
to_unsigned(32707,16),
to_unsigned(32709,16),
to_unsigned(32710,16),
to_unsigned(32711,16),
to_unsigned(32712,16),
to_unsigned(32713,16),
to_unsigned(32715,16),
to_unsigned(32716,16),
to_unsigned(32717,16),
to_unsigned(32718,16),
to_unsigned(32719,16),
to_unsigned(32720,16),
to_unsigned(32721,16),
to_unsigned(32722,16),
to_unsigned(32724,16),
to_unsigned(32725,16),
to_unsigned(32726,16),
to_unsigned(32727,16),
to_unsigned(32728,16),
to_unsigned(32729,16),
to_unsigned(32730,16),
to_unsigned(32731,16),
to_unsigned(32732,16),
to_unsigned(32733,16),
to_unsigned(32733,16),
to_unsigned(32734,16),
to_unsigned(32735,16),
to_unsigned(32736,16),
to_unsigned(32737,16),
to_unsigned(32738,16),
to_unsigned(32739,16),
to_unsigned(32740,16),
to_unsigned(32741,16),
to_unsigned(32741,16),
to_unsigned(32742,16),
to_unsigned(32743,16),
to_unsigned(32744,16),
to_unsigned(32744,16),
to_unsigned(32745,16),
to_unsigned(32746,16),
to_unsigned(32747,16),
to_unsigned(32747,16),
to_unsigned(32748,16),
to_unsigned(32749,16),
to_unsigned(32750,16),
to_unsigned(32750,16),
to_unsigned(32751,16),
to_unsigned(32751,16),
to_unsigned(32752,16),
to_unsigned(32753,16),
to_unsigned(32753,16),
to_unsigned(32754,16),
to_unsigned(32754,16),
to_unsigned(32755,16),
to_unsigned(32756,16),
to_unsigned(32756,16),
to_unsigned(32757,16),
to_unsigned(32757,16),
to_unsigned(32758,16),
to_unsigned(32758,16),
to_unsigned(32759,16),
to_unsigned(32759,16),
to_unsigned(32760,16),
to_unsigned(32760,16),
to_unsigned(32760,16),
to_unsigned(32761,16),
to_unsigned(32761,16),
to_unsigned(32762,16),
to_unsigned(32762,16),
to_unsigned(32762,16),
to_unsigned(32763,16),
to_unsigned(32763,16),
to_unsigned(32763,16),
to_unsigned(32764,16),
to_unsigned(32764,16),
to_unsigned(32764,16),
to_unsigned(32764,16),
to_unsigned(32765,16),
to_unsigned(32765,16),
to_unsigned(32765,16),
to_unsigned(32765,16),
to_unsigned(32766,16),
to_unsigned(32766,16),
to_unsigned(32766,16),
to_unsigned(32766,16),
to_unsigned(32766,16),
to_unsigned(32766,16),
to_unsigned(32766,16),
to_unsigned(32767,16),
to_unsigned(32767,16),
to_unsigned(32767,16),
to_unsigned(32767,16),
to_unsigned(32767,16),
to_unsigned(32767,16),
to_unsigned(32767,16),
to_unsigned(32767,16)
);
 
 
-- Quarter sine lookup table
type lut_65536_x_32_type is array(0 to 16383) of unsigned(31 downto 0);
 
constant sine_lut_65536_x_32 : lut_65536_x_32_type := (
to_unsigned(0,32),
to_unsigned(205887,32),
to_unsigned(411775,32),
to_unsigned(617662,32),
to_unsigned(823550,32),
to_unsigned(1029437,32),
to_unsigned(1235324,32),
to_unsigned(1441212,32),
to_unsigned(1647099,32),
to_unsigned(1852987,32),
to_unsigned(2058874,32),
to_unsigned(2264761,32),
to_unsigned(2470648,32),
to_unsigned(2676536,32),
to_unsigned(2882423,32),
to_unsigned(3088310,32),
to_unsigned(3294197,32),
to_unsigned(3500085,32),
to_unsigned(3705972,32),
to_unsigned(3911859,32),
to_unsigned(4117746,32),
to_unsigned(4323633,32),
to_unsigned(4529520,32),
to_unsigned(4735407,32),
to_unsigned(4941294,32),
to_unsigned(5147180,32),
to_unsigned(5353067,32),
to_unsigned(5558954,32),
to_unsigned(5764841,32),
to_unsigned(5970727,32),
to_unsigned(6176614,32),
to_unsigned(6382501,32),
to_unsigned(6588387,32),
to_unsigned(6794273,32),
to_unsigned(7000160,32),
to_unsigned(7206046,32),
to_unsigned(7411932,32),
to_unsigned(7617818,32),
to_unsigned(7823705,32),
to_unsigned(8029591,32),
to_unsigned(8235476,32),
to_unsigned(8441362,32),
to_unsigned(8647248,32),
to_unsigned(8853134,32),
to_unsigned(9059019,32),
to_unsigned(9264905,32),
to_unsigned(9470790,32),
to_unsigned(9676676,32),
to_unsigned(9882561,32),
to_unsigned(10088446,32),
to_unsigned(10294331,32),
to_unsigned(10500216,32),
to_unsigned(10706101,32),
to_unsigned(10911986,32),
to_unsigned(11117871,32),
to_unsigned(11323755,32),
to_unsigned(11529640,32),
to_unsigned(11735524,32),
to_unsigned(11941409,32),
to_unsigned(12147293,32),
to_unsigned(12353177,32),
to_unsigned(12559061,32),
to_unsigned(12764945,32),
to_unsigned(12970828,32),
to_unsigned(13176712,32),
to_unsigned(13382595,32),
to_unsigned(13588479,32),
to_unsigned(13794362,32),
to_unsigned(14000245,32),
to_unsigned(14206128,32),
to_unsigned(14412011,32),
to_unsigned(14617894,32),
to_unsigned(14823776,32),
to_unsigned(15029659,32),
to_unsigned(15235541,32),
to_unsigned(15441423,32),
to_unsigned(15647305,32),
to_unsigned(15853187,32),
to_unsigned(16059069,32),
to_unsigned(16264950,32),
to_unsigned(16470832,32),
to_unsigned(16676713,32),
to_unsigned(16882594,32),
to_unsigned(17088475,32),
to_unsigned(17294356,32),
to_unsigned(17500237,32),
to_unsigned(17706117,32),
to_unsigned(17911997,32),
to_unsigned(18117878,32),
to_unsigned(18323758,32),
to_unsigned(18529638,32),
to_unsigned(18735517,32),
to_unsigned(18941397,32),
to_unsigned(19147276,32),
to_unsigned(19353155,32),
to_unsigned(19559034,32),
to_unsigned(19764913,32),
to_unsigned(19970791,32),
to_unsigned(20176670,32),
to_unsigned(20382548,32),
to_unsigned(20588426,32),
to_unsigned(20794304,32),
to_unsigned(21000182,32),
to_unsigned(21206059,32),
to_unsigned(21411936,32),
to_unsigned(21617814,32),
to_unsigned(21823690,32),
to_unsigned(22029567,32),
to_unsigned(22235444,32),
to_unsigned(22441320,32),
to_unsigned(22647196,32),
to_unsigned(22853072,32),
to_unsigned(23058947,32),
to_unsigned(23264823,32),
to_unsigned(23470698,32),
to_unsigned(23676573,32),
to_unsigned(23882448,32),
to_unsigned(24088323,32),
to_unsigned(24294197,32),
to_unsigned(24500071,32),
to_unsigned(24705945,32),
to_unsigned(24911819,32),
to_unsigned(25117692,32),
to_unsigned(25323565,32),
to_unsigned(25529438,32),
to_unsigned(25735311,32),
to_unsigned(25941183,32),
to_unsigned(26147056,32),
to_unsigned(26352928,32),
to_unsigned(26558800,32),
to_unsigned(26764671,32),
to_unsigned(26970542,32),
to_unsigned(27176413,32),
to_unsigned(27382284,32),
to_unsigned(27588155,32),
to_unsigned(27794025,32),
to_unsigned(27999895,32),
to_unsigned(28205765,32),
to_unsigned(28411634,32),
to_unsigned(28617504,32),
to_unsigned(28823373,32),
to_unsigned(29029242,32),
to_unsigned(29235110,32),
to_unsigned(29440978,32),
to_unsigned(29646846,32),
to_unsigned(29852714,32),
to_unsigned(30058581,32),
to_unsigned(30264448,32),
to_unsigned(30470315,32),
to_unsigned(30676182,32),
to_unsigned(30882048,32),
to_unsigned(31087914,32),
to_unsigned(31293780,32),
to_unsigned(31499645,32),
to_unsigned(31705510,32),
to_unsigned(31911375,32),
to_unsigned(32117239,32),
to_unsigned(32323104,32),
to_unsigned(32528968,32),
to_unsigned(32734831,32),
to_unsigned(32940695,32),
to_unsigned(33146558,32),
to_unsigned(33352420,32),
to_unsigned(33558283,32),
to_unsigned(33764145,32),
to_unsigned(33970007,32),
to_unsigned(34175868,32),
to_unsigned(34381729,32),
to_unsigned(34587590,32),
to_unsigned(34793451,32),
to_unsigned(34999311,32),
to_unsigned(35205171,32),
to_unsigned(35411031,32),
to_unsigned(35616890,32),
to_unsigned(35822749,32),
to_unsigned(36028607,32),
to_unsigned(36234466,32),
to_unsigned(36440324,32),
to_unsigned(36646181,32),
to_unsigned(36852039,32),
to_unsigned(37057895,32),
to_unsigned(37263752,32),
to_unsigned(37469608,32),
to_unsigned(37675464,32),
to_unsigned(37881320,32),
to_unsigned(38087175,32),
to_unsigned(38293030,32),
to_unsigned(38498884,32),
to_unsigned(38704738,32),
to_unsigned(38910592,32),
to_unsigned(39116446,32),
to_unsigned(39322299,32),
to_unsigned(39528151,32),
to_unsigned(39734004,32),
to_unsigned(39939856,32),
to_unsigned(40145707,32),
to_unsigned(40351559,32),
to_unsigned(40557410,32),
to_unsigned(40763260,32),
to_unsigned(40969110,32),
to_unsigned(41174960,32),
to_unsigned(41380809,32),
to_unsigned(41586658,32),
to_unsigned(41792507,32),
to_unsigned(41998355,32),
to_unsigned(42204203,32),
to_unsigned(42410050,32),
to_unsigned(42615898,32),
to_unsigned(42821744,32),
to_unsigned(43027591,32),
to_unsigned(43233436,32),
to_unsigned(43439282,32),
to_unsigned(43645127,32),
to_unsigned(43850972,32),
to_unsigned(44056816,32),
to_unsigned(44262660,32),
to_unsigned(44468503,32),
to_unsigned(44674346,32),
to_unsigned(44880189,32),
to_unsigned(45086031,32),
to_unsigned(45291873,32),
to_unsigned(45497715,32),
to_unsigned(45703556,32),
to_unsigned(45909396,32),
to_unsigned(46115236,32),
to_unsigned(46321076,32),
to_unsigned(46526915,32),
to_unsigned(46732754,32),
to_unsigned(46938593,32),
to_unsigned(47144431,32),
to_unsigned(47350268,32),
to_unsigned(47556105,32),
to_unsigned(47761942,32),
to_unsigned(47967778,32),
to_unsigned(48173614,32),
to_unsigned(48379449,32),
to_unsigned(48585284,32),
to_unsigned(48791119,32),
to_unsigned(48996953,32),
to_unsigned(49202787,32),
to_unsigned(49408620,32),
to_unsigned(49614452,32),
to_unsigned(49820285,32),
to_unsigned(50026116,32),
to_unsigned(50231948,32),
to_unsigned(50437779,32),
to_unsigned(50643609,32),
to_unsigned(50849439,32),
to_unsigned(51055268,32),
to_unsigned(51261097,32),
to_unsigned(51466926,32),
to_unsigned(51672754,32),
to_unsigned(51878581,32),
to_unsigned(52084409,32),
to_unsigned(52290235,32),
to_unsigned(52496061,32),
to_unsigned(52701887,32),
to_unsigned(52907712,32),
to_unsigned(53113537,32),
to_unsigned(53319361,32),
to_unsigned(53525185,32),
to_unsigned(53731008,32),
to_unsigned(53936831,32),
to_unsigned(54142653,32),
to_unsigned(54348475,32),
to_unsigned(54554296,32),
to_unsigned(54760116,32),
to_unsigned(54965937,32),
to_unsigned(55171756,32),
to_unsigned(55377576,32),
to_unsigned(55583394,32),
to_unsigned(55789212,32),
to_unsigned(55995030,32),
to_unsigned(56200847,32),
to_unsigned(56406664,32),
to_unsigned(56612480,32),
to_unsigned(56818296,32),
to_unsigned(57024111,32),
to_unsigned(57229925,32),
to_unsigned(57435739,32),
to_unsigned(57641553,32),
to_unsigned(57847366,32),
to_unsigned(58053178,32),
to_unsigned(58258990,32),
to_unsigned(58464801,32),
to_unsigned(58670612,32),
to_unsigned(58876423,32),
to_unsigned(59082232,32),
to_unsigned(59288042,32),
to_unsigned(59493850,32),
to_unsigned(59699658,32),
to_unsigned(59905466,32),
to_unsigned(60111273,32),
to_unsigned(60317079,32),
to_unsigned(60522885,32),
to_unsigned(60728691,32),
to_unsigned(60934495,32),
to_unsigned(61140300,32),
to_unsigned(61346103,32),
to_unsigned(61551906,32),
to_unsigned(61757709,32),
to_unsigned(61963511,32),
to_unsigned(62169312,32),
to_unsigned(62375113,32),
to_unsigned(62580914,32),
to_unsigned(62786713,32),
to_unsigned(62992512,32),
to_unsigned(63198311,32),
to_unsigned(63404109,32),
to_unsigned(63609906,32),
to_unsigned(63815703,32),
to_unsigned(64021499,32),
to_unsigned(64227295,32),
to_unsigned(64433090,32),
to_unsigned(64638884,32),
to_unsigned(64844678,32),
to_unsigned(65050471,32),
to_unsigned(65256264,32),
to_unsigned(65462056,32),
to_unsigned(65667847,32),
to_unsigned(65873638,32),
to_unsigned(66079428,32),
to_unsigned(66285218,32),
to_unsigned(66491007,32),
to_unsigned(66696795,32),
to_unsigned(66902583,32),
to_unsigned(67108370,32),
to_unsigned(67314157,32),
to_unsigned(67519943,32),
to_unsigned(67725728,32),
to_unsigned(67931513,32),
to_unsigned(68137297,32),
to_unsigned(68343080,32),
to_unsigned(68548863,32),
to_unsigned(68754645,32),
to_unsigned(68960427,32),
to_unsigned(69166208,32),
to_unsigned(69371988,32),
to_unsigned(69577768,32),
to_unsigned(69783547,32),
to_unsigned(69989325,32),
to_unsigned(70195103,32),
to_unsigned(70400880,32),
to_unsigned(70606656,32),
to_unsigned(70812432,32),
to_unsigned(71018207,32),
to_unsigned(71223982,32),
to_unsigned(71429756,32),
to_unsigned(71635529,32),
to_unsigned(71841301,32),
to_unsigned(72047073,32),
to_unsigned(72252844,32),
to_unsigned(72458615,32),
to_unsigned(72664385,32),
to_unsigned(72870154,32),
to_unsigned(73075922,32),
to_unsigned(73281690,32),
to_unsigned(73487457,32),
to_unsigned(73693224,32),
to_unsigned(73898990,32),
to_unsigned(74104755,32),
to_unsigned(74310519,32),
to_unsigned(74516283,32),
to_unsigned(74722046,32),
to_unsigned(74927808,32),
to_unsigned(75133570,32),
to_unsigned(75339331,32),
to_unsigned(75545092,32),
to_unsigned(75750851,32),
to_unsigned(75956610,32),
to_unsigned(76162368,32),
to_unsigned(76368126,32),
to_unsigned(76573883,32),
to_unsigned(76779639,32),
to_unsigned(76985394,32),
to_unsigned(77191149,32),
to_unsigned(77396903,32),
to_unsigned(77602656,32),
to_unsigned(77808409,32),
to_unsigned(78014161,32),
to_unsigned(78219912,32),
to_unsigned(78425662,32),
to_unsigned(78631412,32),
to_unsigned(78837161,32),
to_unsigned(79042909,32),
to_unsigned(79248657,32),
to_unsigned(79454404,32),
to_unsigned(79660150,32),
to_unsigned(79865895,32),
to_unsigned(80071640,32),
to_unsigned(80277384,32),
to_unsigned(80483127,32),
to_unsigned(80688869,32),
to_unsigned(80894611,32),
to_unsigned(81100352,32),
to_unsigned(81306092,32),
to_unsigned(81511831,32),
to_unsigned(81717570,32),
to_unsigned(81923308,32),
to_unsigned(82129045,32),
to_unsigned(82334782,32),
to_unsigned(82540517,32),
to_unsigned(82746252,32),
to_unsigned(82951986,32),
to_unsigned(83157720,32),
to_unsigned(83363452,32),
to_unsigned(83569184,32),
to_unsigned(83774915,32),
to_unsigned(83980645,32),
to_unsigned(84186375,32),
to_unsigned(84392104,32),
to_unsigned(84597832,32),
to_unsigned(84803559,32),
to_unsigned(85009285,32),
to_unsigned(85215011,32),
to_unsigned(85420736,32),
to_unsigned(85626460,32),
to_unsigned(85832183,32),
to_unsigned(86037906,32),
to_unsigned(86243627,32),
to_unsigned(86449348,32),
to_unsigned(86655069,32),
to_unsigned(86860788,32),
to_unsigned(87066506,32),
to_unsigned(87272224,32),
to_unsigned(87477941,32),
to_unsigned(87683657,32),
to_unsigned(87889372,32),
to_unsigned(88095087,32),
to_unsigned(88300801,32),
to_unsigned(88506514,32),
to_unsigned(88712226,32),
to_unsigned(88917937,32),
to_unsigned(89123647,32),
to_unsigned(89329357,32),
to_unsigned(89535066,32),
to_unsigned(89740774,32),
to_unsigned(89946481,32),
to_unsigned(90152187,32),
to_unsigned(90357893,32),
to_unsigned(90563597,32),
to_unsigned(90769301,32),
to_unsigned(90975004,32),
to_unsigned(91180706,32),
to_unsigned(91386408,32),
to_unsigned(91592108,32),
to_unsigned(91797808,32),
to_unsigned(92003507,32),
to_unsigned(92209205,32),
to_unsigned(92414902,32),
to_unsigned(92620598,32),
to_unsigned(92826293,32),
to_unsigned(93031988,32),
to_unsigned(93237682,32),
to_unsigned(93443374,32),
to_unsigned(93649066,32),
to_unsigned(93854758,32),
to_unsigned(94060448,32),
to_unsigned(94266137,32),
to_unsigned(94471826,32),
to_unsigned(94677513,32),
to_unsigned(94883200,32),
to_unsigned(95088886,32),
to_unsigned(95294571,32),
to_unsigned(95500255,32),
to_unsigned(95705939,32),
to_unsigned(95911621,32),
to_unsigned(96117303,32),
to_unsigned(96322983,32),
to_unsigned(96528663,32),
to_unsigned(96734342,32),
to_unsigned(96940020,32),
to_unsigned(97145697,32),
to_unsigned(97351373,32),
to_unsigned(97557048,32),
to_unsigned(97762723,32),
to_unsigned(97968396,32),
to_unsigned(98174069,32),
to_unsigned(98379741,32),
to_unsigned(98585411,32),
to_unsigned(98791081,32),
to_unsigned(98996750,32),
to_unsigned(99202418,32),
to_unsigned(99408086,32),
to_unsigned(99613752,32),
to_unsigned(99819417,32),
to_unsigned(100025082,32),
to_unsigned(100230745,32),
to_unsigned(100436408,32),
to_unsigned(100642069,32),
to_unsigned(100847730,32),
to_unsigned(101053390,32),
to_unsigned(101259049,32),
to_unsigned(101464707,32),
to_unsigned(101670364,32),
to_unsigned(101876020,32),
to_unsigned(102081675,32),
to_unsigned(102287329,32),
to_unsigned(102492982,32),
to_unsigned(102698635,32),
to_unsigned(102904286,32),
to_unsigned(103109936,32),
to_unsigned(103315586,32),
to_unsigned(103521234,32),
to_unsigned(103726882,32),
to_unsigned(103932529,32),
to_unsigned(104138174,32),
to_unsigned(104343819,32),
to_unsigned(104549463,32),
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to_unsigned(2146434830,32),
to_unsigned(2146441254,32),
to_unsigned(2146447659,32),
to_unsigned(2146454043,32),
to_unsigned(2146460408,32),
to_unsigned(2146466753,32),
to_unsigned(2146473079,32),
to_unsigned(2146479384,32),
to_unsigned(2146485670,32),
to_unsigned(2146491937,32),
to_unsigned(2146498183,32),
to_unsigned(2146504410,32),
to_unsigned(2146510617,32),
to_unsigned(2146516804,32),
to_unsigned(2146522972,32),
to_unsigned(2146529120,32),
to_unsigned(2146535248,32),
to_unsigned(2146541356,32),
to_unsigned(2146547445,32),
to_unsigned(2146553514,32),
to_unsigned(2146559563,32),
to_unsigned(2146565592,32),
to_unsigned(2146571602,32),
to_unsigned(2146577592,32),
to_unsigned(2146583562,32),
to_unsigned(2146589513,32),
to_unsigned(2146595444,32),
to_unsigned(2146601355,32),
to_unsigned(2146607246,32),
to_unsigned(2146613118,32),
to_unsigned(2146618970,32),
to_unsigned(2146624802,32),
to_unsigned(2146630614,32),
to_unsigned(2146636407,32),
to_unsigned(2146642180,32),
to_unsigned(2146647933,32),
to_unsigned(2146653667,32),
to_unsigned(2146659381,32),
to_unsigned(2146665075,32),
to_unsigned(2146670749,32),
to_unsigned(2146676403,32),
to_unsigned(2146682038,32),
to_unsigned(2146687653,32),
to_unsigned(2146693249,32),
to_unsigned(2146698824,32),
to_unsigned(2146704380,32),
to_unsigned(2146709916,32),
to_unsigned(2146715433,32),
to_unsigned(2146720930,32),
to_unsigned(2146726407,32),
to_unsigned(2146731864,32),
to_unsigned(2146737301,32),
to_unsigned(2146742719,32),
to_unsigned(2146748117,32),
to_unsigned(2146753496,32),
to_unsigned(2146758854,32),
to_unsigned(2146764193,32),
to_unsigned(2146769512,32),
to_unsigned(2146774812,32),
to_unsigned(2146780091,32),
to_unsigned(2146785351,32),
to_unsigned(2146790591,32),
to_unsigned(2146795812,32),
to_unsigned(2146801013,32),
to_unsigned(2146806193,32),
to_unsigned(2146811355,32),
to_unsigned(2146816496,32),
to_unsigned(2146821618,32),
to_unsigned(2146826720,32),
to_unsigned(2146831802,32),
to_unsigned(2146836865,32),
to_unsigned(2146841908,32),
to_unsigned(2146846931,32),
to_unsigned(2146851934,32),
to_unsigned(2146856918,32),
to_unsigned(2146861882,32),
to_unsigned(2146866826,32),
to_unsigned(2146871751,32),
to_unsigned(2146876655,32),
to_unsigned(2146881540,32),
to_unsigned(2146886406,32),
to_unsigned(2146891251,32),
to_unsigned(2146896077,32),
to_unsigned(2146900883,32),
to_unsigned(2146905669,32),
to_unsigned(2146910436,32),
to_unsigned(2146915183,32),
to_unsigned(2146919910,32),
to_unsigned(2146924617,32),
to_unsigned(2146929305,32),
to_unsigned(2146933973,32),
to_unsigned(2146938621,32),
to_unsigned(2146943250,32),
to_unsigned(2146947858,32),
to_unsigned(2146952447,32),
to_unsigned(2146957017,32),
to_unsigned(2146961566,32),
to_unsigned(2146966096,32),
to_unsigned(2146970606,32),
to_unsigned(2146975096,32),
to_unsigned(2146979567,32),
to_unsigned(2146984018,32),
to_unsigned(2146988449,32),
to_unsigned(2146992860,32),
to_unsigned(2146997252,32),
to_unsigned(2147001624,32),
to_unsigned(2147005976,32),
to_unsigned(2147010308,32),
to_unsigned(2147014621,32),
to_unsigned(2147018914,32),
to_unsigned(2147023187,32),
to_unsigned(2147027441,32),
to_unsigned(2147031674,32),
to_unsigned(2147035888,32),
to_unsigned(2147040083,32),
to_unsigned(2147044257,32),
to_unsigned(2147048412,32),
to_unsigned(2147052547,32),
to_unsigned(2147056663,32),
to_unsigned(2147060758,32),
to_unsigned(2147064834,32),
to_unsigned(2147068890,32),
to_unsigned(2147072927,32),
to_unsigned(2147076943,32),
to_unsigned(2147080940,32),
to_unsigned(2147084917,32),
to_unsigned(2147088875,32),
to_unsigned(2147092813,32),
to_unsigned(2147096731,32),
to_unsigned(2147100629,32),
to_unsigned(2147104507,32),
to_unsigned(2147108366,32),
to_unsigned(2147112205,32),
to_unsigned(2147116025,32),
to_unsigned(2147119824,32),
to_unsigned(2147123604,32),
to_unsigned(2147127364,32),
to_unsigned(2147131105,32),
to_unsigned(2147134825,32),
to_unsigned(2147138526,32),
to_unsigned(2147142207,32),
to_unsigned(2147145869,32),
to_unsigned(2147149510,32),
to_unsigned(2147153132,32),
to_unsigned(2147156735,32),
to_unsigned(2147160317,32),
to_unsigned(2147163880,32),
to_unsigned(2147167423,32),
to_unsigned(2147170946,32),
to_unsigned(2147174450,32),
to_unsigned(2147177933,32),
to_unsigned(2147181397,32),
to_unsigned(2147184842,32),
to_unsigned(2147188266,32),
to_unsigned(2147191671,32),
to_unsigned(2147195056,32),
to_unsigned(2147198422,32),
to_unsigned(2147201767,32),
to_unsigned(2147205093,32),
to_unsigned(2147208399,32),
to_unsigned(2147211686,32),
to_unsigned(2147214953,32),
to_unsigned(2147218200,32),
to_unsigned(2147221427,32),
to_unsigned(2147224634,32),
to_unsigned(2147227822,32),
to_unsigned(2147230990,32),
to_unsigned(2147234138,32),
to_unsigned(2147237267,32),
to_unsigned(2147240376,32),
to_unsigned(2147243465,32),
to_unsigned(2147246534,32),
to_unsigned(2147249584,32),
to_unsigned(2147252614,32),
to_unsigned(2147255624,32),
to_unsigned(2147258614,32),
to_unsigned(2147261585,32),
to_unsigned(2147264536,32),
to_unsigned(2147267467,32),
to_unsigned(2147270378,32),
to_unsigned(2147273270,32),
to_unsigned(2147276142,32),
to_unsigned(2147278994,32),
to_unsigned(2147281827,32),
to_unsigned(2147284639,32),
to_unsigned(2147287432,32),
to_unsigned(2147290206,32),
to_unsigned(2147292959,32),
to_unsigned(2147295693,32),
to_unsigned(2147298407,32),
to_unsigned(2147301101,32),
to_unsigned(2147303776,32),
to_unsigned(2147306431,32),
to_unsigned(2147309066,32),
to_unsigned(2147311681,32),
to_unsigned(2147314277,32),
to_unsigned(2147316853,32),
to_unsigned(2147319409,32),
to_unsigned(2147321945,32),
to_unsigned(2147324462,32),
to_unsigned(2147326959,32),
to_unsigned(2147329436,32),
to_unsigned(2147331894,32),
to_unsigned(2147334331,32),
to_unsigned(2147336749,32),
to_unsigned(2147339148,32),
to_unsigned(2147341526,32),
to_unsigned(2147343885,32),
to_unsigned(2147346224,32),
to_unsigned(2147348543,32),
to_unsigned(2147350843,32),
to_unsigned(2147353123,32),
to_unsigned(2147355383,32),
to_unsigned(2147357623,32),
to_unsigned(2147359844,32),
to_unsigned(2147362045,32),
to_unsigned(2147364226,32),
to_unsigned(2147366387,32),
to_unsigned(2147368529,32),
to_unsigned(2147370651,32),
to_unsigned(2147372753,32),
to_unsigned(2147374836,32),
to_unsigned(2147376898,32),
to_unsigned(2147378941,32),
to_unsigned(2147380964,32),
to_unsigned(2147382968,32),
to_unsigned(2147384952,32),
to_unsigned(2147386916,32),
to_unsigned(2147388860,32),
to_unsigned(2147390785,32),
to_unsigned(2147392689,32),
to_unsigned(2147394574,32),
to_unsigned(2147396440,32),
to_unsigned(2147398285,32),
to_unsigned(2147400111,32),
to_unsigned(2147401917,32),
to_unsigned(2147403704,32),
to_unsigned(2147405470,32),
to_unsigned(2147407217,32),
to_unsigned(2147408944,32),
to_unsigned(2147410652,32),
to_unsigned(2147412340,32),
to_unsigned(2147414007,32),
to_unsigned(2147415656,32),
to_unsigned(2147417284,32),
to_unsigned(2147418893,32),
to_unsigned(2147420482,32),
to_unsigned(2147422051,32),
to_unsigned(2147423601,32),
to_unsigned(2147425130,32),
to_unsigned(2147426640,32),
to_unsigned(2147428131,32),
to_unsigned(2147429601,32),
to_unsigned(2147431052,32),
to_unsigned(2147432483,32),
to_unsigned(2147433895,32),
to_unsigned(2147435286,32),
to_unsigned(2147436658,32),
to_unsigned(2147438010,32),
to_unsigned(2147439342,32),
to_unsigned(2147440655,32),
to_unsigned(2147441948,32),
to_unsigned(2147443221,32),
to_unsigned(2147444475,32),
to_unsigned(2147445708,32),
to_unsigned(2147446922,32),
to_unsigned(2147448117,32),
to_unsigned(2147449291,32),
to_unsigned(2147450446,32),
to_unsigned(2147451581,32),
to_unsigned(2147452696,32),
to_unsigned(2147453792,32),
to_unsigned(2147454867,32),
to_unsigned(2147455923,32),
to_unsigned(2147456960,32),
to_unsigned(2147457976,32),
to_unsigned(2147458973,32),
to_unsigned(2147459950,32),
to_unsigned(2147460907,32),
to_unsigned(2147461845,32),
to_unsigned(2147462763,32),
to_unsigned(2147463661,32),
to_unsigned(2147464539,32),
to_unsigned(2147465398,32),
to_unsigned(2147466237,32),
to_unsigned(2147467056,32),
to_unsigned(2147467856,32),
to_unsigned(2147468635,32),
to_unsigned(2147469395,32),
to_unsigned(2147470136,32),
to_unsigned(2147470856,32),
to_unsigned(2147471557,32),
to_unsigned(2147472238,32),
to_unsigned(2147472899,32),
to_unsigned(2147473541,32),
to_unsigned(2147474162,32),
to_unsigned(2147474764,32),
to_unsigned(2147475347,32),
to_unsigned(2147475909,32),
to_unsigned(2147476452,32),
to_unsigned(2147476975,32),
to_unsigned(2147477479,32),
to_unsigned(2147477962,32),
to_unsigned(2147478426,32),
to_unsigned(2147478870,32),
to_unsigned(2147479295,32),
to_unsigned(2147479699,32),
to_unsigned(2147480084,32),
to_unsigned(2147480449,32),
to_unsigned(2147480795,32),
to_unsigned(2147481120,32),
to_unsigned(2147481426,32),
to_unsigned(2147481713,32),
to_unsigned(2147481979,32),
to_unsigned(2147482226,32),
to_unsigned(2147482453,32),
to_unsigned(2147482660,32),
to_unsigned(2147482848,32),
to_unsigned(2147483015,32),
to_unsigned(2147483163,32),
to_unsigned(2147483292,32),
to_unsigned(2147483400,32),
to_unsigned(2147483489,32),
to_unsigned(2147483558,32),
to_unsigned(2147483608,32),
to_unsigned(2147483608,32)
);
 
end dds_sine_pack;
 
package body dds_sine_pack is
end dds_sine_pack;
 
 
-------------------------------------------------------------------------------
-- Digital Quadrature (2-phase) sine/cosine oscillator
-------------------------------------------------------------------------------
--
-- Author: John Clayton
-- Update: Jan. 3, 2014 Wrote code and description. Tested in simulation,
-- saw that there is amplitude creep, either growth
-- or shrinkage over time. Applied rounding to
-- mitigate this, with no satisfaction. Ended up
-- using an "amplitude reset" technique mentioned in
-- the book "Digital Signal Processing in VLSI."
-- The inspiration for this module came from that
-- book.
--
-- Description
-------------------------------------------------------------------------------
-- This is a discrete time, discrete amplitude binary recursion oscillator.
--
-- The sine and cosine outputs represent the projections of a rotating vector,
-- or complex phasor if you like, along the real and imaginary axes of a
-- 2-dimensional Cartesian coordinate space. The vector is rotated a fixed
-- amount with each new sample. Is this just as clear as mud?
--
-- Well, it does take some multipliers to implement the rotation matrix, but
-- otherwise, it's a fairly quick implementation...
--
-- The number of samples per cycle is given as a generic quantity, and the
-- initial values for the vector are zero for sin_o, and +1 for cos_o.
--
-- The numerical quantities are represented as signed 2's complement numbers,
-- in Q1.(AMPL_BITS-1) notation.
--
-- The frequency of the oscillator has been fixed at the lowest possible value.
-- The intention is that by varying the sample rate, sine and cosine waves of
-- different frequencies can be produced.
--
-- For example, if the system clock is at 50 MHz, and SAMPLES_PER_CYCLE=1000,
-- then it should be possible to create output at 50 kHz by setting the
-- clk_en_i input to '1'. For lower frequencies, just provide a stream of
-- clock enable pulses at the appropriate rate.
--
 
library ieee;
use ieee.std_logic_1164.all;
use ieee.numeric_std.all;
use ieee.math_real.all;
 
library work;
use work.convert_pack.all;
 
entity quadrature_oscillator is
generic(
AMPL_BITS : natural := 16;
AMPL_VALUE : natural := 31768; -- Set to some value below full scale. There is no saturation!
 
SAMPLES_PER_CYCLE : natural := 5000
);
port(
clk_i : in std_logic; -- System clock
rst_n_i : in std_logic; -- Low asserted reset
clk_en_i : in std_logic; -- clock enable, determines sample rate
 
-- Sine and Cosine outputs
sin_o : out signed(AMPL_BITS-1 downto 0);
cos_o : out signed(AMPL_BITS-1 downto 0)
);
end quadrature_oscillator;
 
architecture beh of quadrature_oscillator is
 
-- Constants
constant alpha : real := MATH_2_PI/real(SAMPLES_PER_CYCLE);
constant CA : real := COS(alpha);
constant SA : real := SIN(alpha);
constant FULLSCALE : real := 2.0**real(AMPL_BITS-1);
constant ROUNDVAL : integer := integer(FULLSCALE);
constant C_INT : integer := integer(CA * FULLSCALE);
constant S_INT : integer := integer(SA * FULLSCALE);
constant C_VECT : signed(AMPL_BITS-1 downto 0) := to_signed(C_INT,AMPL_BITS);
constant S_VECT : signed(AMPL_BITS-1 downto 0) := to_signed(S_INT,AMPL_BITS);
 
-- Signals
signal sine : signed(AMPL_BITS-1 downto 0);
signal cosine : signed(AMPL_BITS-1 downto 0);
signal s_sop : signed(2*AMPL_BITS-1 downto 0);
signal c_sop : signed(2*AMPL_BITS-1 downto 0);
signal s_rnd : signed(2*AMPL_BITS-1 downto 0);
signal c_rnd : signed(2*AMPL_BITS-1 downto 0);
signal last_sine_sign : std_logic;
 
begin
 
-- Calculate the sum of products, which is a vector twice as long, with two adjacent sign bits
s_sop <= S_VECT*cosine + C_VECT*sine;
c_sop <= C_VECT*cosine - S_VECT*sine;
-- Get rid of the duplicated sign bit
-- These signals were named "_rnd" because rounding was tried here...
-- Alas, although the rounding itself seemed to work, the amplitude decayed anyway.
-- So, I pulled out the rounding, but kept the names.
-- To implement rounding, add ROUNDVAL to these.
s_rnd <= (s_sop(2*AMPL_BITS-2 downto 0) & '0');
c_rnd <= (c_sop(2*AMPL_BITS-2 downto 0) & '0');
 
process (clk_i, rst_n_i)
begin
if (rst_n_i = '0') then
sine <= (others=>'0');
last_sine_sign <= '0';
cosine <= to_signed(AMPL_VALUE,cosine'length);
elsif (clk_i'event and clk_i = '1') then
if (clk_en_i = '1') then
sine <= s_rnd(2*AMPL_BITS-1 downto AMPL_BITS); -- select the upper half
cosine <= c_rnd(2*AMPL_BITS-1 downto AMPL_BITS); -- select the upper half
end if;
-- Prevent amplitude creep by resetting the cosine component at the
-- positive zero crossing of the sine signal.
if s_rnd(2*AMPL_BITS-1)='0' and sine(sine'length-1)='1' then
cosine <= to_signed(AMPL_VALUE,cosine'length);
end if;
 
end if;
end process;
 
sin_o <= sine;
cos_o <= cosine;
 
end beh;
 
-------------------------------------------------------------------------------
-- Sinewave Generator Direct Digital Synthesizer (DDS) method
-------------------------------------------------------------------------------
--
-- Author: John Clayton
-- Update: Oct. 15, 2013 Copied code from dds_sine to make this module.
--
-- Description
-------------------------------------------------------------------------------
-- This is a direct digital synthesizer module, which uses a 1/4 wave lookup
-- to produce sinewave samples. This module is the same as "dds_sine" except
-- that this module uses an internal lookup table instead of an external one.
--
 
library ieee;
use ieee.std_logic_1164.all;
use ieee.numeric_std.all;
 
library work;
use work.convert_pack.all;
use work.dds_sine_pack.all;
 
entity sine_generator_dds is
generic(
PHI_BITS : natural := 24; -- Bits in phase accumulator, must be >= PHASE_BITS
AMPL_BITS : natural := 16;
PHASE_BITS : natural := 10
);
port(
clk_i : in std_logic;
rst_n_i : in std_logic;
clk_en_i : in std_logic;
 
-- Frequency Tuning Word input
ftw_i : in unsigned(PHI_BITS-1 downto 0);
 
-- Outputs
accum_o : out unsigned(PHI_BITS-1 downto 0);
sine_o : out signed(AMPL_BITS-1 downto 0)
);
end sine_generator_dds;
 
architecture beh of sine_generator_dds is
 
-- Constants
constant Q_PHASE_BITS : integer := PHASE_BITS-2; -- Quarter phase takes two bits less to represent
constant Q_PHASE_LUT_BITS : integer := PHASE_BITS-2; -- Quarter phase takes two bits less to represent
 
-- Signals
signal accum : unsigned(PHI_BITS-1 downto 0);
signal lut_val : unsigned(AMPL_BITS-1 downto 0);
signal lut_val_neg : unsigned(AMPL_BITS-1 downto 0);
signal q_phase : unsigned(Q_PHASE_BITS-1 downto 0);
signal q_phase_neg : unsigned(Q_PHASE_BITS-1 downto 0);
signal phase_value : unsigned(Q_PHASE_BITS-1 downto 0);
signal lut_adr : unsigned(Q_PHASE_LUT_BITS-1 downto 0);
 
begin
 
q_phase <= u_resize(u_resize_l(accum,PHASE_BITS),q_phase'length); -- Discard the fractional portion
q_phase_neg <= (not q_phase)+1;
 
process (clk_i, rst_n_i)
begin
if (rst_n_i = '0') then
accum <= (others=>'0');
elsif (clk_i'event and clk_i = '1') then
if (clk_en_i = '1') then
accum <= accum + ftw_i;
end if;
end if;
end process;
 
phase_value <= q_phase when accum(accum'length-2)='0' else q_phase_neg;
lut_adr <= u_resize_l(phase_value,lut_adr'length);
lut_val <= u_resize_l(sine_lut_65536_x_32(to_integer(lut_adr)),lut_val'length);
lut_val_neg <= (not lut_val) + 1;
sine_o <= signed(lut_val) when accum(accum'length-1)='0' else signed(lut_val_neg);
accum_o <= accum;
 
end beh;
 
 
-------------------------------------------------------------------------------
-- Direct Digital Synthesizer Power of 2 Length Sinewave Look Up Table module
-------------------------------------------------------------------------------
--
-- Author: John Clayton
-- Update: Sep. 5, 2013 Copied code from dds_sine_non_power_of_two to make
-- this module.
--
-- Description
-------------------------------------------------------------------------------
-- This is a direct digital synthesizer module, which uses a 1/4 wave lookup
-- to produce sinewave samples. An external look up table provides the
-- sinewave samples to be used. The lookup table must be 2**(PHASE_BITS-2)
-- entries long.
--
-- An address bus is provided for indexing into the look up table, and the
-- response data is input via the lut_dat_i bus.
--
 
library ieee;
use ieee.std_logic_1164.all;
use ieee.numeric_std.all;
 
library work;
use work.convert_pack.all;
 
entity dds_sine is
generic(
PHI_BITS : natural := 24; -- Bits in phase accumulator, must be >= PHASE_BITS
AMPL_BITS : natural := 16;
PHASE_BITS : natural := 10
);
port(
clk_i : in std_logic;
rst_n_i : in std_logic;
clk_en_i : in std_logic;
 
-- Look Up Table interface
lut_adr_o : out unsigned(PHASE_BITS-3 downto 0); -- Quarter wave LUT
lut_dat_i : in unsigned(AMPL_BITS-1 downto 0);
 
-- Frequency Tuning Word input
ftw_i : in unsigned(PHI_BITS-1 downto 0);
 
-- Outputs
accum_o : out unsigned(PHI_BITS-1 downto 0);
sine_o : out signed(AMPL_BITS-1 downto 0)
);
end dds_sine;
 
architecture beh of dds_sine is
 
-- Constants
constant Q_PHASE_BITS : integer := PHASE_BITS-2; -- Quarter phase takes two bits less to represent
 
-- Signals
signal accum : unsigned(PHI_BITS-1 downto 0);
signal lut_out : unsigned(AMPL_BITS-1 downto 0);
signal lut_out_neg : unsigned(AMPL_BITS-1 downto 0);
signal q_phase : unsigned(Q_PHASE_BITS-1 downto 0);
signal q_phase_neg : unsigned(Q_PHASE_BITS-1 downto 0);
 
begin
 
q_phase <= u_resize(u_resize_l(accum,PHASE_BITS),q_phase'length); -- Discard the fractional portion
q_phase_neg <= (not q_phase)+1;
 
process (clk_i, rst_n_i)
begin
if (rst_n_i = '0') then
accum <= (others=>'0');
elsif (clk_i'event and clk_i = '1') then
if (clk_en_i = '1') then
accum <= accum + ftw_i;
end if;
end if;
end process;
 
lut_adr_o <= q_phase when accum(accum'length-2)='0' else q_phase_neg;
lut_out <= lut_dat_i;
lut_out_neg <= (not lut_out) + 1;
sine_o <= signed(lut_out) when accum(accum'length-1)='0' else signed(lut_out_neg);
accum_o <= accum;
 
end beh;
 
 
-------------------------------------------------------------------------------
-- Direct Digital Synthesizer Arbitrary Length Sinewave Look Up Table module
-------------------------------------------------------------------------------
--
-- Author: John Clayton
-- Update: Jan. 24, 2013 Modified Matlab script "sine_arbitrary_length_lut_gen"
-- to produce VHDL output which uses the "unsigned" type
-- from ieee.numeric_std library.
-- Jan. 26, 2013 Rewrote accumulator folding logic. Added saturation
-- check to avoid indices beyond the end of the lookup
-- table.
-- Sep. 5, 2013 Restructured the module to use external look up
-- tables. Created generics for AMPL_BITS, PHASE_LENGTH
-- and PHASE_BITS.
--
-- Description
-------------------------------------------------------------------------------
-- This is a direct digital synthesizer module, which uses a 1/4 wave lookup
-- to produce waveform samples. An external look up table provides the
-- sinewave samples to be used. The lookup table can be any length, being
-- one quarter of PHASE_LENGTH entries long.
--
-- An address bus is provided for indexing into the look up table, and the
-- response data is input via the lut_dat_i bus.
--
 
library ieee;
use ieee.std_logic_1164.all;
use ieee.numeric_std.all;
 
library work;
use work.convert_pack.all;
 
entity dds_sine_non_power_of_two is
generic(
PHI_BITS : natural := 24; -- Bits in phase accumulator, must be >= PHASE_BITS
AMPL_BITS : natural := 16;
PHASE_LENGTH : natural := 1024;
PHASE_BITS : natural := 10
);
port(
clk_i : in std_logic;
rst_n_i : in std_logic;
clk_en_i : in std_logic;
 
-- Look Up Table interface
lut_adr_o : out unsigned(PHASE_BITS-3 downto 0); -- Quarter wave LUT
lut_dat_i : in unsigned(AMPL_BITS-1 downto 0);
 
-- Frequency Tuning Word input
ftw_i : in unsigned(PHI_BITS-1 downto 0);
 
-- Outputs
accum_o : out unsigned(PHI_BITS-1 downto 0);
sine_o : out signed(AMPL_BITS-1 downto 0)
);
end dds_sine_non_power_of_two;
 
architecture beh of dds_sine_non_power_of_two is
 
constant FRAC_BITS : natural := PHI_BITS - PHASE_BITS;
constant Q_PHASE_BITS : integer := PHASE_BITS-2; -- Quarter phase takes two bits less to represent
constant Q_LENGTH : unsigned(Q_PHASE_BITS-1 downto 0) := to_unsigned(PHASE_LENGTH/4,Q_PHASE_BITS); -- Quadrant Length
constant Q_THRESH : unsigned(PHI_BITS-1 downto 0) := to_unsigned(2**FRAC_BITS*PHASE_LENGTH/4,PHI_BITS); -- Quadrant Length
 
signal accum : unsigned(PHI_BITS-1 downto 0);
signal q_accum : unsigned(PHI_BITS-1 downto 0);
signal q_accum_next : unsigned(PHI_BITS-1 downto 0);
signal accum_incr : unsigned(PHI_BITS-1 downto 0);
signal accum_folded : unsigned(PHI_BITS-1 downto 0);
signal lut_out : unsigned(AMPL_BITS-1 downto 0);
signal lut_out_neg : unsigned(AMPL_BITS-1 downto 0);
 
signal q_phase : unsigned(Q_PHASE_BITS-1 downto 0);
signal q_phase_sat : unsigned(Q_PHASE_BITS-1 downto 0);
signal q_count : unsigned(1 downto 0);
signal q_count_r1 : unsigned(1 downto 0);
 
begin
 
accum_incr <= unsigned(ftw_i);
q_accum_next <= q_accum + accum_incr;
accum_folded <= q_accum when q_count(0)='0' else
Q_THRESH - q_accum;
q_phase <= u_resize(u_resize_l(accum_folded,PHASE_BITS),q_phase'length); -- Discard the fractional portion
 
process (clk_i, rst_n_i)
begin
if (rst_n_i = '0') then
accum <= (others=>'0');
q_accum <= (others=>'0');
q_count <= (others=>'0');
q_count_r1 <= (others=>'0');
q_phase_sat <= (others=>'0');
elsif (clk_i'event and clk_i = '1') then
if (clk_en_i = '1') then
if (q_accum_next > Q_THRESH) then
q_accum <= q_accum_next - Q_THRESH;
q_count <= q_count+1;
if (q_count="11") then
accum <= (others=>'0');
else
accum <= accum + Q_THRESH;
end if;
else
q_accum <= q_accum_next;
end if;
 
-- Delayed q_count, to match delayed q_phase
q_count_r1 <= q_count;
-- Saturate the quarter phase signal, to avoid overflows when looking up sine values
if (q_phase>=(PHASE_LENGTH/4)) then
q_phase_sat <= to_unsigned(PHASE_LENGTH/4-1,q_phase_sat'length);
else
q_phase_sat <= q_phase;
end if;
end if;
end if;
end process;
 
lut_adr_o <= q_phase_sat;
lut_out <= lut_dat_i;
lut_out_neg <= (not lut_out) + 1;
sine_o <= signed(lut_out_neg) when q_count_r1(1) = '1' else signed(lut_out);
accum_o <= accum+q_accum;
 
end beh;
 
-------------------------------------------------------------------------------
-- Direct Digital Synthesizer Arbitrary Waveform Look Up Table module
-------------------------------------------------------------------------------
--
-- Author: John Clayton
-- Update: Sep. 5, 2013 Copied code from dds_sine to make this module.
--
-- Description
-------------------------------------------------------------------------------
-- This is a direct digital synthesizer module, which uses a full wave lookup
-- to produce waveform samples. The lookup table is external.
-- The lookup table must be 2**PHASE_BITS entries long.
--
-- An address bus is provided for indexing into the look up table, and the
-- response data is input via the lut_dat_i bus.
--
 
library ieee;
use ieee.std_logic_1164.all;
use ieee.numeric_std.all;
 
library work;
use work.convert_pack.all;
 
entity dds_arb is
generic(
PHI_BITS : natural := 24; -- Bits in phase accumulator, must be >= PHASE_BITS
AMPL_BITS : natural := 16;
PHASE_BITS : natural := 10
);
port(
clk_i : in std_logic;
rst_n_i : in std_logic;
clk_en_i : in std_logic;
 
-- Look Up Table interface
lut_adr_o : out unsigned(PHASE_BITS-1 downto 0); -- Full wave LUT
lut_dat_i : in unsigned(AMPL_BITS-1 downto 0);
 
-- Frequency Tuning Word input
ftw_i : in unsigned(PHI_BITS-1 downto 0);
 
-- Outputs
accum_o : out unsigned(PHI_BITS-1 downto 0);
arb_o : out signed(AMPL_BITS-1 downto 0)
);
end dds_arb;
 
architecture beh of dds_arb is
 
-- Constants
constant Q_PHASE_BITS : integer := PHASE_BITS-2; -- Quarter phase takes two bits less to represent
 
-- Signals
signal accum : unsigned(PHI_BITS-1 downto 0);
 
begin
 
process (clk_i, rst_n_i)
begin
if (rst_n_i = '0') then
accum <= (others=>'0');
elsif (clk_i'event and clk_i = '1') then
if (clk_en_i = '1') then
accum <= accum + ftw_i;
end if;
end if;
end process;
 
lut_adr_o <= u_resize_l(accum,PHASE_BITS); -- Discard the fractional portion
accum_o <= accum;
arb_o <= signed(lut_dat_i);
 
end beh;
 
/trunk/README.txt
1,0 → 5,20783
The Quadrature Oscillator generates fixed frequency complex harmonic signals with minimal hardware consumption.
 
The Quadrature Oscillator is given as one module in the VHDL package file "dds_sine_pack.vhd"
Because there is a very long sinewave lookup table inside the "dds_sine_pack.vhd" file, the entity
for the Quadrature Oscillator starts around line 20000.
/trunk/source_new_cordic_pack.zip Cannot display: file marked as a binary type. svn:mime-type = application/octet-stream
/trunk/source_new_cordic_pack.zip
trunk/source_new_cordic_pack.zip Property changes : Added: svn:mime-type ## -0,0 +1 ## +application/octet-stream \ No newline at end of property

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