| 1 |
2 |
feddischso |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
| 2 |
|
|
%%%% %%%%
|
| 3 |
|
|
%%%% File : cordic_iterative_code.m %%%%
|
| 4 |
|
|
%%%% Project : YAC (Yet Another CORDIC Core) %%%%
|
| 5 |
|
|
%%%% Creation : Feb. 2014 %%%%
|
| 6 |
|
|
%%%% Limitations : %%%%
|
| 7 |
|
|
%%%% Platform : Linux, Mac, Windows %%%%
|
| 8 |
|
|
%%%% Target : Octave, Matlab %%%%
|
| 9 |
|
|
%%%% %%%%
|
| 10 |
|
|
%%%% Author(s): : Christian Haettich %%%%
|
| 11 |
|
|
%%%% Email : feddischson@opencores.org %%%%
|
| 12 |
|
|
%%%% %%%%
|
| 13 |
|
|
%%%% %%%%
|
| 14 |
|
|
%%%%% %%%%%
|
| 15 |
|
|
%%%% %%%%
|
| 16 |
|
|
%%%% Description %%%%
|
| 17 |
|
|
%%%% Script to create VHDL and C code. %%%%
|
| 18 |
|
|
%%%% Two functionalities are created: %%%%
|
| 19 |
|
|
%%%% %%%%
|
| 20 |
|
|
%%%% - A division by a fixed value %%%%
|
| 21 |
|
|
%%%% (to remove the cordic gain) %%%%
|
| 22 |
|
|
%%%% %%%%
|
| 23 |
|
|
%%%% - Atan/Atanh/Linear lookup table %%%%
|
| 24 |
|
|
%%%%% %%%%%
|
| 25 |
|
|
%%%% %%%%
|
| 26 |
|
|
%%%% TODO %%%%
|
| 27 |
|
|
%%%% Some documentation and function description %%%%
|
| 28 |
|
|
%%%% %%%%
|
| 29 |
|
|
%%%% %%%%
|
| 30 |
|
|
%%%% %%%%
|
| 31 |
|
|
%%%% %%%%
|
| 32 |
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
| 33 |
|
|
%%%% %%%%
|
| 34 |
|
|
%%%% Copyright Notice %%%%
|
| 35 |
|
|
%%%% %%%%
|
| 36 |
|
|
%%%% This file is part of YAC - Yet Another CORDIC Core %%%%
|
| 37 |
|
|
%%%% Copyright (c) 2014, Author(s), All rights reserved. %%%%
|
| 38 |
|
|
%%%% %%%%
|
| 39 |
|
|
%%%% YAC is free software; you can redistribute it and/or %%%%
|
| 40 |
|
|
%%%% modify it under the terms of the GNU Lesser General Public %%%%
|
| 41 |
|
|
%%%% License as published by the Free Software Foundation; either %%%%
|
| 42 |
|
|
%%%% version 3.0 of the License, or (at your option) any later version. %%%%
|
| 43 |
|
|
%%%% %%%%
|
| 44 |
|
|
%%%% YAC is distributed in the hope that it will be useful, %%%%
|
| 45 |
|
|
%%%% but WITHOUT ANY WARRANTY; without even the implied warranty of %%%%
|
| 46 |
|
|
%%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU %%%%
|
| 47 |
|
|
%%%% Lesser General Public License for more details. %%%%
|
| 48 |
|
|
%%%% %%%%
|
| 49 |
|
|
%%%% You should have received a copy of the GNU Lesser General Public %%%%
|
| 50 |
|
|
%%%% License along with this library. If not, download it from %%%%
|
| 51 |
|
|
%%%% http://www.gnu.org/licenses/lgpl %%%%
|
| 52 |
|
|
%%%% %%%%
|
| 53 |
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
| 54 |
|
|
|
| 55 |
|
|
|
| 56 |
|
|
|
| 57 |
|
|
|
| 58 |
|
|
|
| 59 |
|
|
|
| 60 |
|
|
function cordic_iterative_code( outfile )
|
| 61 |
|
|
|
| 62 |
|
|
if ~exist( 'outfile', 'var' )
|
| 63 |
|
|
outfile = 'autogen_code.txt';
|
| 64 |
|
|
end
|
| 65 |
|
|
|
| 66 |
|
|
fid = fopen( outfile, 'w' );
|
| 67 |
|
|
|
| 68 |
|
|
% TODO: calculate these values
|
| 69 |
|
|
K0 = 0.607252935009;
|
| 70 |
|
|
K1 = 0.207497067763;
|
| 71 |
3 |
feddischso |
<<<<<<< HEAD
|
| 72 |
2 |
feddischso |
%prod( sqrt( 1-2.^(-2 .* [ 1 : 100000 ] ) ) )
|
| 73 |
|
|
|
| 74 |
3 |
feddischso |
=======
|
| 75 |
|
|
>>>>>>> initial commit
|
| 76 |
2 |
feddischso |
|
| 77 |
|
|
signs = get_rm_gain_shifts( K0, 30 );
|
| 78 |
|
|
print_rm_gain_code( fid, signs, K0, 1, 1, 0 );
|
| 79 |
|
|
|
| 80 |
|
|
signs = get_rm_gain_shifts( K1, 30 );
|
| 81 |
|
|
print_rm_gain_code( fid, signs, K1, 1, 1, 1 );
|
| 82 |
|
|
|
| 83 |
|
|
signs = get_rm_gain_shifts( K0, 30 );
|
| 84 |
|
|
print_rm_gain_code( fid, signs, K0, 1, 0, 0 );
|
| 85 |
|
|
|
| 86 |
|
|
signs = get_rm_gain_shifts( K1, 30 );
|
| 87 |
|
|
print_rm_gain_code( fid, signs, K1, 1, 0, 1 );
|
| 88 |
|
|
|
| 89 |
|
|
MAX_A_WIDTH = 32;
|
| 90 |
3 |
feddischso |
<<<<<<< HEAD
|
| 91 |
2 |
feddischso |
print_angular_lut( fid, MAX_A_WIDTH );
|
| 92 |
3 |
feddischso |
=======
|
| 93 |
|
|
print_angular_lut( fid, MAX_A_WIDTH )
|
| 94 |
|
|
>>>>>>> initial commit
|
| 95 |
2 |
feddischso |
|
| 96 |
|
|
|
| 97 |
|
|
fclose( fid );
|
| 98 |
|
|
|
| 99 |
|
|
end
|
| 100 |
|
|
|
| 101 |
|
|
|
| 102 |
|
|
|
| 103 |
|
|
|
| 104 |
|
|
function print_angular_lut( fid, MAX_A_WIDTH )
|
| 105 |
|
|
|
| 106 |
|
|
|
| 107 |
|
|
values = round( atan( 2.^-[0:MAX_A_WIDTH] ) / pi * 2^(MAX_A_WIDTH-1) );
|
| 108 |
|
|
|
| 109 |
|
|
|
| 110 |
|
|
fprintf( fid, '-- Auto-generated function \n' );
|
| 111 |
|
|
fprintf( fid, '-- by matlab (see c_octave/cordic_iterative_code.m)\n' );
|
| 112 |
|
|
fprintf( fid, 'function angular_lut( n : integer; mode : std_logic_vector; ANG_WIDTH : natural ) return signed is\n' );
|
| 113 |
|
|
fprintf( fid, ' variable result : signed( ANG_WIDTH-1 downto 0 );\n' );
|
| 114 |
|
|
fprintf( fid, ' variable temp : signed( MAX_A_WIDTH-1 downto 0 );\n' );
|
| 115 |
|
|
fprintf( fid, ' begin\n' );
|
| 116 |
|
|
fprintf( fid, ' if mode = VAL_MODE_CIR then\n' );
|
| 117 |
|
|
fprintf( fid, ' case n is\n' );
|
| 118 |
|
|
for x = 0 : 10
|
| 119 |
|
|
val = floor( atan( 2^-x ) * 2^(MAX_A_WIDTH+2-1) );
|
| 120 |
|
|
fprintf( fid, ' when %d => temp := "', x );
|
| 121 |
|
|
fprintf( fid, '%c', dec2bin( val, MAX_A_WIDTH+2 ) );
|
| 122 |
|
|
fprintf( fid, '"; \t-- %d\n', val );
|
| 123 |
|
|
end
|
| 124 |
|
|
fprintf( fid, ' when others => temp := to_signed( 2**(MAX_A_WIDTH-1-n), MAX_A_WIDTH );\n' );
|
| 125 |
|
|
fprintf( fid, ' end case;\n' );
|
| 126 |
|
|
fprintf( fid, ' elsif mode = VAL_MODE_HYP then\n' );
|
| 127 |
|
|
fprintf( fid, ' case n is\n' );
|
| 128 |
|
|
for x = 1 : 10
|
| 129 |
|
|
val = floor( atanh( 2^-x ) * 2^(MAX_A_WIDTH+2-1) );
|
| 130 |
|
|
fprintf( fid, ' when %d => temp := "', x );
|
| 131 |
|
|
fprintf( fid, '%c', dec2bin( val, MAX_A_WIDTH+2 ) );
|
| 132 |
|
|
fprintf( fid, '"; \t-- %d\n', val);
|
| 133 |
|
|
end
|
| 134 |
|
|
fprintf( fid, ' when others => temp := to_signed( 2**(MAX_A_WIDTH-1-n), MAX_A_WIDTH );\n' );
|
| 135 |
|
|
fprintf( fid, ' end case;\n' );
|
| 136 |
|
|
fprintf( fid, ' elsif mode = VAL_MODE_LIN then\n' );
|
| 137 |
|
|
fprintf( fid, ' temp := ( others => ''0'' );\n' );
|
| 138 |
|
|
fprintf( fid, ' temp( temp''high-1-n downto 0 ) := ( others => ''1'' );\n' );
|
| 139 |
|
|
fprintf( fid, ' end if;\n' );
|
| 140 |
|
|
fprintf( fid, ' result := temp( temp''high downto temp''high-result''length+1 );\n' );
|
| 141 |
|
|
fprintf( fid, ' return result;\n' );
|
| 142 |
|
|
fprintf( fid, 'end function angular_lut;\n' );
|
| 143 |
|
|
end
|
| 144 |
|
|
|
| 145 |
|
|
|
| 146 |
|
|
function print_rm_gain_code( fid, signs, value, force_pos_err, c_or_vhdl, plus_one )
|
| 147 |
|
|
|
| 148 |
|
|
|
| 149 |
|
|
% Default values for arguments
|
| 150 |
|
|
if ~exist( 'force_pos_err', 'var' )
|
| 151 |
|
|
force_neg_err = 0;
|
| 152 |
|
|
end
|
| 153 |
|
|
|
| 154 |
|
|
if ~exist( 'c_or_vhdl', 'var' )
|
| 155 |
|
|
c_or_vhdl = 0;
|
| 156 |
|
|
end
|
| 157 |
|
|
|
| 158 |
|
|
val_str = sprintf( '%4.2f', value );
|
| 159 |
|
|
val_str( val_str == '.' ) = ('_' );
|
| 160 |
|
|
|
| 161 |
|
|
if c_or_vhdl
|
| 162 |
|
|
fprintf( fid, '/* Auto-generated procedure to multiply "x" with %f */\n', value );
|
| 163 |
|
|
fprintf( fid, '/* "shifts" defines the number of shifts, which are used */\n' );
|
| 164 |
|
|
fprintf( fid, 'switch( shifts )\n{\n' );
|
| 165 |
|
|
end
|
| 166 |
|
|
i_shift = 1;
|
| 167 |
|
|
for x = 1 : length( signs )
|
| 168 |
|
|
if signs( x ) ~= 0
|
| 169 |
|
|
|
| 170 |
|
|
tmp = signs( 1 : x );
|
| 171 |
|
|
|
| 172 |
|
|
|
| 173 |
|
|
err = value - sum( tmp .* 2.^-( 1 : length( tmp ) ) );
|
| 174 |
|
|
if force_pos_err
|
| 175 |
|
|
if err < 0
|
| 176 |
|
|
|
| 177 |
|
|
if( tmp( end ) == 1 )
|
| 178 |
|
|
tmp( end+1 ) = -1;
|
| 179 |
|
|
tmp( end-1 ) = 0;
|
| 180 |
|
|
else
|
| 181 |
|
|
tmp( end-1 ) = -1;
|
| 182 |
|
|
tmp( end ) = 0;
|
| 183 |
|
|
end
|
| 184 |
|
|
end
|
| 185 |
|
|
err = value - sum( tmp .* 2.^-( 1 : length( tmp ) ) );
|
| 186 |
|
|
end
|
| 187 |
|
|
|
| 188 |
|
|
index = 1 : length( tmp );
|
| 189 |
|
|
index( tmp == 0 ) = [];
|
| 190 |
|
|
tmp( tmp == 0 ) = [];
|
| 191 |
|
|
tmp2 = cell( size ( tmp ) );
|
| 192 |
|
|
tmp2( tmp == 1 ) = { '+' };
|
| 193 |
|
|
tmp2( tmp == -1 ) = { '-' };
|
| 194 |
|
|
|
| 195 |
|
|
if c_or_vhdl
|
| 196 |
|
|
|
| 197 |
|
|
% C-Code
|
| 198 |
|
|
if plus_one
|
| 199 |
|
|
fprintf( fid, ' case %d: x = x ', i_shift );
|
| 200 |
|
|
else
|
| 201 |
|
|
fprintf( fid, ' case %d: x = ', i_shift );
|
| 202 |
|
|
end
|
| 203 |
|
|
|
| 204 |
|
|
for y = 1 : length( tmp2 )
|
| 205 |
3 |
feddischso |
<<<<<<< HEAD
|
| 206 |
2 |
feddischso |
fprintf( fid, '%c ( x >> %d ) ', tmp2{ y }, index( y ) );
|
| 207 |
3 |
feddischso |
=======
|
| 208 |
|
|
fprintf( fid, '%c ( x >> %d ) ', tmp2{ y }, index( y ) )
|
| 209 |
|
|
>>>>>>> initial commit
|
| 210 |
2 |
feddischso |
end
|
| 211 |
|
|
fprintf( fid, '; break; /* error: %.10f */ \n', err );
|
| 212 |
|
|
else
|
| 213 |
|
|
|
| 214 |
|
|
% VHDL CODE
|
| 215 |
|
|
|
| 216 |
|
|
fprintf( fid, '\n\n--\n' );
|
| 217 |
|
|
fprintf( fid, '-- Auto-generated procedure to multiply "a" with %f iteratively\n', value );
|
| 218 |
|
|
fprintf( fid, '-- a_sh is a temporary register to store the shifted value, and \n' );
|
| 219 |
|
|
fprintf( fid, '-- sum is a temporary register to sum up the result\n' );
|
| 220 |
|
|
fprintf( fid, '--\n' );
|
| 221 |
|
|
fprintf( fid, 'procedure mult_%s_%.2d( signal a : in signed; \n', val_str, i_shift );
|
| 222 |
|
|
fprintf( fid, ' signal a_sh : inout signed; \n' );
|
| 223 |
|
|
fprintf( fid, ' signal sum : inout signed; \n' );
|
| 224 |
|
|
fprintf( fid, ' cnt : in natural ) is \n' );
|
| 225 |
|
|
fprintf( fid, ' begin\n' );
|
| 226 |
|
|
fprintf( fid, ' case cnt is\n' );
|
| 227 |
|
|
|
| 228 |
|
|
if plus_one
|
| 229 |
|
|
fprintf( fid, ' when 0 => sum <= a;\n' );
|
| 230 |
|
|
else
|
| 231 |
|
|
fprintf( fid, ' when 0 => sum <= to_signed( 0, sum''length );\n' );
|
| 232 |
|
|
end
|
| 233 |
|
|
fprintf( fid, ' a_sh <= SHIFT_RIGHT( a, %d ); \n', index( 1 ) );
|
| 234 |
|
|
fprintf( fid, ' when 1 => sum <= sum %c a_sh; \n', tmp2{ 1 } );
|
| 235 |
|
|
|
| 236 |
|
|
for y = 2 : length( tmp2 )
|
| 237 |
|
|
fprintf( fid, ' a_sh <= SHIFT_RIGHT( a, %d );\n', index( y ) );
|
| 238 |
|
|
fprintf( fid, ' when %3.d => sum <= sum %c a_sh; \n', y, tmp2{ y } );
|
| 239 |
|
|
end
|
| 240 |
|
|
fprintf( fid, ' when others => sum <= sum;\n' );
|
| 241 |
|
|
fprintf( fid, ' end case;\n' );
|
| 242 |
|
|
fprintf( fid, 'end procedure mult_%s_%.2d;\n', val_str, i_shift );
|
| 243 |
|
|
end
|
| 244 |
|
|
i_shift = i_shift+1;
|
| 245 |
|
|
end
|
| 246 |
|
|
|
| 247 |
|
|
end
|
| 248 |
|
|
if c_or_vhdl
|
| 249 |
|
|
fprintf( fid, ' default: x = x; break;\n}\n' );
|
| 250 |
|
|
end
|
| 251 |
|
|
|
| 252 |
|
|
|
| 253 |
|
|
if ~c_or_vhdl
|
| 254 |
|
|
fprintf( fid, '\n\n--\n' );
|
| 255 |
|
|
fprintf( fid, '-- Auto-generated procedure to multiply "a" with %f iteratively\n', value );
|
| 256 |
|
|
fprintf( fid, '-- a_sh is a temporary register to store the shifted value, and \n' );
|
| 257 |
|
|
fprintf( fid, '-- sum is a temporary register to sum up the result\n' );
|
| 258 |
|
|
fprintf( fid, '--\n' );
|
| 259 |
|
|
fprintf( fid, 'procedure mult_%s( signal a : in signed; \n', val_str );
|
| 260 |
|
|
fprintf( fid, ' signal a_sh : inout signed; \n' );
|
| 261 |
|
|
fprintf( fid, ' signal sum : inout signed; \n' );
|
| 262 |
|
|
fprintf( fid, ' cnt : in natural; \n' );
|
| 263 |
|
|
fprintf( fid, ' constant RM_GAIN : in natural ) is \n' );
|
| 264 |
|
|
fprintf( fid, ' begin\n' );
|
| 265 |
|
|
fprintf( fid, ' case RM_GAIN is\n' );
|
| 266 |
|
|
for y = 1 : length( tmp2 )
|
| 267 |
|
|
fprintf( fid, ' when %d => mult_%s_%.2d( a, a_sh, sum, cnt );\n', y, val_str, y );
|
| 268 |
|
|
end
|
| 269 |
|
|
fprintf( fid, ' when others => mult_%s_%.2d( a, a_sh, sum, cnt );\n', val_str, y );
|
| 270 |
|
|
fprintf( fid, ' end case;\n' );
|
| 271 |
|
|
fprintf( fid, 'end procedure mult_%s;\n', val_str );
|
| 272 |
|
|
end
|
| 273 |
|
|
|
| 274 |
|
|
|
| 275 |
|
|
end
|
| 276 |
|
|
|
| 277 |
|
|
function signs = get_rm_gain_shifts( value, N_shifts )
|
| 278 |
|
|
%N_steps = 50;
|
| 279 |
|
|
%signs = zeros( 1, N_steps );
|
| 280 |
|
|
signs = [ ];
|
| 281 |
|
|
from_p_n = 1; % comming from pos or neg
|
| 282 |
|
|
|
| 283 |
|
|
prev_pos_err = inf;
|
| 284 |
|
|
prev_neg_err = inf;
|
| 285 |
|
|
i_shift = 0;
|
| 286 |
|
|
x = 0;
|
| 287 |
|
|
|
| 288 |
|
|
while i_shift < N_shifts
|
| 289 |
|
|
x = x + 1;
|
| 290 |
|
|
if isempty( signs )
|
| 291 |
|
|
tmp = 0;
|
| 292 |
|
|
else
|
| 293 |
|
|
tmp = sum( signs .* 2.^-( 1 : length( signs ) ) );
|
| 294 |
|
|
end;
|
| 295 |
|
|
|
| 296 |
|
|
pos_err = value - ( tmp + 2^-x );
|
| 297 |
|
|
neg_err = value - ( tmp - 2^-x );
|
| 298 |
|
|
signs( end+1 ) = 0;
|
| 299 |
|
|
if from_p_n == 1 && pos_err < 0 ...
|
| 300 |
|
|
|| from_p_n == 0 && neg_err > 0
|
| 301 |
|
|
prev_pos_err = pos_err;
|
| 302 |
|
|
prev_neg_err = neg_err;
|
| 303 |
|
|
continue
|
| 304 |
|
|
end
|
| 305 |
|
|
i_shift = i_shift+1;
|
| 306 |
|
|
|
| 307 |
|
|
if from_p_n == 1 && abs( prev_pos_err ) < abs( pos_err )
|
| 308 |
|
|
signs( x-1 ) = 1;
|
| 309 |
|
|
from_p_n = 0;
|
| 310 |
|
|
neg_err2 = value - ( tmp - 2^-x );
|
| 311 |
|
|
if neg_err2 < 0
|
| 312 |
|
|
signs( x ) = -1;
|
| 313 |
|
|
end
|
| 314 |
|
|
|
| 315 |
|
|
elseif from_p_n == 0 && abs( prev_neg_err ) < abs( neg_err )
|
| 316 |
|
|
signs( x-1 ) = -1;
|
| 317 |
|
|
from_p_n = 1;
|
| 318 |
|
|
pos_err2 = value - ( tmp + 2^-x );
|
| 319 |
|
|
if pos_err2 > 0
|
| 320 |
|
|
signs( x ) = 1;
|
| 321 |
|
|
end
|
| 322 |
|
|
|
| 323 |
|
|
|
| 324 |
|
|
elseif from_p_n == 1 && abs( prev_pos_err ) >= abs( pos_err )
|
| 325 |
|
|
signs( x ) = 1;
|
| 326 |
|
|
|
| 327 |
|
|
elseif from_p_n == 0 && abs( prev_pos_err ) >= abs( pos_err )
|
| 328 |
|
|
signs( x ) = -1;
|
| 329 |
|
|
|
| 330 |
|
|
end
|
| 331 |
|
|
prev_pos_err = pos_err;
|
| 332 |
|
|
prev_neg_err = neg_err;
|
| 333 |
|
|
|
| 334 |
|
|
end
|
| 335 |
|
|
|
| 336 |
|
|
end
|
| 337 |
|
|
|
| 338 |
|
|
|
| 339 |
|
|
|
| 340 |
|
|
|
| 341 |
|
|
|
