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feddischso |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%% %%%%
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%%%% File : cordic_iterative_code.m %%%%
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%%%% Project : YAC (Yet Another CORDIC Core) %%%%
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%%%% Creation : Feb. 2014 %%%%
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%%%% Limitations : %%%%
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%%%% Platform : Linux, Mac, Windows %%%%
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%%%% Target : Octave, Matlab %%%%
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%%%% %%%%
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%%%% Author(s): : Christian Haettich %%%%
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%%%% Email : feddischson@opencores.org %%%%
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%%%% %%%%
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%%%% %%%%
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%%%%% %%%%%
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%%%% %%%%
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%%%% Description %%%%
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%%%% Script to create VHDL and C code. %%%%
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%%%% Two functionalities are created: %%%%
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%%%% %%%%
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%%%% - A division by a fixed value %%%%
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%%%% (to remove the cordic gain) %%%%
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%%%% %%%%
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%%%% - Atan/Atanh/Linear lookup table %%%%
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%%%%% %%%%%
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%%%% %%%%
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%%%% TODO %%%%
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%%%% Some documentation and function description %%%%
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%%%% %%%%
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%%%% %%%%
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%%%% %%%%
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%%%% %%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%% %%%%
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%%%% Copyright Notice %%%%
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%%%% %%%%
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%%%% This file is part of YAC - Yet Another CORDIC Core %%%%
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%%%% Copyright (c) 2014, Author(s), All rights reserved. %%%%
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%%%% %%%%
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%%%% YAC is free software; you can redistribute it and/or %%%%
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%%%% modify it under the terms of the GNU Lesser General Public %%%%
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%%%% License as published by the Free Software Foundation; either %%%%
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%%%% version 3.0 of the License, or (at your option) any later version. %%%%
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%%%% %%%%
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%%%% YAC is distributed in the hope that it will be useful, %%%%
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%%%% but WITHOUT ANY WARRANTY; without even the implied warranty of %%%%
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%%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU %%%%
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%%%% Lesser General Public License for more details. %%%%
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%%%% %%%%
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%%%% You should have received a copy of the GNU Lesser General Public %%%%
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%%%% License along with this library. If not, download it from %%%%
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%%%% http://www.gnu.org/licenses/lgpl %%%%
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%%%% %%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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function cordic_iterative_code( outfile )
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if ~exist( 'outfile', 'var' )
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outfile = 'autogen_code.txt';
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end
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fid = fopen( outfile, 'w' );
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% TODO: calculate these values
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K0 = 0.607252935009;
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K1 = 0.207497067763;
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%prod( sqrt( 1-2.^(-2 .* [ 1 : 100000 ] ) ) )
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signs = get_rm_gain_shifts( K0, 30 );
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print_rm_gain_code( fid, signs, K0, 1, 1, 0 );
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signs = get_rm_gain_shifts( K1, 30 );
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print_rm_gain_code( fid, signs, K1, 1, 1, 1 );
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signs = get_rm_gain_shifts( K0, 30 );
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print_rm_gain_code( fid, signs, K0, 1, 0, 0 );
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signs = get_rm_gain_shifts( K1, 30 );
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print_rm_gain_code( fid, signs, K1, 1, 0, 1 );
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MAX_A_WIDTH = 32;
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print_angular_lut( fid, MAX_A_WIDTH );
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fclose( fid );
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end
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function print_angular_lut( fid, MAX_A_WIDTH )
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values = round( atan( 2.^-[0:MAX_A_WIDTH] ) / pi * 2^(MAX_A_WIDTH-1) );
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fprintf( fid, '-- Auto-generated function \n' );
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fprintf( fid, '-- by matlab (see c_octave/cordic_iterative_code.m)\n' );
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fprintf( fid, 'function angular_lut( n : integer; mode : std_logic_vector; ANG_WIDTH : natural ) return signed is\n' );
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fprintf( fid, ' variable result : signed( ANG_WIDTH-1 downto 0 );\n' );
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fprintf( fid, ' variable temp : signed( MAX_A_WIDTH-1 downto 0 );\n' );
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fprintf( fid, ' begin\n' );
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fprintf( fid, ' if mode = VAL_MODE_CIR then\n' );
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fprintf( fid, ' case n is\n' );
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for x = 0 : 10
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val = floor( atan( 2^-x ) * 2^(MAX_A_WIDTH+2-1) );
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fprintf( fid, ' when %d => temp := "', x );
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fprintf( fid, '%c', dec2bin( val, MAX_A_WIDTH+2 ) );
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fprintf( fid, '"; \t-- %d\n', val );
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end
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fprintf( fid, ' when others => temp := to_signed( 2**(MAX_A_WIDTH-1-n), MAX_A_WIDTH );\n' );
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fprintf( fid, ' end case;\n' );
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fprintf( fid, ' elsif mode = VAL_MODE_HYP then\n' );
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fprintf( fid, ' case n is\n' );
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for x = 1 : 10
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val = floor( atanh( 2^-x ) * 2^(MAX_A_WIDTH+2-1) );
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fprintf( fid, ' when %d => temp := "', x );
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fprintf( fid, '%c', dec2bin( val, MAX_A_WIDTH+2 ) );
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fprintf( fid, '"; \t-- %d\n', val);
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end
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fprintf( fid, ' when others => temp := to_signed( 2**(MAX_A_WIDTH-1-n), MAX_A_WIDTH );\n' );
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fprintf( fid, ' end case;\n' );
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fprintf( fid, ' elsif mode = VAL_MODE_LIN then\n' );
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fprintf( fid, ' temp := ( others => ''0'' );\n' );
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fprintf( fid, ' temp( temp''high-1-n downto 0 ) := ( others => ''1'' );\n' );
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fprintf( fid, ' end if;\n' );
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fprintf( fid, ' result := temp( temp''high downto temp''high-result''length+1 );\n' );
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fprintf( fid, ' return result;\n' );
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fprintf( fid, 'end function angular_lut;\n' );
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end
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function print_rm_gain_code( fid, signs, value, force_pos_err, c_or_vhdl, plus_one )
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% Default values for arguments
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if ~exist( 'force_pos_err', 'var' )
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force_neg_err = 0;
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end
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if ~exist( 'c_or_vhdl', 'var' )
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c_or_vhdl = 0;
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end
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val_str = sprintf( '%4.2f', value );
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val_str( val_str == '.' ) = ('_' );
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if c_or_vhdl
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fprintf( fid, '/* Auto-generated procedure to multiply "x" with %f */\n', value );
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fprintf( fid, '/* "shifts" defines the number of shifts, which are used */\n' );
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fprintf( fid, 'switch( shifts )\n{\n' );
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end
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i_shift = 1;
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for x = 1 : length( signs )
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if signs( x ) ~= 0
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tmp = signs( 1 : x );
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err = value - sum( tmp .* 2.^-( 1 : length( tmp ) ) );
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if force_pos_err
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if err < 0
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if( tmp( end ) == 1 )
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tmp( end+1 ) = -1;
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tmp( end-1 ) = 0;
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else
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tmp( end-1 ) = -1;
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tmp( end ) = 0;
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end
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end
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err = value - sum( tmp .* 2.^-( 1 : length( tmp ) ) );
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end
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index = 1 : length( tmp );
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index( tmp == 0 ) = [];
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tmp( tmp == 0 ) = [];
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tmp2 = cell( size ( tmp ) );
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tmp2( tmp == 1 ) = { '+' };
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tmp2( tmp == -1 ) = { '-' };
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if c_or_vhdl
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% C-Code
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if plus_one
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fprintf( fid, ' case %d: x = x ', i_shift );
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else
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fprintf( fid, ' case %d: x = ', i_shift );
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end
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for y = 1 : length( tmp2 )
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fprintf( fid, '%c ( x >> %d ) ', tmp2{ y }, index( y ) );
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end
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fprintf( fid, '; break; /* error: %.10f */ \n', err );
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else
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% VHDL CODE
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fprintf( fid, '\n\n--\n' );
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fprintf( fid, '-- Auto-generated procedure to multiply "a" with %f iteratively\n', value );
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fprintf( fid, '-- a_sh is a temporary register to store the shifted value, and \n' );
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fprintf( fid, '-- sum is a temporary register to sum up the result\n' );
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fprintf( fid, '--\n' );
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fprintf( fid, 'procedure mult_%s_%.2d( signal a : in signed; \n', val_str, i_shift );
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fprintf( fid, ' signal a_sh : inout signed; \n' );
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fprintf( fid, ' signal sum : inout signed; \n' );
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fprintf( fid, ' cnt : in natural ) is \n' );
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fprintf( fid, ' begin\n' );
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fprintf( fid, ' case cnt is\n' );
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if plus_one
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fprintf( fid, ' when 0 => sum <= a;\n' );
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else
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fprintf( fid, ' when 0 => sum <= to_signed( 0, sum''length );\n' );
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end
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fprintf( fid, ' a_sh <= SHIFT_RIGHT( a, %d ); \n', index( 1 ) );
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fprintf( fid, ' when 1 => sum <= sum %c a_sh; \n', tmp2{ 1 } );
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for y = 2 : length( tmp2 )
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fprintf( fid, ' a_sh <= SHIFT_RIGHT( a, %d );\n', index( y ) );
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fprintf( fid, ' when %3.d => sum <= sum %c a_sh; \n', y, tmp2{ y } );
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end
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fprintf( fid, ' when others => sum <= sum;\n' );
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fprintf( fid, ' end case;\n' );
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fprintf( fid, 'end procedure mult_%s_%.2d;\n', val_str, i_shift );
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end
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i_shift = i_shift+1;
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end
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| 236 |
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end
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if c_or_vhdl
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fprintf( fid, ' default: x = x; break;\n}\n' );
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end
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| 240 |
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| 241 |
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| 242 |
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if ~c_or_vhdl
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| 243 |
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fprintf( fid, '\n\n--\n' );
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| 244 |
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fprintf( fid, '-- Auto-generated procedure to multiply "a" with %f iteratively\n', value );
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fprintf( fid, '-- a_sh is a temporary register to store the shifted value, and \n' );
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| 246 |
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fprintf( fid, '-- sum is a temporary register to sum up the result\n' );
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| 247 |
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fprintf( fid, '--\n' );
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| 248 |
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fprintf( fid, 'procedure mult_%s( signal a : in signed; \n', val_str );
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| 249 |
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fprintf( fid, ' signal a_sh : inout signed; \n' );
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| 250 |
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fprintf( fid, ' signal sum : inout signed; \n' );
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| 251 |
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fprintf( fid, ' cnt : in natural; \n' );
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| 252 |
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fprintf( fid, ' constant RM_GAIN : in natural ) is \n' );
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| 253 |
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fprintf( fid, ' begin\n' );
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| 254 |
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fprintf( fid, ' case RM_GAIN is\n' );
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| 255 |
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for y = 1 : length( tmp2 )
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| 256 |
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fprintf( fid, ' when %d => mult_%s_%.2d( a, a_sh, sum, cnt );\n', y, val_str, y );
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end
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| 258 |
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fprintf( fid, ' when others => mult_%s_%.2d( a, a_sh, sum, cnt );\n', val_str, y );
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| 259 |
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fprintf( fid, ' end case;\n' );
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| 260 |
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fprintf( fid, 'end procedure mult_%s;\n', val_str );
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| 261 |
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end
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| 262 |
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| 263 |
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| 264 |
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end
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| 265 |
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| 266 |
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function signs = get_rm_gain_shifts( value, N_shifts )
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| 267 |
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%N_steps = 50;
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| 268 |
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%signs = zeros( 1, N_steps );
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| 269 |
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signs = [ ];
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| 270 |
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from_p_n = 1; % comming from pos or neg
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| 271 |
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| 272 |
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prev_pos_err = inf;
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| 273 |
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prev_neg_err = inf;
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| 274 |
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i_shift = 0;
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| 275 |
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x = 0;
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| 276 |
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| 277 |
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while i_shift < N_shifts
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| 278 |
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x = x + 1;
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| 279 |
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if isempty( signs )
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| 280 |
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tmp = 0;
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| 281 |
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else
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| 282 |
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tmp = sum( signs .* 2.^-( 1 : length( signs ) ) );
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| 283 |
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end;
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| 284 |
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| 285 |
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pos_err = value - ( tmp + 2^-x );
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| 286 |
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neg_err = value - ( tmp - 2^-x );
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| 287 |
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signs( end+1 ) = 0;
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| 288 |
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if from_p_n == 1 && pos_err < 0 ...
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| 289 |
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|| from_p_n == 0 && neg_err > 0
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| 290 |
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prev_pos_err = pos_err;
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| 291 |
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prev_neg_err = neg_err;
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| 292 |
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continue
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| 293 |
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end
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| 294 |
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i_shift = i_shift+1;
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| 295 |
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| 296 |
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if from_p_n == 1 && abs( prev_pos_err ) < abs( pos_err )
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| 297 |
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signs( x-1 ) = 1;
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| 298 |
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from_p_n = 0;
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| 299 |
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neg_err2 = value - ( tmp - 2^-x );
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| 300 |
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if neg_err2 < 0
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| 301 |
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signs( x ) = -1;
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| 302 |
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end
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| 303 |
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| 304 |
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elseif from_p_n == 0 && abs( prev_neg_err ) < abs( neg_err )
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| 305 |
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signs( x-1 ) = -1;
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| 306 |
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from_p_n = 1;
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| 307 |
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pos_err2 = value - ( tmp + 2^-x );
|
| 308 |
|
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if pos_err2 > 0
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| 309 |
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signs( x ) = 1;
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| 310 |
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end
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| 311 |
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| 312 |
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| 313 |
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elseif from_p_n == 1 && abs( prev_pos_err ) >= abs( pos_err )
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| 314 |
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signs( x ) = 1;
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| 315 |
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|
| 316 |
|
|
elseif from_p_n == 0 && abs( prev_pos_err ) >= abs( pos_err )
|
| 317 |
|
|
signs( x ) = -1;
|
| 318 |
|
|
|
| 319 |
|
|
end
|
| 320 |
|
|
prev_pos_err = pos_err;
|
| 321 |
|
|
prev_neg_err = neg_err;
|
| 322 |
|
|
|
| 323 |
|
|
end
|
| 324 |
|
|
|
| 325 |
|
|
end
|
| 326 |
|
|
|
| 327 |
|
|
|
| 328 |
|
|
|
| 329 |
|
|
|
| 330 |
|
|
|
