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URL https://opencores.org/ocsvn/yac/yac/trunk

Subversion Repositories yac

Compare Revisions

  • This comparison shows the changes necessary to convert path
    /yac/trunk/c_octave
    from Rev 3 to Rev 4
    Reverse comparison

Rev 3 → Rev 4

/cordic_iterative.c
60,10 → 60,14
 
/* enable debug output */
<<<<<<< HEAD
<<<<<<< HEAD
#define PRINT_DEBUG 0
=======
#define PRINT_DEBUG 0
>>>>>>> initial commit
=======
#define PRINT_DEBUG 0
>>>>>>> Updated C and RTL model as well as the documentation
 
 
/* #define CORDIC_ROUNDING 0.5 */
85,6 → 89,7
 
 
<<<<<<< HEAD
<<<<<<< HEAD
=======
 
long long int ov_check( long long int * value, long long int length )
102,6 → 107,8
 
 
>>>>>>> initial commit
=======
>>>>>>> Updated C and RTL model as well as the documentation
void cordic_int( long long int x_i,
long long int y_i,
long long int a_i,
125,11 → 132,16
long long int *a,
int mode,
<<<<<<< HEAD
<<<<<<< HEAD
int A_WIDTH,
int XY_WIDTH );
=======
int A_WIDTH );
>>>>>>> initial commit
=======
int A_WIDTH,
int XY_WIDTH );
>>>>>>> Updated C and RTL model as well as the documentation
void cordic_int_rm_gain( long long int *x,
long long int *y,
int mode,
259,10 → 271,14
long long int s;
int ov;
<<<<<<< HEAD
<<<<<<< HEAD
int it = 0;
=======
int it;
>>>>>>> initial commit
=======
int it = 0;
>>>>>>> Updated C and RTL model as well as the documentation
 
 
273,6 → 289,7
cordic_int_dbg( x_i, y_i, a_i, mode, 0, "input" );
 
<<<<<<< HEAD
<<<<<<< HEAD
if( !cordic_int_init( &x_i, &y_i, &a_i, mode, A_WIDTH, XY_WIDTH ) )
{
 
284,10 → 301,19
cordic_int_init( &x_i, &y_i, &a_i, mode, A_WIDTH );
 
it = cordic_int_rotate( &x_i, &y_i, &a_i, mode, A_WIDTH );
=======
if( !cordic_int_init( &x_i, &y_i, &a_i, mode, A_WIDTH, XY_WIDTH ) )
{
>>>>>>> Updated C and RTL model as well as the documentation
 
cordic_int_rm_gain( &x_i, &y_i, mode, RM_GAIN );
it = cordic_int_rotate( &x_i, &y_i, &a_i, mode, A_WIDTH );
 
<<<<<<< HEAD
>>>>>>> initial commit
=======
cordic_int_rm_gain( &x_i, &y_i, mode, RM_GAIN );
}
>>>>>>> Updated C and RTL model as well as the documentation
 
*x_o = x_i;
*y_o = y_i;
307,11 → 333,16
long long int *a,
int mode,
<<<<<<< HEAD
<<<<<<< HEAD
int A_WIDTH,
int XY_WIDTH )
=======
int A_WIDTH )
>>>>>>> initial commit
=======
int A_WIDTH,
int XY_WIDTH )
>>>>>>> Updated C and RTL model as well as the documentation
{
int already_done = 0;
 
319,6 → 350,7
long long int PI = ( long long int )( M_PI * pow( 2, A_WIDTH-1 ) + 0.5 );
long long int PI_H = (long long int)( M_PI * pow( 2, A_WIDTH-2 ) + 0.5 );
<<<<<<< HEAD
<<<<<<< HEAD
long long int XY_MAX = pow( 2, XY_WIDTH-1 )-1;
330,6 → 362,14
cordic_int_dbg( *x, *y, *a, mode, 0, "before init" );
>>>>>>> initial commit
=======
long long int XY_MAX = pow( 2, XY_WIDTH-1 )-1;
cordic_int_dbg( *x, *y, *a, mode, 0, "before init" );
 
 
>>>>>>> Updated C and RTL model as well as the documentation
/* Circular rotation mode */
if( 0 == ( mode & C_FLAG_VEC_ROT ) &&
C_MODE_CIR == ( mode & C_MODE_MSK ) )
365,6 → 405,9
C_MODE_CIR == ( mode & C_MODE_MSK ) )
{
<<<<<<< HEAD
<<<<<<< HEAD
=======
>>>>>>> Updated C and RTL model as well as the documentation
 
if( *x == 0 && *y == 0 )
{
434,9 → 477,12
#endif
}
else if( *x < 0 && *y >= 0 )
<<<<<<< HEAD
=======
if( *x < 0 && *y > 0 )
>>>>>>> initial commit
=======
>>>>>>> Updated C and RTL model as well as the documentation
{
*x = -*x;
*y = -*y;
443,6 → 489,7
*a = PI;
#if PRINT_DEBUG > 0
<<<<<<< HEAD
<<<<<<< HEAD
PRINT("pre-rotation from second to the fourth quadrant\n" );
#endif
}
453,6 → 500,12
}
else if( *x < 0 && *y < 0 )
>>>>>>> initial commit
=======
PRINT("pre-rotation from second to the fourth quadrant\n" );
#endif
}
else if( *x < 0 && *y < 0 )
>>>>>>> Updated C and RTL model as well as the documentation
{
*x = -*x;
*y = -*y;
459,6 → 512,7
*a = -PI;
#if PRINT_DEBUG > 0
<<<<<<< HEAD
<<<<<<< HEAD
PRINT("pre-rotation from third to first quadrand\n" );
#endif
}
472,6 → 526,11
already_done = 1;
}
>>>>>>> initial commit
=======
PRINT("pre-rotation from third to first quadrand\n" );
#endif
}
>>>>>>> Updated C and RTL model as well as the documentation
else
*a = 0;
}
489,10 → 548,14
 
cordic_int_dbg( *x, *y, *a, mode, 0, "after init" );
<<<<<<< HEAD
<<<<<<< HEAD
return already_done;
=======
>>>>>>> initial commit
=======
return already_done;
>>>>>>> Updated C and RTL model as well as the documentation
}
 
 
610,10 → 673,14
/* abort condition */
if( ( mode & C_FLAG_VEC_ROT ) == 0 &&
<<<<<<< HEAD
<<<<<<< HEAD
( *a == 0 /* || *a == -1 */ ) )
=======
( *a == 0 || *a == -1 ) )
>>>>>>> initial commit
=======
( *a == 0 /* || *a == -1 */ ) )
>>>>>>> Updated C and RTL model as well as the documentation
break;
if( ( mode & C_FLAG_VEC_ROT ) == 0 &&
( *a == alst ) )
621,10 → 688,14
if( ( mode & C_FLAG_VEC_ROT ) != 0 &&
<<<<<<< HEAD
<<<<<<< HEAD
( *y == 0 /*|| *y == -1 */ ) )
=======
( *y == 0 || *y == -1 ) )
>>>>>>> initial commit
=======
( *y == 0 /*|| *y == -1 */ ) )
>>>>>>> Updated C and RTL model as well as the documentation
break;
if( ( mode & C_FLAG_VEC_ROT ) != 0 &&
( *y == ylst ) )
/cordic_iterative_code.m
69,11 → 69,16
K0 = 0.607252935009;
K1 = 0.207497067763;
<<<<<<< HEAD
<<<<<<< HEAD
%prod( sqrt( 1-2.^(-2 .* [ 1 : 100000 ] ) ) )
 
=======
>>>>>>> initial commit
=======
%prod( sqrt( 1-2.^(-2 .* [ 1 : 100000 ] ) ) )
 
>>>>>>> Updated C and RTL model as well as the documentation
 
signs = get_rm_gain_shifts( K0, 30 );
print_rm_gain_code( fid, signs, K0, 1, 1, 0 );
 
88,10 → 93,14
 
MAX_A_WIDTH = 32;
<<<<<<< HEAD
<<<<<<< HEAD
print_angular_lut( fid, MAX_A_WIDTH );
=======
print_angular_lut( fid, MAX_A_WIDTH )
>>>>>>> initial commit
=======
print_angular_lut( fid, MAX_A_WIDTH );
>>>>>>> Updated C and RTL model as well as the documentation
 
 
fclose( fid );
203,10 → 212,14
for y = 1 : length( tmp2 )
<<<<<<< HEAD
<<<<<<< HEAD
fprintf( fid, '%c ( x >> %d ) ', tmp2{ y }, index( y ) );
=======
fprintf( fid, '%c ( x >> %d ) ', tmp2{ y }, index( y ) )
>>>>>>> initial commit
=======
fprintf( fid, '%c ( x >> %d ) ', tmp2{ y }, index( y ) );
>>>>>>> Updated C and RTL model as well as the documentation
end
fprintf( fid, '; break; /* error: %.10f */ \n', err );
else
/cordic_iterative_test.m
21,6 → 21,9
%%%% implementation. %%%%
%%%% %%%%
<<<<<<< HEAD
<<<<<<< HEAD
=======
>>>>>>> Updated C and RTL model as well as the documentation
%%%% Three tests are implemented: %%%%
%%%% - Random test values %%%%
%%%% - Linear increasing values %%%%
29,17 → 32,24
%%%% %%%%
%%%% Please do 'mex cordic_iterative.c' to create %%%%
%%%% the cordic_iterative.mex. %%%%
<<<<<<< HEAD
=======
>>>>>>> initial commit
=======
>>>>>>> Updated C and RTL model as well as the documentation
%%%% %%%%
%%%%% %%%%%
%%%% %%%%
%%%% TODO %%%%
<<<<<<< HEAD
<<<<<<< HEAD
%%%% The linear test is not complete %%%%
=======
%%%% Some documentation and function description %%%%
>>>>>>> initial commit
=======
%%%% The linear test is not complete %%%%
>>>>>>> Updated C and RTL model as well as the documentation
%%%% %%%%
%%%% %%%%
%%%% %%%%
67,6 → 77,7
%%%% %%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
<<<<<<< HEAD
<<<<<<< HEAD
function cordic_iterative_test( )
 
 
75,17 → 86,12
 
 
 
=======
>>>>>>> Updated C and RTL model as well as the documentation
function cordic_iterative_test( )
%
%
% Please do 'mex cordic_iterative.c' to create
% the cordic_iterative.mex
%
%
%
%
 
 
 
>>>>>>> initial commit
% global flags/values, they are static
% through the whole script and defined below
120,6 → 126,7
% open test file
tb_fid = fopen( './tb_data.txt', 'w' );
<<<<<<< HEAD
<<<<<<< HEAD
%tb_fid = 0;
 
 
197,13 → 204,51
0, 0, ...
'Limit Value Test' );
=======
=======
%tb_fid = 0;
 
>>>>>>> Updated C and RTL model as well as the documentation
 
 
 
 
%
% run test, which uses random values
run_random_test( N_TESTS, tb_fid );
%
% run tests, which test limits
run_limit_test( tb_fid );
%
% run linear value test
run_linear_test( 1000, tb_fid );
 
% close file
fclose( tb_fid );
if tb_fid > 0
fclose( tb_fid );
end
 
end
 
 
 
 
function run_limit_test( tb_fid )
%RUN_LIMIT_TEST Test the range limit
%
% run_limit_test( fid )
%
% This function is used to generate a test pattern
% with values, which are at the range limit.
% This values are then processed by the fixed-point YAC
% implementation. All input and outputs are logged into
% a testbench pattern file.
%
% The argument fid is the file-descriptor of the testbench pattern
% file.
%
 
 
<<<<<<< HEAD
>>>>>>> initial commit
 
end
237,7 → 282,43
[ atanh_res, sqrt_res, atanh_err, sqrt_err, it_6 ] = catanh( data_a_h, data_b_h, tb_fid );
[ sinh_res, cosh_res, sinh_err, cosh_err, it_7 ] = csinhcosh( data_c_h, tb_fid );
 
=======
data_a = [ 0 1 0 1 -1 0 -1 1 -1 ];
data_b = [ 0 0 1 1 0 -1 -1 -1 1 ];
 
data_c = [ 0 0 0 0 0 0 0 0 0 ...
1 1 1 1 1 1 1 1 1 ...
-1 -1 -1 -1 -1 -1 -1 -1 -1 ];
 
data_d = data_a * pi;
data_a_div = [ 0.5 ,1 -0.5, -1, -0.5, -1 ];
data_b_div = [ 1 ,1, 1, 1, -1, -1 ];
 
[ ~, ~, atan_err, abs_err, it_1 ] = ccart2pol( data_a, data_b, tb_fid );
[ ~, ~, sin_err, cos_err, it_2 ] = cpol2cart( data_d, data_b, tb_fid );
[ ~, ~, x_err, y_err, it_3 ] = crot( [ data_a, data_a, data_a], ...
[ data_b, data_b, data_b], ...
data_c, tb_fid );
[ ~, div_err, it_4 ] = cdiv( data_a_div, data_b_div, tb_fid );
[ ~, mul_err, it_5 ] = cmul( data_a, data_b, tb_fid );
print_result_info( ...
atan_err, it_1, ...
abs_err, it_1, ...
sin_err, it_2, ...
cos_err, it_2, ...
x_err, it_3, ...
y_err, it_3, ...
div_err, it_4, ...
mul_err, it_5, ...
0, 0, ...
0, 0, ...
0, 0, ...
0, 0, ...
'Limit Value Test' );
>>>>>>> Updated C and RTL model as well as the documentation
 
figure; plot( data_b_h, atanh_res ); title( 'atanh' );
figure; plot( data_b_h, atanh_err ); title( 'atanh-error' );
figure; plot( data_c_h, sinh_res, data_c_h, cosh_res ); title( 'sinh and cosh' );
246,6 → 327,7
 
 
 
<<<<<<< HEAD
function run_random_test( N_TESTS, tb_fid )
%RUN_RANDOM_TEST Generates a random test pattern
%
256,12 → 338,28
% These values are then processed by the fixed-point YAC
% implementation. All input and outputs are logged into
% a testbench pattern file.
=======
function run_linear_test( N_TESTS, tb_fid )
%RUN_LINEAR_TEST Generates a linear test pattern
%
% run_linear_test( N, fid )
%
% This function is used to generate linear increasing test
% values.
% These values are then processed by the fixed-point YAC
% implementation. All input and outputs are logged into
% a testbench pattern file. In addition, the result is plotted.
%
% NOTE: only the hyperbolic functions are processed at the moment.
% This function needs to be extended in future.
>>>>>>> Updated C and RTL model as well as the documentation
%
%
% The argument fid is the file-descriptor of the testbench pattern
% file. The argument N defines the number of values, which are processed.
%
%
<<<<<<< HEAD
data_a = -1 + 2 .* rand( 1, N_TESTS );
data_b = -1 + 2 .* rand( 1, N_TESTS );
data_c = -1 + 2 .* rand( 1, N_TESTS );
268,11 → 366,49
data_d = -pi + 2*pi .* rand( 1, N_TESTS );
=======
function run_random_test( N_TESTS, tb_fid )
=======
 
data_a_h = ones( 1, N_TESTS );
data_b_h = linspace( -1, 1, N_TESTS ) * 0.78;
data_c_h = linspace( -1, 1, N_TESTS );
[ atanh_res, sqrt_res, atanh_err, sqrt_err, it_6 ] = catanh( data_a_h, data_b_h, tb_fid );
[ sinh_res, cosh_res, sinh_err, cosh_err, it_7 ] = csinhcosh( data_c_h, tb_fid );
 
 
figure; plot( data_b_h, atanh_res ); title( 'atanh' );
figure; plot( data_b_h, atanh_err ); title( 'atanh-error' );
figure; plot( data_c_h, sinh_res, data_c_h, cosh_res ); title( 'sinh and cosh' );
figure; plot( data_c_h, sinh_err, data_c_h, cosh_err ); title( 'sinh and cosh errors' );
end
 
 
>>>>>>> Updated C and RTL model as well as the documentation
 
function run_random_test( N_TESTS, tb_fid )
%RUN_RANDOM_TEST Generates a random test pattern
%
% run_random_test( N, fid )
%
% This function is used to generate random test
% values (uniform distributed).
% These values are then processed by the fixed-point YAC
% implementation. All input and outputs are logged into
% a testbench pattern file.
%
%
% The argument fid is the file-descriptor of the testbench pattern
% file. The argument N defines the number of values, which are processed.
%
%
data_a = -1 + 2 .* rand( 1, N_TESTS );
data_b = -1 + 2 .* rand( 1, N_TESTS );
<<<<<<< HEAD
 
>>>>>>> initial commit
=======
data_c = -1 + 2 .* rand( 1, N_TESTS );
data_d = -pi + 2*pi .* rand( 1, N_TESTS );
>>>>>>> Updated C and RTL model as well as the documentation
% adapat data for division
data_a_div = data_a;
data_b_div = data_b;
282,15 → 418,22
 
data_a_h = ones( size( data_a ) );
<<<<<<< HEAD
<<<<<<< HEAD
data_b_h = data_b .* 0.80694; %0.78;
=======
data_b_h = data_b .* 0.78;
>>>>>>> initial commit
=======
data_b_h = data_b .* 0.80694; %0.78;
>>>>>>> Updated C and RTL model as well as the documentation
 
 
 
[ ~, ~, atan_err, abs_err, it_1 ] = ccart2pol( data_a, data_b, tb_fid );
<<<<<<< HEAD
<<<<<<< HEAD
=======
>>>>>>> Updated C and RTL model as well as the documentation
[ ~, ~, sin_err, cos_err, it_2 ] = cpol2cart( data_d, data_b, tb_fid );
[ ~, ~, x_err, y_err, it_3 ] = crot( data_a, data_b, data_c, tb_fid );
[ ~, div_err, it_4 ] = cdiv( data_a_div, data_b_div, tb_fid );
330,6 → 473,7
sinh_err, sinh_it, ...
cosh_err, cosh_it, ...
title )
<<<<<<< HEAD
 
fprintf( ' ___________________________________________________________________\n' );
fprintf( ' %s\n', title);
356,22 → 500,26
[ ~, mul_err, it_4 ] = cmul( data_a, data_b, tb_fid );
[ ~, ~, atanh_err, sqrt_err, it_5 ] = catanh( data_a_h, data_b_h, tb_fid );
[ ~, ~, sinh_err, cosh_err, it_6 ] = csinhcosh( data_a, tb_fid );
=======
>>>>>>> Updated C and RTL model as well as the documentation
 
fprintf( ' ___________________________________________________________________\n' );
fprintf( ' Random Value Test \n' );
fprintf( ' %s\n', title);
fprintf( ' -----+-------------------+--------------------+-------------------\n' );
fprintf( ' | max error | mean error | max iterations \n' );
fprintf( ' atan | % .14f | % .14f | %.5f \n', max( atan_err ), mean( atan_err ), max( it_1 ) );
fprintf( ' abs | % .14f | % .14f | %.5f \n', max( abs_err ), mean( abs_err ), max( it_1 ) );
fprintf( ' sin | % .14f | % .14f | %.5f \n', max( sin_err ), mean( sin_err ), max( it_2 ) );
fprintf( ' cos | % .14f | % .14f | %.5f \n', max( cos_err ), mean( cos_err ), max( it_2 ) );
fprintf( ' div | % .14f | % .14f | %.5f \n', max( div_err ), mean( div_err ), max( it_3 ) );
fprintf( ' mul | % .14f | % .14f | %.5f \n', max( mul_err ), mean( mul_err ), mean( it_4 ) );
fprintf( ' atanh| % .14f | % .14f | %.5f \n', max( atanh_err), mean( atanh_err ), mean( it_5 ) );
fprintf( ' sinh | % .14f | % .14f | %.5f \n', max( sinh_err ), mean( sinh_err ), mean( it_6 ) );
fprintf( ' cosh | % .14f | % .14f | %.5f \n', max( cosh_err ), mean( cosh_err ), mean( it_6 ) );
fprintf( ' atan | % .14f | % .14f | %.5f \n', max( atan_err ), mean( atan_err ), max( atan_it ) );
fprintf( ' abs | % .14f | % .14f | %.5f \n', max( abs_err ), mean( abs_err ), max( abs_it ) );
fprintf( ' sin | % .14f | % .14f | %.5f \n', max( sin_err ), mean( sin_err ), max( sin_it ) );
fprintf( ' cos | % .14f | % .14f | %.5f \n', max( cos_err ), mean( cos_err ), max( cos_it ) );
fprintf( ' x | % .14f | % .14f | %.5f \n', max( x_err ), mean( x_err ), max( x_it ) );
fprintf( ' y | % .14f | % .14f | %.5f \n', max( y_err ), mean( y_err ), max( y_it ) );
fprintf( ' div | % .14f | % .14f | %.5f \n', max( div_err ), mean( div_err ), max( div_it ) );
fprintf( ' mul | % .14f | % .14f | %.5f \n', max( mul_err ), mean( mul_err ), max( mul_it ) );
fprintf( ' atanh| % .14f | % .14f | %.5f \n', max( atanh_err ), mean( atanh_err ), max( atanh_it ) );
fprintf( ' sqrt | % .14f | % .14f | %.5f \n', max( sqrt_err ), mean( sqrt_err ), max( sqrt_it ) );
fprintf( ' sinh | % .14f | % .14f | %.5f \n', max( sinh_err ), mean( sinh_err ), max( sinh_it ) );
fprintf( ' cosh | % .14f | % .14f | %.5f \n', max( cosh_err ), mean( cosh_err ), max( cosh_it ) );
 
 
end
>>>>>>> initial commit
 
378,6 → 526,7
 
 
 
 
function [sinh_res, cosh_res, sinh_err, cosh_err, it ]= csinhcosh( th, fid )
global C_FLAG_VEC_ROT C_FLAG_ATAN_3 C_MODE_CIRC C_MODE_LIN C_MODE_HYP
global XY_WIDTH ANGLEWIDTH GUARDBITS RM_GAIN
539,6 → 688,9
 
 
<<<<<<< HEAD
<<<<<<< HEAD
=======
>>>>>>> Updated C and RTL model as well as the documentation
function [x_res, y_res, x_err, y_err, it ] = crot( x, y, th, fid )
%
% does a multiplication with exp( th * i )
584,6 → 736,7
% does the Matlab equivalent pol2cart
%
 
<<<<<<< HEAD
=======
 
 
590,6 → 743,8
 
function [sin_res, cos_res, sin_err, cos_err, it ]= cpol2cart( th, r, fid )
>>>>>>> initial commit
=======
>>>>>>> Updated C and RTL model as well as the documentation
global C_FLAG_VEC_ROT C_FLAG_ATAN_3 C_MODE_CIRC C_MODE_LIN C_MODE_HYP
global XY_WIDTH ANGLEWIDTH GUARDBITS RM_GAIN
 
598,6 → 753,7
ai = round( th .* (2^(ANGLEWIDTH-1)-1) );
 
<<<<<<< HEAD
<<<<<<< HEAD
mode = C_MODE_CIRC;
 
=======
608,6 → 764,10
 
% cordic version
>>>>>>> initial commit
=======
mode = C_MODE_CIRC;
 
>>>>>>> Updated C and RTL model as well as the documentation
[ rcos rsin ra, it ] = cordic_iterative( ...
xi, ...
yi, ...
636,9 → 796,13
 
 
<<<<<<< HEAD
<<<<<<< HEAD
 
=======
>>>>>>> initial commit
=======
 
>>>>>>> Updated C and RTL model as well as the documentation
function [atan_res, abs_res, atan_err, abs_err, it ] = ccart2pol( x, y, fid )
 
global C_FLAG_VEC_ROT C_FLAG_ATAN_3 C_MODE_CIRC C_MODE_LIN C_MODE_HYP
665,14 → 829,20
GUARDBITS, ...
RM_GAIN );
<<<<<<< HEAD
<<<<<<< HEAD
=======
>>>>>>> Updated C and RTL model as well as the documentation
% matlab version:
m_th = atan2( y, x );
m_r = sqrt( x.^2 + y.^2 );
 
<<<<<<< HEAD
=======
% matlab version
[m_th, m_r ] = cart2pol( x, y );
>>>>>>> initial commit
=======
>>>>>>> Updated C and RTL model as well as the documentation
 
% comparison
atan_res = ra ./ 2^( (ANGLEWIDTH)-1);
681,10 → 851,15
abs_err = abs( m_r - abs_res );
 
<<<<<<< HEAD
<<<<<<< HEAD
% TODO: ATAN oder ATAN2 atan( 0 / x ) != atan2( 0, x )!!!!
 
=======
>>>>>>> initial commit
=======
% TODO: ATAN oder ATAN2 atan( 0 / x ) != atan2( 0, x )!!!!
 
>>>>>>> Updated C and RTL model as well as the documentation
% write TB data
write_tb( fid, xi, yi, ai, rx, ry, ra, mode )
 

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