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fxpf.c
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/*
============================================================================
Name : FXPF.c
Author : Anastasia Lozanova Volkova
Version : 0.1
Copyright :
Description : This program determines the Fixed-Point Format of a
LTI filter given in state-space representation:
|x(k+1) = Ax(k) + Bu(k)
|y(k) = Cx(k) + Du(k)
where
*u(k) is an input vector of size q x 1
*x(k) is internal state vector of size n x 1
*y(k) is the filter output vector of size p x 1
Input of the algorithm:
* ur such that for all k |u(k)| <= ur,
ur is a 1 x q vector
* w_u, w_x, w_y the restrictions on the wordlengths
of vectors u(k), x(k), y(k) respectively
w_u is a 1 x q vector
w_x is a n x 1 vector
w_y is a p x 1 vector
============================================================================
*/
#include "fxpf.h"
#include <time.h>
/*Allocates the space for the result structure fields.
If length is zero, exit with error.
*/
void fxpf_result_allocate(fxpf_result *result, uint64_t length )
{
if(!length)
{
fprintf(stderr, "ERROR: Trying to initialize fxpf_result with length = 0.\n");
return;
}
result->length = length;
result->error = allocateMPFIMatrix(1, length, 64);
result->w = (uint64_t*)calloc(length, length * sizeof(uint64_t));
result->msb = (uint64_t*)calloc(length, length * sizeof(uint64_t));
result->lsb = (int*)calloc(length, length * sizeof(int));
}
/* Frees the space by the pointer of the fxpf_result. */
void fxpf_result_free(fxpf_result *result)
{
if(!result->w) free(result->w);
if(!result->msb) free(result->msb);
if(!result->lsb) free(result->lsb);
freeMPFIMatrix(result->error, 1, result->length);
}
/* Copies the values of an array of wordlength constraints
w (which muct be non-null pointer for an array of length elements)
to the fxpf_result structure.
If w is a null pointer, print an error.
*/
void fxpf_result_setW(fxpf_result *result, uint64_t *w)
{
if(!w)
{
fprintf(stderr, "ERROR: Null pointer occured while trying to initialize wordlength constraints.\n");
return;
}
int i;
for(i = 0; i < result->length; ++i)
{
if(w[i] < 4 || isnan(w[i]))
{
fprintf(stderr, "ERROR: wordlength constraint must be >=4 bits but it is w[%i] = %llu \n", i, w[i]);
return;
}
result->w[i] = w[i];
}
}
/* Copies the values of an array of MSB msb (which muct be non-null pointer for an array of length elements)
to the fxpf_result structure.
If msb is a null pointer, print an error.
*/
void fxpf_result_setMSB(fxpf_result *result, uint64_t *msb)
{
if(!msb)
{
fprintf(stderr, "ERROR: Null pointer occured while trying to copy MSBs to fxpf_result.\n");
return;
}
UINT64MatrixCopy(result->msb, msb, 1, result->length);
}
/* Copies the values of an array of LSBs lsb (which muct be non-null pointer for an array of length elements)
to the fxpf_result structure.
If lsb is a null pointer, print an error.
*/
void fxpf_result_setLSB(fxpf_result *result, int *lsb)
{
if(!lsb)
{
fprintf(stderr, "ERROR: Null pointer occured while trying to copy LSBs to fxpf_result.\n");
return;
}
INTMatrixCopy(result->lsb, lsb, 1, result->length);
}
/* Copies the values of an array of error-vector (which muct be non-null pointer for an array of length elements)
to the fxpf_result structure.
If error is a null pointer, print an error.
*/
void fxpf_result_setError(fxpf_result *result, mpfi_t *error)
{
if(!error)
{
fprintf(stderr, "ERROR: Null pointer occured while trying to copy error vector to fxpf_result.\n");
return;
}
int i;
mp_prec_t prec;
for(i = 0; i < result->length; ++i)
{
prec = mpfi_get_prec(error[i]) > mpfi_get_prec(result->error[i]) ? mpfi_get_prec(error[i]) : mpfr_get_default_prec();
mpfi_set_prec(result->error[i], prec);
mpfi_set(result->error[i], error[i]);
}
}
/* Sets the number of additional steps. The integer value steps
must be positive or zero, otherwise print an error.
*/
void fxpf_result_setAdditionalSteps(fxpf_result *result, int steps)
{
if(steps < 0) fprintf(stderr, "WARNING: Trying to set negative numver of additional steps. \n");
result->additionalSteps = steps;
}
/* Prints results in format
wordlengths
msb
lsb
errors
additional steps
(empty line)
*/
void fxpf_result_print(FILE *file, fxpf_result *result)
{
// fprintf(file, "Printing result:\n");
// fprintf(file, "%llu\n",result->length);
UINT64MatrixPrint(file, result->w, 1, result->length);
// fprintf(file, "\n");
// UINT64MatrixPrint(file, result->msb, 1, result->length);
// fprintf(file, "\n");
// INT64MatrixPrint(file, result->lsb, 1, result->length);
int i;
double d;
for(i = 0; i < result->length; ++i)
{
d = mpfi_get_d(result->error[i]);
fprintf(file, "%e \t", d);
}
fprintf(file, "\n");
}
/* Computes the precision of WCPG computation of filter H such that
the MSB computed with above mentioned WCPG is either exact, either overestimated by one.
The precision eps is computed via following formula:
eps = max_i {eps_i}
eps_i <= (WCPGLowerBound(H) * ur)_i / alpha * sum_j {ur_j} for i=1:p
with alpha = 1 or 2.
Note: we are going to compute WCPG lower bound with precision 64.
Returns non-zero if epsilon was computied; and zero otherwise.
*/
int getWCPGeps(mpfr_t epsWCPG, filter *H, uint64_t alpha)
{
mp_exp_t res;
mp_prec_t prec = 64;
/* computing the WCPG lower bound matrix */
mp_exp_t epsWCPGLowerBound = -prec;
mpfr_t *WLowerBound;
WLowerBound = allocateMPFRMatrix(H->p, H->q, prec);
//fprintf(stderr, "Filter for the getWCPGeps: \n");
//filter_print(stderr, H);
if(!WCPGLowerBound_double(WLowerBound, H->A, H->B, H->C, H->D, H->n, H->p, H->q, -64))
{
fprintf(stderr, "Could not compute lower bound on the Worst Case Peak Gain matrix. \n");
freeMPFRMatrix(WLowerBound, H->p, H->q);
return 0;
}
//fprintf(stderr, "WLowerBound: \n");
//writeMPFRMatrix(stderr, WLowerBound, H->p, H->q, 5, MPFR_RNDN);
//fprintf(stderr, "\n");
mpfi_t *eps;
eps = allocateMPFIMatrix(H->p, 1, prec);
mpfi_t tmp;
mpfi_init(tmp);
/* computing denumerator sum_j (ur_j) */
mpfi_t sum_ur;
mpfi_init_set_ui(sum_ur, 0);
int i, j;
for(i = 0; i < H->q; ++i)
{
mpfi_add_d(sum_ur, sum_ur, H->ur[i]);
}
// fprintf(stderr, "Denum sum_j U_r: \n");
// mpfi_out_str(stderr, 10, 10, sum_ur);
// fprintf(stderr, "\n");
/* computing the epsilon vector */
mpfi_t *WCPG_ur;
WCPG_ur = allocateMPFIMatrix(H->p, 1, prec);
for(i = 0; i < H->p; ++i)
{
mpfi_set_ui(WCPG_ur[i], 0);
for(j = 0; j < H->q; ++j)
{
mpfi_set_fr(tmp, WLowerBound[i * H->q + j]);
mpfi_mul_d(tmp, tmp, H->ur[j]);
mpfi_add(WCPG_ur[i], WCPG_ur[i], tmp);
}
mpfi_div(eps[i], WCPG_ur[i],sum_ur);
if(mpfi_nan_p(eps[i]))
{
fprintf(stderr, "\n Could not compute the epsWCPG: eps[%d] is NaN \n", i);
freeMPFRMatrix(WLowerBound, H->p, H->q);
mpfi_clear(tmp);
mpfi_clear(sum_ur);
freeMPFIMatrix(eps, 1, H->p);
freeMPFIMatrix(WCPG_ur, H->p, 1);
return 0;
}
//fprintf(stderr, "\n eps[%d] = \n", i);
//mpfi_out_str(stderr, 10, 5, eps[i]);
//fprintf(stderr, "\n");
}
mpfr_t curr, min;
mpfr_init_set_ui(curr, 1, MPFR_RNDN);
mpfr_init(min); //setting min
mpfi_get_left(min, eps[0]);
int successflag = 1;
if(alpha == (uint64_t)2)
{
for(i = 0; i < H->p; ++i)
{
mpfi_div_ui(eps[i], eps[i], 2);
mpfi_get_left(curr, eps[i]);
if(mpfr_cmp(min, curr)) mpfr_set(min, curr, MPFR_RNDD);
}
mpfr_div_ui(epsWCPG, min, 4, MPFR_RNDN); //just adding additional 2 bits
if(mpfr_nan_p(epsWCPG))
{
fprintf(stderr, "\n epsWCPG is NaN \n");
successflag = 0;
}
}
if (alpha == (uint64_t)1)
{
for(i = 0; i < H->p; ++i)
{
mpfi_get_left(curr, eps[i]);
if(mpfr_cmp(min, curr)) mpfr_set(min, curr, MPFR_RNDD);
}
mpfr_div_ui(epsWCPG, min, 4, MPFR_RNDN); //just adding additional 2 bits
if(mpfr_nan_p(epsWCPG))
{
fprintf(stderr, "\n epsWCPG is NaN \n");
successflag = 0;
}
}
mpfr_clear(curr);
mpfr_clear(min);
freeMPFRMatrix(WLowerBound, H->p, H->q);
mpfi_clear(tmp);
mpfi_clear(sum_ur);
freeMPFIMatrix(eps, 1, H->p);
freeMPFIMatrix(WCPG_ur, H->p, 1);
return successflag;
}
/* Computes MSB for the Step 1 of the algorithm: a modification Hz1 of filter is
considered instead of filter H. This filter Hz1 does not take into account
any computational errors.
Given wordlength constraints, the MSBs of this filter are evaluated with
m_i = ceil[log2(WCPG(Hz1)*u_bound) - log2(A - 2^(1-w_i)) ] (1)
If the WCPG of filter Hz1 is computed with epsWCPG satisfying condifiton
epsWCPG <= min_i {WCPGLowerBound(Hz1)*u_bound / 2*sum_j u_bound_j }
then, the difference between the exact MSBs and the MSBs computed with (1)
is 0 or 1.
Inputs:
* filter Hz1
* wordlengths w
Outputs:
* msb_implemented
Returns non-zero value in case of success and zero otherwise
*/
int msb_step1(mpfi_t *msb, uint64_t *msb_left, uint64_t *msb_right, filter *H, uint64_t *w)
{
mp_prec_t defaultPrec = 64;
mpfr_t epsWCPG;
mpfr_init2(epsWCPG, defaultPrec);
if(!getWCPGeps(epsWCPG, H, (uint64_t)1) || mpfr_cmp_ui(epsWCPG, (uint64_t)0) <= 0 )
{
fprintf(stderr, "Could not determine the epsilon for WCPG computation. Exit with error. \n");
fprintf(stderr, "epsWCPG = %f", mpfr_get_d(epsWCPG, MPFR_RNDN));
mpfr_clear(epsWCPG);
return 0;
}
fprintf(stderr, "\n epsWCPG: \n");fflush(stdout);
mpfr_out_str(stderr, 10, 20, epsWCPG, MPFR_RNDN);
mpfr_t *WCPG;
WCPG = allocateMPFRMatrix(H->p, H->q, defaultPrec);
if (!WCPG_ABCD_mprec(WCPG, H->A, H->B, H->C, H->D, H->n, H->p, H->q, epsWCPG))
{
fprintf(stderr, "Could not compute WCPG. Exit with error\n");
freeMPFRMatrix(WCPG, H->p, H->q);
mpfr_clear(epsWCPG);
return 0;
}
fprintf(stderr, "\n Step 1: WCPG matrix of the initial filter \n");
writeMPFRMatrix(stderr, WCPG, H->p, H->q, 10, MPFR_RNDN);
mpfr_t tmp_mpfr;
mpfr_init(tmp_mpfr);
mp_prec_t WCPGprec = getMaxPrecMPFRMatrix(WCPG, H->p, H->q);
defaultPrec = WCPGprec >= defaultPrec ? WCPGprec : defaultPrec; //set default precision to the max precision of the WCPG matrix or leave it unchanged
mpfi_t WCPG_ur, tmp;
mpfi_init2(WCPG_ur, 2 * defaultPrec); //we will store [(<<H>> * ur)_i] in this variable
mpfi_set_ui(WCPG_ur, 0);
mpfi_init2(tmp, 2 * defaultPrec);
mpfi_set_ui(tmp, 0);
mpfi_t WCPG_ij_interval; //we will store interval values of the WCPG_ij
mpfi_init2(WCPG_ij_interval, defaultPrec); //with precision being at least the max precision of the WCPG matrix
mpfi_t log2WCPG_ur, log2const;
mpfi_init2(log2WCPG_ur, defaultPrec);
mpfi_init2(log2const, defaultPrec);
int i, j;
for(i = 0; i < H->p; ++i)
{
/* Compute [log2[(<<H>> * ur)_i]] */
mpfi_set_ui(WCPG_ur, 0);
for(j = 0; j < H->q; ++j)
{
mpfi_set_fr(WCPG_ij_interval, WCPG[i * H->q + j]); // convert WCPG_ij to interval
/* Here precision of H->ur[j] is at most defaultprec.
Setting precision of tmp equal to 2 * defaultprec guarantees the
interval bounds to be exact. */
mpfi_mul_d(tmp, WCPG_ij_interval, H->ur[j]);
mpfi_add(WCPG_ur, WCPG_ur, tmp); //WCPG_ur = [(<<H>> * ur)_i]
}
mpfi_log2(log2WCPG_ur,WCPG_ur);
if(mpfi_nan_p(log2WCPG_ur))
{
fprintf(stderr, "\n Could not compute MSB: log2WCPG_ur is NaN \n");
mpfi_clear(WCPG_ur);
mpfi_clear(tmp);
mpfi_clear(log2WCPG_ur);
mpfi_clear(log2const);
freeMPFRMatrix(WCPG, H->p, H->q);
mpfr_clear(tmp_mpfr);
mpfr_clear(epsWCPG);
mpfi_clear(WCPG_ij_interval);
return 0;
}
//fprintf(stderr, "Step 1: [log2[(<<H>> * ur)_i]]_%d: \n", i);
//mpfi_out_str(stderr, 10, 10, log2WCPG_ur);
//fprintf(stderr,"\n");
/* Compute log2const = [log2(1 - 2^(1 - w_j))] */
mpfi_set_prec(tmp, defaultPrec);
mpfi_set_si(tmp, 1 - w[i]);
if(mpfi_cmp_ui(tmp, 0) == 0)
{
/* Here w[i] is <= 1, which is violation of input constraints. */
fprintf(stderr, "ERROR: wordlength is 1: 1 - w = %f.\n", mpfi_get_d(tmp));
mpfi_clear(WCPG_ur);
mpfi_clear(tmp);
mpfi_clear(log2WCPG_ur);
mpfi_clear(log2const);
freeMPFRMatrix(WCPG, H->p, H->q);
mpfr_clear(tmp_mpfr);
mpfr_clear(epsWCPG);
mpfi_clear(WCPG_ij_interval);
}
mpfi_exp2(tmp, tmp);
mpfi_neg(tmp,tmp);
mpfi_add_ui(tmp, tmp, (unsigned long int)1);
mpfi_log2(log2const, tmp);
//mpfi_log1p(log2const, tmp);
if(mpfi_nan_p(log2const))
{
fprintf(stderr, "\n ERROR: Could not compute MSB: log2(1 - 2^(1-w)) is NaN \n");
mpfi_clear(WCPG_ur);
mpfi_clear(tmp);
mpfi_clear(log2WCPG_ur);
mpfi_clear(log2const);
freeMPFRMatrix(WCPG, H->p, H->q);
mpfr_clear(tmp_mpfr);
mpfr_clear(epsWCPG);
mpfi_clear(WCPG_ij_interval);
return 0;
}
//fprintf(stderr, "\n [log2(1 - 2^(1 - w_j))] = ");
//mpfi_out_str(stderr, 10, 10, log2const);
/* Compute [log2[(<<H>> * ur)_i]] - [log2(1 - 2^(1 - w_j))] */
mpfi_set_prec(msb[i], mpfi_get_prec(log2WCPG_ur));
mpfi_sub(msb[i], log2WCPG_ur, log2const);
if(mpfi_nan_p(msb[i]))
{
fprintf(stderr, "\n ERROR: Could not compute MSB: msb[%d] is NaN \n", i);
mpfi_clear(WCPG_ur);
mpfi_clear(tmp);
mpfi_clear(log2WCPG_ur);
mpfi_clear(log2const);
freeMPFRMatrix(WCPG, H->p, H->q);
mpfr_clear(tmp_mpfr);
mpfr_clear(epsWCPG);
mpfi_clear(WCPG_ij_interval);
return 0;
}
mpfr_set_prec(tmp_mpfr, 2 * defaultPrec);
if(mpfi_get_left(tmp_mpfr, msb[i]) < 0)
{
fprintf(stderr, "Could not correctly round inf of the MSB interval. \n");
}
if(mpfr_ceil(tmp_mpfr, tmp_mpfr) < 0)
{
fprintf(stderr, "Could not correctly round ceil(inf(MSB)). \n");
}
msb_left[i] = mpfr_get_ui(tmp_mpfr, MPFR_RNDD);
mpfr_set_prec(tmp_mpfr, 2 * defaultPrec);
if(mpfi_get_right(tmp_mpfr, msb[i]) < 0)
{
fprintf(stderr, "Could not correctly round sup of the MSB interval. \n");
}
if(mpfr_ceil(tmp_mpfr,tmp_mpfr) < 0)
{
fprintf(stderr, "Could not correctly round ceil(sup(MSB)). \n");
}
msb_right[i] = mpfr_get_ui(tmp_mpfr, MPFR_RNDU);
}
freeMPFRMatrix(WCPG, H->p, H->q);
mpfr_clear(epsWCPG);
mpfi_clear(WCPG_ur);
mpfi_clear(tmp);
mpfr_clear(tmp_mpfr);
mpfi_clear(log2WCPG_ur);
mpfi_clear(log2const);
mpfi_clear(WCPG_ij_interval);
return 1;
}
/* Computes MSB for the Step 2 of the algorithm: output of the
implemented filter Hz1 is represented as sum of the outputs of the
filter Hz1, which does not take into account computational errors,
and error-filter Delta.
Then, MSB of the implemented filter, taking into account the computational
errors is evaluated with:
m_i = ceil[log2{WCPG(Hz1)*u_bound)_i + WCPG(Delta)*eps_bound)_i } - log2{A - 2^(1-w_i)} ] (1)
If the WCPGs of filters are computes with epsWCPG satisfying condifiton
epsWCPG_Hz1 <= min_i {WCPGLowerBound(Hz1)*u_bound / 2*sum_j u_bound_j }
epsWCPG_Delta <= min_i {WCPGLowerBound(Delta)*u_bound / 2*sum_j u_bound_j }
then, the difference between the exact MSBs and the MSBs computed with (1)
is 0 or 1.
Inputs:
* filter Hz1
* filter Delta
* msb_Hz1
Outputs:
* msb_implemented
*/
int msb_step2(mpfi_t *msb, uint64_t *msb_left, uint64_t *msb_right, filter *Hz1, filter *Delta, uint64_t *w, uint64_t *lsb_max, fxpf_result *result)
{
mp_prec_t defaultPrec = 64;
mpfr_t epsWCPG_Hz1;
mpfr_init2(epsWCPG_Hz1, defaultPrec);
if(!getWCPGeps(epsWCPG_Hz1, Hz1, (uint64_t)2) || mpfr_cmp_ui(epsWCPG_Hz1, (uint64_t)0) <= 0 )
{
fprintf(stderr, "Could not determine the epsilon for WCPG_Hz1 computation. Exit with error. \n");
mpfr_clear(epsWCPG_Hz1);
return 0;
}
mpfr_t epsWCPG_Delta;
mpfr_init2(epsWCPG_Delta, defaultPrec);
if(!getWCPGeps(epsWCPG_Delta, Delta, (uint64_t)2) || mpfr_cmp_ui(epsWCPG_Delta, (uint64_t)0) <= 0 )
{
fprintf(stderr, "Could not determine the epsilon for WCPG_Delta computation. Exit with error. \n");
mpfr_clear(epsWCPG_Hz1);
mpfr_clear(epsWCPG_Delta);
return 0;
}
fprintf(stderr,"\n ...epsWCPG_Hz1: \n");
mpfr_out_str(stderr, 10, 20, epsWCPG_Hz1, MPFR_RNDN);
fprintf(stderr, "\n ...epsWCPG_Delta: \n");
mpfr_out_str(stderr, 10, 20, epsWCPG_Delta, MPFR_RNDN);
/* Computing WCPGs */
mpfr_t *WCPG_Hz1;
WCPG_Hz1 = allocateMPFRMatrix(Hz1->p, Hz1->q, defaultPrec);
if (!WCPG_ABCD_mprec(WCPG_Hz1, Hz1->A, Hz1->B, Hz1->C, Hz1->D, Hz1->n, Hz1->p, Hz1->q, epsWCPG_Hz1))
{
fprintf(stderr,"\nERROR: Could not compute WCPG_Hz1. Exiting.\n");
freeMPFRMatrix(WCPG_Hz1,Hz1->p, Hz1->q);
mpfr_clear(epsWCPG_Hz1);
mpfr_clear(epsWCPG_Delta);
return 0;
}
mpfr_t *WCPG_Delta;
WCPG_Delta = allocateMPFRMatrix(Delta->p, Delta->q, defaultPrec);
if (!WCPG_ABCD_mprec(WCPG_Delta, Delta->A, Delta->B, Delta->C, Delta->D, Delta->n, Delta->p, Delta->q, epsWCPG_Delta))
{
fprintf(stderr, "\nERROR: Could not compute WCPG_Delta. Exiting.\n");
freeMPFRMatrix(WCPG_Delta,Delta->p, Delta->q);
freeMPFRMatrix(WCPG_Hz1,Hz1->p, Hz1->q);
mpfr_clear(epsWCPG_Hz1);
mpfr_clear(epsWCPG_Delta);
return 0;
}
fprintf(stderr, "\n <---------Debug-------->\nWCPG_Hz1 matrix: \n");
writeMPFRMatrix(stderr, WCPG_Hz1, Hz1->p, Hz1->q, 10, MPFR_RNDN);
fprintf(stderr, "\n <---------Debug-------->\nWCPG_Delta matrix: \n");
writeMPFRMatrix(stderr, WCPG_Delta, Delta->p, Delta->q, 10, MPFR_RNDN);
mp_prec_t precDelta = getMaxPrecMPFRMatrix(WCPG_Delta, Delta->p, Delta->q);
mp_prec_t precHz1 = getMaxPrecMPFRMatrix(WCPG_Hz1, Hz1->p, Hz1->q);
defaultPrec = precHz1 >= precDelta ? precHz1 : precDelta;
mpfr_t tmp_mpfr;
mpfr_init2(tmp_mpfr, defaultPrec);
/* Computing element by element the MSB:
m_i = ceil[log2{WCPG(Hz1)*u_bound)_i + WCPG(Delta)*eps_bound)_i } - log2{A - 2^(1-w_i)} ]
*/
mpfi_t WCPG_ij_interval; //we will store interval values of the WCPG_ij
mpfi_init2(WCPG_ij_interval, defaultPrec); //with precision being at least the max precision of the WCPG matrices
mpfi_t WCPG_Hz1_ur, tmp;
mpfi_init2(WCPG_Hz1_ur, 2 * defaultPrec);
mpfi_set_ui(WCPG_Hz1_ur, 0);
mpfi_init2(tmp, 2 * defaultPrec);
mpfi_set_ui(tmp, 0);
mpfi_t WCPG_Delta_eps;
mpfi_init2(WCPG_Delta_eps, 2 * defaultPrec);
mpfi_set_ui(WCPG_Delta_eps, 0);
mpfi_t log2WCPGs, log2const;
mpfi_init2(log2WCPGs, 2 * defaultPrec);
mpfi_init2(log2const, defaultPrec);
int i, j;
mpfi_t *Deltaeps_vector;
Deltaeps_vector = allocateMPFIMatrix(Hz1->p, 1, 2 * defaultPrec);
mpfi_t *Hz1ur_vector;
Hz1ur_vector = allocateMPFIMatrix(Hz1->p, 1, 2 * defaultPrec);
/* Compute the interval vectors
Hz1ur_vector = [<<Hz1>> * u ]
Deltaeps_vector = [(<<Delta>> * eps)]
*/
for(i = 0; i < Hz1->p; ++i)
{
mpfi_set_ui(WCPG_Hz1_ur, 0);
mpfi_set_ui(WCPG_Delta_eps, 0);
/* Compute [(<<Hz1>> * ur)_i] = sum_{j=1}^{q} [<<Hz1>>_ij * u_j]*/
for(j = 0; j < Hz1->q; ++j)
{
/* convert WCPG_ij to interval */
mpfi_set_fr(WCPG_ij_interval, WCPG_Hz1[i * Hz1->q + j]);
//fprintf(stderr,"\n ...Multiplying the WCPG_Hz1[%llu] = \n", i * Hz1->q + j);
//mpfi_out_str(stderr, 10, 10,WCPG_ij_interval);
//fprintf(stderr,"\t by ur[%d] = %f \n", j,Hz1->ur[j]);
//mpfi_set_ui(tmp, 0);
/* compute the interval [tmp] = <<H_z>>_ij * u_j */
mpfi_mul_d(tmp, WCPG_ij_interval, Hz1->ur[j]);
/* add the [tmp] interval to the [(<<Hz1>> * ur)_i] */
mpfi_add(WCPG_Hz1_ur, WCPG_Hz1_ur, tmp);
}
/* copy the i-th element of the result vector to variable Hz1ur_vector */
mpfi_set(Hz1ur_vector[i], WCPG_Hz1_ur);
//fprintf(stderr,"\n ++Step i = %d. [<<Hz1>> * u ]: \n", i);
//mpfi_out_str(stderr, 10, 10, Hz1ur_vector[i]);
/* Compute [(<<Delta>> * eps)_i] = sum_{j=1}^{q} [<<Delta>>_ij * eps_j]*/
for(j = 0; j < Delta->q; ++j)
{
/* convert WCPG_ij to interval */
mpfi_set_fr(WCPG_ij_interval, WCPG_Delta[i * Delta->q + j]);
//printf("\nIteration %d: WCPG_Delta[%d * %d + %d] = ",i,i,Delta->q, j);
//mpfi_out_str(stderr, 10, 10, tmp);
mpfi_set_ui(tmp, 0);
/* compute the interval [tmp] = <<Delta>>_ij * eps_j */
mpfi_mul_d(tmp, WCPG_ij_interval, Delta->ur[j]);
//printf("\nIteration %d: WCPG_Delta[%d * %d + %d] * %f = \n",i,i,Delta->q, j, j, Delta->ur[j]);
//mpfi_out_str(stderr, 10, 10, tmp);
/* add the [tmp] interval to the [(<<Delta>> * eps)_i] */
mpfi_add(WCPG_Delta_eps, WCPG_Delta_eps, tmp);
}
/* copy the i-th element of the result vector to variable Deltaeps_vector */
mpfi_set(Deltaeps_vector[i], WCPG_Delta_eps);
//printf("\n --Step i = %d. Deltaeps_vector[i]: \n", i);
//mpfi_out_str(stderr, 10, 10, WCPG_Delta_eps);
/* Compute [<<Hz1>> * u ] + [(<<Delta>> * eps)] */
mpfi_add(log2WCPGs, WCPG_Hz1_ur, WCPG_Delta_eps);
/* Compute log2{(<<Hz1>> * ur)_i]] + [(<<Delta>> * eps)_i]} */
mpfi_log2(log2WCPGs, log2WCPGs);
if(mpfi_nan_p(log2WCPGs))
{
fprintf(stderr, "\n Could not compute MSB: log2WCPGs is NaN \n");
mpfr_clear(tmp_mpfr);
mpfi_clear(WCPG_Hz1_ur);
mpfi_clear(tmp);
mpfi_clear(WCPG_Delta_eps);
mpfi_clear(log2WCPGs);
mpfi_clear(log2const);
freeMPFIMatrix(Deltaeps_vector, Hz1->p, 1);
freeMPFIMatrix(Hz1ur_vector, Hz1->p, 1);
freeMPFRMatrix(WCPG_Delta,Delta->p, Delta->q);
freeMPFRMatrix(WCPG_Hz1,Hz1->p, Hz1->q);
mpfr_clear(epsWCPG_Hz1);
mpfr_clear(epsWCPG_Delta);
mpfi_clear(WCPG_ij_interval);
return 0;
}
/* Compute log2const = [log2(1 - 2^(1 - w_j))] */
mpfi_set_prec(tmp, defaultPrec);
mpfi_set_si(tmp, 1 - w[i]);
mpfi_exp2(tmp, tmp);
mpfi_neg(tmp,tmp);
mpfi_log1p(log2const, tmp);
if(mpfi_nan_p(log2const))
{
fprintf(stderr, "\n Could not compute MSB: log2const is NaN \n");
mpfr_clear(tmp_mpfr);
mpfi_clear(WCPG_Hz1_ur);
mpfi_clear(tmp);
mpfi_clear(WCPG_Delta_eps);
mpfi_clear(log2WCPGs);
mpfi_clear(log2const);
freeMPFIMatrix(Deltaeps_vector, Hz1->p, 1);
freeMPFIMatrix(Hz1ur_vector, Hz1->p, 1);
freeMPFRMatrix(WCPG_Delta,Delta->p, Delta->q);
freeMPFRMatrix(WCPG_Hz1,Hz1->p, Hz1->q);
mpfr_clear(epsWCPG_Hz1);
mpfr_clear(epsWCPG_Delta);
mpfi_clear(WCPG_ij_interval);
return 0;
}
/* Compute [log2[(<<Hz1>> * ur)_i]] + [(<<Delta>> * eps)_i]] - [log2(1 - 2^(1 - w_j))] */
mpfi_sub(msb[i], log2WCPGs, log2const);
if(mpfi_nan_p(msb[i]))
{
fprintf(stderr, "\n Could not compute MSB: msb[%d] is NaN \n", i);
mpfr_clear(tmp_mpfr);
mpfi_clear(WCPG_Hz1_ur);
mpfi_clear(tmp);
mpfi_clear(WCPG_Delta_eps);
mpfi_clear(log2WCPGs);
mpfi_clear(log2const);
freeMPFIMatrix(Deltaeps_vector, Hz1->p, 1);
freeMPFIMatrix(Hz1ur_vector, Hz1->p, 1);
freeMPFRMatrix(WCPG_Delta,Delta->p, Delta->q);
freeMPFRMatrix(WCPG_Hz1,Hz1->p, Hz1->q);
mpfr_clear(epsWCPG_Hz1);
mpfr_clear(epsWCPG_Delta);
mpfi_clear(WCPG_ij_interval);
return 0;
}
/* Now we compute the mpfr left and right bounds of the MSB interval. */
mpfr_set_prec(tmp_mpfr, 2 * defaultPrec);
if(mpfi_get_left(tmp_mpfr, msb[i]) < 0)
{
fprintf(stderr, "Could not correctly round inf of the MSB interval. \n");
}
if(mpfr_ceil(tmp_mpfr, tmp_mpfr) < 0)
{
fprintf(stderr, "Could not correctly round ceil(inf(MSB)). \n");
}
msb_left[i] = mpfr_get_ui(tmp_mpfr, MPFR_RNDD);
mpfr_set_prec(tmp_mpfr, 2 * defaultPrec);
if(mpfi_get_right(tmp_mpfr, msb[i]) < 0)
{
fprintf(stderr, "Could not correctly round sup of the MSB interval. \n");
}
if(mpfr_ceil(tmp_mpfr,tmp_mpfr) < 0)
{
fprintf(stderr, "Could not correctly round ceil(sup(MSB)). \n");
}
msb_right[i] = mpfr_get_ui(tmp_mpfr, MPFR_RNDU);
/* Check the stopping criteria for the algorithm.
If the lsb[i] on this iteration of the Step 2
has moved more to the right than the lsb_max constraint
(which is the msb[i] position deduced from the Step 1
of the algorithm), then the algorithm stops.
*/
int64_t lsb_current = msb_right[i] - w[i] + 1;
int64_t lsb_max_tmp = (int64_t)lsb_max[i];
if(lsb_current > lsb_max_tmp)
{
fprintf(stderr, "Error: LSB reached point when it is larger than initial MSB estimation on Step 1!\n");
fprintf(stderr, "msb_step1 = %llu and lsb_current = %lld \n",lsb_max[i], lsb_current);
// fprintf(stderr, "Error!!! LSB reached point when it is larger than wordlength.\n");
mpfr_clear(tmp_mpfr);
mpfi_clear(WCPG_Hz1_ur);
mpfi_clear(tmp);
mpfi_clear(WCPG_Delta_eps);
mpfi_clear(log2WCPGs);
mpfi_clear(log2const);
freeMPFIMatrix(Deltaeps_vector, Hz1->p, 1);
freeMPFIMatrix(Hz1ur_vector, Hz1->p, 1);
freeMPFRMatrix(WCPG_Delta,Delta->p, Delta->q);
freeMPFRMatrix(WCPG_Hz1,Hz1->p, Hz1->q);
mpfr_clear(epsWCPG_Hz1);
mpfr_clear(epsWCPG_Delta);
return 0;
}
}
//fprintf(stderr, "\n <+++++++++++++++++++++++Debug++++++++++++++++++++++++>\n The bound on the output (eps * WCPG_Delta) [p-1]= \n");
//mpfi_out_str(stderr, 10, 10, Deltaeps_vector[Hz1->p-1]);
//fprintf(stderr, "\n <++++++++++++++++++++++++++++++++++++++++++++++++++++>\n");
//fprintf(stderr, "\n The <<Delta>>*eps vector is: \n");
//writeMPFIMatrix(stderr, Deltaeps_vector, 1, Hz1->p, 10);
//fprintf(stderr, "\n The <<Hz1>>*ur vector is: \n");
//writeMPFIMatrix(stderr, Hz1ur_vector, 1, Hz1->p, 10);
/* Set the error vector in the fxpf_result structure to
error = <<Delta>> * eps
*/
fxpf_result_setError(result, Deltaeps_vector);
mpfr_clear(tmp_mpfr);
mpfi_clear(WCPG_Hz1_ur);
mpfi_clear(tmp);
mpfi_clear(WCPG_Delta_eps);
mpfi_clear(log2WCPGs);
mpfi_clear(log2const);
freeMPFIMatrix(Deltaeps_vector, Hz1->p, 1);
freeMPFIMatrix(Hz1ur_vector, Hz1->p, 1);
freeMPFRMatrix(WCPG_Delta,Delta->p, Delta->q);
freeMPFRMatrix(WCPG_Hz1,Hz1->p, Hz1->q);
mpfr_clear(epsWCPG_Hz1);
mpfr_clear(epsWCPG_Delta);
mpfi_clear(WCPG_ij_interval);
return 1;
}
/* Computes the LSB vector given wordlegths and MSB positions in the input.
Space for lsb vector is assumed preallocated output the function.
Returns non-zero value if succeed, zero otherwise.*/
int computeLSB(int *lsb, uint64_t *msb, uint64_t *w, uint64_t length)
{
if(!msb || !w || length < 1)
{
fprintf(stderr, "ERROR: Null pointer occured in LSB computation function. \n");
return 0;
}
int i;
for(i = 0; i < length; ++i)
{
lsb[i] = msb[i] - w[i] + 1;
fprintf(stderr, "compute LSB: lsb[%d] = %d = msb[i] - w[i] + 1 = %llu - %llu + 1 \n", i, lsb[i], msb[i], w[i] );
}
return 1;
}
/* For a LTI IIR filter in state-space representation H={A,B,C,D}, bound on input values
u and wordlegths for state- and output-variable representation the function, if possible,
determines Fixed-Point Formats for its state- and output-variables such that no overflow
occurs. <<<<>
Algorithm consists in a loop around step1 and step2 parts.
TODO: finish description
Returns a negative number if failed, otherwise number of additional algorithm
iterations required to determine FXPF.
*/
int determineFXPF(uint64_t *msb, int *lsb, filter *H, uint64_t *wl, fxpf_result *result)
{
clock_t begin, end;
begin = clock();
// fprintf(stderr, "------------------------------ Computing MSB on step 1 --------------------- \n");
/* Construct modification Hz1 of initial filter H. */
filter Hz1;
filter_allocate(&Hz1, H->n, H->p + H->n, H->q);
createFilterHz1(&Hz1, H);
fprintf(stderr,"++++++++++++++++Filter H:\n");fflush(stdout);
filter_print(stderr, H);
fprintf(stderr,"++++++++++++++++Filter Hz1:\n");
filter_print(stderr, &Hz1);
fflush(stderr);
mpfi_t *msb_Hz1;
msb_Hz1 = allocateMPFIMatrix(Hz1.p, 1, 64);
uint64_t *msb_inf_Hz1;
msb_inf_Hz1 = (uint64_t*)calloc(Hz1.p, Hz1.p * sizeof(uint64_t));
uint64_t *msb_sup_Hz1;
msb_sup_Hz1 = (uint64_t*)calloc(Hz1.p, Hz1.p * sizeof(uint64_t));
if (!msb_step1(msb_Hz1, msb_inf_Hz1, msb_sup_Hz1, &Hz1, wl))
{
fprintf(stderr, "Could not determine the MSB for step 1. \n");
filter_free(&Hz1);
free(msb_inf_Hz1);
free(msb_sup_Hz1);
freeMPFIMatrix(msb_Hz1,Hz1.p, 1);
return -1;
}
fprintf(stderr, "\n Step 1: MSB in mpfi format\n");
writeMPFIMatrix(stderr, msb_Hz1, Hz1.p, 1, 5);
fprintf(stderr, "---------------------------");
//fprintf("Step 1: MSB interval infinum \n");
//UINT64MatrixPrint(stderr, msb_inf_Hz1, 1, Hz1.p);
//printf("\n Step 1: interval supremum \n");
//UINT64MatrixPrint(stderr, msb_sup_Hz1, 1, Hz1.p);
fprintf(stderr, "------------------------------ Computing MSB on step 2 --------------------- \n");
filter Delta;
filter_allocate(&Delta, H->n, H->p + H->n, H->p + H->n);
// first, we try to set MSB to inferior part of MSB interval from step 1
createFilterDelta(&Delta, H, msb_inf_Hz1, wl);
mpfi_t *msb_step2_interval;
msb_step2_interval = allocateMPFIMatrix(Hz1.p, 1, 64);
uint64_t *msb_inf_step2;
msb_inf_step2 = (uint64_t*)malloc(Hz1.p * sizeof(uint64_t));
uint64_t *msb_sup_step2;
msb_sup_step2 = (uint64_t*)malloc(Hz1.p * sizeof(uint64_t));
/* We set the LSB constraint to the supremum of the MSB interval, obtained on the step 1.
Then, the condition of breaking from the refinement loop is successful MSB check,
or if the LSB after refinment became larger than initially estimated MSB.
*/
uint64_t *lsb_max;
lsb_max = (uint64_t*)calloc(Hz1.p, Hz1.p * sizeof(uint64_t));
UINT64MatrixCopy(lsb_max, msb_sup_Hz1, 1, Hz1.p);
if (!msb_step2(msb_step2_interval, msb_inf_step2, msb_sup_step2, &Hz1, &Delta, wl,lsb_max, result))
{
fprintf(stderr, "Could not determine the MSB for step 2. \n");
filter_free(&Hz1);
free(msb_inf_Hz1);
free(msb_sup_Hz1);
freeMPFIMatrix(msb_Hz1,Hz1.p, 1);
filter_free(&Delta);
free(msb_inf_step2);
free(msb_sup_step2);
freeMPFIMatrix(msb_step2_interval,Hz1.p, 1);
free(lsb_max);
return -1;
}
fprintf(stderr, "\n Step 2: MSB in mpfi format\n");
writeMPFIMatrix(stderr, msb_step2_interval, Hz1.p, 1, 5);
//printf("Step 2: MSB \n");
//UINT64MatrixPrint(stderr, msb_sup_step2, 1, Hz1.p);
uint64_t *msb_new = (uint64_t*)calloc(Hz1.p, Hz1.p * sizeof(uint64_t));
uint64_t *msb_z = (uint64_t*)calloc(Hz1.p, Hz1.p * sizeof(uint64_t));
int flag_OK = 0;
int steps = 0;
if(!checkMSB(msb_new, msb_inf_Hz1, msb_sup_Hz1, msb_sup_step2, 1, Hz1.p)) //if format changed
{
/*We are in the case when first check of MSB has not passed. */
//fprintf(stderr, "\n <-----Result----> The first check if msb_step2 is equal has not passed.\n");