/**
* Find the live intervals for each temporary register in the program.
* For register R, the interval [A,B] indicates that R is referenced
* from instruction A through instruction B.
* Special consideration is needed for loops and subroutines.
* \return GL_TRUE if success, GL_FALSE if we cannot proceed for some reason
*/
static GLboolean
find_live_intervals(struct gl_program *prog,
struct interval_list *liveIntervals)
{
GLint intBegin[REG_ALLOCATE_MAX_PROGRAM_TEMPS];
GLint intEnd[REG_ALLOCATE_MAX_PROGRAM_TEMPS];
GLuint i;
/*
* Note: we'll return GL_FALSE below if we find relative indexing
* into the TEMP register file. We can't handle that yet.
* We also give up on subroutines for now.
*/
if (dbg) {
printf("Optimize: Begin find intervals\n");
}
/* build intermediate arrays */
if (!_mesa_find_temp_intervals(prog->Instructions, prog->NumInstructions,
intBegin, intEnd))
return GL_FALSE;
/* Build live intervals list from intermediate arrays */
liveIntervals->Num = 0;
for (i = 0; i < REG_ALLOCATE_MAX_PROGRAM_TEMPS; i++) {
if (intBegin[i] >= 0) {
struct interval inv;
inv.Reg = i;
inv.Start = intBegin[i];
inv.End = intEnd[i];
append_interval(liveIntervals, &inv);
}
}
/* Sort the list according to interval starts */
sort_interval_list_by_start(liveIntervals);
if (dbg) {
/* print interval info */
for (i = 0; i < liveIntervals->Num; i++) {
const struct interval *inv = liveIntervals->Intervals + i;
printf("Reg[%d] live [%d, %d]:",
inv->Reg, inv->Start, inv->End);
if (1) {
GLuint j;
for (j = 0; j < inv->Start; j++)
printf(" ");
for (j = inv->Start; j <= inv->End; j++)
printf("x");
}
printf("\n");
}
}
return GL_TRUE;
}
int
gsl_integration_qawf (gsl_function * f,
const double a,
const double epsabs,
const size_t limit,
gsl_integration_workspace * workspace,
gsl_integration_workspace * cycle_workspace,
gsl_integration_qawo_table * wf,
double *result, double *abserr)
{
double area, errsum;
double res_ext, err_ext;
double correc, total_error = 0.0, truncation_error;
size_t ktmin = 0;
size_t iteration = 0;
struct extrapolation_table table;
double cycle;
double omega = wf->omega;
const double p = 0.9;
double factor = 1;
double initial_eps, eps;
int error_type = 0;
/* Initialize results */
initialise (workspace, a, a);
*result = 0;
*abserr = 0;
if (limit > workspace->limit)
{
GSL_ERROR ("iteration limit exceeds available workspace", GSL_EINVAL) ;
}
/* Test on accuracy */
if (epsabs <= 0)
{
GSL_ERROR ("absolute tolerance epsabs must be positive", GSL_EBADTOL) ;
}
if (omega == 0.0)
{
if (wf->sine == GSL_INTEG_SINE)
{
/* The function sin(w x) f(x) is always zero for w = 0 */
*result = 0;
*abserr = 0;
return GSL_SUCCESS;
}
else
{
/* The function cos(w x) f(x) is always f(x) for w = 0 */
int status = gsl_integration_qagiu (f, a, epsabs, 0.0,
cycle_workspace->limit,
cycle_workspace,
result, abserr);
return status;
}
}
if (epsabs > GSL_DBL_MIN / (1 - p))
{
eps = epsabs * (1 - p);
}
else
{
eps = epsabs;
}
initial_eps = eps;
area = 0;
errsum = 0;
res_ext = 0;
err_ext = GSL_DBL_MAX;
correc = 0;
cycle = (2 * floor (fabs (omega)) + 1) * M_PI / fabs (omega);
gsl_integration_qawo_table_set_length (wf, cycle);
initialise_table (&table);
for (iteration = 0; iteration < limit; iteration++)
{
double area1, error1, reseps, erreps;
double a1 = a + iteration * cycle;
double b1 = a1 + cycle;
double epsabs1 = eps * factor;
int status = gsl_integration_qawo (f, a1, epsabs1, 0.0, limit,
cycle_workspace, wf,
&area1, &error1);
append_interval (workspace, a1, b1, area1, error1);
factor *= p;
area = area + area1;
errsum = errsum + error1;
/* estimate the truncation error as 50 times the final term */
truncation_error = 50 * fabs (area1);
total_error = errsum + truncation_error;
if (total_error < epsabs && iteration > 4)
{
goto compute_result;
}
if (error1 > correc)
{
correc = error1;
}
if (status)
{
eps = GSL_MAX_DBL (initial_eps, correc * (1.0 - p));
}
if (status && total_error < 10 * correc && iteration > 3)
{
goto compute_result;
}
append_table (&table, area);
if (table.n < 2)
{
continue;
}
qelg (&table, &reseps, &erreps);
ktmin++;
if (ktmin >= 15 && err_ext < 0.001 * total_error)
{
error_type = 4;
}
if (erreps < err_ext)
{
ktmin = 0;
err_ext = erreps;
res_ext = reseps;
if (err_ext + 10 * correc <= epsabs)
break;
if (err_ext <= epsabs && 10 * correc >= epsabs)
break;
}
}
if (iteration == limit)
error_type = 1;
if (err_ext == GSL_DBL_MAX)
goto compute_result;
err_ext = err_ext + 10 * correc;
*result = res_ext;
*abserr = err_ext;
if (error_type == 0)
{
return GSL_SUCCESS ;
}
if (res_ext != 0.0 && area != 0.0)
{
if (err_ext / fabs (res_ext) > errsum / fabs (area))
goto compute_result;
}
else if (err_ext > errsum)
{
goto compute_result;
}
else if (area == 0.0)
{
goto return_error;
}
if (error_type == 4)
{
err_ext = err_ext + truncation_error;
}
goto return_error;
compute_result:
*result = area;
*abserr = total_error;
return_error:
if (error_type > 2)
error_type--;
if (error_type == 0)
{
return GSL_SUCCESS;
}
else if (error_type == 1)
{
GSL_ERROR ("number of iterations was insufficient", GSL_EMAXITER);
}
else if (error_type == 2)
{
GSL_ERROR ("cannot reach tolerance because of roundoff error",
GSL_EROUND);
}
else if (error_type == 3)
{
GSL_ERROR ("bad integrand behavior found in the integration interval",
GSL_ESING);
}
else if (error_type == 4)
{
GSL_ERROR ("roundoff error detected in the extrapolation table",
GSL_EROUND);
}
else if (error_type == 5)
{
GSL_ERROR ("integral is divergent, or slowly convergent",
GSL_EDIVERGE);
}
else
{
GSL_ERROR ("could not integrate function", GSL_EFAILED);
}
}
int
gsl_integration_qaws (gsl_function * f,
const double a, const double b,
gsl_integration_qaws_table * t,
const double epsabs, const double epsrel,
const size_t limit,
gsl_integration_workspace * workspace,
double *result, double *abserr)
{
double area, errsum;
double result0, abserr0;
double tolerance;
size_t iteration = 0;
int roundoff_type1 = 0, roundoff_type2 = 0, error_type = 0;
/* Initialize results */
initialise (workspace, a, b);
*result = 0;
*abserr = 0;
if (limit > workspace->limit)
{
GSL_ERROR ("iteration limit exceeds available workspace", GSL_EINVAL) ;
}
if (b <= a)
{
GSL_ERROR ("limits must form an ascending sequence, a < b", GSL_EINVAL) ;
}
if (epsabs <= 0 && (epsrel < 50 * GSL_DBL_EPSILON || epsrel < 0.5e-28))
{
GSL_ERROR ("tolerance cannot be acheived with given epsabs and epsrel",
GSL_EBADTOL);
}
/* perform the first integration */
{
double area1, area2;
double error1, error2;
int err_reliable1, err_reliable2;
double a1 = a;
double b1 = 0.5 * (a + b);
double a2 = b1;
double b2 = b;
qc25s (f, a, b, a1, b1, t, &area1, &error1, &err_reliable1);
qc25s (f, a, b, a2, b2, t, &area2, &error2, &err_reliable2);
if (error1 > error2)
{
append_interval (workspace, a1, b1, area1, error1);
append_interval (workspace, a2, b2, area2, error2);
}
else
{
append_interval (workspace, a2, b2, area2, error2);
append_interval (workspace, a1, b1, area1, error1);
}
result0 = area1 + area2;
abserr0 = error1 + error2;
}
/* Test on accuracy */
tolerance = GSL_MAX_DBL (epsabs, epsrel * fabs (result0));
/* Test on accuracy, use 0.01 relative error as an extra safety
margin on the first iteration (ignored for subsequent iterations) */
if (abserr0 < tolerance && abserr0 < 0.01 * fabs(result0))
{
*result = result0;
*abserr = abserr0;
return GSL_SUCCESS;
}
else if (limit == 1)
{
*result = result0;
*abserr = abserr0;
GSL_ERROR ("a maximum of one iteration was insufficient", GSL_EMAXITER);
}
area = result0;
errsum = abserr0;
iteration = 2;
do
{
double a1, b1, a2, b2;
double a_i, b_i, r_i, e_i;
double area1 = 0, area2 = 0, area12 = 0;
double error1 = 0, error2 = 0, error12 = 0;
int err_reliable1, err_reliable2;
/* Bisect the subinterval with the largest error estimate */
retrieve (workspace, &a_i, &b_i, &r_i, &e_i);
a1 = a_i;
b1 = 0.5 * (a_i + b_i);
a2 = b1;
b2 = b_i;
qc25s (f, a, b, a1, b1, t, &area1, &error1, &err_reliable1);
qc25s (f, a, b, a2, b2, t, &area2, &error2, &err_reliable2);
area12 = area1 + area2;
error12 = error1 + error2;
errsum += (error12 - e_i);
area += area12 - r_i;
if (err_reliable1 && err_reliable2)
{
double delta = r_i - area12;
if (fabs (delta) <= 1.0e-5 * fabs (area12) && error12 >= 0.99 * e_i)
{
roundoff_type1++;
}
if (iteration >= 10 && error12 > e_i)
{
roundoff_type2++;
}
}
tolerance = GSL_MAX_DBL (epsabs, epsrel * fabs (area));
if (errsum > tolerance)
{
if (roundoff_type1 >= 6 || roundoff_type2 >= 20)
{
error_type = 2; /* round off error */
}
/* set error flag in the case of bad integrand behaviour at
a point of the integration range */
if (subinterval_too_small (a1, a2, b2))
{
error_type = 3;
}
}
update (workspace, a1, b1, area1, error1, a2, b2, area2, error2);
retrieve (workspace, &a_i, &b_i, &r_i, &e_i);
iteration++;
}
while (iteration < limit && !error_type && errsum > tolerance);
*result = sum_results (workspace);
*abserr = errsum;
if (errsum <= tolerance)
{
return GSL_SUCCESS;
}
else if (error_type == 2)
{
GSL_ERROR ("roundoff error prevents tolerance from being achieved",
GSL_EROUND);
}
else if (error_type == 3)
{
GSL_ERROR ("bad integrand behavior found in the integration interval",
GSL_ESING);
}
else if (iteration == limit)
{
GSL_ERROR ("maximum number of subdivisions reached", GSL_EMAXITER);
}
else
{
GSL_ERROR ("could not integrate function", GSL_EFAILED);
}
}
static int
qagp (const gsl_function * f,
const double *pts, const size_t npts,
const double epsabs, const double epsrel,
const size_t limit,
gsl_integration_workspace * workspace,
double *result, double *abserr,
gsl_integration_rule * q)
{
double area, errsum;
double res_ext, err_ext;
double result0, abserr0, resabs0;
double tolerance;
double ertest = 0;
double error_over_large_intervals = 0;
double reseps = 0, abseps = 0, correc = 0;
size_t ktmin = 0;
int roundoff_type1 = 0, roundoff_type2 = 0, roundoff_type3 = 0;
int error_type = 0, error_type2 = 0;
size_t iteration = 0;
int positive_integrand = 0;
int extrapolate = 0;
int disallow_extrapolation = 0;
struct extrapolation_table table;
const size_t nint = npts - 1; /* number of intervals */
size_t *ndin = workspace->level; /* temporarily alias ndin to level */
size_t i;
/* Initialize results */
*result = 0;
*abserr = 0;
/* Test on validity of parameters */
if (limit > workspace->limit)
{
GSL_ERROR ("iteration limit exceeds available workspace", GSL_EINVAL) ;
}
if (npts > workspace->limit)
{
GSL_ERROR ("npts exceeds size of workspace", GSL_EINVAL);
}
if (epsabs <= 0 && (epsrel < 50 * GSL_DBL_EPSILON || epsrel < 0.5e-28))
{
GSL_ERROR ("tolerance cannot be acheived with given epsabs and epsrel",
GSL_EBADTOL);
}
/* Check that the integration range and break points are an
ascending sequence */
for (i = 0; i < nint; i++)
{
if (pts[i + 1] < pts[i])
{
GSL_ERROR ("points are not in an ascending sequence", GSL_EINVAL);
}
}
/* Perform the first integration */
result0 = 0;
abserr0 = 0;
resabs0 = 0;
initialise (workspace, 0.0, 0.0) ;
for (i = 0; i < nint; i++)
{
double area1, error1, resabs1, resasc1;
const double a1 = pts[i];
const double b1 = pts[i + 1];
q (f, a1, b1, &area1, &error1, &resabs1, &resasc1);
result0 = result0 + area1;
abserr0 = abserr0 + error1;
resabs0 = resabs0 + resabs1;
append_interval (workspace, a1, b1, area1, error1);
if (error1 == resasc1 && error1 != 0.0)
{
ndin[i] = 1;
}
else
{
ndin[i] = 0;
}
}
/* Compute the initial error estimate */
errsum = 0.0;
for (i = 0; i < nint; i++)
{
if (ndin[i])
{
workspace->elist[i] = abserr0;
}
errsum = errsum + workspace->elist[i];
}
for (i = 0; i < nint; i++)
{
workspace->level[i] = 0;
}
/* Sort results into order of decreasing error via the indirection
array order[] */
sort_results (workspace);
/* Test on accuracy */
tolerance = GSL_MAX_DBL (epsabs, epsrel * fabs (result0));
if (abserr0 <= 100 * GSL_DBL_EPSILON * resabs0 && abserr0 > tolerance)
{
*result = result0;
*abserr = abserr0;
GSL_ERROR ("cannot reach tolerance because of roundoff error"
"on first attempt", GSL_EROUND);
}
else if (abserr0 <= tolerance)
{
*result = result0;
*abserr = abserr0;
return GSL_SUCCESS;
}
else if (limit == 1)
{
*result = result0;
*abserr = abserr0;
GSL_ERROR ("a maximum of one iteration was insufficient", GSL_EMAXITER);
}
/* Initialization */
initialise_table (&table);
append_table (&table, result0);
area = result0;
res_ext = result0;
err_ext = GSL_DBL_MAX;
error_over_large_intervals = errsum;
ertest = tolerance;
positive_integrand = test_positivity (result0, resabs0);
iteration = nint - 1;
do
{
size_t current_level;
double a1, b1, a2, b2;
double a_i, b_i, r_i, e_i;
double area1 = 0, area2 = 0, area12 = 0;
double error1 = 0, error2 = 0, error12 = 0;
double resasc1, resasc2;
double resabs1, resabs2;
double last_e_i;
/* Bisect the subinterval with the largest error estimate */
retrieve (workspace, &a_i, &b_i, &r_i, &e_i);
current_level = workspace->level[workspace->i] + 1;
a1 = a_i;
b1 = 0.5 * (a_i + b_i);
a2 = b1;
b2 = b_i;
iteration++;
q (f, a1, b1, &area1, &error1, &resabs1, &resasc1);
q (f, a2, b2, &area2, &error2, &resabs2, &resasc2);
area12 = area1 + area2;
error12 = error1 + error2;
last_e_i = e_i;
/* Improve previous approximations to the integral and test for
accuracy.
We write these expressions in the same way as the original
QUADPACK code so that the rounding errors are the same, which
makes testing easier. */
errsum = errsum + error12 - e_i;
area = area + area12 - r_i;
tolerance = GSL_MAX_DBL (epsabs, epsrel * fabs (area));
if (resasc1 != error1 && resasc2 != error2)
{
double delta = r_i - area12;
if (fabs (delta) <= 1.0e-5 * fabs (area12) && error12 >= 0.99 * e_i)
{
if (!extrapolate)
{
roundoff_type1++;
}
else
{
roundoff_type2++;
}
}
if (i > 10 && error12 > e_i)
{
roundoff_type3++;
}
}
/* Test for roundoff and eventually set error flag */
if (roundoff_type1 + roundoff_type2 >= 10 || roundoff_type3 >= 20)
{
error_type = 2; /* round off error */
}
if (roundoff_type2 >= 5)
{
error_type2 = 1;
}
/* set error flag in the case of bad integrand behaviour at
a point of the integration range */
if (subinterval_too_small (a1, a2, b2))
{
error_type = 4;
}
/* append the newly-created intervals to the list */
update (workspace, a1, b1, area1, error1, a2, b2, area2, error2);
if (errsum <= tolerance)
{
goto compute_result;
}
if (error_type)
{
break;
}
if (iteration >= limit - 1)
{
error_type = 1;
break;
}
if (disallow_extrapolation)
{
continue;
}
error_over_large_intervals += -last_e_i;
if (current_level < workspace->maximum_level)
{
error_over_large_intervals += error12;
}
if (!extrapolate)
{
/* test whether the interval to be bisected next is the
smallest interval. */
if (large_interval (workspace))
continue;
extrapolate = 1;
workspace->nrmax = 1;
}
/* The smallest interval has the largest error. Before
bisecting decrease the sum of the errors over the larger
intervals (error_over_large_intervals) and perform
extrapolation. */
if (!error_type2 && error_over_large_intervals > ertest)
{
if (increase_nrmax (workspace))
continue;
}
/* Perform extrapolation */
append_table (&table, area);
if (table.n < 3)
{
goto skip_extrapolation;
}
qelg (&table, &reseps, &abseps);
ktmin++;
if (ktmin > 5 && err_ext < 0.001 * errsum)
{
error_type = 5;
}
if (abseps < err_ext)
{
ktmin = 0;
err_ext = abseps;
res_ext = reseps;
correc = error_over_large_intervals;
ertest = GSL_MAX_DBL (epsabs, epsrel * fabs (reseps));
if (err_ext <= ertest)
break;
}
/* Prepare bisection of the smallest interval. */
if (table.n == 1)
{
disallow_extrapolation = 1;
}
if (error_type == 5)
{
break;
}
skip_extrapolation:
reset_nrmax (workspace);
extrapolate = 0;
error_over_large_intervals = errsum;
}
while (iteration < limit);
*result = res_ext;
*abserr = err_ext;
if (err_ext == GSL_DBL_MAX)
goto compute_result;
if (error_type || error_type2)
{
if (error_type2)
{
err_ext += correc;
}
if (error_type == 0)
error_type = 3;
if (result != 0 && area != 0)
{
if (err_ext / fabs (res_ext) > errsum / fabs (area))
goto compute_result;
}
else if (err_ext > errsum)
{
goto compute_result;
}
else if (area == 0.0)
{
goto return_error;
}
}
/* Test on divergence. */
{
double max_area = GSL_MAX_DBL (fabs (res_ext), fabs (area));
if (!positive_integrand && max_area < 0.01 * resabs0)
goto return_error;
}
{
double ratio = res_ext / area;
if (ratio < 0.01 || ratio > 100 || errsum > fabs (area))
error_type = 6;
}
goto return_error;
compute_result:
*result = sum_results (workspace);
*abserr = errsum;
return_error:
if (error_type > 2)
error_type--;
if (error_type == 0)
{
return GSL_SUCCESS;
}
else if (error_type == 1)
{
GSL_ERROR ("number of iterations was insufficient", GSL_EMAXITER);
}
else if (error_type == 2)
{
GSL_ERROR ("cannot reach tolerance because of roundoff error",
GSL_EROUND);
}
else if (error_type == 3)
{
GSL_ERROR ("bad integrand behavior found in the integration interval",
GSL_ESING);
}
else if (error_type == 4)
{
GSL_ERROR ("roundoff error detected in the extrapolation table",
GSL_EROUND);
}
else if (error_type == 5)
{
GSL_ERROR ("integral is divergent, or slowly convergent",
GSL_EDIVERGE);
}
else
{
GSL_ERROR ("could not integrate function", GSL_EFAILED);
}
}