Module: ppl/ppl Branch: floating_point Commit: cf40c1ee096f612eab5f8353298f39e84e3f5880 URL: http://www.cs.unipr.it/git/gitweb.cgi?p=ppl/ppl.git;a=commit;h=cf40c1ee096f6...

Author: Fabio Bossi bossi@cs.unipr.it Date: Tue Sep 15 16:16:15 2009 +0200

Added a first implementation of refine_with_linear_form_inequality. Two small optimizations for affine_image.

---

src/Octagonal_Shape.templates.hh | 138 ++++++++++++++++++++++++++++++-------- 1 files changed, 110 insertions(+), 28 deletions(-)

diff --git a/src/Octagonal_Shape.templates.hh b/src/Octagonal_Shape.templates.hh index 761a468..ce65f96 100644 --- a/src/Octagonal_Shape.templates.hh +++ b/src/Octagonal_Shape.templates.hh @@ -490,6 +490,8 @@ Octagonal_Shape<T>::refine_with_linear_form_inequality( // Check that T is a floating point type. PPL_ASSERT(std::numeric_limits<T>::max_exponent);

+ // FIXME: what to do when empty? + // Dimension-compatibility checks. // The dimensions of `left' and `right' should not be greater than the // dimension of `*this'. @@ -503,6 +505,10 @@ Octagonal_Shape<T>::refine_with_linear_form_inequality( throw_dimension_incompatible( "refine_with_linear_form_inequality(left, right)", "right", right);

+ // FIXME: maybe it would be best to create a no_check variant. + if (marked_empty()) + return; + /* FIXME: these are not really necessary right now. They will come in handy when we optimize the most common cases. @@ -546,6 +552,9 @@ Octagonal_Shape<T>::refine_with_linear_form_inequality(

// General case.

+ // In the following, strong closure will be definitely lost. + reset_strongly_closed(); + // FIRST, update the binary constraints for each pair of DIFFERENT variables // in `left' and `right'.

@@ -558,19 +567,22 @@ Octagonal_Shape<T>::refine_with_linear_form_inequality( PPL_DIRTY_TEMP(N, rf_ub); PPL_DIRTY_TEMP(N, rs_lb); PPL_DIRTY_TEMP(N, rs_ub); + PPL_DIRTY_TEMP(N, upper_bound);

- // FIXME: to complete. + Linear_Form<FP_Interval_Type> right_minus_left(right); + right_minus_left -= left;

dimension_type max_w_id = std::max(left_w_id, right_w_id); - for (dimension_type first_v = 0; first_v <= max_w_id; ++first_v) { - for (dimension_type second_v = first_v; second_v <= max_w_id; ++second_v) { - FP_Interval_Type* lfv_coefficient = + for (dimension_type first_v = 0; first_v < max_w_id; ++first_v) { + for (dimension_type second_v = first_v+1; + second_v <= max_w_id; ++second_v) { + const FP_Interval_Type* lfv_coefficient = &(left.coefficient(Variable(first_v))); - FP_Interval_Type* lsv_coefficient = + const FP_Interval_Type* lsv_coefficient = &(left.coefficient(Variable(second_v))); - FP_Interval_Type* rfv_coefficient = + const FP_Interval_Type* rfv_coefficient = &(right.coefficient(Variable(first_v))); - FP_Interval_Type* rsv_coefficient = + const FP_Interval_Type* rsv_coefficient = &(right.coefficient(Variable(second_v))); assign_r(lf_lb, lfv_coefficient->lower(), ROUND_NOT_NEEDED); assign_r(lf_ub, lfv_coefficient->upper(), ROUND_NOT_NEEDED); @@ -580,10 +592,82 @@ Octagonal_Shape<T>::refine_with_linear_form_inequality( assign_r(rf_ub, rfv_coefficient->upper(), ROUND_NOT_NEEDED); assign_r(rs_lb, rsv_coefficient->lower(), ROUND_NOT_NEEDED); assign_r(rs_ub, rsv_coefficient->upper(), ROUND_NOT_NEEDED); + // true when both variables appear in at least one argument. + if ((lf_lb != 0 || lf_ub != 0 || rf_lb != 0 || rf_ub != 0) + && + (ls_lb != 0 || ls_ub != 0 || rs_lb != 0 || rs_lb != 0)) { + Variable first(first_v); + Variable second(second_v); + dimension_type n_first_var = first_v * 2; + dimension_type n_second_var = second_v * 2; + linear_form_upper_bound(right_minus_left - first + second, + upper_bound); + assign_r(matrix[n_second_var+1][n_first_var+1], + upper_bound, ROUND_NOT_NEEDED); + linear_form_upper_bound(right_minus_left + first + second, + upper_bound); + assign_r(matrix[n_second_var+1][n_first_var], + upper_bound, ROUND_NOT_NEEDED); + linear_form_upper_bound(right_minus_left - first - second, + upper_bound); + assign_r(matrix[n_second_var][n_first_var+1], + upper_bound, ROUND_NOT_NEEDED); + linear_form_upper_bound(right_minus_left + first - second, + upper_bound); + assign_r(matrix[n_second_var][n_first_var], + upper_bound, ROUND_NOT_NEEDED); + } } }

// Finally, update the unary constraints. + for (dimension_type v = 0; v <= max_w_id; ++v) { + const FP_Interval_Type* lv_coefficient = + &(left.coefficient(Variable(v))); + const FP_Interval_Type* rv_coefficient = + &(right.coefficient(Variable(v))); + assign_r(lf_lb, lv_coefficient->lower(), ROUND_NOT_NEEDED); + assign_r(lf_ub, lv_coefficient->upper(), ROUND_NOT_NEEDED); + assign_r(rf_lb, rv_coefficient->lower(), ROUND_NOT_NEEDED); + assign_r(rf_ub, rv_coefficient->upper(), ROUND_NOT_NEEDED); + // true if variable v appears in one of the two arguments. + if (lf_lb != 0 || lf_ub != 0 || rf_lb != 0 || rf_ub != 0) { + Variable var(v); + dimension_type n_var = 2 * v; + /* + VERY DIRTY trick: since we need to keep the old unary constraints + while computing the new ones, we momentarily keep the new coefficients + in the main diagonal of the matrix. They will be moved later. + */ + linear_form_upper_bound(right_minus_left + var, upper_bound); + assign_r(matrix[n_var+1][n_var+1], upper_bound, ROUND_NOT_NEEDED); + linear_form_upper_bound(right_minus_left - var, upper_bound); + assign_r(matrix[n_var][n_var], upper_bound, ROUND_NOT_NEEDED); + } + } + + /* + Now move the newly computed coefficients from the main diagonal to + their proper place, and restore +infinity on the diagonal. + */ + Row_Iterator m_ite = matrix.row_begin(); + Row_Iterator m_end = matrix.row_end(); + for (dimension_type i = 0; m_ite != m_end; i += 2) { + Row_Reference upper = *m_ite; + N& ul = upper[i]; + N& ur = upper[i+1]; + assign_r(ur, ul, ROUND_NOT_NEEDED); + assign_r(ul, PLUS_INFINITY, ROUND_NOT_NEEDED); + ++m_ite; + Row_Reference lower = *m_ite; + N& ll = lower[i]; + N& lr = lower[i+1]; + assign_r(ll, lr, ROUND_NOT_NEEDED); + assign_r(lr, PLUS_INFINITY, ROUND_NOT_NEEDED); + ++m_ite; + } + + PPL_ASSERT(OK());

}

@@ -4980,13 +5064,11 @@ Octagonal_Shape<T>::affine_image(Variable var, // In the following, strong closure will be definitely lost. reset_strongly_closed();

- Linear_Form<FP_Interval_Type> minus_lf(-lf); + Linear_Form<FP_Interval_Type> minus_lf(lf); + minus_lf.negate();

// Declare temporaries outside the loop. - PPL_DIRTY_TEMP(N, lf_plus_var_ub); - PPL_DIRTY_TEMP(N, lf_minus_var_ub); - PPL_DIRTY_TEMP(N, var_minus_lf_ub); - PPL_DIRTY_TEMP(N, minus_lf_minus_var_ub); + PPL_DIRTY_TEMP(N, upper_bound);

Row_Iterator m_iter = matrix.row_begin(); m_iter += n_var; @@ -5000,14 +5082,14 @@ Octagonal_Shape<T>::affine_image(Variable var, for (dimension_type curr_var = var_id, n_curr_var = n_var - 2; curr_var-- > 0; ) { Variable current(curr_var); - linear_form_upper_bound(lf + current, lf_plus_var_ub); - linear_form_upper_bound(lf - current, lf_minus_var_ub); - linear_form_upper_bound(minus_lf + current, var_minus_lf_ub); - linear_form_upper_bound(minus_lf - current, minus_lf_minus_var_ub); - assign_r(var_ite[n_curr_var], var_minus_lf_ub, ROUND_NOT_NEEDED); - assign_r(var_ite[n_curr_var+1], minus_lf_minus_var_ub, ROUND_NOT_NEEDED); - assign_r(var_cv_ite[n_curr_var], lf_plus_var_ub, ROUND_NOT_NEEDED); - assign_r(var_cv_ite[n_curr_var+1], lf_minus_var_ub, ROUND_NOT_NEEDED); + linear_form_upper_bound(lf + current, upper_bound); + assign_r(var_cv_ite[n_curr_var], upper_bound, ROUND_NOT_NEEDED); + linear_form_upper_bound(lf - current, upper_bound); + assign_r(var_cv_ite[n_curr_var+1], upper_bound, ROUND_NOT_NEEDED); + linear_form_upper_bound(minus_lf + current, upper_bound); + assign_r(var_ite[n_curr_var], upper_bound, ROUND_NOT_NEEDED); + linear_form_upper_bound(minus_lf - current, upper_bound); + assign_r(var_ite[n_curr_var+1], upper_bound, ROUND_NOT_NEEDED); n_curr_var -= 2; } for (dimension_type curr_var = var_id+1; m_iter != m_end; ++m_iter) { @@ -5015,14 +5097,14 @@ Octagonal_Shape<T>::affine_image(Variable var, ++m_iter; Row_Reference m_cv_ite = *m_iter; Variable current(curr_var); - linear_form_upper_bound(lf + current, lf_plus_var_ub); - linear_form_upper_bound(lf - current, lf_minus_var_ub); - linear_form_upper_bound(minus_lf + current, var_minus_lf_ub); - linear_form_upper_bound(minus_lf - current, minus_lf_minus_var_ub); - assign_r(m_v_ite[n_var], lf_minus_var_ub, ROUND_NOT_NEEDED); - assign_r(m_v_ite[n_var+1], minus_lf_minus_var_ub, ROUND_NOT_NEEDED); - assign_r(m_cv_ite[n_var], lf_plus_var_ub, ROUND_NOT_NEEDED); - assign_r(m_cv_ite[n_var+1], var_minus_lf_ub, ROUND_NOT_NEEDED); + linear_form_upper_bound(lf + current, upper_bound); + assign_r(m_cv_ite[n_var], upper_bound, ROUND_NOT_NEEDED); + linear_form_upper_bound(lf - current, upper_bound); + assign_r(m_v_ite[n_var], upper_bound, ROUND_NOT_NEEDED); + linear_form_upper_bound(minus_lf + current, upper_bound); + assign_r(m_cv_ite[n_var+1], upper_bound, ROUND_NOT_NEEDED); + linear_form_upper_bound(minus_lf - current, upper_bound); + assign_r(m_v_ite[n_var+1], upper_bound, ROUND_NOT_NEEDED); ++curr_var; }