/* BEGIN OUTFILE1 */ load("stringproc"); /* Begin Function number 3*/ display_poles() := ( block([rad_given], if (glob_type_given_pole = 4) then ( /* if number 1*/ rad_given : sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) , omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "), omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," ") ) elseif (glob_type_given_pole = 3) then ( /* if number 2*/ omniout_str(ALWAYS,"NO POLE (given) for Equation 1") ) else ( omniout_str(ALWAYS,"NO INFO (given) for Equation 1") )/* end if 2*/ , if (array_poles[1,1] # glob_large_float) then ( /* if number 2*/ omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "), omniout_str(ALWAYS,"Order of pole (ratio test) Not computed") ) else ( omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1") )/* end if 2*/ , if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] # glob_large_float)) then ( /* if number 2*/ omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "), omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," ") ) else ( omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1") )/* end if 2*/ , if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] # glob_large_float)) then ( /* if number 2*/ omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "), omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," ") ) else ( omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1") )/* end if 2*/ ) ); /* End Function number3 */ /* Begin Function number 4*/ check_sign( x0 ,xf) := ( block( [ret], if (xf > x0) then ( /* if number 2*/ ret : 1.0 ) else ( ret : -1.0 )/* end if 2*/ , ret ) ); /* End Function number4 */ /* Begin Function number 5*/ est_size_answer() := ( block( [ min_size], min_size : glob_large_float, if (omniabs(array_y[1]) < min_size) then ( /* if number 2*/ min_size : omniabs(array_y[1]), omniout_float(ALWAYS,"min_size",32,min_size,32,"") )/* end if 2*/ , if (min_size < 1.0) then ( /* if number 2*/ min_size : 1.0, omniout_float(ALWAYS,"min_size",32,min_size,32,"") )/* end if 2*/ , min_size ) ); /* End Function number5 */ /* Begin Function number 6*/ test_suggested_h() := ( block ([max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp], max_estimated_step_error : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""), omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""), omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""), est_tmp : omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3), if (est_tmp >= max_estimated_step_error) then ( /* if number 2*/ max_estimated_step_error : est_tmp )/* end if 2*/ , omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""), max_estimated_step_error ) ); /* End Function number6 */ /* Begin Function number 7*/ reached_interval() := ( block([ret], if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then ( /* if number 2*/ ret : true ) else ( ret : false )/* end if 2*/ , return(ret) ) ); /* End Function number7 */ /* Begin Function number 8*/ display_alot(iter) := ( block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], /* TOP DISPLAY ALOT */ if (reached_interval()) then ( /* if number 2*/ if (iter >= 0) then ( /* if number 3*/ ind_var : array_x[1], omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "), term_no : 1, numeric_val : array_y[term_no], abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "), if (omniabs(analytic_val_y) # 0.0) then ( /* if number 4*/ relerr : abserr*100.0/omniabs(analytic_val_y), if (relerr > 0.0000000000000000000000000000000001) then ( /* if number 5*/ glob_good_digits : -floor(log10(relerr)) + 3 ) else ( glob_good_digits : 16 )/* end if 5*/ ) else ( relerr : -1.0 , glob_good_digits : -1 )/* end if 4*/ , if (glob_iter = 1) then ( /* if number 4*/ array_1st_rel_error[1] : relerr ) else ( array_last_rel_error[1] : relerr )/* end if 4*/ , omniout_float(ALWAYS,"absolute error ",4,abserr,20," "), omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"), omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") , omniout_float(ALWAYS,"h ",4,glob_h,20," ") )/* end if 3*/ /* BOTTOM DISPLAY ALOT */ )/* end if 2*/ ) ); /* End Function number8 */ /* Begin Function number 9*/ adjust_for_pole(h_param) := ( block([hnew, sz2, tmp], /* TOP ADJUST FOR POLE */ hnew : h_param, glob_normmax : glob_small_float, if (omniabs(array_y_higher[1,1]) > glob_small_float) then ( /* if number 2*/ tmp : omniabs(array_y_higher[1,1]), if (tmp < glob_normmax) then ( /* if number 3*/ glob_normmax : tmp )/* end if 3*/ )/* end if 2*/ , if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] # glob_large_float)) then ( /* if number 2*/ sz2 : array_pole[1]/10.0, if (sz2 < hnew) then ( /* if number 3*/ omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."), omniout_str(INFO,"Reached Optimal"), return(hnew) )/* end if 3*/ )/* end if 2*/ , if ( not glob_reached_optimal_h) then ( /* if number 2*/ glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x[1] )/* end if 2*/ , hnew : sz2 ),/* END block */ return(hnew) /* BOTTOM ADJUST FOR POLE */ ); /* End Function number9 */ /* Begin Function number 10*/ prog_report(x_start,x_end) := ( block([ clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], /* TOP PROGRESS REPORT */ clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1), expect_sec : comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)), glob_total_exp_sec : glob_optimal_expect_sec + total_clock_sec, percent_done : comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)), glob_percent_done : percent_done, omniout_str_noeol(INFO,"Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO,"Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if (convfloat(percent_done) < convfloat(100.0)) then ( /* if number 2*/ omniout_str_noeol(INFO,"Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO,"Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO,"Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec)) )/* end if 2*/ , omniout_str_noeol(INFO,"Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ",33,percent_done,4,"%") /* BOTTOM PROGRESS REPORT */ ) ); /* End Function number10 */ /* Begin Function number 11*/ check_for_pole() := ( block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad], /* TOP CHECK FOR POLE */ array_pole[1] : glob_large_float, array_pole[2] : glob_large_float, tmp_rad : glob_large_float, prev_tmp_rad : glob_large_float, tmp_ratio : glob_large_float, rad_c : glob_large_float, array_poles[1,1] : glob_large_float, array_poles[1,2] : glob_large_float, /* TOP radius ratio test in Henrici1 */ found_sing : 1, n : glob_max_terms - 2 - 10, cnt : 0, while ((cnt < 5) and (found_sing = 1)) do ( /* do number 1*/ if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then ( /* if number 2*/ found_sing : 0 ) else ( tmp_rad : omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]), tmp_ratio : tmp_rad / prev_tmp_rad, if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then ( /* if number 3*/ if (tmp_rad < rad_c) then ( /* if number 4*/ rad_c : tmp_rad )/* end if 4*/ ) elseif (cnt = 0) then ( /* if number 4*/ if (tmp_rad < rad_c) then ( /* if number 5*/ rad_c : tmp_rad )/* end if 5*/ ) elseif (cnt > 0) then ( /* if number 5*/ found_sing : 0 )/* end if 5*/ )/* end if 4*/ , prev_tmp_rad : tmp_rad, cnt : cnt + 1, n : n + 1 )/* end do number 1*/ , if (found_sing = 1) then ( /* if number 4*/ if (rad_c < array_pole[1]) then ( /* if number 5*/ array_pole[1] : rad_c, array_poles[1,1] : rad_c )/* end if 5*/ )/* end if 4*/ , /* BOTTOM radius ratio test in Henrici1 */ /* IN RADII REAL EQ = 1 */ /* Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 */ /* Applies to pole of arbitrary r_order on the real axis, */ /* Due to Prof. George Corliss. */ n : glob_max_terms, m : n - 2 - 1, while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do ( /* do number 1*/ m : m - 1 )/* end do number 1*/ , if (m > 10) then ( /* if number 4*/ rm0 : array_y_higher[1,m]/array_y_higher[1,m-1], rm1 : array_y_higher[1,m-1]/array_y_higher[1,m-2], hdrc : convfloat(m)*rm0-convfloat(m-1)*rm1, if (omniabs(hdrc) > 0.0) then ( /* if number 5*/ rcs : glob_h/hdrc, ord_no : (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc, array_real_poles[1,1] : rcs, array_real_poles[1,2] : ord_no ) else ( array_real_poles[1,1] : glob_large_float, array_real_poles[1,2] : glob_large_float )/* end if 5*/ ) else ( array_real_poles[1,1] : glob_large_float, array_real_poles[1,2] : glob_large_float )/* end if 4*/ , /* BOTTOM RADII REAL EQ = 1 */ /* TOP RADII COMPLEX EQ = 1 */ /* Computes radius of convergence for complex conjugate pair of poles. */ /* from 6 adjacent Taylor series terms */ /* Also computes r_order of poles. */ /* Due to Manuel Prieto. */ /* With a correction by Dennis J. Darland */ n : glob_max_terms - 2 - 1, cnt : 0, while ((cnt < 5) and (n >= 10)) do ( /* do number 1*/ if (omniabs(array_y_higher[1,n]) # 0.0) then ( /* if number 4*/ cnt : cnt + 1 ) else ( cnt : 0 )/* end if 4*/ , n : n - 1 )/* end do number 1*/ , m : n + cnt, if (m <= 10) then ( /* if number 4*/ rad_c : glob_large_float, ord_no : glob_large_float ) else ( rm0 : (array_y_higher[1,m])/(array_y_higher[1,m-1]), rm1 : (array_y_higher[1,m-1])/(array_y_higher[1,m-2]), rm2 : (array_y_higher[1,m-2])/(array_y_higher[1,m-3]), rm3 : (array_y_higher[1,m-3])/(array_y_higher[1,m-4]), rm4 : (array_y_higher[1,m-4])/(array_y_higher[1,m-5]), nr1 : convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2, nr2 : convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3, dr1 : (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3, dr2 : (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4, ds1 : 3.0/rm1 - 8.0/rm2 + 5.0/rm3, ds2 : 3.0/rm2 - 8.0/rm3 + 5.0/rm4, if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then ( /* if number 5*/ rad_c : glob_large_float, ord_no : glob_large_float ) else ( if (omniabs(nr1*dr2 - nr2 * dr1) # 0.0) then ( /* if number 6*/ rcs : ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)), /* (Manuels) rcs : (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) */ ord_no : (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0, if (omniabs(rcs) # 0.0) then ( /* if number 7*/ if (rcs > 0.0) then ( /* if number 8*/ rad_c : sqrt(rcs) * omniabs(glob_h) ) else ( rad_c : glob_large_float )/* end if 8*/ ) else ( rad_c : glob_large_float, ord_no : glob_large_float )/* end if 7*/ ) else ( rad_c : glob_large_float, ord_no : glob_large_float )/* end if 6*/ )/* end if 5*/ , array_complex_poles[1,1] : rad_c, array_complex_poles[1,2] : ord_no )/* end if 4*/ , /* BOTTOM RADII COMPLEX EQ = 1 */ /* START ADJUST ALL SERIES */ if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then ( /* if number 4*/ h_new : array_pole[1] * glob_ratio_of_radius, term : 1, ratio : 1.0, while (term <= glob_max_terms) do ( /* do number 1*/ array_y[term] : array_y[term]* ratio, array_y_higher[1,term] : array_y_higher[1,term]* ratio, array_x[term] : array_x[term]* ratio, ratio : ratio * h_new / omniabs(glob_h), term : term + 1 )/* end do number 1*/ , glob_h : h_new )/* end if 4*/ /* BOTTOM ADJUST ALL SERIES */ , if (reached_interval()) then ( /* if number 4*/ display_poles() )/* end if 4*/ ) ); /* End Function number11 */ /* Begin Function number 12*/ get_norms() := ( block([ iii], if ( not glob_initial_pass) then ( /* if number 4*/ iii : 1, while (iii <= glob_max_terms) do ( /* do number 1*/ array_norms[iii] : 0.0, iii : iii + 1 )/* end do number 1*/ , /* TOP GET NORMS */ iii : 1, while (iii <= glob_max_terms) do ( /* do number 1*/ if (omniabs(array_y[iii]) > array_norms[iii]) then ( /* if number 5*/ array_norms[iii] : omniabs(array_y[iii]) )/* end if 5*/ , iii : iii + 1 )/* end do number 1*/ /* BOTTOM GET NORMS */ )/* end if 4*/ ) ); /* End Function number12 */ /* Begin Function number 13*/ atomall() := ( block([ kkk, order_d, adj2, adj3, temporary, term,temp,temp2], /* TOP ATOMALL */ /* END OUTFILE1 */ /* BEGIN ATOMHDR1 */ /* emit pre diff $eq_no = 1 i = 1 order_d = 1 */ array_tmp1[1] : array_y_higher[2,1], /* emit pre add CONST FULL $eq_no = 1 i = 1 */ array_tmp2[1] : array_const_0D0[1] + array_tmp1[1], /* emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 */ if ( not array_y_set_initial[1,3]) then ( /* if number 1*/ if (1 <= glob_max_terms) then ( /* if number 2*/ temporary : array_tmp2[1] * expt(glob_h , (2)) * factorial_3(0,2), array_y[3] : temporary, array_y_higher[1,3] : temporary, temporary : temporary / glob_h * (2.0), array_y_higher[2,2] : temporary, temporary : temporary / glob_h * (1.0), array_y_higher[3,1] : temporary, 0 )/* end if 2*/ )/* end if 1*/ , kkk : 2, /* END ATOMHDR1 */ /* BEGIN ATOMHDR2 */ /* emit pre diff $eq_no = 1 i = 2 order_d = 1 */ array_tmp1[2] : array_y_higher[2,2], /* emit pre add CONST FULL $eq_no = 1 i = 2 */ array_tmp2[2] : array_tmp1[2], /* emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 */ if ( not array_y_set_initial[1,4]) then ( /* if number 1*/ if (2 <= glob_max_terms) then ( /* if number 2*/ temporary : array_tmp2[2] * expt(glob_h , (2)) * factorial_3(1,3), array_y[4] : temporary, array_y_higher[1,4] : temporary, temporary : temporary / glob_h * (3.0), array_y_higher[2,3] : temporary, temporary : temporary / glob_h * (2.0), array_y_higher[3,2] : temporary, 0 )/* end if 2*/ )/* end if 1*/ , kkk : 3, /* END ATOMHDR2 */ /* BEGIN ATOMHDR3 */ /* emit pre diff $eq_no = 1 i = 3 order_d = 1 */ array_tmp1[3] : array_y_higher[2,3], /* emit pre add CONST FULL $eq_no = 1 i = 3 */ array_tmp2[3] : array_tmp1[3], /* emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 */ if ( not array_y_set_initial[1,5]) then ( /* if number 1*/ if (3 <= glob_max_terms) then ( /* if number 2*/ temporary : array_tmp2[3] * expt(glob_h , (2)) * factorial_3(2,4), array_y[5] : temporary, array_y_higher[1,5] : temporary, temporary : temporary / glob_h * (4.0), array_y_higher[2,4] : temporary, temporary : temporary / glob_h * (3.0), array_y_higher[3,3] : temporary, 0 )/* end if 2*/ )/* end if 1*/ , kkk : 4, /* END ATOMHDR3 */ /* BEGIN ATOMHDR4 */ /* emit pre diff $eq_no = 1 i = 4 order_d = 1 */ array_tmp1[4] : array_y_higher[2,4], /* emit pre add CONST FULL $eq_no = 1 i = 4 */ array_tmp2[4] : array_tmp1[4], /* emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 */ if ( not array_y_set_initial[1,6]) then ( /* if number 1*/ if (4 <= glob_max_terms) then ( /* if number 2*/ temporary : array_tmp2[4] * expt(glob_h , (2)) * factorial_3(3,5), array_y[6] : temporary, array_y_higher[1,6] : temporary, temporary : temporary / glob_h * (5.0), array_y_higher[2,5] : temporary, temporary : temporary / glob_h * (4.0), array_y_higher[3,4] : temporary, 0 )/* end if 2*/ )/* end if 1*/ , kkk : 5, /* END ATOMHDR4 */ /* BEGIN ATOMHDR5 */ /* emit pre diff $eq_no = 1 i = 5 order_d = 1 */ array_tmp1[5] : array_y_higher[2,5], /* emit pre add CONST FULL $eq_no = 1 i = 5 */ array_tmp2[5] : array_tmp1[5], /* emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 */ if ( not array_y_set_initial[1,7]) then ( /* if number 1*/ if (5 <= glob_max_terms) then ( /* if number 2*/ temporary : array_tmp2[5] * expt(glob_h , (2)) * factorial_3(4,6), array_y[7] : temporary, array_y_higher[1,7] : temporary, temporary : temporary / glob_h * (6.0), array_y_higher[2,6] : temporary, temporary : temporary / glob_h * (5.0), array_y_higher[3,5] : temporary, 0 )/* end if 2*/ )/* end if 1*/ , kkk : 6, /* END ATOMHDR5 */ /* BEGIN OUTFILE3 */ /* Top Atomall While Loop-- outfile3 */ while (kkk <= glob_max_terms) do ( /* do number 1*/ /* END OUTFILE3 */ /* BEGIN OUTFILE4 */ /* emit diff $eq_no = 1 */ array_tmp1[kkk] : array_y_higher[2,kkk], /* emit NOT FULL - FULL add $eq_no = 1 */ array_tmp2[kkk] : array_tmp1[kkk], /* emit assign $eq_no = 1 */ order_d : 2, if (kkk + order_d < glob_max_terms) then ( /* if number 1*/ if ( not array_y_set_initial[1,kkk + order_d]) then ( /* if number 2*/ temporary : array_tmp2[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)), array_y[kkk + order_d] : temporary, array_y_higher[1,kkk + order_d] : temporary, term : kkk + order_d - 1, adj2 : kkk + order_d - 1, adj3 : 2, while (term >= 1) do ( /* do number 1*/ if (adj3 <= order_d + 1) then ( /* if number 3*/ if (adj2 > 0) then ( /* if number 4*/ temporary : temporary / glob_h * convfp(adj2) ) else ( temporary : temporary )/* end if 4*/ , array_y_higher[adj3,term] : temporary )/* end if 3*/ , term : term - 1, adj2 : adj2 - 1, adj3 : adj3 + 1 )/* end do number 1*/ )/* end if 2*/ )/* end if 1*/ , kkk : kkk + 1 )/* end do number 1*/ /* BOTTOM ATOMALL */ /* END OUTFILE4 */ /* BEGIN OUTFILE5 */ ) /* BOTTOM ATOMALL ??? */ ); /* End Function number13 */ /* BEGIN ATS LIBRARY BLOCK */ log10(x) := (log(x)/log(10.0)); /* Begin Function number 2*/ omniout_str(iolevel,str) := ( if (glob_iolevel) >= iolevel then ( /* if number 1*/ printf(true,"~a~%",string(str)) )/* end if 1*/ ); /* End Function number2 */ /* Begin Function number 3*/ omniout_str_noeol(iolevel,str) := ( if (glob_iolevel >= iolevel) then ( /* if number 1*/ printf(true,"~a",string(str)) )/* end if 1*/ ); /* End Function number3 */ /* Begin Function number 4*/ omniout_labstr(iolevel,label,str) := ( if (glob_iolevel >= iolevel) then ( /* if number 1*/ printf(true,"~a = ~a~%",string(label),string(str)) )/* end if 1*/ ); /* End Function number4 */ /* Begin Function number 5*/ omniout_float(iolevel,prelabel,prelen,value,vallen,postlabel) := ( if (glob_iolevel >= iolevel) then ( /* if number 1*/ if vallen = 4 then ( printf(true,"~a = ~g ~s ~%",prelabel,value, postlabel) ) else ( printf(true,"~a = ~g ~s ~%",prelabel,value, postlabel) )/* end if 1*/ )/* end if 0*/ ); /* End Function number5 */ omniout_int(iolevel,prelabel,prelen,value,vallen,postlabel) := ( if (glob_iolevel >= iolevel) then ( /* if number 0*/ printf(true,"~a = ~d ~a~%",prelabel,value, postlabel), newline() )/* end if 0*/ ); /* End Function number5 */ /* Begin Function number 6*/ omniout_float_arr(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) := ( if (glob_iolevel >= iolevel) then ( /* if number 0*/ sprint(prelabel,"[",elemnt,"]=",value, postlabel), newline() )/* end if 0*/ ); /* End Function number6 */ /*Function Start*/ /* Begin Function number 7*/ dump_series(iolevel,dump_label,series_name,arr_series,numb) := ( block([i], if (glob_iolevel >= iolevel) then ( /* if number 0*/ i : 1, while (i <= numb) do ( sprint(dump_label,series_name,"i = ",i,"series = ",array_series[i]), newline(), i : i + 1 ) ) )/* end if 0*/ ); /* End Function number7 */ /* Begin Function number 8*/ dump_series_2(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) := ( /*Function Start*/ array_series2,numb,subnum ) := ( block([i,sub,ts_term], if (glob_iolevel >= iolevel) then ( /* if number 0*/ sub : 1, while (sub <= subnum) do ( /* do number 1*/ i : 1, while (i <= num) do ( /* do number 2*/ sprint(dump_label,series_name,"sub = ",sub,"i = ",i,"series2 = ",array_series2[sub,i]), i : i + 1 )/* end do number 2*/ , sub : sub + 1 )/* end do number 1*/ )/* end if 0*/ ) ); /* End Function number8 */ /* Begin Function number 9*/ cs_info(iolevel,str) := ( if (glob_iolevel >= iolevel) then ( /* if number 0*/ sprint(concat("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)) )/* end if 0*/ ); /* End Function number9 */ logitem_time(fd,secs_in) := ( block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd,"~%"), if (secs >= 0) then ( /* if number 0*/ years_int : trunc(secs / glob_sec_in_year), sec_temp : mod(trunc(secs) , trunc(glob_sec_in_year)), days_int : trunc(sec_temp / glob_sec_in_day) , sec_temp : mod(sec_temp , trunc(glob_sec_in_day)) , hours_int : trunc(sec_temp / glob_sec_in_hour), sec_temp : mod(sec_temp , trunc(glob_sec_in_hour)), minutes_int : trunc(sec_temp / glob_sec_in_minute), sec_int : mod(sec_temp , trunc(glob_sec_in_minute)), if (years_int > 0) then ( /* if number 1*/ printf(fd,"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",years_int,days_int,hours_int,minutes_int,sec_int) ) elseif (days_int > 0) then ( /* if number 2*/ printf(fd,"= ~d Days ~d Hours ~d Minutes ~d Seconds~%",days_int,hours_int,minutes_int,sec_int) ) elseif (hours_int > 0) then ( /* if number 3*/ printf(fd,"= ~d Hours ~d Minutes ~d Seconds~%",hours_int,minutes_int,sec_int) ) elseif (minutes_int > 0) then ( /* if number 4*/ printf(fd,"= ~d Minutes ~d Seconds~%",minutes_int,sec_int) ) else ( printf(fd,"= ~d Seconds~%",sec_int) )/* end if 4*/ ) else ( printf(fd," Unknown~%") )/* end if 3*/ , printf(fd,"~%") ) ); /* End Function number9 */ /* Begin Function number 10*/ omniout_timestr(secs_in) := ( block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if (secs >= 0) then ( /* if number 3*/ years_int : trunc(secs / glob_sec_in_year), sec_temp : mod(trunc(secs) , trunc(glob_sec_in_year)), days_int : trunc(sec_temp / glob_sec_in_day) , sec_temp : mod(sec_temp , trunc(glob_sec_in_day)) , hours_int : trunc(sec_temp / glob_sec_in_hour), sec_temp : mod(sec_temp , trunc(glob_sec_in_hour)), minutes_int : trunc(sec_temp / glob_sec_in_minute), sec_int : mod(sec_temp , trunc(glob_sec_in_minute)), if (years_int > 0) then ( /* if number 4*/ printf(true,"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%",years_int,days_int,hours_int,minutes_int,sec_int) ) elseif (days_int > 0) then ( /* if number 5*/ printf(true,"= ~d Days ~d Hours ~d Minutes ~d Seconds~%",days_int,hours_int,minutes_int,sec_int) ) elseif (hours_int > 0) then ( /* if number 6*/ printf(true,"= ~d Hours ~d Minutes ~d Seconds~%",hours_int,minutes_int,sec_int) ) elseif (minutes_int > 0) then ( /* if number 7*/ printf(true,"= ~d Minutes ~d Seconds~%",minutes_int,sec_int) ) else ( printf(true,"= ~d Seconds~%",sec_int) )/* end if 7*/ ) else ( printf(true," Unknown~%") )/* end if 6*/ ) ); /* End Function number10 */ /* Begin Function number 11*/ ats(mmm_ats,arr_a,arr_b,jjj_ats) := ( block([ iii_ats, lll_ats,ma_ats, ret_ats], ret_ats : 0.0, if (jjj_ats <= mmm_ats) then ( /* if number 6*/ ma_ats : mmm_ats + 1, iii_ats : jjj_ats, while (iii_ats <= mmm_ats) do ( /* do number 1*/ lll_ats : ma_ats - iii_ats, ret_ats : ret_ats + arr_a[iii_ats]*arr_b[lll_ats], iii_ats : iii_ats + 1 )/* end do number 1*/ )/* end if 6*/ , ret_ats ) ); /* End Function number11 */ /* Begin Function number 12*/ att(mmm_att,arr_aa,arr_bb,jjj_att) := ( block([ al_att, iii_att,lll_att, ma_att, ret_att], ret_att : 0.0, if (jjj_att <= mmm_att) then ( /* if number 6*/ ma_att : mmm_att + 2, iii_att : jjj_att, while (iii_att <= mmm_att) do ( /* do number 1*/ lll_att : ma_att - iii_att, al_att : (lll_att - 1), if (lll_att <= glob_max_terms) then ( /* if number 7*/ ret_att : ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att) )/* end if 7*/ , iii_att : iii_att + 1 )/* end do number 1*/ , ret_att : ret_att / convfp(mmm_att) )/* end if 6*/ , ret_att ) ); /* End Function number12 */ /* Begin Function number 13*/ display_pole_debug(typ,m,radius,order2) := ( if (typ = 1) then ( /* if number 6*/ omniout_str(ALWAYS,"Real") ) else ( omniout_str(ALWAYS,"Complex") )/* end if 6*/ , omniout_int(ALWAYS,"m",4, m ,4," "), omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "), omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ") ); /* End Function number13 */ /* Begin Function number 14*/ logditto(file) := ( printf(file,""), printf(file,"ditto"), printf(file,"") ); /* End Function number14 */ /* Begin Function number 15*/ logitem_integer(file,n) := ( printf(file,""), printf(file,"~d",n), printf(file,"") ); /* End Function number15 */ /* Begin Function number 16*/ logitem_str(file,str) := ( printf(file,""), printf(file,str), printf(file,"") ); /* End Function number16 */ /* Begin Function number 17*/ logitem_good_digits(file,rel_error) := ( block([good_digits], printf(file,""), if (rel_error # -1.0) then ( /* if number 6*/ if (rel_error > + 0.0000000000000000000000000000000001) then ( /* if number 7*/ good_digits : 1-floor(log10(rel_error)), printf(file,"~d",good_digits) ) else ( good_digits : 16, printf(file,"~d",good_digits) )/* end if 7*/ ) else ( printf(file,"Unknown") )/* end if 6*/ , printf(file,"") ) ); /* End Function number17 */ /* Begin Function number 18*/ log_revs(file,revs) := ( printf(file,revs) ); /* End Function number18 */ /* Begin Function number 19*/ logitem_float(file,x) := ( printf(file,""), printf(file,"~g",x), printf(file,"") ); /* End Function number19 */ /* Begin Function number 20*/ logitem_pole(file,pole) := ( printf(file,""), if pole = 0 then ( /* if number 6*/ printf(file,"NA") ) elseif pole = 1 then ( /* if number 7*/ printf(file,"Real") ) elseif pole = 2 then ( /* if number 8*/ printf(file,"Complex") ) elseif pole = 4 then ( /* if number 9*/ printf(file,"Yes") ) else ( printf(file,"No") )/* end if 9*/ , printf(file,"") ); /* End Function number20 */ /* Begin Function number 21*/ logstart(file) := ( printf(file,"") ); /* End Function number21 */ /* Begin Function number 22*/ logend(file) := ( printf(file,"~%") ); /* End Function number22 */ /* Begin Function number 23*/ chk_data() := ( block([ errflag], errflag : false, if ((glob_max_terms < 15) or (glob_max_terms > 512)) then ( /* if number 9*/ omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"), glob_max_terms : 30 )/* end if 9*/ , if (glob_max_iter < 2) then ( /* if number 9*/ omniout_str(ALWAYS,"Illegal max_iter"), errflag : true )/* end if 9*/ , if (errflag) then ( /* if number 9*/ quit() )/* end if 9*/ ) ); /* End Function number23 */ /* Begin Function number 24*/ comp_expect_sec(t_end2,t_start2,t2,clock_sec2) := ( block([ ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : (t_end2-t_start2), sub2 : (t2-t_start2), if (sub1 = 0.0) then ( /* if number 9*/ sec_left : 0.0 ) else ( if (sub2 > 0.0) then ( /* if number 10*/ rrr : (sub1/sub2), sec_left : rrr * ms2 - ms2 ) else ( sec_left : 0.0 )/* end if 10*/ )/* end if 9*/ , sec_left ) ); /* End Function number24 */ /* Begin Function number 25*/ comp_percent(t_end2,t_start2, t2) := ( block([ rrr, sub1, sub2], sub1 : (t_end2-t_start2), sub2 : (t2-t_start2), if (sub2 > glob_small_float) then ( /* if number 9*/ rrr : (100.0*sub2)/sub1 ) else ( rrr : 0.0 )/* end if 9*/ , rrr ) ); /* End Function number25 */ /* Begin Function number 26*/ factorial_2(nnn) := ( nnn! ); /* End Function number26 */ /* Begin Function number 27*/ factorial_1(nnn) := ( block([ ret], if (nnn <= glob_max_terms) then ( /* if number 9*/ if (array_fact_1[nnn] = 0) then ( /* if number 10*/ ret : factorial_2(nnn), array_fact_1[nnn] : ret ) else ( ret : array_fact_1[nnn] )/* end if 10*/ ) else ( ret : factorial_2(nnn) )/* end if 9*/ , ret ) ); /* End Function number27 */ /* Begin Function number 28*/ factorial_3(mmm,nnn) := ( block([ ret], if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then ( /* if number 9*/ if (array_fact_2[mmm,nnn] = 0) then ( /* if number 10*/ ret : factorial_1(mmm)/factorial_1(nnn), array_fact_2[mmm,nnn] : ret ) else ( ret : array_fact_2[mmm,nnn] )/* end if 10*/ ) else ( ret : factorial_2(mmm)/factorial_2(nnn) )/* end if 9*/ , ret ) ); /* End Function number28 */ /* Begin Function number 29*/ convfp(mmm) := ( (mmm) ); /* End Function number29 */ /* Begin Function number 30*/ convfloat(mmm) := ( (mmm) ); /* End Function number30 */ /* Begin Function number 31*/ elapsed_time_seconds() := ( block([t], t: elapsed_real_time(), t) ); /* End Function number31 */ /* Begin Function number 32*/ Si(x) := ( 0.0 ); /* End Function number32 */ /* Begin Function number 33*/ Ci(x) := ( 0.0 ); /* End Function number33 */ /* Begin Function number 34*/ ln(x) := ( log(x) ); /* End Function number34 */ /* Begin Function number 35*/ arcsin(x) := ( asin(x) ); /* End Function number35 */ /* Begin Function number 36*/ arccos(x) := ( acos(x) ); /* End Function number36 */ /* Begin Function number 37*/ arctan(x) := ( atan(x) ); /* End Function number37 */ /* Begin Function number 38*/ omniabs(x) := ( abs(x) ); /* End Function number38 */ /* Begin Function number 39*/ expt(x,y) := ( if ((x <= 0.0) and (y < 0.0)) then ( /* if number 9*/ print("expt error x = ",x,"y = ",y) )/* end if 9*/ , (x^y) ); /* End Function number39 */ /* Begin Function number 40*/ estimated_needed_step_error(x_start,x_end,estimated_h,estimated_answer) := ( block ([ desired_abs_gbl_error,range,estimated_steps,step_error], omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""), desired_abs_gbl_error : expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer), omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""), range : (x_end - x_start), omniout_float(ALWAYS,"range",32,range,32,""), estimated_steps : range / estimated_h, omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""), step_error : omniabs(desired_abs_gbl_error / estimated_steps), omniout_float(ALWAYS,"step_error",32,step_error,32,""), (step_error) ) ); /* End Function number40 */ /* END ATS LIBRARY BLOCK */ /* BEGIN USER DEF BLOCK */ /* BEGIN USER DEF BLOCK */ exact_soln_y (x) := (block( (1.0 + exp(x)) )); exact_soln_yp (x) := (block( (exp(x)) )); /* END USER DEF BLOCK */ /* END USER DEF BLOCK */ /* END OUTFILE5 */ /* Begin Function number 2*/ main() := ( /* BEGIN OUTFIEMAIN */ block([ d1,d2,d3,d4,est_err_2,niii,done_once, term,ord,order_diff,term_no,html_log_file,iiif,jjjf, rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, x_start,x_end ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it], define_variable(glob_max_terms,30,fixnum ), define_variable(glob_iolevel,5,fixnum ), define_variable(glob_yes_pole,4,fixnum ), define_variable(glob_no_pole,3,fixnum ), define_variable(glob_not_given,0,fixnum ), define_variable(ALWAYS,1,fixnum ), define_variable(INFO,2,fixnum ), define_variable(DEBUGL,3,fixnum ), define_variable(DEBUGMASSIVE,4,fixnum ), /* Top Generate Globals Definition */ define_variable(MAX_UNCHANGED,10,fixnum ), define_variable(glob_check_sign,1.0,float ), define_variable(glob_desired_digits_correct,8.0,float ), define_variable(glob_max_estimated_step_error,0.0,float ), define_variable(glob_ratio_of_radius,0.1,float ), define_variable(glob_percent_done,0.0,float ), define_variable(glob_subiter_method,3,fixnum ), define_variable(glob_total_exp_sec,0.1,float ), define_variable(glob_optimal_expect_sec,0.1,float ), define_variable(glob_html_log,true,boolean ), define_variable(glob_good_digits,0,fixnum ), define_variable(glob_max_opt_iter,10,fixnum ), define_variable(glob_dump,false,boolean ), define_variable(glob_djd_debug,true,boolean ), define_variable(glob_display_flag,true,boolean ), define_variable(glob_djd_debug2,true,boolean ), define_variable(glob_sec_in_minute,60,fixnum ), define_variable(glob_min_in_hour,60,fixnum ), define_variable(glob_hours_in_day,24,fixnum ), define_variable(glob_days_in_year,365,fixnum ), define_variable(glob_sec_in_hour,3600,fixnum ), define_variable(glob_sec_in_day,86400,fixnum ), define_variable(glob_sec_in_year,31536000,fixnum ), define_variable(glob_almost_1,0.9990,float ), define_variable(glob_clock_sec,0.0,float ), define_variable(glob_clock_start_sec,0.0,float ), define_variable(glob_not_yet_finished,true,boolean ), define_variable(glob_initial_pass,true,boolean ), define_variable(glob_not_yet_start_msg,true,boolean ), define_variable(glob_reached_optimal_h,false,boolean ), define_variable(glob_optimal_done,false,boolean ), define_variable(glob_disp_incr,0.1,float ), define_variable(glob_h,0.1,float ), define_variable(glob_max_h,0.1,float ), define_variable(glob_min_h,0.000001,float ), define_variable(glob_type_given_pole,0,fixnum ), define_variable(glob_large_float,9.0e100,float ), define_variable(glob_last_good_h,0.1,float ), define_variable(glob_look_poles,false,boolean ), define_variable(glob_neg_h,false,boolean ), define_variable(glob_display_interval,0.0,float ), define_variable(glob_next_display,0.0,float ), define_variable(glob_dump_analytic,false,boolean ), define_variable(glob_abserr,0.1e-10,float ), define_variable(glob_relerr,0.1e-10,float ), define_variable(glob_max_hours,0.0,float ), define_variable(glob_max_iter,1000,fixnum ), define_variable(glob_max_rel_trunc_err,0.1e-10,float ), define_variable(glob_max_trunc_err,0.1e-10,float ), define_variable(glob_no_eqs,0,fixnum ), define_variable(glob_optimal_clock_start_sec,0.0,float ), define_variable(glob_optimal_start,0.0,float ), define_variable(glob_small_float,0.0,float ), define_variable(glob_smallish_float,0.0,float ), define_variable(glob_unchanged_h_cnt,0,fixnum ), define_variable(glob_warned,false,boolean ), define_variable(glob_warned2,false,boolean ), define_variable(glob_max_sec,10000.0,float ), define_variable(glob_orig_start_sec,0.0,float ), define_variable(glob_start,0,fixnum ), define_variable(glob_curr_iter_when_opt,0,fixnum ), define_variable(glob_current_iter,0,fixnum ), define_variable(glob_iter,0,fixnum ), define_variable(glob_normmax,0.0,float ), define_variable(glob_max_minutes,0.0,float ), /* Bottom Generate Globals Deninition */ ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, /* Write Set Defaults */ glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : -1, opt_iter : -1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS,"##############temp/diffpostode.ode#################"), omniout_str(ALWAYS,"diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"Digits:32,"), omniout_str(ALWAYS,"max_terms:30,"), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"x_start:-5.0,"), omniout_str(ALWAYS,"x_end:5.0,"), omniout_str(ALWAYS,"array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS,"array_y_init[1 + 1] : exact_soln_yp(x_start),"), omniout_str(ALWAYS,"glob_look_poles:true,"), omniout_str(ALWAYS,"glob_max_iter:10000000,"), omniout_str(ALWAYS,"glob_display_interval:0.1,"), omniout_str(ALWAYS,"glob_max_minutes:10,"), omniout_str(ALWAYS,"/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS,"/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS,"glob_desired_digits_correct:10,"), omniout_str(ALWAYS,"glob_display_interval:0.01,"), omniout_str(ALWAYS,"glob_look_poles:true,"), omniout_str(ALWAYS,"glob_max_iter:10000000,"), omniout_str(ALWAYS,"glob_max_minutes:3,"), omniout_str(ALWAYS,"glob_subiter_method:3,"), omniout_str(ALWAYS,"/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS,"!"), omniout_str(ALWAYS,"/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS,"exact_soln_y (x) := (block("), omniout_str(ALWAYS," (1.0 + exp(x)) "), omniout_str(ALWAYS,"));"), omniout_str(ALWAYS,"exact_soln_yp (x) := (block("), omniout_str(ALWAYS," (exp(x)) "), omniout_str(ALWAYS,"));"), omniout_str(ALWAYS,""), omniout_str(ALWAYS,"/* END USER DEF BLOCK */"), omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 0.0, glob_smallish_float : 0.0, glob_large_float : 1.0e100, glob_almost_1 : 0.99, /* BEGIN FIRST INPUT BLOCK */ /* BEGIN FIRST INPUT BLOCK */ Digits:32, max_terms:30, /* END FIRST INPUT BLOCK */ /* START OF INITS AFTER INPUT BLOCK */ glob_max_terms : max_terms, glob_html_log : true, /* END OF INITS AFTER INPUT BLOCK */ array(array_y_init,max_terms+ 1), array(array_norms,max_terms+ 1), array(array_fact_1,max_terms+ 1), array(array_pole,4+ 1), array(array_real_pole,4+ 1), array(array_complex_pole,4+ 1), array(array_1st_rel_error,2+ 1), array(array_last_rel_error,2+ 1), array(array_type_pole,2+ 1), array(array_type_real_pole,2+ 1), array(array_type_complex_pole,2+ 1), array(array_y,max_terms+ 1), array(array_x,max_terms+ 1), array(array_tmp0,max_terms+ 1), array(array_tmp1,max_terms+ 1), array(array_tmp2,max_terms+ 1), array(array_m1,max_terms+ 1), array(array_y_higher,3+ 1,max_terms+ 1), array(array_y_higher_work,3+ 1,max_terms+ 1), array(array_y_higher_work2,3+ 1,max_terms+ 1), array(array_y_set_initial,2+ 1,max_terms+ 1), array(array_poles,2+ 1,3+ 1), array(array_given_rad_poles,2+ 1,3+ 1), array(array_given_ord_poles,2+ 1,3+ 1), array(array_real_poles,2+ 1,3+ 1), array(array_complex_poles,2+ 1,3+ 1), array(array_fact_2,max_terms+ 1,max_terms+ 1), term : 1, while (term <= max_terms) do ( /* do number 1*/ array_y_init[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= max_terms) do ( /* do number 1*/ array_norms[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= max_terms) do ( /* do number 1*/ array_fact_1[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 4) do ( /* do number 1*/ array_pole[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 4) do ( /* do number 1*/ array_real_pole[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 4) do ( /* do number 1*/ array_complex_pole[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_1st_rel_error[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_last_rel_error[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_type_pole[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_type_real_pole[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= 2) do ( /* do number 1*/ array_type_complex_pole[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= max_terms) do ( /* do number 1*/ array_y[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= max_terms) do ( /* do number 1*/ array_x[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= max_terms) do ( /* do number 1*/ array_tmp0[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= max_terms) do ( /* do number 1*/ array_tmp1[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= max_terms) do ( /* do number 1*/ array_tmp2[term] : 0.0, term : term + 1 )/* end do number 1*/ , term : 1, while (term <= max_terms) do ( /* do number 1*/ array_m1[term] : 0.0, term : term + 1 )/* end do number 1*/ , ord : 1, while (ord <=3) do ( /* do number 1*/ term : 1, while (term <= max_terms) do ( /* do number 2*/ array_y_higher[ord,term] : 0.0, term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=3) do ( /* do number 1*/ term : 1, while (term <= max_terms) do ( /* do number 2*/ array_y_higher_work[ord,term] : 0.0, term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=3) do ( /* do number 1*/ term : 1, while (term <= max_terms) do ( /* do number 2*/ array_y_higher_work2[ord,term] : 0.0, term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= max_terms) do ( /* do number 2*/ array_y_set_initial[ord,term] : 0.0, term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 3) do ( /* do number 2*/ array_poles[ord,term] : 0.0, term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 3) do ( /* do number 2*/ array_given_rad_poles[ord,term] : 0.0, term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 3) do ( /* do number 2*/ array_given_ord_poles[ord,term] : 0.0, term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 3) do ( /* do number 2*/ array_real_poles[ord,term] : 0.0, term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=2) do ( /* do number 1*/ term : 1, while (term <= 3) do ( /* do number 2*/ array_complex_poles[ord,term] : 0.0, term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , ord : 1, while (ord <=max_terms) do ( /* do number 1*/ term : 1, while (term <= max_terms) do ( /* do number 2*/ array_fact_2[ord,term] : 0.0, term : term + 1 )/* end do number 2*/ , ord : ord + 1 )/* end do number 1*/ , /* BEGIN ARRAYS DEFINED AND INITIALIZATED */ array(array_y,max_terms+1 + 1), term : 1, while (term <= max_terms + 1) do ( /* do number 1*/ array_y[term] : 0.0, term : term + 1 )/* end do number 1*/ , array(array_x,max_terms+1 + 1), term : 1, while (term <= max_terms + 1) do ( /* do number 1*/ array_x[term] : 0.0, term : term + 1 )/* end do number 1*/ , array(array_tmp0,max_terms+1 + 1), term : 1, while (term <= max_terms + 1) do ( /* do number 1*/ array_tmp0[term] : 0.0, term : term + 1 )/* end do number 1*/ , array(array_tmp1,max_terms+1 + 1), term : 1, while (term <= max_terms + 1) do ( /* do number 1*/ array_tmp1[term] : 0.0, term : term + 1 )/* end do number 1*/ , array(array_tmp2,max_terms+1 + 1), term : 1, while (term <= max_terms + 1) do ( /* do number 1*/ array_tmp2[term] : 0.0, term : term + 1 )/* end do number 1*/ , array(array_m1,max_terms+1 + 1), term : 1, while (term <= max_terms + 1) do ( /* do number 1*/ array_m1[term] : 0.0, term : term + 1 )/* end do number 1*/ , array(array_const_2,max_terms+1 + 1), term : 1, while (term <= max_terms + 1) do ( /* do number 1*/ array_const_2[term] : 0.0, term : term + 1 )/* end do number 1*/ , array_const_2[1] : 2, array(array_const_0D0,max_terms+1 + 1), term : 1, while (term <= max_terms + 1) do ( /* do number 1*/ array_const_0D0[term] : 0.0, term : term + 1 )/* end do number 1*/ , array_const_0D0[1] : 0.0, array(array_const_1,max_terms+1 + 1), term : 1, while (term <= max_terms + 1) do ( /* do number 1*/ array_const_1[term] : 0.0, term : term + 1 )/* end do number 1*/ , array_const_1[1] : 1, array(array_m1,max_terms+1 + 1), term : 1, while (term <= max_terms) do ( /* do number 1*/ array_m1[term] : 0.0, term : term + 1 )/* end do number 1*/ , array_m1[1] : -1.0, /* END ARRAYS DEFINED AND INITIALIZATED */ /* Initing Factorial Tables */ iiif : 0, while (iiif <= glob_max_terms) do ( /* do number 1*/ jjjf : 0, while (jjjf <= glob_max_terms) do ( /* do number 2*/ array_fact_1[iiif] : 0, array_fact_2[iiif,jjjf] : 0, jjjf : jjjf + 1 )/* end do number 2*/ , iiif : iiif + 1 )/* end do number 1*/ , /* Done Initing Factorial Tables */ /* TOP SECOND INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start:-5.0, x_end:5.0, array_y_init[0 + 1] : exact_soln_y(x_start), array_y_init[1 + 1] : exact_soln_yp(x_start), glob_look_poles:true, glob_max_iter:10000000, glob_display_interval:0.1, glob_max_minutes:10, /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct:10, glob_display_interval:0.01, glob_look_poles:true, glob_max_iter:10000000, glob_max_minutes:3, glob_subiter_method:3, /* END OVERRIDE BLOCK */ /* END SECOND INPUT BLOCK */ /* BEGIN INITS AFTER SECOND INPUT BLOCK */ glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours), if (glob_h > 0.0) then ( /* if number 1*/ glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval) ) else ( glob_neg_h : true, glob_display_interval : -omniabs(glob_display_interval) )/* end if 1*/ , chk_data(), /* AFTER INITS AFTER SECOND INPUT BLOCK */ array_y_set_initial[1,1] : true, array_y_set_initial[1,2] : true, array_y_set_initial[1,3] : false, array_y_set_initial[1,4] : false, array_y_set_initial[1,5] : false, array_y_set_initial[1,6] : false, array_y_set_initial[1,7] : false, array_y_set_initial[1,8] : false, array_y_set_initial[1,9] : false, array_y_set_initial[1,10] : false, array_y_set_initial[1,11] : false, array_y_set_initial[1,12] : false, array_y_set_initial[1,13] : false, array_y_set_initial[1,14] : false, array_y_set_initial[1,15] : false, array_y_set_initial[1,16] : false, array_y_set_initial[1,17] : false, array_y_set_initial[1,18] : false, array_y_set_initial[1,19] : false, array_y_set_initial[1,20] : false, array_y_set_initial[1,21] : false, array_y_set_initial[1,22] : false, array_y_set_initial[1,23] : false, array_y_set_initial[1,24] : false, array_y_set_initial[1,25] : false, array_y_set_initial[1,26] : false, array_y_set_initial[1,27] : false, array_y_set_initial[1,28] : false, array_y_set_initial[1,29] : false, array_y_set_initial[1,30] : false, /* BEGIN OPTIMIZE CODE */ omniout_str(ALWAYS,"START of Optimize"), /* Start Series -- INITIALIZE FOR OPTIMIZE */ glob_check_sign : check_sign(x_start,x_end), glob_h : check_sign(x_start,x_end), found_h : false, glob_h : glob_min_h, if (glob_max_h < glob_h) then ( /* if number 4*/ glob_h : glob_max_h )/* end if 4*/ , if (glob_display_interval < glob_h) then ( /* if number 4*/ glob_h : glob_display_interval )/* end if 4*/ , best_h : glob_h, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, est_needed_step_err : estimated_needed_step_error(x_start,x_end,glob_h,est_answer), omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""), estimated_step_error : 0.0, while ((opt_iter <= 100) and ( not found_h)) do ( /* do number 1*/ omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""), array_x[1] : x_start, array_x[2] : glob_h, glob_next_display : x_start, order_diff : 2, /* Start Series array_y */ term_no : 1, while (term_no <= order_diff) do ( /* do number 2*/ array_y[term_no] : array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1), term_no : term_no + 1 )/* end do number 2*/ , rows : order_diff, r_order : 1, while (r_order <= rows) do ( /* do number 2*/ term_no : 1, while (term_no <= (rows - r_order + 1)) do ( /* do number 3*/ it : term_no + r_order - 1, array_y_higher[r_order,term_no] : array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))), term_no : term_no + 1 )/* end do number 3*/ , r_order : r_order + 1 )/* end do number 2*/ , atomall(), estimated_step_error : test_suggested_h(), omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""), if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then ( /* if number 4*/ found_h : true, glob_h : glob_max_h, best_h : glob_h ) elseif ((estimated_step_error > est_needed_step_err) and ( not found_h)) then ( /* if number 5*/ glob_h : glob_h/2.0, best_h : glob_h, found_h : true ) else ( glob_h : glob_h*2.0, best_h : glob_h )/* end if 5*/ , omniout_float(ALWAYS,"best_h",32,best_h,32,""), opt_iter : opt_iter + 1 )/* end do number 1*/ , if (( not found_h) and (opt_iter = 1)) then ( /* if number 5*/ omniout_str(ALWAYS,"Beginning glob_h too large."), found_h : false )/* end if 5*/ , if (opt_iter > 100) then ( /* if number 5*/ glob_h : glob_max_h, found_h : false )/* end if 5*/ , if (glob_display_interval < glob_h) then ( /* if number 5*/ glob_h : glob_display_interval )/* end if 5*/ , /* END OPTIMIZE CODE */ if (glob_html_log) then ( /* if number 5*/ html_log_file : openw("entry.html") )/* end if 5*/ , /* BEGIN SOLUTION CODE */ if (found_h) then ( /* if number 5*/ omniout_str(ALWAYS,"START of Soultion"), /* Start Series -- INITIALIZE FOR SOLUTION */ array_x[1] : x_start, array_x[2] : glob_h, glob_next_display : x_start, order_diff : 2, /* Start Series array_y */ term_no : 1, while (term_no <= order_diff) do ( /* do number 1*/ array_y[term_no] : array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1), term_no : term_no + 1 )/* end do number 1*/ , rows : order_diff, r_order : 1, while (r_order <= rows) do ( /* do number 1*/ term_no : 1, while (term_no <= (rows - r_order + 1)) do ( /* do number 2*/ it : term_no + r_order - 1, array_y_higher[r_order,term_no] : array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))), term_no : term_no + 1 )/* end do number 2*/ , r_order : r_order + 1 )/* end do number 1*/ , current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL," "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do ( /* do number 1*/ /* left paren 0001C */ if (reached_interval()) then ( /* if number 6*/ omniout_str(INFO," "), omniout_str(INFO,"TOP MAIN SOLVE Loop") )/* end if 6*/ , glob_iter : glob_iter + 1, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : glob_current_iter + 1, atomall(), display_alot(current_iter), if (glob_look_poles) then ( /* if number 6*/ /* left paren 0004C */ check_for_pole() )/* end if 6*/ ,/* was right paren 0004C */ if (reached_interval()) then ( /* if number 6*/ glob_next_display : glob_next_display + glob_display_interval )/* end if 6*/ , array_x[1] : array_x[1] + glob_h, array_x[2] : glob_h /* Jump Series array_y */, order_diff : 3, /* START PART 1 SUM AND ADJUST */ /* START SUM AND ADJUST EQ =1 */ /* sum_and_adjust array_y */ /* BEFORE ADJUST SUBSERIES EQ =1 */ ord : 3, calc_term : 1, /* adjust_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 2*/ array_y_higher_work[3,iii] : array_y_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1), iii : iii - 1 )/* end do number 2*/ , /* AFTER ADJUST SUBSERIES EQ =1 */ /* BEFORE SUM SUBSERIES EQ =1 */ temp_sum : 0.0, ord : 3, calc_term : 1, /* sum_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 2*/ temp_sum : temp_sum + array_y_higher_work[ord,iii], iii : iii - 1 )/* end do number 2*/ , array_y_higher_work2[ord,calc_term] : temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)), /* AFTER SUM SUBSERIES EQ =1 */ /* BEFORE ADJUST SUBSERIES EQ =1 */ ord : 2, calc_term : 2, /* adjust_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 2*/ array_y_higher_work[2,iii] : array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1), iii : iii - 1 )/* end do number 2*/ , /* AFTER ADJUST SUBSERIES EQ =1 */ /* BEFORE SUM SUBSERIES EQ =1 */ temp_sum : 0.0, ord : 2, calc_term : 2, /* sum_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 2*/ temp_sum : temp_sum + array_y_higher_work[ord,iii], iii : iii - 1 )/* end do number 2*/ , array_y_higher_work2[ord,calc_term] : temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)), /* AFTER SUM SUBSERIES EQ =1 */ /* BEFORE ADJUST SUBSERIES EQ =1 */ ord : 2, calc_term : 1, /* adjust_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 2*/ array_y_higher_work[2,iii] : array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1), iii : iii - 1 )/* end do number 2*/ , /* AFTER ADJUST SUBSERIES EQ =1 */ /* BEFORE SUM SUBSERIES EQ =1 */ temp_sum : 0.0, ord : 2, calc_term : 1, /* sum_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 2*/ temp_sum : temp_sum + array_y_higher_work[ord,iii], iii : iii - 1 )/* end do number 2*/ , array_y_higher_work2[ord,calc_term] : temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)), /* AFTER SUM SUBSERIES EQ =1 */ /* BEFORE ADJUST SUBSERIES EQ =1 */ ord : 1, calc_term : 3, /* adjust_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 2*/ array_y_higher_work[1,iii] : array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1), iii : iii - 1 )/* end do number 2*/ , /* AFTER ADJUST SUBSERIES EQ =1 */ /* BEFORE SUM SUBSERIES EQ =1 */ temp_sum : 0.0, ord : 1, calc_term : 3, /* sum_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 2*/ temp_sum : temp_sum + array_y_higher_work[ord,iii], iii : iii - 1 )/* end do number 2*/ , array_y_higher_work2[ord,calc_term] : temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)), /* AFTER SUM SUBSERIES EQ =1 */ /* BEFORE ADJUST SUBSERIES EQ =1 */ ord : 1, calc_term : 2, /* adjust_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 2*/ array_y_higher_work[1,iii] : array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1), iii : iii - 1 )/* end do number 2*/ , /* AFTER ADJUST SUBSERIES EQ =1 */ /* BEFORE SUM SUBSERIES EQ =1 */ temp_sum : 0.0, ord : 1, calc_term : 2, /* sum_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 2*/ temp_sum : temp_sum + array_y_higher_work[ord,iii], iii : iii - 1 )/* end do number 2*/ , array_y_higher_work2[ord,calc_term] : temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)), /* AFTER SUM SUBSERIES EQ =1 */ /* BEFORE ADJUST SUBSERIES EQ =1 */ ord : 1, calc_term : 1, /* adjust_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 2*/ array_y_higher_work[1,iii] : array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1), iii : iii - 1 )/* end do number 2*/ , /* AFTER ADJUST SUBSERIES EQ =1 */ /* BEFORE SUM SUBSERIES EQ =1 */ temp_sum : 0.0, ord : 1, calc_term : 1, /* sum_subseriesarray_y */ iii : glob_max_terms, while (iii >= calc_term) do ( /* do number 2*/ temp_sum : temp_sum + array_y_higher_work[ord,iii], iii : iii - 1 )/* end do number 2*/ , array_y_higher_work2[ord,calc_term] : temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)), /* AFTER SUM SUBSERIES EQ =1 */ /* END SUM AND ADJUST EQ =1 */ /* END PART 1 */ /* START PART 2 MOVE TERMS to REGULAR Array */ term_no : glob_max_terms, while (term_no >= 1) do ( /* do number 2*/ array_y[term_no] : array_y_higher_work2[1,term_no], ord : 1, while (ord <= order_diff) do ( /* do number 3*/ array_y_higher[ord,term_no] : array_y_higher_work2[ord,term_no], ord : ord + 1 )/* end do number 3*/ , term_no : term_no - 1 )/* end do number 2*/ /* END PART 2 HEVE MOVED TERMS to REGULAR Array */ )/* end do number 1*/ ,/* right paren 0001C */ omniout_str(ALWAYS,"Finished!"), if (glob_iter >= glob_max_iter) then ( /* if number 6*/ omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") )/* end if 6*/ , if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then ( /* if number 6*/ omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") )/* end if 6*/ , glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO,"diff ( y , x , 2 ) = diff ( y , x , 1 ) ;"), omniout_int(INFO,"Iterations ",32,glob_iter,4," ") , prog_report(x_start,x_end), if (glob_html_log) then ( /* if number 6*/ logstart(html_log_file), logitem_str(html_log_file,"2013-05-26T00:22:34-05:00") , logitem_str(html_log_file,"Maxima") , logitem_str(html_log_file,"diff") , logitem_str(html_log_file,"diff ( y , x , 2 ) = diff ( y , x , 1 ) ;") , logitem_float(html_log_file,x_start) , logitem_float(html_log_file,x_end) , logitem_float(html_log_file,array_x[1]) , logitem_float(html_log_file,glob_h) , logitem_str(html_log_file,"16") , logitem_good_digits(html_log_file,array_last_rel_error[1]) , logitem_integer(html_log_file,glob_max_terms) , logitem_float(html_log_file,array_1st_rel_error[1]) , logitem_float(html_log_file,array_last_rel_error[1]) , logitem_integer(html_log_file,glob_iter) , logitem_time(html_log_file,convfloat(glob_clock_sec)) , if (glob_percent_done < 100.0) then ( /* if number 7*/ logitem_time(html_log_file,convfloat(glob_total_exp_sec)) , 0 ) else ( logitem_str(html_log_file,"Done") , 0 )/* end if 7*/ , log_revs(html_log_file," 189 ") , logitem_str(html_log_file,"diff diffeq.max") , logitem_str(html_log_file,"diff maxima results") , logitem_str(html_log_file,"All Tests - All Languages") , logend(html_log_file) )/* end if 6*/ , if (glob_html_log) then ( /* if number 6*/ close(html_log_file) )/* end if 6*/ )/* end if 5*/ /* END OUTFILEMAIN */ ) ); /* End Function number13 */ main();