|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 1 > ret := 1.0; > else > ret := -1.0; > fi;# end if 1; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 3 > # Begin Function number 4 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 1 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (min_size < 1.0) then # if number 1 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 4 > # Begin Function number 5 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms; > max_value3 := 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,""); > value3 := 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 (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > omniout_float(ALWAYS,"max_value3",32,max_value3,32,""); > max_value3; > end; test_suggested_h := proc() local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; max_value3 := 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, ""); value3 := 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 max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""); max_value3 end proc > # End Function number 5 > # Begin Function number 6 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 6 > # Begin Function number 7 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 1 > if (iter >= 0) then # if number 2 > 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 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3; > 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," "); > fi;# end if 2; > #BOTTOM DISPLAY ALOT > fi;# end if 1; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then 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. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 2 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; 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 end if end proc > # End Function number 7 > # Begin Function number 8 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local 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 1 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1; > if ( not glob_reached_optimal_h) then # if number 1 > 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]; > fi;# end if 1; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then 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; hnew := sz2; return hnew end proc > # End Function number 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local 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 1 > 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)); > fi;# end if 1; > 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; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; 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 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; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term; > #TOP CHECK FOR POLE > #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 - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2; > if (m > 10) then # if number 1 > 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) > glob_small_float * glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1; > #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 - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 1 > rad_c := glob_large_float; > ord_no := glob_large_float; > elif > (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2 > 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) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > 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) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2; > #BOTTOM RADII COMPLEX EQ = 1 > found_sing := 0; > #TOP WHICH RADII EQ = 1 > if (1 <> found_sing and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found_sing := 1; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found_sing := 1; > if (glob_display_flag) then # if number 3 > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 4; > fi;# end if 3; > fi;# end if 2; > if (1 <> found_sing ) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 3 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 3; > fi;# end if 2; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2; > #BOTTOM WHICH RADIUS EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 2 > 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; > od;# end do number 2; > glob_h := h_new; > fi;# end if 2; > #BOTTOM ADJUST ALL SERIES > if (reached_interval()) then # if number 2 > display_pole(); > fi;# end if 2 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and ( omniabs(array_y_higher[1, m]) < glob_small_float*glob_small_float or omniabs(array_y_higher[1, m - 1]) < glob_small_float*glob_small_float or omniabs(array_y_higher[1, m - 2]) < glob_small_float*glob_small_float) do m := m - 1 end do; if 10 < m then 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 glob_small_float*glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float elif glob_large_float <= omniabs(array_y_higher[1, m]) or glob_large_float <= omniabs(array_y_higher[1, m - 1]) or glob_large_float <= omniabs(array_y_higher[1, m - 2]) or glob_large_float <= omniabs(array_y_higher[1, m - 3]) or glob_large_float <= omniabs(array_y_higher[1, m - 4]) or glob_large_float <= omniabs(array_y_higher[1, m - 5]) or omniabs(array_y_higher[1, m]) <= glob_small_float or omniabs(array_y_higher[1, m - 1]) <= glob_small_float or omniabs(array_y_higher[1, m - 2]) <= glob_small_float or omniabs(array_y_higher[1, m - 3]) <= glob_small_float or omniabs(array_y_higher[1, m - 4]) <= glob_small_float or omniabs(array_y_higher[1, m - 5]) <= glob_small_float then 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)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(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) <= glob_small_float or omniabs(dr1) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found_sing := 0; if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found_sing := 1; array_type_pole[1] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found_sing := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do 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; glob_h := h_new end if; if reached_interval() then display_pole() end if end proc > # End Function number 10 > # Begin Function number 11 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 2 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 3; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 2; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > #emit pre sqrt 1 $eq_no = 1 > array_tmp4[1] := sqrt(array_tmp3[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0; > #emit pre sqrt ID_FULL iii = 2 $eq_no = 1 > #emit pre sqrt 2 $eq_no = 1 > array_tmp4[2] := 0.0; > array_tmp4[2] := (array_tmp3[2]-ats(2,array_tmp4,array_tmp4,2)) / array_tmp4[1] / 2.0; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0.0; > array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre sqrt ID_FULL iii = 3 $eq_no = 1 > #emit pre sqrt 3 $eq_no = 1 > array_tmp4[3] := 0.0; > array_tmp4[3] := (array_tmp3[3]-ats(3,array_tmp4,array_tmp4,2)) / array_tmp4[1] / 2.0; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0.0; > array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre sqrt ID_FULL iii = 4 $eq_no = 1 > #emit pre sqrt 4 $eq_no = 1 > array_tmp4[4] := 0.0; > array_tmp4[4] := (array_tmp3[4]-ats(4,array_tmp4,array_tmp4,2)) / array_tmp4[1] / 2.0; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0.0; > array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre sqrt ID_FULL iii = 5 $eq_no = 1 > #emit pre sqrt 5 $eq_no = 1 > array_tmp4[5] := 0.0; > array_tmp4[5] := (array_tmp3[5]-ats(5,array_tmp4,array_tmp4,2)) / array_tmp4[1] / 2.0; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# 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 sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0.0; > array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0; > #emit sqrt FULL $eq_no = 1 > array_tmp4[kkk] := 0.0; > array_tmp4[kkk] := (array_tmp3[kkk] - ats(kkk,array_tmp4,array_tmp4,2)) / array_tmp4[1] / 2.0; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp5[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 2 > 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; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4[1] := sqrt(array_tmp3[1]); array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0); array_tmp4[2] := 0.; array_tmp4[2] := (array_tmp3[2] - ats(2, array_tmp4, array_tmp4, 2))/( array_tmp4[1]*2.0); array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp3[3] := 0.; array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4[3] := 0.; array_tmp4[3] := (array_tmp3[3] - ats(3, array_tmp4, array_tmp4, 2))/( array_tmp4[1]*2.0); array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp3[4] := 0.; array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4[4] := 0.; array_tmp4[4] := (array_tmp3[4] - ats(4, array_tmp4, array_tmp4, 2))/( array_tmp4[1]*2.0); array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp3[5] := 0.; array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4[5] := 0.; array_tmp4[5] := (array_tmp3[5] - ats(5, array_tmp4, array_tmp4, 2))/( array_tmp4[1]*2.0); array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp3[kkk] := 0.; array_tmp3[kkk] := -ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0); array_tmp4[kkk] := 0.; array_tmp4[kkk] := ( array_tmp3[kkk] - ats(kkk, array_tmp4, array_tmp4, 2))/( array_tmp4[1]*2.0); array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp5[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 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 12 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local 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 <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("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 end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, "\n") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local 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; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do 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 end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local 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); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 6 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # End Function number 16 > # Begin Function number 17 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 20 > # Begin Function number 21 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 21 > # Begin Function number 22 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 8 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 24 > # Begin Function number 25 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc > # End Function number 25 > # Begin Function number 26 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 8 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 8; > if (glob_max_iter < 2) then # if number 8 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 8; > if (errflag) then # if number 8 > quit; > fi;# end if 8 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 26 > # Begin Function number 27 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local 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 8 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 9 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 9 > fi;# end if 8; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 27 > # Begin Function number 28 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 8 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 8; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 28 > # Begin Function number 29 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 29 > # Begin Function number 30 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 8 > if (array_fact_1[nnn] = 0) then # if number 9 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 9; > else > ret := factorial_2(nnn); > fi;# end if 8; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 8 > if (array_fact_2[mmm,nnn] = 0) then # if number 9 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 9; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 8; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 31 > # Begin Function number 32 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 33 > # Begin Function number 34 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 34 > # Begin Function number 35 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 35 > # Begin Function number 36 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 36 > # Begin Function number 37 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > 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; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; 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 proc > # End Function number 37 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(0.8 * (x + 2.0) * sqrt(sqrt(0.1 * x + 0.2))); > end; exact_soln_y := proc(x) return 0.8*(x + 2.0)*sqrt(sqrt(0.1*x + 0.2)) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local 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,value3,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.1e-200; > glob_smallish_float := 0.1e-100; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #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/sqrt_sqrtpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));"); > 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 := 0.1;"); > omniout_str(ALWAYS,"x_end := 0.5 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > 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:=0.001;"); > 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 := proc(x)"); > omniout_str(ALWAYS,"return(0.8 * (x + 2.0) * sqrt(sqrt(0.1 * x + 0.2)));"); > omniout_str(ALWAYS,"end;"); > 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 := 1.0e-200; > glob_smallish_float := 1.0e-64; > 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_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=1) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_const_0D1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D1[1] := 0.1; > array_const_0D2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D2[1] := 0.2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 0.5 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > 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); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > 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); > if (glob_display_interval < glob_h) then # if number 2 > glob_h := glob_display_interval; > fi;# end if 2; > if (glob_max_h < glob_h) then # if number 2 > glob_h := glob_max_h; > fi;# end if 2; > found_h := -1.0; > best_h := 0.0; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2 > 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 := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 3 > 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; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > 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; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > atomall(); > 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,""); > value3 := test_suggested_h(); > omniout_float(ALWAYS,"value3",32,value3,32,""); > if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2 > best_h := glob_h; > found_h := 1.0; > fi;# end if 2; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > glob_h := glob_h * 0.5; > od;# end do number 2; > if (found_h > 0.0) then # if number 2 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 2; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 2 > 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 := 1; > #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; > od;# 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; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > 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 2 > #left paren 0001C > if (reached_interval()) then # if number 3 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 3; > 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 3 > #left paren 0004C > check_for_pole(); > fi;# end if 3;#was right paren 0004C > if (reached_interval()) then # if number 3 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 3; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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; > od;# end do number 3; > #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 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > 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 3 > 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; > od;# end do number 3; > #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 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > 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 3 > 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; > od;# end do number 3; > #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 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > 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 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 2;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 3 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 3; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 3; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 3 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-28T19:38:02-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sqrt_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));") > ; > 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_integer(html_log_file,Digits) > ; > ; > 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_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 4; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 4 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 4; > log_revs(html_log_file," 165 ") > ; > logitem_str(html_log_file,"sqrt_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"sqrt_sqrt maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 3; > if (glob_html_log) then # if number 3 > fclose(html_log_file); > fi;# end if 3 > ; > ;; > fi;# end if 2 > #END OUTFILEMAIN > end; main := proc() local 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, value3, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.1*10^(-200); glob_smallish_float := 0.1*10^(-100); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; 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.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sqrt_sqrtpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));"); 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 := 0.1;"); omniout_str(ALWAYS, "x_end := 0.5 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); 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:=0.001;"); 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 := proc(x)"); omniout_str(ALWAYS, "return(0.8 * (x + 2.0) * sqrt(sqrt(0.1 * x + 0.2)));"); omniout_str(ALWAYS, "end;"); 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 := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_0D1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D1[term] := 0.; term := term + 1 end do; array_const_0D1[1] := 0.1; array_const_0D2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D2[term] := 0.; term := term + 1 end do; array_const_0D2[1] := 0.2; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 0.5; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; 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 0. < glob_h then 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; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; 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; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_max_h < glob_h then glob_h := glob_max_h end if; found_h := -1.0; best_h := 0.; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; while opt_iter <= 20 and found_h < 0. do 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 := 1; term_no := 1; while term_no <= order_diff do 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; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do 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; r_order := r_order + 1 end do; atomall(); 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, ""); value3 := test_suggested_h(); omniout_float(ALWAYS, "value3", 32, value3, 32, ""); if value3 < est_needed_step_err and found_h < 0. then best_h := glob_h; found_h := 1.0 end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1; glob_h := glob_h*0.5 end do; if 0. < found_h then glob_h := best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found") end if; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; if 0. < found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do 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; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do 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; r_order := r_order + 1 end do; 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 if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; 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 check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do 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; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do 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; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do 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; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));") ; omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-01-28T19:38:02-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sqrt_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));"); 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_integer(html_log_file, Digits); 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_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 165 "); logitem_str(html_log_file, "sqrt_sqrt diffeq.mxt"); logitem_str(html_log_file, "sqrt_sqrt maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrtpostode.ode################# diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2)); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 0.5 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(0.8 * (x + 2.0) * sqrt(sqrt(0.1 * x + 0.2))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.4 estimated_steps = 400 step_error = 2.5000000000000000000000000000000e-13 est_needed_step_err = 2.5000000000000000000000000000000e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 8.4135105462372732904425552992627e-91 max_value3 = 8.4135105462372732904425552992627e-91 value3 = 8.4135105462372732904425552992627e-91 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.1372713678556830191114874919567 y[1] (numeric) = 1.1372713678556830191114874919567 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.101 y[1] (analytic) = 1.1379483553881370327381823752768 y[1] (numeric) = 1.1379483553881370327381823752767 absolute error = 1e-31 relative error = 8.7877450260817422782925078054484e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.102 y[1] (analytic) = 1.1386254234807807318966501493581 y[1] (numeric) = 1.138625423480780731896650149358 absolute error = 1e-31 relative error = 8.7825195132478030402489174324988e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.103 y[1] (analytic) = 1.1393025721048682840552323014437 y[1] (numeric) = 1.1393025721048682840552323014436 absolute error = 1e-31 relative error = 8.7772995908584147857677139498219e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.31 x[1] = 0.104 y[1] (analytic) = 1.1399798012316777787949962525529 y[1] (numeric) = 1.1399798012316777787949962525528 absolute error = 1e-31 relative error = 8.7720852502786606600717227238068e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.105 y[1] (analytic) = 1.1406571108325111965408527226457 y[1] (numeric) = 1.1406571108325111965408527226456 absolute error = 1e-31 relative error = 8.7668764828910566903865648477940e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.106 y[1] (analytic) = 1.1413345008786943773483810753456 y[1] (numeric) = 1.1413345008786943773483810753455 absolute error = 1e-31 relative error = 8.7616732800955083304820187665424e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.107 y[1] (analytic) = 1.1420119713415769897462369875802 y[1] (numeric) = 1.1420119713415769897462369875801 absolute error = 1e-31 relative error = 8.7564756333092671341077793554186e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.108 y[1] (analytic) = 1.1426895221925324996340171324293 y[1] (numeric) = 1.1426895221925324996340171324292 absolute error = 1e-31 relative error = 8.7512835339668875568803369706057e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.109 y[1] (analytic) = 1.1433671534029581392354559053057 y[1] (numeric) = 1.1433671534029581392354559053055 absolute error = 2e-31 relative error = 1.7492193947040367772358865799070e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 1.1440448649442748761068295643318 y[1] (numeric) = 1.1440448649442748761068295643316 absolute error = 2e-31 relative error = 1.7481831886876374597228547905684e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.111 y[1] (analytic) = 1.1447226567879273822004434954263 y[1] (numeric) = 1.1447226567879273822004434954261 absolute error = 2e-31 relative error = 1.7471480870414206089242815374622e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.112 y[1] (analytic) = 1.1454005289053840029830786511756 y[1] (numeric) = 1.1454005289053840029830786511754 absolute error = 2e-31 relative error = 1.7461140880660535519515741940474e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.8MB, time=0.65 x[1] = 0.113 y[1] (analytic) = 1.1460784812681367266092735500495 y[1] (numeric) = 1.1460784812681367266092735500492 absolute error = 3e-31 relative error = 2.6176217850984320706764784977597e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.114 y[1] (analytic) = 1.1467565138477011531493185589201 y[1] (numeric) = 1.1467565138477011531493185589198 absolute error = 3e-31 relative error = 2.6160740870214276949198238341360e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.115 y[1] (analytic) = 1.147434626615616463871839517175 y[1] (numeric) = 1.1474346266156164638718395171748 absolute error = 2e-31 relative error = 1.7430186902229399842622741560147e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.116 y[1] (analytic) = 1.1481128195434453905808480949712 y[1] (numeric) = 1.148112819543445390580848094971 absolute error = 2e-31 relative error = 1.7419890850058735049376788461171e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.117 y[1] (analytic) = 1.1487910926027741850071366113705 y[1] (numeric) = 1.1487910926027741850071366113703 absolute error = 2e-31 relative error = 1.7409605740140905522177393675705e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.118 y[1] (analytic) = 1.1494694457652125882538953702266 y[1] (numeric) = 1.1494694457652125882538953702264 absolute error = 2e-31 relative error = 1.7399331555686382308653317487888e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.119 y[1] (analytic) = 1.1501478790023938002964309027649 y[1] (numeric) = 1.1501478790023938002964309027647 absolute error = 2e-31 relative error = 1.7389068279939308607112445994080e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 1.150826392285974449535863835812 y[1] (numeric) = 1.1508263922859744495358638358118 absolute error = 2e-31 relative error = 1.7378815896177416385238359388435e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.121 y[1] (analytic) = 1.1515049855876345624066854335994 y[1] (numeric) = 1.1515049855876345624066854335992 absolute error = 2e-31 relative error = 1.7368574387711943244474037464540e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=3.9MB, time=1.00 x[1] = 0.122 y[1] (analytic) = 1.1521836588790775330380521889825 y[1] (numeric) = 1.1521836588790775330380521889824 absolute error = 1e-31 relative error = 8.6791718689437747646266700269721e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.123 y[1] (analytic) = 1.1528624121320300929686981667934 y[1] (numeric) = 1.1528624121320300929686981667933 absolute error = 1e-31 relative error = 8.6740619650411178401220808503540e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.124 y[1] (analytic) = 1.1535412453182422809153451278806 y[1] (numeric) = 1.1535412453182422809153451278804 absolute error = 2e-31 relative error = 1.7337914947707259830770407246176e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.125 y[1] (analytic) = 1.1542201584094874125944907871906 y[1] (numeric) = 1.1542201584094874125944907871905 absolute error = 1e-31 relative error = 8.6638583871035278227915841191867e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.126 y[1] (analytic) = 1.1548991513775620505974558830157 y[1] (numeric) = 1.1548991513775620505974558830156 absolute error = 1e-31 relative error = 8.6587646965295752005773496269984e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.127 y[1] (analytic) = 1.1555782241942859743185710572699 y[1] (numeric) = 1.1555782241942859743185710572699 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.128 y[1] (analytic) = 1.156257376831502149936384868377 y[1] (numeric) = 1.156257376831502149936384868377 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.129 y[1] (analytic) = 1.1569366092610767004477745790449 y[1] (numeric) = 1.1569366092610767004477745790449 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 1.1576159214548988757548416808844 y[1] (numeric) = 1.1576159214548988757548416808843 absolute error = 1e-31 relative error = 8.6384437313473867282260833355837e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.131 y[1] (analytic) = 1.1582953133848810228044744364931 y[1] (numeric) = 1.1582953133848810228044744364931 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 memory used=15.2MB, alloc=4.0MB, time=1.35 TOP MAIN SOLVE Loop x[1] = 0.132 y[1] (analytic) = 1.1589747850229585557804600372856 y[1] (numeric) = 1.1589747850229585557804600372856 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.133 y[1] (analytic) = 1.1596543363410899263480292919964 y[1] (numeric) = 1.1596543363410899263480292919964 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.134 y[1] (analytic) = 1.1603339673112565939507170764376 y[1] (numeric) = 1.1603339673112565939507170764376 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.135 y[1] (analytic) = 1.1610136779054629961594220897376 y[1] (numeric) = 1.1610136779054629961594220897376 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.136 y[1] (analytic) = 1.1616934680957365190735497759466 y[1] (numeric) = 1.1616934680957365190735497759466 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.137 y[1] (analytic) = 1.1623733378541274677741225825563 y[1] (numeric) = 1.1623733378541274677741225825562 absolute error = 1e-31 relative error = 8.6030879015696712557973159547285e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.138 y[1] (analytic) = 1.1630532871527090368287420391593 y[1] (numeric) = 1.1630532871527090368287420391592 absolute error = 1e-31 relative error = 8.5980583267007256171678630405016e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.139 y[1] (analytic) = 1.163733315963577280848287450166 y[1] (numeric) = 1.1637333159635772808482874501659 absolute error = 1e-31 relative error = 8.5930340420991966045736928213812e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 1.164413424258851085095236305207 y[1] (numeric) = 1.1644134242588510850952363052069 absolute error = 1e-31 relative error = 8.5880150397312690103024371237498e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.1MB, time=1.71 x[1] = 0.141 y[1] (analytic) = 1.1650936120106721361434918195869 y[1] (numeric) = 1.1650936120106721361434918195868 absolute error = 1e-31 relative error = 8.5830013115790742499436682767902e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.142 y[1] (analytic) = 1.1657738791912048925896033249146 y[1] (numeric) = 1.1657738791912048925896033249144 absolute error = 2e-31 relative error = 1.7155985699281302559619409568178e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.143 y[1] (analytic) = 1.1664542257726365558152655368274 y[1] (numeric) = 1.1664542257726365558152655368272 absolute error = 2e-31 relative error = 1.7145979291859815256666044297918e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.144 y[1] (analytic) = 1.1671346517271770408009830325533 y[1] (numeric) = 1.1671346517271770408009830325532 absolute error = 1e-31 relative error = 8.5679916924765805410548760445488e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.145 y[1] (analytic) = 1.1678151570270589469907865759154 y[1] (numeric) = 1.1678151570270589469907865759153 absolute error = 1e-31 relative error = 8.5629989813261982388212272134392e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.146 y[1] (analytic) = 1.168495741644537529207888231287 y[1] (numeric) = 1.1684957416445375292078882312869 absolute error = 1e-31 relative error = 8.5580115045400412888035332866001e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.147 y[1] (analytic) = 1.1691764055518906686211625109537 y[1] (numeric) = 1.1691764055518906686211625109536 absolute error = 1e-31 relative error = 8.5530292541951040879634421588999e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.148 y[1] (analytic) = 1.1698571487214188437623411023315 y[1] (numeric) = 1.1698571487214188437623411023315 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.149 y[1] (analytic) = 1.1705379711254451015938090225373 y[1] (numeric) = 1.1705379711254451015938090225372 absolute error = 1e-31 relative error = 8.5430804012152053554745212267391e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 1.1712188727363150286268903479054 y[1] (numeric) = 1.1712188727363150286268903479053 absolute error = 1e-31 relative error = 8.5381137828124566845169473309408e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 memory used=22.8MB, alloc=4.1MB, time=2.06 TOP MAIN SOLVE Loop x[1] = 0.151 y[1] (analytic) = 1.1718998535263967220905119652055 y[1] (numeric) = 1.1718998535263967220905119652054 absolute error = 1e-31 relative error = 8.5331523593152772321045077484615e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.152 y[1] (analytic) = 1.1725809134680807611501340895319 y[1] (numeric) = 1.1725809134680807611501340895318 absolute error = 1e-31 relative error = 8.5281961228786567051730065970526e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.153 y[1] (analytic) = 1.1732620525337801781768365911193 y[1] (numeric) = 1.1732620525337801781768365911193 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.154 y[1] (analytic) = 1.1739432706959304300664504696929 y[1] (numeric) = 1.1739432706959304300664504696928 absolute error = 1e-31 relative error = 8.5182991798844388692720476398411e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.155 y[1] (analytic) = 1.1746245679269893696086241103793 y[1] (numeric) = 1.1746245679269893696086241103792 absolute error = 1e-31 relative error = 8.5133584577140954774797948128212e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.156 y[1] (analytic) = 1.1753059441994372169057142497069 y[1] (numeric) = 1.1753059441994372169057142497068 absolute error = 1e-31 relative error = 8.5084228913787436935540190724381e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.157 y[1] (analytic) = 1.1759873994857765308413918737946 y[1] (numeric) = 1.1759873994857765308413918737945 absolute error = 1e-31 relative error = 8.5034924731104222710948719073512e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.158 y[1] (analytic) = 1.1766689337585321805988535634873 y[1] (numeric) = 1.1766689337585321805988535634872 absolute error = 1e-31 relative error = 8.4985671951564674253977963004130e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.159 y[1] (analytic) = 1.1773505469902513172285290929364 y[1] (numeric) = 1.1773505469902513172285290929363 absolute error = 1e-31 relative error = 8.4936470497794756370560720280396e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.1MB, time=2.43 x[1] = 0.16 y[1] (analytic) = 1.1780322391535033452651763789517 y[1] (numeric) = 1.1780322391535033452651763789517 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.161 y[1] (analytic) = 1.1787140102208798943942551683725 y[1] (numeric) = 1.1787140102208798943942551683725 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.162 y[1] (analytic) = 1.1793958601649947911674711397168 y[1] (numeric) = 1.1793958601649947911674711397168 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.163 y[1] (analytic) = 1.1800777889584840307673823834842 y[1] (numeric) = 1.1800777889584840307673823834842 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.164 y[1] (analytic) = 1.1807597965740057488209605126949 y[1] (numeric) = 1.180759796574005748820960512695 absolute error = 1e-31 relative error = 8.4691230418033937586174318744938e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.165 y[1] (analytic) = 1.1814418829842401932619989415693 y[1] (numeric) = 1.1814418829842401932619989415694 absolute error = 1e-31 relative error = 8.4642335302526215626148491224170e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.166 y[1] (analytic) = 1.1821240481618896962422611556721 y[1] (numeric) = 1.1821240481618896962422611556722 absolute error = 1e-31 relative error = 8.4593490975411732290483049456261e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.167 y[1] (analytic) = 1.1828062920796786460912620813829 y[1] (numeric) = 1.182806292079678646091262081383 absolute error = 1e-31 relative error = 8.4544697360524011297800864148847e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.168 y[1] (analytic) = 1.1834886147103534593245759462016 y[1] (numeric) = 1.1834886147103534593245759462017 absolute error = 1e-31 relative error = 8.4495954381845879343562673649608e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.169 y[1] (analytic) = 1.1841710160266825527005643041608 y[1] (numeric) = 1.184171016026682552700564304161 absolute error = 2e-31 relative error = 1.6889452392701820947497385613197e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.1MB, time=2.78 x[1] = 0.17 y[1] (analytic) = 1.1848534960014563153254181825059 y[1] (numeric) = 1.184853496001456315325418182506 absolute error = 1e-31 relative error = 8.4398620029794037081700491484886e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.171 y[1] (analytic) = 1.1855360546074870808064085868064 y[1] (numeric) = 1.1855360546074870808064085868065 absolute error = 1e-31 relative error = 8.4350028505129247986144907942547e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.172 y[1] (analytic) = 1.186218691817609099453239881802 y[1] (numeric) = 1.1862186918176090994532398818021 absolute error = 1e-31 relative error = 8.4301487314091172817776136392571e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.173 y[1] (analytic) = 1.1869014076046785105274008445452 y[1] (numeric) = 1.1869014076046785105274008445453 absolute error = 1e-31 relative error = 8.4252996381403753480108803334011e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.174 y[1] (analytic) = 1.1875842019415733145394084648024 y[1] (numeric) = 1.1875842019415733145394084648025 absolute error = 1e-31 relative error = 8.4204555631938082219669109254873e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.175 y[1] (analytic) = 1.188267074801193345593839845205 y[1] (numeric) = 1.188267074801193345593839845205 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.176 y[1] (analytic) = 1.1889500261564602437820478303121 y[1] (numeric) = 1.1889500261564602437820478303122 absolute error = 1e-31 relative error = 8.4107824382889974631343645688272e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.177 y[1] (analytic) = 1.1896330559803174276224562695611 y[1] (numeric) = 1.1896330559803174276224562695612 absolute error = 1e-31 relative error = 8.4059533733782283077999598360029e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.178 y[1] (analytic) = 1.1903161642457300665483310940344 y[1] (numeric) = 1.1903161642457300665483310940345 absolute error = 1e-31 relative error = 8.4011292968845123897649051480075e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.1MB, time=3.15 x[1] = 0.179 y[1] (analytic) = 1.1909993509256850534429236610809 y[1] (numeric) = 1.190999350925685053442923661081 absolute error = 1e-31 relative error = 8.3963102013680033851599454356908e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 1.1916826159931909772218830940816 y[1] (numeric) = 1.1916826159931909772218830940817 absolute error = 1e-31 relative error = 8.3914960794033584257195677508535e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.181 y[1] (analytic) = 1.19236595942127809546283461706 y[1] (numeric) = 1.1923659594212780954628346170601 absolute error = 1e-31 relative error = 8.3866869235797031887517035609200e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.182 y[1] (analytic) = 1.1930493811829983070820211554049 y[1] (numeric) = 1.193049381182998307082021155405 absolute error = 1e-31 relative error = 8.3818827265005970870960579232523e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.183 y[1] (analytic) = 1.193732881251425125057905744697 y[1] (numeric) = 1.1937328812514251250579057446971 absolute error = 1e-31 relative error = 8.3770834807839985587390105634742e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.184 y[1] (analytic) = 1.1944164595996536492016325595221 y[1] (numeric) = 1.1944164595996536492016325595221 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.185 y[1] (analytic) = 1.1951001162008005389742446432057 y[1] (numeric) = 1.1951001162008005389742446432057 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.186 y[1] (analytic) = 1.1957838510280039863505566876305 y[1] (numeric) = 1.1957838510280039863505566876306 absolute error = 1e-31 relative error = 8.3627153782040920309227207476675e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.187 y[1] (analytic) = 1.1964676640544236887295814796907 y[1] (numeric) = 1.1964676640544236887295814796907 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.188 y[1] (analytic) = 1.1971515552532408218914088975071 y[1] (numeric) = 1.1971515552532408218914088975072 absolute error = 1e-31 relative error = 8.3531612652707439166224494851863e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=3.51 x[1] = 0.189 y[1] (analytic) = 1.1978355245976580130004366052779 y[1] (numeric) = 1.197835524597658013000436605278 absolute error = 1e-31 relative error = 8.3483915735083148864997529778832e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 1.198519572060899313654851860562 y[1] (numeric) = 1.1985195720608993136548518605621 absolute error = 1e-31 relative error = 8.3436267818343803029643356027310e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.191 y[1] (analytic) = 1.1992036976162101729822641119094 y[1] (numeric) = 1.1992036976162101729822641119095 absolute error = 1e-31 relative error = 8.3388668829808530815113847808570e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.192 y[1] (analytic) = 1.1998879012368574107813883280455 y[1] (numeric) = 1.1998879012368574107813883280456 absolute error = 1e-31 relative error = 8.3341118696937371996902118725977e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.193 y[1] (analytic) = 1.2005721828961291907096792623069 y[1] (numeric) = 1.200572182896129190709679262307 absolute error = 1e-31 relative error = 8.3293617347330939652951765188355e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.194 y[1] (analytic) = 1.201256542567334993516817117702 y[1] (numeric) = 1.2012565425673349935168171177021 absolute error = 1e-31 relative error = 8.3246164708730083806422032339102e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.195 y[1] (analytic) = 1.2019409802238055903239453388463 y[1] (numeric) = 1.2019409802238055903239453388464 absolute error = 1e-31 relative error = 8.3198760709015556026135413433460e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.196 y[1] (analytic) = 1.2026254958388930159485615170905 y[1] (numeric) = 1.2026254958388930159485615170906 absolute error = 1e-31 relative error = 8.3151405276207674981546115178262e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.197 y[1] (analytic) = 1.2033100893859705422749626544348 y[1] (numeric) = 1.2033100893859705422749626544349 absolute error = 1e-31 relative error = 8.3104098338465992949079692939664e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.1MB, time=3.86 x[1] = 0.198 y[1] (analytic) = 1.2039947608384326516701462902951 y[1] (numeric) = 1.2039947608384326516701462902952 absolute error = 1e-31 relative error = 8.3056839824088963266705981159508e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.199 y[1] (analytic) = 1.2046795101696950104450692528708 y[1] (numeric) = 1.2046795101696950104450692528709 absolute error = 1e-31 relative error = 8.3009629661513608733619216032221e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 1.2053643373531944423611660537526 y[1] (numeric) = 1.2053643373531944423611660537527 absolute error = 1e-31 relative error = 8.2962467779315190951910969713868e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.201 y[1] (analytic) = 1.2060492423623889021820292005117 y[1] (numeric) = 1.2060492423623889021820292005118 absolute error = 1e-31 relative error = 8.2915354106206880607133188293019e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.202 y[1] (analytic) = 1.2067342251707574492701539573293 y[1] (numeric) = 1.2067342251707574492701539573294 absolute error = 1e-31 relative error = 8.2868288571039428684660249679102e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.203 y[1] (analytic) = 1.2074192857518002212286503382576 y[1] (numeric) = 1.2074192857518002212286503382577 absolute error = 1e-31 relative error = 8.2821271102800838618770532686036e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.204 y[1] (analytic) = 1.2081044240790384075878253714596 y[1] (numeric) = 1.2081044240790384075878253714597 absolute error = 1e-31 relative error = 8.2774301630616039371379515133794e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.205 y[1] (analytic) = 1.2087896401260142235365389257509 y[1] (numeric) = 1.208789640126014223536538925751 absolute error = 1e-31 relative error = 8.2727380083746559437367896984340e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.206 y[1] (analytic) = 1.2094749338662908836982366429694 y[1] (numeric) = 1.2094749338662908836982366429695 absolute error = 1e-31 relative error = 8.2680506391590201773459674595544e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.207 y[1] (analytic) = 1.2101603052734525759515637711297 y[1] (numeric) = 1.2101603052734525759515637711299 absolute error = 2e-31 relative error = 1.6526736096736143929523294868134e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.1MB, time=4.22 x[1] = 0.208 y[1] (analytic) = 1.2108457543211044352954639439812 y[1] (numeric) = 1.2108457543211044352954639439814 absolute error = 2e-31 relative error = 1.6517380457937498681185157664867e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.209 y[1] (analytic) = 1.2115312809828725177586672024823 y[1] (numeric) = 1.2115312809828725177586672024825 absolute error = 2e-31 relative error = 1.6508034347883041630794408389963e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 1.2122168852324037743534718028387 y[1] (numeric) = 1.212216885232403774353471802839 absolute error = 3e-31 relative error = 2.4748046628841059704907198863005e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.211 y[1] (analytic) = 1.2129025670433660250737246041205 y[1] (numeric) = 1.2129025670433660250737246041207 absolute error = 2e-31 relative error = 1.6489370657985359460943302734412e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.212 y[1] (analytic) = 1.2135883263894479329369050760871 y[1] (numeric) = 1.2135883263894479329369050760873 absolute error = 2e-31 relative error = 1.6480053050198735518249839284040e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.213 y[1] (analytic) = 1.2142741632443589780702182147076 y[1] (numeric) = 1.2142741632443589780702182147078 absolute error = 2e-31 relative error = 1.6470744915269374470293767386110e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.214 y[1] (analytic) = 1.2149600775818294318406018989639 y[1] (numeric) = 1.2149600775818294318406018989641 absolute error = 2e-31 relative error = 1.6461446239292557501309401838096e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.215 y[1] (analytic) = 1.2156460693756103310285544678818 y[1] (numeric) = 1.215646069375610331028554467882 absolute error = 2e-31 relative error = 1.6452157008390243772461693511693e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.216 y[1] (analytic) = 1.216332138599473452045688541338 y[1] (numeric) = 1.2163321385994734520456885413381 absolute error = 1e-31 relative error = 8.2214386043555036108610315101826e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.1MB, time=4.58 x[1] = 0.217 y[1] (analytic) = 1.2170182852272112851959173520527 y[1] (numeric) = 1.2170182852272112851959173520528 absolute error = 1e-31 relative error = 8.2168034132149867709516151661266e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.218 y[1] (analytic) = 1.2177045092326370089801800992967 y[1] (numeric) = 1.2177045092326370089801800992968 absolute error = 1e-31 relative error = 8.2121729238743786681353614884423e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.219 y[1] (analytic) = 1.2183908105895844644446130772175 y[1] (numeric) = 1.2183908105895844644446130772176 absolute error = 1e-31 relative error = 8.2075471294476997255754551822598e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 1.2190771892719081295720735723323 y[1] (numeric) = 1.2190771892719081295720735723324 absolute error = 1e-31 relative error = 8.2029260230621522424787837937666e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.221 y[1] (analytic) = 1.2197636452534830937169237656406 y[1] (numeric) = 1.2197636452534830937169237656407 absolute error = 1e-31 relative error = 8.1983095978580892365305594728316e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.222 y[1] (analytic) = 1.2204501785082050320829821149841 y[1] (numeric) = 1.2204501785082050320829821149842 absolute error = 1e-31 relative error = 8.1936978469889833739634246863157e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.223 y[1] (analytic) = 1.2211367890099901802445499327237 y[1] (numeric) = 1.2211367890099901802445499327238 absolute error = 1e-31 relative error = 8.1890907636213959869752504908989e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.224 y[1] (analytic) = 1.2218234767327753087104211125236 y[1] (numeric) = 1.2218234767327753087104211125237 absolute error = 1e-31 relative error = 8.1844883409349461782108960670311e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.225 y[1] (analytic) = 1.2225102416505176975307831970228 y[1] (numeric) = 1.2225102416505176975307831970229 absolute error = 1e-31 relative error = 8.1798905721222800120242539015435e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.226 y[1] (analytic) = 1.223197083737195110946918215446 y[1] (numeric) = 1.223197083737195110946918215446 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.2MB, time=4.94 x[1] = 0.227 y[1] (analytic) = 1.2238840029668057720836119567557 y[1] (numeric) = 1.2238840029668057720836119567558 absolute error = 1e-31 relative error = 8.1707089689538334261191658889956e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.228 y[1] (analytic) = 1.2245709993133683376841805797846 y[1] (numeric) = 1.2245709993133683376841805797847 absolute error = 1e-31 relative error = 8.1661251210482038742909151935291e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.229 y[1] (analytic) = 1.2252580727509218728880236969013 y[1] (numeric) = 1.2252580727509218728880236969014 absolute error = 1e-31 relative error = 8.1615458999165986862994989582388e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 1.2259452232535258260506133021762 y[1] (numeric) = 1.2259452232535258260506133021763 absolute error = 1e-31 relative error = 8.1569712988163396215594564309159e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.231 y[1] (analytic) = 1.226632450795260003605828148707 y[1] (numeric) = 1.226632450795260003605828148707 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.232 y[1] (analytic) = 1.2273197553502245449705434127573 y[1] (numeric) = 1.2273197553502245449705434127573 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.233 y[1] (analytic) = 1.228007136892539897491385714647 y[1] (numeric) = 1.228007136892539897491385714647 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.234 y[1] (analytic) = 1.2286945953963467914335637979161 y[1] (numeric) = 1.2286945953963467914335637979161 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.235 y[1] (analytic) = 1.2293821308358062150116853991695 y[1] (numeric) = 1.2293821308358062150116853991695 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.2MB, time=5.30 x[1] = 0.236 y[1] (analytic) = 1.2300697431850993894624710711956 y[1] (numeric) = 1.2300697431850993894624710711956 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.237 y[1] (analytic) = 1.2307574324184277441592759514452 y[1] (numeric) = 1.2307574324184277441592759514452 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.238 y[1] (analytic) = 1.2314451985100128917683306967536 y[1] (numeric) = 1.2314451985100128917683306967537 absolute error = 1e-31 relative error = 8.1205400062459132742455207113913e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.239 y[1] (analytic) = 1.2321330414340966034466130333025 y[1] (numeric) = 1.2321330414340966034466130333026 absolute error = 1e-31 relative error = 8.1160066841165645397825111271839e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 1.2328209611649407840812615982348 y[1] (numeric) = 1.2328209611649407840812615982349 absolute error = 1e-31 relative error = 8.1114779152932381659867770917633e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.241 y[1] (analytic) = 1.2335089576768274475704439760761 y[1] (numeric) = 1.2335089576768274475704439760762 absolute error = 1e-31 relative error = 8.1069536931728913455129517331991e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.242 y[1] (analytic) = 1.2341970309440586921455910591666 y[1] (numeric) = 1.2341970309440586921455910591667 absolute error = 1e-31 relative error = 8.1024340111649974917081246924421e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.243 y[1] (analytic) = 1.2348851809409566757349100866823 y[1] (numeric) = 1.2348851809409566757349100866824 absolute error = 1e-31 relative error = 8.0979188626915169445881328106856e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.244 y[1] (analytic) = 1.2355734076418635913680889415159 y[1] (numeric) = 1.235573407641863591368088941516 absolute error = 1e-31 relative error = 8.0934082411868677583991647740256e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.245 y[1] (analytic) = 1.2362617110211416426221045083093 y[1] (numeric) = 1.2362617110211416426221045083094 absolute error = 1e-31 relative error = 8.0889021400978965705012228896295e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.2MB, time=5.66 x[1] = 0.246 y[1] (analytic) = 1.2369500910531730191080481192722 y[1] (numeric) = 1.2369500910531730191080481192722 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.247 y[1] (analytic) = 1.2376385477123598719988813370951 y[1] (numeric) = 1.2376385477123598719988813370952 absolute error = 1e-31 relative error = 8.0799034730163434350423159735309e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.248 y[1] (analytic) = 1.2383270809731242895980355462716 y[1] (numeric) = 1.2383270809731242895980355462717 absolute error = 1e-31 relative error = 8.0754108939793366309845383458246e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.249 y[1] (analytic) = 1.2390156908099082729487690454794 y[1] (numeric) = 1.2390156908099082729487690454795 absolute error = 1e-31 relative error = 8.0709228092691004150577266458651e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 1.2397043771971737114841955543462 y[1] (numeric) = 1.2397043771971737114841955543463 absolute error = 1e-31 relative error = 8.0664392123941902013874928160453e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.251 y[1] (analytic) = 1.2403931401094023587178982679372 y[1] (numeric) = 1.2403931401094023587178982679373 absolute error = 1e-31 relative error = 8.0619600968754168936408772543494e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.252 y[1] (analytic) = 1.2410819795210958079750438116511 y[1] (numeric) = 1.2410819795210958079750438116513 absolute error = 2e-31 relative error = 1.6114970912491636631733608925018e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.253 y[1] (analytic) = 1.2417708954067754681639106679091 y[1] (numeric) = 1.2417708954067754681639106679093 absolute error = 2e-31 relative error = 1.6106030568101261445170490387817e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.254 y[1] (analytic) = 1.2424598877409825395877468640566 y[1] (numeric) = 1.2424598877409825395877468640567 absolute error = 1e-31 relative error = 8.0485495738472603878701954644021e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.2MB, time=6.02 x[1] = 0.255 y[1] (analytic) = 1.2431489564982779897968719282862 y[1] (numeric) = 1.2431489564982779897968719282864 absolute error = 2e-31 relative error = 1.6088176638410510546345030521061e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.256 y[1] (analytic) = 1.2438381016532425294809383371257 y[1] (numeric) = 1.2438381016532425294809383371259 absolute error = 2e-31 relative error = 1.6079263027412553547259196855741e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.257 y[1] (analytic) = 1.2445273231804765884012678941185 y[1] (numeric) = 1.2445273231804765884012678941187 absolute error = 2e-31 relative error = 1.6070358301888143085219540129611e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.258 y[1] (analytic) = 1.245216621054600291363178694769 y[1] (numeric) = 1.2452166210546002913631786947692 absolute error = 2e-31 relative error = 1.6061462449048886788480457602080e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.259 y[1] (analytic) = 1.2459059952502534342282185476181 y[1] (numeric) = 1.2459059952502534342282185476184 absolute error = 3e-31 relative error = 2.4078863184195675851004805869116e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 1.2465954457420954599662209354707 y[1] (numeric) = 1.246595445742095459966220935471 absolute error = 3e-31 relative error = 2.4065545965588754094419285311587e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.261 y[1] (analytic) = 1.2472849725048054347470998143103 y[1] (numeric) = 1.2472849725048054347470998143106 absolute error = 3e-31 relative error = 2.4052241998677987375939382059262e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.262 y[1] (analytic) = 1.2479745755130820240722997603158 y[1] (numeric) = 1.2479745755130820240722997603161 absolute error = 3e-31 relative error = 2.4038951264424634795683749221340e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.263 y[1] (analytic) = 1.2486642547416434689458181876344 y[1] (numeric) = 1.2486642547416434689458181876347 absolute error = 3e-31 relative error = 2.4025673743825708957044139444436e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.264 y[1] (analytic) = 1.2493540101652275620847165711768 y[1] (numeric) = 1.249354010165227562084716571177 absolute error = 2e-31 relative error = 1.6008272945275928708201235042958e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.2MB, time=6.38 x[1] = 0.265 y[1] (analytic) = 1.2500438417585916241690378196762 y[1] (numeric) = 1.2500438417585916241690378196765 absolute error = 3e-31 relative error = 2.3999158267757458236996407496590e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.266 y[1] (analytic) = 1.2507337494965124801310471546051 y[1] (numeric) = 1.2507337494965124801310471546053 absolute error = 2e-31 relative error = 1.5990613516306787388209728521002e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.267 y[1] (analytic) = 1.251423733353786435483714060262 y[1] (numeric) = 1.2514237333537864354837140602622 absolute error = 2e-31 relative error = 1.5981796946107507636513808912603e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.268 y[1] (analytic) = 1.2521137933052292526883530794448 y[1] (numeric) = 1.252113793305229252688353079445 absolute error = 2e-31 relative error = 1.5972989122023493648301002349248e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.269 y[1] (analytic) = 1.2528039293256761275613414375964 y[1] (numeric) = 1.2528039293256761275613414375966 absolute error = 2e-31 relative error = 1.5964190031527945831401211487583e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 1.2534941413899816657198316861694 y[1] (numeric) = 1.2534941413899816657198316861696 absolute error = 2e-31 relative error = 1.5955399662117516560886558801739e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.271 y[1] (analytic) = 1.2541844294730198590663777631917 y[1] (numeric) = 1.2541844294730198590663777631919 absolute error = 2e-31 relative error = 1.5946618001312255966808781066607e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.272 y[1] (analytic) = 1.2548747935496840623123930756359 y[1] (numeric) = 1.2548747935496840623123930756361 absolute error = 2e-31 relative error = 1.5937845036655557871059859295899e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.273 y[1] (analytic) = 1.255565233594886969540359414205 y[1] (numeric) = 1.2555652335948869695403594142052 absolute error = 2e-31 relative error = 1.5929080755714105872880264263223e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.2MB, time=6.73 x[1] = 0.274 y[1] (analytic) = 1.2562557495835605908047057165415 y[1] (numeric) = 1.2562557495835605908047057165417 absolute error = 2e-31 relative error = 1.5920325146077819582540923173320e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.275 y[1] (analytic) = 1.2569463414906562287712758996526 y[1] (numeric) = 1.2569463414906562287712758996528 absolute error = 2e-31 relative error = 1.5911578195359801002726731474413e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.276 y[1] (analytic) = 1.257637009291144455395305186524 y[1] (numeric) = 1.2576370092911444553953051865242 absolute error = 2e-31 relative error = 1.5902839891196281057151145242847e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.277 y[1] (analytic) = 1.2583277529600150886378245554674 y[1] (numeric) = 1.2583277529600150886378245554677 absolute error = 3e-31 relative error = 2.3841165331869849398899641089013e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.278 y[1] (analytic) = 1.2590185724722771692204131437156 y[1] (numeric) = 1.2590185724722771692204131437159 absolute error = 3e-31 relative error = 2.3828083759789478350903727795236e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.279 y[1] (analytic) = 1.2597094678029589374182186391469 y[1] (numeric) = 1.2597094678029589374182186391472 absolute error = 3e-31 relative error = 2.3815015102111255927403390926115e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 1.2604004389271078098911658957906 y[1] (numeric) = 1.2604004389271078098911658957909 absolute error = 3e-31 relative error = 2.3801959340427504361734978142455e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.281 y[1] (analytic) = 1.2610914858197903565532742099348 y[1] (numeric) = 1.2610914858197903565532742099351 absolute error = 3e-31 relative error = 2.3788916456364841521565435156001e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.282 y[1] (analytic) = 1.2617826084560922774800038942346 y[1] (numeric) = 1.2617826084560922774800038942349 absolute error = 3e-31 relative error = 2.3775886431584102012216738463880e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.283 y[1] (analytic) = 1.2624738068111183798535529872006 y[1] (numeric) = 1.2624738068111183798535529872009 absolute error = 3e-31 relative error = 2.3762869247780258495968081376295e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.2MB, time=7.10 x[1] = 0.284 y[1] (analytic) = 1.2631650808599925549460251348393 y[1] (numeric) = 1.2631650808599925549460251348396 absolute error = 3e-31 relative error = 2.3749864886682343226650282265537e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.285 y[1] (analytic) = 1.263856430577857755140389880019 y[1] (numeric) = 1.2638564305778577551403898800193 absolute error = 3e-31 relative error = 2.3736873330053369798849358941047e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.286 y[1] (analytic) = 1.264547855939875970989156793349 y[1] (numeric) = 1.2645478559398759709891567933493 absolute error = 3e-31 relative error = 2.3723894559690255111038678017885e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.287 y[1] (analytic) = 1.2652393569212282083106850769888 y[1] (numeric) = 1.2652393569212282083106850769891 absolute error = 3e-31 relative error = 2.3710928557423741541961543139277e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.288 y[1] (analytic) = 1.265930933497114465323050469851 y[1] (numeric) = 1.2659309334971144653230504698513 absolute error = 3e-31 relative error = 2.3697975305118319339588530982650e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.289 y[1] (analytic) = 1.266622585642753709815391479126 y[1] (numeric) = 1.2666225856427537098153914791263 absolute error = 3e-31 relative error = 2.3685034784672149221976319167204e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 1.2673143133333838563566571589405 y[1] (numeric) = 1.2673143133333838563566571589407 absolute error = 2e-31 relative error = 1.5781404652011323459571450355827e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.291 y[1] (analytic) = 1.268006116544261743541678852271 y[1] (numeric) = 1.2680061165442617435416788522712 absolute error = 2e-31 relative error = 1.5772794578078731697860462552164e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.292 y[1] (analytic) = 1.2686979952506631112744885069661 y[1] (numeric) = 1.2686979952506631112744885069663 absolute error = 2e-31 relative error = 1.5764192955982797424474511088894e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.2MB, time=7.45 x[1] = 0.293 y[1] (analytic) = 1.2693899494278825780888063708884 y[1] (numeric) = 1.2693899494278825780888063708886 absolute error = 2e-31 relative error = 1.5755599773744902520474121666536e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.294 y[1] (analytic) = 1.2700819790512336185056210647754 y[1] (numeric) = 1.2700819790512336185056210647756 absolute error = 2e-31 relative error = 1.5747015019408619953258413784847e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.295 y[1] (analytic) = 1.2707740840960485404277852244368 y[1] (numeric) = 1.270774084096048540427785224437 absolute error = 2e-31 relative error = 1.5738438681039663015408129114651e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.296 y[1] (analytic) = 1.2714662645376784625715500963538 y[1] (numeric) = 1.271466264537678462571550096354 absolute error = 2e-31 relative error = 1.5729870746725834701699370075461e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.297 y[1] (analytic) = 1.2721585203514932919349626626315 y[1] (numeric) = 1.2721585203514932919349626626316 absolute error = 1e-31 relative error = 7.8606556022884886119259827104198e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.298 y[1] (analytic) = 1.2728508515128817013030490625742 y[1] (numeric) = 1.2728508515128817013030490625743 absolute error = 1e-31 relative error = 7.8563800213624608312889725605424e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.299 y[1] (analytic) = 1.2735432579972511067897082689142 y[1] (numeric) = 1.2735432579972511067897082689143 absolute error = 1e-31 relative error = 7.8521086246617188782485830110266e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 1.2742357397800276454162401669183 y[1] (numeric) = 1.2742357397800276454162401669184 absolute error = 1e-31 relative error = 7.8478414062740919137443413389558e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.301 y[1] (analytic) = 1.2749282968366561527264323742409 y[1] (numeric) = 1.274928296836656152726432374241 absolute error = 1e-31 relative error = 7.8435783602983284210240022160570e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.302 y[1] (analytic) = 1.275620929142600140438130328472 y[1] (numeric) = 1.2756209291426001404381303284721 absolute error = 1e-31 relative error = 7.8393194808440713041109601414549e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.2MB, time=7.82 x[1] = 0.303 y[1] (analytic) = 1.2763136366733417741312153578603 y[1] (numeric) = 1.2763136366733417741312153578603 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.304 y[1] (analytic) = 1.2770064194043818509719156386655 y[1] (numeric) = 1.2770064194043818509719156386655 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.305 y[1] (analytic) = 1.2776992773112397774733751300222 y[1] (numeric) = 1.2776992773112397774733751300222 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.306 y[1] (analytic) = 1.2783922103694535472924057640721 y[1] (numeric) = 1.2783922103694535472924057640721 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.307 y[1] (analytic) = 1.279085218554579719062348355452 y[1] (numeric) = 1.279085218554579719062348355452 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.308 y[1] (analytic) = 1.2797783018421933942619678800099 y[1] (numeric) = 1.2797783018421933942619678800099 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.309 y[1] (analytic) = 1.2804714602078881951203089578621 y[1] (numeric) = 1.2804714602078881951203089578621 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 1.2811646936272762425574375606039 y[1] (numeric) = 1.281164693627276242557437560604 absolute error = 1e-31 relative error = 7.8053977367169448183082794045992e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.311 y[1] (analytic) = 1.2818580020759881341609951466463 y[1] (numeric) = 1.2818580020759881341609951466464 absolute error = 1e-31 relative error = 7.8011760926755155400248654199778e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.312 y[1] (analytic) = 1.2825513855296729221984916122726 y[1] (numeric) = 1.2825513855296729221984916122727 absolute error = 1e-31 relative error = 7.7969585568457845273271131598811e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 memory used=87.7MB, alloc=4.2MB, time=8.17 TOP MAIN SOLVE Loop x[1] = 0.313 y[1] (analytic) = 1.2832448439639980916652636290957 y[1] (numeric) = 1.2832448439639980916652636290959 absolute error = 2e-31 relative error = 1.5585490246911217974253731268210e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.314 y[1] (analytic) = 1.2839383773546495383680251211478 y[1] (numeric) = 1.283938377354649538368025121148 absolute error = 2e-31 relative error = 1.5577071573486893878659401099838e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.315 y[1] (analytic) = 1.2846319856773315470439368168513 y[1] (numeric) = 1.2846319856773315470439368168515 absolute error = 2e-31 relative error = 1.5568661081916666354825855626058e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.316 y[1] (analytic) = 1.2853256689077667695151219926121 y[1] (numeric) = 1.2853256689077667695151219926123 absolute error = 2e-31 relative error = 1.5560258760719710587746616686071e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.317 y[1] (analytic) = 1.2860194270216962028785557057307 y[1] (numeric) = 1.2860194270216962028785557057309 absolute error = 2e-31 relative error = 1.5551864598436259540683049612417e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.318 y[1] (analytic) = 1.2867132599948791677312549947625 y[1] (numeric) = 1.2867132599948791677312549947627 absolute error = 2e-31 relative error = 1.5543478583627556264322314436680e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.319 y[1] (analytic) = 1.2874071678030932864306977053628 y[1] (numeric) = 1.287407167803093286430697705363 absolute error = 2e-31 relative error = 1.5535100704875806334461271678463e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 1.288101150422134461390397779036 y[1] (numeric) = 1.2881011504221344613903977790363 absolute error = 3e-31 relative error = 2.3290096426176195626722081142284e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.321 y[1] (analytic) = 1.2887952078278168534105650210692 y[1] (numeric) = 1.2887952078278168534105650210695 absolute error = 3e-31 relative error = 2.3277553964964775448321664885314e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.2MB, time=8.54 x[1] = 0.322 y[1] (analytic) = 1.2894893399959728600437775422702 y[1] (numeric) = 1.2894893399959728600437775422705 absolute error = 3e-31 relative error = 2.3265023656646662551200417433525e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.323 y[1] (analytic) = 1.2901835469024530939955952469539 y[1] (numeric) = 1.2901835469024530939955952469542 absolute error = 3e-31 relative error = 2.3252505484220230849708810374681e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.324 y[1] (analytic) = 1.2908778285231263615600429169253 y[1] (numeric) = 1.2908778285231263615600429169256 absolute error = 3e-31 relative error = 2.3239999430714944199314749205046e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.325 y[1] (analytic) = 1.2915721848338796410898916179975 y[1] (numeric) = 1.2915721848338796410898916179978 absolute error = 3e-31 relative error = 2.3227505479191286197286577089917e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.326 y[1] (analytic) = 1.2922666158106180615016673318623 y[1] (numeric) = 1.2922666158106180615016673318626 absolute error = 3e-31 relative error = 2.3215023612740690171992648654824e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.327 y[1] (analytic) = 1.2929611214292648808153158918937 y[1] (numeric) = 1.292961121429264880815315891894 absolute error = 3e-31 relative error = 2.3202553814485469360229851703227e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.328 y[1] (analytic) = 1.2936557016657614647284534767233 y[1] (numeric) = 1.2936557016657614647284534767236 absolute error = 3e-31 relative error = 2.3190096067578747271995537068278e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.329 y[1] (analytic) = 1.294350356496067265225132090172 y[1] (numeric) = 1.2943503564960672652251320901723 absolute error = 3e-31 relative error = 2.3177650355204388242119390848293e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 1.295045085896159799219049630365 y[1] (numeric) = 1.2950450858961597992190496303653 absolute error = 3e-31 relative error = 2.3165216660576928168173849084140e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.331 y[1] (analytic) = 1.295739889842034627231134324592 y[1] (numeric) = 1.2957398898420346272311343245923 absolute error = 3e-31 relative error = 2.3152794966941505434083712548184e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 memory used=95.3MB, alloc=4.2MB, time=8.91 TOP MAIN SOLVE Loop x[1] = 0.332 y[1] (analytic) = 1.2964347683097053321014334797088 y[1] (numeric) = 1.2964347683097053321014334797091 absolute error = 3e-31 relative error = 2.3140385257573792018857668764575e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.333 y[1] (analytic) = 1.297129721275203497735236670608 y[1] (numeric) = 1.2971297212752034977352366706083 absolute error = 3e-31 relative error = 2.3127987515779924789866469705590e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.334 y[1] (analytic) = 1.297824748714578687883363661518 y[1] (numeric) = 1.2978247487145786878833636615183 absolute error = 3e-31 relative error = 2.3115601724896436980094546843924e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.335 y[1] (analytic) = 1.2985198506038984249565475266234 y[1] (numeric) = 1.2985198506038984249565475266236 absolute error = 2e-31 relative error = 1.5402151912193459899195913614630e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.336 y[1] (analytic) = 1.2992150269192481688738436077372 y[1] (numeric) = 1.2992150269192481688738436077374 absolute error = 2e-31 relative error = 1.5393910619572203016647251307446e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.337 y[1] (analytic) = 1.2999102776367312959449951174991 y[1] (numeric) = 1.2999102776367312959449951174993 absolute error = 2e-31 relative error = 1.5385677261018729355426198809247e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.338 y[1] (analytic) = 1.3006056027324690777866863668207 y[1] (numeric) = 1.3006056027324690777866863668208 absolute error = 1e-31 relative error = 7.6887259127523318335912419962561e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.339 y[1] (analytic) = 1.3013010021826006602726147650581 y[1] (numeric) = 1.3013010021826006602726147650582 absolute error = 1e-31 relative error = 7.6846171510108341823002468663105e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 1.3019964759632830425173129106615 y[1] (numeric) = 1.3019964759632830425173129106616 absolute error = 1e-31 relative error = 7.6805123397906992837554720390223e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.2MB, time=9.27 x[1] = 0.341 y[1] (analytic) = 1.3026920240506910558936522588267 y[1] (numeric) = 1.3026920240506910558936522588268 absolute error = 1e-31 relative error = 7.6764114736077286345069977386231e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.342 y[1] (analytic) = 1.3033876464210173430839600209711 y[1] (numeric) = 1.3033876464210173430839600209712 absolute error = 1e-31 relative error = 7.6723145469876753106211600510395e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.343 y[1] (analytic) = 1.3040833430504723371646811186614 y[1] (numeric) = 1.3040833430504723371646811186615 absolute error = 1e-31 relative error = 7.6682215544662216701969681557478e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.344 y[1] (analytic) = 1.3047791139152842407245171819456 y[1] (numeric) = 1.3047791139152842407245171819457 absolute error = 1e-31 relative error = 7.6641324905889571153329640709543e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.345 y[1] (analytic) = 1.3054749589916990050159747488845 y[1] (numeric) = 1.3054749589916990050159747488846 absolute error = 1e-31 relative error = 7.6600473499113559133607327071080e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.346 y[1] (analytic) = 1.3061708782559803091402549894398 y[1] (numeric) = 1.3061708782559803091402549894399 absolute error = 1e-31 relative error = 7.6559661269987550771619163173833e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.347 y[1] (analytic) = 1.3068668716844095392654174427593 y[1] (numeric) = 1.3068668716844095392654174427595 absolute error = 2e-31 relative error = 1.5303777632852664608772462360720e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.348 y[1] (analytic) = 1.3075629392532857678777504223066 y[1] (numeric) = 1.3075629392532857678777504223068 absolute error = 2e-31 relative error = 1.5295630825558167950777251121594e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.349 y[1] (analytic) = 1.3082590809389257330662809082126 y[1] (numeric) = 1.3082590809389257330662809082128 absolute error = 2e-31 relative error = 1.5287491821303606419408713360434e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = 1.3089552967176638178403569106841 y[1] (numeric) = 1.3089552967176638178403569106842 absolute error = 1e-31 relative error = 7.6396803046490579808814006009853e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 memory used=103.0MB, alloc=4.2MB, time=9.63 TOP MAIN SOLVE Loop x[1] = 0.351 y[1] (analytic) = 1.3096515865658520294802354522885 y[1] (numeric) = 1.3096515865658520294802354522886 absolute error = 1e-31 relative error = 7.6356185893851692894902425966730e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.352 y[1] (analytic) = 1.310347950459859978920609480448 y[1] (numeric) = 1.3103479504598599789206094804481 absolute error = 1e-31 relative error = 7.6315607594841893941317267585840e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.353 y[1] (analytic) = 1.3110443883760748601670071845194 y[1] (numeric) = 1.3110443883760748601670071845195 absolute error = 1e-31 relative error = 7.6275068095798801002642722843537e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.354 y[1] (analytic) = 1.3117409002909014297449973544145 y[1] (numeric) = 1.3117409002909014297449973544146 absolute error = 1e-31 relative error = 7.6234567343156911066723901201737e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.355 y[1] (analytic) = 1.312437486180761986182134579825 y[1] (numeric) = 1.3124374861807619861821345798251 absolute error = 1e-31 relative error = 7.6194105283447384093990573943209e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.356 y[1] (analytic) = 1.3131341460220963495225782507613 y[1] (numeric) = 1.3131341460220963495225782507614 absolute error = 1e-31 relative error = 7.6153681863297827629651283969124e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.357 y[1] (analytic) = 1.3138308797913618408743194812988 y[1] (numeric) = 1.3138308797913618408743194812989 absolute error = 1e-31 relative error = 7.6113297029432081986995797398232e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.358 y[1] (analytic) = 1.3145276874650332619889502391439 y[1] (numeric) = 1.314527687465033261988950239144 absolute error = 1e-31 relative error = 7.6072950728670006000050037821232e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.359 y[1] (analytic) = 1.3152245690196028748739091238953 y[1] (numeric) = 1.3152245690196028748739091238954 absolute error = 1e-31 relative error = 7.6032642907927263343833784407045e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.2MB, time=9.99 x[1] = 0.36 y[1] (analytic) = 1.3159215244315803814371383966764 y[1] (numeric) = 1.3159215244315803814371383966765 absolute error = 1e-31 relative error = 7.5992373514215109420477531335459e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.361 y[1] (analytic) = 1.316618553677492903164087023161 y[1] (numeric) = 1.3166185536774929031640870231611 absolute error = 1e-31 relative error = 7.5952142494640178809460998346796e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.362 y[1] (analytic) = 1.317315656733884960826994650903 y[1] (numeric) = 1.3173156567338849608269946509031 absolute error = 1e-31 relative error = 7.5911949796404273280241850658349e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.363 y[1] (analytic) = 1.318012833577318454226391600318 y[1] (numeric) = 1.3180128335773184542263916003181 absolute error = 1e-31 relative error = 7.5871795366804150365549231202430e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.364 y[1] (analytic) = 1.3187100841843726419647501066459 y[1] (numeric) = 1.318710084184372641964750106646 absolute error = 1e-31 relative error = 7.5831679153231312493622729195295e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.365 y[1] (analytic) = 1.319407408531644121252222207756 y[1] (numeric) = 1.3194074085316441212522222077561 absolute error = 1e-31 relative error = 7.5791601103171796677683406552238e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.366 y[1] (analytic) = 1.3201048065957468077443998297385 y[1] (numeric) = 1.3201048065957468077443998297386 absolute error = 1e-31 relative error = 7.5751561164205964760929477723802e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.367 y[1] (analytic) = 1.3208022783533119154120327788604 y[1] (numeric) = 1.3208022783533119154120327788604 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.368 y[1] (analytic) = 1.3214998237809879364426405046496 y[1] (numeric) = 1.3214998237809879364426405046496 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.369 y[1] (analytic) = 1.3221974428554406211739536546161 y[1] (numeric) = 1.3221974428554406211739536546161 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 memory used=110.6MB, alloc=4.3MB, time=10.35 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 1.3228951355533529580591215964133 y[1] (numeric) = 1.3228951355533529580591215964132 absolute error = 1e-31 relative error = 7.5591781474176382178853346158170e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.371 y[1] (analytic) = 1.3235929018514251536636222381021 y[1] (numeric) = 1.3235929018514251536636222381021 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.372 y[1] (analytic) = 1.3242907417263746126938106315943 y[1] (numeric) = 1.3242907417263746126938106315943 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.373 y[1] (analytic) = 1.3249886551549359180570429983252 y[1] (numeric) = 1.3249886551549359180570429983251 absolute error = 1e-31 relative error = 7.5472344318530503225396464440830e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.374 y[1] (analytic) = 1.3256866421138608109533129697468 y[1] (numeric) = 1.3256866421138608109533129697467 absolute error = 1e-31 relative error = 7.5432607392457366369066826129869e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.375 y[1] (analytic) = 1.3263847025799181709983369883317 y[1] (numeric) = 1.3263847025799181709983369883316 absolute error = 1e-31 relative error = 7.5392908109911450579030022538775e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.376 y[1] (analytic) = 1.3270828365298939963780259674428 y[1] (numeric) = 1.3270828365298939963780259674427 absolute error = 1e-31 relative error = 7.5353246419404950479491647174456e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.377 y[1] (analytic) = 1.327781043940591384034280460659 y[1] (numeric) = 1.3277810439405913840342804606588 absolute error = 2e-31 relative error = 1.5062724453908422880361363300955e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.378 y[1] (analytic) = 1.3284793247888305098820467429434 y[1] (numeric) = 1.3284793247888305098820467429432 absolute error = 2e-31 relative error = 1.5054807121803808232947427765942e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.3MB, time=10.71 x[1] = 0.379 y[1] (analytic) = 1.3291776790514486090575713574133 y[1] (numeric) = 1.3291776790514486090575713574131 absolute error = 2e-31 relative error = 1.5046897277324695477713846619003e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 1.3298761067052999561977918324065 y[1] (numeric) = 1.3298761067052999561977918324063 absolute error = 2e-31 relative error = 1.5038994910246923068293724836611e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.381 y[1] (analytic) = 1.3305746077272558457508014240532 y[1] (numeric) = 1.3305746077272558457508014240529 absolute error = 3e-31 relative error = 2.2546650015546867394934542649281e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.382 y[1] (analytic) = 1.3312731820942045723173258896451 y[1] (numeric) = 1.3312731820942045723173258896448 absolute error = 3e-31 relative error = 2.2534818851234935361201469619097e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.383 y[1] (analytic) = 1.3319718297830514110231504467548 y[1] (numeric) = 1.3319718297830514110231504467545 absolute error = 3e-31 relative error = 2.2522998857180284977642851394775e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.384 y[1] (analytic) = 1.3326705507707185979224352222904 y[1] (numeric) = 1.3326705507707185979224352222901 absolute error = 3e-31 relative error = 2.2511190018155805417656628303732e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.385 y[1] (analytic) = 1.3333693450341453104318576444875 y[1] (numeric) = 1.3333693450341453104318576444872 absolute error = 3e-31 relative error = 2.2499392318961518696637581312300e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.386 y[1] (analytic) = 1.3340682125502876477955203792281 y[1] (numeric) = 1.3340682125502876477955203792277 absolute error = 4e-31 relative error = 2.9983474325899359965008644685204e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.387 y[1] (analytic) = 1.3347671532961186115805635600503 y[1] (numeric) = 1.33476715329611861158056356005 absolute error = 3e-31 relative error = 2.2475830279398918010041862666266e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.388 y[1] (analytic) = 1.335466167248628086203420208766 y[1] (numeric) = 1.3354661672486280862034202087657 absolute error = 3e-31 relative error = 2.2464065908765775782289862808670e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.3MB, time=11.07 x[1] = 0.389 y[1] (analytic) = 1.3361652543848228194866538907371 y[1] (numeric) = 1.3361652543848228194866538907368 absolute error = 3e-31 relative error = 2.2452312617433051252329331549874e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 1.3368644146817264032463177955853 y[1] (numeric) = 1.336864414681726403246317795585 absolute error = 3e-31 relative error = 2.2440570390335538291170891835458e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.391 y[1] (analytic) = 1.3375636481163792539097745804138 y[1] (numeric) = 1.3375636481163792539097745804134 absolute error = 4e-31 relative error = 2.9905118949913077010093843876469e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.392 y[1] (analytic) = 1.338262954665838593163916458512 y[1] (numeric) = 1.3382629546658385931639164585116 absolute error = 4e-31 relative error = 2.9889492091625531640718233046960e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.393 y[1] (analytic) = 1.3389623343071784286337251619986 y[1] (numeric) = 1.3389623343071784286337251619982 absolute error = 4e-31 relative error = 2.9873879925604679860441965274615e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.394 y[1] (analytic) = 1.3396617870174895345911115519247 y[1] (numeric) = 1.3396617870174895345911115519243 absolute error = 4e-31 relative error = 2.9858282431905921443272460107864e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.395 y[1] (analytic) = 1.3403613127738794326939747940252 y[1] (numeric) = 1.3403613127738794326939747940249 absolute error = 3e-31 relative error = 2.2382024692965034959219774446706e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.396 y[1] (analytic) = 1.3410609115534723727554211625573 y[1] (numeric) = 1.3410609115534723727554211625569 absolute error = 4e-31 relative error = 2.9827131381873158497859594163366e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.397 y[1] (analytic) = 1.3417605833334093135430826785133 y[1] (numeric) = 1.341760583333409313543082678513 absolute error = 3e-31 relative error = 2.2358683339369946848478486368254e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.3MB, time=11.43 x[1] = 0.398 y[1] (analytic) = 1.3424603280908479036084759319405 y[1] (numeric) = 1.3424603280908479036084759319402 absolute error = 3e-31 relative error = 2.2347029087007641730153028294198e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.399 y[1] (analytic) = 1.3431601458029624621463415811339 y[1] (numeric) = 1.3431601458029624621463415811336 absolute error = 3e-31 relative error = 2.2335385764491637483447997126112e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 1.3438600364469439598839051641098 y[1] (numeric) = 1.3438600364469439598839051641096 absolute error = 2e-31 relative error = 1.4882502238014581093444081138903e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.401 y[1] (analytic) = 1.34456 y[1] (numeric) = 1.3445599999999999999999999999998 absolute error = 2e-31 relative error = 1.4874754566549651930743142738145e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.402 y[1] (analytic) = 1.3452600364393547990739930998413 y[1] (numeric) = 1.3452600364393547990739930998411 absolute error = 2e-31 relative error = 1.4867014152101152571794220921651e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.403 y[1] (analytic) = 1.3459601457422491680644551476744 y[1] (numeric) = 1.3459601457422491680644551476742 absolute error = 2e-31 relative error = 1.4859280984854652624915321202184e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.404 y[1] (analytic) = 1.3466603278859404933175157539028 y[1] (numeric) = 1.3466603278859404933175157539027 absolute error = 1e-31 relative error = 7.4257775275065357992199448401484e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.405 y[1] (analytic) = 1.3473605828477027176048453235069 y[1] (numeric) = 1.3473605828477027176048453235068 absolute error = 1e-31 relative error = 7.4219181763983205143419773321750e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.406 y[1] (analytic) = 1.3480609106048263211912050219563 y[1] (numeric) = 1.3480609106048263211912050219562 absolute error = 1e-31 relative error = 7.4180624342214333531436462875130e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.407 y[1] (analytic) = 1.34876131113461830293150646152 y[1] (numeric) = 1.3487613111346183029315064615199 absolute error = 1e-31 relative error = 7.4142102961032455003161631140308e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.3MB, time=11.79 x[1] = 0.408 y[1] (analytic) = 1.3494617844144021613973228701345 y[1] (numeric) = 1.3494617844144021613973228701345 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.409 y[1] (analytic) = 1.350162330421517876032793644064 y[1] (numeric) = 1.350162330421517876032793644064 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 1.3508629491333218883398643242667 y[1] (numeric) = 1.3508629491333218883398643242667 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.411 y[1] (analytic) = 1.3515636405271870830928041746783 y[1] (numeric) = 1.3515636405271870830928041746782 absolute error = 1e-31 relative error = 7.3988376870655001798352825658508e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.412 y[1] (analytic) = 1.3522644045805027695819436785256 y[1] (numeric) = 1.3522644045805027695819436785255 absolute error = 1e-31 relative error = 7.3950034964517042698416163139299e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.413 y[1] (analytic) = 1.3529652412706746628865744063092 y[1] (numeric) = 1.3529652412706746628865744063091 absolute error = 1e-31 relative error = 7.3911728808407700786912038447339e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.414 y[1] (analytic) = 1.3536661505751248651769538462248 y[1] (numeric) = 1.3536661505751248651769538462247 absolute error = 1e-31 relative error = 7.3873458354198734469267875292212e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.415 y[1] (analytic) = 1.3543671324712918470453579245486 y[1] (numeric) = 1.3543671324712918470453579245485 absolute error = 1e-31 relative error = 7.3835223553846595499262840611748e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.416 y[1] (analytic) = 1.3550681869366304288661240798815 y[1] (numeric) = 1.3550681869366304288661240798815 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.3MB, time=12.15 x[1] = 0.417 y[1] (analytic) = 1.355769313948611762184627891135 y[1] (numeric) = 1.355769313948611762184627891135 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.418 y[1] (analytic) = 1.3564705134847233111351363947518 y[1] (numeric) = 1.3564705134847233111351363947518 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.419 y[1] (analytic) = 1.3571717855224688338874813618851 y[1] (numeric) = 1.3571717855224688338874813618851 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 1.3578731300393683641224959411132 y[1] (numeric) = 1.3578731300393683641224959411131 absolute error = 1e-31 relative error = 7.3644582684319508740285957366140e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.421 y[1] (analytic) = 1.3585745470129581925361582067434 y[1] (numeric) = 1.3585745470129581925361582067434 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.422 y[1] (analytic) = 1.3592760364207908483723852868626 y[1] (numeric) = 1.3592760364207908483723852868626 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.423 y[1] (analytic) = 1.3599775982404350809844218790175 y[1] (numeric) = 1.3599775982404350809844218790175 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.424 y[1] (analytic) = 1.3606792324494758414247670947673 y[1] (numeric) = 1.3606792324494758414247670947673 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.425 y[1] (analytic) = 1.3613809390255142640635837073331 y[1] (numeric) = 1.3613809390255142640635837073331 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.426 y[1] (analytic) = 1.3620827179461676482355340091838 y[1] (numeric) = 1.3620827179461676482355340091838 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.3MB, time=12.51 x[1] = 0.427 y[1] (analytic) = 1.3627845691890694399149866186437 y[1] (numeric) = 1.3627845691890694399149866186437 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.428 y[1] (analytic) = 1.3634864927318692134195387064848 y[1] (numeric) = 1.3634864927318692134195387064848 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.429 y[1] (analytic) = 1.3641884885522326531417982449768 y[1] (numeric) = 1.3641884885522326531417982449768 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 1.3648905566278415353093710130139 y[1] (numeric) = 1.3648905566278415353093710130138 absolute error = 1e-31 relative error = 7.3265947598805566776644902186824e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.431 y[1] (analytic) = 1.3655926969363937097729972217184 y[1] (numeric) = 1.3655926969363937097729972217184 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.432 y[1] (analytic) = 1.3662949094556030818227827553402 y[1] (numeric) = 1.3662949094556030818227827553402 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.433 y[1] (analytic) = 1.366997194163199594032470152324 y[1] (numeric) = 1.366997194163199594032470152324 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.434 y[1] (analytic) = 1.3676995510369292081316945811159 y[1] (numeric) = 1.3676995510369292081316945811158 absolute error = 1e-31 relative error = 7.3115473295421081460182505979664e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.435 y[1] (analytic) = 1.3684019800545538869061701946116 y[1] (numeric) = 1.3684019800545538869061701946116 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.436 y[1] (analytic) = 1.3691044811938515761257523761302 y[1] (numeric) = 1.3691044811938515761257523761302 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.3MB, time=12.87 x[1] = 0.437 y[1] (analytic) = 1.3698070544326161865003215184119 y[1] (numeric) = 1.3698070544326161865003215184119 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.438 y[1] (analytic) = 1.3705096997486575756634341054058 y[1] (numeric) = 1.3705096997486575756634341054058 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.439 y[1] (analytic) = 1.3712124171198015301836869945193 y[1] (numeric) = 1.3712124171198015301836869945193 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 1.3719152065238897476037409245554 y[1] (numeric) = 1.3719152065238897476037409245554 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.441 y[1] (analytic) = 1.3726180679387798185069494017657 y[1] (numeric) = 1.3726180679387798185069494017657 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.442 y[1] (analytic) = 1.3733210013423452086115392432959 y[1] (numeric) = 1.3733210013423452086115392432959 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.443 y[1] (analytic) = 1.3740240067124752408922891837997 y[1] (numeric) = 1.3740240067124752408922891837997 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.444 y[1] (analytic) = 1.3747270840270750777296530771457 y[1] (numeric) = 1.3747270840270750777296530771457 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.445 y[1] (analytic) = 1.3754302332640657030862743509443 y[1] (numeric) = 1.3754302332640657030862743509442 absolute error = 1e-31 relative error = 7.2704523705784522209262292246604e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.3MB, time=13.23 x[1] = 0.446 y[1] (analytic) = 1.3761334544013839047108384970719 y[1] (numeric) = 1.3761334544013839047108384970718 absolute error = 1e-31 relative error = 7.2667370799076938190324769408461e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.447 y[1] (analytic) = 1.3768367474169822563692105064816 y[1] (numeric) = 1.3768367474169822563692105064815 absolute error = 1e-31 relative error = 7.2630252052471166081170907799967e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.448 y[1] (analytic) = 1.3775401122888291001028042813472 y[1] (numeric) = 1.3775401122888291001028042813471 absolute error = 1e-31 relative error = 7.2593167420618079816967732809906e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.449 y[1] (analytic) = 1.3782435489949085285141311820078 y[1] (numeric) = 1.3782435489949085285141311820077 absolute error = 1e-31 relative error = 7.2556116858247248288124678689506e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 1.3789470575132203670794749902563 y[1] (numeric) = 1.3789470575132203670794749902562 absolute error = 1e-31 relative error = 7.2519100320166766716853538846947e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.451 y[1] (analytic) = 1.3796506378217801564886406942458 y[1] (numeric) = 1.3796506378217801564886406942456 absolute error = 2e-31 relative error = 1.4496423552252617692738561909133e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.452 y[1] (analytic) = 1.3803542898986191350117246236822 y[1] (numeric) = 1.380354289898619135011724623682 absolute error = 2e-31 relative error = 1.4489033827300171452545037207342e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.453 y[1] (analytic) = 1.3810580137217842208928535870252 y[1] (numeric) = 1.3810580137217842208928535870251 absolute error = 1e-31 relative error = 7.2408254400922739884221245411439e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.454 y[1] (analytic) = 1.381761809269337994770840785131 y[1] (numeric) = 1.3817618092693379947708407851309 absolute error = 1e-31 relative error = 7.2371373509649259223446609603019e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.455 y[1] (analytic) = 1.3824656765193586821267063981491 y[1] (numeric) = 1.382465676519358682126706398149 absolute error = 1e-31 relative error = 7.2334526417878627814374125060106e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.3MB, time=13.59 x[1] = 0.456 y[1] (analytic) = 1.3831696154499401357580108645258 y[1] (numeric) = 1.3831696154499401357580108645257 absolute error = 1e-31 relative error = 7.2297713080886581767046822731401e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.457 y[1] (analytic) = 1.3838736260391918182799489926703 y[1] (numeric) = 1.3838736260391918182799489926703 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.458 y[1] (analytic) = 1.3845777082652387846531531672111 y[1] (numeric) = 1.3845777082652387846531531672111 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.459 y[1] (analytic) = 1.3852818621062216647381540328061 y[1] (numeric) = 1.385281862106221664738154032806 absolute error = 1e-31 relative error = 7.2187475152498695038899931076433e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 1.3859860875402966458764471591757 y[1] (numeric) = 1.3859860875402966458764471591757 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.461 y[1] (analytic) = 1.3866903845456354554981143114027 y[1] (numeric) = 1.3866903845456354554981143114027 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.462 y[1] (analytic) = 1.3873947531004253437559480695824 y[1] (numeric) = 1.3873947531004253437559480695823 absolute error = 1e-31 relative error = 7.2077539414452137781164542234389e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.463 y[1] (analytic) = 1.3880991931828690661860286616249 y[1] (numeric) = 1.3880991931828690661860286616249 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.464 y[1] (analytic) = 1.3888037047711848663947019923967 y[1] (numeric) = 1.3888037047711848663947019923966 absolute error = 1e-31 relative error = 7.2004416215519600818263660809596e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.3MB, time=13.95 x[1] = 0.465 y[1] (analytic) = 1.389508287843606458771907971444 y[1] (numeric) = 1.3895082878436064587719079714439 absolute error = 1e-31 relative error = 7.1967904671652678523904932680740e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.466 y[1] (analytic) = 1.3902129423783830112308083602804 y[1] (numeric) = 1.3902129423783830112308083602803 absolute error = 1e-31 relative error = 7.1931426439549266015735281978826e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.467 y[1] (analytic) = 1.3909176683537791279736634786215 y[1] (numeric) = 1.3909176683537791279736634786215 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.468 y[1] (analytic) = 1.3916224657480748322839072270408 y[1] (numeric) = 1.3916224657480748322839072270407 absolute error = 1e-31 relative error = 7.1858569735179154712190135617093e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.469 y[1] (analytic) = 1.3923273345395655493443700012748 y[1] (numeric) = 1.3923273345395655493443700012747 absolute error = 1e-31 relative error = 7.1822191175374295972374269746653e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 1.3930322747065620890815991908521 y[1] (numeric) = 1.393032274706562089081599190852 absolute error = 1e-31 relative error = 7.1785845752256306201557783074584e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.471 y[1] (analytic) = 1.3937372862273906290362270718319 y[1] (numeric) = 1.3937372862273906290362270718318 absolute error = 1e-31 relative error = 7.1749533422244131927500222411538e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.472 y[1] (analytic) = 1.3944423690803926972593360202417 y[1] (numeric) = 1.3944423690803926972593360202416 absolute error = 1e-31 relative error = 7.1713254141831642861028058580696e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.473 y[1] (analytic) = 1.3951475232439251552347710892789 y[1] (numeric) = 1.3951475232439251552347710892788 absolute error = 1e-31 relative error = 7.1677007867587472847582740535941e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.474 y[1] (analytic) = 1.3958527486963601808273501095053 y[1] (numeric) = 1.3958527486963601808273501095052 absolute error = 1e-31 relative error = 7.1640794556154861220548287742098e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.3MB, time=14.32 x[1] = 0.475 y[1] (analytic) = 1.3965580454160852512569215871056 y[1] (numeric) = 1.3965580454160852512569215871056 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.476 y[1] (analytic) = 1.3972634133815031260982207908118 y[1] (numeric) = 1.3972634133815031260982207908118 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.477 y[1] (analytic) = 1.3979688525710318303064745333054 y[1] (numeric) = 1.3979688525710318303064745333054 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.478 y[1] (analytic) = 1.3986743629631046372687052678137 y[1] (numeric) = 1.3986743629631046372687052678136 absolute error = 1e-31 relative error = 7.1496270074007126716967718816258e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.479 y[1] (analytic) = 1.3993799445361700518806852351971 y[1] (numeric) = 1.399379944536170051880685235197 absolute error = 1e-31 relative error = 7.1460220928881034211218212970223e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 1.4000855972686917936494915111048 y[1] (numeric) = 1.4000855972686917936494915111047 absolute error = 1e-31 relative error = 7.1424204487983817453794981529973e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.481 y[1] (analytic) = 1.4007913211391487798216129167341 y[1] (numeric) = 1.400791321139148779821612916734 absolute error = 1e-31 relative error = 7.1388220708476545590176089829043e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.482 y[1] (analytic) = 1.401497116126035108536559870386 y[1] (numeric) = 1.401497116126035108536559870386 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.483 y[1] (analytic) = 1.4022029822078600420059283703526 y[1] (numeric) = 1.4022029822078600420059283703526 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.484 y[1] (analytic) = 1.4029089193631479897178694127062 y[1] (numeric) = 1.4029089193631479897178694127062 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 memory used=156.4MB, alloc=4.3MB, time=14.67 TOP MAIN SOLVE Loop x[1] = 0.485 y[1] (analytic) = 1.4036149275704384916669152602927 y[1] (numeric) = 1.4036149275704384916669152602926 absolute error = 1e-31 relative error = 7.1244611350132308305121732918885e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.486 y[1] (analytic) = 1.40432100680828620160911409165 y[1] (numeric) = 1.4043210068082862016091140916499 absolute error = 1e-31 relative error = 7.1208790237552650706207838950575e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.487 y[1] (analytic) = 1.4050271570552608703424246706942 y[1] (numeric) = 1.4050271570552608703424246706941 absolute error = 1e-31 relative error = 7.1173001530864301999055036918454e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.488 y[1] (analytic) = 1.4057333782899473290123227898256 y[1] (numeric) = 1.4057333782899473290123227898255 absolute error = 1e-31 relative error = 7.1137245187738542667314040744104e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.489 y[1] (analytic) = 1.406439670490945472442571350618 y[1] (numeric) = 1.4064396704909454724425713506179 absolute error = 1e-31 relative error = 7.1101521165918926405007081540131e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 1.4071460336368702424911060574628 y[1] (numeric) = 1.4071460336368702424911060574628 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.491 y[1] (analytic) = 1.4078524677063516114309888104441 y[1] (numeric) = 1.407852467706351611430988810444 absolute error = 1e-31 relative error = 7.1030169917532790045204195510243e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.492 y[1] (analytic) = 1.4085589726780345653563809943253 y[1] (numeric) = 1.4085589726780345653563809943252 absolute error = 1e-31 relative error = 7.0994542606813373917378464076023e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.493 y[1] (analytic) = 1.4092655485305790876134889708371 y[1] (numeric) = 1.4092655485305790876134889708371 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.3MB, time=15.03 x[1] = 0.494 y[1] (analytic) = 1.4099721952426601422564341914594 y[1] (numeric) = 1.4099721952426601422564341914594 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.495 y[1] (analytic) = 1.4106789127929676575280004576013 y[1] (numeric) = 1.4106789127929676575280004576013 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.496 y[1] (analytic) = 1.4113857011602065093652109644962 y[1] (numeric) = 1.4113857011602065093652109644962 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.497 y[1] (analytic) = 1.4120925603230965049296878742438 y[1] (numeric) = 1.4120925603230965049296878742438 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.498 y[1] (analytic) = 1.4127994902603723661627472722537 y[1] (numeric) = 1.4127994902603723661627472722537 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 0.499 y[1] (analytic) = 1.4135064909507837133651824698724 y[1] (numeric) = 1.4135064909507837133651824698724 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 Finished! diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2)); Iterations = 400 Total Elapsed Time = 15 Seconds Elapsed Time(since restart) = 15 Seconds Time to Timeout = 2 Minutes 44 Seconds Percent Done = 100.2 % > quit memory used=162.4MB, alloc=4.3MB, time=15.22