|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > 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 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > 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_min_h, > glob_type_given_pole, > 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, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, 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_min_h, glob_type_given_pole, 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_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, 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 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > 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_min_h, > glob_type_given_pole, > 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, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, 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_min_h, glob_type_given_pole, 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_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > 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_min_h, > glob_type_given_pole, > 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, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, 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_min_h, glob_type_given_pole, 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_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, 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 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > 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_min_h, > glob_type_given_pole, > 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, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > 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 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, 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_min_h, glob_type_given_pole, 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_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, 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)) + 3 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 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > 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_min_h, > glob_type_given_pole, > 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, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > 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 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > 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, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, 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_min_h, glob_type_given_pole, 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_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, 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 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > 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_min_h, > glob_type_given_pole, > 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, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > 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 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; 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, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, 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_min_h, glob_type_given_pole, 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_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, 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 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > 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_min_h, > glob_type_given_pole, > 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, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, 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_min_h, glob_type_given_pole, 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_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) 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 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. 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 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) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. 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 omniabs(rcs) <> 0. 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_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no 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_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > 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_min_h, > glob_type_given_pole, > 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, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, 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_min_h, glob_type_given_pole, 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_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, 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 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > 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_min_h, > glob_type_given_pole, > 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, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre tan $eq_no = 1 > array_tmp1_a1[1] := sin(array_x[1]); > array_tmp1_a2[1] := cos(array_x[1]); > array_tmp1[1] := (array_tmp1_a1[1] / array_tmp1_a2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[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 tan $eq_no = 1 > array_tmp1_a1[2] := array_tmp1_a2[1] * array_x[2] / 1; > array_tmp1_a2[2] := -array_tmp1_a1[1] * array_x[2] / 1; > array_tmp1[2] := (array_tmp1_a1[2] - ats(2,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[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 tan $eq_no = 1 > array_tmp1_a1[3] := array_tmp1_a2[2] * array_x[2] / 2; > array_tmp1_a2[3] := -array_tmp1_a1[2] * array_x[2] / 2; > array_tmp1[3] := (array_tmp1_a1[3] - ats(3,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[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 tan $eq_no = 1 > array_tmp1_a1[4] := array_tmp1_a2[3] * array_x[2] / 3; > array_tmp1_a2[4] := -array_tmp1_a1[3] * array_x[2] / 3; > array_tmp1[4] := (array_tmp1_a1[4] - ats(4,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[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 tan $eq_no = 1 > array_tmp1_a1[5] := array_tmp1_a2[4] * array_x[2] / 4; > array_tmp1_a2[5] := -array_tmp1_a1[4] * array_x[2] / 4; > array_tmp1[5] := (array_tmp1_a1[5] - ats(5,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[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 > array_tmp1_a1[kkk] := array_tmp1_a2[kkk-1] * array_x[2] / (kkk - 1); > array_tmp1_a2[kkk] := -array_tmp1_a1[kkk-1] * array_x[2] / (kkk - 1); > array_tmp1[kkk] := (array_tmp1_a1[kkk] - ats(kkk ,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp2[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > 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 1 > 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, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, 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_min_h, glob_type_given_pole, 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_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1_a1[1] := sin(array_x[1]); array_tmp1_a2[1] := cos(array_x[1]); array_tmp1[1] := array_tmp1_a1[1]/array_tmp1_a2[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[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_a1[2] := array_tmp1_a2[1]*array_x[2]; array_tmp1_a2[2] := -array_tmp1_a1[1]*array_x[2]; array_tmp1[2] := ( array_tmp1_a1[2] - ats(2, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[2] := array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[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_tmp1_a1[3] := 1/2*array_tmp1_a2[2]*array_x[2]; array_tmp1_a2[3] := -1/2*array_tmp1_a1[2]*array_x[2]; array_tmp1[3] := ( array_tmp1_a1[3] - ats(3, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[3] := array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[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_tmp1_a1[4] := 1/3*array_tmp1_a2[3]*array_x[2]; array_tmp1_a2[4] := -1/3*array_tmp1_a1[3]*array_x[2]; array_tmp1[4] := ( array_tmp1_a1[4] - ats(4, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[4] := array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[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_tmp1_a1[5] := 1/4*array_tmp1_a2[4]*array_x[2]; array_tmp1_a2[5] := -1/4*array_tmp1_a1[4]*array_x[2]; array_tmp1[5] := ( array_tmp1_a1[5] - ats(5, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[5] := array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[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_tmp1_a1[kkk] := array_tmp1_a2[kkk - 1]*array_x[2]/(kkk - 1); array_tmp1_a2[kkk] := -array_tmp1_a1[kkk - 1]*array_x[2]/(kkk - 1); array_tmp1[kkk] := ( array_tmp1_a1[kkk] - ats(kkk, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[kkk] := array_tmp1[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 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 13 > #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 ", 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 ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", 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 ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", 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, " ") 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 Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") 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,m,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_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, 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_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > 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 16 > # Begin Function number 17 > 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 17 > # Begin Function number 18 > 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 18 > # Begin Function number 19 > 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 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > 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 21 > # Begin Function number 22 > 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"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > 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") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > 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 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > 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 25 > # Begin Function number 26 > 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 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > 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 26 > # Begin Function number 27 > 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 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > 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 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > 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 29 > # Begin Function number 30 > 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 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > 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 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > 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 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(-ln(cos(x))); > end; exact_soln_y := proc(x) return -ln(cos(x)) 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,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > 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_min_h, > glob_type_given_pole, > 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, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > 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; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > 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_min_h := 0.000001; > glob_type_given_pole := 0; > 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 := 0.0; > glob_smallish_float := 0.0; > 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/tanpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = tan ( x ) ;"); > 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 := 1.5 ;"); > 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 := 10000;"); > omniout_str(ALWAYS,"glob_max_h := 0.001;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"## Not Given = 0"); > omniout_str(ALWAYS,"## No Pole = 3"); > omniout_str(ALWAYS,"## Pole = 4"); > omniout_str(ALWAYS,"glob_type_given_pole := 4;"); > omniout_str(ALWAYS,"## Real Part"); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := 1.570796327;"); > omniout_str(ALWAYS,"## Imag Part"); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := 0.0;"); > omniout_str(ALWAYS,"## Order"); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := 0.0;"); > omniout_str(ALWAYS,"## Not Used"); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := 0.0;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(-ln(cos(x)));"); > 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 := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_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..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_tmp1_a1:= Array(0..(max_terms + 1),[]); > array_tmp1_a2:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= 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..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 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 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 1.5 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 10000; > glob_max_h := 0.001; > ## Not Given = 0 > ## No Pole = 3 > ## Pole = 4 > glob_type_given_pole := 4; > ## Real Part > array_given_rad_poles[1,1] := 1.570796327; > ## Imag Part > array_given_rad_poles[1,2] := 0.0; > ## Order > array_given_ord_poles[1,1] := 0.0; > ## Not Used > array_given_ord_poles[1,2] := 0.0; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > 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); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 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 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > 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 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = tan ( x ) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T05:36:15-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"tan") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = tan ( x ) ;") > ; > 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_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"tan diffeq.mxt") > ; > logitem_str(html_log_file,"tan maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #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, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, 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_min_h, glob_type_given_pole, 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_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, 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; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; 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_min_h := 0.1*10^(-5); glob_type_given_pole := 0; 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.; glob_smallish_float := 0.; 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/tanpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = tan ( x ) ;"); 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 := 1.5 ;"); 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 := 10000;"); omniout_str(ALWAYS, "glob_max_h := 0.001;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "## Not Given = 0"); omniout_str(ALWAYS, "## No Pole = 3"); omniout_str(ALWAYS, "## Pole = 4"); omniout_str(ALWAYS, "glob_type_given_pole := 4;"); omniout_str(ALWAYS, "## Real Part"); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := 1.570796327;"); omniout_str(ALWAYS, "## Imag Part"); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := 0.0;"); omniout_str(ALWAYS, "## Order"); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := 0.0;"); omniout_str(ALWAYS, "## Not Used"); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := 0.0;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(-ln(cos(x)));"); 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.; glob_smallish_float := 0.; 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 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_tmp1_a1 := Array(0 .. max_terms + 1, []); array_tmp1_a2 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := 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 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 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 <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_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_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_a2[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_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 <= 2 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 <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[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_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_tmp1_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_a1[term] := 0.; term := term + 1 end do; array_tmp1_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_a2[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_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_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 := 1.5; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 10000; glob_max_h := 0.001; glob_type_given_pole := 4; array_given_rad_poles[1, 1] := 1.570796327; array_given_rad_poles[1, 2] := 0.; array_given_ord_poles[1, 1] := 0.; array_given_ord_poles[1, 2] := 0.; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; 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); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h 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(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if 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 ) = tan ( x ) ;"); 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, "2013-05-26T05:36:15-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "tan"); logitem_str(html_log_file, "diff ( y , x , 1 ) = tan ( x ) ;") ; 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_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, " 189 "); logitem_str(html_log_file, "tan diffeq.mxt"); logitem_str(html_log_file, "tan 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 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/tanpostode.ode################# diff ( y , x , 1 ) = tan ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 1.5 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 10000; glob_max_h := 0.001; ## Not Given = 0 ## No Pole = 3 ## Pole = 4 glob_type_given_pole := 4; ## Real Part array_given_rad_poles[1,1] := 1.570796327; ## Imag Part array_given_rad_poles[1,2] := 0.0; ## Order array_given_ord_poles[1,1] := 0.0; ## Not Used array_given_ord_poles[1,2] := 0.0; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(-ln(cos(x))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 1.4 estimated_steps = 1400000 step_error = 7.1428571428571428571428571428571e-17 est_needed_step_err = 7.1428571428571428571428571428571e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.7545349881333858732823046613652e-162 estimated_step_error = 1.7545349881333858732823046613652e-162 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1774488590573532239307284745361e-154 estimated_step_error = 1.1774488590573532239307284745361e-154 best_h = 4.00e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.9017303673035447986682384028776e-147 estimated_step_error = 7.9017303673035447986682384028776e-147 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.3027679717378352124110150784201e-139 estimated_step_error = 5.3027679717378352124110150784201e-139 best_h = 1.60000e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.5586360516496029956506643574241e-131 estimated_step_error = 3.5586360516496029956506643574241e-131 best_h = 3.200000e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.3881719122569965421151336516878e-123 estimated_step_error = 2.3881719122569965421151336516878e-123 best_h = 6.4000000e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.6026907230790530667830817420081e-115 estimated_step_error = 1.6026907230790530667830817420081e-115 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0755685869512843352017551453386e-107 estimated_step_error = 1.0755685869512843352017551453386e-107 best_h = 0.000256 opt_iter = 9 bytes used=4000036, alloc=2883056, time=0.28 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.2183011397030182533279186888254e-100 estimated_step_error = 7.2183011397030182533279186888254e-100 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.8444991607453669861841049715834e-92 estimated_step_error = 4.8444991607453669861841049715834e-92 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.2515975312764918051583899910931e-84 estimated_step_error = 3.2515975312764918051583899910931e-84 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.0050083556232353090791329977212671 y[1] (numeric) = 0.0050083556232353090791329977212671 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.309 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=8001488, alloc=4062488, time=0.58 x[1] = 0.11 y[1] (analytic) = 0.0060622403465323032306356113409113 y[1] (numeric) = 0.0060622403465323032306356113409134 absolute error = 2.1e-33 relative error = 3.4640658897683477849595778723851e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.461 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.349 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0.0072173466466277368000894604662206 y[1] (numeric) = 0.0072173466466277368000894604662168 absolute error = 3.8e-33 relative error = 5.2650928188069335365755048237809e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.451 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.379 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=12002528, alloc=4259060, time=0.90 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0.008473908649082293939847075567037 y[1] (numeric) = 0.0084739086490822939398470755670326 absolute error = 4.4e-33 relative error = 5.1924090549129421234068325682876e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.441 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.401 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=16003572, alloc=4324584, time=1.21 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0.0098321816582955505386607580817523 y[1] (numeric) = 0.0098321816582955505386607580817521 absolute error = 2e-34 relative error = 2.0341365421300691197282114176828e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.431 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.416 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=20004552, alloc=4390108, time=1.53 x[1] = 0.15 y[1] (analytic) = 0.011292442366641786981368027419826 y[1] (numeric) = 0.011292442366641786981368027419827 absolute error = 1e-33 relative error = 8.8554802188234314590609468704173e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.421 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.425 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 5.301 Order of pole (three term test) = 2373 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.012854989082009649242948557584918 y[1] (numeric) = 0.01285498908200964924294855758492 absolute error = 2e-33 relative error = 1.5558161794154830346126250679557e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.411 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.431 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 2.964 Order of pole (three term test) = 1330 NO COMPLEX POLE (six term test) for Equation 1 bytes used=24008020, alloc=4390108, time=1.85 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0.014520141974147117510638725229194 y[1] (numeric) = 0.01452014197414711751063872522919 absolute error = 4e-33 relative error = 2.7547940007211613759040100212574e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.401 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.432 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 2.241 Order of pole (three term test) = 1010 NO COMPLEX POLE (six term test) for Equation 1 bytes used=28009432, alloc=4455632, time=2.18 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0.016288243340248848521775773334465 y[1] (numeric) = 0.016288243340248848521775773334461 absolute error = 4e-33 relative error = 2.4557589891328875496598955846129e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.391 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.431 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 860.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0.018159657890259910149161840872723 y[1] (numeric) = 0.018159657890259910149161840872717 absolute error = 6e-33 relative error = 3.3040270010913322249437818052116e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.381 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.428 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.708 Order of pole (three term test) = 777.5 NO COMPLEX POLE (six term test) for Equation 1 bytes used=32010404, alloc=4455632, time=2.50 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0.020134773052408348925755928105682 y[1] (numeric) = 0.020134773052408348925755928105681 absolute error = 1e-33 relative error = 4.9665322643425006151950931220052e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.371 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.423 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.588 Order of pole (three term test) = 727.2 NO COMPLEX POLE (six term test) for Equation 1 bytes used=36011140, alloc=4455632, time=2.83 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0.022213999299519054687682950444782 y[1] (numeric) = 0.022213999299519054687682950444785 absolute error = 3e-33 relative error = 1.3504997274691332376701629135856e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.361 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.417 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.507 Order of pole (three term test) = 694.9 NO COMPLEX POLE (six term test) for Equation 1 bytes used=40012376, alloc=4455632, time=3.15 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0.024397770496703150585626911321445 y[1] (numeric) = 0.024397770496703150585626911321446 absolute error = 1e-33 relative error = 4.0987351698186075094151270232649e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.351 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.408 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.451 Order of pole (three term test) = 673.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 0.026686544271060789125605597428335 y[1] (numeric) = 0.026686544271060789125605597428335 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.341 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.41 Order of pole (three term test) = 658.9 NO COMPLEX POLE (six term test) for Equation 1 bytes used=44013460, alloc=4455632, time=3.48 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 0.029080802404080932719476939417643 y[1] (numeric) = 0.029080802404080932719476939417643 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.331 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.378 Order of pole (three term test) = 648.9 NO COMPLEX POLE (six term test) for Equation 1 bytes used=48015648, alloc=4455632, time=3.80 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 0.031581051247469607713948928307465 y[1] (numeric) = 0.031581051247469607713948928307466 absolute error = 1e-33 relative error = 3.1664557084056020807309863415846e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.321 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.381 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.354 Order of pole (three term test) = 641.9 NO COMPLEX POLE (six term test) for Equation 1 bytes used=52016640, alloc=4521156, time=4.12 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 0.034187822163188422429682548760632 y[1] (numeric) = 0.034187822163188422429682548760626 absolute error = 6e-33 relative error = 1.7550108840979265212372091952948e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.311 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.371 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.333 Order of pole (three term test) = 637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 0.036901671988538022962828423907479 y[1] (numeric) = 0.036901671988538022962828423907476 absolute error = 3e-33 relative error = 8.1297129326059421630631290100100e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.301 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.361 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.316 Order of pole (three term test) = 633.5 NO COMPLEX POLE (six term test) for Equation 1 bytes used=56017588, alloc=4521156, time=4.44 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0.039723183527176829264819318516813 y[1] (numeric) = 0.039723183527176829264819318516815 absolute error = 2e-33 relative error = 5.0348431883151793787126812218300e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.291 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.301 Order of pole (three term test) = 631 NO COMPLEX POLE (six term test) for Equation 1 bytes used=60018764, alloc=4521156, time=4.77 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 0.04265296606702406673056111562254 y[1] (numeric) = 0.042652966067024066730561115622538 absolute error = 2e-33 relative error = 4.6890056763162442361124474062756e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.281 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.34 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.287 Order of pole (three term test) = 629.3 NO COMPLEX POLE (six term test) for Equation 1 bytes used=64020432, alloc=4521156, time=5.09 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0.045691655926058019453301984654094 y[1] (numeric) = 0.045691655926058019453301984654094 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.271 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.329 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.275 Order of pole (three term test) = 628.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 0.048839917027085832016946896893199 y[1] (numeric) = 0.048839917027085832016946896893201 absolute error = 2e-33 relative error = 4.0950110519041876860802642675505e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.261 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.318 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.263 Order of pole (three term test) = 627.2 NO COMPLEX POLE (six term test) for Equation 1 bytes used=68021208, alloc=4521156, time=5.42 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 0.052098441502630347658225662533815 y[1] (numeric) = 0.052098441502630347658225662533814 absolute error = 1e-33 relative error = 1.9194432139577763959996581380792e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.251 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.308 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.252 Order of pole (three term test) = 626.6 NO COMPLEX POLE (six term test) for Equation 1 bytes used=72022952, alloc=4521156, time=5.74 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0.055467950331152682936048083594259 y[1] (numeric) = 0.055467950331152682936048083594266 absolute error = 7e-33 relative error = 1.2619900245473037588847466038327e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.241 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.297 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.241 Order of pole (three term test) = 626.1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=76023952, alloc=4521156, time=6.07 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 0.05894919400590681631636664753468 y[1] (numeric) = 0.058949194005906816316366647534685 absolute error = 5e-33 relative error = 8.4818801754931389186751276571028e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.231 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.287 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.231 Order of pole (three term test) = 625.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = 0.062542953237804748550628956240186 y[1] (numeric) = 0.062542953237804748550628956240192 absolute error = 6e-33 relative error = 9.5934069137835925515673590119066e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.221 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.276 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.22 Order of pole (three term test) = 625.6 NO COMPLEX POLE (six term test) for Equation 1 bytes used=80024952, alloc=4521156, time=6.40 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 0.066250039693758141520080425462836 y[1] (numeric) = 0.066250039693758141520080425462837 absolute error = 1e-33 relative error = 1.5094330578857248221729736638924e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.211 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.266 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.21 Order of pole (three term test) = 625.4 NO COMPLEX POLE (six term test) for Equation 1 bytes used=84025908, alloc=4521156, time=6.73 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 0.070071296772055153862035972018276 y[1] (numeric) = 0.07007129677205515386203597201828 absolute error = 4e-33 relative error = 5.7084714915611831164887372594294e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.201 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.255 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.2 Order of pole (three term test) = 625.3 NO COMPLEX POLE (six term test) for Equation 1 bytes used=88027368, alloc=4521156, time=7.05 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 0.074007600416429892867616152336733 y[1] (numeric) = 0.074007600416429892867616152336735 absolute error = 2e-33 relative error = 2.7024251411291460336078626552939e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.191 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.245 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.189 Order of pole (three term test) = 625.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 0.078059859970586954708407708121751 y[1] (numeric) = 0.078059859970586954708407708121749 absolute error = 2e-33 relative error = 2.5621362897058773963001112408045e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.181 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.234 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.179 Order of pole (three term test) = 625.2 NO COMPLEX POLE (six term test) for Equation 1 bytes used=92029948, alloc=4521156, time=7.38 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0.082229019075055429399409173994342 y[1] (numeric) = 0.082229019075055429399409173994339 absolute error = 3e-33 relative error = 3.6483470601317978122022328021689e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.171 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.224 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.169 Order of pole (three term test) = 625.1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=96030872, alloc=4521156, time=7.70 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 0.086516056608366045624893433143116 y[1] (numeric) = 0.086516056608366045624893433143118 absolute error = 2e-33 relative error = 2.3117096160004607963261615715471e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.161 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.214 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.159 Order of pole (three term test) = 625.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=100031716, alloc=4521156, time=8.04 x[1] = 0.42 y[1] (analytic) = 0.090921987674672412487058343650493 y[1] (numeric) = 0.090921987674672412487058343650495 absolute error = 2e-33 relative error = 2.1996879425427782290544313905053e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.151 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.203 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.149 Order of pole (three term test) = 625.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 0.095447864640073219965858582901525 y[1] (numeric) = 0.095447864640073219965858582901526 absolute error = 1e-33 relative error = 1.0476923750687618106997094118368e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.141 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.193 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.139 Order of pole (three term test) = 625.1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=104032644, alloc=4521156, time=8.36 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 0.1000947782200374826708000675464 y[1] (numeric) = 0.1000947782200374826708000675464 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.131 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.182 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.129 Order of pole (three term test) = 625.1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=108033624, alloc=4521156, time=8.69 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 0.1048638586204902087536765449528 y[1] (numeric) = 0.10486385862049020875367654495281 absolute error = 1e-32 relative error = 9.5361739798176929228709214477871e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.121 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.172 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.119 Order of pole (three term test) = 625.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=112034812, alloc=4521156, time=9.02 x[1] = 0.46 y[1] (analytic) = 0.10975627673528207129354998536697 y[1] (numeric) = 0.10975627673528207129354998536699 absolute error = 2e-32 relative error = 1.8222192474911854457753939988704e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.111 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.161 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.109 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 0.11477324540294465066547177211419 y[1] (numeric) = 0.11477324540294465066547177211421 absolute error = 2e-32 relative error = 1.7425663907807276373990099461198e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.151 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.099 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=116035740, alloc=4521156, time=9.34 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 0.11991602072582358236478155761168 y[1] (numeric) = 0.11991602072582358236478155761168 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.091 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.14 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.089 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=120036548, alloc=4521156, time=9.67 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 0.12518590345488655415521215776159 y[1] (numeric) = 0.1251859034548865541552121577616 absolute error = 1e-32 relative error = 7.9881198473785957229312899573591e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.081 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.13 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.079 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0.13058424044372271678761259182601 y[1] (numeric) = 0.130584240443722716787612591826 absolute error = 1e-32 relative error = 7.6578919217358801615068075265730e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.071 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.119 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.069 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=124039520, alloc=4521156, time=10.00 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 0.13611242617548598054384463663251 y[1] (numeric) = 0.1361124261754859805438446366325 absolute error = 1e-32 relative error = 7.3468677922964043087651262237556e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.061 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.109 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.059 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=128040772, alloc=4521156, time=10.32 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 0.14177190436678826263712043626926 y[1] (numeric) = 0.14177190436678826263712043626925 absolute error = 1e-32 relative error = 7.0535837440176318233430622044113e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.051 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.099 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.049 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=132041556, alloc=4521156, time=10.65 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 0.14756416965282155837629888639352 y[1] (numeric) = 0.14756416965282155837629888639349 absolute error = 3e-32 relative error = 2.0330138454735900908122135190440e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.041 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.088 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.039 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 0.15349076935828140966659957147956 y[1] (numeric) = 0.15349076935828140966659957147954 absolute error = 2e-32 relative error = 1.3030099519089369968591266716306e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.031 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.078 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.029 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=136042212, alloc=4521156, time=10.98 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 0.15955330535898077874467619601204 y[1] (numeric) = 0.15955330535898077874467619601202 absolute error = 2e-32 relative error = 1.2534995721337000661899541168466e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.021 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.067 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.019 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=140043248, alloc=4521156, time=11.30 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 0.16575343603938452477904084553625 y[1] (numeric) = 0.16575343603938452477904084553624 absolute error = 1e-32 relative error = 6.0330574369655353622983370220351e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 1.011 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.057 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.009 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=144044136, alloc=4521156, time=11.63 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = 0.17209287835166284853206403837245 y[1] (numeric) = 0.17209287835166284853206403837243 absolute error = 2e-32 relative error = 1.1621631407158546065857100512740e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 1.001 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.046 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9994 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 0.17857340998225966096732308406808 y[1] (numeric) = 0.17857340998225966096732308406807 absolute error = 1e-32 relative error = 5.5999378636457958453221053068043e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.9908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.036 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9894 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=148045208, alloc=4521156, time=11.96 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 0.18519687163240153853967239844412 y[1] (numeric) = 0.18519687163240153853967239844411 absolute error = 1e-32 relative error = 5.3996592447031526038026899738309e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.9808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.025 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9794 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=152046432, alloc=4586680, time=12.29 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0.19196516941943771967052566250649 y[1] (numeric) = 0.1919651694194377196705256625065 absolute error = 1e-32 relative error = 5.2092783447346751220031869080219e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.9708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.015 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9694 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=156047724, alloc=4586680, time=12.62 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 0.19888027740640474945477660860593 y[1] (numeric) = 0.19888027740640474945477660860592 absolute error = 1e-32 relative error = 5.0281506695434444056176029093369e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.9608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 1.004 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9594 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 0.2059442402677545113221722854327 y[1] (numeric) = 0.20594424026775451132217228543269 absolute error = 1e-32 relative error = 4.8556832601866840341514871911572e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.9508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.994 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9494 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=160048748, alloc=4586680, time=12.94 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 0.21315917609977549587585267775296 y[1] (numeric) = 0.21315917609977549587585267775295 absolute error = 1e-32 relative error = 4.6913298235489531097560011142313e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.9408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9836 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9395 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=164050128, alloc=4586680, time=13.27 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 0.22052727938487867644382399752528 y[1] (numeric) = 0.22052727938487867644382399752526 absolute error = 2e-32 relative error = 9.0691727825176167118275975948168e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.9308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9731 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9295 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=168051128, alloc=4586680, time=13.60 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 0.22805082411961619408242495471385 y[1] (numeric) = 0.22805082411961619408242495471384 absolute error = 1e-32 relative error = 4.3849874424285548340639618231153e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.9208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9627 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9195 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 0.23573216711705864347290962598666 y[1] (numeric) = 0.23573216711705864347290962598665 absolute error = 1e-32 relative error = 4.2421024344268860157420143879628e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.9108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9522 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9095 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=172052904, alloc=4586680, time=13.94 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 0.24357375149498113754754544323105 y[1] (numeric) = 0.24357375149498113754754544323104 absolute error = 1e-32 relative error = 4.1055326933313054624520373142816e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.9008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9417 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8995 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=176053860, alloc=4586680, time=14.26 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 0.25157811036220622931999672046961 y[1] (numeric) = 0.25157811036220622931999672046959 absolute error = 2e-32 relative error = 7.9498172441176486786750190360357e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.8908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9313 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8895 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=180055080, alloc=4586680, time=14.59 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 0.25974787071643065894544560756899 y[1] (numeric) = 0.25974787071643065894544560756896 absolute error = 3e-32 relative error = 1.1549661568833917104472994049817e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.8808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9208 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8795 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0.26808575756793110052941329261424 y[1] (numeric) = 0.26808575756793110052941329261419 absolute error = 5e-32 relative error = 1.8650748347692563037572436643028e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.8708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.9104 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8696 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=184056216, alloc=4586680, time=14.92 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 0.27659459830471089647622620475432 y[1] (numeric) = 0.27659459830471089647622620475427 absolute error = 5e-32 relative error = 1.8076997998680154028977902519084e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.8608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8999 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8596 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=188057012, alloc=4586680, time=15.24 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 0.28527732731592556251069378115938 y[1] (numeric) = 0.28527732731592556251069378115934 absolute error = 4e-32 relative error = 1.4021443756623068379972593372306e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.8508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8895 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8496 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=192058260, alloc=4586680, time=15.57 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 0.29413699089182122586533133649918 y[1] (numeric) = 0.29413699089182122586533133649913 absolute error = 5e-32 relative error = 1.6998881999982512285977634552204e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.8408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.879 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8396 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 0.30317675241995011257089763534277 y[1] (numeric) = 0.30317675241995011257089763534272 absolute error = 5e-32 relative error = 1.6492029682652482134406878673694e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.8308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8686 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8296 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=196059356, alloc=4586680, time=15.89 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 0.31239989789910529045450249364086 y[1] (numeric) = 0.3123998978991052904545024936408 absolute error = 6e-32 relative error = 1.9206152243807067927165326175636e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.8208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8581 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8196 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=200060028, alloc=4586680, time=16.22 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 0.32180984179425945068151423381541 y[1] (numeric) = 0.32180984179425945068151423381537 absolute error = 4e-32 relative error = 1.2429700650849868786083279752077e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.8108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8477 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8096 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=204061140, alloc=4586680, time=16.55 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 0.33141013325781794977317349320871 y[1] (numeric) = 0.33141013325781794977317349320868 absolute error = 3e-32 relative error = 9.0522277351917094352483658436037e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.8008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8372 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7997 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 0.34120446274472532274703956801391 y[1] (numeric) = 0.34120446274472532274703956801388 absolute error = 3e-32 relative error = 8.7923820687083817390578760451850e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.7908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8267 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7897 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=208062696, alloc=4586680, time=16.87 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 0.35119666905142033592219992599373 y[1] (numeric) = 0.3511966690514203359221999259937 absolute error = 3e-32 relative error = 8.5422222485850401458553333666287e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.7808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8163 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7797 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=212063440, alloc=4586680, time=17.20 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 0.36139074681134370073955187701716 y[1] (numeric) = 0.36139074681134370073955187701713 absolute error = 3e-32 relative error = 8.3012640098560291785317531038220e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.7708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.8058 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7697 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=216064784, alloc=4586680, time=17.52 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 0.37179085448269458146368508643973 y[1] (numeric) = 0.3717908544826945814636850864397 absolute error = 3e-32 relative error = 8.0690527048444069090164142013195e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.7608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7954 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7597 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 0.38240132286744070218141983186178 y[1] (numeric) = 0.38240132286744070218141983186177 absolute error = 1e-32 relative error = 2.6150537150381398764755980197267e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.7508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7849 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7497 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=220066656, alloc=4586680, time=17.85 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 0.39322666420425041395821766021091 y[1] (numeric) = 0.39322666420425041395821766021089 absolute error = 2e-32 relative error = 5.0861250827109650082452479904619e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.7408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7745 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7397 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=224067576, alloc=4586680, time=18.18 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = 0.40427158188207693854781095755977 y[1] (numeric) = 0.40427158188207693854781095755976 absolute error = 1e-32 relative error = 2.4735847010183680947066511350799e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.7308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.764 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7298 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=228068612, alloc=4586680, time=18.50 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 0.41554098082563456072414008672357 y[1] (numeric) = 0.41554098082563456072414008672356 absolute error = 1e-32 relative error = 2.4065015152370993074744156440428e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.7208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7536 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7198 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 0.42703997860902009961970846262481 y[1] (numeric) = 0.4270399786090200996197084626248 absolute error = 1e-32 relative error = 2.3417011289136422379392072638076e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.7108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7431 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7098 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=232070988, alloc=4586680, time=18.83 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 0.43877391735931483133143230370915 y[1] (numeric) = 0.43877391735931483133143230370915 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.7008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7327 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6998 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=236072696, alloc=4586680, time=19.16 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 0.45074837651822568140685167564968 y[1] (numeric) = 0.45074837651822568140685167564969 absolute error = 1e-32 relative error = 2.2185326716524862077584661218965e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.6908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7222 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6898 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=240073612, alloc=4586680, time=19.49 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 0.46296918653677419992400132049904 y[1] (numeric) = 0.46296918653677419992400132049905 absolute error = 1e-32 relative error = 2.1599709636843591446046130781641e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.6808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7117 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6798 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 0.47544244358581428500971793610522 y[1] (numeric) = 0.47544244358581428500971793610523 absolute error = 1e-32 relative error = 2.1033040139579092287837196962823e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.6708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.7013 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6698 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=244074524, alloc=4586680, time=19.82 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 0.48817452537386607244011633638259 y[1] (numeric) = 0.4881745253738660724401163363826 absolute error = 1e-32 relative error = 2.0484477333882895493558612541152e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.6608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6908 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6599 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=248075352, alloc=4586680, time=20.15 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 0.50117210817352206486580922236454 y[1] (numeric) = 0.50117210817352206486580922236455 absolute error = 1e-32 relative error = 1.9953225323021518071425780477080e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.6508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6804 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6499 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=252076712, alloc=4586680, time=20.47 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 0.51444218516866049589961060443574 y[1] (numeric) = 0.51444218516866049589961060443575 absolute error = 1e-32 relative error = 1.9438530292226108637170845310439e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.6408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6699 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6399 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 0.52799208624706146590424159189259 y[1] (numeric) = 0.52799208624706146590424159189264 absolute error = 5e-32 relative error = 9.4698389052376207741018584733058e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.6308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6595 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6299 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=256077628, alloc=4586680, time=20.80 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 0.54182949937696228955735782951295 y[1] (numeric) = 0.541829499376962289557357829513 absolute error = 5e-32 relative error = 9.2279951640680121311163537073748e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.6208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.649 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6199 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=260079596, alloc=4586680, time=21.13 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 0.55596249372184078297003425326856 y[1] (numeric) = 0.5559624937218407829700342532686 absolute error = 4e-32 relative error = 7.1947299416231492178750215311288e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.6108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6386 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6099 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=264080940, alloc=4586680, time=21.46 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 0.57039954466554805723971068073415 y[1] (numeric) = 0.57039954466554805723971068073416 absolute error = 1e-32 relative error = 1.7531570797209292852374561767918e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.6008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6281 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.5999 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 0.58514956094014013115956949852153 y[1] (numeric) = 0.58514956094014013115956949852154 absolute error = 1e-32 relative error = 1.7089647959289820069389438382598e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.5908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6177 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.59 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=268081852, alloc=4586680, time=21.79 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 0.60022191407174835977683955432996 y[1] (numeric) = 0.60022191407174835977683955432998 absolute error = 2e-32 relative error = 3.3321009331907318922592495494910e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.5808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.6072 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.58 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=272082996, alloc=4586680, time=22.12 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 0.61562647038601426214703751640889 y[1] (numeric) = 0.61562647038601426214703751640891 absolute error = 2e-32 relative error = 3.2487232050726254656885231606205e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.5708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5967 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.57 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=276084340, alloc=4586680, time=22.44 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 0.63137362584450315188279089363379 y[1] (numeric) = 0.6313736258445031518827908936338 absolute error = 1e-32 relative error = 1.5838482303761662159127203336818e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.5608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5863 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.56 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = 0.64747434401770284367387505983639 y[1] (numeric) = 0.64747434401770284367387505983641 bytes used=280086088, alloc=4586680, time=22.77 absolute error = 2e-32 relative error = 3.0889254817258322672268823959777e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.5508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5758 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.55 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = 0.66394019753941837193284368197813 y[1] (numeric) = 0.66394019753941837193284368197815 absolute error = 2e-32 relative error = 3.0123194941533258645616326942854e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.5408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5654 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.54 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=284087284, alloc=4586680, time=23.10 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = 0.68078341343243336216822163902211 y[1] (numeric) = 0.68078341343243336216822163902212 absolute error = 1e-32 relative error = 1.4688959517361219623537727973747e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.5308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5549 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.53 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=288088120, alloc=4586680, time=23.43 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 0.6980169227472259234768425271063 y[1] (numeric) = 0.69801692274722592347684252710631 absolute error = 1e-32 relative error = 1.4326300228714250399781130143757e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.5208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5445 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.5201 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=292089048, alloc=4586680, time=23.76 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 0.7156544150154985808589391935345 y[1] (numeric) = 0.71565441501549858085893919353452 absolute error = 2e-32 relative error = 2.7946449543760405211816886542539e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.5108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.534 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.5101 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = 0.73371039808974145199588183609803 y[1] (numeric) = 0.73371039808974145199588183609807 absolute error = 4e-32 relative error = 5.4517422819878760007801684848994e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.5008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5236 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.5001 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=296089988, alloc=4586680, time=24.09 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 0.75220026402071845962429762508506 y[1] (numeric) = 0.75220026402071845962429762508511 absolute error = 5e-32 relative error = 6.6471659731593512976606625454245e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.4908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5131 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4901 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=300091148, alloc=4586680, time=24.42 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = 0.77114036171872549545405346664079 y[1] (numeric) = 0.77114036171872549545405346664083 absolute error = 4e-32 relative error = 5.1871231212496247031462113180340e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.4808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.5027 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4801 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=304092436, alloc=4586680, time=24.75 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0.79054807725423157832360761284218 y[1] (numeric) = 0.79054807725423157832360761284223 absolute error = 5e-32 relative error = 6.3247260272471131690939094290130e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.4708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4922 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4701 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 0.8104419227821336686144201585331 y[1] (numeric) = 0.81044192278213366861442015853312 absolute error = 2e-32 relative error = 2.4677894168335714623164795292032e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.4608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4817 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4601 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=308093348, alloc=4586680, time=25.08 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 0.8308416352250578146554749380697 y[1] (numeric) = 0.83084163522505781465547493806973 absolute error = 3e-32 relative error = 3.6107964175234935705964526984736e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.4508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4713 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4502 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=312094532, alloc=4586680, time=25.41 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 0.85176828602948452590182842787181 y[1] (numeric) = 0.85176828602948452590182842787183 absolute error = 2e-32 relative error = 2.3480564289649646211425483134459e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.4408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4608 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4402 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=316095472, alloc=4586680, time=25.75 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = 0.87324440351957250437741676966729 y[1] (numeric) = 0.87324440351957250437741676966732 absolute error = 3e-32 relative error = 3.4354643303852096881547049181364e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.4308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4504 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4302 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=320096580, alloc=4586680, time=26.08 x[1] = 1.15 y[1] (analytic) = 0.89529410962432754843323878013503 y[1] (numeric) = 0.89529410962432754843323878013507 absolute error = 4e-32 relative error = 4.4678055590898855209791356180875e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.4208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4399 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4202 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 0.9179432730528043730621826802488 y[1] (numeric) = 0.91794327305280437306218268024884 absolute error = 4e-32 relative error = 4.3575677467488792927370114281950e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.4108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4295 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4102 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=324097636, alloc=4586680, time=26.41 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 0.94121968135004839415224478118841 y[1] (numeric) = 0.94121968135004839415224478118844 absolute error = 3e-32 relative error = 3.1873536640212604822423854789607e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.4008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.419 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4002 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=328098880, alloc=4586680, time=26.73 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 0.9651532346968997068056452965941 y[1] (numeric) = 0.96515323469689970680564529659414 absolute error = 4e-32 relative error = 4.1444196177368403072870306854722e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.3908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.4086 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3902 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=332100040, alloc=4586680, time=27.06 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 0.98977616483648983560036133331333 y[1] (numeric) = 0.9897761648364898356003613333134 absolute error = 7e-32 relative error = 7.0723060917075063448710753500221e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.3808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3981 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3803 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 1.0151232831406596166642531887589 y[1] (numeric) = 1.015123283140659616664253188759 absolute error = 1e-31 relative error = 9.8510202318099714696838520120862e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.3708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3877 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3703 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=336100932, alloc=4586680, time=27.39 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 1.0412322625978628317573860361734 y[1] (numeric) = 1.0412322625978628317573860361736 absolute error = 2e-31 relative error = 1.9208010276304946632342586423945e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.3608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3772 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3603 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=340102312, alloc=4586680, time=27.72 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 1.0681439594453074953144590293971 y[1] (numeric) = 1.0681439594453074953144590293972 absolute error = 1e-31 relative error = 9.3620339389393261696122831330832e-30 % Correct digits = 32 h = 0.001 Radius of convergence (given) for eq 1 = 0.3508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3667 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3503 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=344103180, alloc=4586680, time=28.05 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 1.0959027813271406152089727445301 y[1] (numeric) = 1.0959027813271406152089727445303 absolute error = 2e-31 relative error = 1.8249793997036814859923563484792e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.3408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3563 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3403 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 1.1245571102958336035990707821674 y[1] (numeric) = 1.1245571102958336035990707821677 absolute error = 3e-31 relative error = 2.6677168927514936953581750871937e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.3308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3458 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3303 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=348104232, alloc=4586680, time=28.38 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 1.1541597907619533834757535760123 y[1] (numeric) = 1.1541597907619533834757535760125 absolute error = 2e-31 relative error = 1.7328623090219073569901017154433e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.3208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3354 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3203 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=352105292, alloc=4586680, time=28.71 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = 1.1847686947387932103640751409307 y[1] (numeric) = 1.1847686947387932103640751409309 absolute error = 2e-31 relative error = 1.6880932192768153875077449544539e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.3108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3249 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3104 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=356106712, alloc=4586680, time=29.04 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 1.2164473795563924951328697040191 y[1] (numeric) = 1.2164473795563924951328697040195 absolute error = 4e-31 relative error = 3.2882638963460125520618266235853e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.3008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.3145 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3004 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 1.2492658568129765948943342669988 y[1] (numeric) = 1.2492658568129765948943342669993 absolute error = 5e-31 relative error = 4.0023506387628211989853966864742e-29 % Correct digits = 31 h = 0.001 bytes used=360108588, alloc=4586680, time=29.37 Radius of convergence (given) for eq 1 = 0.2908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.304 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2904 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 1.2833014959320560732328761350587 y[1] (numeric) = 1.2833014959320560732328761350592 absolute error = 5e-31 relative error = 3.8962005544679293081279135251741e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.2808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2936 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2804 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=364109456, alloc=4586680, time=29.64 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 1.3186400916291685666027959482477 y[1] (numeric) = 1.3186400916291685666027959482483 absolute error = 6e-31 relative error = 4.5501422549552935741970886524303e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.2708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2831 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2704 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=368110444, alloc=4586680, time=29.78 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 1.3553771323162041613521307414069 y[1] (numeric) = 1.3553771323162041613521307414074 absolute error = 5e-31 relative error = 3.6890101513336729654060881921967e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.2608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2727 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2604 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=372111340, alloc=4586680, time=29.92 x[1] = 1.32 y[1] (analytic) = 1.3936193166132841894311591204205 y[1] (numeric) = 1.3936193166132841894311591204211 absolute error = 6e-31 relative error = 4.3053364204085165271785848502106e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.2508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2622 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2504 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 1.4334863785846989858939593092082 y[1] (numeric) = 1.4334863785846989858939593092089 absolute error = 7e-31 relative error = 4.8831995229080566756789880993088e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.2408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2517 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2405 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=376113320, alloc=4586680, time=30.05 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 1.4751133003293379102707928607389 y[1] (numeric) = 1.4751133003293379102707928607397 absolute error = 8e-31 relative error = 5.4233122284328245728256241380044e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.2308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2413 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2305 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=380114572, alloc=4586680, time=30.19 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 1.5186530149603870751898958988672 y[1] (numeric) = 1.518653014960387075189895898868 absolute error = 8e-31 relative error = 5.2678261072090085038270403325028e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.2208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2308 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2205 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=384115588, alloc=4586680, time=30.33 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 1.5642797364730061261017717087599 y[1] (numeric) = 1.5642797364730061261017717087608 absolute error = 9e-31 relative error = 5.7534466439438581918796116009730e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.2108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2204 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2105 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 1.6121930994906972389671884851212 y[1] (numeric) = 1.6121930994906972389671884851221 absolute error = 9e-31 relative error = 5.5824578351334968427682401344631e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.2008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.2099 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2005 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=388116888, alloc=4586680, time=30.47 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 1.6626233574003796274966328950026 y[1] (numeric) = 1.6626233574003796274966328950035 absolute error = 9e-31 relative error = 5.4131321805030387011338955865748e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.1908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1995 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1905 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=392117940, alloc=4586680, time=30.61 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 1.7158379811678190697045444588912 y[1] (numeric) = 1.7158379811678190697045444588921 absolute error = 9e-31 relative error = 5.2452504833087425073870157145904e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.1808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.189 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1805 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=396119660, alloc=4586680, time=30.75 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 1.7721501376696990272141106868693 y[1] (numeric) = 1.7721501376696990272141106868704 absolute error = 1.1e-30 relative error = 6.2071490254570221754740733219416e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.1708 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1786 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1706 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 1.8319297289558808289320648371267 y[1] (numeric) = 1.8319297289558808289320648371278 absolute error = 1.1e-30 relative error = 6.0045971339029008400052528782541e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.1608 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1681 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1606 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=400122088, alloc=4586680, time=30.89 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 1.8956179807145446725622651027797 y[1] (numeric) = 1.8956179807145446725622651027807 absolute error = 1.0e-30 relative error = 5.2753245125004274192185554763821e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.1508 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1577 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1506 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=404122988, alloc=4586680, time=31.03 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 1.9637470439243689010155627224162 y[1] (numeric) = 1.9637470439243689010155627224171 absolute error = 9e-31 relative error = 4.5830750084870009355542948859559e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.1408 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1472 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1406 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 2.469 Order of pole (six term test) = -4.473e-24 bytes used=408123684, alloc=4586680, time=31.17 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 2.0369668305394392250598441967529 y[1] (numeric) = 2.0369668305394392250598441967538 absolute error = 9e-31 relative error = 4.4183340961013966433334485953978e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.1308 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1367 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1306 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 2.1160825440137191518804053682086 y[1] (numeric) = 2.1160825440137191518804053682096 absolute error = 1.0e-30 relative error = 4.7257135730784456666013892843209e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.1208 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1263 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1206 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=412124876, alloc=4586680, time=31.31 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 2.2021084657468975855988513433722 y[1] (numeric) = 2.2021084657468975855988513433732 absolute error = 1.0e-30 relative error = 4.5411023823516620443418311533001e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.1108 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1158 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1106 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 0.1606 Order of pole (six term test) = 5.539e-27 bytes used=416125924, alloc=4586680, time=31.45 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = 2.2963472549526355919112295036683 y[1] (numeric) = 2.2963472549526355919112295036695 absolute error = 1.2e-30 relative error = 5.2256904847988732160056597219459e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.1008 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.1054 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1007 Order of pole (three term test) = 625 Radius of convergence (six term test) for eq 1 = 0.03162 Order of pole (six term test) = 0 bytes used=420127048, alloc=4586680, time=31.59 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = 2.4005108212575825445957134843943 y[1] (numeric) = 2.4005108212575825445957134843953 absolute error = 1.0e-30 relative error = 4.1657800129229110373776367044288e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.0908 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.09492 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.09067 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 2.5169120195352477327155332172207 y[1] (numeric) = 2.5169120195352477327155332172217 absolute error = 1.0e-30 relative error = 3.9731225892617882334872187302527e-29 % Correct digits = 31 h = 0.001 Radius of convergence (given) for eq 1 = 0.0808 Order of pole (given) = 0 Radius of convergence (ratio test) for eq 1 = 0.08447 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.08068 Order of pole (three term test) = 625 NO COMPLEX POLE (six term test) for Equation 1 bytes used=424128900, alloc=4586680, time=31.73 Finished! diff ( y , x , 1 ) = tan ( x ) ; Iterations = 1400 Total Elapsed Time = 31 Seconds Elapsed Time(since restart) = 31 Seconds Time to Timeout = 2 Minutes 28 Seconds Percent Done = 100.1 % > quit bytes used=426569192, alloc=4586680, time=31.81