|\^/| 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, > array_const_2D0, > array_const_1D0, > #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_const_2D0, array_const_1D0, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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, > array_const_2D0, > array_const_1D0, > #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_const_2D0, array_const_1D0, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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, > array_const_2D0, > array_const_1D0, > #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_const_2D0, array_const_1D0, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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, > array_const_2D0, > array_const_1D0, > #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_const_2D0, array_const_1D0, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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, > array_const_2D0, > array_const_1D0, > #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_const_2D0, array_const_1D0, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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, > array_const_2D0, > array_const_1D0, > #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_const_2D0, array_const_1D0, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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, > array_const_2D0, > array_const_1D0, > #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_const_2D0, array_const_1D0, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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, > array_const_2D0, > array_const_1D0, > #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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_const_2D0, array_const_1D0, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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, > array_const_2D0, > array_const_1D0, > #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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 mult FULL CONST $eq_no = 1 i = 1 > array_tmp1[1] := array_m1[1] * array_const_2D0[1]; > #emit pre mult FULL LINEAR $eq_no = 1 i = 1 > #emit pre mult LINEAR - FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_x[1] * array_tmp1[1]; > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_x[1] * array_x[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp3[1] + array_const_1D0[1]; > #emit pre div FULL - FULL $eq_no = 1 i = 1 > array_tmp5[1] := (array_tmp2[1] / (array_tmp4[1])); > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1 > array_tmp6[1] := array_x[1] * array_x[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp7[1] := array_tmp6[1] + array_const_1D0[1]; > #emit pre div FULL - FULL $eq_no = 1 i = 1 > array_tmp8[1] := (array_tmp5[1] / (array_tmp7[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp9[1] := array_const_0D0[1] + array_tmp8[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_tmp9[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult FULL CONST $eq_no = 1 i = 2 > array_tmp1[2] := array_m1[2] * array_const_2D0[1]; > #emit pre mult LINEAR FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_x[2] * array_tmp1[kkk - 1] + array_x[1] * array_tmp1[kkk]; > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre div FULL - FULL $eq_no = 1 i = 2 > array_tmp5[2] := ((array_tmp2[2] - ats(2,array_tmp4,array_tmp5,2))/array_tmp4[1]); > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2 > array_tmp6[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp7[2] := array_tmp6[2]; > #emit pre div FULL - FULL $eq_no = 1 i = 2 > array_tmp8[2] := ((array_tmp5[2] - ats(2,array_tmp7,array_tmp8,2))/array_tmp7[1]); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp9[2] := array_tmp8[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_tmp9[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 mult FULL CONST $eq_no = 1 i = 3 > array_tmp1[3] := array_m1[3] * array_const_2D0[1]; > #emit pre mult LINEAR FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_x[2] * array_tmp1[kkk - 1] + array_x[1] * array_tmp1[kkk]; > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3 > array_tmp3[3] := array_x[2] * array_x[2]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[3]; > #emit pre div FULL - FULL $eq_no = 1 i = 3 > array_tmp5[3] := ((array_tmp2[3] - ats(3,array_tmp4,array_tmp5,2))/array_tmp4[1]); > #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3 > array_tmp6[3] := array_x[2] * array_x[2]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp7[3] := array_tmp6[3]; > #emit pre div FULL - FULL $eq_no = 1 i = 3 > array_tmp8[3] := ((array_tmp5[3] - ats(3,array_tmp7,array_tmp8,2))/array_tmp7[1]); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp9[3] := array_tmp8[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_tmp9[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 mult FULL CONST $eq_no = 1 i = 4 > array_tmp1[4] := array_m1[4] * array_const_2D0[1]; > #emit pre mult LINEAR FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_x[2] * array_tmp1[kkk - 1] + array_x[1] * array_tmp1[kkk]; > #emit pre add FULL CONST $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[4]; > #emit pre div FULL - FULL $eq_no = 1 i = 4 > array_tmp5[4] := ((array_tmp2[4] - ats(4,array_tmp4,array_tmp5,2))/array_tmp4[1]); > #emit pre add FULL CONST $eq_no = 1 i = 4 > array_tmp7[4] := array_tmp6[4]; > #emit pre div FULL - FULL $eq_no = 1 i = 4 > array_tmp8[4] := ((array_tmp5[4] - ats(4,array_tmp7,array_tmp8,2))/array_tmp7[1]); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp9[4] := array_tmp8[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_tmp9[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 mult FULL CONST $eq_no = 1 i = 5 > array_tmp1[5] := array_m1[5] * array_const_2D0[1]; > #emit pre mult LINEAR FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_x[2] * array_tmp1[kkk - 1] + array_x[1] * array_tmp1[kkk]; > #emit pre add FULL CONST $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[5]; > #emit pre div FULL - FULL $eq_no = 1 i = 5 > array_tmp5[5] := ((array_tmp2[5] - ats(5,array_tmp4,array_tmp5,2))/array_tmp4[1]); > #emit pre add FULL CONST $eq_no = 1 i = 5 > array_tmp7[5] := array_tmp6[5]; > #emit pre div FULL - FULL $eq_no = 1 i = 5 > array_tmp8[5] := ((array_tmp5[5] - ats(5,array_tmp7,array_tmp8,2))/array_tmp7[1]); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp9[5] := array_tmp8[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_tmp9[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult FULL CONST $eq_no = 1 i = 1 > array_tmp1[kkk] := array_m1[kkk] * array_const_2D0[1]; > #emit mult FULL LINEAR $eq_no = 1 i = 1 > array_tmp2[kkk] := array_tmp1[kkk-1] * array_x[2] + array_tmp1[kkk] * array_x[1]; > #emit mult LINEAR - LINEAR $eq_no = 1 i = 1 > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp3[kkk]; > #emit div FULL FULL $eq_no = 1 > array_tmp5[kkk] := ((array_tmp2[kkk] - ats(kkk,array_tmp4,array_tmp5,2))/array_tmp4[1]); > #emit mult LINEAR - LINEAR $eq_no = 1 i = 1 > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp7[kkk] := array_tmp6[kkk]; > #emit div FULL FULL $eq_no = 1 > array_tmp8[kkk] := ((array_tmp5[kkk] - ats(kkk,array_tmp7,array_tmp8,2))/array_tmp7[1]); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp9[kkk] := array_tmp8[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_tmp9[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_const_2D0, array_const_1D0, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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[1] := array_m1[1]*array_const_2D0[1]; array_tmp2[1] := array_x[1]*array_tmp1[1]; array_tmp3[1] := array_x[1]*array_x[1]; array_tmp4[1] := array_tmp3[1] + array_const_1D0[1]; array_tmp5[1] := array_tmp2[1]/array_tmp4[1]; array_tmp6[1] := array_x[1]*array_x[1]; array_tmp7[1] := array_tmp6[1] + array_const_1D0[1]; array_tmp8[1] := array_tmp5[1]/array_tmp7[1]; array_tmp9[1] := array_const_0D0[1] + array_tmp8[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp9[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_m1[2]*array_const_2D0[1]; array_tmp2[2] := array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk]; array_tmp3[2] := 2*array_x[1]*array_x[2]; array_tmp4[2] := array_tmp3[2]; array_tmp5[2] := (array_tmp2[2] - ats(2, array_tmp4, array_tmp5, 2))/array_tmp4[1]; array_tmp6[2] := 2*array_x[1]*array_x[2]; array_tmp7[2] := array_tmp6[2]; array_tmp8[2] := (array_tmp5[2] - ats(2, array_tmp7, array_tmp8, 2))/array_tmp7[1]; array_tmp9[2] := array_tmp8[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp9[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[3] := array_m1[3]*array_const_2D0[1]; array_tmp2[3] := array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk]; array_tmp3[3] := array_x[2]*array_x[2]; array_tmp4[3] := array_tmp3[3]; array_tmp5[3] := (array_tmp2[3] - ats(3, array_tmp4, array_tmp5, 2))/array_tmp4[1]; array_tmp6[3] := array_x[2]*array_x[2]; array_tmp7[3] := array_tmp6[3]; array_tmp8[3] := (array_tmp5[3] - ats(3, array_tmp7, array_tmp8, 2))/array_tmp7[1]; array_tmp9[3] := array_tmp8[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp9[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[4] := array_m1[4]*array_const_2D0[1]; array_tmp2[4] := array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk]; array_tmp4[4] := array_tmp3[4]; array_tmp5[4] := (array_tmp2[4] - ats(4, array_tmp4, array_tmp5, 2))/array_tmp4[1]; array_tmp7[4] := array_tmp6[4]; array_tmp8[4] := (array_tmp5[4] - ats(4, array_tmp7, array_tmp8, 2))/array_tmp7[1]; array_tmp9[4] := array_tmp8[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp9[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[5] := array_m1[5]*array_const_2D0[1]; array_tmp2[5] := array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk]; array_tmp4[5] := array_tmp3[5]; array_tmp5[5] := (array_tmp2[5] - ats(5, array_tmp4, array_tmp5, 2))/array_tmp4[1]; array_tmp7[5] := array_tmp6[5]; array_tmp8[5] := (array_tmp5[5] - ats(5, array_tmp7, array_tmp8, 2))/array_tmp7[1]; array_tmp9[5] := array_tmp8[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp9[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[kkk] := array_m1[kkk]*array_const_2D0[1]; array_tmp2[kkk] := array_x[2]*array_tmp1[kkk - 1] + array_x[1]*array_tmp1[kkk]; array_tmp4[kkk] := array_tmp3[kkk]; array_tmp5[kkk] := ( array_tmp2[kkk] - ats(kkk, array_tmp4, array_tmp5, 2))/ array_tmp4[1]; array_tmp7[kkk] := array_tmp6[kkk]; array_tmp8[kkk] := ( array_tmp5[kkk] - ats(kkk, array_tmp7, array_tmp8, 2))/ array_tmp7[1]; array_tmp9[kkk] := array_tmp8[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_tmp9[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(1.0 / (x * x + 1.0)); > end; exact_soln_y := proc(x) return 1.0/(x*x + 1.0) 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, > array_const_2D0, > array_const_1D0, > #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > 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/sing4postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"); > 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 := -2.0;"); > omniout_str(ALWAYS,"x_end := 1.0;"); > 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 := 50;"); > 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] := 0.0;"); > omniout_str(ALWAYS,"## Imag Part"); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := 1.0;"); > omniout_str(ALWAYS,"## Order"); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := 1.0;"); > 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(1.0 / (x * x + 1.0));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_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:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_tmp6:= Array(0..(max_terms + 1),[]); > array_tmp7:= Array(0..(max_terms + 1),[]); > array_tmp8:= Array(0..(max_terms + 1),[]); > array_tmp9:= 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[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_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp9[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_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_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 := 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_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp6 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp6[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp7 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp7[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp8 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp8[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp9 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp9[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_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_2D0[1] := 2.0; > array_const_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1D0[1] := 1.0; > 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 := -2.0; > x_end := 1.0; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 50; > ## Not Given = 0 > ## No Pole = 3 > ## Pole = 4 > glob_type_given_pole := 4; > ## Real Part > array_given_rad_poles[1,1] := 0.0; > ## Imag Part > array_given_rad_poles[1,2] := 1.0; > ## Order > array_given_ord_poles[1,1] := 1.0; > ## 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 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"); > 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,"2013-05-26T04:44:14-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing4") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);") > ; > 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,"sing4 diffeq.mxt") > ; > logitem_str(html_log_file,"sing4 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_const_2D0, array_const_1D0, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, 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/sing4postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.\ 0) /( x * x + 1.0);"); 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 := -2.0;"); omniout_str(ALWAYS, "x_end := 1.0;"); 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 := 50;"); 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] := 0.0;"); omniout_str(ALWAYS, "## Imag Part"); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := 1.0;"); omniout_str(ALWAYS, "## Order"); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := 1.0;"); 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(1.0 / (x * x + 1.0));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; 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 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_tmp6 := Array(0 .. max_terms + 1, []); array_tmp7 := Array(0 .. max_terms + 1, []); array_tmp8 := Array(0 .. max_terms + 1, []); array_tmp9 := 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[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp6[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp7[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp8[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp9[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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp6 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1 end do; array_tmp7 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1 end do; array_tmp8 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1 end do; array_tmp9 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 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 := -2.0; x_end := 1.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 50; glob_type_given_pole := 4; array_given_rad_poles[1, 1] := 0.; array_given_rad_poles[1, 2] := 1.0; array_given_ord_poles[1, 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 ) = m1 * 2.0 * x / (x * x + \ 1.0) /( x * x + 1.0);"); 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, "2013-05-26T04:44:14-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing4") ; logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x\ / (x * x + 1.0) /( x * x + 1.0);"); 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, "sing4 diffeq.mxt"); logitem_str(html_log_file, "sing4 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/sing4postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -2.0; x_end := 1.0; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 50; ## Not Given = 0 ## No Pole = 3 ## Pole = 4 glob_type_given_pole := 4; ## Real Part array_given_rad_poles[1,1] := 0.0; ## Imag Part array_given_rad_poles[1,2] := 1.0; ## Order array_given_ord_poles[1,1] := 1.0; ## 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(1.0 / (x * x + 1.0)); 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 = 3 estimated_steps = 3000000 step_error = 3.3333333333333333333333333333333e-17 est_needed_step_err = 3.3333333333333333333333333333333e-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 = 1.7536349118946956400132850974720e-167 estimated_step_error = 1.7536349118946956400132850974720e-167 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 = 1.1768422476818998532806619425966e-159 estimated_step_error = 1.1768422476818998532806619425966e-159 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 = 7.8976248331978607456552549900645e-152 estimated_step_error = 7.8976248331978607456552549900645e-152 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 = 5.2999663092524575208633246162456e-144 estimated_step_error = 5.2999663092524575208633246162456e-144 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 = 3.5566934961110163673014159657443e-136 estimated_step_error = 3.5566934961110163673014159657443e-136 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 = 2.3867845437832855688549009745458e-128 estimated_step_error = 2.3867845437832855688549009745458e-128 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 = 1.6016472776504198132722139440060e-120 estimated_step_error = 1.6016472776504198132722139440060e-120 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 = 1.0747174782404312690568160248973e-112 estimated_step_error = 1.0747174782404312690568160248973e-112 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.2105644174211882780809733062789e-105 estimated_step_error = 7.2105644174211882780809733062789e-105 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 = 4.8365887535281934083191811061483e-97 estimated_step_error = 4.8365887535281934083191811061483e-97 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 = 3.2426392338306994156972057118205e-89 estimated_step_error = 3.2426392338306994156972057118205e-89 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.1718804391371197797340892547020e-81 estimated_step_error = 2.1718804391371197797340892547020e-81 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.4518556937502212755611441418922e-73 estimated_step_error = 1.4518556937502212755611441418922e-73 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.6669571696462781799470723894923e-66 estimated_step_error = 9.6669571696462781799470723894923e-66 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.3844681200204431030174531732561e-58 estimated_step_error = 6.3844681200204431030174531732561e-58 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.1449782952624452806899791734192e-50 estimated_step_error = 4.1449782952624452806899791734192e-50 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.5904796231726051492296620955938e-42 estimated_step_error = 2.5904796231726051492296620955938e-42 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.4715350520328429807965831058381e-34 estimated_step_error = 1.4715350520328429807965831058381e-34 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = 0.2 y[1] (numeric) = 0.2 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 bytes used=4000712, alloc=3145152, time=0.17 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (analytic) = 0.20160883853148122013669079252434 y[1] (numeric) = 0.20160883853148122013669079252434 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.227 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001107 Order of pole (three term test) = -0.8975 Radius of convergence (six term test) for eq 1 = 2.227 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (analytic) = 0.20323550930818632631493374522397 y[1] (numeric) = 0.20323550930818632631493374522396 absolute error = 1e-32 relative error = 4.9203999999999999999999999999999e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.218 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009404 Order of pole (three term test) = -1.319 Radius of convergence (six term test) for eq 1 = 2.218 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (analytic) = 0.20488024749533897436948103833309 y[1] (numeric) = 0.20488024749533897436948103833309 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.209 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01548 Order of pole (three term test) = -2.421 Radius of convergence (six term test) for eq 1 = 2.209 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (analytic) = 0.20654329147389292795769993390615 y[1] (numeric) = 0.20654329147389292795769993390614 absolute error = 1e-32 relative error = 4.8415999999999999999999999999999e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01931 Order of pole (three term test) = -4.197 Radius of convergence (six term test) for eq 1 = 2.2 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (analytic) = 0.20822488287350338365434669442998 y[1] (numeric) = 0.20822488287350338365434669442998 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02086 Order of pole (three term test) = -6.636 Radius of convergence (six term test) for eq 1 = 2.191 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (analytic) = 0.20992526660508858846250734738433 y[1] (numeric) = 0.20992526660508858846250734738433 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.183 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02011 Order of pole (three term test) = -9.722 Radius of convergence (six term test) for eq 1 = 2.183 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (analytic) = 0.21164469089292895087726724375119 y[1] (numeric) = 0.21164469089292895087726724375119 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.174 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01708 Order of pole (three term test) = -13.43 Radius of convergence (six term test) for eq 1 = 2.174 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.92 y[1] (analytic) = 0.21338340730624786616592693752134 y[1] (numeric) = 0.21338340730624786616592693752134 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.165 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01178 Order of pole (three term test) = -17.73 Radius of convergence (six term test) for eq 1 = 2.165 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (analytic) = 0.21514167079021535681246100557217 y[1] (numeric) = 0.21514167079021535681246100557217 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.156 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004254 Order of pole (three term test) = -22.59 Radius of convergence (six term test) for eq 1 = 2.156 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = 0.21691973969631236442516268980477 y[1] (numeric) = 0.21691973969631236442516268980477 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.147 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (analytic) = 0.21871787581199011395201329804685 y[1] (numeric) = 0.21871787581199011395201329804685 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.138 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 0.909 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.138 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (analytic) = 0.22053634438955539872971065631616 y[1] (numeric) = 0.22053634438955539872971065631616 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.129 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 0.8403 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.129 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (analytic) = 0.22237541417420889946407525184016 y[1] (numeric) = 0.22237541417420889946407525184016 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.121 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.121 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.86 y[1] (analytic) = 0.22423535743115974526863395820253 y[1] (numeric) = 0.22423535743115974526863395820253 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.112 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.112 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (analytic) = 0.22611644997173544375353306953081 y[1] (numeric) = 0.22611644997173544375353306953081 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.103 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (analytic) = 0.22801897117840204304998175848231 y[1] (numeric) = 0.22801897117840204304998175848231 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.094 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (analytic) = 0.2299432040286049345811584538619 y[1] (numeric) = 0.2299432040286049345811584538619 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.085 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.085 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (analytic) = 0.2318894351173360541693720434097 y[1] (numeric) = 0.23188943511733605416937204340971 absolute error = 1e-32 relative error = 4.3124000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.077 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (analytic) = 0.23385795467832838333995930871589 y[1] (numeric) = 0.23385795467832838333995930871589 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.068 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = 0.23584905660377358490566037735849 y[1] (numeric) = 0.23584905660377358490566037735849 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.059 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (analytic) = 0.23786303846245331937870174353607 y[1] (numeric) = 0.23786303846245331937870174353607 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 0.7474 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.05 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (analytic) = 0.23990020151616927358218980903944 y[1] (numeric) = 0.23990020151616927358218980903944 bytes used=8002132, alloc=4324584, time=0.37 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.042 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 0.8325 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.042 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (analytic) = 0.24196085073435118197875583730552 y[1] (numeric) = 0.24196085073435118197875583730552 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.033 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.033 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (analytic) = 0.24404529480671612651308082780164 y[1] (numeric) = 0.24404529480671612651308082780164 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.024 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.024 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (analytic) = 0.24615384615384615384615384615385 y[1] (numeric) = 0.24615384615384615384615384615385 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.016 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.016 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (analytic) = 0.24828682093554474128513258516238 y[1] (numeric) = 0.24828682093554474128513258516238 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 2.007 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.007 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (analytic) = 0.25044453905682586591199378897543 y[1] (numeric) = 0.25044453905682586591199378897543 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.998 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.998 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (analytic) = 0.2526273241713823767178658043654 y[1] (numeric) = 0.2526273241713823767178658043654 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.99 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (analytic) = 0.25483550368237302821029025763869 y[1] (numeric) = 0.25483550368237302821029025763869 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.981 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.273 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.981 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = 0.25706940874035989717223650385604 y[1] (numeric) = 0.25706940874035989717223650385604 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.322 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.972 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (analytic) = 0.25932937423821996317522885817277 y[1] (numeric) = 0.25932937423821996317522885817276 absolute error = 1e-32 relative error = 3.8560999999999999999999999999999e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.964 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.964 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (analytic) = 0.26161573880284637923817496860611 y[1] (numeric) = 0.26161573880284637923817496860611 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.955 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.955 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (analytic) = 0.26392884478344638285518224286732 y[1] (numeric) = 0.26392884478344638285518224286732 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.947 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.947 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (analytic) = 0.26626903823623389072318670784961 y[1] (numeric) = 0.26626903823623389072318670784961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.938 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.938 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (analytic) = 0.26863666890530557421087978509066 y[1] (numeric) = 0.26863666890530557421087978509066 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.929 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.929 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (analytic) = 0.2710320901994796183868169991327 y[1] (numeric) = 0.27103209019947961838681699913269 absolute error = 1e-32 relative error = 3.6896000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.921 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.921 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (analytic) = 0.27345565916486641691049796275534 y[1] (numeric) = 0.27345565916486641691049796275533 absolute error = 1e-32 relative error = 3.6569000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.912 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.912 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (analytic) = 0.27590773645293014016113011808851 y[1] (numeric) = 0.2759077364529301401611301180885 absolute error = 1e-32 relative error = 3.6244000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.904 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.904 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (analytic) = 0.27838868628378942679769494167757 y[1] (numeric) = 0.27838868628378942679769494167756 absolute error = 1e-32 relative error = 3.5921000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.895 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.895 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = 0.28089887640449438202247191011236 y[1] (numeric) = 0.28089887640449438202247191011235 absolute error = 1e-32 relative error = 3.5600000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.887 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (analytic) = 0.28343867804200561208582523171112 y[1] (numeric) = 0.28343867804200561208582523171111 absolute error = 1e-32 relative error = 3.5281000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.878 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.878 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (analytic) = 0.28600846585058917743965221370553 y[1] (numeric) = 0.28600846585058917743965221370552 absolute error = 1e-32 relative error = 3.4963999999999999999999999999999e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.87 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (analytic) = 0.28860861785332910040693815117319 y[1] (numeric) = 0.28860861785332910040693815117319 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.861 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.861 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop bytes used=12003172, alloc=4455632, time=0.56 x[1] = -1.56 y[1] (analytic) = 0.2912395153774464119291705498602 y[1] (numeric) = 0.2912395153774464119291705498602 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.853 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.853 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (analytic) = 0.29390154298310066127847171197649 y[1] (numeric) = 0.29390154298310066127847171197648 absolute error = 1e-32 relative error = 3.4025000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.845 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = 0.29659508838533633883022897140823 y[1] (numeric) = 0.29659508838533633883022897140823 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.836 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = 0.29932054236882277230686342003652 y[1] (numeric) = 0.29932054236882277230686342003651 absolute error = 1e-32 relative error = 3.3409000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.828 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.828 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = 0.30207829869502174963750604156597 y[1] (numeric) = 0.30207829869502174963750604156597 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.819 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0004087 Order of pole (three term test) = -0.8938 Radius of convergence (six term test) for eq 1 = 1.819 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = 0.30486875400140239626840645102283 y[1] (numeric) = 0.30486875400140239626840645102283 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.811 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008677 Order of pole (three term test) = -1.449 Radius of convergence (six term test) for eq 1 = 1.811 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (analytic) = 0.30769230769230769230769230769231 y[1] (numeric) = 0.3076923076923076923076923076923 absolute error = 1e-32 relative error = 3.2500000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.803 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01432 Order of pole (three term test) = -3.018 Radius of convergence (six term test) for eq 1 = 1.803 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.49 y[1] (analytic) = 0.31054936182106145771870438806248 y[1] (numeric) = 0.31054936182106145771870438806247 absolute error = 1e-32 relative error = 3.2201000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.794 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01723 Order of pole (three term test) = -5.572 Radius of convergence (six term test) for eq 1 = 1.794 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.48 y[1] (analytic) = 0.31344032096288866599799398194584 y[1] (numeric) = 0.31344032096288866599799398194582 absolute error = 2e-32 relative error = 6.3807999999999999999999999999999e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.786 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01735 Order of pole (three term test) = -9.06 Radius of convergence (six term test) for eq 1 = 1.786 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.47 y[1] (analytic) = 0.31636559207820557436173241798222 y[1] (numeric) = 0.3163655920782055743617324179822 absolute error = 2e-32 relative error = 6.3218000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.778 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01468 Order of pole (three term test) = -13.41 Radius of convergence (six term test) for eq 1 = 1.778 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.46 y[1] (analytic) = 0.31932558436581938944948269255333 y[1] (numeric) = 0.31932558436581938944948269255331 absolute error = 2e-32 relative error = 6.2631999999999999999999999999999e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009248 Order of pole (three term test) = -18.52 Radius of convergence (six term test) for eq 1 = 1.77 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.45 y[1] (analytic) = 0.322320709105560032232070910556 y[1] (numeric) = 0.32232070910556003223207091055599 absolute error = 1e-32 relative error = 3.1025000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.761 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001185 Order of pole (three term test) = -24.28 Radius of convergence (six term test) for eq 1 = 1.761 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.44 y[1] (analytic) = 0.32535137948984903695991671004685 y[1] (numeric) = 0.32535137948984903695991671004684 absolute error = 1e-32 relative error = 3.0736000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.753 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.753 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.43 y[1] (analytic) = 0.32841801044369273210942888107984 y[1] (numeric) = 0.32841801044369273210942888107983 absolute error = 1e-32 relative error = 3.0449000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.745 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.745 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.42 y[1] (analytic) = 0.33152101843256862485081554170534 y[1] (numeric) = 0.33152101843256862485081554170534 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.737 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.737 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.41 y[1] (analytic) = 0.3346608212576553662862688665038 y[1] (numeric) = 0.33466082125765536628626886650379 absolute error = 1e-32 relative error = 2.9881000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.729 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.729 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.4 y[1] (analytic) = 0.33783783783783783783783783783784 y[1] (numeric) = 0.33783783783783783783783783783783 absolute error = 1e-32 relative error = 2.9600000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.72 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.39 y[1] (analytic) = 0.34105248797789979877903209303912 y[1] (numeric) = 0.34105248797789979877903209303911 absolute error = 1e-32 relative error = 2.9321000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.712 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.712 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.38 y[1] (analytic) = 0.3443051921222972042418399669467 y[1] (numeric) = 0.34430519212229720424183996694669 absolute error = 1e-32 relative error = 2.9044000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.704 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.704 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.37 y[1] (analytic) = 0.34759637109388577983245854913275 y[1] (numeric) = 0.34759637109388577983245854913274 absolute error = 1e-32 relative error = 2.8769000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.696 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.696 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.36 y[1] (analytic) = 0.35092644581695676586187535092645 y[1] (numeric) = 0.35092644581695676586187535092644 absolute error = 1e-32 relative error = 2.8496000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.688 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.688 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.35 y[1] (analytic) = 0.35429583702391496899911426040744 y[1] (numeric) = 0.35429583702391496899911426040743 absolute error = 1e-32 relative error = 2.8225000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.68 Order of pole (six term test) = 1 bytes used=16004188, alloc=4455632, time=0.76 TOP MAIN SOLVE Loop x[1] = -1.34 y[1] (analytic) = 0.35770496494491343539848333094863 y[1] (numeric) = 0.35770496494491343539848333094862 absolute error = 1e-32 relative error = 2.7956000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.672 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.672 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.33 y[1] (analytic) = 0.36115424897973924663223662826393 y[1] (numeric) = 0.36115424897973924663223662826392 absolute error = 1e-32 relative error = 2.7689000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.664 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.664 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.32 y[1] (analytic) = 0.36464410735122520420070011668611 y[1] (numeric) = 0.3646441073512252042007001166861 absolute error = 1e-32 relative error = 2.7424000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.656 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.656 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.31 y[1] (analytic) = 0.36817495673944258311549648392916 y[1] (numeric) = 0.36817495673944258311549648392915 absolute error = 1e-32 relative error = 2.7161000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.648 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.648 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.3 y[1] (analytic) = 0.37174721189591078066914498141264 y[1] (numeric) = 0.37174721189591078066914498141263 absolute error = 1e-32 relative error = 2.6900000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.64 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.29 y[1] (analytic) = 0.37536128523704065162719117150257 y[1] (numeric) = 0.37536128523704065162719117150256 absolute error = 1e-32 relative error = 2.6641000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.632 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.632 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.28 y[1] (analytic) = 0.37901758641600970285021224984839 y[1] (numeric) = 0.37901758641600970285021224984838 absolute error = 1e-32 relative error = 2.6384000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.624 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.624 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.27 y[1] (analytic) = 0.38271652187224922499904320869532 y[1] (numeric) = 0.38271652187224922499904320869531 absolute error = 1e-32 relative error = 2.6129000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.616 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.616 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.26 y[1] (analytic) = 0.38645849435770598237749265728861 y[1] (numeric) = 0.3864584943577059823774926572886 absolute error = 1e-32 relative error = 2.5876000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.609 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.609 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.25 y[1] (analytic) = 0.39024390243902439024390243902439 y[1] (numeric) = 0.39024390243902439024390243902438 absolute error = 1e-32 relative error = 2.5625000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.601 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.601 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.24 y[1] (analytic) = 0.39407313997477931904161412358134 y[1] (numeric) = 0.39407313997477931904161412358133 absolute error = 1e-32 relative error = 2.5376000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.593 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.593 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.23 y[1] (analytic) = 0.39794659556687492538501333121095 y[1] (numeric) = 0.39794659556687492538501333121094 absolute error = 1e-32 relative error = 2.5129000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.585 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.585 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.22 y[1] (analytic) = 0.4018646519852113808069442211863 y[1] (numeric) = 0.40186465198521138080694422118629 absolute error = 1e-32 relative error = 2.4884000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.577 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.577 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.21 y[1] (analytic) = 0.40582768556470922446329288584067 y[1] (numeric) = 0.40582768556470922446329288584066 absolute error = 1e-32 relative error = 2.4641000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.57 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.2 y[1] (analytic) = 0.40983606557377049180327868852459 y[1] (numeric) = 0.40983606557377049180327868852458 absolute error = 1e-32 relative error = 2.4400000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.562 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.562 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.19 y[1] (analytic) = 0.41389015355324696825462522246596 y[1] (numeric) = 0.41389015355324696825462522246595 absolute error = 1e-32 relative error = 2.4161000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.554 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00165 Order of pole (three term test) = -0.9144 Radius of convergence (six term test) for eq 1 = 1.554 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.18 y[1] (analytic) = 0.41799030262497910048486875104498 y[1] (numeric) = 0.41799030262497910048486875104497 absolute error = 1e-32 relative error = 2.3924000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.547 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009409 Order of pole (three term test) = -1.857 Radius of convergence (six term test) for eq 1 = 1.547 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.17 y[1] (analytic) = 0.42213685676896449829034573008569 y[1] (numeric) = 0.42213685676896449829034573008569 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.539 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01416 Order of pole (three term test) = -4.162 Radius of convergence (six term test) for eq 1 = 1.539 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.16 y[1] (analytic) = 0.42633015006821282401091405184175 y[1] (numeric) = 0.42633015006821282401091405184174 absolute error = 1e-32 relative error = 2.3456000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.532 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01572 Order of pole (three term test) = -7.735 Radius of convergence (six term test) for eq 1 = 1.532 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.15 y[1] (analytic) = 0.43057050592034445640473627556512 y[1] (numeric) = 0.43057050592034445640473627556512 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.524 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01401 Order of pole (three term test) = -12.43 Radius of convergence (six term test) for eq 1 = 1.524 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.14 y[1] (analytic) = 0.43485823621499391198469299008523 y[1] (numeric) = 0.43485823621499391198469299008523 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.516 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009089 Order of pole (three term test) = -18.02 Radius of convergence (six term test) for eq 1 = 1.516 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.13 y[1] (analytic) = 0.43919364047608590627607712240327 y[1] (numeric) = 0.43919364047608590627607712240327 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.509 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001168 Order of pole (three term test) = -24.24 Radius of convergence (six term test) for eq 1 = 1.509 Order of pole (six term test) = 1 bytes used=20005684, alloc=4521156, time=0.96 TOP MAIN SOLVE Loop x[1] = -1.12 y[1] (analytic) = 0.44357700496806245564229950319375 y[1] (numeric) = 0.44357700496806245564229950319376 absolute error = 1e-32 relative error = 2.2544000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.501 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.501 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.11 y[1] (analytic) = 0.44800860176515389095470633036154 y[1] (numeric) = 0.44800860176515389095470633036155 absolute error = 1e-32 relative error = 2.2321000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.494 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.494 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.1 y[1] (analytic) = 0.45248868778280542986425339366516 y[1] (numeric) = 0.45248868778280542986425339366517 absolute error = 1e-32 relative error = 2.2100000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.487 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.487 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.09 y[1] (analytic) = 0.45701750377039440610575385037247 y[1] (numeric) = 0.45701750377039440610575385037248 absolute error = 1e-32 relative error = 2.1881000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.479 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.479 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.08 y[1] (analytic) = 0.46159527326440177252584933530281 y[1] (numeric) = 0.46159527326440177252584933530282 absolute error = 1e-32 relative error = 2.1664000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.472 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.472 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.07 y[1] (analytic) = 0.46622220150123548883397827404541 y[1] (numeric) = 0.46622220150123548883397827404542 absolute error = 1e-32 relative error = 2.1449000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.465 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.465 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.06 y[1] (analytic) = 0.47089847428894330382369561122622 y[1] (numeric) = 0.47089847428894330382369561122623 absolute error = 1e-32 relative error = 2.1236000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.457 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.05 y[1] (analytic) = 0.4756242568370986920332936979786 y[1] (numeric) = 0.47562425683709869203329369797861 absolute error = 1e-32 relative error = 2.1025000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.45 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.04 y[1] (analytic) = 0.48039969254419677171406610299769 y[1] (numeric) = 0.48039969254419677171406610299771 absolute error = 2e-32 relative error = 4.1632000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.443 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.443 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.03 y[1] (analytic) = 0.48522490174195739725362705614052 y[1] (numeric) = 0.48522490174195739725362705614054 absolute error = 2e-32 relative error = 4.1218000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.436 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.436 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.02 y[1] (analytic) = 0.49009998039600078415996863360125 y[1] (numeric) = 0.49009998039600078415996863360127 absolute error = 2e-32 relative error = 4.0808000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.428 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.428 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.01 y[1] (analytic) = 0.49502499876243750309390624226523 y[1] (numeric) = 0.49502499876243750309390624226525 absolute error = 2e-32 relative error = 4.0402000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.421 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.421 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = 0.5 y[1] (numeric) = 0.50000000000000000000000000000002 absolute error = 2e-32 relative error = 4.0000000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = 0.50502499873743750315640624210898 y[1] (numeric) = 0.505024998737437503156406242109 absolute error = 2e-32 relative error = 3.9602000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.407 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.407 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = 0.51009997959600081615996735360131 y[1] (numeric) = 0.51009997959600081615996735360132 absolute error = 1e-32 relative error = 1.9604000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.4 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (analytic) = 0.51522489566695862744087794322222 y[1] (numeric) = 0.51522489566695862744087794322223 absolute error = 1e-32 relative error = 1.9409000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.393 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.393 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (analytic) = 0.52039966694421315570358034970858 y[1] (numeric) = 0.52039966694421315570358034970859 absolute error = 1e-32 relative error = 1.9216000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.386 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.386 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = 0.52562417871222076215505913272011 y[1] (numeric) = 0.52562417871222076215505913272012 absolute error = 1e-32 relative error = 1.9025000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.379 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.379 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.94 y[1] (analytic) = 0.53089827988957315778296878318114 y[1] (numeric) = 0.53089827988957315778296878318116 absolute error = 2e-32 relative error = 3.7672000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.372 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.003163 Order of pole (three term test) = -0.9998 Radius of convergence (six term test) for eq 1 = 1.372 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.93 y[1] (analytic) = 0.53622178132875757413266126870073 y[1] (numeric) = 0.53622178132875757413266126870075 absolute error = 2e-32 relative error = 3.7298000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.366 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0103 Order of pole (three term test) = -2.501 Radius of convergence (six term test) for eq 1 = 1.366 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.92 y[1] (analytic) = 0.54159445407279029462738301559792 y[1] (numeric) = 0.54159445407279029462738301559794 absolute error = 2e-32 relative error = 3.6928000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.359 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01407 Order of pole (three term test) = -5.68 Radius of convergence (six term test) for eq 1 = 1.359 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.91 y[1] (analytic) = 0.54701602756960778950823259121492 y[1] (numeric) = 0.54701602756960778950823259121494 absolute error = 2e-32 bytes used=24007408, alloc=4521156, time=1.16 relative error = 3.6562000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.352 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01421 Order of pole (three term test) = -10.31 Radius of convergence (six term test) for eq 1 = 1.352 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.9 y[1] (analytic) = 0.55248618784530386740331491712707 y[1] (numeric) = 0.55248618784530386740331491712709 absolute error = 2e-32 relative error = 3.6200000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.345 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01067 Order of pole (three term test) = -16.04 Radius of convergence (six term test) for eq 1 = 1.345 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.89 y[1] (analytic) = 0.55800457563752022766586686010825 y[1] (numeric) = 0.55800457563752022766586686010827 absolute error = 2e-32 relative error = 3.5842000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.339 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.003703 Order of pole (three term test) = -22.39 Radius of convergence (six term test) for eq 1 = 1.339 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.88 y[1] (analytic) = 0.56357078449053201082055906221821 y[1] (numeric) = 0.56357078449053201082055906221823 absolute error = 2e-32 relative error = 3.5488000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.332 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.332 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.87 y[1] (analytic) = 0.56918435881381979623199954465251 y[1] (numeric) = 0.56918435881381979623199954465253 absolute error = 2e-32 relative error = 3.5138000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.325 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.325 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.86 y[1] (analytic) = 0.57484479190618532996091055415038 y[1] (numeric) = 0.5748447919061853299609105541504 absolute error = 2e-32 relative error = 3.4792000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.319 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.319 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.85 y[1] (analytic) = 0.58055152394775036284470246734398 y[1] (numeric) = 0.580551523947750362844702467344 absolute error = 2e-32 relative error = 3.4450000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.312 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.312 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.84 y[1] (analytic) = 0.58630393996247654784240150093809 y[1] (numeric) = 0.58630393996247654784240150093811 absolute error = 2e-32 relative error = 3.4112000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.306 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.306 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.83 y[1] (analytic) = 0.59210136775415951210847297057256 y[1] (numeric) = 0.59210136775415951210847297057259 absolute error = 3e-32 relative error = 5.0667000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.3 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.82 y[1] (analytic) = 0.59794307581918201387227935900502 y[1] (numeric) = 0.59794307581918201387227935900505 absolute error = 3e-32 relative error = 5.0172000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.293 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.293 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.81 y[1] (analytic) = 0.60382827123965944085502083207536 y[1] (numeric) = 0.60382827123965944085502083207539 absolute error = 3e-32 relative error = 4.9683000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.287 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.287 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (analytic) = 0.60975609756097560975609756097561 y[1] (numeric) = 0.60975609756097560975609756097564 absolute error = 3e-32 relative error = 4.9200000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.281 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.281 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.79 y[1] (analytic) = 0.61572563265808755618496398005049 y[1] (numeric) = 0.61572563265808755618496398005052 absolute error = 3e-32 relative error = 4.8723000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.274 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.274 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.78 y[1] (analytic) = 0.62173588659537428500373041531957 y[1] (numeric) = 0.6217358865953742850037304153196 absolute error = 3e-32 relative error = 4.8252000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.268 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.268 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.77 y[1] (analytic) = 0.62778579948521564442212317157386 y[1] (numeric) = 0.62778579948521564442212317157389 absolute error = 3e-32 relative error = 4.7787000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.262 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.262 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.76 y[1] (analytic) = 0.63387423935091277890466531440162 y[1] (numeric) = 0.63387423935091277890466531440165 absolute error = 3e-32 relative error = 4.7328000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.256 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.256 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.75 y[1] (analytic) = 0.64 y[1] (numeric) = 0.64000000000000000000000000000003 absolute error = 3e-32 relative error = 4.6875000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.25 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.74 y[1] (analytic) = 0.64616179891444817782372706125614 y[1] (numeric) = 0.64616179891444817782372706125617 absolute error = 3e-32 relative error = 4.6428000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.244 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00404 Order of pole (three term test) = -1.111 Radius of convergence (six term test) for eq 1 = 1.244 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.73 y[1] (analytic) = 0.65235827516472046447909191728097 y[1] (numeric) = 0.652358275164720464479091917281 absolute error = 3e-32 relative error = 4.5987000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.238 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0108 Order of pole (three term test) = -3.139 Radius of convergence (six term test) for eq 1 = 1.238 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.72 y[1] (analytic) = 0.65858798735511064278187565858799 y[1] (numeric) = 0.65858798735511064278187565858802 absolute error = 3e-32 relative error = 4.5552000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.232 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01389 Order of pole (three term test) = -7.098 Radius of convergence (six term test) for eq 1 = 1.232 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.71 y[1] (analytic) = 0.6648494116082707266804068878399 y[1] (numeric) = 0.66484941160827072668040688783994 absolute error = 4e-32 relative error = 6.0164000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.226 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01295 Order of pole (three term test) = -12.55 Radius of convergence (six term test) for eq 1 = 1.226 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.7 y[1] (analytic) = 0.67114093959731543624161073825503 y[1] (numeric) = 0.67114093959731543624161073825507 absolute error = 4e-32 relative error = 5.9600000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.221 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008057 Order of pole (three term test) = -18.85 Radius of convergence (six term test) for eq 1 = 1.221 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop bytes used=28008824, alloc=4586680, time=1.35 x[1] = -0.69 y[1] (analytic) = 0.67746087663437436488042815527403 y[1] (numeric) = 0.67746087663437436488042815527407 absolute error = 4e-32 relative error = 5.9044000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.215 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.215 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.68 y[1] (analytic) = 0.68380743982494529540481400437637 y[1] (numeric) = 0.6838074398249452954048140043764 absolute error = 3e-32 relative error = 4.3872000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.209 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.209 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.67 y[1] (analytic) = 0.69017875629788115121816550486576 y[1] (numeric) = 0.69017875629788115121816550486579 absolute error = 3e-32 relative error = 4.3467000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.204 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.204 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.66 y[1] (analytic) = 0.69657286152131512956255224296461 y[1] (numeric) = 0.69657286152131512956255224296464 absolute error = 3e-32 relative error = 4.3068000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.198 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.198 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.65 y[1] (analytic) = 0.70298769771528998242530755711775 y[1] (numeric) = 0.70298769771528998242530755711778 absolute error = 3e-32 relative error = 4.2675000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.193 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.193 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.64 y[1] (analytic) = 0.70942111237230419977298524404086 y[1] (numeric) = 0.70942111237230419977298524404089 absolute error = 3e-32 relative error = 4.2288000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.187 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.187 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.63 y[1] (analytic) = 0.71587085689741570620660032930059 y[1] (numeric) = 0.71587085689741570620660032930062 absolute error = 3e-32 relative error = 4.1907000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.182 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.182 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.62 y[1] (analytic) = 0.72233458537994799190985264374458 y[1] (numeric) = 0.72233458537994799190985264374461 absolute error = 3e-32 relative error = 4.1532000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.177 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.177 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.61 y[1] (analytic) = 0.72880985350921944464689162597478 y[1] (numeric) = 0.72880985350921944464689162597481 absolute error = 3e-32 relative error = 4.1163000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.171 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.171 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.6 y[1] (analytic) = 0.73529411764705882352941176470588 y[1] (numeric) = 0.73529411764705882352941176470591 absolute error = 3e-32 relative error = 4.0800000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.166 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.166 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.59 y[1] (analytic) = 0.74178473407017283584303835027075 y[1] (numeric) = 0.74178473407017283584303835027078 absolute error = 3e-32 relative error = 4.0443000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.161 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.161 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.58 y[1] (analytic) = 0.74827895839568991319964082609997 y[1] (numeric) = 0.7482789583956899131996408261 absolute error = 3e-32 relative error = 4.0092000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.156 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.156 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.57 y[1] (analytic) = 0.75477394520341157823231942033361 y[1] (numeric) = 0.75477394520341157823231942033364 absolute error = 3e-32 relative error = 3.9747000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.151 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.006371 Order of pole (three term test) = -1.576 Radius of convergence (six term test) for eq 1 = 1.151 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.56 y[1] (analytic) = 0.76126674786845310596833130328867 y[1] (numeric) = 0.7612667478684531059683313032887 absolute error = 3e-32 relative error = 3.9408000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.146 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01217 Order of pole (three term test) = -4.588 Radius of convergence (six term test) for eq 1 = 1.146 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.55 y[1] (analytic) = 0.76775431861804222648752399232246 y[1] (numeric) = 0.76775431861804222648752399232248 absolute error = 2e-32 relative error = 2.6050000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.141 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0139 Order of pole (three term test) = -9.574 Radius of convergence (six term test) for eq 1 = 1.141 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.54 y[1] (analytic) = 0.77423350882626200061938680706101 y[1] (numeric) = 0.77423350882626200061938680706103 absolute error = 2e-32 relative error = 2.5832000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.136 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01127 Order of pole (three term test) = -15.75 Radius of convergence (six term test) for eq 1 = 1.136 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.53 y[1] (analytic) = 0.78070106956046529783745803731751 y[1] (numeric) = 0.78070106956046529783745803731753 absolute error = 2e-32 relative error = 2.5618000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.132 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004646 Order of pole (three term test) = -22.09 Radius of convergence (six term test) for eq 1 = 1.132 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.52 y[1] (analytic) = 0.78715365239294710327455919395466 y[1] (numeric) = 0.78715365239294710327455919395468 absolute error = 2e-32 relative error = 2.5408000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.127 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.127 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.51 y[1] (analytic) = 0.79358781049123085469407189905563 y[1] (numeric) = 0.79358781049123085469407189905565 absolute error = 2e-32 relative error = 2.5202000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.123 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.123 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.5 y[1] (analytic) = 0.8 y[1] (numeric) = 0.80000000000000000000000000000002 absolute error = 2e-32 relative error = 2.5000000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.118 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.118 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.49 y[1] (analytic) = 0.80638658172728005805983388436416 y[1] (numeric) = 0.80638658172728005805983388436418 absolute error = 2e-32 relative error = 2.4802000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.114 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.114 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.48 y[1] (analytic) = 0.81274382314694408322496749024707 y[1] (numeric) = 0.81274382314694408322496749024709 absolute error = 2e-32 relative error = 2.4608000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.109 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.109 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop bytes used=32010700, alloc=4586680, time=1.55 x[1] = -0.47 y[1] (analytic) = 0.81906790072897043164878368416742 y[1] (numeric) = 0.81906790072897043164878368416743 absolute error = 1e-32 relative error = 1.2209000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.105 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.105 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.46 y[1] (analytic) = 0.82535490260812149224166391548366 y[1] (numeric) = 0.82535490260812149224166391548367 absolute error = 1e-32 relative error = 1.2116000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.101 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.45 y[1] (analytic) = 0.83160083160083160083160083160083 y[1] (numeric) = 0.83160083160083160083160083160084 absolute error = 1e-32 relative error = 1.2025000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.097 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.097 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.44 y[1] (analytic) = 0.83780160857908847184986595174263 y[1] (numeric) = 0.83780160857908847184986595174264 absolute error = 1e-32 relative error = 1.1936000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.093 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.093 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.43 y[1] (analytic) = 0.84395307620896278166933918474133 y[1] (numeric) = 0.84395307620896278166933918474134 absolute error = 1e-32 relative error = 1.1849000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.089 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001291 Order of pole (three term test) = -0.9192 Radius of convergence (six term test) for eq 1 = 1.089 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.42 y[1] (analytic) = 0.85005100306018361101666099965998 y[1] (numeric) = 0.85005100306018361101666099965999 absolute error = 1e-32 relative error = 1.1764000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.085 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009287 Order of pole (three term test) = -2.703 Radius of convergence (six term test) for eq 1 = 1.085 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.41 y[1] (analytic) = 0.85609108809177296464343806180978 y[1] (numeric) = 0.85609108809177296464343806180979 absolute error = 1e-32 relative error = 1.1681000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.081 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01366 Order of pole (three term test) = -6.971 Radius of convergence (six term test) for eq 1 = 1.081 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.4 y[1] (analytic) = 0.86206896551724137931034482758621 y[1] (numeric) = 0.86206896551724137931034482758622 absolute error = 1e-32 relative error = 1.1600000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.077 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01356 Order of pole (three term test) = -12.9 Radius of convergence (six term test) for eq 1 = 1.077 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.39 y[1] (analytic) = 0.86798021005121083239302143911119 y[1] (numeric) = 0.8679802100512108323930214391112 absolute error = 1e-32 relative error = 1.1521000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.073 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00894 Order of pole (three term test) = -19.28 Radius of convergence (six term test) for eq 1 = 1.073 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.38 y[1] (analytic) = 0.87382034253757427472911569381335 y[1] (numeric) = 0.87382034253757427472911569381336 absolute error = 1e-32 relative error = 1.1444000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0007173 Order of pole (three term test) = -24.71 Radius of convergence (six term test) for eq 1 = 1.07 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.37 y[1] (analytic) = 0.87958483595742809393966048025332 y[1] (numeric) = 0.87958483595742809393966048025333 absolute error = 1e-32 relative error = 1.1369000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.066 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.066 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.36 y[1] (analytic) = 0.88526912181303116147308781869688 y[1] (numeric) = 0.88526912181303116147308781869689 absolute error = 1e-32 relative error = 1.1296000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.063 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.063 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.35 y[1] (analytic) = 0.89086859688195991091314031180401 y[1] (numeric) = 0.89086859688195991091314031180402 absolute error = 1e-32 relative error = 1.1225000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.059 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.059 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.34 y[1] (analytic) = 0.89637863033345285048404446038006 y[1] (numeric) = 0.89637863033345285048404446038008 absolute error = 2e-32 relative error = 2.2312000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.056 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.056 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.33 y[1] (analytic) = 0.9017945711966813959779962124628 y[1] (numeric) = 0.90179457119668139597799621246282 absolute error = 2e-32 relative error = 2.2178000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.053 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.053 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.32 y[1] (analytic) = 0.90711175616835994194484760522496 y[1] (numeric) = 0.90711175616835994194484760522498 absolute error = 2e-32 relative error = 2.2048000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.05 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.31 y[1] (analytic) = 0.91232551774473132013502417662622 y[1] (numeric) = 0.91232551774473132013502417662624 absolute error = 2e-32 relative error = 2.1922000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.047 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.047 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.3 y[1] (analytic) = 0.91743119266055045871559633027523 y[1] (numeric) = 0.91743119266055045871559633027525 absolute error = 2e-32 relative error = 2.1800000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.044 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.044 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.29 y[1] (analytic) = 0.92242413061525689512037634904529 y[1] (numeric) = 0.92242413061525689512037634904531 absolute error = 2e-32 relative error = 2.1682000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.041 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008117 Order of pole (three term test) = -2.242 Radius of convergence (six term test) for eq 1 = 1.041 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.28 y[1] (analytic) = 0.92729970326409495548961424332344 y[1] (numeric) = 0.92729970326409495548961424332346 absolute error = 2e-32 relative error = 2.1568000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.038 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01362 Order of pole (three term test) = -6.349 Radius of convergence (six term test) for eq 1 = 1.038 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.27 y[1] (analytic) = 0.9320533134495293130767079876969 y[1] (numeric) = 0.93205331344952931307670798769691 absolute error = 1e-32 relative error = 1.0729000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.036 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01467 Order of pole (three term test) = -12.29 Radius of convergence (six term test) for eq 1 = 1.036 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.26 y[1] (analytic) = 0.93668040464593480704383664293743 y[1] (numeric) = 0.93668040464593480704383664293744 absolute error = 1e-32 relative error = 1.0676000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.033 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01095 Order of pole (three term test) = -18.65 Radius of convergence (six term test) for eq 1 = 1.033 Order of pole (six term test) = 1 bytes used=36013004, alloc=4586680, time=1.75 TOP MAIN SOLVE Loop x[1] = -0.25 y[1] (analytic) = 0.94117647058823529411764705882353 y[1] (numeric) = 0.94117647058823529411764705882354 absolute error = 1e-32 relative error = 1.0625000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.031 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.003299 Order of pole (three term test) = -23.79 Radius of convergence (six term test) for eq 1 = 1.031 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.24 y[1] (analytic) = 0.94553706505295007564296520423601 y[1] (numeric) = 0.94553706505295007564296520423602 absolute error = 1e-32 relative error = 1.0576000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.028 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.028 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.23 y[1] (analytic) = 0.94975781175800170956406116440308 y[1] (numeric) = 0.94975781175800170956406116440309 absolute error = 1e-32 relative error = 1.0529000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.026 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.026 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.22 y[1] (analytic) = 0.95383441434566959175887066005341 y[1] (numeric) = 0.95383441434566959175887066005343 absolute error = 2e-32 relative error = 2.0968000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.024 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.024 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.21 y[1] (analytic) = 0.95776266641126328895699645627813 y[1] (numeric) = 0.95776266641126328895699645627815 absolute error = 2e-32 relative error = 2.0882000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.022 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.022 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.2 y[1] (analytic) = 0.96153846153846153846153846153846 y[1] (numeric) = 0.96153846153846153846153846153848 absolute error = 2e-32 relative error = 2.0800000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.02 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.19 y[1] (analytic) = 0.96515780330083968728887173052794 y[1] (numeric) = 0.96515780330083968728887173052796 absolute error = 2e-32 relative error = 2.0722000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.018 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.018 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.18 y[1] (analytic) = 0.96861681518791166214645486245641 y[1] (numeric) = 0.96861681518791166214645486245643 absolute error = 2e-32 relative error = 2.0648000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.016 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.016 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.17 y[1] (analytic) = 0.97191175041306249392555155991836 y[1] (numeric) = 0.97191175041306249392555155991838 absolute error = 2e-32 relative error = 2.0578000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.014 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005819 Order of pole (three term test) = -1.546 Radius of convergence (six term test) for eq 1 = 1.014 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.16 y[1] (analytic) = 0.97503900156006240249609984399376 y[1] (numeric) = 0.97503900156006240249609984399378 absolute error = 2e-32 relative error = 2.0512000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.013 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01292 Order of pole (three term test) = -5.045 Radius of convergence (six term test) for eq 1 = 1.013 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.15 y[1] (analytic) = 0.97799511002444987775061124694377 y[1] (numeric) = 0.97799511002444987775061124694379 absolute error = 2e-32 relative error = 2.0450000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.011 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01595 Order of pole (three term test) = -10.74 Radius of convergence (six term test) for eq 1 = 1.011 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.14 y[1] (analytic) = 0.98077677520596312279325225578658 y[1] (numeric) = 0.98077677520596312279325225578661 absolute error = 3e-32 relative error = 3.0588000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01408 Order of pole (three term test) = -17.15 Radius of convergence (six term test) for eq 1 = 1.01 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.13 y[1] (analytic) = 0.98338086340839807257350771953978 y[1] (numeric) = 0.9833808634083980725735077195398 absolute error = 2e-32 relative error = 2.0338000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.008 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007745 Order of pole (three term test) = -22.5 Radius of convergence (six term test) for eq 1 = 1.008 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.12 y[1] (analytic) = 0.9858044164037854889589905362776 y[1] (numeric) = 0.98580441640378548895899053627762 absolute error = 2e-32 relative error = 2.0288000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.007 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.007 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.11 y[1] (analytic) = 0.98804465961861476138721470210454 y[1] (numeric) = 0.98804465961861476138721470210455 absolute error = 1e-32 relative error = 1.0121000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.006 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.006 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.1 y[1] (analytic) = 0.99009900990099009900990099009901 y[1] (numeric) = 0.99009900990099009900990099009902 absolute error = 1e-32 relative error = 1.0100000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.005 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.005 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.09 y[1] (analytic) = 0.99196508282908441622854875508382 y[1] (numeric) = 0.99196508282908441622854875508383 absolute error = 1e-32 relative error = 1.0081000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.004 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.004 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.08 y[1] (analytic) = 0.99364069952305246422893481717011 y[1] (numeric) = 0.99364069952305246422893481717012 absolute error = 1e-32 relative error = 1.0064000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.003 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.003 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.07 y[1] (analytic) = 0.99512389292466912130560254751717 y[1] (numeric) = 0.99512389292466912130560254751717 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.002 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.002 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.06 y[1] (analytic) = 0.99641291351135910721402949382224 y[1] (numeric) = 0.99641291351135910721402949382224 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.002 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.002 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.05 y[1] (analytic) = 0.99750623441396508728179551122195 y[1] (numeric) = 0.99750623441396508728179551122195 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.001 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007614 Order of pole (three term test) = -2.026 Radius of convergence (six term test) for eq 1 = 1.001 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.04 y[1] (analytic) = 0.99840255591054313099041533546326 y[1] (numeric) = 0.99840255591054313099041533546326 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 bytes used=40014300, alloc=4586680, time=1.95 Radius of convergence (given) for eq 1 = 1.001 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 0.7409 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.01468 Order of pole (three term test) = -6.126 Radius of convergence (six term test) for eq 1 = 1.001 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.03 y[1] (analytic) = 0.99910080927165551004096313318014 y[1] (numeric) = 0.99910080927165551004096313318014 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01764 Order of pole (three term test) = -12.17 Radius of convergence (six term test) for eq 1 = 1 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.02 y[1] (analytic) = 0.9996001599360255897640943622551 y[1] (numeric) = 0.9996001599360255897640943622551 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01564 Order of pole (three term test) = -18.49 Radius of convergence (six term test) for eq 1 = 1 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.01 y[1] (analytic) = 0.99990000999900009999000099990001 y[1] (numeric) = 0.99990000999900009999000099990001 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009154 Order of pole (three term test) = -23.26 Radius of convergence (six term test) for eq 1 = 1 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 0.99990000999900009999000099990001 y[1] (numeric) = 0.99990000999900009999000099990001 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 0.9996001599360255897640943622551 y[1] (numeric) = 0.9996001599360255897640943622551 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 0.99910080927165551004096313318014 y[1] (numeric) = 0.99910080927165551004096313318014 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 0.99840255591054313099041533546326 y[1] (numeric) = 0.99840255591054313099041533546326 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.001 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 0.7409 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.001 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (analytic) = 0.99750623441396508728179551122195 y[1] (numeric) = 0.99750623441396508728179551122195 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.001 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.001 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (analytic) = 0.99641291351135910721402949382224 y[1] (numeric) = 0.99641291351135910721402949382224 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.002 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001696 Order of pole (three term test) = -0.945 Radius of convergence (six term test) for eq 1 = 1.002 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.07 y[1] (analytic) = 0.99512389292466912130560254751717 y[1] (numeric) = 0.99512389292466912130560254751717 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.002 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01089 Order of pole (three term test) = -3.162 Radius of convergence (six term test) for eq 1 = 1.002 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 0.99364069952305246422893481717011 y[1] (numeric) = 0.99364069952305246422893481717012 absolute error = 1e-32 relative error = 1.0064000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.003 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01761 Order of pole (three term test) = -8.108 Radius of convergence (six term test) for eq 1 = 1.003 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 0.99196508282908441622854875508382 y[1] (numeric) = 0.99196508282908441622854875508383 absolute error = 1e-32 relative error = 1.0081000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.004 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02009 Order of pole (three term test) = -14.48 Radius of convergence (six term test) for eq 1 = 1.004 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.99009900990099009900990099009901 y[1] (numeric) = 0.99009900990099009900990099009902 absolute error = 1e-32 relative error = 1.0100000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.005 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01758 Order of pole (three term test) = -20.52 Radius of convergence (six term test) for eq 1 = 1.005 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0.98804465961861476138721470210454 y[1] (numeric) = 0.98804465961861476138721470210455 absolute error = 1e-32 relative error = 1.0121000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.006 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0107 Order of pole (three term test) = -24.5 Radius of convergence (six term test) for eq 1 = 1.006 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0.9858044164037854889589905362776 y[1] (numeric) = 0.98580441640378548895899053627762 absolute error = 2e-32 relative error = 2.0288000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.007 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001374 Order of pole (three term test) = -25.22 Radius of convergence (six term test) for eq 1 = 1.007 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0.98338086340839807257350771953978 y[1] (numeric) = 0.9833808634083980725735077195398 absolute error = 2e-32 relative error = 2.0338000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.008 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.008 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0.98077677520596312279325225578658 y[1] (numeric) = 0.98077677520596312279325225578661 absolute error = 3e-32 relative error = 3.0588000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.01 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0.97799511002444987775061124694377 y[1] (numeric) = 0.97799511002444987775061124694379 absolute error = 2e-32 relative error = 2.0450000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.011 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.011 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.97503900156006240249609984399376 y[1] (numeric) = 0.97503900156006240249609984399378 absolute error = 2e-32 relative error = 2.0512000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.013 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.013 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0.97191175041306249392555155991836 y[1] (numeric) = 0.97191175041306249392555155991838 absolute error = 2e-32 relative error = 2.0578000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.014 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.014 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0.96861681518791166214645486245641 y[1] (numeric) = 0.96861681518791166214645486245643 absolute error = 2e-32 relative error = 2.0648000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.016 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.003585 Order of pole (three term test) = -1.114 Radius of convergence (six term test) for eq 1 = 1.016 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop bytes used=44017928, alloc=4652204, time=2.15 x[1] = 0.19 y[1] (analytic) = 0.96515780330083968728887173052794 y[1] (numeric) = 0.96515780330083968728887173052796 absolute error = 2e-32 relative error = 2.0722000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.018 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01304 Order of pole (three term test) = -3.855 Radius of convergence (six term test) for eq 1 = 1.018 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0.96153846153846153846153846153846 y[1] (numeric) = 0.96153846153846153846153846153848 absolute error = 2e-32 relative error = 2.0800000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02027 Order of pole (three term test) = -9.108 Radius of convergence (six term test) for eq 1 = 1.02 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0.95776266641126328895699645627813 y[1] (numeric) = 0.95776266641126328895699645627815 absolute error = 2e-32 relative error = 2.0882000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.022 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02348 Order of pole (three term test) = -15.57 Radius of convergence (six term test) for eq 1 = 1.022 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0.95383441434566959175887066005341 y[1] (numeric) = 0.95383441434566959175887066005343 absolute error = 2e-32 relative error = 2.0968000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.024 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02178 Order of pole (three term test) = -21.58 Radius of convergence (six term test) for eq 1 = 1.024 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 0.94975781175800170956406116440308 y[1] (numeric) = 0.94975781175800170956406116440309 absolute error = 1e-32 relative error = 1.0529000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.026 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01554 Order of pole (three term test) = -25.52 Radius of convergence (six term test) for eq 1 = 1.026 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 0.94553706505295007564296520423601 y[1] (numeric) = 0.94553706505295007564296520423602 absolute error = 1e-32 relative error = 1.0576000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.028 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.006372 Order of pole (three term test) = -26.33 Radius of convergence (six term test) for eq 1 = 1.028 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 0.94117647058823529411764705882353 y[1] (numeric) = 0.94117647058823529411764705882354 absolute error = 1e-32 relative error = 1.0625000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.031 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.031 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 0.93668040464593480704383664293743 y[1] (numeric) = 0.93668040464593480704383664293744 absolute error = 1e-32 relative error = 1.0676000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.033 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.033 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 0.9320533134495293130767079876969 y[1] (numeric) = 0.93205331344952931307670798769691 absolute error = 1e-32 relative error = 1.0729000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.036 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.036 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0.92729970326409495548961424332344 y[1] (numeric) = 0.92729970326409495548961424332346 absolute error = 2e-32 relative error = 2.1568000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.038 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.038 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 0.92242413061525689512037634904529 y[1] (numeric) = 0.92242413061525689512037634904531 absolute error = 2e-32 relative error = 2.1682000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.041 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.041 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0.91743119266055045871559633027523 y[1] (numeric) = 0.91743119266055045871559633027525 absolute error = 2e-32 relative error = 2.1800000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.044 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0006003 Order of pole (three term test) = -0.8988 Radius of convergence (six term test) for eq 1 = 1.044 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 0.91232551774473132013502417662622 y[1] (numeric) = 0.91232551774473132013502417662624 absolute error = 2e-32 relative error = 2.1922000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.047 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01065 Order of pole (three term test) = -2.614 Radius of convergence (six term test) for eq 1 = 1.047 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 0.90711175616835994194484760522496 y[1] (numeric) = 0.90711175616835994194484760522498 absolute error = 2e-32 relative error = 2.2048000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0199 Order of pole (three term test) = -7.023 Radius of convergence (six term test) for eq 1 = 1.05 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0.9017945711966813959779962124628 y[1] (numeric) = 0.90179457119668139597799621246282 absolute error = 2e-32 relative error = 2.2178000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.053 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02635 Order of pole (three term test) = -13.17 Radius of convergence (six term test) for eq 1 = 1.053 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 0.89637863033345285048404446038006 y[1] (numeric) = 0.89637863033345285048404446038008 absolute error = 2e-32 relative error = 2.2312000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.056 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02853 Order of pole (three term test) = -19.69 Radius of convergence (six term test) for eq 1 = 1.056 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = 0.89086859688195991091314031180401 y[1] (numeric) = 0.89086859688195991091314031180402 absolute error = 1e-32 relative error = 1.1225000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.059 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02588 Order of pole (three term test) = -25.07 Radius of convergence (six term test) for eq 1 = 1.059 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 0.88526912181303116147308781869688 y[1] (numeric) = 0.88526912181303116147308781869689 absolute error = 1e-32 relative error = 1.1296000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.063 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01895 Order of pole (three term test) = -28.04 Radius of convergence (six term test) for eq 1 = 1.063 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 0.87958483595742809393966048025332 y[1] (numeric) = 0.87958483595742809393966048025333 absolute error = 1e-32 relative error = 1.1369000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.066 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009342 Order of pole (three term test) = -27.89 Radius of convergence (six term test) for eq 1 = 1.066 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 0.87382034253757427472911569381335 y[1] (numeric) = 0.87382034253757427472911569381336 absolute error = 1e-32 relative error = 1.1444000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.07 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 0.86798021005121083239302143911119 y[1] (numeric) = 0.8679802100512108323930214391112 absolute error = 1e-32 relative error = 1.1521000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.073 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.073 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0.86206896551724137931034482758621 y[1] (numeric) = 0.86206896551724137931034482758622 absolute error = 1e-32 relative error = 1.1600000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.077 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.077 Order of pole (six term test) = 1 bytes used=48018568, alloc=4652204, time=2.35 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 0.85609108809177296464343806180978 y[1] (numeric) = 0.85609108809177296464343806180979 absolute error = 1e-32 relative error = 1.1681000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.081 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.081 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 0.85005100306018361101666099965998 y[1] (numeric) = 0.85005100306018361101666099965999 absolute error = 1e-32 relative error = 1.1764000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.085 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.085 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 0.84395307620896278166933918474133 y[1] (numeric) = 0.84395307620896278166933918474134 absolute error = 1e-32 relative error = 1.1849000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.089 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.089 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 0.83780160857908847184986595174263 y[1] (numeric) = 0.83780160857908847184986595174264 absolute error = 1e-32 relative error = 1.1936000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.093 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008874 Order of pole (three term test) = -1.95 Radius of convergence (six term test) for eq 1 = 1.093 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 0.83160083160083160083160083160083 y[1] (numeric) = 0.83160083160083160083160083160084 absolute error = 1e-32 relative error = 1.2025000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.097 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01941 Order of pole (three term test) = -5.613 Radius of convergence (six term test) for eq 1 = 1.097 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 0.82535490260812149224166391548366 y[1] (numeric) = 0.82535490260812149224166391548367 absolute error = 1e-32 relative error = 1.2116000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02843 Order of pole (three term test) = -11.26 Radius of convergence (six term test) for eq 1 = 1.101 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 0.81906790072897043164878368416742 y[1] (numeric) = 0.81906790072897043164878368416743 absolute error = 1e-32 relative error = 1.2209000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.105 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0343 Order of pole (three term test) = -17.85 Radius of convergence (six term test) for eq 1 = 1.105 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 0.81274382314694408322496749024707 y[1] (numeric) = 0.81274382314694408322496749024709 absolute error = 2e-32 relative error = 2.4608000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.109 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03585 Order of pole (three term test) = -24.15 Radius of convergence (six term test) for eq 1 = 1.109 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 0.80638658172728005805983388436416 y[1] (numeric) = 0.80638658172728005805983388436418 absolute error = 2e-32 relative error = 2.4802000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.114 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03275 Order of pole (three term test) = -28.95 Radius of convergence (six term test) for eq 1 = 1.114 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0.8 y[1] (numeric) = 0.80000000000000000000000000000002 absolute error = 2e-32 relative error = 2.5000000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.118 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02554 Order of pole (three term test) = -31.28 Radius of convergence (six term test) for eq 1 = 1.118 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 0.79358781049123085469407189905563 y[1] (numeric) = 0.79358781049123085469407189905565 absolute error = 2e-32 relative error = 2.5202000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.123 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01561 Order of pole (three term test) = -30.72 Radius of convergence (six term test) for eq 1 = 1.123 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 0.78715365239294710327455919395466 y[1] (numeric) = 0.78715365239294710327455919395468 absolute error = 2e-32 relative error = 2.5408000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.127 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004877 Order of pole (three term test) = -27.43 Radius of convergence (six term test) for eq 1 = 1.127 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 0.78070106956046529783745803731751 y[1] (numeric) = 0.78070106956046529783745803731753 absolute error = 2e-32 relative error = 2.5618000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.132 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.132 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 0.77423350882626200061938680706101 y[1] (numeric) = 0.77423350882626200061938680706103 absolute error = 2e-32 relative error = 2.5832000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.136 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.136 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 0.76775431861804222648752399232246 y[1] (numeric) = 0.76775431861804222648752399232248 absolute error = 2e-32 relative error = 2.6050000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.141 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.141 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 0.76126674786845310596833130328867 y[1] (numeric) = 0.7612667478684531059683313032887 absolute error = 3e-32 relative error = 3.9408000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.146 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.146 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = 0.75477394520341157823231942033361 y[1] (numeric) = 0.75477394520341157823231942033364 absolute error = 3e-32 relative error = 3.9747000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.151 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.151 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 0.74827895839568991319964082609997 y[1] (numeric) = 0.7482789583956899131996408261 absolute error = 3e-32 relative error = 4.0092000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.156 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.002633 Order of pole (three term test) = -0.9822 Radius of convergence (six term test) for eq 1 = 1.156 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 0.74178473407017283584303835027075 y[1] (numeric) = 0.74178473407017283584303835027078 absolute error = 3e-32 relative error = 4.0443000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.161 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01359 Order of pole (three term test) = -2.892 Radius of convergence (six term test) for eq 1 = 1.161 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0.73529411764705882352941176470588 y[1] (numeric) = 0.73529411764705882352941176470591 absolute error = 3e-32 relative error = 4.0800000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.166 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02499 Order of pole (three term test) = -7.044 Radius of convergence (six term test) for eq 1 = 1.166 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 0.72880985350921944464689162597478 y[1] (numeric) = 0.72880985350921944464689162597481 absolute error = 3e-32 relative error = 4.1163000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.171 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03527 Order of pole (three term test) = -12.86 Radius of convergence (six term test) for eq 1 = 1.171 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 0.72233458537994799190985264374458 y[1] (numeric) = 0.72233458537994799190985264374461 absolute error = 3e-32 relative error = 4.1532000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 bytes used=52019372, alloc=4652204, time=2.56 Radius of convergence (given) for eq 1 = 1.177 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04296 Order of pole (three term test) = -19.53 Radius of convergence (six term test) for eq 1 = 1.177 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 0.71587085689741570620660032930059 y[1] (numeric) = 0.71587085689741570620660032930062 absolute error = 3e-32 relative error = 4.1907000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.182 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04691 Order of pole (three term test) = -26.07 Radius of convergence (six term test) for eq 1 = 1.182 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 0.70942111237230419977298524404086 y[1] (numeric) = 0.70942111237230419977298524404089 absolute error = 3e-32 relative error = 4.2288000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.187 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04648 Order of pole (three term test) = -31.51 Radius of convergence (six term test) for eq 1 = 1.187 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 0.70298769771528998242530755711775 y[1] (numeric) = 0.70298769771528998242530755711778 absolute error = 3e-32 relative error = 4.2675000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.193 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0417 Order of pole (three term test) = -35.01 Radius of convergence (six term test) for eq 1 = 1.193 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 0.69657286152131512956255224296461 y[1] (numeric) = 0.69657286152131512956255224296464 absolute error = 3e-32 relative error = 4.3068000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.198 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03327 Order of pole (three term test) = -36.05 Radius of convergence (six term test) for eq 1 = 1.198 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 0.69017875629788115121816550486576 y[1] (numeric) = 0.69017875629788115121816550486579 absolute error = 3e-32 relative error = 4.3467000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.204 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02246 Order of pole (three term test) = -34.52 Radius of convergence (six term test) for eq 1 = 1.204 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 0.68380743982494529540481400437637 y[1] (numeric) = 0.6838074398249452954048140043764 absolute error = 3e-32 relative error = 4.3872000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.209 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0109 Order of pole (three term test) = -30.69 Radius of convergence (six term test) for eq 1 = 1.209 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 0.67746087663437436488042815527403 y[1] (numeric) = 0.67746087663437436488042815527407 absolute error = 4e-32 relative error = 5.9044000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.215 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0002417 Order of pole (three term test) = -25.19 Radius of convergence (six term test) for eq 1 = 1.215 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0.67114093959731543624161073825503 y[1] (numeric) = 0.67114093959731543624161073825507 absolute error = 4e-32 relative error = 5.9600000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.221 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.221 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 0.6648494116082707266804068878399 y[1] (numeric) = 0.66484941160827072668040688783994 absolute error = 4e-32 relative error = 6.0164000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.226 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.226 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 0.65858798735511064278187565858799 y[1] (numeric) = 0.65858798735511064278187565858802 absolute error = 3e-32 relative error = 4.5552000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.232 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.232 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 0.65235827516472046447909191728097 y[1] (numeric) = 0.652358275164720464479091917281 absolute error = 3e-32 relative error = 4.5987000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.238 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.238 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 0.64616179891444817782372706125614 y[1] (numeric) = 0.64616179891444817782372706125617 absolute error = 3e-32 relative error = 4.6428000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.244 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.244 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 0.64 y[1] (numeric) = 0.64000000000000000000000000000003 absolute error = 3e-32 relative error = 4.6875000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005697 Order of pole (three term test) = -1.226 Radius of convergence (six term test) for eq 1 = 1.25 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 0.63387423935091277890466531440162 y[1] (numeric) = 0.63387423935091277890466531440165 absolute error = 3e-32 relative error = 4.7328000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.256 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01744 Order of pole (three term test) = -3.474 Radius of convergence (six term test) for eq 1 = 1.256 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 0.62778579948521564442212317157386 y[1] (numeric) = 0.62778579948521564442212317157389 absolute error = 3e-32 relative error = 4.7787000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.262 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03004 Order of pole (three term test) = -7.635 Radius of convergence (six term test) for eq 1 = 1.262 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 0.62173588659537428500373041531957 y[1] (numeric) = 0.6217358865953742850037304153196 absolute error = 3e-32 relative error = 4.8252000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.268 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04226 Order of pole (three term test) = -13.3 Radius of convergence (six term test) for eq 1 = 1.268 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 0.61572563265808755618496398005049 y[1] (numeric) = 0.61572563265808755618496398005052 absolute error = 3e-32 relative error = 4.8723000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.274 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05287 Order of pole (three term test) = -19.9 Radius of convergence (six term test) for eq 1 = 1.274 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 0.60975609756097560975609756097561 y[1] (numeric) = 0.60975609756097560975609756097564 absolute error = 3e-32 relative error = 4.9200000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.281 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06075 Order of pole (three term test) = -26.75 Radius of convergence (six term test) for eq 1 = 1.281 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 0.60382827123965944085502083207536 y[1] (numeric) = 0.60382827123965944085502083207539 absolute error = 3e-32 relative error = 4.9683000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.287 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06504 Order of pole (three term test) = -33.13 Radius of convergence (six term test) for eq 1 = 1.287 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 0.59794307581918201387227935900502 y[1] (numeric) = 0.59794307581918201387227935900505 absolute error = 3e-32 relative error = 5.0172000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.293 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06522 Order of pole (three term test) = -38.34 Radius of convergence (six term test) for eq 1 = 1.293 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 0.59210136775415951210847297057256 y[1] (numeric) = 0.59210136775415951210847297057259 absolute error = 3e-32 relative error = 5.0667000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06125 Order of pole (three term test) = -41.81 Radius of convergence (six term test) for eq 1 = 1.3 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop bytes used=56021772, alloc=4652204, time=2.76 x[1] = 0.84 y[1] (analytic) = 0.58630393996247654784240150093809 y[1] (numeric) = 0.58630393996247654784240150093811 absolute error = 2e-32 relative error = 3.4112000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.306 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05355 Order of pole (three term test) = -43.17 Radius of convergence (six term test) for eq 1 = 1.306 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 0.58055152394775036284470246734398 y[1] (numeric) = 0.580551523947750362844702467344 absolute error = 2e-32 relative error = 3.4450000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.312 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04297 Order of pole (three term test) = -42.3 Radius of convergence (six term test) for eq 1 = 1.312 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 0.57484479190618532996091055415038 y[1] (numeric) = 0.5748447919061853299609105541504 absolute error = 2e-32 relative error = 3.4792000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.319 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03067 Order of pole (three term test) = -39.34 Radius of convergence (six term test) for eq 1 = 1.319 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 0.56918435881381979623199954465251 y[1] (numeric) = 0.56918435881381979623199954465253 absolute error = 2e-32 relative error = 3.5138000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.325 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01795 Order of pole (three term test) = -34.66 Radius of convergence (six term test) for eq 1 = 1.325 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 0.56357078449053201082055906221821 y[1] (numeric) = 0.56357078449053201082055906221823 absolute error = 2e-32 relative error = 3.5488000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.332 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.006124 Order of pole (three term test) = -28.81 Radius of convergence (six term test) for eq 1 = 1.332 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 0.55800457563752022766586686010825 y[1] (numeric) = 0.55800457563752022766586686010827 absolute error = 2e-32 relative error = 3.5842000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.339 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.339 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 0.55248618784530386740331491712707 y[1] (numeric) = 0.55248618784530386740331491712709 absolute error = 2e-32 relative error = 3.6200000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.345 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.345 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 0.54701602756960778950823259121492 y[1] (numeric) = 0.54701602756960778950823259121494 absolute error = 2e-32 relative error = 3.6562000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.352 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.352 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 0.54159445407279029462738301559792 y[1] (numeric) = 0.54159445407279029462738301559794 absolute error = 2e-32 relative error = 3.6928000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.359 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.359 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 0.53622178132875757413266126870073 y[1] (numeric) = 0.53622178132875757413266126870075 absolute error = 2e-32 relative error = 3.7298000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.366 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.366 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 0.53089827988957315778296878318114 y[1] (numeric) = 0.53089827988957315778296878318116 absolute error = 2e-32 relative error = 3.7672000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.372 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.372 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 0.52562417871222076215505913272011 y[1] (numeric) = 0.52562417871222076215505913272012 absolute error = 1e-32 relative error = 1.9025000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.379 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.006862 Order of pole (three term test) = -1.277 Radius of convergence (six term test) for eq 1 = 1.379 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 0.52039966694421315570358034970858 y[1] (numeric) = 0.52039966694421315570358034970859 absolute error = 1e-32 relative error = 1.9216000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.386 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01913 Order of pole (three term test) = -3.316 Radius of convergence (six term test) for eq 1 = 1.386 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 0.51522489566695862744087794322222 y[1] (numeric) = 0.51522489566695862744087794322223 absolute error = 1e-32 relative error = 1.9409000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.393 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03288 Order of pole (three term test) = -6.989 Radius of convergence (six term test) for eq 1 = 1.393 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 0.51009997959600081615996735360131 y[1] (numeric) = 0.51009997959600081615996735360132 absolute error = 1e-32 relative error = 1.9604000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04723 Order of pole (three term test) = -12.06 Radius of convergence (six term test) for eq 1 = 1.4 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 0.50502499873743750315640624210898 y[1] (numeric) = 0.505024998737437503156406242109 absolute error = 2e-32 relative error = 3.9602000000000000000000000000000e-30 % Correct digits = 32 h = 0.01 Radius of convergence (given) for eq 1 = 1.407 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06127 Order of pole (three term test) = -18.21 Radius of convergence (six term test) for eq 1 = 1.407 Order of pole (six term test) = 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0); Iterations = 300 Total Elapsed Time = 2 Seconds Elapsed Time(since restart) = 2 Seconds Time to Timeout = 2 Minutes 57 Seconds Percent Done = 100.3 % > quit bytes used=58889548, alloc=4652204, time=2.89