|\^/| 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_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10_g, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > 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_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10_g, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, 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_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10_g, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > 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_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10_g, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, 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_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10_g, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > 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_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10_g, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, 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_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10_g, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > 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_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10_g, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, 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_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10_g, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > 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_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10_g, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, 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_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10_g, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > 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_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10_g, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, 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_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10_g, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > 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_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10_g, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, 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_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10_g, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > 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_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10_g, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, 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_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10_g, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > 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 CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; > #emit pre sin 1 $eq_no = 1 > array_tmp3[1] := sin(array_x[1]); > array_tmp3_g[1] := cos(array_x[1]); > #emit pre expt LINEAR - FULL $eq_no = 1 i = 1 > array_tmp4[1] := expt(array_tmp2[1] , array_tmp3[1] ) ; > array_tmp4_a1[1] := ln(array_tmp2[1] ) ; > array_tmp4_a1[2] := array_tmp2[2] / array_tmp2[1]; > #emit pre cos 1 $eq_no = 1 > array_tmp5[1] := cos(array_x[1]); > array_tmp5_g[1] := sin(array_x[1]); > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp6[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp7[1] := array_tmp6[1] + array_const_1D0[1]; > #emit pre ln 1 LINEAR $eq_no = 1 > array_tmp8[1] := ln(array_tmp7[1]); > # emit pre mult FULL FULL $eq_no = 1 i = 1 > array_tmp9[1] := (array_tmp5[1] * (array_tmp8[1])); > #emit pre sin 1 $eq_no = 1 > array_tmp10[1] := sin(array_x[1]); > array_tmp10_g[1] := cos(array_x[1]); > #emit pre mult CONST FULL $eq_no = 1 i = 1 > array_tmp11[1] := array_const_2D0[1] * array_tmp10[1]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp12[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp13[1] := array_tmp12[1] + array_const_1D0[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp14[1] := array_tmp11[1] / array_tmp13[1]; > #emit pre add FULL FULL $eq_no = 1 i = 1 > array_tmp15[1] := array_tmp9[1] + array_tmp14[1]; > # emit pre mult FULL FULL $eq_no = 1 i = 1 > array_tmp16[1] := (array_tmp4[1] * (array_tmp15[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp17[1] := array_const_0D0[1] + array_tmp16[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_tmp17[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp3[2] := array_tmp3_g[1] * array_x[2] / 1; > array_tmp3_g[2] := -array_tmp3[1] * array_x[2] / 1; > #emit pre expt LINEAR - FULL $eq_no = 1 i = 2 > array_tmp4_a2[1] := (array_tmp4_a1[1] * array_tmp3[2] + array_tmp4_a1[2] * array_tmp3[1]) / glob_h; > array_tmp4[2] := array_tmp4[1] * array_tmp4_a2[1] * glob_h; > #emit pre cos ID_LINEAR iii = 2 $eq_no = 1 > array_tmp5[2] := -array_tmp5_g[1] * array_x[2] / 1; > array_tmp5_g[2] := array_tmp5[1] * array_x[2] / 1; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp6[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp7[2] := array_tmp6[2]; > #emit pre ln 2 LINEAR $eq_no = 1 > array_tmp8[2] := array_tmp7[2] / array_tmp7[1]; > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp9[2] := ats(2,array_tmp5,array_tmp8,1); > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp10[2] := array_tmp10_g[1] * array_x[2] / 1; > array_tmp10_g[2] := -array_tmp10[1] * array_x[2] / 1; > #emit pre mult CONST FULL $eq_no = 1 i = 2 > array_tmp11[2] := array_const_2D0[1] * array_tmp10[2]; > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp12[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp13[2] := array_tmp12[2]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp14[2] := (array_tmp11[2] - array_tmp14[1] * array_tmp13[2]) / array_tmp13[1]; > #emit pre add FULL FULL $eq_no = 1 i = 2 > array_tmp15[2] := array_tmp9[2] + array_tmp14[2]; > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp16[2] := ats(2,array_tmp4,array_tmp15,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp17[2] := array_tmp16[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_tmp17[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 sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := array_tmp3_g[2] * array_x[2] / 2; > array_tmp3_g[3] := -array_tmp3[2] * array_x[2] / 2; > #emit pre expt LINEAR - FULL $eq_no = 1 i = 3 > array_tmp4_a1[3] := -array_tmp4_a1[2] * array_tmp2[2] * 1 / array_tmp2[1] / 2; > array_tmp4_a2[2] := ats(3,array_tmp3,array_tmp4_a1,1)*2 / glob_h; > array_tmp4[3] := ats(2,array_tmp4,array_tmp4_a2,1)*glob_h/2; > #emit pre cos ID_LINEAR iii = 3 $eq_no = 1 > array_tmp5[3] := -array_tmp5_g[2] * array_x[2] / 2; > array_tmp5_g[3] := array_tmp5[2] * array_x[2] / 2; > #emit pre ln ID_LINEAR iii = 3 $eq_no = 1 > array_tmp8[3] := - array_tmp7[2] * array_tmp8[2] * 1 / array_tmp7[1] / 2; > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp9[3] := ats(3,array_tmp5,array_tmp8,1); > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp10[3] := array_tmp10_g[2] * array_x[2] / 2; > array_tmp10_g[3] := -array_tmp10[2] * array_x[2] / 2; > #emit pre mult CONST FULL $eq_no = 1 i = 3 > array_tmp11[3] := array_const_2D0[1] * array_tmp10[3]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp14[3] := (array_tmp11[3] - array_tmp14[2] * array_tmp13[2]) / array_tmp13[1]; > #emit pre add FULL FULL $eq_no = 1 i = 3 > array_tmp15[3] := array_tmp9[3] + array_tmp14[3]; > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp16[3] := ats(3,array_tmp4,array_tmp15,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp17[3] := array_tmp16[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_tmp17[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 sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := array_tmp3_g[3] * array_x[2] / 3; > array_tmp3_g[4] := -array_tmp3[3] * array_x[2] / 3; > #emit pre expt LINEAR - FULL $eq_no = 1 i = 4 > array_tmp4_a1[4] := -array_tmp4_a1[3] * array_tmp2[2] * 2 / array_tmp2[1] / 3; > array_tmp4_a2[3] := ats(4,array_tmp3,array_tmp4_a1,1)*3 / glob_h; > array_tmp4[4] := ats(3,array_tmp4,array_tmp4_a2,1)*glob_h/3; > #emit pre cos ID_LINEAR iii = 4 $eq_no = 1 > array_tmp5[4] := -array_tmp5_g[3] * array_x[2] / 3; > array_tmp5_g[4] := array_tmp5[3] * array_x[2] / 3; > #emit pre ln ID_LINEAR iii = 4 $eq_no = 1 > array_tmp8[4] := - array_tmp7[2] * array_tmp8[3] * 2 / array_tmp7[1] / 3; > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp9[4] := ats(4,array_tmp5,array_tmp8,1); > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp10[4] := array_tmp10_g[3] * array_x[2] / 3; > array_tmp10_g[4] := -array_tmp10[3] * array_x[2] / 3; > #emit pre mult CONST FULL $eq_no = 1 i = 4 > array_tmp11[4] := array_const_2D0[1] * array_tmp10[4]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp14[4] := (array_tmp11[4] - array_tmp14[3] * array_tmp13[2]) / array_tmp13[1]; > #emit pre add FULL FULL $eq_no = 1 i = 4 > array_tmp15[4] := array_tmp9[4] + array_tmp14[4]; > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp16[4] := ats(4,array_tmp4,array_tmp15,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp17[4] := array_tmp16[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_tmp17[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 sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := array_tmp3_g[4] * array_x[2] / 4; > array_tmp3_g[5] := -array_tmp3[4] * array_x[2] / 4; > #emit pre expt LINEAR - FULL $eq_no = 1 i = 5 > array_tmp4_a1[5] := -array_tmp4_a1[4] * array_tmp2[2] * 3 / array_tmp2[1] / 4; > array_tmp4_a2[4] := ats(5,array_tmp3,array_tmp4_a1,1)*4 / glob_h; > array_tmp4[5] := ats(4,array_tmp4,array_tmp4_a2,1)*glob_h/4; > #emit pre cos ID_LINEAR iii = 5 $eq_no = 1 > array_tmp5[5] := -array_tmp5_g[4] * array_x[2] / 4; > array_tmp5_g[5] := array_tmp5[4] * array_x[2] / 4; > #emit pre ln ID_LINEAR iii = 5 $eq_no = 1 > array_tmp8[5] := - array_tmp7[2] * array_tmp8[4] * 3 / array_tmp7[1] / 4; > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp9[5] := ats(5,array_tmp5,array_tmp8,1); > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp10[5] := array_tmp10_g[4] * array_x[2] / 4; > array_tmp10_g[5] := -array_tmp10[4] * array_x[2] / 4; > #emit pre mult CONST FULL $eq_no = 1 i = 5 > array_tmp11[5] := array_const_2D0[1] * array_tmp10[5]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp14[5] := (array_tmp11[5] - array_tmp14[4] * array_tmp13[2]) / array_tmp13[1]; > #emit pre add FULL FULL $eq_no = 1 i = 5 > array_tmp15[5] := array_tmp9[5] + array_tmp14[5]; > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp16[5] := ats(5,array_tmp4,array_tmp15,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp17[5] := array_tmp16[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_tmp17[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 sin LINEAR $eq_no = 1 > array_tmp3[kkk] := array_tmp3_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp3_g[kkk] := -array_tmp3[kkk - 1] * array_x[2] / (kkk - 1); > #emit expt LINEAR FULL $eq_no = 1 i = 1 > array_tmp4_a1[kkk] := -array_tmp4_a1[kkk-1] * array_tmp2[2] * (kkk-2) / array_tmp2[1] / (kkk - 1); > array_tmp4_a2[kkk-1] := ats(kkk,array_tmp3,array_tmp4_a1,1) * (kkk-1) / glob_h; > array_tmp4[kkk] := ats(kkk-1,array_tmp4,array_tmp4_a2,1) * glob_h/(kkk-1); > #emit cos LINEAR $eq_no = 1 > array_tmp5[kkk] := -array_tmp5_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp5_g[kkk] := array_tmp5[kkk - 1] * array_x[2] / (kkk - 1); > #emit ln LINEAR $eq_no = 1 > array_tmp8[kkk] := - array_tmp7[2] * array_tmp8[kkk - 1] * (kkk - 2)/ array_tmp7[1] / (kkk - 1); > #emit mult FULL FULL $eq_no = 1 > array_tmp9[kkk] := ats(kkk,array_tmp5,array_tmp8,1); > #emit sin LINEAR $eq_no = 1 > array_tmp10[kkk] := array_tmp10_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp10_g[kkk] := -array_tmp10[kkk - 1] * array_x[2] / (kkk - 1); > #emit mult CONST FULL $eq_no = 1 i = 1 > array_tmp11[kkk] := array_const_2D0[1] * array_tmp10[kkk]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp14[kkk] := -ats(kkk,array_tmp13,array_tmp14,2) / array_tmp13[1]; > #emit FULL - FULL add $eq_no = 1 > array_tmp15[kkk] := array_tmp9[kkk] + array_tmp14[kkk]; > #emit mult FULL FULL $eq_no = 1 > array_tmp16[kkk] := ats(kkk,array_tmp4,array_tmp15,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp17[kkk] := array_tmp16[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_tmp17[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_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10_g, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, 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_const_2D0[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_1D0[1]; array_tmp3[1] := sin(array_x[1]); array_tmp3_g[1] := cos(array_x[1]); array_tmp4[1] := expt(array_tmp2[1], array_tmp3[1]); array_tmp4_a1[1] := ln(array_tmp2[1]); array_tmp4_a1[2] := array_tmp2[2]/array_tmp2[1]; array_tmp5[1] := cos(array_x[1]); array_tmp5_g[1] := sin(array_x[1]); array_tmp6[1] := array_const_2D0[1]*array_x[1]; array_tmp7[1] := array_tmp6[1] + array_const_1D0[1]; array_tmp8[1] := ln(array_tmp7[1]); array_tmp9[1] := array_tmp5[1]*array_tmp8[1]; array_tmp10[1] := sin(array_x[1]); array_tmp10_g[1] := cos(array_x[1]); array_tmp11[1] := array_const_2D0[1]*array_tmp10[1]; array_tmp12[1] := array_const_2D0[1]*array_x[1]; array_tmp13[1] := array_tmp12[1] + array_const_1D0[1]; array_tmp14[1] := array_tmp11[1]/array_tmp13[1]; array_tmp15[1] := array_tmp9[1] + array_tmp14[1]; array_tmp16[1] := array_tmp4[1]*array_tmp15[1]; array_tmp17[1] := array_const_0D0[1] + array_tmp16[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp17[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_2D0[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp3_g[1]*array_x[2]; array_tmp3_g[2] := -array_tmp3[1]*array_x[2]; array_tmp4_a2[1] := ( array_tmp4_a1[1]*array_tmp3[2] + array_tmp4_a1[2]*array_tmp3[1])/ glob_h; array_tmp4[2] := array_tmp4[1]*array_tmp4_a2[1]*glob_h; array_tmp5[2] := -array_tmp5_g[1]*array_x[2]; array_tmp5_g[2] := array_tmp5[1]*array_x[2]; array_tmp6[2] := array_const_2D0[1]*array_x[2]; array_tmp7[2] := array_tmp6[2]; array_tmp8[2] := array_tmp7[2]/array_tmp7[1]; array_tmp9[2] := ats(2, array_tmp5, array_tmp8, 1); array_tmp10[2] := array_tmp10_g[1]*array_x[2]; array_tmp10_g[2] := -array_tmp10[1]*array_x[2]; array_tmp11[2] := array_const_2D0[1]*array_tmp10[2]; array_tmp12[2] := array_const_2D0[1]*array_x[2]; array_tmp13[2] := array_tmp12[2]; array_tmp14[2] := (array_tmp11[2] - array_tmp14[1]*array_tmp13[2])/array_tmp13[1]; array_tmp15[2] := array_tmp9[2] + array_tmp14[2]; array_tmp16[2] := ats(2, array_tmp4, array_tmp15, 1); array_tmp17[2] := array_tmp16[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp17[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp3[3] := 1/2*array_tmp3_g[2]*array_x[2]; array_tmp3_g[3] := -1/2*array_tmp3[2]*array_x[2]; array_tmp4_a1[3] := -1/2*array_tmp4_a1[2]*array_tmp2[2]/array_tmp2[1]; array_tmp4_a2[2] := 2*ats(3, array_tmp3, array_tmp4_a1, 1)/glob_h; array_tmp4[3] := 1/2*ats(2, array_tmp4, array_tmp4_a2, 1)*glob_h; array_tmp5[3] := -1/2*array_tmp5_g[2]*array_x[2]; array_tmp5_g[3] := 1/2*array_tmp5[2]*array_x[2]; array_tmp8[3] := -1/2*array_tmp7[2]*array_tmp8[2]/array_tmp7[1]; array_tmp9[3] := ats(3, array_tmp5, array_tmp8, 1); array_tmp10[3] := 1/2*array_tmp10_g[2]*array_x[2]; array_tmp10_g[3] := -1/2*array_tmp10[2]*array_x[2]; array_tmp11[3] := array_const_2D0[1]*array_tmp10[3]; array_tmp14[3] := (array_tmp11[3] - array_tmp14[2]*array_tmp13[2])/array_tmp13[1]; array_tmp15[3] := array_tmp9[3] + array_tmp14[3]; array_tmp16[3] := ats(3, array_tmp4, array_tmp15, 1); array_tmp17[3] := array_tmp16[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp17[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp3[4] := 1/3*array_tmp3_g[3]*array_x[2]; array_tmp3_g[4] := -1/3*array_tmp3[3]*array_x[2]; array_tmp4_a1[4] := -2/3*array_tmp4_a1[3]*array_tmp2[2]/array_tmp2[1]; array_tmp4_a2[3] := 3*ats(4, array_tmp3, array_tmp4_a1, 1)/glob_h; array_tmp4[4] := 1/3*ats(3, array_tmp4, array_tmp4_a2, 1)*glob_h; array_tmp5[4] := -1/3*array_tmp5_g[3]*array_x[2]; array_tmp5_g[4] := 1/3*array_tmp5[3]*array_x[2]; array_tmp8[4] := -2/3*array_tmp7[2]*array_tmp8[3]/array_tmp7[1]; array_tmp9[4] := ats(4, array_tmp5, array_tmp8, 1); array_tmp10[4] := 1/3*array_tmp10_g[3]*array_x[2]; array_tmp10_g[4] := -1/3*array_tmp10[3]*array_x[2]; array_tmp11[4] := array_const_2D0[1]*array_tmp10[4]; array_tmp14[4] := (array_tmp11[4] - array_tmp14[3]*array_tmp13[2])/array_tmp13[1]; array_tmp15[4] := array_tmp9[4] + array_tmp14[4]; array_tmp16[4] := ats(4, array_tmp4, array_tmp15, 1); array_tmp17[4] := array_tmp16[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp17[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp3[5] := 1/4*array_tmp3_g[4]*array_x[2]; array_tmp3_g[5] := -1/4*array_tmp3[4]*array_x[2]; array_tmp4_a1[5] := -3/4*array_tmp4_a1[4]*array_tmp2[2]/array_tmp2[1]; array_tmp4_a2[4] := 4*ats(5, array_tmp3, array_tmp4_a1, 1)/glob_h; array_tmp4[5] := 1/4*ats(4, array_tmp4, array_tmp4_a2, 1)*glob_h; array_tmp5[5] := -1/4*array_tmp5_g[4]*array_x[2]; array_tmp5_g[5] := 1/4*array_tmp5[4]*array_x[2]; array_tmp8[5] := -3/4*array_tmp7[2]*array_tmp8[4]/array_tmp7[1]; array_tmp9[5] := ats(5, array_tmp5, array_tmp8, 1); array_tmp10[5] := 1/4*array_tmp10_g[4]*array_x[2]; array_tmp10_g[5] := -1/4*array_tmp10[4]*array_x[2]; array_tmp11[5] := array_const_2D0[1]*array_tmp10[5]; array_tmp14[5] := (array_tmp11[5] - array_tmp14[4]*array_tmp13[2])/array_tmp13[1]; array_tmp15[5] := array_tmp9[5] + array_tmp14[5]; array_tmp16[5] := ats(5, array_tmp4, array_tmp15, 1); array_tmp17[5] := array_tmp16[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp17[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp3[kkk] := array_tmp3_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp3_g[kkk] := -array_tmp3[kkk - 1]*array_x[2]/(kkk - 1); array_tmp4_a1[kkk] := -array_tmp4_a1[kkk - 1]*array_tmp2[2]* (kkk - 2)/(array_tmp2[1]*(kkk - 1)); array_tmp4_a2[kkk - 1] := ats(kkk, array_tmp3, array_tmp4_a1, 1)*(kkk - 1)/glob_h; array_tmp4[kkk] := ats(kkk - 1, array_tmp4, array_tmp4_a2, 1)*glob_h/(kkk - 1); array_tmp5[kkk] := -array_tmp5_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp5_g[kkk] := array_tmp5[kkk - 1]*array_x[2]/(kkk - 1); array_tmp8[kkk] := -array_tmp7[2]*array_tmp8[kkk - 1]*(kkk - 2)/( array_tmp7[1]*(kkk - 1)); array_tmp9[kkk] := ats(kkk, array_tmp5, array_tmp8, 1); array_tmp10[kkk] := array_tmp10_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp10_g[kkk] := -array_tmp10[kkk - 1]*array_x[2]/(kkk - 1); array_tmp11[kkk] := array_const_2D0[1]*array_tmp10[kkk]; array_tmp14[kkk] := -ats(kkk, array_tmp13, array_tmp14, 2)/array_tmp13[1]; array_tmp15[kkk] := array_tmp9[kkk] + array_tmp14[kkk]; array_tmp16[kkk] := ats(kkk, array_tmp4, array_tmp15, 1); array_tmp17[kkk] := array_tmp16[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_tmp17[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(expt(2.0*x+1.0,sin(x))); > end; exact_soln_y := proc(x) return expt(2.0*x + 1.0, sin(x)) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > 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_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5_g, > array_tmp5, > array_tmp6, > array_tmp7, > array_tmp8, > array_tmp9, > array_tmp10_g, > array_tmp10, > array_tmp11, > array_tmp12, > array_tmp13, > array_tmp14, > array_tmp15, > array_tmp16, > array_tmp17, > 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/expt_lin_sin_newpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = expt ( 2.0 * x + 1.0 , sin ( x ) ) * ( cos ( x ) * ln ( 2.0* x + 1.0 )+ ( 2.0 * sin ( x ) ) / ( 2.0 * 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 := 0.1;"); > 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 := 1000000;"); > omniout_str(ALWAYS,"glob_max_h := 0.00001;"); > 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(expt(2.0*x+1.0,sin(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3_g:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4_c1:= Array(0..(max_terms + 1),[]); > array_tmp4_a1:= Array(0..(max_terms + 1),[]); > array_tmp4_a2:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5_g:= 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_tmp10_g:= Array(0..(max_terms + 1),[]); > array_tmp10:= Array(0..(max_terms + 1),[]); > array_tmp11:= Array(0..(max_terms + 1),[]); > array_tmp12:= Array(0..(max_terms + 1),[]); > array_tmp13:= Array(0..(max_terms + 1),[]); > array_tmp14:= Array(0..(max_terms + 1),[]); > array_tmp15:= Array(0..(max_terms + 1),[]); > array_tmp16:= Array(0..(max_terms + 1),[]); > array_tmp17:= 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_g[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_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4_a2[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_g[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_tmp10_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := 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_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3_g[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_c1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_a2[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_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5_g[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_tmp10_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp10_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp10 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp10[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp11 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp11[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp12 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp12[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp13 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp13[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp14 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp14[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp15 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp15[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp16 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp16[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp17 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp17[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_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 := 0.1; > x_end := 1.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > glob_max_h := 0.00001; > #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 ) = expt ( 2.0 * x + 1.0 , sin ( x ) ) * ( cos ( x ) * ln ( 2.0* x + 1.0 )+ ( 2.0 * sin ( x ) ) / ( 2.0 * 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,"2013-05-26T01:24:05-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"expt_lin_sin_new") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = expt ( 2.0 * x + 1.0 , sin ( x ) ) * ( cos ( x ) * ln ( 2.0* x + 1.0 )+ ( 2.0 * sin ( x ) ) / ( 2.0 * 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,"expt_lin_sin_new diffeq.mxt") > ; > logitem_str(html_log_file,"expt_lin_sin_new 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_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5_g, array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10_g, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16, array_tmp17, 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/expt_lin_sin_newpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt ( 2.0 * x + 1.0 , sin \ ( x ) ) * ( cos ( x ) * ln ( 2.0* x + 1.0 )+ ( 2.0 * sin ( x ) )\ / ( 2.0 * 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 := 0.1;"); 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 := 1000000;"); omniout_str(ALWAYS, "glob_max_h := 0.00001;"); 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(expt(2.0*x+1.0,sin(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3_g := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4_c1 := Array(0 .. max_terms + 1, []); array_tmp4_a1 := Array(0 .. max_terms + 1, []); array_tmp4_a2 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5_g := 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_tmp10_g := Array(0 .. max_terms + 1, []); array_tmp10 := Array(0 .. max_terms + 1, []); array_tmp11 := Array(0 .. max_terms + 1, []); array_tmp12 := Array(0 .. max_terms + 1, []); array_tmp13 := Array(0 .. max_terms + 1, []); array_tmp14 := Array(0 .. max_terms + 1, []); array_tmp15 := Array(0 .. max_terms + 1, []); array_tmp16 := Array(0 .. max_terms + 1, []); array_tmp17 := 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_g[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_c1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_a2[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_g[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_tmp10_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp10[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp11[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp12[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp13[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp14[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp15[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp16[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp17[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := 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_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3_g[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_c1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_c1[term] := 0.; term := term + 1 end do; array_tmp4_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_a1[term] := 0.; term := term + 1 end do; array_tmp4_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_a2[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_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5_g[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_tmp10_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10_g[term] := 0.; term := term + 1 end do; array_tmp10 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp10[term] := 0.; term := term + 1 end do; array_tmp11 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp11[term] := 0.; term := term + 1 end do; array_tmp12 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp12[term] := 0.; term := term + 1 end do; array_tmp13 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp13[term] := 0.; term := term + 1 end do; array_tmp14 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp14[term] := 0.; term := term + 1 end do; array_tmp15 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp15[term] := 0.; term := term + 1 end do; array_tmp16 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp16[term] := 0.; term := term + 1 end do; array_tmp17 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp17[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_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 := 0.1; x_end := 1.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_max_h := 0.00001; 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 ) = expt ( 2.0 * x + 1.0 , si\ n ( x ) ) * ( cos ( x ) * ln ( 2.0* x + 1.0 )+ ( 2.0 * sin (\ x ) ) / ( 2.0 * 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, "2013-05-26T01:24:05-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "expt_lin_sin_new"); logitem_str(html_log_file, "diff ( y , x , 1 ) = expt ( 2.0 *\ x + 1.0 , sin ( x ) ) * ( cos ( x ) * ln ( 2.0* x + 1.0\ )+ ( 2.0 * sin ( x ) ) / ( 2.0 * 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, "expt_lin_sin_new diffeq.mxt"); logitem_str(html_log_file, "expt_lin_sin_new 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/expt_lin_sin_newpostode.ode################# diff ( y , x , 1 ) = expt ( 2.0 * x + 1.0 , sin ( x ) ) * ( cos ( x ) * ln ( 2.0* x + 1.0 )+ ( 2.0 * sin ( x ) ) / ( 2.0 * x + 1.0 ) ); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 1.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_max_h := 0.00001; #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(expt(2.0*x+1.0,sin(x))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.9 estimated_steps = 900000 step_error = 1.1111111111111111111111111111111e-16 est_needed_step_err = 1.1111111111111111111111111111111e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0318900514724224979569277853977e-152 estimated_step_error = 1.0318900514724224979569277853977e-152 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 = 1.6681238136644616876934102340032e-144 estimated_step_error = 1.6681238136644616876934102340032e-144 best_h = 4.00e-06 opt_iter = 3 bytes used=4000004, alloc=2883056, time=0.12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1194571309197240476269175333955e-136 estimated_step_error = 1.1194571309197240476269175333955e-136 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 = 7.5125253346803874883867670952866e-129 estimated_step_error = 7.5125253346803874883867670952866e-129 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 = 5.0415377944308556393866414083964e-121 estimated_step_error = 5.0415377944308556393866414083964e-121 best_h = 1e-05 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.0183684460594404010081485732561 y[1] (numeric) = 1.0183684460594404010081485732561 absolute error = 0 relative error = 0 % Correct digits = 32 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6055 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 = 0.675 Order of pole (six term test) = 0.02195 bytes used=8001532, alloc=4062488, time=0.24 bytes used=12002448, alloc=4324584, time=0.37 bytes used=16003820, alloc=4390108, time=0.50 bytes used=20004688, alloc=4390108, time=0.62 bytes used=24005632, alloc=4455632, time=0.75 bytes used=28006608, alloc=4455632, time=0.88 bytes used=32007768, alloc=4521156, time=1.01 bytes used=36008548, alloc=4521156, time=1.14 bytes used=40011028, alloc=4521156, time=1.27 bytes used=44011948, alloc=4521156, time=1.40 bytes used=48012724, alloc=4521156, time=1.53 bytes used=52013416, alloc=4521156, time=1.66 bytes used=56014504, alloc=4586680, time=1.79 bytes used=60015536, alloc=4586680, time=1.92 bytes used=64016688, alloc=4586680, time=2.05 bytes used=68017676, alloc=4586680, time=2.18 bytes used=72018900, alloc=4586680, time=2.31 bytes used=76020112, alloc=4586680, time=2.44 bytes used=80021120, alloc=4586680, time=2.57 bytes used=84022132, alloc=4586680, time=2.70 bytes used=88023388, alloc=4586680, time=2.83 bytes used=92024364, alloc=4586680, time=2.96 bytes used=96025384, alloc=4586680, time=3.09 bytes used=100026612, alloc=4586680, time=3.22 bytes used=104027788, alloc=4652204, time=3.34 bytes used=108028700, alloc=4652204, time=3.47 bytes used=112029776, alloc=4652204, time=3.60 bytes used=116031248, alloc=4652204, time=3.73 bytes used=120031900, alloc=4652204, time=3.87 bytes used=124034308, alloc=4652204, time=4.00 bytes used=128035328, alloc=4652204, time=4.13 bytes used=132036112, alloc=4652204, time=4.26 bytes used=136037024, alloc=4652204, time=4.39 bytes used=140038172, alloc=4652204, time=4.52 bytes used=144039712, alloc=4652204, time=4.65 bytes used=148040632, alloc=4652204, time=4.78 bytes used=152041668, alloc=4652204, time=4.91 bytes used=156042916, alloc=4652204, time=5.04 bytes used=160043656, alloc=4652204, time=5.17 bytes used=164044564, alloc=4652204, time=5.30 bytes used=168045768, alloc=4652204, time=5.43 bytes used=172046552, alloc=4652204, time=5.56 bytes used=176047584, alloc=4652204, time=5.69 bytes used=180048736, alloc=4652204, time=5.82 bytes used=184049640, alloc=4652204, time=5.95 bytes used=188051448, alloc=4652204, time=6.08 bytes used=192052804, alloc=4652204, time=6.21 bytes used=196054260, alloc=4652204, time=6.35 bytes used=200055608, alloc=4652204, time=6.48 bytes used=204056536, alloc=4652204, time=6.61 bytes used=208057888, alloc=4652204, time=6.74 bytes used=212059200, alloc=4652204, time=6.87 bytes used=216060352, alloc=4652204, time=6.99 bytes used=220061344, alloc=4652204, time=7.12 bytes used=224063740, alloc=4652204, time=7.26 bytes used=228064512, alloc=4652204, time=7.39 bytes used=232065412, alloc=4652204, time=7.52 bytes used=236067408, alloc=4652204, time=7.65 bytes used=240068648, alloc=4652204, time=7.78 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alloc=4717728, time=24.10 bytes used=744225924, alloc=4717728, time=24.23 bytes used=748226720, alloc=4717728, time=24.36 bytes used=752227872, alloc=4717728, time=24.50 bytes used=756229188, alloc=4717728, time=24.63 bytes used=760232680, alloc=4717728, time=24.76 bytes used=764233712, alloc=4717728, time=24.89 bytes used=768234772, alloc=4717728, time=25.02 bytes used=772235632, alloc=4717728, time=25.15 bytes used=776237216, alloc=4717728, time=25.28 bytes used=780238220, alloc=4717728, time=25.41 bytes used=784239180, alloc=4717728, time=25.54 bytes used=788240336, alloc=4717728, time=25.67 bytes used=792241112, alloc=4717728, time=25.80 bytes used=796241904, alloc=4717728, time=25.93 bytes used=800242696, alloc=4717728, time=26.06 bytes used=804243840, alloc=4717728, time=26.19 bytes used=808245464, alloc=4717728, time=26.32 bytes used=812246268, alloc=4717728, time=26.46 bytes used=816247032, alloc=4717728, time=26.59 bytes used=820248328, alloc=4717728, time=26.72 bytes used=824249564, alloc=4717728, time=26.85 bytes used=828250612, alloc=4717728, time=26.98 bytes used=832251832, alloc=4717728, time=27.11 bytes used=836252504, alloc=4717728, time=27.24 bytes used=840253288, alloc=4717728, time=27.37 bytes used=844255320, alloc=4717728, time=27.50 bytes used=848256208, alloc=4717728, time=27.63 bytes used=852257292, alloc=4717728, time=27.76 bytes used=856258608, alloc=4717728, time=27.89 bytes used=860259652, alloc=4717728, time=28.02 bytes used=864260788, alloc=4717728, time=28.15 bytes used=868261740, alloc=4717728, time=28.28 bytes used=872262820, alloc=4717728, time=28.42 bytes used=876263772, alloc=4717728, time=28.55 bytes used=880264752, alloc=4717728, time=28.68 bytes used=884265828, alloc=4717728, time=28.81 bytes used=888267024, alloc=4717728, time=28.94 TOP MAIN SOLVE Loop bytes used=892267924, alloc=4717728, time=29.07 x[1] = 0.11 y[1] (analytic) = 1.0220695163631402783684403429253 y[1] (numeric) = 1.0220695163649084843882526158594 absolute error = 1.7682060198122729341e-12 relative error = 1.7300252003446222548940957754466e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6247 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 = 0.6913 Order of pole (six term test) = 0.2368 bytes used=896268980, alloc=4717728, time=29.20 bytes used=900270432, alloc=4717728, time=29.34 bytes used=904271080, alloc=4717728, time=29.47 bytes used=908272192, alloc=4717728, time=29.60 bytes used=912273424, alloc=4717728, time=29.73 bytes used=916274492, alloc=4717728, time=29.86 bytes used=920275440, alloc=4717728, time=29.99 bytes used=924276384, alloc=4717728, time=30.12 bytes used=928277456, alloc=4717728, time=30.26 bytes used=932278352, alloc=4717728, time=30.39 bytes used=936279980, alloc=4717728, time=30.52 bytes used=940281040, alloc=4717728, time=30.65 bytes used=944281940, 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used=1516446936, alloc=4783252, time=49.52 bytes used=1520448764, alloc=4783252, time=49.65 bytes used=1524449636, alloc=4783252, time=49.78 bytes used=1528451484, alloc=4783252, time=49.91 bytes used=1532452300, alloc=4783252, time=50.04 bytes used=1536453236, alloc=4783252, time=50.17 bytes used=1540454244, alloc=4783252, time=50.30 bytes used=1544455268, alloc=4783252, time=50.43 bytes used=1548456572, alloc=4783252, time=50.56 bytes used=1552457720, alloc=4783252, time=50.69 bytes used=1556458932, alloc=4783252, time=50.82 bytes used=1560460368, alloc=4783252, time=50.95 bytes used=1564461012, alloc=4783252, time=51.08 bytes used=1568462184, alloc=4783252, time=51.21 bytes used=1572463076, alloc=4783252, time=51.34 bytes used=1576464052, alloc=4783252, time=51.48 bytes used=1580467792, alloc=4783252, time=51.61 bytes used=1584468796, alloc=4783252, time=51.74 bytes used=1588469680, alloc=4783252, time=51.87 bytes used=1592470456, alloc=4783252, time=52.00 bytes used=1596471340, alloc=4783252, time=52.13 bytes used=1600473864, alloc=4783252, time=52.26 bytes used=1604475168, alloc=4783252, time=52.39 bytes used=1608476188, alloc=4783252, time=52.52 bytes used=1612477200, alloc=4783252, time=52.65 bytes used=1616478132, alloc=4783252, time=52.78 bytes used=1620479420, alloc=4783252, time=52.92 bytes used=1624480268, alloc=4783252, time=53.05 bytes used=1628481284, alloc=4783252, time=53.18 bytes used=1632482264, alloc=4783252, time=53.31 bytes used=1636483164, alloc=4783252, time=53.44 bytes used=1640484216, alloc=4783252, time=53.57 bytes used=1644485152, alloc=4783252, time=53.70 bytes used=1648486200, alloc=4783252, time=53.83 bytes used=1652487016, alloc=4783252, time=53.97 bytes used=1656488424, alloc=4783252, time=54.10 bytes used=1660489928, alloc=4783252, time=54.23 bytes used=1664490892, alloc=4783252, time=54.36 bytes used=1668492076, alloc=4783252, time=54.49 bytes used=1672493176, alloc=4783252, time=54.62 bytes used=1676494060, alloc=4783252, time=54.76 bytes used=1680495436, alloc=4783252, time=54.89 bytes used=1684496540, alloc=4783252, time=55.02 bytes used=1688497396, alloc=4783252, time=55.15 bytes used=1692498560, alloc=4783252, time=55.28 bytes used=1696499416, alloc=4783252, time=55.41 bytes used=1700500632, alloc=4783252, time=55.54 bytes used=1704501552, alloc=4783252, time=55.67 bytes used=1708502924, alloc=4783252, time=55.80 bytes used=1712504136, alloc=4783252, time=55.93 bytes used=1716505864, alloc=4783252, time=56.06 bytes used=1720506656, alloc=4783252, time=56.19 bytes used=1724507656, alloc=4783252, time=56.32 bytes used=1728508588, alloc=4783252, time=56.45 bytes used=1732509420, alloc=4783252, time=56.59 bytes used=1736510564, alloc=4783252, time=56.72 bytes used=1740511668, alloc=4783252, time=56.85 bytes used=1744512444, alloc=4783252, time=56.98 bytes used=1748513672, alloc=4783252, time=57.11 bytes used=1752514872, alloc=4783252, time=57.24 bytes used=1756515864, alloc=4783252, time=57.37 bytes used=1760516664, alloc=4783252, time=57.50 bytes used=1764517568, alloc=4783252, time=57.63 bytes used=1768518572, alloc=4783252, time=57.76 bytes used=1772519724, alloc=4783252, time=57.89 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 1.0260858914075993513803283482295 y[1] (numeric) = 1.0260858914093675574001406211619 absolute error = 1.7682060198122729324e-12 relative error = 1.7232534182753673170300190943162e-10 % Correct digits = 12 h = 1e-05 bytes used=1776521208, alloc=4783252, time=58.03 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.635 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 = 0.7032 Order of pole (six term test) = 0.2358 bytes used=1780522352, alloc=4783252, time=58.16 bytes used=1784525280, alloc=4783252, time=58.29 bytes used=1788525960, alloc=4783252, time=58.42 bytes used=1792527840, alloc=4783252, time=58.55 bytes used=1796528644, alloc=4783252, time=58.69 bytes used=1800532204, alloc=4783252, time=58.81 bytes used=1804533208, alloc=4783252, time=58.95 bytes used=1808534392, alloc=4783252, time=59.08 bytes used=1812535360, alloc=4783252, time=59.21 bytes used=1816536640, alloc=4783252, time=59.34 bytes used=1820537664, alloc=4783252, time=59.47 bytes used=1824538404, alloc=4783252, time=59.60 bytes used=1828539512, alloc=4783252, time=59.73 bytes used=1832540420, alloc=4783252, time=59.86 bytes used=1836541328, alloc=4783252, time=60.00 bytes used=1840542268, alloc=4783252, time=60.13 bytes used=1844543308, alloc=4783252, time=60.26 bytes used=1848544480, alloc=4783252, time=60.39 bytes used=1852545660, alloc=4783252, time=60.52 bytes used=1856547564, alloc=4783252, time=60.65 bytes used=1860548424, alloc=4783252, time=60.79 bytes used=1864549224, alloc=4783252, time=60.92 bytes used=1868550772, alloc=4783252, time=61.05 bytes used=1872551908, alloc=4783252, time=61.18 bytes used=1876552804, alloc=4783252, time=61.31 bytes used=1880554272, alloc=4783252, time=61.44 bytes used=1884555328, alloc=4783252, time=61.57 bytes used=1888556376, alloc=4783252, time=61.70 bytes used=1892557476, alloc=4783252, time=61.83 bytes used=1896559300, alloc=4783252, time=61.96 bytes used=1900560252, alloc=4783252, time=62.09 bytes used=1904561340, alloc=4783252, time=62.23 bytes used=1908562264, alloc=4783252, time=62.36 bytes used=1912563568, alloc=4783252, time=62.49 bytes used=1916564932, alloc=4783252, time=62.62 bytes used=1920566052, alloc=4783252, time=62.75 bytes used=1924566812, alloc=4783252, time=62.88 bytes used=1928567728, alloc=4783252, time=63.01 bytes used=1932568604, alloc=4783252, time=63.14 bytes used=1936569532, alloc=4783252, time=63.27 bytes used=1940570792, alloc=4783252, time=63.40 bytes used=1944571828, alloc=4783252, time=63.53 bytes used=1948573036, alloc=4783252, time=63.66 bytes used=1952573900, alloc=4783252, time=63.80 bytes used=1956575060, alloc=4783252, time=63.92 bytes used=1960575988, alloc=4783252, time=64.06 bytes used=1964577220, alloc=4783252, time=64.19 bytes used=1968578348, alloc=4783252, time=64.32 bytes used=1972579316, alloc=4783252, time=64.45 bytes used=1976580116, alloc=4783252, time=64.58 bytes used=1980581376, alloc=4783252, time=64.72 bytes used=1984582520, alloc=4783252, time=64.85 bytes used=1988583552, alloc=4783252, time=64.98 bytes used=1992584520, alloc=4783252, time=65.11 bytes used=1996585340, alloc=4783252, time=65.24 bytes used=2000586328, alloc=4783252, time=65.37 bytes used=2004587356, alloc=4783252, time=65.50 bytes used=2008588588, alloc=4783252, time=65.63 bytes used=2012589316, alloc=4783252, time=65.77 bytes used=2016590284, alloc=4783252, time=65.90 bytes used=2020591852, alloc=4783252, time=66.03 bytes used=2024592840, alloc=4783252, time=66.16 bytes used=2028593964, alloc=4783252, time=66.30 bytes used=2032594784, alloc=4783252, time=66.43 bytes used=2036595888, alloc=4783252, time=66.56 bytes used=2040596856, alloc=4783252, time=66.69 bytes used=2044597836, alloc=4783252, time=66.82 bytes used=2048599864, alloc=4783252, time=66.95 bytes used=2052602004, alloc=4783252, time=67.08 bytes used=2056603292, alloc=4783252, time=67.21 bytes used=2060604104, alloc=4783252, time=67.34 bytes used=2064606128, alloc=4783252, time=67.47 bytes used=2068607240, alloc=4783252, time=67.60 bytes used=2072609112, alloc=4783252, time=67.74 bytes used=2076610128, alloc=4783252, time=67.87 bytes used=2080611132, alloc=4783252, time=68.00 bytes used=2084612440, alloc=4783252, time=68.13 bytes used=2088613428, alloc=4783252, time=68.26 bytes used=2092614160, alloc=4783252, time=68.39 bytes used=2096615380, alloc=4783252, time=68.52 bytes used=2100616524, alloc=4783252, time=68.65 bytes used=2104617612, alloc=4783252, time=68.78 bytes used=2108618868, alloc=4783252, time=68.92 bytes used=2112619764, alloc=4783252, time=69.05 bytes used=2116620800, alloc=4783252, time=69.18 bytes used=2120621712, alloc=4783252, time=69.31 bytes used=2124623000, alloc=4783252, time=69.44 bytes used=2128624084, alloc=4783252, time=69.57 bytes used=2132624952, alloc=4783252, time=69.70 bytes used=2136625768, alloc=4783252, time=69.83 bytes used=2140626972, alloc=4783252, time=69.96 bytes used=2144628052, alloc=4783252, time=70.10 bytes used=2148629592, alloc=4783252, time=70.23 bytes used=2152630588, alloc=4783252, time=70.36 bytes used=2156632700, alloc=4783252, time=70.49 bytes used=2160633732, alloc=4783252, time=70.62 bytes used=2164634700, alloc=4783252, time=70.75 bytes used=2168635572, alloc=4783252, time=70.88 bytes used=2172636752, alloc=4783252, time=71.02 bytes used=2176638928, alloc=4783252, time=71.15 bytes used=2180639740, alloc=4783252, time=71.28 bytes used=2184640768, alloc=4783252, time=71.41 bytes used=2188641844, alloc=4783252, time=71.54 bytes used=2192642712, alloc=4783252, time=71.67 bytes used=2196643468, alloc=4783252, time=71.81 bytes used=2200644408, alloc=4783252, time=71.94 bytes used=2204645560, alloc=4783252, time=72.07 bytes used=2208646904, alloc=4783252, time=72.21 bytes used=2212648200, alloc=4783252, time=72.34 bytes used=2216649228, alloc=4783252, time=72.47 bytes used=2220650920, alloc=4783252, time=72.60 bytes used=2224651812, alloc=4783252, time=72.73 bytes used=2228652864, alloc=4783252, time=72.86 bytes used=2232654048, alloc=4783252, time=72.99 bytes used=2236655164, alloc=4783252, time=73.12 bytes used=2240656452, alloc=4783252, time=73.25 bytes used=2244657516, alloc=4783252, time=73.38 bytes used=2248658768, alloc=4783252, time=73.52 bytes used=2252659584, alloc=4783252, time=73.65 bytes used=2256660396, alloc=4783252, time=73.78 bytes used=2260661540, alloc=4783252, time=73.91 bytes used=2264662536, alloc=4783252, time=74.04 bytes used=2268664048, alloc=4783252, time=74.17 bytes used=2272664980, alloc=4783252, time=74.30 bytes used=2276666088, alloc=4783252, time=74.43 bytes used=2280667064, alloc=4783252, time=74.57 bytes used=2284668204, alloc=4783252, time=74.70 bytes used=2288669144, alloc=4783252, time=74.83 bytes used=2292670104, alloc=4783252, time=74.96 bytes used=2296671252, alloc=4783252, time=75.09 bytes used=2300672260, alloc=4783252, time=75.22 bytes used=2304673388, alloc=4783252, time=75.36 bytes used=2308675032, alloc=4783252, time=75.49 bytes used=2312675892, alloc=4783252, time=75.62 bytes used=2316676780, alloc=4783252, time=75.75 bytes used=2320678892, alloc=4783252, time=75.88 bytes used=2324680064, alloc=4783252, time=76.01 bytes used=2328681176, alloc=4783252, time=76.14 bytes used=2332682092, alloc=4783252, time=76.27 bytes used=2336683176, alloc=4783252, time=76.40 bytes used=2340684240, alloc=4783252, time=76.53 bytes used=2344685348, alloc=4783252, time=76.67 bytes used=2348686500, alloc=4783252, time=76.80 bytes used=2352687316, alloc=4783252, time=76.93 bytes used=2356688620, alloc=4783252, time=77.06 bytes used=2360689508, alloc=4783252, time=77.19 bytes used=2364690488, alloc=4783252, time=77.32 bytes used=2368691552, alloc=4783252, time=77.45 bytes used=2372692484, alloc=4783252, time=77.59 bytes used=2376693272, alloc=4783252, time=77.72 bytes used=2380694316, alloc=4783252, time=77.85 bytes used=2384695088, alloc=4783252, time=77.99 bytes used=2388696596, alloc=4783252, time=78.12 bytes used=2392697592, alloc=4783252, time=78.25 bytes used=2396698752, alloc=4783252, time=78.38 bytes used=2400699804, alloc=4783252, time=78.51 bytes used=2404701048, alloc=4783252, time=78.64 bytes used=2408701932, alloc=4783252, time=78.77 bytes used=2412702880, alloc=4783252, time=78.90 bytes used=2416704232, alloc=4783252, time=79.03 bytes used=2420705820, alloc=4783252, time=79.16 bytes used=2424707192, alloc=4783252, time=79.29 bytes used=2428709860, alloc=4783252, time=79.42 bytes used=2432710600, alloc=4783252, time=79.56 bytes used=2436711500, alloc=4783252, time=79.69 bytes used=2440712340, alloc=4783252, time=79.82 bytes used=2444713020, alloc=4783252, time=79.95 bytes used=2448714024, alloc=4783252, time=80.08 bytes used=2452715144, alloc=4783252, time=80.22 bytes used=2456717644, alloc=4783252, time=80.35 bytes used=2460718440, alloc=4783252, time=80.48 bytes used=2464719780, alloc=4783252, time=80.61 bytes used=2468721104, alloc=4783252, time=80.74 bytes used=2472722088, alloc=4783252, time=80.87 bytes used=2476723028, alloc=4848776, time=81.00 bytes used=2480727104, alloc=4848776, time=81.13 bytes used=2484728120, alloc=4848776, time=81.26 bytes used=2488729116, alloc=4848776, time=81.39 bytes used=2492729876, alloc=4848776, time=81.53 bytes used=2496730860, alloc=4848776, time=81.66 bytes used=2500731740, alloc=4848776, time=81.79 bytes used=2504732880, alloc=4848776, time=81.92 bytes used=2508733660, alloc=4848776, time=82.05 bytes used=2512735120, alloc=4848776, time=82.18 bytes used=2516736588, alloc=4848776, time=82.31 bytes used=2520737380, alloc=4848776, time=82.45 bytes used=2524738404, alloc=4848776, time=82.58 bytes used=2528739184, alloc=4848776, time=82.71 bytes used=2532740124, alloc=4848776, time=82.84 bytes used=2536741128, alloc=4848776, time=82.97 bytes used=2540742520, alloc=4848776, time=83.10 bytes used=2544743680, alloc=4848776, time=83.23 bytes used=2548744832, alloc=4848776, time=83.37 bytes used=2552745756, alloc=4848776, time=83.50 bytes used=2556749880, alloc=4848776, time=83.63 bytes used=2560750732, alloc=4848776, time=83.76 bytes used=2564752088, alloc=4848776, time=83.89 bytes used=2568753180, alloc=4848776, time=84.02 bytes used=2572754296, alloc=4848776, time=84.15 bytes used=2576755352, alloc=4848776, time=84.28 bytes used=2580756512, alloc=4848776, time=84.42 bytes used=2584757388, alloc=4848776, time=84.55 bytes used=2588758380, alloc=4848776, time=84.68 bytes used=2592759388, alloc=4848776, time=84.81 bytes used=2596760828, alloc=4848776, time=84.94 bytes used=2600763420, alloc=4848776, time=85.07 bytes used=2604764312, alloc=4848776, time=85.20 bytes used=2608765408, alloc=4848776, time=85.34 bytes used=2612766608, alloc=4848776, time=85.47 bytes used=2616767880, alloc=4848776, time=85.60 bytes used=2620769024, alloc=4848776, time=85.73 bytes used=2624770356, alloc=4848776, time=85.86 bytes used=2628771484, alloc=4848776, time=85.99 bytes used=2632772532, alloc=4848776, time=86.12 bytes used=2636773432, alloc=4848776, time=86.25 bytes used=2640775048, alloc=4848776, time=86.38 bytes used=2644776168, alloc=4848776, time=86.51 bytes used=2648777020, alloc=4848776, time=86.64 bytes used=2652779176, alloc=4848776, time=86.78 bytes used=2656780448, alloc=4848776, time=86.91 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 1.0304132854743725006293351711328 y[1] (numeric) = 1.0304132854761407066491474440635 absolute error = 1.7682060198122729307e-12 relative error = 1.7160163254283372086820451656389e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6452 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 = 0.715 Order of pole (six term test) = 0.2348 bytes used=2660781340, alloc=4848776, time=87.04 bytes used=2664782252, alloc=4848776, time=87.17 bytes used=2668783188, alloc=4848776, time=87.30 bytes used=2672784292, alloc=4848776, time=87.44 bytes used=2676785216, alloc=4848776, time=87.57 bytes used=2680786412, alloc=4848776, time=87.70 bytes used=2684787412, alloc=4848776, time=87.83 bytes used=2688788352, alloc=4848776, time=87.96 bytes used=2692789444, alloc=4848776, time=88.09 bytes used=2696790476, alloc=4848776, time=88.22 bytes used=2700792860, alloc=4848776, time=88.36 bytes used=2704793800, alloc=4848776, time=88.49 bytes used=2708794592, alloc=4848776, time=88.62 bytes used=2712795624, alloc=4848776, time=88.75 bytes used=2716797308, alloc=4848776, time=88.88 bytes used=2720798380, alloc=4848776, time=89.01 bytes used=2724799484, alloc=4848776, time=89.15 bytes used=2728800816, alloc=4848776, time=89.28 bytes used=2732803132, alloc=4848776, time=89.41 bytes used=2736804080, alloc=4848776, time=89.54 bytes used=2740804980, alloc=4848776, time=89.67 bytes used=2744806004, alloc=4848776, time=89.81 bytes used=2748806796, alloc=4848776, time=89.94 bytes used=2752807692, alloc=4848776, time=90.07 bytes used=2756808452, alloc=4848776, time=90.20 bytes used=2760809412, alloc=4848776, time=90.33 bytes used=2764810628, alloc=4848776, time=90.46 bytes used=2768813152, alloc=4848776, time=90.59 bytes used=2772814264, alloc=4848776, time=90.72 bytes used=2776815540, alloc=4848776, time=90.85 bytes used=2780816376, alloc=4848776, time=90.99 bytes used=2784817744, alloc=4848776, time=91.12 bytes used=2788818620, alloc=4848776, time=91.25 bytes used=2792819524, alloc=4848776, time=91.38 bytes used=2796821040, alloc=4848776, time=91.51 bytes used=2800822372, alloc=4848776, time=91.64 bytes used=2804823316, alloc=4848776, time=91.77 bytes used=2808824232, alloc=4848776, time=91.90 bytes used=2812825376, alloc=4848776, time=92.04 bytes used=2816826884, alloc=4848776, time=92.17 bytes used=2820828244, alloc=4848776, time=92.30 bytes used=2824829664, alloc=4848776, time=92.43 bytes used=2828830800, alloc=4848776, time=92.56 bytes used=2832831724, alloc=4848776, time=92.70 bytes used=2836833556, alloc=4848776, time=92.83 bytes used=2840834572, alloc=4848776, time=92.96 bytes used=2844835756, alloc=4848776, time=93.09 bytes used=2848836652, alloc=4848776, time=93.22 bytes used=2852837724, alloc=4848776, time=93.35 bytes used=2856838572, alloc=4848776, time=93.48 bytes used=2860839680, alloc=4848776, time=93.62 bytes used=2864840636, alloc=4848776, time=93.75 bytes used=2868841828, alloc=4848776, time=93.87 bytes used=2872843368, alloc=4848776, time=94.01 bytes used=2876844808, alloc=4848776, time=94.14 bytes used=2880845796, alloc=4848776, time=94.27 bytes used=2884846604, alloc=4848776, time=94.40 bytes used=2888847644, alloc=4848776, time=94.53 bytes used=2892849104, alloc=4848776, time=94.66 bytes used=2896850584, alloc=4848776, time=94.79 bytes used=2900851284, alloc=4848776, time=94.93 bytes used=2904852404, alloc=4848776, time=95.06 bytes used=2908853328, alloc=4848776, time=95.19 bytes used=2912854668, alloc=4848776, time=95.32 bytes used=2916855764, alloc=4848776, time=95.45 bytes used=2920857096, alloc=4848776, time=95.59 bytes used=2924857908, alloc=4848776, time=95.72 bytes used=2928858740, alloc=4848776, time=95.85 bytes used=2932859672, alloc=4848776, time=95.98 bytes used=2936861344, alloc=4848776, time=96.12 bytes used=2940862428, alloc=4848776, time=96.25 bytes used=2944863272, alloc=4848776, time=96.38 bytes used=2948864316, alloc=4848776, time=96.51 bytes used=2952865380, alloc=4848776, time=96.64 bytes used=2956866440, alloc=4848776, time=96.77 bytes used=2960867960, alloc=4848776, time=96.91 bytes used=2964871388, alloc=4848776, time=97.04 bytes used=2968872304, alloc=4848776, time=97.17 bytes used=2972873320, alloc=4848776, time=97.30 bytes used=2976874360, alloc=4848776, time=97.43 bytes used=2980875816, alloc=4848776, time=97.56 bytes used=2984876620, alloc=4848776, time=97.69 bytes used=2988878244, alloc=4848776, time=97.82 bytes used=2992880796, alloc=4848776, time=97.95 bytes used=2996881588, alloc=4848776, time=98.09 bytes used=3000883280, alloc=4848776, time=98.22 bytes used=3004884516, alloc=4848776, time=98.35 bytes used=3008885520, alloc=4848776, time=98.48 bytes used=3012886292, alloc=4848776, time=98.61 bytes used=3016887364, alloc=4848776, time=98.74 bytes used=3020888188, alloc=4848776, time=98.87 bytes used=3024890252, alloc=4848776, time=99.01 bytes used=3028891692, alloc=4848776, time=99.14 bytes used=3032892396, alloc=4848776, time=99.27 bytes used=3036893256, alloc=4848776, time=99.40 bytes used=3040894720, alloc=4848776, time=99.53 bytes used=3044895524, alloc=4848776, time=99.66 bytes used=3048897036, alloc=4848776, time=99.79 bytes used=3052897828, alloc=4848776, time=99.92 bytes used=3056898712, alloc=4848776, time=100.06 bytes used=3060901080, alloc=4848776, time=100.19 bytes used=3064902080, alloc=4848776, time=100.32 bytes used=3068903008, alloc=4848776, time=100.45 bytes used=3072903956, alloc=4848776, time=100.58 bytes used=3076905108, alloc=4848776, time=100.72 bytes used=3080906008, alloc=4848776, time=100.85 bytes used=3084907148, alloc=4848776, time=100.98 bytes used=3088908228, alloc=4848776, time=101.11 bytes used=3092911048, alloc=4848776, time=101.24 bytes used=3096912864, alloc=4848776, time=101.37 bytes used=3100914720, alloc=4848776, time=101.51 bytes used=3104915668, alloc=4848776, time=101.64 bytes used=3108916720, alloc=4848776, time=101.77 bytes used=3112917668, alloc=4848776, time=101.91 bytes used=3116918792, alloc=4848776, time=102.04 bytes used=3120919744, alloc=4848776, time=102.17 bytes used=3124920744, alloc=4848776, time=102.30 bytes used=3128921688, alloc=4848776, time=102.43 bytes used=3132922624, alloc=4848776, time=102.56 bytes used=3136923920, alloc=4848776, time=102.70 bytes used=3140925076, alloc=4848776, time=102.83 bytes used=3144928024, alloc=4848776, time=102.96 bytes used=3148928856, alloc=4848776, time=103.09 bytes used=3152932452, alloc=4848776, time=103.22 bytes used=3156933328, alloc=4848776, time=103.35 bytes used=3160934548, alloc=4848776, time=103.48 bytes used=3164935712, alloc=4848776, time=103.62 bytes used=3168938452, alloc=4848776, time=103.75 bytes used=3172940808, alloc=4848776, time=103.88 bytes used=3176941604, alloc=4848776, time=104.01 bytes used=3180942540, alloc=4848776, time=104.14 bytes used=3184943644, alloc=4848776, time=104.27 bytes used=3188944580, alloc=4848776, time=104.41 bytes used=3192945624, alloc=4848776, time=104.53 bytes used=3196946324, alloc=4848776, time=104.67 bytes used=3200947200, alloc=4848776, time=104.80 bytes used=3204948396, alloc=4848776, time=104.93 bytes used=3208949324, alloc=4848776, time=105.06 bytes used=3212950360, alloc=4848776, time=105.19 bytes used=3216952604, alloc=4848776, time=105.32 bytes used=3220953756, alloc=4848776, time=105.46 bytes used=3224954684, alloc=4848776, time=105.59 bytes used=3228955748, alloc=4848776, time=105.72 bytes used=3232956708, alloc=4848776, time=105.85 bytes used=3236958132, alloc=4848776, time=105.98 bytes used=3240959496, alloc=4848776, time=106.11 bytes used=3244961852, alloc=4848776, time=106.25 bytes used=3248962712, alloc=4848776, time=106.38 bytes used=3252963816, alloc=4848776, time=106.51 bytes used=3256964664, alloc=4848776, time=106.64 bytes used=3260965672, alloc=4848776, time=106.77 bytes used=3264966664, alloc=4848776, time=106.90 bytes used=3268967780, alloc=4848776, time=107.03 bytes used=3272969060, alloc=4848776, time=107.16 bytes used=3276969960, alloc=4848776, time=107.29 bytes used=3280972456, alloc=4848776, time=107.43 bytes used=3284973416, alloc=4848776, time=107.56 bytes used=3288974556, alloc=4848776, time=107.69 bytes used=3292975540, alloc=4848776, time=107.82 bytes used=3296976540, alloc=4848776, time=107.96 bytes used=3300977328, alloc=4848776, time=108.09 bytes used=3304978416, alloc=4848776, time=108.22 bytes used=3308979472, alloc=4848776, time=108.35 bytes used=3312980276, alloc=4848776, time=108.48 bytes used=3316981256, alloc=4848776, time=108.61 bytes used=3320982980, alloc=4848776, time=108.75 bytes used=3324983736, alloc=4848776, time=108.88 bytes used=3328984856, alloc=4848776, time=109.01 bytes used=3332985964, alloc=4848776, time=109.14 bytes used=3336987044, alloc=4848776, time=109.27 bytes used=3340988588, alloc=4848776, time=109.40 bytes used=3344989316, alloc=4848776, time=109.53 bytes used=3348990408, alloc=4848776, time=109.67 bytes used=3352991488, alloc=4848776, time=109.80 bytes used=3356992496, alloc=4848776, time=109.93 bytes used=3360993296, alloc=4848776, time=110.06 bytes used=3364995292, alloc=4848776, time=110.19 bytes used=3368996188, alloc=4848776, time=110.32 bytes used=3372997236, alloc=4848776, time=110.45 bytes used=3376998268, alloc=4848776, time=110.59 bytes used=3380999216, alloc=4848776, time=110.72 bytes used=3385000552, alloc=4848776, time=110.85 bytes used=3389001392, alloc=4848776, time=110.98 bytes used=3393002724, alloc=4848776, time=111.11 bytes used=3397003740, alloc=4848776, time=111.24 bytes used=3401004716, alloc=4848776, time=111.38 bytes used=3405005744, alloc=4848776, time=111.51 bytes used=3409007172, alloc=4848776, time=111.64 bytes used=3413009260, alloc=4848776, time=111.77 bytes used=3417010028, alloc=4848776, time=111.90 bytes used=3421010840, alloc=4848776, time=112.03 bytes used=3425012504, alloc=4848776, time=112.17 bytes used=3429013584, alloc=4848776, time=112.30 bytes used=3433014516, alloc=4848776, time=112.43 bytes used=3437015520, alloc=4848776, time=112.56 bytes used=3441016444, alloc=4848776, time=112.69 bytes used=3445017408, alloc=4848776, time=112.82 bytes used=3449018408, alloc=4848776, time=112.95 bytes used=3453019312, alloc=4848776, time=113.08 bytes used=3457020924, alloc=4848776, time=113.21 bytes used=3461021780, alloc=4848776, time=113.35 bytes used=3465022728, alloc=4848776, time=113.48 bytes used=3469023836, alloc=4848776, time=113.61 bytes used=3473024888, alloc=4848776, time=113.74 bytes used=3477028592, alloc=4848776, time=113.87 bytes used=3481029868, alloc=4848776, time=114.00 bytes used=3485030820, alloc=4848776, time=114.14 bytes used=3489031860, alloc=4848776, time=114.27 bytes used=3493032680, alloc=4848776, time=114.40 bytes used=3497033600, alloc=4848776, time=114.53 bytes used=3501034740, alloc=4848776, time=114.67 bytes used=3505035752, alloc=4848776, time=114.80 bytes used=3509036888, alloc=4848776, time=114.93 bytes used=3513037828, alloc=4848776, time=115.06 bytes used=3517038852, alloc=4848776, time=115.19 bytes used=3521039812, alloc=4848776, time=115.32 bytes used=3525041000, alloc=4848776, time=115.45 bytes used=3529041920, alloc=4848776, time=115.59 bytes used=3533042856, alloc=4848776, time=115.72 bytes used=3537045120, alloc=4848776, time=115.85 bytes used=3541046432, alloc=4848776, time=115.98 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 1.0350478154533681990734601547946 y[1] (numeric) = 1.0350478154551364050932724277223 absolute error = 1.7682060198122729277e-12 relative error = 1.7083326909276835797153951504224e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6554 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 = 0.7268 Order of pole (six term test) = 0.2338 bytes used=3545047600, alloc=4848776, time=116.11 bytes used=3549048424, alloc=4848776, time=116.24 bytes used=3553049392, alloc=4848776, time=116.37 bytes used=3557050332, alloc=4848776, time=116.50 bytes used=3561051688, alloc=4848776, time=116.64 bytes used=3565052648, alloc=4848776, time=116.77 bytes used=3569054448, alloc=4848776, time=116.90 bytes used=3573055472, alloc=4848776, time=117.03 bytes used=3577056292, alloc=4848776, time=117.17 bytes used=3581057096, alloc=4848776, time=117.30 bytes used=3585057880, alloc=4848776, time=117.43 bytes used=3589059088, alloc=4848776, time=117.56 bytes used=3593060256, alloc=4848776, time=117.69 bytes used=3597061420, alloc=4848776, time=117.82 bytes used=3601062368, alloc=4848776, time=117.96 bytes used=3605064012, alloc=4848776, time=118.09 bytes used=3609065836, alloc=4848776, time=118.22 bytes used=3613067344, alloc=4848776, time=118.35 bytes used=3617069416, alloc=4848776, time=118.48 bytes used=3621070260, alloc=4848776, time=118.61 bytes used=3625071200, alloc=4848776, time=118.74 bytes used=3629072348, alloc=4848776, time=118.88 bytes used=3633073424, alloc=4848776, time=119.01 bytes used=3637074404, alloc=4848776, time=119.14 bytes used=3641075440, alloc=4848776, time=119.27 bytes used=3645076524, alloc=4848776, time=119.41 bytes used=3649077676, alloc=4848776, time=119.54 bytes used=3653078720, alloc=4848776, time=119.67 bytes used=3657079820, alloc=4848776, time=119.81 bytes used=3661080852, alloc=4848776, time=119.94 bytes used=3665081972, alloc=4848776, time=120.07 bytes used=3669082960, alloc=4848776, time=120.20 bytes used=3673085700, alloc=4848776, time=120.34 bytes used=3677086516, alloc=4848776, time=120.47 bytes used=3681087780, alloc=4848776, time=120.60 bytes used=3685088628, alloc=4848776, time=120.73 bytes used=3689091816, alloc=4848776, time=120.86 bytes used=3693093364, alloc=4848776, time=120.99 bytes used=3697094196, alloc=4848776, time=121.12 bytes used=3701095244, alloc=4848776, time=121.26 bytes used=3705096436, alloc=4848776, time=121.39 bytes used=3709097440, alloc=4848776, time=121.51 bytes used=3713099372, alloc=4848776, time=121.64 bytes used=3717100444, alloc=4848776, time=121.78 bytes used=3721102648, alloc=4848776, time=121.91 bytes used=3725103520, alloc=4848776, time=122.04 bytes used=3729104468, alloc=4848776, time=122.17 bytes used=3733105412, alloc=4848776, time=122.30 bytes used=3737106760, alloc=4848776, time=122.44 bytes used=3741107692, alloc=4848776, time=122.57 bytes used=3745108576, alloc=4848776, time=122.70 bytes used=3749109512, alloc=4848776, time=122.83 bytes used=3753111744, alloc=4848776, time=122.96 bytes used=3757113140, alloc=4848776, time=123.09 bytes used=3761114064, alloc=4848776, time=123.22 bytes used=3765115056, alloc=4848776, time=123.36 bytes used=3769115884, alloc=4848776, time=123.49 bytes used=3773117040, alloc=4848776, time=123.62 bytes used=3777118028, alloc=4848776, time=123.75 bytes used=3781119840, alloc=4848776, time=123.88 bytes used=3785120824, alloc=4848776, time=124.02 bytes used=3789121644, alloc=4848776, time=124.15 bytes used=3793123288, alloc=4848776, time=124.28 bytes used=3797124124, alloc=4848776, time=124.41 bytes used=3801125040, alloc=4848776, time=124.54 bytes used=3805125968, alloc=4848776, time=124.68 bytes used=3809127704, alloc=4848776, time=124.81 bytes used=3813128452, alloc=4848776, time=124.94 bytes used=3817130188, alloc=4848776, time=125.07 bytes used=3821131456, alloc=4848776, time=125.20 bytes used=3825132268, alloc=4848776, time=125.34 bytes used=3829133356, alloc=4848776, time=125.47 bytes used=3833134348, alloc=4848776, time=125.60 bytes used=3837135328, alloc=4848776, time=125.73 bytes used=3841136428, alloc=4848776, time=125.87 bytes used=3845137656, alloc=4848776, time=126.00 bytes used=3849138816, alloc=4848776, time=126.13 bytes used=3853142316, alloc=4848776, time=126.26 bytes used=3857143188, alloc=4848776, time=126.39 bytes used=3861144692, alloc=4848776, time=126.52 bytes used=3865145508, alloc=4848776, time=126.65 bytes used=3869146820, alloc=4848776, time=126.78 bytes used=3873147896, alloc=4848776, time=126.92 bytes used=3877148912, alloc=4848776, time=127.05 bytes used=3881150120, alloc=4848776, time=127.18 bytes used=3885151056, alloc=4848776, time=127.31 bytes used=3889151948, alloc=4848776, time=127.44 bytes used=3893153152, alloc=4848776, time=127.58 bytes used=3897154488, alloc=4848776, time=127.71 bytes used=3901155640, alloc=4848776, time=127.84 bytes used=3905156444, alloc=4848776, time=127.97 bytes used=3909158808, alloc=4848776, time=128.10 bytes used=3913160596, alloc=4848776, time=128.24 bytes used=3917161532, alloc=4848776, time=128.37 bytes used=3921162532, alloc=4848776, time=128.50 bytes used=3925165136, alloc=4848776, time=128.63 bytes used=3929167712, alloc=4848776, time=128.76 bytes used=3933169196, alloc=4848776, time=128.89 bytes used=3937170160, alloc=4848776, time=129.02 bytes used=3941171160, alloc=4848776, time=129.16 bytes used=3945172324, alloc=4848776, time=129.29 bytes used=3949173224, alloc=4848776, time=129.42 bytes used=3953174196, alloc=4848776, time=129.55 bytes used=3957175392, alloc=4848776, time=129.68 bytes used=3961176376, alloc=4848776, time=129.81 bytes used=3965178232, alloc=4848776, time=129.94 bytes used=3969179280, alloc=4848776, time=130.08 bytes used=3973181868, alloc=4848776, time=130.21 bytes used=3977182604, alloc=4848776, time=130.34 bytes used=3981183900, alloc=4848776, time=130.47 bytes used=3985184688, alloc=4848776, time=130.60 bytes used=3989185760, alloc=4848776, time=130.74 bytes used=3993186904, alloc=4848776, time=130.87 bytes used=3997187832, alloc=4848776, time=131.00 bytes used=4001188912, alloc=4848776, time=131.13 bytes used=4005190784, alloc=4848776, time=131.26 bytes used=4009191576, alloc=4848776, time=131.39 bytes used=4013192376, alloc=4848776, time=131.52 bytes used=4017193268, alloc=4848776, time=131.65 bytes used=4021194484, alloc=4848776, time=131.78 bytes used=4025195336, alloc=4848776, time=131.91 bytes used=4029196420, alloc=4848776, time=132.05 bytes used=4033200564, alloc=4848776, time=132.18 bytes used=4037201564, alloc=4848776, time=132.31 bytes used=4041202640, alloc=4848776, time=132.44 bytes used=4045203864, alloc=4848776, time=132.57 bytes used=4049204612, alloc=4848776, time=132.70 bytes used=4053205800, alloc=4848776, time=132.84 bytes used=4057206664, alloc=4848776, time=132.97 bytes used=4061207812, alloc=4848776, time=133.10 bytes used=4065209440, alloc=4848776, time=133.23 bytes used=4069210444, alloc=4848776, time=133.36 bytes used=4073211160, alloc=4848776, time=133.49 bytes used=4077212408, alloc=4848776, time=133.62 bytes used=4081214048, alloc=4848776, time=133.76 bytes used=4085215108, alloc=4848776, time=133.89 bytes used=4089216436, alloc=4848776, time=134.02 bytes used=4093218528, alloc=4848776, time=134.15 bytes used=4097219240, alloc=4848776, time=134.28 bytes used=4101220564, alloc=4848776, time=134.41 bytes used=4105221660, alloc=4848776, time=134.54 bytes used=4109222532, alloc=4848776, time=134.68 bytes used=4113223644, alloc=4848776, time=134.81 bytes used=4117225924, alloc=4848776, time=134.94 bytes used=4121226864, alloc=4848776, time=135.07 bytes used=4125227672, alloc=4848776, time=135.20 bytes used=4129229496, alloc=4848776, time=135.33 bytes used=4133230332, alloc=4848776, time=135.46 bytes used=4137231564, alloc=4848776, time=135.59 bytes used=4141232464, alloc=4848776, time=135.73 bytes used=4145233416, alloc=4848776, time=135.86 bytes used=4149234980, alloc=4848776, time=135.99 bytes used=4153235868, alloc=4848776, time=136.12 bytes used=4157236820, alloc=4848776, time=136.25 bytes used=4161238732, alloc=4848776, time=136.38 bytes used=4165239552, alloc=4848776, time=136.51 bytes used=4169240580, alloc=4848776, time=136.64 bytes used=4173241376, alloc=4848776, time=136.77 bytes used=4177242428, alloc=4848776, time=136.90 bytes used=4181243572, alloc=4848776, time=137.04 bytes used=4185244760, alloc=4848776, time=137.17 bytes used=4189245896, alloc=4848776, time=137.30 bytes used=4193247032, alloc=4848776, time=137.44 bytes used=4197247864, alloc=4848776, time=137.57 bytes used=4201248848, alloc=4848776, time=137.70 bytes used=4205249824, alloc=4848776, time=137.83 bytes used=4209250808, alloc=4848776, time=137.96 bytes used=4213251864, alloc=4848776, time=138.10 bytes used=4217252956, alloc=4848776, time=138.23 bytes used=4221254324, alloc=4848776, time=138.36 bytes used=4225256400, alloc=4848776, time=138.49 bytes used=4229257992, alloc=4848776, time=138.62 bytes used=4233259520, alloc=4848776, time=138.75 bytes used=4237260176, alloc=4848776, time=138.88 bytes used=4241261308, alloc=4848776, time=139.02 bytes used=4245262056, alloc=4848776, time=139.14 bytes used=4249263164, alloc=4848776, time=139.28 bytes used=4253264444, alloc=4848776, time=139.41 bytes used=4257265616, alloc=4848776, time=139.54 bytes used=4261266560, alloc=4848776, time=139.67 bytes used=4265267632, alloc=4848776, time=139.80 bytes used=4269268740, alloc=4848776, time=139.94 bytes used=4273269772, alloc=4848776, time=140.07 bytes used=4277270744, alloc=4848776, time=140.20 bytes used=4281271968, alloc=4848776, time=140.33 bytes used=4285272948, alloc=4848776, time=140.46 bytes used=4289274808, alloc=4848776, time=140.59 bytes used=4293275728, alloc=4848776, time=140.72 bytes used=4297276504, alloc=4848776, time=140.86 bytes used=4301277624, alloc=4848776, time=140.99 bytes used=4305278440, alloc=4848776, time=141.12 bytes used=4309279456, alloc=4848776, time=141.25 bytes used=4313280432, alloc=4848776, time=141.38 bytes used=4317281652, alloc=4848776, time=141.51 bytes used=4321283084, alloc=4848776, time=141.64 bytes used=4325283804, alloc=4848776, time=141.77 bytes used=4329285632, alloc=4848776, time=141.91 bytes used=4333286356, alloc=4848776, time=142.04 bytes used=4337288660, alloc=4848776, time=142.17 bytes used=4341289636, alloc=4848776, time=142.30 bytes used=4345290584, alloc=4848776, time=142.43 bytes used=4349292492, alloc=4848776, time=142.56 bytes used=4353293852, alloc=4848776, time=142.70 bytes used=4357296072, alloc=4848776, time=142.83 bytes used=4361296992, alloc=4848776, time=142.96 bytes used=4365298040, alloc=4848776, time=143.09 bytes used=4369298840, alloc=4848776, time=143.22 bytes used=4373300868, alloc=4848776, time=143.36 bytes used=4377301872, alloc=4848776, time=143.49 bytes used=4381303700, alloc=4848776, time=143.62 bytes used=4385304468, alloc=4848776, time=143.75 bytes used=4389306284, alloc=4848776, time=143.88 bytes used=4393307196, alloc=4848776, time=144.02 bytes used=4397308184, alloc=4848776, time=144.15 bytes used=4401309372, alloc=4848776, time=144.28 bytes used=4405310632, alloc=4848776, time=144.41 bytes used=4409311780, alloc=4848776, time=144.54 bytes used=4413312664, alloc=4848776, time=144.67 bytes used=4417315356, alloc=4848776, time=144.80 bytes used=4421316608, alloc=4848776, time=144.93 TOP MAIN SOLVE Loop bytes used=4425317376, alloc=4848776, time=145.06 x[1] = 0.15 y[1] (analytic) = 1.0399859731534054175306843407257 y[1] (numeric) = 1.0399859731551736235504966136515 absolute error = 1.7682060198122729258e-12 relative error = 1.7002210274536556746318950861623e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6657 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 = 0.7386 Order of pole (six term test) = 0.2328 bytes used=4429318872, alloc=4848776, time=145.20 bytes used=4433319936, alloc=4848776, time=145.33 bytes used=4437321400, alloc=4848776, time=145.46 bytes used=4441322252, alloc=4848776, time=145.59 bytes used=4445323348, alloc=4848776, time=145.72 bytes used=4449325000, alloc=4848776, time=145.85 bytes used=4453326680, alloc=4848776, time=145.98 bytes used=4457327460, alloc=4848776, time=146.11 bytes used=4461328396, alloc=4848776, time=146.25 bytes used=4465329552, alloc=4848776, time=146.38 bytes used=4469330780, alloc=4848776, time=146.51 bytes used=4473331708, alloc=4848776, time=146.64 bytes used=4477333732, alloc=4848776, time=146.77 bytes used=4481334852, alloc=4848776, time=146.90 bytes used=4485335536, alloc=4848776, time=147.03 bytes used=4489336508, alloc=4848776, time=147.17 bytes used=4493337388, alloc=4848776, time=147.30 bytes used=4497338208, alloc=4848776, time=147.43 bytes used=4501339256, alloc=4848776, time=147.56 bytes used=4505340724, alloc=4848776, time=147.69 bytes used=4509341584, alloc=4848776, time=147.82 bytes used=4513343632, alloc=4848776, time=147.95 bytes used=4517344324, alloc=4848776, time=148.08 bytes used=4521345120, alloc=4848776, time=148.22 bytes used=4525346028, alloc=4848776, time=148.35 bytes used=4529346988, alloc=4848776, time=148.48 bytes used=4533348180, alloc=4848776, time=148.61 bytes used=4537351176, alloc=4848776, time=148.74 bytes used=4541352044, alloc=4848776, time=148.87 bytes used=4545353024, alloc=4848776, time=149.00 bytes used=4549353940, alloc=4848776, time=149.14 bytes used=4553355152, alloc=4848776, time=149.27 bytes used=4557356452, alloc=4848776, time=149.40 bytes used=4561357620, alloc=4848776, time=149.53 bytes used=4565358696, alloc=4848776, time=149.66 bytes used=4569359720, alloc=4848776, time=149.79 bytes used=4573360760, alloc=4848776, time=149.92 bytes used=4577362636, alloc=4848776, time=150.06 bytes used=4581363612, alloc=4848776, time=150.19 bytes used=4585364616, alloc=4848776, time=150.32 bytes used=4589365776, alloc=4848776, time=150.45 bytes used=4593366968, alloc=4848776, time=150.58 bytes used=4597368944, alloc=4848776, time=150.71 bytes used=4601369936, alloc=4848776, time=150.84 bytes used=4605371012, alloc=4848776, time=150.98 bytes used=4609372228, alloc=4848776, time=151.11 bytes used=4613373168, alloc=4848776, time=151.24 bytes used=4617374212, alloc=4848776, time=151.37 bytes used=4621375556, alloc=4848776, time=151.50 bytes used=4625376624, alloc=4848776, time=151.63 bytes used=4629377504, alloc=4848776, time=151.76 bytes used=4633378572, alloc=4848776, time=151.90 bytes used=4637379544, alloc=4848776, time=152.03 bytes used=4641380760, alloc=4848776, time=152.16 bytes used=4645381632, alloc=4848776, time=152.29 bytes used=4649383908, alloc=4848776, time=152.42 bytes used=4653384736, alloc=4848776, time=152.55 bytes used=4657385980, alloc=4848776, time=152.68 bytes used=4661387068, alloc=4848776, time=152.81 bytes used=4665389144, alloc=4848776, time=152.95 bytes used=4669389940, alloc=4848776, time=153.08 bytes used=4673391116, alloc=4848776, time=153.21 bytes used=4677392040, alloc=4848776, time=153.34 bytes used=4681393240, alloc=4848776, time=153.47 bytes used=4685394260, alloc=4848776, time=153.60 bytes used=4689395448, alloc=4848776, time=153.73 bytes used=4693396696, alloc=4848776, time=153.86 bytes used=4697398168, alloc=4848776, time=154.00 bytes used=4701398932, alloc=4848776, time=154.13 bytes used=4705400028, alloc=4848776, time=154.26 bytes used=4709401396, alloc=4848776, time=154.39 bytes used=4713402280, alloc=4848776, time=154.52 bytes used=4717403312, alloc=4848776, time=154.65 bytes used=4721405108, alloc=4848776, time=154.78 bytes used=4725406120, alloc=4848776, time=154.91 bytes used=4729407644, alloc=4848776, time=155.04 bytes used=4733408516, alloc=4848776, time=155.18 bytes used=4737409744, alloc=4848776, time=155.31 bytes used=4741410708, alloc=4848776, time=155.44 bytes used=4745411708, alloc=4848776, time=155.57 bytes used=4749412756, alloc=4848776, time=155.70 bytes used=4753413916, alloc=4848776, time=155.83 bytes used=4757414968, alloc=4848776, time=155.96 bytes used=4761416856, alloc=4848776, time=156.09 bytes used=4765418020, alloc=4848776, time=156.22 bytes used=4769418976, alloc=4848776, time=156.36 bytes used=4773419812, alloc=4848776, time=156.49 bytes used=4777420996, alloc=4848776, time=156.62 bytes used=4781422248, alloc=4848776, time=156.75 bytes used=4785423400, alloc=4848776, time=156.88 bytes used=4789424228, alloc=4848776, time=157.01 bytes used=4793425180, alloc=4848776, time=157.15 bytes used=4797426128, alloc=4848776, time=157.28 bytes used=4801427404, alloc=4848776, time=157.41 bytes used=4805428636, alloc=4848776, time=157.54 bytes used=4809429564, alloc=4848776, time=157.67 bytes used=4813430980, alloc=4848776, time=157.81 bytes used=4817431804, alloc=4848776, time=157.94 bytes used=4821433656, alloc=4848776, time=158.07 bytes used=4825434512, alloc=4848776, time=158.20 bytes used=4829435492, alloc=4848776, time=158.33 bytes used=4833436488, alloc=4848776, time=158.47 bytes used=4837437444, alloc=4848776, time=158.60 bytes used=4841438808, alloc=4848776, time=158.73 bytes used=4845439668, alloc=4848776, time=158.86 bytes used=4849440900, alloc=4848776, time=158.99 bytes used=4853442040, alloc=4848776, time=159.12 bytes used=4857443316, alloc=4848776, time=159.26 bytes used=4861444408, alloc=4848776, time=159.39 bytes used=4865445772, alloc=4848776, time=159.52 bytes used=4869446592, alloc=4848776, time=159.65 bytes used=4873447908, alloc=4848776, time=159.78 bytes used=4877448716, alloc=4848776, time=159.91 bytes used=4881449492, alloc=4848776, time=160.05 bytes used=4885450572, alloc=4848776, time=160.18 bytes used=4889451672, alloc=4848776, time=160.31 bytes used=4893452864, alloc=4848776, time=160.44 bytes used=4897454888, alloc=4848776, time=160.57 bytes used=4901455820, alloc=4848776, time=160.70 bytes used=4905457316, alloc=4848776, time=160.83 bytes used=4909458188, alloc=4848776, time=160.97 bytes used=4913459080, alloc=4848776, time=161.10 bytes used=4917460404, alloc=4848776, time=161.23 bytes used=4921461184, alloc=4848776, time=161.36 bytes used=4925462260, alloc=4848776, time=161.49 bytes used=4929463200, alloc=4848776, time=161.62 bytes used=4933464292, alloc=4848776, time=161.75 bytes used=4937465456, alloc=4848776, time=161.89 bytes used=4941467184, alloc=4848776, time=162.02 bytes used=4945468644, alloc=4848776, time=162.15 bytes used=4949469948, alloc=4848776, time=162.28 bytes used=4953470924, alloc=4848776, time=162.41 bytes used=4957471848, alloc=4848776, time=162.54 bytes used=4961472972, alloc=4848776, time=162.67 bytes used=4965475144, alloc=4848776, time=162.81 bytes used=4969476136, alloc=4848776, time=162.94 bytes used=4973476924, alloc=4848776, time=163.07 bytes used=4977478104, alloc=4848776, time=163.20 bytes used=4981478908, alloc=4848776, time=163.33 bytes used=4985479884, alloc=4848776, time=163.46 bytes used=4989480864, alloc=4848776, time=163.59 bytes used=4993482040, alloc=4848776, time=163.73 bytes used=4997483192, alloc=4848776, time=163.86 bytes used=5001484312, alloc=4848776, time=163.99 bytes used=5005485536, alloc=4848776, time=164.12 bytes used=5009486524, alloc=4848776, time=164.25 bytes used=5013487540, alloc=4848776, time=164.38 bytes used=5017489188, alloc=4848776, time=164.52 bytes used=5021490028, alloc=4848776, time=164.65 bytes used=5025491004, alloc=4848776, time=164.78 bytes used=5029492288, alloc=4848776, time=164.91 bytes used=5033493480, alloc=4848776, time=165.04 bytes used=5037495328, alloc=4848776, time=165.17 bytes used=5041496112, alloc=4848776, time=165.31 bytes used=5045497144, alloc=4848776, time=165.44 bytes used=5049498292, alloc=4848776, time=165.57 bytes used=5053499628, alloc=4848776, time=165.70 bytes used=5057500624, alloc=4848776, time=165.83 bytes used=5061503168, alloc=4848776, time=165.96 bytes used=5065504100, alloc=4848776, time=166.09 bytes used=5069505028, alloc=4848776, time=166.22 bytes used=5073505984, alloc=4848776, time=166.36 bytes used=5077507192, alloc=4848776, time=166.49 bytes used=5081508888, alloc=4848776, time=166.62 bytes used=5085509704, alloc=4848776, time=166.75 bytes used=5089511400, alloc=4848776, time=166.89 bytes used=5093512316, alloc=4848776, time=167.02 bytes used=5097513336, alloc=4848776, time=167.16 bytes used=5101514316, alloc=4848776, time=167.29 bytes used=5105515832, alloc=4848776, time=167.42 bytes used=5109516648, alloc=4848776, time=167.55 bytes used=5113517664, alloc=4848776, time=167.68 bytes used=5117518760, alloc=4848776, time=167.81 bytes used=5121519720, alloc=4848776, time=167.95 bytes used=5125521044, alloc=4848776, time=168.08 bytes used=5129521972, alloc=4848776, time=168.21 bytes used=5133523036, alloc=4848776, time=168.34 bytes used=5137524868, alloc=4848776, time=168.47 bytes used=5141526232, alloc=4848776, time=168.61 bytes used=5145527156, alloc=4848776, time=168.74 bytes used=5149528180, alloc=4848776, time=168.87 bytes used=5153529032, alloc=4848776, time=169.00 bytes used=5157530252, alloc=4848776, time=169.13 bytes used=5161531312, alloc=4848776, time=169.26 bytes used=5165532528, alloc=4848776, time=169.39 bytes used=5169533388, alloc=4848776, time=169.52 bytes used=5173535988, alloc=4848776, time=169.65 bytes used=5177537096, alloc=4848776, time=169.78 bytes used=5181538208, alloc=4848776, time=169.92 bytes used=5185539352, alloc=4848776, time=170.05 bytes used=5189540708, alloc=4914300, time=170.18 bytes used=5193541528, alloc=4914300, time=170.31 bytes used=5197542564, alloc=4914300, time=170.44 bytes used=5201545188, alloc=4914300, time=170.57 bytes used=5205546932, alloc=4914300, time=170.71 bytes used=5209548136, alloc=4914300, time=170.84 bytes used=5213550124, alloc=4914300, time=170.97 bytes used=5217550968, alloc=4914300, time=171.10 bytes used=5221552008, alloc=4914300, time=171.23 bytes used=5225553564, alloc=4914300, time=171.37 bytes used=5229554760, alloc=4914300, time=171.50 bytes used=5233555904, alloc=4914300, time=171.63 bytes used=5237557048, alloc=4914300, time=171.76 bytes used=5241558340, alloc=4914300, time=171.89 bytes used=5245559116, alloc=4914300, time=172.03 bytes used=5249560060, alloc=4914300, time=172.16 bytes used=5253561260, alloc=4914300, time=172.29 bytes used=5257563232, alloc=4914300, time=172.42 bytes used=5261564432, alloc=4914300, time=172.55 bytes used=5265566968, alloc=4914300, time=172.69 bytes used=5269567796, alloc=4914300, time=172.81 bytes used=5273568848, alloc=4914300, time=172.95 bytes used=5277569884, alloc=4914300, time=173.08 bytes used=5281571112, alloc=4914300, time=173.21 bytes used=5285572196, alloc=4914300, time=173.34 bytes used=5289573304, alloc=4914300, time=173.47 bytes used=5293574480, alloc=4914300, time=173.60 bytes used=5297576764, alloc=4914300, time=173.74 bytes used=5301577740, alloc=4914300, time=173.87 bytes used=5305579340, alloc=4914300, time=174.00 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 1.0452245998132813045112197869812 y[1] (numeric) = 1.0452245998150495105310320599047 absolute error = 1.7682060198122729235e-12 relative error = 1.6916995831595858563092287824560e-10 % Correct digits = 12 h = 1e-05 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6759 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 = 0.7503 Order of pole (six term test) = 0.2318 bytes used=5309580624, alloc=4914300, time=174.13 bytes used=5313582104, alloc=4914300, time=174.26 bytes used=5317583112, alloc=4914300, time=174.39 bytes used=5321584120, alloc=4914300, time=174.53 bytes used=5325585172, alloc=4914300, time=174.66 bytes used=5329586172, alloc=4914300, time=174.79 bytes used=5333587444, alloc=4914300, time=174.92 bytes used=5337588284, alloc=4914300, time=175.05 bytes used=5341589184, alloc=4914300, time=175.18 bytes used=5345590996, alloc=4914300, time=175.31 bytes used=5349592404, alloc=4914300, time=175.44 bytes used=5353593804, alloc=4914300, time=175.58 bytes used=5357596524, alloc=4914300, time=175.71 bytes used=5361597196, alloc=4914300, time=175.84 bytes used=5365598192, alloc=4914300, time=175.97 bytes used=5369599116, alloc=4914300, time=176.10 bytes used=5373600072, alloc=4914300, time=176.23 bytes used=5377601212, alloc=4914300, time=176.36 bytes used=5381603560, alloc=4914300, time=176.50 bytes used=5385604548, alloc=4914300, time=176.62 bytes used=5389605776, alloc=4914300, time=176.76 bytes used=5393606904, alloc=4914300, time=176.89 bytes used=5397608064, alloc=4914300, time=177.02 bytes used=5401609132, alloc=4914300, time=177.15 bytes used=5405610216, alloc=4914300, time=177.28 bytes used=5409611840, alloc=4914300, time=177.42 bytes used=5413612972, alloc=4914300, time=177.55 bytes used=5417613944, alloc=4914300, time=177.68 bytes used=5421615056, alloc=4914300, time=177.81 bytes used=5425615988, alloc=4914300, time=177.94 bytes used=5429617116, alloc=4914300, time=178.08 bytes used=5433618136, alloc=4914300, time=178.21 bytes used=5437619116, alloc=4914300, time=178.34 bytes used=5441620312, alloc=4914300, time=178.47 bytes used=5445621272, alloc=4914300, time=178.60 bytes used=5449622072, alloc=4914300, time=178.74 bytes used=5453623072, alloc=4914300, time=178.87 bytes used=5457624008, alloc=4914300, time=179.00 bytes used=5461627220, alloc=4914300, time=179.14 bytes used=5465627988, alloc=4914300, time=179.27 bytes used=5469628932, alloc=4914300, time=179.40 bytes used=5473629952, alloc=4914300, time=179.53 bytes used=5477631020, alloc=4914300, time=179.66 bytes used=5481631980, alloc=4914300, time=179.80 bytes used=5485633468, alloc=4914300, time=179.93 bytes used=5489634180, alloc=4914300, time=180.06 Finished! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = expt ( 2.0 * x + 1.0 , sin ( x ) ) * ( cos ( x ) * ln ( 2.0* x + 1.0 )+ ( 2.0 * sin ( x ) ) / ( 2.0 * x + 1.0 ) ); Iterations = 6208 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 2 Minutes 59 Seconds Expected Time Remaining = 40 Minutes 29 Seconds Optimized Time Remaining = 40 Minutes 27 Seconds Expected Total Time = 43 Minutes 28 Seconds Time to Timeout Unknown Percent Done = 6.899 % > quit bytes used=5490804240, alloc=4914300, time=180.10