|\^/| 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_new_sm_hpostode.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,"2013-05-26T01:33:27-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"expt_lin_sin_new_sm_h") > ; > 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_sm_h diffeq.mxt") > ; > logitem_str(html_log_file,"expt_lin_sin_new_sm_h 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_new_sm_hpostode.\ 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, "2013-05-26T01:33:27-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "expt_lin_sin_new_sm_h"); 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_sm_h diffeq.mxt"); logitem_str(html_log_file, "expt_lin_sin_new_sm_h 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_new_sm_hpostode.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=4000532, 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=8001876, alloc=4062488, time=0.23 bytes used=12003000, alloc=4324584, time=0.36 bytes used=16003828, alloc=4390108, time=0.49 bytes used=20004980, alloc=4390108, time=0.61 bytes used=24005872, alloc=4455632, time=0.74 bytes used=28006692, alloc=4455632, time=0.87 bytes used=32007720, alloc=4521156, time=1.00 bytes used=36008752, alloc=4521156, time=1.13 bytes used=40009528, alloc=4521156, time=1.26 bytes used=44010464, alloc=4521156, time=1.39 bytes used=48011520, alloc=4521156, time=1.52 bytes used=52012552, alloc=4521156, time=1.65 bytes used=56013440, alloc=4586680, time=1.78 bytes used=60014340, alloc=4586680, time=1.91 bytes used=64015680, alloc=4586680, time=2.04 bytes used=68016692, alloc=4586680, time=2.17 bytes used=72017632, alloc=4586680, time=2.30 bytes used=76018592, alloc=4586680, time=2.43 bytes used=80019764, alloc=4586680, time=2.56 bytes used=84021168, alloc=4586680, time=2.69 bytes used=88021916, alloc=4586680, time=2.82 bytes used=92022996, alloc=4586680, time=2.96 bytes used=96023952, alloc=4652204, time=3.08 bytes used=100025156, alloc=4652204, time=3.22 bytes used=104026464, alloc=4652204, time=3.35 bytes used=108027364, alloc=4652204, time=3.48 bytes used=112028496, alloc=4652204, time=3.61 bytes used=116031172, alloc=4652204, time=3.73 bytes used=120032260, alloc=4652204, time=3.87 bytes used=124035408, alloc=4652204, time=4.00 bytes used=128036176, alloc=4652204, time=4.13 bytes used=132037304, alloc=4652204, time=4.26 bytes used=136038116, alloc=4652204, time=4.39 bytes used=140039796, alloc=4652204, time=4.52 bytes used=144040944, alloc=4652204, time=4.65 bytes used=148042956, alloc=4652204, time=4.78 bytes used=152043732, alloc=4652204, time=4.91 bytes used=156044680, alloc=4652204, time=5.04 bytes used=160046068, alloc=4652204, time=5.17 bytes used=164047200, alloc=4652204, time=5.30 bytes used=168047912, alloc=4652204, time=5.44 bytes used=172049148, alloc=4652204, time=5.57 bytes used=176050360, alloc=4652204, time=5.70 bytes used=180051896, alloc=4652204, time=5.83 bytes used=184052880, alloc=4652204, time=5.96 bytes used=188053936, alloc=4652204, time=6.09 bytes used=192055184, alloc=4652204, time=6.22 bytes used=196056096, alloc=4652204, time=6.35 bytes used=200057256, alloc=4652204, time=6.48 bytes used=204058148, alloc=4652204, time=6.61 bytes used=208059048, alloc=4652204, time=6.75 bytes used=212059880, alloc=4652204, time=6.88 bytes used=216060876, alloc=4652204, time=7.01 bytes used=220061836, alloc=4652204, time=7.14 bytes used=224064552, alloc=4652204, time=7.27 bytes used=228065464, alloc=4652204, time=7.40 bytes used=232066904, alloc=4652204, time=7.53 bytes used=236068008, alloc=4652204, time=7.66 bytes used=240069144, 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time=24.07 bytes used=740220528, alloc=4717728, time=24.20 bytes used=744221816, alloc=4717728, time=24.33 bytes used=748222728, alloc=4717728, time=24.47 bytes used=752224552, alloc=4717728, time=24.59 bytes used=756225396, alloc=4717728, time=24.73 bytes used=760226924, alloc=4717728, time=24.86 bytes used=764227936, alloc=4717728, time=24.99 bytes used=768229212, alloc=4717728, time=25.12 bytes used=772230084, alloc=4717728, time=25.25 bytes used=776231048, alloc=4717728, time=25.38 bytes used=780231964, alloc=4717728, time=25.52 bytes used=784232804, alloc=4717728, time=25.65 bytes used=788233764, alloc=4717728, time=25.78 bytes used=792235008, alloc=4717728, time=25.91 bytes used=796237320, alloc=4717728, time=26.04 bytes used=800238100, alloc=4717728, time=26.17 bytes used=804239340, alloc=4717728, time=26.31 bytes used=808240316, alloc=4717728, time=26.44 bytes used=812242720, alloc=4717728, time=26.57 bytes used=816243496, alloc=4717728, time=26.71 bytes used=820245000, alloc=4717728, time=26.84 bytes used=824245776, alloc=4717728, time=26.97 bytes used=828247332, alloc=4717728, time=27.10 bytes used=832248296, alloc=4717728, time=27.23 bytes used=836251492, alloc=4717728, time=27.36 bytes used=840252612, alloc=4717728, time=27.49 bytes used=844253580, alloc=4717728, time=27.62 bytes used=848255936, alloc=4717728, time=27.76 bytes used=852257068, alloc=4717728, time=27.89 bytes used=856258084, alloc=4717728, time=28.01 bytes used=860259880, alloc=4717728, time=28.15 bytes used=864260964, alloc=4717728, time=28.28 bytes used=868262136, alloc=4717728, time=28.41 bytes used=872263048, alloc=4717728, time=28.54 bytes used=876264000, alloc=4717728, time=28.67 bytes used=880265004, alloc=4717728, time=28.80 bytes used=884266160, alloc=4717728, time=28.93 bytes used=888267924, alloc=4717728, time=29.07 TOP MAIN SOLVE Loop bytes used=892268932, alloc=4717728, time=29.20 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=896270276, alloc=4717728, time=29.33 bytes used=900271248, alloc=4717728, time=29.46 bytes used=904272484, alloc=4717728, time=29.59 bytes used=908273692, alloc=4717728, time=29.73 bytes used=912274684, alloc=4717728, time=29.86 bytes used=916275924, alloc=4717728, time=29.99 bytes used=920278592, alloc=4717728, time=30.12 bytes used=924279308, alloc=4717728, time=30.25 bytes used=928280324, alloc=4717728, time=30.38 bytes used=932281064, alloc=4717728, time=30.51 bytes used=936282392, alloc=4717728, time=30.64 bytes used=940283160, alloc=4717728, 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alloc=4783252, time=49.60 bytes used=1516450188, alloc=4783252, time=49.73 bytes used=1520451840, alloc=4783252, time=49.86 bytes used=1524453064, alloc=4783252, time=49.99 bytes used=1528453844, alloc=4783252, time=50.13 bytes used=1532455144, alloc=4783252, time=50.26 bytes used=1536456024, alloc=4783252, time=50.39 bytes used=1540456720, alloc=4783252, time=50.52 bytes used=1544457808, alloc=4783252, time=50.66 bytes used=1548459080, alloc=4783252, time=50.79 bytes used=1552460076, alloc=4783252, time=50.92 bytes used=1556460724, alloc=4783252, time=51.05 bytes used=1560461716, alloc=4783252, time=51.18 bytes used=1564462892, alloc=4783252, time=51.31 bytes used=1568463820, alloc=4783252, time=51.45 bytes used=1572464948, alloc=4783252, time=51.58 bytes used=1576466008, alloc=4783252, time=51.71 bytes used=1580471032, alloc=4783252, time=51.84 bytes used=1584471744, alloc=4783252, time=51.97 bytes used=1588472692, alloc=4783252, time=52.11 bytes used=1592473604, alloc=4783252, time=52.24 bytes used=1596474904, alloc=4783252, time=52.37 bytes used=1600475680, alloc=4783252, time=52.50 bytes used=1604476780, alloc=4783252, time=52.63 bytes used=1608477724, alloc=4783252, time=52.76 bytes used=1612478752, alloc=4783252, time=52.89 bytes used=1616479712, alloc=4783252, time=53.03 bytes used=1620480744, alloc=4783252, time=53.16 bytes used=1624481764, alloc=4783252, time=53.29 bytes used=1628482812, alloc=4783252, time=53.42 bytes used=1632483688, alloc=4783252, time=53.55 bytes used=1636484540, alloc=4783252, time=53.69 bytes used=1640485484, alloc=4783252, time=53.82 bytes used=1644486372, alloc=4783252, time=53.95 bytes used=1648487036, alloc=4783252, time=54.08 bytes used=1652487960, alloc=4783252, time=54.21 bytes used=1656489596, alloc=4783252, time=54.35 bytes used=1660490740, alloc=4783252, time=54.48 bytes used=1664491960, alloc=4783252, time=54.61 bytes used=1668492812, alloc=4783252, time=54.74 bytes used=1672493956, alloc=4783252, time=54.87 bytes used=1676495032, alloc=4783252, time=55.00 bytes used=1680495944, alloc=4783252, time=55.13 bytes used=1684497056, alloc=4783252, time=55.27 bytes used=1688498300, alloc=4783252, time=55.40 bytes used=1692499400, alloc=4783252, time=55.53 bytes used=1696500552, alloc=4783252, time=55.66 bytes used=1700501480, alloc=4783252, time=55.79 bytes used=1704502424, alloc=4783252, time=55.92 bytes used=1708503832, alloc=4783252, time=56.06 bytes used=1712504640, alloc=4783252, time=56.19 bytes used=1716505612, alloc=4783252, time=56.32 bytes used=1720506340, alloc=4783252, time=56.45 bytes used=1724507312, alloc=4783252, time=56.58 bytes used=1728508096, alloc=4783252, time=56.71 bytes used=1732508812, alloc=4783252, time=56.85 bytes used=1736509760, alloc=4783252, time=56.98 bytes used=1740510704, alloc=4783252, time=57.11 bytes used=1744511748, alloc=4783252, time=57.24 bytes used=1748512836, alloc=4783252, time=57.38 bytes used=1752513900, alloc=4783252, time=57.51 bytes used=1756516472, alloc=4783252, time=57.64 bytes used=1760517292, alloc=4783252, time=57.77 bytes used=1764518460, alloc=4783252, time=57.90 bytes used=1768519616, alloc=4783252, time=58.03 bytes used=1772520580, alloc=4783252, time=58.16 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=1776522064, alloc=4783252, time=58.30 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=1780523100, alloc=4783252, time=58.43 bytes used=1784525620, alloc=4783252, time=58.56 bytes used=1788526584, alloc=4783252, time=58.69 bytes used=1792527656, alloc=4783252, time=58.83 bytes used=1796528444, alloc=4783252, time=58.96 bytes used=1800529884, alloc=4783252, time=59.09 bytes used=1804530856, alloc=4783252, time=59.22 bytes used=1808532060, alloc=4783252, time=59.35 bytes used=1812532964, alloc=4783252, time=59.49 bytes used=1816534316, alloc=4783252, time=59.62 bytes used=1820535084, alloc=4783252, time=59.75 bytes used=1824536860, alloc=4783252, time=59.88 bytes used=1828537636, alloc=4783252, time=60.01 bytes used=1832538748, alloc=4783252, time=60.14 bytes used=1836539696, alloc=4783252, time=60.27 bytes used=1840540896, alloc=4783252, time=60.41 bytes used=1844542024, alloc=4783252, time=60.54 bytes used=1848543140, alloc=4783252, time=60.67 bytes used=1852545168, alloc=4783252, time=60.80 bytes used=1856545944, alloc=4783252, time=60.93 bytes used=1860547220, alloc=4783252, time=61.06 bytes used=1864548976, alloc=4783252, time=61.20 bytes used=1868550260, alloc=4783252, time=61.33 bytes used=1872551160, alloc=4783252, time=61.46 bytes used=1876552512, alloc=4783252, time=61.59 bytes used=1880553576, alloc=4783252, time=61.73 bytes used=1884554464, alloc=4783252, time=61.86 bytes used=1888555712, alloc=4783252, time=61.99 bytes used=1892556392, alloc=4783252, time=62.13 bytes used=1896557412, alloc=4783252, time=62.26 bytes used=1900558416, alloc=4783252, time=62.39 bytes used=1904559344, alloc=4783252, time=62.52 bytes used=1908560644, alloc=4783252, time=62.65 bytes used=1912561668, alloc=4783252, time=62.78 bytes used=1916562560, alloc=4783252, time=62.91 bytes used=1920563488, alloc=4783252, time=63.05 bytes used=1924564336, alloc=4783252, time=63.18 bytes used=1928565396, alloc=4783252, time=63.31 bytes used=1932566448, alloc=4783252, time=63.44 bytes used=1936569036, alloc=4783252, time=63.57 bytes used=1940569848, alloc=4783252, time=63.70 bytes used=1944570868, alloc=4783252, time=63.83 bytes used=1948571976, alloc=4783252, time=63.96 bytes used=1952573172, alloc=4783252, time=64.09 bytes used=1956574144, alloc=4783252, time=64.23 bytes used=1960575212, alloc=4783252, time=64.35 bytes used=1964577192, alloc=4783252, time=64.48 bytes used=1968578092, alloc=4783252, time=64.62 bytes used=1972579136, alloc=4783252, time=64.75 bytes used=1976580232, alloc=4783252, time=64.88 bytes used=1980583928, alloc=4783252, time=65.01 bytes used=1984584596, alloc=4783252, time=65.14 bytes used=1988585504, alloc=4783252, time=65.27 bytes used=1992586868, alloc=4783252, time=65.40 bytes used=1996587964, alloc=4783252, time=65.53 bytes used=2000588744, alloc=4783252, time=65.67 bytes used=2004589768, alloc=4783252, time=65.80 bytes used=2008590600, alloc=4783252, time=65.93 bytes used=2012591612, alloc=4783252, time=66.06 bytes used=2016592568, alloc=4783252, time=66.19 bytes used=2020594400, alloc=4783252, time=66.33 bytes used=2024595308, alloc=4783252, time=66.46 bytes used=2028598964, alloc=4783252, time=66.59 bytes used=2032600052, alloc=4783252, time=66.72 bytes used=2036600940, alloc=4783252, time=66.85 bytes used=2040603072, alloc=4783252, time=66.98 bytes used=2044604208, alloc=4783252, time=67.12 bytes used=2048605304, alloc=4783252, time=67.25 bytes used=2052607580, alloc=4783252, time=67.38 bytes used=2056608384, alloc=4783252, time=67.51 bytes used=2060609288, alloc=4783252, time=67.64 bytes used=2064610780, alloc=4783252, time=67.78 bytes used=2068611716, alloc=4783252, time=67.91 bytes used=2072612760, alloc=4783252, time=68.04 bytes used=2076613420, alloc=4783252, time=68.18 bytes used=2080614476, alloc=4783252, time=68.31 bytes used=2084615792, alloc=4783252, time=68.44 bytes used=2088616864, alloc=4783252, time=68.57 bytes used=2092617808, alloc=4783252, time=68.70 bytes used=2096618812, alloc=4783252, time=68.84 bytes used=2100619920, alloc=4783252, time=68.97 bytes used=2104620892, alloc=4783252, time=69.10 bytes used=2108621932, alloc=4783252, time=69.23 bytes used=2112623216, alloc=4783252, time=69.36 bytes used=2116625004, alloc=4783252, time=69.49 bytes used=2120626004, alloc=4783252, time=69.63 bytes used=2124627072, alloc=4783252, time=69.76 bytes used=2128628076, alloc=4783252, time=69.89 bytes used=2132629076, alloc=4783252, time=70.02 bytes used=2136629900, alloc=4783252, time=70.15 bytes used=2140631408, alloc=4783252, time=70.29 bytes used=2144632360, alloc=4783252, time=70.42 bytes used=2148633680, alloc=4783252, time=70.55 bytes used=2152634712, alloc=4783252, time=70.68 bytes used=2156635928, alloc=4783252, time=70.81 bytes used=2160636844, alloc=4783252, time=70.95 bytes used=2164638048, alloc=4783252, time=71.08 bytes used=2168639156, alloc=4783252, time=71.21 bytes used=2172641400, alloc=4783252, time=71.34 bytes used=2176643348, alloc=4783252, time=71.47 bytes used=2180644696, alloc=4783252, time=71.61 bytes used=2184646044, alloc=4783252, time=71.74 bytes used=2188646908, alloc=4783252, time=71.87 bytes used=2192649736, alloc=4783252, time=72.00 bytes used=2196650816, alloc=4783252, time=72.13 bytes used=2200651916, alloc=4783252, time=72.27 bytes used=2204652904, alloc=4783252, time=72.40 bytes used=2208654188, alloc=4783252, time=72.53 bytes used=2212655844, alloc=4783252, time=72.66 bytes used=2216656880, alloc=4783252, time=72.79 bytes used=2220657700, alloc=4783252, time=72.92 bytes used=2224658736, alloc=4783252, time=73.06 bytes used=2228659648, alloc=4783252, time=73.19 bytes used=2232661572, alloc=4783252, time=73.32 bytes used=2236662660, alloc=4783252, time=73.45 bytes used=2240664044, alloc=4783252, time=73.58 bytes used=2244664836, alloc=4783252, time=73.72 bytes used=2248666956, alloc=4783252, time=73.85 bytes used=2252668740, alloc=4783252, time=73.98 bytes used=2256669576, alloc=4783252, time=74.11 bytes used=2260670576, alloc=4783252, time=74.25 bytes used=2264671576, alloc=4783252, time=74.38 bytes used=2268673388, alloc=4783252, time=74.51 bytes used=2272674116, alloc=4783252, time=74.64 bytes used=2276675444, alloc=4783252, time=74.77 bytes used=2280677076, alloc=4783252, time=74.90 bytes used=2284677868, alloc=4783252, time=75.04 bytes used=2288679104, alloc=4783252, time=75.17 bytes used=2292680136, alloc=4783252, time=75.30 bytes used=2296681124, alloc=4783252, time=75.43 bytes used=2300682364, alloc=4783252, time=75.56 bytes used=2304683476, alloc=4783252, time=75.69 bytes used=2308684636, alloc=4783252, time=75.83 bytes used=2312685772, alloc=4783252, time=75.96 bytes used=2316687388, alloc=4783252, time=76.09 bytes used=2320688644, alloc=4783252, time=76.22 bytes used=2324689932, alloc=4783252, time=76.36 bytes used=2328690964, alloc=4783252, time=76.49 bytes used=2332692176, alloc=4783252, time=76.62 bytes used=2336693356, alloc=4783252, time=76.75 bytes used=2340694388, alloc=4783252, time=76.88 bytes used=2344696652, alloc=4783252, time=77.02 bytes used=2348697424, alloc=4783252, time=77.15 bytes used=2352698468, alloc=4783252, time=77.28 bytes used=2356699464, alloc=4783252, time=77.41 bytes used=2360700492, alloc=4783252, time=77.54 bytes used=2364701636, alloc=4783252, time=77.68 bytes used=2368702616, alloc=4783252, time=77.81 bytes used=2372703500, alloc=4783252, time=77.94 bytes used=2376704520, alloc=4783252, time=78.07 bytes used=2380705824, alloc=4783252, time=78.20 bytes used=2384707656, alloc=4783252, time=78.34 bytes used=2388708436, alloc=4783252, time=78.47 bytes used=2392709580, alloc=4848776, time=78.60 bytes used=2396711312, alloc=4848776, time=78.73 bytes used=2400712452, alloc=4848776, time=78.86 bytes used=2404716352, alloc=4848776, time=78.99 bytes used=2408717420, alloc=4848776, time=79.12 bytes used=2412718632, alloc=4848776, time=79.26 bytes used=2416719780, alloc=4848776, time=79.39 bytes used=2420720808, alloc=4848776, time=79.52 bytes used=2424721844, alloc=4848776, time=79.65 bytes used=2428723620, alloc=4848776, time=79.78 bytes used=2432724684, alloc=4848776, time=79.92 bytes used=2436726124, alloc=4848776, time=80.05 bytes used=2440728340, alloc=4848776, time=80.18 bytes used=2444729148, alloc=4848776, time=80.32 bytes used=2448731208, alloc=4848776, time=80.45 bytes used=2452732088, alloc=4848776, time=80.58 bytes used=2456733356, alloc=4848776, time=80.71 bytes used=2460734324, alloc=4848776, time=80.84 bytes used=2464736672, alloc=4848776, time=80.98 bytes used=2468737848, alloc=4848776, time=81.11 bytes used=2472739632, alloc=4848776, time=81.24 bytes used=2476740720, alloc=4848776, time=81.37 bytes used=2480742656, alloc=4848776, time=81.51 bytes used=2484743420, alloc=4848776, time=81.64 bytes used=2488744380, alloc=4848776, time=81.77 bytes used=2492745468, alloc=4848776, time=81.90 bytes used=2496746460, alloc=4848776, time=82.03 bytes used=2500747388, alloc=4848776, time=82.16 bytes used=2504748312, alloc=4848776, time=82.29 bytes used=2508749460, alloc=4848776, time=82.43 bytes used=2512750456, alloc=4848776, time=82.56 bytes used=2516751616, alloc=4848776, time=82.69 bytes used=2520752764, alloc=4848776, time=82.82 bytes used=2524754200, alloc=4848776, time=82.95 bytes used=2528755112, alloc=4848776, time=83.09 bytes used=2532757372, alloc=4848776, time=83.22 bytes used=2536758320, alloc=4848776, time=83.35 bytes used=2540759232, alloc=4848776, time=83.48 bytes used=2544760300, alloc=4848776, time=83.62 bytes used=2548761252, alloc=4848776, time=83.75 bytes used=2552762184, alloc=4848776, time=83.88 bytes used=2556763784, alloc=4848776, time=84.01 bytes used=2560764792, alloc=4848776, time=84.15 bytes used=2564765992, alloc=4848776, time=84.28 bytes used=2568767728, alloc=4848776, time=84.41 bytes used=2572768572, alloc=4848776, time=84.54 bytes used=2576769672, alloc=4848776, time=84.67 bytes used=2580770584, alloc=4848776, time=84.81 bytes used=2584771632, alloc=4848776, time=84.93 bytes used=2588772896, alloc=4848776, time=85.07 bytes used=2592773784, alloc=4848776, time=85.20 bytes used=2596774688, alloc=4848776, time=85.33 bytes used=2600775720, alloc=4848776, time=85.46 bytes used=2604777556, alloc=4848776, time=85.59 bytes used=2608778520, alloc=4848776, time=85.72 bytes used=2612779536, alloc=4848776, time=85.86 bytes used=2616780564, alloc=4848776, time=85.99 bytes used=2620781892, alloc=4848776, time=86.12 bytes used=2624782836, alloc=4848776, time=86.25 bytes used=2628783812, alloc=4848776, time=86.38 bytes used=2632785076, alloc=4848776, time=86.52 bytes used=2636786136, alloc=4848776, time=86.65 bytes used=2640787276, alloc=4848776, time=86.78 bytes used=2644788924, alloc=4848776, time=86.91 bytes used=2648789816, alloc=4848776, time=87.04 bytes used=2652791128, alloc=4848776, time=87.18 bytes used=2656792004, alloc=4848776, time=87.31 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=2660792956, alloc=4848776, time=87.44 bytes used=2664793908, alloc=4848776, time=87.57 bytes used=2668795484, alloc=4848776, time=87.70 bytes used=2672796920, alloc=4848776, time=87.84 bytes used=2676797572, alloc=4848776, time=87.97 bytes used=2680798920, alloc=4848776, time=88.10 bytes used=2684800864, alloc=4848776, time=88.23 bytes used=2688801576, alloc=4848776, time=88.36 bytes used=2692802508, alloc=4848776, time=88.50 bytes used=2696803792, alloc=4848776, time=88.63 bytes used=2700805004, alloc=4848776, time=88.76 bytes used=2704805972, alloc=4848776, time=88.89 bytes used=2708806944, alloc=4848776, time=89.02 bytes used=2712808028, alloc=4848776, time=89.16 bytes used=2716808940, alloc=4848776, time=89.29 bytes used=2720809944, alloc=4848776, time=89.42 bytes used=2724810872, alloc=4848776, time=89.55 bytes used=2728812852, alloc=4848776, time=89.68 bytes used=2732815592, alloc=4848776, time=89.82 bytes used=2736816504, alloc=4848776, time=89.95 bytes used=2740817316, alloc=4848776, time=90.08 bytes used=2744818408, alloc=4848776, time=90.21 bytes used=2748819572, alloc=4848776, time=90.35 bytes used=2752821196, alloc=4848776, time=90.48 bytes used=2756822564, alloc=4848776, time=90.61 bytes used=2760823924, alloc=4848776, time=90.74 bytes used=2764824972, alloc=4848776, time=90.87 bytes used=2768826660, alloc=4848776, time=91.00 bytes used=2772827484, alloc=4848776, time=91.14 bytes used=2776828576, alloc=4848776, time=91.27 bytes used=2780829636, alloc=4848776, time=91.40 bytes used=2784830688, alloc=4848776, time=91.53 bytes used=2788831588, alloc=4848776, time=91.66 bytes used=2792832708, alloc=4848776, time=91.80 bytes used=2796833788, alloc=4848776, time=91.93 bytes used=2800835572, alloc=4848776, time=92.06 bytes used=2804836424, alloc=4848776, time=92.19 bytes used=2808837476, alloc=4848776, time=92.32 bytes used=2812838504, alloc=4848776, time=92.46 bytes used=2816839460, alloc=4848776, time=92.59 bytes used=2820840360, alloc=4848776, time=92.72 bytes used=2824841316, alloc=4848776, time=92.85 bytes used=2828842572, alloc=4848776, time=92.98 bytes used=2832844328, alloc=4848776, time=93.12 bytes used=2836845160, alloc=4848776, time=93.25 bytes used=2840846396, alloc=4848776, time=93.38 bytes used=2844847472, alloc=4848776, time=93.51 bytes used=2848848548, alloc=4848776, time=93.64 bytes used=2852849732, alloc=4848776, time=93.78 bytes used=2856850892, alloc=4848776, time=93.91 bytes used=2860851832, alloc=4848776, time=94.04 bytes used=2864852744, alloc=4848776, time=94.17 bytes used=2868853840, alloc=4848776, time=94.30 bytes used=2872855068, alloc=4848776, time=94.44 bytes used=2876855856, alloc=4848776, time=94.57 bytes used=2880857008, alloc=4848776, time=94.70 bytes used=2884858456, alloc=4848776, time=94.83 bytes used=2888859256, alloc=4848776, time=94.96 bytes used=2892860432, alloc=4848776, time=95.09 bytes used=2896863748, alloc=4848776, time=95.23 bytes used=2900864876, alloc=4848776, time=95.36 bytes used=2904865784, alloc=4848776, time=95.49 bytes used=2908866952, alloc=4848776, time=95.62 bytes used=2912867764, alloc=4848776, time=95.75 bytes used=2916868840, alloc=4848776, time=95.88 bytes used=2920869640, alloc=4848776, time=96.02 bytes used=2924870632, alloc=4848776, time=96.15 bytes used=2928871804, alloc=4848776, time=96.28 bytes used=2932872980, alloc=4848776, time=96.41 bytes used=2936873872, alloc=4848776, time=96.54 bytes used=2940874836, alloc=4848776, time=96.67 bytes used=2944875928, alloc=4848776, time=96.81 bytes used=2948877276, alloc=4848776, time=96.94 bytes used=2952877940, alloc=4848776, time=97.07 bytes used=2956879676, alloc=4848776, time=97.20 bytes used=2960881152, alloc=4848776, time=97.33 bytes used=2964882464, alloc=4848776, time=97.46 bytes used=2968883212, alloc=4848776, time=97.59 bytes used=2972885192, alloc=4848776, time=97.73 bytes used=2976886744, alloc=4848776, time=97.86 bytes used=2980888536, alloc=4848776, time=98.00 bytes used=2984889276, alloc=4848776, time=98.13 bytes used=2988890432, alloc=4848776, time=98.26 bytes used=2992891872, alloc=4848776, time=98.39 bytes used=2996892796, alloc=4848776, time=98.52 bytes used=3000894000, alloc=4848776, time=98.65 bytes used=3004894904, alloc=4848776, time=98.78 bytes used=3008895992, alloc=4848776, time=98.91 bytes used=3012896968, alloc=4848776, time=99.05 bytes used=3016897948, alloc=4848776, time=99.18 bytes used=3020898752, alloc=4848776, time=99.31 bytes used=3024901032, alloc=4848776, time=99.44 bytes used=3028901784, alloc=4848776, time=99.57 bytes used=3032903228, alloc=4848776, time=99.71 bytes used=3036904212, alloc=4848776, time=99.84 bytes used=3040905328, alloc=4848776, time=99.97 bytes used=3044906624, alloc=4848776, time=100.10 bytes used=3048907652, alloc=4848776, time=100.23 bytes used=3052908416, alloc=4848776, time=100.37 bytes used=3056909584, alloc=4848776, time=100.50 bytes used=3060910544, alloc=4848776, time=100.63 bytes used=3064912040, alloc=4848776, time=100.76 bytes used=3068912904, alloc=4848776, time=100.89 bytes used=3072914904, alloc=4848776, time=101.03 bytes used=3076915872, alloc=4848776, time=101.16 bytes used=3080917304, alloc=4848776, time=101.29 bytes used=3084919116, alloc=4848776, time=101.42 bytes used=3088920096, alloc=4848776, time=101.55 bytes used=3092921852, alloc=4848776, time=101.69 bytes used=3096923200, alloc=4848776, time=101.82 bytes used=3100925384, alloc=4848776, time=101.95 bytes used=3104926352, alloc=4848776, time=102.08 bytes used=3108927500, alloc=4848776, time=102.21 bytes used=3112928556, alloc=4848776, time=102.35 bytes used=3116929292, alloc=4848776, time=102.48 bytes used=3120931020, alloc=4848776, time=102.61 bytes used=3124931980, alloc=4848776, time=102.74 bytes used=3128933088, alloc=4848776, time=102.87 bytes used=3132933872, alloc=4848776, time=103.00 bytes used=3136934980, alloc=4848776, time=103.13 bytes used=3140936188, alloc=4848776, time=103.27 bytes used=3144937028, alloc=4848776, time=103.40 bytes used=3148938036, alloc=4848776, time=103.53 bytes used=3152940392, alloc=4848776, time=103.66 bytes used=3156941440, alloc=4848776, time=103.80 bytes used=3160942212, alloc=4848776, time=103.93 bytes used=3164942996, alloc=4848776, time=104.06 bytes used=3168944296, alloc=4848776, time=104.20 bytes used=3172946204, alloc=4848776, time=104.33 bytes used=3176948176, alloc=4848776, time=104.46 bytes used=3180949200, alloc=4848776, time=104.59 bytes used=3184950136, alloc=4848776, time=104.72 bytes used=3188951320, alloc=4848776, time=104.85 bytes used=3192952592, alloc=4848776, time=104.99 bytes used=3196953976, alloc=4848776, time=105.12 bytes used=3200954804, alloc=4848776, time=105.25 bytes used=3204955780, alloc=4848776, time=105.38 bytes used=3208957204, alloc=4848776, time=105.51 bytes used=3212958332, alloc=4848776, time=105.65 bytes used=3216959108, alloc=4848776, time=105.78 bytes used=3220960200, alloc=4848776, time=105.91 bytes used=3224961196, alloc=4848776, time=106.04 bytes used=3228962688, alloc=4848776, time=106.17 bytes used=3232964124, alloc=4848776, time=106.30 bytes used=3236965140, alloc=4848776, time=106.43 bytes used=3240966256, alloc=4848776, time=106.57 bytes used=3244967292, alloc=4848776, time=106.70 bytes used=3248968328, alloc=4848776, time=106.83 bytes used=3252969440, alloc=4848776, time=106.96 bytes used=3256970408, alloc=4848776, time=107.09 bytes used=3260971876, alloc=4848776, time=107.23 bytes used=3264972972, alloc=4848776, time=107.36 bytes used=3268973952, alloc=4848776, time=107.49 bytes used=3272975400, alloc=4848776, time=107.62 bytes used=3276976240, alloc=4848776, time=107.75 bytes used=3280977448, alloc=4848776, time=107.89 bytes used=3284978600, alloc=4848776, time=108.02 bytes used=3288979708, alloc=4848776, time=108.15 bytes used=3292980556, alloc=4848776, time=108.28 bytes used=3296981532, alloc=4848776, time=108.42 bytes used=3300982704, alloc=4848776, time=108.55 bytes used=3304984884, alloc=4848776, time=108.68 bytes used=3308986004, alloc=4848776, time=108.81 bytes used=3312986812, alloc=4848776, time=108.94 bytes used=3316988000, alloc=4848776, time=109.07 bytes used=3320988928, alloc=4848776, time=109.21 bytes used=3324989884, alloc=4848776, time=109.34 bytes used=3328991308, alloc=4848776, time=109.47 bytes used=3332992204, alloc=4848776, time=109.60 bytes used=3336992900, alloc=4848776, time=109.73 bytes used=3340996740, alloc=4848776, time=109.87 bytes used=3344997532, alloc=4848776, time=110.00 bytes used=3348998564, alloc=4848776, time=110.13 bytes used=3353001132, alloc=4848776, time=110.26 bytes used=3357002832, alloc=4848776, time=110.39 bytes used=3361003764, alloc=4848776, time=110.52 bytes used=3365004760, alloc=4848776, time=110.66 bytes used=3369005680, alloc=4848776, time=110.79 bytes used=3373007016, alloc=4848776, time=110.92 bytes used=3377008356, alloc=4848776, time=111.05 bytes used=3381009924, alloc=4848776, time=111.18 bytes used=3385010896, alloc=4848776, time=111.31 bytes used=3389011908, alloc=4848776, time=111.45 bytes used=3393012956, alloc=4848776, time=111.58 bytes used=3397014152, alloc=4848776, time=111.71 bytes used=3401015164, alloc=4848776, time=111.84 bytes used=3405016268, alloc=4848776, time=111.97 bytes used=3409017064, alloc=4848776, time=112.10 bytes used=3413018524, alloc=4848776, time=112.23 bytes used=3417020792, alloc=4848776, time=112.37 bytes used=3421021708, alloc=4848776, time=112.50 bytes used=3425022508, alloc=4848776, time=112.63 bytes used=3429023528, alloc=4848776, time=112.76 bytes used=3433024536, alloc=4848776, time=112.89 bytes used=3437025412, alloc=4848776, time=113.02 bytes used=3441028300, alloc=4848776, time=113.16 bytes used=3445029248, alloc=4848776, time=113.29 bytes used=3449030192, alloc=4848776, time=113.42 bytes used=3453031116, alloc=4848776, time=113.55 bytes used=3457032820, alloc=4848776, time=113.69 bytes used=3461033764, alloc=4848776, time=113.82 bytes used=3465034924, alloc=4848776, time=113.95 bytes used=3469036004, alloc=4848776, time=114.08 bytes used=3473036968, alloc=4848776, time=114.21 bytes used=3477039040, alloc=4848776, time=114.35 bytes used=3481039736, alloc=4848776, time=114.48 bytes used=3485041108, alloc=4848776, time=114.61 bytes used=3489042000, alloc=4848776, time=114.74 bytes used=3493043120, alloc=4848776, time=114.88 bytes used=3497043992, alloc=4848776, time=115.01 bytes used=3501044948, alloc=4848776, time=115.14 bytes used=3505045932, alloc=4848776, time=115.27 bytes used=3509046904, alloc=4848776, time=115.40 bytes used=3513047936, alloc=4848776, time=115.53 bytes used=3517049116, alloc=4848776, time=115.67 bytes used=3521050144, alloc=4848776, time=115.80 bytes used=3525052208, alloc=4848776, time=115.94 bytes used=3529054044, alloc=4848776, time=116.07 bytes used=3533054868, alloc=4848776, time=116.20 bytes used=3537057388, alloc=4848776, time=116.33 bytes used=3541058164, alloc=4848776, time=116.46 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=3545059524, alloc=4848776, time=116.60 bytes used=3549060692, alloc=4848776, time=116.73 bytes used=3553063156, alloc=4848776, time=116.86 bytes used=3557063980, alloc=4848776, time=116.99 bytes used=3561065096, alloc=4848776, time=117.13 bytes used=3565066076, alloc=4848776, time=117.26 bytes used=3569067900, alloc=4848776, time=117.39 bytes used=3573068628, alloc=4848776, time=117.52 bytes used=3577069684, alloc=4848776, time=117.66 bytes used=3581070716, alloc=4848776, time=117.79 bytes used=3585071616, alloc=4848776, time=117.92 bytes used=3589072792, alloc=4848776, time=118.05 bytes used=3593075024, alloc=4848776, time=118.19 bytes used=3597075968, alloc=4848776, time=118.32 bytes used=3601076920, alloc=4848776, time=118.45 bytes used=3605078072, alloc=4848776, time=118.58 bytes used=3609079096, alloc=4848776, time=118.71 bytes used=3613080084, alloc=4848776, time=118.84 bytes used=3617080992, alloc=4848776, time=118.97 bytes used=3621083644, alloc=4848776, time=119.10 bytes used=3625084576, alloc=4848776, time=119.24 bytes used=3629085656, alloc=4848776, time=119.37 bytes used=3633086748, alloc=4848776, time=119.50 bytes used=3637087780, alloc=4848776, time=119.63 bytes used=3641088788, alloc=4848776, time=119.77 bytes used=3645089700, alloc=4848776, time=119.90 bytes used=3649090860, alloc=4848776, time=120.03 bytes used=3653091984, alloc=4848776, time=120.16 bytes used=3657093064, alloc=4848776, time=120.29 bytes used=3661094104, alloc=4848776, time=120.42 bytes used=3665095024, alloc=4848776, time=120.56 bytes used=3669096172, alloc=4848776, time=120.69 bytes used=3673097400, alloc=4848776, time=120.82 bytes used=3677098584, alloc=4848776, time=120.95 bytes used=3681100108, alloc=4848776, time=121.09 bytes used=3685101156, alloc=4848776, time=121.22 bytes used=3689102212, alloc=4848776, time=121.35 bytes used=3693103348, alloc=4848776, time=121.48 bytes used=3697104252, alloc=4848776, time=121.62 bytes used=3701105340, alloc=4848776, time=121.75 bytes used=3705106692, alloc=4848776, time=121.88 bytes used=3709107804, alloc=4848776, time=122.02 bytes used=3713108568, alloc=4848776, time=122.15 bytes used=3717109568, alloc=4848776, time=122.28 bytes used=3721110920, alloc=4848776, time=122.41 bytes used=3725111560, alloc=4848776, time=122.54 bytes used=3729112632, alloc=4848776, time=122.67 bytes used=3733114264, alloc=4848776, time=122.81 bytes used=3737116032, alloc=4848776, time=122.94 bytes used=3741117312, alloc=4848776, time=123.07 bytes used=3745118248, alloc=4848776, time=123.20 bytes used=3749119468, alloc=4848776, time=123.34 bytes used=3753121352, alloc=4848776, time=123.47 bytes used=3757122208, alloc=4848776, time=123.60 bytes used=3761123248, alloc=4848776, time=123.73 bytes used=3765124440, alloc=4848776, time=123.86 bytes used=3769125760, alloc=4848776, time=124.00 bytes used=3773126716, alloc=4848776, time=124.13 bytes used=3777127680, alloc=4848776, time=124.26 bytes used=3781128944, alloc=4848776, time=124.39 bytes used=3785130512, alloc=4848776, time=124.52 bytes used=3789131472, alloc=4848776, time=124.66 bytes used=3793134020, alloc=4848776, time=124.79 bytes used=3797136388, alloc=4848776, time=124.92 bytes used=3801137364, alloc=4848776, time=125.05 bytes used=3805138276, alloc=4848776, time=125.18 bytes used=3809139320, alloc=4848776, time=125.32 bytes used=3813140124, alloc=4848776, time=125.45 bytes used=3817141752, alloc=4848776, time=125.58 bytes used=3821142924, alloc=4848776, time=125.71 bytes used=3825144204, alloc=4848776, time=125.84 bytes used=3829145028, alloc=4848776, time=125.98 bytes used=3833146288, alloc=4848776, time=126.11 bytes used=3837147368, alloc=4848776, time=126.24 bytes used=3841148400, alloc=4848776, time=126.38 bytes used=3845149716, alloc=4848776, time=126.51 bytes used=3849150680, alloc=4848776, time=126.64 bytes used=3853156612, alloc=4848776, time=126.77 bytes used=3857158188, alloc=4848776, time=126.90 bytes used=3861159108, alloc=4848776, time=127.03 bytes used=3865160284, alloc=4848776, time=127.16 bytes used=3869161132, alloc=4848776, time=127.30 bytes used=3873163604, alloc=4848776, time=127.43 bytes used=3877164868, alloc=4848776, time=127.56 bytes used=3881165892, alloc=4848776, time=127.70 bytes used=3885168724, alloc=4848776, time=127.83 bytes used=3889169584, alloc=4848776, time=127.96 bytes used=3893170628, alloc=4848776, time=128.09 bytes used=3897171812, alloc=4848776, time=128.22 bytes used=3901173172, alloc=4848776, time=128.35 bytes used=3905173896, alloc=4848776, time=128.48 bytes used=3909174860, alloc=4848776, time=128.62 bytes used=3913176340, alloc=4848776, time=128.75 bytes used=3917176980, alloc=4848776, time=128.88 bytes used=3921178236, alloc=4848776, time=129.01 bytes used=3925179160, alloc=4848776, time=129.15 bytes used=3929180112, alloc=4848776, time=129.28 bytes used=3933181380, alloc=4848776, time=129.41 bytes used=3937182296, alloc=4848776, time=129.54 bytes used=3941183240, alloc=4848776, time=129.67 bytes used=3945184280, alloc=4848776, time=129.81 bytes used=3949185408, alloc=4848776, time=129.94 bytes used=3953186364, alloc=4848776, time=130.07 bytes used=3957187392, alloc=4848776, time=130.20 bytes used=3961188480, alloc=4848776, time=130.34 bytes used=3965189448, alloc=4848776, time=130.47 bytes used=3969190240, alloc=4848776, time=130.60 bytes used=3973191260, alloc=4848776, time=130.73 bytes used=3977192796, alloc=4848776, time=130.86 bytes used=3981194028, alloc=4848776, time=130.99 bytes used=3985195076, alloc=4848776, time=131.12 bytes used=3989197508, alloc=4848776, time=131.25 bytes used=3993198472, alloc=4848776, time=131.39 bytes used=3997200588, alloc=4848776, time=131.52 bytes used=4001201644, alloc=4848776, time=131.65 bytes used=4005202704, alloc=4848776, time=131.78 bytes used=4009203808, alloc=4848776, time=131.91 bytes used=4013204712, alloc=4848776, time=132.05 bytes used=4017205632, alloc=4848776, time=132.18 bytes used=4021206512, alloc=4848776, time=132.31 bytes used=4025207420, alloc=4848776, time=132.44 bytes used=4029208340, alloc=4848776, time=132.58 bytes used=4033210456, alloc=4848776, time=132.71 bytes used=4037211540, alloc=4848776, time=132.84 bytes used=4041212880, alloc=4848776, time=132.97 bytes used=4045213860, alloc=4848776, time=133.10 bytes used=4049214892, alloc=4848776, time=133.24 bytes used=4053215896, alloc=4848776, time=133.37 bytes used=4057216896, alloc=4848776, time=133.50 bytes used=4061217840, alloc=4848776, time=133.63 bytes used=4065218876, alloc=4848776, time=133.76 bytes used=4069219712, alloc=4848776, time=133.89 bytes used=4073220880, alloc=4848776, time=134.03 bytes used=4077222316, alloc=4848776, time=134.16 bytes used=4081223328, alloc=4848776, time=134.29 bytes used=4085224596, alloc=4848776, time=134.42 bytes used=4089225920, alloc=4848776, time=134.55 bytes used=4093229212, alloc=4848776, time=134.69 bytes used=4097229980, alloc=4848776, time=134.82 bytes used=4101231192, alloc=4848776, time=134.95 bytes used=4105232160, alloc=4848776, time=135.09 bytes used=4109233272, alloc=4848776, time=135.22 bytes used=4113234140, alloc=4848776, time=135.35 bytes used=4117235500, alloc=4848776, time=135.48 bytes used=4121236616, alloc=4848776, time=135.61 bytes used=4125237640, alloc=4848776, time=135.75 bytes used=4129238640, alloc=4848776, time=135.88 bytes used=4133239704, alloc=4848776, time=136.01 bytes used=4137241120, alloc=4848776, time=136.14 bytes used=4141241980, alloc=4848776, time=136.28 bytes used=4145243236, alloc=4848776, time=136.41 bytes used=4149244220, alloc=4848776, time=136.54 bytes used=4153245212, alloc=4848776, time=136.67 bytes used=4157247088, alloc=4848776, time=136.81 bytes used=4161248116, alloc=4848776, time=136.94 bytes used=4165249032, alloc=4848776, time=137.07 bytes used=4169250692, alloc=4848776, time=137.20 bytes used=4173251544, alloc=4848776, time=137.34 bytes used=4177253084, alloc=4848776, time=137.47 bytes used=4181255020, alloc=4848776, time=137.60 bytes used=4185255940, alloc=4848776, time=137.73 bytes used=4189257272, alloc=4848776, time=137.86 bytes used=4193258048, alloc=4848776, time=138.00 bytes used=4197259268, alloc=4848776, time=138.13 bytes used=4201260544, alloc=4848776, time=138.26 bytes used=4205261480, alloc=4848776, time=138.39 bytes used=4209262660, alloc=4848776, time=138.52 bytes used=4213264240, alloc=4848776, time=138.66 bytes used=4217265272, alloc=4848776, time=138.79 bytes used=4221268388, alloc=4848776, time=138.92 bytes used=4225269236, alloc=4848776, time=139.05 bytes used=4229270168, alloc=4848776, time=139.19 bytes used=4233271216, alloc=4848776, time=139.32 bytes used=4237272424, alloc=4848776, time=139.45 bytes used=4241273736, alloc=4848776, time=139.59 bytes used=4245274712, alloc=4848776, time=139.72 bytes used=4249275844, alloc=4848776, time=139.85 bytes used=4253276928, alloc=4848776, time=139.98 bytes used=4257278644, alloc=4848776, time=140.11 bytes used=4261279744, alloc=4848776, time=140.25 bytes used=4265280532, alloc=4848776, time=140.38 bytes used=4269281812, alloc=4848776, time=140.51 bytes used=4273282880, alloc=4848776, time=140.65 bytes used=4277284104, alloc=4848776, time=140.78 bytes used=4281285280, alloc=4848776, time=140.91 bytes used=4285286360, alloc=4848776, time=141.04 bytes used=4289289220, alloc=4848776, time=141.17 bytes used=4293290032, alloc=4848776, time=141.30 bytes used=4297291208, alloc=4848776, time=141.44 bytes used=4301292168, alloc=4848776, time=141.57 bytes used=4305293252, alloc=4848776, time=141.70 bytes used=4309294488, alloc=4848776, time=141.83 bytes used=4313295588, alloc=4848776, time=141.96 bytes used=4317296812, alloc=4848776, time=142.09 bytes used=4321297920, alloc=4848776, time=142.23 bytes used=4325300604, alloc=4848776, time=142.36 bytes used=4329302660, alloc=4848776, time=142.49 bytes used=4333303728, alloc=4848776, time=142.62 bytes used=4337304692, alloc=4848776, time=142.76 bytes used=4341305776, alloc=4848776, time=142.89 bytes used=4345307732, alloc=4848776, time=143.02 bytes used=4349310924, alloc=4848776, time=143.15 bytes used=4353311932, alloc=4848776, time=143.28 bytes used=4357314084, alloc=4848776, time=143.41 bytes used=4361315060, alloc=4848776, time=143.54 bytes used=4365316120, alloc=4848776, time=143.68 bytes used=4369317064, alloc=4848776, time=143.81 bytes used=4373318192, alloc=4848776, time=143.94 bytes used=4377319356, alloc=4848776, time=144.07 bytes used=4381320768, alloc=4848776, time=144.20 bytes used=4385321976, alloc=4848776, time=144.34 bytes used=4389323032, alloc=4848776, time=144.47 bytes used=4393324696, alloc=4848776, time=144.60 bytes used=4397325800, alloc=4848776, time=144.73 bytes used=4401326736, alloc=4848776, time=144.87 bytes used=4405327748, alloc=4848776, time=145.00 bytes used=4409330056, alloc=4848776, time=145.13 bytes used=4413331100, alloc=4848776, time=145.26 bytes used=4417332344, alloc=4848776, time=145.40 bytes used=4421333072, alloc=4848776, time=145.53 TOP MAIN SOLVE Loop bytes used=4425334132, alloc=4848776, time=145.66 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=4429335576, alloc=4848776, time=145.80 bytes used=4433336704, alloc=4848776, time=145.93 bytes used=4437337676, alloc=4848776, time=146.06 bytes used=4441338600, alloc=4848776, time=146.19 bytes used=4445339836, alloc=4848776, time=146.32 bytes used=4449341764, alloc=4848776, time=146.46 bytes used=4453342924, alloc=4848776, time=146.59 bytes used=4457343800, alloc=4848776, time=146.72 bytes used=4461344804, alloc=4848776, time=146.85 bytes used=4465345712, alloc=4848776, time=146.98 bytes used=4469346980, alloc=4848776, time=147.12 bytes used=4473348032, alloc=4848776, time=147.25 bytes used=4477349452, alloc=4848776, time=147.38 bytes used=4481350328, alloc=4848776, time=147.52 bytes used=4485351656, alloc=4848776, time=147.65 bytes used=4489352908, alloc=4848776, time=147.78 bytes used=4493353924, alloc=4848776, time=147.91 bytes used=4497355100, alloc=4848776, time=148.05 bytes used=4501356084, alloc=4848776, time=148.18 bytes used=4505357180, alloc=4848776, time=148.31 bytes used=4509358804, alloc=4848776, time=148.44 bytes used=4513359872, alloc=4848776, time=148.58 bytes used=4517360836, alloc=4848776, time=148.71 bytes used=4521363300, alloc=4848776, time=148.84 bytes used=4525364580, alloc=4848776, time=148.97 bytes used=4529365520, alloc=4848776, time=149.10 bytes used=4533366320, alloc=4848776, time=149.24 bytes used=4537367756, alloc=4848776, time=149.37 bytes used=4541368560, alloc=4848776, time=149.50 bytes used=4545370196, alloc=4848776, time=149.64 bytes used=4549371308, alloc=4848776, time=149.77 bytes used=4553372228, alloc=4848776, time=149.90 bytes used=4557373224, alloc=4848776, time=150.03 bytes used=4561374288, alloc=4848776, time=150.16 bytes used=4565375160, alloc=4848776, time=150.29 bytes used=4569377136, alloc=4848776, time=150.43 bytes used=4573377796, alloc=4848776, time=150.56 bytes used=4577378868, alloc=4848776, time=150.69 bytes used=4581380312, alloc=4848776, time=150.82 bytes used=4585381276, alloc=4848776, time=150.96 bytes used=4589383204, alloc=4848776, time=151.09 bytes used=4593384268, alloc=4848776, time=151.22 bytes used=4597385628, alloc=4848776, time=151.35 bytes used=4601386540, alloc=4848776, time=151.48 bytes used=4605387664, alloc=4848776, time=151.61 bytes used=4609388620, alloc=4848776, time=151.74 bytes used=4613389688, alloc=4848776, time=151.87 bytes used=4617390804, alloc=4848776, time=152.00 bytes used=4621391872, alloc=4848776, time=152.14 bytes used=4625392828, alloc=4848776, time=152.27 bytes used=4629393932, alloc=4848776, time=152.40 bytes used=4633394996, alloc=4848776, time=152.53 bytes used=4637397592, alloc=4848776, time=152.66 bytes used=4641398596, alloc=4848776, time=152.80 bytes used=4645399564, alloc=4848776, time=152.93 bytes used=4649401312, alloc=4848776, time=153.06 bytes used=4653403816, alloc=4848776, time=153.19 bytes used=4657404628, alloc=4848776, time=153.32 bytes used=4661405696, alloc=4848776, time=153.45 bytes used=4665406836, alloc=4848776, time=153.58 bytes used=4669408000, alloc=4848776, time=153.72 bytes used=4673408832, alloc=4848776, time=153.85 bytes used=4677409800, alloc=4848776, time=153.98 bytes used=4681411412, alloc=4848776, time=154.11 bytes used=4685412612, alloc=4848776, time=154.24 bytes used=4689413520, alloc=4848776, time=154.38 bytes used=4693415108, alloc=4848776, time=154.51 bytes used=4697416136, alloc=4848776, time=154.64 bytes used=4701417700, alloc=4848776, time=154.77 bytes used=4705418844, alloc=4848776, time=154.90 bytes used=4709421224, alloc=4848776, time=155.03 bytes used=4713422692, alloc=4848776, time=155.17 bytes used=4717423516, alloc=4848776, time=155.30 bytes used=4721424836, alloc=4848776, time=155.43 bytes used=4725425992, alloc=4848776, time=155.56 bytes used=4729426908, alloc=4848776, time=155.69 bytes used=4733427964, alloc=4848776, time=155.83 bytes used=4737428840, alloc=4848776, time=155.96 bytes used=4741430048, alloc=4848776, time=156.09 bytes used=4745430944, alloc=4848776, time=156.22 bytes used=4749432128, alloc=4848776, time=156.36 bytes used=4753433212, alloc=4848776, time=156.49 bytes used=4757434656, alloc=4848776, time=156.62 bytes used=4761436160, alloc=4848776, time=156.75 bytes used=4765437124, alloc=4848776, time=156.88 bytes used=4769438544, alloc=4848776, time=157.02 bytes used=4773439540, alloc=4848776, time=157.15 bytes used=4777440840, alloc=4848776, time=157.28 bytes used=4781441736, alloc=4848776, time=157.42 bytes used=4785442960, alloc=4848776, time=157.55 bytes used=4789443856, alloc=4848776, time=157.68 bytes used=4793444836, alloc=4848776, time=157.81 bytes used=4797446024, alloc=4848776, time=157.94 bytes used=4801446892, alloc=4914300, time=158.08 bytes used=4805448028, alloc=4914300, time=158.21 bytes used=4809449180, alloc=4914300, time=158.34 bytes used=4813450140, alloc=4914300, time=158.47 bytes used=4817450928, alloc=4914300, time=158.60 bytes used=4821451956, alloc=4914300, time=158.74 bytes used=4825453092, alloc=4914300, time=158.87 bytes used=4829454028, alloc=4914300, time=159.00 bytes used=4833455180, alloc=4914300, time=159.13 bytes used=4837456068, alloc=4914300, time=159.27 bytes used=4841457152, alloc=4914300, time=159.40 bytes used=4845458012, alloc=4914300, time=159.53 bytes used=4849460896, alloc=4914300, time=159.66 bytes used=4853462136, alloc=4914300, time=159.80 bytes used=4857463376, alloc=4914300, time=159.93 bytes used=4861464304, alloc=4914300, time=160.06 bytes used=4865466548, alloc=4914300, time=160.20 bytes used=4869467492, alloc=4914300, time=160.33 bytes used=4873468420, alloc=4914300, time=160.46 bytes used=4877469372, alloc=4914300, time=160.59 bytes used=4881470308, alloc=4914300, time=160.72 bytes used=4885472524, alloc=4914300, time=160.86 bytes used=4889473852, alloc=4914300, time=160.99 bytes used=4893474772, alloc=4914300, time=161.12 bytes used=4897477056, alloc=4914300, time=161.25 bytes used=4901477952, alloc=4914300, time=161.39 bytes used=4905478904, alloc=4914300, time=161.52 bytes used=4909480240, alloc=4914300, time=161.65 bytes used=4913481132, alloc=4914300, time=161.78 bytes used=4917482104, alloc=4914300, time=161.91 bytes used=4921483004, alloc=4914300, time=162.04 bytes used=4925483988, alloc=4914300, time=162.17 bytes used=4929485144, alloc=4914300, time=162.31 bytes used=4933485840, alloc=4914300, time=162.44 bytes used=4937487548, alloc=4914300, time=162.57 bytes used=4941488892, alloc=4914300, time=162.71 bytes used=4945491472, alloc=4914300, time=162.84 bytes used=4949492360, alloc=4914300, time=162.97 bytes used=4953493428, alloc=4914300, time=163.10 bytes used=4957494556, alloc=4914300, time=163.23 bytes used=4961495564, alloc=4914300, time=163.37 bytes used=4965496556, alloc=4914300, time=163.50 bytes used=4969497628, alloc=4914300, time=163.63 bytes used=4973499740, alloc=4914300, time=163.76 bytes used=4977500808, alloc=4914300, time=163.90 bytes used=4981501908, alloc=4914300, time=164.03 bytes used=4985502764, alloc=4914300, time=164.16 bytes used=4989503720, alloc=4914300, time=164.29 bytes used=4993505084, alloc=4914300, time=164.42 bytes used=4997506216, alloc=4914300, time=164.56 bytes used=5001507112, alloc=4914300, time=164.69 bytes used=5005508168, alloc=4914300, time=164.82 bytes used=5009509164, alloc=4914300, time=164.95 bytes used=5013510536, alloc=4914300, time=165.08 bytes used=5017511348, alloc=4914300, time=165.22 bytes used=5021512316, alloc=4914300, time=165.35 bytes used=5025513392, alloc=4914300, time=165.48 bytes used=5029515164, alloc=4914300, time=165.61 bytes used=5033515972, alloc=4914300, time=165.75 bytes used=5037517640, alloc=4914300, time=165.88 bytes used=5041518676, alloc=4914300, time=166.01 bytes used=5045520456, alloc=4914300, time=166.14 bytes used=5049521440, alloc=4914300, time=166.28 bytes used=5053523196, alloc=4914300, time=166.41 bytes used=5057524104, alloc=4914300, time=166.54 bytes used=5061525084, alloc=4914300, time=166.67 bytes used=5065526348, alloc=4914300, time=166.81 bytes used=5069527288, alloc=4914300, time=166.94 bytes used=5073528480, alloc=4914300, time=167.07 bytes used=5077529544, alloc=4914300, time=167.20 bytes used=5081530596, alloc=4914300, time=167.34 bytes used=5085531808, alloc=4914300, time=167.47 bytes used=5089533960, alloc=4914300, time=167.60 bytes used=5093535508, alloc=4914300, time=167.73 bytes used=5097536456, alloc=4914300, time=167.87 bytes used=5101537552, alloc=4914300, time=168.00 bytes used=5105538708, alloc=4914300, time=168.13 bytes used=5109539632, alloc=4914300, time=168.26 bytes used=5113540440, alloc=4914300, time=168.40 bytes used=5117541616, alloc=4914300, time=168.53 bytes used=5121542936, alloc=4914300, time=168.66 bytes used=5125545108, alloc=4914300, time=168.79 bytes used=5129545828, alloc=4914300, time=168.92 bytes used=5133546992, alloc=4914300, time=169.05 bytes used=5137547944, alloc=4914300, time=169.19 bytes used=5141549728, alloc=4914300, time=169.32 bytes used=5145550916, alloc=4914300, time=169.46 bytes used=5149551744, alloc=4914300, time=169.59 bytes used=5153553732, alloc=4914300, time=169.72 bytes used=5157554632, alloc=4914300, time=169.85 bytes used=5161555864, alloc=4914300, time=169.98 bytes used=5165557016, alloc=4914300, time=170.12 bytes used=5169558164, alloc=4914300, time=170.25 bytes used=5173559784, alloc=4914300, time=170.38 bytes used=5177560944, alloc=4914300, time=170.51 bytes used=5181562348, alloc=4914300, time=170.65 bytes used=5185563088, alloc=4914300, time=170.78 bytes used=5189564160, alloc=4914300, time=170.91 bytes used=5193566704, alloc=4914300, time=171.04 bytes used=5197567880, alloc=4914300, time=171.17 bytes used=5201569536, alloc=4914300, time=171.31 bytes used=5205570592, alloc=4914300, time=171.44 bytes used=5209571748, alloc=4914300, time=171.57 bytes used=5213572728, alloc=4914300, time=171.70 bytes used=5217573912, alloc=4914300, time=171.84 bytes used=5221574956, alloc=4914300, time=171.97 bytes used=5225576024, alloc=4914300, time=172.10 bytes used=5229577132, alloc=4914300, time=172.23 bytes used=5233578380, alloc=4914300, time=172.36 bytes used=5237579744, alloc=4914300, time=172.50 bytes used=5241580500, alloc=4914300, time=172.63 bytes used=5245582760, alloc=4914300, time=172.76 bytes used=5249583708, alloc=4914300, time=172.89 bytes used=5253585572, alloc=4914300, time=173.02 bytes used=5257586372, alloc=4914300, time=173.16 bytes used=5261587424, alloc=4914300, time=173.29 bytes used=5265588580, alloc=4914300, time=173.42 bytes used=5269590212, alloc=4914300, time=173.55 bytes used=5273591208, alloc=4914300, time=173.69 bytes used=5277594580, alloc=4914300, time=173.82 bytes used=5281595496, alloc=4914300, time=173.95 bytes used=5285596528, alloc=4914300, time=174.08 bytes used=5289597708, alloc=4914300, time=174.21 bytes used=5293600048, alloc=4914300, time=174.35 bytes used=5297601156, alloc=4914300, time=174.48 bytes used=5301603616, alloc=4914300, time=174.61 bytes used=5305604588, alloc=4914300, time=174.74 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=5309605744, alloc=4914300, time=174.88 bytes used=5313607100, alloc=4914300, time=175.01 bytes used=5317607956, alloc=4914300, time=175.14 bytes used=5321608920, alloc=4914300, time=175.28 bytes used=5325609876, alloc=4914300, time=175.41 bytes used=5329610944, alloc=4914300, time=175.54 bytes used=5333612432, alloc=4914300, time=175.68 bytes used=5337613404, alloc=4914300, time=175.81 bytes used=5341614376, alloc=4914300, time=175.94 bytes used=5345615284, alloc=4914300, time=176.07 bytes used=5349616596, alloc=4914300, time=176.20 bytes used=5353617696, alloc=4914300, time=176.34 bytes used=5357619964, alloc=4914300, time=176.47 bytes used=5361620816, alloc=4914300, time=176.60 bytes used=5365621644, alloc=4914300, time=176.73 bytes used=5369622720, alloc=4914300, time=176.86 bytes used=5373623540, alloc=4914300, time=177.00 bytes used=5377624592, alloc=4914300, time=177.13 bytes used=5381626116, alloc=4914300, time=177.26 bytes used=5385626916, alloc=4914300, time=177.39 bytes used=5389628260, alloc=4914300, time=177.53 bytes used=5393630096, alloc=4914300, time=177.66 bytes used=5397630932, alloc=4914300, time=177.79 bytes used=5401632036, alloc=4914300, time=177.92 bytes used=5405633196, alloc=4914300, time=178.05 bytes used=5409636552, alloc=4914300, time=178.18 bytes used=5413637320, alloc=4914300, time=178.32 bytes used=5417638484, alloc=4914300, time=178.45 bytes used=5421639480, alloc=4914300, time=178.58 bytes used=5425642304, alloc=4914300, time=178.72 bytes used=5429643280, alloc=4914300, time=178.85 bytes used=5433644244, alloc=4914300, time=178.98 bytes used=5437645560, alloc=4914300, time=179.11 bytes used=5441646700, alloc=4914300, time=179.25 bytes used=5445647844, alloc=4914300, time=179.38 bytes used=5449649156, alloc=4914300, time=179.51 bytes used=5453650492, alloc=4914300, time=179.64 bytes used=5457651600, alloc=4914300, time=179.78 bytes used=5461653704, alloc=4914300, time=179.91 bytes used=5465655648, alloc=4914300, time=180.04 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 = 6181 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 2 Minutes 59 Seconds Expected Time Remaining = 40 Minutes 41 Seconds Optimized Time Remaining = 40 Minutes 39 Seconds Expected Total Time = 43 Minutes 39 Seconds Time to Timeout Unknown Percent Done = 6.869 % > quit bytes used=5467001492, alloc=4914300, time=180.08