(%i1) batch(diffeq.max)
read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max
(%i2) load(stringproc)
(%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac
(%i3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%o3) check_sign(x0, xf) := block([ret],
if xf > x0 then ret : 1.0 else ret : - 1.0, ret)
(%i4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%o4) est_size_answer() := block([min_size], min_size : glob_large_float,
if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ),
1 1
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")),
if min_size < 1.0 then (min_size : 1.0,
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size)
(%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2,
hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms,
hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125,
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""),
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""),
value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2
no_terms no_terms - 1
+ array_y hn_div_ho + array_y ),
no_terms - 2 no_terms - 3
if value3 > max_value3 then (max_value3 : value3,
omniout_float(ALWAYS, "value3", 32, value3, 32, "")),
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3)
(%i6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%o6) reached_interval() := block([ret],
if glob_check_sign array_x >= glob_check_sign glob_next_display
1
then ret : true else ret : false, return(ret))
(%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 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) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"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, " "))))
(%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var,
numeric_val, relerr, term_no], if reached_interval()
then (if iter >= 0 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) # 0.0
abserr 100.0
then (relerr : -----------------------,
omniabs(analytic_val_y)
if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr))
else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1),
if glob_iter = 1 then array_1st_rel_error : relerr
1
else array_last_rel_error : relerr, omniout_float(ALWAYS,
1
"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, " "))))
(%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
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))), 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 ), hnew : sz2), return(hnew))
1
(%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp],
block(hnew : h_param, glob_normmax : glob_small_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ),
1, 1
if tmp < glob_normmax then glob_normmax : tmp),
if glob_look_poles and (omniabs(array_pole ) > glob_small_float)
1
array_pole
1
and (array_pole # glob_large_float) then (sz2 : -----------,
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))), 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 ), hnew : sz2), return(hnew))
1
(%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
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(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
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(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
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))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec,
clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec],
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(clock_sec1) + convfloat(glob_orig_start_sec)
+ convfloat(glob_max_sec), expect_sec :
comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x ),
1
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(glob_h) + convfloat(array_x ),
1
convfloat(opt_clock_sec)), glob_total_exp_sec :
total_clock_sec + glob_optimal_expect_sec,
percent_done : comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done,
1
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))),
omniout_str_noeol(INFO, "Time to Timeout "),
omniout_timestr(convfloat(left_sec)), omniout_float(INFO,
"Percent Done ", 33, percent_done, 4, "%"))
(%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1,
nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term],
n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10)
and ((omniabs(array_y_higher ) < glob_small_float)
1, m
or (omniabs(array_y_higher ) < glob_small_float)
1, m - 1
or (omniabs(array_y_higher ) < glob_small_float)) do m :
1, m - 2
array_y_higher
1, m
m - 1, if m > 10 then (rm0 : ----------------------,
array_y_higher
1, m - 1
array_y_higher
1, m - 1
rm1 : ----------------------, hdrc : convfloat(m - 1) rm0
array_y_higher
1, m - 2
- convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float
glob_h convfloat(m - 1) rm0
then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------,
hdrc hdrc
array_real_pole : rcs, array_real_pole : ord_no)
1, 1 1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float))
1, 2
else (array_real_pole : glob_large_float,
1, 1
array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms,
1, 2
cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) >
1, n
glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n,
if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float)
elseif ((omniabs(array_y_higher ) >= glob_large_float)
1, m
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 1
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 2
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 3
or (omniabs(array_y_higher ) >= glob_large_float)
1, m - 4
or (omniabs(array_y_higher ) >= glob_large_float))
1, m - 5
or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float))
1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5
then (rad_c : glob_large_float, ord_no : glob_large_float)
array_y_higher array_y_higher
1, m 1, m - 1
else (rm0 : ----------------------, rm1 : ----------------------,
array_y_higher array_y_higher
1, m - 1 1, m - 2
array_y_higher array_y_higher
1, m - 2 1, m - 3
rm2 : ----------------------, rm3 : ----------------------,
array_y_higher array_y_higher
1, m - 3 1, m - 4
array_y_higher
1, m - 4
rm4 : ----------------------, nr1 : convfloat(m - 3) rm2
array_y_higher
1, m - 5
- 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0,
nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1,
- 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0
dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---,
rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1
5.0 8.0 3.0
ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float)
rm4 rm3 rm2
or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float,
ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) >
dr1 dr2 - ds2 dr1 + ds1 dr2
glob_small_float then (rcs : ---------------------------,
nr1 dr2 - nr2 dr1
rcs nr1 - ds1 convfloat(m)
ord_no : ------------- - ------------,
2.0 dr1 2.0
if omniabs(rcs) > glob_small_float then (if rcs > 0.0
then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float)
else (rad_c : glob_large_float, ord_no : glob_large_float))
else (rad_c : glob_large_float, ord_no : glob_large_float)),
array_complex_pole : rad_c, array_complex_pole : ord_no),
1, 1 1, 2
found : false, if (not found) and ((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float))
1, 1 1, 2
and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0))
1, 1 1, 2
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , found : true, array_type_pole : 2,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if (not found) and ((array_real_pole # glob_large_float)
1, 1
and (array_real_pole # glob_large_float) and (array_real_pole > 0.0)
1, 2 1, 1
and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <=
1, 2 1, 1 1, 2 1, 1 1, 2
0.0)))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and (((array_real_pole = glob_large_float)
1, 1
or (array_real_pole = glob_large_float))
1, 2
and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float)))
1, 1 1, 2
then (array_poles : glob_large_float, array_poles : glob_large_float,
1, 1 1, 2
found : true, array_type_pole : 3, if reached_interval()
1
then omniout_str(ALWAYS, "NO POLE")),
if (not found) and ((array_real_pole < array_complex_pole )
1, 1 1, 1
and (array_real_pole > 0.0) and (array_real_pole >
1, 1 1, 2
0.0))
then (array_poles : array_real_pole ,
1, 1 1, 1
array_poles : array_real_pole , found : true, array_type_pole : 1,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Real estimate of pole used"))),
if (not found) and ((array_complex_pole # glob_large_float)
1, 1
and (array_complex_pole # glob_large_float)
1, 2
and (array_complex_pole > 0.0) and (array_complex_pole >
1, 1 1, 2
0.0))
then (array_poles : array_complex_pole ,
1, 1 1, 1
array_poles : array_complex_pole , array_type_pole : 2, found : true,
1, 2 1, 2 1
if glob_display_flag then (if reached_interval()
then omniout_str(ALWAYS, "Complex estimate of poles used"))),
if not found then (array_poles : glob_large_float,
1, 1
array_poles : glob_large_float, array_type_pole : 3,
1, 2 1
if reached_interval() then omniout_str(ALWAYS, "NO POLE")),
array_pole : glob_large_float, array_pole : glob_large_float,
1 2
if array_pole > array_poles then (array_pole : array_poles ,
1 1, 1 1 1, 1
array_pole : array_poles ), if array_pole glob_ratio_of_radius <
2 1, 2 1
omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1,
1
ratio : 1.0, while term <= glob_max_terms do (array_y :
term
array_y ratio, array_y_higher : array_y_higher ratio,
term 1, term 1, term
ratio h_new
array_x : array_x ratio, ratio : ---------------, term : 1 + term),
term term omniabs(glob_h)
glob_h : h_new), if reached_interval() then display_pole())
(%i11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%o11) get_norms() := block([iii], if not glob_initial_pass
then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0,
iii
iii : 1 + iii), iii : 1, while iii <=
glob_max_terms do (if omniabs(array_y ) > array_norms
iii iii
then array_norms : omniabs(array_y ), iii : 1 + iii)))
iii iii
(%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_0D2 + array_tmp1 , omniout_str(ALWAYS, "WARNING: ar\
1 1 1
ccos of linear function has low precision in testing."),
array_tmp3 : arccos(array_tmp2 ), array_tmp3_a1 : sin(array_tmp3 ),
1 1 1 1
array_tmp4 : array_tmp3 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
- array_tmp2
2
array_tmp3 : --------------, array_tmp3_a1 : array_tmp2 array_tmp3 ,
2 array_tmp3_a1 2 1 2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
att(2, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : ------------------------------------,
3 array_tmp3_a1
1
array_tmp3 array_tmp2 1
2 2
array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 ,
3 2 3 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
att(3, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : ------------------------------------,
4 array_tmp3_a1
1
array_tmp3 array_tmp2 2
3 2
array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 ,
4 3 4 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
att(4, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : ------------------------------------,
5 array_tmp3_a1
1
array_tmp3 array_tmp2 3
4 2
array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 ,
5 4 5 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp3 :
kkk
att(kkk - 1, array_tmp3_a1, array_tmp3, 2)
------------------------------------------,
array_tmp3_a1
1
array_tmp3 array_tmp2 (kkk - 2)
kkk - 1 2
array_tmp3_a1 : ---------------------------------------
kkk kkk - 1
+ array_tmp3 array_tmp2 , array_tmp4 : array_tmp3 , order_d : 1,
kkk 1 kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp4 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
(%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp,
temp2], array_tmp1 : array_const_0D1 array_x ,
1 1 1
array_tmp2 : array_const_0D2 + array_tmp1 , omniout_str(ALWAYS, "WARNING: ar\
1 1 1
ccos of linear function has low precision in testing."),
array_tmp3 : arccos(array_tmp2 ), array_tmp3_a1 : sin(array_tmp3 ),
1 1 1 1
array_tmp4 : array_tmp3 + array_const_0D0 ,
1 1 1
if not array_y_set_initial then (if 1 <= glob_max_terms
1, 2
then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1),
1
array_y : temporary, array_y_higher : temporary,
2 1, 2
temporary 1.0
temporary : -------------, array_y_higher : temporary, 0)), kkk : 2,
glob_h 2, 1
array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 ,
2 1 2 2 2
- array_tmp2
2
array_tmp3 : --------------, array_tmp3_a1 : array_tmp2 array_tmp3 ,
2 array_tmp3_a1 2 1 2
1
array_tmp4 : array_tmp3 , if not array_y_set_initial
2 2 1, 3
then (if 2 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary,
2 3
temporary 2.0
array_y_higher : temporary, temporary : -------------,
1, 3 glob_h
array_y_higher : temporary, 0)), kkk : 3,
2, 2
att(2, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : ------------------------------------,
3 array_tmp3_a1
1
array_tmp3 array_tmp2 1
2 2
array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 ,
3 2 3 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
3 3 1, 4
then (if 3 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary,
3 4
temporary 3.0
array_y_higher : temporary, temporary : -------------,
1, 4 glob_h
array_y_higher : temporary, 0)), kkk : 4,
2, 3
att(3, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : ------------------------------------,
4 array_tmp3_a1
1
array_tmp3 array_tmp2 2
3 2
array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 ,
4 3 4 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
4 4 1, 5
then (if 4 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary,
4 5
temporary 4.0
array_y_higher : temporary, temporary : -------------,
1, 5 glob_h
array_y_higher : temporary, 0)), kkk : 5,
2, 4
att(4, array_tmp3_a1, array_tmp3, 2)
array_tmp3 : ------------------------------------,
5 array_tmp3_a1
1
array_tmp3 array_tmp2 3
4 2
array_tmp3_a1 : ------------------------- + array_tmp3 array_tmp2 ,
5 4 5 1
array_tmp4 : array_tmp3 , if not array_y_set_initial
5 5 1, 6
then (if 5 <= glob_max_terms then (temporary :
array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary,
5 6
temporary 5.0
array_y_higher : temporary, temporary : -------------,
1, 6 glob_h
array_y_higher : temporary, 0)), kkk : 6,
2, 5
while kkk <= glob_max_terms do (array_tmp3 :
kkk
att(kkk - 1, array_tmp3_a1, array_tmp3, 2)
------------------------------------------,
array_tmp3_a1
1
array_tmp3 array_tmp2 (kkk - 2)
kkk - 1 2
array_tmp3_a1 : ---------------------------------------
kkk kkk - 1
+ array_tmp3 array_tmp2 , array_tmp4 : array_tmp3 , order_d : 1,
kkk 1 kkk kkk
if 1 + order_d + kkk <= glob_max_terms
then (if not array_y_set_initial
1, order_d + kkk
then (temporary : array_tmp4 expt(glob_h, order_d)
kkk
factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary,
order_d + kkk
array_y_higher : temporary, term : - 1 + order_d + kkk,
1, order_d + kkk
adj2 : - 1 + order_d + kkk, adj3 : 2, while term >=
1 do (if adj3 <= 1 + order_d then (if adj2 > 0
temporary convfp(adj2)
then temporary : ---------------------- else temporary : temporary,
glob_h
array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1,
adj3, term
adj3 : 1 + adj3))), kkk : 1 + kkk))
log(x)
(%i13) log10(x) := ---------
log(10.0)
log(x)
(%o13) log10(x) := ---------
log(10.0)
(%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel
then printf(true, "~a~%", string(str))
(%i15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%o15) omniout_str_noeol(iolevel, str) :=
if glob_iolevel >= iolevel then printf(true, "~a", string(str))
(%i16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%o16) omniout_labstr(iolevel, label, str) :=
if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label),
string(str))
(%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (if vallen = 4
then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)
else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel))
(%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) :=
if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value,
postlabel), newline())
(%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen,
postlabel) := if glob_iolevel >= iolevel
then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline())
(%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) :=
block([i], if glob_iolevel >= iolevel then (i : 1,
while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ",
array_series ), newline(), i : 1 + i)))
i
(%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb,
subnum, arr_x) := (array_series2, numb, subnum) :=
block([i, sub, ts_term], if glob_iolevel >= iolevel
then (sub : 1, while sub <= subnum do (i : 1,
while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i,
"series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)))
sub, i
(%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel
then sprint(concat("cs_info ", str, " glob_correct_start_flag = ",
glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h))
(%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "| ~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), printf(fd, "~%"),
secs
if secs >= 0 then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(fd,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int,
sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%",
minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int))
else printf(fd, " Unknown~%"), printf(fd, " | ~%"))
(%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int,
minutes, minutes_int, sec_int, seconds, secs, years, years_int],
secs : convfloat(secs_in), if secs >= 0
secs
then (years_int : trunc(----------------),
glob_sec_in_year
sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)),
sec_temp
days_int : trunc(---------------), sec_temp :
glob_sec_in_day
sec_temp
mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------),
glob_sec_in_hour
sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)),
sec_temp
minutes_int : trunc(------------------),
glob_sec_in_minute
sec_int : mod(sec_temp, trunc(glob_sec_in_minute)),
if years_int > 0 then printf(true,
"= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int,
hours_int, minutes_int, sec_int) elseif days_int > 0
then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int,
hours_int, minutes_int, sec_int) elseif hours_int > 0
then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int,
minutes_int, sec_int) elseif minutes_int > 0
then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int)
else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%"))
(%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) :=
block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0,
if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats,
while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats,
ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)),
iii_ats lll_ats
ret_ats)
(%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, 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 : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) :=
block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0,
if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, 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 : arr_aa arr_bb convfp(al_att) + ret_att,
iii_att lll_att
ret_att
iii_att : 1 + iii_att), ret_att : ---------------), ret_att)
convfp(mmm_att)
(%i27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%o27) display_pole() := if (array_pole # glob_large_float)
1
and (array_pole > 0.0) and (array_pole # glob_large_float)
1 2
and (array_pole > 0.0) and glob_display_flag
2
then (omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole , 4, " "), omniout_float(ALWAYS,
1
"Order of pole ", 4, array_pole , 4, " "))
2
(%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"),
printf(file, " | "))
(%i29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%o29) logitem_integer(file, n) := (printf(file, ""),
printf(file, "~d", n), printf(file, " | "))
(%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str),
printf(file, " | "))
(%i31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%o31) logitem_good_digits(file, rel_error) :=
block([good_digits], printf(file, ""),
if rel_error # - 1.0 then (if rel_error > + 1.0E-34
then (good_digits : 1 - floor(log10(rel_error)),
printf(file, "~d", good_digits)) else (good_digits : 16,
printf(file, "~d", good_digits))) else printf(file, "Unknown"),
printf(file, " | "))
(%i32) log_revs(file, revs) := printf(file, revs)
(%o32) log_revs(file, revs) := printf(file, revs)
(%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x),
printf(file, " | "))
(%i34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%o34) logitem_pole(file, pole) := (printf(file, ""),
if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real")
elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"),
printf(file, " | "))
(%i35) logstart(file) := printf(file, "")
(%o35) logstart(file) := printf(file, "
")
(%i36) logend(file) := printf(file, "
~%")
(%o36) logend(file) := printf(file, "~%")
(%i37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%o37) chk_data() := block([errflag], errflag : false,
if (glob_max_terms < 15) or (glob_max_terms > 512)
then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"),
glob_max_terms : 30), if glob_max_iter < 2
then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true),
if errflag then quit())
(%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) :=
block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2,
sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0
sub1
then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left)
sub2
(%i39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%o39) comp_percent(t_end2, t_start2, t2) :=
block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2,
100.0 sub2
if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr)
sub1
(%i40) factorial_2(nnn) := nnn!
(%o40) factorial_2(nnn) := nnn!
(%i41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%o41) factorial_1(nnn) := block([ret],
if nnn <= glob_max_terms then (if array_fact_1 = 0
nnn
then (ret : factorial_2(nnn), array_fact_1 : ret)
nnn
else ret : array_fact_1 ) else ret : factorial_2(nnn), ret)
nnn
(%i42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%o42) factorial_3(mmm, nnn) := block([ret],
if (nnn <= glob_max_terms) and (mmm <= glob_max_terms)
factorial_1(mmm)
then (if array_fact_2 = 0 then (ret : ----------------,
mmm, nnn factorial_1(nnn)
array_fact_2 : ret) else ret : array_fact_2 )
mmm, nnn mmm, nnn
factorial_2(mmm)
else ret : ----------------, ret)
factorial_2(nnn)
(%i43) convfp(mmm) := mmm
(%o43) convfp(mmm) := mmm
(%i44) convfloat(mmm) := mmm
(%o44) convfloat(mmm) := mmm
(%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t)
(%i46) Si(x) := 0.0
(%o46) Si(x) := 0.0
(%i47) Ci(x) := 0.0
(%o47) Ci(x) := 0.0
(%i48) ln(x) := log(x)
(%o48) ln(x) := log(x)
(%i49) arcsin(x) := asin(x)
(%o49) arcsin(x) := asin(x)
(%i50) arccos(x) := acos(x)
(%o50) arccos(x) := acos(x)
(%i51) arctan(x) := atan(x)
(%o51) arctan(x) := atan(x)
(%i52) omniabs(x) := abs(x)
(%o52) omniabs(x) := abs(x)
(%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0)
y
then print("expt error x = ", x, "y = ", y), x )
(%i54) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], 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,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%o54) estimated_needed_step_error(x_start, x_end, estimated_h,
estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps,
step_error], 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,
range
""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps",
estimated_h
desired_abs_gbl_error
32, estimated_steps, 32, ""), step_error : omniabs(---------------------),
estimated_steps
omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error)
(%i55) exact_soln_y(x) := block(10.0 (0.2 + 0.1 x) arccos(0.2 + 0.1 x)
- 10.0 sqrt(1.0 - expt(0.2 + 0.1 x, 2)))
(%o55) exact_soln_y(x) := block(10.0 (0.2 + 0.1 x) arccos(0.2 + 0.1 x)
- 10.0 sqrt(1.0 - expt(0.2 + 0.1 x, 2)))
(%i56) main() := block([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, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
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/lin_arccospostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-0.8,"), omniout_str(ALWAYS, "x_end:0.8,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (10.\
0 * (0.1 * x + 0.2) * arccos(0.1 * x + 0.2 ) - 10.0 * sqrt(1.0 -"),
omniout_str(ALWAYS, "expt((0.1 * x + 0.2) , 2 ))) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, max_terms : 30, Digits : 32,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3_a1, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3_a1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 0.8, x_end : 0.8, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), 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 < glob_check_sign x_end)
1
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")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-12T23:37:26-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_arccos"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
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), log_revs(html_log_file, " 156 | "), logitem_str(html_log_file, "lin_arccos diffeq.max"),
logitem_str(html_log_file,
"lin_arccos maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%o56) main() := block([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, log10norm,
max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value,
est_answer, best_h, found_h, repeat_it],
define_variable(glob_max_terms, 30, fixnum),
define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum),
define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum),
define_variable(DEBUGMASSIVE, 4, fixnum),
define_variable(MAX_UNCHANGED, 10, fixnum),
define_variable(glob_check_sign, 1.0, float),
define_variable(glob_desired_digits_correct, 8.0, float),
define_variable(glob_max_value3, 0.0, float),
define_variable(glob_ratio_of_radius, 0.01, float),
define_variable(glob_percent_done, 0.0, float),
define_variable(glob_subiter_method, 3, fixnum),
define_variable(glob_log10normmin, 0.1, float),
define_variable(glob_total_exp_sec, 0.1, float),
define_variable(glob_optimal_expect_sec, 0.1, float),
define_variable(glob_html_log, true, boolean),
define_variable(glob_good_digits, 0, fixnum),
define_variable(glob_max_opt_iter, 10, fixnum),
define_variable(glob_dump, false, boolean),
define_variable(glob_djd_debug, true, boolean),
define_variable(glob_display_flag, true, boolean),
define_variable(glob_djd_debug2, true, boolean),
define_variable(glob_sec_in_minute, 60, fixnum),
define_variable(glob_min_in_hour, 60, fixnum),
define_variable(glob_hours_in_day, 24, fixnum),
define_variable(glob_days_in_year, 365, fixnum),
define_variable(glob_sec_in_hour, 3600, fixnum),
define_variable(glob_sec_in_day, 86400, fixnum),
define_variable(glob_sec_in_year, 31536000, fixnum),
define_variable(glob_almost_1, 0.999, float),
define_variable(glob_clock_sec, 0.0, float),
define_variable(glob_clock_start_sec, 0.0, float),
define_variable(glob_not_yet_finished, true, boolean),
define_variable(glob_initial_pass, true, boolean),
define_variable(glob_not_yet_start_msg, true, boolean),
define_variable(glob_reached_optimal_h, false, boolean),
define_variable(glob_optimal_done, false, boolean),
define_variable(glob_disp_incr, 0.1, float),
define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float),
define_variable(glob_hmin, 1.0E-11, float),
define_variable(glob_hmin_init, 0.001, float),
define_variable(glob_large_float, 9.0E+100, float),
define_variable(glob_last_good_h, 0.1, float),
define_variable(glob_look_poles, false, boolean),
define_variable(glob_neg_h, false, boolean),
define_variable(glob_display_interval, 0.0, float),
define_variable(glob_next_display, 0.0, float),
define_variable(glob_dump_analytic, false, boolean),
define_variable(glob_log10_abserr, 1.0E-11, float),
define_variable(glob_log10_relerr, 1.0E-11, float),
define_variable(glob_abserr, 1.0E-11, float),
define_variable(glob_relerr, 1.0E-11, float),
define_variable(glob_max_hours, 0.0, float),
define_variable(glob_max_iter, 1000, fixnum),
define_variable(glob_max_rel_trunc_err, 1.0E-11, float),
define_variable(glob_max_trunc_err, 1.0E-11, float),
define_variable(glob_no_eqs, 0, fixnum),
define_variable(glob_optimal_clock_start_sec, 0.0, float),
define_variable(glob_optimal_start, 0.0, float),
define_variable(glob_small_float, 1.0E-51, float),
define_variable(glob_smallish_float, 1.0E-101, float),
define_variable(glob_unchanged_h_cnt, 0, fixnum),
define_variable(glob_warned, false, boolean),
define_variable(glob_warned2, false, boolean),
define_variable(glob_max_sec, 10000.0, float),
define_variable(glob_orig_start_sec, 0.0, float),
define_variable(glob_start, 0, fixnum),
define_variable(glob_curr_iter_when_opt, 0, fixnum),
define_variable(glob_current_iter, 0, fixnum),
define_variable(glob_iter, 0, fixnum),
define_variable(glob_normmax, 0.0, float),
define_variable(glob_log10abserr, 0.0, float),
define_variable(glob_log10relerr, 0.0, float),
define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2,
DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO,
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/lin_arccospostode.ode#################"),
omniout_str(ALWAYS, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"),
omniout_str(ALWAYS, "!"), omniout_str(ALWAYS,
"/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "max_terms:30,"),
omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "x_start:-0.8,"), omniout_str(ALWAYS, "x_end:0.8,"),
omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"),
omniout_str(ALWAYS, "glob_h:0.00001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:100,"),
omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"),
omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"),
omniout_str(ALWAYS, "glob_desired_digits_correct:10,"),
omniout_str(ALWAYS, "glob_display_interval:0.001,"),
omniout_str(ALWAYS, "glob_look_poles:true,"),
omniout_str(ALWAYS, "glob_max_iter:10000000,"),
omniout_str(ALWAYS, "glob_max_minutes:3,"),
omniout_str(ALWAYS, "glob_subiter_method:3,"),
omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"),
omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"),
omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (10.\
0 * (0.1 * x + 0.2) * arccos(0.1 * x + 0.2 ) - 10.0 * sqrt(1.0 -"),
omniout_str(ALWAYS, "expt((0.1 * x + 0.2) , 2 ))) "),
omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""),
omniout_str(ALWAYS, "/* END USER DEF BLOCK */"),
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"),
glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false,
glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64,
glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0,
glob_log10_relerr : - 8.0, glob_hmax : 0.01, max_terms : 30, Digits : 32,
glob_max_terms : max_terms, glob_html_log : true,
array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms),
array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms),
array(array_1st_rel_error, 1 + max_terms),
array(array_last_rel_error, 1 + max_terms),
array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms),
array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms),
array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms),
array(array_tmp3_a1, 1 + max_terms), array(array_tmp3, 1 + max_terms),
array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms),
array(array_y_higher, 1 + 2, 1 + max_terms),
array(array_y_higher_work, 1 + 2, 1 + max_terms),
array(array_y_higher_work2, 1 + 2, 1 + max_terms),
array(array_y_set_initial, 1 + 2, 1 + max_terms),
array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3),
array(array_complex_pole, 1 + 1, 1 + 3),
array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1,
while term <= max_terms do (array_y_init : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_norms : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_last_rel_error : 0.0,
term
term : 1 + term), term : 1, while term <=
max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1,
term
while term <= max_terms do (array_tmp3_a1 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_higher_work : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 2 do (term : 1, while term <=
max_terms do (array_y_higher_work2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1,
while term <= max_terms do (array_y_set_initial : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0,
ord, term
term : 1 + term), ord : 1 + ord), ord : 1,
while ord <= 1 do (term : 1, while term <=
3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord),
ord, term
ord : 1, while ord <= 1 do (term : 1,
while term <= 3 do (array_complex_pole : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1,
while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term),
ord, term
ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term),
term
array(array_x, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term),
term
array(array_tmp0, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term),
term
array(array_tmp1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term),
term
array(array_tmp2, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term),
term
array(array_tmp3_a1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term),
term
array(array_tmp3, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term),
term
array(array_tmp4, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term),
term
array(array_m1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term),
term
array(array_const_1, 1 + 1 + max_terms), term : 1,
while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term),
term
array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term),
term
array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term),
term
array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1,
1
while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term),
term
array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1,
1
while term <= max_terms do (array_m1 : 0.0, term : 1 + term),
term
array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0,
1
while jjjf <= glob_max_terms do (array_fact_1 : 0,
iiif
array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif),
iiif, jjjf
x_start : - 0.8, x_end : 0.8, array_y_init : exact_soln_y(x_start),
1 + 0
glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100,
glob_desired_digits_correct : 10, glob_display_interval : 0.001,
glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3,
glob_subiter_method : 3, glob_last_good_h : glob_h,
glob_max_terms : max_terms, glob_max_sec :
convfloat(3600.0) convfloat(glob_max_hours)
+ convfloat(60.0) convfloat(glob_max_minutes),
glob_abserr : expt(10.0, glob_log10_abserr),
glob_relerr : expt(10.0, glob_log10_relerr),
if glob_h > 0.0 then (glob_neg_h : false,
glob_display_interval : omniabs(glob_display_interval))
else (glob_neg_h : true, glob_display_interval :
- omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true,
1, 1
array_y_set_initial : false, array_y_set_initial : false,
1, 2 1, 3
array_y_set_initial : false, array_y_set_initial : false,
1, 4 1, 5
array_y_set_initial : false, array_y_set_initial : false,
1, 6 1, 7
array_y_set_initial : false, array_y_set_initial : false,
1, 8 1, 9
array_y_set_initial : false, array_y_set_initial : false,
1, 10 1, 11
array_y_set_initial : false, array_y_set_initial : false,
1, 12 1, 13
array_y_set_initial : false, array_y_set_initial : false,
1, 14 1, 15
array_y_set_initial : false, array_y_set_initial : false,
1, 16 1, 17
array_y_set_initial : false, array_y_set_initial : false,
1, 18 1, 19
array_y_set_initial : false, array_y_set_initial : false,
1, 20 1, 21
array_y_set_initial : false, array_y_set_initial : false,
1, 22 1, 23
array_y_set_initial : false, array_y_set_initial : false,
1, 24 1, 25
array_y_set_initial : false, array_y_set_initial : false,
1, 26 1, 27
array_y_set_initial : false, array_y_set_initial : false,
1, 28 1, 29
array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"),
1, 30
glob_check_sign : check_sign(x_start, x_end),
glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h
then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0,
min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1,
while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS,
"opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h,
1 2
glob_next_display : x_start, order_diff : 1, term_no : 1,
while term_no <= order_diff do (array_y :
term_no
array_y_init expt(glob_h, term_no - 1)
term_no
---------------------------------------------, term_no : 1 + term_no),
factorial_1(term_no - 1)
rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), atomall(),
est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h,
est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, ""), value3 : test_suggested_h(),
omniout_float(ALWAYS, "value3", 32, value3, 32, ""),
if (value3 < est_needed_step_err) and (found_h < 0.0)
then (best_h : glob_h, found_h : 1.0),
omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter,
glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h
else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"),
if glob_html_log then html_log_file : openw("html/entry.html"),
if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"),
array_x : x_start, array_x : glob_h, glob_next_display : x_start,
1 2
order_diff : 1, term_no : 1, while term_no <=
order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1))
term_no term_no
/factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff,
r_order : 1, while r_order <= rows do (term_no : 1,
while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no,
array_y_init expt(glob_h, term_no - 1)
it
array_y_higher : ----------------------------------------,
r_order, term_no factorial_1(term_no - 1)
term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1,
glob_clock_start_sec : elapsed_time_seconds(),
glob_log10normmin : - glob_large_float,
if omniabs(array_y_higher ) > glob_small_float
1, 1
then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp),
1, 1
if log10norm < glob_log10normmin then glob_log10normmin : log10norm),
display_alot(current_iter), 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 < glob_check_sign x_end)
1
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")),
glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(),
glob_current_iter : 1 + glob_current_iter, atomall(),
display_alot(current_iter), if glob_look_poles then check_for_pole(),
if reached_interval() then glob_next_display :
glob_display_interval + glob_next_display, array_x : glob_h + array_x ,
1 1
array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1,
2
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
2, iii
array_y_higher
2, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 2, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 2,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 2, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, ord : 1, calc_term : 1,
factorial_1(calc_term - 1)
iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work :
1, iii
array_y_higher
1, iii
---------------------------
expt(glob_h, calc_term - 1)
-------------------------------------, iii : iii - 1), temp_sum : 0.0,
factorial_3(iii - calc_term, iii - 1)
ord : 1, calc_term : 1, iii : glob_max_terms,
while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum,
ord, iii
iii : iii - 1), array_y_higher_work2 :
ord, calc_term
temp_sum expt(glob_h, calc_term - 1)
------------------------------------, term_no : glob_max_terms,
factorial_1(calc_term - 1)
while term_no >= 1 do (array_y : array_y_higher_work2 ,
term_no 1, term_no
ord : 1, while ord <= order_diff do (array_y_higher :
ord, term_no
array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)),
ord, term_no
omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter
then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!"),
if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >=
convfloat(glob_max_sec) then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!"),
glob_clock_sec : elapsed_time_seconds(),
omniout_str(INFO, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"),
omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "),
prog_report(x_start, x_end), if glob_html_log
then (logstart(html_log_file), logitem_str(html_log_file,
"2013-01-12T23:37:26-06:00"), logitem_str(html_log_file, "Maxima"),
logitem_str(html_log_file, "lin_arccos"),
logitem_str(html_log_file, "diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"),
logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end),
logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h),
1
logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file,
array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms),
1
logitem_float(html_log_file, array_1st_rel_error ),
1
logitem_float(html_log_file, array_last_rel_error ),
1
logitem_integer(html_log_file, glob_iter),
logitem_pole(html_log_file, array_type_pole ),
1
if (array_type_pole = 1) or (array_type_pole = 2)
1 1
then (logitem_float(html_log_file, array_pole ),
1
logitem_float(html_log_file, array_pole ), 0)
2
else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0),
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), log_revs(html_log_file, " 156 | "), logitem_str(html_log_file, "lin_arccos diffeq.max"),
logitem_str(html_log_file,
"lin_arccos maxima results"),
logitem_str(html_log_file, "Languages compared - single equations"),
logend(html_log_file)), if glob_html_log then close(html_log_file)))
(%i57) main()
"##############ECHO OF PROBLEM#################"
"##############temp/lin_arccospostode.ode#################"
"diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"
"!"
"/* BEGIN FIRST INPUT BLOCK */"
"max_terms:30,"
"Digits:32,"
"!"
"/* END FIRST INPUT BLOCK */"
"/* BEGIN SECOND INPUT BLOCK */"
"x_start:-0.8,"
"x_end:0.8,"
"array_y_init[0 + 1] : exact_soln_y(x_start),"
"glob_h:0.00001,"
"glob_look_poles:true,"
"glob_max_iter:100,"
"/* END SECOND INPUT BLOCK */"
"/* BEGIN OVERRIDE BLOCK */"
"glob_desired_digits_correct:10,"
"glob_display_interval:0.001,"
"glob_look_poles:true,"
"glob_max_iter:10000000,"
"glob_max_minutes:3,"
"glob_subiter_method:3,"
"/* END OVERRIDE BLOCK */"
"!"
"/* BEGIN USER DEF BLOCK */"
"exact_soln_y (x) := (block("
" (10.0 * (0.1 * x + 0.2) * arccos(0.1 * x + 0.2 ) - 10.0 * sqrt(1.0 -"
"expt((0.1 * x + 0.2) , 2 ))) "
"));"
""
"/* END USER DEF BLOCK */"
"#######END OF ECHO OF PROBLEM#################"
"START of Optimize"
min_size = 0.0 ""
min_size = 1. ""
opt_iter = 1
"WARNING: arccos of linear function has low precision in testing."
glob_desired_digits_correct = 10. ""
desired_abs_gbl_error = 1.0000000000E-10 ""
range = 1.6 ""
estimated_steps = 1600. ""
step_error = 6.2500000000000000E-14 ""
est_needed_step_err = 6.2500000000000000E-14 ""
hn_div_ho = 0.5 ""
hn_div_ho_2 = 0.25 ""
hn_div_ho_3 = 0.125 ""
value3 = 2.93939858910162700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-107 ""
max_value3 = 2.93939858910162700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-107 ""
value3 = 2.93939858910162700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-107 ""
best_h = 1.000E-3 ""
"START of Soultion"
x[1] = -0.8 " "
y[1] (analytic) = -8.187131183512555 " "
y[1] (numeric) = -8.187131183512555 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.8 " "
y[1] (analytic) = -8.187131183512555 " "
y[1] (numeric) = -8.187131183512555 " "
absolute error = 0.0 " "
relative error = 0.0 "%"
Correct digits = 16
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.799 " "
y[1] (analytic) = -8.185680727432294 " "
y[1] (numeric) = -8.185680727431887 " "
absolute error = 4.06785716222657360000000000000E-13 " "
relative error = 4.96947938440128970000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.798 " "
y[1] (analytic) = -8.184230372081132 " "
y[1] (numeric) = -8.184230372080314 " "
absolute error = 8.1712414612411520000000000000E-13 " "
relative error = 9.984129343567493000000000000E-12 "%"
Correct digits = 14
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.797 " "
y[1] (analytic) = -8.182780117460295 " "
y[1] (numeric) = -8.182780117459068 " "
absolute error = 1.227462576025573100000000000E-12 " "
relative error = 1.50005567595105200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.796 " "
y[1] (analytic) = -8.181329963571011 " "
y[1] (numeric) = -8.181329963569375 " "
absolute error = 1.6360246490876307000000000000E-12 " "
relative error = 1.999705006853841300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.795 " "
y[1] (analytic) = -8.179879910414513 " "
y[1] (numeric) = -8.179879910412467 " "
absolute error = 2.0463630789890885000000000000E-12 " "
relative error = 2.501703082931188700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.794 " "
y[1] (analytic) = -8.17842995799203 " "
y[1] (numeric) = -8.178429957989573 " "
absolute error = 2.4567015088905464000000000000E-12 " "
relative error = 3.00387913268100700000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.793 " "
y[1] (analytic) = -8.176980106304796 " "
y[1] (numeric) = -8.176980106301928 " "
absolute error = 2.8688162956314045000000000000E-12 " "
relative error = 3.5084056195996200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.792 " "
y[1] (analytic) = -8.175530355354045 " "
y[1] (numeric) = -8.175530355350764 " "
absolute error = 3.2809310823722626000000000000E-12 " "
relative error = 4.01311100291325400000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.791 " "
y[1] (analytic) = -8.174080705141007 " "
y[1] (numeric) = -8.174080705137316 " "
absolute error = 3.6912695122737205000000000000E-12 " "
relative error = 4.515822201207449500000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.79 " "
y[1] (analytic) = -8.172631155666924 " "
y[1] (numeric) = -8.172631155662819 " "
absolute error = 4.105160655853979000000000000E-12 " "
relative error = 5.0230587648721300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.789 " "
y[1] (analytic) = -8.171181706933025 " "
y[1] (numeric) = -8.17118170692851 " "
absolute error = 4.515499085755436700000000000E-12 " "
relative error = 5.52612736775166600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.788 " "
y[1] (analytic) = -8.169732358940553 " "
y[1] (numeric) = -8.169732358935624 " "
absolute error = 4.929390229335695000000000000E-12 " "
relative error = 6.03372303125843900000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.787 " "
y[1] (analytic) = -8.168283111690746 " "
y[1] (numeric) = -8.168283111685403 " "
absolute error = 5.343281372915953000000000000E-12 " "
relative error = 6.5414987456402610000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.786 " "
y[1] (analytic) = -8.166833965184843 " "
y[1] (numeric) = -8.166833965179086 " "
absolute error = 5.757172516496212000000000000E-12 " "
relative error = 7.04945458795783000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.785 " "
y[1] (analytic) = -8.165384919424083 " "
y[1] (numeric) = -8.165384919417912 " "
absolute error = 6.17106366007647000000000000E-12 " "
relative error = 7.55759063531291000000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.784 " "
y[1] (analytic) = -8.16393597440971 " "
y[1] (numeric) = -8.163935974403126 " "
absolute error = 6.5849548036567280000000000000E-12 " "
relative error = 8.0659069648483510000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.783 " "
y[1] (analytic) = -8.162487130142967 " "
y[1] (numeric) = -8.162487130135968 " "
absolute error = 6.998845947236987000000000000E-12 " "
relative error = 8.5744036537481200000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.782 " "
y[1] (analytic) = -8.161038386625098 " "
y[1] (numeric) = -8.161038386617683 " "
absolute error = 7.414513447656645000000000000E-12 " "
relative error = 9.08525741014536600000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.781 " "
y[1] (analytic) = -8.159589743857348 " "
y[1] (numeric) = -8.159589743849518 " "
absolute error = 7.830180948076304000000000000E-12 " "
relative error = 9.59629245327067300000000000E-11 "%"
Correct digits = 13
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.78 " "
y[1] (analytic) = -8.158141201840962 " "
y[1] (numeric) = -8.158141201832716 " "
absolute error = 8.245848448495963000000000000E-12 " "
relative error = 1.01075088607625570000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.779 " "
y[1] (analytic) = -8.156692760577188 " "
y[1] (numeric) = -8.156692760568527 " "
absolute error = 8.661515948915621000000000000E-12 " "
relative error = 1.0618906710300940000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.778 " "
y[1] (analytic) = -8.155244420067273 " "
y[1] (numeric) = -8.155244420058196 " "
absolute error = 9.07718344933528000000000000E-12 " "
relative error = 1.11304860796071660000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.777 " "
y[1] (analytic) = -8.15379618031247 " "
y[1] (numeric) = -8.153796180302976 " "
absolute error = 9.494627306594339000000000000E-12 " "
relative error = 1.1644425610636841000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.776 " "
y[1] (analytic) = -8.152348041314024 " "
y[1] (numeric) = -8.152348041304116 " "
absolute error = 9.908518450174597000000000000E-12 " "
relative error = 1.2154189688615780000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.775 " "
y[1] (analytic) = -8.150900003073192 " "
y[1] (numeric) = -8.150900003062866 " "
absolute error = 1.032596230743365600000000000E-11 " "
relative error = 1.26684934222483230000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.774 " "
y[1] (analytic) = -8.149452065591223 " "
y[1] (numeric) = -8.14945206558048 " "
absolute error = 1.074340616469271500000000000E-11 " "
relative error = 1.31829797613679270000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.773 " "
y[1] (analytic) = -8.148004228869373 " "
y[1] (numeric) = -8.14800422885821 " "
absolute error = 1.116262637879117400000000000E-11 " "
relative error = 1.36998288970452740000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.772 " "
y[1] (analytic) = -8.146556492908896 " "
y[1] (numeric) = -8.146556492897314 " "
absolute error = 1.158184659288963300000000000E-11 " "
relative error = 1.42168615696349230000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.771 " "
y[1] (analytic) = -8.145108857711048 " "
y[1] (numeric) = -8.145108857699046 " "
absolute error = 1.200106680698809200000000000E-11 " "
relative error = 1.47340778578134960000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.77 " "
y[1] (analytic) = -8.143661323277081 " "
y[1] (numeric) = -8.143661323264663 " "
absolute error = 1.241851066424715100000000000E-11 " "
relative error = 1.52492965648647980000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.769 " "
y[1] (analytic) = -8.142213889608259 " "
y[1] (numeric) = -8.142213889595421 " "
absolute error = 1.28377308783456100000000000E-11 " "
relative error = 1.5766879932655840000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.768 " "
y[1] (analytic) = -8.14076655670584 " "
y[1] (numeric) = -8.140766556692581 " "
absolute error = 1.32587274492834700000000000E-11 " "
relative error = 1.62868292032791200000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.767 " "
y[1] (analytic) = -8.139319324571082 " "
y[1] (numeric) = -8.139319324557404 " "
absolute error = 1.367794766338192900000000000E-11 " "
relative error = 1.68047807414199450000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.766 " "
y[1] (analytic) = -8.137872193205247 " "
y[1] (numeric) = -8.137872193191148 " "
absolute error = 1.409894423431978800000000000E-11 " "
relative error = 1.73250991163166280000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.765 " "
y[1] (analytic) = -8.136425162609598 " "
y[1] (numeric) = -8.136425162595078 " "
absolute error = 1.451994080525764700000000000E-11 " "
relative error = 1.78456023561589070000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.764 " "
y[1] (analytic) = -8.134978232785398 " "
y[1] (numeric) = -8.134978232770456 " "
absolute error = 1.494271373303490700000000000E-11 " "
relative error = 1.83684741439296470000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.763 " "
y[1] (analytic) = -8.13353140373391 " "
y[1] (numeric) = -8.133531403718546 " "
absolute error = 1.536371030397276600000000000E-11 " "
relative error = 1.88893477400476430000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.762 " "
y[1] (analytic) = -8.132084675456401 " "
y[1] (numeric) = -8.132084675440614 " "
absolute error = 1.578648323175002600000000000E-11 " "
relative error = 1.94125908199105580000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.761 " "
y[1] (analytic) = -8.130638047954136 " "
y[1] (numeric) = -8.130638047937927 " "
absolute error = 1.620925615952728500000000000E-11 " "
relative error = 1.99360198596048980000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.76 " "
y[1] (analytic) = -8.129191521228385 " "
y[1] (numeric) = -8.129191521211752 " "
absolute error = 1.663380544414394500000000000E-11 " "
relative error = 2.04618200970007960000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.759 " "
y[1] (analytic) = -8.127745095280414 " "
y[1] (numeric) = -8.127745095263357 " "
absolute error = 1.705657837192120500000000000E-11 " "
relative error = 2.09856216846977030000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.758 " "
y[1] (analytic) = -8.126298770111495 " "
y[1] (numeric) = -8.126298770094014 " "
absolute error = 1.748112765653786500000000000E-11 " "
relative error = 2.15117954078102660000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.757 " "
y[1] (analytic) = -8.124852545722895 " "
y[1] (numeric) = -8.124852545704991 " "
absolute error = 1.790390058431512400000000000E-11 " "
relative error = 2.20359698635271100000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.756 " "
y[1] (analytic) = -8.12340642211589 " "
y[1] (numeric) = -8.123406422097561 " "
absolute error = 1.832844986893178400000000000E-11 " "
relative error = 2.25625173929901720000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.755 " "
y[1] (analytic) = -8.12196039929175 " "
y[1] (numeric) = -8.121960399272998 " "
absolute error = 1.875122279670904400000000000E-11 " "
relative error = 2.30870650370865960000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.754 " "
y[1] (analytic) = -8.120514477251751 " "
y[1] (numeric) = -8.120514477232575 " "
absolute error = 1.917577208132570400000000000E-11 " "
relative error = 2.36139866938768340000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.753 " "
y[1] (analytic) = -8.119068655997168 " "
y[1] (numeric) = -8.119068655977566 " "
absolute error = 1.960209772278176400000000000E-11 " "
relative error = 2.41432836120958640000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.752 " "
y[1] (analytic) = -8.117622935529276 " "
y[1] (numeric) = -8.117622935509248 " "
absolute error = 2.002842336423782400000000000E-11 " "
relative error = 2.46727687690164340000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.751 " "
y[1] (analytic) = -8.116177315849352 " "
y[1] (numeric) = -8.116177315828898 " "
absolute error = 2.045474900569388400000000000E-11 " "
relative error = 2.52024422455010200000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.75 " "
y[1] (analytic) = -8.114731796958676 " "
y[1] (numeric) = -8.114731796937795 " "
absolute error = 2.088107464714994400000000000E-11 " "
relative error = 2.57323041224553740000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.749 " "
y[1] (analytic) = -8.113286378858525 " "
y[1] (numeric) = -8.113286378837218 " "
absolute error = 2.130740028860600400000000000E-11 " "
relative error = 2.626235448082850400000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.748 " "
y[1] (analytic) = -8.111841061550182 " "
y[1] (numeric) = -8.111841061528446 " "
absolute error = 2.173550228690146500000000000E-11 " "
relative error = 2.67947832335213240000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.747 " "
y[1] (analytic) = -8.110395845034924 " "
y[1] (numeric) = -8.110395845012764 " "
absolute error = 2.216005157151812500000000000E-11 " "
relative error = 2.7323020965843750000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.746 " "
y[1] (analytic) = -8.10895072931404 " "
y[1] (numeric) = -8.108950729291452 " "
absolute error = 2.258815356981358500000000000E-11 " "
relative error = 2.7855827867046840000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.745 " "
y[1] (analytic) = -8.10750571438881 " "
y[1] (numeric) = -8.107505714365793 " "
absolute error = 2.301625556810904500000000000E-11 " "
relative error = 2.8388824354771540000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.744 " "
y[1] (analytic) = -8.106060800260519 " "
y[1] (numeric) = -8.106060800237072 " "
absolute error = 2.344613392324390600000000000E-11 " "
relative error = 2.8924201903951150000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.743 " "
y[1] (analytic) = -8.104615986930451 " "
y[1] (numeric) = -8.104615986906577 " "
absolute error = 2.387423592153936600000000000E-11 " "
relative error = 2.945757819992840000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.742 " "
y[1] (analytic) = -8.103171274399898 " "
y[1] (numeric) = -8.103171274375592 " "
absolute error = 2.430589063351362700000000000E-11 " "
relative error = 2.9995528676905160000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.741 " "
y[1] (analytic) = -8.10172666267014 " "
y[1] (numeric) = -8.101726662645406 " "
absolute error = 2.473399263180908700000000000E-11 " "
relative error = 3.0529285498823950000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.74 " "
y[1] (analytic) = -8.100282151742475 " "
y[1] (numeric) = -8.100282151717309 " "
absolute error = 2.516564734378335000000000000E-11 " "
relative error = 3.10676182290389600000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.739 " "
y[1] (analytic) = -8.098837741618187 " "
y[1] (numeric) = -8.09883774159259 " "
absolute error = 2.55973020557576100000000000E-11 " "
relative error = 3.16061426002135770000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.738 " "
y[1] (analytic) = -8.097393432298567 " "
y[1] (numeric) = -8.09739343227254 " "
absolute error = 2.60271804108924700000000000E-11 " "
relative error = 3.21426649557081800000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.737 " "
y[1] (analytic) = -8.095949223784912 " "
y[1] (numeric) = -8.095949223758453 " "
absolute error = 2.64588351228667300000000000E-11 " "
relative error = 3.2681572464824630000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.736 " "
y[1] (analytic) = -8.09450511607851 " "
y[1] (numeric) = -8.09450511605162 " "
absolute error = 2.68904898348409900000000000E-11 " "
relative error = 3.32206718622329370000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.735 " "
y[1] (analytic) = -8.09306110918066 " "
y[1] (numeric) = -8.093061109153338 " "
absolute error = 2.732214454681525000000000000E-11 " "
relative error = 3.3759963230502954000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.734 " "
y[1] (analytic) = -8.091617203092653 " "
y[1] (numeric) = -8.0916172030649 " "
absolute error = 2.775379925878951300000000000E-11 " "
relative error = 3.429944665224880000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.733 " "
y[1] (analytic) = -8.09017339781579 " "
y[1] (numeric) = -8.090173397787602 " "
absolute error = 2.818723032760317400000000000E-11 " "
relative error = 3.48413179069972160000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.732 " "
y[1] (analytic) = -8.088729693351363 " "
y[1] (numeric) = -8.088729693322744 " "
absolute error = 2.861888503957743500000000000E-11 " "
relative error = 3.53811860756097500000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.731 " "
y[1] (analytic) = -8.087286089700676 " "
y[1] (numeric) = -8.087286089671624 " "
absolute error = 2.905231610839109600000000000E-11 " "
relative error = 3.59234430266907660000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.73 " "
y[1] (analytic) = -8.085842586865027 " "
y[1] (numeric) = -8.085842586835541 " "
absolute error = 2.94857471772047600000000000E-11 " "
relative error = 3.64658931465010300000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.729 " "
y[1] (analytic) = -8.084399184845717 " "
y[1] (numeric) = -8.084399184815796 " "
absolute error = 2.99209546028578200000000000E-11 " "
relative error = 3.70107337833403050000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.728 " "
y[1] (analytic) = -8.082955883644045 " "
y[1] (numeric) = -8.08295588361369 " "
absolute error = 3.03543856716714800000000000E-11 " "
relative error = 3.7553570882520750000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.727 " "
y[1] (analytic) = -8.081512683261318 " "
y[1] (numeric) = -8.081512683230528 " "
absolute error = 3.07895930973245400000000000E-11 " "
relative error = 3.80987994501288300000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.726 " "
y[1] (analytic) = -8.080069583698837 " "
y[1] (numeric) = -8.080069583667614 " "
absolute error = 3.1223024166138200000000000E-11 " "
relative error = 3.8642023862182073000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.725 " "
y[1] (analytic) = -8.078626584957911 " "
y[1] (numeric) = -8.078626584926251 " "
absolute error = 3.166000794863066400000000000E-11 " "
relative error = 3.9189839529877970000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.724 " "
y[1] (analytic) = -8.077183687039842 " "
y[1] (numeric) = -8.077183687007746 " "
absolute error = 3.209521537428372500000000000E-11 " "
relative error = 3.9735651209445390000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.723 " "
y[1] (analytic) = -8.07574088994594 " "
y[1] (numeric) = -8.075740889913408 " "
absolute error = 3.25321991567761870000000000E-11 " "
relative error = 4.02838570480608340000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.722 " "
y[1] (analytic) = -8.07429819367751 " "
y[1] (numeric) = -8.074298193644545 " "
absolute error = 3.29656302255898500000000000E-11 " "
relative error = 4.0827858266868590000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.721 " "
y[1] (analytic) = -8.072855598235867 " "
y[1] (numeric) = -8.072855598202464 " "
absolute error = 3.34026140080823100000000000E-11 " "
relative error = 4.13764542194730500000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.72 " "
y[1] (analytic) = -8.07141310362232 " "
y[1] (numeric) = -8.071413103588476 " "
absolute error = 3.38431505042535700000000000E-11 " "
relative error = 4.1929647348944780000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.719 " "
y[1] (analytic) = -8.069970709838174 " "
y[1] (numeric) = -8.069970709803895 " "
absolute error = 3.42783579299066330000000000E-11 " "
relative error = 4.2476434131436910000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.718 " "
y[1] (analytic) = -8.068528416884748 " "
y[1] (numeric) = -8.068528416850032 " "
absolute error = 3.471534171239909500000000000E-11 " "
relative error = 4.3025617459252450000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.717 " "
y[1] (analytic) = -8.067086224763354 " "
y[1] (numeric) = -8.0670862247282 " "
absolute error = 3.515410185173095700000000000E-11 " "
relative error = 4.357719859720750000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.716 " "
y[1] (analytic) = -8.065644133475306 " "
y[1] (numeric) = -8.065644133439715 " "
absolute error = 3.55910856342234200000000000E-11 " "
relative error = 4.41267740619843250000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.715 " "
y[1] (analytic) = -8.064202143021923 " "
y[1] (numeric) = -8.064202142985893 " "
absolute error = 3.60298457735552800000000000E-11 " "
relative error = 4.46787482934470500000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.714 " "
y[1] (analytic) = -8.06276025340452 " "
y[1] (numeric) = -8.062760253368051 " "
absolute error = 3.64686059128871400000000000E-11 " "
relative error = 4.52309193957344650000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.713 " "
y[1] (analytic) = -8.061318464624415 " "
y[1] (numeric) = -8.061318464587506 " "
absolute error = 3.690914240905840400000000000E-11 " "
relative error = 4.578549100997219600000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.712 " "
y[1] (analytic) = -8.059876776682925 " "
y[1] (numeric) = -8.059876776645577 " "
absolute error = 3.734790254839026600000000000E-11 " "
relative error = 4.6338056502845126000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.711 " "
y[1] (analytic) = -8.058435189581376 " "
y[1] (numeric) = -8.058435189543586 " "
absolute error = 3.77902154014009300000000000E-11 " "
relative error = 4.689522781080290300000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.71 " "
y[1] (analytic) = -8.05699370332108 " "
y[1] (numeric) = -8.056993703282853 " "
absolute error = 3.82271991838933900000000000E-11 " "
relative error = 4.7445983690090510000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.709 " "
y[1] (analytic) = -8.05555231790337 " "
y[1] (numeric) = -8.0555523178647 " "
absolute error = 3.86695120369040500000000000E-11 " "
relative error = 4.8003551477111656000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.708 " "
y[1] (analytic) = -8.054111033329562 " "
y[1] (numeric) = -8.054111033290452 " "
absolute error = 3.911004853307531400000000000E-11 " "
relative error = 4.8559112695653084000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.707 " "
y[1] (analytic) = -8.052669849600981 " "
y[1] (numeric) = -8.05266984956143 " "
absolute error = 3.955058502924657700000000000E-11 " "
relative error = 4.9114872170260837000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.706 " "
y[1] (analytic) = -8.051228766718957 " "
y[1] (numeric) = -8.051228766678964 " "
absolute error = 3.99928978822572400000000000E-11 " "
relative error = 4.9673036304190340000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.705 " "
y[1] (analytic) = -8.049787784684813 " "
y[1] (numeric) = -8.049787784644378 " "
absolute error = 4.0435210735267900000000000E-11 " "
relative error = 5.0231399655278150000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.704 " "
y[1] (analytic) = -8.04834690349988 " "
y[1] (numeric) = -8.048346903459 " "
absolute error = 4.087929994511796400000000000E-11 " "
relative error = 5.0792169417226930000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.703 " "
y[1] (analytic) = -8.046906123165481 " "
y[1] (numeric) = -8.04690612312416 " "
absolute error = 4.132161279812862600000000000E-11 " "
relative error = 5.1350931855874060000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.702 " "
y[1] (analytic) = -8.045465443682952 " "
y[1] (numeric) = -8.045465443641186 " "
absolute error = 4.17657020079786900000000000E-11 " "
relative error = 5.1912101668116430000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.701 " "
y[1] (analytic) = -8.04402486505362 " "
y[1] (numeric) = -8.04402486501141 " "
absolute error = 4.22097912178287500000000000E-11 " "
relative error = 5.247347183274450000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.7 " "
y[1] (analytic) = -8.042584387278819 " "
y[1] (numeric) = -8.042584387236165 " "
absolute error = 4.265388042767881400000000000E-11 " "
relative error = 5.3035042436291570000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.699 " "
y[1] (analytic) = -8.04114401035988 " "
y[1] (numeric) = -8.041144010316783 " "
absolute error = 4.309619328068947700000000000E-11 " "
relative error = 5.3594604480613850000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.698 " "
y[1] (analytic) = -8.03970373429814 " "
y[1] (numeric) = -8.039703734254598 " "
absolute error = 4.35420588473789400000000000E-11 " "
relative error = 5.4158785306508720000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.697 " "
y[1] (analytic) = -8.038263559094933 " "
y[1] (numeric) = -8.038263559050945 " "
absolute error = 4.3987924414068400000000000E-11 " "
relative error = 5.4723167622810830000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.696 " "
y[1] (analytic) = -8.036823484751595 " "
y[1] (numeric) = -8.036823484707162 " "
absolute error = 4.443378998075786500000000000E-11 " "
relative error = 5.5287751516582230000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.695 " "
y[1] (analytic) = -8.035383511269465 " "
y[1] (numeric) = -8.035383511224586 " "
absolute error = 4.48796555474473300000000000E-11 " "
relative error = 5.5852537074931770000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.694 " "
y[1] (analytic) = -8.03394363864988 " "
y[1] (numeric) = -8.033943638604555 " "
absolute error = 4.53255211141367900000000000E-11 " "
relative error = 5.6417524385015270000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.693 " "
y[1] (analytic) = -8.032503866894181 " "
y[1] (numeric) = -8.032503866848408 " "
absolute error = 4.577316303766565400000000000E-11 " "
relative error = 5.698492499495570000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.692 " "
y[1] (analytic) = -8.031064196003706 " "
y[1] (numeric) = -8.031064195957487 " "
absolute error = 4.62190286043551170000000000E-11 " "
relative error = 5.7550316466594690000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.691 " "
y[1] (analytic) = -8.0296246259798 " "
y[1] (numeric) = -8.029624625933133 " "
absolute error = 4.66666705278839800000000000E-11 " "
relative error = 5.8118122205730840000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.69 " "
y[1] (analytic) = -8.028185156823803 " "
y[1] (numeric) = -8.028185156776688 " "
absolute error = 4.71143124514128430000000000E-11 " "
relative error = 5.8686130839130670000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.689 " "
y[1] (analytic) = -8.02674578853706 " "
y[1] (numeric) = -8.026745788489498 " "
absolute error = 4.756195437494170600000000000E-11 " "
relative error = 5.9254342454528210000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.688 " "
y[1] (analytic) = -8.025306521120914 " "
y[1] (numeric) = -8.025306521072906 " "
absolute error = 4.80078199416311700000000000E-11 " "
relative error = 5.9820543695477190000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6869999999999999 " "
y[1] (analytic) = -8.023867354576716 " "
y[1] (numeric) = -8.023867354528258 " "
absolute error = 4.84572382219994300000000000E-11 " "
relative error = 6.0391374982488980000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6859999999999999 " "
y[1] (analytic) = -8.022428288905813 " "
y[1] (numeric) = -8.022428288856903 " "
absolute error = 4.891020921604649600000000000E-11 " "
relative error = 6.0966838785812830000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6849999999999999 " "
y[1] (analytic) = -8.020989324109546 " "
y[1] (numeric) = -8.020989324060187 " "
absolute error = 4.93596274964147600000000000E-11 " "
relative error = 6.1538079034775970000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6839999999999999 " "
y[1] (analytic) = -8.019550460189272 " "
y[1] (numeric) = -8.019550460139461 " "
absolute error = 4.981082213362242300000000000E-11 " "
relative error = 6.2111738533093310000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6829999999999999 " "
y[1] (analytic) = -8.018111697146336 " "
y[1] (numeric) = -8.018111697096076 " "
absolute error = 5.026024041399069000000000000E-11 " "
relative error = 6.2683387700720630000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6819999999999999 " "
y[1] (analytic) = -8.016673034982093 " "
y[1] (numeric) = -8.016673034931383 " "
absolute error = 5.07096586943589500000000000E-11 " "
relative error = 6.3255241261654160000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6809999999999999 " "
y[1] (analytic) = -8.015234473697895 " "
y[1] (numeric) = -8.015234473646734 " "
absolute error = 5.116085333156661000000000000E-11 " "
relative error = 6.3829515530021840000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6799999999999999 " "
y[1] (analytic) = -8.013796013295094 " "
y[1] (numeric) = -8.013796013243482 " "
absolute error = 5.16120479687742800000000000E-11 " "
relative error = 6.4403995164274910000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6789999999999999 " "
y[1] (analytic) = -8.012357653775046 " "
y[1] (numeric) = -8.012357653722983 " "
absolute error = 5.20632426059819400000000000E-11 " "
relative error = 6.4978680253311190000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6779999999999999 " "
y[1] (analytic) = -8.010919395139108 " "
y[1] (numeric) = -8.010919395086592 " "
absolute error = 5.251621360002900000000000000E-11 " "
relative error = 6.555578830551580000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6769999999999999 " "
y[1] (analytic) = -8.009481237388632 " "
y[1] (numeric) = -8.009481237335667 " "
absolute error = 5.29656318803972700000000000E-11 " "
relative error = 6.6128667151564350000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6759999999999999 " "
y[1] (analytic) = -8.008043180524984 " "
y[1] (numeric) = -8.008043180471564 " "
absolute error = 5.34203792312837300000000000E-11 " "
relative error = 6.6708405570537450000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6749999999999999 " "
y[1] (analytic) = -8.006605224549515 " "
y[1] (numeric) = -8.006605224495642 " "
absolute error = 5.387335022533080000000000000E-11 " "
relative error = 6.7286132779653730000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6739999999999999 " "
y[1] (analytic) = -8.00516736946359 " "
y[1] (numeric) = -8.005167369409264 " "
absolute error = 5.43263212193778600000000000E-11 " "
relative error = 6.7864066685988790000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6729999999999999 " "
y[1] (analytic) = -8.00372961526857 " "
y[1] (numeric) = -8.00372961521379 " "
absolute error = 5.478106857026432000000000000E-11 " "
relative error = 6.8444426790429650000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6719999999999999 " "
y[1] (analytic) = -8.002291961965815 " "
y[1] (numeric) = -8.00229196191058 " "
absolute error = 5.52358159211507900000000000E-11 " "
relative error = 6.9024994568658240000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6709999999999999 " "
y[1] (analytic) = -8.00085440955669 " "
y[1] (numeric) = -8.000854409500999 " "
absolute error = 5.56905632720372500000000000E-11 " "
relative error = 6.9605770110648660000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6699999999999999 " "
y[1] (analytic) = -7.999416958042560 " "
y[1] (numeric) = -7.999416957986412 " "
absolute error = 5.614708697976312000000000000E-11 " "
relative error = 7.0188974114311200000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6689999999999999 " "
y[1] (analytic) = -7.997979607424789 " "
y[1] (numeric) = -7.997979607368185 " "
absolute error = 5.66036106874889800000000000E-11 " "
relative error = 7.0772386859978960000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6679999999999999 " "
y[1] (analytic) = -7.996542357704742 " "
y[1] (numeric) = -7.996542357647684 " "
absolute error = 5.705835803837545000000000000E-11 " "
relative error = 7.1353787031965380000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6669999999999999 " "
y[1] (analytic) = -7.995105208883789 " "
y[1] (numeric) = -7.995105208826276 " "
absolute error = 5.75131053892619100000000000E-11 " "
relative error = 7.1935395328326660000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6659999999999999 " "
y[1] (analytic) = -7.9936681609633 " "
y[1] (numeric) = -7.99366816090533 " "
absolute error = 5.796962909698777000000000000E-11 " "
relative error = 7.2519434044159750000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6649999999999999 " "
y[1] (analytic) = -7.992231213944644 " "
y[1] (numeric) = -7.9922312138862175 " "
absolute error = 5.84261528047136400000000000E-11 " "
relative error = 7.3103681863924510000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6639999999999999 " "
y[1] (analytic) = -7.990794367829192 " "
y[1] (numeric) = -7.990794367770308 " "
absolute error = 5.8884452869278900000000000E-11 " "
relative error = 7.3690361882351450000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6629999999999999 " "
y[1] (analytic) = -7.989357622618314 " "
y[1] (numeric) = -7.989357622558972 " "
absolute error = 5.93418647554244700000000000E-11 " "
relative error = 7.4276140283699850000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6619999999999999 " "
y[1] (analytic) = -7.987920978313386 " "
y[1] (numeric) = -7.987920978253586 " "
absolute error = 5.98001648199897300000000000E-11 " "
relative error = 7.4863240362971480000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6609999999999999 " "
y[1] (analytic) = -7.986484434915779 " "
y[1] (numeric) = -7.986484434855521 " "
absolute error = 6.0257576706135300000000000E-11 " "
relative error = 7.5449438607427450000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6599999999999999 " "
y[1] (analytic) = -7.985047992426874 " "
y[1] (numeric) = -7.985047992366155 " "
absolute error = 6.07185413059596600000000000E-11 " "
relative error = 7.6040296017689480000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6589999999999999 " "
y[1] (analytic) = -7.98361165084804 " "
y[1] (numeric) = -7.983611650786863 " "
absolute error = 6.11768413705249300000000000E-11 " "
relative error = 7.6628027571990630000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6579999999999999 " "
y[1] (analytic) = -7.982175410180658 " "
y[1] (numeric) = -7.982175410119023 " "
absolute error = 6.16351414350901900000000000E-11 " "
relative error = 7.7215969667215350000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6569999999999999 " "
y[1] (analytic) = -7.980739270426107 " "
y[1] (numeric) = -7.980739270364013 " "
absolute error = 6.20943296780751600000000000E-11 " "
relative error = 7.780523529715540000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6559999999999999 " "
y[1] (analytic) = -7.979303231585767 " "
y[1] (numeric) = -7.979303231523213 " "
absolute error = 6.25544060994798200000000000E-11 " "
relative error = 7.8395825154081860000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6549999999999999 " "
y[1] (analytic) = -7.977867293661018 " "
y[1] (numeric) = -7.9778672935980035 " "
absolute error = 6.30144825208844800000000000E-11 " "
relative error = 7.8986626627587510000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6539999999999999 " "
y[1] (analytic) = -7.976431456653243 " "
y[1] (numeric) = -7.976431456589766 " "
absolute error = 6.34772234775482500000000000E-11 " "
relative error = 7.9580980319966380000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6529999999999999 " "
y[1] (analytic) = -7.974995720563821 " "
y[1] (numeric) = -7.974995720499884 " "
absolute error = 6.39372998989529200000000000E-11 " "
relative error = 8.0172205903619760000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6519999999999999 " "
y[1] (analytic) = -7.973560085394139 " "
y[1] (numeric) = -7.973560085329740 " "
absolute error = 6.43982644987772800000000000E-11 " "
relative error = 8.0764757284191240000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6509999999999999 " "
y[1] (analytic) = -7.9721245511455825 " "
y[1] (numeric) = -7.9721245510807215 " "
absolute error = 6.48610054554410500000000000E-11 " "
relative error = 8.135974926046610000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6499999999999999 " "
y[1] (analytic) = -7.970689117819537 " "
y[1] (numeric) = -7.970689117754213 " "
absolute error = 6.53246345905245100000000000E-11 " "
relative error = 8.1956068822810550000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6489999999999999 " "
y[1] (analytic) = -7.969253785417388 " "
y[1] (numeric) = -7.969253785351602 " "
absolute error = 6.57864873687685800000000000E-11 " "
relative error = 8.2550373146791460000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6479999999999999 " "
y[1] (analytic) = -7.967818553940526 " "
y[1] (numeric) = -7.9678185538742765 " "
absolute error = 6.62492283254323400000000000E-11 " "
relative error = 8.314600524213550000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6469999999999999 " "
y[1] (analytic) = -7.96638342339034 " "
y[1] (numeric) = -7.966383423323627 " "
absolute error = 6.6712857460515810000000000E-11 " "
relative error = 8.3742965803827820000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6459999999999999 " "
y[1] (analytic) = -7.96494839376822 " "
y[1] (numeric) = -7.964948393701044 " "
absolute error = 6.71764865955992700000000000E-11 " "
relative error = 8.4340140418434080000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6449999999999999 " "
y[1] (analytic) = -7.963513465075560 " "
y[1] (numeric) = -7.963513465007917 " "
absolute error = 6.76418920875221400000000000E-11 " "
relative error = 8.4939759798447620000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6439999999999999 " "
y[1] (analytic) = -7.962078637313747 " "
y[1] (numeric) = -7.962078637245641 " "
absolute error = 6.8105521222605600000000000E-11 " "
relative error = 8.5537363199898140000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6429999999999999 " "
y[1] (analytic) = -7.960643910484179 " "
y[1] (numeric) = -7.960643910415609 " "
absolute error = 6.85700385361087700000000000E-11 " "
relative error = 8.6136296645302690000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6419999999999999 " "
y[1] (analytic) = -7.95920928458825 " "
y[1] (numeric) = -7.959209284519215 " "
absolute error = 6.90354440280316300000000000E-11 " "
relative error = 8.6736560831121570000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6409999999999999 " "
y[1] (analytic) = -7.957774759627357 " "
y[1] (numeric) = -7.957774759557855 " "
absolute error = 6.9501737698374200000000000E-11 " "
relative error = 8.7338156454215590000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6399999999999999 " "
y[1] (analytic) = -7.956340335602894 " "
y[1] (numeric) = -7.956340335532928 " "
absolute error = 6.99662550118773700000000000E-11 " "
relative error = 8.7937735266041330000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6389999999999999 " "
y[1] (analytic) = -7.954906012516262 " "
y[1] (numeric) = -7.9549060124458295 " "
absolute error = 7.04325486822199300000000000E-11 " "
relative error = 8.8539762218939160000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6379999999999999 " "
y[1] (analytic) = -7.953471790368859 " "
y[1] (numeric) = -7.95347179029796 " "
absolute error = 7.0898842352562500000000000E-11 " "
relative error = 8.9142005178689920000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6369999999999999 " "
y[1] (analytic) = -7.952037669162084 " "
y[1] (numeric) = -7.952037669090719 " "
absolute error = 7.13651360229050600000000000E-11 " "
relative error = 8.9744464239220470000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6359999999999999 " "
y[1] (analytic) = -7.95060364889734 " "
y[1] (numeric) = -7.950603648825508 " "
absolute error = 7.18323178716673300000000000E-11 " "
relative error = 9.0348256615244140000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6349999999999999 " "
y[1] (analytic) = -7.94916972957603 " "
y[1] (numeric) = -7.94916972950373 " "
absolute error = 7.2300387898849290000000000E-11 " "
relative error = 9.0953383005328590000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6339999999999999 " "
y[1] (analytic) = -7.947735911199558 " "
y[1] (numeric) = -7.947735911126788 " "
absolute error = 7.27702342828706600000000000E-11 " "
relative error = 9.1560961632263630000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6329999999999999 " "
y[1] (analytic) = -7.946302193769327 " "
y[1] (numeric) = -7.946302193696087 " "
absolute error = 7.32400806668920300000000000E-11 " "
relative error = 9.2168758349411080000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6319999999999999 " "
y[1] (analytic) = -7.944868577286740 " "
y[1] (numeric) = -7.9448685772130325 " "
absolute error = 7.37081506940739900000000000E-11 " "
relative error = 9.2774537397377730000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6309999999999999 " "
y[1] (analytic) = -7.943435061753208 " "
y[1] (numeric) = -7.943435061679032 " "
absolute error = 7.41762207212559600000000000E-11 " "
relative error = 9.3380533918388210000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6299999999999999 " "
y[1] (analytic) = -7.942001647170137 " "
y[1] (numeric) = -7.942001647095492 " "
absolute error = 7.46451789268576200000000000E-11 " "
relative error = 9.3987866337770030000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6289999999999999 " "
y[1] (analytic) = -7.9405683335389385 " "
y[1] (numeric) = -7.940568333463823 " "
absolute error = 7.51159134892986900000000000E-11 " "
relative error = 9.4597653888359860000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6279999999999999 " "
y[1] (analytic) = -7.939135120861020 " "
y[1] (numeric) = -7.9391351207854335 " "
absolute error = 7.55857598733200600000000000E-11 " "
relative error = 9.5206541673172330000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6269999999999999 " "
y[1] (analytic) = -7.937702009137792 " "
y[1] (numeric) = -7.937702009061735 " "
absolute error = 7.60564944357611200000000000E-11 " "
relative error = 9.5816767054502370000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6259999999999999 " "
y[1] (analytic) = -7.936268998370668 " "
y[1] (numeric) = -7.936268998294140 " "
absolute error = 7.65272289982021900000000000E-11 " "
relative error = 9.6427211595163140000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6249999999999999 " "
y[1] (analytic) = -7.934836088561061 " "
y[1] (numeric) = -7.9348360884840625 " "
absolute error = 7.69988517390629600000000000E-11 " "
relative error = 9.7038994731176950000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6239999999999999 " "
y[1] (analytic) = -7.933403279710386 " "
y[1] (numeric) = -7.933403279632916 " "
absolute error = 7.74695863015040200000000000E-11 " "
relative error = 9.7649878078972570000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6229999999999999 " "
y[1] (analytic) = -7.931970571820058 " "
y[1] (numeric) = -7.9319705717421165 " "
absolute error = 7.79412090423647900000000000E-11 " "
relative error = 9.8262100617552480000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6219999999999999 " "
y[1] (analytic) = -7.930537964891494 " "
y[1] (numeric) = -7.930537964813080 " "
absolute error = 7.84146081400649600000000000E-11 " "
relative error = 9.887678299657170000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6209999999999999 " "
y[1] (analytic) = -7.929105458926111 " "
y[1] (numeric) = -7.929105458847223 " "
absolute error = 7.88880072377651200000000000E-11 " "
relative error = 9.949168622666980000000000E-10 "%"
Correct digits = 12
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6199999999999999 " "
y[1] (analytic) = -7.927673053925329 " "
y[1] (numeric) = -7.927673053845967 " "
absolute error = 7.93614063354652900000000000E-11 " "
relative error = 1.0010681040405682000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6189999999999999 " "
y[1] (analytic) = -7.9262407498905665 " "
y[1] (numeric) = -7.926240749810730 " "
absolute error = 7.98356936115851600000000000E-11 " "
relative error = 1.0072327617942643000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6179999999999999 " "
y[1] (analytic) = -7.924808546823244 " "
y[1] (numeric) = -7.924808546742935 " "
absolute error = 8.03090927092853200000000000E-11 " "
relative error = 1.0133884274274133000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6169999999999999 " "
y[1] (analytic) = -7.923376444724784 " "
y[1] (numeric) = -7.923376444644001 " "
absolute error = 8.07833799854051900000000000E-11 " "
relative error = 1.019557515018600900000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6159999999999999 " "
y[1] (analytic) = -7.921944443596608 " "
y[1] (numeric) = -7.921944443515352 " "
absolute error = 8.12558909046856600000000000E-11 " "
relative error = 1.0257063967466429000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6149999999999999 " "
y[1] (analytic) = -7.920512543440147 " "
y[1] (numeric) = -7.920512543358414 " "
absolute error = 8.17328427160646200000000000E-11 " "
relative error = 1.0319135569548038000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6139999999999999 " "
y[1] (analytic) = -7.919080744256818 " "
y[1] (numeric) = -7.91908074417461 " "
absolute error = 8.22080181706041900000000000E-11 " "
relative error = 1.0381005172882495000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6129999999999999 " "
y[1] (analytic) = -7.9176490460480515 " "
y[1] (numeric) = -7.917649045965368 " "
absolute error = 8.26831936251437600000000000E-11 " "
relative error = 1.044289701959113000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6119999999999999 " "
y[1] (analytic) = -7.916217448815274 " "
y[1] (numeric) = -7.916217448732115 " "
absolute error = 8.31592572581030300000000000E-11 " "
relative error = 1.0504923316696976000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6109999999999999 " "
y[1] (analytic) = -7.914785952559915 " "
y[1] (numeric) = -7.914785952476280 " "
absolute error = 8.36353208910622900000000000E-11 " "
relative error = 1.0566971917163691000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6099999999999999 " "
y[1] (analytic) = -7.913354557283403 " "
y[1] (numeric) = -7.91335455719929 " "
absolute error = 8.41131608808609600000000000E-11 " "
relative error = 1.062926730654874000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6089999999999999 " "
y[1] (analytic) = -7.91192326298717 " "
y[1] (numeric) = -7.9119232629025795 " "
absolute error = 8.45901126922399300000000000E-11 " "
relative error = 1.0691472841750323000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6079999999999999 " "
y[1] (analytic) = -7.910492069672646 " "
y[1] (numeric) = -7.910492069587578 " "
absolute error = 8.5067952682038600000000000E-11 " "
relative error = 1.0753813028670275000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6069999999999999 " "
y[1] (analytic) = -7.909060977341266 " "
y[1] (numeric) = -7.909060977255720 " "
absolute error = 8.55466808502569600000000000E-11 " "
relative error = 1.081628793801696000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6059999999999999 " "
y[1] (analytic) = -7.907629985994461 " "
y[1] (numeric) = -7.907629985908437 " "
absolute error = 8.60245208400556300000000000E-11 " "
relative error = 1.087867300220386000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6049999999999999 " "
y[1] (analytic) = -7.906199095633668 " "
y[1] (numeric) = -7.906199095547166 " "
absolute error = 8.6502360829854300000000000E-11 " "
relative error = 1.094108050954936000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6039999999999999 " "
y[1] (analytic) = -7.9047683062603245 " "
y[1] (numeric) = -7.9047683061733425 " "
absolute error = 8.69819771764923600000000000E-11 " "
relative error = 1.1003735189506492000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6029999999999999 " "
y[1] (analytic) = -7.903337617875868 " "
y[1] (numeric) = -7.903337617788405 " "
absolute error = 8.74633698799698300000000000E-11 " "
relative error = 1.1066637173912965000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6019999999999999 " "
y[1] (analytic) = -7.901907030481732 " "
y[1] (numeric) = -7.901907030393791 " "
absolute error = 8.7941209869768500000000000E-11 " "
relative error = 1.1129112191592976000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.6009999999999999 " "
y[1] (analytic) = -7.9004765440793605 " "
y[1] (numeric) = -7.90047654399094 " "
absolute error = 8.84208262164065700000000000E-11 " "
relative error = 1.119183453340790900000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.5999999999999999 " "
y[1] (analytic) = -7.899046158670194 " "
y[1] (numeric) = -7.899046158581291 " "
absolute error = 8.89022189198840400000000000E-11 " "
relative error = 1.1254804331318245000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
" "
"TOP MAIN SOLVE Loop"
"WARNING: arccos of linear function has low precision in testing."
x[1] = -0.5989999999999999 " "
y[1] (analytic) = -7.897615874255670 " "
y[1] (numeric) = -7.897615874166289 " "
absolute error = 8.9381835266522100000000000E-11 " "
relative error = 1.1317571871010516000000000E-9 "%"
Correct digits = 11
h = 1.000E-3 " "
"NO POLE"
"Finished!"
"Maximum Time Reached before Solution Completed!"
"diff ( y , x , 1 ) = arccos(0.1 * x + 0.2) ;"
Iterations = 202
"Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds
"Expected Time Remaining "= 0 Years 0 Days 0 Hours 20 Minutes 44 Seconds
"Optimized Time Remaining "= 0 Years 0 Days 0 Hours 20 Minutes 38 Seconds
"Expected Total Time "= 0 Years 0 Days 0 Hours 23 Minutes 39 Seconds
"Time to Timeout " Unknown
Percent Done = 12.68750000000001 "%"
(%o57) true
(%o57) diffeq.max