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t_chkmpc.pas
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{Test program for MPArith/mp_cmplx, (c) W.Ehrhardt 2014-2017}
program t_chkmpc;
{$i STD.INC}
{$i mp_conf.inc}
{$x+} {pchar I/O}
{$i+} {RTE on I/O error}
{$ifdef BIT16}
{$N+,F+}
{$endif}
{$ifdef APPCONS}
{$apptype console}
{$endif}
uses
{$ifdef WINCRT}
WinCRT,
{$endif}
{$ifdef MPC_Diagnostic}
mp_supp,
{$endif}
mp_types, mp_base, mp_real, mp_cmplx;
{---------------------------------------------------------------------------}
function mpc_reldev(const a,b: mp_complex): double;
{-Return abs((a-b)/b)*2^b.re.bitprec, special if b=0, or a-b=0}
var
c: mp_complex;
begin
mpc_reldev := -1;
mpc_initp(c,b.re.bitprec);
if mp_error<>MP_OKAY then exit;
mpc_sub(a,b,c);
if mpc_is0(c) then mpc_reldev := 0.0
else begin
if not mpc_is0(b) then mpc_div(c,b,c);
mpc_abs(c,c.re);
mpf_mul_2k(c.re,b.re.bitprec,c.re);
mpc_reldev := abs(mpf_todouble(c.re));
end;
mpc_clear(c);
end;
{---------------------------------------------------------------------------}
procedure mpc_writeln(const s: string; const a: mp_complex);
begin
write(s);
mpf_output_decimal_alt(a.re, 28);
if mp_show_plus or s_mpf_is_neg(a.im) then write(' ')
else write(' + ');
mpf_output_decimal_alt(a.im, 28);
writeln('*I');
end;
{---------------------------------------------------------------------------}
procedure mpf_randomx(var a: mp_float);
{-random numbers u*2^x for test, u and x are uniform random}
{ u from -0.5 .. 0.5, x from -0.5..0.5*2^(default_prec/4)}
begin
mpf_random(a);
mpf_sub_dbl(a,0.5,a);
mpf_mul_2k(a,round((random-0.5)*0.25*mpf_get_default_prec),a);
end;
{---------------------------------------------------------------------------}
procedure mpc_randomx(var z: mp_complex);
{-random numbers u*2^x for test, u and x are uniform random}
{ u from -0.5 .. 0.5, x from -0.5..0.5*2^(default_prec/4)}
begin
mpf_randomx(z.re);
mpf_randomx(z.im);
end;
{---------------------------------------------------------------------------}
procedure func_test;
{-Tests for other elementary functions}
type
t_testfunc = procedure(const a: mp_complex; var b: mp_complex);
const
NUMFUN = 36;
var
z,u,v,w: mp_complex;
f,i,k,cnt: integer;
tf: t_testfunc;
ts: string[20];
skip: boolean;
rd: double;
fcnt: array[0..NUMFUN-1] of integer;
dp,dpq: longint;
{$ifndef BIT16}
const
imax = 20000;
imsk = $FF;
{$else}
{$ifdef IN_IDE}
const
imax = 600;
imsk = $07;
{$else}
const
imax = 2400;
imsk = $1f;
{$endif}
{$endif}
function ldxc(const c: mp_complex): longint;
{-Maximum ldx(c.re) und ldx(c.tm)}
var
mi, ma: longint;
begin
mi := s_mpf_ldx(c.re);
ma := s_mpf_ldx(c.im);
if mi>ma then ma := mi;
ldxc := ma;
end;
begin
writeln('Function test (compare with double precision): ');
dp := mpf_get_default_prec;
mpc_initp2(z,w,dp);
mpc_initp2(u,v,dp*2);
fillchar(fcnt,sizeof(fcnt),0);
f := 0;
cnt := 0;
tf := nil;
for i:=1 to imax do begin
skip := false;
if i and imsk = 0 then write('.');
mpc_randomx(z);
k := random(NUMFUN);
dpq := random(dp div 2);
inc(fcnt[k]);
case k of
0: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_sqrt;
ts := 'mpc_sqrt';
end;
1: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_sqr;
ts := 'mpc_sqr';
end;
2: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_ln;
ts := 'mpc_ln';
skip := mpc_is0(z);
while skip do begin
mpc_randomx(z);
skip := mpc_is0(z);
end;
end;
3: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_exp;
ts := 'mpc_exp';
skip := ldxc(z) > 22;
while skip do begin
mpc_randomx(z);
skip := ldxc(z) > 22;
end;
end;
4: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arctan;
ts := 'mpc_arctan';
end;
5: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_cos;
ts := 'mpc_cos';
skip := ldxc(z) > 20;
while skip do begin
mpc_randomx(z);
skip := ldxc(z) > 20;
end;
end;
6: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_sin;
ts := 'mpc_sin';
skip := ldxc(z) > 22;
while skip do begin
mpc_randomx(z);
skip := ldxc(z) > 22;
end;
end;
7: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_tan;
ts := 'mpc_tan';
end;
8: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_cosh;
ts := 'mpc_cosh';
skip := ldxc(z) > 22;
while skip do begin
mpc_randomx(z);
skip := ldxc(z) > 22;
end;
end;
9: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_sinh;
ts := 'mpc_sinh';
skip := ldxc(z) > 22;
while skip do begin
mpc_randomx(z);
skip := ldxc(z) > 22;
end;
end;
10: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_tanh;
ts := 'mpc_tanh';
end;
11: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arctanh;
ts := 'mpf_arctanh';
skip := mpc_is1a(z);
while skip do begin
mpc_randomx(z);
skip := mpc_is1a(z);
end;
end;
12: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arccosh;
ts := 'mpc_arccosh';
end;
13: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arcsinh;
ts := 'mpc_arcsinh';
end;
14: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arcsin;
ts := 'mpc_arcsin';
end;
15: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arccos;
ts := 'mpc_arccos';
end;
16: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_cot;
ts := 'mpc_cot';
skip := mpc_is0(z);
{skip := (ldxc(z) < -25) or (s_mpf_ldx(z.im) < -25);}
while skip do begin
mpc_randomx(z);
skip := mpc_is0(z);
end;
end;
17: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_coth;
ts := 'mpc_coth';
skip := mpc_is0(z);
while skip do begin
mpc_randomx(z);
skip := mpc_is0(z);
end;
end;
18: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_sec;
ts := 'mpc_sec';
skip := ldxc(z) > 22;
while skip do begin
mpc_randomx(z);
skip := ldxc(z) > 22;
end;
end;
19: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_sech;
ts := 'mpc_sech';
skip := ldxc(z) > 22;
while skip do begin
mpc_randomx(z);
skip := ldxc(z) > 22;
end;
end;
20: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_csc;
ts := 'mpc_csc';
skip := ldxc(z) > 22;
while skip do begin
mpc_randomx(z);
skip := ldxc(z) > 22;
end;
end;
21: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_csch;
ts := 'mpc_csch';
skip := ldxc(z) > 22;
while skip do begin
mpc_randomx(z);
skip := ldxc(z) > 22;
end;
end;
22: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arccoth;
ts := 'mpc_arccoth';
end;
23: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arccothc;
ts := 'mpc_arccothc';
end;
24: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arccotc;
ts := 'mpc_arccotc';
end;
25: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arccothc;
ts := 'mpc_arccothc';
end;
26: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arccsc;
ts := 'mpc_arccsc';
end;
27: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arccsch;
ts := 'mpc_arccsch';
end;
28: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arcsec;
ts := 'mpc_arcsec';
end;
29: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_arcsech;
ts := 'mpc_arcsech';
end;
30: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_agm1;
ts := 'mpc_agm1';
end;
31: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_exp;
ts := 'mpc_exp2';
skip := ldxc(z) > 22;
while skip do begin
mpc_randomx(z);
skip := ldxc(z) > 22;
end;
end;
32: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_exp;
ts := 'mpc_exp10';
skip := ldxc(z) > 22;
while skip do begin
mpc_randomx(z);
skip := ldxc(z) > 22;
end;
end;
33: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_ln1p;
ts := 'mpc_ln1p';
mpf_random(z.re);
mpf_sub_dbl(z.re,0.5,z.re);
mpf_mul_2k(z.re,2-dpq,z.re);
mpf_random(z.im);
mpf_sub_dbl(z.im,0.5,z.im);
mpf_mul_2k(z.im,2-dpq,z.im);
{mpc_writeln(' ln1p: ', z);}
end;
34: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_expm1;
ts := 'mpc_expm1';
mpf_random(z.re);
mpf_sub_dbl(z.re,0.5,z.re);
mpf_mul_2k(z.re,2-dpq,z.re);
mpf_random(z.im);
mpf_sub_dbl(z.im,0.5,z.im);
mpf_mul_2k(z.im,2-dpq,z.im);
{mpc_writeln('expm1: ', z);}
end;
35: begin
tf := {$ifdef FPC_ProcVar}@{$endif}mpc_log10;
ts := 'mpc_log10';
skip := mpc_is0(z);
while skip do begin
mpc_randomx(z);
skip := mpc_is0(z);
end;
end;
end;
if not skip then begin
inc(cnt);
mpc_copyp(z,u);
tf(z,w);
if mp_error<>MP_OKAY then begin
set_mp_error(0); {clear error variable}
writeln(i, ', test of ',ts);
writeln(' z.re: ', mpf_decimal(z.re,50));
writeln(' z.im: ', mpf_decimal(z.im,50));
end;
tf(u,v);
rd := mpc_reldev(v,w);
if rd>4 then begin
if rd>8 then begin
write('Failed! #');
inc(f);
end
else write('Bad precision: #');
writeln(i, ', test of ',ts, ': rd=',rd:1:1);
mpc_writeln('z=',z);
end;
end;
end;
k := imax;
for i:=0 to NUMFUN-1 do begin
if fcnt[i]<k then k := fcnt[i];
end;
writeln;
{$ifdef debug}
if z.re.bitprec <> dp then begin
writeln('z.re.bitprec changed to ', z.re.bitprec);
end;
if w.re.bitprec <> dp then begin
writeln('w.re.bitprec changed to ', w.re.bitprec);
end;
if u.re.bitprec <> 2*dp then begin
writeln('u.re.bitprec changed to ', u.re.bitprec);
end;
if v.re.bitprec <> 2*dp then begin
writeln('v.re.bitprec changed to ', v.re.bitprec);
end;
{$endif}
writeln('No. of checks: ',cnt,', failed: ',f, ', min fct cnt: ',k);
writeln;
mpc_clear4(z,u,v,w);
end;
{---------------------------------------------------------------------------}
{----------------------- Basic function test -------------------------------}
{---------------------------------------------------------------------------}
var
d,z,v,w,cxx: mp_complex;
x,y: mp_float;
const
eps_d = 2.2e-16;
{.$define fullwrite}
type
FNamStr = string[12];
type
complex = record
re: double; {real part }
im: double; {imaginary part}
end;
type
cfunc1 = procedure(const z: mp_complex; var w: mp_complex);
cfuncx = procedure(const z: mp_complex; var x: mp_float);
var
maxr: double;
{Test cases from GO V1.1 \math\cmplx\cmath_test.go}
{Taken from DAMath/DAMCmplx test program}
const zv: array[0..9] of complex = (
(re: 4.979011924883673501; im: +7.738872474578104566),
(re: 7.738872474578104566; im: -0.276880057192001594),
(re: -0.276880057192001594; im: -5.010603618271074922),
(re: -5.010603618271074922; im: +9.636293707198417380),
(re: 9.636293707198417380; im: +2.926377239243964645),
(re: 2.926377239243964645; im: +5.229083431459306652),
(re: 5.229083431459306652; im: +2.727939910436010251),
(re: 2.727939910436010251; im: +1.825308091680855060),
(re: 1.825308091680855060; im: -8.685924768575601362),
(re: -8.685924768575601362; im: +4.979011924883673501));
const t_abs: array[0..9] of double = (
9.202212066993265031e+00,
7.743823974229610662e+00,
5.018247820255774690e+00,
1.086113737279954516e+01,
1.007084108492219961e+01,
5.992244761316694218e+00,
5.897878405673676230e+00,
3.282286670067870902e+00,
8.875643002899041729e+00,
1.001178549677773199e+01);
const t_arg: array[0..9] of double = (
0.4995455752345964553*2, {!! 16-bit}
-3.576257502185697130e-02,
-1.625999007401905844e+00,
2.050293635965911176e+00,
2.948321315544675621e-01,
1.060586036725255628e+00,
4.808455608335830782e-01,
5.896963416477665942e-01,
-1.363664772458245503e+00,
2.621091389538601329e+00);
const t_acos: array[0..9] of complex = (
(re: 1.001767980470745633; im: -2.913823271855495378),
(re: 3.606427612041407370e-2; im: +2.735858443457626093),
(re: 1.624936546233379670; im: +2.315953745433590119),
(re: 2.048565084965074012; im: -3.079557679120411791),
(re: 2.962113208907306728e-1; im: -3.000739250820062252),
(re: 1.066455591493415660; im: -2.487286502479601136),
(re: 4.868130745223138770e-1; im: -2.463655912283054555),
(re: 6.116977071277574248e-1; im: -1.873445885173705526),
(re: 1.364931128037018133; im: +2.879352863232879542),
(re: 2.618931048568298831; im: -2.995654330289876780));
const t_acosh: array[0..9] of complex = (
(re: 2.913823271855495378; im: +1.001767980470745633),
(re: 2.735858443457626093; im: -3.606427612041407370e-2),
(re: 2.315953745433590119; im: -1.624936546233379670),
(re: 3.079557679120411791; im: +2.048565084965074012),
(re: 3.000739250820062252; im: +2.962113208907306728e-1),
(re: 2.487286502479601136; im: +1.066455591493415660),
(re: 2.463655912283054555; im: +4.868130745223138769e-1),
(re: 1.873445885173705526; im: +6.116977071277574248e-1),
(re: 2.879352863232879542; im: -1.364931128037018133),
(re: 2.995654330289876779; im: +2.618931048568298831));
const t_asin: array[0..9] of complex = (
(re: 5.690283463241509864e-1; im: +2.913823271855495378),
(re: 1.534732050674482545; im: -2.735858443457626093),
(re: -5.414021943848305114e-2; im: -2.315953745433590119),
(re: -4.777687581701773928e-1; im: +3.079557679120411791),
(re: 1.274585005904165946; im: +3.000739250820062252),
(re: 5.043407353014809591e-1; im: +2.487286502479601136),
(re: 1.083983252272582742; im: +2.463655912283054555),
(re: 9.590986196671391944e-1; im: +1.873445885173705526),
(re: 2.058651987578784861e-1; im: -2.879352863232879542),
(re: -1.048134721773402212; im: +2.995654330289876780));
const t_asinh: array[0..9] of complex = (
(re: 2.911376046941529568; im: +9.963945954570432676e-1),
(re: 2.744175542399425906; im: -3.546830878900050060e-2),
(re: -2.296213646252069051; im: -1.514466356569015189),
(re: -3.077123345929572597; im: +1.089557796719401385),
(re: 3.004836610092364742; im: +2.934697916981922004e-1),
(re: 2.480005937079536316; im: +1.054586860604916571),
(re: 2.471877383830958561; im: +4.750234436425080336e-1),
(re: 1.891074358808015914; im: +5.688292557256360234e-1),
(re: 2.873542642336734188; im: -1.362376149648891421),
(re: -2.998175058617247722; im: +5.183571985225367506e-1));
const t_atan: array[0..9] of complex = (
(re: 1.511574707933274136; im: +9.132440360395449438e-2),
(re: 1.442450432348260256; im: -4.541613264280391150e-3),
(re: -1.559348870363053267; im: -2.016329540924836246e-1),
(re: -1.528061947244588987; im: +8.172155623067200375e-2),
(re: 1.475990916324079968; im: +2.860296932069164436e-2),
(re: 1.487735377204654893; im: +1.456687715320728166e-1),
(re: 1.420698392777919189; im: +7.683048612788070225e-2),
(re: 1.316223606049893336; im: +1.603131300046753064e-1),
(re: 1.547345068430370358; im: -1.106490750793908248e-1),
(re: -1.484146234018525399; im: +4.934185030502439949e-2));
const t_atanh: array[0..9] of complex = (
(re: 5.837502793896850906e-2; im: +1.479348849510533446),
(re: 1.297734349779038123e-1; im: -1.566100941046356133),
(re: -1.057645606734725207e-2; im: -1.374369865840228455),
(re: -4.221859567868835888e-2; im: +1.489143396816640561),
(re: 9.521899799131672206e-2; im: +1.541688409877711033),
(re: 7.996545936689032386e-2; im: +1.425251035387319270),
(re: 1.505124547198072622e-1; im: +1.490743253301630380),
(re: 2.508207293399398771e-1; im: +1.392057665392187516),
(re: 2.289610881579713585e-2; im: -1.460922498928286421),
(re: -8.665624101841876131e-2; im: +1.520790203693509348));
const t_conj: array[0..9] of complex = (
(re: 4.979011924883673501; im: -7.738872474578104566),
(re: 7.738872474578104566; im: +0.276880057192001594),
(re: -0.276880057192001594; im: +5.010603618271074922),
(re: -5.010603618271074922; im: -9.636293707198417380),
(re: 9.636293707198417380; im: -2.926377239243964645),
(re: 2.926377239243964645; im: -5.229083431459306652),
(re: 5.229083431459306652; im: -2.727939910436010251),
(re: 2.727939910436010251; im: -1.825308091680855060),
(re: 1.825308091680855060; im: +8.685924768575601362),
(re: -8.685924768575601362; im: -4.979011924883673501));
const t_cos: array[0..9] of complex = (
(re: 3.024540920601483938e+02; im: +1.107379757251707165e+03),
(re: 1.192858682649064973e-01; im: +2.785755412233306554e-01),
(re: 7.214439430452830660e+01; im: -2.050012966707604417e+01),
(re: 2.249219525384039842e+03; im: -7.317363745602773587e+03),
(re: -9.148222970032421760e+00; im: +1.953124661113563542e+00),
(re: -9.116081175857732248e+01; im: -1.992669213569952232e+01),
(re: 3.795639179042704640e+00; im: +6.623513350981458399e+00),
(re: -2.914484073249886956e+00; im: -1.214620271628002918e+00),
(re: -7.451234825012997439e+02; im: +2.864169231448808081e+03),
(re: -5.371977967039319076e+01; im: +4.893348341339375831e+01));
const t_cosh: array[0..9] of complex = (
(re: 8.346383835230182494e+00; im: +7.218105788642584642e+01),
(re: 1.104219673799193670e+03; im: -3.137963868927757538e+02),
(re: 3.051485206773701585e-01; im: -2.680538473010529785e-01),
(re: -7.332947286841879334e+01; im: +1.574445942284918251e+01),
(re: -7.478643293945957536e+03; im: +1.634838220991335393e+03),
(re: 4.622316522966235702e+00; im: -8.088695185566375256e+00),
(re: -8.544333183278877406e+01; im: +3.750583612012816646e+01),
(re: -1.934457815021493925e+00; im: +7.372585961176722818e+00),
(re: -2.352958770061749348e+00; im: -2.034982010440878359e+00),
(re: 7.797564575321347482e+02; im: +2.854935071681917656e+03));
const t_exp: array[0..9] of complex = (
(re: 1.669197736864670815e+01; im: +1.443689510950766369e+02),
(re: 2.208438928625258345e+03; im: -6.275928928490921124e+02),
(re: 2.227538273122775173e-01; im: +7.246828402833419125e-01),
(re: -6.518298595815354900e-03; im: -1.399658379151938609e-03),
(re: -1.495728652408401575e+04; im: +3.269676455931135689e+03),
(re: 9.218158701983105936e+00; im: -1.622398529108495601e+01),
(re: -1.708817571685304084e+02; im: +7.501382609870410714e+01),
(re: -3.852461315830959613e+00; im: +1.480842042315607322e+01),
(re: -4.586775503301407380e+00; im: -4.178501081246873415e+00),
(re: 4.451337963005453491e-05; im: -1.629775742054429159e-04));
const t_exp2: array[0..9] of complex = (
(re: 19.13114851867412526; im: -25.07258411828447256),
(re: 209.6935289144531275; im: -40.74558517972284900),
(re: -0.7804385630056867110; im: +0.2686222841553663176),
(re: 0.2861826306152657883e-1; im: +0.1197110279008295110e-1),
(re: -351.5990610189685966; im: +713.9352210484824750),
(re: -6.732606237487401262; im: -3.530194636296673789),
(re: -11.80081515033121407; im: +35.60206402414627666),
(re: 1.993191920305541285; im: +6.318148050158053523),
(re: 3.422374229625497396; im: +0.9198168024611665233),
(re: -0.2312711405020745712e-2; im: -0.7397935321601635477e-3));
const t_exp10: array[0..9] of complex = (
(re: 49041.36455339954630; im: -81692.40122564724781),
(re: 44044545.49543944410; im: -32624981.77369520256),
(re: 0.2725684221615126522; im: +0.4528963789852567103),
(re: -0.9569591974910356937e-5; im: -0.1912347033434410590e-5),
(re: 3887641543.827246551; im: 1902205053.527650575),
(re: 729.9849992944069395; im: -423.7594183570774552),
(re: 169466.0359719999248; im: -317.1619584673702657),
(re: -260.6749487307233164; im: -466.6139307539978187),
(re: 27.28833232049515759; im: -61.06164877299231211),
(re: 0.9315994876725179977e-9; im: -0.1838420354078803348e-8));
const t_expm1: array[0..9] of complex = ( {exp(a[i]/16)-1}
(re: 0.2084614314764963823; im: +0.6348007474939909575),
(re: 0.6217888859800103407; im: -0.2806786428857771341e-1),
(re: -0.6495773464318968003e-1; im: -0.3027838022489718850),
(re: -0.3975095971688073819; im: +0.4141953035763729656),
(re: 0.7957958947511262505; im: +0.3321606008092035376),
(re: 0.1371384618852060061; im: +0.3854593328378902681),
(re: 0.3664447065220901995; im: +0.2352576867156370654),
(re: 0.1781845733786736222; im: +0.1349955131114415004),
(re: -0.4030059291753222991e-1; im: -0.5790231209681929250),
(re: -0.4468309463182119146; im: +0.1779202851051918940));
const t_log: array[0..9] of complex = (
(re: 2.219443897217919443e+00; im: +9.990911504691929106e-01),
(re: 2.046895619115416726e+00; im: -3.576257502185697130e-02),
(re: 1.613080832985386044e+00; im: -1.625999007401905844e+00),
(re: 2.385191039482300871e+00; im: +2.050293635965911176e+00),
(re: 2.309644227067992300e+00; im: +2.948321315544675621e-01),
(re: 1.790466093397465611e+00; im: +1.060586036725255628e+00),
(re: 1.774592693984175167e+00; im: +4.808455608335830782e-01),
(re: 1.188540335004534243e+00; im: +5.896963416477665942e-01),
(re: 2.183310783767908259e+00; im: -1.363664772458245503e+00),
(re: 2.303762948727325917e+00; im: +2.621091389538601329e+00));
const t_sin: array[0..9] of complex = (
(re: -1.107380177424023354e+03; im: +3.024539773002502192e+02),
(re: 1.031703752140075936e+00; im: -3.220897979992957024e-02),
(re: -2.050195209727142980e+01; im: -7.213798134824079884e+01),
(re: 7.317363808034633864e+03; im: +2.249219506193664343e+03),
(re: -1.964375633631808178e+00; im: -9.095826471387040446e+00),
(re: 1.992783647158514838e+01; im: -9.115557694101913504e+01),
(re: -6.680335650741921444e+00; im: +3.763353833142432513e+00),
(re: 1.279402816665745915e+00; im: -2.766909209979578116e+00),
(re: 2.864169394953525959e+03; im: +7.451234399649871203e+02),
(re: -4.893811726244659136e+01; im: -5.371469305562194636e+01));
const t_sinh: array[0..9] of complex = (
(re: 8.345593533416525658e+00; im: +7.218789320865079048e+01),
(re: 1.104219254826064675e+03; im: -3.137965059563163586e+02),
(re: -8.239469336509264113e-02; im: +9.927366875843948910e-01),
(re: 7.332295456982297798e+01; im: -1.574585908122833445e+01),
(re: -7.478643230138058210e+03; im: +1.634838234939800296e+03),
(re: 4.595842179016870234e+00; im: -8.135290105518580753e+00),
(re: -8.543842533574163435e+01; im: +3.750798997857594068e+01),
(re: -1.918003500809465688e+00; im: +7.435834461979350404e+00),
(re: -2.233816733239658031e+00; im: -2.143519070805995056e+00),
(re: -7.797564130187551181e+02; im: -2.854935234659491861e+03));
const t_sqrt: array[0..9] of complex = (
(re: 2.662820308608613054e+00; im: +1.453134567428218523e+00),
(re: 2.782327842725198625e+00; im: -4.975690731700522453e-02),
(re: 1.539702530208964276e+00; im: -1.627133657301663754e+00),
(re: 1.710341158150687526e+00; im: +2.817067712273758968e+00),
(re: 3.139039247295310338e+00; im: +4.661262584985865325e-01),
(re: 2.111708076482241764e+00; im: +1.238117022351427323e+00),
(re: 2.358703228167225670e+00; im: +5.782711190325734994e-01),
(re: 1.733526258887341048e+00; im: +5.264725822072126914e-01),
(re: 2.313109497470871653e+00; im: -1.877542930430378557e+00),
(re: 8.142053574504808624e-01; im: +3.057589758727724852e+00));
const t_tan: array[0..9] of complex = (
(re: -1.928757919086441129e-07; im: +1.000000326749916907e+00),
(re: 1.242412685364183792e+00; im: -3.171496938831333701e+00),
(re: -4.674512625158779523e-05; im: -9.999243922526395929e-01),
(re: 4.792363401193648193e-09; im: +1.000000007058933345e+00),
(re: 2.345740824080089140e-03; im: +9.947733046570988661e-01),
(re: -2.396030789494815566e-05; im: +9.999478134541859143e-01),
(re: -7.370204836644931341e-03; im: +1.004355341341713899e+00),
(re: -3.691803847992048527e-02; im: +9.647507199346954807e-01),
(re: -2.781955256713729368e-08; im: -1.000000049848910609e+00),
(re: 9.428159006403047888e-05; im: +9.999911934086371818e-01));
const t_tanh: array[0..9] of complex = (
(re: 1.000092198122514475e+00; im: +2.160986245871518020e-05),
(re: 9.999996772753199321e-01; im: -1.995376322295965887e-07),
(re: -1.765485739548037261e+00; im: +1.702421632555285245e+00),
(re: -9.999189442732736453e-01; im: +3.649060704944737019e-05),
(re: 9.999999922462233374e-01; im: -3.560088949517914775e-09),
(re: 1.002932493336732686e+00; im: -4.948790309797102353e-03),
(re: 9.999611306478801249e-01; im: -4.226995742097032481e-05),
(re: 1.007478418931634003e+00; im: -4.194050814891697808e-03),
(re: 9.938553422971832711e-01; im: +5.144217985914355503e-02),
(re: -1.000000049160498243e+00; im: -2.901873195374433112e-08));
{computed with Maple V}
const t_cbrt: array[0..9] of complex = (
(re: 1.980409351452068568; im: +0.6850519424925463137),
(re: 1.978279414982640533; im: -0.2358390581971672100e-1),
(re: 1.466680172613141937; im: -0.8831630365740902142),
(re: 1.717210422352255150; im: +1.398414056434914519),
(re: 2.149089778617387532; im: +0.2118895207076571871),
(re: 1.704009405612443111; im: +0.6288349012096719349),
(re: 1.783593916153138361; im: +0.2883512525266128085),
(re: 1.457518627100494964; im: +0.2902456331911219456),
(re: 1.860217302730305655; im: -0.9090607999413698775),
(re: 1.383682302674507700; im: +1.652470362294393105));
const t_cot: array[0..9] of complex = (
(re: -0.1928756658644007560e-6; im: -0.9999996732501526571),
(re: 0.1070862438142847477; im: +0.2733581992914031586),
(re: -0.4675219553854650241e-4; im: +1.000075611278721583),
(re: 0.4792363333535701170e-8; im: -0.9999999929410666817),
(re: 0.2370442182397188751e-2; im: -1.005248567563544041),
(re: -0.2396280888837780351e-4; im: -1.000052188695205540),
(re: -0.7306028886391044333e-2; im: -0.9956099319736191871),
(re: -0.3960708664430225805e-1; im: -1.035021548487447295),
(re: -0.2781954979358870134e-7; im: +0.9999999501510911020),
(re: 0.9428324984674023356e-4; im: -1.000008797779666557));
const t_coth: array[0..9] of complex = (
(re: 0.9999078099103386497; im: -0.2160587822215018317e-4),
(re: 1.000000322724744404; im: +0.1995377610210880360e-6),
(re: -0.2935050890604510592; im: -0.2830209282854317464),
(re: -1.000081060965401525; im: -0.3649652326549915645e-4),
(re: 1.000000007753776710; im: +0.35600890047261845990e-8),
(re: 0.9970518052990871675; im: +0.49197731105648616632e-2),
(re: 1.000038869076047474; im: +0.42273243548748589534e-4),
(re: 0.9925598917226418365; im: +0.41319461980362737256e-2),
(re: 1.003494165385392379; im: -0.51941087547045132368e-1),
(re: -0.9999999508395033317; im: +0.29018729100593874631e-7));
const t_acot: array[0..9] of complex = ({arccot(z) = arctan(1/z)}
(re: 0.5922161886162248337e-1; im: -0.9132440360395449438e-1),
(re: 0.1283458944466363632; im: +0.4541613264280391150e-2),
(re: -0.1144745643184335178e-1; im: +0.2016329540924836246),
(re: -0.4273437955030763245e-1; im: -0.8172155623067200375e-1),
(re: 0.9480541047081665141e-1; im: -0.2860296932069164436e-1),
(re: 0.8306094959024172596e-1; im: -0.1456687715320728166),
(re: 0.1500979340169774302; im: -0.7683048612788070225e-1),
(re: 0.2545727207450032827; im: -0.1603131300046753064),
(re: 0.2345125836452626135e-1; im: +0.1106490750793908248),
(re: -0.8665009277637122049e-1; im: -0.4934185030502439949e-1));
const t_acotc: array[0..9] of complex = ( {arccotc(z) = Pi/2 - arctan(z)}
(re: 0.5922161886162248337e-1; im: -0.9132440360395449438e-1),
(re: 0.1283458944466363632; im: +0.4541613264280391150e-2),
(re: 0.3130145197157949887e1; im: +0.2016329540924836246),
(re: 0.3098858274039485606e1; im: -0.8172155623067200375e-1),
(re: 0.9480541047081665141e-1; im: -0.2860296932069164436e-1),
(re: 0.8306094959024172596e-1; im: -0.1456687715320728166),
(re: 0.1500979340169774302; im: -0.7683048612788070225e-1),
(re: 0.2545727207450032827; im: -0.1603131300046753064),
(re: 0.2345125836452626135e-1; im: +0.1106490750793908248),
(re: 0.3054942560813422018e1; im: -0.4934185030502439949e-1));
const t_acoth: array[0..9] of complex = ({arccoth(z) = arctanh(1/z)}
(re: 0.5837502793896850906e-1; im: -0.9144747728436317341e-1),
(re: 0.1297734349779038123; im: +0.4695385748540486505e-2),
(re: -0.1057645606734725207e-1; im: +0.1964264609546681643),
(re: -0.4221859567868835888e-1; im: -0.8165292997825605856e-1),
(re: 0.9521899799131672206e-1; im: -0.2910791691718558618e-1),
(re: 0.7996545936689032386e-1; im: -0.1455452914075773492),
(re: 0.1505124547198072622; im: -0.8005307349326623874e-1),
(re: 0.2508207293399398771; im: -0.1787386614027091028),
(re: 0.2289610881579713585e-1; im: +0.1098738278666101983),
(re: -0.8665624101841876131e-1; im: -0.5000612310138727122e-1));
const t_acothc: array[0..9] of complex = ( {arccothc(z) = arctanh(z) - Pi/2}
(re: 0.5837502793896850906e-1; im: +3.050145176305430065),
(re: 0.1297734349779038123; im: +4.695385748540486505e-3),
(re: -0.1057645606734725207e-1; im: +1.964264609546681643e-1),
(re: -0.4221859567868835888e-1; im: +3.059939723611537180),
(re: 0.9521899799131672206e-1; im: +3.112484736672607652),
(re: 0.7996545936689032386e-1; im: +2.996047362182215889),
(re: 0.1505124547198072622; im: +3.061539580096527000),
(re: 0.2508207293399398771; im: +2.962853992187084136),
(re: 0.2289610881579713585e-1; im: +1.098738278666101983e-1),
(re: -0.8665624101841876131e-1; im: +3.091586530488405967));
const t_sec: array[0..9] of complex = (
(re: 0.2295199148880376835e-3; im: -0.8403447475347837991e-3),
(re: 0.12989370166232056268e1; im: -0.3033486595555792470e1),
(re: 0.1282551289556627290e-1; im: +0.3644422826478168455e-2),
(re: 0.3838075143333806804e-4; im: +0.1248637209030750447e-3),
(re: -0.1045455286208551367; im: -0.2232023102491372549e-1),
(re: -0.1046938934796870726e-1; im: +0.2288486624474527028e-2),
(re: 0.6513009749079909522e-1; im: -0.1136541304196971542),
(re: -0.2923394633451341215; im: +0.1218333775212251219),
(re: -0.8507263191619357876e-4; im: -0.3270094427232153096e-3),
(re: -0.1017362163340791656e-1; im: -0.9267177723122378378e-2));
const t_csc: array[0..9] of complex = (
(re: -0.8403445172210722399e-3; im: -0.2295196778103877952e-3),
(re: 0.9683267193972526473; im: +0.3023039867801472170e-1),
(re: -0.3645298006835056261e-2; im: +0.1282631226422795817e-1),
(re: 0.1248637202056048708e-3; im: -0.3838075056401858522e-4),
(re: -0.2268519939650578464e-1; im: +0.1050413340741458162),
(re: 0.2288856933581577076e-2; im: +0.1046988089317075064e-1),
(re: -0.1136310234293167699; im: -0.6401381157234571038e-1),
(re: 0.1376788855137337301; im: +0.2977521788958189069),
(re: 0.3270094287888337102e-3; im: -0.8507261857816022584e-4),
(re: -0.9268218455820426031e-2; im: +0.1017283739905681490e-1));
const t_sech: array[0..9] of complex = (
(re: 0.1580824202030253160e-2; im: -0.1367125757545055034e-1),
(re: 0.8379461465333227632e-3; im: +0.2381269591839372671e-3),
(re: 1.849738276901817540; im: +1.624879126147844399),
(re: -0.1303611992058492371e-1; im: -0.2798965451304095563e-2),
(re: -0.1276157982057134419e-3; im: -0.2789692947087167673e-4),
(re: 0.5325691222430206498e-1; im: +0.9319546321990157438e-1),
(re: -0.9812894425422896831e-2; im: -0.4307425779044763368e-2),
(re: -0.3329694810529869903e-1; im: -0.1269009901611255701),
(re: -0.2431353695905795505; im: +0.2102782715592330703),
(re: 0.8902676617781153125e-4; im: -0.3259551551312227504e-3));
const t_csch: array[0..9] of complex = (
(re: 0.1580383086179010325e-2; im: -0.1367003137608408583e-1),
(re: 0.8379463694439584530e-3; im: +0.2381272032352972409e-3),
(re: -0.8303279906660916594e-1; im: -1.000424936846338354),
(re: 0.1303707448854306353e-1; im: +0.2799668111199677253e-2),
(re: -0.1276157990959022940e-3; im: -0.2789693014150183876e-4),
(re: 0.5264139994391948945e-1; im: +0.9318271677380037815e-1),
(re: -0.9813093754703538708e-2; im: -0.4308008027580901967e-2),
(re: -0.3252486714226639958e-1; im: -0.1260944142519527329),
(re: -0.2330628426706680808; im: +0.2236417341347029484),
(re: -0.8902675234240714349e-4; im: +0.3259551416905490430e-3));
const t_powxx: array[0..9] of complex = ( {(2-0.75*I),)^a[i]}
(re: -411.5034488394179369; im: -569.8659411483985571),
(re: -317.9550520992117476; im: -49.67441240169941263),
(re: -1.136453275749506582e-1; im: +0.7153440743397040163e-1),
(re: -6.732970677690146106e-1; im: +0.2184973370139234927),
(re: 1407.2720056523953442; im: -4048.893677791971718),
(re: -58.66890468069053621; im: +13.30164259070217028),
(re: 138.13717633016558385; im: +27.18131225346363694),
(re: 14.015416563592191076; im: +6.034734380815592956),
(re: 1.0103523461390175547e-1; im: -0.1454685283138031456),
(re: 6.6984084283828055675e-3; im: +0.4699792933223983569e-2));
const t_asec: array[0..9] of complex = (
(re: 1.512210183685502006; im: +0.9141852458058421885e-1),
(re: 1.441384210511503894; im: -0.4656140008081491080e-2),
(re: 1.581579935950300462; im: -0.1976905676742241681),
(re: 1.613143307981322738; im: +0.8167069354626031696e-1),
(re: 1.475680840833964570; im: +0.2898047671654966331e-1),
(re: 1.490066035968365363; im: +0.1455895139329430183),
(re: 1.420374427615751175; im: +0.7923568279285739895e-1),
(re: 1.318713053844599337; im: +0.1740762424309732395),
(re: 1.547763376821836497; im: -0.1100664831786344994),
(re: 1.657452099507347186; im: +0.4983941833819650269e-1));
const t_acsc: array[0..9] of complex = (
(re: 0.5858614310939461327e-1; im: -0.9141852458058421885e-1),
(re: 0.1294121162833927252; im: +0.4656140008081491080e-2),
(re: -0.1078360915540384276e-1; im: +0.1976905676742241681),
(re: -0.4234698118642611903e-1; im: -0.8167069354626031696e-1),
(re: 0.9511548596093204879e-1; im: -0.2898047671654966331e-1),
(re: 0.8073029082653125666e-1; im: -0.1455895139329430183),
(re: 0.1504218991791454444; im: -0.7923568279285739895e-1),
(re: 0.2520832729502972825; im: -0.1740762424309732395),
(re: 0.2303294997306012269e-1; im: +0.1100664831786344994),
(re: -0.8665577271245056663e-1; im: -0.4983941833819650269e-1));
const t_asech: array[0..9] of complex = (
(re: 0.9141852458058421885e-1; im: -1.512210183685502006),
(re: 0.4656140008081491080e-2; im: +1.441384210511503894),
(re: 0.1976905676742241681; im: +1.581579935950300463),
(re: 0.8167069354626031696e-1; im: -1.613143307981322738),
(re: 0.2898047671654966331e-1; im: -1.475680840833964570),
(re: 0.1455895139329430183; im: -1.490066035968365363),
(re: 0.7923568279285739895e-1; im: -1.420374427615751175),
(re: 0.1740762424309732395; im: -1.318713053844599337),
(re: 0.1100664831786344994; im: +1.547763376821836497),
(re: 0.4983941833819650269e-1; im: -1.657452099507347186));
const t_acsch: array[0..9] of complex = (
(re: 0.5900944583838133397e-1; im: -0.9135699399171889898e-1),
(re: 0.1286983771056428065; im: +0.4579261716317799017e-2),
(re: -0.1121885689753266316e-1; im: +0.2002931943353766317),
(re: -0.4260487376311824908e-1; im: -0.8170500960799509011e-1),
(re: 0.9490868978698757836e-1; im: -0.2872800740986223793e-1),
(re: 0.8227811649941698836e-1; im: -0.1456514294348292370),
(re: 0.1502144285132965397; im: -0.7762434097558978131e-1),
(re: 0.2539521606134725062; im: -0.1648526110697654025),
(re: 0.2331051248997436416e-1; im: +0.1104541052974145886),
(re: -0.8665269393397101588e-1; im: -0.4950727938358179074e-1));
const t_sqr: array[0..9] of complex = (
(re: -35.09958742964881212; im: +77.06387667215681207),
(re: 59.81348461171198962; im: -4.285478906725584989),
(re: -25.02948605336054182; im: +2.774672432786690695),
(re: -67.75200779196063026; im: -96.56729623202236066),
(re: 84.29447266502668985; im: +56.39886115083058811),
(re: -18.77962978679710908; im: +30.60454147186048605),
(re: 19.90165737821260974; im: +28.52925077535505228),
(re: 4.10990652539402285; im: +9.958661584275993084),
(re: -72.11353945579950930; im: -31.70897752762440709),
(re: 50.65472933722129051; im: -86.49464600276076246));
const t_inv: array[0..9] of complex = (
(re: 0.5879747708341167711e-1; im: -0.9138885060735870098e-1),
(re: 0.1290525960549594605; im: +0.4617221732733286767e-2),
(re: -0.1099480336617089353e-1; im: +0.1989691929690424442),
(re: -0.4247559138301920663e-1; im: -0.8168821665740785727e-1),
(re: 0.9501201804472894140e-1; im: -0.2885352143771125834e-1),
(re: 0.8149880137464069725e-1; im: -0.1456285355957822296),
(re: 0.1503259447498211211; im: -0.7842294919027377673e-1),
(re: 0.2532105413089933676; im: -0.1694272106882013405),
(re: 0.2317055986689894902e-1; im: +0.1102595998817552844),
(re: -0.8665487317820390140e-1; im: -0.4967296613764175193e-1));
const t_neg: array[0..9] of complex = (
(re: -4.979011924883673501; im: -7.738872474578104566),
(re: -7.738872474578104566; im: +0.276880057192001594),
(re: 0.276880057192001594; im: +5.010603618271074922),
(re: 5.010603618271074922; im: -9.636293707198417380),
(re: -9.636293707198417380; im: -2.926377239243964645),
(re: -2.926377239243964645; im: -5.229083431459306652),
(re: -5.229083431459306652; im: -2.727939910436010251),
(re: -2.727939910436010251; im: -1.825308091680855060),
(re: -1.825308091680855060; im: +8.685924768575601362),
(re: 8.685924768575601362; im: -4.979011924883673501));
const t_add: array[0..9] of complex = (
(re: 6.979011924883673501; im: +6.988872474578104566),
(re: 2*4.869436237289052283; im: -1.026880057192001594), {!! 16-bit}
(re: 1.723119942807998406; im: -5.760603618271074922),
(re: -3.010603618271074922; im: +8.886293707198417380),
(re: 11.63629370719841738; im: +2.176377239243964645),
(re: 4.926377239243964645; im: +4.479083431459306652),
(re: 7.229083431459306652; im: +1.977939910436010251),
(re: 4.727939910436010251; im: +1.075308091680855060),
(re: 3.825308091680855060; im: -9.435924768575601362),
(re: -6.685924768575601362; im: +4.229011924883673501));
const t_sub: array[0..9] of complex = (
(re: 2.979011924883673501; im: +8.488872474578104566),
(re: 5.738872474578104566; im: +0.4731199428079984060),
(re: -2.276880057192001594; im: -4.260603618271074922),
(re: -7.010603618271074922; im: +10.38629370719841738),
(re: 7.636293707198417380; im: +3.676377239243964645),
(re: 0.9263772392439646453; im: +5.979083431459306652),
(re: 3.229083431459306652; im: +3.477939910436010251),
(re: 0.7279399104360102513; im: +2.575308091680855060),
(re: -0.1746919083191449396; im: -7.935924768575601362),
(re: -10.68592476857560136; im: +5.729011924883673501));
const t_mul: array[0..9] of complex = (
(re: 15.76217820570092543; im: +11.74348600549345401),
(re: 15.27008490626220794; im: -6.357914470317581612),
(re: -4.311712828087309379; im: -4.906773596824074324*2), {!! 16-bit}
(re: -2.793986956143336808; im: +23.03054012810014095),
(re: 21.46737034382980824; im: -1.374465801910883744),
(re: 9.774567052082409280; im: +8.263383933485639821),
(re: 12.50412179574562099; im: +1.534067247277540513),
(re: 6.824860889632661798; im: +1.604661250534702432),
(re: -2.863827393069990901; im: -18.74083060591184402),
(re: -13.63759059348844760; im: +16.47246742619904802));
const t_div: array[0..9] of complex = (
(re: 0.4905331621130432848e-1; im: -0.2268758090272761598),
(re: 0.2615681084094688860; im: -0.8755500357575302183e-1),