45 #include <cln/output.h> 46 #include <cln/integer_io.h> 47 #include <cln/integer_ring.h> 48 #include <cln/rational_io.h> 49 #include <cln/rational_ring.h> 50 #include <cln/lfloat_class.h> 51 #include <cln/lfloat_io.h> 52 #include <cln/real_io.h> 53 #include <cln/real_ring.h> 54 #include <cln/complex_io.h> 55 #include <cln/complex_ring.h> 56 #include <cln/numtheory.h> 94 #if cl_value_len >= 32 97 if (i < (1L << (cl_value_len-1)) && i >= -(1L << (cl_value_len-1)))
100 value = cln::cl_I(static_cast<long>(i));
115 #if cl_value_len >= 32 116 value = cln::cl_I(i);
118 if (i < (1UL << (cl_value_len-1)))
119 value = cln::cl_I(i);
121 value = cln::cl_I(static_cast<unsigned long>(i));
129 value = cln::cl_I(i);
136 value = cln::cl_I(i);
142 value = cln::cl_I(i);
148 value = cln::cl_I(i);
158 throw std::overflow_error(
"division by zero");
169 value = cln::cl_float(d, cln::default_float_format);
178 cln::cl_N ctorval = 0;
183 std::string::size_type delim;
186 if (ss.at(0) !=
'+' && ss.at(0) !=
'-' && ss.at(0) !=
'#')
191 while ((delim = ss.find(
"e"))!=std::string::npos)
192 ss.replace(delim,1,
"E");
198 bool imaginary =
false;
199 delim = ss.find_first_of(std::string(
"+-"),1);
201 if (delim!=std::string::npos && ss.at(delim-1)==
'E')
202 delim = ss.find_first_of(std::string(
"+-"),delim+1);
203 term = ss.substr(0,delim);
204 if (delim!=std::string::npos)
205 ss = ss.substr(delim);
207 if (term.find(
"I")!=std::string::npos) {
209 term.erase(term.find(
"I"),1);
211 if (term.find(
"*")!=std::string::npos)
212 term.erase(term.find(
"*"),1);
218 if (term.find(
'.')!=std::string::npos || term.find(
'E')!=std::string::npos) {
229 if (term.find(
"E")==std::string::npos)
232 term = term.replace(term.find(
"E"),1,
"e");
234 term +=
"_" + std::to_string((
unsigned)
Digits);
237 ctorval = ctorval + cln::complex(cln::cl_I(0),cln::cl_F(term.c_str()));
239 ctorval = ctorval + cln::cl_F(term.c_str());
243 ctorval = ctorval + cln::complex(cln::cl_I(0),cln::cl_R(term.c_str()));
245 ctorval = ctorval + cln::cl_R(term.c_str());
247 }
while (delim != std::string::npos);
271 cln::cl_F
x = cln::cl_float(dec.mantissa, cln::default_float_format);
272 x = cln::scale_float(
x, dec.exponent);
273 cln::cl_F sign = cln::cl_float(dec.sign, cln::default_float_format);
274 x = cln::float_sign(sign,
x);
283 cln::cl_idecoded_float dec;
284 s >> dec.sign >> dec.mantissa >> dec.exponent;
291 inherited::read_archive(
n, sym_lst);
296 if (
n.find_string(
"number", str)) {
297 std::istringstream s(str);
311 value = cln::complex(re, im);
318 value = cln::complex(re, im);
325 value = cln::complex(re, im);
340 const cln::cl_idecoded_float dec = cln::integer_decode_float(cln::the<cln::cl_F>(
n));
341 s << dec.sign <<
' ' << dec.mantissa <<
' ' << dec.exponent;
346 inherited::archive(
n);
350 const cln::cl_R re = cln::realpart(
value);
351 const cln::cl_R im = cln::imagpart(
value);
352 const bool re_rationalp = cln::instanceof(re, cln::cl_RA_ring);
353 const bool im_rationalp = cln::instanceof(im, cln::cl_RA_ring);
357 std::ostringstream s;
358 if (re_rationalp && im_rationalp)
360 else if (zerop(im)) {
364 }
else if (re_rationalp) {
370 }
else if (im_rationalp) {
383 n.add_string(
"number", s.str());
399 cln::cl_print_flags ourflags;
400 if (cln::instanceof(
x, cln::cl_RA_ring)) {
402 if (cln::instanceof(
x, cln::cl_I_ring) ||
403 !is_a<print_latex>(
c)) {
404 cln::print_real(
c.s, ourflags,
x);
409 cln::print_real(
c.s, ourflags,
cln::abs(cln::numerator(cln::the<cln::cl_RA>(
x))));
411 cln::print_real(
c.s, ourflags, cln::denominator(cln::the<cln::cl_RA>(
x)));
418 ourflags.default_float_format = cln::float_format(cln::the<cln::cl_F>(
x));
419 cln::print_real(
c.s, ourflags,
x);
430 const int max_cln_int = 536870911;
431 if (
x >= cln::cl_I(-max_cln_int) &&
x <= cln::cl_I(max_cln_int))
432 c.s << cln::cl_I_to_int(
x) <<
".0";
434 c.s << cln::double_approx(
x);
442 if (cln::instanceof(
x, cln::cl_I_ring)) {
447 }
else if (cln::instanceof(
x, cln::cl_RA_ring)) {
450 const cln::cl_I
numer = cln::numerator(cln::the<cln::cl_RA>(
x));
451 const cln::cl_I
denom = cln::denominator(cln::the<cln::cl_RA>(
x));
466 c.s << cln::double_approx(
x);
470 template<
typename T1,
typename T2>
471 static inline bool coerce(T1& dst,
const T2& arg);
479 inline bool coerce<int, cln::cl_I>(
int& dst,
const cln::cl_I& arg)
481 static const cln::cl_I cl_max_int =
482 (cln::cl_I)(
long)(std::numeric_limits<int>::max());
483 static const cln::cl_I cl_min_int =
484 (cln::cl_I)(
long)(std::numeric_limits<int>::min());
485 if ((arg >= cl_min_int) && (arg <= cl_max_int)) {
486 dst = cl_I_to_int(arg);
493 inline bool coerce<unsigned int, cln::cl_I>(
unsigned int& dst,
const cln::cl_I& arg)
495 static const cln::cl_I cl_max_uint =
496 (cln::cl_I)(
unsigned long)(std::numeric_limits<unsigned int>::max());
497 if ((! minusp(arg)) && (arg <= cl_max_uint)) {
498 dst = cl_I_to_uint(arg);
509 if (cln::instanceof(
x, cln::cl_I_ring)) {
513 if (
coerce(dst, cln::the<cln::cl_I>(
x))) {
516 c.s <<
'(' << dst <<
')';
521 c.s <<
"cln::cl_I(\"";
525 }
else if (cln::instanceof(
x, cln::cl_RA_ring)) {
528 cln::cl_print_flags ourflags;
529 c.s <<
"cln::cl_RA(\"";
530 cln::print_rational(
c.s, ourflags, cln::the<cln::cl_RA>(
x));
536 c.s <<
"cln::cl_F(\"";
544 const cln::cl_R
r = cln::realpart(
value);
545 const cln::cl_R i = cln::imagpart(
value);
568 c.s <<
"-" << imag_sym;
571 c.s << mul_sym << imag_sym;
585 c.s <<
"-" << imag_sym;
588 c.s << mul_sym << imag_sym;
592 c.s <<
"+" << imag_sym;
596 c.s << mul_sym << imag_sym;
617 std::ios::fmtflags oldflags =
c.s.flags();
618 c.s.setf(std::ios::scientific);
619 int oldprec =
c.s.precision();
622 if (is_a<print_csrc_double>(
c))
623 c.s.precision(std::numeric_limits<double>::digits10 + 1);
625 c.s.precision(std::numeric_limits<float>::digits10 + 1);
635 c.s <<
"std::complex<";
636 if (is_a<print_csrc_double>(
c))
648 c.s.precision(oldprec);
661 c.s <<
"cln::complex(";
671 c.s << std::string(level,
' ') <<
value 672 <<
" (" << class_name() <<
")" <<
" @" <<
this 673 << std::hex <<
", hash=0x" <<
hashvalue <<
", flags=0x" <<
flags << std::dec
679 c.s << class_name() <<
"('";
745 return n==0 ? *this :
_ex0;
756 if (!is_exactly_a<numeric>(other))
758 const numeric &o = ex_to<numeric>(other);
797 return numeric(cln::cl_float(1.0, cln::default_float_format) *
value);
892 if (cln::zerop(other.
value))
893 throw std::overflow_error(
"numeric::div(): division by zero");
907 if (cln::zerop(
value)) {
908 if (cln::zerop(other.
value))
909 throw std::domain_error(
"numeric::eval(): pow(0,0) is undefined");
910 else if (cln::zerop(cln::realpart(other.
value)))
911 throw std::domain_error(
"numeric::eval(): pow(0,I) is undefined");
912 else if (cln::minusp(cln::realpart(other.
value)))
913 throw std::overflow_error(
"numeric::eval(): division by zero");
934 return dynallocate<numeric>(
value + other.
value);
949 return dynallocate<numeric>(
value - other.
value);
966 return dynallocate<numeric>(
value * other.
value);
982 if (cln::zerop(cln::the<cln::cl_N>(other.
value)))
983 throw std::overflow_error(
"division by zero");
985 return dynallocate<numeric>(
value / other.
value);
1001 if (cln::zerop(
value)) {
1002 if (cln::zerop(other.
value))
1003 throw std::domain_error(
"numeric::eval(): pow(0,0) is undefined");
1004 else if (cln::zerop(cln::realpart(other.
value)))
1005 throw std::domain_error(
"numeric::eval(): pow(0,I) is undefined");
1006 else if (cln::minusp(cln::realpart(other.
value)))
1007 throw std::overflow_error(
"numeric::eval(): division by zero");
1012 return dynallocate<numeric>(cln::expt(
value, other.
value));
1055 if (cln::zerop(
value))
1056 throw std::overflow_error(
"numeric::inverse(): division by zero");
1065 { cln::cl_R
r = cln::realpart(
value);
1080 if (cln::zerop(
value))
1082 cln::cl_R
r = cln::realpart(
value);
1083 if (!cln::zerop(
r)) {
1089 if (cln::plusp(cln::imagpart(
value)))
1107 if (cln::instanceof(
value, cln::cl_R_ring) &&
1108 cln::instanceof(other.
value, cln::cl_R_ring))
1110 return cln::compare(cln::the<cln::cl_R>(
value), cln::the<cln::cl_R>(other.
value));
1113 cl_signean real_cmp = cln::compare(cln::realpart(
value), cln::realpart(other.
value));
1117 return cln::compare(cln::imagpart(
value), cln::imagpart(other.
value));
1131 return cln::zerop(
value);
1138 if (cln::instanceof(
value, cln::cl_R_ring))
1139 return cln::plusp(cln::the<cln::cl_R>(
value));
1147 if (cln::instanceof(
value, cln::cl_R_ring))
1148 return cln::minusp(cln::the<cln::cl_R>(
value));
1156 return cln::instanceof(
value, cln::cl_I_ring);
1163 return (cln::instanceof(
value, cln::cl_I_ring) && cln::plusp(cln::the<cln::cl_I>(
value)));
1170 return (cln::instanceof(
value, cln::cl_I_ring) && !cln::minusp(cln::the<cln::cl_I>(
value)));
1177 return (cln::instanceof(
value, cln::cl_I_ring) && cln::evenp(cln::the<cln::cl_I>(
value)));
1184 return (cln::instanceof(
value, cln::cl_I_ring) && cln::oddp(cln::the<cln::cl_I>(
value)));
1193 return (cln::instanceof(
value, cln::cl_I_ring)
1194 && cln::plusp(cln::the<cln::cl_I>(
value))
1195 && cln::isprobprime(cln::the<cln::cl_I>(
value)));
1203 return cln::instanceof(
value, cln::cl_RA_ring);
1210 return cln::instanceof(
value, cln::cl_R_ring);
1230 if (cln::instanceof(
value, cln::cl_I_ring))
1233 if (cln::instanceof(cln::realpart(
value), cln::cl_I_ring) &&
1234 cln::instanceof(cln::imagpart(
value), cln::cl_I_ring))
1245 if (cln::instanceof(
value, cln::cl_RA_ring))
1248 if (cln::instanceof(cln::realpart(
value), cln::cl_RA_ring) &&
1249 cln::instanceof(cln::imagpart(
value), cln::cl_RA_ring))
1262 return (cln::the<cln::cl_R>(
value) < cln::the<cln::cl_R>(other.
value));
1263 throw std::invalid_argument(
"numeric::operator<(): complex inequality");
1273 return (cln::the<cln::cl_R>(
value) <= cln::the<cln::cl_R>(other.
value));
1274 throw std::invalid_argument(
"numeric::operator<=(): complex inequality");
1284 return (cln::the<cln::cl_R>(
value) > cln::the<cln::cl_R>(other.
value));
1285 throw std::invalid_argument(
"numeric::operator>(): complex inequality");
1295 return (cln::the<cln::cl_R>(
value) >= cln::the<cln::cl_R>(other.
value));
1296 throw std::invalid_argument(
"numeric::operator>=(): complex inequality");
1306 return cln::cl_I_to_int(cln::the<cln::cl_I>(
value));
1316 return cln::cl_I_to_long(cln::the<cln::cl_I>(
value));
1325 return cln::double_approx(cln::realpart(
value));
1358 if (cln::instanceof(
value, cln::cl_I_ring))
1361 else if (cln::instanceof(
value, cln::cl_RA_ring))
1362 return numeric(cln::numerator(cln::the<cln::cl_RA>(
value)));
1365 const cln::cl_RA
r = cln::the<cln::cl_RA>(cln::realpart(
value));
1366 const cln::cl_RA i = cln::the<cln::cl_RA>(cln::imagpart(
value));
1367 if (cln::instanceof(
r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_I_ring))
1369 if (cln::instanceof(
r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_RA_ring))
1370 return numeric(cln::complex(
r*cln::denominator(i), cln::numerator(i)));
1371 if (cln::instanceof(
r, cln::cl_RA_ring) && cln::instanceof(i, cln::cl_I_ring))
1372 return numeric(cln::complex(cln::numerator(
r), i*cln::denominator(
r)));
1373 if (cln::instanceof(
r, cln::cl_RA_ring) && cln::instanceof(i, cln::cl_RA_ring)) {
1374 const cln::cl_I s =
cln::lcm(cln::denominator(
r), cln::denominator(i));
1375 return numeric(cln::complex(cln::numerator(
r)*(cln::exquo(s,cln::denominator(
r))),
1376 cln::numerator(i)*(cln::exquo(s,cln::denominator(i)))));
1389 if (cln::instanceof(
value, cln::cl_I_ring))
1392 if (cln::instanceof(
value, cln::cl_RA_ring))
1393 return numeric(cln::denominator(cln::the<cln::cl_RA>(
value)));
1396 const cln::cl_RA
r = cln::the<cln::cl_RA>(cln::realpart(
value));
1397 const cln::cl_RA i = cln::the<cln::cl_RA>(cln::imagpart(
value));
1398 if (cln::instanceof(
r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_I_ring))
1400 if (cln::instanceof(
r, cln::cl_I_ring) && cln::instanceof(i, cln::cl_RA_ring))
1401 return numeric(cln::denominator(i));
1402 if (cln::instanceof(
r, cln::cl_RA_ring) && cln::instanceof(i, cln::cl_I_ring))
1403 return numeric(cln::denominator(
r));
1404 if (cln::instanceof(
r, cln::cl_RA_ring) && cln::instanceof(i, cln::cl_RA_ring))
1420 if (cln::instanceof(
value, cln::cl_I_ring))
1421 return cln::integer_length(cln::the<cln::cl_I>(
value));
1453 throw pole_error(
"log(): logarithmic pole",0);
1513 throw pole_error(
"atan(): logarithmic pole",0);
1531 cln::the<cln::cl_R>(y.
to_cl_N())));
1537 const cln::cl_N aux_p =
x.to_cl_N()+cln::complex(0,1)*y.
to_cl_N();
1538 if (cln::zerop(aux_p)) {
1540 throw pole_error(
"atan(): logarithmic pole",0);
1542 const cln::cl_N aux_m =
x.to_cl_N()-cln::complex(0,1)*y.
to_cl_N();
1543 if (cln::zerop(aux_m)) {
1545 throw pole_error(
"atan(): logarithmic pole",0);
1634 const cln::float_format_t &prec)
1638 cln::cl_N num = cln::complex(cln::cl_float(1, prec), 0);
1647 }
while (acc != acc+aug);
1653 const cln::float_format_t &prec)
1655 const cln::cl_R re = cln::realpart(
x);
1656 const cln::cl_R im = cln::imagpart(
x);
1657 if (re > cln::cl_F(
".5"))
1662 if ((re <= 0 &&
cln::abs(im) > cln::cl_F(
".75")) || (re < cln::cl_F(
"-.5")))
1666 if (re > 0 &&
cln::abs(im) > cln::cl_LF(
".75"))
1686 cln::float_format_t prec = cln::default_float_format;
1688 if (!instanceof(realpart(
value), cln::cl_RA_ring))
1689 prec = cln::float_format(cln::the<cln::cl_F>(cln::realpart(
value)));
1690 else if (!instanceof(imagpart(
value), cln::cl_RA_ring))
1691 prec = cln::float_format(cln::the<cln::cl_F>(cln::imagpart(
value)));
1707 const cln::cl_N x_ =
x.to_cl_N();
1710 const cln::cl_N result =
Li2_(x_);
1725 const int aux = (int)(cln::double_approx(cln::the<cln::cl_R>(
x.to_cl_N())));
1726 if (cln::zerop(
x.to_cl_N()-aux))
1773 cln::cl_N A = (*current_vector)[0];
1775 for (
int i=1; i<size; ++i)
1787 coeffs =
new std::vector<cln::cl_N>[4];
1788 std::vector<cln::cl_N> coeffs_12(12);
1790 coeffs_12[0] =
"1.000000000000000002194974863102775496587";
1791 coeffs_12[1] =
"133550.502942477423232096703994753698903";
1792 coeffs_12[2] =
"-492930.93529936026920053070245469905582";
1793 coeffs_12[3] =
"741287.473697611642492293025524275986598";
1794 coeffs_12[4] =
"-585097.37760399665198416642641725036094";
1795 coeffs_12[5] =
"260425.270330385275465083772352301818652";
1796 coeffs_12[6] =
"-65413.3533961142651069690504470463782994";
1797 coeffs_12[7] =
"8801.45963508441793636152568413199291892";
1798 coeffs_12[8] =
"-564.805024129362118607692062642312799553";
1799 coeffs_12[9] =
"13.80379833961490898061357227729422691903";
1800 coeffs_12[10] =
"-0.0807817619724537563116612761921260762075";
1801 coeffs_12[11] =
"3.47974801622326717770813986587340515986E-5";
1802 coeffs[0].swap(coeffs_12);
1803 std::vector<cln::cl_N> coeffs_30(30);
1805 coeffs_30[0] =
"1.0000000000000000000000000000000000000000000000445658922238202528026977308762";
1806 coeffs_30[1] =
"1.40445649204966682962030786915579421135474600150789821268713805046080310901683E13";
1807 coeffs_30[2] =
"-1.4473384178280338809560100504713144673757322488310852336205875273000116908753E14";
1808 coeffs_30[3] =
"6.9392104219998816400402602197781299548036066538116472480223222192156630720206E14";
1809 coeffs_30[4] =
"-2.05552680548452350127164925238339710431333013110755662640014074226849466382297E15";
1810 coeffs_30[5] =
"4.21346047774975891986783355395961145235696863271597017695734168781011785582523E15";
1811 coeffs_30[6] =
"-6.3439111294220458481092019992445750626799029041090235945435769621790257585491E15";
1812 coeffs_30[7] =
"7.2684029986336427327225410026373012514882246322145965580608264703248155838791E15";
1813 coeffs_30[8] =
"-6.4784969409198000751978874152931803231807770528527455966624850088042561231024E15";
1814 coeffs_30[9] =
"4.5545745239457403086706103662737668418631761744785802123770605916210445083544E15";
1815 coeffs_30[10] =
"-2.54592491966737919409139938046543941491145224466411852277136834553178078105403E15";
1816 coeffs_30[11] =
"1.1356718195163150156198936885250451780214219874255251444701005988134747787666E15";
1817 coeffs_30[12] =
"-4.04275236298036712070700727222520609783336229393218886420197964965371362011123E14";
1818 coeffs_30[13] =
"1.14472757259832757229433124273590647229089622322597383276758880048004748372644E14";
1819 coeffs_30[14] =
"-2.56166271828342920179612184110684658183432315551120625854181503468327037516717E13";
1820 coeffs_30[15] =
"4.4861708254018935131376878973710146069395814469656232761173409397653101421558E12";
1821 coeffs_30[16] =
"-6.0657495816705687896607821799338217335976369800808791959096705890743701166037E11";
1822 coeffs_30[17] =
"6.21975328147406581536747878587069711930541459818297675578654403265380823122363E10";
1823 coeffs_30[18] =
"-4.7255003764027411113501086372508071116675161078057298991208060427341079636661E9";
1824 coeffs_30[19] =
"2.5814613908651936680441351265410235295992556406609945442133129515256889464315E8";
1825 coeffs_30[20] =
"-9752115.5047412418881417732027953903591189993329461844657371497174389592441887";
1826 coeffs_30[21] =
"242056.60372411758318197954509546521913927205056839365620249547101194072057318";
1827 coeffs_30[22] =
"-3686.17673045938850138289555088011327333352145765167200561022138925168680049115";
1828 coeffs_30[23] =
"31.3494924501834034405048975310989414795238339283146314931357877820190435258517";
1829 coeffs_30[24] =
"-0.130254774344853676030752542814176943723937677940441021884132211221409382350105";
1830 coeffs_30[25] =
"2.16625679868432886771581352257834967866602495378408740265571976698475288337338E-4";
1831 coeffs_30[26] =
"-1.05077239977528252603869373455592388508233760416601143477182890107978206726294E-7";
1832 coeffs_30[27] =
"8.5728436055212340846907439451102962820713733082683634385104363203776378266115E-12";
1833 coeffs_30[28] =
"-3.9175430218003196379961975369936752665267219444417121562332986822123821080906E-17";
1834 coeffs_30[29] =
"1.06841715008998384033789050831892757796251622802680860264598247667384268519263E-24";
1835 coeffs[1].swap(coeffs_30);
1836 std::vector<cln::cl_N> coeffs_60(60);
1838 coeffs_60[0] =
"1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000007301368866363013444179014835363181183419450549774";
1839 coeffs_60[1] =
"2.13152397525281235754468356918725048606852617746577461250754322057711822075135461598274984226013367948201688447853106595646692682568953E26";
1840 coeffs_60[2] =
"-4.548529924829267669336610112411669181387790087825260737133755173032543313325682598833009521765336124891170163525664509845740222794717604E27";
1841 coeffs_60[3] =
"4.6879437426294973235875133160595324795437824160731608900005486977197800919261614723948577079551305728583507312310069280623018775850412E28";
1842 coeffs_60[4] =
"-3.10861265267020467624457768823845414206135580030123228715133927538323570190367768297139526311161786169387040978744732051184844409191231E29";
1843 coeffs_60[5] =
"1.490599577483981276717037178787147902256911799467742317379590487947009001487476793680630580522955117318124168494382267800788736334308E30";
1844 coeffs_60[6] =
"-5.50755504045738806940255910881807353185463857314393682608295373644157298562106198431098170107741597645409216199785852260920496247655646E30";
1845 coeffs_60[7] =
"1.631668518639067070100242032960081591016027803392225476881353619523143028349554534276268195490790113905102273979193269720381236708853746E31";
1846 coeffs_60[8] =
"-3.9823057865511431381368541930378720290638930941334849821428293955264049587073723565727061718251925950255036781219414607001763225298119E31";
1847 coeffs_60[9] =
"8.16425963140638737297557821827674142140347732117757126331775708561852858085860735359056658172512163756926693444882201094206795155146202E31";
1848 coeffs_60[10] =
"-1.426548236351667330492229413193359354309705120770113917370333660827270957172393778178051742077714657388432785747112574456061555034588373E32";
1849 coeffs_60[11] =
"2.14821861694536170414714365485614715949416083667308573285807894910742621740039595483105992136915471547998283891842897000924199509164799E32";
1850 coeffs_60[12] =
"-2.81233281290021706519566203146379395136352592819625378308636458418501787286411189089807465993150834399778687427813779950602826375635436E32";
1851 coeffs_60[13] =
"3.222783358826786224404373038021509245352188734386849874296356404770508945395436142634892645963851510893216093037595555902121365717716154E32";
1852 coeffs_60[14] =
"-3.250409075716999887328836263791911196138647661969351655925350981785153422033954649154242209471752219326556302767677017396179477496948985E32";
1853 coeffs_60[15] =
"2.897783210826628399578158893643627107049805015801395657097255344786041806868455726759715576609013221857885740543509045196763816109465777E32";
1854 coeffs_60[16] =
"-2.29136919195969647663887561122314618826917230275433296293059354280077561407373070937197721317435316121212106870152659174216557412788874E32";
1855 coeffs_60[17] =
"1.611288006928200619663496306945576194382628760891807800193737346171844871295031418730500946186238469256168610033434708290528870722514911E32";
1856 coeffs_60[18] =
"-1.009632466053186015034182792930705530447465885425278324598880797572411588461783484686932989855033967294215840157892487264656571258327313E32";
1857 coeffs_60[19] =
"5.64520651042784179741815642438421132518008517154942873706221206276337451930555926854271086501686252334516011905237101877044320182980053E31";
1858 coeffs_60[20] =
"-2.81912877441595327683492797147781153304080114512116755424671954256427789550109614317215500473322621746416096887803928883800132453510579E31";
1859 coeffs_60[21] =
"1.257934257434294354026338893625531254891110662111965279263894740714811495074726866375858553579650295684850594211744093582249745250079168E31";
1860 coeffs_60[22] =
"-5.01544407232599962845688086323662774702854661522104499328570796808858930542190600193190967249971520736397504227594619670310759235566195E30";
1861 coeffs_60[23] =
"1.786035425040937365122699272239542501767986628253845452136132211710520249195280548478081559036323184490150479070929923213045153333111476E30";
1862 coeffs_60[24] =
"-5.67605430104368150038863866362066081946938075036837029856903803768657069745962581310398542442108872722631658677177822712376500859930109E29";
1863 coeffs_60[25] =
"1.607878222558573982505999018371559631909289246981490321219650132406126936263403946310818841465409950661433241956831540547593847161412447E29";
1864 coeffs_60[26] =
"-4.05332042374309456146169816144083508836132423024788116321074411679252452773181941601763924562378611113519038766273534176937279867894066E28";
1865 coeffs_60[27] =
"9.07493596543985672039002802030098143847503854224661484396413496012780904911929710460264147600378604646912175235271954302119768907744722E27";
1866 coeffs_60[28] =
"-1.800074018924350353143489874038038169034914082090587278672411654146678304871125651069902339241049552886098125667720181441150399048551683E27";
1867 coeffs_60[29] =
"3.154250688078046681602499411296013099183808016176992164829953752437167774310360166977972581670851790753785195101324694758021403186162394E26";
1868 coeffs_60[30] =
"-4.86629244083379932983782216256143990390210226006560452979433243294026128577640975980482675864760717747936401374948595060083674140963469E25";
1869 coeffs_60[31] =
"6.58428611248406176613133080039790689602908099995907522692286902207707012485115422092589779128693214784991500936878932461139361901566087E24";
1870 coeffs_60[32] =
"-7.77846893445970039116628280774361378296946997639645747353868461156972352366479641995295874152354776734003001337605345817120316052066992E23";
1871 coeffs_60[33] =
"7.98268735994772082084918485121285571015813651374688487489679943603727447378945977989630573952891101472578977333720105112837324185659362E22";
1872 coeffs_60[34] =
"-7.07562692971089746095546542541499489835693326760069291570193808615779224025348460132750549389189539682228913778397783434269420284483726E21";
1873 coeffs_60[35] =
"5.381346729881846847476909845563262674288431852755093265786345982700437823098162630059919716651136095720390719236493773958116646152386075E20";
1874 coeffs_60[36] =
"-3.4856856542678356876484367392130359114150104987588151214926676834365219571876912071608359944324610844909103855562977795837329347647911E19";
1875 coeffs_60[37] =
"1.90665542883474657677037950113781854248329048412482665873254624417996252139138481002200079466749149325431679310476862249520001277129217E18";
1876 coeffs_60[38] =
"-8.72254994006151131395107200045641306281165826830744222866994799005490857259177347821280095689079457417603257537321939951004603693393316E16";
1877 coeffs_60[39] =
"3.30066663941625244322555483012774856710545517350986120571194216206848716066355962922968824538055042855044917677713272771363157100391997E15";
1878 coeffs_60[40] =
"-1.020092089391030771746960980075254826475625668908623135552682999358854102567810002206013823466362488147261886160954607897574298699485318E14";
1879 coeffs_60[41] =
"2.537518136375035057088980117582986067754938584307761188810498418760131416720976321039509027979006220650166651208980823946300429957067604E12";
1880 coeffs_60[42] =
"-4.99523339577986301543863423322168947825482352498610406809585164155176248614834684219539096936869521198401912030883142734471627752449382E10";
1881 coeffs_60[43] =
"7.62961024898383965152735310352890448678585029645218309944823403624458716639413808284778269959424212699922000610764015063766429510499158E8";
1882 coeffs_60[44] =
"-8834336.1370238009649936481782352367054397712953420330251745022286767420934395739052638862442455545176778475848478708230456099596423988";
1883 coeffs_60[45] =
"75445.9196169409678879362111492280315111800786619928588067631801224813888137547544321383450353324917130013984795690223150786036557545929";
1884 coeffs_60[46] =
"-459.8458738886001056822131294892698769439281099450630714273592488999986769567563218319365007529495798105783705491469742412340762305916056";
1885 coeffs_60[47] =
"1.922366163948404706136462977961544621491268971185908661903800938507393909575693892375103171073678191394626251633433930639174604982075991";
1886 coeffs_60[48] =
"-0.00524987734300376305383172698735851896799115189212445098242699916121836353753886238290792298378658233479210271064792489583846726184351881";
1887 coeffs_60[49] =
"8.81521840386771771843311455937479573971716020932982441671173279504850522350287085310420429874536637110755391716691475171030099411021337E-6";
1888 coeffs_60[50] =
"-8.42883518072336499031504944519862331274440110738275125460829656821173301216150526266773841539372995424665091651911614576906895281293397E-9";
1889 coeffs_60[51] =
"4.1559932977982056953309753711587342647729282359841592558743510304569204546713517319749817560490538963802716194154620384631597656968764E-12";
1890 coeffs_60[52] =
"-9.26494376646923216540342478135986593801117330292329759013854851055518195892306285985326338987592590319793280515888731024676428929933443E-16";
1891 coeffs_60[53] =
"7.80165274836868312019654872701978288745672229459298320116385383568401529728308916875595120085091565550085090877341856355815270191309086E-20";
1892 coeffs_60[54] =
"-1.922049272463411538721456378153955404697617250978865956250065913541261535132290272529565880980548519758359440057376306817458561627984943E-24";
1893 coeffs_60[55] =
"9.46189821976955264154519811789356895736753858729897267240554901027053652869864043679401817030067356960879571432881603836052222728024736E-30";
1894 coeffs_60[56] =
"-5.06814507370603015985813829025522226614719112357562650414521252967497371724973383019436312018485582224796590023220166954083973156538672E-36";
1895 coeffs_60[57] =
"1.022249951013180267209479446016461291488484443236553319305574600271584296178678167457933405768832443689762998392188667506451117069946568E-43";
1896 coeffs_60[58] =
"-1.158776990252157075591666544736990249102708476419363164106801472497162421792350234416969073422311477683246469337273059290064112071625785E-47";
1897 coeffs_60[59] =
"4.27222387142756413870104074160770434521893587460314314301300261552300727494374933435001642531897059406263033431558827297492879960920275E-49";
1898 coeffs[2].swap(coeffs_60);
1899 std::vector<cln::cl_N> coeffs_120(120);
1901 coeffs_120[0] =
"1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000060166025676976656004344991957470171590616719251813003320122316373430327091055571";
1902 coeffs_120[1] =
"3.4497260317073952007403696383770947678893302981614719279265682622766639811173298171511730607823612517530376844024218507032522459279662180470113961839690189982241536061314319614353993672315096520499373373015802582693649149063603309572777186560148513524E52";
1903 coeffs_120[2] =
"-1.4975581565000729527538170857594663742319328925831469933998274880997450758924704742659571258591716460336677591345828722528085692201176737000527729600671680178988361119859420301844184208079614468449296788394212801103162564922199859549237082372776667464E54";
1904 coeffs_120[3] =
"3.1957762163065481328529158845807843312720427291703934903666695190945338610786360201875291048323381336567812569171891600400186742244091402566230953251621720778096033490814848238417212345597975915378369497445590090951446115848410773972658485451963575288E55";
1905 coeffs_120[4] =
"-4.4689623509319752841609439083871154399631153121231062689347162975834499076693093642474289117173045421812089871506249999929076992135798925381959196225961791389783472385803138226317976820364502651110639008585046458007356178875618627927171581950486124233E56";
1906 coeffs_120[5] =
"4.606068718424276543329442566011849623375399823565351941825685310847310447457609082356012685588953435307896055516214072529445026693975872604267789672469025113562486157850515006504573881812473997762948360804814769118883992998548055557441646946685125118E57";
1907 coeffs_120[6] =
"-3.7314461146854666499272326592212099391213696621869706562566612605818861385928266960370453310708465394226398321257508947092784006446784523328681347046673172481746936234783770854350210504707173921547794426833735429199925024679815789545465854297845328325E58";
1908 coeffs_120[7] =
"2.474425401670711256989398808079221298913654027234786607507813220440957186918973475366048940039541074278444160674001228864321389049663140487504402096319272526201782217412803784224929141788255724630940381342478088455751340159338461174261577243566175687E59";
1909 coeffs_120[8] =
"-1.3811875718622847750042362590249762290599823842851465148429257970104907280458901604054390293828410620002370526629527048636126473391278330353375163563724888073254512227198849135923692811222561965740181944727170495185714496890490479692693474125883791901E60";
1910 coeffs_120[9] =
"6.623089858532754482582703479109160446021743439335073883710993620625687271109284320721410901325182604938578905712329203551531862389936804947105415805829404869727743706364603519433193421234231031076682156125442577335383798263985569601899041876776866622E60";
1911 coeffs_120[10] =
"-2.7709515004299938864490083840820063124223529009388282231525445615826433364331567602934962481829061542793349831611106716261513624279121506887680318284535361848032886450351898892264386237450622827397559067350672965967202437971930333676917000390477963866E61";
1912 coeffs_120[11] =
"1.02386112293172223921263435003659366453292875147351461165091656394534393086780717052422266565203902889367201592668259202439166666819852985689989767402099479793087277263747942659943270101657408462079787397068550734516045511611701546009078868077038808757E62";
1913 coeffs_120[12] =
"-3.3740197731917655541744976218513993073761175468772389726802124778433432226803314067431898210976006853342921093194297198044021414900546886804610561082663076825192459864843102368108908666053756409152492134638014803233805912009476407113691438596300794146E62";
1914 coeffs_120[13] =
"9.996217786487670355655374796561399578704294298563457268841140703036898520360123177193155340144551120260016445533739357030180277693840431766824113840895797510199955331557143980793267795747200088810293047731873192410526786931879590684673414288653913515E62";
1915 coeffs_120[14] =
"-2.6804750990199908441443350402311488850281543531194918304012545530803283220192092419107511475988099394746800512008906823331244710178292896561401750166818497729239682879419868799442954945496319510685448344062610897698253544876306888341881254056091234759E63";
1916 coeffs_120[15] =
"6.5422964482833531603879610057815197301035372862466791995455246163778529556707384145891730234453157337303612060344197138180893720879196243783337539071284141345021864817147590781643393947019750353147151780290464319306645652085743359080495090595200531486E63";
1917 coeffs_120[16] =
"-1.4604487304348366496825146715570516556564950771546738885215899741781982964860978993963272314092830563320794184042847908967120542212316261920409301852237223308467032419706968676861616456179895880956772385510853673982424825597152850339588189159102980666E64";
1918 coeffs_120[17] =
"2.9942297466313630831467808691292548682230644559492580161942357031681185068971393754352871129412787966878287389513657398203481589163498279625760316093736277896138061249076616695157422053188087353540756151586375196486093987258640269607104978950906670704E64";
1919 coeffs_120[18] =
"-5.658399283776588293772725313973093187743120982052603944865098913586526167668102733207163739469977271584007101869254711458133873627143366757941713180350370056955237604551850024423889291598422917971467957836705917204903687959901869098540153925178692732E64";
1920 coeffs_120[19] =
"9.887368951584101622633538892976576123080629424367489037686110916264512731398396560326756128205833849608930564615629875435100785011872254223744155330328477703592008501954532369042429700051416733748454350165515933757314793533786385104271308839525639768E64";
1921 coeffs_120[20] =
"-1.6019504550228766725078575508839635707919311420327486864048705642201106895239857903763208049376932672160478820626774934879424498715258948985194011690204294886396827446040036506699933786721588971678753877371518212675519147446728054067639530675249526082E65";
1922 coeffs_120[21] =
"2.4124568469636899540706437405441629738413207418758399778576327598069435452295650039157974716832514441625728576753250737726840109004878753294786785674578138926529507088264657400701828947949531197915861820274684954206665488761473274445827472596875582911E65";
1923 coeffs_120[22] =
"-3.3841653726400000079488483558717068873181168418395106876260246491163166726612427450773591871178866824643300679819366574162583413250423974373322308130319007820863363304629451933781204964221002853140392226489420463827400812929748772154909106349410663293E65";
1924 coeffs_120[23] =
"4.4305670380812288478773282114598811227924298131011853412998479811262358077680067168455361591598296346480072528806092976336961470360354620203822421524751468329936930212919915114854135818230382164555078957880154875221176513434392525189922941290050575762E65";
1925 coeffs_120[24] =
"-5.4228176962574428947233160003094662570284359565811627941401342797491445636152854865132166939274138115146035207618348708829039395974942115203986578386666664945394109693178927438991059414217518334491360514633536224841961444935232548483014691997071543828E65";
1926 coeffs_120[25] =
"6.214554789078092267222051275213928685756510105900211846145778269883351640710249139978059486185007208670776100912863866582278800642692097830681092656540813877576256048148229340562594504915197956922387464825593941922429396202734006609196778697870436014E65";
1927 coeffs_120[26] =
"-6.6773485088895517986512141063848395783979405189075416643094283756118912554557672721632998501682483143868731647507940026369035991063923616298815637819145806214374157182512600196214559297579802178103007615921637577873304407436850546650711237281572008424E65";
1928 coeffs_120[27] =
"6.734925330317694704469314845373778479111077864464012553672292377883525864326847400954413754291163739900219432201437895152976917857427306427115230048061308424221525123820493252697918698598513232640014129066982507718245232516657455821629338155744427538E65";
1929 coeffs_120[28] =
"-6.383582878496429871173501676061533991181960023885889537277705274319508246322757005217436814481703326467002683699047193244918123789600842413060331898515872574523803039779899326755393070345055586059441271293717500426377884349137309244757708993087958455E65";
1930 coeffs_120[29] =
"5.6913529405959275511022780614007027176288843526260372650173869440228336395668389555081751187360483397341349300975285817498083216487282169140596290796279875175764991375447348355187090404486257481827615256024271536396461908482904537799521891879785332367E65";
1931 coeffs_120[30] =
"-4.776996734587211249165031248400648409423153869394988746115380756083311986805300361459383722536698540926452976310737678416019979202990255666249869917768885659350216400547190883549730059461513588008706974008085270389354525600694962352952715682056375518E65";
1932 coeffs_120[31] =
"3.7775367524287124255443145064623569295746034916892464094281613465046063954544055573214473155479196552309207209647540614474216985097792266203411723082566949978062697757983354600199199984244302856099811940389910544756210676400851240882142140969864764468E65";
1933 coeffs_120[32] =
"-2.8161966171919236962021901287860232075259781334554793534017516884995332700369401674058517414969240048359891934178343992080557338603528540157030635217682829894098359736903943078409166055640608627322968554856315650475005062493399450913753277478547118352E65";
1934 coeffs_120[33] =
"1.9804651678733327456903212258413521470612733719543558365536494344764973229749132899499862883369665827727506916597326744330471802598610837032598656197205238983585794266213317465548361566327435762497208877015986690267754534342053368396181078097467171858E65";
1935 coeffs_120[34] =
"-1.3144275813663231527166312401997093907605894997476799416306355417933431514642211250592825223377757973148122542735038736133300194844844655961425683877005418926364412294006123974642296395931311307760050290069031276972832755406161248577410950671224318855E65";
1936 coeffs_120[35] =
"8.2367260670024829522614096155108151082106397954565823313893008773930966293786646885943761866773022391428854862805955553810619924412431932999726399857050871862122529700098570542876369425991842818202826823540112018849926644955200888291063471724203391548E64";
1937 coeffs_120[36] =
"-4.8749964750377069822933994525197085013480654713783888755556109773660249389776804499013517227967180500633060271953473316017147397601291325922904139209860429881054757911243087427393920494271315804033914011087815785282473032714919188637172020633929566123E64";
1938 coeffs_120[37] =
"2.7259664773094932979328467102942769029907299417406744864696200699394594868759231280169149208728483197299648608091313447896342349454038879581019820193316159535211365363553004387852005780736869678460092714636910972426808304270369152189989142121207224142E64";
1939 coeffs_120[38] =
"-1.440426226855027726783521340050349148103881707415523724377763633849488875095817796257895327883428230885349760692732068174527147156893314818583058727424251827006457849321094911262818557954829248070170426870959233263267490276774734065709978749400927185E64";
1940 coeffs_120[39] =
"7.193790858249547212173205531149034887209275529426061411129294234841122474820371873361100215884757249851960370114629943083807936135915003201800204713978377250292881453568756354858194614039311248345228434431020394729104593125888325843724239404594830488E63";
1941 coeffs_120[40] =
"-3.3960029336234301755324970935705944032408435186630159101426062821929524761770439420961993430248258136340087498829339209014794230274407979103789924433683527009234592433480445831820377517333956042612961562022604325181492952329031432513768020816986814393E63";
1942 coeffs_120[41] =
"1.5154618904112106565112797443687014834429200069480460967081898435635890576815349145926430052596468033907024005478559584915319911380449387176530845634833237204659108290330613043367085829373476690728522550189678729181372902816898536141595215616716630939E63";
1943 coeffs_120[42] =
"-6.3927647843464050458917092484911245813170740434503951669888756878206365814594631676413018245438405308353724023007754523096143775098898268650326908751515418318201372985246418468844138298345777180517875695389655616000832495210812684049030674085212697428E62";
1944 coeffs_120[43] =
"2.5490394366379355452002449693074954071810215414182359403355645652443600688717811337587901850157210686351097591461582890354662732336749618027675479531031836144519267481752770036252137747675754903974915999567019837855523058289177148692481402871253211324E62";
1945 coeffs_120[44] =
"-9.606466879185328464666445215840505657671157752044466089989040292763536710311599947887918708456526669882072519263973105599580140713596301388561639705589314111762600854460059589939760935803484446888352368360433606245369171819922425771642408570388554052E61";
1946 coeffs_120[45] =
"3.4212392804723358445152430359637323789304939688937873921904941412927756295848104328630952153624979489607759834359194243032109828811134607612715016533909375981353098879969472700079242226099049323998286020341979178782935852542355220403299144612362244738E61";
1947 coeffs_120[46] =
"-1.15119134701605919461057899755821946453925102458815313053351247263978303346790555715641513756644038607667203392289423834966320935498856390723555744530789850290369071103208529608463210398231590077340268751005311531529356083188150256469829678612245577446E61";
1948 coeffs_120[47] =
"3.6588622583411432033523084711047679684233731128914152509273818448610176621874654252431411048902598388935105893946323641003087000410095802098177375492833543391040706755511234323104846636415419597151008153829618275459606044459923718022154035121167198784E60";
1949 coeffs_120[48] =
"-1.0981148514467449476248066871827754422009180048705085132882492434176164929454140182025449006310206725429473330511884213470600326782740663313311256352613244044500057688932314549669435095761340307817735687643806167483576999980691227831561891265615422486E60";
1950 coeffs_120[49] =
"3.110998209448997739767747906196101611409160829345058138064861244336130082424927251851805875584197897229644157110035272012393338413235208343342708685139492629786435072305986349067452739209758702078026647999828517440754895711519542954337931090643534216E59";
1951 coeffs_120[50] =
"-8.3162485922574890007748232799240657004521608654422032389269811102140449056333167761296051794842882201869698963586030628312914066893199727852512779320175952962772072653493447297721128265231294406156925752496310087025926300388984242024436858845487466277E58";
1952 coeffs_120[51] =
"2.0966904516945699848169820408710416999765756367767199815424586610234585829069218729220161654233351574517459523275756901094737085187558904179251813051891939079067686519817858153690134828671544815635956527611986498479411756457222935682849773436423295467E58";
1953 coeffs_120[52] =
"-4.983121305881207125553776640558094509942884568949257704810973508397697839859902664482541160531856121365759763455699578413261749913567077796586919935391984240753355552646184306812426079133011894826183873855851966310877619118554510972675999316631346679E57";
1954 coeffs_120[53] =
"1.1158023601951707374356047495258406415892974604387009613173591921419195864040428221070481312383179580486787822935456571355463718115785982888531393271665510645725283439572279946304699780331972095822869500426555507626639723865965516308476400920600382357E57";
1955 coeffs_120[54] =
"-2.3524850615012075127499506758220926725372558166170912192116695445007095502575329450463479860779122789467638956004572617263549199692255055063165454868102165975951768676031140009643202074220557325155838768661030361538572755082660730808847591840060467064E56";
1956 coeffs_120[55] =
"4.6669318431895615057208826641721251136909284138581355667925884903657855204100373961676117747969449100495897986226609480142908763981931305129946569690612924941456739524153327260627627771254850382983581593260532259539447965597396206625726656509884058042E55";
1957 coeffs_120[56] =
"-8.7053773217442419007560462613131691749734845382618514999712446313788486289774350240165530159591402631439776213579542026449818009956904779042347595401565525081115611496250192338958392965746523979241969677734430475813057146574920495171984815351708574336E54";
1958 coeffs_120[57] =
"1.5256552489620511464542280446639568546874380361953025589702692266626310669215652044048704882910412155084167930513006634430352568411276836880182348033924636960897794333644980768878022821035659978039286230061734024129667272393315169114199838321062607299E54";
1959 coeffs_120[58] =
"-2.5099934505534008439782195609383796207770494575364994376922414269548303512602084430128307108303305643530918354709126474742035537827601791192999467996479881350277448357927640707861695639576629921988481117017137420422963638277868648516492581097660522547E53";
1960 coeffs_120[59] =
"3.872963359882179682964169603201046384616694634651871844057456079738892419308420856725974686574980381399016464501318163662938118593626674643538005780375691959391996340141057698193381380484420715733863044826589570328349973407598034428591146829028071358E52";
1961 coeffs_120[60] =
"-5.59947633823301408044455223877913062308847941596689956112764416031828413291312481723036534632655608672535030921469531903033364444816678754679807809159478411100820014592865068932440734964265842594875758737421026093110624848762070026616564150314951394E51";
1962 coeffs_120[61] =
"7.57762861280525531438216991274899157834431478755285945898172885086150762425529113816148806028462888396660067975773261101497666568988246606837690320098870044112671149076084444095163491848634465373822951831018725769263871497616640732007420499659069842E50";
1963 coeffs_120[62] =
"-9.587786106526273406187878833167940811862067040706459726637556599860244751467528905534431960251166924163661188573831350928972391892492380823531476387272791432306808700507685765850397294118719242350333451452137838374120658600691461454898577711260078952E49";
1964 coeffs_120[63] =
"1.13288726401696728230264357306938076698155303500407071418573081766541065136778223998897791839613776442037036668986628122296219518360439574147622758002647495909592177914657175019781723803408732148262293125845657503039410078589916085532057725749397276232E49";
1965 coeffs_120[64] =
"-1.24849787223197441956280303618704887038709792250544105638342097080498907831514597860418910331910245753340059089147824955071899315894649696314820492532126554883819507650973976145456660786429117569053901704116877128391672511345177517877672824534972448216E48";
1966 coeffs_120[65] =
"1.2815463720972693091316233381473056495608681859925407504190742949467232967966271661733907550222983737930524555721493736920130260377888287772008209963158064973076933575966719577456540496444474944074979736374259087350416613616719928507635667369740203319E47";
1967 coeffs_120[66] =
"-1.2234887340201843394744986892310393596065877342193196880417674427168862926389642850813687099959036354499094230765541977493433449153438766822382486040215211159359175689369230076522107734270943423777076523650345103234411047700646432924770659676420158487E46";
1968 coeffs_120[67] =
"1.0847187881607033339631651118075716564835185723270640503055198532318419482330026641941088359447807553514405522074008969583213861070993661224871455023365601323302778638456843760403418046238489404394483720438784739822580385277055304353975028280477740796E45";
1969 coeffs_120[68] =
"-8.9160881476675795743767277986448579964735858351472748620623279571408606135698760493224031735408212513500922230670883171668702983221921543376953865813604783695111225412173880768170509738290662806468458720236121755965944855709552219268353813402612336565E43";
1970 coeffs_120[69] =
"6.782864920104031936272293608616215844503387641476821968620772153274069873138756405621471099960069602613619793775294358177761533027360002770186566164041138064221354961783144649476276625776241973967317262115970868665380343599565811072109785000646703404E42";
1971 coeffs_120[70] =
"-4.7667808452660756441368384708874451089976319738852731080495062883240643961463680300964077232336439626019128672679703771884184482488932861160134911816225569323838390204451496983578077563176966732010513231048738892639707790407292070646798259086924770995E41";
1972 coeffs_120[71] =
"3.0885057140860079424719232591765602418793465632939298397987628606701994268384966881159469651774584648643122830739130127593326652998108850492039117928976417052691273804304806596509726701594300563830431015215234640024338277573401498998072908815285293868E40";
1973 coeffs_120[72] =
"-1.8410405906573614531857309495652487774337134256805076777639383854080936219680656594060736479739035202182601529001321266214227848431889644620036213870966329509961114940541333851155401637197303308322414678191211465563854205816313387785764908216851396633E39";
1974 coeffs_120[73] =
"1.0073694433024942271325653907485159683302928496826793112696958500366488338508211620934892875328717073528902110227362794694820010124321343709182901273795782541866547318841893692957109947576483162095037812781379193423759617638948859880051822460818418552E38";
1975 coeffs_120[74] =
"-5.0475051506252944853315611134428802424958512917967945464108691542854207821486654807141339210375899950551724141366521361887864357385178212628348794663127149312605456165451981719848656127310229221238908657530297751682848475855876378576874607521597136906E36";
1976 coeffs_120[75] =
"2.3099766115359817610656986443137072041797751710805647712896098246833051023271876304983288225638204962631413469467959017768113430777226924099787875749611560913177631681394153889301715579572842026181746028117354815826836594637709952294015960031772162547E35";
1977 coeffs_120[76] =
"-9.629053850440590569772960665435833408449876392175761493622541259322053209458881628458334353756739601360772251654643632187697620334088992038575944303101187678397564511853344433267011583960451100374611538881978045643233876974513962362084978095067025623E33";
1978 coeffs_120[77] =
"3.6452126546120530579393646694066971671091434168707822859890104373691687449831950255953317231572802167174179528347370588567969602221261721708890001616085516755796796282628169745443137768549800602834096924025507345446292715781107949529692160434800323E32";
1979 coeffs_120[78] =
"-1.2492564030201607643388368733220662634846470405464496879151879822123866671204541555507638492613046717628358162773937737774832271305618491107140304474323049182605167775847584622690299098207979849043605983558768056117581593008210986863088433891075743152E31";
1980 coeffs_120[79] =
"3.8627447638297686357472526935538070834588578920414538227245516723308987020816841052950727259618753144711425856434270832495754300189881199851254605718213699755258867641301730599979474865704144160112269948588154919128986989885090481959424806312935273075E29";
1981 coeffs_120[80] =
"-1.0736758703963497284148841547397192249226725101007524773889805877171959717011395181953504058502607435217886087332761920207901621377557079619638699346496468750455986591040017334237734940082333954589067611955107878899677189289648293223359861027746438121E28";
1982 coeffs_120[81] =
"2.6722714785740082059347577649909834926335247252399259683264830680945466475595847553753509546415283809619181144796536494882020159787371993099998263815645014317923922311421330376008111312767167437401741178863083976628261471599264811824656877164988491393E26";
1983 coeffs_120[82] =
"-5.9304047185329750657632568788530498935629656326502947505210292278638825286675833282579834326765999907183142489791905921257123760969245535649745876992946512033156167841406724363867902645010435996961270021857807247440211477908060243655541266857227638988E24";
1984 coeffs_120[83] =
"1.16817022089143274700208191285335154155497013626172270535715899131321522799010543339535307798264602677955894930046454353008462671803498794203612585729705145312299224155123919877760274781582850868001155383467754608529345730226972329454404720862870618607E23";
1985 coeffs_120[84] =
"-2.03239515657536501213472165328009690017090356606547792466197690386716728380893226886179282271040418637806139515373566132123131620086873213475424131345589653019635327048678766191769576650893957440830876852296666120473866301097954633389040518870395767125E21";
1986 coeffs_120[85] =
"3.1065334503269182605978912331263087603258864771943471481540265718169544724355602987297631515907391374943512439350265433478241465606056187134785807375293801936399644663199667496663518171930757047012102683120173353568660795955174938680248863153863947508E19";
1987 coeffs_120[86] =
"-4.1476244154347831048636005592317388215032295704489937704602030038303705695463546496640638505584602502764898113504560236629804442607426019604639559875021291459916615723777004493344143132459204229291886967479716413925814352313734234340863490128872380307E17";
1988 coeffs_120[87] =
"4.8067293487250079673131214670887682215073707729621636364424152483295071605326220176372385638491275365750175037404843071051780212494354459897540110089573898336327006157766256896984455454193271731091632286742192439925748114360605084629432813597189767538E15";
1989 coeffs_120[88] =
"-4.8023544548381246628003457039588616467438691159189277447469028024236284353593054364114519649309416187375157096932150251663679454372678125518452171003992957433311257042292636706448339781439297178835786059318810522834929923770539615271536113963729385909E13";
1990 coeffs_120[89] =
"4.1055087514683476865343055835875083237542317413651906253058979029083965525058905726360233143503628224856307545474786181299719957472120906835233967660557875100202077212004953379299507351564181758434304881046845705855303854083493519588411179065109026834E11";
1991 coeffs_120[90] =
"-2.9787503393847675871205038539267895335240592213878943742323972872214441728681744433089698206110260166068266926018988659692353298939109421567999207730700359726920482465669373553804927535369930188390246988033893916611435406224816632683980860607732310186E9";
1992 coeffs_120[91] =
"1.8178328110729629877907010659834277046059726898311908447099830056830012488194646687474150289147446390570639168063598563291822008033517936194534129929881015025633519502485415000390171249019651579295905194415531994026553693578406432674734610095421683863E7";
1993 coeffs_120[92] =
"-92391.136314434380495997449781381513978328604842061708454699991154771188446049720445502194923435235472458378926242100033122111143321209059959788378033220861638093951546784186137626553022963832352496255851690092415165826965388502958309163995296640164754";
1994 coeffs_120[93] =
"386.82763074890451546182061419449593717951707520472938425276820204065379182568600735469831672149785863654956632602671563997131280046154927653332261114114005498875447205079045401364007035880825957300757663780618819785476980699579657587509130753204519233";
1995 coeffs_120[94] =
"-1.3181204292571874302358432444324779303744749959754136019600954846045028319805074783759764870805734807693739252625657350494147444011046941331047057337345953605042408524072436811726898109072388160378243068564382623631658424851676817690976343859083960324";
1996 coeffs_120[95] =
"0.003606538673252695455085947121496196507159591230095595764694813152630524319596509155920374890595867709349176662036024214476302717902368680224618116411588086562230407996267622244422187853090635901906175373997993725355114393033631058067900506212434600015";
1997 coeffs_120[96] =
"-7.805244503909439374422205381130511738566245024242591464192744568789876715121004646510755612128565674260161510215430132815223049297785205382643947556846567064565241387424696940674258789227398935846571768027456535982674711768030751512030174841314425949E-6";
1998 coeffs_120[97] =
"1.31373705470989377112938364152965446631228819123896570245455699237549295870321627234421140232628798373711221392827979836922621437205363811871692678679625916100572037589291239046725228767017131155814257944742981208252138821140381478767814046301821211856E-8";
1999 coeffs_120[98] =
"-1.6872873094408224472617181717534409090015431593544429529131126514352910895332010213914243717484771690790552077128803350550170014347729272790464826195676369023970955260051387240496705602732313607409271794413329062030561818907163134089683283286623809325E-11";
2000 coeffs_120[99] =
"1.6183083251905685095057354853863188515437903228178486856957070037813756492593759658405336450433607296873747595037080703825755020175480385843762609522889527239577435110258291566585028919336090916225831079571865425410181260759913688103716786795647286451E-14";
2001 coeffs_120[100] =
"-1.13097359411474028225398794102354853670936316496817819635688647804142428962171772690717075128208102537660772310780986623575005236651312181907812813813504742701120603881086064664411899253566047514905519888629604717647221817372977488600336785871295304013E-17";
2002 coeffs_120[101] =
"5.599216369109121957949255319730053610385733330502739423509794477602247233276045188197007198417289907263120960704056657544648432653622931077692740961599655386871075693202473992087883485704436336279135221721374640982826144708808646466699352755417123702E-21";
2003 coeffs_120[102] =
"-1.9009180102993021108185348502624676395148544369474718879637745630712451378711342634099259114111847962752555305470572286326367888004493816251811794947276966269738750207359305252041104539066278002044545942171476984766923991983055271262414217352967659228E-24";
2004 coeffs_120[103] =
"4.261262509940940316499754264112111685174274727656165126333137554124192224955656564229887938745508952447664695831728428607673797269945824475565104978593072684829487175697371245288754204324544164474840153141042852153497051337607734150135978754952561336E-28";
2005 coeffs_120[104] =
"-6.033854291373449912236926137860325602686312455380825767485673949251953414778800668020214699151728472172651816317924130614791108454134597377848088327850505473503152696524861086193124979489104732214189466703901268332265826882296309653009237279831825243E-32";
2006 coeffs_120[105] =
"5.1208402745272379096703574714836785944518835939702823617280147111145234914591060871138496110227453241036619229980622243972303295470574470937679143516006222494480144845809123492603651773613707216680534850900104861326332900592715684757980394834998321888E-36";
2007 coeffs_120[106] =
"-2.4463535717946588550832618025289907099586319384566637643650142186828541109926588999585266911960640972919441499109750654299062004147686492034166034659422424525984094382368955916181276646903453872999065929058429821759475215620044891133652431220664754175E-40";
2008 coeffs_120[107] =
"6.0973480699773886324239008989591793773608942051497498591908583910660358857815864266160341286217871697703362816166340947142517661604423899536979689047275448159991318658879804351288744125363072102852651926942302209139318098544348348564409845011546432615E-45";
2009 coeffs_120[108] =
"-7.2234185761285078775026471720270426097727212523472472797635230392183067756271499246654638332288950167477129840028892565652782123508855602380279653475510712205780583313834027906297063690370430285856541927759405826980856379432703473274890527421175151858E-50";
2010 coeffs_120[109] =
"3.6217112680215791206171182969894344487335819731880124290544082848140757826983885738735436324684863867140575000400288923606439193119990961489053513339202655922248092157737577138929144240507796562250602457839068582279379672722261563501188150876583184441E-55";
2011 coeffs_120[110] =
"-6.6329300032795486066608594142675837603786558782159646987663521197523704085781830169369726460621246948945196657495305819768951424025780824076252490918306538895670861455244641773606980519824591785816943621538721352987553804824051051144609050417497894495E-61";
2012 coeffs_120[111] =
"3.6664720904335295532012711597888717227860988776477301054518326674835421172405060906940404374163713097964932859351917152390238690399278248344863365606468942320103392909602843987855082225592776850615943708151738327210634139824601616072015258461809772448E-67";
2013 coeffs_120[112] =
"-4.7466013179695826928232672846686064011594588664906398407027593213652099998530859940288723349213099851532139911079905393494419637612780994270110734378146177806681489226896952731800026849872070824592339117757940119304241732812925979963178130104280115315E-74";
2014 coeffs_120[113] =
"1.0163707785221910939390789816391472677729665860532352695801597334766068288835382195560328979864550624486740471947632369344045378626680607890520366137741785540226552923584183986350590955499329375427326072319268396685478606934920507703868118038891818762E-81";
2015 coeffs_120[114] =
"-3.4814151260242800905467399051937942442621710748397374123807284826536707678408888416026868585492229216524609739211131993326633970334388991812593549702868877534701822990946125111761892723042376117665640296993581745994557803052315791392349639065203872505E-90";
2016 coeffs_120[115] =
"1.18525924288117432386770939895670573772658621857195305986011196724304231598127227408839423385042572374412446842112646168302015480830234100570192462192015131968307084609177540911503689228342834030959242458698413980031135644018348590823980902427540799814E-91";
2017 coeffs_120[116] =
"-8.5714961216566153236700116412888006837408819915951896129362859520462766617634320531162919426026429378433105901035364956643086394331335747930198070611009941831387116980941022864465946989065467218665543814574849964435089931072761832853235509961870476035E-93";
2018 coeffs_120[117] =
"4.5681983751743456413033268196376305093509590040595182930261094908859252761697530924655649930852283295534503341542929581967081012867692190108698698006237799801339418962091877730207560007839789937153876806052229193448161273005984514504886230869730232561E-94";
2019 coeffs_120[118] =
"-1.5943139155457706045530478744891549581317663177038648406493256399589001327414318955746453934207742828511041930090849236963271943244329753764497401819704943705370596846318480510254313447057477914171472190541408193443142906466279172123681623644325254209E-95";
2020 coeffs_120[119] =
"2.7319125666863032595604997603472305262880292377469053594326527505796348018540179196191192420176181194669607935656210005192217186286873953583571180312679155204061051208771126804209623533044988888808754656646355388901404252058383561064953226611421609762E-97";
2021 coeffs[3].swap(coeffs_120);
2026 cln::float_format_t prec = cln::default_float_format;
2027 if (!instanceof(realpart(
x), cln::cl_RA_ring))
2028 prec = cln::float_format(cln::the<cln::cl_F>(realpart(
x)));
2029 if (!instanceof(imagpart(
x), cln::cl_RA_ring))
2030 prec = cln::float_format(cln::the<cln::cl_F>(imagpart(
x)));
2044 cln::cl_N pi_val = cln::pi(prec);
2045 if (realpart(
x) < 0.5)
2049 cln::cl_N temp =
x + lc.
get_order() - cln::cl_N(1)/2;
2050 cln::cl_N result =
log(cln::cl_I(2)*pi_val)/2
2051 + (
x-cln::cl_N(1)/2)*
log(temp)
2062 const cln::cl_N x_ =
x.to_cl_N();
2063 const cln::cl_N result =
lgamma(x_);
2072 cln::cl_N pi_val = cln::pi(prec);
2073 if (realpart(
x) < 0.5)
2076 cln::cl_N temp =
x + lc.
get_order() - cln::cl_N(1)/2;
2077 cln::cl_N result =
sqrt(cln::cl_I(2)*pi_val)
2078 * expt(temp,
x - cln::cl_N(1)/2)
2088 const cln::cl_N x_ =
x.to_cl_N();
2089 const cln::cl_N result =
tgamma(x_);
2115 if (!
n.is_nonneg_integer())
2116 throw std::range_error(
"numeric::factorial(): argument must be integer >= 0");
2132 if (!
n.is_nonneg_integer())
2133 throw std::range_error(
"numeric::doublefactorial(): argument must be integer >= -1");
2145 if (
n.is_integer() &&
k.is_integer()) {
2146 if (
n.is_nonneg_integer()) {
2147 if (
k.compare(
n)!=1 &&
k.compare(*
_num0_p)!=-1)
2157 throw std::range_error(
"numeric::binomial(): don't know how to evaluate that.");
2169 throw std::range_error(
"numeric::bernoulli(): argument must be integer >= 0");
2205 const unsigned n = nn.
to_int();
2209 return (
n==1) ? (*_num_1_2_p) : (*_num0_p);
2214 static std::vector< cln::cl_RA > results;
2215 static unsigned next_r = 0;
2219 results.push_back(cln::recip(cln::cl_RA(6)));
2225 results.reserve(
n/2);
2226 for (
unsigned p=next_r; p<=
n; p+=2) {
2228 cln::cl_RA b = cln::cl_RA(p-1)/-2;
2234 if (p < (1UL<<cl_value_len/2)) {
2235 for (
unsigned k=1;
k<=p/2-1; ++
k) {
2236 c = cln::exquo(
c * ((p+3-2*
k) * (p/2-
k+1)), (2*
k-1)*
k);
2237 b = b +
c*results[
k-1];
2240 for (
unsigned k=1;
k<=p/2-1; ++
k) {
2241 c = cln::exquo((
c * (p+3-2*
k)) * (p/2-
k+1), cln::cl_I(2*
k-1)*
k);
2242 b = b +
c*results[
k-1];
2245 results.push_back(-b/(p+1));
2260 if (!
n.is_integer())
2261 throw std::range_error(
"numeric::fibonacci(): argument must be integer");
2280 if (
n.is_negative()) {
2291 cln::cl_I
m = cln::the<cln::cl_I>(
n.to_cl_N()) >> 1L;
2292 for (uintL bit=cln::integer_length(
m); bit>0; --bit) {
2295 cln::cl_I u2 = cln::square(u);
2296 cln::cl_I v2 = cln::square(v);
2297 if (cln::logbitp(bit-1,
m)) {
2298 v = cln::square(u + v) - u2;
2301 u = v2 - cln::square(v - u);
2308 return numeric(u * ((v << 1) - u));
2310 return numeric(cln::square(u) + cln::square(v));
2332 cln::the<cln::cl_I>(b.
to_cl_N())));
2344 const cln::cl_I a = cln::the<cln::cl_I>(a_.
to_cl_N());
2345 const cln::cl_I b = cln::the<cln::cl_I>(b_.
to_cl_N());
2346 const cln::cl_I b2 = b >> 1;
2348 const cln::cl_I m_b =
m - b;
2349 const cln::cl_I ret =
m > b2 ? m_b :
m;
2366 throw std::overflow_error(
"numeric::irem(): division by zero");
2369 cln::the<cln::cl_I>(b.
to_cl_N())));
2386 throw std::overflow_error(
"numeric::irem(): division by zero");
2388 const cln::cl_I_div_t rem_quo = cln::truncate2(cln::the<cln::cl_I>(a.
to_cl_N()),
2389 cln::the<cln::cl_I>(b.
to_cl_N()));
2390 q =
numeric(rem_quo.quotient);
2391 return numeric(rem_quo.remainder);
2407 throw std::overflow_error(
"numeric::iquo(): division by zero");
2410 cln::the<cln::cl_I>(b.
to_cl_N())));
2426 throw std::overflow_error(
"numeric::iquo(): division by zero");
2428 const cln::cl_I_div_t rem_quo = cln::truncate2(cln::the<cln::cl_I>(a.
to_cl_N()),
2429 cln::the<cln::cl_I>(b.
to_cl_N()));
2431 return numeric(rem_quo.quotient);
2447 cln::the<cln::cl_I>(b.
to_cl_N())));
2461 cln::the<cln::cl_I>(b.
to_cl_N())));
2484 if (
x.is_integer()) {
2486 cln::isqrt(cln::the<cln::cl_I>(
x.to_cl_N()), &root);
2496 return numeric(cln::pi(cln::default_float_format));
2503 return numeric(cln::eulerconst(cln::default_float_format));
2510 return numeric(cln::catalanconst(cln::default_float_format));
2522 throw(std::runtime_error(
"I told you not to do instantiate me!"));
2524 cln::default_float_format = cln::float_format(17);
2534 long digitsdiff = prec -
digits;
2536 cln::default_float_format = cln::float_format(prec);
2548 _numeric_digits::operator long()
2551 return (
long)digits;
bool is_cinteger() const
True if object is element of the domain of integers extended by I, i.e.
bool is_crational() const
True if object is an exact rational number, may even be complex (denominator may be unity)...
const numeric zeta(const numeric &x)
Numeric evaluation of Riemann's Zeta function.
const numeric exp(const numeric &x)
Exponential function.
const numeric asinh(const numeric &x)
Numeric inverse hyperbolic sine (trigonometric function).
bool is_negative() const
True if object is not complex and less than zero.
static void write_real_float(std::ostream &s, const cln::cl_R &n)
unsigned calchash() const override
Compute the hash value of an object and if it makes sense to store it in the objects status_flags...
const numeric sinh(const numeric &x)
Numeric hyperbolic sine (trigonometric function).
static bool coerce(T1 &dst, const T2 &arg)
unsigned hashvalue
hash value
ex PiEvalf()
Floating point evaluation of Archimedes' constant Pi.
bool operator>(const numeric &other) const
Numerical comparison: greater.
const numeric acos(const numeric &x)
Numeric inverse cosine (trigonometric function).
const numeric & sub_dyn(const numeric &other) const
Numerical subtraction method.
bool is_pos_integer() const
True if object is an exact integer greater than zero.
const basic & hold() const
Stop further evaluation.
const numeric bernoulli(const numeric &nn)
Bernoulli number.
const basic & setflag(unsigned f) const
Set some status_flags.
void do_print_csrc_cl_N(const print_csrc_cl_N &c, unsigned level) const
bool operator<(const numeric &other) const
Numerical comparison: less.
ex EulerEvalf()
Floating point evaluation of Euler's constant gamma.
const numeric doublefactorial(const numeric &n)
The double factorial combinatorial function.
const cln::cl_N Li2_(const cln::cl_N &value)
Numeric evaluation of Dilogarithm.
ex denom(const ex &thisex)
void print_numeric(const print_context &c, const char *par_open, const char *par_close, const char *imag_sym, const char *mul_sym, unsigned level) const
bool is_even() const
True if object is an exact even integer.
ex lcm(const ex &a, const ex &b, bool check_args)
Compute LCM (Least Common Multiple) of multivariate polynomials in Z[X].
static const cln::cl_F read_real_float(std::istream &s)
Read serialized floating point number.
std::ostream & operator<<(std::ostream &os, const archive_node &n)
Write archive_node to binary data stream.
ex imag_part() const override
static cln::cl_N Li2_projection(const cln::cl_N &x, const cln::float_format_t &prec)
Folds Li2's argument inside a small rectangle to enhance convergence.
const numeric sin(const numeric &x)
Numeric sine (trigonometric function).
const cln::cl_N lgamma(const cln::cl_N &x)
The Gamma function.
std::vector< digits_changed_callback > callbacklist
const numeric power(const numeric &other) const
Numerical exponentiation.
const numeric fibonacci(const numeric &n)
Fibonacci number.
Archiving of GiNaC expressions.
This class is the ABC (abstract base class) of GiNaC's class hierarchy.
Context for python-parsable output.
const numeric denom() const
Denominator.
const cln::cl_N tgamma(const cln::cl_N &x)
function zeta(const T1 &p1)
void do_print_tree(const print_tree &c, unsigned level) const
int ldegree(const ex &s) const override
Return degree of lowest power in object s.
_numeric_digits & operator=(long prec)
Assign a native long to global Digits object.
bool is_polynomial(const ex &var) const override
Check whether this is a polynomial in the given variables.
static const cln::cl_F make_real_float(const cln::cl_idecoded_float &dec)
Construct a floating point number from sign, mantissa, and exponent.
const numeric asin(const numeric &x)
Numeric inverse sine (trigonometric function).
function psi(const T1 &p1)
bool sufficiently_accurate(int digits)
const numeric add(const numeric &other) const
Numerical addition method.
ex real_part() const override
const numeric irem(const numeric &a, const numeric &b)
Numeric integer remainder.
int compare(const numeric &other) const
This method establishes a canonical order on all numbers.
ex rem(const ex &a, const ex &b, const ex &x, bool check_args)
Remainder r(x) of polynomials a(x) and b(x) in Q[x].
Interface to several small and furry utilities needed within GiNaC but not of any interest to the use...
bool info(unsigned inf) const override
Information about the object.
bool is_equal(const numeric &other) const
static void print_real_number(const print_context &c, const cln::cl_R &x)
Helper function to print a real number in a nicer way than is CLN's default.
int to_int() const
Converts numeric types to machine's int.
bool operator<=(const numeric &other) const
Numerical comparison: less or equal.
ex numer(const ex &thisex)
void do_print_python_repr(const print_python_repr &c, unsigned level) const
ex gcd(const ex &a, const ex &b, ex *ca, ex *cb, bool check_args, unsigned options)
Compute GCD (Greatest Common Divisor) of multivariate polynomials a(X) and b(X) in Z[X]...
ex evalf() const override
Cast numeric into a floating-point object.
int degree(const ex &s) const override
Return degree of highest power in object s.
This class is a wrapper around CLN-numbers within the GiNaC class hierarchy.
Context for latex-parsable output.
const numeric & power_dyn(const numeric &other) const
Numerical exponentiation.
ex conjugate(const ex &thisex)
bool is_equal_same_type(const basic &other) const override
Returns true if two objects of same type are equal.
cln::cl_N calc_lanczos_A(const cln::cl_N &) const
bool is_integer() const
True if object is a non-complex integer.
const numeric mul(const numeric &other) const
Numerical multiplication method.
int csgn() const
Return the complex half-plane (left or right) in which the number lies.
print_func< print_context >(&varidx::do_print). print_func< print_latex >(&varidx
const numeric gcd(const numeric &a, const numeric &b)
Greatest Common Divisor.
static bool too_late
Already one object present.
bool is_positive() const
True if object is not complex and greater than zero.
const numeric div(const numeric &other) const
Numerical division method.
#define GINAC_ASSERT(X)
Assertion macro for checking invariances.
_numeric_digits Digits
Accuracy in decimal digits.
ex conjugate() const override
const numeric acosh(const numeric &x)
Numeric inverse hyperbolic cosine (trigonometric function).
ex eval() const override
Evaluation of numbers doesn't do anything at all.
long to_long() const
Converts numeric types to machine's long.
static void print_real_cl_N(const print_context &c, const cln::cl_R &x)
Helper function to print real number in C++ source format using cl_N types.
static void print_integer_csrc(const print_context &c, const cln::cl_I &x)
Helper function to print integer number in C++ source format.
bool is_odd() const
True if object is an exact odd integer.
ex coeff(const ex &s, int n=1) const override
Return coefficient of degree n in object s.
const numeric log(const numeric &x)
Natural logarithm.
const numeric tanh(const numeric &x)
Numeric hyperbolic tangent (trigonometric function).
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(add, expairseq, print_func< print_context >(&add::do_print). print_func< print_latex >(&add::do_print_latex). print_func< print_csrc >(&add::do_print_csrc). print_func< print_tree >(&add::do_print_tree). print_func< print_python_repr >(&add::do_print_python_repr)) add
const numeric real() const
Real part of a number.
const numeric smod(const numeric &a_, const numeric &b_)
Modulus (in symmetric representation).
const numeric numer() const
Numerator.
static ex Li2_series(const ex &x, const relational &rel, int order, unsigned options)
const numeric abs(const numeric &x)
Absolute value.
This class is used to instantiate a global singleton object Digits which behaves just like Maple's Di...
void read_archive(const archive_node &n, lst &syms) override
Read (a.k.a.
const numeric cosh(const numeric &x)
Numeric hyperbolic cosine (trigonometric function).
const numeric isqrt(const numeric &x)
Integer numeric square root.
Interface to GiNaC's overloaded operators.
bool is_real() const
True if object is a real integer, rational or float (but not complex).
const numeric & mul_dyn(const numeric &other) const
Numerical multiplication method.
const numeric sqrt(const numeric &x)
Numeric square root.
const numeric & div_dyn(const numeric &other) const
Numerical division method.
const numeric binomial(const numeric &n, const numeric &k)
The Binomial coefficients.
numeric step() const
Return the step function of a numeric.
bool operator==(const numeric &other) const
const numeric Li2(const numeric &x)
unsigned golden_ratio_hash(uintptr_t n)
Truncated multiplication with golden ratio, for computing hash values.
Interface to GiNaC's light-weight expression handles.
Base class for print_contexts.
void print(std::ostream &os) const
Append global Digits object to ostream.
const numeric I
Imaginary unit.
const numeric cos(const numeric &x)
Numeric cosine (trigonometric function).
const numeric & operator=(int i)
void archive(archive_node &n) const override
Save (a.k.a.
ex CatalanEvalf()
Floating point evaluation of Catalan's constant.
Exception class thrown when a singularity is encountered.
_numeric_digits()
_numeric_digits default ctor, checking for singleton invariance.
bool is_prime() const
Probabilistic primality test.
void do_print_latex(const print_latex &c, unsigned level) const
bool is_zero() const
True if object is zero.
This class stores all properties needed to record/retrieve the state of one object of class basic (or...
const numeric atan(const numeric &y, const numeric &x)
Numeric arcustangent of two arguments, analytically continued in a suitable way.
Lightweight wrapper for GiNaC's symbolic objects.
const numeric atanh(const numeric &x)
Numeric inverse hyperbolic tangent (trigonometric function).
cln::cl_N to_cl_N() const
Returns a new CLN object of type cl_N, representing the value of *this.
Exception class thrown by functions to signal unimplemented functionality so the expression may just ...
.calchash() has already done its job
void do_print_csrc(const print_csrc &c, unsigned level) const
virtual int compare_same_type(const basic &other) const
Returns order relation between two objects of same type.
const numeric mod(const numeric &a, const numeric &b)
Modulus (in positive representation).
const numeric & add_dyn(const numeric &other) const
Numerical addition method.
bool is_nonneg_integer() const
True if object is an exact integer greater or equal zero.
Context for C source output using CLN numbers.
Wrapper template for making GiNaC classes out of STL containers.
.expand(0) has already done its job (other expand() options ignore this flag)
Base context for C source output.
const numeric lcm(const numeric &a, const numeric &b)
Least Common Multiple.
Makes the interface to the underlying bignum package available.
const numeric imag() const
Imaginary part of a number.
void do_print(const print_context &c, unsigned level) const
const numeric atan(const numeric &x)
Numeric arcustangent.
double to_double() const
Converts numeric types to machine's double.
void add_callback(digits_changed_callback callback)
Add a new callback function.
void(* digits_changed_callback)(long)
Function pointer to implement callbacks in the case 'Digits' gets changed.
static cln::float_format_t guess_precision(const cln::cl_N &x)
long digits
Number of decimal digits.
unsigned precedence() const override
Return relative operator precedence (for parenthezing output).
const numeric factorial(const numeric &n)
Factorial combinatorial function.
const numeric inverse() const
Inverse of a number.
const numeric sub(const numeric &other) const
Numerical subtraction method.
bool operator>=(const numeric &other) const
Numerical comparison: greater or equal.
static void print_real_csrc(const print_context &c, const cln::cl_R &x)
Helper function to print real number in C++ source format.
bool is_rational() const
True if object is an exact rational number, may even be complex (denominator may be unity)...
std::ostream & s
stream to output to
bool has(const ex &other, unsigned options=0) const override
Disassemble real part and imaginary part to scan for the occurrence of a single number.
.eval() has already done its job
static std::vector< cln::cl_N > * coeffs
Context for tree-like output for debugging.
std::vector< cln::cl_N > * current_vector
bool operator!=(const numeric &other) const
unsigned flags
of type status_flags
GINAC_BIND_UNARCHIVER(add)
const numeric tan(const numeric &x)
Numeric tangent (trigonometric function).
int int_length() const
Size in binary notation.
const numeric iquo(const numeric &a, const numeric &b)
Numeric integer quotient.