glucat 0.12.0
pade Namespace Reference

Classes

struct  pade_log_denom
 Coefficients of denominator polynomials of Pade approximations produced by Pade1(log(1+x),x,n,n) More...
 
struct  pade_log_denom< dd_real >
 
struct  pade_log_denom< float >
 
struct  pade_log_denom< long double >
 
struct  pade_log_denom< qd_real >
 
struct  pade_log_numer
 Coefficients of numerator polynomials of Pade approximations produced by Pade1(log(1+x),x,n,n) More...
 
struct  pade_log_numer< dd_real >
 
struct  pade_log_numer< float >
 
struct  pade_log_numer< long double >
 
struct  pade_log_numer< qd_real >
 
struct  pade_sqrt_denom
 Coefficients of denominator polynomials of Pade approximations produced by Pade1(sqrt(1+x),x,n,n) More...
 
struct  pade_sqrt_denom< dd_real >
 
struct  pade_sqrt_denom< float >
 
struct  pade_sqrt_denom< long double >
 
struct  pade_sqrt_denom< qd_real >
 
struct  pade_sqrt_numer
 Coefficients of numerator polynomials of Pade approximations produced by Pade1(sqrt(1+x),x,n,n) More...
 
struct  pade_sqrt_numer< dd_real >
 
struct  pade_sqrt_numer< float >
 
struct  pade_sqrt_numer< long double >
 
struct  pade_sqrt_numer< qd_real >
 

Variables

template<typename Scalar_T>
const pade_sqrt_numer< Scalar_T >::array pade_sqrt_numer< Scalar_T >::numer
 
template<typename Scalar_T>
const pade_sqrt_denom< Scalar_T >::array pade_sqrt_denom< Scalar_T >::denom
 
const pade_sqrt_numer< float >::array pade_sqrt_numer< float >::numer
 
const pade_sqrt_denom< float >::array pade_sqrt_denom< float >::denom
 
const pade_sqrt_numer< longdouble >::array pade_sqrt_numer< longdouble >::numer
 
const pade_sqrt_denom< longdouble >::array pade_sqrt_denom< longdouble >::denom
 
const pade_sqrt_numer< dd_real >::array pade_sqrt_numer< dd_real >::numer
 
const pade_sqrt_denom< dd_real >::array pade_sqrt_denom< dd_real >::denom
 
const pade_sqrt_numer< qd_real >::array pade_sqrt_numer< qd_real >::numer
 
const pade_sqrt_denom< qd_real >::array pade_sqrt_denom< qd_real >::denom
 
template<typename Scalar_T>
const pade_log_numer< Scalar_T >::array pade_log_numer< Scalar_T >::numer
 
template<typename Scalar_T>
const pade_log_denom< Scalar_T >::array pade_log_denom< Scalar_T >::denom
 
const pade_log_numer< float >::array pade_log_numer< float >::numer
 
const pade_log_denom< float >::array pade_log_denom< float >::denom
 
const pade_log_numer< longdouble >::array pade_log_numer< longdouble >::numer
 
const pade_log_denom< longdouble >::array pade_log_denom< longdouble >::denom
 
const pade_log_numer< dd_real >::array pade_log_numer< dd_real >::numer
 
const pade_log_denom< dd_real >::array pade_log_denom< dd_real >::denom
 
const pade_log_numer< qd_real >::array pade_log_numer< qd_real >::numer
 
const pade_log_denom< qd_real >::array pade_log_denom< qd_real >::denom
 

Variable Documentation

◆ pade_log_denom< dd_real >::denom

const pade_log_denom<dd_real>::array pade::pade_log_denom< dd_real >::denom
Initial value:
=
{
dd_real("1"), dd_real("21")/dd_real("2"),
dd_real("2100")/dd_real("41"), dd_real("12635")/dd_real("82"),
dd_real("341145")/dd_real("1066"), dd_real("1037799")/dd_real("2132"),
dd_real("11069856")/dd_real("19721"), dd_real("9883800")/dd_real("19721"),
dd_real("6918660")/dd_real("19721"), dd_real("293930")/dd_real("1517"),
dd_real("1410864")/dd_real("16687"), dd_real("88179")/dd_real("3034"),
dd_real("734825")/dd_real("94054"), dd_real("305235")/dd_real("188108"),
dd_real("348840")/dd_real("1363783"), dd_real("40698")/dd_real("1363783"),
dd_real("6783")/dd_real("2727566"), dd_real("9975")/dd_real("70916716"),
dd_real("266")/dd_real("53187537"), dd_real("7")/dd_real("70916716"),
dd_real("7")/dd_real("8155422340"), dd_real("1")/dd_real("538257874440")
}

Definition at line 1825 of file matrix_multi_imp.h.

◆ pade_log_denom< float >::denom

const pade_log_denom<float>::array pade::pade_log_denom< float >::denom
Initial value:
=
{
1.0, 9.0/2.0, 144.0/17.0, 147.0/17.0,
441.0/85.0, 63.0/34.0, 84.0/221.0, 9.0/221.0,
9.0/4862.0, 1.0/48620.0
}

Definition at line 1763 of file matrix_multi_imp.h.

◆ pade_log_denom< longdouble >::denom

const pade_log_denom<longdouble>::array pade::pade_log_denom< longdouble >::denom
Initial value:
=
{
1.0L, 17.0L/2.0L, 1088.0L/33.0L, 850.0L/11.0L,
41650.0L/341.0L, 140777.0L/1023.0L, 1126216.0L/9889.0L, 63206.0L/899.0L,
790075.0L/24273.0L, 60775.0L/5394.0L, 38896.0L/13485.0L, 21658.0L/40455.0L,
21658.0L/310155.0L, 4165.0L/682341.0L, 680.0L/2047023.0L, 34.0L/3411705.0L,
17.0L/129644790.0L, 1.0L/2333606220
}

Definition at line 1790 of file matrix_multi_imp.h.

◆ pade_log_denom< qd_real >::denom

const pade_log_denom<qd_real>::array pade::pade_log_denom< qd_real >::denom
Initial value:
=
{
qd_real("1"), qd_real("33")/qd_real("2"),
qd_real("8448")/qd_real("65"), qd_real("42284")/qd_real("65"),
qd_real("211420")/qd_real("91"), qd_real("573562")/qd_real("91"),
qd_real("32119472")/qd_real("2379"), qd_real("92917044")/qd_real("3965"),
qd_real("603960786")/qd_real("17995"), qd_real("144626625")/qd_real("3599"),
qd_real("2776831200")/qd_real("68381"), qd_real("16692542100")/qd_real("478667"),
qd_real("12241197540")/qd_real("478667"), qd_real("1098569010")/qd_real("68381"),
qd_real("31387686000")/qd_real("3624193"), qd_real("9939433900")/qd_real("2479711"),
qd_real("67091178825")/qd_real("42155087"), qd_real("2683647153")/qd_real("4959422"),
qd_real("19083713088")/qd_real("121505839"), qd_real("4708152900")/qd_real("121505839"),
qd_real("941630580")/qd_real("116546417"), qd_real("88704330")/qd_real("62755763"),
qd_real("12902448")/qd_real("62755763"), qd_real("1542684")/qd_real("62755763"),
qd_real("6427850")/qd_real("2698497809"), qd_real("3471039")/qd_real("18889484663"),
qd_real("8544096")/qd_real("774468871183"), qd_real("39556")/qd_real("79027435835"),
qd_real("118668")/qd_real("7191496660985"), qd_real("10230")/qd_real("27327687311743"),
qd_real("5456")/qd_real("1011124430534491"), qd_real("44")/qd_real("1011124430534491"),
qd_real("11")/qd_real("70778710137414370"), qd_real("1")/qd_real("7219428434016265740")
}

Definition at line 1872 of file matrix_multi_imp.h.

◆ pade_log_denom< Scalar_T >::denom

template<typename Scalar_T>
const pade_log_denom<Scalar_T>::array pade::pade_log_denom< Scalar_T >::denom
Initial value:
=
{
1.0, 13.0/2.0, 468.0/25.0, 1573.0/50.0,
1573.0/46.0, 11583.0/460.0, 10296.0/805.0, 2574.0/575.0,
11583.0/10925.0, 143.0/874.0, 572.0/37145.0, 117.0/148580.0,
13.0/742900.0, 1.0/10400600.0
}

Definition at line 1737 of file matrix_multi_imp.h.

◆ pade_log_numer< dd_real >::numer

const pade_log_numer<dd_real>::array pade::pade_log_numer< dd_real >::numer
Initial value:
=
{
dd_real("0"), dd_real("1"),
dd_real("10"), dd_real("22781")/dd_real("492"),
dd_real("21603")/dd_real("164"), dd_real("5492649")/dd_real("21320"),
dd_real("978724")/dd_real("2665"), dd_real("4191605")/dd_real("10619"),
dd_real("12874933")/dd_real("39442"), dd_real("11473457")/dd_real("54612"),
dd_real("2406734")/dd_real("22755"), dd_real("166770367")/dd_real("4004880"),
dd_real("30653165")/dd_real("2402928"), dd_real("647746389")/dd_real("215195552"),
dd_real("25346331")/dd_real("47074027"), dd_real("278270613")/dd_real("3900419380"),
dd_real("105689791")/dd_real("15601677520"), dd_real("606046475")/dd_real("1379188292768"),
dd_real("969715")/dd_real("53502994116"), dd_real("11098301")/dd_real("26204577562592"),
dd_real("118999")/dd_real("26204577562592"), dd_real("18858053")/dd_real("1392249205900512960")
}

Definition at line 1805 of file matrix_multi_imp.h.

◆ pade_log_numer< float >::numer

const pade_log_numer<float>::array pade::pade_log_numer< float >::numer
Initial value:
=
{
0.0, 1.0, 4.0, 1337.0/204.0,
385.0/68.0, 1879.0/680.0, 193.0/255.0, 197.0/1820.0,
419.0/61880.0, 7129.0/61261200.0
}

Definition at line 1751 of file matrix_multi_imp.h.

◆ pade_log_numer< longdouble >::numer

const pade_log_numer<longdouble>::array pade::pade_log_numer< longdouble >::numer
Initial value:
=
{
0.0L, 1.0L, 8.0L, 3835.0L/132.0L,
8365.0L/132.0L, 11363807.0L/122760.0L, 162981.0L/1705.0L, 9036157.0L/125860.0L,
18009875.0L/453096.0L, 44211925.0L/2718576.0L, 4149566.0L/849555.0L, 16973929.0L/16020180.0L,
172459.0L/1068012.0L, 116317061.0L/7025382936.0L, 19679783.0L/18441630207.0L, 23763863.0L/614721006900.0L,
50747.0L/79318839600.0L, 42142223.0L/14295951736466400.0L
}

Definition at line 1776 of file matrix_multi_imp.h.

◆ pade_log_numer< qd_real >::numer

const pade_log_numer<qd_real>::array pade::pade_log_numer< qd_real >::numer
Initial value:
=
{
qd_real("0"), qd_real("1"),
qd_real("16"), qd_real("95201")/qd_real("780"),
qd_real("30721")/qd_real("52"), qd_real("7416257")/qd_real("3640"),
qd_real("1039099")/qd_real("195"), qd_real("6097772319")/qd_real("555100"),
qd_real("1564058073")/qd_real("85400"), qd_real("30404640205")/qd_real("1209264"),
qd_real("725351278")/qd_real("25193"), qd_real("4092322670789")/qd_real("147429436"),
qd_real("4559713849589")/qd_real("201040140"), qd_real("5049361751189")/qd_real("320023080"),
qd_real("74979677195")/qd_real("8000577"), qd_real("16569850691873")/qd_real("3481514244"),
qd_real("1065906022369")/qd_real("515779888"), qd_real("335956770855841")/qd_real("438412904800"),
qd_real("1462444287585964")/qd_real("6041877844275"), qd_real("397242326339851")/qd_real("6122436215532"),
qd_real("64211291334131")/qd_real("4373168725380"), qd_real("142322343550859")/qd_real("51080680851480"),
qd_real("154355972958659")/qd_real("351179680853925"), qd_real("167483568676259")/qd_real("2937139148960100"),
qd_real("4230788929433")/qd_real("704913395750424"), qd_real("197968763176019")/qd_real("392923948371995600"),
qd_real("10537522306718")/qd_real("319250708052246425"), qd_real("236648286272519")/qd_real("144249197475035425500"),
qd_real("260715545088119")/qd_real("4375558990076074573500"), qd_real("289596255666839")/qd_real("192874640282553367199880"),
qd_real("8802625510547")/qd_real("361639950529787563499775"), qd_real("373831661521439")/qd_real("1659204093030665341336967700"),
qd_real("446033437968239")/qd_real("464577146048586295574350956000"), qd_real("53676090078349")/qd_real("47386868896955802148583797512000")
}

Definition at line 1846 of file matrix_multi_imp.h.

◆ pade_log_numer< Scalar_T >::numer

template<typename Scalar_T>
const pade_log_numer<Scalar_T>::array pade::pade_log_numer< Scalar_T >::numer
Initial value:
=
{
0.0, 1.0, 6.0, 4741.0/300.0,
1441.0/60.0, 107091.0/4600.0, 8638.0/575.0, 263111.0/40250.0,
153081.0/80500.0, 395243.0/1101240.0, 28549.0/688275.0, 605453.0/228813200.0,
785633.0/10296594000.0, 1145993.0/1873980108000.0
}

Definition at line 1720 of file matrix_multi_imp.h.

◆ pade_sqrt_denom< dd_real >::denom

const pade_sqrt_denom<dd_real>::array pade::pade_sqrt_denom< dd_real >::denom
Initial value:
=
{
dd_real("1"), dd_real("41")/dd_real("4"),
dd_real("195")/dd_real("4"), dd_real("9139")/dd_real("64"),
dd_real("73815")/dd_real("256"), dd_real("435897")/dd_real("1024"),
dd_real("121737")/dd_real("256"), dd_real("840565")/dd_real("2048"),
dd_real("4539051")/dd_real("16384"), dd_real("9641775")/dd_real("65536"),
dd_real("4032015")/dd_real("65536"), dd_real("84672315")/dd_real("4194304"),
dd_real("86493225")/dd_real("16777216"), dd_real("67863915")/dd_real("67108864"),
dd_real("5014575")/dd_real("33554432"), dd_real("4345965")/dd_real("268435456"),
dd_real("5311735")/dd_real("4294967296"), dd_real("1081575")/dd_real("17179869184"),
dd_real("33649")/dd_real("17179869184"), dd_real("8855")/dd_real("274877906944"),
dd_real("231")/dd_real("1099511627776"), dd_real("1")/dd_real("4398046511104")
}

Definition at line 1496 of file matrix_multi_imp.h.

◆ pade_sqrt_denom< float >::denom

const pade_sqrt_denom<float>::array pade::pade_sqrt_denom< float >::denom
Initial value:
=
{
1.0, 17.0/4.0, 15.0/2.0, 455.0/64.0,
1001.0/256.0, 1287.0/1024.0, 231.0/1024.0, 165.0/8192.0,
45.0/65536, 1.0/262144.0
}

Definition at line 1433 of file matrix_multi_imp.h.

◆ pade_sqrt_denom< longdouble >::denom

const pade_sqrt_denom<longdouble>::array pade::pade_sqrt_denom< longdouble >::denom
Initial value:
=
{
1.0L, 33.0L/4.0L, 31.0L, 4495.0L/64.0L,
27405.0L/256.0L, 118755.0L/1024.0L, 94185.0L/1024.0L, 444015.0L/8192.0L,
1562275.0L/65536.0L, 2042975.0L/262144.0L, 245157.0L/131072.0L, 676039.0L/2097152.0L,
323323.0L/8388608.0L, 101745.0L/33554432.0L, 4845.0L/33554432.0L, 969.0L/268435456.0L,
153.0L/4294967296.0L, 1.0L/17179869184.0L
}

Definition at line 1460 of file matrix_multi_imp.h.

◆ pade_sqrt_denom< qd_real >::denom

const pade_sqrt_denom<qd_real>::array pade::pade_sqrt_denom< qd_real >::denom
Initial value:
=
{
qd_real("1"), qd_real("65")/qd_real("4"),
qd_real("126"), qd_real("39711")/qd_real("64"),
qd_real("557845")/qd_real("256"), qd_real("5949147")/qd_real("1024"),
qd_real("12515965")/qd_real("1024"), qd_real("170574723")/qd_real("8192"),
qd_real("1916797311")/qd_real("65536"), qd_real("8996462475")/qd_real("262144"),
qd_real("4450881435")/qd_real("131072"), qd_real("59826782925")/qd_real("2097152"),
qd_real("171503444385")/qd_real("8388608"), qd_real("420696483235")/qd_real("33554432"),
qd_real("221120793075")/qd_real("33554432"), qd_real("797168807855")/qd_real("268435456"),
qd_real("4923689695575")/qd_real("4294967296"), qd_real("6499270398159")/qd_real("17179869184"),
qd_real("456864812569")/qd_real("4294967296"), qd_real("3486599885395")/qd_real("137438953472"),
qd_real("2804116503573")/qd_real("549755813888"), qd_real("1886827875075")/qd_real("2199023255552"),
qd_real("263012370465")/qd_real("2199023255552"), qd_real("240141729555")/qd_real("17592186044416"),
qd_real("176848560525")/qd_real("140737488355328"), qd_real("51538723353")/qd_real("562949953421312"),
qd_real("1450433115")/qd_real("281474976710656"), qd_real("977699359")/qd_real("4503599627370496"),
qd_real("118183439")/qd_real("18014398509481984"), qd_real("9652005")/qd_real("72057594037927936"),
qd_real("121737")/qd_real("72057594037927936"), qd_real("6545")/qd_real("576460752303423488"),
qd_real("561")/qd_real("18446744073709551616"), qd_real("1")/qd_real("73786976294838206464")
}

Definition at line 1543 of file matrix_multi_imp.h.

◆ pade_sqrt_denom< Scalar_T >::denom

template<typename Scalar_T>
const pade_sqrt_denom<Scalar_T>::array pade::pade_sqrt_denom< Scalar_T >::denom
Initial value:
=
{
1.0, 25.0/4.0, 69.0/4.0, 1771.0/64.0,
7315.0/256.0, 20349.0/1024.0, 4845.0/512.0, 12597.0/4096.0,
21879.0/32768.0, 12155.0/131072.0, 1001.0/131072.0, 1365.0/4194304.0,
91.0/16777216.0, 1.0/67108864.0
}

Definition at line 1407 of file matrix_multi_imp.h.

◆ pade_sqrt_numer< dd_real >::numer

const pade_sqrt_numer<dd_real>::array pade::pade_sqrt_numer< dd_real >::numer
Initial value:
=
{
dd_real("1"), dd_real("43")/dd_real("4"),
dd_real("215")/dd_real("4"), dd_real("10621")/dd_real("64"),
dd_real("90687")/dd_real("256"), dd_real("567987")/dd_real("1024"),
dd_real("168861")/dd_real("256"), dd_real("1246355")/dd_real("2048"),
dd_real("7228859")/dd_real("16384"), dd_real("16583853")/dd_real("65536"),
dd_real("7538115")/dd_real("65536"), dd_real("173376645")/dd_real("4194304"),
dd_real("195747825")/dd_real("16777216"), dd_real("171655785")/dd_real("67108864"),
dd_real("14375115")/dd_real("33554432"), dd_real("14375115")/dd_real("268435456"),
dd_real("20764055")/dd_real("4294967296"), dd_real("5167525")/dd_real("17179869184"),
dd_real("206701")/dd_real("17179869184"), dd_real("76153")/dd_real("274877906944"),
dd_real("3311")/dd_real("1099511627776") , dd_real("43")/dd_real("4398046511104")
}

Definition at line 1476 of file matrix_multi_imp.h.

◆ pade_sqrt_numer< float >::numer

const pade_sqrt_numer<float>::array pade::pade_sqrt_numer< float >::numer
Initial value:
=
{
1.0, 19.0/4.0, 19.0/2.0, 665.0/64.0,
1729.0/256.0, 2717.0/1024.0, 627.0/1024.0, 627.0/8192.0,
285.0/65536.0, 19.0/262144.0
}

Definition at line 1421 of file matrix_multi_imp.h.

◆ pade_sqrt_numer< longdouble >::numer

const pade_sqrt_numer<longdouble>::array pade::pade_sqrt_numer< longdouble >::numer
Initial value:
=
{
1.0L, 35.0L/4.0L, 35.0L, 5425.0L/64.0L,
35525.0L/256.0L, 166257.0L/1024.0L, 143325.0L/1024.0L, 740025.0L/8192.0L,
2877875.0L/65536.0L, 4206125.0L/262144.0L, 572033.0L/131072.0L, 1820105.0L/2097152.0L,
1028755.0L/8388608.0L, 395675.0L/33554432.0L, 24225.0L/33554432.0L, 6783.0L/268435456.0L,
1785.0L/4294967296.0L, 35.0L/17179869184.0L
}

Definition at line 1446 of file matrix_multi_imp.h.

◆ pade_sqrt_numer< qd_real >::numer

const pade_sqrt_numer<qd_real>::array pade::pade_sqrt_numer< qd_real >::numer
Initial value:
=
{
qd_real("1"), qd_real("67")/qd_real("4"),
qd_real("134"), qd_real("43617")/qd_real("64"),
qd_real("633485")/qd_real("256"), qd_real("6992857")/qd_real("1024"),
qd_real("15246721")/qd_real("1024"), qd_real("215632197")/qd_real("8192"),
qd_real("2518145487")/qd_real("65536"), qd_real("12301285425")/qd_real("262144"),
qd_real("6344873535")/qd_real("131072"), qd_real("89075432355")/qd_real("2097152"),
qd_real("267226297065")/qd_real("8388608"), qd_real("687479618945")/qd_real("33554432"),
qd_real("379874182975")/qd_real("33554432"), qd_real("1443521895305")/qd_real("268435456"),
qd_real("9425348845815")/qd_real("4294967296"), qd_real("13195488384141")/qd_real("17179869184"),
qd_real("987417498133")/qd_real("4294967296"), qd_real("8055248011085")/qd_real("137438953472"),
qd_real("6958363175533")/qd_real("549755813888"), qd_real("5056698705201")/qd_real("2199023255552"),
qd_real("766166470485")/qd_real("2199023255552"), qd_real("766166470485")/qd_real("17592186044416"),
qd_real("623623871325")/qd_real("140737488355328"), qd_real("203123203803")/qd_real("562949953421312"),
qd_real("6478601247")/qd_real("281474976710656"), qd_real("5038912081")/qd_real("4503599627370496"),
qd_real("719844583")/qd_real("18014398509481984"), qd_real("71853815")/qd_real("72057594037927936"),
qd_real("1165197")/qd_real("72057594037927936"), qd_real("87703")/qd_real("576460752303423488"),
qd_real("12529")/qd_real("18446744073709551616"), qd_real("67")/qd_real("73786976294838206464")
}

Definition at line 1517 of file matrix_multi_imp.h.

◆ pade_sqrt_numer< Scalar_T >::numer

template<typename Scalar_T>
const pade_sqrt_numer<Scalar_T>::array pade::pade_sqrt_numer< Scalar_T >::numer
Initial value:
=
{
1.0, 27.0/4.0, 81.0/4.0, 2277.0/64.0,
10395.0/256.0, 32319.0/1024.0, 8721.0/512.0, 26163.0/4096.0,
53703.0/32768.0, 36465.0/131072.0, 3861.0/131072.0, 7371.0/4194304.0,
819.0/16777216.0, 27.0/67108864.0
}

Definition at line 1390 of file matrix_multi_imp.h.