/* fi_lib: interval library version 1.2, for copyright see fi_lib.h */ # include "fi_lib.h" /* RCS $Id: q_glbl.c,v 1.4 1997/07/15 14:57:04 ae13 Exp $ */ /* $Log: q_glbl.c,v $ * Revision 1.4 1997/07/15 14:57:04 ae13 * *** empty log message *** * * Revision 1.3 1997/07/15 09:08:31 ae13 * *** empty log message *** * * Revision 1.2 1997/06/10 14:04:11 ae13 * new approximation for arctan and new error bounds for arcus-functions * */ /****************************************************************/ /* */ /* Description : Constants for fast real functions */ /* for double IEEE Floating-Point */ /* Arithmetic */ /* */ /* Date : 1997-06-10 */ /* */ /* Author : W. Hofschuster */ /* */ /****************************************************************/ /* --------------------------------------------------------------------- */ /* ---- relative worst case error bounds for the standard functions --- */ /* --------------------------------------------------------------------- */ // # undef RND_TO_NRST // // # ifdef RND_TO_NRST // // # else /* worst case relative error bound for q_exp */ /* eps(q_exp) = 2.357962555295842e-16; */ /* q_exem = 1 - eps(q_exp) = 9.999999999999993E-001 */ double q_exem = 9007199254740986.0 / 9007199254740992.0; /* q_exep = 1 + eps(q_exp) = 1.000000000000001E+000 */ double q_exep = 4503599627370501.0 / 4503599627370496.0; /* worst case relative error bound for q_expm */ /* eps(q_expm) = 2.592561649228397E-016; */ /* q_exmm = 1 - eps(q_expm) = 9.999999999999993E-001 */ double q_exmm = 9007199254740986.0 / 9007199254740992.0; /* q_exmp = 1 + eps(q_expm) = 1.000000000000001E+000 */ double q_exmp = 4503599627370501.0 / 4503599627370496.0; /* worst case relative error bound for q_log */ /* eps(q_log) = 2.9398E-016; */ /* q_logm = 1 - eps(q_log) */ double q_logm = 9007199254740986.0 / 9007199254740992.0; /* q_logp = 1 + eps(q_log) */ double q_logp = 4503599627370501.0 / 4503599627370496.0; /* worst case relative error bound for q_lg1p */ /* eps(q_lg1p) = 2.5082E-016; */ /* q_lgpm = 1 - eps(q_lg1p) */ double q_lgpm = 9007199254740986.0 / 9007199254740992.0; /* q_lgpp = 1 + eps(q_lg1p) */ double q_lgpp = 4503599627370501.0 / 4503599627370496.0; /* worst case relative error bound for sqrt */ /* eps(sqrt) = 2.220447e-16; */ /* q_sqtm = 1 - eps(sqrt) */ double q_sqtm = 9007199254740986.0 / 9007199254740992.0; /* q_sqtp = 1 + eps(sqrt) */ double q_sqtp = 4503599627370501.0 / 4503599627370496.0; /* worst case relative error bound for q_sinh */ /* eps(q_sinh) = 7.093289735801012E-016; */ /* q_snhm = 1 - eps(q_sinh) = 9.999999999999989E-001 */ double q_snhm = 9007199254740982.0 / 9007199254740992.0; /* q_snhp = 1 + eps(q_sinh) = 1.000000000000002E+000 */ double q_snhp = 4503599627370503.0 / 4503599627370496.0; /* worst case relative error bound for q_cosh */ /* eps(q_cosh) = 4.581660384746620E-016; */ /* q_cshm = 1 - eps(q_cosh) = 9.999999999999991E-001 */ double q_cshm = 9007199254740984.0 / 9007199254740992.0; /* q_cshp = 1 + eps(q_cosh) = 1.000000000000001E+000 */ double q_cshp = 4503599627370502.0 / 4503599627370496.0; /* worst case relative error bound for q_coth */ /* eps(q_coth) = 8.325226430245611E-016; */ /* q_cthm = 1 - eps(q_coth) = 9.999999999999988E-001 */ double q_cthm = 9007199254740981.0 / 9007199254740992.0; /* q_cthp = 1 + eps(q_coth) = 1.000000000000002E+000 */ double q_cthp = 4503599627370503.0 / 4503599627370496.0; /* worst case relative error bound for q_tanh */ /* eps(q_tanh) = 1.054585718561371E-015; */ /* q_tnhm = 1 - eps(q_tanh) = 9.999999999999986E-001 */ double q_tnhm = 9007199254740979.0 / 9007199254740992.0; /* q_tnhp = 1 + eps(q_tnhp) = 1.000000000000002E+000 */ double q_tnhp = 4503599627370504.0 / 4503599627370496.0; /* worst case relative error bound for q_asnh */ /* eps(q_asnh) = 7.2075e-16; */ double q_asnm = 9007199254740982.0 / 9007199254740992.0; double q_asnp = 4503599627370503.0 / 4503599627370496.0; /* worst case relative error bound for q_acnh */ /* eps(q_acnh) = 1.6180e-15; */ double q_acsm = 9007199254740974.0 / 9007199254740992.0; double q_acsp = 4503599627370507.0 / 4503599627370496.0; /* worst case relative error bound for q_acth */ /* eps(q_acth) = 1.147880588000001E-015; */ double q_actm = 9007199254740978.0 / 9007199254740992.0; double q_actp = 4503599627370505.0 / 4503599627370496.0; /* worst case relative error bound for q_atnh */ /* eps(q_atnh) = 1.264618646263405E-015; */ double q_atnm = 9007199254740977.0 / 9007199254740992.0; double q_atnp = 4503599627370505.0 / 4503599627370496.0; /* worst case relative error bound for q_asin */ /* eps(q_asin) = 2.148875977690793E-015; */ /* q_csnm = 1 - eps(q_asin) = 9.999999999999974E-001 */ double q_csnm = 9007199254740969.0 / 9007199254740992.0; /* q_csnp = 1 + eps(q_asin) = 1.000000000000003E+000 */ double q_csnp = 4503599627370509.0 / 4503599627370496.0; /* worst case relative error bound for q_acos */ /* eps(q_acos) = 2.148489042525242E-015; */ /* q_ccsm = 1 - eps(q_acos) = 9.999999999999974E-001 */ double q_ccsm = 9007199254740969.0 / 9007199254740992.0; /* q_ccsp = 1 + eps(q_acos) = 1.000000000000003E+000 */ double q_ccsp = 4503599627370509.0 / 4503599627370496.0; /* worst case relative error bound for q_acot */ /* eps(q_acot) = 1.802884893838539E-015; */ /* q_cctm = 1 - eps(q_acot) = 9.999999999999978E-001 */ double q_cctm = 9007199254740972.0 / 9007199254740992.0; /* q_cctp = 1 + eps(q_acot) = 1.000000000000003E+000 */ double q_cctp = 4503599627370508.0 / 4503599627370496.0; /* worst case relative error bound for q_atan */ /* eps(q_atan) = 1.358774060669230E-015; */ /* q_ctnm = 1 - eps(q_atan) = 9.999999999999982E-001 */ double q_ctnm = 9007199254740976.0 / 9007199254740992.0; /* q_ctnp = 1 + eps(q_atan) = 1.000000000000002E+000 */ double q_ctnp = 4503599627370506.0 / 4503599627370496.0; /* worst case relative error bound for q_sin */ /* eps(q_sin) = 1.071713978232866e-15; */ double q_sinm = 9007199254740979.0 / 9007199254740992.0; double q_sinp = 4503599627370504.0 / 4503599627370496.0; /* worst case relative error bound for q_cos */ /* eps(q_cos) = 1.071713978232866e-15; */ double q_cosm = 9007199254740979.0 / 9007199254740992.0; double q_cosp = 4503599627370504.0 / 4503599627370496.0; /* worst case relative error bound for q_cot */ /* eps(q_cot) = 2.97768e-15; */ double q_cotm = 9007199254740962.0 / 9007199254740992.0; double q_cotp = 4503599627370513.0 / 4503599627370496.0; /* worst case relative error bound for q_tan */ /* eps(q_tan) = 2.97768e-15; */ double q_tanm = 9007199254740962.0 / 9007199254740992.0; double q_tanp = 4503599627370513.0 / 4503599627370496.0; /* worst case relative error bound for q_lg2 */ /* eps(q_lg2) = 2.7754e-15; */ double q_lg2m = 9007199254740964.0 / 9007199254740992.0; double q_lg2p = 4503599627370512.0 / 4503599627370496.0; /* worst case relative error bound for q_lg10 */ /* eps(q_lg10) = 2.7754e-15; */ double q_l10m = 9007199254740964.0 / 9007199254740992.0; double q_l10p = 4503599627370512.0 / 4503599627370496.0; /* worst case relative error bound for q_exp2 */ /* eps(q_exp2) = 2.350296792932261e-16 */ double q_e2em = 9007199254740986.0 / 9007199254740992.0; double q_e2ep = 4503599627370501.0 / 4503599627370496.0; /* worst case relative error bound for q_ex10 */ /* eps(q_ex10) = 2.418059815583812e-16; */ double q_e10m = 9007199254740986.0 / 9007199254740992.0; double q_e10p = 4503599627370501.0 / 4503599627370496.0; // # endif /* --------------------------------------------------------------------- */ /* ---- global constants for the standard functions ------------------- */ /* --------------------------------------------------------------------- */ /* q_minr = smallest positive normalised number */ double q_minr = 2.2250738585072013e-308; /* q_mine = ln( q_minr ) = -708.3964185322641062617539 */ double q_mine = -6231120794008786.0 / 8796093022208.0; /* q_sqra = 1.3407807929942596e154; */ double q_sqra = 1.3407807929942596e154; /* q_ctht = 5.562684646268013e-309; */ double q_ctht = 5.562684646268013e-309; /* q_ln2h = ln( 2.0 ) / 2 = 0.346573590279972654708616 */ double q_ln2h = 6243314768165359.0 / 18014398509481984.0; /* q_l10i = 1 / ln( 10 ) = 4.342944819032518E-001 */ double q_l10i = 7823553867474190.0 / 18014398509481984.0; /* q_l2i = 1 / ln( 2 ) = 1.442695040888963E+000 */ double q_l2i = 6497320848556798.0 / 4503599627370496.0; /* q_l10 = ln( 10 ) = 2.302585092994046E+000 */ double q_l10 = 5184960683398422.0 / 2251799813685248.0; /* q_l2 = ln( 2 ) = 6.931471805599453E-001 */ double q_l2 = 6243314768165359.0 / 9007199254740992.0; /* q_p2h = 2^(100) */ double q_p2h = 1267650600228229401496703205376.0; /* q_p2mh = 2^(-100) */ double q_p2mh = 1.0/1267650600228229401496703205376.0; /* q_pi = pi ( rounding towards -infinity ) */ double q_pi = 7074237752028440.0 / 2251799813685248.0; /* q_piha = pi/2 */ double q_piha = 7074237752028440.0 / 4503599627370496.0; /* q_pih[7] = pi/2 with 7*22 bits */ double q_pih[7] = { 7074236338274304.0 / 4503599627370496.0, 5929713453236224.0 / 18889465931478580854784.0, 4930663257997312.0 / 79228162514264337593543950336.0, 5376096463749120.0 / 2658455991569831745807614120560689152.0, 4908338017992704.0 / 1393796574908163946345982392040522594123776.0, 8111234717057024.0 / 187072209578355573530071658587684226515959365500928.0, 5071617642201088.0 / 24519928653854221733733552434404946937899825954937634816.0 }; /* q_pi2i = 2/pi */ double q_pi2i = 5734161139222659.0 / 9007199254740992.0; /* q_pi2p[3]= */ double q_pi2p[3]={ 5734160907894784.0 / 9007199254740992.0, 7762075350728704.0 / 302231454903657293676544.0, 5957137356292096.0 / 20282409603651670423947251286016.0}; /* --------------------------------------------------------------------- */ /* ---- global constants and table values for q_expm1 and q_exp ------- */ /* --------------------------------------------------------------------- */ /* q_ext1 = 5.551115123125783E-017 */ double q_ext1 = 4503599627370496.0 / 81129638414606681695789005144064.0; /* q_ext2 = 1.809114141261457E+003 */ double q_ext2 = 7956568137163861.0 / 4398046511104.0; /* q_ex2a = 7.097827128933840E+002 */ double q_ex2a = 6243314768165359.0 / 8796093022208.0; /* q_ex2b =-744.44008 */ double q_ex2b =-6548164193139965.0 / 8796093022208.0; /* q_ex2c = 7.090895657128240E+002 */ double q_ex2c = 6237217781087072.0 / 8796093022208.0; /* q_ext3 =-3.742994775023704E+001 */ double q_ext3 =-5267796835639521.0 / 140737488355328.0; /* q_ext4 =-2.876820724517810E-001 */ double q_ext4 =-5182419497180051.0 / 18014398509481984.0; /* q_ext5 = 2.231435513142098E-001 */ double q_ext5 = 8039593716390434.0 / 36028797018963968.0; /* q_extm = 307.9536855642527627036 */ double q_extm = 5417578529509920.0 / 17592186044416.0; /* q_extn =-307.65265556858878150844 */ double q_extn =-5412282753821250.0 / 17592186044416.0; /* q_exil = 4.616624130844683E+001 */ double q_exil = 6497320848556798.0 / 140737488355328.0; /* q_exl1 = 2.166084939017310E-002 */ double q_exl1 = 6243314767495168.0 / 288230376151711744.0; /* q_exl2 = 2.325192846878874E-012 */ double q_exl2 = 5756898648422637.0 / 2475880078570760549798248448.0; /* q_e10i = 32/lg10(2) = 1.063016990363956E+002 */ double q_e10i = 7480317065143153.0 / 70368744177664.0; /* q_e1l1 = lg10(2)/32 ( lead ) = 9.407187363649427E-003 */ double q_e1l1 = 5422874304708608.0 / 576460752303423488.0; /* q_e1l2 = lg10(2)/32 ( trail ) = 8.499849253130399E-013 */ double q_e1l2 = 8417842974672045.0 / 9903520314283042199192993792.0; double q_exa[5]={ /* q_exa[0] = 5.000000000000000E-001 */ 4503599627370496.0 / 9007199254740992.0, /* q_exa[1] = 1.666666666658136E-001 */ 6004799503129925.0 / 36028797018963968.0, /* q_exa[2] = 4.166666666638950E-002 */ 6004799503120717.0 / 144115188075855872.0, /* q_exa[3] = 8.333362425159880E-003 */ 4803856372824746.0 / 576460752303423488.0, /* q_exa[4] = 1.388893979532449E-003 */ 6405142946487772.0 / 4611686018427387904.0 }; double q_exb[9]={ /* q_exb[0] = 1.666666666666666E-001 */ 6004799503160660.0 / 36028797018963968.0, /* q_exb[1] = 4.166666666666610E-002 */ 6004799503160579.0 / 144115188075855872.0, /* q_exb[2] = 8.333333333354122E-003 */ 4803839602540513.0 / 576460752303423488.0, /* q_exb[3] = 1.388888889017890E-003 */ 6405119470632951.0 / 4611686018427387904.0, /* q_exb[4] = 1.984126964158297E-004 */ 7320136463514879.0 / 36893488147419103232.0, /* q_exb[5] = 2.480157863209126E-005 */ 7320133978402734.0 / 295147905179352825856.0, /* q_exb[6] = 2.755792722352050E-006 */ 6506931592885707.0 / 2361183241434822606848.0, /* q_exb[7] = 2.758025508816736E-007 */ 5209762888694261.0 / 18889465931478580854784.0, /* q_exb[8] = 2.448136759253856E-008 */ 7399039345524175.0 / 302231454903657293676544.0}; /* approximation for function q_exp2 */ double q_exc[7]={ /* q_exc[0] = 6.931471805599453E-001 */ 6243314768165359.0 / 9007199254740992.0, /* q_exc[1] = 2.402265069591007E-001 */ 8655072057804175.0 / 36028797018963968.0, /* q_exc[2] = 5.550410866482158E-002 */ 7998985059213504.0 / 144115188075855872.0, /* q_exc[3] = 9.618129107559553E-003 */ 5544473941095235.0 / 576460752303423488.0, /* q_exc[4] = 1.333355814632986E-003 */ 6149018367931802.0 / 4611686018427387904.0, /* q_exc[5] = 1.540358685612716E-004 */ 5682920491042682.0 / 36893488147419103232.0, /* q_exc[6] = 1.525278971414304E-005 */ 9003657864540998.0 / 590295810358705651712.0}; /* approximation for function q_ex10 */ double q_exd[7]={ /* q_exd[0] = 1.302585092994046E+000 */ 5866321739426347.0 / 4503599627370496.0, /* q_exd[1] = 2.650949055239199E+000 */ 5969406588676713.0 / 2251799813685248.0, /* q_exd[2] = 2.034678592293476E+000 */ 4581688875035812.0 / 2251799813685248.0, /* q_exd[3] = 1.171255148903874E+000 */ 5274864252159260.0 / 4503599627370496.0, /* q_exd[4] = 5.393829291915935E-001 */ 4858329517834534.0 / 9007199254740992.0, /* q_exd[5] = 2.069966074549993E-001 */ 7457838753610334.0 / 36028797018963968.0, /* q_exd[6] = 6.808961466129955E-002 */ 4906373811462869.0 / 72057594037927936.0}; double q_exld[32]={ /* qExpLead [ 0]:= 1.000000000000000E+000 */ 4503599627370496.0 / 4503599627370496.0, /* qExpLead [ 1]:= 1.021897148654105E+000 */ 4602215617889600.0 / 4503599627370496.0, /* qExpLead [ 2]:= 1.044273782427410E+000 */ 4702991017412864.0 / 4503599627370496.0, /* qExpLead [ 3]:= 1.067140400676820E+000 */ 4805973110840128.0 / 4503599627370496.0, /* qExpLead [ 4]:= 1.090507732665245E+000 */ 4911210218475840.0 / 4503599627370496.0, /* qExpLead [ 5]:= 1.114386742595883E+000 */ 5018751718701440.0 / 4503599627370496.0, /* qExpLead [ 6]:= 1.138788634756679E+000 */ 5128648071143936.0 / 4503599627370496.0, /* qExpLead [ 7]:= 1.163724858777570E+000 */ 5240950840352448.0 / 4503599627370496.0, /* qExpLead [ 8]:= 1.189207115002716E+000 */ 5355712719992576.0 / 4503599627370496.0, /* qExpLead [ 9]:= 1.215247359980467E+000 */ 5472987557571008.0 / 4503599627370496.0, /* qExpLead [10]:= 1.241857812073476E+000 */ 5592830379701248.0 / 4503599627370496.0, /* qExpLead [11]:= 1.269050957191723E+000 */ 5715297417922816.0 / 4503599627370496.0, /* qExpLead [12]:= 1.296839554651001E+000 */ 5840446135085568.0 / 4503599627370496.0, /* qExpLead [13]:= 1.325236643159741E+000 */ 5968335252311936.0 / 4503599627370496.0, /* qExpLead [14]:= 1.354255546936884E+000 */ 6099024776549376.0 / 4503599627370496.0, /* qExpLead [15]:= 1.383909881963831E+000 */ 6232576028726656.0 / 4503599627370496.0, /* qExpLead [16]:= 1.414213562373092E+000 */ 6369051672525760.0 / 4503599627370496.0, /* qExpLead [17]:= 1.445180806977035E+000 */ 6508515743784768.0 / 4503599627370496.0, /* qExpLead [18]:= 1.476826145939498E+000 */ 6651033680544128.0 / 4503599627370496.0, /* qExpLead [19]:= 1.509164427593419E+000 */ 6796672353750528.0 / 4503599627370496.0, /* qExpLead [20]:= 1.542210825407935E+000 */ 6945500098633920.0 / 4503599627370496.0, /* qExpLead [21]:= 1.575980845107878E+000 */ 7097586746770880.0 / 4503599627370496.0, /* qExpLead [22]:= 1.610490331949251E+000 */ 7253003658850432.0 / 4503599627370496.0, /* qExpLead [23]:= 1.645755478153959E+000 */ 7411823758157120.0 / 4503599627370496.0, /* qExpLead [24]:= 1.681792830507419E+000 */ 7574121564787584.0 / 4503599627370496.0, /* qExpLead [25]:= 1.718619298122476E+000 */ 7739973230616128.0 / 4503599627370496.0, /* qExpLead [26]:= 1.756252160373293E+000 */ 7909456575025792.0 / 4503599627370496.0, /* qExpLead [27]:= 1.794709075003098E+000 */ 8082651121422400.0 / 4503599627370496.0, /* qExpLead [28]:= 1.834008086409341E+000 */ 8259638134547584.0 / 4503599627370496.0, /* qExpLead [29]:= 1.874167634110293E+000 */ 8440500658608960.0 / 4503599627370496.0, /* qExpLead [30]:= 1.915206561397142E+000 */ 8625323556245696.0 / 4503599627370496.0, /* qExpLead [31]:= 1.957144124175400E+000 */ 8814193548346688.0 / 4503599627370496.0 }; double q_extl[32]={ /* qExpTrail[ 0]:= 0.000000000000000E+000 */ 0.0, /* qExpTrail[ 1]:= 1.159741170639136E-014 */ 7350732955350452.0 / 633825300114114700748351602688.0, /* qExpTrail[ 2]:= 3.416187970930849E-015 */ 8661065463685896.0 / 2535301200456458802993406410752.0, /* qExpTrail[ 3]:= 3.695759744057116E-015 */ 4684932057853331.0 / 1267650600228229401496703205376.0, /* qExpTrail[ 4]:= 1.307016386977872E-014 */ 8284200537303158.0 / 633825300114114700748351602688.0, /* qExpTrail[ 5]:= 9.429976191419770E-015 */ 5976957489595592.0 / 633825300114114700748351602688.0, /* qExpTrail[ 6]:= 1.252362600256201E-014 */ 7937791009590795.0 / 633825300114114700748351602688.0, /* qExpTrail[ 7]:= 7.365764010895274E-015 */ 4668607584775442.0 / 633825300114114700748351602688.0, /* qExpTrail[ 8]:= 4.702756855740314E-015 */ 5961452550906630.0 / 1267650600228229401496703205376.0, /* qExpTrail[ 9]:= 2.365364347248530E-015 */ 5996911069096105.0 / 2535301200456458802993406410752.0, /* qExpTrail[10]:= 7.596096843369434E-015 */ 4814598361444511.0 / 633825300114114700748351602688.0, /* qExpTrail[11]:= 9.994675153757751E-015 */ 6334877978873592.0 / 633825300114114700748351602688.0, /* qExpTrail[12]:= 8.685122094871109E-015 */ 5504850118309409.0 / 633825300114114700748351602688.0, /* qExpTrail[13]:= 4.155018977496740E-016 */ 8427379681253482.0 / 20282409603651670423947251286016.0, /* qExpTrail[14]:= 9.180838285724313E-015 */ 5819047581748367.0 / 633825300114114700748351602688.0, /* qExpTrail[15]:= 1.042517908037209E-015 */ 5286193807488183.0 / 5070602400912917605986812821504.0, /* qExpTrail[16]:= 2.789906930890878E-015 */ 7073254391049437.0 / 2535301200456458802993406410752.0, /* qExpTrail[17]:= 1.151608187475169E-014 */ 7299184050403205.0 / 633825300114114700748351602688.0, /* qExpTrail[18]:= 1.519472288906291E-015 */ 7704639836248887.0 / 5070602400912917605986812821504.0, /* qExpTrail[19]:= 4.117201960800166E-015 */ 5219173536869173.0 / 1267650600228229401496703205376.0, /* qExpTrail[20]:= 6.074702681072822E-015 */ 7700600499869997.0 / 1267650600228229401496703205376.0, /* qExpTrail[21]:= 8.205513465754880E-015 */ 5200862035022496.0 / 633825300114114700748351602688.0, /* qExpTrail[22]:= 3.577420871370299E-015 */ 4534919714861555.0 / 1267650600228229401496703205376.0, /* qExpTrail[23]:= 6.338036743689160E-015 */ 8034416082406136.0 / 1267650600228229401496703205376.0, /* qExpTrail[24]:= 1.007399732183222E-014 */ 6385154375859097.0 / 633825300114114700748351602688.0, /* qExpTrail[25]:= 1.535798430292588E-015 */ 7787423207959887.0 / 5070602400912917605986812821504.0, /* qExpTrail[26]:= 6.246850344855366E-015 */ 7918823589191826.0 / 1267650600228229401496703205376.0, /* qExpTrail[27]:= 9.122056260354196E-015 */ 5781790046876837.0 / 633825300114114700748351602688.0, /* qExpTrail[28]:= 1.587143306717675E-015 */ 8047772661635512.0 / 5070602400912917605986812821504.0, /* qExpTrail[29]:= 6.822155118545929E-015 */ 8648109030874835.0 / 1267650600228229401496703205376.0, /* qExpTrail[30]:= 5.666960267488855E-015 */ 7183725584551774.0 / 1267650600228229401496703205376.0, /* qExpTrail[31]:= 8.960767791036668E-017 */ 7269838508040587.0 / 81129638414606681695789005144064.0 }; /* --------------------------------------------------------------------- */ /* ---- global constants and table values for q_lg1p and q_log -------- */ /* --------------------------------------------------------------------- */ /* qLogT1= 9.394130628134757E-001 */ double q_lgt1= 8461480639267491.0 / 9007199254740992.0; /* qLogT2= 1.064494458917860E+000 */ double q_lgt2= 4794056848520430.0 / 4503599627370496.0; /* qLogT3=-6.058693718652422E-002 */ double q_lgt3=-8731497847576004.0 / 144115188075855872.0; /* qLogT4= 6.449445891785943E-002 */ double q_lgt4= 4647315538398936.0 / 72057594037927936.0; /* qLogT5= 2^-53 = 1.110223024625157E-016 */ double q_lgt5= 4503599627370496.0 / 40564819207303340847894502572032.0; /* qLogT6= 2^55 = 3.60287970189639680E+016 */ double q_lgt6= 3.60287970189639680E+016; double q_lgb[2]={ /* qLogB[1]= 8.333333333326792E-002 */ 6004799503155948.0 / 72057594037927936.0, /* qLogB[2]= 1.250003418826767E-002 */ 7205779111987292.0 / 576460752303423488.0}; double q_lgc[4]={ /* qLogC[1]= 8.333333333333318E-002 */ 6004799503160650.0 / 72057594037927936.0, /* qLogC[2]= 1.250000000132536E-002 */ 7205759404556812.0 / 576460752303423488.0, /* qLogC[3]= 2.232141161100800E-003 */ 5146967091902417.0 / 2305843009213693952.0, /* qLogC[4]= 4.347221829254529E-004 */ 8019208851590178.0 / 18446744073709551616.0}; double q_lgld[129]={0.0, /* qLogLead [ 1]= 7.782140442941454E-003 = 3F7FE02A6B200000 */ 8972197068537856.0 / 1152921504606846976.0, /* qLogLead [ 2]= 1.550418653641827E-002 = 3F8FC0A8B1000000 */ 8937555034636288.0 / 576460752303423488.0, /* qLogLead [ 3]= 2.316705928205920E-002 = 3F97B91B07D80000 */ 6677450211196928.0 / 288230376151711744.0, /* qLogLead [ 4]= 3.077165866670839E-002 = 3F9F829B0E780000 */ 8869326752317440.0 / 288230376151711744.0, /* qLogLead [ 5]= 3.831886430270970E-002 = 3FA39E87BA000000 */ 5522330335838208.0 / 144115188075855872.0, /* qLogLead [ 6]= 4.580953603181115E-002 = 3FA77458F6340000 */ 6601849900892160.0 / 144115188075855872.0, /* qLogLead [ 7]= 5.324451451815548E-002 = 3FAB42DD71180000 */ 7673343223791616.0 / 144115188075855872.0, /* qLogLead [ 8]= 6.062462181580486E-002 = 3FAF0A30C0100000 */ 8736928775012352.0 / 144115188075855872.0, /* qLogLead [ 9]= 6.795066190898069E-002 = 3FB16536EEA40000 */ 4896361210445824.0 / 72057594037927936.0, /* qLogLead [ 10]= 7.522342123775161E-002 = 3FB341D7961C0000 */ 5420418749693952.0 / 72057594037927936.0, /* qLogLead [ 11]= 8.244366921098845E-002 = 3FB51B073F060000 */ 5940692447002624.0 / 72057594037927936.0, /* qLogLead [ 12]= 8.961215869021544E-002 = 3FB6F0D28AE60000 */ 6457236551761920.0 / 72057594037927936.0, /* qLogLead [ 13]= 9.672962645890948E-002 = 3FB8C345D6320000 */ 6970104154816512.0 / 72057594037927936.0, /* qLogLead [ 14]= 1.037967936808855E-001 = 3FBA926D3A4A0000 */ 7479347221495808.0 / 72057594037927936.0, /* qLogLead [ 15]= 1.108143663404917E-001 = 3FBC5E548F5C0000 */ 7985016623333376.0 / 72057594037927936.0, /* qLogLead [ 16]= 1.177830356555205E-001 = 3FBE27076E2A0000 */ 8487162167820288.0 / 72057594037927936.0, /* qLogLead [ 17]= 1.247034785010328E-001 = 3FBFEC9131DC0000 */ 8985832628944896.0 / 72057594037927936.0, /* qLogLead [ 18]= 1.315763577895268E-001 = 3FC0D77E7CD10000 */ 4740537887293440.0 / 36028797018963968.0, /* qLogLead [ 19]= 1.384023228583828E-001 = 3FC1B72AD52F0000 */ 4986469197217792.0 / 36028797018963968.0, /* qLogLead [ 20]= 1.451820098445751E-001 = 3FC29552F8200000 */ 5230733163495424.0 / 36028797018963968.0, /* qLogLead [ 21]= 1.519160420266417E-001 = 3FC371FC201F0000 */ 5473352242102272.0 / 36028797018963968.0, /* qLogLead [ 22]= 1.586050301757496E-001 = 3FC44D2B6CCB0000 */ 5714348438388736.0 / 36028797018963968.0, /* qLogLead [ 23]= 1.652495728958456E-001 = 3FC526E5E3A20000 */ 5953743319334912.0 / 36028797018963968.0, /* qLogLead [ 24]= 1.718502569274278E-001 = 3FC5FF3070A80000 */ 6191558024495104.0 / 36028797018963968.0, /* qLogLead [ 25]= 1.784076574731444E-001 = 3FC6D60FE71A0000 */ 6427813277728768.0 / 36028797018963968.0, /* qLogLead [ 26]= 1.849223384942889E-001 = 3FC7AB8902110000 */ 6662529397882880.0 / 36028797018963968.0, /* qLogLead [ 27]= 1.913948530000198E-001 = 3FC87FA065210000 */ 6895726309212160.0 / 36028797018963968.0, /* qLogLead [ 28]= 1.978257433293038E-001 = 3FC9525A9CF40000 */ 7127423551537152.0 / 36028797018963968.0, /* qLogLead [ 29]= 2.042155414292210E-001 = 3FCA23BC1FE30000 */ 7357640290271232.0 / 36028797018963968.0, /* qLogLead [ 30]= 2.105647691078048E-001 = 3FCAF3C94E810000 */ 7586395325530112.0 / 36028797018963968.0, /* qLogLead [ 31]= 2.168739383014326E-001 = 3FCBC286742E0000 */ 7813707101765632.0 / 36028797018963968.0, /* qLogLead [ 32]= 2.231435513149336E-001 = 3FCC8FF7C79B0000 */ 8039593716416512.0 / 36028797018963968.0, /* qLogLead [ 33]= 2.293741010653321E-001 = 3FCD5C216B500000 */ 8264072928690176.0 / 36028797018963968.0, /* qLogLead [ 34]= 2.355660713128600E-001 = 3FCE27076E2B0000 */ 8487162167885824.0 / 36028797018963968.0, /* qLogLead [ 35]= 2.417199368865113E-001 = 3FCEF0ADCBDC0000 */ 8708878541520896.0 / 36028797018963968.0, /* qLogLead [ 36]= 2.478361639041395E-001 = 3FCFB9186D5E0000 */ 8929238843260928.0 / 36028797018963968.0, /* qLogLead [ 37]= 2.539152099816420E-001 = 3FD0402594B50000 */ 4574129780228096.0 / 18014398509481984.0, /* qLogLead [ 38]= 2.599575244366861E-001 = 3FD0A324E2738000 */ 4682978440740864.0 / 18014398509481984.0, /* qLogLead [ 39]= 2.659635484978935E-001 = 3FD1058BF9AE8000 */ 4791173351636992.0 / 18014398509481984.0, /* qLogLead [ 40]= 2.719337154831010E-001 = 3FD1675CABAB8000 */ 4898722318876672.0 / 18014398509481984.0, /* qLogLead [ 41]= 2.778684510030871E-001 = 3FD1C898C1698000 */ 5005633009582080.0 / 18014398509481984.0, /* qLogLead [ 42]= 2.837681731307384E-001 = 3FD22941FBCF8000 */ 5111912955084800.0 / 18014398509481984.0, /* qLogLead [ 43]= 2.896332925829483E-001 = 3FD2895A13DE8000 */ 5217569554202624.0 / 18014398509481984.0, /* qLogLead [ 44]= 2.954642128934211E-001 = 3FD2E8E2BAE10000 */ 5322610076352512.0 / 18014398509481984.0, /* qLogLead [ 45]= 3.012613305781997E-001 = 3FD347DD9A988000 */ 5427041664532480.0 / 18014398509481984.0, /* qLogLead [ 46]= 3.070250352957373E-001 = 3FD3A64C55698000 */ 5530871338205184.0 / 18014398509481984.0, /* qLogLead [ 47]= 3.127557100033300E-001 = 3FD4043086868000 */ 5634105996115968.0 / 18014398509481984.0, /* qLogLead [ 48]= 3.184537311190070E-001 = 3FD4618BC21C8000 */ 5736752419209216.0 / 18014398509481984.0, /* qLogLead [ 49]= 3.241194686543167E-001 = 3FD4BE5F95778000 */ 5838817273020416.0 / 18014398509481984.0, /* qLogLead [ 50]= 3.297532863725792E-001 = 3FD51AAD872E0000 */ 5940307110526976.0 / 18014398509481984.0, /* qLogLead [ 51]= 3.353555419216718E-001 = 3FD5767717458000 */ 6041228374540288.0 / 18014398509481984.0, /* qLogLead [ 52]= 3.409265869704541E-001 = 3FD5D1BDBF580000 */ 6141587400163328.0 / 18014398509481984.0, /* qLogLead [ 53]= 3.464667673470103E-001 = 3FD62C82F2BA0000 */ 6241390417281024.0 / 18014398509481984.0, /* qLogLead [ 54]= 3.519764231568843E-001 = 3FD686C81E9B0000 */ 6340643552690176.0 / 18014398509481984.0, /* qLogLead [ 55]= 3.574558889213222E-001 = 3FD6E08EAA2B8000 */ 6439352832589824.0 / 18014398509481984.0, /* qLogLead [ 56]= 3.629054936900502E-001 = 3FD739D7F6BC0000 */ 6537524184612864.0 / 18014398509481984.0, /* qLogLead [ 57]= 3.683255611595087E-001 = 3FD792A55FDD8000 */ 6635163439955968.0 / 18014398509481984.0, /* qLogLead [ 58]= 3.737164097929053E-001 = 3FD7EAF83B828000 */ 6732276335542272.0 / 18014398509481984.0, /* qLogLead [ 59]= 3.790783529348118E-001 = 3FD842D1DA1E8000 */ 6828868516085760.0 / 18014398509481984.0, /* qLogLead [ 60]= 3.844116989112081E-001 = 3FD89A3386C18000 */ 6924945535893504.0 / 18014398509481984.0, /* qLogLead [ 61]= 3.897167511404405E-001 = 3FD8F11E87368000 */ 7020512860864512.0 / 18014398509481984.0, /* qLogLead [ 62]= 3.949938082405424E-001 = 3FD947941C210000 */ 7115575870423040.0 / 18014398509481984.0, /* qLogLead [ 63]= 4.002431641274597E-001 = 3FD99D9581180000 */ 7210139859288064.0 / 18014398509481984.0, /* qLogLead [ 64]= 4.054651081078191E-001 = 3FD9F323ECBF8000 */ 7304210039144448.0 / 18014398509481984.0, /* qLogLead [ 65]= 4.106599249844294E-001 = 3FDA484090E58000 */ 7397791540543488.0 / 18014398509481984.0, /* qLogLead [ 66]= 4.158278951435932E-001 = 3FDA9CEC9A9A0000 */ 7490889414475776.0 / 18014398509481984.0, /* qLogLead [ 67]= 4.209692946442374E-001 = 3FDAF12932478000 */ 7583508633976832.0 / 18014398509481984.0, /* qLogLead [ 68]= 4.260843953106814E-001 = 3FDB44F77BCC8000 */ 7675654095798272.0 / 18014398509481984.0, /* qLogLead [ 69]= 4.311734648181300E-001 = 3FDB985896930000 */ 7767330621947904.0 / 18014398509481984.0, /* qLogLead [ 70]= 4.362367667745275E-001 = 3FDBEB4D9DA70000 */ 7858542961164288.0 / 18014398509481984.0, /* qLogLead [ 71]= 4.412745608042314E-001 = 3FDC3DD7A7CD8000 */ 7949295790424064.0 / 18014398509481984.0, /* qLogLead [ 72]= 4.462871026280482E-001 = 3FDC8FF7C79A8000 */ 8039593716383744.0 / 18014398509481984.0, /* qLogLead [ 73]= 4.512746441396303E-001 = 3FDCE1AF0B860000 */ 8129441276755968.0 / 18014398509481984.0, /* qLogLead [ 74]= 4.562374334818742E-001 = 3FDD32FE7E010000 */ 8218842941685760.0 / 18014398509481984.0, /* qLogLead [ 75]= 4.611757151214988E-001 = 3FDD83E7258A0000 */ 8307803115094016.0 / 18014398509481984.0, /* qLogLead [ 76]= 4.660897299254430E-001 = 3FDDD46A04C20000 */ 8396326136053760.0 / 18014398509481984.0, /* qLogLead [ 77]= 4.709797152190731E-001 = 3FDE24881A7C8000 */ 8484416279838720.0 / 18014398509481984.0, /* qLogLead [ 78]= 4.758459048698569E-001 = 3FDE744261D68000 */ 8572077759430656.0 / 18014398509481984.0, /* qLogLead [ 79]= 4.806885293455707E-001 = 3FDEC399D2468000 */ 8659314726567936.0 / 18014398509481984.0, /* qLogLead [ 80]= 4.855078157816024E-001 = 3FDF128F5FAF0000 */ 8746131272957952.0 / 18014398509481984.0, /* qLogLead [ 81]= 4.903039880446158E-001 = 3FDF6123FA700000 */ 8832531431424000.0 / 18014398509481984.0, /* qLogLead [ 82]= 4.950772667980345E-001 = 3FDFAF588F790000 */ 8918519177084928.0 / 18014398509481984.0, /* qLogLead [ 83]= 4.998278695566114E-001 = 3FDFFD2E08580000 */ 9004098428338176.0 / 18014398509481984.0, /* qLogLead [ 84]= 5.045560107519123E-001 = 3FE02552A5A5C000 */ 4544636524019712.0 / 9007199254740992.0, /* qLogLead [ 85]= 5.092619017905236E-001 = 3FE04BDF9DA94000 */ 4587023422275584.0 / 9007199254740992.0, /* qLogLead [ 86]= 5.139457511013461E-001 = 3FE0723E5C1CC000 */ 4629211786297344.0 / 9007199254740992.0, /* qLogLead [ 87]= 5.186077642083546E-001 = 3FE0986F4F574000 */ 4671203467280384.0 / 9007199254740992.0, /* qLogLead [ 88]= 5.232481437651586E-001 = 3FE0BE72E4254000 */ 4713000290566144.0 / 9007199254740992.0, /* qLogLead [ 89]= 5.278670896204858E-001 = 3FE0E44985D1C000 */ 4754604056231936.0 / 9007199254740992.0, /* qLogLead [ 90]= 5.324647988691140E-001 = 3FE109F39E2D4000 */ 4796016539549696.0 / 9007199254740992.0, /* qLogLead [ 91]= 5.370414658973459E-001 = 3FE12F7195940000 */ 4837239491395584.0 / 9007199254740992.0, /* qLogLead [ 92]= 5.415972824321216E-001 = 3FE154C3D2F4C000 */ 4878274638692352.0 / 9007199254740992.0, /* qLogLead [ 93]= 5.461324375974073E-001 = 3FE179EABBD88000 */ 4919123684917248.0 / 9007199254740992.0, /* qLogLead [ 94]= 5.506471179523942E-001 = 3FE19EE6B467C000 */ 4959788310446080.0 / 9007199254740992.0, /* qLogLead [ 95]= 5.551415075406112E-001 = 3FE1C3B81F714000 */ 5000270172995584.0 / 9007199254740992.0, /* qLogLead [ 96]= 5.596157879353996E-001 = 3FE1E85F5E704000 */ 5040570908033024.0 / 9007199254740992.0, /* qLogLead [ 97]= 5.640701382853877E-001 = 3FE20CDCD192C000 */ 5080692129185792.0 / 9007199254740992.0, /* qLogLead [ 98]= 5.685047353526897E-001 = 3FE23130D7BEC000 */ 5120635428585472.0 / 9007199254740992.0, /* qLogLead [ 99]= 5.729197535620187E-001 = 3FE2555BCE990000 */ 5160402377310208.0 / 9007199254740992.0, /* qLogLead [100]= 5.773153650352469E-001 = 3FE2795E1289C000 */ 5199994525696000.0 / 9007199254740992.0, /* qLogLead [101]= 5.816917396350618E-001 = 3FE29D37FEC2C000 */ 5239413403729920.0 / 9007199254740992.0, /* qLogLead [102]= 5.860490450031648E-001 = 3FE2C0E9ED448000 */ 5278660521394176.0 / 9007199254740992.0, /* qLogLead [103]= 5.903874466021080E-001 = 3FE2E47436E40000 */ 5317737369042944.0 / 9007199254740992.0, /* qLogLead [104]= 5.947071077462169E-001 = 3FE307D7334F0000 */ 5356645417680896.0 / 9007199254740992.0, /* qLogLead [105]= 5.990081896452466E-001 = 3FE32B1339120000 */ 5395386119356416.0 / 9007199254740992.0, /* qLogLead [106]= 6.032908514389419E-001 = 3FE34E289D9D0000 */ 5433960907472896.0 / 9007199254740992.0, /* qLogLead [107]= 6.075552502243227E-001 = 3FE37117B5474000 */ 5472371197034496.0 / 9007199254740992.0, /* qLogLead [108]= 6.118015411066153E-001 = 3FE393E0D3564000 */ 5510618385104896.0 / 9007199254740992.0, /* qLogLead [109]= 6.160298772156239E-001 = 3FE3B6844A000000 */ 5548703850954752.0 / 9007199254740992.0, /* qLogLead [110]= 6.202404097512044E-001 = 3FE3D9026A714000 */ 5586628956471296.0 / 9007199254740992.0, /* qLogLead [111]= 6.244332880123693E-001 = 3FE3FB5B84D18000 */ 5624395046420480.0 / 9007199254740992.0, /* qLogLead [112]= 6.286086594227527E-001 = 3FE41D8FE8468000 */ 5662003448676352.0 / 9007199254740992.0, /* qLogLead [113]= 6.327666695706284E-001 = 3FE43F9FE2F9C000 */ 5699455474581504.0 / 9007199254740992.0, /* qLogLead [114]= 6.369074622361950E-001 = 3FE4618BC21C4000 */ 5736752419192832.0 / 9007199254740992.0, /* qLogLead [115]= 6.410311794206791E-001 = 3FE48353D1EA8000 */ 5773895561543680.0 / 9007199254740992.0, /* qLogLead [116]= 6.451379613736208E-001 = 3FE4A4F85DB04000 */ 5810886164889600.0 / 9007199254740992.0, /* qLogLead [117]= 6.492279466256150E-001 = 3FE4C679AFCD0000 */ 5847725477003264.0 / 9007199254740992.0, /* qLogLead [118]= 6.533012720119586E-001 = 3FE4E7D811B74000 */ 5884414730387456.0 / 9007199254740992.0, /* qLogLead [119]= 6.573580727090302E-001 = 3FE50913CC018000 */ 5920955142602752.0 / 9007199254740992.0, /* qLogLead [120]= 6.613984822452039E-001 = 3FE52A2D265BC000 */ 5957347916365824.0 / 9007199254740992.0, /* qLogLead [121]= 6.654226325445052E-001 = 3FE54B2467998000 */ 5993594239942656.0 / 9007199254740992.0, /* qLogLead [122]= 6.694306539429817E-001 = 3FE56BF9D5B40000 */ 6029695287296000.0 / 9007199254740992.0, /* qLogLead [123]= 6.734226752123504E-001 = 3FE58CADB5CD8000 */ 6065652218298368.0 / 9007199254740992.0, /* qLogLead [124]= 6.773988235909201E-001 = 3FE5AD404C358000 */ 6101466179010560.0 / 9007199254740992.0, /* qLogLead [125]= 6.813592248072382E-001 = 3FE5CDB1DC6C0000 */ 6137138301894656.0 / 9007199254740992.0, /* qLogLead [126]= 6.853040030982811E-001 = 3FE5EE02A9240000 */ 6172669705977856.0 / 9007199254740992.0, /* qLogLead [127]= 6.892332812385575E-001 = 3FE60E32F4478000 */ 6208061497114624.0 / 9007199254740992.0, /* qLogLead [128]= 6.931471805601177E-001 = 3FE62E42FEFA4000 */ 6243314768166912.0 / 9007199254740992.0}; double q_lgtl[129]={0.0, /* qLogTrail [ 1]=-8.865052917267247E-013 = BD6F30EE07912DF9 */ -8779523165335033.0 / 9903520314283042199192993792.0, /* qLogTrail [ 2]=-4.530198941364935E-013 = BD5FE0E183092C59 */ -8972983448710233.0 / 19807040628566084398385987584.0, /* qLogTrail [ 3]=-5.248209479295644E-013 = BD62772AB6C0559C */ -5197574919181724.0 / 9903520314283042199192993792.0, /* qLogTrail [ 4]= 4.529814257790929E-014 = 3D2980267C7E09E4 */ 7177777203513828.0 / 158456325028528675187087900672.0, /* qLogTrail [ 5]=-5.730994833076631E-013 = BD642A056FEA4DFD */ -5675702375042557.0 / 9903520314283042199192993792.0, /* qLogTrail [ 6]=-5.169456928812220E-013 = BD62303B9CB0D5E1 */ -5119582170830305.0 / 9903520314283042199192993792.0, /* qLogTrail [ 7]= 6.567993368985218E-013 = 3D671BEC28D14C7E */ 6504625575382142.0 / 9903520314283042199192993792.0, /* qLogTrail [ 8]= 6.299848199383311E-013 = 3D662A6617CC9717 */ 6239067461949207.0 / 9903520314283042199192993792.0, /* qLogTrail [ 9]=-4.729424109166329E-013 = BD60A3E2F3B47D18 */ -4683794773998872.0 / 9903520314283042199192993792.0, /* qLogTrail [ 10]=-1.640830158559866E-013 = BD4717B6B33E44F8 */ -6499997923034360.0 / 39614081257132168796771975168.0, /* qLogTrail [ 11]= 8.614512936087814E-014 = 3D383F69278E686A */ 6825120308815978.0 / 79228162514264337593543950336.0, /* qLogTrail [ 12]=-5.283050530808144E-013 = BD62968C836CC8C2 */ -5232079825324226.0 / 9903520314283042199192993792.0, /* qLogTrail [ 13]=-3.583666743009414E-013 = BD5937C294D2F567 */ -7098183277802855.0 / 19807040628566084398385987584.0, /* qLogTrail [ 14]= 7.581073923016376E-013 = 3D6AAC6CA17A4554 */ 7507931960067412.0 / 9903520314283042199192993792.0, /* qLogTrail [ 15]=-2.015736841601622E-013 = BD4C5E7514F4083F */ -7985156303620159.0 / 39614081257132168796771975168.0, /* qLogTrail [ 16]= 8.629474042969438E-013 = 3D6E5CBD3D50FFFC */ 8546217148612604.0 / 9903520314283042199192993792.0, /* qLogTrail [ 17]=-7.556920687451337E-014 = BD354555D1AE6607 */ -5987209403328007.0 / 79228162514264337593543950336.0, /* qLogTrail [ 18]=-8.075373495358435E-013 = BD6C69A65A23A170 */ -7997462545670512.0 / 9903520314283042199192993792.0, /* qLogTrail [ 19]= 7.363043577087051E-013 = 3D69E80A41811A39 */ 7292005164063289.0 / 9903520314283042199192993792.0, /* qLogTrail [ 20]=-7.718001336828099E-014 = BD35B967F4471DFC */ -6114830641995260.0 / 79228162514264337593543950336.0, /* qLogTrail [ 21]=-7.996871607743758E-013 = BD6C22F10C9A4EA8 */ -7919718041800360.0 / 9903520314283042199192993792.0, /* qLogTrail [ 22]= 8.890223439724663E-013 = 3D6F4799F4F6543E */ 8804450843382846.0 / 9903520314283042199192993792.0, /* qLogTrail [ 23]=-5.384682618788232E-013 = BD62F21746FF8A47 */ -5332731370113607.0 / 9903520314283042199192993792.0, /* qLogTrail [ 24]=-7.686134224018169E-013 = BD6B0B0DE3077D7E */ -7611978642587006.0 / 9903520314283042199192993792.0, /* qLogTrail [ 25]=-3.260571793105816E-013 = BD56F1B955C4D1DA */ -6458227797840346.0 / 19807040628566084398385987584.0, /* qLogTrail [ 26]=-2.768588431044831E-013 = BD537B720E4A694B */ -5483754353748299.0 / 19807040628566084398385987584.0, /* qLogTrail [ 27]=-3.903387893794952E-013 = BD5B77B7EFFB7F41 */ -7731456260144961.0 / 19807040628566084398385987584.0, /* qLogTrail [ 28]= 6.160755775588723E-013 = 3D65AD1D904C1D4E */ 6101316997487950.0 / 9903520314283042199192993792.0, /* qLogTrail [ 29]=-5.301565160060260E-013 = BD62A739B23B93E1 */ -5250415826015201.0 / 9903520314283042199192993792.0, /* qLogTrail [ 30]=-4.551124227747820E-013 = BD600349CC67F9B2 */ -4507215124232626.0 / 9903520314283042199192993792.0, /* qLogTrail [ 31]=-8.182853292737783E-013 = BD6CCA75818C5DBC */ -8103905381342652.0 / 9903520314283042199192993792.0, /* qLogTrail [ 32]=-7.238189921749681E-013 = BD697794F689F843 */ -7168356092868675.0 / 9903520314283042199192993792.0, /* qLogTrail [ 33]=-4.862400015383790E-013 = BD611BA91BBCA682 */ -4815487732852354.0 / 9903520314283042199192993792.0, /* qLogTrail [ 34]=-9.309459495196889E-014 = BD3A342C2AF0003C */ -7375713698054204.0 / 79228162514264337593543950336.0, /* qLogTrail [ 35]= 6.338907368997553E-013 = 3D664D948637950E */ 6277749789922574.0 / 9903520314283042199192993792.0, /* qLogTrail [ 36]= 4.417175537131555E-013 = 3D5F1546AAA3361C */ 8749117532747292.0 / 19807040628566084398385987584.0, /* qLogTrail [ 37]=-6.785208495970588E-013 = BD67DF928EC217A5 */ -6719745017649061.0 / 9903520314283042199192993792.0, /* qLogTrail [ 38]= 2.399954048421174E-013 = 3D50E35F73F7A018 */ 4753598734376984.0 / 19807040628566084398385987584.0, /* qLogTrail [ 39]=-7.555569400283742E-013 = BD6A9573B02FAA5A */ -7482673504168538.0 / 9903520314283042199192993792.0, /* qLogTrail [ 40]= 5.407904186145515E-013 = 3D630701CE63EAB9 */ 5355728896518841.0 / 9903520314283042199192993792.0, /* qLogTrail [ 41]= 3.692037508208009E-013 = 3D59FAFBC68E7540 */ 7312833692726592.0 / 19807040628566084398385987584.0, /* qLogTrail [ 42]=-9.383417223663700E-014 = BD3A6976F5EB0963 */ -7434309047355747.0 / 79228162514264337593543950336.0, /* qLogTrail [ 43]= 9.433398189512690E-014 = 3D3A8D7AD24C13F0 */ 7473908048204784.0 / 79228162514264337593543950336.0, /* qLogTrail [ 44]= 4.148131870425857E-013 = 3D5D309C2CC91A85 */ 8216221649017477.0 / 19807040628566084398385987584.0, /* qLogTrail [ 45]=-3.792316480209315E-014 = BD25594DD4C58092 */ -6009165327990930.0 / 158456325028528675187087900672.0, /* qLogTrail [ 46]=-8.254631387250040E-013 = BD6D0B1C68651946 */ -8174990963054918.0 / 9903520314283042199192993792.0, /* qLogTrail [ 47]= 5.668653582900739E-013 = 3D63F1DE86093EFA */ 5613962591289082.0 / 9903520314283042199192993792.0, /* qLogTrail [ 48]=-4.723727821986367E-013 = BD609EC17A426426 */ -4678153444418598.0 / 9903520314283042199192993792.0, /* qLogTrail [ 49]=-1.047575005877654E-013 = BD3D7C92CD9AD824 */ -8299744281155620.0 / 79228162514264337593543950336.0, /* qLogTrail [ 50]=-1.111867138955932E-013 = BD3F4BD8DB0A7CC1 */ -8809119037947073.0 / 79228162514264337593543950336.0, /* qLogTrail [ 51]=-5.339989292003297E-013 = BD62C9D5B2A49AF9 */ -5288469243140857.0 / 9903520314283042199192993792.0, /* qLogTrail [ 52]= 1.391284121219757E-013 = 3D4394A11B1C1EE4 */ 5511444222975716.0 / 39614081257132168796771975168.0, /* qLogTrail [ 53]=-8.017372713972018E-013 = BD6C356848506EAD */ -7940021354000045.0 / 9903520314283042199192993792.0, /* qLogTrail [ 54]= 2.939185918764800E-013 = 3D54AEC442BE1015 */ 5821657490788373.0 / 19807040628566084398385987584.0, /* qLogTrail [ 55]= 4.815896111723205E-013 = 3D60F1C609C98C6C */ 4769432497392748.0 / 9903520314283042199192993792.0, /* qLogTrail [ 56]=-6.817539406325327E-013 = BD67FCB18ED9D603 */ -6751764000396803.0 / 9903520314283042199192993792.0, /* qLogTrail [ 57]=-8.009990055432491E-013 = BD6C2EC1F512DC03 */ -7932709923118083.0 / 9903520314283042199192993792.0, /* qLogTrail [ 58]= 6.787566823158706E-013 = 3D67E1B259D2F3DA */ 6722080591770586.0 / 9903520314283042199192993792.0, /* qLogTrail [ 59]= 1.576120377396944E-013 = 3D462E927628CBC2 */ 6243656070122434.0 / 39614081257132168796771975168.0, /* qLogTrail [ 60]=-8.760375990774874E-013 = BD6ED2A52C73BF78 */ -8675856158539640.0 / 9903520314283042199192993792.0, /* qLogTrail [ 61]=-4.152515806343612E-013 = BD5D3881E8962A96 */ -8224904928701078.0 / 19807040628566084398385987584.0, /* qLogTrail [ 62]= 3.265569889690715E-013 = 3D56FABA4CDD147D */ 6468127548052605.0 / 19807040628566084398385987584.0, /* qLogTrail [ 63]=-4.470426501045244E-013 = BD5F753456D113B8 */ -8854591933322168.0 / 19807040628566084398385987584.0, /* qLogTrail [ 64]= 3.452764795203977E-013 = 3D584BF2B68D766F */ 6838905257948783.0 / 19807040628566084398385987584.0, /* qLogTrail [ 65]= 8.390050778518307E-013 = 3D6D8515FE535B87 */ 8309103832292231.0 / 9903520314283042199192993792.0, /* qLogTrail [ 66]= 1.177697875136921E-013 = 3D40931A909FEA5E */ 4665341932202590.0 / 39614081257132168796771975168.0, /* qLogTrail [ 67]=-1.077434146160958E-013 = BD3E53BB31EED7A9 */ -8536312763045801.0 / 79228162514264337593543950336.0, /* qLogTrail [ 68]= 2.186334329321591E-013 = 3D4EC5197DDB55D3 */ 8660962577700307.0 / 39614081257132168796771975168.0, /* qLogTrail [ 69]= 2.413263949133313E-013 = 3D50FB598FB14F89 */ 4779961708793737.0 / 19807040628566084398385987584.0, /* qLogTrail [ 70]= 3.905746220983070E-013 = 3D5B7BF7861D37AC */ 7736127408388012.0 / 19807040628566084398385987584.0, /* qLogTrail [ 71]= 6.437879097373207E-013 = 3D66A6B9D9E0A5BD */ 6375766642173373.0 / 9903520314283042199192993792.0, /* qLogTrail [ 72]= 3.713514191959202E-013 = 3D5A21AC25D81EF3 */ 7355372647489267.0 / 19807040628566084398385987584.0, /* qLogTrail [ 73]=-1.716692133608243E-013 = BD48290905A86AA6 */ -6800518167423654.0 / 39614081257132168796771975168.0, /* qLogTrail [ 74]=-2.865828515791435E-013 = BD542A9E21373414 */ -5676358184678420.0 / 19807040628566084398385987584.0, /* qLogTrail [ 75]= 6.713692791384601E-013 = 3D679F2828ADD176 */ 6648919294333302.0 / 9903520314283042199192993792.0, /* qLogTrail [ 76]=-8.437281040871276E-013 = BD6DAFA08CECADB1 */ -8355878418558385.0 / 9903520314283042199192993792.0, /* qLogTrail [ 77]=-2.821014384618127E-013 = BD53D9E34270BA6B */ -5587594652990059.0 / 19807040628566084398385987584.0, /* qLogTrail [ 78]= 1.070193176211425E-013 = 3D3E1F8DF68DBCF3 */ 8478943888653555.0 / 79228162514264337593543950336.0, /* qLogTrail [ 79]= 1.811934636644111E-013 = 3D49802EB9DCA7E7 */ 7177812592863207.0 / 39614081257132168796771975168.0, /* qLogTrail [ 80]= 9.840465278232627E-014 = 3D3BB2CD720EC44C */ 7796419822797900.0 / 79228162514264337593543950336.0, /* qLogTrail [ 81]= 5.780031989454028E-013 = 3D645630A2B61E5B */ 5724266422476379.0 / 9903520314283042199192993792.0, /* qLogTrail [ 82]=-1.830285735604167E-013 = BD49C24CA098362B */ -7250508785399339.0 / 39614081257132168796771975168.0, /* qLogTrail [ 83]=-1.620740015674495E-013 = BD46CF54D05F9367 */ -6420412667761511.0 / 39614081257132168796771975168.0, /* qLogTrail [ 84]= 4.830331494955320E-013 = 3D60FEC69C695D7F */ 4783728608501119.0 / 9903520314283042199192993792.0, /* qLogTrail [ 85]=-7.156055317238212E-013 = BD692D9A033EFF75 */ -7087013920440181.0 / 9903520314283042199192993792.0, /* qLogTrail [ 86]= 8.882123951857185E-013 = 3D6F404E57963891 */ 8796429499119761.0 / 9903520314283042199192993792.0, /* qLogTrail [ 87]=-3.090058051323824E-013 = BD55BE8DC04AD601 */ -6120490536719873.0 / 19807040628566084398385987584.0, /* qLogTrail [ 88]=-6.107655197285150E-013 = BD657D49676844CC */ -6048728731894988.0 / 9903520314283042199192993792.0, /* qLogTrail [ 89]= 3.565996966334783E-013 = 3D5917EDD5CBBD2D */ 7063184679353645.0 / 19807040628566084398385987584.0, /* qLogTrail [ 90]= 3.578239659127638E-013 = 3D592DFBC7D93617 */ 7087433830708759.0 / 19807040628566084398385987584.0, /* qLogTrail [ 91]=-4.622608700154458E-013 = BD6043ACFEDCE638 */ -4578009916696120.0 / 9903520314283042199192993792.0, /* qLogTrail [ 92]= 6.227976291722515E-013 = 3D65E9A98F33A396 */ 6167888972194710.0 / 9903520314283042199192993792.0, /* qLogTrail [ 93]= 7.283894727206574E-013 = 3D69A0BFC60E6FA0 */ 7213619939798944.0 / 9903520314283042199192993792.0, /* qLogTrail [ 94]= 2.680964661521167E-013 = 3D52DD98B97BAEF0 */ 5310197597449968.0 / 19807040628566084398385987584.0, /* qLogTrail [ 95]=-1.096082504605928E-013 = BD3EDA1B58389902 */ -8684060280396034.0 / 79228162514264337593543950336.0, /* qLogTrail [ 96]= 2.311949383800538E-014 = 3D1A07BD8B34BE7C */ 7326860060180092.0 / 316912650057057350374175801344.0, /* qLogTrail [ 97]=-5.846905800529924E-013 = BD64926CAFC2F08A */ -5790495037124746.0 / 9903520314283042199192993792.0, /* qLogTrail [ 98]=-2.103748251144494E-014 = BD17AFA4392F1BA7 */ -6667044333231015.0 / 316912650057057350374175801344.0, /* qLogTrail [ 99]=-2.332318294558741E-013 = BD506987F78A4A5E */ -4619632321907294.0 / 19807040628566084398385987584.0, /* qLogTrail [100]=-4.233369428814192E-013 = BD5DCA290F81848D */ -8385052027225229.0 / 19807040628566084398385987584.0, /* qLogTrail [101]=-4.393393796973784E-013 = BD5EEA6F465268B4 */ -8702012943394996.0 / 19807040628566084398385987584.0, /* qLogTrail [102]= 4.134164707383556E-013 = 3D5D1772F5386374 */ 8188556832433012.0 / 19807040628566084398385987584.0, /* qLogTrail [103]= 6.841763641591467E-014 = 3D334202A10C3491 */ 5420603616801937.0 / 79228162514264337593543950336.0, /* qLogTrail [104]= 4.758553400443064E-013 = 3D60BE1FB590A1F5 */ 4712643026788853.0 / 9903520314283042199192993792.0, /* qLogTrail [105]= 8.367967867475769E-013 = 3D6D71320556B67B */ 8287233976481403.0 / 9903520314283042199192993792.0, /* qLogTrail [106]=-8.576373464665864E-013 = BD6E2CE9146D277A */ -8493628883019642.0 / 9903520314283042199192993792.0, /* qLogTrail [107]= 2.191328122934009E-013 = 3D4ED71774092113 */ 8680745032294675.0 / 39614081257132168796771975168.0, /* qLogTrail [108]=-6.224284253643115E-013 = BD65E6563BBD9FC9 */ -6164232554782665.0 / 9903520314283042199192993792.0, /* qLogTrail [109]=-1.098359432543843E-013 = BD3EEA838909F3D3 */ -8702099962065875.0 / 79228162514264337593543950336.0, /* qLogTrail [110]= 6.531043137763365E-013 = 3D66FAA404263D0B */ 6468031838829835.0 / 9903520314283042199192993792.0, /* qLogTrail [111]=-4.758019902171077E-013 = BD60BDA4B162AFA3 */ -4712114675691427.0 / 9903520314283042199192993792.0, /* qLogTrail [112]=-3.785425126545704E-013 = BD5AA33736867A17 */ -7497806927788567.0 / 19807040628566084398385987584.0, /* qLogTrail [113]= 4.093923321867867E-013 = 3D5CCEF4E4F736C2 */ 8108850556647106.0 / 19807040628566084398385987584.0, /* qLogTrail [114]= 8.742438391485829E-013 = 3D6EC27D0B7B37B3 */ 8658091620644787.0 / 9903520314283042199192993792.0, /* qLogTrail [115]= 2.521818845684288E-013 = 3D51BEE7ABD17660 */ 4994976833435232.0 / 19807040628566084398385987584.0, /* qLogTrail [116]=-3.608131360422557E-014 = BD244FDD840B8591 */ -5717312355927441.0 / 158456325028528675187087900672.0, /* qLogTrail [117]=-5.051855592428090E-013 = BD61C64E971322CE */ -5003115448443598.0 / 9903520314283042199192993792.0, /* qLogTrail [118]= 7.869940332335532E-013 = 3D6BB09CB0985646 */ 7794011395348038.0 / 9903520314283042199192993792.0, /* qLogTrail [119]=-6.702087696194906E-013 = BD6794B434C5A4F5 */ -6637426164737269.0 / 9903520314283042199192993792.0, /* qLogTrail [120]= 1.610857575393246E-013 = 3D46ABB9DF22BC57 */ 6381264288529495.0 / 39614081257132168796771975168.0, /* qLogTrail [121]= 5.852718843625151E-013 = 3D6497A915428B44 */ 5796251996162884.0 / 9903520314283042199192993792.0, /* qLogTrail [122]=-3.524675729790479E-013 = BD58CD7DC73BD194 */ -6981339538248084.0 / 19807040628566084398385987584.0, /* qLogTrail [123]=-1.837208449562906E-013 = BD49DB3DB43689B4 */ -7277932480727476.0 / 39614081257132168796771975168.0, /* qLogTrail [124]= 8.860668981349492E-013 = 3D6F2CFB29AAA5F0 */ 8775181525493232.0 / 9903520314283042199192993792.0, /* qLogTrail [125]= 6.648626807146870E-013 = 3D67648CF6E3C5D7 */ 6584481064666583.0 / 9903520314283042199192993792.0, /* qLogTrail [126]= 6.383161517064652E-013 = 3D667570D6095FD2 */ 6321576975359954.0 / 9903520314283042199192993792.0, /* qLogTrail [127]= 2.514423072837607E-013 = 3D51B194F912B417 */ 4980327996109847.0 / 19807040628566084398385987584.0, /* qLogTrail [128]=-1.723944452561483E-013 = BD48432A1B0E2634 */ -6829247562655284.0 / 39614081257132168796771975168.0}; /* --------------------------------------------------------------------- */ /* ---- global constants and table values for q_atan ------------------ */ /* --------------------------------------------------------------------- */ double q_atnt=1.807032e-8; /* for |x|<=q_atnt approx. x=arctan(x) */ /* used in q_atan, q_atn1, j_atan, q_asin, */ /* j_asin, ... */ double q_atna[7]={0, 8960721713639278.0 / 36028797018963968.0, /* = 0.24871... */ 8960721713639278.0 / 18014398509481984.0, /* = 0.49742... */ 6720541285229458.0 / 9007199254740992.0, /* = 0.74613... */ 8960721713639278.0 / 9007199254740992.0, /* = 0.99484... */ 5600451071024549.0 / 4503599627370496.0, /* = 1.24355... */ 6720541285229458.0 / 4503599627370496.0}; /* = 1.49226... */ double q_atnb[8]={0, 4503599627370496.0 / 36028797018963968.0, /* = 0.12500... */ 7050717449407908.0 / 18014398509481984.0, /* = 0.39139... */ 6454487157372003.0 / 9007199254740992.0, /* = 0.71659... */ 5343484307627230.0 / 4503599627370496.0, /* = 1.18649... */ 4642583338069965.0 / 2251799813685248.0, /* = 2.06172... */ 5472919125137495.0 / 1125899906842624.0, /* = 4.86093... */ 4503599627370496.0 / 562949953421312.0}; /* = 8.00000... */ double q_atnc[7]={0, 4575085335741456.0 / 18014398509481984.0, /* = 0.25397... */ 4890523484394786.0 / 9007199254740992.0, /* = 0.54296... */ 8326197945442628.0 / 9007199254740992.0, /* = 0.92439... */ 6934969934934130.0 / 4503599627370496.0, /* = 1.53987... */ 6633650527568543.0 / 2251799813685248.0, /* = 2.94593... */ 7153270512133541.0 / 562949953421312.0}; /* = 12.70676... */ double q_atnd[6]={ -6004799503160653.0 / 18014398509481984.0, /* = -0.33333... */ 7205759403717662.0 / 36028797018963968.0, /* = 0.20000... */ -5146970946471129.0 / 36028797018963968.0, /* = -0.14286... */ 8006368526669049.0 / 72057594037927936.0, /* = 0.11111... */ -6546869189017288.0 / 72057594037927936.0, /* = -0.09086... */ 5323534481176937.0 / 72057594037927936.0}; /* = 0.07388... */ /* --------------------------------------------------------------------- */ /* ---- global constants for q_sin and q_cos --------------------------- */ /* --------------------------------------------------------------------- */ double q_sinc[6]={ 6004799503160652.0 / 144115188075855872.0, -6405119470031391.0 / 4611686018427387904.0, 7320136533669489.0 / 295147905179352825856.0, -5205429515405659.0 / 18889465931478580854784.0, 5047441620321680.0 / 2417851639229258349412352.0, -7031457305697611.0 / 618970019642690137449562112.0}; double q_sins[6]={ -6004799503160666.0 / 36028797018963968.0, 4803839602527639.0 / 576460752303423488.0, -7320136535288236.0 / 36893488147419103232.0, 6506787178212600.0 / 2361183241434822606848.0, -7571207865408408.0 / 302231454903657293676544.0, 6155219321001458.0 / 38685626227668133590597632.0}; double q_sint[5]={ 4704863629888981.0 / 9007199254740992.0, 4600683640854786.0 / 18014398509481984.0, 7074237750381340.0 / 2097152.0, 7800291619608491.0 / 302231454903657293676544.0, /* 2.580900000000000E-008 */ 5515724051991746.0 / 302231454903657293676544.0 /* 1.825000000000000E-008 */ }; /* q_sint[2]= 3.373259425345106E+009 */ /* --------------------------------------------------------------------- */ /* ---- global constants for q_atnh ------------------------------------ */ /* --------------------------------------------------------------------- */ /* q_at3i = 3.333333333333333E-001 */ double q_at3i = 6004799503160661.0 / 18014398509481984.0; /* ------------------------------------------------------------------- */ /* ---- global constants for the errorfunctions ------ */ /* ------------------------------------------------------------------- */ /* ---- worst case relative error bound for q_erf and q_erfc ---- */ /* eps(q_erf) = 2.8452e-15 */ /* q_erfm = 1 - eps(q_erf) = 9.999999999999969e-001 */ double q_erfm = 9007199254740964.0 / 9007199254740992.0; /* q_erfp = 1 + eps(q_erf) = 1.000000000000003e+000 */ double q_erfp = 4503599627370510.0 / 4503599627370496.0; /* eps(q_erfc) = 6.1641e-15 */ /* q_efcm = 1 - eps(q_erfc) = 9.999999999999936e-001 */ double q_efcm = 9007199254740934.0 / 9007199254740992.0; /* q_efcp = 1 + eps(q_erfc) = 1.000000000000006e+000 */ double q_efcp = 4503599627370525.0 / 4503599627370496.0; double q_erft[7]={ 0.0, 1.97193e-308, /*1.00000000000000003643E-010 = */ 7737125245533627.0 / 77371252455336267000000000.0, /*6.50000000000000022204E-001 = */ 5854679515581645.0 / 9007199254740992.0, /*2.64999999999999991118E+000 = */ 5967269506265907.0 / 2251799813685248.0, 8.0, /*2.65432500000000004547E+001 = */ 7471260675575120.0 / 281474976710656.0}; /* ---------- rational approximation in A2 = [1e-10, 0.65] ----------- */ double q_epA2[5]={ /*1.12837916709551255856e+000 = */ 5081767996463981.0 / 4503599627370496.0, /*1.35895070707443554880e-001 = */ 4896135918396240.0 / 36028797018963968.0, /*4.03259658325609282592e-002 = */ 5811584150300056.0 / 144115188075855872.0, /*1.20339912078812403921e-003 = */ 5549698899926403.0 / 4611686018427387904.0, /*6.49254346257748833756e-005 = */ 4790651505664119.0 / 73786976294838206000.0 }; double q_eqA2[5]={ /*1.00000000000000000000e+000 = */ 1.0, /*4.53767204030574855533e-001 = */ 8174343243940195.0 / 18014398509481984.0, /*8.69936913926476762526e-002 = */ 6268556098232192.0 / 72057594037927936.0, /*8.49718523810939763141e-003 = */ 4898293794822088.0 / 576460752303423488.0, /*3.64916054139638153589e-004 = */ 6731513059101844.0 / 18446744073709552000.0 }; /* --------- rational approximation in B1 = [0.65, 2.65] ------------ */ double q_epB1[7]={ /*9.99999995053825307956e-001 = */ 9007199210189811.0 / 9007199254740992.0, /*1.29137515241946498890e+000 = */ 5815836655231820.0 / 4503599627370496.0, /*8.33965460258685453709e-001 = */ 7511693072121760.0 / 9007199254740992.0, /*3.07821064389492415891e-001 = */ 5545211323525230.0 / 18014398509481984.0, /*6.45809354861053702690e-002 = */ 4653546831847395.0 / 72057594037927936.0, /*6.19734297263174228887e-003 = */ 7145049984571258.0 / 1152921504606846976.0, /*2.42699360423408255789e-008 = */ 7335138080495378.0 / 302231454903657290000000.0 }; double q_eqB1[7]={ /*1.00000000000000000000e+000 = */ 1.0, /*2.41975425418358591756e+000 = */ 5448802178734685.0 / 2251799813685248.0, /*2.56436615659663313949e+000 = */ 5774439233645054.0 / 2251799813685248.0, /*1.53389534613813460773e+000 = */ 6908050509293041.0 / 4503599627370496.0, /*5.51301602659725609179e-001 = */ 4965683384614195.0 / 9007199254740992.0, /*1.14445507239651106390e-001 = */ 8246667900139522.0 / 72057594037927936.0, /*1.09858799707619209790e-002 = */ 6332928632660529.0 / 576460752303423488.0 }; /* --------- rational approximation in B2 = [2.65, 8.0] ------------- */ double q_epB2[6]={ /*9.99652529969472625204e-001 = */ 9004069522940981.0 / 9007199254740992.0, /*1.70250355161751087962e+000 = */ 7667394360661568.0 / 4503599627370496.0, /*1.38625072852174180404e+000 = */ 6243118264412595.0 / 4503599627370496.0, /*6.69754557785788517954e-001 = */ 6032612753747537.0 / 9007199254740992.0, /*1.90685363469095009448e-001 = */ 6870164254915391.0 / 36028797018963968.0, /*3.08079405409659168313e-002 = */ 8879784290582176.0 / 288230376151711744.0 }; double q_eqB2[7]={ /*1.00000000000000000000e+000 = */ 1.0, /*2.82886373185141204445e+000 = */ 6370034824323965.0 / 2251799813685248.0, /*3.58414377512046788965e+000 = */ 8070774285037411.0 / 2251799813685248.0, /*2.62603304307128482264e+000 = */ 5913300717119224.0 / 2251799813685248.0, /*1.21441313373848980284e+000 = */ 5469230536578499.0 / 4503599627370496.0, /*3.37980964348375101380e-001 = */ 6088523780390652.0 / 18014398509481984.0, /*5.46056535072178828027e-002 = */ 7869504025197724.0 / 144115188075855872.0 }; /* --------- rational approximation in B3 = [8.0, 26.54325] --------- */ double q_epB3[5]={ /*5.64189583547756279280e-001 = */ 5081767996463981.0 / 9007199254740992.0, /*9.21322629916612534373e+000 = */ 5186585315975577.0 / 562949953421312.0, /*4.22557691999395714788e+001 = */ 5946970825721923.0 / 140737488355328.0, /*5.52670521664883693802e+001 = */ 7778146110714462.0 / 140737488355328.0, /*9.95533599990016782044e+000 = */ 5604355937437310.0 / 562949953421312.0 }; double q_eqB3[5]={ /*1.00000000000000000000e+000 = */ 1.0, /*1.68300184332209603610e+001 = */ 4737229046530781.0 / 281474976710656.0, /*8.25614100580297787246e+001 = */ 5809742743320713.0 / 70368744177664.0, /*1.28491490639781432037e+002 = */ 4520892416918744.0 / 35184372088832.0, /*4.49638472416869063863e+001 = */ 6328098927587658.0 / 140737488355328.0 }; /* -------- constants for the function e^(-z*z), z is integer -------- */ double q_expz[28] = { 1.0, .3678794411714423215955238, .1831563888873418029371802e-1, .1234098040866795494976367e-3, .1125351747192591145137752e-6, .1388794386496402059466176e-10, .2319522830243569388312264e-15, .5242885663363463937171805e-21, .1603810890548637852976087e-27, .6639677199580734400702255e-35, .3720075976020835962959696e-43, .2820770088460135401118447e-52, .2894640311648300280293837e-62, .4020060215743355247830339e-73, .7555819019711960355051515e-85, .1921947727823849068480597e-97, .6616261056709485261029531e-111, .3082440696949098412671082e-125, .1943514850049292733293510e-140, .1658410477681145141135306e-156, .1915169596714005695019840e-173, .2993184452260192731479412e-191, .6330977336210591368573409e-210, .1812254025793992329712749e-229, .7020667798504734713841204e-250, .3680855854801800602843630e-271, .2611741761284055470541587e-293, .4626391858469564202755058e-297 };