13 April 2013 1:00:49.195 PM SPECFUN_PRB2 FORTRAN77 version Test the SPECFUN library. TEST01: BESI0 computes the Bessel I0 function. BESSEL_I0_VALUES returns selected values. X FX FX2 (table) (BESI0) 0.00000000 1.000000000000000 1.000000000000000 0.20000000 1.010025027795146 1.010025027795146 0.40000000 1.040401782229341 1.040401782229341 0.60000000 1.092045364317340 1.092045364317339 0.80000000 1.166514922869803 1.166514922869803 1.00000000 1.266065877752008 1.266065877752008 1.20000000 1.393725584134064 1.393725584134064 1.40000000 1.553395099731217 1.553395099731216 1.60000000 1.749980639738909 1.749980639738909 1.80000000 1.989559356618051 1.989559356618051 2.00000000 2.279585302336067 2.279585302336067 2.50000000 3.289839144050123 3.289839144050123 3.00000000 4.880792585865024 4.880792585865024 3.50000000 7.378203432225480 7.378203432225480 4.00000000 11.30192195213633 11.30192195213633 4.50000000 17.48117185560928 17.48117185560928 5.00000000 27.23987182360445 27.23987182360445 6.00000000 67.23440697647798 67.23440697647796 8.00000000 427.5641157218048 427.5641157218047 10.00000000 2815.716628466254 2815.716628466254 TEST02: RIBESL returns values of Bessel functsions of non-integer order. BESSEL_I0_SPHERICAL_VALUES returns values of the spherical Bessel i0 function. X FX FX2 (table) (RIBESL) 0.1000000000000000 1.001667500198440 1.001667500198440 0.2000000000000000 1.006680012705470 1.006680012705470 0.4000000000000000 1.026880814507039 1.026880814507039 0.6000000000000000 1.061089303580402 1.061089303580402 0.8000000000000000 1.110132477734529 1.110132477734529 1.0000000000000000 1.175201193643801 1.175201193643801 1.2000000000000000 1.257884462843477 1.257884462843477 1.3999999999999999 1.360215358179667 1.360215358179667 1.6000000000000001 1.484729970750144 1.484729970750144 1.8000000000000000 1.634541271164267 1.634541271164267 2.0000000000000000 1.813430203923509 1.813430203923509 2.2000000000000002 2.025956895698133 2.025956895698133 2.3999999999999999 2.277595505698373 2.277595505698372 2.6000000000000001 2.574897010920645 2.574897010920645 2.7999999999999998 2.925685126512827 2.925685126512827 3.0000000000000000 3.339291642469967 3.339291642469967 3.2000000000000002 3.826838748926716 3.826838748926717 3.3999999999999999 4.401577467270101 4.401577467270101 3.6000000000000001 5.079293155726485 5.079293155726487 3.7999999999999998 5.878791279137455 5.878791279137454 4.0000000000000000 6.822479299281938 6.822479299281937 TEST03: BESI1 computes the Bessel I1 function. BESSEL_I1_VALUES returns selected values. X FX FX2 (table) (BESI1) 0.00000000 0.000000000000000 0.000000000000000 0.20000000 0.1005008340281251 0.1005008340281251 0.40000000 0.2040267557335706 0.2040267557335706 0.60000000 0.3137040256049221 0.3137040256049221 0.80000000 0.4328648026206398 0.4328648026206398 1.00000000 0.5651591039924850 0.5651591039924849 1.20000000 0.7146779415526431 0.7146779415526432 1.40000000 0.8860919814143274 0.8860919814143273 1.60000000 1.084810635129880 1.084810635129880 1.80000000 1.317167230391899 1.317167230391899 2.00000000 1.590636854637329 1.590636854637329 2.50000000 2.516716245288698 2.516716245288698 3.00000000 3.953370217402609 3.953370217402608 3.50000000 6.205834922258365 6.205834922258364 4.00000000 9.759465153704451 9.759465153704447 4.50000000 15.38922275373592 15.38922275373592 5.00000000 24.33564214245053 24.33564214245052 6.00000000 61.34193677764024 61.34193677764024 8.00000000 399.8731367825601 399.8731367825602 10.00000000 2670.988303701255 2670.988303701254 TEST04: RIBESL returns values of Bessel functsions of non-integer order. BESSEL_I1_SPHERICAL_VALUES returns values of the spherical Bessel i1 function. X FX FX2 (table) (RIBESL) 0.1000000000000000 0.3336667857363341E-01 0.3336667857363342E-01 0.2000000000000000 0.6693371456802955E-01 0.6693371456802953E-01 0.4000000000000000 0.1354788933285401 0.1354788933285401 0.6000000000000000 0.2072931911031093 0.2072931911031093 0.8000000000000000 0.2841280857128948 0.2841280857128948 1.0000000000000000 0.3678794411714423 0.3678794411714422 1.2000000000000000 0.4606425870674146 0.4606425870674146 1.3999999999999999 0.5647736480096238 0.5647736480096237 1.6000000000000001 0.6829590627779635 0.6829590627779635 1.8000000000000000 0.8182955028627777 0.8182955028627776 2.0000000000000000 0.9743827435800611 0.9743827435800606 2.2000000000000002 1.155432469636406 1.155432469636406 2.3999999999999999 1.366396525527973 1.366396525527972 2.6000000000000001 1.613118767572064 1.613118767572064 2.7999999999999998 1.902515460838681 1.902515460838681 3.0000000000000000 2.242790117769266 2.242790117769266 3.2000000000000002 2.643689828630357 2.643689828630357 3.3999999999999999 3.116811526884873 3.116811526884873 3.6000000000000001 3.675968313148932 3.675968313148932 3.7999999999999998 4.337627987747642 4.337627987747640 4.0000000000000000 5.121438384183637 5.121438384183637 TEST05: RIBESL computes values of Bessel functions of NONINTEGER order. BESSEL_IX_VALUES returns selected values of the Bessel function In for NONINTEGER order. ALPHA X FX FX2 (table) (RIBESL) 0.50000000 0.20000000 0.3592084175833614 0.3592084175833614 0.50000000 1.00000000 0.9376748882454876 0.9376748882454875 0.50000000 2.00000000 2.046236863089055 2.046236863089054 0.50000000 2.50000000 3.053093538196718 3.053093538196719 0.50000000 3.00000000 4.614822903407601 4.614822903407601 0.50000000 5.00000000 26.47754749755907 26.47754749755907 0.50000000 10.00000000 2778.784603874571 2778.784603874571 0.50000000 20.00000000 43279746.27242893 43279746.27242893 1.50000000 1.00000000 0.2935253263474798 0.2935253263474797 1.50000000 2.00000000 1.099473188633110 1.099473188633109 1.50000000 5.00000000 21.18444226479414 21.18444226479414 1.50000000 10.00000000 2500.906154942118 2500.906154942118 1.50000000 50.00000000 0.2866653715931464E+21 0.2866653715931463E+21 2.50000000 1.00000000 0.5709890920304825E-01 0.5709890920304823E-01 2.50000000 2.00000000 0.3970270801393905 0.3970270801393904 2.50000000 5.00000000 13.76688213868258 13.76688213868258 2.50000000 10.00000000 2028.512757391936 2028.512757391936 2.50000000 50.00000000 0.2753157630035402E+21 0.2753157630035401E+21 1.25000000 1.00000000 0.4139416015642352 0.4139416015642352 1.25000000 2.00000000 1.340196758982897 1.340196758982897 1.25000000 5.00000000 22.85715510364670 22.85715510364670 1.25000000 10.00000000 2593.006763432002 2593.006763432002 1.25000000 50.00000000 0.2886630075077766E+21 0.2886630075077766E+21 2.75000000 1.00000000 0.3590910483251082E-01 0.3590910483251082E-01 2.75000000 2.00000000 0.2931108636266483 0.2931108636266483 2.75000000 5.00000000 11.99397010023068 11.99397010023068 2.75000000 10.00000000 1894.575731562383 1894.575731562383 2.75000000 50.00000000 0.2716911375760483E+21 0.2716911375760485E+21 TEST06: BESJ0 computes the Bessel J0 function. BESSEL_J0_VALUES returns selected values. X FX FX2 (table) (BESJ0) -5.00000000 -0.1775967713143383 -0.1775967713143383 -4.00000000 -0.3971498098638474 -0.3971498098638474 -3.00000000 -0.2600519549019334 -0.2600519549019335 -2.00000000 0.2238907791412357 0.2238907791412357 -1.00000000 0.7651976865579666 0.7651976865579666 0.00000000 1.000000000000000 1.000000000000000 1.00000000 0.7651976865579666 0.7651976865579666 2.00000000 0.2238907791412357 0.2238907791412357 3.00000000 -0.2600519549019334 -0.2600519549019335 4.00000000 -0.3971498098638474 -0.3971498098638474 5.00000000 -0.1775967713143383 -0.1775967713143383 6.00000000 0.1506452572509969 0.1506452572509970 7.00000000 0.3000792705195556 0.3000792705195556 8.00000000 0.1716508071375539 0.1716508071375539 9.00000000 -0.9033361118287613E-01 -0.9033361118287614E-01 10.00000000 -0.2459357644513483 -0.2459357644513483 11.00000000 -0.1711903004071961 -0.1711903004071961 12.00000000 0.4768931079683354E-01 0.4768931079683354E-01 13.00000000 0.2069261023770678 0.2069261023770678 14.00000000 0.1710734761104587 0.1710734761104586 15.00000000 -0.1422447282678077E-01 -0.1422447282678077E-01 TEST07: BESJ1 computes the Bessel J1 function. BESSEL_J1_VALUES returns selected values. X FX FX2 (table) (BESJ1) -5.00000000 0.3275791375914652 0.3275791375914652 -4.00000000 0.6604332802354913E-01 0.6604332802354915E-01 -3.00000000 -0.3390589585259365 -0.3390589585259364 -2.00000000 -0.5767248077568734 -0.5767248077568733 -1.00000000 -0.4400505857449335 -0.4400505857449335 0.00000000 0.000000000000000 0.000000000000000 1.00000000 0.4400505857449335 0.4400505857449335 2.00000000 0.5767248077568734 0.5767248077568733 3.00000000 0.3390589585259365 0.3390589585259364 4.00000000 -0.6604332802354913E-01 -0.6604332802354915E-01 5.00000000 -0.3275791375914652 -0.3275791375914652 6.00000000 -0.2766838581275656 -0.2766838581275656 7.00000000 -0.4682823482345833E-02 -0.4682823482345837E-02 8.00000000 0.2346363468539146 0.2346363468539146 9.00000000 0.2453117865733253 0.2453117865733253 10.00000000 0.4347274616886144E-01 0.4347274616886144E-01 11.00000000 -0.1767852989567215 -0.1767852989567215 12.00000000 -0.2234471044906276 -0.2234471044906276 13.00000000 -0.7031805212177837E-01 -0.7031805212177837E-01 14.00000000 0.1333751546987933 0.1333751546987932 15.00000000 0.2051040386135228 0.2051040386135228 TEST08: RJBESL computes values of Bessel functions of NONINTEGER order. BESSEL_JX_VALUES returns selected values of the Bessel function Jn for NONINTEGER order. ALPHA X FX FX2 (table) (RJBESL) 0.50000000 0.20000000 0.3544507442114011 0.3544507442114011 0.50000000 1.00000000 0.6713967071418031 0.6713967071418029 0.50000000 2.00000000 0.5130161365618278 0.5130161365618278 0.50000000 2.50000000 0.3020049060623657 0.3020049060623657 0.50000000 3.00000000 0.6500818287737578E-01 0.6500818287737570E-01 0.50000000 5.00000000 -0.3421679847981618 -0.3421679847981620 0.50000000 10.00000000 -0.1372637357550505 -0.1372637357550505 0.50000000 20.00000000 0.1628807638550299 0.1628807638550298 1.50000000 1.00000000 0.2402978391234270 0.2402978391234269 1.50000000 2.00000000 0.4912937786871623 0.4912937786871623 1.50000000 5.00000000 -0.1696513061447408 -0.1696513061447408 1.50000000 10.00000000 0.1979824927558931 0.1979824927558931 1.50000000 50.00000000 -0.1094768729883180 -0.1094768729883180 2.50000000 1.00000000 0.4949681022847794E-01 0.4949681022847793E-01 2.50000000 2.00000000 0.2239245314689158 0.2239245314689158 2.50000000 5.00000000 0.2403772011113174 0.2403772011113175 2.50000000 10.00000000 0.1966584835818184 0.1966584835818184 2.50000000 50.00000000 0.2303721950962553E-01 0.2303721950962553E-01 1.25000000 1.00000000 0.3314145508558904 0.3314145508558904 1.25000000 2.00000000 0.5461734240402840 0.5461734240402840 1.25000000 5.00000000 -0.2616584152094124 -0.2616584152094124 1.25000000 10.00000000 0.1296035513791289 0.1296035513791290 1.25000000 50.00000000 -0.1117432171933552 -0.1117432171933552 2.75000000 1.00000000 0.3142623570527935E-01 0.3142623570527934E-01 2.75000000 2.00000000 0.1717922192746527 0.1717922192746527 2.75000000 5.00000000 0.3126634069544786 0.3126634069544785 2.75000000 10.00000000 0.1340289119304364 0.1340289119304366 2.75000000 50.00000000 0.6235967135106445E-01 0.6235967135106444E-01 TEST09: BESK0 computes the Bessel K0 function. BESSEL_K0_VALUES returns selected values. X FX FX2 (table) (BESK0) 0.10000000 2.427069024702017 2.427069024702016 0.20000000 1.752703855528146 1.752703855528146 0.40000000 1.114529134524434 1.114529134524434 0.60000000 0.7775220919047293 0.7775220919047294 0.80000000 0.5653471052658957 0.5653471052658956 1.00000000 0.4210244382407083 0.4210244382407083 1.20000000 0.3185082202865936 0.3185082202865938 1.40000000 0.2436550611815419 0.2436550611815420 1.60000000 0.1879547519693323 0.1879547519693324 1.80000000 0.1459314004898280 0.1459314004898280 2.00000000 0.1138938727495334 0.1138938727495334 2.50000000 0.6234755320036619E-01 0.6234755320036619E-01 3.00000000 0.3473950438627925E-01 0.3473950438627926E-01 3.50000000 0.1959889717036849E-01 0.1959889717036849E-01 4.00000000 0.1115967608585302E-01 0.1115967608585302E-01 4.50000000 0.6399857243233975E-02 0.6399857243233976E-02 5.00000000 0.3691098334042594E-02 0.3691098334042593E-02 6.00000000 0.1243994328013123E-02 0.1243994328013123E-02 8.00000000 0.1464707052228154E-03 0.1464707052228154E-03 10.00000000 0.1778006231616765E-04 0.1778006231616765E-04 TEST10: BESK1 computes the Bessel K1 function. BESSEL_K1_VALUES returns selected values. X FX FX2 (table) (BESK1) 0.10000000 9.853844780870606 9.853844780870604 0.20000000 4.775972543220472 4.775972543220472 0.40000000 2.184354424732687 2.184354424732687 0.60000000 1.302834939763502 1.302834939763502 0.80000000 0.8617816344721803 0.8617816344721805 1.00000000 0.6019072301972346 0.6019072301972346 1.20000000 0.4345923910607150 0.4345923910607150 1.40000000 0.3208359022298758 0.3208359022298757 1.60000000 0.2406339113576119 0.2406339113576118 1.80000000 0.1826230998017470 0.1826230998017470 2.00000000 0.1398658818165224 0.1398658818165224 2.50000000 0.7389081634774707E-01 0.7389081634774705E-01 3.00000000 0.4015643112819418E-01 0.4015643112819418E-01 3.50000000 0.2223939292592383E-01 0.2223939292592384E-01 4.00000000 0.1248349888726843E-01 0.1248349888726843E-01 4.50000000 0.7078094908968090E-02 0.7078094908968089E-02 5.00000000 0.4044613445452164E-02 0.4044613445452164E-02 6.00000000 0.1343919717735509E-02 0.1343919717735509E-02 8.00000000 0.1553692118050011E-03 0.1553692118050011E-03 10.00000000 0.1864877345382558E-04 0.1864877345382558E-04 TEST11: RKBESL computes values of Bessel functions of NONINTEGER order. BESSEL_KX_VALUES returns selected values of the Bessel function Kn for NONINTEGER order. ALPHA X FX FX2 (table) (RKBESL) 0.50000000 0.20000000 2.294489339798475 2.294489339798474 0.50000000 1.00000000 0.4610685044478946 0.4610685044478946 0.50000000 2.00000000 0.1199377719680614 0.1199377719680615 0.50000000 2.50000000 0.6506594315400999E-01 0.6506594315400999E-01 0.50000000 3.00000000 0.3602598513176459E-01 0.3602598513176459E-01 0.50000000 5.00000000 0.3776613374642883E-02 0.3776613374642883E-02 0.50000000 10.00000000 0.1799347809370518E-04 0.1799347809370518E-04 0.50000000 20.00000000 0.5776373974707445E-09 0.5776373974707445E-09 1.50000000 1.00000000 0.9221370088957891 0.9221370088957892 1.50000000 2.00000000 0.1799066579520922 0.1799066579520922 1.50000000 5.00000000 0.4531936049571459E-02 0.4531936049571459E-02 1.50000000 10.00000000 0.1979282590307570E-04 0.1979282590307570E-04 1.50000000 50.00000000 0.3486992497366216E-22 0.3486992497366216E-22 2.50000000 1.00000000 3.227479531135262 3.227479531135262 2.50000000 2.00000000 0.3897977588961997 0.3897977588961997 2.50000000 5.00000000 0.6495775004385758E-02 0.6495775004385758E-02 2.50000000 10.00000000 0.2393132586462789E-04 0.2393132586462789E-04 2.50000000 50.00000000 0.3627839645299048E-22 0.3627839645299047E-22 1.25000000 1.00000000 0.7311451879202114 0.7311451879202115 1.25000000 2.00000000 0.1567475478393932 0.1567475478393932 1.25000000 5.00000000 0.4257389528177461E-02 0.4257389528177460E-02 1.25000000 10.00000000 0.1915541065869563E-04 0.1915541065869563E-04 1.25000000 50.00000000 0.3463337593569306E-22 0.3463337593569306E-22 2.75000000 1.00000000 4.731184839919541 4.731184839919541 2.75000000 2.00000000 0.4976876225514758 0.4976876225514759 2.75000000 5.00000000 0.7300864610941163E-02 0.7300864610941163E-02 2.75000000 10.00000000 0.2546421294106458E-04 0.2546421294106457E-04 2.75000000 50.00000000 0.3675275677913656E-22 0.3675275677913655E-22 TEST12: BESY0 computes the Bessel Y0 function. BESSEL_Y0_VALUES returns selected values. X FX FX2 (table) (BESY0) 0.10000000 -1.534238651350367 -1.534238651350367 1.00000000 0.8825696421567696E-01 0.8825696421567698E-01 2.00000000 0.5103756726497451 0.5103756726497451 3.00000000 0.3768500100127904 0.3768500100127904 4.00000000 -0.1694073932506499E-01 -0.1694073932506500E-01 5.00000000 -0.3085176252490338 -0.3085176252490338 6.00000000 -0.2881946839815792 -0.2881946839815792 7.00000000 -0.2594974396720926E-01 -0.2594974396720926E-01 8.00000000 0.2235214893875662 0.2235214893875662 9.00000000 0.2499366982850247 0.2499366982850247 10.00000000 0.5567116728359939E-01 0.5567116728359939E-01 11.00000000 -0.1688473238920795 -0.1688473238920795 12.00000000 -0.2252373126343614 -0.2252373126343614 13.00000000 -0.7820786452787591E-01 -0.7820786452787593E-01 14.00000000 0.1271925685821837 0.1271925685821837 15.00000000 0.2054642960389183 0.2054642960389182 TEST13: BESY1 computes the Bessel Y1 function. BESSEL_Y1_VALUES returns selected values. X FX FX2 (table) (BESY1) 0.10000000 -6.458951094702027 -6.458951094702027 1.00000000 -0.7812128213002887 -0.7812128213002887 2.00000000 -0.1070324315409375 -0.1070324315409376 3.00000000 0.3246744247918000 0.3246744247917999 4.00000000 0.3979257105571000 0.3979257105571000 5.00000000 0.1478631433912268 0.1478631433912268 6.00000000 -0.1750103443003983 -0.1750103443003983 7.00000000 -0.3026672370241849 -0.3026672370241849 8.00000000 -0.1580604617312475 -0.1580604617312475 9.00000000 0.1043145751967159 0.1043145751967159 10.00000000 0.2490154242069539 0.2490154242069538 11.00000000 0.1637055374149429 0.1637055374149428 12.00000000 -0.5709921826089652E-01 -0.5709921826089653E-01 13.00000000 -0.2100814084206935 -0.2100814084206935 14.00000000 -0.1666448418561723 -0.1666448418561722 15.00000000 0.2107362803687351E-01 0.2107362803687351E-01 TEST14: RYBESL computes values of Bessel functions of NONINTEGER order. BESSEL_YX_VALUES returns selected values of the Bessel function Yn for NONINTEGER order. ALPHA X FX FX2 (table) (RYBESL) 0.50000000 0.20000000 -1.748560416961876 -1.748560416961876 0.50000000 1.00000000 -0.4310988680183761 -0.4310988680183762 0.50000000 2.00000000 0.2347857104062485 0.2347857104062485 0.50000000 2.50000000 0.4042783022390569 0.4042783022390569 0.50000000 3.00000000 0.4560488207946332 0.4560488207946332 0.50000000 5.00000000 -0.1012177091851084 -0.1012177091851084 0.50000000 10.00000000 0.2117088663313982 0.2117088663313982 0.50000000 20.00000000 -0.7280690478506185E-01 -0.7280690478506185E-01 1.50000000 1.00000000 -1.102495575160179 -1.102495575160179 1.50000000 2.00000000 -0.3956232813587035 -0.3956232813587035 1.50000000 5.00000000 0.3219244429611401 0.3219244429611401 1.50000000 10.00000000 0.1584346223881903 0.1584346223881903 1.50000000 50.00000000 0.2742813676191382E-01 0.2742813676191382E-01 2.50000000 1.00000000 -2.876387857462161 -2.876387857462162 2.50000000 2.00000000 -0.8282206324443037 -0.8282206324443038 2.50000000 5.00000000 0.2943723749617925 0.2943723749617925 2.50000000 10.00000000 -0.1641784796149411 -0.1641784796149411 2.50000000 50.00000000 0.1105304445562544 0.1105304445562544 1.25000000 1.00000000 -0.9319659251969881 -0.9319659251969881 1.25000000 2.00000000 -0.2609445010948933 -0.2609445010948932 1.25000000 5.00000000 0.2492796362185881 0.2492796362185881 1.25000000 10.00000000 0.2174410301416733 0.2174410301416734 1.25000000 50.00000000 -0.1578576650557229E-01 -0.1578576650557230E-01 2.75000000 1.00000000 -4.023453301501028 -4.023453301501029 2.75000000 2.00000000 -0.9588998694752389 -0.9588998694752390 2.75000000 5.00000000 0.2264260361047367 0.2264260361047366 2.75000000 10.00000000 -0.2193617736566760 -0.2193617736566760 2.75000000 50.00000000 0.9413988344515077E-01 0.9413988344515081E-01 TEST15: DAW computes the Dawson function. DAWSON_VALUES returns selected values. X FX FX2 (table) (DAW) 0.00000000 0.000000000000000 0.000000000000000 0.10000000 0.9933599239785286E-01 0.9933599239785287E-01 0.20000000 0.1947510333680280 0.1947510333680280 0.30000000 0.2826316650213119 0.2826316650213119 0.40000000 0.3599434819348881 0.3599434819348881 0.50000000 0.4244363835020223 0.4244363835020223 0.60000000 0.4747632036629779 0.4747632036629779 0.70000000 0.5105040575592318 0.5105040575592318 0.80000000 0.5321017070563654 0.5321017070563654 0.90000000 0.5407243187262987 0.5407243187262987 1.00000000 0.5380795069127684 0.5380795069127684 1.10000000 0.5262066799705525 0.5262066799705526 1.20000000 0.5072734964077396 0.5072734964077396 1.30000000 0.4833975173848241 0.4833975173848242 1.40000000 0.4565072375268973 0.4565072375268973 1.50000000 0.4282490710853986 0.4282490710853987 1.60000000 0.3999398943230814 0.3999398943230814 1.70000000 0.3725593489740788 0.3725593489740788 1.80000000 0.3467727691148722 0.3467727691148723 1.90000000 0.3229743193228178 0.3229743193228179 2.00000000 0.3013403889237920 0.3013403889237920 TEST16: EONE computes the exponential integral E1. E1_VALUES returns selected values. X FX FX2 (table) (E1) 0.50000000 0.5597735947761608 0.5597735947761608 0.60000000 0.4543795031894021 0.4543795031894021 0.70000000 0.3737688432335091 0.3737688432335091 0.80000000 0.3105965785455430 0.3105965785455431 0.90000000 0.2601839393259996 0.2601839393259997 1.00000000 0.2193839343955203 0.2193839343955203 1.10000000 0.1859909045360402 0.1859909045360401 1.20000000 0.1584084368514626 0.1584084368514626 1.30000000 0.1354509578491291 0.1354509578491291 1.40000000 0.1162193125713579 0.1162193125713579 1.50000000 0.1000195824066327 0.1000195824066326 1.60000000 0.8630833369753979E-01 0.8630833369753976E-01 1.70000000 0.7465464440125305E-01 0.7465464440125305E-01 1.80000000 0.6471312936386886E-01 0.6471312936386886E-01 1.90000000 0.5620437817453485E-01 0.5620437817453486E-01 2.00000000 0.4890051070806112E-01 0.4890051070806112E-01 TEST17: EI computes the exponential integral Ei. EI_VALUES returns selected values. X FX FX2 (table) (Ei) 0.50000000 0.4542199048631736 0.4542199048631735 0.60000000 0.7698812899373594 0.7698812899373594 0.70000000 1.064907194624291 1.064907194624291 0.80000000 1.347396548212326 1.347396548212326 0.90000000 1.622811713696867 1.622811713696868 1.00000000 1.895117816355937 1.895117816355937 1.10000000 2.167378279563403 2.167378279563403 1.20000000 2.442092285192652 2.442092285192651 1.30000000 2.721398880232024 2.721398880232024 1.40000000 3.007207464150646 3.007207464150645 1.50000000 3.301285449129798 3.301285449129798 1.60000000 3.605319949019469 3.605319949019469 1.70000000 3.920963201354904 3.920963201354905 1.80000000 4.249867557487934 4.249867557487933 1.90000000 4.593713686953585 4.593713686953585 2.00000000 4.954234356001890 4.954234356001889 TEST18: R8_ERF computes the error function. ERF_VALUES returns selected values. X FX FX2 (table) (R8_ERF) 0.00000000 0.000000000000000 0.000000000000000 0.10000000 0.1124629160182849 0.1124629160182849 0.20000000 0.2227025892104785 0.2227025892104785 0.30000000 0.3286267594591274 0.3286267594591273 0.40000000 0.4283923550466685 0.4283923550466684 0.50000000 0.5204998778130465 0.5204998778130465 0.60000000 0.6038560908479259 0.6038560908479259 0.70000000 0.6778011938374185 0.6778011938374184 0.80000000 0.7421009647076605 0.7421009647076605 0.90000000 0.7969082124228321 0.7969082124228322 1.00000000 0.8427007929497149 0.8427007929497148 1.10000000 0.8802050695740817 0.8802050695740817 1.20000000 0.9103139782296354 0.9103139782296354 1.30000000 0.9340079449406524 0.9340079449406524 1.40000000 0.9522851197626488 0.9522851197626487 1.50000000 0.9661051464753106 0.9661051464753108 1.60000000 0.9763483833446440 0.9763483833446440 1.70000000 0.9837904585907746 0.9837904585907746 1.80000000 0.9890905016357306 0.9890905016357308 1.90000000 0.9927904292352575 0.9927904292352574 2.00000000 0.9953222650189527 0.9953222650189527 TEST19: R8_GAMMA computes the gamma function. GAMMA_VALUES returns selected values. X FX FX2 DIFF (table) (R8_GAMMA) -0.50000000 -3.544907701811032 -3.544907701811032 0.4441E-15 -0.01000000 -100.5871979644108 -100.5871979644108 0.2842E-13 0.01000000 99.43258511915060 99.43258511915060 0.000 0.10000000 9.513507698668732 9.513507698668731 0.1776E-14 0.20000000 4.590843711998803 4.590843711998803 0.000 0.40000000 2.218159543757688 2.218159543757688 0.000 0.50000000 1.772453850905516 1.772453850905516 0.000 0.60000000 1.489192248812817 1.489192248812817 0.000 0.80000000 1.164229713725303 1.164229713725303 0.2220E-15 1.00000000 1.000000000000000 1.000000000000000 0.000 1.10000000 0.9513507698668732 0.9513507698668732 0.000 1.20000000 0.9181687423997607 0.9181687423997607 0.000 1.30000000 0.8974706963062772 0.8974706963062772 0.000 1.40000000 0.8872638175030753 0.8872638175030754 0.1110E-15 1.50000000 0.8862269254527581 0.8862269254527581 0.000 1.60000000 0.8935153492876903 0.8935153492876903 0.000 1.70000000 0.9086387328532904 0.9086387328532904 0.000 1.80000000 0.9313837709802427 0.9313837709802427 0.000 1.90000000 0.9617658319073874 0.9617658319073874 0.000 2.00000000 1.000000000000000 1.000000000000000 0.000 3.00000000 2.000000000000000 2.000000000000000 0.000 4.00000000 6.000000000000000 6.000000000000000 0.000 10.00000000 362880.0000000000 362880.0000000000 0.000 20.00000000 0.1216451004088320E+18 0.1216451004088321E+18 80.00 30.00000000 0.8841761993739702E+31 0.8841761993739751E+31 0.4954E+17 TEST20: R8_GAMMA_LOG computes the log of the gamma function. GAMMA_LOG_VALUES returns selected values. X FX FX2 (table) (R8_GAMMA_LOG) 0.20000000 1.524063822430784 1.524063822430784 0.40000000 0.7966778177017837 0.7966778177017837 0.60000000 0.3982338580692348 0.3982338580692349 0.80000000 0.1520596783998375 0.1520596783998376 1.00000000 0.000000000000000 0.000000000000000 1.10000000 -0.4987244125983972E-01 -0.4987244125983976E-01 1.20000000 -0.8537409000331583E-01 -0.8537409000331585E-01 1.30000000 -0.1081748095078604 -0.1081748095078605 1.40000000 -0.1196129141723712 -0.1196129141723713 1.50000000 -0.1207822376352452 -0.1207822376352453 1.60000000 -0.1125917656967557 -0.1125917656967558 1.70000000 -0.9580769740706586E-01 -0.9580769740706586E-01 1.80000000 -0.7108387291437215E-01 -0.7108387291437215E-01 1.90000000 -0.3898427592308333E-01 -0.3898427592308337E-01 2.00000000 0.000000000000000 0.000000000000000 3.00000000 0.6931471805599453 0.6931471805599454 4.00000000 1.791759469228055 1.791759469228055 10.00000000 12.80182748008147 12.80182748008147 20.00000000 39.33988418719949 39.33988418719949 30.00000000 71.25703896716801 71.25703896716800 TEST21 MACHAR computes double precision machine constants. IBETA is the internal base for machine arithmetic. IBETA = 2 IT is the number of digits, base IBETA, in the floating point significand. IT = 53 IRND reports on floating point addition rounding: 0, for chopping; 1, for non-IEEE rounding; 2, for IEEE rounding; 3, for chopping with partial underflow; 4, for non-IEEE rounding with partial underflow. 5, for IEEE rounding with partial underflow. IRND = 5 NGRD is the number of guard digits for floating point multiplication with truncating arithmetic. NGRD = 0 MACHEP is the largest negative integer such that 1.0 < 1.0 + BETA**MACHEP. MACHEP = -52 NEGEPS is the largest negative integer such that 1.0 - BETA**NEGEPS < 1.0: NEGEP = -53 IEXP is the number of bits reserved for the exponent of a floating point number: IEXP = 11 MINEXP is the most negative power of BETA such that BETA**MINEXP is positive and normalized. MINEXP = -1022 MAXEXP is the smallest positive power of BETA that overflows: MAXEXP = 1024 EPS is a small positive floating point number such that 1.0 < 1.0 + EPS. EPS = 0.2220446049250E-15 EPSNEG is a small positive floating point number such that 1.0 - EPSNEG < 1.0. EPSNEG = 0.1110223024625E-15 XMIN is the smallest positive normalized floating point power of the radix: XMIN = 0.2225073858507-307 XMAX is the largest finite floating point number: XMAX = 0.1797693134862+309 TEST22: R8_PSI computes the PSI function. PSI_VALUES returns selected values. X PSI PSI DIFF (table) (R8_PSI) 1.00000000 -0.5772156649015329 -0.5772156649015329 0.000 1.10000000 -0.4237549404110768 -0.4237549404110768 0.5551E-16 1.20000000 -0.2890398965921883 -0.2890398965921884 0.5551E-16 1.30000000 -0.1691908888667997 -0.1691908888667995 0.1665E-15 1.40000000 -0.6138454458511615E-01 -0.6138454458511624E-01 0.9021E-16 1.50000000 0.3648997397857652E-01 0.3648997397857652E-01 0.000 1.60000000 0.1260474527734763 0.1260474527734763 0.2776E-16 1.70000000 0.2085478748734940 0.2085478748734940 0.2776E-16 1.80000000 0.2849914332938615 0.2849914332938615 0.000 1.90000000 0.3561841611640597 0.3561841611640596 0.1110E-15 2.00000000 0.4227843350984671 0.4227843350984672 0.1110E-15 TEST23 REN is a random number generator. It cannot be controlled by an external seed value, although it has an argument that "looks" like a seed. 10 sample values: 0.470393 0.799067 0.883262 0.407668 0.958390 0.798617 0.827025 0.378046 0.255645 0.955567 Expected mean = 0.500000 Expected variance = 0.833333E-01 Sample size = 1000 Sample mean = 0.496233 Sample variance = 0.812630E-01 Sample maximum = 0.994303 Sample minimum = 0.166226E-02 SPECFUN_PRB2 Normal end of execution. 13 April 2013 1:00:49.199 PM