| Path: | libsrc/utils/dlgamma.f90 |
| Last Update: | Mon Aug 19 17:49:26 +0900 2013 |
Copyright(C) 1996 Takuya OOURA <ooura@mmm.t.u-tokyo.ac.jp>
2011 Youhei SASAKI <uwabami@gfd-dennou.org>
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
!
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE HOLDERS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
++
HISTORY 2009/02/06 S.Takehiro:
downloaded from http://www.kurims.kyoto-u.ac.jp/~ooura/gamerf.tar.gz
2011/02/18 Y.SASAKI
rewrite fortran >= 90
+++
* rewrite for Fortran 90 by Youhei SASAKI <uwabami@gfd-dennou.org>
| Function : | |
| dlgamma : | real(8) |
| x : | real(8), intent(in) |
real(8) function dlgamma(x)
implicit none
real(8), intent(in) :: x
real(8) :: a(0 : 21)
real(8) :: b(0 : 97)
real(8) :: c(0 : 64)
real(8) :: d(0 : 6)
real(8) :: y, t, v, w
integer :: i, k
real(8), parameter :: pi = 3.141592653589793238d0
data (a(i), i = 0, 10) / 0.00009967270908702825d0, -0.00019831672170162227d0, -0.00117085315349625822d0, 0.00722012810948319552d0, -0.00962213009367802970d0, -0.04219772092994235254d0, 0.16653861065243609743d0, -0.04200263501129018037d0, -0.65587807152061930091d0, 0.57721566490153514421d0, 0.99999999999999999764d0 /
data (a(i), i = 11, 21) / 0.00004672097259011420d0, -0.00006812300803992063d0, -0.00132531159076610073d0, 0.00733521178107202770d0, -0.00968095666383935949d0, -0.04217642811873540280d0, 0.16653313644244428256d0, -0.04200165481709274859d0, -0.65587818792782740945d0, 0.57721567315209190522d0, 0.99999999973565236061d0 /
data (b(i), i = 0, 13) / -0.00000000004587497028d0, 0.00000000019023633960d0, 0.00000000086377323367d0, 0.00000001155136788610d0, -0.00000002556403058605d0, -0.00000015236723372486d0, -0.00000316805106385740d0, 0.00000122903704923381d0, 0.00002334372474572637d0, 0.00111544038088797696d0, 0.00344717051723468982d0, 0.03198287045148788384d0, -0.32705333652955399526d0, 0.40120442440953927615d0 /
data (b(i), i = 14, 27) / -0.00000000005184290387d0, -0.00000000083355121068d0, -0.00000000256167239813d0, 0.00000001455875381397d0, 0.00000013512178394703d0, 0.00000029898826810905d0, -0.00000358107254612779d0, -0.00002445260816156224d0, -0.00004417127762011821d0, 0.00112859455189416567d0, 0.00804694454346728197d0, 0.04919775747126691372d0, -0.24818372840948854178d0, 0.11071780856646862561d0 /
data (b(i), i = 28, 41) / 0.00000000030279161576d0, 0.00000000160742167357d0, -0.00000000405596009522d0, -0.00000005089259920266d0, -0.00000002029496209743d0, 0.00000135130272477793d0, 0.00000391430041115376d0, -0.00002871505678061895d0, -0.00023052137536922035d0, 0.00045534656385400747d0, 0.01153444585593040046d0, 0.07924014651650476036d0, -0.12152192626936502982d0, -0.07916438300260539592d0 /
data (b(i), i = 42, 55) / -0.00000000050919149580d0, -0.00000000115274986907d0, 0.00000001237873512188d0, 0.00000002937383549209d0, -0.00000030621450667958d0, -0.00000077409414949954d0, 0.00000816753874325579d0, 0.00002412433382517375d0, -0.00026061217606063700d0, -0.00091000087658659231d0, 0.01068093850598380797d0, 0.11395654404408482305d0, 0.07209569059984075595d0, -0.10971041451764266684d0 /
data (b(i), i = 56, 69) / 0.00000000040119897187d0, -0.00000000013224526679d0, -0.00000001002723190355d0, 0.00000002569249716518d0, 0.00000020336011868466d0, -0.00000118097682726060d0, -0.00000300660303810663d0, 0.00004402212897757763d0, -0.00001462405876235375d0, -0.00164873795596001280d0, 0.00513927520866443706d0, 0.13843580753590579416d0, 0.32730190978254056722d0, 0.08588339725978624973d0 /
data (b(i), i = 70, 83) / -0.00000000015413428348d0, 0.00000000064905779353d0, 0.00000000160702811151d0, -0.00000002655645793815d0, 0.00000007619544277956d0, 0.00000047604380765353d0, -0.00000490748870866195d0, 0.00000821513040821212d0, 0.00014804944070262948d0, -0.00122152255762163238d0, -0.00087425289205498532d0, 0.14438703699657968310d0, 0.61315889733595543766d0, 0.55513708159976477557d0 /
data (b(i), i = 84, 97) / 0.00000000001049740243d0, -0.00000000025832017855d0, 0.00000000139591845075d0, -0.00000000021177278325d0, -0.00000005082950464905d0, 0.00000037801785193343d0, -0.00000073982266659145d0, -0.00001088918441519888d0, 0.00012491810452478905d0, -0.00049171790705139895d0, -0.00425707089448266460d0, 0.13595080378472757216d0, 0.89518356003149514744d0, 1.31073912535196238583d0 /
data (c(i), i = 0, 12) / 0.0000000116333640008d0, -0.0000000833156123568d0, 0.0000003832869977018d0, -0.0000015814047847688d0, 0.0000065010672324100d0, -0.0000274514060128677d0, 0.0001209015360925566d0, -0.0005666333178228163d0, 0.0029294103665559733d0, -0.0180340086069185819d0, 0.1651788780501166204d0, 1.1031566406452431944d0, 1.2009736023470742248d0 /
data (c(i), i = 13, 25) / 0.0000000013842760642d0, -0.0000000069417501176d0, 0.0000000342976459827d0, -0.0000001785317236779d0, 0.0000009525947257118d0, -0.0000052483007560905d0, 0.0000302364659535708d0, -0.0001858396115473822d0, 0.0012634378559425382d0, -0.0102594702201954322d0, 0.1243625515195050218d0, 1.3888709263595291174d0, 2.4537365708424422209d0 /
data (c(i), i = 26, 38) / 0.0000000001298977078d0, -0.0000000008029574890d0, 0.0000000049454846150d0, -0.0000000317563534834d0, 0.0000002092136698089d0, -0.0000014252023958462d0, 0.0000101652510114008d0, -0.0000774550502862323d0, 0.0006537746948291078d0, -0.0066014912535521830d0, 0.0996711934948138193d0, 1.6110931485817511402d0, 3.9578139676187162939d0 /
data (c(i), i = 39, 51) / 0.0000000000183995642d0, -0.0000000001353537034d0, 0.0000000009984676809d0, -0.0000000076346363974d0, 0.0000000599311464148d0, -0.0000004868554120177d0, 0.0000041441957716669d0, -0.0000377160856623282d0, 0.0003805693126824884d0, -0.0045979851178130194d0, 0.0831422678749791178d0, 1.7929113303999329439d0, 5.6625620598571415285d0 /
data (c(i), i = 52, 64) / 0.0000000000034858778d0, -0.0000000000297587783d0, 0.0000000002557677575d0, -0.0000000022705728282d0, 0.0000000207024992450d0, -0.0000001954426390917d0, 0.0000019343161886722d0, -0.0000204790249102570d0, 0.0002405181940241215d0, -0.0033842087561074799d0, 0.0713079483483518997d0, 1.9467574842460867884d0, 7.5343642367587329552d0 /
data (d(i), i = 0, 6) / -0.00163312359200500807d0, 0.00083644533703385956d0, -0.00059518947575728181d0, 0.00079365057505415415d0, -0.00277777777735463043d0, 0.08333333333333309869d0, 0.91893853320467274178d0 /
!! main loop
w = x
if (x .lt. 0.0d0) w = 1 - x
if (w .lt. 0.5d0) then
k = 0
if (w .ge. 0.25d0) k = 11
y = ((((((((((a(k) * w + a(k + 1)) * w + a(k + 2)) * w + a(k + 3)) * w + a(k + 4)) * w + a(k + 5)) * w + a(k + 6)) * w + a(k + 7)) * w + a(k + 8)) * w + a(k + 9)) * w + a(k + 10)) * w
y = -dlog(y)
else if (w .lt. 3.5d0) then
t = w - 4.5d0 / (w + 0.5d0)
k = idint(t + 4)
t = t - (k - 3.5d0)
k = k * 14
y = ((((((((((((b(k) * t + b(k + 1)) * t + b(k + 2)) * t + b(k + 3)) * t + b(k + 4)) * t + b(k + 5)) * t + b(k + 6)) * t + b(k + 7)) * t + b(k + 8)) * t + b(k + 9)) * t + b(k + 10)) * t + b(k + 11)) * t + b(k + 12)) * t + b(k + 13)
else if (w .lt. 8) then
k = (idint(w)) - 3
t = w - (k + 3.5d0)
k = k * 13
y = (((((((((((c(k) * t + c(k + 1)) * t + c(k + 2)) * t + c(k + 3)) * t + c(k + 4)) * t + c(k + 5)) * t + c(k + 6)) * t + c(k + 7)) * t + c(k + 8)) * t + c(k + 9)) * t + c(k + 10)) * t + c(k + 11)) * t + c(k + 12)
else
v = 1 / w
t = v * v
y = (((((d(0) * t + d(1)) * t + d(2)) * t + d(3)) * t + d(4)) * t + d(5)) * v + d(6)
y = y + ((w - 0.5d0) * dlog(w) - w)
end if
if (x .lt. 0) y = dlog(pi / dsin(pi * x)) - y
dlgamma = y
end function dlgamma