dlgamma.f90

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

+++

TITLE Gamma function produced by Dr. Ooura, RIMS, Kyoto Univ.

 * rewrite for Fortran 90 by Youhei SASAKI <uwabami@gfd-dennou.org>

Methods

dlgamma  

Public Instance methods

Function :
dlgamma :real(8)
x :real(8), intent(in)

[Source]

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