HERWIG/src/hwuli2.f

   1
   2 CDECK  ID>, HWULI2.
   3
   4 *CMZ :-        -23/08/94  13.22.29  by  Mike Seymour
   5
   6 *-- Author :    Ulrich Baur & Nigel Glover, adapted by Ian Knowles
   7
   8 C-----------------------------------------------------------------------
   9
  10       FUNCTION HWULI2(X)
  11
  12 C-----------------------------------------------------------------------
  13
  14 C     Complex dilogarithm function, Li_2 (Spence function)
  15
  16 C-----------------------------------------------------------------------
  17
  18       IMPLICIT NONE
  19
  20       DOUBLE COMPLEX HWULI2,PROD,Y,Y2,X,Z
  21
  22       DOUBLE PRECISION XR,XI,R2,A1,A2,A3,A4,A5,A6,A7,A8,A9,A10,ZETA2,
  23
  24      & ZERO,ONE,HALF
  25
  26       PARAMETER (ZERO=0.0D0, ONE=1.0D0, HALF=0.5D0)
  27
  28       DATA A1,A2,A3,A4,A5,A6,A7,A8,A9,A10,ZETA2/ -0.250000000000000D0,
  29
  30      & -0.111111111111111D0,-0.010000000000000D0,-0.017006802721088D0,
  31
  32      & -0.019444444444444D0,-0.020661157024793D0,-0.021417300648069D0,
  33
  34      & -0.021948866377231D0,-0.022349233811171D0,-0.022663689135191D0,
  35
  36      &  1.644934066848226D0/
  37
  38       PROD(Y,Y2)=Y*(ONE+A1*Y*(ONE+A2*Y*(ONE+A3*Y2*(ONE+A4*Y2*(ONE+A5*Y2*
  39
  40      & (ONE+A6*Y2*(ONE+A7*Y2*(ONE+A8*Y2*(ONE+A9*Y2*(ONE+A10*Y2))))))))))
  41
  42       XR=DBLE(X)
  43
  44       XI=IMAG(X)
  45
  46       R2=XR*XR+XI*XI
  47
  48       IF (R2.GT.ONE.AND.(XR/R2).GT.HALF) THEN
  49
  50          Z=-LOG(ONE/X)
  51
  52          HWULI2=PROD(Z,Z*Z)+ZETA2-LOG(X)*LOG(ONE-X)+HALF*LOG(X)**2
  53
  54       ELSEIF (R2.GT.ONE.AND.(XR/R2).LE.HALF) THEN
  55
  56          Z=-LOG(ONE-ONE/X)
  57
  58          HWULI2=-PROD(Z,Z*Z)-ZETA2-HALF*LOG(-X)**2
  59
  60       ELSEIF (R2.EQ.ONE.AND.XI.EQ.ZERO) THEN
  61
  62          HWULI2=ZETA2
  63
  64       ELSEIF (R2.LE.ONE.AND.XR.GT.HALF) THEN
  65
  66          Z=-LOG(X)
  67
  68          HWULI2=-PROD(Z,Z*Z)+ZETA2-LOG(X)*LOG(ONE-X)
  69
  70       ELSE
  71
  72          Z=-LOG(ONE-X)
  73
  74          HWULI2=PROD(Z,Z*Z)
  75
  76       ENDIF
  77
  78       END