from math import log,sqrt,exp

def LambertW(z):
  " Lambert W function, principal branch "
  eps=4.0e-16
  em1=0.3678794411714423215955237701614608
  if z<-em1:
    print >>stderr,'LambertW.py: bad argument %g, exiting.'%z
    exit(1)
  if 0.0==z: return 0.0
  if z<-em1+1e-4:
    q=z+em1
    r=sqrt(q)
    q2=q*q
    q3=q2*q
    return\
     -1.0\
     +2.331643981597124203363536062168*r\
     -1.812187885639363490240191647568*q\
     +1.936631114492359755363277457668*r*q\
     -2.353551201881614516821543561516*q2\
     +3.066858901050631912893148922704*r*q2\
     -4.175335600258177138854984177460*q3\
     +5.858023729874774148815053846119*r*q3\
     -8.401032217523977370984161688514*q3*q
  if z<1.0:
    p=sqrt(2.0*(2.7182818284590452353602874713526625*z+1.0))
    w=-1.0+p*(1.0+p*(-0.333333333333333333333+p*0.152777777777777777777777))
  else:
    w=log(z)
  if z>3.0: w-=log(w)
  for i in xrange(10):
    e=exp(w)
    t=w*e-z
    p=w+1.0
    t/=e*p-0.5*(p+1.0)*t/p
    w-=t
    if abs(t)<eps*(1.0+abs(w)): return w