Division of the Intervals

The calculation of the sub-intervals is processed according to the following rules:

• The entire, current interval Jcurr is defined by its size, the lower and the upper endpoint:
  Jcurr_s, Jcurr_l, Jcurr_u
• The sub-interval of the first symbol (0) of the alphabet starts with a closed lower endpoint at the beginning of the current interval:
  J_l(0) = Jcurr_l
• The open upper endpoint of the first sub-interval results from the probability of the first symbol p(0) and the size of the current interval:
  J_u(0) = J_l(0) + Jcurr_s * p(0)
• The closed upper endpoint of each sub-interval is equal to the closed lower endpoint of sub-interval immediately following:
  J_u(x) = J_l(x+1)
• For all further sub-interval applies:
  J(x) = [ J_u(x-1); J_u(x-1) + Jges_s * p(x) )
• The sub-interval of the last symbol of the alphabet J(max) ends at the open upper endpoint of the current interval:
  J_u(z) = Jcurr_u

Example "abcd":

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