Since a few days I am fighting my way through implementing arithmetic coding. I found a really great source of information which made me understand how it should work.

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Long story short, it implements arithmetic coding on integers using two registers: HIGH and LOW. Those register store a fraction, ex. HIGH = 98765 //means 0.98765(9) LOW = 91234 // means 0.91234(0) Then comes magic, when the most significant numbers match (in this case it would be 9s) they are printed out. It's all clear to me. However, when we take the following example HIGH LOW RANGE CUMULATIVE OUTPUT Initial state 0 100000 Encode B (0.2-0.3) 0 Shift out 2 0 100000.2 Encode I (0.5-0.6) 0.2 Shift out 5 0 100000.25 Encode L (0.6-0.8) 0 20000.25 //here starts problems Encode L (0.6-0.8) 0.25 //how possible? Shift out 7 0 40000.257 Encode SPACE (0.0-0.1) 0.257 Shift out 2 0 40000.2572 Encode G (0.4-0.5) 0.2572 Shift out 1 0 40000.25721 Encode A (0.1-0.2) 0.25721 Shift out 6 0 40000.257216 Encode T (0.9-1.0) 0.257216 Shift out 7 0 40000.2572167 Encode E (0.3-0.4) 0.2572167 Shift out 7 0 40000.25721677 Encode S (0.8-0.9) 0.25721677 Shift out 5 0.257216775 Shift out 2. Shift out 0.0 I really don't know how the marked lines are achieved on computers, on paper it's easy, since: /* range, HIGH, LOw - integer symbol->high, symbol->low - real */ HIGH = HIGH - (range - symbol->high*range) LOW = LOW + range*symbol->low But on computers?