Arithmetic Operators in C - Learn C programming in simple and easy steps starting from basic to advanced concepts with examples including C Overview, language basics.

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. Epson805 End Service Life here.

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. Epson Adjustment Program L100 Mower. 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? The real-number inaccuracy comes in and my intervals are much different. You shouldn't use floating point in such cases. Probabilities can be represented as rational numbers with denominator 10^something, this allows you to divide current interval exactly without rounding errors. So in your case 0.6 becomes 6/10, 0.8 - 8/10.

How you will store such things is your choice. Installer Canon Pixma Ip1000 Ubuntu Live Cd here. Usually some kind of fixed point format is used. For example you store 60 and know that this is actually probability*100, so whenever you multiply by it, you also divide by 100. Also note that later you will encounter another type of overflow - when you cannot shift out anything, but number of digits doesn't allow to divide interval without rounding errors. In such cases you either allow some inaccuracy in dividing interval or artificially narrow it to make shift out possible. If decode does everything in the same way, this doesn't impact correctness, but reduces compression a bit.