per9000 at gmail
Jun 21, 2006, 4:20 AM
Post #12 of 14
(974 views)
Permalink

Re: How to truncate/roundoff decimal numbers?
[In reply to]


Nick Maclaren wrote: > > just a thought: if you *always* work with "floats" with two decimals, > > you are in fact working with integers, but you represent them as a > > floats  confusing for the internal representation. > > No, you aren't  you are working with fixedpoint Nick, your answer has so many layers, I'll try to explain how I think :D 1) if you use integers you can think of them as having one part bigger than 100 and one part smaller than 100, like so: >>> a = 11122 >>> (a/100,a%100) (111, 22) Here the output 111,22 looks like something else than an integer, but this is just a matter of representation. a *is* an integer, but we represent it *as if it was* a "decimal" number. (Compare with (minutes,seconds) or (euro,cents) or (feet,inch) or any other "arbitrary" position system) 2) If we use floats with two decimals >>> b = 222.33 >>> b 222.33000000000001 they look like fixpoint numbers (I had to look it up http://en.wikipedia.org/wiki/Fixedpoint :D) but python stores it (correct me if I am wrong) as a float (or double or quad or whatever). If we want to work with fixpoint aritmetics we have to invent new functions to do most math. 3) Most "decimal numbers" cannot be stored exactly as floats  that is why b gave the ugly print. But some can, f.x >>> quart = 0.25 >>> quart 0.25 quart translates to a finite "decimal" number in binary (0.01 I think). The point is: representing shouldbe integers as floats makes you loose precision (negligable probalby but still...). 4) > > So why not work with int(float * 100) instead? This way you only have > > to take care of roundoffs etc when dividing. > > And multiplying, and calling most mathematical functions. You are correct of course. My mistake. But, the multiplication is exact before you start rounding off  I wont start counting ordos for int*int vs. float*float, but it could have some advantages >>> a 11122 >>> b 22233 >>> a*b 247275426 >>> (a*b/10000,a*b%10000) (24727, 5426) On the other hand you will quickly loose accuracy if you perform multiple multiplications or divisions or use other mathematical functions. 5) So, when could this way of thinking be useful? Well, rarely, but if you only add/subtract "decimals" and/or multiply "decimals" with whole numbers or if you want to use some nonmetric system to do scientific stuff (compute square feet when having (feet1,inch1) * (feet2,inch2) assuming that inches are atomic.) This could of course be extended to (feet, inch, quarter_of_afoot, sixteeth_of_a_foot) if you'd like  it is all a matter of representation. Regards, Per  "It is a gift. A gift to the foes of 'the Terrorists'. Why not use this 'terrorism'? Long has my father, 'George Bush Sr', kept the forces of 'the terrorists' at bay. By the blood of our people are your lands kept safe. Give 'the land of the brave' the weapon of the enemy. Let us use it against him."  http://mail.python.org/mailman/listinfo/pythonlist
