On 31 Aug, 02:12, Wildemar Wildenburger <[EMAIL PROTECTED]> wrote: > I've heard (ok, read) that several times now and I understand the > argument. But what use is there for floats, then? When is it OK to use them?
There are fractions that can be exactly represented by floats that cannot be exactly represented by decimals. There are fractions that can be exactly represented by decimals that cannot be exactly represented by floats. Which one is better? Which do we prefer? What a float cannot do is to represent a decimal fractional number (e.g. 1.1) exactly. If we need that, we cannot use floats. A notable example is monetary computations, it covers 99% of the use for decimal numbers in computers. For this reason, we should never use floats to add 10 cents to a dollar. The use of decimals for monetary calculations is mandatory. Floats are written as decimal fractional numbers in program code, and they are printed as decimal fractional numbers on the screen. A novice programmer may for this reason easily mistake floats for being decimals. But inside the computer floats are something very different. Floats do not represent decimal fractional numbers. Floats represent binary fractional numbers. Decimal numbers are base-10, binary numbers are base-2. Floats and decimals are similar but different. It is much easier to manipulate for computers than decimals. Digital electronics by convention only has two states, TTL voltage levels 0.0 V and 5.0 V, which are taken to mean 0 and 1 in binary (or false and true in boolean) respectively. Computers work internally with binary numbers. Floats are preferred to decimals in e.g. numerical maths and other scientific computing for their better performance speed wise. Knowledge of the behaviour of floats, e.g. how they cause rounding and truncation errors, is pivotal in that field of computer science. For most purposes, we could replace floats with decimals. But then we would suffer a major speed penalty. Decimals are only "precise" if the input values can be represented precisely by decimal fractions. If we typed 1.1 and took that to mean "one dollar and 10 cents", then certainly "exactly 1.1" was what we meant. But if we ment "1.1 centigrades read from a mercury thermometer", we would actually (by convention) mean "something between 1.05 and 1.14 centigrades". Decimals also fail to be exact if we try to compute things like "1.0/3.0". 1/3 does not have an exact representation in decimal, and we get an approximation from the computer. For purposes where exact precision is not needed, decimals are neither better nor worse than floats. This accounts for 99% of the cases where fractional numbers are used on a computer. More about floating point numbers here: http://www.math.byu.edu/~schow/work/IEEEFloatingPoint.htm Sturla Molden -- http://mail.python.org/mailman/listinfo/python-list
