Inequalities From Manipulating Real Value

[Dragon20942]

Does anyone get a different output from mine? I posted mine at the bottom. Better yet, anyone have an explanation?

Turing:

var a : int := 0 var b : int := 3 var x : real := a if x = a then %x is set = to a. This should output.     put "x = a" end if for i : 1 .. 10 %modification of x. x becomes 3     x += 0.3 end for if x = b then %Comparing 3 with 3     put "x = b" end if var c : real := 3 %Comparison of reals if x = c then     put "x = c" end if var d : real := 3.0 %Set to a real value if x = d then     put "x = d" end if var e : real := x %set equal to x if x = e then     put "x = e" end if if round (x) = b then %round x     put "round(x) = b" end if var f : real := 0.3 %compare to similar process f *= 10 if x = f then     put "x = f" end if var g : real := 0 %compare to identical process for i : 1 .. 10     g += 0.3 end for if x = g then     put "x = g" end if /* OUTPUT x = a x = e round(x) = b x = g So only works for setting equal, rounding the real, and identical process */

Please specify what version of Turing you are using
4.1.1

[Insectoid]

Real values are inaccurate due to the way they are stored in memory. Typically they are so many bits of data multiplied by some exponent. For example, the number 12340000 could be represented as 1234*10^4. If you only have 4 digits of precision, then 12343000 would also be represented as 1234*10^4. You lose the 3 because the Real cannot be precise enough to store it (Reals can store more than 4 digits ofc). Same for decimals, 1.234 is 1234*10^-3. 1.2345 is also 1234*10^-3. This is how reals work. Because we're using computers of course, this is all stored in binary. instead of 4 decimal digits of precision, we have so many bits (binary digits) of precision. Some numbers are very difficult to store in binary, like 0.1, which is more often stored as 0.999999999 or 1.000000001.

Can you see now why comparing reals to integers might not give you the answers you expect?

[Dragon20942]

Yes. Thank you so much! Now I just have to figure out how to work around it

[Tony]

Depends on what exactly you want to do.

If precision matters, use integers with smaller units. E.g. money is never implemented as floats -- it's all integers. Instead of $1.25 it's 125 cents (the actual unit might be a small fraction of a cent, if it matters).

Otherwise you check for how far away two floats are:

code:

abs(float_1 - float_2) < some_small_value