Numerical issue in simple summation/addition

below code prints 1. But if you have b = 0.2 at the second line, it does not print 1.

a = 0;
b = 0.1;
c = a;

while c < 1
    c
    c = c+b;
end

Answer 1

[Star Strider]

See: Why is 0.3 - 0.2 - 0.1 (or similar) not equal to zero?

Answer 2

[Image Analyst]

It has nothing to do with the version. It has everything to do with digitization/quantization differences as discussed in the FAQ: http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

Answer 3

[Ali]

So, what is the fix? how can i have such a while loop with 0.1 increments and stop before 1?

[Star Strider]

There is no fix, and even the most recent version of round (that my ‘roundn’ function emulates) will not produce an ‘exact’ decimal equivalent of a decimal fraction. Computers (most of them, at least) do everything in binary, and so have to express decimal fractions in binary approximations. (The only computer that I’m aware of that used decimal calculations was the IBM 1620 that I first learned FORTRAN on. The first several cards in a compiled deck loaded the lookup tables it used. IBM engineers called it the ‘CADET’ — Can’t Add, Doesn’t Even Try!)

roundn = @(x,n) round(x .* 10.^n)./10.^n;   % Round ‘x’ To ‘n’ Digits, Emulates Latest ‘round’ Function

Run your code using format long E to see the reason b=0.1 is actually stopping before 1, just as you want it to:

format long E
a = 0;
b = 0.1;
c = a;

while c < 1
    c
    c = c+b;
end

[Ali]

thank you

[Star Strider]

My pleasure.

[Image Analyst]

"What's the fix?" Did you read the FAQ like both Star and I pointed you to? In there is the "fix" or way to deal with the reality of it -- you check against a tolerance.