float inaccuracy?

General Discussion Other

woberndt

in General Discussion • Other • 2 years ago

Hi there.

Adding a float value n times gives a different result than multiplying it by n. Can anyone help me with this difference?

int ct = 100000;
float sum=0.0;
for (int i=0; i<ct; i++) {
sum += 255.0;
}
println (nfc (sum,0));
// prints 25.534.204

sum = ct * 255.0;
println (nfc (sum,0));
// prints 25.500.000

Replies(2)

mbraendle

Re: float inaccuracy?

2 years ago

See this thread: http://forum.processing.org/topic/bug-or-my-own-mistake

With datatype float, you have a mantissa of 23bits, allowing 2^23 = 8388608 distinct values (7.22 significant digits).

In the loop, at a certain point (loop count 65794), you add a 3-digit number to a 7-to-8-digit number. This can't be exact.

In your multiplication, the int 100'000 is converted to a float 1e5 (1 significant digit in the mantissa), and multiplied with a 3-digit number, so no problem there.

You can check what happens by adding the following line to the loop:

println(i + " " + sum / (i + 1));

woberndt

Re: float inaccuracy?

2 years ago

I understand.
Thank you very much.

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