fmod function returning wrong result

Question

I'm getting fmod returning wrong result, am i doing anything wrong?

for($i = 0.00; $i < 1; $i = $i + 0.05) {
    var_dump($i." = ".fmod($i, 0.05));
}

Output:

0.= 0
0.05 = 0
0.1 = 0
0.15 = 1.3877787807814E-17
0.2 = 0
0.25 = 0.05
0.3 = 0.05
0.35 = 0.05
0.4 = 0.05
0.45 = 0.05
0.5 = 0.05
0.55 = 0.05
0.6 = 0.05
0.65 = 0.05
0.7 = 2.7755575615629E-17
0.75 = 6.9388939039072E-17
0.8 = 1.1102230246252E-16
0.85 = 1.5265566588596E-16
0.9 = 1.942890293094E-16
0.95 = 2.3592239273285E-16

I was expecting every result to be the same: 0.

The answer is here: http://stackoverflow.com/q/588004/3933332 (Also add this line in your loop: `echo sprintf("%.20f", $i);` and you will see it) — Rizier123, Feb 06 '15 at 18:32
The operands shown above are not exactly respresentable as binary floating-point numbers. `fmod()` always delivers an exact result based on the actual value stored in the double-precision floating-point source operands. — njuffa, Feb 06 '15 at 18:33

Pascal Cuoq · Answer 1 · 2015-02-06T22:46:50.530

First, fmod is exact. Because it can: when x and y are floating-point numbers, the mathematical result of fmod(x,y) can be represented exactly as a floating-point number.

Second, when you write 0.05, you do not get exactly that number, because 5/100 on the other hand cannot be represented exactly as a floating-point number; and when you write +, you do not get mathematical addition in general because the result of that mathematical addition cannot always be represented as a floating-point number(*).

Starting from 0.0 and repeatedly adding 0.05 will soon get you into inaccurate + territory, because in binary, the best representation of 0.05 has many digits. As the sum gets larger, the last digits progressively have to be dropped. This is where the inaccuracy of + comes from, and ultimately is the reason why fmod does not give you the results you expect.

It wouldn't matter that 0.05 is not exactly 5/100 if repeatedly adding it to zero always was exact. But since the floating-point number 0.05 has many digits in binary (as opposed to decimal) and since some of these digits must be lost when computing multiples of 0.05, the value you get for most multiples y of 0.05 when computing fmod(y, 0.05) is not zero but represents the difference between the mathematical multiplication of the appropriate integer by 0.05 and the approximation y of that number.

(*) when the mathematical sum can be represented, the mathematical sum is what you get, but sometimes it just cannot.

score 0 · Answer 2 · edited May 23 '17 at 11:43

0

This answer relates to the first revision of the question:

https://stackoverflow.com/revisions/28372286/1

All is working fine! You can calculate it for yourself:

fmod(0.5, 0.25);
fmod(0.5, 0.23);
fmod(0.5, 0.20);

0.25 * 2 = 0.50   | Rest 0.00
0.23 * 2 = 0.46   | Rest 0.04
0.20 * 2 = 0.40   | Rest 0.10

edited May 23 '17 at 11:43

Community

1
1

answered Feb 06 '15 at 18:28

Rizier123

58,877
16
101
156

fmod function returning wrong result

2 Answers2

This answer relates to the first revision of the question:

Linked