floating accuracy - php intval() and floor() return value that is too low?

Question

Because the float data type in PHP is inaccurate, and a FLOAT in MySQL takes up more space than an INT (and is inaccurate), I always store prices as INTs, multipling by 100 before storing to ensure we have exactly 2 decimal places of precision. However I believe PHP is misbehaving. Example code:

echo "<pre>";

$price = "1.15";
echo "Price = ";
var_dump($price);

$price_corrected = $price*100;
echo "Corrected price = ";
var_dump($price_corrected);


$price_int = intval(floor($price_corrected));
echo "Integer price = ";
var_dump($price_int);

echo "</pre>";

Produced output:

Price = string(4) "1.15"
Corrected price = float(115)
Integer price = int(114)

I was surprised. When the final result was lower than expected by 1, I was expecting the output of my test to look more like:

Price = string(4) "1.15"
Corrected price = float(114.999999999)
Integer price = int(114)

which would demonstrate the inaccuracy of the float type. But why is floor(115) returning 114??

Answer 1

Try this as a quick fix:

$price_int = intval(floor($price_corrected + 0.5));

The problem you are experiencing is not PHP's fault, all programming languages using real numbers with floating point arithmetics have similar issues.

The general rule of thumb for monetary calculations is to never use floats (neither in the database nor in your script). You can avoid all kinds of problems by always storing the cents instead of dollars. The cents are integers, and you can freely add them together, and multiply by other integers. Whenever you display the number, make sure you insert a dot in front of the last two digits.

The reason why you are getting 114 instead of 115 is that floor rounds down, towards the nearest integer, thus floor(114.999999999) becomes 114. The more interesting question is why 1.15 * 100 is 114.999999999 instead of 115. The reason for that is that 1.15 is not exactly 115/100, but it is a very little less, so if you multiply by 100, you get a number a tiny bit smaller than 115.

Here is a more detailed explanation what echo 1.15 * 100; does:

• It parses 1.15 to a binary floating point number. This involves rounding, it happens to round down a little bit to get the binary floating point number nearest to 1.15. The reason why you cannot get an exact number (without rounding error) is that 1.15 has infinite number of numerals in base 2.
• It parses 100 to a binary floating point number. This involves rounding, but since 100 is a small integer, the rounding error is zero.
• It computes the product of the previous two numbers. This also involves a little rounding, to find the nearest binary floating point number. The rounding error happens to be zero in this operation.
• It converts the binary floating point number to a base 10 decimal number with a dot, and prints this representation. This also involves a little rounding.

The reason why PHP prints the surprising Corrected price = float(115) (instead of 114.999...) is that var_dump doesn't print the exact number (!), but it prints the number rounded to n - 2 (or n - 1) digits, where n digits is the precision of the calculation. You can easily verify this:

echo 1.15 * 100;  # this prints 115
printf("%.30f", 1.15 * 100);  # you 114.999....
echo 1.15 * 100 == 115.0 ? "same" : "different";  # this prints `different'
echo 1.15 * 100 < 115.0 ? "less" : "not-less";    # this prints `less'

If you are printing floats, remember: you don't always see all digits when you print the float.

See also the big warning near the beginning of the PHP float docs.