Why is 14 the magic precision number?

[ramsey]

Originally posted at moontoast#9, @lhfeng asks:

why is the 14 is the magic precision number?

[ramsey]

I admit that the code comment "14 is the magic precision number" is very mysterious. I should probably update that with more explanation.

According to the PHP manual page for the float type:

The size of a float is platform-dependent, although a maximum of ~1.8e308 with a precision of roughly 14 decimal digits is a common value (the 64 bit IEEE format).

So, the default floating-point precision in PHP is 14 (unless this is changed in php.ini).

Consider the following (using psysh):

>>> ceil(23.000000000000000999)
=> 23.0
>>> ceil(23.000000000000001999)
=> 24.0

The two places where this is used in BigNumber is in the ceil() and floor() methods. In order to ensure that BigNumber properly handles the rounding according to PHP's default rules, I need to use a precision of 14. If I were to use a precision less than 14, then BigNumber would calculate the ceil() of 23.000000000000001999 as 23.0, which is incorrect.

[lhfeng]

I have another problem.
1/3 * 0.15 result is 0.05 in Calculator,

but ,
$bn = new \Moontoast\Math\BigNumber(1,2);
$bn->divide(3)->multiply(0.15);
result is 0.04
how to do it the result is 0.05 in Moontoast\Math.

[ramsey]

This library uses bcmath, and this is an unfortunate problem with any kind of arbitrary precision arithmetic.

I recommend reading http://floating-point-gui.de/ for more information on what's going on.

This should illustrate the problem, though:

>>> $value = bcdiv(1, 3, 2);
=> "0.33"
>>> bcmul($value, 0.15, 2);
=> "0.04"
>>> $value = bcdiv(1, 3, 50);
=> "0.33333333333333333333333333333333333333333333333333"
>>> bcmul($value, 0.15, 50);
=> "0.04999999999999999999999999999999999999999999999999"