Store values in integer form to avoid issues with float rounding

Currently Ledger stores values in float columns in the database. Float values have an inherently limited precision, which can become a problem when performing comparisons, rounding, or very precise arithmetic with them. The PHP documentation explains it like this:

Floating point numbers have limited precision. Although it depends on the system, PHP typically uses the IEEE 754 double precision format, which will give a maximum relative error due to rounding in the order of 1.11e-16. Non elementary arithmetic operations may give larger errors, and, of course, error propagation must be considered when several operations are compounded.

Additionally, rational numbers that are exactly representable as floating point numbers in base 10, like 0.1 or 0.7, do not have an exact representation as floating point numbers in base 2, which is used internally, no matter the size of the mantissa. Hence, they cannot be converted into their internal binary counterparts without a small loss of precision. This can lead to confusing results: for example, floor((0.1+0.7)*10) will usually return 7 instead of the expected 8, since the internal representation will be something like 7.9999999999999991118....

So never trust floating number results to the last digit, and do not compare floating point numbers directly for equality. If higher precision is necessary, the arbitrary precision math functions and gmp functions are available.

(from http://php.net/manual/en/language.types.float.php)

A serious bookkeeping program cannot be subject to these kinds of inconsistencies, so another approach is necessary.

GnuCash overcomes this problem by storing two integer values: a value and a denominator. For example, a value of 99.99 is stored like this:
value = 9999
denominator = 100

I suggest we move towards this kind of storage scheme with Ledger.