#Arithmetic

#Adding

add, subtract, sum, negate and absolute are exact. Amounts must be in the same currency:

def total as money.Money init money.sum($lines, "EUR");   # zero for no lines
def due as money.Money init money.subtract($total, $paid);

sum takes the currency so that an empty list still has one.

#Rounding modes

Multiplying, dividing and exchanging can land between two minor units, so each takes a mode. There is no default: whether a tax rounds half up, half to even or always up is the program's rule, not the deck's.

money.MODES lists them.

#Multiplying and dividing

The factor is a decimal string, computed exactly; only the result is rounded:

money.multiply(money.fromMinor(1999, "EUR"), "1.19", "half-up");   # 23.79 EUR
money.multiply(money.fromMinor(1000, "EUR"), "0.075", "down");     # 0.75 EUR
money.divide(money.fromMinor(1000, "EUR"), "3", "half-even");      # 3.33 EUR

Dividing and multiplying back does not give the amount again: 3 x 3.33 is 9.99. To share an amount out, allocate it.

#Allocating

allocate splits an amount by ratios, allocateTo into equal parts. The parts always add up to the amount:

money.allocateTo(money.fromMinor(1000, "EUR"), 3);              # 3.34, 3.33, 3.33
money.allocate(money.fromMinor(1000, "EUR"), ["50", "30", "20"]);   # 5.00, 3.00, 2.00
money.allocate(money.fromMinor(5, "EUR"), ["0.7", "0.3"]);        # 0.04, 0.01

Each part first gets its exact share rounded toward zero. The minor units left over then go one each to the parts whose share was cut the most, the earlier part on a tie; allocateTo therefore gives them to the first parts. A ratio of zero gets nothing. A negative amount splits like its positive mirror.

Ratios are decimal strings, not negative and not all zero. There can be at most MAX_PARTS (100000) parts.

#Exchanging

exchange takes a rate the caller supplies: units of the target currency per unit of the amount's. The deck fetches no rates; take them from a source the program trusts and pass them in as text:

money.exchange(money.fromMinor(10000, "EUR"), "USD", "1.0832", "half-even");   # 108.32 USD
money.exchange(money.fromMinor(10000, "EUR"), "JPY", "162.345", "half-even");  # 16234 JPY

The minor units of both currencies are taken into account, so EUR to JPY and JPY to KWD need no adjusting. The rate must be above zero.

#Limits

Amounts, factors, rates and ratios are at most MAX_TEXT (50) characters, so a hostile string cannot become a number with a million digits.