用十进制换钱如何避免python中的浮点问题？

Question

So currency/money has lot's of known math issues when using a floating point. It seems in python that decimal is used in money libraries, but according to the python docs , decimal is based on a floating point. So how does this not have the same problems?

context a lot of currency libraries measure their monetary values as integers (so cents of USD, not dollars). We've just had the issue of a python application representing it's money as decimal, it goes into javascript, which then needs to convert it to an integer for another service.

10.05 / 100, became 1050.0000...1 which is of course, not an integer. So of course I was wondering why python chose this route, as most recommendations I've seen recommend treating money as integers.

Answer 1

You are confusing binary floating point with decimal floating point. From the module documentation :

The decimal module provides support for fast correctly-rounded decimal floating point arithmetic.

[...]

• Decimal numbers can be represented exactly. In contrast, numbers like 1.1 and 2.2 do not have exact representations in binary floating point

(bold emphasis mine).

The floating point aspect refers to the variability of the exponent; the number 12300000 can be represented as 123 with a decimal exponent of 5 (10 ** 5). Both float and decimal use a floating point representation. But float adds up a number of binary fractions (1/2 + 1/4 + 1/8 + 1/16 + ...), and that makes them unsuitable for representing currencies as binary fractions can not predicisely model 1/100ths or 1/10ths, which currency values tend to use a lot.

The DZone article on floating point issues for currency you link also teaches you about the Java java.math.BigDecimal package . Python's decimal is essentially the same thing ; where the BigDecimal documentation talks about values consist[ing] of an arbitrary precision integer unscaled value and a 32-bit integer scale , the scale is essentially the position of the floating point.

Because decimal can represent 1/100ths (cents) in currency values exactly, it is far more suitable to model currency values.

Answer 2

Decimal avoids some of the problems of binary floating-point, but not all, possibly not even most.

The actual problem is not floating-point but numerical formats. No numerical format can represent all real numbers, or even all rational numbers, so no numerical format can handle all the operations we want to do with numbers.

Money is commonly represented in decimal fractions of a unit of currency. For example, the US dollar and many other currencies have as a “cent” which is 1/100 ^th of a dollar. A decimal format can represent 1/100 ^th exactly. A binary format cannot. So, with a decimal format, you can:

• Represent decimal units of currency exactly (within bounds of the format).
• Add and subtract decimal amounts of currency exactly (within bounds of the format).
• Multiply decimal units of currency by integers exactly (within bounds of the format).

However, problems arise when you try:

• To average numbers or divide by numbers other than powers of ten (or two or five). For example, if a grocery wants to sell a product at three for a dollar, there is no way to represent ⅓ exactly in a decimal format.
• Multiplying numbers with decimal fractions more than a few times. Each multiplication will increase the number of digits after the decimal point. For example, interest compounded monthly for a year cannot be computed exactly with typical decimal formats.
• Any complex (in the general sense, not mathematical) operations such as exponentiation that may be involved in considering the time value of money, stock market options evaluation, and so on.

There is no general solution to how to compute numerically. Studying numerical computing and its errors is an entire field of study with textbooks, courses, and research papers. So you cannot solve numerical problems merely by choosing a format. It is important to understand whatever format(s) you use, what errors arise in using them, how to deal with those errors, and what results you need to achieve.

Answer 3

Decimal types allow decimal floating point rather than binary floating point. The class of problems you are referring to relate to the latter.