Python 3 decimal模块底层运算：基于处理器浮点类型还是整数？

Great question—your intuition is spot-on! The decimal module in Python 3 is entirely implemented using integer arithmetic, not relying on the processor's native floating-point types (like IEEE 754 single/double-precision floats). Here's why that makes sense, and how it works:

Why integers instead of hardware floats? #

• Exact decimal representation: Hardware floats use binary fractions, which can't precisely represent many common decimal values (e.g., 0.1 is a repeating fraction in binary). By using integers to store each digit of the decimal number plus an exponent tracking the decimal point position, decimal avoids this inherent imprecision.
• Arbitrary precision support: Hardware floats have fixed precision (e.g., 64 bits for doubles). The decimal module lets you adjust the precision dynamically (via getcontext().prec) by simply using larger integers to store more digits—something hardware floats can't do natively.

How it works under the hood (CPython example) #

In CPython's reference implementation, the decimal module uses Python's arbitrary-precision integers to represent the significant digits of the decimal number, paired with a separate integer exponent to track the scale (how many places to shift the decimal point). All arithmetic operations—addition, subtraction, multiplication, division—are implemented using integer operations to manipulate these digits and exponents, completely bypassing the CPU's floating-point unit.

For a quick demonstration of the difference:

from decimal import Decimal

# Decimal gives exact result
print(Decimal("0.1") + Decimal("0.2"))  # Output: 0.3

# Hardware float gives imprecise result
print(0.1 + 0.2)  # Output: 0.30000000000000004

This contrast directly stems from the decimal module's integer-based foundation, which prioritizes decimal precision over the speed of hardware float operations.

内容的提问来源于stack exchange，提问作者Paul Uszak