对于大数，为什么整数除法和除法转换为int的结果不同？ [英] Why are the results of integer division and converting to an int after division different for large numbers?
问题描述
print(10**40//2)
print(int(10**40/2))
代码输出：
5000000000000000000000000000000000000000
5000000000000000151893014213501833445376
为什么值不同？为什么第二个 print（）的输出看起来如此？
Why different values? Why the output of the second print() looks so?
推荐答案
10 ** 40 // 2 的浮点表示不准确：
>>> format(float(10**40//2), '.0f')
'5000000000000000151893014213501833445376'
那是因为浮点算法只是一个近似值，尤其是当您超出了CPU可以准确建模的范围时（因为浮点是在硬件中处理的。）
That's because floating point arithmetic is only ever an approximation, especially when you go beyond what your CPU can accurately model (as floating point is handled in hardware).
整数除法不必将 10 ** 40 数字表示为浮点数，它只需要除以整数即可，在Python中整数可以任意取大而不会造成精度损失。
The integer division never has to represent the 10**40 number as a float, it only has to divide the integer, which in Python can be arbitrarily large without precision loss.
另请参见：
- 浮点算术：问题和局限性 在Python教程中
- > 每个程序员应了解的浮点算法
- 每位计算机科学家应该了解的浮点运算
- Floating Point Arithmetic: Issues and Limitations in the Python tutorial
- What Every Programmer Should Know About Floating-Point Arithmetic
- What Every Computer Scientist Should Know About Floating-Point Arithmetic
Also look at the decimal module if you must use higher-precision floating point arithmetic.
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