如何在不使用小数、分数或任何其他外部库的情况下修复浮点数中的 Python 舍入错误？

Question

我有一个 class 模拟器：

class Simulator: # we use a class just to hold variables between calls
    def __init__(self):
        # initialise accumulators
        self.a_sum = 0
        self.b_sum = 0
        
    def update(self, a, b):
        # increment
        self.a_sum += a
        self.b_sum += b
       
    def results(self):
        # return a  pair of results
        return self.a_sum, self.a_sum - self.b_sum

如果我打印结果

a_error, d_error = simulate(Simulator())
print(f"Error in a_sum is {a_error} and {d_error} in d_sum")

我得到Error in a_sum is 13.7734375 and 4.101232676410264e-08 in d_sum，这是使用浮点数造成的。我知道计算是如何进行的，但我想知道是否可以在不转换为十进制的情况下修复错误？我试过四舍五入：

def update(self, a, b):
        # increment
        self.a_sum += round(a, 3)
        self.b_sum += round(b, 3)

它得到了稍微低一些的错误：Error in a_sum is 5.375 and 4.101232676410264e-08 in d_sum 但在那之后我再也无法得到它了。

有什么想法吗？

Answer 1

如何在不使用小数、分数或任何其他外部库的情况下修复浮点数中的 Python 舍入错误？

Floating Point Arithmetic: Issues and Limitations

(...)there are many different decimal numbers that share the same nearest approximate binary fraction. For example, the numbers 0.1 and 0.10000000000000001 and 0.1000000000000000055511151231257827021181583404541015625 are all approximated by 3602879701896397 / 2 ** 55. Since all of these decimal values share the same approximation, any one of them could be displayed while still preserving the invariant eval(repr(x)) == x.(...)this is in the very nature of binary floating-point: this is not a bug in Python, and it is not a bug in your code either. You’ll see the same kind of thing in all languages that support your hardware’s floating-point arithmetic (although some languages may not display the difference by default, or in all output modes).

强调由我添加，所以我想在这种情况下修复 float 的唯一方法是根本不使用 float。如果没有 decimal、fractions 或任何其他外部库.

，这通常是不可行的