python里面mod函数,Mod函数在Python中失败大量

最新推荐文章于 2024-10-18 10:41:41 发布

吴钧泽

最新推荐文章于 2024-10-18 10:41:41 发布

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文章标签： python里面mod函数

本文探讨了在Python中使用`math.pow()`进行浮点数计算时遇到的精度问题，导致大于22的`math.factorial(x)%math.pow(2,x)`结果始终为0。解决方案是使用`**`操作符保持整数运算，以避免浮点数精度损失。通过示例展示了修正后的代码能正确计算大数值的阶乘和取模运算。

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This python code

for x in range(20, 50):

print(x,math.factorial(x),math.pow(2,x), math.factorial(x) % math.pow(2,x) )

calculates fine up to x=22 but the mod when x>22 is always 0.

Wolframalpha says the results for x>22 are nonzero.

For example, when x=23 we get 6815744.

I guess this problem results from how python actually calculates the mod function but was wondering if anyone actually knew.

解决方案

You are running into floating point limitations; math.pow() returns a floating point number, so both operands are coerced to floats. For x = 23, math.factorial(x) returns an integer larger than what a float can model:

>>> math.factorial(23)

25852016738884976640000

>>> float(math.factorial(23))

2.585201673888498e+22

The right-hand-side operator is a much smaller floating point number (only 7 digits), it is that difference in exponents that causes the modulus operator error out.

Use ** to stick to integers:

for x in range(20, 50):

print(x, math.factorial(x), 2 ** x, math.factorial(x) % (2 ** x))

Integer operations are only limited to how much memory is available, and for x = 23 the correct value is calculated, continuing to work correctly all the way to x = 49:

>>> x = 23

>>> print(x, math.factorial(x), 2 ** x, math.factorial(x) % (2 ** x))

23 25852016738884976640000 8388608 6815744

>>> x = 49

>>> print(x, math.factorial(x), 2 ** x, math.factorial(x) % (2 ** x))

49 608281864034267560872252163321295376887552831379210240000000000 562949953421312 492581209243648

Note that for even for smaller floating point modulus calculations, you really should be using the math.fmod() function, for reasons explained in the documentation. It too fails for this case however, again because you are reaching beyond the limits of floating point math:

>>> print(x, math.factorial(x), math.pow(2, x), math.fmod(math.factorial(x), math.pow(2, x)))

23 25852016738884976640000 8388608.0 0.0