Python 等语言如何克服 C 的 Integral 数据限制？

发布于 2024-07-20 11:19:08 字数 889 浏览 6 评论 0原文

使用 C、Python 和 Scheme 中的阶乘程序进行一些随机实验。我发现了这个事实：

在 C 中，使用“unsigned long long”数据类型，我可以打印的最大阶乘是 65。即“9223372036854775808”，即指定的 19 位数字此处。

在Python中，我可以找到一个大到999的数字的阶乘，这个数字由大量数字组成，远远超过19。CPython

是如何实现这一点的？它是否使用像 'octaword' 这样的数据类型？

我可能在这里遗漏了一些基本事实。因此，我希望能阅读一些见解和/或参考资料。谢谢！

更新：谢谢大家的解释。这是否意味着 CPython 正在使用 GNU 多精度库（或其他类似的库）？

更新 2：我正在源代码中寻找 Python 的“bignum”实现。它到底在哪里？它位于 http://svn.python.org /view/python/trunk/Objects/longobject.c?view=markup。谢谢拜山帕扬。

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怪异←思 2024-07-27 11:19:08

这称为任意精度算术。这里还有更多内容：http://en.wikipedia.org/wiki/Arbitrary- precision_arithmetic

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怕倦 2024-07-27 11:19:08

查看Python源代码，似乎long类型（至少在Python 3之前的代码中）是在longintrepr.h 像这样 -

/* Long integer representation.
   The absolute value of a number is equal to
    SUM(for i=0 through abs(ob_size)-1) ob_digit[i] * 2**(SHIFT*i)
   Negative numbers are represented with ob_size < 0;
   zero is represented by ob_size == 0.
   In a normalized number, ob_digit[abs(ob_size)-1] (the most significant
   digit) is never zero.  Also, in all cases, for all valid i,
    0 <= ob_digit[i] <= MASK.
   The allocation function takes care of allocating extra memory
   so that ob_digit[0] ... ob_digit[abs(ob_size)-1] are actually available.

   CAUTION:  Generic code manipulating subtypes of PyVarObject has to
   aware that longs abuse  ob_size's sign bit.
*/

struct _longobject {
    PyObject_VAR_HEAD
    digit ob_digit[1];
};

long 类型的实际可用接口然后在 < a href="http://svn.python.org/view/python/trunk/Include/longobject.h?view=markup" rel="nofollow noreferrer">longobject.h 通过创建新类型 PyLongObject像这样 -

typedef struct _longobject PyLongObject;

等等。

longobject.c，您可以查看这些内容以了解更多详细信息。

Looking at the Python source code, it seems the long type (at least in pre-Python 3 code) is defined in longintrepr.h like this -

/* Long integer representation.
   The absolute value of a number is equal to
    SUM(for i=0 through abs(ob_size)-1) ob_digit[i] * 2**(SHIFT*i)
   Negative numbers are represented with ob_size < 0;
   zero is represented by ob_size == 0.
   In a normalized number, ob_digit[abs(ob_size)-1] (the most significant
   digit) is never zero.  Also, in all cases, for all valid i,
    0 <= ob_digit[i] <= MASK.
   The allocation function takes care of allocating extra memory
   so that ob_digit[0] ... ob_digit[abs(ob_size)-1] are actually available.

   CAUTION:  Generic code manipulating subtypes of PyVarObject has to
   aware that longs abuse  ob_size's sign bit.
*/

struct _longobject {
    PyObject_VAR_HEAD
    digit ob_digit[1];
};

The actual usable interface of the long type is then defined in longobject.h by creating a new type PyLongObject like this -

typedef struct _longobject PyLongObject;

And so on.

There is more stuff happening inside longobject.c, you can take a look at those for more details.

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手心的温暖 2024-07-27 11:19:08

C 中的int 等数据类型直接（或多或少）映射到处理器支持的数据类型。因此，C 的 int 的限制本质上是处理器硬件施加的限制。

但我们可以完全在软件中实现自己的 int 数据类型。例如，您可以使用数字数组作为基础表示。可能是这样的：

class MyInt {
    private int [] digits;
    public MyInt(int noOfDigits) {
       digits = new int[noOfDigits];
    }
}

一旦你这样做了，你就可以使用这个类并存储包含任意数量数字的整数，只要你不耗尽内存。

也许Python正在其虚拟机中做类似的事情。您可能需要阅读关于任意精度算术的这篇文章以获取详细信息。

Data types such as int in C are directly mapped (more or less) to the data types supported by the processor. So the limits on C's int are essentially the limits imposed by the processor hardware.

But one can implement one's own int data type entirely in software. You can for example use an array of digits as your underlying representation. May be like this:

class MyInt {
    private int [] digits;
    public MyInt(int noOfDigits) {
       digits = new int[noOfDigits];
    }
}

Once you do that you may use this class and store integers containing as many digits as you want, as long as you don't run out memory.

Perhaps Python is doing something like this inside its virtual machine. You may want to read this article on Arbitrary Precision Arithmetic to get the details.

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