标题: Python大数存放格式

创建: 2023-03-17 20:20
更新: 2023-03-21 14:02
链接: https://scz.617.cn/python/202303172020.txt

获取大数的地址，一正一负

python3-dbg

>>> x=3215031751
>>> hex(id(x))
'0x7f466c804bc0'

>>> x=-3215031751
>>> hex(id(x))
'0x7f466c804e40'

在gdb中查看大数

gdb -q -nx -x gdbinit_x64.txt -x gdbhelper.py -p $(pidof python3-dbg)

(gdb) p/x *(PyLongObject *)0x7f466c804bc0
$2 = {
  ob_base = {
    ob_base = {
      ob_refcnt = 0x1,
      ob_type = 0x9af720
    },
    ob_size = 0x2
  },
  ob_digit = {
    [0x0] = 0x3fa17dc7
  }
}

(gdb) p/x ((PyLongObject *)0x7f466c804bc0)->ob_digit@2
$3 = {
  [0x0] = {
    [0x0] = 0x3fa17dc7
  },
  [0x1] = {
    [0x0] = 0x2
  }
}

Python解释器内部以"2**30"进制存放大数，ob_size的绝对值表示有多少个系数，
ob_size的符号对应大数的符号，ob_size为负时表示大数为负，ob_digit[]以
little-endian序存放ABS(ob_size)个系数。

下例是负数

(gdb) p/x *(PyLongObject *)0x7f466c804e40
$4 = {
  ob_base = {
    ob_base = {
      ob_refcnt = 0x1,
      ob_type = 0x9af720
    },
    ob_size = 0xfffffffffffffffe
  },
  ob_digit = {
    [0x0] = 0x3fa17dc7
  }
}

(gdb) p/x ((PyLongObject *)0x7f466c804e40)->ob_digit@(-(signed long long)0xfffffffffffffffe)
(gdb) p/x ((PyLongObject *)0x7f466c804e40)->ob_digit@2
$5 = {
  [0x0] = {
    [0x0] = 0x3fa17dc7
  },
  [0x1] = {
    [0x0] = 0x2
  }
}

--------------------------------------------------------------------------
def show_coefficient ( large, base ) :
    coefficient = []
    while large > 0 :
        large, digit    = divmod( large, base )
        coefficient.append( hex( digit ) )
    #
    # end of while
    #
    return coefficient[::-1] if coefficient else ['0x0']
#
# end of show_coefficient
#
--------------------------------------------------------------------------

>>> show_coefficient( 3215031751, 2**30 )
['0x2', '0x3fa17dc7']

Python序列化大数时没有用"2**30"进制，用的是"2**15"进制，pyc中TYPE_LONG型以
ushort[]存放"2**15"进制的系数。

>>> show_coefficient( 3215031751, 2**15 )
['0x2', '0x7f42', '0x7dc7']

>>> hex(0xf*(2**15)**4+0x7fff*(2**15)**3+0x7fff*(2**15)**2+0x7fff*(2**15)**1+0x7fff)
'0xffffffffffffffff'

>>> show_coefficient( 0xffffffffffffffff, 2**15 )
['0xf', '0x7fff', '0x7fff', '0x7fff', '0x7fff']