如何使用 bitstring 包将浮点数输入为“0”和“1”字符的字符串？

Question

我想使用包 bitstring 和 mpmath（或任何其他方式来保证任意设置的输出精度和指定的舍入模式）来计算 rcp、sqrt、sin、cos、ln、exp、...在以二进制 bitstrings 给出的浮点输入上并获得二进制 bitstring回答。

我的目标是 C 中的 MPFR，但我想探索 Python 的浮点高精度包，希望更容易处理。我的第一个问题是如何将以下十进制浮点数反转为 bitstring 转换：

>>> from bitstring import *
>>> a = BitArray(float=1.2,length=32)
>>> a.bin
'00111111100110011001100110011010'

即如何以一种将 '00111111100110011001100110011010' 解释为（刚好超过）1.2 的方式将 '00111111100110011001100110011010' 提供给 bitstring 或 mpmath，然后将其提供给函数 [=15] =]、cos 或 ln（再次将我的答案变成 bitstring）。

我发现很难从 Python bitstring/mpmath 文档中了解二进制 input。它只说了十进制浮点数表示的困难，但没有说如何绕过这些简单地输入精确的二进制浮点数。

Answer 1

根据BitArray文档字符串，您可以指定bin参数：

__init__(self, auto=None, length=None, offset=None, **kwargs)
    Either specify an 'auto' initialiser:
    auto -- a string of comma separated tokens, an integer, a file object,
            a bytearray, a boolean iterable or another bitstring.

    Or initialise via **kwargs with one (and only one) of:
    bytes -- raw data as a string, for example read from a binary file.
    bin -- binary string representation, e.g. '0b001010'.   <--------------
    hex -- hexadecimal string representation, e.g. '0x2ef'
    oct -- octal string representation, e.g. '0o777'.
    uint -- an unsigned integer.
    int -- a signed integer.
    float -- a floating point number.
    uintbe -- an unsigned big-endian whole byte integer.
    intbe -- a signed big-endian whole byte integer.
    floatbe - a big-endian floating point number.
    uintle -- an unsigned little-endian whole byte integer.
    intle -- a signed little-endian whole byte integer.
    floatle -- a little-endian floating point number.
    uintne -- an unsigned native-endian whole byte integer.
    intne -- a signed native-endian whole byte integer.
    floatne -- a native-endian floating point number.
    se -- a signed exponential-Golomb code.
    ue -- an unsigned exponential-Golomb code.
    sie -- a signed interleaved exponential-Golomb code.
    uie -- an unsigned interleaved exponential-Golomb code.
    bool -- a boolean (True or False).
    filename -- a file which will be opened in binary read-only mode.

    Other keyword arguments:
    length -- length of the bitstring in bits, if needed and appropriate.
              It must be supplied for all integer and float initialisers.
    offset -- bit offset to the data. These offset bits are
              ignored and this is intended for use when
              initialising using 'bytes' or 'filename'.

>>> a = BitArray(bin='00111111100110011001100110011010')
>>> a.bin
'00111111100110011001100110011010'

使用float 属性得到浮点值：

>>> a.float
1.2000000476837158
>>>

Answer 2

BitArray 采用 bin 参数，该参数从二进制字符串表示形式对其进行初始化：

>>> from bitstring import *
>>> a = BitArray(float=1.2, length=32)
>>> a.bin
'00111111100110011001100110011010'
>>> b = BitArray(bin=a.bin)
>>> b.float
1.2000000476837158

所以一个通用函数可以做到这一点：

def float_from_bitstring(bitstring):
    return BitArray(bin=bitstring).float

如何使用 bitstring 包将浮点数输入为“0”和“1”字符的字符串？

How to input a float as a string of '0' and '1' characters with the bitstring package?

python

binary

floating-point

bitstring

mpmath