python 内置类型(二)---int,float,complex

一、int

1.int.bit_length()

获取数字的二进制表示长度
例子：

>>>bin(10)
'0b1010'
>>>int.bit_length(10)
4

方法等价于:

def bit_length(self):
    s = bin(self)       # binary representation:  bin(-37) --> '-0b100101'
    s = s.lstrip('-0b') # remove leading zeros and minus sign
    return len(s)       # len('100101') --> 6

2.int.to_bytes(length, byteorder, *, signed=False)

将数字转换为十六进制表示，
length代表将要转换的数据长度，不足补0,超出报错(OverflowError)
byteorder表示转换后的数字的排列顺序，big表示正常表示,little表示反向表示
signed如果传入的是负数或者其他会引起OverflowError的数字，则设置signed为True可避免报错
例子：

>>> (1024).to_bytes(2, byteorder='big')
b'\x04\x00'
>>> (1024).to_bytes(10, byteorder='big')
b'\x00\x00\x00\x00\x00\x00\x00\x00\x04\x00'
>>> (-1024).to_bytes(10, byteorder='big', signed=True)
b'\xff\xff\xff\xff\xff\xff\xff\xff\xfc\x00'
>>> x = 1000
>>> x.to_bytes((x.bit_length() + 7) // 8, byteorder='little')
b'\xe8\x03'

3.int.from_bytes(bytes, byteorder, *, signed=False

将byte-like类型的十六进制数字转换为十进制表示，
bytes代表要转换的数据
byteorder表示bytes的读取顺序，big表示正常读取,little表示反向读取
signed设置signed为True表示返回的是负数表示
例子：

>>> int.from_bytes(b'\x00\x10', byteorder='big')
16
>>> int.from_bytes(b'\x00\x10', byteorder='little')
4096
>>> int.from_bytes(b'\xfc\x00', byteorder='big', signed=True)
-1024
>>> int.from_bytes(b'\xfc\x00', byteorder='big', signed=False)
64512
>>> int.from_bytes([255, 0, 0], byteorder='big')
16711680

二、float

1.float.as_integer_ratio()

返回一对整数，其比值与原浮点数完全相等，且具有正分母
传入必须为浮点数，否则会报错TypeError

>>>float.as_integer_ratio(1.5)
(3, 2)
>>>float.as_integer_ratio(2)
Traceback (most recent call last):
  File "", line 1, in 
TypeError: descriptor 'as_integer_ratio' requires a 'float' object but received a 'int'
>>>float.as_integer_ratio(2.0)
(2, 1)
>>>float.as_integer_ratio(2.1)
(4728779608739021, 2251799813685248)

2.float.is_integer()

判断浮点数是否是整数

>>> (-2.0).is_integer()
True
>>> (3.2).is_integer()
False

3.float.hex()

浮点数转化为十六进制的浮点数...

>>>float.hex(1.0)
'0x1.0000000000000p+0'
>>>float.hex(2.1)
'0x1.0cccccccccccdp+1'

4.float.fromhex(s)

十六进制转化为浮点数

>>> float.fromhex('0x3.a7p10')
3740.0
>>> float.hex(3740.0)
'0x1.d380000000000p+11'
>>>float.fromhex('0x1.0cccccccccccdp+1')
2.1

三、数字的hash值(Hashing of numeric types)

python 官方文档上写的：
python定义的hash值的计算规则:

• If x = m / n is a nonnegative rational number and n is not divisible by P, define hash(x) as m * invmod(n, P) % P, where invmod(n, P) gives the inverse of n modulo P.
• If x = m / n is a nonnegative rational number and n is divisible by P (but m is not) then n has no inverse modulo P and the rule above doesn’t apply; in this case define hash(x) to be the constant value sys.hash_info.inf.
• If x = m / n is a negative rational number define hash(x) as -hash(-x). If the resulting hash is -1, replace it with -2.
• The particular values sys.hash_info.inf, -sys.hash_info.inf and sys.hash_info.nan are used as hash values for positive infinity, negative infinity, or nans (respectively). (All hashable nans have the same hash value.)
• For a complex number z, the hash values of the real and imaginary parts are combined by computing hash(z.real) +sys.hash_info.imag * hash(z.imag), reduced modulo 2**sys.hash_info.width so that it lies in range(-2**(sys.hash_info.width - 1), 2**(sys.hash_info.width - 1)). Again, if the result is -1, it’s replaced with -2.
  下面是根据上面的设定的规则实现的计算hash的方法

import sys, math

def hash_fraction(m, n):
    """Compute the hash of a rational number m / n.

    Assumes m and n are integers, with n positive.
    Equivalent to hash(fractions.Fraction(m, n)).

    """
    P = sys.hash_info.modulus
    # Remove common factors of P.  (Unnecessary if m and n already coprime.)
    while m % P == n % P == 0:
        m, n = m // P, n // P

    if n % P == 0:
        hash_value = sys.hash_info.inf
    else:
        # Fermat's Little Theorem: pow(n, P-1, P) is 1, so
        # pow(n, P-2, P) gives the inverse of n modulo P.
        hash_value = (abs(m) % P) * pow(n, P - 2, P) % P
    if m < 0:
        hash_value = -hash_value
    if hash_value == -1:
        hash_value = -2
    return hash_value

def hash_float(x):
    """Compute the hash of a float x."""

    if math.isnan(x):
        return sys.hash_info.nan
    elif math.isinf(x):
        return sys.hash_info.inf if x > 0 else -sys.hash_info.inf
    else:
        return hash_fraction(*x.as_integer_ratio())

def hash_complex(z):
    """Compute the hash of a complex number z."""

    hash_value = hash_float(z.real) + sys.hash_info.imag * hash_float(z.imag)
    # do a signed reduction modulo 2**sys.hash_info.width
    M = 2**(sys.hash_info.width - 1)
    hash_value = (hash_value & (M - 1)) - (hash_value & M)
    if hash_value == -1:
        hash_value = -2
    return hash_value