python-math函数

Math函数

• math.ceil(x) 【向上取整】

  Return the ceiling of x, the smallest integer greater than or equal to x. If x is not a float, delegates to x.__ceil__(), which should return an Integral value

  >>> math.ceil(5)
  5
  

• math.copysign(x, y)

  Return a float with the magnitude (absolute value) of x but the sign of y. On platforms that support signed zeros, copysign(1.0, -0.0) returns -1.0.

  返回一个浮点数，绝对值是x，符号为y，在支持带符号零的平台上，copsign（1.0,-0.0）返回-1.0

  >>> math.copysign(3.4,-0)
  3.4
  >>> math.copysign(3.4,-0.0)
  -3.4
  >>> math.copysign(3.4,-1)
  -3.4
  >>> math.copysign(3.4,1)
  3.4
  

  这里-0表示正数，-0.0表示复数

• math.fabs(x)

  Return the absolute value of x.

  返回关于x的绝对值小数

  >>> math.fabs(-1241)
  1241.0
  

  python自己有abs绝对值，返回的是整数

  >>> abs(-1241)
  1241
  

• math.factorial(x)

  Return x factorial. Raises ValueError if x is not integral or is negative.

  返回关于x的阶乘，如果x不是整数或者是复数，则引发valueerror错误

  >>> math.factorial(5)
  120
  >>> math.factorial(1)
  1
  >>> math.factorial(2)
  2
  >>> math.factorial(3)
  6
  >>> math.factorial(4)
  24
  

• math.floor(x)【向下取整】

  Return the floor of x, the largest integer less than or equal to x. If x is not a float, delegates to x.__floor__(), which should return an Integral value.

  >>> math.floor(2.51512)
  2
  >>> math.floor(0.2)
  0
  >>> math.floor(3.999999)
  3
  >>> math.floor(3)
  3
  类似于python自带的int函数
  >>> int(3.9)
  3
  

• math.fmod(x, y)

  Return fmod(x, y), as defined by the platform C library. Note that the Python expression x % y may not return the same result. The intent of the C standard is that fmod(x, y) be exactly (mathematically; to infinite precision) equal to x - n*y for some integer n such that the result has the same sign as x and magnitude less than abs(y). Python’s x % y returns a result with the sign of y instead, and may not be exactly computable for float arguments. For example, fmod(-1e-100, 1e100) is -1e-100, but the result of Python’s -1e-100 % 1e100 is 1e100-1e-100, which cannot be represented exactly as a float, and rounds to the surprising 1e100. For this reason, function fmod() is generally preferred when working with floats, while Python’s x % y is preferred when working with integers.

  返回x%y的取余值，并且带一位小数

  >>> 5%3
  2
  >>> math.fmod(5.5,3)
  2.5
  

• math.frexp(x)

  Return the mantissa and exponent of x as the pair (m, e). m is a float and e is an integer such that x == m * 2**e exactly. If x is zero, returns (0.0, 0), otherwise 0.5 <= abs(m) < 1. This is used to “pick apart” the internal representation of a float in a portable way.

  >>> 0.625*2**3
  5.0
  >>> math.frexp(5)
  (0.625, 3)
  

• math.fsum(iterable)

  Return an accurate floating point sum of values in the iterable. Avoids loss of precision by tracking multiple intermediate partial sums:>>> sum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1]) 0.9999999999999999 >>> fsum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1]) 1.0The algorithm’s accuracy depends on IEEE-754 arithmetic guarantees and the typical case where the rounding mode is half-even. On some non-Windows builds, the underlying C library uses extended precision addition and may occasionally double-round an intermediate sum causing it to be off in its least significant bit.For further discussion and two alternative approaches, see the ASPN cookbook recipes for accurate floating point summation.

  列表小数求和总所周知，python里的小数进行加减所得到的值未必是自己想要的，有时候使用sum求和一个列表里的所有小数得到的值也可能是错误的，因此出现了fsum，用来进行小数的求和

  >>> sum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1]) 0.9999999999999999 
  >>> fsum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
  1.0
  >>> sum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1,.1])
  1.0999999999999999
  >>> math.fsum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1,.1])
  1.1
  

• math.gcd(a, b)

  Return the greatest common divisor of the integers a and b. If either a or b is nonzero, then the value of gcd(a, b) is the largest positive integer that divides both a and b. gcd(0, 0) returns 0.New in version 3.5.

  返回最小公约数

  >>> math.gcd(50,25)
  25
  

• math.isclose(a, b, ***, rel_tol=1e-09, abs_tol=0.0)

  Return True if the values a and b are close to each other and False otherwise.Whether or not two values are considered close is determined according to given absolute and relative tolerances.rel_tol is the relative tolerance – it is the maximum allowed difference between a and b, relative to the larger absolute value of a or b. For example, to set a tolerance of 5%, pass rel_tol=0.05. The default tolerance is 1e-09, which assures that the two values are the same within about 9 decimal digits. rel_tol must be greater than zero.abs_tol is the minimum absolute tolerance – useful for comparisons near zero. abs_tol must be at least zero.If no errors occur, the result will be: abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol).The IEEE 754 special values of NaN, inf, and -inf will be handled according to IEEE rules. Specifically, NaN is not considered close to any other value, including NaN. inf and -inf are only considered close to themselves.New in version 3.5.See also PEP 485 – A function for testing approximate equality

  返回a与b的值是否接近，如果接近，则返回true，如果不接近则返回True，后面的rel_tol是允许a与b之间的最大的差别指数，默认为小数点后9位，如果想把这个值提高，可以传入一个大于0的参数。

  >>> math.isclose(0.3,0.1+0.2)
  True
  >>> 0.1+0.2
  0.30000000000000004
  >>> math.isclose(0.33333,0.333333,rel_tol=0.000001)
  False
  >>> math.isclose(0.33333,0.333333,rel_tol=0.00001)
  True
  

• math.isfinite(x)

  Return True if x is neither an infinity nor a NaN, and False otherwise. (Note that 0.0 is considered finite.)New in version 3.2.

• math.isinf(x)

  Return True if x is a positive or negative infinity, and False otherwise.

• math.isnan(x)

  Return True if x is a NaN (not a number), and False otherwise.

• math.ldexp(x, i)

  Return x * (2**i). This is essentially the inverse of function frexp().

• math.modf(x)

  Return the fractional and integer parts of x. Both results carry the sign of x and are floats.

  返回x的小数部分与整数部分，并且都带一位小数

  >>> math.modf(5)
  (0.0, 5.0)
  >>> math.modf(3.4)
  (0.3999999999999999, 3.0)
  >>> math.modf(3.7)
  (0.7000000000000002, 3.0)
  

• math.remainder(x, y)

  Return the IEEE 754-style remainder of x with respect to y. For finite x and finite nonzero y, this is the difference x - n*y, where n is the closest integer to the exact value of the quotient x / y. If x / y is exactly halfway between two consecutive integers, the nearest even integer is used for n. The remainder r = remainder(x, y) thus always satisfies abs(r) <= 0.5 * abs(y).Special cases follow IEEE 754: in particular, remainder(x, math.inf) is x for any finite x, and remainder(x, 0) and remainder(math.inf, x) raise ValueError for any non-NaN x. If the result of the remainder operation is zero, that zero will have the same sign as x.On platforms using IEEE 754 binary floating-point, the result of this operation is always exactly representable: no rounding error is introduced.New in version 3.7.

  返回x%y的值，并且带一位小数

  >>> math.remainder(1,2)
  1.0
  >>> math.remainder(4,2)
  0.0
  >>> math.remainder(9,4)
  1.0
  

• math.trunc(x)

  Return the Real value x truncated to an Integral (usually an integer). Delegates to x.__trunc__().

  返回x的整数部分，且整数部分为int型

  >>> math.trunc(10.5)
  10
  >>> math.trunc(12.5555555555)
  12
  >>> math.trunc(10)
  10
  

Note that frexp() and modf() have a different call/return pattern than their C equivalents: they take a single argument and return a pair of values, rather than returning their second return value through an ‘output parameter’ (there is no such thing in Python).

For the ceil(), floor(), and modf() functions, note that all floating-point numbers of sufficiently large magnitude are exact integers. Python floats typically carry no more than 53 bits of precision (the same as the platform C double type), in which case any float x with abs(x) >= 2**52 necessarily has no fractional bits.