1.8. math
— Mathematical functions¶
This module provides access to the mathematical functions defined by the C standard.

math.
ceil
(x)¶ 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.
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.

math.
fabs
(x)¶ Return the absolute value of x.

math.
floor
(x)¶ 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.
fmod
(x, y)¶ Return
fmod(x, y)
, as defined by the platform C library. Note that the Python expressionx % y
may not return the same result. The intent of the C standard is thatfmod(x, y)
be exactly (mathematically; to infinite precision) equal tox  n*y
for some integer n such that the result has the same sign as x and magnitude less thanabs(y)
. Python’sx % y
returns a result with the sign of y instead, and may not be exactly computable for float arguments. For example,fmod(1e100, 1e100)
is1e100
, but the result of Python’s1e100 % 1e100
is1e1001e100
, which cannot be represented exactly as a float, and rounds to the surprising1e100
. For this reason, functionfmod()
is generally preferred when working with floats, while Python’sx % y
is preferred when working with integers.

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 thatx == m * 2**e
exactly. If x is zero, returns(0.0, 0)
, otherwise0.5 <= abs(m) < 1
. This is used to “pick apart” the internal representation of a float in a portable way.

math.
isinf
(x)¶ Return
True
if x is a positive or negative infinity, andFalse
otherwise.

math.
isnan
(x)¶ Return
True
if x is a NaN (not a number), andFalse
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.

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

math.
log
(x[, base])¶ With one argument, return the natural logarithm of x (to base e).
With two arguments, return the logarithm of x to the given base, calculated as
log(x)/log(base)
.

math.
pow
(x, y)¶ Return x raised to the power y. If both x and y are finite, x is negative, and y is not an integer then
pow(x, y)
is undefined, and raises ValueError.Unlike the builtin ** operator,
math.pow()
converts both its arguments to type float. Use ** or the builtinpow()
function for computing exact integer powers.

math.
sqrt
(x)¶ Return the square root of x.

math.
acos
(x)¶ Return the arc cosine of x, in radians.

math.
asin
(x)¶ Return the arc sine of x, in radians.

math.
atan
(x)¶ Return the arc tangent of x, in radians.

math.
atan2
(y, x)¶ Return
atan(y/x)
, in radians. The result is between π and π. The vector in the plane from the origin to point(x, y)
makes this angle with the positive X axis. The point ofatan2()
is that the signs of both inputs are known to it, so it can compute the correct quadrant for the angle. For example,atan(1)
andatan2(1, 1)
are bothpi/4
, butatan2(1, 1)
is3*pi/4
.

math.
cos
(x)¶ Return the cosine of x radians.

math.
sin
(x)¶ Return the sine of x radians.

math.
tan
(x)¶ Return the tangent of x radians.

math.
degrees
(x)¶ Convert angle x from radians to degrees.

math.
radians
(x)¶ Convert angle x from degrees to radians.

math.
pi
()¶ The mathematical constant π = 3.141592..., to available precision.

math.
e
()¶ The mathematical constant e = 2.718281..., to available precision.