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(-1e-100, 1e100)
is-1e-100
, but the result of Python’s-1e-100 % 1e100
is1e100-1e-100
, 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 built-in ** operator,
math.pow()
converts both its arguments to type float. Use ** or the built-inpow()
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)
is-3*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.