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 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.

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.

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.

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-in pow() 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 of atan2() 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) and atan2(1, 1) are both pi/4, but atan2(-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.