# Mathematical functions and constants¶

This page describes the mathematical functions and constants that are available in Phonometrica. Functions that usually accept a Number, such as log(), can also work with arrays, in which case the operation is applied to each element in the array.

## Global functions¶

abs(x)

Returns the absolute value of x. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

acos(x)

Returns the arccosine of x. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

asin(x)

Returns the arcsine of x. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

atan(x)

Returns the arctangent of x. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

atan2(y, x)

Returns the four-quadrant inverse tangent of y and x.

ceil(x)

Returns the smallest integer no smaller than x. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

cos(x)

Returns the cosine of x. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

exp(x)

Returns the exponential of x. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

floor(x)

Returns the largest integer that is no larger than x. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

log(x)

Returns the natural logarithm of x. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

log2(x)

Returns the logarithm of x in base 2. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

log10(x)

Returns the logarithm of x in base 10. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

max(x, y[, ...])

Returns the maximum value among the arguments passed to the function.

min(x, y[, ...])

Returns the minimum value among the arguments passed to the function.

pow(x, y)

Returns x raised to the power of y.

random()

Returns a pseudo-random value in the interval [0, 1[ according to a uniform distribution.

round(x)

Rounds x to the nearest integer. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

sin(x)

Returns the sine of x. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

sqrt(x)

Returns the square root of x. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

tan(x)

Returns the tangent of x. If x is an array, the function returns a copy of the array in which the function has been applied to each element.

## Constants¶

E

Returns the value of e, the base of the natural logarithm (approximately 2.718281).

PHI

Returns the value of the golden ratio $$\phi$$ (approximately 1.618033).

PI

Returns the value of pi (approximately 3.141593).

SQRT2

Returns the square root of 2 (approximately 1.414214).