The R Book

Built-in Functions

All the mathematical functions you could ever want are here (see Table 2.1). The log function gives logs to the base e e = 2 718282, for which the antilog function is exp

log(10)

[1] 2.302585

exp(1)

[1] 2.718282

If you are old fashioned, and want logs to the base 10, then there is a separate function

log 10(6)

[1] 0.7781513

Logs to other bases are possible by providing the log function with a second argument which is the base of the logs you want to take. Suppose you want log to base 3 of 9:

log(9,3)

[1]   2

The trigonometric functions in R measure angles in radians. A circle is 2π radians, and this is 360°, so a right angle (90°) is π/2 radians. R knows the value of π as pi:

pi

[1]  3.141593

sin(pi/2)

[1]     1

cos(pi/2)

[1]  6.123032e-017

Notice that the cosine of a right angle does not come out as exactly zero, even though the sine came out as exactly 1. The e–017 means ‘times 10⁻¹⁷’. While this is a very smallnumber it is clearly not exactly zero (so you need to be careful when testing for exact equality of real numbers; see p. 77).

Table 2.1. Mathematical functions used in R.

Function	Meaning
log(x)	log to base e of x
exp(x)	antilog of x(ex)
log(x,n)	log to base n of x
log10(x)	log to base 10 of x
sqrt(x)	square root of x
factorial(x)	x!
choose(n,x)	binomial coefficients n!/(x! (n – x)!)
gamma(x)	Γ(x), for real x(x – 1)!, for integer x
lgamma(x)	natural log of Γ(x)
floor(x)	greatest integer < x
ceiling(x)	smallest integer > x