Basic arithmetic and logic

TODO

• link to vector

R as a pocket calculator

Arithmetic operators

See help(Arithmetic)

3 + 7

[1] 10

9 / 3

[1] 3

12^2 + 1.5*10

[1] 159

10 %/% 3

[1] 3

10 %% 3

[1] 1

Also see help(Syntax) for operator precendence / associativity: This determines the order in which computations are carried out when multiple operators are present. Use parentheses to make execution order explicit.

9 * (3+2)

[1] 45

(9*3) + 2

[1] 29

Using operators in function notation

"/"(1, 10)

[1] 0.1

"+"(2, 3)

[1] 5

Standard math functions

sqrt(4)

[1] 2

sin(pi/2)

[1] 1

abs(-4)

[1] 4

log10(100)

[1] 2

exp(1)

[1] 2.718282

Rounding numbers

round(1.271)

[1] 1

round(pi, digits=3)

[1] 3.142

ceiling(1.2)

[1] 2

floor(3.7)

[1] 3

trunc(22.913)

[1] 22

Complex numbers

exp(1)^((0+1i)*pi)

[1] -1+0i

exp(1)^(-pi/2) - (0+1i)^(0+1i)

[1] 0+0i

sqrt(-1)

[1] NaN

sqrt(-1+0i)

[1] 0+1i

Special values

.Machine$integer.max

[1] 2147483647

.Machine$double.eps

[1] 2.220446e-16

1/0

[1] Inf

is.infinite(1/0)

[1] TRUE

0/0

[1] NaN

is.nan(0/0)

[1] TRUE

NULL

NULL

is.null(NULL)

[1] TRUE

Using variables (objects)

x1 <- 2
x2 <- 10
x3 <- -7
x1 * 2

[1] 4

x2^x1 + x3

[1] 93

Logic

Logical values

TRUE

[1] TRUE

FALSE

[1] FALSE

!TRUE

[1] FALSE

!FALSE

[1] TRUE

isTRUE(TRUE)

[1] TRUE

isTRUE(FALSE)

[1] FALSE

Logical comparisons

TRUE == TRUE

[1] TRUE

TRUE == FALSE

[1] FALSE

TRUE != TRUE

[1] FALSE

TRUE != FALSE

[1] TRUE

TRUE & TRUE

[1] TRUE

TRUE & FALSE

[1] FALSE

FALSE & FALSE

[1] FALSE

FALSE & TRUE

[1] FALSE

TRUE | TRUE

[1] TRUE

TRUE | FALSE

[1] TRUE

FALSE | FALSE

[1] FALSE

FALSE | TRUE

[1] TRUE

xor(TRUE, FALSE)

[1] TRUE

xor(TRUE, TRUE)

[1] FALSE

Short-circuit logical comparisons with vectors

c(TRUE,  FALSE, FALSE) && c(TRUE,  TRUE, FALSE)

[1] TRUE

c(FALSE, FALSE, TRUE)  || c(FALSE, TRUE, FALSE)

[1] FALSE

Arithmetic comparisons

4 < 8

[1] TRUE

7 < 3

[1] FALSE

4 > 4

[1] FALSE

4 >= 4

[1] TRUE

Checking whether any or all elements are TRUE

any(c(FALSE, FALSE, FALSE))

[1] FALSE

any(c(FALSE, FALSE, TRUE))

[1] TRUE

all(c(TRUE, TRUE, FALSE))

[1] FALSE

any(c(TRUE, TRUE, TRUE))

[1] TRUE

In an empty vector, there is no element that is FALSE, therefore:

all(numeric(0))

[1] TRUE

In an empty vector, you cannot pick an element that is TRUE, therefore:

any(numeric(0))

[1] FALSE

Numeric representations

Integers vs. decimal numbers

4L == 4

[1] TRUE

identical(4L, 4)

[1] FALSE

Floating point arithmetic

0.1 + 0.2 == 0.3

[1] FALSE

1 %/% 0.1

[1] 9

sin(pi)

[1] 1.224647e-16

1 - ((1/49) * 49)

[1] 1.110223e-16

1 - ((1/48) * 48)

[1] 0

What every computer scientist should know about floating-point arithmetic

Checking decimal numbers for equality

isTRUE(all.equal(0.123450001, 0.123450000))

[1] TRUE

0.123400001 == 0.123400000

[1] FALSE

all.equal(0.12345001, 0.12345000)

[1] "Mean relative difference: 8.100445e-08"

isTRUE(all.equal(0.12345001,  0.12345000))

[1] FALSE

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