3.6 Numeric operations

3.6.1 Arithmethic operators

Common arithmethic aperation such as sum (+), substruction (-), multiplication (*), division (/), left division (\), integer division (÷), remainder (%), exponentiation (^), rational division (//) can be done. See in the examples below that the output type will depend of the arguments type.

4 + 3
# 7

4 - 3
# 1

4.0 * 3
# 12.0

4.0 / 3
# 1.3333333333333333

3 \ 4
# 1.3333333333333333

10 ÷ 4
# 2

4.4 % 3
# 1.4000000000000004

3.0 ^ 4
# 81

4 // 3
# 4 // 3

Negation is available for Bool types:

!true

3.6.2 Bitwise operators

Common bitwise operators are not (~), and (&), or (|), xor (⊻). See examples below.

~ false
# true

true & false
# false

true | false
# true

true ⊻ false
# true

3.6.3 Updating operators

The updating version of binary operators is obtained by appending = at the end of the operator. Some examples are +=, -=, /= and *=.

x = 1
x += 3
x

3.6.4 Numeric literal coefficients

Julia allows to use literal numbers to define polinomials. This means that:

a number preceding a variable will be consider a coefficient,
unary operators (-, +, √) have greater priority,
literal coefficient have greater priority than unary operators when using exponentiation,
parenthesized expressions can be used in the variable or coefficient part,

x = 3
2x + 2
# 8

√4x
# 6.0

2 ^ 2x
# 64

3(x + 1)
# 12

(x + 2)x
# 15

3.6.5 Vectorized dot operator (element-wise)

x = [1, 3, 5]

2x .^2 .-3x .+ 1
# 3-element Array{Int64,1}:
#   0
#   10
#   36

sin.(x)
# 3-element Array{Float64,1}:
#   0.8414709848078965
#   0.1411200080598672
#   -0.9589242746631385

sum.([1:2, 2:4, 3:5])
# 3-element Array{Int64,1}:
#   3
#   9
#   12

Similarly we can use the macro @. that will convert every function into a dot call.

x = [1, 3, 5]

@. 2x ^ 2 - 3x + 1
# 3-element Array{Int64,1}:
#   0
#   10
#   36

@. sin(x)
# 3-element Array{Float64,1}:
#   0.8414709848078965
#   0.1411200080598672
#   -0.9589242746631385

@. sum([1:2, 2:4, 3:5])
# 3-element Array{Int64,1}:
#   3
#   9
#   12

3.6.6 Numeric comparisons

Stardard comparison operators are equality (==), inequality (!=), less than (<), greater than (>).

10.5 == 10.5
# true

10.4 != 10.41
10.4 ≢ 10.41
# true

3 > 3
# false

2 ≥ 1
# true

4 < 5
# true

4 ≤ 5
# true

There is also useful comparison function for special values (e.g. NaN, Inf) such as isequal, isfinite, isinf, isnan.

isequal(NaN, NaN)
# true

isinf(Inf)
# true

isnan(NaN)
# true

Comparisons can also be arbitrarily chained.

8 > 4 <= 10 == 10 < 20