Julia Basic Operators

Julia provides a rich set of operators, including arithmetic, comparison, logical, and bitwise operators.

Arithmetic Operators

Basic Arithmetic

a = 10
b = 3

# Addition
println(a + b)   # 13

# Subtraction
println(a - b)   # 7

# Multiplication
println(a * b)   # 30

# Division
println(a / b)   # 3.333... (returns float)

# Integer division (floor)
println(a ÷ b)   # 3 (same as div(a, b))

# Remainder (modulo)
println(a % b)   # 1 (same as rem(a, b))

# Power
println(a ^ 2)   # 100

# Negation
println(-a)      # -10

Division Variants

a = 10
b = 3

# Standard division (always returns float)
println(10 / 3)      # 3.333...

# Integer division (floor, ÷ or div)
println(10 ÷ 3)      # 3
println(div(10, 3))  # 3

# Remainder
println(10 % 3)      # 1
println(rem(10, 3))  # 1

# Modulo (different from rem for negatives)
println(mod(10, 3))  # 1
println(rem(-10, 3)) # -1
println(mod(-10, 3)) # 2

# Get quotient and remainder together
q, r = divrem(10, 3)
println("Quotient: $q, Remainder: $r")  # Quotient: 3, Remainder: 1

# Float division rounding
println(fld(10, 3))  # 3 (floor toward -∞)
println(cld(10, 3))  # 4 (ceiling toward +∞)

Compound Assignment Operators

x = 10

x += 5   # x = x + 5
println(x)  # 15

x -= 3   # x = x - 3
println(x)  # 12

x *= 2   # x = x * 2
println(x)  # 24

x /= 4   # x = x / 4
println(x)  # 6.0

x ^= 2   # x = x ^ 2
println(x)  # 36.0

# Integer division assignment
x = 10
x ÷= 3
println(x)  # 3

# Remainder assignment
x = 10
x %= 3
println(x)  # 1

Comparison Operators

Basic Comparison

a = 5
b = 3

# Equal
println(a == b)  # false

# Not equal
println(a != b)  # true
println(a ≠ b)   # true (Unicode)

# Greater than
println(a > b)   # true

# Less than
println(a < b)   # false

# Greater or equal
println(a >= b)  # true
println(a ≥ b)   # true (Unicode)

# Less or equal
println(a <= b)  # false
println(a ≤ b)   # false (Unicode)

Chained Comparison

Julia supports mathematical-style chained comparison:

x = 5

# Chained comparison
println(1 < x < 10)     # true
println(1 ≤ x ≤ 10)     # true
println(1 < 5 < 3)      # false

# Equivalent to
println(1 < x && x < 10)  # true

# Multiple chained
println(1 < 2 < 3 < 4)   # true

Approximate Comparison

# Float comparison (considering precision)
a = 0.1 + 0.2
b = 0.3

println(a == b)              # false (float precision issue)
println(isapprox(a, b))      # true
println(a ≈ b)               # true (≈ is infix form of isapprox)

# Specify tolerance
println(isapprox(1.0, 1.001, atol=0.01))  # true (absolute tolerance)
println(isapprox(1.0, 1.001, rtol=0.01))  # true (relative tolerance)

Object Comparison

# === checks object identity
a = [1, 2, 3]
b = [1, 2, 3]
c = a

println(a == b)   # true (values equal)
println(a === b)  # false (not same object)
println(a === c)  # true (same object)

# For immutable types
x = 5
y = 5
println(x === y)  # true (immutable with equal values)

Logical Operators

Basic Logical Operations

a = true
b = false

# Logical AND
println(a && b)  # false
println(a & b)   # false (bitwise, same for booleans)

# Logical OR
println(a || b)  # true
println(a | b)   # true (bitwise)

# Logical NOT
println(!a)      # false
println(!b)      # true

Short-Circuit Evaluation

# && short-circuit: if first is false, skip second
x = 5
x > 0 && println("x is positive")  # will print
x < 0 && println("x is negative")  # won't print

# || short-circuit: if first is true, skip second
x > 0 || println("x is not positive")  # won't print
x < 0 || println("x is not negative")  # will print

# Common pattern
function validate(x)
    x === nothing && return false
    x < 0 && return false
    return true
end

Ternary Operator

x = 10

# condition ? value_if_true : value_if_false
result = x > 5 ? "greater than 5" : "5 or less"
println(result)  # greater than 5

# Can be nested
grade = 85
level = grade >= 90 ? "A" : grade >= 80 ? "B" : grade >= 70 ? "C" : "D"
println(level)  # B

Bitwise Operators

Bitwise Operations

a = 0b1010  # 10 in binary
b = 0b1100  # 12 in binary

# Bitwise AND
println(a & b)   # 8 (0b1000)

# Bitwise OR
println(a | b)   # 14 (0b1110)

# Bitwise XOR
println(a ⊻ b)   # 6 (0b0110)
println(xor(a, b))  # same

# Bitwise NOT
println(~a)      # -11 (inversion)

# View binary representation
println(bitstring(UInt8(10)))  # "00001010"
println(bitstring(UInt8(12)))  # "00001100"

Shift Operations

a = 8  # 0b1000

# Left shift
println(a << 1)   # 16 (0b10000)
println(a << 2)   # 32 (0b100000)

# Right shift (arithmetic, preserves sign)
println(a >> 1)   # 4 (0b100)
println(a >> 2)   # 2 (0b10)

# Unsigned right shift
println(a >>> 1)  # 4

Special Operators

Range Operator

# Using : to create range
r = 1:10
println(collect(r))  # [1, 2, 3, ..., 10]

# Range with step
r = 1:2:10
println(collect(r))  # [1, 3, 5, 7, 9]

# Using range function
r = range(0, 1, length=5)
println(collect(r))  # [0.0, 0.25, 0.5, 0.75, 1.0]

String Operators

# String concatenation
s1 = "Hello"
s2 = "World"
println(s1 * " " * s2)  # "Hello World"

# String repetition
println("ab" ^ 3)  # "ababab"

# String interpolation
name = "Julia"
println("Hello, $name!")  # "Hello, Julia!"

Dot Operator (Vectorization)

# Dot operator for element-wise operations
a = [1, 2, 3, 4, 5]

# Element-wise operations
println(a .+ 10)     # [11, 12, 13, 14, 15]
println(a .* 2)      # [2, 4, 6, 8, 10]
println(a .^ 2)      # [1, 4, 9, 16, 25]

# Element-wise comparison
println(a .> 3)      # [false, false, false, true, true]

# Function vectorization
println(sqrt.(a))    # [1.0, 1.414..., ...]
println(sin.(a))

# @. macro for auto-vectorization
result = @. sin(a) + cos(a)

Membership Operator

# in operator
arr = [1, 2, 3, 4, 5]
println(3 in arr)     # true
println(3 ∈ arr)      # true (Unicode)
println(6 in arr)     # false
println(6 ∉ arr)      # true (not in)

# For strings
println('a' in "hello")  # false
println('e' in "hello")  # true

# For dictionaries
d = Dict("a" => 1, "b" => 2)
println("a" in keys(d))  # true

Pipe Operator

# |> pipe operator
result = [1, 2, 3, 4, 5] |> sum |> sqrt
println(result)  # 3.872...

# Equivalent to
result = sqrt(sum([1, 2, 3, 4, 5]))

# Chained operations
[1, 2, 3, 4, 5] |> 
    x -> filter(n -> n > 2, x) |>
    sum |>
    println  # 12

Operator Precedence

From highest to lowest:

1. ^ Power
2. Unary operators + - ! ~
3. * / ÷ % & Multiplication, division, bitwise AND
4. + - | ⊻ Addition, subtraction, bitwise OR
5. : .. Range
6. < > <= >= == != === Comparison
7. && Logical AND
8. || Logical OR
9. ? : Conditional
10. = += -= *= /= Assignment

# Precedence examples
println(2 + 3 * 4)      # 14 (multiplication first)
println((2 + 3) * 4)    # 20

println(2 ^ 3 ^ 2)      # 512 (power is right-associative)
println((2 ^ 3) ^ 2)    # 64

println(true || false && false)  # true (&& before ||)

Custom Operators

Julia allows defining custom operators:

# Define infix operator
⊕(a, b) = a + b + 1
println(3 ⊕ 4)  # 8

# Using Unicode symbols
∥(a, b) = a * b / (a + b)  # Parallel resistance
println(100 ∥ 100)  # 50.0

Next Steps

After learning operators, continue with:

• Math Functions - Built-in mathematical functions
• Control Flow - Conditionals and loops
• Functions - Defining your own functions