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Operators, expressions, and dunder methods

Mojo includes a variety of operators for manipulating values of different types. Generally, the operators are equivalent to those found in Python, though many operators also work with additional Mojo types such as SIMD vectors. Additionally, Mojo allows you to define the behavior of most of these operators for your own custom types by implementing special dunder (double underscore) methods.

This document contains the following three sections:

Operators and expressions​

This section lists the operators that Mojo supports, their order or precedence and associativity, and describes how these operators behave with several commonly used built-in types.

Operator precedence and associativity​

The table below lists the various Mojo operators, along with their order of precedence and associativity (also referred to as grouping). This table lists operators from the highest precedence to the lowest precedence.

OperatorsDescriptionAssociativity (Grouping)
()Parenthesized expressionLeft to right
x[index], x[index:index]Subscripting, slicingLeft to right
**ExponentiationRight to left
+x, -x, ~xPositive, negative, bitwise NOTRight to left
*, @, /, //, %Multiplication, matrix, division, floor division, remainderLeft to right
+, –Addition and subtractionLeft to right
<<, >>ShiftsLeft to right
&Bitwise ANDLeft to right
^Bitwise XORLeft to right
|Bitwise ORLeft to right
in, not in, is, is not, <, <=, >, >=, !=, ==Comparisons, membership tests, identity testsLeft to Right
not xBoolean NOTRight to left
x and yBoolean ANDLeft to right
x or yBoolean ORLeft to right
if-elseConditional expressionRight to left
:=Assignment expression (walrus operator)Right to left

Mojo supports the same operators as Python (plus a few extensions), and they have the same precedence levels. For example, the following arithmetic expression evaluates to 40:

5 + 4 * 3 ** 2 - 1
5 + 4 * 3 ** 2 - 1

It is equivalent to the following parenthesized expression to explicitly control the order of evaluation:

(5 + (4 * (3 ** 2))) - 1
(5 + (4 * (3 ** 2))) - 1

Associativity defines how operators of the same precedence level are grouped into expressions. The table indicates whether operators of a given level are left- or right-associative. For example, multiplication and division are left associative, so the following expression results in a value of 3:

3 * 4 / 2 / 2
3 * 4 / 2 / 2

It is equivalent to the following parenthesized expression to explicitly control the order of evaluation:

((3 * 4) / 2) / 2
((3 * 4) / 2) / 2

Whereas in the following, exponentiation operators are right associative resulting in a value of 264,144:

4 ** 3 ** 2
4 ** 3 ** 2

It is equivalent to the following parenthesized expression to explicitly control the order of evaluation:

4 ** (3 ** 2)
4 ** (3 ** 2)

Arithmetic and bitwise operators​

Numeric types describes the different numeric types provided by the Mojo standard library. The arithmetic and bitwise operators have slightly different behavior depending on the types of values provided.

Int and UInt values​

The Int and UInt types represent signed and unsigned integers of the word size of the CPU, typically 64 bits or 32 bits.

The Int and UInt types support all arithmetic operators except matrix multiplication (@), as well as all bitwise and shift operators. If both operands to a binary operator are Int values the result is an Int, if both operands are UInt values the result is a UInt, and if one operand is Int and the other UInt the result is an Int. The one exception for these types is true division, /, which always returns a Float64 type value.

var a_int: Int = -7
var b_int: Int = 4
sum_int = a_int + b_int  # Result is type Int
print("Int sum:", sum_int)

var i_uint: UInt = 9
var j_uint: UInt = 8
sum_uint = i_uint + j_uint  # Result is type UInt
print("UInt sum:", sum_uint)

sum_mixed = a_int + i_uint  # Result is type Int
print("Mixed sum:", sum_mixed)

quotient_int = a_int / b_int  # Result is type Float64
print("Int quotient:", quotient_int)
quotient_uint = i_uint / j_uint  # Result is type Float64
print("UInt quotient:", quotient_uint)
var a_int: Int = -7
var b_int: Int = 4
sum_int = a_int + b_int  # Result is type Int
print("Int sum:", sum_int)

var i_uint: UInt = 9
var j_uint: UInt = 8
sum_uint = i_uint + j_uint  # Result is type UInt
print("UInt sum:", sum_uint)

sum_mixed = a_int + i_uint  # Result is type Int
print("Mixed sum:", sum_mixed)

quotient_int = a_int / b_int  # Result is type Float64
print("Int quotient:", quotient_int)
quotient_uint = i_uint / j_uint  # Result is type Float64
print("UInt quotient:", quotient_uint)
Int sum: -3
UInt sum: 17
Mixed sum: 2
Int quotient: -1.75
UInt quotient: 1.125
Int sum: -3
UInt sum: 17
Mixed sum: 2
Int quotient: -1.75
UInt quotient: 1.125

SIMD values​

The Mojo standard library defines the SIMD type to represent a fixed-size array of values that can fit into a processor's register. This allows you to take advantage of single instruction, multiple data operations in hardware to efficiently process multiple values in parallel. SIMD values of a numeric DType support all arithmetic operators except for matrix multiplication (@), though the left shift (<<) and right shift (>>) operators support only integral types. Additionally, SIMD values of an integral or boolean type support all bitwise operators. SIMD values apply the operators in an elementwise fashion, as shown in the following example:

simd1 = SIMD[DType.int32, 4](2, 3, 4, 5)
simd2 = SIMD[DType.int32, 4](-1, 2, -3, 4)
simd3 = simd1 * simd2
print(simd3)
simd1 = SIMD[DType.int32, 4](2, 3, 4, 5)
simd2 = SIMD[DType.int32, 4](-1, 2, -3, 4)
simd3 = simd1 * simd2
print(simd3)
[-2, 6, -12, 20]
[-2, 6, -12, 20]

Scalar values are simply aliases for single-element SIMD vectors, so Float16 is just an alias for SIMD[DType.float16, 1]. Therefore Scalar values support the same set of arithmetic and bitwise operators.

var f1: Float16 = 2.5
var f2: Float16 = -4.0
var f3 = f1 * f2  # Implicitly of type Float16
print(f3)
var f1: Float16 = 2.5
var f2: Float16 = -4.0
var f3 = f1 * f2  # Implicitly of type Float16
print(f3)
-10.0
-10.0

When using these operators on SIMD values, Mojo requires both to have the same size and DType, and the result is a SIMD of the same size and DType. The operators do not automatically widen lower precision SIMD values to higher precision. This means that the DType of each value must be the same or else the result is a compilation error.

var i8: Int8 = 8
var f64: Float64 = 64.0
result = i8 * f64
var i8: Int8 = 8
var f64: Float64 = 64.0
result = i8 * f64
error: invalid call to '__mul__': could not deduce parameter 'type' of parent struct 'SIMD'
    result = i8 * f64
             ~~~^~~~~
error: invalid call to '__mul__': could not deduce parameter 'type' of parent struct 'SIMD'
    result = i8 * f64
             ~~~^~~~~

If you need to perform an arithmetic or bitwise operator on two SIMD values of different types, you can explicitly cast() a SIMD so that they have the same type.

simd1 = SIMD[DType.float32, 4](2.2, 3.3, 4.4, 5.5)
simd2 = SIMD[DType.int16, 4](-1, 2, -3, 4)
simd3 = simd1 * simd2.cast[DType.float32]()  # Result is SIMD[DType.float32, 4]
print(simd3)
simd1 = SIMD[DType.float32, 4](2.2, 3.3, 4.4, 5.5)
simd2 = SIMD[DType.int16, 4](-1, 2, -3, 4)
simd3 = simd1 * simd2.cast[DType.float32]()  # Result is SIMD[DType.float32, 4]
print(simd3)
[-2.2000000476837158, 6.5999999046325684, -13.200000762939453, 22.0]
[-2.2000000476837158, 6.5999999046325684, -13.200000762939453, 22.0]

One exception is that the exponentiation operator, **, is overloaded so that you can specify an Int type exponent. All values in the SIMD are exponentiated to the same power.

base_simd = SIMD[DType.float64, 4](1.1, 2.2, 3.3, 4.4)
var power: Int = 2
pow_simd = base_simd ** power  # Result is SIMD[DType.float64, 4]
print(pow_simd)
base_simd = SIMD[DType.float64, 4](1.1, 2.2, 3.3, 4.4)
var power: Int = 2
pow_simd = base_simd ** power  # Result is SIMD[DType.float64, 4]
print(pow_simd)
[1.2100000000000002, 4.8400000000000007, 10.889999999999999, 19.360000000000003]
[1.2100000000000002, 4.8400000000000007, 10.889999999999999, 19.360000000000003]

There are three operators related to division:

  • /, the "true division" operator, performs floating point division for SIMD values with a floating point DType. For SIMD values with an integral DType, true division truncates the quotient to an integral result.

    num_float16 = SIMD[DType.float16, 4](3.5, -3.5, 3.5, -3.5)
    denom_float16 = SIMD[DType.float16, 4](2.5, 2.5, -2.5, -2.5)

    num_int32 = SIMD[DType.int32, 4](5, -6, 7, -8)
    denom_int32 = SIMD[DType.int32, 4](2, 3, -4, -5)

    # Result is SIMD[DType.float16, 4]
    true_quotient_float16 = num_float16 / denom_float16
    print("True float16 division:", true_quotient_float16)

    # Result is SIMD[DType.int32, 4]
    true_quotient_int32 = num_int32 / denom_int32
    print("True int32 division:", true_quotient_int32)
    num_float16 = SIMD[DType.float16, 4](3.5, -3.5, 3.5, -3.5)
    denom_float16 = SIMD[DType.float16, 4](2.5, 2.5, -2.5, -2.5)

    num_int32 = SIMD[DType.int32, 4](5, -6, 7, -8)
    denom_int32 = SIMD[DType.int32, 4](2, 3, -4, -5)

    # Result is SIMD[DType.float16, 4]
    true_quotient_float16 = num_float16 / denom_float16
    print("True float16 division:", true_quotient_float16)

    # Result is SIMD[DType.int32, 4]
    true_quotient_int32 = num_int32 / denom_int32
    print("True int32 division:", true_quotient_int32)
    True float16 division: [1.400390625, -1.400390625, -1.400390625, 1.400390625]
    True int32 division: [2, -2, -1, 1]
    True float16 division: [1.400390625, -1.400390625, -1.400390625, 1.400390625]
    True int32 division: [2, -2, -1, 1]

  • //, the "floor division" operator, performs division and rounds down the result to the nearest integer. The resulting SIMD is still the same type as the original operands. For example:

    # Result is SIMD[DType.float16, 4]
    var floor_quotient_float16 = num_float16 // denom_float16
    print("Floor float16 division:", floor_quotient_float16)

    # Result is SIMD[DType.int32, 4]
    var floor_quotient_int32 = num_int32 // denom_int32
    print("Floor int32 division:", floor_quotient_int32)
    # Result is SIMD[DType.float16, 4]
    var floor_quotient_float16 = num_float16 // denom_float16
    print("Floor float16 division:", floor_quotient_float16)

    # Result is SIMD[DType.int32, 4]
    var floor_quotient_int32 = num_int32 // denom_int32
    print("Floor int32 division:", floor_quotient_int32)
    Floor float16 division: [1.0, -2.0, -2.0, 1.0]
    Floor int32 division: [2, -2, -2, 1]
    Floor float16 division: [1.0, -2.0, -2.0, 1.0]
    Floor int32 division: [2, -2, -2, 1]

  • %, the modulo operator, returns the remainder after dividing the numerator by the denominator an integral number of times. The relationship between the // and % operators can be defined as num == denom * (num // denom) + (num % denom). For example:

    # Result is SIMD[DType.float16, 4]
    var remainder_float16 = num_float16 % denom_float16
    print("Modulo float16:", remainder_float16)

    # Result is SIMD[DType.int32, 4]
    var remainder_int32 = num_int32 % denom_int32
    print("Modulo int32:", remainder_int32)

    print()

    # Result is SIMD[DType.float16, 4]
    var result_float16 = denom_float16 * floor_quotient_float16 + remainder_float16
    print("Result float16:", result_float16)

    # Result is SIMD[DType.int32, 4]
    var result_int32 = denom_int32 * floor_quotient_int32 + remainder_int32
    print("Result int32:", result_int32)
    # Result is SIMD[DType.float16, 4]
    var remainder_float16 = num_float16 % denom_float16
    print("Modulo float16:", remainder_float16)

    # Result is SIMD[DType.int32, 4]
    var remainder_int32 = num_int32 % denom_int32
    print("Modulo int32:", remainder_int32)

    print()

    # Result is SIMD[DType.float16, 4]
    var result_float16 = denom_float16 * floor_quotient_float16 + remainder_float16
    print("Result float16:", result_float16)

    # Result is SIMD[DType.int32, 4]
    var result_int32 = denom_int32 * floor_quotient_int32 + remainder_int32
    print("Result int32:", result_int32)
    Modulo float16: [1.0, 1.5, -1.5, -1.0]
    Modulo int32: [1, 0, -1, -3]

    Result float16: [3.5, -3.5, 3.5, -3.5]
    Result int32: [5, -6, 7, -8]
    Modulo float16: [1.0, 1.5, -1.5, -1.0]
    Modulo int32: [1, 0, -1, -3]

    Result float16: [3.5, -3.5, 3.5, -3.5]
    Result int32: [5, -6, 7, -8]

IntLiteral and FloatLiteral values​

IntLiteral and FloatLiteral are compile-time, numeric values. When they are used in a compile-time context, they are arbitrary-precision values. When they are used in a run-time context, they are materialized as Int and Float64 type values, respectively.

As an example, the following code causes a compile-time error because the calculated IntLiteral value is too large to store in an Int variable:

alias big_int = (1 << 65) + 123456789  # IntLiteral
var too_big_int: Int = big_int
print("Result:", too_big_int)
alias big_int = (1 << 65) + 123456789  # IntLiteral
var too_big_int: Int = big_int
print("Result:", too_big_int)
note: integer value 36893488147542560021 requires 67 bits to store, but the destination bit width is only 64 bits wide
note: integer value 36893488147542560021 requires 67 bits to store, but the destination bit width is only 64 bits wide

However in the following example, taking that same IntLiteral value, dividing by the IntLiteral 10 and then assigning the result to an Int variable compiles and runs successfully, because the final IntLiteral quotient can fit in a 64-bit Int.

alias big_int = (1 << 65) + 123456789  # IntLiteral
var not_too_big_int: Int = big_int // 10
print("Result:", not_too_big_int)
alias big_int = (1 << 65) + 123456789  # IntLiteral
var not_too_big_int: Int = big_int // 10
print("Result:", not_too_big_int)
Result: 3689348814754256002
Result: 3689348814754256002

In a compile-time context, IntLiteral and FloatLiteral values support all arithmetic operators except exponentiation (**), and IntLiteral values support all bitwise and shift operators. In a run-time context, materialized IntLiteral values are Int values and therefore support the same operators as Int, and materialized FloatLiteral values are Float64 values and therefore support the same operators as Float64.

Comparison operators​

Mojo supports a standard set of comparison operators: ==, !=, <, <=, >, and >=. However their behavior depends on the type of values being compared.

  • Int, UInt, IntLiteral, and any type that can be implicitly converted to Int or UInt do standard numerical comparison with a Bool result.

  • Two SIMD values can be compared only if they are the same DType and size. (If you need to compare two SIMD values of different types, you can explicitly cast() a SIMD so that they have the same type.) Mojo performs elementwise comparison with a SIMD[DType.bool] result. For example:

    simd1 = SIMD[DType.int16, 4](-1, 2, -3, 4)
    simd2 = SIMD[DType.int16, 4](0, 1, 2, 3)
    simd3 = simd1 > simd2  # SIMD[DType.bool, 4]
    print(simd3)
    simd1 = SIMD[DType.int16, 4](-1, 2, -3, 4)
    simd2 = SIMD[DType.int16, 4](0, 1, 2, 3)
    simd3 = simd1 > simd2  # SIMD[DType.bool, 4]
    print(simd3)
    [False, True, False, True]
    [False, True, False, True]

  • An integral type SIMD can be compared to an IntLiteral, Int, UInt, or any type that can be implicitly converted to Int or UInt. Mojo performs elementwise comparison against the value provided and produces a SIMD[DType.bool] result. For example:

    simd1 = SIMD[DType.int16, 4](-1, 2, -3, 4)
    simd2 = simd1 > 2  # SIMD[DType.bool, 4]
    print(simd2)
    simd1 = SIMD[DType.int16, 4](-1, 2, -3, 4)
    simd2 = simd1 > 2  # SIMD[DType.bool, 4]
    print(simd2)
    [False, False, False, True]
    [False, False, False, True]

  • A floating point type SIMD can be compared to a FloatLiteral, IntLiteral, Int, UInt, or any type that can be implicitly converted to Int or UInt. Mojo performs elementwise comparison against the value provided and produces a SIMD[DType.bool] result. For example:

    simd1 = SIMD[DType.float32, 4](1.1, -2.2, 3.3, -4.4)
    simd2 = simd1 > 0.5  # SIMD[DType.bool, 4]
    print(simd2)
    simd1 = SIMD[DType.float32, 4](1.1, -2.2, 3.3, -4.4)
    simd2 = simd1 > 0.5  # SIMD[DType.bool, 4]
    print(simd2)
    [True, False, True, False]
    [True, False, True, False]

  • Scalar values are simply aliases for single-element SIMD vectors. Therefore, the same restrictions apply against comparing different types. In other words, you can't compare a Float16 value to a Float32 value unless you cast the values to the same type. For example:

    var float1: Float16 = 12.345  # SIMD[DType.float16, 1]
    var float2: Float32 = 0.5     # SIMD[DType.float32, 1]
    result = float1.cast[DType.float32]() > float2  # SIMD[DType.bool, 1]
    print(result)
    var float1: Float16 = 12.345  # SIMD[DType.float16, 1]
    var float2: Float32 = 0.5     # SIMD[DType.float32, 1]
    result = float1.cast[DType.float32]() > float2  # SIMD[DType.bool, 1]
    print(result)
    True
    True

  • String and StringLiteral values can be compared using standard lexicographical ordering, producing a Bool. (For example, "Zebra" is treated as less than "ant" because upper case letters occur before lower case letters in the character encoding.) String comparisons are discussed further in the String operators section below.

Several other types in the Mojo standard library support various comparison operators, in particular the equality and inequality comparisons. Consult the API documentation for a type to determine whether any comparison operators are supported.

String operators​

As discussed in Strings, the String type represents a mutable string value. In contrast, the StringLiteral type represents a literal string that is embedded into your compiled program. At run-time a StringLiteral is loaded into memory as a constant that persists for the duration of your program's execution.

The String type has a constructor that accepts a StringLiteral value, which means that a StringLiteral can be implicitly converted to a String at run-time if you pass it as an argument to a function or assign it to a String type variable. You also can use the String constructor to explicitly convert the StringLiteral to a String value at run-time.

String concatenation​

The + operator performs string concatenation. The StringLiteral type supports compile-time string concatenation.

alias last_name = "Curie"

# Compile-time StringLiteral alias
alias marie = "Marie " + last_name
print(marie)

# Compile-time concatenation assigned to a run-time StringLiteral type variable
pierre = "Pierre " + last_name
print(pierre)
alias last_name = "Curie"

# Compile-time StringLiteral alias
alias marie = "Marie " + last_name
print(marie)

# Compile-time concatenation assigned to a run-time StringLiteral type variable
pierre = "Pierre " + last_name
print(pierre)
Marie Curie
Pierre Curie
Marie Curie
Pierre Curie

With the String type the + operator performs run-time string concatenation to produce a new String value. You can also concatenate a String and a StringLiteral to produce a new String result.

var first_name: String = "Grace"
var last_name: String = " Hopper"

# String type result
programmer = first_name + last_name
print(programmer)

# String type result
singer = first_name + " Slick"
print(singer)
var first_name: String = "Grace"
var last_name: String = " Hopper"

# String type result
programmer = first_name + last_name
print(programmer)

# String type result
singer = first_name + " Slick"
print(singer)
Grace Hopper
Grace Slick
Grace Hopper
Grace Slick

String replication​

The * operator replicates a String a specified number of times. For example:

var str1: String = "la"
str2 = str1 * 5
print(str2)
var str1: String = "la"
str2 = str1 * 5
print(str2)
lalalalala
lalalalala

StringLiteral supports the * operator for string replication only at compile time. So the following examples compile and run successfully:

alias divider1 = "=" * 40
alias symbol = "#"
alias divider2 = symbol * 40

# You must define the following function using `fn` because an alias
# initializer cannot call a function that can potentially raise an error.
fn generate_divider(char: StringLiteral, repeat: Int) -> StringLiteral:
    return char * repeat

alias divider3 = generate_divider("~", 40)  # Evaluated at compile-time

print(divider1)
print(divider2)
print(divider3)
alias divider1 = "=" * 40
alias symbol = "#"
alias divider2 = symbol * 40

# You must define the following function using `fn` because an alias
# initializer cannot call a function that can potentially raise an error.
fn generate_divider(char: StringLiteral, repeat: Int) -> StringLiteral:
    return char * repeat

alias divider3 = generate_divider("~", 40)  # Evaluated at compile-time

print(divider1)
print(divider2)
print(divider3)
========================================
########################################
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
========================================
########################################
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

However, the following examples fail to compile because the replication operators would be evaluated at run-time:

# Both of these statements would fail to compile
var div1 = "^" * 40
print("_" * 40)
# Both of these statements would fail to compile
var div1 = "^" * 40
print("_" * 40)

String comparison​

String values can be compared using standard lexicographical ordering, producing a Bool. (For example, "Zebra" is treated as less than "ant" because upper case letters occur before lower case letters in the character encoding.) StringLiteral values can be directly compared against each other as well. However when comparing a String to a StringLiteral value, the String value must be the left-hand operand to avoid a compilation error. For example:

var str: String = "bird"
# Compilation error:
# result = "cat" >= str
# You could explicitly convert the StringLiteral to a String:
# result = String("cat") >= str
result = str < "cat"  # Successful comparison
print(result)
var str: String = "bird"
# Compilation error:
# result = "cat" >= str
# You could explicitly convert the StringLiteral to a String:
# result = String("cat") >= str
result = str < "cat"  # Successful comparison
print(result)
True
True

Substring testing​

Both String and StringLiteral support using the in operator to produce a Bool result indicating whether a given substring appears within another string. The operator is overloaded so that you can use any combination of String and StringLiteral for both the substring and the string to test.

var food: String = "peanut butter"

if "nut" in food:
    print("It contains a nut")
else:
    print("It doesn't contain a nut")
var food: String = "peanut butter"

if "nut" in food:
    print("It contains a nut")
else:
    print("It doesn't contain a nut")
It contains a nut
It contains a nut

String indexing and slicing​

Both the String and StringLiteral types allow you to use indexing to return a single character. Character positions are identified with a zero-based index starting from the first character. You can also specify a negative index to count backwards from the end of the string, with the last character identified by index -1. Specifying an index beyond the bounds of the string results in a run-time error.

alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"  # StringLiteral type value
print(alphabet[0], alphabet[-1])

# The following would produce a run-time error
# print(alphabet[45])
alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"  # StringLiteral type value
print(alphabet[0], alphabet[-1])

# The following would produce a run-time error
# print(alphabet[45])
A Z
A Z

The String type—but not the StringLiteral type—also supports slices to return a substring from the original String. Providing a slice in the form [start:end] returns a substring starting with the character index specified by start and continuing up to but not including the character at index end. You can use positive or negative indexing for both the start and end values. Omitting start is the same as specifying 0, and omitting end is the same as specifying 1 plus the length of the string.

var alphabet: String = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
print(alphabet[1:4])  # The 2nd through 4th characters
print(alphabet[:6])   # The first 6 characters
print(alphabet[-6:])  # The last 6 characters
var alphabet: String = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
print(alphabet[1:4])  # The 2nd through 4th characters
print(alphabet[:6])   # The first 6 characters
print(alphabet[-6:])  # The last 6 characters
BCD
ABCDEF
UVWXYZ
BCD
ABCDEF
UVWXYZ

You can also specify a slice with a step value, as in [start:end:step] indicating the increment between subsequent indices of the slide. (This is also sometimes referred to as a "stride.") If you provide a negative value for step, characters are selected in reverse order starting with start but then with decreasing index values up to but not including end.

print(alphabet[1:6:2])     # The 2nd, 4th, and 6th characters
print(alphabet[-1:-4:-1])  # The last 3 characters in reverse order
print(alphabet[::-1])      # The entire string reversed
print(alphabet[1:6:2])     # The 2nd, 4th, and 6th characters
print(alphabet[-1:-4:-1])  # The last 3 characters in reverse order
print(alphabet[::-1])      # The entire string reversed
BDF
ZYX
ZYXWVUTSRQPONMLKJIHGFEDCBA
BDF
ZYX
ZYXWVUTSRQPONMLKJIHGFEDCBA

In-place assignment operators​

Mutable types that support binary arithmetic, bitwise, and shift operators typically support equivalent in-place assignment operators. That means that for a type that supports the + operator, the following two statements are essentially equivalent:

a = a + b
a += b
a = a + b
a += b

However there is a subtle difference between the two. In the first example, the expression a + b produces a new value, which is then assigned to a. In contrast, the second example does an in-place modification of the value currently assigned to a. For register-passable types, the compiled results might be equivalent at run-time. But for a memory-only type, the first example allocates storage for the result of a + b and then assigns the value to the variable, whereas the second example can do an in-place modification of the existing value.

Assignment expressions​

The "walrus" operator, :=, allows you to assign a value to a variable within an expression. The value provided is both assigned to the variable and becomes the result of the expression. This often can simplify conditional or looping logic. For example, consider the following prompting loop:

while True:
    name = input("Enter a name or 'quit' to exit: ")
    if name == "quit":
        break
    print("Hello,", name)
while True:
    name = input("Enter a name or 'quit' to exit: ")
    if name == "quit":
        break
    print("Hello,", name)
Enter a name or 'quit' to exit: Coco
Hello, Coco
Enter a name or 'quit' to exit: Vivienne
Hello, Vivienne
Enter a name or 'quit' to exit: quit
Enter a name or 'quit' to exit: Coco
Hello, Coco
Enter a name or 'quit' to exit: Vivienne
Hello, Vivienne
Enter a name or 'quit' to exit: quit

Using the walrus operator, you can implement the same behavior like this:

while (name := input("Enter a name or 'quit' to exit: ")) != "quit":
    print("Hello,", name)
while (name := input("Enter a name or 'quit' to exit: ")) != "quit":
    print("Hello,", name)
Enter a name or 'quit' to exit: Donna
Hello, Donna
Enter a name or 'quit' to exit: Vera
Hello, Vera
Enter a name or 'quit' to exit: quit
Enter a name or 'quit' to exit: Donna
Hello, Donna
Enter a name or 'quit' to exit: Vera
Hello, Vera
Enter a name or 'quit' to exit: quit

Implement operators for custom types​

When you create a custom struct, Mojo allows you to define the behavior of many of the built-in operators for that type by implementing special dunder (double underscore) methods. This section lists the dunder methods associated with the operators and briefly describes the requirements for implementing them.

Unary operator dunder methods​

A unary operator invokes an associated dunder method on the value to which it applies. The supported unary operators and their corresponding methods are shown in the table below.

OperatorDunder method
+ positive__pos__()
- negative__neg__()
~ bitwise NOT__invert__()

For each of these methods that you decide to implement, you should return either the original value if unchanged, or a new value representing the result of the operator. For example, you could implement the - negative operator for a MyInt struct like this:

@value
struct MyInt:
    var value: Int

    def __neg__(self) -> Self:
        return Self(-self.value)
@value
struct MyInt:
    var value: Int

    def __neg__(self) -> Self:
        return Self(-self.value)

Binary arithmetic, shift, and bitwise operator dunder methods​

When you have a binary expression like a + b, there are two possible dunder methods that could be invoked.

Mojo first determines whether the left-hand side value (a in this example) has a "normal" version of the + operator's dunder method defined that accepts a value of the right-hand side's type. If so, it then invokes that method on the left-hand side value and passes the right-hand side value as an argument.

If Mojo doesn't find a matching "normal" dunder method on the left-hand side value, it then checks whether the right-hand side value has a "reflected" (sometimes referred to as "reversed") version of the + operator's dunder method defined that accepts a value of the left-hand side's type. If so, it then invokes that method on the right-hand side value and passes the left-hand side value as an argument.

For both the normal and the reflected versions, the dunder method should return a new value representing the result of the operator.

Additionally, there are dunder methods corresponding to the in-place assignment versions of the operators. These methods receive the right-hand side value as an argument and the methods should modify the existing left-hand side value to reflect the result of the operator.

The table below lists the various binary arithmetic, shift, and bitwise operators and their corresponding normal, reflected, and in-place dunder methods.

OperatorNormalReflectedIn-place
+ addition__add__()__radd__()__iadd__()
- subtraction__sub__()__rsub__()__isub__()
* multiplication__mul__()__rmul__()__imul__()
/ division__truediv__()__rtruediv__()__itruediv__()
// floor division__floordiv__()__rfloordiv__()__ifloordiv__()
% modulus/remainder__mod__()__rmod__()__imod__()
** exponentiation__pow__()__rpow__()__ipow__()
@ matrix multiplication__matmul__()__rmatmul__()__imatmul__()
<< left shift__lshift__()__rlshift__()__ilshift__()
>> right shift__rshift__()__rrshift__()__irshift__()
& bitwise AND__and__()__rand__()__iand__()
| bitwise OR__or__()__ror__()__ior__()
^ bitwise XOR__xor__()__rxor__()__ixor__()

As an example, consider implementing support for all of the + operator dunder methods for a custom MyInt struct. This shows supporting adding two MyInt instances as well as adding a MyInt and an Int. We can support the case of having the Int as the right-hand side argument by overloaded the definition of __add__(). But to support the case of having the Int as the left-hand side argument, we need to implement an __radd__() method, because the built-in Int type doesn't have an __add__() method that supports our custom MyInt type.

@value
struct MyInt:
    var value: Int

    def __add__(self, rhs: MyInt) -> Self:
        return MyInt(self.value + rhs.value)

    def __add__(self, rhs: Int) -> Self:
        return MyInt(self.value + rhs)

    def __radd__(self, lhs: Int) -> Self:
        return MyInt(self.value + lhs)

    def __iadd__(inout self, rhs: MyInt) -> None:
        self.value += rhs.value

    def __iadd__(inout self, rhs: Int) -> None:
        self.value += rhs
@value
struct MyInt:
    var value: Int

    def __add__(self, rhs: MyInt) -> Self:
        return MyInt(self.value + rhs.value)

    def __add__(self, rhs: Int) -> Self:
        return MyInt(self.value + rhs)

    def __radd__(self, lhs: Int) -> Self:
        return MyInt(self.value + lhs)

    def __iadd__(inout self, rhs: MyInt) -> None:
        self.value += rhs.value

    def __iadd__(inout self, rhs: Int) -> None:
        self.value += rhs

Comparison operator dunder methods​

When you have a comparison expression like a < b, Mojo invokes as associated dunder method on the left-hand side value and passes the right-hand side value as an argument. Mojo doesn't support "reflected" versions of these dunder methods because you should only compare values of the same type. The comparison dunder methods must return a Bool result representing the result of the comparison.

There are two traits associated with the comparison dunder methods. A type that implements the Comparable trait must define all of the comparison methods. However, some types don't have a natural ordering (for example, complex numbers). For those types you can decide to implement the EqualityComparable trait, which requires defining only the equality and inequality comparison methods.

The supported comparison operators and their corresponding methods are shown in the table below.

OperatorDunder method
== equality__eq__()
!= inequality__ne__()
< less than__lt__()
<= less than or equal__le__()
> greater than__gt__()
>= greater than or equal__ge__()

As an example, consider implementing support for all of the comparison operator dunder methods for a custom MyInt struct.

@value
struct MyInt(
    Comparable
):
    var value: Int

    fn __eq__(self, rhs: MyInt) -> Bool:
        return self.value == rhs.value

    fn __ne__(self, rhs: MyInt) -> Bool:
        return self.value != rhs.value

    fn __lt__(self, rhs: MyInt) -> Bool:
        return self.value < rhs.value

    fn __le__(self, rhs: MyInt) -> Bool:
        return self.value <= rhs.value

    fn __gt__(self, rhs: MyInt) -> Bool:
        return self.value > rhs.value

    fn __ge__(self, rhs: MyInt) -> Bool:
        return self.value >= rhs.value
@value
struct MyInt(
    Comparable
):
    var value: Int

    fn __eq__(self, rhs: MyInt) -> Bool:
        return self.value == rhs.value

    fn __ne__(self, rhs: MyInt) -> Bool:
        return self.value != rhs.value

    fn __lt__(self, rhs: MyInt) -> Bool:
        return self.value < rhs.value

    fn __le__(self, rhs: MyInt) -> Bool:
        return self.value <= rhs.value

    fn __gt__(self, rhs: MyInt) -> Bool:
        return self.value > rhs.value

    fn __ge__(self, rhs: MyInt) -> Bool:
        return self.value >= rhs.value

Membership operator dunder methods​

The in and not in operators depend on a type implementing the __contains__() dunder method. Typically only collection types (such as List, Dict, and Set) implement this method. It should accept the right-hand side value as an argument and return a Bool indicating whether the value is present in the collection or not.

Subscript and slicing dunder methods​

Subscripting and slicing typically apply only to sequential collection types, like List and String. Subscripting references a single element of a collection or a dimension of a multi-dimensional container, whereas slicing refers to a range of values. A type supports both subscripting and slicing by implementing the __getitem__() method for retrieving values and the __setitem__() method for setting values.

Subscripting​

In the simple case of a one-dimensional sequence, the __getitem__() and __setitem__() methods should have signatures similar to this:

struct MySeq[type: CollectionElement]:
    fn __getitem__(self, idx: Int) -> type:
        # Return element at the given index
        ...
    fn __setitem__(inout self, idx: Int, value: type):
        # Assign the element at the given index the provided value
struct MySeq[type: CollectionElement]:
    fn __getitem__(self, idx: Int) -> type:
        # Return element at the given index
        ...
    fn __setitem__(inout self, idx: Int, value: type):
        # Assign the element at the given index the provided value

It's also possible to support multi-dimensional collections, in which case you can implement both __getitem__() and __setitem__() methods to accept multiple index arguments—or even variadic index arguments for arbitrary—dimension collections.

struct MySeq[type: CollectionElement]:
    # 2-dimension support
    fn __getitem__(self, x_idx: Int, y_idx: Int) -> type:
        ...
    # Arbitrary-dimension support
    fn __getitem__(self, *indices: Int) -> type:
        ...
struct MySeq[type: CollectionElement]:
    # 2-dimension support
    fn __getitem__(self, x_idx: Int, y_idx: Int) -> type:
        ...
    # Arbitrary-dimension support
    fn __getitem__(self, *indices: Int) -> type:
        ...

Slicing​

You provide slicing support for a collection type also by implementing __getitem__() and __setitem__() methods. But for slicing, instead of accepting an Int index (or indices, in the case of a multi-dimensional collection) you implement to methods to accept a Slice (or multiple Slices in the case of a multi-dimensional collection).

struct MySeq[type: CollectionElement]:
    # Return a new MySeq with a subset of elements
    fn __getitem__(self, span: Slice) -> Self:
        ...

struct MySeq[type: CollectionElement]:
    # Return a new MySeq with a subset of elements
    fn __getitem__(self, span: Slice) -> Self:
        ...

A Slice contains three fields:

  • start (Optional[Int]): The starting index of the slice
  • end (Optional[Int]): The ending index of the slice
  • step (Optional[Int]): The step increment value of the slice.

Because the start, end, and step values are all optional when using slice syntax, they are represented as Optional[Int] values in the Slice. And if present, the index values might be negative representing a relative position from the end of the sequence. As a convenience, Slice provides an indices() method that accepts a length value and returns a 3-tuple of "normalized" start, end, and step values for the given length, all represented as non-negative values. You can then use these normalized values to determine the corresponding elements of your collection being referenced.

struct MySeq[type: CollectionElement]:
    var size: Int

    # Return a new MySeq with a subset of elements
    fn __getitem__(self, span: Slice) -> Self:
        var start: Int
        var end: Int
        var step: Int
        start, end, step = span.indices(self.size)
        ...

struct MySeq[type: CollectionElement]:
    var size: Int

    # Return a new MySeq with a subset of elements
    fn __getitem__(self, span: Slice) -> Self:
        var start: Int
        var end: Int
        var step: Int
        start, end, step = span.indices(self.size)
        ...

An example of implementing operators for a custom type​

As an example of implementing operators for a custom Mojo type, let's create a Complex struct to represent a single complex number, with both the real and imaginary components stored as Float64 values. We'll implement most of the arithmetic operators, the associated in-place assignment operators, the equality comparison operators, and a few additional convenience methods to support operations like printing complex values. We'll also allow mixing Complex and Float64 values in arithmetic expressions to produce a Complex result.

This example builds our Complex struct incrementally. You can also find the complete example in the public Mojo GitHub repo.

Implement lifecycle methods​

Our Complex struct is an example of a simple value type consisting of trivial numeric fields and requiring no special constructor or destructor behaviors. This means that we can take advantage of Mojo's @value decorator, which is described in Simple value types, to automatically implement a member-wise initializer (a constructor with arguments for each field), a copy constructor, a move constructor, and a destructor.

@value
struct Complex():
    var re: Float64
    var im: Float64
@value
struct Complex():
    var re: Float64
    var im: Float64

This definition is enough for us to create Complex instances and access their real and imaginary fields.

c1 = Complex(-1.2, 6.5)
print(String("c1: Real: {}; Imaginary: {}").format(c1.re, c1.im))
c1 = Complex(-1.2, 6.5)
print(String("c1: Real: {}; Imaginary: {}").format(c1.re, c1.im))
c1: Real: -1.2; Imaginary: 6.5
c1: Real: -1.2; Imaginary: 6.5

As a convenience, let's add an explicit constructor to handle the case of creating a Complex instance with an imaginary component of 0.

@value
struct Complex():
    var re: Float64
    var im: Float64

    fn __init__(out self, re: Float64, im: Float64 = 0.0):
        self.re = re
        self.im = im
@value
struct Complex():
    var re: Float64
    var im: Float64

    fn __init__(out self, re: Float64, im: Float64 = 0.0):
        self.re = re
        self.im = im

Now we can create a Complex instance and provide just a real component.

c2 = Complex(3.14159)
print(String("c2: Real: {}; Imaginary: {}").format(c2.re, c2.im))
c2 = Complex(3.14159)
print(String("c2: Real: {}; Imaginary: {}").format(c2.re, c2.im))
c2: Real: 3.1415899999999999; Imaginary: 0.0
c2: Real: 3.1415899999999999; Imaginary: 0.0

Implement the Writable and Stringable traits​

To make it simpler to print Complex values, let's implement the Writable trait. While we're at it, let's also implement the Stringable trait so that we can use the str() function to generate a String representation of a Complex value. You can find out more about these traits and their associated methods in The Stringable, Representable, and Writable traits.

@value
struct Complex(
    Writable,
    Stringable,
):
    # ...

    fn __str__(self) -> String:
        return String.write(self)

    fn write_to[W: Writer](self, inout writer: W):
        writer.write("(", self.re)
        if self.im < 0:
            writer.write(" - ", -self.im)
        else:
            writer.write(" + ", self.im)
        writer.write("i)")
@value
struct Complex(
    Writable,
    Stringable,
):
    # ...

    fn __str__(self) -> String:
        return String.write(self)

    fn write_to[W: Writer](self, inout writer: W):
        writer.write("(", self.re)
        if self.im < 0:
            writer.write(" - ", -self.im)
        else:
            writer.write(" + ", self.im)
        writer.write("i)")

Now we can print a Complex value directly, and we can explicitly generate a String representation by passing a Complex value to str().

c3 = Complex(3.14159, -2.71828)
print("c3 =", c3)

var msg: String = "The value is: " + str(c3)
print(msg)
c3 = Complex(3.14159, -2.71828)
print("c3 =", c3)

var msg: String = "The value is: " + str(c3)
print(msg)
c3 = (3.1415899999999999 - 2.71828i)
The value is: (3.1415899999999999 - 2.71828i)
c3 = (3.1415899999999999 - 2.71828i)
The value is: (3.1415899999999999 - 2.71828i)

Implement basic indexing​

Indexing usually is supported only by collection types. But as an example, let's implement support for accessing the real component as index 0 and the imaginary component as index 1. We'll not implement slicing or variadic assignment for this example.

    # ...
    def __getitem__(self, idx: Int) -> Float64:
        if idx == 0:
            return self.re
        elif idx == 1:
            return self.im
        else:
            raise "index out of bounds"

    def __setitem__(inout self, idx: Int, value: Float64) -> None:
        if idx == 0:
            self.re = value
        elif idx == 1:
            self.im = value
        else:
            raise "index out of bounds"
    # ...
    def __getitem__(self, idx: Int) -> Float64:
        if idx == 0:
            return self.re
        elif idx == 1:
            return self.im
        else:
            raise "index out of bounds"

    def __setitem__(inout self, idx: Int, value: Float64) -> None:
        if idx == 0:
            self.re = value
        elif idx == 1:
            self.im = value
        else:
            raise "index out of bounds"

Now let's try getting and setting the real and imaginary components of a Complex value using indexing.

c2 = Complex(3.14159)
print(String("c2[0]: {}; c2[1]: {}").format(c2[0], c2[1]))
c2[0] = 2.71828
c2[1] = 42
print("c2[0] = 2.71828; c2[1] = 42; c2:", c2)
c2 = Complex(3.14159)
print(String("c2[0]: {}; c2[1]: {}").format(c2[0], c2[1]))
c2[0] = 2.71828
c2[1] = 42
print("c2[0] = 2.71828; c2[1] = 42; c2:", c2)
c2[0]: 3.1415899999999999; c2[1]: 0.0
c2[0] = 2.71828; c2[1] = 42; c2: (2.71828 + 42.0i)
c2[0]: 3.1415899999999999; c2[1]: 0.0
c2[0] = 2.71828; c2[1] = 42; c2: (2.71828 + 42.0i)

Implement arithmetic operators​

Now let's implement the dunder methods that allow us to perform arithmetic operations on Complex values. (Refer to the Wikipedia page on complex numbers for a more in-depth explanation of the formulas for these operators.)

Implement basic operators for Complex values​

The unary + operator simply returns the original value, whereas the unary - operator returns a new Complex value with the real and imaginary components negated.

    # ...
    def __pos__(self) -> Self:
        return self

    def __neg__(self) -> Self:
        return Self(-self.re, -self.im)
    # ...
    def __pos__(self) -> Self:
        return self

    def __neg__(self) -> Self:
        return Self(-self.re, -self.im)

Let's test these out by printing the result of applying each operator.

c1 = Complex(-1.2, 6.5)
print("+c1:", +c1)
print("-c1:", -c1)
c1 = Complex(-1.2, 6.5)
print("+c1:", +c1)
print("-c1:", -c1)
+c1: (-1.2 + 6.5i)
-c1: (1.2 - 6.5i)
+c1: (-1.2 + 6.5i)
-c1: (1.2 - 6.5i)

Next we'll implement the basic binary operators: +, -, *, and /. Dividing complex numbers is a bit tricky, so we'll also define a helper method called norm() to calculate the Euclidean norm of a Complex instance, which can also be useful for other types of analysis with complex numbers.

For all of these dunder methods, the left-hand side operand is self and the right-hand side operand is passed as an argument. We return a new Complex value representing the result.

from math import sqrt

# ...

    def __add__(self, rhs: Self) -> Self:
        return Self(self.re + rhs.re, self.im + rhs.im)

    def __sub__(self, rhs: Self) -> Self:
        return Self(self.re - rhs.re, self.im - rhs.im)

    def __mul__(self, rhs: Self) -> Self:
        return Self(
            self.re * rhs.re - self.im * rhs.im,
            self.re * rhs.im + self.im * rhs.re
        )

    def __truediv__(self, rhs: Self) -> Self:
        denom = rhs.squared_norm()
        return Self(
            (self.re * rhs.re + self.im * rhs.im) / denom,
            (self.im * rhs.re - self.re * rhs.im) / denom
        )

    def squared_norm(self) -> Float64:
        return self.re * self.re + self.im * self.im

    def norm(self) -> Float64:
        return sqrt(self.squared_norm())
from math import sqrt

# ...

    def __add__(self, rhs: Self) -> Self:
        return Self(self.re + rhs.re, self.im + rhs.im)

    def __sub__(self, rhs: Self) -> Self:
        return Self(self.re - rhs.re, self.im - rhs.im)

    def __mul__(self, rhs: Self) -> Self:
        return Self(
            self.re * rhs.re - self.im * rhs.im,
            self.re * rhs.im + self.im * rhs.re
        )

    def __truediv__(self, rhs: Self) -> Self:
        denom = rhs.squared_norm()
        return Self(
            (self.re * rhs.re + self.im * rhs.im) / denom,
            (self.im * rhs.re - self.re * rhs.im) / denom
        )

    def squared_norm(self) -> Float64:
        return self.re * self.re + self.im * self.im

    def norm(self) -> Float64:
        return sqrt(self.squared_norm())

Now we can try them out.

c1 = Complex(-1.2, 6.5)
c3 = Complex(3.14159, -2.71828)
print("c1 + c3 =", c1 + c3)
print("c1 - c3 =", c1 - c3)
print("c1 * c3 =", c1 * c3)
print("c1 / c3 =", c1 / c3)
c1 = Complex(-1.2, 6.5)
c3 = Complex(3.14159, -2.71828)
print("c1 + c3 =", c1 + c3)
print("c1 - c3 =", c1 - c3)
print("c1 * c3 =", c1 * c3)
print("c1 / c3 =", c1 / c3)
c1 + c3 = (1.9415899999999999 + 3.78172i)
c1 - c3 = (-4.3415900000000001 + 9.21828i)
c1 * c3 = (13.898912000000001 + 23.682270999999997i)
c1 / c3 = (-1.2422030701265261 + 0.99419218883955773i)
c1 + c3 = (1.9415899999999999 + 3.78172i)
c1 - c3 = (-4.3415900000000001 + 9.21828i)
c1 * c3 = (13.898912000000001 + 23.682270999999997i)
c1 / c3 = (-1.2422030701265261 + 0.99419218883955773i)

Implement overloaded arithmetic operators for Float64 values​

Our initial set of binary arithmetic operators work fine if both operands are Complex instances. But if we have a Float64 value representing just a real value, we'd first need to use it to create a Complex value before we could add, subtract, multiply, or divide it with another Complex value. If we think that this will be a common use case, it makes sense to overload our arithmetic methods to accept a Float64 as the second operand.

For the case where we have complex1 + float1, we can just create an overloaded definition of __add__(). But what about the case of float1 + complex1? By default, when Mojo encounters a + operator it tries to invoke the __add__() method of the left-hand operand, but the built-in Float64 type doesn't implement support for addition with a Complex value. This is an example where we need to implement the __radd__() method on the Complex type. When Mojo can't find an __add__(self, rhs: Complex) -> Complex method defined on Float64, it uses the __radd__(self, lhs: Float64) -> Complex method defined on Complex.

So we can support arithmetic operations on Complex and Float64 values by implementing the following eight methods.

    # ...
    def __add__(self, rhs: Float64) -> Self:
        return Self(self.re + rhs, self.im)

    def __radd__(self, lhs: Float64) -> Self:
        return Self(self.re + lhs, self.im)

    def __sub__(self, rhs: Float64) -> Self:
        return Self(self.re - rhs, self.im)

    def __rsub__(self, lhs: Float64) -> Self:
        return Self(lhs - self.re, -self.im)

    def __mul__(self, rhs: Float64) -> Self:
        return Self(self.re * rhs, self.im * rhs)

    def __rmul__(self, lhs: Float64) -> Self:
        return Self(lhs * self.re, lhs * self.im)

    def __truediv__(self, rhs: Float64) -> Self:
        return Self(self.re / rhs, self.im / rhs)

    def __rtruediv__(self, lhs: Float64) -> Self:
        denom = self.squared_norm()
        return Self(
            (lhs * self.re) / denom,
            (-lhs * self.im) / denom
        )
    # ...
    def __add__(self, rhs: Float64) -> Self:
        return Self(self.re + rhs, self.im)

    def __radd__(self, lhs: Float64) -> Self:
        return Self(self.re + lhs, self.im)

    def __sub__(self, rhs: Float64) -> Self:
        return Self(self.re - rhs, self.im)

    def __rsub__(self, lhs: Float64) -> Self:
        return Self(lhs - self.re, -self.im)

    def __mul__(self, rhs: Float64) -> Self:
        return Self(self.re * rhs, self.im * rhs)

    def __rmul__(self, lhs: Float64) -> Self:
        return Self(lhs * self.re, lhs * self.im)

    def __truediv__(self, rhs: Float64) -> Self:
        return Self(self.re / rhs, self.im / rhs)

    def __rtruediv__(self, lhs: Float64) -> Self:
        denom = self.squared_norm()
        return Self(
            (lhs * self.re) / denom,
            (-lhs * self.im) / denom
        )

Let's see them in action.

c1 = Complex(-1.2, 6.5)
f1 = 2.5
print("c1 + f1 =", c1 + f1)
print("f1 + c1 =", f1 + c1)
print("c1 - f1 =", c1 - f1)
print("f1 - c1 =", f1 - c1)
print("c1 * f1 =", c1 * f1)
print("f1 * c1 =", f1 * c1)
print("c1 / f1 =", c1 / f1)
print("f1 / c1 =", f1 / c1)
c1 = Complex(-1.2, 6.5)
f1 = 2.5
print("c1 + f1 =", c1 + f1)
print("f1 + c1 =", f1 + c1)
print("c1 - f1 =", c1 - f1)
print("f1 - c1 =", f1 - c1)
print("c1 * f1 =", c1 * f1)
print("f1 * c1 =", f1 * c1)
print("c1 / f1 =", c1 / f1)
print("f1 / c1 =", f1 / c1)
c1 + f1 = (1.3 + 6.5i)
f1 + c1 = (1.3 + 6.5i)
c1 - f1 = (-3.7000000000000002 + 6.5i)
f1 - c1 = (3.7000000000000002 - 6.5i)
c1 * f1 = (-3.0 + 16.25i)
f1 * c1 = (-3.0 + 16.25i)
c1 / f1 = (-0.47999999999999998 + 2.6000000000000001i)
f1 / c1 = (-0.068665598535133904 - 0.37193865873197529i)
c1 + f1 = (1.3 + 6.5i)
f1 + c1 = (1.3 + 6.5i)
c1 - f1 = (-3.7000000000000002 + 6.5i)
f1 - c1 = (3.7000000000000002 - 6.5i)
c1 * f1 = (-3.0 + 16.25i)
f1 * c1 = (-3.0 + 16.25i)
c1 / f1 = (-0.47999999999999998 + 2.6000000000000001i)
f1 / c1 = (-0.068665598535133904 - 0.37193865873197529i)

Implement in-place assignment operators​

Now let's implement support for the in-place assignment operators: +=, -=, *=, and /=. These modify the original value, so we need to mark self as being an inout argument and update the re and im fields instead of returning a new Complex instance. And once again, we'll overload the definitions to support both a Complex and a Float64 operand.

    # ...
    def __iadd__(inout self, rhs: Self) -> None:
        self.re += rhs.re
        self.im += rhs.im

    def __iadd__(inout self, rhs: Float64) -> None:
        self.re += rhs

    def __isub__(inout self, rhs: Self) -> None:
        self.re -= rhs.re
        self.im -= rhs.im

    def __isub__(inout self, rhs: Float64) -> None:
        self.re -= rhs

    def __imul__(inout self, rhs: Self) -> None:
        new_re = self.re * rhs.re - self.im * rhs.im
        new_im = self.re * rhs.im + self.im * rhs.re
        self.re = new_re
        self.im = new_im

    def __imul__(inout self, rhs: Float64) -> None:
        self.re *= rhs
        self.im *= rhs

    def __itruediv__(inout self, rhs: Self) -> None:
        denom = rhs.squared_norm()
        new_re = (self.re * rhs.re + self.im * rhs.im) / denom
        new_im = (self.im * rhs.re - self.re * rhs.im) / denom
        self.re = new_re
        self.im = new_im

    def __itruediv__(inout self, rhs: Float64) -> None:
        self.re /= rhs
        self.im /= rhs
    # ...
    def __iadd__(inout self, rhs: Self) -> None:
        self.re += rhs.re
        self.im += rhs.im

    def __iadd__(inout self, rhs: Float64) -> None:
        self.re += rhs

    def __isub__(inout self, rhs: Self) -> None:
        self.re -= rhs.re
        self.im -= rhs.im

    def __isub__(inout self, rhs: Float64) -> None:
        self.re -= rhs

    def __imul__(inout self, rhs: Self) -> None:
        new_re = self.re * rhs.re - self.im * rhs.im
        new_im = self.re * rhs.im + self.im * rhs.re
        self.re = new_re
        self.im = new_im

    def __imul__(inout self, rhs: Float64) -> None:
        self.re *= rhs
        self.im *= rhs

    def __itruediv__(inout self, rhs: Self) -> None:
        denom = rhs.squared_norm()
        new_re = (self.re * rhs.re + self.im * rhs.im) / denom
        new_im = (self.im * rhs.re - self.re * rhs.im) / denom
        self.re = new_re
        self.im = new_im

    def __itruediv__(inout self, rhs: Float64) -> None:
        self.re /= rhs
        self.im /= rhs

And now to try them out.

c4 = Complex(-1, -1)
print("c4 =", c4)
c4 += Complex(0.5, -0.5)
print("c4 += Complex(0.5, -0.5) =>", c4)
c4 += 2.75
print("c4 += 2.75 =>", c4)
c4 -= Complex(0.25, 1.5)
print("c4 -= Complex(0.25, 1.5) =>", c4)
c4 -= 3
print("c4 -= 3 =>", c4)
c4 *= Complex(-3.0, 2.0)
print("c4 *= Complex(-3.0, 2.0) =>", c4)
c4 *= 0.75
print("c4 *= 0.75 =>", c4)
c4 /= Complex(1.25, 2.0)
print("c4 /= Complex(1.25, 2.0) =>", c4)
c4 /= 2.0
print("c4 /= 2.0 =>", c4)
c4 = Complex(-1, -1)
print("c4 =", c4)
c4 += Complex(0.5, -0.5)
print("c4 += Complex(0.5, -0.5) =>", c4)
c4 += 2.75
print("c4 += 2.75 =>", c4)
c4 -= Complex(0.25, 1.5)
print("c4 -= Complex(0.25, 1.5) =>", c4)
c4 -= 3
print("c4 -= 3 =>", c4)
c4 *= Complex(-3.0, 2.0)
print("c4 *= Complex(-3.0, 2.0) =>", c4)
c4 *= 0.75
print("c4 *= 0.75 =>", c4)
c4 /= Complex(1.25, 2.0)
print("c4 /= Complex(1.25, 2.0) =>", c4)
c4 /= 2.0
print("c4 /= 2.0 =>", c4)
c4 = (-1.0 - 1.0i)
c4 += Complex(0.5, -0.5) => (-0.5 - 1.5i)
c4 += 2.75 => (2.25 - 1.5i)
c4 -= Complex(0.25, 1.5) => (2.0 - 3.0i)
c4 -= 3 => (-1.0 - 3.0i)
c4 *= Complex(-3.0, 2.0) => (9.0 + 7.0i)
c4 *= 0.75 => (6.75 + 5.25i)
c4 /= Complex(1.25, 2.0) => (3.404494382022472 - 1.247191011235955i)
c4 /= 2.0 => (1.702247191011236 - 0.6235955056179775i)
c4 = (-1.0 - 1.0i)
c4 += Complex(0.5, -0.5) => (-0.5 - 1.5i)
c4 += 2.75 => (2.25 - 1.5i)
c4 -= Complex(0.25, 1.5) => (2.0 - 3.0i)
c4 -= 3 => (-1.0 - 3.0i)
c4 *= Complex(-3.0, 2.0) => (9.0 + 7.0i)
c4 *= 0.75 => (6.75 + 5.25i)
c4 /= Complex(1.25, 2.0) => (3.404494382022472 - 1.247191011235955i)
c4 /= 2.0 => (1.702247191011236 - 0.6235955056179775i)

Implement equality operators​

The field of complex numbers is not an ordered field, so it doesn't make sense for us to implement the Comparable trait and the >, >=, <, and <= operators. However, we can implement the EqualityComparable trait and the == and != operators. (Of course, this suffers the same limitation of comparing floating point numbers for equality because of the limited precision of representing floating point numbers when performing arithmetic operations. But we'll go ahead and implement the operators for completeness.)

@value
struct Complex(
    EqualityComparable,
    Formattable,
    Stringable,
):
    # ...
    fn __eq__(self, other: Self) -> Bool:
        return self.re == other.re and self.im == other.im

    fn __ne__(self, other: Self) -> Bool:
        return self.re != other.re and self.im != other.im
@value
struct Complex(
    EqualityComparable,
    Formattable,
    Stringable,
):
    # ...
    fn __eq__(self, other: Self) -> Bool:
        return self.re == other.re and self.im == other.im

    fn __ne__(self, other: Self) -> Bool:
        return self.re != other.re and self.im != other.im

And now to try them out.

c1 = Complex(-1.2, 6.5)
c3 = Complex(3.14159, -2.71828)
c5 = Complex(-1.2, 6.5)

if c1 == c5:
    print("c1 is equal to c5")
else:
    print("c1 is not equal to c5")

if c1 != c3:
    print("c1 is not equal to c3")
else:
    print("c1 is equal to c3")
c1 = Complex(-1.2, 6.5)
c3 = Complex(3.14159, -2.71828)
c5 = Complex(-1.2, 6.5)

if c1 == c5:
    print("c1 is equal to c5")
else:
    print("c1 is not equal to c5")

if c1 != c3:
    print("c1 is not equal to c3")
else:
    print("c1 is equal to c3")
c1 is equal to c5
c1 is not equal to c3
c1 is equal to c5
c1 is not equal to c3

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