Update Swift tools version to 6.0 and add new Position struct for sad…

…dle points exercise

exercises/practice/complex-numbers/.docs/instructions.append.md

@@ -0,0 +1,11 @@
+# Append
+
+You will have to implement your own equality operator for the `ComplexNumber` object.
+This will pose the challenge of comparing two floating point numbers.
+It might be useful to use the method `isApproximatelyEqual(to:absoluteTolerance:)` which can be found in the [Numerics][swift-numberics] library.
+With a given tolerance of `0.00001` should be enough to pass the tests.
+The library is already imported in the project so it is just to import it in your file.
+
+You are aLso free to implement your own method to compare the two complex numbers.
+
+[swift-numberics]: https://github.com/apple/swift-numerics

exercises/practice/complex-numbers/.docs/instructions.md

@@ -1,29 +1,100 @@
 # Instructions
 
-A complex number is a number in the form `a + b * i` where `a` and `b` are real and `i` satisfies `i^2 = -1`.
+A **complex number** is expressed in the form `z = a + b * i`, where:
 
-`a` is called the real part and `b` is called the imaginary part of `z`.
-The conjugate of the number `a + b * i` is the number `a - b * i`.
-The absolute value of a complex number `z = a + b * i` is a real number `|z| = sqrt(a^2 + b^2)`. The square of the absolute value `|z|^2` is the result of multiplication of `z` by its complex conjugate.
+- `a` is the **real part** (a real number),
 
-The sum/difference of two complex numbers involves adding/subtracting their real and imaginary parts separately:
-`(a + i * b) + (c + i * d) = (a + c) + (b + d) * i`,
-`(a + i * b) - (c + i * d) = (a - c) + (b - d) * i`.
+- `b` is the **imaginary part** (also a real number), and
 
-Multiplication result is by definition
-`(a + i * b) * (c + i * d) = (a * c - b * d) + (b * c + a * d) * i`.
+- `i` is the **imaginary unit** satisfying `i^2 = -1`.
 
-The reciprocal of a non-zero complex number is
-`1 / (a + i * b) = a/(a^2 + b^2) - b/(a^2 + b^2) * i`.
+## Operations on Complex Numbers
 
-Dividing a complex number `a + i * b` by another `c + i * d` gives:
-`(a + i * b) / (c + i * d) = (a * c + b * d)/(c^2 + d^2) + (b * c - a * d)/(c^2 + d^2) * i`.
+### Conjugate
 
-Raising e to a complex exponent can be expressed as `e^(a + i * b) = e^a * e^(i * b)`, the last term of which is given by Euler's formula `e^(i * b) = cos(b) + i * sin(b)`.
+The conjugate of the complex number `z = a + b * i` is given by:
 
-Implement the following operations:
+```text
+zc = a - b * i
+```
 
-- addition, subtraction, multiplication and division of two complex numbers,
-- conjugate, absolute value, exponent of a given complex number.
+### Absolute Value
 
-Assume the programming language you are using does not have an implementation of complex numbers.
+The absolute value (or modulus) of `z` is defined as:
+
+```text
+|z| = sqrt(a^2 + b^2)
+```
+
+The square of the absolute value is computed as the product of `z` and its conjugate `zc`:
+
+```text
+|z|^2 = z * zc = a^2 + b^2
+```
+
+### Addition
+
+The sum of two complex numbers `z1 = a + b * i` and `z2 = c + d * i` is computed by adding their real and imaginary parts separately:
+
+```text
+z1 + z2 = (a + b * i) + (c + d * i)
+        = (a + c) + (b + d) * i
+```
+
+### Subtraction
+
+The difference of two complex numbers is obtained by subtracting their respective parts:
+
+```text
+z1 - z2 = (a + b * i) - (c + d * i)
+        = (a - c) + (b - d) * i
+```
+
+### Multiplication
+
+The product of two complex numbers is defined as:
+
+```text
+z1 * z2 = (a + b * i) * (c + d * i)
+        = (a * c - b * d) + (b * c + a * d) * i
+```
+
+### Reciprocal
+
+The reciprocal of a non-zero complex number is given by:
+
+```text
+1 / z = 1 / (a + b * i)
+      = a / (a^2 + b^2) - b / (a^2 + b^2) * i
+```
+
+### Division
+
+The division of one complex number by another is given by:
+
+```text
+z1 / z2 = z1 * (1 / z2)
+        = (a + b * i) / (c + d * i)
+        = (a * c + b * d) / (c^2 + d^2) + (b * c - a * d) / (c^2 + d^2) * i
+```
+
+### Exponentiation
+
+Raising _e_ (the base of the natural logarithm) to a complex exponent can be expressed using Euler's formula:
+
+```text
+e^(a + b * i) = e^a * e^(b * i)
+              = e^a * (cos(b) + i * sin(b))
+```
+
+## Implementation Requirements
+
+Given that you should not use built-in support for complex numbers, implement the following operations:
+
+- **addition** of two complex numbers
+- **subtraction** of two complex numbers
+- **multiplication** of two complex numbers
+- **division** of two complex numbers
+- **conjugate** of a complex number
+- **absolute value** of a complex number
+- **exponentiation** of _e_ (the base of the natural logarithm) to a complex number

exercises/practice/complex-numbers/.meta/Sources/ComplexNumbers/ComplexNumbersExample.swift

@@ -1,66 +1,51 @@
 import Foundation
+import Numerics
 
-struct ComplexNumber {
+struct ComplexNumbers: Equatable {
 
-    var realComponent: Double
+    var real: Double
+    var imaginary: Double
 
-    var imaginaryComponent: Double
-
-    func getRealComponent() -> Double {
-
-        return self.realComponent
+    init(realComponent: Double, imaginaryComponent: Double? = 0) {
+        real = realComponent
+        imaginary = imaginaryComponent ?? 0
     }
 
-    func getImaginaryComponent() -> Double {
-
-        return self.imaginaryComponent
+    func add(complexNumber: ComplexNumbers) -> ComplexNumbers {
+        ComplexNumbers(realComponent: real + complexNumber.real, imaginaryComponent: imaginary + complexNumber.imaginary)
     }
 
-    func add(complexNumber: ComplexNumber) -> ComplexNumber {
-
-        return ComplexNumber(realComponent: self.realComponent + complexNumber.realComponent, imaginaryComponent: self.imaginaryComponent + complexNumber.imaginaryComponent)
 
+    func sub(complexNumber: ComplexNumbers) -> ComplexNumbers {
+        ComplexNumbers(realComponent: real - complexNumber.real, imaginaryComponent: imaginary - complexNumber.imaginary)
     }
 
-    func subtract(complexNumber: ComplexNumber) -> ComplexNumber {
-
-        return ComplexNumber(realComponent: self.realComponent - complexNumber.realComponent, imaginaryComponent: self.imaginaryComponent - complexNumber.imaginaryComponent)
+    func mul(complexNumber: ComplexNumbers) -> ComplexNumbers {
+        ComplexNumbers(realComponent: real * complexNumber.real - imaginary * complexNumber.imaginary, imaginaryComponent: real * complexNumber.imaginary + imaginary * complexNumber.real)
     }
 
-    func multiply(complexNumber: ComplexNumber) -> ComplexNumber {
-
-        return ComplexNumber(realComponent: self.realComponent * complexNumber.realComponent - self.imaginaryComponent * complexNumber.imaginaryComponent, imaginaryComponent: self.imaginaryComponent * complexNumber.realComponent + self.realComponent * complexNumber.imaginaryComponent)
+    func div(complexNumber: ComplexNumbers) -> ComplexNumbers {
+        let denominator = complexNumber.real * complexNumber.real + complexNumber.imaginary * complexNumber.imaginary
+        let realComponent = (real * complexNumber.real + imaginary * complexNumber.imaginary) / denominator
+        let imaginaryComponent = (imaginary * complexNumber.real - real * complexNumber.imaginary) / denominator
+        return ComplexNumbers(realComponent: realComponent, imaginaryComponent: imaginaryComponent)
     }
 
-    func divide(complexNumber: ComplexNumber) -> ComplexNumber {
-
-        let amplitudeOfComplexNumber = (complexNumber.realComponent *  complexNumber.realComponent) + (complexNumber.imaginaryComponent * complexNumber.imaginaryComponent)
-
-        let realPartOfQuotient = (self.realComponent * complexNumber.realComponent + self.imaginaryComponent * complexNumber.imaginaryComponent) / amplitudeOfComplexNumber
-
-        let imaginaryPartOfQuotient = (self.imaginaryComponent * complexNumber.realComponent - self.realComponent * self.realComponent * complexNumber.imaginaryComponent) / amplitudeOfComplexNumber
-
-        return ComplexNumber(realComponent: realPartOfQuotient, imaginaryComponent: imaginaryPartOfQuotient)
+    func absolute() -> Double {
+        sqrt(Double(real * real + imaginary * imaginary))
     }
 
-    func conjugate() -> ComplexNumber {
-
-        return ComplexNumber(realComponent: self.realComponent, imaginaryComponent: (-1 * self.imaginaryComponent))
+    func conjugate() -> ComplexNumbers {
+        ComplexNumbers(realComponent: real, imaginaryComponent: -imaginary)
     }
 
-    func absolute() -> Double {
-
-        return sqrt(pow(self.realComponent, 2.0) + pow(self.imaginaryComponent, 2.0))
+    func exponent() -> ComplexNumbers {
+        let expReal = exp(Double(real)) * cos(Double(imaginary))
+        let expImaginary = exp(Double(real)) * sin(Double(imaginary))
+        return ComplexNumbers(realComponent: expReal, imaginaryComponent: expImaginary)
     }
 
-    func exponent() -> ComplexNumber {
-
-        let realPartOfResult = cos(self.imaginaryComponent)
-        let imaginaryPartOfResult = sin(self.imaginaryComponent)
-        let factor = exp(self.realComponent)
-
-        return ComplexNumber(realComponent: realPartOfResult * factor, imaginaryComponent: imaginaryPartOfResult * factor)
-
+    static func == (lhs: ComplexNumbers, rhs: ComplexNumbers) -> Bool {
+        lhs.real.isApproximatelyEqual(to: rhs.real, absoluteTolerance: 0.0001) && lhs.imaginary.isApproximatelyEqual(to: rhs.imaginary, absoluteTolerance: 0.0001)
     }
-
-}
+}

exercises/practice/complex-numbers/.meta/config.json

@@ -1,6 +1,7 @@
 {
   "authors": [
-    "AlwynC"
+    "AlwynC",
+    "meatball133"
   ],
   "contributors": [
     "bhargavg",

exercises/practice/complex-numbers/.meta/template.swift

@@ -0,0 +1,72 @@
+import Testing
+import Foundation
+
+@testable import {{exercise|camelCase}}
+
+let RUNALL = Bool(ProcessInfo.processInfo.environment["RUNALL", default: "false"]) ?? false
+
+@Suite struct {{exercise|camelCase}}Tests {
+    {% outer: for case in cases %}
+        {%- if case.cases %}
+        {%- for subCases in case.cases %}
+        {%- if subCases.cases %}
+            {%- for subSubCases in subCases.cases %}
+                @Test("{{subSubCases.description}}", .enabled(if: RUNALL))
+                func test{{subSubCases.description |camelCase }}() {
+                    let complexNumberOne = {{exercise|camelCase}}(realComponent: {{subSubCases.input.z1[0]}}, imaginaryComponent: {{subSubCases.input.z1[1]}})
+                    let complexNumberTwo = {{exercise|camelCase}}(realComponent: {{subSubCases.input.z2[0]}}, imaginaryComponent: {{subSubCases.input.z2[1]}})
+                    let result = complexNumberOne.{{subSubCases.property}}(complexNumber: complexNumberTwo)
+                    let expected = {{exercise|camelCase}}(realComponent: {{subSubCases.expected[0]}}, imaginaryComponent: {{subSubCases.expected[1]}})
+                    #expect(expected == result)
+                }
+            {%- endfor %}
+        {%- else %}
+        {%- if forloop.outer.first and forloop.first %}
+            @Test("{{subCases.description}}")
+        {%- else %}
+            @Test("{{subCases.description}}", .enabled(if: RUNALL))
+        {%- endif %}
+            func test{{subCases.description |camelCase }}() {
+                {%- if subCases.property == "real" or subCases.property == "imaginary" or subCases.property == "abs" or subCases.property == "conjugate" or subCases.property == "exp" %}
+                let complexNumber = {{exercise|camelCase}}(realComponent: {{subCases.input.z[0] | complexNumber}}, imaginaryComponent: {{subCases.input.z[1] | complexNumber}})
+                {%- if subCases.property == "real" %}
+                #expect(complexNumber.real == {{subCases.expected}})
+                {%- elif subCases.property == "imaginary" %}
+                #expect(complexNumber.imaginary == {{subCases.expected}})
+                {%- elif subCases.property == "abs" %}
+                #expect(complexNumber.absolute() == {{subCases.expected}})
+                {%- elif subCases.property == "conjugate" %}
+                let expected = {{exercise|camelCase}}(realComponent: {{subCases.expected[0]}}, imaginaryComponent: {{subCases.expected[1]}})
+                #expect(complexNumber.conjugate() == expected)
+                {%- elif subCases.property == "exp" %}
+                let expected = {{exercise|camelCase}}(realComponent: {{subCases.expected[0] | complexNumber}}, imaginaryComponent: {{subCases.expected[1]}})
+                #expect(complexNumber.exponent() == expected)
+                {%- elif subCases.property == "add" or subCases.property == "sub" or subCases.property == "mul" or subCases.property == "div" %}
+                {%- endif %}
+                {%- else %}
+                {%- if subCases.input.z1[0] %}
+                let complexNumberOne = {{exercise|camelCase}}(realComponent: {{subCases.input.z1[0]}}, imaginaryComponent: {{subCases.input.z1[1]}})
+                let complexNumberTwo = {{exercise|camelCase}}(realComponent: {{subCases.input.z2}}, imaginaryComponent: nil)
+                {%- else %}
+                let complexNumberOne = {{exercise|camelCase}}(realComponent: {{subCases.input.z1}}, imaginaryComponent: nil)
+                let complexNumberTwo = {{exercise|camelCase}}(realComponent: {{subCases.input.z2[0]}}, imaginaryComponent: {{subCases.input.z2[1]}})
+                {%- endif %}
+                let result = complexNumberOne.{{subCases.property}}(complexNumber: complexNumberTwo)
+                let expected = {{exercise|camelCase}}(realComponent: {{subCases.expected[0]}}, imaginaryComponent: {{subCases.expected[1]}})
+                #expect(expected == result)
+                {%- endif %}
+        }
+        {%- endif %}
+        {% endfor -%}
+        {%- else %}
+            @Test("{{case.description}}", .enabled(if: RUNALL))
+            func test{{case.description |camelCase }}() {
+                let complexNumberOne = {{exercise|camelCase}}(realComponent: {{case.input.z1[0]}}, imaginaryComponent: {{case.input.z1[1]}})
+                let complexNumberTwo = {{exercise|camelCase}}(realComponent: {{case.input.z2[0]}}, imaginaryComponent: {{case.input.z2[1]}})
+                let result = complexNumberOne.{{case.property}}(complexNumber: complexNumberTwo)
+                let expected = {{exercise|camelCase}}(realComponent: {{case.expected[0]}}, imaginaryComponent: {{case.expected[1]}})
+                #expect(expected == result)
+        }
+        {%- endif %}
+    {% endfor -%}
+}

exercises/practice/complex-numbers/.meta/tests.toml

@@ -101,3 +101,30 @@ description = "Complex exponential function -> Exponential of a purely real numb
 
 [08eedacc-5a95-44fc-8789-1547b27a8702]
 description = "Complex exponential function -> Exponential of a number with real and imaginary part"
+
+[d2de4375-7537-479a-aa0e-d474f4f09859]
+description = "Complex exponential function -> Exponential resulting in a number with real and imaginary part"
+
+[06d793bf-73bd-4b02-b015-3030b2c952ec]
+description = "Operations between real numbers and complex numbers -> Add real number to complex number"
+
+[d77dbbdf-b8df-43f6-a58d-3acb96765328]
+description = "Operations between real numbers and complex numbers -> Add complex number to real number"
+
+[20432c8e-8960-4c40-ba83-c9d910ff0a0f]
+description = "Operations between real numbers and complex numbers -> Subtract real number from complex number"
+
+[b4b38c85-e1bf-437d-b04d-49bba6e55000]
+description = "Operations between real numbers and complex numbers -> Subtract complex number from real number"
+
+[dabe1c8c-b8f4-44dd-879d-37d77c4d06bd]
+description = "Operations between real numbers and complex numbers -> Multiply complex number by real number"
+
+[6c81b8c8-9851-46f0-9de5-d96d314c3a28]
+description = "Operations between real numbers and complex numbers -> Multiply real number by complex number"
+
+[8a400f75-710e-4d0c-bcb4-5e5a00c78aa0]
+description = "Operations between real numbers and complex numbers -> Divide complex number by real number"
+
+[9a867d1b-d736-4c41-a41e-90bd148e9d5e]
+description = "Operations between real numbers and complex numbers -> Divide real number by complex number"

exercises/practice/complex-numbers/Package.swift

@@ -1,4 +1,4 @@
-// swift-tools-version:5.3
+// swift-tools-version:6.0
 
 import PackageDescription
 
@@ -9,13 +9,18 @@ let package = Package(
             name: "ComplexNumbers",
             targets: ["ComplexNumbers"]),
     ],
-    dependencies: [],
+    dependencies: [
+        .package(url: "https://github.com/apple/swift-numerics", from: "1.0.2"),
+    ],
     targets: [
         .target(
             name: "ComplexNumbers",
-            dependencies: []),
+            dependencies: [
+                .product(name: "Numerics", package: "swift-numerics"),
+            ]),
         .testTarget(
             name: "ComplexNumbersTests",
-            dependencies: ["ComplexNumbers"]),
+            dependencies: ["ComplexNumbers",
+            .product(name: "Numerics", package: "swift-numerics"),]),
     ]
 )