[docs] Extensions.md: Numbers & Geometry section

Documentation/Extensions.md

@@ -1118,7 +1118,274 @@ false.string  // "false"
 
 ## Numbers & Geometry
 
-<!-- batch 5 -->
+<details>
+<summary><b>Int</b> — conversions, digits, primes, roman numerals, operators</summary>
+
+### `var double: Double` / `var float: Float` / `var cgFloat: CGFloat` / `var uInt: UInt` / `var uInt32: UInt32` / `var uInt64: UInt64`
+Straight numeric conversions (`uInt32`/`uInt64` truncate).
+
+```swift
+5.double    // 5.0
+(-1).uInt32 // 4294967295
+```
+
+### `var countableRange: CountableRange<Int>`
+`0..<self`.
+
+```swift
+3.countableRange   // 0..<3
+```
+
+### `var degreesToRadians: Double` / `var radiansToDegrees: Double`
+Angle conversion.
+
+```swift
+180.degreesToRadians   // 3.14159…
+```
+
+### `var digits: [Int]` / `var digitsCount: Int`
+Decimal digits of `abs(self)`, and how many.
+
+```swift
+1234.digits       // [1, 2, 3, 4]
+1234.digitsCount  // 4
+```
+
+### `var kFormatted: String`
+Compact "k"/"kk" formatting for values ≥ 1000.
+
+```swift
+5300.kFormatted     // "5k"
+2_500_000.kFormatted // "25kk"
+```
+
+### `var timestampToDate: Date`
+`Date(timeIntervalSince1970:)`.
+
+```swift
+1_700_000_000.timestampToDate   // 2023-11-14 …
+```
+
+### `var satsToBTC: String` / `var convertToBTC: String` / `var toBTC: String`
+Satoshis → BTC string, 8 decimal places. All three are the same.
+
+```swift
+150_000_000.satsToBTC   // "1.50000000"
+```
+
+### `func isPrime() -> Bool`
+Primality test (trial division up to √n).
+
+```swift
+7.isPrime()   // true
+9.isPrime()   // false
+```
+
+### `func romanNumeral() -> String?`
+Roman numerals for positive integers, `nil` for 0 or negative.
+
+```swift
+2024.romanNumeral()   // "MMXXIV"
+```
+
+### `func roundToNearest(_ number: Int) -> Int`
+Round to the closest multiple of `number`.
+
+```swift
+47.roundToNearest(10)   // 50
+```
+
+### Operators
+| Operator | Meaning | Example |
+|---|---|---|
+| `a ** b` | exponentiation → `Double` | `2 ** 3` → `8.0` |
+| `√ n` (prefix) | square root → `Double` | `√ 9` → `3.0` |
+| `a ± b` (infix) | `(a+b, a-b)` | `5 ± 3` → `(8, 2)` |
+| `± n` (prefix) | `(n, -n)` | `± 2` → `(2, -2)` |
+
+</details>
+
+<details>
+<summary><b>Float / Double</b></summary>
+
+### `var int: Int` / `var double: Double` (Float) / `var float: Float` (Double) / `var cgFloat: CGFloat`
+Numeric conversions.
+
+### `var satsToBTC / convertToBTC / toBTC`
+Satoshis → BTC (`Double` here, unlike `Int` which returns a `String`).
+
+```swift
+150_000_000.0.satsToBTC   // 1.5
+```
+
+### `func rounded(toPlaces places: Int) -> Float` — *(Float only)*
+Round to N decimal places.
+
+```swift
+Float(3.14159).rounded(toPlaces: 2)   // 3.14
+```
+
+### Operator `a ** b`
+Exponentiation, staying in the same type (`Float ** Float → Float`, `Double ** Double → Double`).
+
+```swift
+4.4 ** 0.5   // 2.0976…
+```
+
+</details>
+
+<details>
+<summary><b>Decimal</b></summary>
+
+### `mutating func round(_ scale: Int, _ roundingMode:)` / `func rounded(_ scale:, _ roundingMode:) -> Decimal`
+Decimal rounding via `NSDecimalRound` — mutating and non-mutating.
+
+```swift
+Decimal(2.567).rounded(2, .plain)   // 2.57
+```
+
+</details>
+
+<details>
+<summary><b>BinaryInteger</b></summary>
+
+### `var bytes: [UInt8]`
+Big-endian raw byte representation.
+
+```swift
+Int16(-128).bytes   // [255, 128]
+```
+
+### `init?(bytes: [UInt8])`
+Reconstruct an integer from bytes (traps if the byte count exceeds the type size;
+`nil` if the value doesn't fit exactly).
+
+```swift
+Int16(bytes: [0xFF, 0xFD])   // -3
+```
+
+</details>
+
+<details>
+<summary><b>BinaryFloatingPoint</b></summary>
+
+### `func rounded(numberOfDecimalPlaces: Int, rule: FloatingPointRoundingRule) -> Self`
+Round to N places with an explicit rule (negative places treated as 0).
+
+```swift
+3.1415927.rounded(numberOfDecimalPlaces: 3, rule: .up)   // 3.142
+```
+
+</details>
+
+<details>
+<summary><b>SignedNumeric</b></summary>
+
+### `var string: String`
+`String(describing:)`.
+
+### `var asLocaleCurrency: String?` / `func asCurrency(locale: Locale = pt_BR) -> String?`
+Currency formatting in the current locale / a specified locale.
+
+```swift
+1234.5.asCurrency()                                  // "R$ 1.234,50"
+1234.5.asCurrency(locale: Locale(identifier: "en_US")) // "$1,234.50"
+```
+
+### `func spelledOutString(locale: Locale = .current) -> String?`
+Number spelled out in words.
+
+```swift
+92.spelledOutString(locale: Locale(identifier: "en"))   // "ninety-two"
+```
+
+</details>
+
+<details>
+<summary><b>CGFloat</b></summary>
+
+### `var abs / ceil / floor` / `var int / float / double`
+Math and numeric conversions.
+
+```swift
+CGFloat(-3.2).abs    // 3.2
+CGFloat(3.2).ceil    // 4.0
+```
+
+### `var isPositive: Bool` / `var isNegative: Bool`
+Sign checks.
+
+### `var degreesToRadians: CGFloat` / `var radiansToDegrees: CGFloat`
+Angle conversion.
+
+</details>
+
+<details>
+<summary><b>CGRect</b></summary>
+
+### `var center: CGPoint`
+Rect centre.
+
+### `init(center: CGPoint, size: CGSize)`
+Build a rect from its centre and size.
+
+```swift
+CGRect(center: CGPoint(x: 50, y: 50), size: CGSize(width: 20, height: 10))
+// origin (40, 45), size 20×10
+```
+
+### `func resizing(to size: CGSize, anchor: CGPoint = (0.5, 0.5)) -> CGRect`
+Resize while keeping the given normalised anchor point fixed.
+
+```swift
+rect.resizing(to: CGSize(width: 100, height: 100), anchor: CGPoint(x: 0, y: 1))
+// grows from the bottom-left corner
+```
+
+</details>
+
+<details>
+<summary><b>CGSize</b></summary>
+
+### `var aspectRatio: CGFloat` / `var maxDimension: CGFloat` / `var minDimension: CGFloat`
+`width / height` (0 when height is 0), and the larger / smaller side.
+
+```swift
+CGSize(width: 16, height: 9).aspectRatio   // 1.777…
+```
+
+### `func aspectFit(to boundingSize:) -> CGSize` / `func aspectFill(to boundingSize:) -> CGSize`
+Scale to fit inside / fill a bounding size, preserving ratio.
+
+```swift
+CGSize(width: 120, height: 80).aspectFit(to: CGSize(width: 100, height: 50))
+// 75 × 50
+```
+
+### Operators
+`+`, `-`, `*` and their `+=`/`-=`/`*=` forms, between two `CGSize`s, a `CGSize`
+and a `(width, height)` tuple, or a `CGSize` and a scalar.
+
+```swift
+CGSize(width: 5, height: 10) + CGSize(width: 3, height: 4)   // 8 × 14
+CGSize(width: 5, height: 10) * 3                              // 15 × 30
+```
+
+</details>
+
+<details>
+<summary><b>CGPoint / CGRect / CGSize — <code>Hashable</code></summary>
+
+When SwiftUI is available, `CGPoint`, `CGRect`, and `CGSize` are made
+`Hashable` (retroactive conformance) so they can be used as dictionary keys or
+in `Set`s and as SwiftUI identifiers.
+
+```swift
+var seen: Set<CGPoint> = []
+seen.insert(CGPoint(x: 1, y: 2))
+```
+
+</details>
 
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