axiom-localization

name	axiom-localization
description	Use when localizing apps, using String Catalogs, generating type-safe symbols (Xcode 26+), handling plurals, RTL layouts, locale-aware formatting, or migrating from .strings files - comprehensive i18n patterns for Xcode 15-26
license	MIT
metadata	{"version":"1.1.0","last-updated":"2025-12-16"}

Localization & Internationalization

Comprehensive guide to app localization using String Catalogs. Apple Design Award Inclusivity winners always support multiple languages with excellent RTL (Right-to-Left) support.

Overview

String Catalogs (.xcstrings) are Xcode 15's unified format for managing app localization. They replace legacy .strings and .stringsdict files with a single JSON-based format that's easier to maintain, diff, and integrate with translation workflows.

This skill covers String Catalogs, SwiftUI/UIKit localization APIs, plural handling, RTL support, locale-aware formatting, and migration strategies from legacy formats.

When to Use This Skill

• Setting up String Catalogs in Xcode 15+
• Localizing SwiftUI and UIKit apps
• Handling plural forms correctly (critical for many languages)
• Supporting RTL languages (Arabic, Hebrew)
• Formatting dates, numbers, and currencies by locale
• Migrating from legacy .strings/.stringsdict files
• Preparing App Shortcuts and App Intents for localization
• Debugging missing translations or incorrect plural forms

System Requirements

• Xcode 15+ for String Catalogs (.xcstrings)
• Xcode 26+ for automatic symbol generation, #bundle macro, and AI-powered comment generation
• iOS 15+ for LocalizedStringResource
• iOS 16+ for App Shortcuts localization
• Earlier iOS versions use legacy .strings files

---

Part 1: String Catalogs (WWDC 2023/10155)

Creating a String Catalog

Method 1: Xcode Navigator

1. File → New → File
2. Choose "String Catalog"
3. Name it (e.g., Localizable.xcstrings)
4. Add to target

Method 2: Automatic Extraction

Xcode 15 can automatically extract strings from:

• SwiftUI views (string literals in Text, Label, Button)
• Swift code (String(localized:))
• Objective-C (NSLocalizedString)
• C (CFCopyLocalizedString)
• Interface Builder files (.storyboard, .xib)
• Info.plist values
• App Shortcuts phrases

Build Settings Required:

• "Use Compiler to Extract Swift Strings" → Yes
• "Localization Prefers String Catalogs" → Yes

String Catalog Structure

Each entry has:

• Key: Unique identifier (default: the English string)
• Default Value: Fallback if translation missing
• Comment: Context for translators
• String Table: Organization container (default: "Localizable")

Example .xcstrings JSON:

{
  "sourceLanguage" : "en",
  "strings" : {
    "Thanks for shopping with us!" : {
      "comment" : "Label above checkout button",
      "localizations" : {
        "en" : {
          "stringUnit" : {
            "state" : "translated",
            "value" : "Thanks for shopping with us!"
          }
        },
        "es" : {
          "stringUnit" : {
            "state" : "translated",
            "value" : "¡Gracias por comprar con nosotros!"
          }
        }
      }
    }
  },
  "version"  

Translation States

Xcode tracks state for each translation:

• New (⚪) - String hasn't been translated yet
• Needs Review (🟡) - Source changed, translation may be outdated
• Reviewed (✅) - Translation approved and current
• Stale (🔴) - String no longer found in source code

Workflow:

1. Developer adds string → New
2. Translator adds translation → Reviewed
3. Developer changes source → Needs Review
4. Translator updates → Reviewed
5. Developer removes code → Stale

---

Part 2: SwiftUI Localization

LocalizedStringKey (Automatic)

SwiftUI views with String parameters automatically support localization:

// ✅ Automatically localizable
Text("Welcome to WWDC!")
Label("Thanks for shopping with us!", systemImage: "bag")
Button("Checkout") { }

// Xcode extracts these strings to String Catalog

How it works: SwiftUI uses LocalizedStringKey internally, which looks up strings in String Catalogs.

String(localized:) with Comments

For explicit localization in Swift code:

// Basic
let title = String(localized: "Welcome to WWDC!")

// With comment for translators
let title = String(localized: "Welcome to WWDC!",
                   comment: "Notification banner title")

// With custom table
let title = String(localized: "Welcome to WWDC!",
                   table: "WWDCNotifications",
                   comment: "Notification banner title")

// With default value (key ≠ English text)
let title = String(localized: "WWDC_NOTIFICATION_TITLE",
                   defaultValue: "Welcome to WWDC!",
                   comment: "Notification banner title")

Best practice: Always include comment to give translators context.

LocalizedStringResource (Deferred Localization)

For passing localizable strings to other functions:

import Foundation

struct CardView: View {
    let title: LocalizedStringResource
    let subtitle: LocalizedStringResource

    var body: some View {
        ZStack {
            RoundedRectangle(cornerRadius: 10.0)
            VStack {
                Text(title)      // Resolved at render time
                Text(subtitle)
            }
            .padding()
        }
    }
}

// Usage
CardView(
    title: "Recent Purchases",
    subtitle: "Items you've ordered in the past week."
)

Key difference: LocalizedStringResource defers lookup until used, allowing custom views to be fully localizable.

AttributedString with Markdown

// Markdown formatting is preserved across localizations
let subtitle = AttributedString(localized: "**Bold** and _italic_ text")

---

Part 3: UIKit & Foundation

NSLocalizedString Macro

// Basic
let title = NSLocalizedString("Recent Purchases", comment: "Button Title")

// With table
let title = NSLocalizedString("Recent Purchases",
                             tableName: "Shopping",
                             comment: "Button Title")

// With bundle
let title = NSLocalizedString("Recent Purchases",
                             tableName: nil,
                             bundle: .main,
                             value: "",
                             comment: "Button Title")

Bundle.localizedString

let customBundle = Bundle(for: MyFramework.self)
let text = customBundle.localizedString(forKey: "Welcome",
                                        value: nil,
                                        table: "MyFramework")

Custom Macros

// Objective-C
#define MyLocalizedString(key, comment) \
    [myBundle localizedStringForKey:key value:nil table:nil]

Info.plist Localization

Localize app name, permissions, etc.:

1. Select Info.plist
2. Editor → Add Localization
3. Create InfoPlist.strings for each language:

// InfoPlist.strings (Spanish)
"CFBundleName" = "Mi Aplicación";
"NSCameraUsageDescription" = "La app necesita acceso a la cámara para tomar fotos.";

---

Part 4: Pluralization

Different languages have different plural rules:

• English: 2 forms (one, other)
• Russian: 3 forms (one, few, many)
• Polish: 3 forms (one, few, other)
• Arabic: 6 forms (zero, one, two, few, many, other)

SwiftUI Plural Handling

// Xcode automatically creates plural variations
Text("\(count) items")

// With custom formatting
Text("\(visitorCount) Recent Visitors")

In String Catalog:

{
  "strings" : {
    "%lld Recent Visitors" : {
      "localizations" : {
        "en" : {
          "variations" : {
            "plural" : {
              "one" : {
                "stringUnit" : {
                  "state" : "translated",
                  "value" : "%lld Recent Visitor"
                }
              },
              "other" : {
                "stringUnit" : {
                  "state" : "translated",
                  "value" : "%lld Recent Visitors"
                }
              }
            }
          }
        }
      
    
  

XLIFF Export Format

When exporting for translation (File → Export Localizations):

Legacy (stringsdict):

<trans-unit id="/%lld Recent Visitors:dict/NSStringLocalizedFormatKey:dict/:string">
    <source>%#@recentVisitors@</source>
</trans-unit>

<trans-unit id="/%lld Recent Visitors:dict/recentVisitors:dict/one:dict/:string">
    <source>%lld Recent Visitor</source>
    <target>%lld Visitante Recente</target>
</trans-unit>

String Catalog (cleaner):

<trans-unit id="%lld Recent Visitors|==|plural.one">
    <source>%lld Recent Visitor</source>
    <target>%lld Visitante Recente</target>
</trans-unit>

<trans-unit id="%lld Recent Visitors|==|plural.other">
    <source>%lld Recent Visitors</source>
    <target>%lld Visitantes Recentes</target>
</trans-unit>

Substitutions with Plural Variables

// Multiple variables with different plural forms
let message = String(localized: "\(songCount) songs on \(albumCount) albums")

Xcode creates variations for each variable's plural form:

• songCount: one, other
• albumCount: one, other
• Total combinations: 2 × 2 = 4 translation entries

---

Part 5: Device & Width Variations

Device-Specific Strings

Different text for different platforms:

// Same code, different strings per device
Text("Bird Food Shop")

String Catalog variations:

{
  "Bird Food Shop" : {
    "localizations" : {
      "en" : {
        "variations" : {
          "device" : {
            "applewatch" : {
              "stringUnit" : {
                "value" : "Bird Food"
              }
            },
            "other" : {
              "stringUnit" : {
                "value" : "Bird Food Shop"
              }
            }
          }
        }
      }
    }
  }
}

Result:

• iPhone/iPad: "Bird Food Shop"
• Apple Watch: "Bird Food" (shorter for small screen)

Width Variations

For dynamic type and size classes:

Text("Application Settings")

String Catalog can provide shorter text for narrow widths.

---

Part 6: RTL Support

Layout Mirroring

SwiftUI automatically mirrors layouts for RTL languages:

// ✅ Automatically mirrors for Arabic/Hebrew
HStack {
    Image(systemName: "chevron.right")
    Text("Next")
}

// iPhone (English): [>] Next
// iPhone (Arabic):  Next [<]

Leading/Trailing vs Left/Right

Always use semantic directions:

// ✅ Correct - mirrors automatically
.padding(.leading, 16)
.frame(maxWidth: .infinity, alignment: .leading)

// ❌ Wrong - doesn't mirror
.padding(.left, 16)
.frame(maxWidth: .infinity, alignment: .left)

Images and Icons

Mark images that should/shouldn't flip:

// ✅ Directional - mirrors for RTL
Image(systemName: "chevron.forward")

// ✅ Non-directional - never mirrors
Image(systemName: "star.fill")

// Custom images
Image("backButton")
    .flipsForRightToLeftLayoutDirection(true)

Testing in RTL Mode

Xcode Scheme:

1. Edit Scheme → Run → Options
2. Application Language: Arabic / Hebrew
3. OR: App Language → Right-to-Left Pseudolanguage

Simulator: Settings → General → Language & Region → Preferred Language Order

SwiftUI Preview:

struct ContentView_Previews: PreviewProvider {
    static var previews: some View {
        ContentView()
            .environment(\.layoutDirection, .rightToLeft)
            .environment(\.locale, Locale(identifier: "ar"))
    }
}

---

Part 7: Locale-Aware Formatting

DateFormatter

let formatter = DateFormatter()
formatter.locale = Locale.current  // ✅ Use current locale
formatter.dateStyle = .long
formatter.timeStyle = .short

let dateString = formatter.string(from: Date())

// US: "January 15, 2024 at 3:30 PM"
// France: "15 janvier 2024 à 15:30"
// Japan: "2024年1月15日 15:30"

Never hardcode date format strings:

// ❌ Wrong - breaks in other locales
formatter.dateFormat = "MM/dd/yyyy"

// ✅ Correct - adapts to locale
formatter.dateStyle = .short

NumberFormatter for Currency

let formatter = NumberFormatter()
formatter.locale = Locale.current
formatter.numberStyle = .currency

let priceString = formatter.string(from: 29.99)

// US: "$29.99"
// UK: "£29.99"
// Japan: "¥30" (rounds to integer)
// France: "29,99 €" (comma decimal, space before symbol)

MeasurementFormatter

let distance = Measurement(value: 100, unit: UnitLength.meters)

let formatter = MeasurementFormatter()
formatter.locale = Locale.current

let distanceString = formatter.string(from: distance)

// US: "328 ft" (converts to imperial)
// Metric countries: "100 m"

Locale-Specific Sorting

let names = ["Ångström", "Zebra", "Apple"]

// ✅ Locale-aware sort
let sorted = names.sorted { (lhs, rhs) in
    lhs.localizedStandardCompare(rhs) == .orderedAscending
}

// Sweden: ["Ångström", "Apple", "Zebra"]  (Å comes first in Swedish)
// US: ["Ångström", "Apple", "Zebra"]      (Å treated as A)

---

Part 8: App Shortcuts Localization

Phrases with Parameters

import AppIntents

struct ShowTopDonutsIntent: AppIntent {
    static var title: LocalizedStringResource = "Show Top Donuts"

    @Parameter(title: "Timeframe")
    var timeframe: Timeframe

    static var parameterSummary: some ParameterSummary {
        Summary("\(.applicationName) Trends for \(\.$timeframe)") {
            \.$timeframe
        }
    }
}

String Catalog automatically extracts:

• Intent title
• Parameter names
• Phrase templates with placeholders

Localized phrases:

English: "Food Truck Trends for this week"
Spanish: "Tendencias de Food Truck para esta semana"

AppShortcutsProvider Localization

struct FoodTruckShortcuts: AppShortcutsProvider {
    static var appShortcuts: [AppShortcut] {
        AppShortcut(
            intent: ShowTopDonutsIntent(),
            phrases: [
                "\(.applicationName) Trends for \(\.$timeframe)",
                "Show trending donuts for \(\.$timeframe) in \(.applicationName)",
                "Give me trends for \(\.$timeframe) in \(.applicationName)"
            ]
        )
    }
}

Xcode extracts all 3 phrases into String Catalog for translation.

---

Part 9: Migration from Legacy

Converting .strings to .xcstrings

Automatic migration:

1. Select .strings file in Navigator
2. Editor → Convert to String Catalog
3. Xcode creates .xcstrings and preserves translations

Manual approach:

1. Create new String Catalog
2. Build project (Xcode extracts strings from code)
3. Import translations via File → Import Localizations (XLIFF)
4. Delete old .strings files

Converting .stringsdict

Plural files automatically merge:

1. Keep .strings and .stringsdict together
2. Convert → Both merge into single .xcstrings
3. Plural variations preserved

Gradual Migration Strategy

Phase 1: New code uses String Catalogs

• Create Localizable.xcstrings
• Write new code with String(localized:)
• Keep legacy .strings files for old code

Phase 2: Migrate existing strings

• Convert one .strings table at a time
• Test translations after each conversion
• Update code using old NSLocalizedString calls

Phase 3: Remove legacy files

• Delete .strings and .stringsdict files
• Verify all strings in String Catalog
• Submit to App Store

Coexistence: .strings and .xcstrings work together - Xcode checks both.

---

Common Mistakes

Hardcoded Strings

// ❌ Wrong - not localizable
Text("Welcome")
let title = "Settings"

// ✅ Correct - localizable
Text("Welcome")  // SwiftUI auto-localizes
let title = String(localized: "Settings")

Concatenating Localized Strings

// ❌ Wrong - word order varies by language
let message = String(localized: "You have") + " \(count) " + String(localized: "items")

// ✅ Correct - single localizable string with substitution
let message = String(localized: "You have \(count) items")

Why wrong: Some languages put numbers before nouns, some after.

Missing Plural Forms

// ❌ Wrong - grammatically incorrect for many languages
Text("\(count) item(s)")

// ✅ Correct - proper plural handling
Text("\(count) items")  // Xcode creates plural variations

Ignoring RTL

// ❌ Wrong - breaks in RTL languages
.padding(.left, 20)
HStack {
    backButton
    Spacer()
    title
}

// ✅ Correct - mirrors automatically
.padding(.leading, 20)
HStack {
    backButton  // Appears on right in RTL
    Spacer()
    title
}

Wrong Date/Number Formats

// ❌ Wrong - US-only format
let formatter = DateFormatter()
formatter.dateFormat = "MM/dd/yyyy"

// ✅ Correct - adapts to locale
formatter.dateStyle = .short
formatter.locale = Locale.current

Forgetting Comments

// ❌ Wrong - translator has no context
String(localized: "Confirm")

// ✅ Correct - clear context
String(localized: "Confirm", comment: "Button to confirm delete action")

Impact: "Confirm" could mean "verify" or "acknowledge" - context matters for accurate translation.

---

Troubleshooting

Strings not appearing in String Catalog

Cause: Build settings not enabled

Solution:

1. Build Settings → "Use Compiler to Extract Swift Strings" → Yes
2. Clean Build Folder (Cmd+Shift+K)
3. Build project

Translations not showing in app

Cause 1: Language not added to project

1. Project → Info → Localizations → + button
2. Add target language

Cause 2: String marked as "Stale"

• Remove stale strings or verify code still uses them

Plural forms incorrect

Cause: Using String.localizedStringWithFormat instead of String Catalog

Solution: Use String Catalog's automatic plural handling:

// ✅ Correct
Text("\(count) items")

// ❌ Wrong
Text(String.localizedStringWithFormat(NSLocalizedString("%d items", comment: ""), count))

XLIFF export missing strings

Cause: "Localization Prefers String Catalogs" not set

Solution:

1. Build Settings → "Localization Prefers String Catalogs" → Yes
2. Export Localizations again

Generated symbols not appearing (Xcode 26+)

Cause 1: Build setting not enabled

Solution:

1. Build Settings → "Generate String Catalog Symbols" → Yes
2. Clean Build Folder (Cmd+Shift+K)
3. Rebuild project

Cause 2: String not manually added to catalog

Solution: Symbols only generate for manually-added strings (+ button in String Catalog). Auto-extracted strings don't generate symbols.

#bundle macro not working (Xcode 26+)

Cause: Wrong syntax or missing import

Solution:

import Foundation  // Required for #bundle
Text("My Collections", bundle: #bundle, comment: "Section title")

Verify you're using #bundle not .module.

Refactoring to symbols fails (Xcode 26+)

Cause 1: String not in String Catalog

1. Ensure string exists in .xcstrings file
2. Build project to refresh catalog
3. Try refactoring again

Cause 2: Build setting not enabled

• Enable "Generate String Catalog Symbols" in Build Settings
• Clean and rebuild

---

Part 10: Xcode 26 Localization Enhancements

Xcode 26 introduces type-safe localization with generated symbols, automatic comment generation using on-device AI, and improved Swift Package support with the #bundle macro. Based on WWDC 2025 session 225 "Explore localization with Xcode".

Generated Symbols (Type-Safe Localization)

The problem: String-based localization fails silently when typos occur.

// ❌ Typo - fails silently at runtime
Text("App.HomeScren.Title")  // Missing 'e' in Screen

The solution: Xcode 26 generates type-safe symbols from manually-added strings.

How It Works

1. Add strings manually to String Catalog using the + button
2. Enable build setting: "Generate String Catalog Symbols" (ON by default in new projects)
3. Use symbols instead of strings

// ✅ Type-safe - compiler catches typos
Text(.appHomeScreenTitle)

Symbol Generation Rules

String Type	Generated Symbol Type	Usage Example
No placeholders	Static property	Text(.introductionTitle)
With placeholders	Function with labeled arguments	.subtitle(friendsPosts: 42)

Key naming conversion:

• App.HomeScreen.Title → .appHomeScreenTitle
• Periods removed, camel-cased
• Available on LocalizedStringResource

Code Examples

// SwiftUI views
struct ContentView: View {
    var body: some View {
        NavigationStack {
            Text(.introductionTitle)
                .navigationSubtitle(.subtitle(friendsPosts: 42))
        }
    }
}

// Foundation String
let message = String(localized: .curatedCollection)

// Custom views with LocalizedStringResource
struct CollectionDetailEditingView: View {
    let title: LocalizedStringResource

    init(title: LocalizedStringResource) {
        self.title = title
    }

    var body: some View {
        Text(title)
    }
}

CollectionDetailEditingView(title: .editingTitle)

---

Automatic Comment Generation

Xcode 26 uses an on-device model to automatically generate contextual comments for localizable strings.

Enabling the Feature

1. Open Xcode Settings → Editing
2. Enable "automatically generate string catalog comments"
3. New strings added to code automatically receive generated comments

Example

For a button string, Xcode generates:

"The text label on a button to cancel the deletion of a collection"

This context helps translators understand where and how the string is used.

XLIFF Export

Auto-generated comments are marked in exported XLIFF files:

<trans-unit id="Grand Canyon" xml:space="preserve">
    <source>Grand Canyon</source>
    <target state="new">Grand Canyon</target>
    <note from="auto-generated">Suggestion for searching landmarks</note>
</trans-unit>

Benefits:

• Saves developer time writing translator context
• Provides consistent, clear descriptions
• Improves translation quality

---

Swift Package & Framework Localization

The Problem

SwiftUI uses the .main bundle by default. Swift Packages and frameworks need to reference their own bundle:

// ❌ Wrong - uses main bundle, strings not found
Text("My Collections", comment: "Section title")

The Solution: #bundle Macro (NEW in Xcode 26)

The #bundle macro automatically references the correct bundle for the current target:

// ✅ Correct - automatically uses package/framework bundle
Text("My Collections", bundle: #bundle, comment: "Section title")

Key advantages:

• Works in main app, frameworks, and Swift Packages
• Backwards-compatible with older OS versions
• Eliminates manual .module bundle management

With Custom Table Names

// Main app
Text("My Collections",
     tableName: "Discover",
     comment: "Section title")

// Framework or Swift Package
Text("My Collections",
     tableName: "Discover",
     bundle: #bundle,
     comment: "Section title")

---

Custom Table Symbol Access

When using multiple String Catalogs for organization:

Default "Localizable" Table

Symbols are directly accessible on LocalizedStringResource:

Text(.welcomeMessage)  // From Localizable.xcstrings

Note: Xcode automatically resolves symbols from the default "Localizable" table. Explicit table selection is rarely needed—use it only for debugging or testing specific catalogs.

Custom Tables

Symbols are nested in the table namespace:

// From Discover.xcstrings
Text(Discover.featuredCollection)

// From Settings.xcstrings
Text(Settings.privacyPolicy)

Organization strategy for large apps:

• Localizable.xcstrings - Core app strings
• FeatureName.xcstrings - Feature-specific strings (e.g., Onboarding, Settings, Discover)
• Benefits: Easier to manage, clearer ownership, better XLIFF organization

---

Two Localization Workflows

Xcode 26 supports two complementary workflows:

Workflow 1: String Extraction (Recommended for new projects)

Process:

1. Write strings directly in code
2. Use SwiftUI views (Text, Button) and String(localized:)
3. Xcode automatically extracts to String Catalog
4. Leverage automatic comment generation

Pros: Simple initial setup, immediate start

Cons: Less control over string organization

// ✅ String extraction workflow
Text("Welcome to WWDC!", comment: "Main welcome message")

Workflow 2: Generated Symbols (Recommended as complexity grows)

Process:

1. Manually add strings to String Catalog
2. Reference via type-safe symbols
3. Organize into custom tables

Pros: Better control, type safety, easier to maintain across frameworks

Cons: Requires planning string catalog structure upfront

// ✅ Generated symbols workflow
Text(.welcomeMessage)

Workflow	Best For	Trade-offs
String Extraction	New projects, simple apps, prototyping	Automatic extraction, less control over organization
Generated Symbols	Large apps, frameworks, multiple teams	Type safety, better organization, requires upfront planning

---

Refactoring Between Workflows

Xcode 26 allows converting between workflows without manual rewriting.

Converting Strings to Symbols

1. Right-click on a string literal in code
2. Select "Refactor > Convert Strings to Symbols"
3. Preview all affected locations
4. Customize symbol names before confirming
5. Apply to entire table or individual strings

Example:

// Before
Text("Welcome to WWDC!", comment: "Main welcome message")

// After refactoring
Text(.welcomeToWWDC)

Benefits:

• Batch conversion of entire String Catalogs
• Preview changes before applying
• Maintain localization without code rewrites

---

Implementation Checklist

After adopting Xcode 26 generated symbols, verify:

Build Configuration:

• "Generate String Catalog Symbols" build setting enabled
• Project builds without "Cannot find 'symbolName' in scope" errors
• Clean build succeeds (Cmd+Shift+K, then Cmd+B)

String Catalog Setup:

• Strings manually added to catalog using + button (not auto-extracted)
• Symbol names follow conventions (camelCase, no periods)
• Custom tables organized by feature (if using multiple catalogs)

Swift Package Integration:

• All Text() and String(localized:) calls in packages use bundle: #bundle
• Import Foundation added where #bundle is used
• Tested package builds independently and as dependency

Refactoring & Migration:

• Tested refactoring tool on sample strings
• Preview showed expected changes before applying
• Old string-based calls still work during transition period

Optional Features:

• Automatic comment generation enabled in Xcode Settings → Editing (optional)
• Tested AI-generated comments for accuracy
• XLIFF export includes auto-generated comments

Testing:

• Symbols resolve correctly in SwiftUI previews
• Localization works across all supported languages
• App runs on minimum supported iOS version

---

Resources

WWDC: 2025-225, 2023-10155, 2022-10110

Docs: /xcode/localization, /xcode/localizing-and-varying-text-with-a-string-catalog

Skills: axiom-app-intents-ref, axiom-hig, axiom-accessibility-diag