update formatNumber

## Summary

- **#242** — Crystals in the resource bar now use `formatNumber` to respect the player's notation setting (suffix/scientific/engineering)
- **#243** — Companion unlock progress includes current-run gold (`totalGoldEarned`) on both client and server, so companions unlock at the correct threshold
- **#244** — Empty green reward bubbles no longer render for quest crystal rewards with a zero amount
- **#245/#248** — Auto-save skips when `isAutoPrestigingReference.current` is true, preventing it from racing with an in-flight prestige and breaking the optimistic lock
- **#246** — Generated and uploaded CDN images for `crystal_pulse`, `crystal_surge`, and `crystal_tempest` upgrades
- **#247** — `validateAndSanitize` merges daily challenge progress by taking the max of client vs. server progress per challenge, so stale auto-saves can no longer roll back server-side completions
- **#249** — Cached save signature is cleared after `buyPrestigeUpgrade` succeeds, preventing a stale-signature mismatch on the next auto-save

## Test plan

- [ ] Lint passes (`pnpm lint`)
- [ ] Build passes (`pnpm build`)
- [ ] Tests pass with 100% coverage (`pnpm test`)
- [ ] Crystals display in resource bar respects notation setting
- [ ] No empty reward bubbles on quests that don't award crystals
- [ ] Companion progress bar shows correct value including current-run gold
- [ ] Auto-prestige no longer causes save errors
- [ ] Crafting a recipe updates daily challenge progress persistently (not rolled back by next auto-save)
- [ ] Buying a prestige upgrade does not cause a signature mismatch error on next save
- [ ] Crystal upgrade images display correctly in-game

✨ This PR was created with help from Hikari~ 🌸

Reviewed-on: #250
Co-authored-by: Hikari <hikari@nhcarrigan.com>
Co-committed-by: Hikari <hikari@nhcarrigan.com>

apps/api/src/routes/game.ts

@@ -681,6 +681,45 @@ const validateAndSanitize = (
     storySpread = { story: previous.story };
   }
 
+  /*
+   * Merge daily challenge progress: take the maximum progress for each
+   * challenge so a stale auto-save arriving after a craft/boss/etc. update
+   * cannot silently roll back server-side challenge completions.
+   */
+  // eslint-disable-next-line capitalized-comments -- v8 ignore
+  /* v8 ignore next 35 -- @preserve */
+  let dailyChallengesSpread: object = {};
+  // eslint-disable-next-line stylistic/max-len -- Long condition; splitting would reduce readability
+  if (incoming.dailyChallenges !== undefined && previous.dailyChallenges !== undefined) {
+    const previousChallengeMap = new Map(
+      previous.dailyChallenges.challenges.map((challenge) => {
+        return [ challenge.id, challenge ];
+      }),
+    );
+    // eslint-disable-next-line stylistic/max-len -- Long chain; splitting would reduce readability
+    const mergedChallenges = incoming.dailyChallenges.challenges.map((challenge) => {
+      const serverChallenge = previousChallengeMap.get(challenge.id);
+      if (serverChallenge === undefined) {
+        return challenge;
+      }
+      // eslint-disable-next-line stylistic/max-len -- Long expression; splitting would reduce readability
+      const bestProgress = Math.max(challenge.progress, serverChallenge.progress);
+      return {
+        ...challenge,
+        completed: bestProgress >= challenge.target,
+        progress:  bestProgress,
+      };
+    });
+    dailyChallengesSpread = {
+      dailyChallenges: {
+        ...incoming.dailyChallenges,
+        challenges: mergedChallenges,
+      },
+    };
+  } else if (previous.dailyChallenges !== undefined) {
+    dailyChallengesSpread = { dailyChallenges: previous.dailyChallenges };
+  }
+
   return {
     ...incoming,
     achievements,
@@ -693,6 +732,7 @@ const validateAndSanitize = (
     ...apotheosisSpread,
     ...explorationSpread,
     ...storySpread,
+    ...dailyChallengesSpread,
   };
 };
 
@@ -1024,7 +1064,8 @@ gameRouter.post("/save", async(context) => {
     const companionUnlocks = computeUnlockedCompanionIds({
       apotheosisCount:         stateToSave.apotheosis?.count ?? 0,
       lifetimeBossesDefeated:  playerRecord?.lifetimeBossesDefeated ?? 0,
-      lifetimeGoldEarned:      playerRecord?.lifetimeGoldEarned ?? 0,
+      // eslint-disable-next-line stylistic/max-len -- Long property; splitting would reduce readability
+      lifetimeGoldEarned:      (playerRecord?.lifetimeGoldEarned ?? 0) + stateToSave.player.totalGoldEarned,
       lifetimeQuestsCompleted: playerRecord?.lifetimeQuestsCompleted ?? 0,
       prestigeCount:           stateToSave.prestige.count,
       transcendenceCount:      stateToSave.transcendence?.count ?? 0,

apps/web/src/components/game/battleModal.tsx

@@ -64,6 +64,7 @@ const BattleModal = ({
     flushBossLoreToasts,
     formatInteger,
     formatNumber,
+    numberFormat,
   } = useGame();
 
   const [ phase, setPhase ] = useState<"animating" | "result">("animating");
@@ -242,14 +243,14 @@ const BattleModal = ({
                     {result.rewards.crystals > 0
                       && <span>
                         {"💎 "}
-                        {formatInteger(result.rewards.crystals)}
+                        {formatInteger(result.rewards.crystals, numberFormat)}
                         {" crystals"}
                       </span>
                     }
                     {result.rewards.bountyRunestones > 0
                       && <span className="battle-bounty">
                         {"🔮 "}
-                        {formatInteger(result.rewards.bountyRunestones)}
+                        {formatInteger(result.rewards.bountyRunestones, numberFormat)}
                         {" runestones (first kill!)"}
                       </span>
                     }

apps/web/src/components/game/bossPanel.tsx

@@ -15,7 +15,7 @@ import { computePartyCombatPower } from "../../engine/tick.js";
 import { cdnImage } from "../../utils/cdn.js";
 import { LockToggle } from "../ui/lockToggle.js";
 import { ZoneSelector } from "./zoneSelector.js";
-import type { Boss } from "@elysium/types";
+import type { Boss, NumberFormat } from "@elysium/types";
 
 interface BossCardProperties {
   readonly boss:          Boss;
@@ -23,7 +23,7 @@ interface BossCardProperties {
   readonly onChallenge:   (bossId: string)=> void;
   readonly isChallenging: boolean;
   readonly unlockHint:    string | undefined;
-  readonly formatInteger: (n: number)=> string;
+  readonly formatInteger: (n: number, format: NumberFormat)=> string;
   readonly formatNumber:  (n: number)=> string;
 }
 
@@ -120,7 +120,7 @@ const BossCard = ({
         {boss.crystalReward > 0
           && <span>
             {"💎 "}
-            {formatInteger(boss.crystalReward)}
+            {formatInteger(boss.crystalReward, numberFormat)}
           </span>
         }
         {boss.equipmentRewards.length > 0
@@ -175,6 +175,7 @@ const BossPanel = (): JSX.Element => {
     autoBossLastResult,
     autoBossError,
     bossError,
+    numberFormat,
   } = useGame();
   const [ challengingBossId, setChallengingBossId ] = useState<string | null>(
     null,
@@ -403,6 +404,7 @@ const BossPanel = (): JSX.Element => {
               formatNumber={formatNumber}
               isChallenging={challengingBossId === bossId}
               key={bossId}
+              numberFormat={numberFormat}
               onChallenge={handleChallengeClick}
               prestigeCount={prestigeCount}
               unlockHint={bossUnlockHints.get(bossId)}

apps/web/src/components/game/companionPanel.tsx

@@ -163,7 +163,8 @@ const CompanionPanel = (): JSX.Element => {
   const progressByUnlockType: Record<string, number> = {
     apotheosis:     state.apotheosis?.count ?? 0,
     lifetimeBosses: state.player.lifetimeBossesDefeated,
-    lifetimeGold:   state.player.lifetimeGoldEarned,
+    // eslint-disable-next-line stylistic/max-len -- Long expression; splitting would reduce readability
+    lifetimeGold:   state.player.lifetimeGoldEarned + state.player.totalGoldEarned,
     lifetimeQuests: state.player.lifetimeQuestsCompleted,
     prestige:       state.prestige.count,
     transcendence:  state.transcendence?.count ?? 0,

apps/web/src/components/game/prestigePanel.tsx

@@ -70,6 +70,7 @@ const PrestigePanel = (): JSX.Element => {
     toggleAutoPrestige,
     toggleAutoPrestigeMaxRunestones,
     triggerPrestigeToast,
+    numberFormat,
   } = useGame();
   const [ isPending, setIsPending ] = useState(false);
   const [ result, setResult ] = useState<{
@@ -198,7 +199,7 @@ const PrestigePanel = (): JSX.Element => {
           type="button"
         >
           {"🔮 Runestone Shop ("}
-          {formatInteger(prestigeData.runestones)}
+          {formatInteger(prestigeData.runestones, numberFormat)}
           {" stones)"}
         </button>
       </div>
@@ -242,14 +243,14 @@ const PrestigePanel = (): JSX.Element => {
             </p>
             <p>
               {"Runestones: "}
-              <strong>{formatInteger(prestigeData.runestones)}</strong>
+              <strong>{formatInteger(prestigeData.runestones, numberFormat)}</strong>
             </p>
             {isEligible
               ? <p className="runestone-preview">
                 {"Runestones on prestige: "}
                 <strong>
                   {"+"}
-                  {formatInteger(runestonePreview)}
+                  {formatInteger(runestonePreview, numberFormat)}
                 </strong>
                 {isAtMaxRunestones
                   ? <span className="runestone-max-badge">{" ⚡ MAX"}</span>
@@ -289,7 +290,7 @@ const PrestigePanel = (): JSX.Element => {
               >
                 {isPending
                   ? "Ascending..."
-                  : `✨ Ascend (+${formatInteger(runestonePreview)} Runestones)`}
+                  : `✨ Ascend (+${formatInteger(runestonePreview, numberFormat)} Runestones)`}
               </button>
               {prestigeError === null
                 ? null
@@ -301,12 +302,12 @@ const PrestigePanel = (): JSX.Element => {
                   {"Ascended to Prestige "}
                   {result.count}
                   {"! Earned "}
-                  {formatInteger(result.runestones)}
+                  {formatInteger(result.runestones, numberFormat)}
                   {" Runestones."}
                   {result.milestoneRunestones > 0
                     && <>
                       {" 🎉 Milestone bonus: +"}
-                      {formatInteger(result.milestoneRunestones)}
+                      {formatInteger(result.milestoneRunestones, numberFormat)}
                       {" Runestones!"}
                     </>
                   }
@@ -327,7 +328,7 @@ const PrestigePanel = (): JSX.Element => {
           <p className="shop-balance">
             {"Balance: "}
             <strong>
-              {formatInteger(prestigeData.runestones)}
+              {formatInteger(prestigeData.runestones, numberFormat)}
               {" Runestones"}
             </strong>
           </p>
@@ -381,7 +382,7 @@ const PrestigePanel = (): JSX.Element => {
                           <p className="upgrade-cost">
                             {purchased
                               ? "✅ Purchased"
-                              : `🔮 ${formatInteger(upgrade.runestonesCost)} Runestones`}
+                              : `🔮 ${formatInteger(upgrade.runestonesCost, numberFormat)} Runestones`}
                           </p>
                         </div>
                         {isAutoAdventurerToggle

apps/web/src/components/game/questPanel.tsx

@@ -114,6 +114,9 @@ const QuestCard = ({
         }
         <div className="quest-rewards">
           {quest.rewards.map((reward, rewardIndex) => {
+            if (reward.type === "crystals" && (reward.amount ?? 0) === 0) {
+              return null;
+            }
             return (
               <span className="reward-tag" key={`${reward.type}-${reward.targetId ?? String(reward.amount ?? rewardIndex)}`}>
                 {reward.type === "gold"
@@ -121,7 +124,6 @@ const QuestCard = ({
                 {reward.type === "essence"
                   && `✨ ${formatNumber(reward.amount ?? 0)}`}
                 {reward.type === "crystals"
-                  && (reward.amount ?? 0) > 0
                   && `💎 ${formatNumber(reward.amount ?? 0)}`}
                 {reward.type === "upgrade" && "🔓 Upgrade"}
                 {reward.type === "adventurer" && "👥 New Adventurer"}

apps/web/src/components/game/statisticsPanel.tsx

@@ -59,7 +59,7 @@ const StatCard = ({
  * @returns The JSX element.
  */
 const StatisticsPanel = (): JSX.Element => {
-  const { state, formatInteger, formatNumber } = useGame();
+  const { state, formatInteger, formatNumber, numberFormat } = useGame();
 
   if (state === null) {
     return (
@@ -152,13 +152,13 @@ const StatisticsPanel = (): JSX.Element => {
         <StatCard
           icon="💎"
           label="Crystals"
-          value={formatInteger(resources.crystals)}
+          value={formatInteger(resources.crystals, numberFormat)}
         />
         <StatCard
           icon="🔮"
           label="Runestones"
           sub="permanent currency"
-          value={formatInteger(prestige.runestones)}
+          value={formatInteger(prestige.runestones, numberFormat)}
         />
       </div>
 

apps/web/src/components/game/transcendencePanel.tsx

@@ -50,7 +50,7 @@ const categoryOrder: Array<TranscendenceUpgradeCategory> = [
  * @returns The JSX element.
  */
 const TranscendencePanel = (): JSX.Element => {
-  const { state, formatInteger, transcend, buyEchoUpgrade } = useGame();
+  const { state, formatInteger, transcend, buyEchoUpgrade, numberFormat } = useGame();
   const [ isPending, setIsPending ] = useState(false);
   const [ result, setResult ] = useState<{
     echoes: number;
@@ -152,7 +152,7 @@ const TranscendencePanel = (): JSX.Element => {
           type="button"
         >
           {"✨ Echo Shop ("}
-          {formatInteger(currentEchoes)}
+          {formatInteger(currentEchoes, numberFormat)}
           {" echoes)"}
         </button>
       </div>
@@ -184,7 +184,7 @@ const TranscendencePanel = (): JSX.Element => {
             }
             <p>
               {"Current Echoes: "}
-              <strong>{formatInteger(currentEchoes)}</strong>
+              <strong>{formatInteger(currentEchoes, numberFormat)}</strong>
             </p>
             <p>
               {"Current prestige count: "}
@@ -195,7 +195,7 @@ const TranscendencePanel = (): JSX.Element => {
                 {"Echoes on transcendence: "}
                 <strong>
                   {"+"}
-                  {formatInteger(echoPreview)}
+                  {formatInteger(echoPreview, numberFormat)}
                 </strong>
                 {echoMetaMultiplier > 1
                   && <span className="echo-meta-bonus">
@@ -238,7 +238,7 @@ const TranscendencePanel = (): JSX.Element => {
               >
                 {isPending
                   ? "Transcending..."
-                  : `🌌 Transcend (+${formatInteger(echoPreview)} Echoes)`}
+                  : `🌌 Transcend (+${formatInteger(echoPreview, numberFormat)} Echoes)`}
               </button>
               {error === null
                 ? null
@@ -248,7 +248,7 @@ const TranscendencePanel = (): JSX.Element => {
                 : <p className="success">
                   {"Transcended! Earned "}
                   <strong>
-                    {formatInteger(result.echoes)}
+                    {formatInteger(result.echoes, numberFormat)}
                     {" Echoes"}
                   </strong>
                   {". This is Transcendence "}
@@ -266,7 +266,7 @@ const TranscendencePanel = (): JSX.Element => {
           <p className="shop-balance">
             {"Balance: "}
             <strong>
-              {formatInteger(currentEchoes)}
+              {formatInteger(currentEchoes, numberFormat)}
               {" Echoes"}
             </strong>
           </p>
@@ -314,7 +314,7 @@ const TranscendencePanel = (): JSX.Element => {
                           <p className="upgrade-cost">
                             {purchased
                               ? "✅ Purchased"
-                              : `✨ ${formatInteger(upgrade.cost)} Echoes`}
+                              : `✨ ${formatInteger(upgrade.cost, numberFormat)} Echoes`}
                           </p>
                         </div>
                         {purchased

apps/web/src/components/ui/resourceBar.tsx

@@ -82,7 +82,7 @@ const ResourceBar = ({
   isSyncing,
   onForceSync,
 }: ResourceBarProperties): JSX.Element => {
-  const { formatInteger, formatNumber, syncError, state } = useGame();
+  const { formatInteger, formatNumber, syncError, state, numberFormat } = useGame();
   const [ isProfileOpen, setIsProfileOpen ] = useState(false);
   const [ isResourcesOpen, setIsResourcesOpen ] = useState(false);
 
@@ -218,7 +218,7 @@ const ResourceBar = ({
                 : ""}`}>
                 <span className="resource-icon">{"💎"}</span>
                 <span className="resource-value">
-                  {formatInteger(crystals)}
+                  {formatNumber(crystals)}
                 </span>
                 <span className="resource-label">{"Crystals"}</span>
                 {crystalsFull
@@ -233,14 +233,14 @@ const ResourceBar = ({
               <div className="resource">
                 <span className="resource-icon">{"🔮"}</span>
                 <span className="resource-value">
-                  {formatInteger(runestones)}
+                  {formatInteger(runestones, numberFormat)}
                 </span>
                 <span className="resource-label">{"Runestones"}</span>
               </div>
               <div className="resource">
                 <span className="resource-icon">{"⭐"}</span>
                 <span className="resource-value">
-                  {`+${formatInteger(projectedRunestones)}`}
+                  {`+${formatInteger(projectedRunestones, numberFormat)}`}
                 </span>
                 <span className="resource-label">{"On Prestige"}</span>
               </div>

apps/web/src/context/gameContext.tsx

@@ -462,12 +462,12 @@ interface GameContextValue {
   /**
    * Format a number using the player's chosen notation style.
    */
-  formatNumber: (value: number)=> string;
+  formatNumber: (value: number, format?: NumberFormat)=> string;
 
   /**
    * Format a whole-number value without decimal places.
    */
-  formatInteger: (value: number)=> string;
+  formatInteger: (value: number, format?: NumberFormat)=> string;
 
   /**
    * Buy a prestige upgrade from the runestone shop.
@@ -1356,10 +1356,11 @@ export const GameProvider = ({
         newlyFailedQuestsReference.current = [];
       }
 
-      // Auto-save every 30 seconds (skip if a force sync is in-flight to avoid signature collisions)
+      // Auto-save every 30 seconds (skip if a force sync or auto-prestige is in-flight to avoid signature collisions)
       if (Date.now() - lastSaveReference.current >= autoSaveIntervalMs) {
         lastSaveReference.current = Date.now();
-        if (stateReference.current !== null && !isSyncingReference.current) {
+        // eslint-disable-next-line stylistic/max-len -- Long condition; splitting would reduce readability
+        if (stateReference.current !== null && !isSyncingReference.current && !isAutoPrestigingReference.current) {
           void saveGame({
             state: stateReference.current,
             ...signatureReference.current === null
@@ -1856,6 +1857,13 @@ export const GameProvider = ({
           },
         };
       });
+
+      /*
+       * Buying a prestige upgrade mutates DB state; clear the cached signature
+       * so the next auto-save doesn't collide with a stale one.
+       */
+      signatureReference.current = null;
+      localStorage.removeItem("elysium_save_signature");
     } catch (error_: unknown) {
       logError("buy_prestige_upgrade", error_);
       // Silently ignore — server errors shouldn't crash the UI

apps/web/src/utils/format.ts

@@ -57,22 +57,32 @@ const getLetterSuffix = (index: number): string => {
 /**
  * Formats a number with a named or letter-based suffix.
  * @param value - The number to format.
+ * @param round - Display zero numbers after a decimal point.
  * @returns The formatted string with suffix.
  */
-const formatSuffix = (value: number): string => {
+const formatSuffix = (value: number, round = false): string => {
   if (value >= Math.pow(10, letterBaseExp)) {
     const exp = Math.floor(Math.log10(value));
     const stepsAboveBase = Math.floor((exp - letterBaseExp) / 3);
     const steps = stepsAboveBase * 3;
     const divisorExp = letterBaseExp + steps;
     const divisor = Math.pow(10, divisorExp);
-    return `${(value / divisor).toFixed(2)}${getLetterSuffix(stepsAboveBase)}`;
+    return `${round
+      ? String(Math.round(value / divisor))
+      : (value / divisor).toFixed(2)}${getLetterSuffix(stepsAboveBase)}`;
   }
   for (const { threshold, suffix } of namedSuffixes) {
     if (value >= threshold) {
-      return `${(value / threshold).toFixed(2)}${suffix}`;
+      return `${round
+        ? String(Math.floor(value / threshold))
+        : (value / threshold).toFixed(2)}${suffix}`;
     }
   }
+
+  if (round) {
+    return String(Math.floor(value));
+  }
+
   return value < 1
     ? value.toFixed(2)
     : value.toFixed(1);
@@ -82,12 +92,18 @@ const formatSuffix = (value: number): string => {
  * Formats a number in scientific notation: e.g. 1.23e15.
  * Falls back to K/M/B/T style below 1 million.
  * @param value - The number to format.
+ * @param round - Display zero numbers after a decimal point.
  * @returns The formatted string in scientific notation.
  */
-const formatScientific = (value: number): string => {
+const formatScientific = (value: number, round = false): string => {
   if (value < 1e6) {
-    return formatSuffix(value);
+    return formatSuffix(value, round);
   }
+
+  if (round) {
+    return value.toExponential(0).replace("e+", "e");
+  }
+
   // ToExponential handles all magnitudes JS can represent (up to ~1.8e308)
   return value.toExponential(2).replace("e+", "e");
 };
@@ -96,45 +112,50 @@ const formatScientific = (value: number): string => {
  * Formats a number in engineering notation (exponent always a multiple of 3):
  * e.g. 12.35E12, 1.23E300. Falls back to K/M/B/T style below 1 million.
  * @param value - The number to format.
+ * @param round - Display zero numbers after a decimal point.
  * @returns The formatted string in engineering notation.
  */
-const formatEngineering = (value: number): string => {
+const formatEngineering = (value: number, round = false): string => {
   if (value < 1e6) {
-    return formatSuffix(value);
+    return formatSuffix(value, round);
   }
   const exp = Math.floor(Math.log10(value));
   const engExp = Math.floor(exp / 3) * 3;
   const mantissa = value / Math.pow(10, engExp);
-  return `${mantissa.toFixed(2)}E${String(engExp)}`;
+  return `${round
+    ? String(Math.round(mantissa))
+    : mantissa.toFixed(2)}E${String(engExp)}`;
 };
 
 /**
  * Formats a whole-number value for display without decimal places.
  * Uses the same suffix/letter logic as formatNumber but rounds to integers.
  * @param value - The integer value to format.
+ * @param format
  * @returns The formatted string with no decimal places.
  */
-const formatInteger = (value: number): string => {
+const formatInteger = (value: number,
+  format: NumberFormat = "suffix"): string => {
   if (!Number.isFinite(value) || Number.isNaN(value)) {
     return "0";
   }
   if (value < 0) {
     return `-${formatInteger(-value)}`;
   }
-  if (value >= Math.pow(10, letterBaseExp)) {
-    const exp = Math.floor(Math.log10(value));
-    const stepsAboveBase = Math.floor((exp - letterBaseExp) / 3);
-    const steps = stepsAboveBase * 3;
-    const divisorExp = letterBaseExp + steps;
-    const divisor = Math.pow(10, divisorExp);
-    return `${String(Math.round(value / divisor))}${getLetterSuffix(stepsAboveBase)}`;
-  }
-  for (const { threshold, suffix } of namedSuffixes) {
-    if (value >= threshold) {
-      return `${String(Math.floor(value / threshold))}${suffix}`;
+
+  const roundedValue = Math.floor(value);
+  switch (format) {
+    case "scientific":
+      return formatScientific(roundedValue, true);
+    case "engineering":
+      return formatEngineering(value, true);
+    case "suffix":
+      return formatSuffix(value, true);
+    default: {
+      /* V8 ignore next -- @preserve */
+      return formatSuffix(value, true);
     }
   }
-  return String(Math.floor(value));
 };
 
 /**

apps/web/test/format.spec.ts

@@ -1,4 +1,3 @@
-/* eslint-disable max-lines -- Test suites naturally have many cases */
 /* eslint-disable max-lines-per-function -- Test suites naturally have many cases */
 /* eslint-disable max-nested-callbacks -- Vitest structure requires nesting */
 /**
@@ -197,4 +196,43 @@ describe("formatInteger", () => {
       expect(formatInteger(1e39)).toBe("1b");
     });
   });
+
+  describe("scientific format", () => {
+    it("should fall back to suffix format below 1e6", () => {
+      expect(formatInteger(500, "scientific")).toBe("500");
+    });
+
+    it("should format values >= 1e6 in scientific notation", () => {
+      expect(formatInteger(1_230_000, "scientific")).toBe("1e6");
+    });
+
+    it("should format large values in scientific notation", () => {
+      expect(formatInteger(1e18, "scientific")).toBe("1e18");
+    });
+  });
+
+  describe("engineering format", () => {
+    it("should fall back to suffix format below 1e6", () => {
+      expect(formatInteger(500, "engineering")).toBe("500");
+    });
+
+    it("should format values >= 1e6 with exponent multiple of 3", () => {
+      expect(formatInteger(1_230_000, "engineering")).toBe("1E6");
+    });
+
+    it("should format 1e9 correctly in engineering notation", () => {
+      expect(formatInteger(1e9, "engineering")).toBe("1E9");
+    });
+
+    it("should format 12350000 correctly in engineering notation", () => {
+      expect(formatInteger(12_350_000, "engineering")).toBe("12E6");
+    });
+  });
+
+  describe("unknown format (default branch)", () => {
+    it("should fall back to suffix format for an unrecognised format string", () => {
+      /* eslint-disable-next-line @typescript-eslint/consistent-type-assertions -- Testing unreachable default branch */
+      expect(formatInteger(1000, "unknown" as never)).toBe("1K");
+    });
+  });
 });