perf: refactor path logic in router + add LRU cache (vercel#41365)

I'm investigating the runtime perf of the node server and this was one of the hot spot I stumbled upon.

This diff:
- refactors getPagePath to not throw when it doesn't find a path: this function is used to check if a path exists, we don't want that kind of overhead there
- adds a LRU cache to cache the result of the evaluation

Results:

before:
> 110k requests in 11.01s, 285 MB read

after
>135k requests in 11.01s, 348 MB read

on an autocannon run



## Bug

- [ ] Related issues linked using `fixes #number`
- [ ] Integration tests added
- [ ] Errors have a helpful link attached, see `contributing.md`

## Feature

- [ ] Implements an existing feature request or RFC. Make sure the feature request has been accepted for implementation before opening a PR.
- [ ] Related issues linked using `fixes #number`
- [ ] Integration tests added
- [ ] Documentation added
- [ ] Telemetry added. In case of a feature if it's used or not.
- [ ] Errors have a helpful link attached, see `contributing.md`

## Documentation / Examples

- [ ] Make sure the linting passes by running `pnpm lint`
- [ ] The "examples guidelines" are followed from [our contributing doc](https://github.com/vercel/next.js/blob/canary/contributing/examples/adding-examples.md)

packages/next/server/next-server.ts

@@ -74,7 +74,7 @@ import BaseServer, {
   NoFallbackError,
   RequestContext,
 } from './base-server'
-import { getPagePath, requireFontManifest } from './require'
+import { getMaybePagePath, getPagePath, requireFontManifest } from './require'
 import { denormalizePagePath } from '../shared/lib/page-path/denormalize-page-path'
 import { normalizePagePath } from '../shared/lib/page-path/normalize-page-path'
 import { loadComponents } from './load-components'
@@ -327,12 +327,12 @@ export default class NextNodeServer extends BaseServer {
   }
 
   protected async hasPage(pathname: string): Promise<boolean> {
-    let found = false
-    try {
-      found = !!this.getPagePath(pathname, this.nextConfig.i18n?.locales)
-    } catch (_) {}
-
-    return found
+    return !!getMaybePagePath(
+      pathname,
+      this.distDir,
+      this.nextConfig.i18n?.locales,
+      this.hasAppDir
+    )
   }
 
   protected getBuildId(): string {

packages/next/server/require.ts

@@ -11,13 +11,33 @@ import { normalizePagePath } from '../shared/lib/page-path/normalize-page-path'
 import { denormalizePagePath } from '../shared/lib/page-path/denormalize-page-path'
 import type { PagesManifest } from '../build/webpack/plugins/pages-manifest-plugin'
 import { PageNotFoundError, MissingStaticPage } from '../shared/lib/utils'
+import LRUCache from 'next/dist/compiled/lru-cache'
 
-export function getPagePath(
+const pagePathCache =
+  process.env.NODE_ENV === 'development'
+    ? {
+        get: (_key: string) => {
+          return null
+        },
+        set: () => {},
+        has: () => false,
+      }
+    : new LRUCache<string, string | null>({
+        max: 1000,
+      })
+
+export function getMaybePagePath(
   page: string,
   distDir: string,
   locales?: string[],
   appDirEnabled?: boolean
-): string {
+): string | null {
+  const cacheKey = `${page}:${locales}`
+
+  if (pagePathCache.has(cacheKey)) {
+    return pagePathCache.get(cacheKey) as string | null
+  }
+
   const serverBuildPath = join(distDir, SERVER_DIRECTORY)
   let appPathsManifest: undefined | PagesManifest
 
@@ -60,10 +80,30 @@ export function getPagePath(
     pagePath = checkManifest(pagesManifest)
   }
 
+  if (!pagePath) {
+    pagePathCache.set(cacheKey, null)
+    return null
+  }
+
+  const path = join(serverBuildPath, pagePath)
+  pagePathCache.set(cacheKey, path)
+
+  return path
+}
+
+export function getPagePath(
+  page: string,
+  distDir: string,
+  locales?: string[],
+  appDirEnabled?: boolean
+): string {
+  const pagePath = getMaybePagePath(page, distDir, locales, appDirEnabled)
+
   if (!pagePath) {
     throw new PageNotFoundError(page)
   }
-  return join(serverBuildPath, pagePath)
+
+  return pagePath
 }
 
 export function requirePage(