tsweb: restore CPU profiling handler

It was accidentally deleted in the earlier 0022c3d2e (#2143) refactor.
Lock it in with a test.

Fixes tailscale/corp#2503

Signed-off-by: Brad Fitzpatrick <bradfitz@tailscale.com>

tsweb/debug.go

@@ -47,6 +47,11 @@ func Debugger(mux *http.ServeMux) *DebugHandler {
 	}
 	mux.Handle("/debug/", ret)
 
+	// Register this one directly on mux, rather than using
+	// ret.URL/etc, as we don't need another line of output on the
+	// index page. The /pprof/ index already covers it.
+	mux.Handle("/debug/pprof/profile", http.HandlerFunc(pprof.Profile))
+
 	ret.KVFunc("Uptime", func() interface{} { return Uptime() })
 	ret.KV("Version", version.Long)
 	ret.Handle("vars", "Metrics (Go)", expvar.Handler())

tsweb/debug_test.go

@@ -9,6 +9,7 @@ import (
 	"io"
 	"net/http"
 	"net/http/httptest"
+	"runtime"
 	"strings"
 	"testing"
 )
@@ -25,6 +26,25 @@ func TestDebugger(t *testing.T) {
 	if dbg2 != dbg1 {
 		t.Fatal("Debugger returned different debuggers for the same mux")
 	}
+
+	t.Run("cpu_pprof", func(t *testing.T) {
+		if testing.Short() {
+			t.Skip("skipping second long test")
+		}
+		switch runtime.GOOS {
+		case "linux", "darwin":
+		default:
+			t.Skipf("skipping test on %v", runtime.GOOS)
+		}
+		req := httptest.NewRequest("GET", "/debug/pprof/profile?seconds=1", nil)
+		req.RemoteAddr = "100.101.102.103:1234"
+		rec := httptest.NewRecorder()
+		mux.ServeHTTP(rec, req)
+		res := rec.Result()
+		if res.StatusCode != 200 {
+			t.Errorf("unexpected %v", res.Status)
+		}
+	})
 }
 
 func get(m http.Handler, path, srcIP string) (int, string) {