add caching to prompt_dir

internal/p10k.zsh

@@ -856,8 +856,11 @@ prompt_dir() {
     ;;
   esac
 
+  [[ $POWERLEVEL9K_DIR_SHOW_WRITABLE == true && ! -w $PWD ]]
+  local w=$?
+  if ! _p9k_cache_get $0 $w $fake_first "$delim" "${parts[@]}"; then
     local state='' icon=''
-  if [[ $POWERLEVEL9K_DIR_SHOW_WRITABLE == true && ! -w $PWD ]]; then
+    if (( ! w )); then
       state=NOT_WRITABLE
       icon=LOCK_ICON
     else
@@ -898,7 +901,9 @@ prompt_dir() {
       sep=$_P9K_RETVAL$sep
     fi
 
-  "$1_prompt_segment" "$0_$state" "$2" blue "$DEFAULT_COLOR" "$icon" 0 "" "${(pj.$sep.)parts}"
+    _p9k_cache_set "$0_$state" "$2" blue "$DEFAULT_COLOR" "$icon" 0 "" "${(pj.$sep.)parts}"
+  fi
+  "$1_prompt_segment" "$_P9K_CACHE_VAL[@]"
 }
 
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