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harfbuzz/src/hb-subset-plan.cc

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/*
* Copyright © 2018 Google, Inc.
*
* This is part of HarfBuzz, a text shaping library.
*
* Permission is hereby granted, without written agreement and without
* license or royalty fees, to use, copy, modify, and distribute this
* software and its documentation for any purpose, provided that the
* above copyright notice and the following two paragraphs appear in
* all copies of this software.
*
* IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE TO ANY PARTY FOR
* DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES
* ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN
* IF THE COPYRIGHT HOLDER HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
* DAMAGE.
*
* THE COPYRIGHT HOLDER SPECIFICALLY DISCLAIMS ANY WARRANTIES, INCLUDING,
* BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
* FITNESS FOR A PARTICULAR PURPOSE. THE SOFTWARE PROVIDED HEREUNDER IS
* ON AN "AS IS" BASIS, AND THE COPYRIGHT HOLDER HAS NO OBLIGATION TO
* PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
*
* Google Author(s): Garret Rieger, Roderick Sheeter
*/
#include "hb-subset-plan.hh"
#include "hb-map.hh"
#include "hb-set.hh"
#include "hb-ot-cmap-table.hh"
#include "hb-ot-glyf-table.hh"
#include "hb-ot-layout-gdef-table.hh"
#include "hb-ot-layout-gpos-table.hh"
#include "hb-ot-layout-gsub-table.hh"
#include "hb-ot-cff1-table.hh"
#include "hb-ot-color-colr-table.hh"
#include "hb-ot-color-colrv1-closure.hh"
#include "hb-ot-var-fvar-table.hh"
#include "hb-ot-stat-table.hh"
#include "hb-ot-math-table.hh"
using OT::Layout::GSUB::GSUB;
typedef hb_hashmap_t<unsigned, hb_set_t *> script_langsys_map;
#ifndef HB_NO_SUBSET_CFF
static inline void
_add_cff_seac_components (const OT::cff1::accelerator_t &cff,
hb_codepoint_t gid,
hb_set_t *gids_to_retain)
{
hb_codepoint_t base_gid, accent_gid;
if (cff.get_seac_components (gid, &base_gid, &accent_gid))
{
gids_to_retain->add (base_gid);
gids_to_retain->add (accent_gid);
}
}
#endif
static void
_remap_palette_indexes (const hb_set_t *palette_indexes,
hb_map_t *mapping /* OUT */)
{
unsigned new_idx = 0;
for (unsigned palette_index : palette_indexes->iter ())
{
if (palette_index == 0xFFFF)
{
mapping->set (palette_index, palette_index);
continue;
}
mapping->set (palette_index, new_idx);
new_idx++;
}
}
static void
_remap_indexes (const hb_set_t *indexes,
hb_map_t *mapping /* OUT */)
{
unsigned count = indexes->get_population ();
for (auto _ : + hb_zip (indexes->iter (), hb_range (count)))
mapping->set (_.first, _.second);
}
#ifndef HB_NO_SUBSET_LAYOUT
typedef void (*layout_collect_func_t) (hb_face_t *face, hb_tag_t table_tag, const hb_tag_t *scripts, const hb_tag_t *languages, const hb_tag_t *features, hb_set_t *lookup_indexes /* OUT */);
template <typename T>
static void _collect_layout_indices (hb_face_t *face,
const T& table,
const hb_set_t *layout_features_to_retain,
layout_collect_func_t layout_collect_func,
hb_set_t *indices /* OUT */)
{
hb_vector_t<hb_tag_t> features;
if (!features.alloc (table.get_feature_count () + 1))
return;
hb_set_t visited_features;
bool retain_all_features = true;
for (unsigned i = 0; i < table.get_feature_count (); i++)
{
hb_tag_t tag = table.get_feature_tag (i);
if (!tag) continue;
if (!layout_features_to_retain->has (tag))
{
retain_all_features = false;
continue;
}
if (visited_features.has (tag))
continue;
features.push (tag);
visited_features.add (tag);
}
if (!features)
return;
// The collect function needs a null element to signal end of the array.
features.push (0);
if (retain_all_features)
{
// Looking for all features, trigger the faster collection method.
layout_collect_func (face,
T::tableTag,
nullptr,
nullptr,
nullptr,
indices);
return;
}
layout_collect_func (face,
T::tableTag,
nullptr,
nullptr,
features.arrayZ,
indices);
}
template <typename T>
static inline void
_closure_glyphs_lookups_features (hb_face_t *face,
hb_set_t *gids_to_retain,
const hb_set_t *layout_features_to_retain,
hb_map_t *lookups,
hb_map_t *features,
script_langsys_map *langsys_map)
{
hb_blob_ptr_t<T> table = hb_sanitize_context_t ().reference_table<T> (face);
hb_tag_t table_tag = table->tableTag;
hb_set_t lookup_indices;
_collect_layout_indices<T> (face,
*table,
layout_features_to_retain,
hb_ot_layout_collect_lookups,
&lookup_indices);
if (table_tag == HB_OT_TAG_GSUB)
hb_ot_layout_lookups_substitute_closure (face,
&lookup_indices,
gids_to_retain);
table->closure_lookups (face,
gids_to_retain,
&lookup_indices);
_remap_indexes (&lookup_indices, lookups);
// Collect and prune features
hb_set_t feature_indices;
_collect_layout_indices<T> (face,
*table,
layout_features_to_retain,
hb_ot_layout_collect_features,
&feature_indices);
table->prune_features (lookups, &feature_indices);
hb_map_t duplicate_feature_map;
table->find_duplicate_features (lookups, &feature_indices, &duplicate_feature_map);
feature_indices.clear ();
table->prune_langsys (&duplicate_feature_map, langsys_map, &feature_indices);
_remap_indexes (&feature_indices, features);
table.destroy ();
}
#endif
#ifndef HB_NO_VAR
static inline void
_collect_layout_variation_indices (hb_face_t *face,
const hb_set_t *glyphset,
const hb_map_t *gpos_lookups,
hb_set_t *layout_variation_indices,
hb_map_t *layout_variation_idx_map)
{
hb_blob_ptr_t<OT::GDEF> gdef = hb_sanitize_context_t ().reference_table<OT::GDEF> (face);
hb_blob_ptr_t<OT::GPOS> gpos = hb_sanitize_context_t ().reference_table<OT::GPOS> (face);
if (!gdef->has_data ())
{
gdef.destroy ();
gpos.destroy ();
return;
}
OT::hb_collect_variation_indices_context_t c (layout_variation_indices, glyphset, gpos_lookups);
gdef->collect_variation_indices (&c);
if (hb_ot_layout_has_positioning (face))
gpos->collect_variation_indices (&c);
gdef->remap_layout_variation_indices (layout_variation_indices, layout_variation_idx_map);
gdef.destroy ();
gpos.destroy ();
}
#endif
static inline void
_cmap_closure (hb_face_t *face,
const hb_set_t *unicodes,
hb_set_t *glyphset)
{
OT::cmap::accelerator_t cmap (face);
cmap.table->closure_glyphs (unicodes, glyphset);
}
static void _colr_closure (hb_face_t *face,
hb_map_t *layers_map,
hb_map_t *palettes_map,
hb_set_t *glyphs_colred)
{
OT::COLR::accelerator_t colr (face);
if (!colr.is_valid ()) return;
unsigned iteration_count = 0;
hb_set_t palette_indices, layer_indices;
unsigned glyphs_num;
{
glyphs_num = glyphs_colred->get_population ();
// Collect all glyphs referenced by COLRv0
hb_set_t glyphset_colrv0;
for (hb_codepoint_t gid : glyphs_colred->iter ())
colr.closure_glyphs (gid, &glyphset_colrv0);
glyphs_colred->union_ (glyphset_colrv0);
//closure for COLRv1
colr.closure_forV1 (glyphs_colred, &layer_indices, &palette_indices);
} while (iteration_count++ <= HB_CLOSURE_MAX_STAGES &&
glyphs_num != glyphs_colred->get_population ());
colr.closure_V0palette_indices (glyphs_colred, &palette_indices);
_remap_indexes (&layer_indices, layers_map);
_remap_palette_indexes (&palette_indices, palettes_map);
}
static inline void
_math_closure (hb_face_t *face,
hb_set_t *glyphset)
{
hb_blob_ptr_t<OT::MATH> math = hb_sanitize_context_t ().reference_table<OT::MATH> (face);
if (math->has_data ())
math->closure_glyphs (glyphset);
math.destroy ();
}
static inline void
_remove_invalid_gids (hb_set_t *glyphs,
unsigned int num_glyphs)
{
glyphs->del_range (num_glyphs, HB_SET_VALUE_INVALID);
}
static void
_populate_unicodes_to_retain (const hb_set_t *unicodes,
const hb_set_t *glyphs,
hb_subset_plan_t *plan)
{
OT::cmap::accelerator_t cmap (plan->source);
unsigned size_threshold = plan->source->get_num_glyphs ();
if (glyphs->is_empty () && unicodes->get_population () < size_threshold)
{
// This is approach to collection is faster, but can only be used if glyphs
// are not being explicitly added to the subset and the input unicodes set is
// not excessively large (eg. an inverted set).
plan->unicode_to_new_gid_list.alloc (unicodes->get_population ());
for (hb_codepoint_t cp : *unicodes)
{
hb_codepoint_t gid;
if (!cmap.get_nominal_glyph (cp, &gid))
{
DEBUG_MSG(SUBSET, nullptr, "Drop U+%04X; no gid", cp);
continue;
}
plan->codepoint_to_glyph->set (cp, gid);
plan->unicode_to_new_gid_list.push (hb_pair (cp, gid));
}
}
else
{
// This approach is slower, but can handle adding in glyphs to the subset and will match
// them with cmap entries.
hb_map_t unicode_glyphid_map;
hb_set_t cmap_unicodes;
cmap.collect_mapping (&cmap_unicodes, &unicode_glyphid_map);
plan->unicode_to_new_gid_list.alloc (hb_min(unicodes->get_population ()
+ glyphs->get_population (),
cmap_unicodes.get_population ()));
for (hb_codepoint_t cp : cmap_unicodes)
{
hb_codepoint_t gid = unicode_glyphid_map[cp];
if (!unicodes->has (cp) && !glyphs->has (gid))
continue;
plan->codepoint_to_glyph->set (cp, gid);
plan->unicode_to_new_gid_list.push (hb_pair (cp, gid));
}
/* Add gids which where requested, but not mapped in cmap */
for (hb_codepoint_t gid : *glyphs)
{
if (gid >= plan->source->get_num_glyphs ())
break;
plan->_glyphset_gsub->add (gid);
}
}
auto &arr = plan->unicode_to_new_gid_list;
if (arr.length)
{
plan->unicodes->add_sorted_array (&arr.arrayZ->first, arr.length, sizeof (*arr.arrayZ));
plan->_glyphset_gsub->add_array (&arr.arrayZ->second, arr.length, sizeof (*arr.arrayZ));
}
}
static void
_populate_gids_to_retain (hb_subset_plan_t* plan,
bool close_over_gsub,
bool close_over_gpos,
bool close_over_gdef)
{
OT::glyf::accelerator_t glyf (plan->source);
#ifndef HB_NO_SUBSET_CFF
OT::cff1::accelerator_t cff (plan->source);
#endif
plan->_glyphset_gsub->add (0); // Not-def
_cmap_closure (plan->source, plan->unicodes, plan->_glyphset_gsub);
#ifndef HB_NO_SUBSET_LAYOUT
if (close_over_gsub)
// closure all glyphs/lookups/features needed for GSUB substitutions.
_closure_glyphs_lookups_features<GSUB> (
plan->source,
plan->_glyphset_gsub,
plan->layout_features,
plan->gsub_lookups,
plan->gsub_features,
plan->gsub_langsys);
if (close_over_gpos)
_closure_glyphs_lookups_features<OT::GPOS> (
plan->source,
plan->_glyphset_gsub,
plan->layout_features,
plan->gpos_lookups,
plan->gpos_features,
plan->gpos_langsys);
#endif
_remove_invalid_gids (plan->_glyphset_gsub, plan->source->get_num_glyphs ());
hb_set_set (plan->_glyphset_mathed, plan->_glyphset_gsub);
_math_closure (plan->source, plan->_glyphset_mathed);
_remove_invalid_gids (plan->_glyphset_mathed, plan->source->get_num_glyphs ());
hb_set_t cur_glyphset = *plan->_glyphset_mathed;
_colr_closure (plan->source, plan->colrv1_layers, plan->colr_palettes, &cur_glyphset);
_remove_invalid_gids (&cur_glyphset, plan->source->get_num_glyphs ());
hb_set_set (plan->_glyphset_colred, &cur_glyphset);
/* Populate a full set of glyphs to retain by adding all referenced
* composite glyphs. */
if (glyf.has_data ())
for (hb_codepoint_t gid : cur_glyphset)
glyf.add_gid_and_children (gid, plan->_glyphset);
else
plan->_glyphset->union_ (cur_glyphset);
#ifndef HB_NO_SUBSET_CFF
if (cff.is_valid ())
for (hb_codepoint_t gid : cur_glyphset)
_add_cff_seac_components (cff, gid, plan->_glyphset);
#endif
_remove_invalid_gids (plan->_glyphset, plan->source->get_num_glyphs ());
#ifndef HB_NO_VAR
if (close_over_gdef)
_collect_layout_variation_indices (plan->source,
plan->_glyphset_gsub,
plan->gpos_lookups,
plan->layout_variation_indices,
plan->layout_variation_idx_map);
#endif
}
static void
_create_glyph_map_gsub (const hb_set_t* glyph_set_gsub,
const hb_map_t* glyph_map,
hb_map_t* out)
{
+ hb_iter (glyph_set_gsub)
| hb_map ([&] (hb_codepoint_t gid) {
return hb_pair_t<hb_codepoint_t, hb_codepoint_t> (gid,
glyph_map->get (gid));
})
| hb_sink (out)
;
}
static void
_create_old_gid_to_new_gid_map (const hb_face_t *face,
bool retain_gids,
const hb_set_t *all_gids_to_retain,
hb_map_t *glyph_map, /* OUT */
hb_map_t *reverse_glyph_map, /* OUT */
unsigned int *num_glyphs /* OUT */)
{
unsigned pop = all_gids_to_retain->get_population ();
reverse_glyph_map->resize (pop);
glyph_map->resize (pop);
if (!retain_gids)
{
+ hb_enumerate (hb_iter (all_gids_to_retain), (hb_codepoint_t) 0)
| hb_sink (reverse_glyph_map)
;
*num_glyphs = reverse_glyph_map->get_population ();
}
else
{
+ hb_iter (all_gids_to_retain)
| hb_map ([] (hb_codepoint_t _) {
return hb_pair_t<hb_codepoint_t, hb_codepoint_t> (_, _);
})
| hb_sink (reverse_glyph_map)
;
hb_codepoint_t max_glyph = HB_SET_VALUE_INVALID;
hb_set_previous (all_gids_to_retain, &max_glyph);
*num_glyphs = max_glyph + 1;
}
+ reverse_glyph_map->iter ()
| hb_map (&hb_pair_t<hb_codepoint_t, hb_codepoint_t>::reverse)
| hb_sink (glyph_map)
;
}
static void
_nameid_closure (hb_face_t *face,
hb_set_t *nameids)
{
#ifndef HB_NO_STYLE
face->table.STAT->collect_name_ids (nameids);
#endif
#ifndef HB_NO_VAR
face->table.fvar->collect_name_ids (nameids);
#endif
}
/**
* hb_subset_plan_create_or_fail:
* @face: font face to create the plan for.
* @input: a #hb_subset_input_t input.
*
* Computes a plan for subsetting the supplied face according
* to a provided input. The plan describes
* which tables and glyphs should be retained.
*
* Return value: (transfer full): New subset plan. Destroy with
* hb_subset_plan_destroy(). If there is a failure creating the plan
* nullptr will be returned.
*
* Since: 4.0.0
**/
hb_subset_plan_t *
hb_subset_plan_create_or_fail (hb_face_t *face,
const hb_subset_input_t *input)
{
hb_subset_plan_t *plan;
if (unlikely (!(plan = hb_object_create<hb_subset_plan_t> ())))
return nullptr;
plan->successful = true;
plan->flags = input->flags;
plan->unicodes = hb_set_create ();
plan->unicode_to_new_gid_list.init ();
plan->name_ids = hb_set_copy (input->sets.name_ids);
_nameid_closure (face, plan->name_ids);
plan->name_languages = hb_set_copy (input->sets.name_languages);
plan->layout_features = hb_set_copy (input->sets.layout_features);
plan->glyphs_requested = hb_set_copy (input->sets.glyphs);
plan->drop_tables = hb_set_copy (input->sets.drop_tables);
plan->no_subset_tables = hb_set_copy (input->sets.no_subset_tables);
plan->source = hb_face_reference (face);
plan->dest = hb_face_builder_create ();
plan->_glyphset = hb_set_create ();
plan->_glyphset_gsub = hb_set_create ();
plan->_glyphset_mathed = hb_set_create ();
plan->_glyphset_colred = hb_set_create ();
plan->codepoint_to_glyph = hb_map_create ();
plan->glyph_map = hb_map_create ();
plan->reverse_glyph_map = hb_map_create ();
plan->glyph_map_gsub = hb_map_create ();
plan->gsub_lookups = hb_map_create ();
plan->gpos_lookups = hb_map_create ();
if (plan->check_success (plan->gsub_langsys = hb_object_create<script_langsys_map> ()))
plan->gsub_langsys->init_shallow ();
if (plan->check_success (plan->gpos_langsys = hb_object_create<script_langsys_map> ()))
plan->gpos_langsys->init_shallow ();
plan->gsub_features = hb_map_create ();
plan->gpos_features = hb_map_create ();
plan->colrv1_layers = hb_map_create ();
plan->colr_palettes = hb_map_create ();
plan->layout_variation_indices = hb_set_create ();
plan->layout_variation_idx_map = hb_map_create ();
if (unlikely (plan->in_error ())) {
hb_subset_plan_destroy (plan);
return nullptr;
}
_populate_unicodes_to_retain (input->sets.unicodes, input->sets.glyphs, plan);
_populate_gids_to_retain (plan,
!input->sets.drop_tables->has (HB_OT_TAG_GSUB),
!input->sets.drop_tables->has (HB_OT_TAG_GPOS),
!input->sets.drop_tables->has (HB_OT_TAG_GDEF));
_create_old_gid_to_new_gid_map (face,
input->flags & HB_SUBSET_FLAGS_RETAIN_GIDS,
plan->_glyphset,
plan->glyph_map,
plan->reverse_glyph_map,
&plan->_num_output_glyphs);
_create_glyph_map_gsub (
plan->_glyphset_gsub,
plan->glyph_map,
plan->glyph_map_gsub);
// Now that we have old to new gid map update the unicode to new gid list.
for (unsigned i = 0; i < plan->unicode_to_new_gid_list.length; i++)
{
// Use raw array access for performance.
plan->unicode_to_new_gid_list.arrayZ[i].second =
plan->glyph_map->get(plan->unicode_to_new_gid_list.arrayZ[i].second);
}
if (unlikely (plan->in_error ())) {
hb_subset_plan_destroy (plan);
return nullptr;
}
return plan;
}
/**
* hb_subset_plan_destroy:
* @plan: a #hb_subset_plan_t
*
* Decreases the reference count on @plan, and if it reaches zero, destroys
* @plan, freeing all memory.
*
* Since: 4.0.0
**/
void
hb_subset_plan_destroy (hb_subset_plan_t *plan)
{
if (!hb_object_destroy (plan)) return;
hb_set_destroy (plan->unicodes);
plan->unicode_to_new_gid_list.fini ();
hb_set_destroy (plan->name_ids);
hb_set_destroy (plan->name_languages);
hb_set_destroy (plan->layout_features);
hb_set_destroy (plan->glyphs_requested);
hb_set_destroy (plan->drop_tables);
hb_set_destroy (plan->no_subset_tables);
hb_face_destroy (plan->source);
hb_face_destroy (plan->dest);
hb_map_destroy (plan->codepoint_to_glyph);
hb_map_destroy (plan->glyph_map);
hb_map_destroy (plan->reverse_glyph_map);
hb_map_destroy (plan->glyph_map_gsub);
hb_set_destroy (plan->_glyphset);
hb_set_destroy (plan->_glyphset_gsub);
hb_set_destroy (plan->_glyphset_mathed);
hb_set_destroy (plan->_glyphset_colred);
hb_map_destroy (plan->gsub_lookups);
hb_map_destroy (plan->gpos_lookups);
hb_map_destroy (plan->gsub_features);
hb_map_destroy (plan->gpos_features);
hb_map_destroy (plan->colrv1_layers);
hb_map_destroy (plan->colr_palettes);
hb_set_destroy (plan->layout_variation_indices);
hb_map_destroy (plan->layout_variation_idx_map);
if (plan->gsub_langsys)
{
for (auto _ : plan->gsub_langsys->iter ())
hb_set_destroy (_.second);
hb_object_destroy (plan->gsub_langsys);
plan->gsub_langsys->fini_shallow ();
hb_free (plan->gsub_langsys);
}
if (plan->gpos_langsys)
{
for (auto _ : plan->gpos_langsys->iter ())
hb_set_destroy (_.second);
hb_object_destroy (plan->gpos_langsys);
plan->gpos_langsys->fini_shallow ();
hb_free (plan->gpos_langsys);
}
hb_free (plan);
}
/**
* hb_subset_plan_old_to_new_glyph_mapping:
* @plan: a subsetting plan.
*
* Returns the mapping between glyphs in the original font to glyphs in the
* subset that will be produced by @plan
*
* Return value: (transfer none):
* A pointer to the #hb_map_t of the mapping.
*
* Since: 4.0.0
**/
const hb_map_t*
hb_subset_plan_old_to_new_glyph_mapping (const hb_subset_plan_t *plan)
{
return plan->glyph_map;
}
/**
* hb_subset_plan_new_to_old_glyph_mapping:
* @plan: a subsetting plan.
*
* Returns the mapping between glyphs in the subset that will be produced by
* @plan and the glyph in the original font.
*
* Return value: (transfer none):
* A pointer to the #hb_map_t of the mapping.
*
* Since: 4.0.0
**/
const hb_map_t*
hb_subset_plan_new_to_old_glyph_mapping (const hb_subset_plan_t *plan)
{
return plan->reverse_glyph_map;
}
/**
* hb_subset_plan_unicode_to_old_glyph_mapping:
* @plan: a subsetting plan.
*
* Returns the mapping between codepoints in the original font and the
* associated glyph id in the original font.
*
* Return value: (transfer none):
* A pointer to the #hb_map_t of the mapping.
*
* Since: 4.0.0
**/
const hb_map_t*
hb_subset_plan_unicode_to_old_glyph_mapping (const hb_subset_plan_t *plan)
{
return plan->codepoint_to_glyph;
}
/**
* hb_subset_plan_reference: (skip)
* @plan: a #hb_subset_plan_t object.
*
* Increases the reference count on @plan.
*
* Return value: @plan.
*
* Since: 4.0.0
**/
hb_subset_plan_t *
hb_subset_plan_reference (hb_subset_plan_t *plan)
{
return hb_object_reference (plan);
}
/**
* hb_subset_plan_set_user_data: (skip)
* @plan: a #hb_subset_plan_t object.
* @key: The user-data key to set
* @data: A pointer to the user data
* @destroy: (nullable): A callback to call when @data is not needed anymore
* @replace: Whether to replace an existing data with the same key
*
* Attaches a user-data key/data pair to the given subset plan object.
*
* Return value: %true if success, %false otherwise
*
* Since: 4.0.0
**/
hb_bool_t
hb_subset_plan_set_user_data (hb_subset_plan_t *plan,
hb_user_data_key_t *key,
void *data,
hb_destroy_func_t destroy,
hb_bool_t replace)
{
return hb_object_set_user_data (plan, key, data, destroy, replace);
}
/**
* hb_subset_plan_get_user_data: (skip)
* @plan: a #hb_subset_plan_t object.
* @key: The user-data key to query
*
* Fetches the user data associated with the specified key,
* attached to the specified subset plan object.
*
* Return value: (transfer none): A pointer to the user data
*
* Since: 4.0.0
**/
void *
hb_subset_plan_get_user_data (const hb_subset_plan_t *plan,
hb_user_data_key_t *key)
{
return hb_object_get_user_data (plan, key);
}
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