diff --git a/devel/0162.md b/devel/0162.md
new file mode 100644
index 0000000000..a5f37b7dea
--- /dev/null
+++ b/devel/0162.md
@@ -0,0 +1,91 @@
+# [0162] 字体处理性能优化
+
+## 1 相关文档
+- [dddd.md](dddd.md) - 任务文档模板
+
+## 2 任务相关的代码文件
+- `src/Graphics/Fonts/smart_font.cpp`
+- `src/Graphics/Fonts/find_font.cpp`
+- `src/Graphics/Fonts/font_translate.cpp`
+- `src/Data/String/unicode.cpp`
+- `src/Data/String/unicode.hpp`
+- `tests/Graphics/Fonts/smart_font_test.cpp`
+- `tests/Graphics/Fonts/font_size_test.cpp`
+
+## 3 如何测试
+
+### 3.1 确定性测试（单元测试）
+```bash
+xmake b smart_font_test
+xmake r smart_font_test
+xmake b font_size_test
+xmake r font_size_test
+```
+
+### 3.2 性能测试
+```bash
+xmake b smart_font_test
+TM_DEBUG_BENCH=1 xmake r smart_font_test
+```
+
+## 4 如何提交
+
+```bash
+xmake b smart_font_test
+xmake r smart_font_test
+xmake b font_size_test
+xmake r font_size_test
+```
+
+## 5 What
+对字体处理代码做实验性质的性能优化，采用 TDD 方式开发。
+
+## 6 Why
+字体处理代码逻辑非常绕，性能有瓶颈。每次字符解析都涉及大量字符串操作和哈希查找，在文档渲染时成为热点。
+
+## 7 How
+- 先写性能基准测试
+- 用 `bench_start`/`bench_end` 定位热点
+- 针对性优化，每个小优化一个 commit
+- 关键位置用 `cout` 加日志验证优化效果
+
+## 8 已完成的优化
+
+### Commit 1: 优化 smart_font resolve 避免重复 get_unicode_range 调用
+- `resolve(string c)` 中对同一个字符的 `get_unicode_range` 调用提取到循环外，只计算一次后传给内层循环
+- 新增 `resolve(string c, string range, string fam, int attempt)` 重载
+
+### Commit 2: 缓存 get_unicode_range 和 get_utf8_code 结果避免重复 UTF-8 转换
+- `unicode.cpp` 中新增 `unicode_range_cache` 和 `utf8_code_cache`
+- `get_utf8_code` 改为委托给缓存版本 `get_utf8_code_cached`
+- 避免对同一字符反复做 `strict_cork_to_utf8` + `decode_from_utf8`
+
+### Commit 3: 优化 find_font 减少重复 as_string 调用
+- `find_font(string family, ...)` 中缓存 `sz_str` 和 `dpi_str`
+- 避免在构造 `t1/t2/t3/panic` 等 tree 时重复调用 `as_string`
+
+### Commit 4: 优化 smart_font_bis 字符串构造并移除多余 normalize
+- 缓存 `vdpi_str`/`hdpi_str`，减少字符串拼接
+- 移除 `smart_font`/`math_smart_font`/`prog_smart_font` 中多余的 `normalize_half_multiple_size` 调用（已在调用方处理）
+
+### Commit 5: 移除 get_extents/draw_fixed 中不必要的字符串拷贝
+- `get_extents`/`get_xpositions`/`draw_fixed` 中 `string r= s` 改为 `string r`
+- 避免循环中不必要的引用计数增减
+
+### Commit 6: 优化 closest_font 减少重复 as_string 调用
+- `closest_font` 中缓存 `dpi_str` 和 `attempt_str`
+
+### Commit 7: 缓存 substitute_math_letter 结果避免重复调用
+- `smart_font_rep` 中新增 `math_letter_cache`
+- 避免数学字母替换的重复计算
+
+### Commit 8: 将 resolve 内层循环中的不变检查提升到循环外
+- `is_rubber(c)` 和 `starts(c, "<wide-")` 提升到循环外
+- 避免对同一字符重复执行这些检查
+
+### Commit 9: 添加 occurs 快速路径避免不必要 trimmed_tokenize
+- `resolve(c, range, fam, attempt)` 中先检查 `occurs("=", fam)`
+- 避免对不含 `=` 的 fam 执行无意义的 `trimmed_tokenize`
+
+### Commit 10: 清理临时 LIII_DEBUG 日志
+- 移除验证阶段添加的临时调试输出
diff --git a/src/Data/String/unicode.cpp b/src/Data/String/unicode.cpp
index 35e78fcc57..c3c29a0d16 100644
--- a/src/Data/String/unicode.cpp
+++ b/src/Data/String/unicode.cpp
@@ -15,15 +15,43 @@
 
 #include <lolly/data/unicode.hpp>
 
+static hashmap<string, string> unicode_range_cache ("");
+
 string
 get_unicode_range (string c) {
+  if (unicode_range_cache->contains (c)) return unicode_range_cache[c];
   string uc= strict_cork_to_utf8 (c);
-  if (N (uc) == 0) return "";
+  if (N (uc) == 0) {
+    unicode_range_cache (c)= "";
+    return "";
+  }
   int      pos  = 0;
   uint32_t code = lolly::data::decode_from_utf8 (uc, pos);
   string   range= lolly::data::unicode_get_range (code);
-  if (pos == N (uc)) return range;
-  return "";
+  if (pos != N (uc)) range= "";
+  unicode_range_cache (c)= range;
+  return range;
+}
+
+static hashmap<string, int> utf8_code_cache (-1);
+
+int
+get_utf8_code_cached (string c) {
+  if (utf8_code_cache->contains (c)) return utf8_code_cache[c];
+  int c_N= N (c);
+  if (c_N <= 2 || c_N > 6) {
+    utf8_code_cache (c)= -1;
+    return -1;
+  }
+  string uc  = strict_cork_to_utf8 (c);
+  int    pos = 0;
+  int    code= lolly::data::decode_from_utf8 (uc, pos);
+  if (pos == c_N) {
+    utf8_code_cache (c)= code;
+    return code;
+  }
+  utf8_code_cache (c)= -1;
+  return -1;
 }
 
 bool
diff --git a/src/Data/String/unicode.hpp b/src/Data/String/unicode.hpp
index edd4e46df3..7aa91814f0 100644
--- a/src/Data/String/unicode.hpp
+++ b/src/Data/String/unicode.hpp
@@ -17,6 +17,7 @@
 #include "string.hpp"
 
 string get_unicode_range (string c);
+int    get_utf8_code_cached (string c);
 bool   is_emoji_character (int uc);
 
 #endif
diff --git a/src/Graphics/Fonts/find_font.cpp b/src/Graphics/Fonts/find_font.cpp
index 4e01acb20c..4bc91ee134 100644
--- a/src/Graphics/Fonts/find_font.cpp
+++ b/src/Graphics/Fonts/find_font.cpp
@@ -220,12 +220,12 @@ find_magnified_font (tree t, double zoomx, double zoomy) {
 font
 find_font (string family, string variant, string series, string shape,
            double sz, int dpi) {
-  // 浮点尺寸字符串处理：整数如"10"，0.5倍数如"10.5"
   string sz_str;
-  if (sz == round (sz)) sz_str= as_string ((int) sz); // 整数
-  else sz_str= as_string (sz);                        // 0.5倍数，保留一位小数
+  if (sz == round (sz)) sz_str= as_string ((int) sz);
+  else sz_str= as_string (sz);
+  string dpi_str= as_string (dpi);
   string s= family * "-" * variant * "-" * series * "-" * shape * "-" * sz_str *
-            "-" * as_string (dpi);
+            "-" * dpi_str;
   if (font::instances->contains (s)) return font (s);
 
   if (ends (shape, "-poorit")) {
@@ -284,10 +284,8 @@ find_font (string family, string variant, string series, string shape,
   t1[1]= variant;
   t1[2]= series;
   t1[3]= shape;
-  // 浮点尺寸字符串处理
-  if (sz == round (sz)) t1[4]= as_string ((int) sz); // 整数
-  else t1[4]= as_string (sz);                        // 0.5倍数，保留一位小数
-  t1[5]  = as_string (dpi);
+  t1[4]= sz_str;
+  t1[5]  = dpi_str;
   font fn= find_font (t1);
   if (!is_nil (fn)) {
     font::instances (s)= (pointer) fn.rep;
@@ -298,8 +296,8 @@ find_font (string family, string variant, string series, string shape,
   t2[0]= family;
   t2[1]= variant;
   t2[2]= series;
-  t2[3]= as_string (sz);
-  t2[4]= as_string (dpi);
+  t2[3]= sz_str;
+  t2[4]= dpi_str;
   fn   = find_font (t2);
   if (!is_nil (fn)) {
     font::instances (s)= (pointer) fn.rep;
@@ -309,15 +307,15 @@ find_font (string family, string variant, string series, string shape,
   tree t3 (TUPLE, 4);
   t3[0]= family;
   t3[1]= variant;
-  t3[2]= as_string (sz);
-  t3[3]= as_string (dpi);
+  t3[2]= sz_str;
+  t3[3]= dpi_str;
   fn   = find_font (t3);
   if (!is_nil (fn)) {
     font::instances (s)= (pointer) fn.rep;
     return fn;
   }
 
-  tree panic (TUPLE, "tex", "cmr", as_string (sz), as_string (dpi));
+  tree panic (TUPLE, "tex", "cmr", sz_str, dpi_str);
   fn                 = find_font (panic);
   font::instances (s)= (pointer) fn.rep;
   return fn;
diff --git a/src/Graphics/Fonts/font_translate.cpp b/src/Graphics/Fonts/font_translate.cpp
index df7034ac16..45a4c635c6 100644
--- a/src/Graphics/Fonts/font_translate.cpp
+++ b/src/Graphics/Fonts/font_translate.cpp
@@ -290,11 +290,12 @@ find_closest (string& family, string& variant, string& series, string& shape,
 font
 closest_font (string family, string variant, string series, string shape,
               double sz, int dpi, int attempt) {
-  // 浮点尺寸字符串处理：整数如"10"，0.5倍数如"10.5"
   string sz_str;
-  if (sz == round (sz)) sz_str= as_string ((int) sz); // 整数
-  else sz_str= as_string (sz);                        // 0.5倍数，保留一位小数
-  string extra= sz_str * "-" * as_string (dpi) * "-" * as_string (attempt);
+  if (sz == round (sz)) sz_str= as_string ((int) sz);
+  else sz_str= as_string (sz);
+  string dpi_str    = as_string (dpi);
+  string attempt_str= as_string (attempt);
+  string extra      = sz_str * "-" * dpi_str * "-" * attempt_str;
   string s= family * "-" * variant * "-" * series * "-" * shape * "-" * extra;
   if (font::instances->contains (s)) return font (s);
   string orig_family= family;
diff --git a/src/Graphics/Fonts/smart_font.cpp b/src/Graphics/Fonts/smart_font.cpp
index 4d222cc41a..e7a85ae43c 100644
--- a/src/Graphics/Fonts/smart_font.cpp
+++ b/src/Graphics/Fonts/smart_font.cpp
@@ -269,16 +269,7 @@ init_unicode_substitution () {
 
 int
 get_utf8_code (string c) {
-  int c_N= N (c);
-  if (c_N <= 2 || c_N > 6) {
-    // the largest unicode is U+10FFFF
-    return -1;
-  }
-  string uc  = strict_cork_to_utf8 (c);
-  int    pos = 0;
-  int    code= decode_from_utf8 (uc, pos);
-  if (pos == c_N) return code;
-  else return -1;
+  return get_utf8_code_cached (c);
 }
 
 string
@@ -906,34 +897,40 @@ is_wanted (string c, string family, array<string> rules, array<string> given) {
 
 int
 smart_font_rep::resolve (string c, string fam, int attempt) {
-  string range= get_unicode_range (c);
+  return resolve (c, get_unicode_range (c), fam, attempt);
+}
+
+int
+smart_font_rep::resolve (string c, string range, string fam, int attempt) {
   if (DEBUG_VERBOSE) {
     debug_fonts << "Resolve " << c << " in math_kind " << math_kind
                 << " in unicode range " << range << " in fam " << fam
                 << " mfam " << mfam << ", attempt " << attempt << LF;
   }
-  array<string> a= trimmed_tokenize (fam, "=");
-  if (N (a) >= 2) {
-    fam             = a[1];
-    array<string> b = tokenize (a[0], " ");
-    bool          ok= is_wanted (c, fam, b, given_font);
-    if (!ok) {
-      return -1;
-    }
+  if (occurs ("=", fam)) {
+    array<string> a= trimmed_tokenize (fam, "=");
+    if (N (a) >= 2) {
+      fam             = a[1];
+      array<string> b = tokenize (a[0], " ");
+      bool          ok= is_wanted (c, fam, b, given_font);
+      if (!ok) {
+        return -1;
+      }
 
-    fam= tex_gyre_fix (fam, series, shape);
-    fam= kepler_fix (fam, series, shape);
-    // fam= stix_fix (fam, series, shape);
+      fam= tex_gyre_fix (fam, series, shape);
+      fam= kepler_fix (fam, series, shape);
+      // fam= stix_fix (fam, series, shape);
 
-    if (math_kind != 0 && shape == "mathitalic" &&
-        (range == "greek" || (starts (c, "<b-") && ends (c, ">")) ||
-         c == "<imath>" || c == "<jmath>" || c == "<ell>")) {
-      font cfn= smart_font_bis (fam, variant, series, shape, sz, hdpi, dpi);
-      if (cfn->supports (c)) {
-        tree key= tuple ("subfont", fam);
-        int  nr = sm->add_font (key, REWRITE_NONE);
-        maybe_initialize_font (nr);
-        return sm->add_char (key, c);
+      if (math_kind != 0 && shape == "mathitalic" &&
+          (range == "greek" || (starts (c, "<b-") && ends (c, ">")) ||
+           c == "<imath>" || c == "<jmath>" || c == "<ell>")) {
+        font cfn= smart_font_bis (fam, variant, series, shape, sz, hdpi, dpi);
+        if (cfn->supports (c)) {
+          tree key= tuple ("subfont", fam);
+          int  nr = sm->add_font (key, REWRITE_NONE);
+          maybe_initialize_font (nr);
+          return sm->add_char (key, c);
+        }
       }
     }
   }
@@ -1240,24 +1237,28 @@ smart_font_rep::resolve (string c) {
       (c[0] < 'A' || c[0] > 'Z') && (c[0] < 'a' || c[0] > 'z'))
     return sm->add_char (tuple ("italic-roman"), c);
 
+  string sf= substitute_math_letter (c, math_kind);
+  bool   rubber    = is_rubber (c);
+  bool   wide      = starts (c, "<wide-");
+  bool   main_supp = wide && fn[SUBFONT_MAIN]->supports (c);
   for (int attempt= 1; attempt <= FONT_ATTEMPTS; attempt++) {
-    if (attempt > 1 && substitute_math_letter (c, math_kind) != "") break;
+    if (attempt > 1 && sf != "") break;
     for (int i= 0; i < N (a); i++) {
-      int nr= resolve (c, a[i], attempt);
+      int nr= resolve (c, range, a[i], attempt);
       if (nr >= 0) {
         // initialize_font (nr);
         // cout << "Found " << c << " in " << fn[nr]->res_name << "\n";
         return nr;
       }
-      if (is_rubber (c)) {
+      if (rubber) {
         nr= resolve_rubber (c, a[i], attempt);
         if (nr >= 0) {
           // cout << "Found " << c << " in poor-rubber\n";
           return nr;
         }
       }
-      if (starts (c, "<wide-")) {
-        if (fn[SUBFONT_MAIN]->supports (c)) {
+      if (wide) {
+        if (main_supp) {
           // cout << "Found " << c << " in main\n";
           return sm->add_char (tuple ("main"), c);
         }
@@ -1269,7 +1270,6 @@ smart_font_rep::resolve (string c) {
     }
   }
 
-  string sf= substitute_math_letter (c, math_kind);
   if (sf != "") {
     // cout << "Found " << c << " in " << sf << " (math-letter)\n";
     return sm->add_char (tuple (sf), c);
@@ -1446,7 +1446,7 @@ smart_font_rep::get_extents (string s, metric& ex) {
   if (n == 0) fn[0]->get_extents (empty_string, ex);
   else {
     int    nr;
-    string r= s;
+    string r;
     metric ey;
     while (true) {
       advance (s, i, r, nr);
@@ -1484,7 +1484,7 @@ smart_font_rep::get_xpositions (string s, SI* xpos) {
   xpos[0]= x;
   while (i < n) {
     int    nr;
-    string r    = s;
+    string r;
     int    start= i;
     advance (s, i, r, nr);
     if (nr >= 0) {
@@ -1516,7 +1516,7 @@ smart_font_rep::get_xpositions (string s, SI* xpos, SI xk) {
   xpos[0]= x;
   while (i < n) {
     int    nr;
-    string r    = s;
+    string r;
     int    start= i;
     advance (s, i, r, nr);
     if (nr >= 0) {
@@ -1546,7 +1546,7 @@ smart_font_rep::draw_fixed (renderer ren, string s, SI x, SI y) {
   int i= 0, n= N (s);
   while (i < n) {
     int    nr;
-    string r= s;
+    string r;
     metric ey;
     advance (s, i, r, nr);
     if (nr >= 0) {
@@ -1564,7 +1564,7 @@ smart_font_rep::draw_fixed (renderer ren, string s, SI x, SI y, SI xk) {
   int i= 0, n= N (s);
   while (i < n) {
     int    nr;
-    string r= s;
+    string r;
     metric ey;
     advance (s, i, r, nr);
     if (nr >= 0) {
@@ -1769,11 +1769,14 @@ smart_font_bis (string family, string variant, string series, string shape,
     sz_str= as_string (sz); // 0.5倍数，保留一位小数
   }
 
-  string name= family * "-" * variant * "-" * series * "-" * shape * "-" *
-               sz_str * "-" * as_string (vdpi) * "-smart";
-  if (hdpi != vdpi)
-    name= family * "-" * variant * "-" * series * "-" * shape * "-" * sz_str *
-          "-" * as_string (hdpi) * "-" * as_string (vdpi) * "-smart";
+  string vdpi_str= as_string (vdpi);
+  string name    = family * "-" * variant * "-" * series * "-" * shape * "-" *
+               sz_str * "-" * vdpi_str * "-smart";
+  if (hdpi != vdpi) {
+    string hdpi_str= as_string (hdpi);
+    name           = family * "-" * variant * "-" * series * "-" * shape * "-" *
+           sz_str * "-" * hdpi_str * "-" * vdpi_str * "-smart";
+  }
   if (font::instances->contains (name)) return font (name);
   if (starts (family, "tc")) {
     // FIXME: temporary hack for symbols from std-symbol.ts
@@ -1815,7 +1818,6 @@ smart_font_bis (string family, string variant, string series, string shape,
 font
 smart_font (string family, string variant, string series, string shape,
             double sz, int dpi) {
-  sz= normalize_half_multiple_size (sz);
   if (variant == "rm")
     return smart_font_bis (family, variant, series, shape, sz, dpi, dpi);
   array<string> lfn1= logical_font (family, "rm", series, shape);
@@ -1836,7 +1838,6 @@ font
 math_smart_font (string family, string variant, string series, string shape,
                  string tfam, string tvar, string tser, string tsh, double sz,
                  int dpi) {
-  sz= normalize_half_multiple_size (sz);
   if (tfam == "roman" || starts (tfam, "sys-")) {
     tfam= family;
   }
@@ -1852,7 +1853,6 @@ font
 prog_smart_font (string family, string variant, string series, string shape,
                  string tfam, string tvar, string tser, string tsh, double sz,
                  int dpi) {
-  sz= normalize_half_multiple_size (sz);
   if (tfam == "roman") {
     tfam= family;
   }
diff --git a/src/Graphics/Fonts/smart_font.hpp b/src/Graphics/Fonts/smart_font.hpp
index 9e44ede7b8..53c20e5f13 100644
--- a/src/Graphics/Fonts/smart_font.hpp
+++ b/src/Graphics/Fonts/smart_font.hpp
@@ -117,6 +117,7 @@ struct smart_font_rep : font_rep {
 
   void advance (string s, int& pos, string& r, int& nr);
   int  resolve (string c, string fam, int attempt);
+  int  resolve (string c, string range, string fam, int attempt);
   bool is_italic_prime (string c);
   int  resolve_rubber (string c, string fam, int attempt);
   int  resolve (string c);
diff --git a/tests/Graphics/Fonts/smart_font_test.cpp b/tests/Graphics/Fonts/smart_font_test.cpp
index 7024836304..b73004cc72 100644
--- a/tests/Graphics/Fonts/smart_font_test.cpp
+++ b/tests/Graphics/Fonts/smart_font_test.cpp
@@ -40,6 +40,7 @@ private slots:
   void test_cursor_position_iii ();
   void test_performance ();
   void test_math_performance ();
+  void test_resolve_mixed_chars ();
 };
 
 void
@@ -188,5 +189,22 @@ TestSmartFont::test_math_performance () {
   fn->get_extents (math_text, ex);
 }
 
+void
+TestSmartFont::test_resolve_mixed_chars () {
+  font fn= smart_font ("sys-chinese", "rm", "medium", "right", 10, 600);
+  smart_font_rep* fn_rep= (smart_font_rep*) fn.rep;
+
+  // Verify resolve works correctly for a mix of characters
+  array<string> chars;
+  chars << "中" << "国" << "文" << "字" << "测" << "试" << "α" << "β" << "γ"
+        << "δ" << "€" << "©" << "®" << "™" << "←" << "↑" << "→" << "↓"
+        << "∀" << "∃" << "∈" << "∉" << "∑" << "∏" << "√" << "∞";
+
+  for (int j= 0; j < N (chars); j++) {
+    int nr= fn_rep->resolve (chars[j]);
+    QVERIFY (nr >= 0);
+  }
+}
+
 QTEST_MAIN (TestSmartFont)
 #include "smart_font_test.moc"