[libc] Combine the function prototype `int (*compar)(const void *, const void *)` (#134238)

Closes #134118.
diff --git a/libc/include/CMakeLists.txt b/libc/include/CMakeLists.txt
index d1e116a..e407de2 100644
--- a/libc/include/CMakeLists.txt
+++ b/libc/include/CMakeLists.txt
@@ -240,13 +240,13 @@
   ../libc/include/search.yaml
   search.h
   DEPENDS
-    .llvm_libc_common_h
     .llvm-libc-types.ACTION
     .llvm-libc-types.ENTRY
-    .llvm-libc-types.struct_hsearch_data
-    .llvm-libc-types.size_t
     .llvm-libc-types.VISIT
-    .llvm-libc-types.__lsearchcompare_t
+    .llvm-libc-types.__search_compare_t
+    .llvm-libc-types.size_t
+    .llvm-libc-types.struct_hsearch_data
+    .llvm_libc_common_h
 )
 
 add_header_macro(
@@ -343,17 +343,17 @@
   ../libc/include/stdlib.yaml
   stdlib.h
   DEPENDS
-    .llvm_libc_common_h
     .llvm-libc-macros.stdlib_macros
+    .llvm-libc-types.__atexithandler_t
+    .llvm-libc-types.__qsortcompare_t
+    .llvm-libc-types.__qsortrcompare_t
+    .llvm-libc-types.__search_compare_t
     .llvm-libc-types.div_t
     .llvm-libc-types.ldiv_t
     .llvm-libc-types.lldiv_t
-    .llvm-libc-types.size_t
-    .llvm-libc-types.__bsearchcompare_t
-    .llvm-libc-types.__qsortcompare_t
-    .llvm-libc-types.__qsortrcompare_t
-    .llvm-libc-types.__atexithandler_t
     .llvm-libc-types.locale_t
+    .llvm-libc-types.size_t
+    .llvm_libc_common_h
 )
 
 add_header_macro(
diff --git a/libc/include/llvm-libc-types/CMakeLists.txt b/libc/include/llvm-libc-types/CMakeLists.txt
index 66e8527..9ed39bc 100644
--- a/libc/include/llvm-libc-types/CMakeLists.txt
+++ b/libc/include/llvm-libc-types/CMakeLists.txt
@@ -2,8 +2,7 @@
 add_header(size_t HDR size_t.h)
 add_header(ssize_t HDR ssize_t.h)
 add_header(__atfork_callback_t HDR __atfork_callback_t.h)
-add_header(__bsearchcompare_t HDR __bsearchcompare_t.h)
-add_header(__lsearchcompare_t HDR __lsearchcompare_t.h)
+add_header(__search_compare_t HDR __search_compare_t.h)
 add_header(__call_once_func_t HDR __call_once_func_t.h)
 add_header(__dl_iterate_phdr_callback_t HDR __dl_iterate_phdr_callback_t.h DEPENDS .size_t)
 add_header(__exec_argv_t HDR __exec_argv_t.h)
diff --git a/libc/include/llvm-libc-types/__bsearchcompare_t.h b/libc/include/llvm-libc-types/__bsearchcompare_t.h
deleted file mode 100644
index 0b1987be..0000000
--- a/libc/include/llvm-libc-types/__bsearchcompare_t.h
+++ /dev/null
@@ -1,14 +0,0 @@
-//===-- Definition of type __bsearchcompare_t -----------------------------===//
-//
-// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
-// See https://llvm.org/LICENSE.txt for license information.
-// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-//===----------------------------------------------------------------------===//
-
-#ifndef LLVM_LIBC_TYPES___BSEARCHCOMPARE_T_H
-#define LLVM_LIBC_TYPES___BSEARCHCOMPARE_T_H
-
-typedef int (*__bsearchcompare_t)(const void *, const void *);
-
-#endif // LLVM_LIBC_TYPES___BSEARCHCOMPARE_T_H
diff --git a/libc/include/llvm-libc-types/__lsearchcompare_t.h b/libc/include/llvm-libc-types/__lsearchcompare_t.h
deleted file mode 100644
index 08dc2db..0000000
--- a/libc/include/llvm-libc-types/__lsearchcompare_t.h
+++ /dev/null
@@ -1,14 +0,0 @@
-//===-- Definition of type __lsearchcompare_t -----------------------------===//
-//
-// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
-// See https://llvm.org/LICENSE.txt for license information.
-// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-//===----------------------------------------------------------------------===//
-
-#ifndef LLVM_LIBC_TYPES___LSEARCHCOMPARE_T_H
-#define LLVM_LIBC_TYPES___LSEARCHCOMPARE_T_H
-
-typedef int (*__lsearchcompare_t)(const void *, const void *);
-
-#endif // LLVM_LIBC_TYPES___LSEARCHCOMPARE_T_H
diff --git a/libc/include/llvm-libc-types/__search_compare_t.h b/libc/include/llvm-libc-types/__search_compare_t.h
new file mode 100644
index 0000000..7033fef
--- /dev/null
+++ b/libc/include/llvm-libc-types/__search_compare_t.h
@@ -0,0 +1,14 @@
+//===-- Definition of type __search_compare_t -----------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_TYPES___SEARCH_COMPARE_T_H
+#define LLVM_LIBC_TYPES___SEARCH_COMPARE_T_H
+
+typedef int (*__search_compare_t)(const void *, const void *);
+
+#endif // LLVM_LIBC_TYPES___SEARCH_COMPARE_T_H
diff --git a/libc/include/search.yaml b/libc/include/search.yaml
index e2e711c..e0247af 100644
--- a/libc/include/search.yaml
+++ b/libc/include/search.yaml
@@ -2,11 +2,11 @@
 header_template: search.h.def
 macros: []
 types:
-  - type_name: struct_hsearch_data
-  - type_name: ENTRY
   - type_name: ACTION
+  - type_name: ENTRY
   - type_name: VISIT
-  - type_name: __lsearchcompare_t
+  - type_name: __search_compare_t
+  - type_name: struct_hsearch_data
 enums: []
 objects: []
 functions:
@@ -69,7 +69,7 @@
       - type: const void *
       - type: size_t *
       - type: size_t
-      - type: __lsearchcompare_t
+      - type: __search_compare_t
   - name: lsearch
     standards:
       - POSIX
@@ -79,4 +79,4 @@
       - type: void *
       - type: size_t *
       - type: size_t
-      - type: __lsearchcompare_t
+      - type: __search_compare_t
diff --git a/libc/include/stdlib.yaml b/libc/include/stdlib.yaml
index a6204ce..5690a94 100644
--- a/libc/include/stdlib.yaml
+++ b/libc/include/stdlib.yaml
@@ -7,9 +7,9 @@
 macros: []
 types:
   - type_name: __atexithandler_t
-  - type_name: __qsortrcompare_t
   - type_name: __qsortcompare_t
-  - type_name: __bsearchcompare_t
+  - type_name: __qsortrcompare_t
+  - type_name: __search_compare_t
   - type_name: div_t
   - type_name: ldiv_t
   - type_name: lldiv_t
@@ -87,7 +87,7 @@
       - type: const void *
       - type: size_t
       - type: size_t
-      - type: __bsearchcompare_t
+      - type: __search_compare_t
   - name: div
     standards:
       - stdc