pw_libc: Facilitate next llvm-libc roll

These are required to roll llvm-libc.

- Remove parser.cpp; this has been removed and replaced by parser.h in
  upstream llvm-libc.
- Define LIBC_NAMESPACE
- Add the proper include dir for headers.

Change-Id: Ic1bee26723075211faf74fe19e7d140a769328f3
Original-Reviewed-on: https://pigweed-review.googlesource.com/c/pigweed/pigweed/+/194603
Original-Reviewed-by: Prabhu Karthikeyan Rajasekaran <prabhukr@google.com>
Reviewed-on: https://pigweed-review.googlesource.com/c/pigweed/llvm-integration/+/235137
Reviewed-by: Keir Mierle <keir@google.com>
Lint: Lint 🤖 <android-build-ayeaye@system.gserviceaccount.com>
Commit-Queue: Prabhu Karthikeyan Rajasekaran <prabhukr@google.com>
diff --git a/pw_libc/BUILD.gn b/pw_libc/BUILD.gn
index d9fd80b..d256469 100644
--- a/pw_libc/BUILD.gn
+++ b/pw_libc/BUILD.gn
@@ -121,7 +121,6 @@
     additional_srcs = [
       "printf_core/printf_main.cpp",
       "printf_core/writer.cpp",
-      "printf_core/parser.cpp",
       "printf_core/converter.cpp",
     ]
 
diff --git a/third_party/llvm_libc/llvm_libc.gni b/third_party/llvm_libc/llvm_libc.gni
index fea2509..a5e0d3b 100644
--- a/third_party/llvm_libc/llvm_libc.gni
+++ b/third_party/llvm_libc/llvm_libc.gni
@@ -74,12 +74,16 @@
       _additional_srcs = invoker.additional_srcs
     }
 
-    include_dirs = [ dir_pw_third_party_llvm_libc ]
+    include_dirs = [
+      dir_pw_third_party_llvm_libc,
+      "$dir_pw_third_party_llvm_libc/include/",
+    ]
 
     defines = [
       "LIBC_COPT_PUBLIC_PACKAGING=1",
       "LIBC_COPT_USE_C_ASSERT=1",
       "LIBC_INLINE=inline",
+      "LIBC_NAMESPACE=__llvm_libc",
     ]
 
     if (defined(invoker.defines)) {