"fatal error: bits/libc-header-start.h: No such file or directory" while compiling HTK

I'm getting the following issue when trying to run make on the HTK library:

(cd HTKLib && make HTKLib.a) \
  || case "" in *k*) fail=yes;; *) exit 1;; esac;
make[1]: Entering directory '/home/william/speech/htk/HTK-3.4.1/htk/HTKLib'
gcc  -m32 -ansi -D_SVID_SOURCE -DOSS_AUDIO -D'ARCH="x86_64"' -Wall -Wno-switch -g -O2 -I. -DPHNALG   -c -o HGraf.o HGraf.c
In file included from HShell.h:40:0,
                 from HGraf.c:54:
/usr/include/stdio.h:27:10: fatal error: bits/libc-header-start.h: No such file or directory
 #include <bits/libc-header-start.h>
          ^~~~~~~~~~~~~~~~~~~~~~~~~~
compilation terminated.
<builtin>: recipe for target 'HGraf.o' failed
make[1]: *** [HGraf.o] Error 1
make[1]: Leaving directory '/home/william/speech/htk/HTK-3.4.1/htk/HTKLib'
Makefile:96: recipe for target 'HTKLib/HTKLib.a' failed
make: *** [HTKLib/HTKLib.a] Error 1

I'm unsure what to do about this error. The libc-header-start.h file is present on my system:

$ find /usr -name libc-header-start.h
/usr/include/x86_64-linux-gnu/bits/libc-header-start.h

Running gcc -H -fsyntax-only /usr/include/stdio.h appropriately returns

. /usr/include/x86_64-linux-gnu/bits/libc-header-start.h
.. /usr/include/features.h
... /usr/include/x86_64-linux-gnu/sys/cdefs.h

etc.

Also, compiling and running a sanity-check C file works fine (simply executing printf("hello!"); in its main method).

Apologies if this is a well-known error - my experience with C libraries stops at compiling and installing them using make.

UPDATE Per the accepted answer below I executed sudo apt-get install gcc-multilib to install the missing 32 bit libraries.

Afterwards I got an error with a similar cause: "/usr/bin/ld: cannot find -lX11" error when installing htk. I resolved this by executing sudo apt-get install libx11-dev:i386 libx11-dev to retrieve the missing 32 bit library.

The -m32 is telling gcc to compile for a 32-bit platform. On a 64-bit machine, gcc normally only comes with 64-bit libraries. You have two options:

1. Install 32-bit headers and libraries. Here's how you'd do this on Ubuntu.

   Run this command:

   sudo apt-get install gcc-multilib
   

2. Compile for 64-bit instead. Modify this line in the file named configure:

    CFLAGS="-m32 -ansi -D_SVID_SOURCE -DOSS_AUDIO -D'ARCH=\"$host_cpu\"' $CFLAGS"
   

   Delete -m32, giving you:

    CFLAGS="-ansi -D_SVID_SOURCE -DOSS_AUDIO -D'ARCH=\"$host_cpu\"' $CFLAGS"
   

   Run ./configure, then make clean, then make

   However, I would not suggest doing this. The library authors went out of their way to make this build for 32 bits on a 64 bit system, and it might not work correctly if you change this. (It does compile, though.)

Below is one way to debug and fix this issue. Since most linux installations differ in one way or another, YMMV.

1. Find which package installed libc-header-start.h.

$ dpkg -S libc-header-start.h
libc6-dev:amd64: /usr/include/x86_64-linux-gnu/bits/libc-header-start.h

On a working system, /usr/include/bits is a symlink to /usr/include/x86_64-linux-gnu/bits. Running dpkg search gives us:

$ dpkg -S /usr/include/bits
libc6-dev-i386: /usr/include/bits

Installing libc6-dev-i386 creates the symlink and the error is addressed.

However, subsequently I ran into a linker error with the linker not being able to find libgcc (-lgcc). Apparently Linux default linker needs libgcc in most cases. Further debugging the issue with linker verbosity enabled lead me to missing lib32gcc-10-dev package.

In short, unless a very controlled build environment is desired, just install gcc-multilib package when using -m32 (needed for gcc or clang). For C++, g++-multilib is also required.