The libgcrypt rsa code is mostly visible
   at [1]https://dev.gnupg.org/source/libgcrypt/browse/master/cipher/rsa.c
   .  (I had to work around some network issues reaching [2]git.gnupg.org,
   and found [3]dev.gnupg.org which works for me.)
   The operations of use start around line 909.  Here's a link to that
   line: [4]https://dev.gnupg.org/source/libgcrypt/browse/master/cipher/rs
   a.c$909
   This source can also be cloned at
   [5]https://dev.gnupg.org/source/libgcrypt.git .  I've cloned it
   locally.
   The basic operations of use are public() and secret().  They basically
   just call out to mpi_powm, which is a wrapper for gcry_mpi_powm().
   There's a #define in gcrypt.h, which is a different file generated from
   [6]gcrypt.h.in .
   Before moving off rsa.c, it's notable that:
   - public() basically just wraps mpi_powm, using the same structures
   - secret() has an additional step to remove leading zeros
   - secret() has a special form that might be used when p and q are known
   called secret_core_crt()
   - there's something else called secret_blinded() that is likely
   documented in a header file or elsewhere
   Basically, everything of interest is likely in mpi_powm.
   I'm taking it slower now, because complexity will increase as we get
   deeper.  mpi_powm could look frighteningly new.

References

   1. https://dev.gnupg.org/source/libgcrypt/browse/master/cipher/rsa.c
   2. http://git.gnupg.org/
   3. http://dev.gnupg.org/
   4. https://dev.gnupg.org/source/libgcrypt/browse/master/cipher/rsa.c$909
   5. https://dev.gnupg.org/source/libgcrypt.git
   6. http://gcrypt.h.in/