Under <a href="http://www.cygwin.com" target="_blank">Cygwin</a>, you can install the 64 bit mingw version of GCC, but you don't get the <a href="http://gmplib.org/" target="_blank">gnu multiprecision library</a> for free with it, you'll much rather have to compile it from source. I ran into a bit of trouble here: It will <b>not</b> suffice to tell the configuration script about the new compiler, there are now mingw-64 versions of all relevant binaries that should be used instead. Basically, you go like
```bash
tar -xjf gmp-5.0.4.tar.bz2
cd gmp-5.0.4
./configure \
AR=x86_64-w64-mingw32-ar \
AS=x86_64-w64-mingw32-as \
DLLTOOL=x86_64-w64-mingw32-dlltool \
DLLWRAP=x86_64-w64-mingw32-dllwrap \
CC=x86_64-w64-mingw32-gcc-4.5.3 \
NM=x86_64-w64-mingw32-nm \
LD=x86_64-w64-mingw32-ld \
OBJDUMP=x86_64-w64-mingw32-objdump \
RANLIB=x86_64-w64-mingw32-ranlib \
STRIP=x86_64-w64-mingw32-strip
```
I am not sure if all of these are needed, but it won't hurt either. After that, you should
```bash
make && make check
```
the whole thing. Worked perfectly for me, so now I can link with `libgmp.a` in `.libs` and native 64 bit bignum action ensues!