I'm +1 in adding fallbacks for important functions like copysign, asinh,
acosh and atanh. expm1 and log1p may be worth adding, too. Windows
doesn't have any of the functions except of _copysign().

But why write our own version if we can reuse existing implementations?
I found a set of very well written and documented implementations in the
uclibc sources of libm. The sources are under a BSDish license:

 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================

In #1381 I suggested two new files Python/pymath.c and Include/pymath.h.
We could stick all the replacement implementations in the files and
maybe move some of the code from Include/pyport.h and Python/hypot.c to
the new files.