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SV *
overload_add_eq (a, b, third)
...
CODE:
  RETVAL = overload_add_eq (aTHX_ a, b, third);
OUTPUT:  RETVAL

void
overload_add_eq (a, b, third)
...
        CODE:
        overload_add_eq (aTHX_ a, b, third);
        XSRETURN_EMPTY; /* return empty stack */

SV * overload_add_eq(pTHX_ SV * a, SV * b, SV * third) {
    /* lengthy code  snipped */
}

void overload_add_eq(pTHX_ SV * a, SV * b, SV * third) {
     PERL_UNUSED_ARG(third); /* UPDATE: This line can be removed as ir
+relevant */
     mpz_add_ui(*(INT2PTR(mpz_t *, SvIVX(SvRV(a)))), *(INT2PTR(mpz_t *
+, SvIVX(SvRV(a)))), SvUV(b));
}

> perl -Mblib -MMath::GMPz -MDevel::Peek -wle "$x = Math::GMPz->new(12
+34); $x++;print $x; $x += 15; print $x; Dump($x);"
1235
...
  FLAGS = ()
  IV = 1837594613288
  PV = 0

> perl -Mblib -MMath::GMPz -MDevel::Peek -wle "$x = Math::GMPz->new(12
+34); $x++; print $x; Math::GMPz::overload_add_eq($x, 15, 0); print $x
+;"
1235
1250

> perl -Mblib -MMath::GMPz -MDevel::Peek -wle "$x = Math::GMPz->new(12
+34); $x++;print $x; $x += 15; print $x; Dump($x);"
1235
...
    NV = 0
    PV = 0
    STASH = 0x2bfffa5e5e8       "Math::GMPz"