X-Git-Url: https://git.distorted.org.uk/~mdw/catacomb-python/blobdiff_plain/963a61481edc7a83698b18b518bf20cd93d268a6..591bf41b5e4fa2d55e00d1e418b1b9ed53b4489c:/mp.c

diff --git a/mp.c b/mp.c
index 4c91865..93dd137 100644
--- a/mp.c
+++ b/mp.c
@@ -1,13 +1,11 @@
 /* -*-c-*-
  *
- * $Id$
- *
  * Multiprecision arithmetic
  *
  * (c) 2004 Straylight/Edgeware
  */
 
-/*----- Licensing notice --------------------------------------------------* 
+/*----- Licensing notice --------------------------------------------------*
  *
  * This file is part of the Python interface to Catacomb.
  *
@@ -15,12 +13,12 @@
  * it under the terms of the GNU General Public License as published by
  * the Free Software Foundation; either version 2 of the License, or
  * (at your option) any later version.
- * 
+ *
  * Catacomb/Python is distributed in the hope that it will be useful,
  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  * GNU General Public License for more details.
- * 
+ *
  * You should have received a copy of the GNU General Public License
  * along with Catacomb/Python; if not, write to the Free Software Foundation,
  * Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
@@ -35,9 +33,10 @@
 PyTypeObject *mp_pytype = 0;
 PyTypeObject *gf_pytype = 0;
 
-mp *mp_frompylong(PyLongObject *l)
+mp *mp_frompylong(PyObject *obj)
 {
   unsigned long bits;
+  PyLongObject *l = (PyLongObject *)obj;
   int sz;
   size_t w;
   mpd r = 0;
@@ -46,12 +45,12 @@ mp *mp_frompylong(PyLongObject *l)
   mp *x;
   mpw *p;
 
-  sz = l->ob_size;
+  sz = Py_SIZE(l);
   if (sz < 0) sz = -sz;
   assert(MPW_BITS >= SHIFT);
   bits = (unsigned long)sz * SHIFT;
   w = (bits + MPW_BITS - 1)/MPW_BITS;
-  x = mp_new(w, l->ob_size < 0 ? MP_NEG : 0);
+  x = mp_new(w, Py_SIZE(l) < 0 ? MP_NEG : 0);
   p = x->v;
   for (i = 0; i < sz; i++) {
     r |= (mpd)l->ob_digit[i] << b;
@@ -71,7 +70,7 @@ mp *mp_frompylong(PyLongObject *l)
   return (x);
 }
 
-PyLongObject *mp_topylong(mp *x)
+PyObject *mp_topylong(mp *x)
 {
   unsigned long bits = mp_bits(x);
   int sz = (bits + SHIFT - 1)/SHIFT;
@@ -83,7 +82,7 @@ PyLongObject *mp_topylong(mp *x)
 
   assert(MPW_BITS >= SHIFT);
   while (i < sz && p < x->vl) {
-    r |= *p << b;
+    r |= (mpd)*p++ << b;
     b += MPW_BITS;
     while (i < sz && b >= SHIFT) {
       l->ob_digit[i++] = r & MASK;
@@ -95,16 +94,14 @@ PyLongObject *mp_topylong(mp *x)
     l->ob_digit[i++] = r & MASK;
     r >>= SHIFT;
   }
-  l->ob_size = (x->f & MP_NEG) ? -sz : sz;
-  return (l);
+  Py_SIZE(l) = (x->f & MP_NEG) ? -sz : sz;
+  return ((PyObject *)l);
 }
 
 mp *mp_frompyobject(PyObject *o, int radix)
 {
   mp *x;
 
-  if ((x = tomp(o)) != 0)
-    return (x);
   if (PyString_Check(o)) {
     mptext_stringctx sc;
     mp *x;
@@ -115,6 +112,8 @@ mp *mp_frompyobject(PyObject *o, int radix)
     if (sc.buf < sc.lim) { MP_DROP(x); return (0); }
     return (x);
   }
+  if ((x = tomp(o)) != 0)
+    return (x);
   return (0);
 }
 
@@ -143,6 +142,13 @@ PyObject *mp_topystring(mp *x, int radix, const char *xpre,
   return (o);
 }
 
+static int good_radix_p(int r, int readp)
+{
+  return ((r >= -255 && r <= -2) ||
+	  (readp && r == 0) ||
+	  (r >= 2 && r <= 62));
+}
+
 PyObject *mp_pywrap(mp *x)
 {
   mp_pyobj *z = PyObject_New(mp_pyobj, mp_pytype);
@@ -157,7 +163,7 @@ PyObject *gf_pywrap(mp *x)
   return ((PyObject *)z);
 }
 
-int mp_tolong_checked(mp *x, long *l)
+int mp_tolong_checked(mp *x, long *l, int must)
 {
   static mp *longmin = 0, *longmax = 0;
   int rc = -1;
@@ -166,8 +172,10 @@ int mp_tolong_checked(mp *x, long *l)
     longmin = mp_fromlong(MP_NEW, LONG_MIN);
     longmax = mp_fromlong(MP_NEW, LONG_MAX);
   }
-  if (MP_CMP(x, <, longmin) || MP_CMP(x, >, longmax))
-    VALERR("mp out of range for int");
+  if (MP_CMP(x, <, longmin) || MP_CMP(x, >, longmax)) {
+    if (must) VALERR("mp out of range for int");
+    else goto end;
+  }
   *l = mp_tolong(x);
   rc = 0;
 end:
@@ -203,6 +211,7 @@ mp *tomp(PyObject *o)
     return (MP_COPY(PFILT_F(o)->m));
   else if (ECPT_PYCHECK(o)) {
     ec p = EC_INIT;
+    if (EC_ATINF(ECPT_P(o))) return (0);
     getecptout(&p, o);
     x = MP_COPY(p.x);
     EC_DESTROY(&p);
@@ -214,7 +223,7 @@ mp *tomp(PyObject *o)
   } else if (PyInt_Check(o))
     return (mp_fromlong(MP_NEW, PyInt_AS_LONG(o)));
   else if ((l = PyNumber_Long(o)) != 0) {
-    x = mp_frompylong((PyLongObject *)l);
+    x = mp_frompylong(l);
     Py_DECREF(l);
     return (x);
   } else {
@@ -229,7 +238,7 @@ mp *getmp(PyObject *o)
   if (!o) return (0);
   if ((x = tomp(o)) == 0) {
     PyErr_Format(PyExc_TypeError, "can't convert %.100s to mp",
-		 o->ob_type->tp_name);
+		 Py_TYPE(o)->tp_name);
   }
   return (x);
 }
@@ -248,7 +257,7 @@ mp *getgf(PyObject *o)
   if (!o) return (0);
   if ((x = tomp(o)) == 0) {
     PyErr_Format(PyExc_TypeError, "can't convert %.100s to gf",
-		 o->ob_type->tp_name);
+		 Py_TYPE(o)->tp_name);
   }
   return (x);
 }
@@ -261,11 +270,44 @@ int convgf(PyObject *o, void *p)
   return (1);
 }
 
+static mp *implicitmp(PyObject *o)
+{
+  if (!o ||
+      GF_PYCHECK(o) ||
+      ECPT_PYCHECK(o) ||
+      FE_PYCHECK(o) ||
+      GE_PYCHECK(o))
+    return (0);
+  return (tomp(o));
+}
+
+static mp *implicitgf(PyObject *o)
+{
+  if (!o ||
+      MP_PYCHECK(o) ||
+      ECPT_PYCHECK(o) ||
+      FE_PYCHECK(o) ||
+      GE_PYCHECK(o))
+    return (0);
+  return (tomp(o));
+}
+
 static int mpbinop(PyObject *x, PyObject *y, mp **xx, mp **yy)
 {
-  if ((*xx = tomp(x)) == 0)
+  if ((*xx = implicitmp(x)) == 0)
     return (-1);
-  if ((*yy = tomp(y)) == 0) {
+  if ((*yy = implicitmp(y)) == 0) {
+    MP_DROP(*xx);
+    return (-1);
+  }
+  return (0);
+}
+
+static int gfbinop(PyObject *x, PyObject *y, mp **xx, mp **yy)
+{
+  if ((*xx = implicitgf(x)) == 0)
+    return (-1);
+  if ((*yy = implicitgf(y)) == 0) {
     MP_DROP(*xx);
     return (-1);
   }
@@ -278,7 +320,7 @@ static int mpbinop(PyObject *x, PyObject *y, mp **xx, mp **yy)
 #define BINOP(pre, name)						\
   static PyObject *pre##_py##name(PyObject *x, PyObject *y) {		\
     mp *xx, *yy, *zz;							\
-    if (mpbinop(x, y, &xx, &yy)) RETURN_NOTIMPL;			\
+    if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL;			\
     zz = pre##_##name(MP_NEW, xx, yy);					\
     MP_DROP(xx); MP_DROP(yy);						\
     return (pre##_pywrap(zz));						\
@@ -322,8 +364,8 @@ static PyObject *mp_pyid(PyObject *x) { RETURN_OBJ(x); }
     mp *xx, *yy;							\
     PyObject *z = 0;							\
     long n;								\
-    if (mpbinop(x, y, &xx, &yy)) RETURN_NOTIMPL;			\
-    if (mp_tolong_checked(yy, &n)) goto end;				\
+    if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL;			\
+    if (mp_tolong_checked(yy, &n, 1)) goto end;				\
     if (n < 0)								\
       z = pre##_pywrap(mp_##rname(MP_NEW, xx, -n));			\
     else								\
@@ -343,7 +385,7 @@ SHIFTOP(gf, lsr, lsl)
     mp *xx, *yy;							\
     PyObject *z = 0;							\
     INIT_##qq(q) INIT_##rr(r)						\
-    if (mpbinop(x, y, &xx, &yy)) RETURN_NOTIMPL;			\
+    if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL;			\
     if (MP_ZEROP(yy))							\
       ZDIVERR("division by zero");					\
     pre##_div(ARG_##qq(q), ARG_##rr(r), xx, yy);			\
@@ -388,7 +430,7 @@ static PyObject *mp_pyexp(PyObject *x, PyObject *y, PyObject *z)
   mp *r = 0;
   PyObject *rc = 0;
 
-  if ((xx = tomp(x)) == 0 || (yy = tomp(y)) == 0 ||
+  if ((xx = implicitmp(x)) == 0 || (yy = implicitmp(y)) == 0 ||
       (z && z != Py_None && (zz = tomp(z)) == 0)) {
     mp_drop(xx); mp_drop(yy); mp_drop(zz);
     RETURN_NOTIMPL;
@@ -444,20 +486,20 @@ static int mp_pynonzerop(PyObject *x) { return !MP_ZEROP(MP_X(x)); }
 static PyObject *mp_pyint(PyObject *x)
 {
   long l;
-  if (mp_tolong_checked(MP_X(x), &l)) return (0);
-  return (PyInt_FromLong(l));
+  if (!mp_tolong_checked(MP_X(x), &l, 0)) return (PyInt_FromLong(l));
+  else return mp_topylong(MP_X(x));
 }
 static PyObject *mp_pylong(PyObject *x)
-  { return (PyObject *)mp_topylong(MP_X(x)); }
+  { return (mp_topylong(MP_X(x))); }
 static PyObject *mp_pyfloat(PyObject *x)
 {
-  PyObject *l = (PyObject *)mp_topylong(MP_X(x));
+  PyObject *l = mp_topylong(MP_X(x));
   double f = PyLong_AsDouble(l);
   Py_DECREF(l);
   return (PyFloat_FromDouble(f));
 }
 
-#define COERCE(pre, PRE) 						\
+#define COERCE(pre, PRE)						\
   static int pre##_pycoerce(PyObject **x, PyObject **y)			\
   {									\
     mp *z;								\
@@ -486,15 +528,15 @@ static PyObject *mp_pynew(PyTypeObject *ty, PyObject *arg, PyObject *kw)
   mp *z;
   mp_pyobj *zz = 0;
   int radix = 0;
-  char *kwlist[] = { "x", "radix", 0 };
+  static const char *const kwlist[] = { "x", "radix", 0 };
 
-  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O|i:mp", kwlist, &x, &radix))
+  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O|i:new", KWLIST, &x, &radix))
     goto end;
   if (MP_PYCHECK(x)) RETURN_OBJ(x);
-  if (radix < -255 || radix > 62) VALERR("radix out of range");
+  if (!good_radix_p(radix, 1)) VALERR("bad radix");
   if ((z = mp_frompyobject(x, radix)) == 0) {
     PyErr_Format(PyExc_TypeError, "can't convert %.100s to mp",
-		 x->ob_type->tp_name);
+		 Py_TYPE(x)->tp_name);
     goto end;
   }
   zz = (mp_pyobj *)ty->tp_alloc(ty, 0);
@@ -503,14 +545,15 @@ end:
   return ((PyObject *)zz);
 }
 
-static long mp_pyhash(PyObject *me)
+long mphash(mp *x)
 {
-  long i = mp_tolong(MP_X(me));
-  if (i == -1)
-    i = -2;
-  return (i);
+  PyObject *l = mp_topylong(x);
+  long h = PyObject_Hash(l);
+  Py_DECREF(l); return (h);
 }
 
+static long mp_pyhash(PyObject *me) { return (mphash(MP_X(me))); }
+
 static PyObject *mpmeth_jacobi(PyObject *me, PyObject *arg)
 {
   mp *y = 0;
@@ -526,49 +569,44 @@ end:
 #define BITOP(pre, name, c)						\
   static PyObject *pre##meth_##name(PyObject *me, PyObject *arg)	\
   {									\
-    int i;								\
-    if (!PyArg_ParseTuple(arg, "i:" #name, &i)) return (0);		\
+    unsigned long i;							\
+    if (!PyArg_ParseTuple(arg, "O&:" #name, convulong, &i)) return (0);	\
     return (pre##_pywrap(mp_##name##c(MP_NEW, MP_X(me), i)));		\
   }
 BITOP(mp, setbit, 2c);
 BITOP(mp, clearbit, 2c);
-BITOP(gf, setbit, ); 
+BITOP(gf, setbit, );
 BITOP(gf, clearbit, );
 #undef BITOP
 
 static PyObject *mpmeth_testbit(PyObject *me, PyObject *arg)
 {
-  int i;
-  if (!PyArg_ParseTuple(arg, "i:testbit", &i)) return (0);
+  unsigned long i;
+  if (!PyArg_ParseTuple(arg, "O&:testbit", convulong, &i)) return (0);
   return (getbool(mp_testbit2c(MP_X(me), i)));
 }
 
 static PyObject *gfmeth_testbit(PyObject *me, PyObject *arg)
 {
-  int i;
-  if (!PyArg_ParseTuple(arg, "i:testbit", &i)) return (0);
+  unsigned long i;
+  if (!PyArg_ParseTuple(arg, "O&:testbit", convulong, &i)) return (0);
   return (getbool(mp_testbit(MP_X(me), i)));
 }
 
-static PyObject *mpmeth_odd(PyObject *me, PyObject *arg)
+static PyObject *mpmeth_odd(PyObject *me)
 {
   mp *t;
   size_t s;
 
-  if (!PyArg_ParseTuple(arg, ":odd")) return (0);
   t = mp_odd(MP_NEW, MP_X(me), &s);
   return (Py_BuildValue("(lN)", (long)s, mp_pywrap(t)));
 }
 
-static PyObject *mpmeth_sqr(PyObject *me, PyObject *arg)
-{
-  if (!PyArg_ParseTuple(arg, ":sqr")) return (0);
-  return (mp_pywrap(mp_sqr(MP_NEW, MP_X(me))));
-}
+static PyObject *mpmeth_sqr(PyObject *me)
+  { return (mp_pywrap(mp_sqr(MP_NEW, MP_X(me)))); }
 
-static PyObject *mpmeth_sqrt(PyObject *me, PyObject *arg)
+static PyObject *mpmeth_sqrt(PyObject *me)
 {
-  if (!PyArg_ParseTuple(arg, ":sqrt")) return (0);
   if (MP_NEGP(MP_X(me))) VALERR("negative root");
   return (mp_pywrap(mp_sqrt(MP_NEW, MP_X(me))));
 end:
@@ -619,11 +657,10 @@ end:
 static PyObject *mpmeth_tostring(PyObject *me, PyObject *arg, PyObject *kw)
 {
   int radix = 10;
-  char *kwlist[] = { "radix", 0 };
-  if (!PyArg_ParseTupleAndKeywords(arg, kw, "|i:tostring", kwlist, &radix))
+  static const char *const kwlist[] = { "radix", 0 };
+  if (!PyArg_ParseTupleAndKeywords(arg, kw, "|i:tostring", KWLIST, &radix))
     goto end;
-  if (radix < -255 || radix > 62 || radix == -1 || radix == 0 || radix == 1)
-    VALERR("bad radix");
+  if (!good_radix_p(radix, 0)) VALERR("bad radix");
   return (mp_topystring(MP_X(me), radix, 0, 0, 0));
 end:
   return (0);
@@ -643,16 +680,29 @@ end:
   return (z);
 }
 
+static PyObject *mpmeth_leastcongruent(PyObject *me, PyObject *arg)
+{
+  mp *z, *b, *m;
+  PyObject *rc = 0;
+
+  if (!PyArg_ParseTuple(arg, "O&O&:leastcongruent", convmp, &b, convmp, &m))
+    goto end;
+  z = mp_leastcongruent(MP_NEW, b, MP_X(me), m);
+  rc = mp_pywrap(z);
+end:
+  return (rc);
+}
+
 #define STOREOP(name, c)						\
   static PyObject *mpmeth_##name(PyObject *me,				\
 				 PyObject *arg, PyObject *kw)		\
   {									\
     long len = -1;							\
-    char *kwlist[] = { "len", 0 };					\
+    static const char *const kwlist[] = { "len", 0 };					\
     PyObject *rc = 0;							\
 									\
     if (!PyArg_ParseTupleAndKeywords(arg, kw, "|l:" #name,		\
-				    kwlist, &len))			\
+				    KWLIST, &len))			\
       goto end;								\
     if (len < 0) {							\
       len = mp_octets##c(MP_X(me));					\
@@ -669,16 +719,16 @@ STOREOP(storel2c, 2c)
 STOREOP(storeb2c, 2c)
 #undef STOREOP
 
-#define BUFOP(ty, pyty)							\
-  static PyObject *meth__##pyty##_frombuf(PyObject *me, PyObject *arg)	\
+#define BUFOP(ty)							\
+  static PyObject *ty##meth_frombuf(PyObject *me, PyObject *arg)	\
   {									\
     buf b;								\
     char *p;								\
-    int sz;								\
+    Py_ssize_t sz;							\
     PyObject *rc = 0;							\
     mp *x;								\
 									\
-    if (!PyArg_ParseTuple(arg, "Os#:frombuf", &me, &p, &sz)) goto end;	\
+    if (!PyArg_ParseTuple(arg, "s#:frombuf", &p, &sz)) goto end;	\
     buf_init(&b, p, sz);						\
     if ((x = buf_getmp(&b)) == 0) VALERR("malformed data");		\
     rc = Py_BuildValue("(NN)", ty##_pywrap(x),				\
@@ -686,18 +736,17 @@ STOREOP(storeb2c, 2c)
   end:									\
     return (rc);							\
   }
-BUFOP(mp, MP)
-BUFOP(gf, GF)
+BUFOP(mp)
+BUFOP(gf)
 #undef BUFOP
 
-static PyObject *mpmeth_tobuf(PyObject *me, PyObject *arg)
+static PyObject *mpmeth_tobuf(PyObject *me)
 {
   buf b;
   PyObject *rc;
   mp *x;
   size_t n;
 
-  if (!PyArg_ParseTuple(arg, ":tobuf")) return (0);
   x = MP_X(me);
   n = mp_octets(x) + 3;
   rc = bytestring_pywrap(0, n);
@@ -711,16 +760,74 @@ static PyObject *mpmeth_tobuf(PyObject *me, PyObject *arg)
 static PyObject *mpmeth_primep(PyObject *me, PyObject *arg, PyObject *kw)
 {
   grand *r = &rand_global;
-  char *kwlist[] = { "rng", 0 };
+  static const char *const kwlist[] = { "rng", 0 };
   PyObject *rc = 0;
 
-  if (!PyArg_ParseTupleAndKeywords(arg, kw, "|O&", kwlist, convgrand, &r))
+  if (!PyArg_ParseTupleAndKeywords(arg, kw, "|O&", KWLIST, convgrand, &r))
     goto end;
   rc = getbool(pgen_primep(MP_X(me), r));
 end:
   return (rc);
 }
 
+static PyObject *mpmeth_fromstring(PyObject *me,
+				   PyObject *arg, PyObject *kw)
+{
+  int r = 0;
+  char *p;
+  Py_ssize_t len;
+  PyObject *z = 0;
+  mp *zz;
+  mptext_stringctx sc;
+  static const char *const kwlist[] = { "x", "radix", 0 };
+
+  if (!PyArg_ParseTupleAndKeywords(arg, kw, "s#|i:fromstring", KWLIST,
+				   &p, &len, &r))
+    goto end;
+  if (!good_radix_p(r, 1)) VALERR("bad radix");
+  sc.buf = p; sc.lim = p + len;
+  if ((zz = mp_read(MP_NEW, r, &mptext_stringops, &sc)) == 0)
+    VALERR("bad integer");
+  z = Py_BuildValue("(Ns#)", mp_pywrap(zz),
+		    sc.buf, (Py_ssize_t)(sc.lim - sc.buf));
+end:
+  return (z);
+}
+
+static PyObject *mpmeth_factorial(PyObject *me, PyObject *arg)
+{
+  unsigned long i;
+  mp *x;
+  if (!PyArg_ParseTuple(arg, "O&:factorial", convulong, &i)) return (0);
+  x = mp_factorial(i);
+  return mp_pywrap(x);
+}
+
+static PyObject *mpmeth_fibonacci(PyObject *me, PyObject *arg)
+{
+  long i;
+  mp *x;
+  if (!PyArg_ParseTuple(arg, "l:fibonacci", &i)) return (0);
+  x = mp_fibonacci(i);
+  return mp_pywrap(x);
+}
+
+#define LOADOP(pre, name)						\
+  static PyObject *pre##meth_##name(PyObject *me, PyObject *arg)	\
+  {									\
+    char *p;								\
+    Py_ssize_t len;							\
+    if (!PyArg_ParseTuple(arg, "s#:" #name, &p, &len)) return (0);	\
+    return (pre##_pywrap(mp_##name(MP_NEW, p, len)));			\
+  }
+LOADOP(mp, loadl)
+LOADOP(mp, loadb)
+LOADOP(mp, loadl2c)
+LOADOP(mp, loadb2c)
+LOADOP(gf, loadl)
+LOADOP(gf, loadb)
+#undef LOADOP
+
 static PyObject *mpget_nbits(PyObject *me, void *hunoz)
   { return (PyInt_FromLong(mp_bits(MP_X(me)))); }
 
@@ -730,7 +837,7 @@ static PyObject *mpget_noctets(PyObject *me, void *hunoz)
 static PyObject *mpget_noctets2c(PyObject *me, void *hunoz)
   { return (PyInt_FromLong(mp_octets2c(MP_X(me)))); }
 
-static PyGetSetDef mp_pygetset[] = {
+static const PyGetSetDef mp_pygetset[] = {
 #define GETSETNAME(op, func) mp##op##_##func
   GET	(nbits,		"X.nbits -> bit length of X")
   GET	(noctets,	"X.noctets -> octet length of X")
@@ -739,34 +846,49 @@ static PyGetSetDef mp_pygetset[] = {
   { 0 }
 };
 
-static PyMethodDef mp_pymethods[] = {
+static const PyMethodDef mp_pymethods[] = {
 #define METHNAME(func) mpmeth_##func
-  METH	(jacobi,	"X.jacobi(Y) -> Jacobi symbol (Y/X) (NB inversion!)")
+  METH	(jacobi,	"X.jacobi(Y) -> Jacobi symbol (Y|X) (NB inversion!)")
   METH	(setbit,	"X.setbit(N) -> X with bit N set")
   METH	(clearbit,	"X.clearbit(N) -> X with bit N clear")
   METH	(testbit,	"X.testbit(N) -> true/false if bit N set/clear in X")
-  METH	(odd,		"X.odd() -> S, T where X = 2^S T with T odd")
-  METH	(sqr,		"X.sqr() -> X^2")
-  METH	(sqrt,		"X.sqrt() -> largest integer <= sqrt(X)")
+  NAMETH(odd,		"X.odd() -> S, T where X = 2^S T with T odd")
+  NAMETH(sqr,		"X.sqr() -> X^2")
+  NAMETH(sqrt,		"X.sqrt() -> largest integer <= sqrt(X)")
   METH	(gcd,		"X.gcd(Y) -> gcd(X, Y)")
-  METH	(gcdx,
-	 "X.gcdx(Y) -> (gcd(X, Y), U, V) with X U + Y V = gcd(X, Y)")
+  METH	(gcdx,		"X.gcdx(Y) -> (gcd(X, Y), U, V) "
+						"with X U + Y V = gcd(X, Y)")
   METH	(modinv,	"X.modinv(Y) -> multiplicative inverse of Y mod X")
   METH	(modsqrt,	"X.modsqrt(Y) -> square root of Y mod X, if X prime")
-  KWMETH(primep,	"X.primep(rng = rand) -> true/false if X is prime")
-  KWMETH(tostring,	"X.tostring(radix = 10) -> STR")
-  KWMETH(storel,	"X.storel(len = -1) -> little-endian bytes")
-  KWMETH(storeb,	"X.storeb(len = -1) -> big-endian bytes")
-  KWMETH(storel2c,
-	 "X.storel2c(len = -1) -> little-endian bytes, two's complement")
-  KWMETH(storeb2c,
-	 "X.storeb2c(len = -1) -> big-endian bytes, two's complement")
-  METH	(tobuf,		"X.tobuf() -> buffer format")
+  METH	(leastcongruent, "X.leastcongruent(B, M) -> "
+				       "smallest Z >= B with Z == X (mod M)")
+  KWMETH(primep,	"X.primep([rng = rand]) -> X is prime?")
+  KWMETH(tostring,	"X.tostring([radix = 10]) -> STR")
+  KWMETH(storel,	"X.storel([len = -1]) -> little-endian bytes")
+  KWMETH(storeb,	"X.storeb([len = -1]) -> big-endian bytes")
+  KWMETH(storel2c,	"X.storel2c([len = -1]) -> "
+				     "little-endian bytes, two's complement")
+  KWMETH(storeb2c,	"X.storeb2c([len = -1]) -> "
+					"big-endian bytes, two's complement")
+  NAMETH(tobuf,		"X.tobuf() -> buffer format")
+  KWSMTH(fromstring,	"fromstring(STR, [radix = 0]) -> (X, REST)\n"
+    "  Parse STR as a large integer, according to RADIX.  If RADIX is\n"
+    "  zero, read a prefix from STR to decide radix: allow `0b' for binary,\n"
+    "  `0' or `0o' for octal, `0x' for hex, or `R_' for other radix R.")
+  SMTH	(factorial,	"factorial(I) -> I!: compute factorial")
+  SMTH	(fibonacci,	"fibonacci(I) -> F(I): compute Fibonacci number")
+  SMTH	(loadl,		"loadl(STR) -> X: read little-endian bytes")
+  SMTH	(loadb,		"loadb(STR) -> X: read big-endian bytes")
+  SMTH	(loadl2c,	"loadl2c(STR) -> X: "
+				"read little-endian bytes, two's complement")
+  SMTH	(loadb2c,	"loadb2c(STR) -> X: "
+				   "read big-endian bytes, two's complement")
+  SMTH	(frombuf,	"frombuf(STR) -> (X, REST): read buffer format")
 #undef METHNAME
   { 0 }
 };
 
-static PyNumberMethods mp_pynumber = {
+static const PyNumberMethods mp_pynumber = {
   mp_pyadd,				/* @nb_add@ */
   mp_pysub,				/* @nb_subtract@ */
   mp_pymul,				/* @nb_multiply@ */
@@ -809,9 +931,9 @@ static PyNumberMethods mp_pynumber = {
   0,					/* @nb_inplace_true_divide@ */
 };
 
-static PyTypeObject mp_pytype_skel = {
-  PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.MP",			/* @tp_name@ */
+static const PyTypeObject mp_pytype_skel = {
+  PyVarObject_HEAD_INIT(0, 0)		/* Header */
+  "MP",					/* @tp_name@ */
   sizeof(mp_pyobj),			/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -821,7 +943,7 @@ static PyTypeObject mp_pytype_skel = {
   0,					/* @tp_setattr@ */
   mp_pycompare,				/* @tp_compare@ */
   mp_pyrepr,				/* @tp_repr@ */
-  &mp_pynumber,				/* @tp_as_number@ */
+  PYNUMBER(mp),				/* @tp_as_number@ */
   0,					/* @tp_as_sequence@ */
   0,					/* @tp_as_mapping@ */
   mp_pyhash,				/* @tp_hash@ */
@@ -835,16 +957,20 @@ static PyTypeObject mp_pytype_skel = {
     Py_TPFLAGS_BASETYPE,
 
   /* @tp_doc@ */
-"Multiprecision integers, similar to `long' but more efficient and\n\
-versatile.  Support all the standard arithmetic operations.\n\
-\n\
-Constructor mp(X, radix = R) attempts to convert X to an `mp'.  If\n\
-X is a string, it's read in radix-R form, or we look for a prefix\n\
-if R = 0.  Other acceptable things are ints and longs.\n\
-\n\
-Notes:\n\
-\n\
-  * Use `//' for division.  MPs don't have `/' division.",
+  "Multiprecision integers, similar to `long' but more efficient and\n"
+  "versatile.  Support all the standard arithmetic operations, with\n"
+  "implicit conversions from `PrimeFilter', and other objects which\n"
+  "convert to `long'.\n"
+  "\n"
+  "Constructor MP(X, [radix = R]) attempts to convert X to an `MP'.  If\n"
+  "X is a string, it's read in radix-R form, or we look for a prefix\n"
+  "if R = 0.  Other acceptable things are field elements, elliptic curve\n"
+  "points, group elements, Python `int' and `long' objects, and anything\n"
+  "with an integer conversion.\n"
+  "\n"
+  "Notes:\n"
+  "\n"
+  "  * Use `//' for integer division: `/' gives exact rational division.",
 
   0,					/* @tp_traverse@ */
   0,					/* @tp_clear@ */
@@ -852,9 +978,9 @@ Notes:\n\
   0,					/* @tp_weaklistoffset@ */
   0,					/* @tp_iter@ */
   0,					/* @tp_iternext@ */
-  mp_pymethods,				/* @tp_methods@ */
+  PYMETHODS(mp),			/* @tp_methods@ */
   0,					/* @tp_members@ */
-  mp_pygetset,				/* @tp_getset@ */
+  PYGETSET(mp),				/* @tp_getset@ */
   0,					/* @tp_base@ */
   0,					/* @tp_dict@ */
   0,					/* @tp_descr_get@ */
@@ -867,79 +993,155 @@ Notes:\n\
   0					/* @tp_is_gc@ */
 };
 
-static PyObject *meth__MP_fromstring(PyObject *me,
-				    PyObject *arg, PyObject *kw)
-{
-  int r = 0;
-  char *p;
-  int len;
-  PyObject *z = 0;
-  mp *zz;
-  mptext_stringctx sc;
-  char *kwlist[] = { "class", "x", "radix", 0 };
+/*----- Products of small integers ----------------------------------------*/
 
-  if (!PyArg_ParseTupleAndKeywords(arg, kw, "Os#|i:fromstring",
-				   kwlist, &me, &p, &len, &r))
-    goto end;
-  if (r < -255 || r > 62) VALERR("radix out of range");
-  sc.buf = p; sc.lim = p + len;
-  if ((zz = mp_read(MP_NEW, r, &mptext_stringops, &sc)) == 0)
-    SYNERR("bad integer");
-  z = Py_BuildValue("(Ns#)", mp_pywrap(zz), sc.buf, (int)(sc.lim - sc.buf));
-end:
-  return (z);
+static PyTypeObject *mpmul_pytype;
+
+typedef struct mpmul_pyobj {
+  PyObject_HEAD
+  int livep;
+  mpmul mm;
+} mpmul_pyobj;
+
+#define MPMUL_LIVEP(o) (((mpmul_pyobj *)(o))->livep)
+#define MPMUL_PY(o) (&((mpmul_pyobj *)(o))->mm)
+
+static void mpmul_pydealloc(PyObject *me)
+{
+  if (MPMUL_LIVEP(me))
+    mp_drop(mpmul_done(MPMUL_PY(me)));
+  FREEOBJ(me);
 }
 
-static PyObject *meth__MP_product(PyObject *me, PyObject *arg)
+static PyObject *mmmeth_factor(PyObject *me, PyObject *arg)
 {
-  mpmul m;
   PyObject *q, *i;
   mp *x;
 
-  if (PyTuple_Size(arg) != 2) {
+  if (!MPMUL_LIVEP(me)) VALERR("MPMul object invalid");
+  if (PyTuple_GET_SIZE(arg) != 1)
     i = PyObject_GetIter(arg);
-    PyIter_Next(i);
-  } else {
-    if ((q = PyTuple_GetItem(arg, 1)) == 0) return (0);
+  else {
+    if ((q = PyTuple_GET_ITEM(arg, 0)) == 0) goto end;
     if ((i = PyObject_GetIter(q)) == 0) {
       PyErr_Clear(); /* that's ok */
       i = PyObject_GetIter(arg);
     }
   }
-  if (!i) return (0);
-  mpmul_init(&m);
+  if (!i) goto end;
   while ((q = PyIter_Next(i)) != 0) {
     x = getmp(q); Py_DECREF(q); if (!x) {
-      MP_DROP(mpmul_done(&m));
       Py_DECREF(i);
-      return (0);
+      goto end;
     }
-    mpmul_add(&m, x);
+    mpmul_add(MPMUL_PY(me), x);
     MP_DROP(x);
   }
-  x = mpmul_done(&m);
   Py_DECREF(i);
+  RETURN_ME;
+end:
+  return (0);
+}
+
+static PyObject *mmmeth_done(PyObject *me)
+{
+  mp *x;
+
+  if (!MPMUL_LIVEP(me)) VALERR("MPMul object invalid");
+  x = mpmul_done(MPMUL_PY(me));
+  MPMUL_LIVEP(me) = 0;
   return (mp_pywrap(x));
+end:
+  return (0);
 }
 
-#define LOADOP(pre, py, name)						\
-  static PyObject *meth__##py##_##name(PyObject *me, PyObject *arg)	\
-  {									\
-    char *p;								\
-    int len;								\
-    if (!PyArg_ParseTuple(arg, "Os#:" #name, &me, &p, &len)) return (0); \
-    return (pre##_pywrap(mp_##name(MP_NEW, p, len)));			\
+static PyObject *mpmul_pynew(PyTypeObject *ty, PyObject *arg, PyObject *kw)
+{
+  mpmul_pyobj *mm;
+
+  if (kw) TYERR("keyword arguments not allowed here");
+  mm = (mpmul_pyobj *)ty->tp_alloc(ty, 0);
+  mpmul_init(&mm->mm);
+  mm->livep = 1;
+  if (mmmeth_factor((PyObject *)mm, arg) == 0) {
+    Py_DECREF(mm);
+    goto end;
   }
-LOADOP(mp, MP, loadl)
-LOADOP(mp, MP, loadb)
-LOADOP(mp, MP, loadl2c)
-LOADOP(mp, MP, loadb2c)
-LOADOP(gf, GF, loadl)
-LOADOP(gf, GF, loadb)
-#undef LOADOP
+  return ((PyObject *)mm);
+end:
+  return (0);
+}
+
+static PyObject *mmget_livep(PyObject *me, void *hunoz)
+  { return (getbool(MPMUL_LIVEP(me))); }
+
+static const PyGetSetDef mpmul_pygetset[] = {
+#define GETSETNAME(op, name) mm##op##_##name
+  GET	(livep,		"MM.livep -> flag: object still valid?")
+#undef GETSETNAME
+  { 0 }
+};
+
+static const PyMethodDef mpmul_pymethods[] = {
+#define METHNAME(name) mmmeth_##name
+  METH	(factor,	"MM.factor(ITERABLE) or MM.factor(I, ...)")
+  NAMETH(done,		"MM.done() -> PRODUCT")
+#undef METHNAME
+  { 0 }
+};
+
+static const PyTypeObject mpmul_pytype_skel = {
+  PyVarObject_HEAD_INIT(0, 0)		/* Header */
+  "MPMul",				/* @tp_name@ */
+  sizeof(mpmul_pyobj),			/* @tp_basicsize@ */
+  0,					/* @tp_itemsize@ */
+
+  mpmul_pydealloc,			/* @tp_dealloc@ */
+  0,					/* @tp_print@ */
+  0,					/* @tp_getattr@ */
+  0,					/* @tp_setattr@ */
+  0,					/* @tp_compare@ */
+  0,					/* @tp_repr@ */
+  0,					/* @tp_as_number@ */
+  0,					/* @tp_as_sequence@ */
+  0,					/* @tp_as_mapping@ */
+  0,					/* @tp_hash@ */
+  0,					/* @tp_call@ */
+  0,					/* @tp_str@ */
+  0,					/* @tp_getattro@ */
+  0,					/* @tp_setattro@ */
+  0,					/* @tp_as_buffer@ */
+  Py_TPFLAGS_DEFAULT |			/* @tp_flags@ */
+    Py_TPFLAGS_BASETYPE,
+
+  /* @tp_doc@ */
+  "MPMul(N_0, N_1, ....): an object for multiplying many small integers.",
+
+  0,					/* @tp_traverse@ */
+  0,					/* @tp_clear@ */
+  0,					/* @tp_richcompare@ */
+  0,					/* @tp_weaklistoffset@ */
+  0,					/* @tp_iter@ */
+  0,					/* @tp_iternext@ */
+  PYMETHODS(mpmul),			/* @tp_methods@ */
+  0,					/* @tp_members@ */
+  PYGETSET(mpmul),			/* @tp_getset@ */
+  0,					/* @tp_base@ */
+  0,					/* @tp_dict@ */
+  0,					/* @tp_descr_get@ */
+  0,					/* @tp_descr_set@ */
+  0,					/* @tp_dictoffset@ */
+  0,					/* @tp_init@ */
+  PyType_GenericAlloc,			/* @tp_alloc@ */
+  mpmul_pynew,				/* @tp_new@ */
+  0,					/* @tp_free@ */
+  0					/* @tp_is_gc@ */
+};
 
 /*----- Montgomery reduction ----------------------------------------------*/
 
+static PyTypeObject *mpmont_pytype;
+
 typedef struct mpmont_pyobj {
   PyObject_HEAD
   mpmont mm;
@@ -1040,7 +1242,7 @@ fail:
 
 static PyObject *mm_mexpr(PyObject *me, void *v, int n)
   { return mp_pywrap(mpmont_mexpr(MPMONT_PY(me), MP_NEW, v, n)); }
-  
+
 static void mp_mexp_drop(void *p)
 {
   mp_expfactor *f = p;
@@ -1080,7 +1282,7 @@ fail:
 
 static PyObject *mm_mexp(PyObject *me, void *v, int n)
   { return mp_pywrap(mpmont_mexp(MPMONT_PY(me), MP_NEW, v, n)); }
-  
+
 static PyObject *mmmeth_mexp(PyObject *me, PyObject *arg)
 {
   return mexp_common(me, arg, sizeof(mp_expfactor),
@@ -1108,10 +1310,10 @@ static void mpmont_pydealloc(PyObject *me)
 static PyObject *mpmont_pynew(PyTypeObject *ty, PyObject *arg, PyObject *kw)
 {
   mpmont_pyobj *mm = 0;
-  char *kwlist[] = { "m", 0 };
+  static const char *const kwlist[] = { "m", 0 };
   mp *xx = 0;
 
-  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O&:new", kwlist, convmp, &xx))
+  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O&:new", KWLIST, convmp, &xx))
     goto end;
   if (!MP_POSP(xx) || !MP_ODDP(xx)) VALERR("m must be positive and odd");
   mm = (mpmont_pyobj *)ty->tp_alloc(ty, 0);
@@ -1130,7 +1332,7 @@ static PyObject *mmget_r(PyObject *me, void *hunoz)
 static PyObject *mmget_r2(PyObject *me, void *hunoz)
   { return (mp_pywrap(MP_COPY(MPMONT_PY(me)->r2))); }
 
-static PyGetSetDef mpmont_pygetset[] = {
+static const PyGetSetDef mpmont_pygetset[] = {
 #define GETSETNAME(op, name) mm##op##_##name
   GET	(m,		"M.m -> modulus for reduction")
   GET	(r,		"M.r -> multiplicative identity")
@@ -1139,27 +1341,27 @@ static PyGetSetDef mpmont_pygetset[] = {
   { 0 }
 };
 
-static PyMethodDef mpmont_pymethods[] = {
+static const PyMethodDef mpmont_pymethods[] = {
 #define METHNAME(name) mmmeth_##name
-  METH	(int,		"M.out(X) -> XR")
+  METH	(int,		"M.int(X) -> XR")
   METH	(mul,		"M.mul(XR, YR) -> ZR where Z = X Y")
   METH	(expr,		"M.expr(XR, N) -> ZR where Z = X^N mod M.m")
-  METH	(mexpr,		"\
-B.mexp([(XR0, N0), (XR1, N1), ...]) = ZR where Z = X0^N0 X1^N1 mod B.m\n\
-\t(the list may be flattened if this more convenient.)")
+  METH	(mexpr,		"M.mexpr([(XR0, N0), (XR1, N1), ...]) = ZR "
+					"where Z = X0^N0 X1^N1 ... mod M.m\n"
+		    "\t(the list may be flattened if this more convenient.)")
   METH	(reduce,	"M.reduce(XR) -> X")
   METH	(ext,		"M.ext(XR) -> X")
   METH	(exp,		"M.exp(X, N) -> X^N mod M.m")
-  METH	(mexp,		"\
-B.mexp([(X0, N0), (X1, N1), ...]) = X0^N0 X1^N1 mod B.m\n\
-\t(the list may be flattened if this more convenient.)")
+  METH	(mexp,		"M.mexp([(X0, N0), (X1, N1), ...]) = "
+						  "X0^N0 X1^N1 ... mod M.m\n"
+		    "\t(the list may be flattened if this more convenient.)")
 #undef METHNAME
   { 0 }
 };
 
-static PyTypeObject *mpmont_pytype, mpmont_pytype_skel = {
-  PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.MPMont",			/* @tp_name@ */
+static const PyTypeObject mpmont_pytype_skel = {
+  PyVarObject_HEAD_INIT(0, 0)		/* Header */
+  "MPMont",				/* @tp_name@ */
   sizeof(mpmont_pyobj),			/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -1182,7 +1384,7 @@ static PyTypeObject *mpmont_pytype, mpmont_pytype_skel = {
     Py_TPFLAGS_BASETYPE,
 
   /* @tp_doc@ */
-"A Montgomery reduction context.",
+  "MPMont(N): a Montgomery reduction context.",
 
   0,					/* @tp_traverse@ */
   0,					/* @tp_clear@ */
@@ -1190,9 +1392,9 @@ static PyTypeObject *mpmont_pytype, mpmont_pytype_skel = {
   0,					/* @tp_weaklistoffset@ */
   0,					/* @tp_iter@ */
   0,					/* @tp_iternext@ */
-  mpmont_pymethods,			/* @tp_methods@ */
+  PYMETHODS(mpmont),			/* @tp_methods@ */
   0,					/* @tp_members@ */
-  mpmont_pygetset,			/* @tp_getset@ */
+  PYGETSET(mpmont),			/* @tp_getset@ */
   0,					/* @tp_base@ */
   0,					/* @tp_dict@ */
   0,					/* @tp_descr_get@ */
@@ -1207,6 +1409,8 @@ static PyTypeObject *mpmont_pytype, mpmont_pytype_skel = {
 
 /*----- Barrett reduction -------------------------------------------------*/
 
+static PyTypeObject *mpbarrett_pytype;
+
 typedef struct mpbarrett_pyobj {
   PyObject_HEAD
   mpbarrett mb;
@@ -1233,7 +1437,7 @@ end:
 
 static PyObject *mb_mexp(PyObject *me, void *v, int n)
   { return mp_pywrap(mpbarrett_mexp(MPBARRETT_PY(me), MP_NEW, v, n)); }
-  
+
 static PyObject *mbmeth_mexp(PyObject *me, PyObject *arg)
 {
   return mexp_common(me, arg, sizeof(mp_expfactor),
@@ -1262,10 +1466,10 @@ static PyObject *mpbarrett_pynew(PyTypeObject *ty,
 				 PyObject *arg, PyObject *kw)
 {
   mpbarrett_pyobj *mb = 0;
-  char *kwlist[] = { "m", 0 };
+  static const char *const kwlist[] = { "m", 0 };
   mp *xx = 0;
 
-  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O&:new", kwlist, convmp, &xx))
+  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O&:new", KWLIST, convmp, &xx))
     goto end;
   if (!MP_POSP(xx)) VALERR("m must be positive");
   mb = (mpbarrett_pyobj *)ty->tp_alloc(ty, 0);
@@ -1278,27 +1482,27 @@ end:
 static PyObject *mbget_m(PyObject *me, void *hunoz)
   { return (mp_pywrap(MP_COPY(MPBARRETT_PY(me)->m))); }
 
-static PyGetSetDef mpbarrett_pygetset[] = {
+static const PyGetSetDef mpbarrett_pygetset[] = {
 #define GETSETNAME(op, name) mb##op##_##name
   GET	(m,		"B.m -> modulus for reduction")
 #undef GETSETNAME
   { 0 }
 };
 
-static PyMethodDef mpbarrett_pymethods[] = {
+static const PyMethodDef mpbarrett_pymethods[] = {
 #define METHNAME(name) mbmeth_##name
   METH	(reduce,	"B.reduce(X) -> X mod B.m")
   METH	(exp,		"B.exp(X, N) -> X^N mod B.m")
-  METH	(mexp,		"\
-B.mexp([(X0, N0), (X1, N1), ...]) = X0^N0 X1^N1 mod B.m\n\
-\t(the list may be flattened if this more convenient.)")
+  METH	(mexp,		"B.mexp([(X0, N0), (X1, N1), ...]) = "
+						  "X0^N0 X1^N1 ... mod B.m\n"
+		    "\t(the list may be flattened if this more convenient.)")
 #undef METHNAME
   { 0 }
 };
 
-static PyTypeObject *mpbarrett_pytype, mpbarrett_pytype_skel = {
-  PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.MPBarrett",			/* @tp_name@ */
+static const PyTypeObject mpbarrett_pytype_skel = {
+  PyVarObject_HEAD_INIT(0, 0)		/* Header */
+  "MPBarrett",				/* @tp_name@ */
   sizeof(mpbarrett_pyobj),		/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -1321,7 +1525,7 @@ static PyTypeObject *mpbarrett_pytype, mpbarrett_pytype_skel = {
     Py_TPFLAGS_BASETYPE,
 
   /* @tp_doc@ */
-"A Barrett reduction context.",
+  "MPBarrett(N): a Barrett reduction context.",
 
   0,					/* @tp_traverse@ */
   0,					/* @tp_clear@ */
@@ -1329,9 +1533,9 @@ static PyTypeObject *mpbarrett_pytype, mpbarrett_pytype_skel = {
   0,					/* @tp_weaklistoffset@ */
   0,					/* @tp_iter@ */
   0,					/* @tp_iternext@ */
-  mpbarrett_pymethods,			/* @tp_methods@ */
+  PYMETHODS(mpbarrett),			/* @tp_methods@ */
   0,					/* @tp_members@ */
-  mpbarrett_pygetset,			/* @tp_getset@ */
+  PYGETSET(mpbarrett),			/* @tp_getset@ */
   0,					/* @tp_base@ */
   0,					/* @tp_dict@ */
   0,					/* @tp_descr_get@ */
@@ -1346,6 +1550,8 @@ static PyTypeObject *mpbarrett_pytype, mpbarrett_pytype_skel = {
 
 /*----- Nice prime reduction ----------------------------------------------*/
 
+static PyTypeObject *mpreduce_pytype;
+
 typedef struct mpreduce_pyobj {
   PyObject_HEAD
   mpreduce mr;
@@ -1392,10 +1598,10 @@ static PyObject *mpreduce_pynew(PyTypeObject *ty,
 {
   mpreduce_pyobj *mr = 0;
   mpreduce r;
-  char *kwlist[] = { "m", 0 };
+  static const char *const kwlist[] = { "m", 0 };
   mp *xx = 0;
 
-  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O&:new", kwlist, convmp, &xx))
+  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O&:new", KWLIST, convmp, &xx))
     goto end;
   if (!MP_POSP(xx)) VALERR("m must be positive");
   if (mpreduce_create(&r, xx)) VALERR("bad modulus (must be 2^k - ...)");
@@ -1409,14 +1615,14 @@ end:
 static PyObject *mrget_m(PyObject *me, void *hunoz)
   { return (mp_pywrap(MP_COPY(MPREDUCE_PY(me)->p))); }
 
-static PyGetSetDef mpreduce_pygetset[] = {
+static const PyGetSetDef mpreduce_pygetset[] = {
 #define GETSETNAME(op, name) mr##op##_##name
   GET	(m,		"R.m -> modulus for reduction")
 #undef GETSETNAME
   { 0 }
 };
 
-static PyMethodDef mpreduce_pymethods[] = {
+static const const PyMethodDef mpreduce_pymethods[] = {
 #define METHNAME(name) mrmeth_##name
   METH	(reduce,	"R.reduce(X) -> X mod B.m")
   METH	(exp,		"R.exp(X, N) -> X^N mod B.m")
@@ -1424,9 +1630,9 @@ static PyMethodDef mpreduce_pymethods[] = {
   { 0 }
 };
 
-static PyTypeObject *mpreduce_pytype, mpreduce_pytype_skel = {
-  PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.MPReduce",			/* @tp_name@ */
+static const PyTypeObject mpreduce_pytype_skel = {
+  PyVarObject_HEAD_INIT(0, 0)		/* Header */
+  "MPReduce",				/* @tp_name@ */
   sizeof(mpreduce_pyobj),		/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -1449,7 +1655,7 @@ static PyTypeObject *mpreduce_pytype, mpreduce_pytype_skel = {
     Py_TPFLAGS_BASETYPE,
 
   /* @tp_doc@ */
-"A reduction context for reduction modulo primes of special form.",
+  "MPReduce(N): a reduction context for reduction modulo Solinas primes.",
 
   0,					/* @tp_traverse@ */
   0,					/* @tp_clear@ */
@@ -1457,9 +1663,9 @@ static PyTypeObject *mpreduce_pytype, mpreduce_pytype_skel = {
   0,					/* @tp_weaklistoffset@ */
   0,					/* @tp_iter@ */
   0,					/* @tp_iternext@ */
-  mpreduce_pymethods,			/* @tp_methods@ */
+  PYMETHODS(mpreduce),			/* @tp_methods@ */
   0,					/* @tp_members@ */
-  mpreduce_pygetset,			/* @tp_getset@ */
+  PYGETSET(mpreduce),			/* @tp_getset@ */
   0,					/* @tp_base@ */
   0,					/* @tp_dict@ */
   0,					/* @tp_descr_get@ */
@@ -1474,6 +1680,8 @@ static PyTypeObject *mpreduce_pytype, mpreduce_pytype_skel = {
 
 /*----- Chinese Remainder Theorem solution --------------------------------*/
 
+static PyTypeObject *mpcrt_pytype;
+
 typedef struct mpcrt_pyobj {
   PyObject_HEAD
   mpcrt c;
@@ -1487,16 +1695,17 @@ static PyObject *mcmeth_solve(PyObject *me, PyObject *arg)
   PyObject *q = 0, *x, *z = 0;
   mp *xx;
   mp **v = 0;
-  int i = 0, n = c->k;
+  Py_ssize_t i = 0, n = c->k;
 
   Py_INCREF(me);
-  if (PyTuple_Size(arg) == n)
+  if (PyTuple_GET_SIZE(arg) == n)
     q = arg;
   else if (!PyArg_ParseTuple(arg, "O:solve", &q))
     goto end;
   Py_INCREF(q);
   if (!PySequence_Check(q)) TYERR("want a sequence of residues");
-  if (PySequence_Size(q) != n) VALERR("residue count mismatch");
+  i = PySequence_Size(q); if (i < 0) goto end;
+  if (i != n) VALERR("residue count mismatch");
   v = xmalloc(n * sizeof(*v));
   for (i = 0; i < n; i++) {
     if ((x = PySequence_GetItem(q, i)) == 0) goto end;
@@ -1526,30 +1735,41 @@ static void mpcrt_pydealloc(PyObject *me)
 static PyObject *mpcrt_pynew(PyTypeObject *ty, PyObject *arg, PyObject *kw)
 {
   mpcrt_mod *v = 0;
-  int n, i = 0;
-  char *kwlist[] = { "mv", 0 };
+  Py_ssize_t n, i = 0, j;
+  static const char *const kwlist[] = { "mv", 0 };
   PyObject *q = 0, *x;
-  mp *xx;
+  mp *xx = MP_NEW, *y = MP_NEW, *g = MP_NEW;
+  mpmul mm;
   mpcrt_pyobj *c = 0;
 
-  if (PyTuple_Size(arg) > 1)
+  if (PyTuple_GET_SIZE(arg) > 1)
     q = arg;
-  else if (!PyArg_ParseTupleAndKeywords(arg, kw, "O:new", kwlist, &q))
+  else if (!PyArg_ParseTupleAndKeywords(arg, kw, "O:new", KWLIST, &q))
     goto end;
   Py_INCREF(q);
   if (!PySequence_Check(q)) TYERR("want a sequence of moduli");
-  n = PySequence_Size(q);
-  if (PyErr_Occurred()) goto end;
+  n = PySequence_Size(q); if (n < 0) goto end;
   if (!n) VALERR("want at least one modulus");
   v = xmalloc(n * sizeof(*v));
   for (i = 0; i < n; i++) {
     if ((x = PySequence_GetItem(q, i)) == 0) goto end;
     xx = getmp(x); Py_DECREF(x); if (!xx) goto end;
-    v[i].m = xx; v[i].n = 0; v[i].ni = 0; v[i].nni = 0;
+    if (MP_CMP(xx, <=, MP_ZERO)) VALERR("moduli must be positive");
+    v[i].m = xx; v[i].n = 0; v[i].ni = 0; v[i].nni = 0; xx = MP_NEW;
   }
+  mpmul_init(&mm);
+  for (j = 0; j < i; j++) mpmul_add(&mm, v[j].m);
+  xx = mpmul_done(&mm);
+  for (j = 0; j < i; j++) {
+    mp_div(&y, 0, xx, v[j].m);
+    mp_gcd(&g, 0, 0, y, v[j].m);
+    if (!MP_EQ(g, MP_ONE)) VALERR("moduli must be pairwise coprime");
+  }
+
   c = (mpcrt_pyobj *)ty->tp_alloc(ty, 0);
   mpcrt_create(&c->c, v, n, 0);
   Py_DECREF(q);
+  mp_drop(xx); mp_drop(y); mp_drop(g);
   return ((PyObject *)c);
 
 end:
@@ -1560,6 +1780,7 @@ end:
     xfree(v);
   }
   Py_XDECREF(q);
+  mp_drop(xx); mp_drop(y); mp_drop(g);
   return (0);
 }
 
@@ -1574,11 +1795,11 @@ static PyObject *mcget_moduli(PyObject *me, void *hunoz)
 
   if ((q = PyList_New(c->k)) == 0) return (0);
   for (i = 0; i < c->k; i++)
-    PyList_SetItem(q, i, mp_pywrap(c->v[i].m));
+    PyList_SET_ITEM(q, i, mp_pywrap(c->v[i].m));
   return (q);
 }
 
-static PyGetSetDef mpcrt_pygetset[] = {
+static const PyGetSetDef mpcrt_pygetset[] = {
 #define GETSETNAME(op, name) mc##op##_##name
   GET	(product,	"C.product -> product of moduli")
   GET	(moduli,	"C.moduli -> list of individual moduli")
@@ -1586,16 +1807,16 @@ static PyGetSetDef mpcrt_pygetset[] = {
   { 0 }
 };
 
-static PyMethodDef mpcrt_pymethods[] = {
+static const PyMethodDef mpcrt_pymethods[] = {
 #define METHNAME(name) mcmeth_##name
   METH	(solve,		"C.solve([R0, R1]) -> X mod C.product")
 #undef METHNAME
   { 0 }
 };
 
-static PyTypeObject *mpcrt_pytype, mpcrt_pytype_skel = {
-  PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.MPCRT",			/* @tp_name@ */
+static const PyTypeObject mpcrt_pytype_skel = {
+  PyVarObject_HEAD_INIT(0, 0)		/* Header */
+  "MPCRT",				/* @tp_name@ */
   sizeof(mpcrt_pyobj),			/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -1618,7 +1839,7 @@ static PyTypeObject *mpcrt_pytype, mpcrt_pytype_skel = {
     Py_TPFLAGS_BASETYPE,
 
   /* @tp_doc@ */
-"A context for the solution of Chinese Remainder Theorem problems.",
+  "MPCRT(SEQ): a context for solving Chinese Remainder Theorem problems.",
 
   0,					/* @tp_traverse@ */
   0,					/* @tp_clear@ */
@@ -1626,9 +1847,9 @@ static PyTypeObject *mpcrt_pytype, mpcrt_pytype_skel = {
   0,					/* @tp_weaklistoffset@ */
   0,					/* @tp_iter@ */
   0,					/* @tp_iternext@ */
-  mpcrt_pymethods,			/* @tp_methods@ */
+  PYMETHODS(mpcrt),			/* @tp_methods@ */
   0,					/* @tp_members@ */
-  mpcrt_pygetset,			/* @tp_getset@ */
+  PYGETSET(mpcrt),			/* @tp_getset@ */
   0,					/* @tp_base@ */
   0,					/* @tp_dict@ */
   0,					/* @tp_descr_get@ */
@@ -1652,7 +1873,7 @@ static PyObject *gf_pyrichcompare(PyObject *x, PyObject *y, int op)
   int xl, yl;
   int b;
 
-  if (mpbinop(x, y, &xx, &yy)) RETURN_NOTIMPL;
+  if (gfbinop(x, y, &xx, &yy)) RETURN_NOTIMPL;
   switch (op) {
     case Py_EQ: b = MP_EQ(xx, yy); break;
     case Py_NE: b = !MP_EQ(xx, yy); break;
@@ -1678,15 +1899,15 @@ static PyObject *gf_pynew(PyTypeObject *ty, PyObject *arg, PyObject *kw)
   mp *z;
   mp_pyobj *zz = 0;
   int radix = 0;
-  char *kwlist[] = { "x", "radix", 0 };
+  static const char *const kwlist[] = { "x", "radix", 0 };
 
-  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O|i:gf", kwlist, &x, &radix))
+  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O|i:gf", KWLIST, &x, &radix))
     goto end;
   if (GF_PYCHECK(x)) RETURN_OBJ(x);
-  if (radix < -255 || radix > 62) VALERR("radix out of range");
+  if (!good_radix_p(radix, 1)) VALERR("radix out of range");
   if ((z = mp_frompyobject(x, radix)) == 0) {
     PyErr_Format(PyExc_TypeError, "can't convert %.100s to gf",
-		 x->ob_type->tp_name);
+		 Py_TYPE(x)->tp_name);
     goto end;
   }
   if (MP_NEGP(z)) {
@@ -1699,15 +1920,6 @@ end:
   return ((PyObject *)zz);
 }
 
-static long gf_pyhash(PyObject *me)
-{
-  long i = mp_tolong(MP_X(me));
-  i ^= 0xc7ecd67c; /* random perturbance */
-  if (i == -1)
-    i = -2;
-  return (i);
-}
-
 static PyObject *gf_pyexp(PyObject *x, PyObject *y, PyObject *z)
 {
   mp *xx = 0, *yy = 0, *zz = 0;
@@ -1739,11 +1951,8 @@ end:
   return (rc);
 }
 
-static PyObject *gfmeth_sqr(PyObject *me, PyObject *arg)
-{
-  if (!PyArg_ParseTuple(arg, ":sqr")) return (0);
-  return (gf_pywrap(gf_sqr(MP_NEW, MP_X(me))));
-}
+static PyObject *gfmeth_sqr(PyObject *me)
+  { return (gf_pywrap(gf_sqr(MP_NEW, MP_X(me)))); }
 
 static PyObject *gfmeth_gcd(PyObject *me, PyObject *arg)
 {
@@ -1787,16 +1996,40 @@ end:
   return (z);
 }
 
-static PyObject *gfmeth_irreduciblep(PyObject *me, PyObject *arg)
+static PyObject *gfmeth_fromstring(PyObject *me,
+				   PyObject *arg, PyObject *kw)
 {
-  if (!PyArg_ParseTuple(arg, ":irreduciblep")) return (0);
-  return getbool(gf_irreduciblep(MP_X(me)));
+  int r = 0;
+  char *p;
+  Py_ssize_t len;
+  PyObject *z = 0;
+  mp *zz;
+  mptext_stringctx sc;
+  static const char *const kwlist[] = { "x", "radix", 0 };
+
+  if (!PyArg_ParseTupleAndKeywords(arg, kw, "s#|i:fromstring", KWLIST,
+				   &p, &len, &r))
+    goto end;
+  if (!good_radix_p(r, 1)) VALERR("bad radix");
+  sc.buf = p; sc.lim = p + len;
+  if ((zz = mp_read(MP_NEW, r, &mptext_stringops, &sc)) == 0 ||
+      MP_NEGP(zz)) {
+    if (zz) MP_DROP(zz);
+    VALERR("bad binary polynomial");
+  }
+  z = Py_BuildValue("(Ns#)", gf_pywrap(zz),
+		    sc.buf, (Py_ssize_t)(sc.lim - sc.buf));
+end:
+  return (z);
 }
 
+static PyObject *gfmeth_irreduciblep(PyObject *me)
+  { return getbool(gf_irreduciblep(MP_X(me))); }
+
 static PyObject *gfget_degree(PyObject *me, void *hunoz)
   { return (PyInt_FromLong(mp_bits(MP_X(me)) - 1)); }
 
-static PyGetSetDef gf_pygetset[] = {
+static const PyGetSetDef gf_pygetset[] = {
 #define GETSETNAME(op, name) gf##op##_##name
   GET	(degree,	"X.degree -> polynomial degree of X")
 #undef GETSETNAME
@@ -1807,32 +2040,38 @@ static PyGetSetDef gf_pygetset[] = {
   { 0 }
 };
 
-static PyMethodDef gf_pymethods[] = {
+static const PyMethodDef gf_pymethods[] = {
 #define METHNAME(func) gfmeth_##func
   METH	(setbit,	"X.setbit(N) -> X with bit N set")
   METH	(clearbit,	"X.clearbit(N) -> X with bit N clear")
   METH	(testbit,	"X.testbit(N) -> true/false if bit N set/clear in X")
-  METH	(sqr,		"X.sqr() -> X^2")
+  NAMETH(sqr,		"X.sqr() -> X^2")
   METH	(gcd,		"X.gcd(Y) -> gcd(X, Y)")
-  METH	(gcdx,
-	 "X.gcdx(Y) -> (gcd(X, Y), U, V) with X U + Y V = gcd(X, Y)")
+  METH	(gcdx,   "X.gcdx(Y) -> (gcd(X, Y), U, V) with X U + Y V = gcd(X, Y)")
   METH	(modinv,	"X.modinv(Y) -> multiplicative inverse of Y mod X")
-  METH	(irreduciblep, 	"X.irreduciblep() -> true/false")
+  NAMETH(irreduciblep,	"X.irreduciblep() -> true/false")
+  KWSMTH(fromstring,	"fromstring(STR, [radix = 0]) -> (X, REST)\n"
+    "  Parse STR as a binary polynomial, according to RADIX.  If RADIX is\n"
+    "  zero, read a prefix from STR to decide radix: allow `0b' for binary,\n"
+    "  `0' or `0o' for octal, `0x' for hex, or `R_' for other radix R.")
+  SMTH	(loadl,		"loadl(STR) -> X: read little-endian bytes")
+  SMTH	(loadb,		"loadb(STR) -> X: read big-endian bytes")
+  SMTH	(frombuf,	"frombuf(STR) -> (X, REST): read buffer format")
 #undef METHNAME
 #define METHNAME(func) mpmeth_##func
-  KWMETH(tostring,	"X.tostring(radix = 10) -> STR")
-  KWMETH(storel,	"X.storel(len = -1) -> little-endian bytes")
-  KWMETH(storeb,	"X.storeb(len = -1) -> big-endian bytes")
-  KWMETH(storel2c,
-	 "X.storel2c(len = -1) -> little-endian bytes, two's complement")
-  KWMETH(storeb2c,
-	 "X.storeb2c(len = -1) -> big-endian bytes, two's complement")
-  METH	(tobuf,		"X.tobuf() -> buffer format")
+  KWMETH(tostring,	"X.tostring([radix = 10]) -> STR")
+  KWMETH(storel,	"X.storel([len = -1]) -> little-endian bytes")
+  KWMETH(storeb,	"X.storeb([len = -1]) -> big-endian bytes")
+  KWMETH(storel2c,	"X.storel2c([len = -1]) -> "
+				     "little-endian bytes, two's complement")
+  KWMETH(storeb2c,	"X.storeb2c([len = -1]) -> "
+					"big-endian bytes, two's complement")
+  NAMETH(tobuf,		"X.tobuf() -> buffer format")
 #undef METHNAME
   { 0 }
 };
 
-static PyNumberMethods gf_pynumber = {
+static const PyNumberMethods gf_pynumber = {
   gf_pyadd,				/* @nb_add@ */
   gf_pysub,				/* @nb_subtract@ */
   gf_pymul,				/* @nb_multiply@ */
@@ -1875,9 +2114,9 @@ static PyNumberMethods gf_pynumber = {
   0,					/* @nb_inplace_true_divide@ */
 };
 
-static PyTypeObject gf_pytype_skel = {
-  PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.GF",			/* @tp_name@ */
+static const PyTypeObject gf_pytype_skel = {
+  PyVarObject_HEAD_INIT(0, 0)		/* Header */
+  "GF",					/* @tp_name@ */
   sizeof(mp_pyobj),			/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -1887,10 +2126,10 @@ static PyTypeObject gf_pytype_skel = {
   0,					/* @tp_setattr@ */
   0,					/* @tp_compare@ */
   gf_pyrepr,				/* @tp_repr@ */
-  &gf_pynumber,				/* @tp_as_number@ */
+  PYNUMBER(gf),				/* @tp_as_number@ */
   0,					/* @tp_as_sequence@ */
   0,					/* @tp_as_mapping@ */
-  gf_pyhash,				/* @tp_hash@ */
+  mp_pyhash,				/* @tp_hash@ */
   0,					/* @tp_call@ */
   mp_pyhex,				/* @tp_str@ */
   0,					/* @tp_getattro@ */
@@ -1901,19 +2140,21 @@ static PyTypeObject gf_pytype_skel = {
     Py_TPFLAGS_BASETYPE,
 
   /* @tp_doc@ */
-"Binary polynomials.  Support almost all the standard arithmetic\n\
-operations.\n\
-\n\
-Constructor gf(X, radix = R) attempts to convert X to a `gf'.  If\n\
-X is a string, it's read in radix-R form, or we look for a prefix\n\
-if R = 0.  Other acceptable things are ints and longs.\n\
-\n\
-The name is hopelessly wrong from a technical point of view, but\n\
-but it's much easier to type than `p2' or `c2' or whatever.\n\
-\n\
-Notes:\n\
-\n\
-  * Use `//' for division.  GFs don't have `/' division.",
+  "Binary polynomials.  Support almost all the standard arithmetic\n"
+  "operations.\n"
+  "\n"
+  "Constructor GF(X, [radix = R]) attempts to convert X to a `GF'.  If\n"
+  "X is a string, it's read in radix-R form, or we look for a prefix\n"
+  "if R = 0.  Other acceptable things are field elements, elliptic curve\n"
+  "points, group elements, Python `int' and `long' objects, and anything\n"
+  "with an integer conversion.\n"
+  "\n"
+  "The name is hopelessly wrong from a technical point of view, but\n"
+  "but it's much easier to type than `p2' or `c2' or whatever.\n"
+  "\n"
+  "Notes:\n"
+  "\n"
+  "  * Use `//' for Euclidean division: `/' gives exact rational division.",
 
   0,					/* @tp_traverse@ */
   0,					/* @tp_clear@ */
@@ -1921,9 +2162,9 @@ Notes:\n\
   0,					/* @tp_weaklistoffset@ */
   0,					/* @tp_iter@ */
   0,					/* @tp_iternext@ */
-  gf_pymethods,				/* @tp_methods@ */
+  PYMETHODS(gf),			/* @tp_methods@ */
   0,					/* @tp_members@ */
-  gf_pygetset,				/* @tp_getset@ */
+  PYGETSET(gf),				/* @tp_getset@ */
   0,					/* @tp_base@ */
   0,					/* @tp_dict@ */
   0,					/* @tp_descr_get@ */
@@ -1936,33 +2177,10 @@ Notes:\n\
   0					/* @tp_is_gc@ */
 };
 
-static PyObject *meth__GF_fromstring(PyObject *me,
-				    PyObject *arg, PyObject *kw)
-{
-  int r = 0;
-  char *p;
-  int len;
-  PyObject *z = 0;
-  mp *zz;
-  mptext_stringctx sc;
-  char *kwlist[] = { "class", "x", "radix", 0 };
-
-  if (!PyArg_ParseTupleAndKeywords(arg, kw, "Os#|i:fromstring",
-				   kwlist, &me, &p, &len, &r))
-    goto end;
-  if (r < -255 || r > 62) VALERR("radix out of range");
-  sc.buf = p; sc.lim = p + len;
-  if ((zz = mp_read(MP_NEW, r, &mptext_stringops, &sc)) == 0 || MP_NEGP(zz))
-    z = Py_BuildValue("(Os#)", Py_None, p, len);
-  else
-    z = Py_BuildValue("(Ns#)", gf_pywrap(zz),
-		      sc.buf, (int)(sc.lim - sc.buf));
-end:
-  return (z);
-}
-
 /*----- Sparse poly reduction ---------------------------------------------*/
 
+static PyTypeObject *gfreduce_pytype;
+
 typedef struct gfreduce_pyobj {
   PyObject_HEAD
   gfreduce mr;
@@ -1987,6 +2205,58 @@ end:
   return (rc);
 }
 
+static PyObject *grmeth_trace(PyObject *me, PyObject *arg)
+{
+  PyObject *rc = 0;
+  mp *xx = 0;
+
+  if (!PyArg_ParseTuple(arg, "O&:trace", convgf, &xx)) goto end;
+  rc = PyInt_FromLong(gfreduce_trace(GFREDUCE_PY(me), xx));
+end:
+  if (xx) MP_DROP(xx);
+  return (rc);
+}
+
+static PyObject *grmeth_halftrace(PyObject *me, PyObject *arg)
+{
+  PyObject *rc = 0;
+  mp *xx = 0;
+
+  if (!PyArg_ParseTuple(arg, "O&:halftrace", convgf, &xx)) goto end;
+  rc = gf_pywrap(gfreduce_halftrace(GFREDUCE_PY(me), MP_NEW, xx));
+end:
+  if (xx) MP_DROP(xx);
+  return (rc);
+}
+
+static PyObject *grmeth_sqrt(PyObject *me, PyObject *arg)
+{
+  PyObject *rc = 0;
+  mp *xx = 0, *yy;
+
+  if (!PyArg_ParseTuple(arg, "O&:sqrt", convgf, &xx)) goto end;
+  if ((yy = gfreduce_sqrt(GFREDUCE_PY(me), MP_NEW, xx)) == 0)
+    VALERR("no modular square root");
+  rc = gf_pywrap(yy);
+end:
+  if (xx) MP_DROP(xx);
+  return (rc);
+}
+
+static PyObject *grmeth_quadsolve(PyObject *me, PyObject *arg)
+{
+  PyObject *rc = 0;
+  mp *xx = 0, *yy;
+
+  if (!PyArg_ParseTuple(arg, "O&:quadsolve", convgf, &xx)) goto end;
+  if ((yy = gfreduce_quadsolve(GFREDUCE_PY(me), MP_NEW, xx)) == 0)
+    VALERR("no solution found");
+  rc = gf_pywrap(yy);
+end:
+  if (xx) MP_DROP(xx);
+  return (rc);
+}
+
 static PyObject *grmeth_reduce(PyObject *me, PyObject *arg)
 {
   PyObject *z = 0;
@@ -2009,10 +2279,10 @@ static PyObject *gfreduce_pynew(PyTypeObject *ty,
 {
   gfreduce_pyobj *mr = 0;
   gfreduce r;
-  char *kwlist[] = { "m", 0 };
+  static const char *const kwlist[] = { "m", 0 };
   mp *xx = 0;
 
-  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O&:new", kwlist, convgf, &xx))
+  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O&:new", KWLIST, convgf, &xx))
     goto end;
   if (MP_ZEROP(xx)) ZDIVERR("modulus is zero!");
   gfreduce_create(&r, xx);
@@ -2026,24 +2296,28 @@ end:
 static PyObject *grget_m(PyObject *me, void *hunoz)
   { return (gf_pywrap(MP_COPY(GFREDUCE_PY(me)->p))); }
 
-static PyGetSetDef gfreduce_pygetset[] = {
+static const PyGetSetDef gfreduce_pygetset[] = {
 #define GETSETNAME(op, name) gr##op##_##name
   GET	(m,		"R.m -> reduction polynomial")
 #undef GETSETNAME
   { 0 }
 };
 
-static PyMethodDef gfreduce_pymethods[] = {
+static const PyMethodDef gfreduce_pymethods[] = {
 #define METHNAME(name) grmeth_##name
   METH	(reduce,	"R.reduce(X) -> X mod B.m")
+  METH	(trace,	       "R.trace(X) -> Tr(X) = x + x^2 + ... + x^{2^{m - 1}}")
+  METH	(halftrace,    "R.halftrace(X) -> x + x^{2^2} + ... + x^{2^{m - 1}}")
+  METH	(sqrt,		"R.sqrt(X) -> Y where Y^2 = X mod R")
+  METH	(quadsolve,	"R.quadsolve(X) -> Y where Y^2 + Y = X mod R")
   METH	(exp,		"R.exp(X, N) -> X^N mod B.m")
 #undef METHNAME
   { 0 }
 };
 
-static PyTypeObject *gfreduce_pytype, gfreduce_pytype_skel = {
-  PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.GFReduce",			/* @tp_name@ */
+static const PyTypeObject gfreduce_pytype_skel = {
+  PyVarObject_HEAD_INIT(0, 0)		/* Header */
+  "GFReduce",				/* @tp_name@ */
   sizeof(gfreduce_pyobj),		/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -2066,7 +2340,7 @@ static PyTypeObject *gfreduce_pytype, gfreduce_pytype_skel = {
     Py_TPFLAGS_BASETYPE,
 
   /* @tp_doc@ */
-"A reduction context for reduction modulo sparse irreducible polynomials.",
+  "GFReduce(N): a context for reduction modulo sparse polynomials.",
 
   0,					/* @tp_traverse@ */
   0,					/* @tp_clear@ */
@@ -2074,9 +2348,9 @@ static PyTypeObject *gfreduce_pytype, gfreduce_pytype_skel = {
   0,					/* @tp_weaklistoffset@ */
   0,					/* @tp_iter@ */
   0,					/* @tp_iternext@ */
-  gfreduce_pymethods,			/* @tp_methods@ */
+  PYMETHODS(gfreduce),			/* @tp_methods@ */
   0,					/* @tp_members@ */
-  gfreduce_pygetset,			/* @tp_getset@ */
+  PYGETSET(gfreduce),			/* @tp_getset@ */
   0,					/* @tp_base@ */
   0,					/* @tp_dict@ */
   0,					/* @tp_descr_get@ */
@@ -2091,14 +2365,14 @@ static PyTypeObject *gfreduce_pytype, gfreduce_pytype_skel = {
 
 /*----- Normal/poly transformation ----------------------------------------*/
 
+static PyTypeObject *gfn_pytype;
+
 typedef struct gfn_pyobj {
   PyObject_HEAD
   mp *p;
   gfn ntop, pton;
 } gfn_pyobj;
 
-static PyTypeObject *gfn_pytype, gfn_pytype_skel;
-
 #define GFN_P(o) (((gfn_pyobj *)(o))->p)
 #define GFN_PTON(o) (&((gfn_pyobj *)(o))->pton)
 #define GFN_NTOP(o) (&((gfn_pyobj *)(o))->ntop)
@@ -2107,14 +2381,15 @@ static PyObject *gfn_pynew(PyTypeObject *ty, PyObject *arg, PyObject *kw)
 {
   mp *p = 0, *beta = 0;
   gfn_pyobj *gg = 0;
-  char *kwlist[] = { "p", "beta", 0 };
+  static const char *const kwlist[] = { "p", "beta", 0 };
 
-  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O&O&:new", kwlist,
+  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O&O&:new", KWLIST,
 				   convgf, &p, convgf, &beta))
     goto end;
   gg = PyObject_New(gfn_pyobj, ty);
+  gg->p = 0;
   if (gfn_create(p, beta, &gg->ntop, &gg->pton)) {
-    FREEOBJ(gg);
+    Py_DECREF(gg);
     gg = 0;
     VALERR("can't invert transformation matrix");
   }
@@ -2146,7 +2421,7 @@ static PyObject *gfnget_beta(PyObject *me, void *hunoz)
   end:									\
     mp_drop(xx);							\
     if (!z) return (0);							\
-    return (mp_pywrap(z));						\
+    return (gf_pywrap(z));						\
   }
 XFORMOP(pton, PTON)
 XFORMOP(ntop, NTOP)
@@ -2154,12 +2429,15 @@ XFORMOP(ntop, NTOP)
 
 static void gfn_pydealloc(PyObject *me)
 {
-  gfn_destroy(GFN_PTON(me));
-  gfn_destroy(GFN_NTOP(me));
+  if (GFN_P(me)) {
+    MP_DROP(GFN_P(me));
+    gfn_destroy(GFN_PTON(me));
+    gfn_destroy(GFN_NTOP(me));
+  }
   FREEOBJ(me);
 }
 
-static PyGetSetDef gfn_pygetset[] = {
+static const PyGetSetDef gfn_pygetset[] = {
 #define GETSETNAME(op, name) gfn##op##_##name
   GET	(p,		"X.p -> polynomial basis, as polynomial")
   GET	(beta,		"X.beta -> normal basis element, in poly form")
@@ -2167,7 +2445,7 @@ static PyGetSetDef gfn_pygetset[] = {
   { 0 }
 };
 
-static PyMethodDef gfn_pymethods[] = {
+static const PyMethodDef gfn_pymethods[] = {
 #define METHNAME(name) gfnmeth_##name
   METH	(pton,		"X.pton(A) -> normal-basis representation of A")
   METH	(ntop,		"X.ntop(A) -> polynomial-basis representation of A")
@@ -2175,9 +2453,9 @@ static PyMethodDef gfn_pymethods[] = {
   { 0 }
 };
 
-static PyTypeObject gfn_pytype_skel = {
-  PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.GFN",			/* @tp_name@ */
+static const PyTypeObject gfn_pytype_skel = {
+  PyVarObject_HEAD_INIT(0, 0)		/* Header */
+  "GFN",				/* @tp_name@ */
   sizeof(gfn_pyobj),			/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -2200,8 +2478,8 @@ static PyTypeObject gfn_pytype_skel = {
     Py_TPFLAGS_BASETYPE,
 
   /* @tp_doc@ */
-"An object for transforming elements of binary fields between polynomial\n\
-and normal basis representations.",
+  "GFN(P, BETA): an object for transforming elements of binary fields\n"
+  "  between polynomial and normal basis representations.",
 
   0,					/* @tp_traverse@ */
   0,					/* @tp_clear@ */
@@ -2209,9 +2487,9 @@ and normal basis representations.",
   0,					/* @tp_weaklistoffset@ */
   0,					/* @tp_iter@ */
   0,					/* @tp_iternext@ */
-  gfn_pymethods,			/* @tp_methods@ */
+  PYMETHODS(gfn),			/* @tp_methods@ */
   0,					/* @tp_members@ */
-  gfn_pygetset,				/* @tp_getset@ */
+  PYGETSET(gfn),			/* @tp_getset@ */
   0,					/* @tp_base@ */
   0,					/* @tp_dict@ */
   0,					/* @tp_descr_get@ */
@@ -2226,39 +2504,8 @@ and normal basis representations.",
 
 /*----- Glue --------------------------------------------------------------*/
 
-static PyMethodDef methods[] = {
-#define METHNAME(func) meth_##func
-  KWMETH(_MP_fromstring,        "\
-fromstring(STR, radix = 0) -> (X, REST)\n\
-\n\
-Parse STR as a large integer, according to radix.  If radix is zero,\n\
-read a prefix from STR to decide radix: allow `0' for octal, `0x' for hex\n\
-or `R_' for other radix R.")
-  KWMETH(_GF_fromstring,        "\
-fromstring(STR, radix = 0) -> (X, REST)\n\
-\n\
-Parse STR as a binary polynomial, according to radix.  If radix is zero,\n\
-read a prefix from STR to decide radix: allow `0' for octal, `0x' for hex\n\
-or `R_' for other radix R.")
-  METH	(_MP_loadl,		"\
-loadl(STR) -> X: read little-endian bytes")
-  METH	(_MP_loadb,		"\
-loadb(STR) -> X: read big-endian bytes")
-  METH	(_MP_loadl2c,		"\
-loadl2c(STR) -> X: read little-endian bytes, two's complement")
-  METH	(_MP_loadb2c,		"\
-loadb2c(STR) -> X: read big-endian bytes, two's complement")
-  METH	(_MP_frombuf,		"\
-frombuf(STR) -> (X, REST): read buffer format")
-  METH	(_MP_product,		"\
-product(ITER) -> X: product of things iterated over")
-  METH	(_GF_loadl,		"\
-loadl(STR) -> X: read little-endian bytes")
-  METH	(_GF_loadb,		"\
-loadb(STR) -> X: read big-endian bytes")
-  METH	(_GF_frombuf,		"\
-frombuf(STR) -> (X, REST): read buffer format")
-#undef METHNAME
+static const struct nameval consts[] = {
+  CONST(MPW_MAX),
   { 0 }
 };
 
@@ -2266,18 +2513,19 @@ void mp_pyinit(void)
 {
   INITTYPE(mp, root);
   INITTYPE(gf, root);
+  INITTYPE(mpmul, root);
   INITTYPE(mpmont, root);
   INITTYPE(mpbarrett, root);
   INITTYPE(mpreduce, root);
   INITTYPE(mpcrt, root);
   INITTYPE(gfreduce, root);
   INITTYPE(gfn, root);
-  addmethods(methods);
 }
 
 void mp_pyinsert(PyObject *mod)
 {
   INSERT("MP", mp_pytype);
+  INSERT("MPMul", mpmul_pytype);
   INSERT("MPMont", mpmont_pytype);
   INSERT("MPBarrett", mpbarrett_pytype);
   INSERT("MPReduce", mpreduce_pytype);
@@ -2285,6 +2533,7 @@ void mp_pyinsert(PyObject *mod)
   INSERT("GF", gf_pytype);
   INSERT("GFReduce", gfreduce_pytype);
   INSERT("GFN", gfn_pytype);
+  setconstants(mod, consts);
 }
 
 /*----- That's all, folks -------------------------------------------------*/