X-Git-Url: https://git.distorted.org.uk/~mdw/catacomb-python/blobdiff_plain/32507e35eeef67236e12adf7d00458e303f8c9aa..2f9acb0c0748743bafe5f4905a0e00e024cc75a7:/mp.c

diff --git a/mp.c b/mp.c
index 4b73223..e0f72d4 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.
@@ -165,7 +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;
@@ -174,8 +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:
@@ -269,11 +269,44 @@ 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 = 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 = tomp(y)) == 0) {
+  if ((*yy = implicitgf(y)) == 0) {
     MP_DROP(*xx);
     return (-1);
   }
@@ -286,7 +319,7 @@ 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));						\
@@ -330,8 +363,8 @@ 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								\
@@ -351,7 +384,7 @@ 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);			\
@@ -396,7 +429,7 @@ 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;
@@ -452,8 +485,8 @@ 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 (mp_topylong(MP_X(x))); }
@@ -465,7 +498,7 @@ static PyObject *mp_pyfloat(PyObject *x)
   return (PyFloat_FromDouble(f));
 }
 
-#define COERCE(pre, PRE) 						\
+#define COERCE(pre, PRE)						\
   static int pre##_pycoerce(PyObject **x, PyObject **y)			\
   {									\
     mp *z;								\
@@ -494,9 +527,9 @@ 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:new", kwlist, &x, &radix))
+  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O|i:new", KWLIST, &x, &radix))
     goto end;
   if (MP_PYCHECK(x)) RETURN_OBJ(x);
   if (!good_radix_p(radix, 1)) VALERR("bad radix");
@@ -524,8 +557,6 @@ static PyObject *mpmeth_jacobi(PyObject *me, PyObject *arg)
   PyObject *z = 0;
 
   if (!PyArg_ParseTuple(arg, "O&:jacobi", convmp, &y)) goto end;
-  if (MP_NEGP(MP_X(me)) || MP_EVENP(MP_X(me)))
-    VALERR("must be positive and odd");
   z = PyInt_FromLong(mp_jacobi(y, MP_X(me)));
 end:
   if (y) MP_DROP(y);
@@ -535,27 +566,27 @@ 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)));
 }
 
@@ -628,8 +659,8 @@ 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 (!good_radix_p(radix, 0)) VALERR("bad radix");
   return (mp_topystring(MP_X(me), radix, 0, 0, 0));
@@ -651,16 +682,29 @@ 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));					\
@@ -682,7 +726,7 @@ STOREOP(storeb2c, 2c)
   {									\
     buf b;								\
     char *p;								\
-    int sz;								\
+    Py_ssize_t sz;							\
     PyObject *rc = 0;							\
     mp *x;								\
 									\
@@ -719,10 +763,10 @@ 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:
@@ -761,6 +805,8 @@ static PyMethodDef mp_pymethods[] = {
 	 "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")
+  METH	(leastcongruent,
+	 "X.leastcongruent(B, M) -> smallest Z >= B with Z == X (mod M)")
   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")
@@ -819,7 +865,7 @@ static PyNumberMethods mp_pynumber = {
 
 static PyTypeObject mp_pytype_skel = {
   PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.MP",			/* @tp_name@ */
+  "MP",					/* @tp_name@ */
   sizeof(mp_pyobj),			/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -846,13 +892,13 @@ static PyTypeObject mp_pytype_skel = {
 "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\
+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.",
+  * Use `//' for integer division.  `/' gives exact rational division.",
 
   0,					/* @tp_traverse@ */
   0,					/* @tp_clear@ */
@@ -876,33 +922,53 @@ Notes:\n\
 };
 
 static PyObject *meth__MP_fromstring(PyObject *me,
-				    PyObject *arg, PyObject *kw)
+				     PyObject *arg, PyObject *kw)
 {
   int r = 0;
   char *p;
-  int len;
+  Py_ssize_t len;
   PyObject *z = 0;
   mp *zz;
   mptext_stringctx sc;
-  char *kwlist[] = { "class", "x", "radix", 0 };
+  static const char *const kwlist[] = { "class", "x", "radix", 0 };
 
   if (!PyArg_ParseTupleAndKeywords(arg, kw, "Os#|i:fromstring",
-				   kwlist, &me, &p, &len, &r))
+				   KWLIST, &me, &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)
-    SYNERR("bad integer");
-  z = Py_BuildValue("(Ns#)", mp_pywrap(zz), sc.buf, (int)(sc.lim - sc.buf));
+    VALERR("bad integer");
+  z = Py_BuildValue("(Ns#)", mp_pywrap(zz),
+		    sc.buf, (Py_ssize_t)(sc.lim - sc.buf));
 end:
   return (z);
 }
 
+static PyObject *meth__MP_factorial(PyObject *me, PyObject *arg)
+{
+  unsigned long i;
+  mp *x;
+  if (!PyArg_ParseTuple(arg, "OO&:factorial", &me, convulong, &i))
+    return (0);
+  x = mp_factorial(i);
+  return mp_pywrap(x);
+}
+
+static PyObject *meth__MP_fibonacci(PyObject *me, PyObject *arg)
+{
+  long i;
+  mp *x;
+  if (!PyArg_ParseTuple(arg, "Ol:fibonacci", &me, &i)) return (0);
+  x = mp_fibonacci(i);
+  return mp_pywrap(x);
+}
+
 #define LOADOP(pre, py, name)						\
   static PyObject *meth__##py##_##name(PyObject *me, PyObject *arg)	\
   {									\
     char *p;								\
-    int len;								\
+    Py_ssize_t len;							\
     if (!PyArg_ParseTuple(arg, "Os#:" #name, &me, &p, &len)) return (0); \
     return (pre##_pywrap(mp_##name(MP_NEW, p, len)));			\
   }
@@ -1012,7 +1078,7 @@ static PyMethodDef mpmul_pymethods[] = {
 
 static PyTypeObject *mpmul_pytype, mpmul_pytype_skel = {
   PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.MPMul",			/* @tp_name@ */
+  "MPMul",				/* @tp_name@ */
   sizeof(mpmul_pyobj),			/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -1035,7 +1101,7 @@ static PyTypeObject *mpmul_pytype, mpmul_pytype_skel = {
     Py_TPFLAGS_BASETYPE,
 
   /* @tp_doc@ */
-"An object for multiplying many small integers.",
+"MPMul(N_0, N_1, ....): an object for multiplying many small integers.",
 
   0,					/* @tp_traverse@ */
   0,					/* @tp_clear@ */
@@ -1160,7 +1226,7 @@ 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;
@@ -1200,7 +1266,7 @@ 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),
@@ -1228,10 +1294,10 @@ 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);
@@ -1261,17 +1327,17 @@ static PyGetSetDef mpmont_pygetset[] = {
 
 static 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\
+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\
+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 }
@@ -1279,7 +1345,7 @@ B.mexp([(X0, N0), (X1, N1), ...]) = X0^N0 X1^N1 mod B.m\n\
 
 static PyTypeObject *mpmont_pytype, mpmont_pytype_skel = {
   PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.MPMont",			/* @tp_name@ */
+  "MPMont",				/* @tp_name@ */
   sizeof(mpmont_pyobj),			/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -1302,7 +1368,7 @@ 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@ */
@@ -1353,7 +1419,7 @@ 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),
@@ -1382,10 +1448,10 @@ 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);
@@ -1410,7 +1476,7 @@ static PyMethodDef mpbarrett_pymethods[] = {
   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\
+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 }
@@ -1418,7 +1484,7 @@ B.mexp([(X0, N0), (X1, N1), ...]) = X0^N0 X1^N1 mod B.m\n\
 
 static PyTypeObject *mpbarrett_pytype, mpbarrett_pytype_skel = {
   PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.MPBarrett",			/* @tp_name@ */
+  "MPBarrett",				/* @tp_name@ */
   sizeof(mpbarrett_pyobj),		/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -1441,7 +1507,7 @@ 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@ */
@@ -1512,10 +1578,10 @@ 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 - ...)");
@@ -1546,7 +1612,7 @@ static PyMethodDef mpreduce_pymethods[] = {
 
 static PyTypeObject *mpreduce_pytype, mpreduce_pytype_skel = {
   PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.MPReduce",			/* @tp_name@ */
+  "MPReduce",				/* @tp_name@ */
   sizeof(mpreduce_pyobj),		/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -1569,7 +1635,7 @@ 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@ */
@@ -1647,14 +1713,14 @@ static PyObject *mpcrt_pynew(PyTypeObject *ty, PyObject *arg, PyObject *kw)
 {
   mpcrt_mod *v = 0;
   int n, i = 0;
-  char *kwlist[] = { "mv", 0 };
+  static const char *const kwlist[] = { "mv", 0 };
   PyObject *q = 0, *x;
   mp *xx;
   mpcrt_pyobj *c = 0;
 
   if (PyTuple_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");
@@ -1715,7 +1781,7 @@ static PyMethodDef mpcrt_pymethods[] = {
 
 static PyTypeObject *mpcrt_pytype, mpcrt_pytype_skel = {
   PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.MPCRT",			/* @tp_name@ */
+  "MPCRT",				/* @tp_name@ */
   sizeof(mpcrt_pyobj),			/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -1738,7 +1804,7 @@ 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@ */
@@ -1772,7 +1838,7 @@ 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;
@@ -1798,9 +1864,9 @@ 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 (!good_radix_p(radix, 1)) VALERR("radix out of range");
@@ -1937,7 +2003,7 @@ static PyMethodDef gf_pymethods[] = {
   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")
+  METH	(irreduciblep,	"X.irreduciblep() -> true/false")
 #undef METHNAME
 #define METHNAME(func) mpmeth_##func
   KWMETH(tostring,	"X.tostring(radix = 10) -> STR")
@@ -1997,7 +2063,7 @@ static PyNumberMethods gf_pynumber = {
 
 static PyTypeObject gf_pytype_skel = {
   PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.GF",			/* @tp_name@ */
+  "GF",					/* @tp_name@ */
   sizeof(mp_pyobj),			/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -2033,7 +2099,7 @@ 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.",
+  * Use `//' for Euclidean division.  `/' gives exact rational division.",
 
   0,					/* @tp_traverse@ */
   0,					/* @tp_clear@ */
@@ -2061,22 +2127,24 @@ static PyObject *meth__GF_fromstring(PyObject *me,
 {
   int r = 0;
   char *p;
-  int len;
+  Py_ssize_t len;
   PyObject *z = 0;
   mp *zz;
   mptext_stringctx sc;
-  char *kwlist[] = { "class", "x", "radix", 0 };
+  static const char *const kwlist[] = { "class", "x", "radix", 0 };
 
   if (!PyArg_ParseTupleAndKeywords(arg, kw, "Os#|i:fromstring",
-				   kwlist, &me, &p, &len, &r))
+				   KWLIST, &me, &p, &len, &r))
     goto end;
-  if (!good_radix_p(r, 1)) VALERR("radix out of range");
+  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))
-    z = Py_BuildValue("(Os#)", Py_None, p, len);
-  else
-    z = Py_BuildValue("(Ns#)", gf_pywrap(zz),
-		      sc.buf, (int)(sc.lim - sc.buf));
+  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);
 }
@@ -2107,6 +2175,58 @@ 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;
@@ -2129,10 +2249,10 @@ 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);
@@ -2156,6 +2276,10 @@ static PyGetSetDef gfreduce_pygetset[] = {
 static 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 }
@@ -2163,7 +2287,7 @@ static PyMethodDef gfreduce_pymethods[] = {
 
 static PyTypeObject *gfreduce_pytype, gfreduce_pytype_skel = {
   PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.GFReduce",			/* @tp_name@ */
+  "GFReduce",				/* @tp_name@ */
   sizeof(gfreduce_pyobj),		/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -2186,7 +2310,7 @@ 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@ */
@@ -2227,9 +2351,9 @@ 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);
@@ -2297,7 +2421,7 @@ static PyMethodDef gfn_pymethods[] = {
 
 static PyTypeObject gfn_pytype_skel = {
   PyObject_HEAD_INIT(0) 0,		/* Header */
-  "catacomb.GFN",			/* @tp_name@ */
+  "GFN",				/* @tp_name@ */
   sizeof(gfn_pyobj),			/* @tp_basicsize@ */
   0,					/* @tp_itemsize@ */
 
@@ -2320,8 +2444,8 @@ 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@ */
@@ -2348,18 +2472,22 @@ and normal basis representations.",
 
 static PyMethodDef methods[] = {
 #define METHNAME(func) meth_##func
-  KWMETH(_MP_fromstring,        "\
+  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,        "\
+  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_factorial,		"\
+factorial(I) -> I!: compute factorial")
+  METH	(_MP_fibonacci,		"\
+fibonacci(I) -> F(I): compute Fibonacci number")
   METH	(_MP_loadl,		"\
 loadl(STR) -> X: read little-endian bytes")
   METH	(_MP_loadb,		"\