.gdbinit: Delete this obsolete file.

[catacomb-python] / mp.c

/* -*-c-*-
 *
 * Multiprecision arithmetic
 *
 * (c) 2004 Straylight/Edgeware
 */

/*----- Licensing notice --------------------------------------------------*
 *
 * This file is part of the Python interface to Catacomb.
 *
 * Catacomb/Python is free software; you can redistribute it and/or modify
 * 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.
 */

/*----- Header files ------------------------------------------------------*/

#include "catacomb-python.h"

/*----- General utilities -------------------------------------------------*/

PyTypeObject *mp_pytype = 0;
PyTypeObject *gf_pytype = 0;

mp *mp_frompylong(PyObject *obj)
{
  unsigned long bits;
  PyLongObject *l = (PyLongObject *)obj;
  int sz;
  size_t w;
  mpd r = 0;
  int b = 0;
  int i;
  mp *x;
  mpw *p;

  sz = l->ob_size;
  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);
  p = x->v;
  for (i = 0; i < sz; i++) {
    r |= (mpd)l->ob_digit[i] << b;
    b += SHIFT;
    while (b >= MPW_BITS) {
      *p++ = MPW(r);
      r >>= MPW_BITS;
      b -= MPW_BITS;
    }
  }
  while (r) {
    *p++ = MPW(r);
    r >>= MPW_BITS;
  }
  x->vl = p;
  MP_SHRINK(x);
  return (x);
}

PyObject *mp_topylong(mp *x)
{
  unsigned long bits = mp_bits(x);
  int sz = (bits + SHIFT - 1)/SHIFT;
  PyLongObject *l = _PyLong_New(sz);
  mpd r = 0;
  int b = 0;
  mpw *p = x->v;
  int i = 0;

  assert(MPW_BITS >= SHIFT);
  while (i < sz && p < x->vl) {
    r |= (mpd)*p++ << b;
    b += MPW_BITS;
    while (i < sz && b >= SHIFT) {
      l->ob_digit[i++] = r & MASK;
      r >>= SHIFT;
      b -= SHIFT;
    }
  }
  while (i < sz && r) {
    l->ob_digit[i++] = r & MASK;
    r >>= SHIFT;
  }
  l->ob_size = (x->f & MP_NEG) ? -sz : sz;
  return ((PyObject *)l);
}

mp *mp_frompyobject(PyObject *o, int radix)
{
  mp *x;

  if (PyString_Check(o)) {
    mptext_stringctx sc;
    mp *x;
    sc.buf = PyString_AS_STRING(o);
    sc.lim = sc.buf + PyString_GET_SIZE(o);
    x = mp_read(MP_NEW, radix, &mptext_stringops, &sc);
    if (!x) return (0);
    if (sc.buf < sc.lim) { MP_DROP(x); return (0); }
    return (x);
  }
  if ((x = tomp(o)) != 0)
    return (x);
  return (0);
}

PyObject *mp_topystring(mp *x, int radix, const char *xpre,
			const char *pre, const char *post)
{
  int len = mptext_len(x, radix) + 1;
  mptext_stringctx sc;
  PyObject *o;
  size_t xprelen = xpre ? strlen(xpre) : 0;
  size_t prelen = pre ? strlen(pre) : 0;
  size_t postlen = post ? strlen(post) : 0;
  char *p;
  MP_COPY(x);
  o = PyString_FromStringAndSize(0, len + 1 + xprelen + prelen + postlen);
  p = PyString_AS_STRING(o);
  sc.buf = p;
  if (xpre) { memcpy(sc.buf, xpre, xprelen); sc.buf += xprelen; }
  if (MP_NEGP(x)) { *sc.buf++ = '-'; x = mp_neg(x, x); }
  if (pre) { memcpy(sc.buf, pre, prelen); sc.buf += prelen; }
  sc.lim = sc.buf + len;
  mp_write(x, radix, &mptext_stringops, &sc);
  if (post) { memcpy(sc.buf, post, postlen); sc.buf += postlen; }
  MP_DROP(x);
  _PyString_Resize(&o, sc.buf - p);
  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);
  z->x = x;
  return ((PyObject *)z);
}

PyObject *gf_pywrap(mp *x)
{
  mp_pyobj *z = PyObject_New(mp_pyobj, gf_pytype);
  z->x = x;
  return ((PyObject *)z);
}

int mp_tolong_checked(mp *x, long *l, int must)
{
  static mp *longmin = 0, *longmax = 0;
  int rc = -1;

  if (!longmax) {
    longmin = mp_fromlong(MP_NEW, LONG_MIN);
    longmax = mp_fromlong(MP_NEW, LONG_MAX);
  }
  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:
  return (rc);
}

/*----- Python interface --------------------------------------------------*/

static void mp_pydealloc(PyObject *o)
{
  MP_DROP(MP_X(o));
  FREEOBJ(o);
}

static PyObject *mp_pyrepr(PyObject *o)
  { return mp_topystring(MP_X(o), 10, "MP(", 0, "L)"); }

static PyObject *mp_pystr(PyObject *o)
  { return mp_topystring(MP_X(o), 10, 0, 0, 0); }

mp *tomp(PyObject *o)
{
  PyObject *l;
  mp *x;

  if (!o)
    return (0);
  else if (MP_PYCHECK(o) || GF_PYCHECK(o))
    return (MP_COPY(MP_X(o)));
  else if (FE_PYCHECK(o))
    return (F_OUT(FE_F(o), MP_NEW, FE_X(o)));
  else if (PFILT_PYCHECK(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);
    return (x);
  } else if (GE_PYCHECK(o)) {
    if ((x = G_TOINT(GE_G(o), MP_NEW, GE_X(o))) == 0)
      return (0);
    return (x);
  } else if (PyInt_Check(o))
    return (mp_fromlong(MP_NEW, PyInt_AS_LONG(o)));
  else if ((l = PyNumber_Long(o)) != 0) {
    x = mp_frompylong(l);
    Py_DECREF(l);
    return (x);
  } else {
    PyErr_Clear();
    return (0);
  }
}

mp *getmp(PyObject *o)
{
  mp *x = 0;
  if (!o) return (0);
  if ((x = tomp(o)) == 0) {
    PyErr_Format(PyExc_TypeError, "can't convert %.100s to mp",
		 o->ob_type->tp_name);
  }
  return (x);
}

int convmp(PyObject *o, void *p)
{
  mp *x;
  if ((x = getmp(o)) == 0) return (0);
  *(mp **)p = x;
  return (1);
}

mp *getgf(PyObject *o)
{
  mp *x = 0;
  if (!o) return (0);
  if ((x = tomp(o)) == 0) {
    PyErr_Format(PyExc_TypeError, "can't convert %.100s to gf",
		 o->ob_type->tp_name);
  }
  return (x);
}

int convgf(PyObject *o, void *p)
{
  mp *x;
  if ((x = getgf(o)) == 0) return (0);
  *(mp **)p = x;
  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 = 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 = implicitgf(y)) == 0) {
    MP_DROP(*xx);
    return (-1);
  }
  return (0);
}

#define gf_and mp_and
#define gf_or mp_or
#define gf_xor mp_xor
#define BINOP(pre, name)						\
  static PyObject *pre##_py##name(PyObject *x, PyObject *y) {		\
    mp *xx, *yy, *zz;							\
    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));						\
  }
BINOP(mp, add)
BINOP(mp, sub)
BINOP(mp, mul)
BINOP(mp, and2c)
BINOP(mp, or2c)
BINOP(mp, xor2c)
BINOP(gf, add)
BINOP(gf, sub)
BINOP(gf, mul)
BINOP(gf, and)
BINOP(gf, or)
BINOP(gf, xor)
#undef BINOP

static mp *mp_abs(mp *d, mp *x)
{
  if (MP_NEGP(x))
    return (mp_neg(d, x));
  MP_COPY(x);
  if (d) MP_DROP(d);
  return (x);
}

#define UNOP(pre, name)							\
  static PyObject *pre##_py##name(PyObject *x)				\
    { return mp_pywrap(pre##_##name(MP_NEW, MP_X(x))); }
UNOP(mp, neg)
UNOP(mp, abs)
UNOP(mp, not2c)
#undef UNOP

static PyObject *mp_pyid(PyObject *x) { RETURN_OBJ(x); }

#define gf_lsr mp_lsr
#define SHIFTOP(pre, name, rname)					\
  static PyObject *pre##_py##name(PyObject *x, PyObject *y) {		\
    mp *xx, *yy;							\
    PyObject *z = 0;							\
    long n;								\
    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								\
      z = pre##_pywrap(mp_##name(MP_NEW, xx, n));			\
  end:									\
    MP_DROP(xx); MP_DROP(yy);						\
    return (z);								\
  }
SHIFTOP(mp, lsl2c, lsr2c)
SHIFTOP(mp, lsr2c, lsl2c)
SHIFTOP(gf, lsl, lsr)
SHIFTOP(gf, lsr, lsl)
#undef SHIFTOP

#define DIVOP(pre, name, qq, rr, gather)				\
  static PyObject *pre##_py##name(PyObject *x, PyObject *y) {		\
    mp *xx, *yy;							\
    PyObject *z = 0;							\
    INIT_##qq(q) INIT_##rr(r)						\
    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);			\
    z = gather;								\
  end:									\
    MP_DROP(xx); MP_DROP(yy);						\
    return (z);								\
  }
#define INIT_YES(p) mp *p = MP_NEW;
#define INIT_NO(p)
#define ARG_YES(p) &p
#define ARG_NO(p) 0
DIVOP(mp, divmod, YES, YES,
      Py_BuildValue("(NN)", mp_pywrap(q), mp_pywrap(r)))
DIVOP(mp, div, YES, NO, mp_pywrap(q))
DIVOP(mp, mod, NO, YES, mp_pywrap(r))
DIVOP(gf, divmod, YES, YES,
      Py_BuildValue("(NN)", gf_pywrap(q), gf_pywrap(r)))
DIVOP(gf, div, YES, NO, gf_pywrap(q))
DIVOP(gf, mod, NO, YES, gf_pywrap(r))
#undef INIT_YES
#undef INIT_NO
#undef ARG_YES
#undef ARG_NO
#undef DIVOP

static mp *mp_modinv_checked(mp *d, mp *x, mp *p)
{
  mp *g = MP_NEW;
  mp_gcd(&g, 0, &d, p, x);
  if (!MP_EQ(g, MP_ONE)) {
    MP_DROP(g); MP_DROP(d);
    PyErr_SetString(PyExc_ZeroDivisionError, "no modular inverse");
    return (0);
  }
  MP_DROP(g); return (d);
}

static PyObject *mp_pyexp(PyObject *x, PyObject *y, PyObject *z)
{
  mp *xx = 0, *yy = 0, *zz = 0;
  mp *r = 0;
  PyObject *rc = 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;
  }
  if (!z || z == Py_None) {
    if (MP_NEGP(yy)) VALERR("negative exponent");
    r = mp_exp(MP_NEW, xx, yy);
  } else {
    if (!MP_POSP(zz)) VALERR("modulus must be positive");
    if (MP_NEGP(yy)) {
      if ((xx = mp_modinv_checked(xx, xx, zz)) == 0) goto end;
      yy = mp_neg(yy, yy);
    }
    if (MP_ODDP(zz)) {
      mpmont mm;
      mpmont_create(&mm, zz);
      r = mpmont_exp(&mm, MP_NEW, xx, yy);
      mpmont_destroy(&mm);
    } else {
      mpbarrett mb;
      mpbarrett_create(&mb, zz);
      r = mpbarrett_exp(&mb, MP_NEW, xx, yy);
      mpbarrett_destroy(&mb);
    }
  }
  rc = mp_pywrap(r);
end:
  mp_drop(xx); mp_drop(yy); mp_drop(zz);
  return (rc);
}

static mp *gf_modinv_checked(mp *d, mp *x, mp *p)
{
  mp *g = MP_NEW;
  gf_gcd(&g, 0, &d, p, x);
  if (!MP_EQ(g, MP_ONE)) {
    MP_DROP(g); MP_DROP(d);
    PyErr_SetString(PyExc_ZeroDivisionError, "no modular inverse");
    return (0);
  }
  MP_DROP(g); return (d);
}

#define BASEOP(name, radix, pre)					\
  static PyObject *mp_py##name(PyObject *x)				\
    { return mp_topystring(MP_X(x), radix, 0, pre, 0); }
BASEOP(oct, 8, "0");
BASEOP(hex, 16, "0x");
#undef BASEOP

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, 0)) return (PyInt_FromLong(l));
  else return mp_topylong(MP_X(x));
}
static PyObject *mp_pylong(PyObject *x)
  { return (mp_topylong(MP_X(x))); }
static PyObject *mp_pyfloat(PyObject *x)
{
  PyObject *l = mp_topylong(MP_X(x));
  double f = PyLong_AsDouble(l);
  Py_DECREF(l);
  return (PyFloat_FromDouble(f));
}

#define COERCE(pre, PRE)						\
  static int pre##_pycoerce(PyObject **x, PyObject **y)			\
  {									\
    mp *z;								\
									\
    if (PRE##_PYCHECK(*y)) {						\
      Py_INCREF(*x); Py_INCREF(*y);					\
      return (0);							\
    }									\
    if ((z = tomp(*y)) != 0) {						\
      Py_INCREF(*x);							\
      *y = pre##_pywrap(z);						\
      return (0);							\
    }									\
    return (1);								\
  }
COERCE(mp, MP)
COERCE(gf, GF)
#undef COERCE

static int mp_pycompare(PyObject *x, PyObject *y)
  { return mp_cmp(MP_X(x), MP_X(y)); }

static PyObject *mp_pynew(PyTypeObject *ty, PyObject *arg, PyObject *kw)
{
  PyObject *x;
  mp *z;
  mp_pyobj *zz = 0;
  int radix = 0;
  static const char *const kwlist[] = { "x", "radix", 0 };

  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");
  if ((z = mp_frompyobject(x, radix)) == 0) {
    PyErr_Format(PyExc_TypeError, "can't convert %.100s to mp",
		 x->ob_type->tp_name);
    goto end;
  }
  zz = (mp_pyobj *)ty->tp_alloc(ty, 0);
  zz->x = z;
end:
  return ((PyObject *)zz);
}

long mphash(mp *x)
{
  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;
  PyObject *z = 0;

  if (!PyArg_ParseTuple(arg, "O&:jacobi", convmp, &y)) goto end;
  z = PyInt_FromLong(mp_jacobi(y, MP_X(me)));
end:
  if (y) MP_DROP(y);
  return (z);
}

#define BITOP(pre, name, c)						\
  static PyObject *pre##meth_##name(PyObject *me, PyObject *arg)	\
  {									\
    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, clearbit, );
#undef BITOP

static PyObject *mpmeth_testbit(PyObject *me, PyObject *arg)
{
  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)
{
  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)
{
  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_sqrt(PyObject *me, PyObject *arg)
{
  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:
  return (0);
}

static PyObject *mpmeth_gcd(PyObject *me, PyObject *arg)
{
  mp *y = 0, *zz = MP_NEW;
  PyObject *z = 0;

  if (!PyArg_ParseTuple(arg, "O&:gcd", convmp, &y)) goto end;
  mp_gcd(&zz, 0, 0, MP_X(me), y);
  z = mp_pywrap(zz);
end:
  if (y) MP_DROP(y);
  return (z);
}

static PyObject *mpmeth_gcdx(PyObject *me, PyObject *arg)
{
  PyObject *z = 0;
  mp *yy = 0, *zz = MP_NEW, *uu = MP_NEW, *vv = MP_NEW;

  if (!PyArg_ParseTuple(arg, "O&:gcdx", convmp, &yy)) goto end;
  mp_gcd(&zz, &uu, &vv, MP_X(me), yy);
  z = Py_BuildValue("(NNN)",
		    mp_pywrap(zz), mp_pywrap(uu), mp_pywrap(vv));
end:
  if (yy) MP_DROP(yy);
  return (z);
}

static PyObject *mpmeth_modinv(PyObject *me, PyObject *arg)
{
  PyObject *z = 0;
  mp *yy = 0, *zz = MP_NEW;

  if (!PyArg_ParseTuple(arg, "O&:modinv", convmp, &yy) ||
      (zz = mp_modinv_checked(MP_NEW, yy, MP_X(me))) == 0)
    goto end;
  z = mp_pywrap(zz);
end:
  if (yy) MP_DROP(yy);
  return (z);
}

static PyObject *mpmeth_tostring(PyObject *me, PyObject *arg, PyObject *kw)
{
  int radix = 10;
  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));
end:
  return (0);
}

static PyObject *mpmeth_modsqrt(PyObject *me, PyObject *arg)
{
  PyObject *z = 0;
  mp *yy = 0, *zz = MP_NEW;

  if (!PyArg_ParseTuple(arg, "O&:modsqrt", convmp, &yy)) goto end;
  if ((zz = mp_modsqrt(MP_NEW, yy, MP_X(me))) == 0)
    VALERR("no modular square root");
  z = mp_pywrap(zz);
end:
  if (yy) MP_DROP(yy);
  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;							\
    static const char *const kwlist[] = { "len", 0 };					\
    PyObject *rc = 0;							\
									\
    if (!PyArg_ParseTupleAndKeywords(arg, kw, "|l:" #name,		\
				    KWLIST, &len))			\
      goto end;								\
    if (len < 0) {							\
      len = mp_octets##c(MP_X(me));					\
      if (!len) len = 1;						\
    }									\
    rc = bytestring_pywrap(0, len);					\
    mp_##name(MP_X(me), PyString_AS_STRING(rc), len);			\
  end:									\
    return (rc);							\
  }
STOREOP(storel, )
STOREOP(storeb, )
STOREOP(storel2c, 2c)
STOREOP(storeb2c, 2c)
#undef STOREOP

#define BUFOP(ty, pyty)							\
  static PyObject *meth__##pyty##_frombuf(PyObject *me, PyObject *arg)	\
  {									\
    buf b;								\
    char *p;								\
    Py_ssize_t sz;							\
    PyObject *rc = 0;							\
    mp *x;								\
									\
    if (!PyArg_ParseTuple(arg, "Os#:frombuf", &me, &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),				\
		       bytestring_pywrapbuf(&b));			\
  end:									\
    return (rc);							\
  }
BUFOP(mp, MP)
BUFOP(gf, GF)
#undef BUFOP

static PyObject *mpmeth_tobuf(PyObject *me, PyObject *arg)
{
  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);
  buf_init(&b, PyString_AS_STRING(rc), n);
  buf_putmp(&b, x);
  assert(BOK(&b));
  _PyString_Resize(&rc, BLEN(&b));
  return (rc);
}

static PyObject *mpmeth_primep(PyObject *me, PyObject *arg, PyObject *kw)
{
  grand *r = &rand_global;
  static const char *const kwlist[] = { "rng", 0 };
  PyObject *rc = 0;

  if (!PyArg_ParseTupleAndKeywords(arg, kw, "|O&", KWLIST, convgrand, &r))
    goto end;
  rc = getbool(pgen_primep(MP_X(me), r));
end:
  return (rc);
}

static PyObject *mpget_nbits(PyObject *me, void *hunoz)
  { return (PyInt_FromLong(mp_bits(MP_X(me)))); }

static PyObject *mpget_noctets(PyObject *me, void *hunoz)
  { return (PyInt_FromLong(mp_octets(MP_X(me)))); }

static PyObject *mpget_noctets2c(PyObject *me, void *hunoz)
  { return (PyInt_FromLong(mp_octets2c(MP_X(me)))); }

static 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")
  GET	(noctets2c,	"X.noctets2c -> two's complement octet length of X")
#undef GETSETNAME
  { 0 }
};

static PyMethodDef mp_pymethods[] = {
#define METHNAME(func) mpmeth_##func
  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)")
  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	(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")
  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")
#undef METHNAME
  { 0 }
};

static PyNumberMethods mp_pynumber = {
  mp_pyadd,				/* @nb_add@ */
  mp_pysub,				/* @nb_subtract@ */
  mp_pymul,				/* @nb_multiply@ */
  0,					/* @nb_divide@ */
  mp_pymod,				/* @nb_remainder@ */
  mp_pydivmod,				/* @nb_divmod@ */
  mp_pyexp,				/* @nb_power@ */
  mp_pyneg,				/* @nb_negative@ */
  mp_pyid,				/* @nb_positive@ */
  mp_pyabs,				/* @nb_absolute@ */
  mp_pynonzerop,			/* @nb_nonzero@ */
  mp_pynot2c,				/* @nb_invert@ */
  mp_pylsl2c,				/* @nb_lshift@ */
  mp_pylsr2c,				/* @nb_rshift@ */
  mp_pyand2c,				/* @nb_and@ */
  mp_pyxor2c,				/* @nb_xor@ */
  mp_pyor2c,				/* @nb_or@ */
  mp_pycoerce,				/* @nb_coerce@ */
  mp_pyint,				/* @nb_int@ */
  mp_pylong,				/* @nb_long@ */
  mp_pyfloat,				/* @nb_float@ */
  mp_pyoct,				/* @nb_oct@ */
  mp_pyhex,				/* @nb_hex@ */

  0,					/* @nb_inplace_add@ */
  0,					/* @nb_inplace_subtract@ */
  0,					/* @nb_inplace_multiply@ */
  0,					/* @nb_inplace_divide@ */
  0,					/* @nb_inplace_remainder@ */
  0,					/* @nb_inplace_power@ */
  0,					/* @nb_inplace_lshift@ */
  0,					/* @nb_inplace_rshift@ */
  0,					/* @nb_inplace_and@ */
  0,					/* @nb_inplace_xor@ */
  0,					/* @nb_inplace_or@ */

  mp_pydiv,				/* @nb_floor_divide@ */
  0,					/* @nb_true_divide@ */
  0,					/* @nb_inplace_floor_divide@ */
  0,					/* @nb_inplace_true_divide@ */
};

static PyTypeObject mp_pytype_skel = {
  PyObject_HEAD_INIT(0) 0,		/* Header */
  "MP",					/* @tp_name@ */
  sizeof(mp_pyobj),			/* @tp_basicsize@ */
  0,					/* @tp_itemsize@ */

  mp_pydealloc,				/* @tp_dealloc@ */
  0,					/* @tp_print@ */
  0,					/* @tp_getattr@ */
  0,					/* @tp_setattr@ */
  mp_pycompare,				/* @tp_compare@ */
  mp_pyrepr,				/* @tp_repr@ */
  &mp_pynumber,				/* @tp_as_number@ */
  0,					/* @tp_as_sequence@ */
  0,					/* @tp_as_mapping@ */
  mp_pyhash,				/* @tp_hash@ */
  0,					/* @tp_call@ */
  mp_pystr,				/* @tp_str@ */
  0,					/* @tp_getattro@ */
  0,					/* @tp_setattro@ */
  0,					/* @tp_as_buffer@ */
  Py_TPFLAGS_DEFAULT |			/* @tp_flags@ */
    Py_TPFLAGS_CHECKTYPES |
    Py_TPFLAGS_BASETYPE,

  /* @tp_doc@ */
"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@ */
  0,					/* @tp_richcompare@ */
  0,					/* @tp_weaklistoffset@ */
  0,					/* @tp_iter@ */
  0,					/* @tp_iternext@ */
  mp_pymethods,				/* @tp_methods@ */
  0,					/* @tp_members@ */
  mp_pygetset,				/* @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@ */
  mp_pynew,				/* @tp_new@ */
  0,					/* @tp_free@ */
  0					/* @tp_is_gc@ */
};

static PyObject *meth__MP_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[] = { "class", "x", "radix", 0 };

  if (!PyArg_ParseTupleAndKeywords(arg, kw, "Os#|i:fromstring",
				   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)
    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;								\
    Py_ssize_t len;							\
    if (!PyArg_ParseTuple(arg, "Os#:" #name, &me, &p, &len)) return (0); \
    return (pre##_pywrap(mp_##name(MP_NEW, p, len)));			\
  }
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

/*----- Products of small integers ----------------------------------------*/

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 *mmmeth_factor(PyObject *me, PyObject *arg)
{
  PyObject *q, *i;
  mp *x;

  if (!MPMUL_LIVEP(me)) VALERR("MPMul object invalid");
  if (PyTuple_Size(arg) != 1)
    i = PyObject_GetIter(arg);
  else {
    if ((q = PyTuple_GetItem(arg, 0)) == 0) goto end;
    if ((i = PyObject_GetIter(q)) == 0) {
      PyErr_Clear(); /* that's ok */
      i = PyObject_GetIter(arg);
    }
  }
  if (!i) goto end;
  while ((q = PyIter_Next(i)) != 0) {
    x = getmp(q); Py_DECREF(q); if (!x) {
      Py_DECREF(i);
      goto end;
    }
    mpmul_add(MPMUL_PY(me), x);
    MP_DROP(x);
  }
  Py_DECREF(i);
  RETURN_ME;
end:
  return (0);
}

static PyObject *mmmeth_done(PyObject *me, PyObject *arg)
{
  mp *x;

  if (!PyArg_ParseTuple(arg, ":done")) goto end;
  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);
}

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;
  }
  return ((PyObject *)mm);
end:
  return (0);
}

static PyObject *mmget_livep(PyObject *me, void *hunoz)
  { return (getbool(MPMUL_LIVEP(me))); }

static PyGetSetDef mpmul_pygetset[] = {
#define GETSETNAME(op, name) mm##op##_##name
  GET	(livep,			"MM.livep -> flag: object still valid?")
#undef GETSETNAME
  { 0 }
};

static PyMethodDef mpmul_pymethods[] = {
#define METHNAME(name) mmmeth_##name
  METH	(factor,		"MM.factor(ITERABLE) or MM.factor(I, ...)")
  METH	(done,			"MM.done() -> PRODUCT")
#undef METHNAME
  { 0 }
};

static PyTypeObject *mpmul_pytype, mpmul_pytype_skel = {
  PyObject_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@ */
  mpmul_pymethods,			/* @tp_methods@ */
  0,					/* @tp_members@ */
  mpmul_pygetset,			/* @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 ----------------------------------------------*/

typedef struct mpmont_pyobj {
  PyObject_HEAD
  mpmont mm;
} mpmont_pyobj;

#define MPMONT_PY(o) (&((mpmont_pyobj *)(o))->mm)

static PyObject *mmmeth_int(PyObject *me, PyObject *arg)
{
  PyObject *z = 0;
  mp *yy = 0;
  mpmont *mm = MPMONT_PY(me);

  if (!PyArg_ParseTuple(arg, "O&:in", convmp, &yy))
    goto end;
  mp_div(0, &yy, yy, mm->m);
  z = mp_pywrap(mpmont_mul(mm, MP_NEW, yy, mm->r2));
end:
  if (yy) MP_DROP(yy);
  return (z);
}

static PyObject *mmmeth_mul(PyObject *me, PyObject *arg)
{
  PyObject *rc = 0;
  mp *yy = 0, *zz = 0;

  if (!PyArg_ParseTuple(arg, "O&O&:mul", convmp, &yy, convmp, &zz))
    goto end;
  rc = mp_pywrap(mpmont_mul(MPMONT_PY(me), MP_NEW, yy, zz));
end:
  if (yy) MP_DROP(yy); if (zz) MP_DROP(zz);
  return (rc);
}

static PyObject *mmmeth_exp(PyObject *me, PyObject *arg)
{
  PyObject *rc = 0;
  mp *yy = 0, *zz = 0;

  if (!PyArg_ParseTuple(arg, "O&O&:exp", convmp, &yy, convmp, &zz))
    goto end;
  if (MP_NEGP(zz)) {
    if ((yy = mp_modinv_checked(yy, yy, MPMONT_PY(me)->m)) == 0) goto end;
    zz = mp_neg(zz, zz);
  }
  rc = mp_pywrap(mpmont_exp(MPMONT_PY(me), MP_NEW, yy, zz));
end:
  if (yy) MP_DROP(yy); if (zz) MP_DROP(zz);
  return (rc);
}

static PyObject *mmmeth_expr(PyObject *me, PyObject *arg)
{
  PyObject *rc = 0;
  mp *yy = 0, *zz = 0;

  if (!PyArg_ParseTuple(arg, "O&O&:expr", convmp, &yy, convmp, &zz))
    goto end;
  if (MP_NEGP(zz)) {
    yy = mpmont_reduce(MPMONT_PY(me), yy, yy);
    if ((yy = mp_modinv_checked(yy, yy, MPMONT_PY(me)->m)) == 0) goto end;
    yy = mpmont_mul(MPMONT_PY(me), yy, yy, MPMONT_PY(me)->r2);
    zz = mp_neg(zz, zz);
  }
  rc = mp_pywrap(mpmont_expr(MPMONT_PY(me), MP_NEW, yy, zz));
end:
  if (yy) MP_DROP(yy); if (zz) MP_DROP(zz);
  return (rc);
}

static PyObject *mm_mexpr_id(PyObject *me)
  { return mp_pywrap(MP_COPY(MPMONT_PY(me)->r)); }

static int mm_mexpr_fill(void *p, PyObject *me, PyObject *x, PyObject *y)
{
  mp *xx = 0, *yy = 0;
  mp_expfactor *f = p;
  mpmont *mm = MPMONT_PY(me);

  if ((xx = getmp(x)) == 0 || (yy = getmp(y)) == 0)
    goto fail;
  if (MP_NEGP(yy)) {
    xx = mpmont_reduce(mm, xx, xx);
    if ((xx = mp_modinv_checked(xx, xx, yy)) == 0)
      goto fail;
    xx = mpmont_mul(mm, xx, xx, mm->r2);
    yy = mp_neg(yy, yy);
  }
  f->base = xx;
  f->exp = yy;
  return (0);

fail:
  mp_drop(xx); mp_drop(yy);
  return (-1);
}

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;
  mp_drop(f->base);
  mp_drop(f->exp);
}

static PyObject *mmmeth_mexpr(PyObject *me, PyObject *arg)
{
  return mexp_common(me, arg, sizeof(mp_expfactor),
		     mm_mexpr_id, mm_mexpr_fill, mm_mexpr, mp_mexp_drop);
}

static PyObject *mp_mexp_id(PyObject *me)
  { return mp_pywrap(MP_ONE); }

static int mp_mexp_fill(void *p, PyObject *me, PyObject *x, PyObject *y)
{
  mp *xx = 0, *yy = 0;
  mp_expfactor *f = p;

  if ((xx = getmp(x)) == 0 || (yy = getmp(y)) == 0)
    goto fail;
  if (MP_NEGP(yy)) {
    if ((xx = mp_modinv_checked(xx, xx, yy)) == 0)
      goto fail;
    yy = mp_neg(yy, yy);
  }
  f->base = xx;
  f->exp = yy;
  return (0);

fail:
  mp_drop(xx); mp_drop(yy);
  return (-1);
}

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),
		     mp_mexp_id, mp_mexp_fill, mm_mexp, mp_mexp_drop);
}

#define mmmeth_ext mmmeth_reduce
static PyObject *mmmeth_reduce(PyObject *me, PyObject *arg)
{
  PyObject *z = 0;
  mp *yy = 0;

  if (!PyArg_ParseTuple(arg, "O&", convmp, &yy)) goto end;
  z = mp_pywrap(mpmont_reduce(MPMONT_PY(me), MP_NEW, yy));
end:
  return (z);
}

static void mpmont_pydealloc(PyObject *me)
{
  mpmont_destroy(MPMONT_PY(me));
  FREEOBJ(me);
}

static PyObject *mpmont_pynew(PyTypeObject *ty, PyObject *arg, PyObject *kw)
{
  mpmont_pyobj *mm = 0;
  static const char *const kwlist[] = { "m", 0 };
  mp *xx = 0;

  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);
  mpmont_create(&mm->mm, xx);
end:
  if (xx) MP_DROP(xx);
  return ((PyObject *)mm);
}

static PyObject *mmget_m(PyObject *me, void *hunoz)
  { return (mp_pywrap(MP_COPY(MPMONT_PY(me)->m))); }

static PyObject *mmget_r(PyObject *me, void *hunoz)
  { return (mp_pywrap(MP_COPY(MPMONT_PY(me)->r))); }

static PyObject *mmget_r2(PyObject *me, void *hunoz)
  { return (mp_pywrap(MP_COPY(MPMONT_PY(me)->r2))); }

static PyGetSetDef mpmont_pygetset[] = {
#define GETSETNAME(op, name) mm##op##_##name
  GET	(m,		"M.m -> modulus for reduction")
  GET	(r,		"M.r -> multiplicative identity")
  GET	(r2,		"M.r2 -> M.r^2, Montgomerization factor")
#undef GETSETNAME
  { 0 }
};

static PyMethodDef mpmont_pymethods[] = {
#define METHNAME(name) mmmeth_##name
  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,		"\
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,		"\
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 */
  "MPMont",				/* @tp_name@ */
  sizeof(mpmont_pyobj),			/* @tp_basicsize@ */
  0,					/* @tp_itemsize@ */

  mpmont_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@ */
"MPMont(N): a Montgomery reduction context.",

  0,					/* @tp_traverse@ */
  0,					/* @tp_clear@ */
  0,					/* @tp_richcompare@ */
  0,					/* @tp_weaklistoffset@ */
  0,					/* @tp_iter@ */
  0,					/* @tp_iternext@ */
  mpmont_pymethods,			/* @tp_methods@ */
  0,					/* @tp_members@ */
  mpmont_pygetset,			/* @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@ */
  mpmont_pynew,				/* @tp_new@ */
  0,					/* @tp_free@ */
  0					/* @tp_is_gc@ */
};

/*----- Barrett reduction -------------------------------------------------*/

typedef struct mpbarrett_pyobj {
  PyObject_HEAD
  mpbarrett mb;
} mpbarrett_pyobj;

#define MPBARRETT_PY(o) (&((mpbarrett_pyobj *)(o))->mb)

static PyObject *mbmeth_exp(PyObject *me, PyObject *arg)
{
  PyObject *rc = 0;
  mp *yy = 0, *zz = 0;

  if (!PyArg_ParseTuple(arg, "O&O&:exp", convmp, &yy, convmp, &zz))
    goto end;
  if (MP_NEGP(zz)) {
    if ((yy = mp_modinv_checked(yy, yy, MPBARRETT_PY(me)->m)) == 0) goto end;
    zz = mp_neg(zz, zz);
  }
  rc = mp_pywrap(mpbarrett_exp(MPBARRETT_PY(me), MP_NEW, yy, zz));
end:
  if (yy) MP_DROP(yy); if (zz) MP_DROP(zz);
  return (rc);
}

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),
		     mp_mexp_id, mp_mexp_fill, mb_mexp, mp_mexp_drop);
}

static PyObject *mbmeth_reduce(PyObject *me, PyObject *arg)
{
  PyObject *z = 0;
  mp *yy = 0;

  if (!PyArg_ParseTuple(arg, "O&:reduce", convmp, &yy))
    goto end;
  z = mp_pywrap(mpbarrett_reduce(MPBARRETT_PY(me), MP_NEW, yy));
end:
  return (z);
}

static void mpbarrett_pydealloc(PyObject *me)
{
  mpbarrett_destroy(MPBARRETT_PY(me));
  FREEOBJ(me);
}

static PyObject *mpbarrett_pynew(PyTypeObject *ty,
				 PyObject *arg, PyObject *kw)
{
  mpbarrett_pyobj *mb = 0;
  static const char *const kwlist[] = { "m", 0 };
  mp *xx = 0;

  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);
  mpbarrett_create(&mb->mb, xx);
end:
  if (xx) MP_DROP(xx);
  return ((PyObject *)mb);
}

static PyObject *mbget_m(PyObject *me, void *hunoz)
  { return (mp_pywrap(MP_COPY(MPBARRETT_PY(me)->m))); }

static PyGetSetDef mpbarrett_pygetset[] = {
#define GETSETNAME(op, name) mb##op##_##name
  GET	(m,		"B.m -> modulus for reduction")
#undef GETSETNAME
  { 0 }
};

static 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.)")
#undef METHNAME
  { 0 }
};

static PyTypeObject *mpbarrett_pytype, mpbarrett_pytype_skel = {
  PyObject_HEAD_INIT(0) 0,		/* Header */
  "MPBarrett",				/* @tp_name@ */
  sizeof(mpbarrett_pyobj),		/* @tp_basicsize@ */
  0,					/* @tp_itemsize@ */

  mpbarrett_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@ */
"MPBarrett(N): a Barrett reduction context.",

  0,					/* @tp_traverse@ */
  0,					/* @tp_clear@ */
  0,					/* @tp_richcompare@ */
  0,					/* @tp_weaklistoffset@ */
  0,					/* @tp_iter@ */
  0,					/* @tp_iternext@ */
  mpbarrett_pymethods,			/* @tp_methods@ */
  0,					/* @tp_members@ */
  mpbarrett_pygetset,			/* @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@ */
  mpbarrett_pynew,			/* @tp_new@ */
  0,					/* @tp_free@ */
  0					/* @tp_is_gc@ */
};

/*----- Nice prime reduction ----------------------------------------------*/

typedef struct mpreduce_pyobj {
  PyObject_HEAD
  mpreduce mr;
} mpreduce_pyobj;

#define MPREDUCE_PY(o) (&((mpreduce_pyobj *)(o))->mr)

static PyObject *mrmeth_exp(PyObject *me, PyObject *arg)
{
  PyObject *rc = 0;
  mp *yy = 0, *zz = 0;

  if (!PyArg_ParseTuple(arg, "O&O&:exp", convmp, &yy, convmp, &zz))
    goto end;
  if (MP_NEGP(zz)) {
    if ((yy = mp_modinv_checked(yy, yy, MPREDUCE_PY(me)->p)) == 0) goto end;
    zz = mp_neg(zz, zz);
  }
  rc = mp_pywrap(mpreduce_exp(MPREDUCE_PY(me), MP_NEW, yy, zz));
end:
  if (yy) MP_DROP(yy); if (zz) MP_DROP(zz);
  return (rc);
}

static PyObject *mrmeth_reduce(PyObject *me, PyObject *arg)
{
  PyObject *z = 0;
  mp *yy = 0;

  if (!PyArg_ParseTuple(arg, "O&:reduce", convmp, &yy)) goto end;
  z = mp_pywrap(mpreduce_do(MPREDUCE_PY(me), MP_NEW, yy));
end:
  return (z);
}

static void mpreduce_pydealloc(PyObject *me)
{
  mpreduce_destroy(MPREDUCE_PY(me));
  FREEOBJ(me);
}

static PyObject *mpreduce_pynew(PyTypeObject *ty,
				 PyObject *arg, PyObject *kw)
{
  mpreduce_pyobj *mr = 0;
  mpreduce r;
  static const char *const kwlist[] = { "m", 0 };
  mp *xx = 0;

  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 - ...)");
  mr = (mpreduce_pyobj *)ty->tp_alloc(ty, 0);
  mr->mr = r;
end:
  if (xx) MP_DROP(xx);
  return ((PyObject *)mr);
}

static PyObject *mrget_m(PyObject *me, void *hunoz)
  { return (mp_pywrap(MP_COPY(MPREDUCE_PY(me)->p))); }

static PyGetSetDef mpreduce_pygetset[] = {
#define GETSETNAME(op, name) mr##op##_##name
  GET	(m,		"R.m -> modulus for reduction")
#undef GETSETNAME
  { 0 }
};

static 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")
#undef METHNAME
  { 0 }
};

static PyTypeObject *mpreduce_pytype, mpreduce_pytype_skel = {
  PyObject_HEAD_INIT(0) 0,		/* Header */
  "MPReduce",				/* @tp_name@ */
  sizeof(mpreduce_pyobj),		/* @tp_basicsize@ */
  0,					/* @tp_itemsize@ */

  mpreduce_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@ */
"MPReduce(N): a reduction context for reduction modulo Solinas primes.",

  0,					/* @tp_traverse@ */
  0,					/* @tp_clear@ */
  0,					/* @tp_richcompare@ */
  0,					/* @tp_weaklistoffset@ */
  0,					/* @tp_iter@ */
  0,					/* @tp_iternext@ */
  mpreduce_pymethods,			/* @tp_methods@ */
  0,					/* @tp_members@ */
  mpreduce_pygetset,			/* @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@ */
  mpreduce_pynew,			/* @tp_new@ */
  0,					/* @tp_free@ */
  0					/* @tp_is_gc@ */
};

/*----- Chinese Remainder Theorem solution --------------------------------*/

typedef struct mpcrt_pyobj {
  PyObject_HEAD
  mpcrt c;
} mpcrt_pyobj;

#define MPCRT_PY(o) (&((mpcrt_pyobj *)(o))->c)

static PyObject *mcmeth_solve(PyObject *me, PyObject *arg)
{
  mpcrt *c = MPCRT_PY(me);
  PyObject *q = 0, *x, *z = 0;
  mp *xx;
  mp **v = 0;
  Py_ssize_t i = 0, n = c->k;

  Py_INCREF(me);
  if (PyTuple_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");
  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;
    xx = getmp(x); Py_DECREF(x); if (!xx) goto end;
    v[i] = xx;
  }
  z = mp_pywrap(mpcrt_solve(c, MP_NEW, v));
end:
  if (v) {
    n = i;
    for (i = 0; i < n; i++)
      MP_DROP(v[i]);
    xfree(v);
  }
  Py_DECREF(me);
  Py_XDECREF(q);
  return (z);
}

static void mpcrt_pydealloc(PyObject *me)
{
  mpcrt *c = MPCRT_PY(me);
  mpcrt_destroy(c);
  xfree(c->v);
}

static PyObject *mpcrt_pynew(PyTypeObject *ty, PyObject *arg, PyObject *kw)
{
  mpcrt_mod *v = 0;
  Py_ssize_t n, i = 0, j;
  static const char *const kwlist[] = { "mv", 0 };
  PyObject *q = 0, *x;
  mp *xx = MP_NEW, *y = MP_NEW, *g = MP_NEW;
  mpmul mm;
  mpcrt_pyobj *c = 0;

  if (PyTuple_Size(arg) > 1)
    q = arg;
  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 (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;
    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:
  if (v) {
    n = i;
    for (i = 0; i < n; i++)
      MP_DROP(v[i].m);
    xfree(v);
  }
  Py_XDECREF(q);
  mp_drop(xx); mp_drop(y); mp_drop(g);
  return (0);
}

static PyObject *mcget_product(PyObject *me, void *hunoz)
  { return (mp_pywrap(MP_COPY(MPCRT_PY(me)->mb.m))); }

static PyObject *mcget_moduli(PyObject *me, void *hunoz)
{
  int i;
  PyObject *q;
  mpcrt *c = MPCRT_PY(me);

  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));
  return (q);
}

static 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")
#undef GETSETNAME
  { 0 }
};

static 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 */
  "MPCRT",				/* @tp_name@ */
  sizeof(mpcrt_pyobj),			/* @tp_basicsize@ */
  0,					/* @tp_itemsize@ */

  mpcrt_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@ */
"MPCRT(SEQ): a context for solving Chinese Remainder Theorem problems.",

  0,					/* @tp_traverse@ */
  0,					/* @tp_clear@ */
  0,					/* @tp_richcompare@ */
  0,					/* @tp_weaklistoffset@ */
  0,					/* @tp_iter@ */
  0,					/* @tp_iternext@ */
  mpcrt_pymethods,			/* @tp_methods@ */
  0,					/* @tp_members@ */
  mpcrt_pygetset,			/* @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@ */
  mpcrt_pynew,				/* @tp_new@ */
  0,					/* @tp_free@ */
  0					/* @tp_is_gc@ */
};

/*----- Binary polynomials ------------------------------------------------*/

static PyObject *gf_pyrepr(PyObject *o)
  { return mp_topystring(MP_X(o), 16, "GF(", "0x", "L)"); }

static PyObject *gf_pyrichcompare(PyObject *x, PyObject *y, int op)
{
  mp *xx, *yy;
  int xl, yl;
  int b;

  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;
    default:
      xl = mp_bits(xx);
      yl = mp_bits(yy);
      switch (op) {
	case Py_LT: b = xl < yl; break;
	case Py_LE: b = xl <= yl; break;
	case Py_GT: b = xl > yl; break;
	case Py_GE: b = xl >= yl; break;
	default: abort();
      }
      break;
  }
  MP_DROP(xx); MP_DROP(yy);
  return (getbool(b));
}

static PyObject *gf_pynew(PyTypeObject *ty, PyObject *arg, PyObject *kw)
{
  PyObject *x;
  mp *z;
  mp_pyobj *zz = 0;
  int radix = 0;
  static const char *const kwlist[] = { "x", "radix", 0 };

  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");
  if ((z = mp_frompyobject(x, radix)) == 0) {
    PyErr_Format(PyExc_TypeError, "can't convert %.100s to gf",
		 x->ob_type->tp_name);
    goto end;
  }
  if (MP_NEGP(z)) {
    MP_DROP(z);
    VALERR("gf cannot be negative");
  }
  zz = (mp_pyobj *)ty->tp_alloc(ty, 0);
  zz->x = z;
end:
  return ((PyObject *)zz);
}

static PyObject *gf_pyexp(PyObject *x, PyObject *y, PyObject *z)
{
  mp *xx = 0, *yy = 0, *zz = 0;
  mp *r = 0;
  PyObject *rc = 0;

  if ((xx = tomp(x)) == 0 || (yy = tomp(y)) == 0 ||
      (z && z != Py_None && (zz = tomp(z)) == 0)) {
    mp_drop(xx); mp_drop(yy); mp_drop(zz);
    RETURN_NOTIMPL;
  }
  if (!z || z == Py_None) {
    if (MP_NEGP(yy)) VALERR("negative exponent");
    r = gf_exp(MP_NEW, xx, yy);
  } else {
    gfreduce gr;
    if (MP_ZEROP(zz)) ZDIVERR("zero modulus");
    if (MP_NEGP(yy)) {
      if ((xx = gf_modinv_checked(xx, xx, zz)) == 0) goto end;
      yy = mp_neg(yy, yy);
    }
    gfreduce_create(&gr, zz);
    r = gfreduce_exp(&gr, MP_NEW, xx, yy);
    gfreduce_destroy(&gr);
  }
  rc = gf_pywrap(r);
end:
  mp_drop(xx); mp_drop(yy); mp_drop(zz);
  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_gcd(PyObject *me, PyObject *arg)
{
  PyObject *z = 0;
  mp *yy = 0, *zz = MP_NEW;

  if (!PyArg_ParseTuple(arg, "O&:gcd", convgf, &yy)) goto end;
  gf_gcd(&zz, 0, 0, MP_X(me), yy);
  z = gf_pywrap(zz);
end:
  if (yy) MP_DROP(yy);
  return (z);
}

static PyObject *gfmeth_gcdx(PyObject *me, PyObject *arg)
{
  PyObject *z = 0;
  mp *yy = 0, *zz = MP_NEW, *uu = MP_NEW, *vv = MP_NEW;

  if (!PyArg_ParseTuple(arg, "O&:gcdx", convgf, &yy))
    goto end;
  gf_gcd(&zz, &uu, &vv, MP_X(me), yy);
  z = Py_BuildValue("(NNN)",
		    gf_pywrap(zz), gf_pywrap(uu), gf_pywrap(vv));
end:
  if (yy) MP_DROP(yy);
  return (z);
}

static PyObject *gfmeth_modinv(PyObject *me, PyObject *arg)
{
  PyObject *z = 0;
  mp *yy = 0, *zz = MP_NEW;

  if (!PyArg_ParseTuple(arg, "O&:modinv", convgf, &yy) ||
      (zz = gf_modinv_checked(MP_NEW, yy, MP_X(me))) == 0)
    goto end;
  z = gf_pywrap(zz);
end:
  if (yy) MP_DROP(yy);
  return (z);
}

static PyObject *gfmeth_irreduciblep(PyObject *me, PyObject *arg)
{
  if (!PyArg_ParseTuple(arg, ":irreduciblep")) return (0);
  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[] = {
#define GETSETNAME(op, name) gf##op##_##name
  GET	(degree,	"X.degree -> polynomial degree of X")
#undef GETSETNAME
#define GETSETNAME(op, name) mp##op##_##name
  GET	(nbits,		"X.nbits -> bit length of X")
  GET	(noctets,	"X.noctets -> octet length of X")
#undef GETSETNAME
  { 0 }
};

static 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")
  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	(modinv,	"X.modinv(Y) -> multiplicative inverse of Y mod X")
  METH	(irreduciblep,	"X.irreduciblep() -> true/false")
#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")
#undef METHNAME
  { 0 }
};

static PyNumberMethods gf_pynumber = {
  gf_pyadd,				/* @nb_add@ */
  gf_pysub,				/* @nb_subtract@ */
  gf_pymul,				/* @nb_multiply@ */
  0,					/* @nb_divide@ */
  gf_pymod,				/* @nb_remainder@ */
  gf_pydivmod,				/* @nb_divmod@ */
  gf_pyexp,				/* @nb_power@ */
  mp_pyid,				/* @nb_negative@ */
  mp_pyid,				/* @nb_positive@ */
  mp_pyid,				/* @nb_absolute@ */
  mp_pynonzerop,			/* @nb_nonzero@ */
  0 /* doesn't make any sense */,	/* @nb_invert@ */
  gf_pylsl,				/* @nb_lshift@ */
  gf_pylsr,				/* @nb_rshift@ */
  gf_pyand,				/* @nb_and@ */
  gf_pyxor,				/* @nb_xor@ */
  gf_pyor,				/* @nb_or@ */
  gf_pycoerce,				/* @nb_coerce@ */
  mp_pyint,				/* @nb_int@ */
  mp_pylong,				/* @nb_long@ */
  0 /* doesn't make any sense */,	/* @nb_float@ */
  mp_pyoct,				/* @nb_oct@ */
  mp_pyhex,				/* @nb_hex@ */

  0,					/* @nb_inplace_add@ */
  0,					/* @nb_inplace_subtract@ */
  0,					/* @nb_inplace_multiply@ */
  0,					/* @nb_inplace_divide@ */
  0,					/* @nb_inplace_remainder@ */
  0,					/* @nb_inplace_power@ */
  0,					/* @nb_inplace_lshift@ */
  0,					/* @nb_inplace_rshift@ */
  0,					/* @nb_inplace_and@ */
  0,					/* @nb_inplace_xor@ */
  0,					/* @nb_inplace_or@ */

  gf_pydiv,				/* @nb_floor_divide@ */
  0,					/* @nb_true_divide@ */
  0,					/* @nb_inplace_floor_divide@ */
  0,					/* @nb_inplace_true_divide@ */
};

static PyTypeObject gf_pytype_skel = {
  PyObject_HEAD_INIT(0) 0,		/* Header */
  "GF",					/* @tp_name@ */
  sizeof(mp_pyobj),			/* @tp_basicsize@ */
  0,					/* @tp_itemsize@ */

  mp_pydealloc,				/* @tp_dealloc@ */
  0,					/* @tp_print@ */
  0,					/* @tp_getattr@ */
  0,					/* @tp_setattr@ */
  0,					/* @tp_compare@ */
  gf_pyrepr,				/* @tp_repr@ */
  &gf_pynumber,				/* @tp_as_number@ */
  0,					/* @tp_as_sequence@ */
  0,					/* @tp_as_mapping@ */
  mp_pyhash,				/* @tp_hash@ */
  0,					/* @tp_call@ */
  mp_pyhex,				/* @tp_str@ */
  0,					/* @tp_getattro@ */
  0,					/* @tp_setattro@ */
  0,					/* @tp_as_buffer@ */
  Py_TPFLAGS_DEFAULT |			/* @tp_flags@ */
    Py_TPFLAGS_CHECKTYPES |
    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 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@ */
  gf_pyrichcompare,			/* @tp_richcompare@ */
  0,					/* @tp_weaklistoffset@ */
  0,					/* @tp_iter@ */
  0,					/* @tp_iternext@ */
  gf_pymethods,				/* @tp_methods@ */
  0,					/* @tp_members@ */
  gf_pygetset,				/* @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@ */
  gf_pynew,				/* @tp_new@ */
  0,					/* @tp_free@ */
  0					/* @tp_is_gc@ */
};

static PyObject *meth__GF_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[] = { "class", "x", "radix", 0 };

  if (!PyArg_ParseTupleAndKeywords(arg, kw, "Os#|i:fromstring",
				   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 ||
      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);
}

/*----- Sparse poly reduction ---------------------------------------------*/

typedef struct gfreduce_pyobj {
  PyObject_HEAD
  gfreduce mr;
} gfreduce_pyobj;

#define GFREDUCE_PY(o) (&((gfreduce_pyobj *)(o))->mr)

static PyObject *grmeth_exp(PyObject *me, PyObject *arg)
{
  PyObject *rc = 0;
  mp *yy = 0, *zz = 0;

  if (!PyArg_ParseTuple(arg, "O&O&:exp", convgf, &yy, convgf, &zz))
    goto end;
  if (MP_NEGP(zz)) {
    if ((yy = gf_modinv_checked(yy, yy, GFREDUCE_PY(me)->p)) == 0) goto end;
    zz = mp_neg(zz, zz);
  }
  rc = gf_pywrap(gfreduce_exp(GFREDUCE_PY(me), MP_NEW, yy, zz));
end:
  if (yy) MP_DROP(yy); if (zz) MP_DROP(zz);
  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;
  mp *yy = 0;

  if (!PyArg_ParseTuple(arg, "O&:reduce", convgf, &yy)) goto end;
  z = gf_pywrap(gfreduce_do(GFREDUCE_PY(me), MP_NEW, yy));
end:
  return (z);
}

static void gfreduce_pydealloc(PyObject *me)
{
  gfreduce_destroy(GFREDUCE_PY(me));
  FREEOBJ(me);
}

static PyObject *gfreduce_pynew(PyTypeObject *ty,
				 PyObject *arg, PyObject *kw)
{
  gfreduce_pyobj *mr = 0;
  gfreduce r;
  static const char *const kwlist[] = { "m", 0 };
  mp *xx = 0;

  if (!PyArg_ParseTupleAndKeywords(arg, kw, "O&:new", KWLIST, convgf, &xx))
    goto end;
  if (MP_ZEROP(xx)) ZDIVERR("modulus is zero!");
  gfreduce_create(&r, xx);
  mr = (gfreduce_pyobj *)ty->tp_alloc(ty, 0);
  mr->mr = r;
end:
  if (xx) MP_DROP(xx);
  return ((PyObject *)mr);
}

static PyObject *grget_m(PyObject *me, void *hunoz)
  { return (gf_pywrap(MP_COPY(GFREDUCE_PY(me)->p))); }

static PyGetSetDef gfreduce_pygetset[] = {
#define GETSETNAME(op, name) gr##op##_##name
  GET	(m,		"R.m -> reduction polynomial")
#undef GETSETNAME
  { 0 }
};

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 }
};

static PyTypeObject *gfreduce_pytype, gfreduce_pytype_skel = {
  PyObject_HEAD_INIT(0) 0,		/* Header */
  "GFReduce",				/* @tp_name@ */
  sizeof(gfreduce_pyobj),		/* @tp_basicsize@ */
  0,					/* @tp_itemsize@ */

  gfreduce_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@ */
"GFReduce(N): a context for reduction modulo sparse polynomials.",

  0,					/* @tp_traverse@ */
  0,					/* @tp_clear@ */
  0,					/* @tp_richcompare@ */
  0,					/* @tp_weaklistoffset@ */
  0,					/* @tp_iter@ */
  0,					/* @tp_iternext@ */
  gfreduce_pymethods,			/* @tp_methods@ */
  0,					/* @tp_members@ */
  gfreduce_pygetset,			/* @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@ */
  gfreduce_pynew,			/* @tp_new@ */
  0,					/* @tp_free@ */
  0					/* @tp_is_gc@ */
};

/*----- Normal/poly transformation ----------------------------------------*/

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)

static PyObject *gfn_pynew(PyTypeObject *ty, PyObject *arg, PyObject *kw)
{
  mp *p = 0, *beta = 0;
  gfn_pyobj *gg = 0;
  static const char *const kwlist[] = { "p", "beta", 0 };

  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)) {
    Py_DECREF(gg);
    gg = 0;
    VALERR("can't invert transformation matrix");
  }
  gg->p = MP_COPY(p);
end:
  mp_drop(p);
  mp_drop(beta);
  return ((PyObject *)gg);
}

static PyObject *gfnget_p(PyObject *me, void *hunoz)
  { return (gf_pywrap(MP_COPY(GFN_P(me)))); }

static PyObject *gfnget_beta(PyObject *me, void *hunoz)
{
  gfn *n = GFN_NTOP(me);
  mp *x = n->r[n->n - 1];
  return (gf_pywrap(MP_COPY(x)));
}

#define XFORMOP(name, NAME)						\
  static PyObject *gfnmeth_##name(PyObject *me, PyObject *arg)		\
  {									\
    mp *xx = 0;								\
    mp *z = 0;								\
									\
    if (!PyArg_ParseTuple(arg, "O&:" #name, convgf, &xx)) goto end;	\
    z = gfn_transform(GFN_##NAME(me), MP_NEW, xx);			\
  end:									\
    mp_drop(xx);							\
    if (!z) return (0);							\
    return (gf_pywrap(z));						\
  }
XFORMOP(pton, PTON)
XFORMOP(ntop, NTOP)
#undef XFORMOP

static void gfn_pydealloc(PyObject *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[] = {
#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")
#undef GETSETNAME
  { 0 }
};

static 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")
#undef METHNAME
  { 0 }
};

static PyTypeObject gfn_pytype_skel = {
  PyObject_HEAD_INIT(0) 0,		/* Header */
  "GFN",				/* @tp_name@ */
  sizeof(gfn_pyobj),			/* @tp_basicsize@ */
  0,					/* @tp_itemsize@ */

  gfn_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@ */
"GFN(P, BETA): an object for transforming elements of binary fields\n\
  between polynomial and normal basis representations.",

  0,					/* @tp_traverse@ */
  0,					/* @tp_clear@ */
  0,					/* @tp_richcompare@ */
  0,					/* @tp_weaklistoffset@ */
  0,					/* @tp_iter@ */
  0,					/* @tp_iternext@ */
  gfn_pymethods,			/* @tp_methods@ */
  0,					/* @tp_members@ */
  gfn_pygetset,				/* @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@ */
  gfn_pynew,				/* @tp_new@ */
  0,					/* @tp_free@ */
  0					/* @tp_is_gc@ */
};

/*----- 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_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,		"\
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	(_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
  { 0 }
};

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);
  INSERT("MPCRT", mpcrt_pytype);
  INSERT("GF", gf_pytype);
  INSERT("GFReduce", gfreduce_pytype);
  INSERT("GFN", gfn_pytype);
}

/*----- That's all, folks -------------------------------------------------*/