3 * Multiprecision arithmetic
5 * (c) 2004 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of the Python interface to Catacomb.
12 * Catacomb/Python is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU General Public License as published by
14 * the Free Software Foundation; either version 2 of the License, or
15 * (at your option) any later version.
17 * Catacomb/Python is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU General Public License for more details.
22 * You should have received a copy of the GNU General Public License
23 * along with Catacomb/Python; if not, write to the Free Software Foundation,
24 * Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
27 /*----- Header files ------------------------------------------------------*/
29 #include "catacomb-python.h"
31 /*----- General utilities -------------------------------------------------*/
33 PyTypeObject
*mp_pytype
= 0;
34 PyTypeObject
*gf_pytype
= 0;
37 # define PyLong_SHIFT SHIFT
41 # define PyLong_MASK MASK
44 STATIC_ASSERT(MPW_BITS
>= PyLong_SHIFT
,
45 "Catacomb's limbs are now narrower than than Python's!");
47 mp
*mp_frompylong(PyObject
*obj
)
50 PyLongObject
*l
= (PyLongObject
*)obj
;
61 bits
= (unsigned long)sz
* PyLong_SHIFT
;
62 w
= (bits
+ MPW_BITS
- 1)/MPW_BITS
;
63 x
= mp_new(w
, Py_SIZE(l
) < 0 ? MP_NEG
: 0);
65 for (i
= 0; i
< sz
; i
++) {
66 r
|= (mpd
)l
->ob_digit
[i
] << b
;
68 while (b
>= MPW_BITS
) {
83 PyObject
*mp_topylong(mp
*x
)
85 unsigned long bits
= mp_bits(x
);
86 int sz
= (bits
+ PyLong_SHIFT
- 1)/PyLong_SHIFT
;
87 PyLongObject
*l
= _PyLong_New(sz
);
93 while (i
< sz
&& p
< x
->vl
) {
96 while (i
< sz
&& b
>= PyLong_SHIFT
) {
97 l
->ob_digit
[i
++] = r
& PyLong_MASK
;
102 while (i
< sz
&& r
) {
103 l
->ob_digit
[i
++] = r
& PyLong_MASK
;
106 Py_SIZE(l
) = (x
->f
& MP_NEG
) ?
-sz
: sz
;
107 return ((PyObject
*)l
);
110 mp
*mp_frompyobject(PyObject
*o
, int radix
)
118 TEXT_PTRLEN(o
, sc
.buf
, sz
); sc
.lim
= sc
.buf
+ sz
;
119 x
= mp_read(MP_NEW
, radix
, &mptext_stringops
, &sc
);
121 if (sc
.buf
< sc
.lim
) { MP_DROP(x
); return (0); }
124 if ((x
= tomp(o
)) != 0)
129 PyObject
*mp_topystring(mp
*x
, int radix
, const char *xpre
,
130 const char *pre
, const char *post
)
132 int len
= mptext_len(x
, radix
) + 1;
135 size_t xprelen
= xpre ?
strlen(xpre
) : 0;
136 size_t prelen
= pre ?
strlen(pre
) : 0;
137 size_t postlen
= post ?
strlen(post
) : 0;
140 TEXT_PREPAREWRITE(o
, p
, len
+ 1 + xprelen
+ prelen
+ postlen
);
142 if (xpre
) { memcpy(sc
.buf
, xpre
, xprelen
); sc
.buf
+= xprelen
; }
143 if (MP_NEGP(x
)) { *sc
.buf
++ = '-'; x
= mp_neg(x
, x
); }
144 if (pre
) { memcpy(sc
.buf
, pre
, prelen
); sc
.buf
+= prelen
; }
145 sc
.lim
= sc
.buf
+ len
;
146 mp_write(x
, radix
, &mptext_stringops
, &sc
);
147 if (post
) { memcpy(sc
.buf
, post
, postlen
); sc
.buf
+= postlen
; }
149 TEXT_DONEWRITE(o
, sc
.buf
- p
);
153 static int good_radix_p(int r
, int readp
)
155 return ((r
>= -255 && r
<= -2) ||
157 (r
>= 2 && r
<= 62));
160 PyObject
*mp_pywrap(mp
*x
)
162 mp_pyobj
*z
= PyObject_New(mp_pyobj
, mp_pytype
);
164 return ((PyObject
*)z
);
167 PyObject
*gf_pywrap(mp
*x
)
169 mp_pyobj
*z
= PyObject_New(mp_pyobj
, gf_pytype
);
171 return ((PyObject
*)z
);
174 int mp_tolong_checked(mp
*x
, long *l
, int must
)
176 static mp
*longmin
= 0, *longmax
= 0;
180 longmin
= mp_fromlong(MP_NEW
, LONG_MIN
);
181 longmax
= mp_fromlong(MP_NEW
, LONG_MAX
);
183 if (MP_CMP(x
, <, longmin
) || MP_CMP(x
, >, longmax
)) {
184 if (must
) VALERR("mp out of range for int");
193 /*----- Python interface --------------------------------------------------*/
195 static void mp_pydealloc(PyObject
*o
)
201 static PyObject
*mp_pyrepr(PyObject
*o
)
202 { return mp_topystring(MP_X(o
), 10, "MP(", 0, "L)"); }
204 static PyObject
*mp_pystr(PyObject
*o
)
205 { return mp_topystring(MP_X(o
), 10, 0, 0, 0); }
207 mp
*tomp(PyObject
*o
)
214 else if (MP_PYCHECK(o
) || GF_PYCHECK(o
))
215 return (MP_COPY(MP_X(o
)));
216 else if (FE_PYCHECK(o
))
217 return (F_OUT(FE_F(o
), MP_NEW
, FE_X(o
)));
218 else if (PFILT_PYCHECK(o
))
219 return (MP_COPY(PFILT_F(o
)->m
));
220 else if (ECPT_PYCHECK(o
)) {
222 if (EC_ATINF(ECPT_P(o
))) return (0);
227 } else if (GE_PYCHECK(o
)) {
228 if ((x
= G_TOINT(GE_G(o
), MP_NEW
, GE_X(o
))) == 0)
231 } else if (PyInt_Check(o
))
232 return (mp_fromlong(MP_NEW
, PyInt_AS_LONG(o
)));
233 else if ((l
= PyNumber_Long(o
)) != 0) {
234 x
= mp_frompylong(l
);
243 mp
*getmp(PyObject
*o
)
247 if ((x
= tomp(o
)) == 0) {
248 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to mp",
249 Py_TYPE(o
)->tp_name
);
254 int convmp(PyObject
*o
, void *p
)
257 if ((x
= getmp(o
)) == 0) return (0);
262 mp
*getgf(PyObject
*o
)
266 if ((x
= tomp(o
)) == 0) {
267 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to gf",
268 Py_TYPE(o
)->tp_name
);
273 int convgf(PyObject
*o
, void *p
)
276 if ((x
= getgf(o
)) == 0) return (0);
281 static mp
*implicitmp(PyObject
*o
)
292 static mp
*implicitgf(PyObject
*o
)
303 static int mpbinop(PyObject
*x
, PyObject
*y
, mp
**xx
, mp
**yy
)
305 if ((*xx
= implicitmp(x
)) == 0)
307 if ((*yy
= implicitmp(y
)) == 0) {
314 static int gfbinop(PyObject
*x
, PyObject
*y
, mp
**xx
, mp
**yy
)
316 if ((*xx
= implicitgf(x
)) == 0)
318 if ((*yy
= implicitgf(y
)) == 0) {
325 #define gf_and mp_and
327 #define gf_xor mp_xor
328 #define BINOP(pre, name) \
329 static PyObject *pre##_py##name(PyObject *x, PyObject *y) { \
331 if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL; \
332 zz = pre##_##name(MP_NEW, xx, yy); \
333 MP_DROP(xx); MP_DROP(yy); \
334 return (pre##_pywrap(zz)); \
350 static mp
*mp_abs(mp
*d
, mp
*x
)
353 return (mp_neg(d
, x
));
359 #define UNOP(pre, name) \
360 static PyObject *pre##_py##name(PyObject *x) \
361 { return mp_pywrap(pre##_##name(MP_NEW, MP_X(x))); }
367 static PyObject
*mp_pyid(PyObject
*x
) { RETURN_OBJ(x
); }
369 #define gf_lsr mp_lsr
370 #define SHIFTOP(pre, name, rname) \
371 static PyObject *pre##_py##name(PyObject *x, PyObject *y) { \
375 if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL; \
376 if (mp_tolong_checked(yy, &n, 1)) goto end; \
378 z = pre##_pywrap(mp_##rname(MP_NEW, xx, -n)); \
380 z = pre##_pywrap(mp_##name(MP_NEW, xx, n)); \
382 MP_DROP(xx); MP_DROP(yy); \
385 SHIFTOP(mp
, lsl2c
, lsr2c
)
386 SHIFTOP(mp
, lsr2c
, lsl2c
)
387 SHIFTOP(gf
, lsl
, lsr
)
388 SHIFTOP(gf
, lsr
, lsl
)
391 #define DIVOP(pre, name, qq, rr, gather) \
392 static PyObject *pre##_py##name(PyObject *x, PyObject *y) { \
395 INIT_##qq(q) INIT_##rr(r) \
396 if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL; \
398 ZDIVERR("division by zero"); \
399 pre##_div(ARG_##qq(q), ARG_##rr(r), xx, yy); \
402 MP_DROP(xx); MP_DROP(yy); \
405 #define INIT_YES(p) mp *p = MP_NEW;
407 #define ARG_YES(p) &p
409 DIVOP(mp
, divmod
, YES
, YES
,
410 Py_BuildValue("(NN)", mp_pywrap(q
), mp_pywrap(r
)))
411 DIVOP(mp
, div
, YES
, NO
, mp_pywrap(q
))
412 DIVOP(mp
, mod
, NO
, YES
, mp_pywrap(r
))
413 DIVOP(gf
, divmod
, YES
, YES
,
414 Py_BuildValue("(NN)", gf_pywrap(q
), gf_pywrap(r
)))
415 DIVOP(gf
, div
, YES
, NO
, gf_pywrap(q
))
416 DIVOP(gf
, mod
, NO
, YES
, gf_pywrap(r
))
423 static mp
*mp_modinv_checked(mp
*d
, mp
*x
, mp
*p
)
426 mp_gcd(&g
, 0, &d
, p
, x
);
427 if (!MP_EQ(g
, MP_ONE
)) {
428 MP_DROP(g
); MP_DROP(d
);
429 PyErr_SetString(PyExc_ZeroDivisionError
, "no modular inverse");
432 MP_DROP(g
); return (d
);
435 static PyObject
*mp_pyexp(PyObject
*x
, PyObject
*y
, PyObject
*z
)
437 mp
*xx
= 0, *yy
= 0, *zz
= 0;
441 if ((xx
= implicitmp(x
)) == 0 || (yy
= implicitmp(y
)) == 0 ||
442 (z
&& z
!= Py_None
&& (zz
= tomp(z
)) == 0)) {
443 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
446 if (!z
|| z
== Py_None
) {
447 if (MP_NEGP(yy
)) VALERR("negative exponent");
448 r
= mp_exp(MP_NEW
, xx
, yy
);
450 if (!MP_POSP(zz
)) VALERR("modulus must be positive");
452 if ((xx
= mp_modinv_checked(xx
, xx
, zz
)) == 0) goto end
;
457 mpmont_create(&mm
, zz
);
458 r
= mpmont_exp(&mm
, MP_NEW
, xx
, yy
);
462 mpbarrett_create(&mb
, zz
);
463 r
= mpbarrett_exp(&mb
, MP_NEW
, xx
, yy
);
464 mpbarrett_destroy(&mb
);
469 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
473 static mp
*gf_modinv_checked(mp
*d
, mp
*x
, mp
*p
)
476 gf_gcd(&g
, 0, &d
, p
, x
);
477 if (!MP_EQ(g
, MP_ONE
)) {
478 MP_DROP(g
); MP_DROP(d
);
479 PyErr_SetString(PyExc_ZeroDivisionError
, "no modular inverse");
482 MP_DROP(g
); return (d
);
485 #define BASEOP(name, radix, pre) \
486 static PyObject *mp_py##name(PyObject *x) \
487 { return mp_topystring(MP_X(x), radix, 0, pre, 0); }
489 BASEOP(hex
, 16, "0x");
492 static int mp_pynonzerop(PyObject
*x
) { return !MP_ZEROP(MP_X(x
)); }
494 static PyObject
*mp_pyint(PyObject
*x
)
497 if (!mp_tolong_checked(MP_X(x
), &l
, 0)) return (PyInt_FromLong(l
));
498 else return mp_topylong(MP_X(x
));
500 static PyObject
*mp_pylong(PyObject
*x
)
501 { return (mp_topylong(MP_X(x
))); }
502 static PyObject
*mp_pyfloat(PyObject
*x
)
504 PyObject
*l
= mp_topylong(MP_X(x
));
505 double f
= PyLong_AsDouble(l
);
507 return (PyFloat_FromDouble(f
));
510 #define COERCE(pre, PRE) \
511 static int pre##_pycoerce(PyObject **x, PyObject **y) \
515 if (PRE##_PYCHECK(*y)) { \
516 Py_INCREF(*x); Py_INCREF(*y); \
519 if ((z = tomp(*y)) != 0) { \
521 *y = pre##_pywrap(z); \
530 static int mp_pycompare(PyObject
*x
, PyObject
*y
)
531 { return mp_cmp(MP_X(x
), MP_X(y
)); }
533 static PyObject
*mp_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
539 static const char *const kwlist
[] = { "x", "radix", 0 };
541 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O|i:new", KWLIST
, &x
, &radix
))
543 if (MP_PYCHECK(x
)) RETURN_OBJ(x
);
544 if (!good_radix_p(radix
, 1)) VALERR("bad radix");
545 if ((z
= mp_frompyobject(x
, radix
)) == 0) {
546 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to mp",
547 Py_TYPE(x
)->tp_name
);
550 zz
= (mp_pyobj
*)ty
->tp_alloc(ty
, 0);
553 return ((PyObject
*)zz
);
556 Py_hash_t
mphash(mp
*x
)
558 PyObject
*l
= mp_topylong(x
);
559 Py_hash_t h
= PyObject_Hash(l
);
560 Py_DECREF(l
); return (h
);
563 static Py_hash_t
mp_pyhash(PyObject
*me
) { return (mphash(MP_X(me
))); }
565 static PyObject
*mpmeth_jacobi(PyObject
*me
, PyObject
*arg
)
570 if (!PyArg_ParseTuple(arg
, "O&:jacobi", convmp
, &y
)) goto end
;
571 z
= PyInt_FromLong(mp_jacobi(y
, MP_X(me
)));
577 #define BITOP(pre, name, c) \
578 static PyObject *pre##meth_##name(PyObject *me, PyObject *arg) \
581 if (!PyArg_ParseTuple(arg, "O&:" #name, convulong, &i)) return (0); \
582 return (pre##_pywrap(mp_##name##c(MP_NEW, MP_X(me), i))); \
584 BITOP(mp
, setbit
, 2c
);
585 BITOP(mp
, clearbit
, 2c
);
587 BITOP(gf
, clearbit
, );
590 static PyObject
*mpmeth_testbit(PyObject
*me
, PyObject
*arg
)
593 if (!PyArg_ParseTuple(arg
, "O&:testbit", convulong
, &i
)) return (0);
594 return (getbool(mp_testbit2c(MP_X(me
), i
)));
597 static PyObject
*gfmeth_testbit(PyObject
*me
, PyObject
*arg
)
600 if (!PyArg_ParseTuple(arg
, "O&:testbit", convulong
, &i
)) return (0);
601 return (getbool(mp_testbit(MP_X(me
), i
)));
604 static PyObject
*mpmeth_odd(PyObject
*me
)
609 t
= mp_odd(MP_NEW
, MP_X(me
), &s
);
610 return (Py_BuildValue("(lN)", (long)s
, mp_pywrap(t
)));
613 static PyObject
*mpmeth_sqr(PyObject
*me
)
614 { return (mp_pywrap(mp_sqr(MP_NEW
, MP_X(me
)))); }
616 static PyObject
*mpmeth_sqrt(PyObject
*me
)
618 if (MP_NEGP(MP_X(me
))) VALERR("negative root");
619 return (mp_pywrap(mp_sqrt(MP_NEW
, MP_X(me
))));
624 static PyObject
*mpmeth_gcd(PyObject
*me
, PyObject
*arg
)
626 mp
*y
= 0, *zz
= MP_NEW
;
629 if (!PyArg_ParseTuple(arg
, "O&:gcd", convmp
, &y
)) goto end
;
630 mp_gcd(&zz
, 0, 0, MP_X(me
), y
);
637 static PyObject
*mpmeth_gcdx(PyObject
*me
, PyObject
*arg
)
640 mp
*yy
= 0, *zz
= MP_NEW
, *uu
= MP_NEW
, *vv
= MP_NEW
;
642 if (!PyArg_ParseTuple(arg
, "O&:gcdx", convmp
, &yy
)) goto end
;
643 mp_gcd(&zz
, &uu
, &vv
, MP_X(me
), yy
);
644 z
= Py_BuildValue("(NNN)",
645 mp_pywrap(zz
), mp_pywrap(uu
), mp_pywrap(vv
));
651 static PyObject
*mpmeth_modinv(PyObject
*me
, PyObject
*arg
)
654 mp
*yy
= 0, *zz
= MP_NEW
;
656 if (!PyArg_ParseTuple(arg
, "O&:modinv", convmp
, &yy
) ||
657 (zz
= mp_modinv_checked(MP_NEW
, yy
, MP_X(me
))) == 0)
665 static PyObject
*mpmeth_tostring(PyObject
*me
, PyObject
*arg
, PyObject
*kw
)
668 static const char *const kwlist
[] = { "radix", 0 };
669 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "|i:tostring", KWLIST
, &radix
))
671 if (!good_radix_p(radix
, 0)) VALERR("bad radix");
672 return (mp_topystring(MP_X(me
), radix
, 0, 0, 0));
677 static PyObject
*mpmeth_modsqrt(PyObject
*me
, PyObject
*arg
)
680 mp
*yy
= 0, *zz
= MP_NEW
;
682 if (!PyArg_ParseTuple(arg
, "O&:modsqrt", convmp
, &yy
)) goto end
;
683 if ((zz
= mp_modsqrt(MP_NEW
, yy
, MP_X(me
))) == 0)
684 VALERR("no modular square root");
691 static PyObject
*mpmeth_leastcongruent(PyObject
*me
, PyObject
*arg
)
696 if (!PyArg_ParseTuple(arg
, "O&O&:leastcongruent", convmp
, &b
, convmp
, &m
))
698 z
= mp_leastcongruent(MP_NEW
, b
, MP_X(me
), m
);
704 #define STOREOP(name, c) \
705 static PyObject *mpmeth_##name(PyObject *me, \
706 PyObject *arg, PyObject *kw) \
709 static const char *const kwlist[] = { "len", 0 }; \
712 if (!PyArg_ParseTupleAndKeywords(arg, kw, "|l:" #name, \
716 len = mp_octets##c(MP_X(me)); \
719 rc = bytestring_pywrap(0, len); \
720 mp_##name(MP_X(me), BIN_PTR(rc), len); \
726 STOREOP(storel2c
, 2c
)
727 STOREOP(storeb2c
, 2c
)
731 static PyObject *ty##meth_frombuf(PyObject *me, PyObject *arg) \
738 if (!PyArg_ParseTuple(arg, "O&:frombuf", convbin, &in)) goto end; \
739 buf_init(&b, (/*unconst*/ void *)in.p, in.sz); \
740 if ((x = buf_getmp(&b)) == 0) VALERR("malformed data"); \
741 rc = Py_BuildValue("(NN)", ty##_pywrap(x), \
742 bytestring_pywrapbuf(&b)); \
750 static PyObject
*mpmeth_tobuf(PyObject
*me
)
758 n
= mp_octets(x
) + 3;
759 rc
= bytestring_pywrap(0, n
);
760 buf_init(&b
, BIN_PTR(rc
), n
);
763 BIN_SETLEN(rc
, BLEN(&b
));
767 static PyObject
*mpmeth_primep(PyObject
*me
, PyObject
*arg
, PyObject
*kw
)
769 grand
*r
= &rand_global
;
770 static const char *const kwlist
[] = { "rng", 0 };
773 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "|O&", KWLIST
, convgrand
, &r
))
775 rc
= getbool(pgen_primep(MP_X(me
), r
));
780 static PyObject
*mpmeth_fromstring(PyObject
*me
,
781 PyObject
*arg
, PyObject
*kw
)
789 static const char *const kwlist
[] = { "x", "radix", 0 };
791 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "s#|i:fromstring", KWLIST
,
794 if (!good_radix_p(r
, 1)) VALERR("bad radix");
795 sc
.buf
= p
; sc
.lim
= p
+ len
;
796 if ((zz
= mp_read(MP_NEW
, r
, &mptext_stringops
, &sc
)) == 0)
797 VALERR("bad integer");
798 z
= Py_BuildValue("(Ns#)", mp_pywrap(zz
),
799 sc
.buf
, (Py_ssize_t
)(sc
.lim
- sc
.buf
));
804 static PyObject
*mpmeth_factorial(PyObject
*me
, PyObject
*arg
)
808 if (!PyArg_ParseTuple(arg
, "O&:factorial", convulong
, &i
)) return (0);
813 static PyObject
*mpmeth_fibonacci(PyObject
*me
, PyObject
*arg
)
817 if (!PyArg_ParseTuple(arg
, "l:fibonacci", &i
)) return (0);
822 #define LOADOP(pre, name) \
823 static PyObject *pre##meth_##name(PyObject *me, PyObject *arg) \
826 if (!PyArg_ParseTuple(arg, "O&:" #name, convbin, &in)) return (0); \
827 return (pre##_pywrap(mp_##name(MP_NEW, in.p, in.sz))); \
837 static PyObject
*mpget_nbits(PyObject
*me
, void *hunoz
)
838 { return (PyInt_FromLong(mp_bits(MP_X(me
)))); }
840 static PyObject
*mpget_noctets(PyObject
*me
, void *hunoz
)
841 { return (PyInt_FromLong(mp_octets(MP_X(me
)))); }
843 static PyObject
*mpget_noctets2c(PyObject
*me
, void *hunoz
)
844 { return (PyInt_FromLong(mp_octets2c(MP_X(me
)))); }
846 static const PyGetSetDef mp_pygetset
[] = {
847 #define GETSETNAME(op, func) mp##op##_##func
848 GET (nbits
, "X.nbits -> bit length of X")
849 GET (noctets
, "X.noctets -> octet length of X")
850 GET (noctets2c
, "X.noctets2c -> two's complement octet length of X")
855 static const PyMethodDef mp_pymethods
[] = {
856 #define METHNAME(func) mpmeth_##func
857 METH (jacobi
, "X.jacobi(Y) -> Jacobi symbol (Y|X) (NB inversion!)")
858 METH (setbit
, "X.setbit(N) -> X with bit N set")
859 METH (clearbit
, "X.clearbit(N) -> X with bit N clear")
860 METH (testbit
, "X.testbit(N) -> true/false if bit N set/clear in X")
861 NAMETH(odd
, "X.odd() -> S, T where X = 2^S T with T odd")
862 NAMETH(sqr
, "X.sqr() -> X^2")
863 NAMETH(sqrt
, "X.sqrt() -> largest integer <= sqrt(X)")
864 METH (gcd
, "X.gcd(Y) -> gcd(X, Y)")
865 METH (gcdx
, "X.gcdx(Y) -> (gcd(X, Y), U, V) "
866 "with X U + Y V = gcd(X, Y)")
867 METH (modinv
, "X.modinv(Y) -> multiplicative inverse of Y mod X")
868 METH (modsqrt
, "X.modsqrt(Y) -> square root of Y mod X, if X prime")
869 METH (leastcongruent
, "X.leastcongruent(B, M) -> "
870 "smallest Z >= B with Z == X (mod M)")
871 KWMETH(primep
, "X.primep([rng = rand]) -> X is prime?")
872 KWMETH(tostring
, "X.tostring([radix = 10]) -> STR")
873 KWMETH(storel
, "X.storel([len = -1]) -> little-endian bytes")
874 KWMETH(storeb
, "X.storeb([len = -1]) -> big-endian bytes")
875 KWMETH(storel2c
, "X.storel2c([len = -1]) -> "
876 "little-endian bytes, two's complement")
877 KWMETH(storeb2c
, "X.storeb2c([len = -1]) -> "
878 "big-endian bytes, two's complement")
879 NAMETH(tobuf
, "X.tobuf() -> buffer format")
880 KWSMTH(fromstring
, "fromstring(STR, [radix = 0]) -> (X, REST)\n"
881 " Parse STR as a large integer, according to RADIX. If RADIX is\n"
882 " zero, read a prefix from STR to decide radix: allow `0b' for binary,\n"
883 " `0' or `0o' for octal, `0x' for hex, or `R_' for other radix R.")
884 SMTH (factorial
, "factorial(I) -> I!: compute factorial")
885 SMTH (fibonacci
, "fibonacci(I) -> F(I): compute Fibonacci number")
886 SMTH (loadl
, "loadl(STR) -> X: read little-endian bytes")
887 SMTH (loadb
, "loadb(STR) -> X: read big-endian bytes")
888 SMTH (loadl2c
, "loadl2c(STR) -> X: "
889 "read little-endian bytes, two's complement")
890 SMTH (loadb2c
, "loadb2c(STR) -> X: "
891 "read big-endian bytes, two's complement")
892 SMTH (frombuf
, "frombuf(STR) -> (X, REST): read buffer format")
897 static const PyNumberMethods mp_pynumber
= {
898 mp_pyadd
, /* @nb_add@ */
899 mp_pysub
, /* @nb_subtract@ */
900 mp_pymul
, /* @nb_multiply@ */
902 mp_pymod
, /* @nb_remainder@ */
903 mp_pydivmod
, /* @nb_divmod@ */
904 mp_pyexp
, /* @nb_power@ */
905 mp_pyneg
, /* @nb_negative@ */
906 mp_pyid
, /* @nb_positive@ */
907 mp_pyabs
, /* @nb_absolute@ */
908 mp_pynonzerop
, /* @nb_nonzero@ */
909 mp_pynot2c
, /* @nb_invert@ */
910 mp_pylsl2c
, /* @nb_lshift@ */
911 mp_pylsr2c
, /* @nb_rshift@ */
912 mp_pyand2c
, /* @nb_and@ */
913 mp_pyxor2c
, /* @nb_xor@ */
914 mp_pyor2c
, /* @nb_or@ */
915 mp_pycoerce
, /* @nb_coerce@ */
916 mp_pyint
, /* @nb_int@ */
917 mp_pylong
, /* @nb_long@ */
918 mp_pyfloat
, /* @nb_float@ */
919 mp_pyoct
, /* @nb_oct@ */
920 mp_pyhex
, /* @nb_hex@ */
922 0, /* @nb_inplace_add@ */
923 0, /* @nb_inplace_subtract@ */
924 0, /* @nb_inplace_multiply@ */
925 0, /* @nb_inplace_divide@ */
926 0, /* @nb_inplace_remainder@ */
927 0, /* @nb_inplace_power@ */
928 0, /* @nb_inplace_lshift@ */
929 0, /* @nb_inplace_rshift@ */
930 0, /* @nb_inplace_and@ */
931 0, /* @nb_inplace_xor@ */
932 0, /* @nb_inplace_or@ */
934 mp_pydiv
, /* @nb_floor_divide@ */
935 0, /* @nb_true_divide@ */
936 0, /* @nb_inplace_floor_divide@ */
937 0, /* @nb_inplace_true_divide@ */
940 static const PyTypeObject mp_pytype_skel
= {
941 PyVarObject_HEAD_INIT(0, 0) /* Header */
942 "MP", /* @tp_name@ */
943 sizeof(mp_pyobj
), /* @tp_basicsize@ */
944 0, /* @tp_itemsize@ */
946 mp_pydealloc
, /* @tp_dealloc@ */
948 0, /* @tp_getattr@ */
949 0, /* @tp_setattr@ */
950 mp_pycompare
, /* @tp_compare@ */
951 mp_pyrepr
, /* @tp_repr@ */
952 PYNUMBER(mp
), /* @tp_as_number@ */
953 0, /* @tp_as_sequence@ */
954 0, /* @tp_as_mapping@ */
955 mp_pyhash
, /* @tp_hash@ */
957 mp_pystr
, /* @tp_str@ */
958 0, /* @tp_getattro@ */
959 0, /* @tp_setattro@ */
960 0, /* @tp_as_buffer@ */
961 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
962 Py_TPFLAGS_CHECKTYPES
|
966 "Multiprecision integers, similar to `long' but more efficient and\n"
967 "versatile. Support all the standard arithmetic operations, with\n"
968 "implicit conversions from `PrimeFilter', and other objects which\n"
969 "convert to `long'.\n"
971 "Constructor MP(X, [radix = R]) attempts to convert X to an `MP'. If\n"
972 "X is a string, it's read in radix-R form, or we look for a prefix\n"
973 "if R = 0. Other acceptable things are field elements, elliptic curve\n"
974 "points, group elements, Python `int' and `long' objects, and anything\n"
975 "with an integer conversion.\n"
979 " * Use `//' for integer division: `/' gives exact rational division.",
981 0, /* @tp_traverse@ */
983 0, /* @tp_richcompare@ */
984 0, /* @tp_weaklistoffset@ */
986 0, /* @tp_iternext@ */
987 PYMETHODS(mp
), /* @tp_methods@ */
988 0, /* @tp_members@ */
989 PYGETSET(mp
), /* @tp_getset@ */
992 0, /* @tp_descr_get@ */
993 0, /* @tp_descr_set@ */
994 0, /* @tp_dictoffset@ */
996 PyType_GenericAlloc
, /* @tp_alloc@ */
997 mp_pynew
, /* @tp_new@ */
1002 /*----- Products of small integers ----------------------------------------*/
1004 static PyTypeObject
*mpmul_pytype
;
1006 typedef struct mpmul_pyobj
{
1012 #define MPMUL_LIVEP(o) (((mpmul_pyobj *)(o))->livep)
1013 #define MPMUL_PY(o) (&((mpmul_pyobj *)(o))->mm)
1015 static void mpmul_pydealloc(PyObject
*me
)
1017 if (MPMUL_LIVEP(me
))
1018 mp_drop(mpmul_done(MPMUL_PY(me
)));
1022 static PyObject
*mmmeth_factor(PyObject
*me
, PyObject
*arg
)
1027 if (!MPMUL_LIVEP(me
)) VALERR("MPMul object invalid");
1028 if (PyTuple_GET_SIZE(arg
) != 1)
1029 i
= PyObject_GetIter(arg
);
1031 if ((q
= PyTuple_GET_ITEM(arg
, 0)) == 0) goto end
;
1032 if ((i
= PyObject_GetIter(q
)) == 0) {
1033 PyErr_Clear(); /* that's ok */
1034 i
= PyObject_GetIter(arg
);
1038 while ((q
= PyIter_Next(i
)) != 0) {
1039 x
= getmp(q
); Py_DECREF(q
); if (!x
) {
1043 mpmul_add(MPMUL_PY(me
), x
);
1052 static PyObject
*mmmeth_done(PyObject
*me
)
1056 if (!MPMUL_LIVEP(me
)) VALERR("MPMul object invalid");
1057 x
= mpmul_done(MPMUL_PY(me
));
1058 MPMUL_LIVEP(me
) = 0;
1059 return (mp_pywrap(x
));
1064 static PyObject
*mpmul_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1068 if (kw
) TYERR("keyword arguments not allowed here");
1069 mm
= (mpmul_pyobj
*)ty
->tp_alloc(ty
, 0);
1070 mpmul_init(&mm
->mm
);
1072 if (mmmeth_factor((PyObject
*)mm
, arg
) == 0) {
1076 return ((PyObject
*)mm
);
1081 static PyObject
*mmget_livep(PyObject
*me
, void *hunoz
)
1082 { return (getbool(MPMUL_LIVEP(me
))); }
1084 static const PyGetSetDef mpmul_pygetset
[] = {
1085 #define GETSETNAME(op, name) mm##op##_##name
1086 GET (livep
, "MM.livep -> flag: object still valid?")
1091 static const PyMethodDef mpmul_pymethods
[] = {
1092 #define METHNAME(name) mmmeth_##name
1093 METH (factor
, "MM.factor(ITERABLE) or MM.factor(I, ...)")
1094 NAMETH(done
, "MM.done() -> PRODUCT")
1099 static const PyTypeObject mpmul_pytype_skel
= {
1100 PyVarObject_HEAD_INIT(0, 0) /* Header */
1101 "MPMul", /* @tp_name@ */
1102 sizeof(mpmul_pyobj
), /* @tp_basicsize@ */
1103 0, /* @tp_itemsize@ */
1105 mpmul_pydealloc
, /* @tp_dealloc@ */
1107 0, /* @tp_getattr@ */
1108 0, /* @tp_setattr@ */
1109 0, /* @tp_compare@ */
1111 0, /* @tp_as_number@ */
1112 0, /* @tp_as_sequence@ */
1113 0, /* @tp_as_mapping@ */
1117 0, /* @tp_getattro@ */
1118 0, /* @tp_setattro@ */
1119 0, /* @tp_as_buffer@ */
1120 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1121 Py_TPFLAGS_BASETYPE
,
1124 "MPMul(N_0, N_1, ....): an object for multiplying many small integers.",
1126 0, /* @tp_traverse@ */
1128 0, /* @tp_richcompare@ */
1129 0, /* @tp_weaklistoffset@ */
1131 0, /* @tp_iternext@ */
1132 PYMETHODS(mpmul
), /* @tp_methods@ */
1133 0, /* @tp_members@ */
1134 PYGETSET(mpmul
), /* @tp_getset@ */
1137 0, /* @tp_descr_get@ */
1138 0, /* @tp_descr_set@ */
1139 0, /* @tp_dictoffset@ */
1141 PyType_GenericAlloc
, /* @tp_alloc@ */
1142 mpmul_pynew
, /* @tp_new@ */
1147 /*----- Montgomery reduction ----------------------------------------------*/
1149 static PyTypeObject
*mpmont_pytype
;
1151 typedef struct mpmont_pyobj
{
1156 #define MPMONT_PY(o) (&((mpmont_pyobj *)(o))->mm)
1158 static PyObject
*mmmeth_int(PyObject
*me
, PyObject
*arg
)
1162 mpmont
*mm
= MPMONT_PY(me
);
1164 if (!PyArg_ParseTuple(arg
, "O&:in", convmp
, &yy
))
1166 mp_div(0, &yy
, yy
, mm
->m
);
1167 z
= mp_pywrap(mpmont_mul(mm
, MP_NEW
, yy
, mm
->r2
));
1169 if (yy
) MP_DROP(yy
);
1173 static PyObject
*mmmeth_mul(PyObject
*me
, PyObject
*arg
)
1176 mp
*yy
= 0, *zz
= 0;
1178 if (!PyArg_ParseTuple(arg
, "O&O&:mul", convmp
, &yy
, convmp
, &zz
))
1180 rc
= mp_pywrap(mpmont_mul(MPMONT_PY(me
), MP_NEW
, yy
, zz
));
1182 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1186 static PyObject
*mmmeth_exp(PyObject
*me
, PyObject
*arg
)
1189 mp
*yy
= 0, *zz
= 0;
1191 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convmp
, &yy
, convmp
, &zz
))
1194 if ((yy
= mp_modinv_checked(yy
, yy
, MPMONT_PY(me
)->m
)) == 0) goto end
;
1195 zz
= mp_neg(zz
, zz
);
1197 rc
= mp_pywrap(mpmont_exp(MPMONT_PY(me
), MP_NEW
, yy
, zz
));
1199 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1203 static PyObject
*mmmeth_expr(PyObject
*me
, PyObject
*arg
)
1206 mp
*yy
= 0, *zz
= 0;
1208 if (!PyArg_ParseTuple(arg
, "O&O&:expr", convmp
, &yy
, convmp
, &zz
))
1211 yy
= mpmont_reduce(MPMONT_PY(me
), yy
, yy
);
1212 if ((yy
= mp_modinv_checked(yy
, yy
, MPMONT_PY(me
)->m
)) == 0) goto end
;
1213 yy
= mpmont_mul(MPMONT_PY(me
), yy
, yy
, MPMONT_PY(me
)->r2
);
1214 zz
= mp_neg(zz
, zz
);
1216 rc
= mp_pywrap(mpmont_expr(MPMONT_PY(me
), MP_NEW
, yy
, zz
));
1218 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1222 static PyObject
*mm_mexpr_id(PyObject
*me
)
1223 { return mp_pywrap(MP_COPY(MPMONT_PY(me
)->r
)); }
1225 static int mm_mexpr_fill(void *p
, PyObject
*me
, PyObject
*x
, PyObject
*y
)
1227 mp
*xx
= 0, *yy
= 0;
1228 mp_expfactor
*f
= p
;
1229 mpmont
*mm
= MPMONT_PY(me
);
1231 if ((xx
= getmp(x
)) == 0 || (yy
= getmp(y
)) == 0)
1234 xx
= mpmont_reduce(mm
, xx
, xx
);
1235 if ((xx
= mp_modinv_checked(xx
, xx
, yy
)) == 0)
1237 xx
= mpmont_mul(mm
, xx
, xx
, mm
->r2
);
1238 yy
= mp_neg(yy
, yy
);
1245 mp_drop(xx
); mp_drop(yy
);
1249 static PyObject
*mm_mexpr(PyObject
*me
, void *v
, int n
)
1250 { return mp_pywrap(mpmont_mexpr(MPMONT_PY(me
), MP_NEW
, v
, n
)); }
1252 static void mp_mexp_drop(void *p
)
1254 mp_expfactor
*f
= p
;
1259 static PyObject
*mmmeth_mexpr(PyObject
*me
, PyObject
*arg
)
1261 return mexp_common(me
, arg
, sizeof(mp_expfactor
),
1262 mm_mexpr_id
, mm_mexpr_fill
, mm_mexpr
, mp_mexp_drop
);
1265 static PyObject
*mp_mexp_id(PyObject
*me
)
1266 { return mp_pywrap(MP_ONE
); }
1268 static int mp_mexp_fill(void *p
, PyObject
*me
, PyObject
*x
, PyObject
*y
)
1270 mp
*xx
= 0, *yy
= 0;
1271 mp_expfactor
*f
= p
;
1273 if ((xx
= getmp(x
)) == 0 || (yy
= getmp(y
)) == 0)
1276 if ((xx
= mp_modinv_checked(xx
, xx
, yy
)) == 0)
1278 yy
= mp_neg(yy
, yy
);
1285 mp_drop(xx
); mp_drop(yy
);
1289 static PyObject
*mm_mexp(PyObject
*me
, void *v
, int n
)
1290 { return mp_pywrap(mpmont_mexp(MPMONT_PY(me
), MP_NEW
, v
, n
)); }
1292 static PyObject
*mmmeth_mexp(PyObject
*me
, PyObject
*arg
)
1294 return mexp_common(me
, arg
, sizeof(mp_expfactor
),
1295 mp_mexp_id
, mp_mexp_fill
, mm_mexp
, mp_mexp_drop
);
1298 #define mmmeth_ext mmmeth_reduce
1299 static PyObject
*mmmeth_reduce(PyObject
*me
, PyObject
*arg
)
1304 if (!PyArg_ParseTuple(arg
, "O&", convmp
, &yy
)) goto end
;
1305 z
= mp_pywrap(mpmont_reduce(MPMONT_PY(me
), MP_NEW
, yy
));
1310 static void mpmont_pydealloc(PyObject
*me
)
1312 mpmont_destroy(MPMONT_PY(me
));
1316 static PyObject
*mpmont_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1318 mpmont_pyobj
*mm
= 0;
1319 static const char *const kwlist
[] = { "m", 0 };
1322 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", KWLIST
, convmp
, &xx
))
1324 if (!MP_POSP(xx
) || !MP_ODDP(xx
)) VALERR("m must be positive and odd");
1325 mm
= (mpmont_pyobj
*)ty
->tp_alloc(ty
, 0);
1326 mpmont_create(&mm
->mm
, xx
);
1328 if (xx
) MP_DROP(xx
);
1329 return ((PyObject
*)mm
);
1332 static PyObject
*mmget_m(PyObject
*me
, void *hunoz
)
1333 { return (mp_pywrap(MP_COPY(MPMONT_PY(me
)->m
))); }
1335 static PyObject
*mmget_r(PyObject
*me
, void *hunoz
)
1336 { return (mp_pywrap(MP_COPY(MPMONT_PY(me
)->r
))); }
1338 static PyObject
*mmget_r2(PyObject
*me
, void *hunoz
)
1339 { return (mp_pywrap(MP_COPY(MPMONT_PY(me
)->r2
))); }
1341 static const PyGetSetDef mpmont_pygetset
[] = {
1342 #define GETSETNAME(op, name) mm##op##_##name
1343 GET (m
, "M.m -> modulus for reduction")
1344 GET (r
, "M.r -> multiplicative identity")
1345 GET (r2
, "M.r2 -> M.r^2, Montgomerization factor")
1350 static const PyMethodDef mpmont_pymethods
[] = {
1351 #define METHNAME(name) mmmeth_##name
1352 METH (int, "M.int(X) -> XR")
1353 METH (mul
, "M.mul(XR, YR) -> ZR where Z = X Y")
1354 METH (expr
, "M.expr(XR, N) -> ZR where Z = X^N mod M.m")
1355 METH (mexpr
, "M.mexpr([(XR0, N0), (XR1, N1), ...]) = ZR "
1356 "where Z = X0^N0 X1^N1 ... mod M.m\n"
1357 "\t(the list may be flattened if this more convenient.)")
1358 METH (reduce
, "M.reduce(XR) -> X")
1359 METH (ext
, "M.ext(XR) -> X")
1360 METH (exp
, "M.exp(X, N) -> X^N mod M.m")
1361 METH (mexp
, "M.mexp([(X0, N0), (X1, N1), ...]) = "
1362 "X0^N0 X1^N1 ... mod M.m\n"
1363 "\t(the list may be flattened if this more convenient.)")
1368 static const PyTypeObject mpmont_pytype_skel
= {
1369 PyVarObject_HEAD_INIT(0, 0) /* Header */
1370 "MPMont", /* @tp_name@ */
1371 sizeof(mpmont_pyobj
), /* @tp_basicsize@ */
1372 0, /* @tp_itemsize@ */
1374 mpmont_pydealloc
, /* @tp_dealloc@ */
1376 0, /* @tp_getattr@ */
1377 0, /* @tp_setattr@ */
1378 0, /* @tp_compare@ */
1380 0, /* @tp_as_number@ */
1381 0, /* @tp_as_sequence@ */
1382 0, /* @tp_as_mapping@ */
1386 0, /* @tp_getattro@ */
1387 0, /* @tp_setattro@ */
1388 0, /* @tp_as_buffer@ */
1389 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1390 Py_TPFLAGS_BASETYPE
,
1393 "MPMont(N): a Montgomery reduction context.",
1395 0, /* @tp_traverse@ */
1397 0, /* @tp_richcompare@ */
1398 0, /* @tp_weaklistoffset@ */
1400 0, /* @tp_iternext@ */
1401 PYMETHODS(mpmont
), /* @tp_methods@ */
1402 0, /* @tp_members@ */
1403 PYGETSET(mpmont
), /* @tp_getset@ */
1406 0, /* @tp_descr_get@ */
1407 0, /* @tp_descr_set@ */
1408 0, /* @tp_dictoffset@ */
1410 PyType_GenericAlloc
, /* @tp_alloc@ */
1411 mpmont_pynew
, /* @tp_new@ */
1416 /*----- Barrett reduction -------------------------------------------------*/
1418 static PyTypeObject
*mpbarrett_pytype
;
1420 typedef struct mpbarrett_pyobj
{
1425 #define MPBARRETT_PY(o) (&((mpbarrett_pyobj *)(o))->mb)
1427 static PyObject
*mbmeth_exp(PyObject
*me
, PyObject
*arg
)
1430 mp
*yy
= 0, *zz
= 0;
1432 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convmp
, &yy
, convmp
, &zz
))
1435 if ((yy
= mp_modinv_checked(yy
, yy
, MPBARRETT_PY(me
)->m
)) == 0) goto end
;
1436 zz
= mp_neg(zz
, zz
);
1438 rc
= mp_pywrap(mpbarrett_exp(MPBARRETT_PY(me
), MP_NEW
, yy
, zz
));
1440 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1444 static PyObject
*mb_mexp(PyObject
*me
, void *v
, int n
)
1445 { return mp_pywrap(mpbarrett_mexp(MPBARRETT_PY(me
), MP_NEW
, v
, n
)); }
1447 static PyObject
*mbmeth_mexp(PyObject
*me
, PyObject
*arg
)
1449 return mexp_common(me
, arg
, sizeof(mp_expfactor
),
1450 mp_mexp_id
, mp_mexp_fill
, mb_mexp
, mp_mexp_drop
);
1453 static PyObject
*mbmeth_reduce(PyObject
*me
, PyObject
*arg
)
1458 if (!PyArg_ParseTuple(arg
, "O&:reduce", convmp
, &yy
))
1460 z
= mp_pywrap(mpbarrett_reduce(MPBARRETT_PY(me
), MP_NEW
, yy
));
1465 static void mpbarrett_pydealloc(PyObject
*me
)
1467 mpbarrett_destroy(MPBARRETT_PY(me
));
1471 static PyObject
*mpbarrett_pynew(PyTypeObject
*ty
,
1472 PyObject
*arg
, PyObject
*kw
)
1474 mpbarrett_pyobj
*mb
= 0;
1475 static const char *const kwlist
[] = { "m", 0 };
1478 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", KWLIST
, convmp
, &xx
))
1480 if (!MP_POSP(xx
)) VALERR("m must be positive");
1481 mb
= (mpbarrett_pyobj
*)ty
->tp_alloc(ty
, 0);
1482 mpbarrett_create(&mb
->mb
, xx
);
1484 if (xx
) MP_DROP(xx
);
1485 return ((PyObject
*)mb
);
1488 static PyObject
*mbget_m(PyObject
*me
, void *hunoz
)
1489 { return (mp_pywrap(MP_COPY(MPBARRETT_PY(me
)->m
))); }
1491 static const PyGetSetDef mpbarrett_pygetset
[] = {
1492 #define GETSETNAME(op, name) mb##op##_##name
1493 GET (m
, "B.m -> modulus for reduction")
1498 static const PyMethodDef mpbarrett_pymethods
[] = {
1499 #define METHNAME(name) mbmeth_##name
1500 METH (reduce
, "B.reduce(X) -> X mod B.m")
1501 METH (exp
, "B.exp(X, N) -> X^N mod B.m")
1502 METH (mexp
, "B.mexp([(X0, N0), (X1, N1), ...]) = "
1503 "X0^N0 X1^N1 ... mod B.m\n"
1504 "\t(the list may be flattened if this more convenient.)")
1509 static const PyTypeObject mpbarrett_pytype_skel
= {
1510 PyVarObject_HEAD_INIT(0, 0) /* Header */
1511 "MPBarrett", /* @tp_name@ */
1512 sizeof(mpbarrett_pyobj
), /* @tp_basicsize@ */
1513 0, /* @tp_itemsize@ */
1515 mpbarrett_pydealloc
, /* @tp_dealloc@ */
1517 0, /* @tp_getattr@ */
1518 0, /* @tp_setattr@ */
1519 0, /* @tp_compare@ */
1521 0, /* @tp_as_number@ */
1522 0, /* @tp_as_sequence@ */
1523 0, /* @tp_as_mapping@ */
1527 0, /* @tp_getattro@ */
1528 0, /* @tp_setattro@ */
1529 0, /* @tp_as_buffer@ */
1530 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1531 Py_TPFLAGS_BASETYPE
,
1534 "MPBarrett(N): a Barrett reduction context.",
1536 0, /* @tp_traverse@ */
1538 0, /* @tp_richcompare@ */
1539 0, /* @tp_weaklistoffset@ */
1541 0, /* @tp_iternext@ */
1542 PYMETHODS(mpbarrett
), /* @tp_methods@ */
1543 0, /* @tp_members@ */
1544 PYGETSET(mpbarrett
), /* @tp_getset@ */
1547 0, /* @tp_descr_get@ */
1548 0, /* @tp_descr_set@ */
1549 0, /* @tp_dictoffset@ */
1551 PyType_GenericAlloc
, /* @tp_alloc@ */
1552 mpbarrett_pynew
, /* @tp_new@ */
1557 /*----- Nice prime reduction ----------------------------------------------*/
1559 static PyTypeObject
*mpreduce_pytype
;
1561 typedef struct mpreduce_pyobj
{
1566 #define MPREDUCE_PY(o) (&((mpreduce_pyobj *)(o))->mr)
1568 static PyObject
*mrmeth_exp(PyObject
*me
, PyObject
*arg
)
1571 mp
*yy
= 0, *zz
= 0;
1573 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convmp
, &yy
, convmp
, &zz
))
1576 if ((yy
= mp_modinv_checked(yy
, yy
, MPREDUCE_PY(me
)->p
)) == 0) goto end
;
1577 zz
= mp_neg(zz
, zz
);
1579 rc
= mp_pywrap(mpreduce_exp(MPREDUCE_PY(me
), MP_NEW
, yy
, zz
));
1581 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1585 static PyObject
*mrmeth_reduce(PyObject
*me
, PyObject
*arg
)
1590 if (!PyArg_ParseTuple(arg
, "O&:reduce", convmp
, &yy
)) goto end
;
1591 z
= mp_pywrap(mpreduce_do(MPREDUCE_PY(me
), MP_NEW
, yy
));
1596 static void mpreduce_pydealloc(PyObject
*me
)
1598 mpreduce_destroy(MPREDUCE_PY(me
));
1602 static PyObject
*mpreduce_pynew(PyTypeObject
*ty
,
1603 PyObject
*arg
, PyObject
*kw
)
1605 mpreduce_pyobj
*mr
= 0;
1607 static const char *const kwlist
[] = { "m", 0 };
1610 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", KWLIST
, convmp
, &xx
))
1612 if (!MP_POSP(xx
)) VALERR("m must be positive");
1613 if (mpreduce_create(&r
, xx
)) VALERR("bad modulus (must be 2^k - ...)");
1614 mr
= (mpreduce_pyobj
*)ty
->tp_alloc(ty
, 0);
1617 if (xx
) MP_DROP(xx
);
1618 return ((PyObject
*)mr
);
1621 static PyObject
*mrget_m(PyObject
*me
, void *hunoz
)
1622 { return (mp_pywrap(MP_COPY(MPREDUCE_PY(me
)->p
))); }
1624 static const PyGetSetDef mpreduce_pygetset
[] = {
1625 #define GETSETNAME(op, name) mr##op##_##name
1626 GET (m
, "R.m -> modulus for reduction")
1631 static const const PyMethodDef mpreduce_pymethods
[] = {
1632 #define METHNAME(name) mrmeth_##name
1633 METH (reduce
, "R.reduce(X) -> X mod B.m")
1634 METH (exp
, "R.exp(X, N) -> X^N mod B.m")
1639 static const PyTypeObject mpreduce_pytype_skel
= {
1640 PyVarObject_HEAD_INIT(0, 0) /* Header */
1641 "MPReduce", /* @tp_name@ */
1642 sizeof(mpreduce_pyobj
), /* @tp_basicsize@ */
1643 0, /* @tp_itemsize@ */
1645 mpreduce_pydealloc
, /* @tp_dealloc@ */
1647 0, /* @tp_getattr@ */
1648 0, /* @tp_setattr@ */
1649 0, /* @tp_compare@ */
1651 0, /* @tp_as_number@ */
1652 0, /* @tp_as_sequence@ */
1653 0, /* @tp_as_mapping@ */
1657 0, /* @tp_getattro@ */
1658 0, /* @tp_setattro@ */
1659 0, /* @tp_as_buffer@ */
1660 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1661 Py_TPFLAGS_BASETYPE
,
1664 "MPReduce(N): a reduction context for reduction modulo Solinas primes.",
1666 0, /* @tp_traverse@ */
1668 0, /* @tp_richcompare@ */
1669 0, /* @tp_weaklistoffset@ */
1671 0, /* @tp_iternext@ */
1672 PYMETHODS(mpreduce
), /* @tp_methods@ */
1673 0, /* @tp_members@ */
1674 PYGETSET(mpreduce
), /* @tp_getset@ */
1677 0, /* @tp_descr_get@ */
1678 0, /* @tp_descr_set@ */
1679 0, /* @tp_dictoffset@ */
1681 PyType_GenericAlloc
, /* @tp_alloc@ */
1682 mpreduce_pynew
, /* @tp_new@ */
1687 /*----- Chinese Remainder Theorem solution --------------------------------*/
1689 static PyTypeObject
*mpcrt_pytype
;
1691 typedef struct mpcrt_pyobj
{
1696 #define MPCRT_PY(o) (&((mpcrt_pyobj *)(o))->c)
1698 static PyObject
*mcmeth_solve(PyObject
*me
, PyObject
*arg
)
1700 mpcrt
*c
= MPCRT_PY(me
);
1701 PyObject
*q
= 0, *x
, *z
= 0;
1704 Py_ssize_t i
= 0, n
= c
->k
;
1707 if (PyTuple_GET_SIZE(arg
) == n
)
1709 else if (!PyArg_ParseTuple(arg
, "O:solve", &q
))
1712 if (!PySequence_Check(q
)) TYERR("want a sequence of residues");
1713 i
= PySequence_Size(q
); if (i
< 0) goto end
;
1714 if (i
!= n
) VALERR("residue count mismatch");
1715 v
= xmalloc(n
* sizeof(*v
));
1716 for (i
= 0; i
< n
; i
++) {
1717 if ((x
= PySequence_GetItem(q
, i
)) == 0) goto end
;
1718 xx
= getmp(x
); Py_DECREF(x
); if (!xx
) goto end
;
1721 z
= mp_pywrap(mpcrt_solve(c
, MP_NEW
, v
));
1725 for (i
= 0; i
< n
; i
++)
1734 static void mpcrt_pydealloc(PyObject
*me
)
1736 mpcrt
*c
= MPCRT_PY(me
);
1741 static PyObject
*mpcrt_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1744 Py_ssize_t n
, i
= 0, j
;
1745 static const char *const kwlist
[] = { "mv", 0 };
1746 PyObject
*q
= 0, *x
;
1747 mp
*xx
= MP_NEW
, *y
= MP_NEW
, *g
= MP_NEW
;
1751 if (PyTuple_GET_SIZE(arg
) > 1)
1753 else if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O:new", KWLIST
, &q
))
1756 if (!PySequence_Check(q
)) TYERR("want a sequence of moduli");
1757 n
= PySequence_Size(q
); if (n
< 0) goto end
;
1758 if (!n
) VALERR("want at least one modulus");
1759 v
= xmalloc(n
* sizeof(*v
));
1760 for (i
= 0; i
< n
; i
++) {
1761 if ((x
= PySequence_GetItem(q
, i
)) == 0) goto end
;
1762 xx
= getmp(x
); Py_DECREF(x
); if (!xx
) goto end
;
1763 if (MP_CMP(xx
, <=, MP_ZERO
)) VALERR("moduli must be positive");
1764 v
[i
].m
= xx
; v
[i
].n
= 0; v
[i
].ni
= 0; v
[i
].nni
= 0; xx
= MP_NEW
;
1767 for (j
= 0; j
< i
; j
++) mpmul_add(&mm
, v
[j
].m
);
1768 xx
= mpmul_done(&mm
);
1769 for (j
= 0; j
< i
; j
++) {
1770 mp_div(&y
, 0, xx
, v
[j
].m
);
1771 mp_gcd(&g
, 0, 0, y
, v
[j
].m
);
1772 if (!MP_EQ(g
, MP_ONE
)) VALERR("moduli must be pairwise coprime");
1775 c
= (mpcrt_pyobj
*)ty
->tp_alloc(ty
, 0);
1776 mpcrt_create(&c
->c
, v
, n
, 0);
1778 mp_drop(xx
); mp_drop(y
); mp_drop(g
);
1779 return ((PyObject
*)c
);
1784 for (i
= 0; i
< n
; i
++)
1789 mp_drop(xx
); mp_drop(y
); mp_drop(g
);
1793 static PyObject
*mcget_product(PyObject
*me
, void *hunoz
)
1794 { return (mp_pywrap(MP_COPY(MPCRT_PY(me
)->mb
.m
))); }
1796 static PyObject
*mcget_moduli(PyObject
*me
, void *hunoz
)
1800 mpcrt
*c
= MPCRT_PY(me
);
1802 if ((q
= PyList_New(c
->k
)) == 0) return (0);
1803 for (i
= 0; i
< c
->k
; i
++)
1804 PyList_SET_ITEM(q
, i
, mp_pywrap(c
->v
[i
].m
));
1808 static const PyGetSetDef mpcrt_pygetset
[] = {
1809 #define GETSETNAME(op, name) mc##op##_##name
1810 GET (product
, "C.product -> product of moduli")
1811 GET (moduli
, "C.moduli -> list of individual moduli")
1816 static const PyMethodDef mpcrt_pymethods
[] = {
1817 #define METHNAME(name) mcmeth_##name
1818 METH (solve
, "C.solve([R0, R1]) -> X mod C.product")
1823 static const PyTypeObject mpcrt_pytype_skel
= {
1824 PyVarObject_HEAD_INIT(0, 0) /* Header */
1825 "MPCRT", /* @tp_name@ */
1826 sizeof(mpcrt_pyobj
), /* @tp_basicsize@ */
1827 0, /* @tp_itemsize@ */
1829 mpcrt_pydealloc
, /* @tp_dealloc@ */
1831 0, /* @tp_getattr@ */
1832 0, /* @tp_setattr@ */
1833 0, /* @tp_compare@ */
1835 0, /* @tp_as_number@ */
1836 0, /* @tp_as_sequence@ */
1837 0, /* @tp_as_mapping@ */
1841 0, /* @tp_getattro@ */
1842 0, /* @tp_setattro@ */
1843 0, /* @tp_as_buffer@ */
1844 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1845 Py_TPFLAGS_BASETYPE
,
1848 "MPCRT(SEQ): a context for solving Chinese Remainder Theorem problems.",
1850 0, /* @tp_traverse@ */
1852 0, /* @tp_richcompare@ */
1853 0, /* @tp_weaklistoffset@ */
1855 0, /* @tp_iternext@ */
1856 PYMETHODS(mpcrt
), /* @tp_methods@ */
1857 0, /* @tp_members@ */
1858 PYGETSET(mpcrt
), /* @tp_getset@ */
1861 0, /* @tp_descr_get@ */
1862 0, /* @tp_descr_set@ */
1863 0, /* @tp_dictoffset@ */
1865 PyType_GenericAlloc
, /* @tp_alloc@ */
1866 mpcrt_pynew
, /* @tp_new@ */
1871 /*----- Binary polynomials ------------------------------------------------*/
1873 static PyObject
*gf_pyrepr(PyObject
*o
)
1874 { return mp_topystring(MP_X(o
), 16, "GF(", "0x", "L)"); }
1876 static PyObject
*gf_pyrichcompare(PyObject
*x
, PyObject
*y
, int op
)
1882 if (gfbinop(x
, y
, &xx
, &yy
)) RETURN_NOTIMPL
;
1884 case Py_EQ
: b
= MP_EQ(xx
, yy
); break;
1885 case Py_NE
: b
= !MP_EQ(xx
, yy
); break;
1890 case Py_LT
: b
= xl
< yl
; break;
1891 case Py_LE
: b
= xl
<= yl
; break;
1892 case Py_GT
: b
= xl
> yl
; break;
1893 case Py_GE
: b
= xl
>= yl
; break;
1898 MP_DROP(xx
); MP_DROP(yy
);
1899 return (getbool(b
));
1902 static PyObject
*gf_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1908 static const char *const kwlist
[] = { "x", "radix", 0 };
1910 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O|i:gf", KWLIST
, &x
, &radix
))
1912 if (GF_PYCHECK(x
)) RETURN_OBJ(x
);
1913 if (!good_radix_p(radix
, 1)) VALERR("radix out of range");
1914 if ((z
= mp_frompyobject(x
, radix
)) == 0) {
1915 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to gf",
1916 Py_TYPE(x
)->tp_name
);
1921 VALERR("gf cannot be negative");
1923 zz
= (mp_pyobj
*)ty
->tp_alloc(ty
, 0);
1926 return ((PyObject
*)zz
);
1929 static PyObject
*gf_pyexp(PyObject
*x
, PyObject
*y
, PyObject
*z
)
1931 mp
*xx
= 0, *yy
= 0, *zz
= 0;
1935 if ((xx
= tomp(x
)) == 0 || (yy
= tomp(y
)) == 0 ||
1936 (z
&& z
!= Py_None
&& (zz
= tomp(z
)) == 0)) {
1937 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
1940 if (!z
|| z
== Py_None
) {
1941 if (MP_NEGP(yy
)) VALERR("negative exponent");
1942 r
= gf_exp(MP_NEW
, xx
, yy
);
1945 if (MP_ZEROP(zz
)) ZDIVERR("zero modulus");
1947 if ((xx
= gf_modinv_checked(xx
, xx
, zz
)) == 0) goto end
;
1948 yy
= mp_neg(yy
, yy
);
1950 gfreduce_create(&gr
, zz
);
1951 r
= gfreduce_exp(&gr
, MP_NEW
, xx
, yy
);
1952 gfreduce_destroy(&gr
);
1956 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
1960 static PyObject
*gfmeth_sqr(PyObject
*me
)
1961 { return (gf_pywrap(gf_sqr(MP_NEW
, MP_X(me
)))); }
1963 static PyObject
*gfmeth_gcd(PyObject
*me
, PyObject
*arg
)
1966 mp
*yy
= 0, *zz
= MP_NEW
;
1968 if (!PyArg_ParseTuple(arg
, "O&:gcd", convgf
, &yy
)) goto end
;
1969 gf_gcd(&zz
, 0, 0, MP_X(me
), yy
);
1972 if (yy
) MP_DROP(yy
);
1976 static PyObject
*gfmeth_gcdx(PyObject
*me
, PyObject
*arg
)
1979 mp
*yy
= 0, *zz
= MP_NEW
, *uu
= MP_NEW
, *vv
= MP_NEW
;
1981 if (!PyArg_ParseTuple(arg
, "O&:gcdx", convgf
, &yy
))
1983 gf_gcd(&zz
, &uu
, &vv
, MP_X(me
), yy
);
1984 z
= Py_BuildValue("(NNN)",
1985 gf_pywrap(zz
), gf_pywrap(uu
), gf_pywrap(vv
));
1987 if (yy
) MP_DROP(yy
);
1991 static PyObject
*gfmeth_modinv(PyObject
*me
, PyObject
*arg
)
1994 mp
*yy
= 0, *zz
= MP_NEW
;
1996 if (!PyArg_ParseTuple(arg
, "O&:modinv", convgf
, &yy
) ||
1997 (zz
= gf_modinv_checked(MP_NEW
, yy
, MP_X(me
))) == 0)
2001 if (yy
) MP_DROP(yy
);
2005 static PyObject
*gfmeth_fromstring(PyObject
*me
,
2006 PyObject
*arg
, PyObject
*kw
)
2013 mptext_stringctx sc
;
2014 static const char *const kwlist
[] = { "x", "radix", 0 };
2016 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "s#|i:fromstring", KWLIST
,
2019 if (!good_radix_p(r
, 1)) VALERR("bad radix");
2020 sc
.buf
= p
; sc
.lim
= p
+ len
;
2021 if ((zz
= mp_read(MP_NEW
, r
, &mptext_stringops
, &sc
)) == 0 ||
2023 if (zz
) MP_DROP(zz
);
2024 VALERR("bad binary polynomial");
2026 z
= Py_BuildValue("(Ns#)", gf_pywrap(zz
),
2027 sc
.buf
, (Py_ssize_t
)(sc
.lim
- sc
.buf
));
2032 static PyObject
*gfmeth_irreduciblep(PyObject
*me
)
2033 { return getbool(gf_irreduciblep(MP_X(me
))); }
2035 static PyObject
*gfget_degree(PyObject
*me
, void *hunoz
)
2036 { return (PyInt_FromLong(mp_bits(MP_X(me
)) - 1)); }
2038 static const PyGetSetDef gf_pygetset
[] = {
2039 #define GETSETNAME(op, name) gf##op##_##name
2040 GET (degree
, "X.degree -> polynomial degree of X")
2042 #define GETSETNAME(op, name) mp##op##_##name
2043 GET (nbits
, "X.nbits -> bit length of X")
2044 GET (noctets
, "X.noctets -> octet length of X")
2049 static const PyMethodDef gf_pymethods
[] = {
2050 #define METHNAME(func) gfmeth_##func
2051 METH (setbit
, "X.setbit(N) -> X with bit N set")
2052 METH (clearbit
, "X.clearbit(N) -> X with bit N clear")
2053 METH (testbit
, "X.testbit(N) -> true/false if bit N set/clear in X")
2054 NAMETH(sqr
, "X.sqr() -> X^2")
2055 METH (gcd
, "X.gcd(Y) -> gcd(X, Y)")
2056 METH (gcdx
, "X.gcdx(Y) -> (gcd(X, Y), U, V) with X U + Y V = gcd(X, Y)")
2057 METH (modinv
, "X.modinv(Y) -> multiplicative inverse of Y mod X")
2058 NAMETH(irreduciblep
, "X.irreduciblep() -> true/false")
2059 KWSMTH(fromstring
, "fromstring(STR, [radix = 0]) -> (X, REST)\n"
2060 " Parse STR as a binary polynomial, according to RADIX. If RADIX is\n"
2061 " zero, read a prefix from STR to decide radix: allow `0b' for binary,\n"
2062 " `0' or `0o' for octal, `0x' for hex, or `R_' for other radix R.")
2063 SMTH (loadl
, "loadl(STR) -> X: read little-endian bytes")
2064 SMTH (loadb
, "loadb(STR) -> X: read big-endian bytes")
2065 SMTH (frombuf
, "frombuf(STR) -> (X, REST): read buffer format")
2067 #define METHNAME(func) mpmeth_##func
2068 KWMETH(tostring
, "X.tostring([radix = 10]) -> STR")
2069 KWMETH(storel
, "X.storel([len = -1]) -> little-endian bytes")
2070 KWMETH(storeb
, "X.storeb([len = -1]) -> big-endian bytes")
2071 KWMETH(storel2c
, "X.storel2c([len = -1]) -> "
2072 "little-endian bytes, two's complement")
2073 KWMETH(storeb2c
, "X.storeb2c([len = -1]) -> "
2074 "big-endian bytes, two's complement")
2075 NAMETH(tobuf
, "X.tobuf() -> buffer format")
2080 static const PyNumberMethods gf_pynumber
= {
2081 gf_pyadd
, /* @nb_add@ */
2082 gf_pysub
, /* @nb_subtract@ */
2083 gf_pymul
, /* @nb_multiply@ */
2084 0, /* @nb_divide@ */
2085 gf_pymod
, /* @nb_remainder@ */
2086 gf_pydivmod
, /* @nb_divmod@ */
2087 gf_pyexp
, /* @nb_power@ */
2088 mp_pyid
, /* @nb_negative@ */
2089 mp_pyid
, /* @nb_positive@ */
2090 mp_pyid
, /* @nb_absolute@ */
2091 mp_pynonzerop
, /* @nb_nonzero@ */
2092 0 /* doesn't make any sense */, /* @nb_invert@ */
2093 gf_pylsl
, /* @nb_lshift@ */
2094 gf_pylsr
, /* @nb_rshift@ */
2095 gf_pyand
, /* @nb_and@ */
2096 gf_pyxor
, /* @nb_xor@ */
2097 gf_pyor
, /* @nb_or@ */
2098 gf_pycoerce
, /* @nb_coerce@ */
2099 mp_pyint
, /* @nb_int@ */
2100 mp_pylong
, /* @nb_long@ */
2101 0 /* doesn't make any sense */, /* @nb_float@ */
2102 mp_pyoct
, /* @nb_oct@ */
2103 mp_pyhex
, /* @nb_hex@ */
2105 0, /* @nb_inplace_add@ */
2106 0, /* @nb_inplace_subtract@ */
2107 0, /* @nb_inplace_multiply@ */
2108 0, /* @nb_inplace_divide@ */
2109 0, /* @nb_inplace_remainder@ */
2110 0, /* @nb_inplace_power@ */
2111 0, /* @nb_inplace_lshift@ */
2112 0, /* @nb_inplace_rshift@ */
2113 0, /* @nb_inplace_and@ */
2114 0, /* @nb_inplace_xor@ */
2115 0, /* @nb_inplace_or@ */
2117 gf_pydiv
, /* @nb_floor_divide@ */
2118 0, /* @nb_true_divide@ */
2119 0, /* @nb_inplace_floor_divide@ */
2120 0, /* @nb_inplace_true_divide@ */
2123 static const PyTypeObject gf_pytype_skel
= {
2124 PyVarObject_HEAD_INIT(0, 0) /* Header */
2125 "GF", /* @tp_name@ */
2126 sizeof(mp_pyobj
), /* @tp_basicsize@ */
2127 0, /* @tp_itemsize@ */
2129 mp_pydealloc
, /* @tp_dealloc@ */
2131 0, /* @tp_getattr@ */
2132 0, /* @tp_setattr@ */
2133 0, /* @tp_compare@ */
2134 gf_pyrepr
, /* @tp_repr@ */
2135 PYNUMBER(gf
), /* @tp_as_number@ */
2136 0, /* @tp_as_sequence@ */
2137 0, /* @tp_as_mapping@ */
2138 mp_pyhash
, /* @tp_hash@ */
2140 mp_pyhex
, /* @tp_str@ */
2141 0, /* @tp_getattro@ */
2142 0, /* @tp_setattro@ */
2143 0, /* @tp_as_buffer@ */
2144 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
2145 Py_TPFLAGS_CHECKTYPES
|
2146 Py_TPFLAGS_BASETYPE
,
2149 "Binary polynomials. Support almost all the standard arithmetic\n"
2152 "Constructor GF(X, [radix = R]) attempts to convert X to a `GF'. If\n"
2153 "X is a string, it's read in radix-R form, or we look for a prefix\n"
2154 "if R = 0. Other acceptable things are field elements, elliptic curve\n"
2155 "points, group elements, Python `int' and `long' objects, and anything\n"
2156 "with an integer conversion.\n"
2158 "The name is hopelessly wrong from a technical point of view, but\n"
2159 "but it's much easier to type than `p2' or `c2' or whatever.\n"
2163 " * Use `//' for Euclidean division: `/' gives exact rational division.",
2165 0, /* @tp_traverse@ */
2167 gf_pyrichcompare
, /* @tp_richcompare@ */
2168 0, /* @tp_weaklistoffset@ */
2170 0, /* @tp_iternext@ */
2171 PYMETHODS(gf
), /* @tp_methods@ */
2172 0, /* @tp_members@ */
2173 PYGETSET(gf
), /* @tp_getset@ */
2176 0, /* @tp_descr_get@ */
2177 0, /* @tp_descr_set@ */
2178 0, /* @tp_dictoffset@ */
2180 PyType_GenericAlloc
, /* @tp_alloc@ */
2181 gf_pynew
, /* @tp_new@ */
2186 /*----- Sparse poly reduction ---------------------------------------------*/
2188 static PyTypeObject
*gfreduce_pytype
;
2190 typedef struct gfreduce_pyobj
{
2195 #define GFREDUCE_PY(o) (&((gfreduce_pyobj *)(o))->mr)
2197 static PyObject
*grmeth_exp(PyObject
*me
, PyObject
*arg
)
2200 mp
*yy
= 0, *zz
= 0;
2202 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convgf
, &yy
, convgf
, &zz
))
2205 if ((yy
= gf_modinv_checked(yy
, yy
, GFREDUCE_PY(me
)->p
)) == 0) goto end
;
2206 zz
= mp_neg(zz
, zz
);
2208 rc
= gf_pywrap(gfreduce_exp(GFREDUCE_PY(me
), MP_NEW
, yy
, zz
));
2210 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
2214 static PyObject
*grmeth_trace(PyObject
*me
, PyObject
*arg
)
2219 if (!PyArg_ParseTuple(arg
, "O&:trace", convgf
, &xx
)) goto end
;
2220 rc
= PyInt_FromLong(gfreduce_trace(GFREDUCE_PY(me
), xx
));
2222 if (xx
) MP_DROP(xx
);
2226 static PyObject
*grmeth_halftrace(PyObject
*me
, PyObject
*arg
)
2231 if (!PyArg_ParseTuple(arg
, "O&:halftrace", convgf
, &xx
)) goto end
;
2232 rc
= gf_pywrap(gfreduce_halftrace(GFREDUCE_PY(me
), MP_NEW
, xx
));
2234 if (xx
) MP_DROP(xx
);
2238 static PyObject
*grmeth_sqrt(PyObject
*me
, PyObject
*arg
)
2243 if (!PyArg_ParseTuple(arg
, "O&:sqrt", convgf
, &xx
)) goto end
;
2244 if ((yy
= gfreduce_sqrt(GFREDUCE_PY(me
), MP_NEW
, xx
)) == 0)
2245 VALERR("no modular square root");
2248 if (xx
) MP_DROP(xx
);
2252 static PyObject
*grmeth_quadsolve(PyObject
*me
, PyObject
*arg
)
2257 if (!PyArg_ParseTuple(arg
, "O&:quadsolve", convgf
, &xx
)) goto end
;
2258 if ((yy
= gfreduce_quadsolve(GFREDUCE_PY(me
), MP_NEW
, xx
)) == 0)
2259 VALERR("no solution found");
2262 if (xx
) MP_DROP(xx
);
2266 static PyObject
*grmeth_reduce(PyObject
*me
, PyObject
*arg
)
2271 if (!PyArg_ParseTuple(arg
, "O&:reduce", convgf
, &yy
)) goto end
;
2272 z
= gf_pywrap(gfreduce_do(GFREDUCE_PY(me
), MP_NEW
, yy
));
2277 static void gfreduce_pydealloc(PyObject
*me
)
2279 gfreduce_destroy(GFREDUCE_PY(me
));
2283 static PyObject
*gfreduce_pynew(PyTypeObject
*ty
,
2284 PyObject
*arg
, PyObject
*kw
)
2286 gfreduce_pyobj
*mr
= 0;
2288 static const char *const kwlist
[] = { "m", 0 };
2291 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", KWLIST
, convgf
, &xx
))
2293 if (MP_ZEROP(xx
)) ZDIVERR("modulus is zero!");
2294 gfreduce_create(&r
, xx
);
2295 mr
= (gfreduce_pyobj
*)ty
->tp_alloc(ty
, 0);
2298 if (xx
) MP_DROP(xx
);
2299 return ((PyObject
*)mr
);
2302 static PyObject
*grget_m(PyObject
*me
, void *hunoz
)
2303 { return (gf_pywrap(MP_COPY(GFREDUCE_PY(me
)->p
))); }
2305 static const PyGetSetDef gfreduce_pygetset
[] = {
2306 #define GETSETNAME(op, name) gr##op##_##name
2307 GET (m
, "R.m -> reduction polynomial")
2312 static const PyMethodDef gfreduce_pymethods
[] = {
2313 #define METHNAME(name) grmeth_##name
2314 METH (reduce
, "R.reduce(X) -> X mod B.m")
2315 METH (trace
, "R.trace(X) -> Tr(X) = x + x^2 + ... + x^{2^{m - 1}}")
2316 METH (halftrace
, "R.halftrace(X) -> x + x^{2^2} + ... + x^{2^{m - 1}}")
2317 METH (sqrt
, "R.sqrt(X) -> Y where Y^2 = X mod R")
2318 METH (quadsolve
, "R.quadsolve(X) -> Y where Y^2 + Y = X mod R")
2319 METH (exp
, "R.exp(X, N) -> X^N mod B.m")
2324 static const PyTypeObject gfreduce_pytype_skel
= {
2325 PyVarObject_HEAD_INIT(0, 0) /* Header */
2326 "GFReduce", /* @tp_name@ */
2327 sizeof(gfreduce_pyobj
), /* @tp_basicsize@ */
2328 0, /* @tp_itemsize@ */
2330 gfreduce_pydealloc
, /* @tp_dealloc@ */
2332 0, /* @tp_getattr@ */
2333 0, /* @tp_setattr@ */
2334 0, /* @tp_compare@ */
2336 0, /* @tp_as_number@ */
2337 0, /* @tp_as_sequence@ */
2338 0, /* @tp_as_mapping@ */
2342 0, /* @tp_getattro@ */
2343 0, /* @tp_setattro@ */
2344 0, /* @tp_as_buffer@ */
2345 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
2346 Py_TPFLAGS_BASETYPE
,
2349 "GFReduce(N): a context for reduction modulo sparse polynomials.",
2351 0, /* @tp_traverse@ */
2353 0, /* @tp_richcompare@ */
2354 0, /* @tp_weaklistoffset@ */
2356 0, /* @tp_iternext@ */
2357 PYMETHODS(gfreduce
), /* @tp_methods@ */
2358 0, /* @tp_members@ */
2359 PYGETSET(gfreduce
), /* @tp_getset@ */
2362 0, /* @tp_descr_get@ */
2363 0, /* @tp_descr_set@ */
2364 0, /* @tp_dictoffset@ */
2366 PyType_GenericAlloc
, /* @tp_alloc@ */
2367 gfreduce_pynew
, /* @tp_new@ */
2372 /*----- Normal/poly transformation ----------------------------------------*/
2374 static PyTypeObject
*gfn_pytype
;
2376 typedef struct gfn_pyobj
{
2382 #define GFN_P(o) (((gfn_pyobj *)(o))->p)
2383 #define GFN_PTON(o) (&((gfn_pyobj *)(o))->pton)
2384 #define GFN_NTOP(o) (&((gfn_pyobj *)(o))->ntop)
2386 static PyObject
*gfn_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
2388 mp
*p
= 0, *beta
= 0;
2390 static const char *const kwlist
[] = { "p", "beta", 0 };
2392 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&O&:new", KWLIST
,
2393 convgf
, &p
, convgf
, &beta
))
2395 gg
= PyObject_New(gfn_pyobj
, ty
);
2397 if (gfn_create(p
, beta
, &gg
->ntop
, &gg
->pton
)) {
2400 VALERR("can't invert transformation matrix");
2406 return ((PyObject
*)gg
);
2409 static PyObject
*gfnget_p(PyObject
*me
, void *hunoz
)
2410 { return (gf_pywrap(MP_COPY(GFN_P(me
)))); }
2412 static PyObject
*gfnget_beta(PyObject
*me
, void *hunoz
)
2414 gfn
*n
= GFN_NTOP(me
);
2415 mp
*x
= n
->r
[n
->n
- 1];
2416 return (gf_pywrap(MP_COPY(x
)));
2419 #define XFORMOP(name, NAME) \
2420 static PyObject *gfnmeth_##name(PyObject *me, PyObject *arg) \
2425 if (!PyArg_ParseTuple(arg, "O&:" #name, convgf, &xx)) goto end; \
2426 z = gfn_transform(GFN_##NAME(me), MP_NEW, xx); \
2429 if (!z) return (0); \
2430 return (gf_pywrap(z)); \
2436 static void gfn_pydealloc(PyObject
*me
)
2440 gfn_destroy(GFN_PTON(me
));
2441 gfn_destroy(GFN_NTOP(me
));
2446 static const PyGetSetDef gfn_pygetset
[] = {
2447 #define GETSETNAME(op, name) gfn##op##_##name
2448 GET (p
, "X.p -> polynomial basis, as polynomial")
2449 GET (beta
, "X.beta -> normal basis element, in poly form")
2454 static const PyMethodDef gfn_pymethods
[] = {
2455 #define METHNAME(name) gfnmeth_##name
2456 METH (pton
, "X.pton(A) -> normal-basis representation of A")
2457 METH (ntop
, "X.ntop(A) -> polynomial-basis representation of A")
2462 static const PyTypeObject gfn_pytype_skel
= {
2463 PyVarObject_HEAD_INIT(0, 0) /* Header */
2464 "GFN", /* @tp_name@ */
2465 sizeof(gfn_pyobj
), /* @tp_basicsize@ */
2466 0, /* @tp_itemsize@ */
2468 gfn_pydealloc
, /* @tp_dealloc@ */
2470 0, /* @tp_getattr@ */
2471 0, /* @tp_setattr@ */
2472 0, /* @tp_compare@ */
2474 0, /* @tp_as_number@ */
2475 0, /* @tp_as_sequence@ */
2476 0, /* @tp_as_mapping@ */
2480 0, /* @tp_getattro@ */
2481 0, /* @tp_setattro@ */
2482 0, /* @tp_as_buffer@ */
2483 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
2484 Py_TPFLAGS_BASETYPE
,
2487 "GFN(P, BETA): an object for transforming elements of binary fields\n"
2488 " between polynomial and normal basis representations.",
2490 0, /* @tp_traverse@ */
2492 0, /* @tp_richcompare@ */
2493 0, /* @tp_weaklistoffset@ */
2495 0, /* @tp_iternext@ */
2496 PYMETHODS(gfn
), /* @tp_methods@ */
2497 0, /* @tp_members@ */
2498 PYGETSET(gfn
), /* @tp_getset@ */
2501 0, /* @tp_descr_get@ */
2502 0, /* @tp_descr_set@ */
2503 0, /* @tp_dictoffset@ */
2505 PyType_GenericAlloc
, /* @tp_alloc@ */
2506 gfn_pynew
, /* @tp_new@ */
2511 /*----- Glue --------------------------------------------------------------*/
2513 static const struct nameval consts
[] = {
2518 void mp_pyinit(void)
2522 INITTYPE(mpmul
, root
);
2523 INITTYPE(mpmont
, root
);
2524 INITTYPE(mpbarrett
, root
);
2525 INITTYPE(mpreduce
, root
);
2526 INITTYPE(mpcrt
, root
);
2527 INITTYPE(gfreduce
, root
);
2528 INITTYPE(gfn
, root
);
2531 void mp_pyinsert(PyObject
*mod
)
2533 INSERT("MP", mp_pytype
);
2534 INSERT("MPMul", mpmul_pytype
);
2535 INSERT("MPMont", mpmont_pytype
);
2536 INSERT("MPBarrett", mpbarrett_pytype
);
2537 INSERT("MPReduce", mpreduce_pytype
);
2538 INSERT("MPCRT", mpcrt_pytype
);
2539 INSERT("GF", gf_pytype
);
2540 INSERT("GFReduce", gfreduce_pytype
);
2541 INSERT("GFN", gfn_pytype
);
2542 setconstants(mod
, consts
);
2545 /*----- That's all, folks -------------------------------------------------*/