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;
36 mp
*mp_frompylong(PyObject
*obj
)
39 PyLongObject
*l
= (PyLongObject
*)obj
;
50 assert(MPW_BITS
>= SHIFT
);
51 bits
= (unsigned long)sz
* SHIFT
;
52 w
= (bits
+ MPW_BITS
- 1)/MPW_BITS
;
53 x
= mp_new(w
, l
->ob_size
< 0 ? MP_NEG
: 0);
55 for (i
= 0; i
< sz
; i
++) {
56 r
|= (mpd
)l
->ob_digit
[i
] << b
;
58 while (b
>= MPW_BITS
) {
73 PyObject
*mp_topylong(mp
*x
)
75 unsigned long bits
= mp_bits(x
);
76 int sz
= (bits
+ SHIFT
- 1)/SHIFT
;
77 PyLongObject
*l
= _PyLong_New(sz
);
83 assert(MPW_BITS
>= SHIFT
);
84 while (i
< sz
&& p
< x
->vl
) {
87 while (i
< sz
&& b
>= SHIFT
) {
88 l
->ob_digit
[i
++] = r
& MASK
;
94 l
->ob_digit
[i
++] = r
& MASK
;
97 l
->ob_size
= (x
->f
& MP_NEG
) ?
-sz
: sz
;
98 return ((PyObject
*)l
);
101 mp
*mp_frompyobject(PyObject
*o
, int radix
)
105 if (PyString_Check(o
)) {
108 sc
.buf
= PyString_AS_STRING(o
);
109 sc
.lim
= sc
.buf
+ PyString_GET_SIZE(o
);
110 x
= mp_read(MP_NEW
, radix
, &mptext_stringops
, &sc
);
112 if (sc
.buf
< sc
.lim
) { MP_DROP(x
); return (0); }
115 if ((x
= tomp(o
)) != 0)
120 PyObject
*mp_topystring(mp
*x
, int radix
, const char *xpre
,
121 const char *pre
, const char *post
)
123 int len
= mptext_len(x
, radix
) + 1;
126 size_t xprelen
= xpre ?
strlen(xpre
) : 0;
127 size_t prelen
= pre ?
strlen(pre
) : 0;
128 size_t postlen
= post ?
strlen(post
) : 0;
131 o
= PyString_FromStringAndSize(0, len
+ 1 + xprelen
+ prelen
+ postlen
);
132 p
= PyString_AS_STRING(o
);
134 if (xpre
) { memcpy(sc
.buf
, xpre
, xprelen
); sc
.buf
+= xprelen
; }
135 if (MP_NEGP(x
)) { *sc
.buf
++ = '-'; x
= mp_neg(x
, x
); }
136 if (pre
) { memcpy(sc
.buf
, pre
, prelen
); sc
.buf
+= prelen
; }
137 sc
.lim
= sc
.buf
+ len
;
138 mp_write(x
, radix
, &mptext_stringops
, &sc
);
139 if (post
) { memcpy(sc
.buf
, post
, postlen
); sc
.buf
+= postlen
; }
141 _PyString_Resize(&o
, sc
.buf
- p
);
145 static int good_radix_p(int r
, int readp
)
147 return ((r
>= -255 && r
<= -2) ||
149 (r
>= 2 && r
<= 62));
152 PyObject
*mp_pywrap(mp
*x
)
154 mp_pyobj
*z
= PyObject_New(mp_pyobj
, mp_pytype
);
156 return ((PyObject
*)z
);
159 PyObject
*gf_pywrap(mp
*x
)
161 mp_pyobj
*z
= PyObject_New(mp_pyobj
, gf_pytype
);
163 return ((PyObject
*)z
);
166 int mp_tolong_checked(mp
*x
, long *l
, int must
)
168 static mp
*longmin
= 0, *longmax
= 0;
172 longmin
= mp_fromlong(MP_NEW
, LONG_MIN
);
173 longmax
= mp_fromlong(MP_NEW
, LONG_MAX
);
175 if (MP_CMP(x
, <, longmin
) || MP_CMP(x
, >, longmax
)) {
176 if (must
) VALERR("mp out of range for int");
185 /*----- Python interface --------------------------------------------------*/
187 static void mp_pydealloc(PyObject
*o
)
193 static PyObject
*mp_pyrepr(PyObject
*o
)
194 { return mp_topystring(MP_X(o
), 10, "MP(", 0, "L)"); }
196 static PyObject
*mp_pystr(PyObject
*o
)
197 { return mp_topystring(MP_X(o
), 10, 0, 0, 0); }
199 mp
*tomp(PyObject
*o
)
206 else if (MP_PYCHECK(o
) || GF_PYCHECK(o
))
207 return (MP_COPY(MP_X(o
)));
208 else if (FE_PYCHECK(o
))
209 return (F_OUT(FE_F(o
), MP_NEW
, FE_X(o
)));
210 else if (PFILT_PYCHECK(o
))
211 return (MP_COPY(PFILT_F(o
)->m
));
212 else if (ECPT_PYCHECK(o
)) {
214 if (EC_ATINF(ECPT_P(o
))) return (0);
219 } else if (GE_PYCHECK(o
)) {
220 if ((x
= G_TOINT(GE_G(o
), MP_NEW
, GE_X(o
))) == 0)
223 } else if (PyInt_Check(o
))
224 return (mp_fromlong(MP_NEW
, PyInt_AS_LONG(o
)));
225 else if ((l
= PyNumber_Long(o
)) != 0) {
226 x
= mp_frompylong(l
);
235 mp
*getmp(PyObject
*o
)
239 if ((x
= tomp(o
)) == 0) {
240 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to mp",
241 o
->ob_type
->tp_name
);
246 int convmp(PyObject
*o
, void *p
)
249 if ((x
= getmp(o
)) == 0) return (0);
254 mp
*getgf(PyObject
*o
)
258 if ((x
= tomp(o
)) == 0) {
259 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to gf",
260 o
->ob_type
->tp_name
);
265 int convgf(PyObject
*o
, void *p
)
268 if ((x
= getgf(o
)) == 0) return (0);
273 static mp
*implicitmp(PyObject
*o
)
284 static mp
*implicitgf(PyObject
*o
)
295 static int mpbinop(PyObject
*x
, PyObject
*y
, mp
**xx
, mp
**yy
)
297 if ((*xx
= implicitmp(x
)) == 0)
299 if ((*yy
= implicitmp(y
)) == 0) {
306 static int gfbinop(PyObject
*x
, PyObject
*y
, mp
**xx
, mp
**yy
)
308 if ((*xx
= implicitgf(x
)) == 0)
310 if ((*yy
= implicitgf(y
)) == 0) {
317 #define gf_and mp_and
319 #define gf_xor mp_xor
320 #define BINOP(pre, name) \
321 static PyObject *pre##_py##name(PyObject *x, PyObject *y) { \
323 if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL; \
324 zz = pre##_##name(MP_NEW, xx, yy); \
325 MP_DROP(xx); MP_DROP(yy); \
326 return (pre##_pywrap(zz)); \
342 static mp
*mp_abs(mp
*d
, mp
*x
)
345 return (mp_neg(d
, x
));
351 #define UNOP(pre, name) \
352 static PyObject *pre##_py##name(PyObject *x) \
353 { return mp_pywrap(pre##_##name(MP_NEW, MP_X(x))); }
359 static PyObject
*mp_pyid(PyObject
*x
) { RETURN_OBJ(x
); }
361 #define gf_lsr mp_lsr
362 #define SHIFTOP(pre, name, rname) \
363 static PyObject *pre##_py##name(PyObject *x, PyObject *y) { \
367 if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL; \
368 if (mp_tolong_checked(yy, &n, 1)) goto end; \
370 z = pre##_pywrap(mp_##rname(MP_NEW, xx, -n)); \
372 z = pre##_pywrap(mp_##name(MP_NEW, xx, n)); \
374 MP_DROP(xx); MP_DROP(yy); \
377 SHIFTOP(mp
, lsl2c
, lsr2c
)
378 SHIFTOP(mp
, lsr2c
, lsl2c
)
379 SHIFTOP(gf
, lsl
, lsr
)
380 SHIFTOP(gf
, lsr
, lsl
)
383 #define DIVOP(pre, name, qq, rr, gather) \
384 static PyObject *pre##_py##name(PyObject *x, PyObject *y) { \
387 INIT_##qq(q) INIT_##rr(r) \
388 if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL; \
390 ZDIVERR("division by zero"); \
391 pre##_div(ARG_##qq(q), ARG_##rr(r), xx, yy); \
394 MP_DROP(xx); MP_DROP(yy); \
397 #define INIT_YES(p) mp *p = MP_NEW;
399 #define ARG_YES(p) &p
401 DIVOP(mp
, divmod
, YES
, YES
,
402 Py_BuildValue("(NN)", mp_pywrap(q
), mp_pywrap(r
)))
403 DIVOP(mp
, div
, YES
, NO
, mp_pywrap(q
))
404 DIVOP(mp
, mod
, NO
, YES
, mp_pywrap(r
))
405 DIVOP(gf
, divmod
, YES
, YES
,
406 Py_BuildValue("(NN)", gf_pywrap(q
), gf_pywrap(r
)))
407 DIVOP(gf
, div
, YES
, NO
, gf_pywrap(q
))
408 DIVOP(gf
, mod
, NO
, YES
, gf_pywrap(r
))
415 static mp
*mp_modinv_checked(mp
*d
, mp
*x
, mp
*p
)
418 mp_gcd(&g
, 0, &d
, p
, x
);
419 if (!MP_EQ(g
, MP_ONE
)) {
420 MP_DROP(g
); MP_DROP(d
);
421 PyErr_SetString(PyExc_ZeroDivisionError
, "no modular inverse");
424 MP_DROP(g
); return (d
);
427 static PyObject
*mp_pyexp(PyObject
*x
, PyObject
*y
, PyObject
*z
)
429 mp
*xx
= 0, *yy
= 0, *zz
= 0;
433 if ((xx
= implicitmp(x
)) == 0 || (yy
= implicitmp(y
)) == 0 ||
434 (z
&& z
!= Py_None
&& (zz
= tomp(z
)) == 0)) {
435 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
438 if (!z
|| z
== Py_None
) {
439 if (MP_NEGP(yy
)) VALERR("negative exponent");
440 r
= mp_exp(MP_NEW
, xx
, yy
);
442 if (!MP_POSP(zz
)) VALERR("modulus must be positive");
444 if ((xx
= mp_modinv_checked(xx
, xx
, zz
)) == 0) goto end
;
449 mpmont_create(&mm
, zz
);
450 r
= mpmont_exp(&mm
, MP_NEW
, xx
, yy
);
454 mpbarrett_create(&mb
, zz
);
455 r
= mpbarrett_exp(&mb
, MP_NEW
, xx
, yy
);
456 mpbarrett_destroy(&mb
);
461 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
465 static mp
*gf_modinv_checked(mp
*d
, mp
*x
, mp
*p
)
468 gf_gcd(&g
, 0, &d
, p
, x
);
469 if (!MP_EQ(g
, MP_ONE
)) {
470 MP_DROP(g
); MP_DROP(d
);
471 PyErr_SetString(PyExc_ZeroDivisionError
, "no modular inverse");
474 MP_DROP(g
); return (d
);
477 #define BASEOP(name, radix, pre) \
478 static PyObject *mp_py##name(PyObject *x) \
479 { return mp_topystring(MP_X(x), radix, 0, pre, 0); }
481 BASEOP(hex
, 16, "0x");
484 static int mp_pynonzerop(PyObject
*x
) { return !MP_ZEROP(MP_X(x
)); }
486 static PyObject
*mp_pyint(PyObject
*x
)
489 if (!mp_tolong_checked(MP_X(x
), &l
, 0)) return (PyInt_FromLong(l
));
490 else return mp_topylong(MP_X(x
));
492 static PyObject
*mp_pylong(PyObject
*x
)
493 { return (mp_topylong(MP_X(x
))); }
494 static PyObject
*mp_pyfloat(PyObject
*x
)
496 PyObject
*l
= mp_topylong(MP_X(x
));
497 double f
= PyLong_AsDouble(l
);
499 return (PyFloat_FromDouble(f
));
502 #define COERCE(pre, PRE) \
503 static int pre##_pycoerce(PyObject **x, PyObject **y) \
507 if (PRE##_PYCHECK(*y)) { \
508 Py_INCREF(*x); Py_INCREF(*y); \
511 if ((z = tomp(*y)) != 0) { \
513 *y = pre##_pywrap(z); \
522 static int mp_pycompare(PyObject
*x
, PyObject
*y
)
523 { return mp_cmp(MP_X(x
), MP_X(y
)); }
525 static PyObject
*mp_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
531 static const char *const kwlist
[] = { "x", "radix", 0 };
533 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O|i:new", KWLIST
, &x
, &radix
))
535 if (MP_PYCHECK(x
)) RETURN_OBJ(x
);
536 if (!good_radix_p(radix
, 1)) VALERR("bad radix");
537 if ((z
= mp_frompyobject(x
, radix
)) == 0) {
538 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to mp",
539 x
->ob_type
->tp_name
);
542 zz
= (mp_pyobj
*)ty
->tp_alloc(ty
, 0);
545 return ((PyObject
*)zz
);
550 PyObject
*l
= mp_topylong(x
);
551 long h
= PyObject_Hash(l
);
552 Py_DECREF(l
); return (h
);
555 static long mp_pyhash(PyObject
*me
) { return (mphash(MP_X(me
))); }
557 static PyObject
*mpmeth_jacobi(PyObject
*me
, PyObject
*arg
)
562 if (!PyArg_ParseTuple(arg
, "O&:jacobi", convmp
, &y
)) goto end
;
563 z
= PyInt_FromLong(mp_jacobi(y
, MP_X(me
)));
569 #define BITOP(pre, name, c) \
570 static PyObject *pre##meth_##name(PyObject *me, PyObject *arg) \
573 if (!PyArg_ParseTuple(arg, "O&:" #name, convulong, &i)) return (0); \
574 return (pre##_pywrap(mp_##name##c(MP_NEW, MP_X(me), i))); \
576 BITOP(mp
, setbit
, 2c
);
577 BITOP(mp
, clearbit
, 2c
);
579 BITOP(gf
, clearbit
, );
582 static PyObject
*mpmeth_testbit(PyObject
*me
, PyObject
*arg
)
585 if (!PyArg_ParseTuple(arg
, "O&:testbit", convulong
, &i
)) return (0);
586 return (getbool(mp_testbit2c(MP_X(me
), i
)));
589 static PyObject
*gfmeth_testbit(PyObject
*me
, PyObject
*arg
)
592 if (!PyArg_ParseTuple(arg
, "O&:testbit", convulong
, &i
)) return (0);
593 return (getbool(mp_testbit(MP_X(me
), i
)));
596 static PyObject
*mpmeth_odd(PyObject
*me
, PyObject
*arg
)
601 if (!PyArg_ParseTuple(arg
, ":odd")) return (0);
602 t
= mp_odd(MP_NEW
, MP_X(me
), &s
);
603 return (Py_BuildValue("(lN)", (long)s
, mp_pywrap(t
)));
606 static PyObject
*mpmeth_sqr(PyObject
*me
, PyObject
*arg
)
608 if (!PyArg_ParseTuple(arg
, ":sqr")) return (0);
609 return (mp_pywrap(mp_sqr(MP_NEW
, MP_X(me
))));
612 static PyObject
*mpmeth_sqrt(PyObject
*me
, PyObject
*arg
)
614 if (!PyArg_ParseTuple(arg
, ":sqrt")) return (0);
615 if (MP_NEGP(MP_X(me
))) VALERR("negative root");
616 return (mp_pywrap(mp_sqrt(MP_NEW
, MP_X(me
))));
621 static PyObject
*mpmeth_gcd(PyObject
*me
, PyObject
*arg
)
623 mp
*y
= 0, *zz
= MP_NEW
;
626 if (!PyArg_ParseTuple(arg
, "O&:gcd", convmp
, &y
)) goto end
;
627 mp_gcd(&zz
, 0, 0, MP_X(me
), y
);
634 static PyObject
*mpmeth_gcdx(PyObject
*me
, PyObject
*arg
)
637 mp
*yy
= 0, *zz
= MP_NEW
, *uu
= MP_NEW
, *vv
= MP_NEW
;
639 if (!PyArg_ParseTuple(arg
, "O&:gcdx", convmp
, &yy
)) goto end
;
640 mp_gcd(&zz
, &uu
, &vv
, MP_X(me
), yy
);
641 z
= Py_BuildValue("(NNN)",
642 mp_pywrap(zz
), mp_pywrap(uu
), mp_pywrap(vv
));
648 static PyObject
*mpmeth_modinv(PyObject
*me
, PyObject
*arg
)
651 mp
*yy
= 0, *zz
= MP_NEW
;
653 if (!PyArg_ParseTuple(arg
, "O&:modinv", convmp
, &yy
) ||
654 (zz
= mp_modinv_checked(MP_NEW
, yy
, MP_X(me
))) == 0)
662 static PyObject
*mpmeth_tostring(PyObject
*me
, PyObject
*arg
, PyObject
*kw
)
665 static const char *const kwlist
[] = { "radix", 0 };
666 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "|i:tostring", KWLIST
, &radix
))
668 if (!good_radix_p(radix
, 0)) VALERR("bad radix");
669 return (mp_topystring(MP_X(me
), radix
, 0, 0, 0));
674 static PyObject
*mpmeth_modsqrt(PyObject
*me
, PyObject
*arg
)
677 mp
*yy
= 0, *zz
= MP_NEW
;
679 if (!PyArg_ParseTuple(arg
, "O&:modsqrt", convmp
, &yy
)) goto end
;
680 if ((zz
= mp_modsqrt(MP_NEW
, yy
, MP_X(me
))) == 0)
681 VALERR("no modular square root");
688 static PyObject
*mpmeth_leastcongruent(PyObject
*me
, PyObject
*arg
)
693 if (!PyArg_ParseTuple(arg
, "O&O&:leastcongruent", convmp
, &b
, convmp
, &m
))
695 z
= mp_leastcongruent(MP_NEW
, b
, MP_X(me
), m
);
701 #define STOREOP(name, c) \
702 static PyObject *mpmeth_##name(PyObject *me, \
703 PyObject *arg, PyObject *kw) \
706 static const char *const kwlist[] = { "len", 0 }; \
709 if (!PyArg_ParseTupleAndKeywords(arg, kw, "|l:" #name, \
713 len = mp_octets##c(MP_X(me)); \
716 rc = bytestring_pywrap(0, len); \
717 mp_##name(MP_X(me), PyString_AS_STRING(rc), len); \
723 STOREOP(storel2c
, 2c
)
724 STOREOP(storeb2c
, 2c
)
727 #define BUFOP(ty, pyty) \
728 static PyObject *meth__##pyty##_frombuf(PyObject *me, PyObject *arg) \
736 if (!PyArg_ParseTuple(arg, "Os#:frombuf", &me, &p, &sz)) goto end; \
737 buf_init(&b, p, sz); \
738 if ((x = buf_getmp(&b)) == 0) VALERR("malformed data"); \
739 rc = Py_BuildValue("(NN)", ty##_pywrap(x), \
740 bytestring_pywrapbuf(&b)); \
748 static PyObject
*mpmeth_tobuf(PyObject
*me
, PyObject
*arg
)
755 if (!PyArg_ParseTuple(arg
, ":tobuf")) return (0);
757 n
= mp_octets(x
) + 3;
758 rc
= bytestring_pywrap(0, n
);
759 buf_init(&b
, PyString_AS_STRING(rc
), n
);
762 _PyString_Resize(&rc
, BLEN(&b
));
766 static PyObject
*mpmeth_primep(PyObject
*me
, PyObject
*arg
, PyObject
*kw
)
768 grand
*r
= &rand_global
;
769 static const char *const kwlist
[] = { "rng", 0 };
772 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "|O&", KWLIST
, convgrand
, &r
))
774 rc
= getbool(pgen_primep(MP_X(me
), r
));
779 static PyObject
*mpget_nbits(PyObject
*me
, void *hunoz
)
780 { return (PyInt_FromLong(mp_bits(MP_X(me
)))); }
782 static PyObject
*mpget_noctets(PyObject
*me
, void *hunoz
)
783 { return (PyInt_FromLong(mp_octets(MP_X(me
)))); }
785 static PyObject
*mpget_noctets2c(PyObject
*me
, void *hunoz
)
786 { return (PyInt_FromLong(mp_octets2c(MP_X(me
)))); }
788 static PyGetSetDef mp_pygetset
[] = {
789 #define GETSETNAME(op, func) mp##op##_##func
790 GET (nbits
, "X.nbits -> bit length of X")
791 GET (noctets
, "X.noctets -> octet length of X")
792 GET (noctets2c
, "X.noctets2c -> two's complement octet length of X")
797 static PyMethodDef mp_pymethods
[] = {
798 #define METHNAME(func) mpmeth_##func
799 METH (jacobi
, "X.jacobi(Y) -> Jacobi symbol (Y|X) (NB inversion!)")
800 METH (setbit
, "X.setbit(N) -> X with bit N set")
801 METH (clearbit
, "X.clearbit(N) -> X with bit N clear")
802 METH (testbit
, "X.testbit(N) -> true/false if bit N set/clear in X")
803 METH (odd
, "X.odd() -> S, T where X = 2^S T with T odd")
804 METH (sqr
, "X.sqr() -> X^2")
805 METH (sqrt
, "X.sqrt() -> largest integer <= sqrt(X)")
806 METH (gcd
, "X.gcd(Y) -> gcd(X, Y)")
808 "X.gcdx(Y) -> (gcd(X, Y), U, V) with X U + Y V = gcd(X, Y)")
809 METH (modinv
, "X.modinv(Y) -> multiplicative inverse of Y mod X")
810 METH (modsqrt
, "X.modsqrt(Y) -> square root of Y mod X, if X prime")
811 METH (leastcongruent
,
812 "X.leastcongruent(B, M) -> smallest Z >= B with Z == X (mod M)")
813 KWMETH(primep
, "X.primep([rng = rand]) -> true/false if X is prime")
814 KWMETH(tostring
, "X.tostring([radix = 10]) -> STR")
815 KWMETH(storel
, "X.storel([len = -1]) -> little-endian bytes")
816 KWMETH(storeb
, "X.storeb([len = -1]) -> big-endian bytes")
818 "X.storel2c([len = -1]) -> little-endian bytes, two's complement")
820 "X.storeb2c([len = -1]) -> big-endian bytes, two's complement")
821 METH (tobuf
, "X.tobuf() -> buffer format")
826 static PyNumberMethods mp_pynumber
= {
827 mp_pyadd
, /* @nb_add@ */
828 mp_pysub
, /* @nb_subtract@ */
829 mp_pymul
, /* @nb_multiply@ */
831 mp_pymod
, /* @nb_remainder@ */
832 mp_pydivmod
, /* @nb_divmod@ */
833 mp_pyexp
, /* @nb_power@ */
834 mp_pyneg
, /* @nb_negative@ */
835 mp_pyid
, /* @nb_positive@ */
836 mp_pyabs
, /* @nb_absolute@ */
837 mp_pynonzerop
, /* @nb_nonzero@ */
838 mp_pynot2c
, /* @nb_invert@ */
839 mp_pylsl2c
, /* @nb_lshift@ */
840 mp_pylsr2c
, /* @nb_rshift@ */
841 mp_pyand2c
, /* @nb_and@ */
842 mp_pyxor2c
, /* @nb_xor@ */
843 mp_pyor2c
, /* @nb_or@ */
844 mp_pycoerce
, /* @nb_coerce@ */
845 mp_pyint
, /* @nb_int@ */
846 mp_pylong
, /* @nb_long@ */
847 mp_pyfloat
, /* @nb_float@ */
848 mp_pyoct
, /* @nb_oct@ */
849 mp_pyhex
, /* @nb_hex@ */
851 0, /* @nb_inplace_add@ */
852 0, /* @nb_inplace_subtract@ */
853 0, /* @nb_inplace_multiply@ */
854 0, /* @nb_inplace_divide@ */
855 0, /* @nb_inplace_remainder@ */
856 0, /* @nb_inplace_power@ */
857 0, /* @nb_inplace_lshift@ */
858 0, /* @nb_inplace_rshift@ */
859 0, /* @nb_inplace_and@ */
860 0, /* @nb_inplace_xor@ */
861 0, /* @nb_inplace_or@ */
863 mp_pydiv
, /* @nb_floor_divide@ */
864 0, /* @nb_true_divide@ */
865 0, /* @nb_inplace_floor_divide@ */
866 0, /* @nb_inplace_true_divide@ */
869 static PyTypeObject mp_pytype_skel
= {
870 PyObject_HEAD_INIT(0) 0, /* Header */
871 "MP", /* @tp_name@ */
872 sizeof(mp_pyobj
), /* @tp_basicsize@ */
873 0, /* @tp_itemsize@ */
875 mp_pydealloc
, /* @tp_dealloc@ */
877 0, /* @tp_getattr@ */
878 0, /* @tp_setattr@ */
879 mp_pycompare
, /* @tp_compare@ */
880 mp_pyrepr
, /* @tp_repr@ */
881 &mp_pynumber
, /* @tp_as_number@ */
882 0, /* @tp_as_sequence@ */
883 0, /* @tp_as_mapping@ */
884 mp_pyhash
, /* @tp_hash@ */
886 mp_pystr
, /* @tp_str@ */
887 0, /* @tp_getattro@ */
888 0, /* @tp_setattro@ */
889 0, /* @tp_as_buffer@ */
890 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
891 Py_TPFLAGS_CHECKTYPES
|
895 "Multiprecision integers, similar to `long' but more efficient and\n\
896 versatile. Support all the standard arithmetic operations, with\n\
897 implicit conversions from `PrimeFilter', and other objects which\n\
898 convert to `long'.\n\
900 Constructor MP(X, [radix = R]) attempts to convert X to an `MP'. If\n\
901 X is a string, it's read in radix-R form, or we look for a prefix\n\
902 if R = 0. Other acceptable things are field elements, elliptic curve\n\
903 points, group elements, Python `int' and `long' objects, and anything\n\
904 with an integer conversion.\n\
908 * Use `//' for integer division: `/' gives exact rational division.",
910 0, /* @tp_traverse@ */
912 0, /* @tp_richcompare@ */
913 0, /* @tp_weaklistoffset@ */
915 0, /* @tp_iternext@ */
916 mp_pymethods
, /* @tp_methods@ */
917 0, /* @tp_members@ */
918 mp_pygetset
, /* @tp_getset@ */
921 0, /* @tp_descr_get@ */
922 0, /* @tp_descr_set@ */
923 0, /* @tp_dictoffset@ */
925 PyType_GenericAlloc
, /* @tp_alloc@ */
926 mp_pynew
, /* @tp_new@ */
931 static PyObject
*meth__MP_fromstring(PyObject
*me
,
932 PyObject
*arg
, PyObject
*kw
)
940 static const char *const kwlist
[] = { "class", "x", "radix", 0 };
942 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "Os#|i:fromstring",
943 KWLIST
, &me
, &p
, &len
, &r
))
945 if (!good_radix_p(r
, 1)) VALERR("bad radix");
946 sc
.buf
= p
; sc
.lim
= p
+ len
;
947 if ((zz
= mp_read(MP_NEW
, r
, &mptext_stringops
, &sc
)) == 0)
948 VALERR("bad integer");
949 z
= Py_BuildValue("(Ns#)", mp_pywrap(zz
),
950 sc
.buf
, (Py_ssize_t
)(sc
.lim
- sc
.buf
));
955 static PyObject
*meth__MP_factorial(PyObject
*me
, PyObject
*arg
)
959 if (!PyArg_ParseTuple(arg
, "OO&:factorial", &me
, convulong
, &i
))
965 static PyObject
*meth__MP_fibonacci(PyObject
*me
, PyObject
*arg
)
969 if (!PyArg_ParseTuple(arg
, "Ol:fibonacci", &me
, &i
)) return (0);
974 #define LOADOP(pre, py, name) \
975 static PyObject *meth__##py##_##name(PyObject *me, PyObject *arg) \
979 if (!PyArg_ParseTuple(arg, "Os#:" #name, &me, &p, &len)) return (0); \
980 return (pre##_pywrap(mp_##name(MP_NEW, p, len))); \
982 LOADOP(mp
, MP
, loadl
)
983 LOADOP(mp
, MP
, loadb
)
984 LOADOP(mp
, MP
, loadl2c
)
985 LOADOP(mp
, MP
, loadb2c
)
986 LOADOP(gf
, GF
, loadl
)
987 LOADOP(gf
, GF
, loadb
)
990 /*----- Products of small integers ----------------------------------------*/
992 typedef struct mpmul_pyobj
{
998 #define MPMUL_LIVEP(o) (((mpmul_pyobj *)(o))->livep)
999 #define MPMUL_PY(o) (&((mpmul_pyobj *)(o))->mm)
1001 static void mpmul_pydealloc(PyObject
*me
)
1003 if (MPMUL_LIVEP(me
))
1004 mp_drop(mpmul_done(MPMUL_PY(me
)));
1008 static PyObject
*mmmeth_factor(PyObject
*me
, PyObject
*arg
)
1013 if (!MPMUL_LIVEP(me
)) VALERR("MPMul object invalid");
1014 if (PyTuple_Size(arg
) != 1)
1015 i
= PyObject_GetIter(arg
);
1017 if ((q
= PyTuple_GetItem(arg
, 0)) == 0) goto end
;
1018 if ((i
= PyObject_GetIter(q
)) == 0) {
1019 PyErr_Clear(); /* that's ok */
1020 i
= PyObject_GetIter(arg
);
1024 while ((q
= PyIter_Next(i
)) != 0) {
1025 x
= getmp(q
); Py_DECREF(q
); if (!x
) {
1029 mpmul_add(MPMUL_PY(me
), x
);
1038 static PyObject
*mmmeth_done(PyObject
*me
, PyObject
*arg
)
1042 if (!PyArg_ParseTuple(arg
, ":done")) goto end
;
1043 if (!MPMUL_LIVEP(me
)) VALERR("MPMul object invalid");
1044 x
= mpmul_done(MPMUL_PY(me
));
1045 MPMUL_LIVEP(me
) = 0;
1046 return (mp_pywrap(x
));
1051 static PyObject
*mpmul_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1055 if (kw
) TYERR("keyword arguments not allowed here");
1056 mm
= (mpmul_pyobj
*)ty
->tp_alloc(ty
, 0);
1057 mpmul_init(&mm
->mm
);
1059 if (mmmeth_factor((PyObject
*)mm
, arg
) == 0) {
1063 return ((PyObject
*)mm
);
1068 static PyObject
*mmget_livep(PyObject
*me
, void *hunoz
)
1069 { return (getbool(MPMUL_LIVEP(me
))); }
1071 static PyGetSetDef mpmul_pygetset
[] = {
1072 #define GETSETNAME(op, name) mm##op##_##name
1073 GET (livep
, "MM.livep -> flag: object still valid?")
1078 static PyMethodDef mpmul_pymethods
[] = {
1079 #define METHNAME(name) mmmeth_##name
1080 METH (factor
, "MM.factor(ITERABLE) or MM.factor(I, ...)")
1081 METH (done
, "MM.done() -> PRODUCT")
1086 static PyTypeObject
*mpmul_pytype
, mpmul_pytype_skel
= {
1087 PyObject_HEAD_INIT(0) 0, /* Header */
1088 "MPMul", /* @tp_name@ */
1089 sizeof(mpmul_pyobj
), /* @tp_basicsize@ */
1090 0, /* @tp_itemsize@ */
1092 mpmul_pydealloc
, /* @tp_dealloc@ */
1094 0, /* @tp_getattr@ */
1095 0, /* @tp_setattr@ */
1096 0, /* @tp_compare@ */
1098 0, /* @tp_as_number@ */
1099 0, /* @tp_as_sequence@ */
1100 0, /* @tp_as_mapping@ */
1104 0, /* @tp_getattro@ */
1105 0, /* @tp_setattro@ */
1106 0, /* @tp_as_buffer@ */
1107 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1108 Py_TPFLAGS_BASETYPE
,
1111 "MPMul(N_0, N_1, ....): an object for multiplying many small integers.",
1113 0, /* @tp_traverse@ */
1115 0, /* @tp_richcompare@ */
1116 0, /* @tp_weaklistoffset@ */
1118 0, /* @tp_iternext@ */
1119 mpmul_pymethods
, /* @tp_methods@ */
1120 0, /* @tp_members@ */
1121 mpmul_pygetset
, /* @tp_getset@ */
1124 0, /* @tp_descr_get@ */
1125 0, /* @tp_descr_set@ */
1126 0, /* @tp_dictoffset@ */
1128 PyType_GenericAlloc
, /* @tp_alloc@ */
1129 mpmul_pynew
, /* @tp_new@ */
1134 /*----- Montgomery reduction ----------------------------------------------*/
1136 typedef struct mpmont_pyobj
{
1141 #define MPMONT_PY(o) (&((mpmont_pyobj *)(o))->mm)
1143 static PyObject
*mmmeth_int(PyObject
*me
, PyObject
*arg
)
1147 mpmont
*mm
= MPMONT_PY(me
);
1149 if (!PyArg_ParseTuple(arg
, "O&:in", convmp
, &yy
))
1151 mp_div(0, &yy
, yy
, mm
->m
);
1152 z
= mp_pywrap(mpmont_mul(mm
, MP_NEW
, yy
, mm
->r2
));
1154 if (yy
) MP_DROP(yy
);
1158 static PyObject
*mmmeth_mul(PyObject
*me
, PyObject
*arg
)
1161 mp
*yy
= 0, *zz
= 0;
1163 if (!PyArg_ParseTuple(arg
, "O&O&:mul", convmp
, &yy
, convmp
, &zz
))
1165 rc
= mp_pywrap(mpmont_mul(MPMONT_PY(me
), MP_NEW
, yy
, zz
));
1167 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1171 static PyObject
*mmmeth_exp(PyObject
*me
, PyObject
*arg
)
1174 mp
*yy
= 0, *zz
= 0;
1176 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convmp
, &yy
, convmp
, &zz
))
1179 if ((yy
= mp_modinv_checked(yy
, yy
, MPMONT_PY(me
)->m
)) == 0) goto end
;
1180 zz
= mp_neg(zz
, zz
);
1182 rc
= mp_pywrap(mpmont_exp(MPMONT_PY(me
), MP_NEW
, yy
, zz
));
1184 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1188 static PyObject
*mmmeth_expr(PyObject
*me
, PyObject
*arg
)
1191 mp
*yy
= 0, *zz
= 0;
1193 if (!PyArg_ParseTuple(arg
, "O&O&:expr", convmp
, &yy
, convmp
, &zz
))
1196 yy
= mpmont_reduce(MPMONT_PY(me
), yy
, yy
);
1197 if ((yy
= mp_modinv_checked(yy
, yy
, MPMONT_PY(me
)->m
)) == 0) goto end
;
1198 yy
= mpmont_mul(MPMONT_PY(me
), yy
, yy
, MPMONT_PY(me
)->r2
);
1199 zz
= mp_neg(zz
, zz
);
1201 rc
= mp_pywrap(mpmont_expr(MPMONT_PY(me
), MP_NEW
, yy
, zz
));
1203 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1207 static PyObject
*mm_mexpr_id(PyObject
*me
)
1208 { return mp_pywrap(MP_COPY(MPMONT_PY(me
)->r
)); }
1210 static int mm_mexpr_fill(void *p
, PyObject
*me
, PyObject
*x
, PyObject
*y
)
1212 mp
*xx
= 0, *yy
= 0;
1213 mp_expfactor
*f
= p
;
1214 mpmont
*mm
= MPMONT_PY(me
);
1216 if ((xx
= getmp(x
)) == 0 || (yy
= getmp(y
)) == 0)
1219 xx
= mpmont_reduce(mm
, xx
, xx
);
1220 if ((xx
= mp_modinv_checked(xx
, xx
, yy
)) == 0)
1222 xx
= mpmont_mul(mm
, xx
, xx
, mm
->r2
);
1223 yy
= mp_neg(yy
, yy
);
1230 mp_drop(xx
); mp_drop(yy
);
1234 static PyObject
*mm_mexpr(PyObject
*me
, void *v
, int n
)
1235 { return mp_pywrap(mpmont_mexpr(MPMONT_PY(me
), MP_NEW
, v
, n
)); }
1237 static void mp_mexp_drop(void *p
)
1239 mp_expfactor
*f
= p
;
1244 static PyObject
*mmmeth_mexpr(PyObject
*me
, PyObject
*arg
)
1246 return mexp_common(me
, arg
, sizeof(mp_expfactor
),
1247 mm_mexpr_id
, mm_mexpr_fill
, mm_mexpr
, mp_mexp_drop
);
1250 static PyObject
*mp_mexp_id(PyObject
*me
)
1251 { return mp_pywrap(MP_ONE
); }
1253 static int mp_mexp_fill(void *p
, PyObject
*me
, PyObject
*x
, PyObject
*y
)
1255 mp
*xx
= 0, *yy
= 0;
1256 mp_expfactor
*f
= p
;
1258 if ((xx
= getmp(x
)) == 0 || (yy
= getmp(y
)) == 0)
1261 if ((xx
= mp_modinv_checked(xx
, xx
, yy
)) == 0)
1263 yy
= mp_neg(yy
, yy
);
1270 mp_drop(xx
); mp_drop(yy
);
1274 static PyObject
*mm_mexp(PyObject
*me
, void *v
, int n
)
1275 { return mp_pywrap(mpmont_mexp(MPMONT_PY(me
), MP_NEW
, v
, n
)); }
1277 static PyObject
*mmmeth_mexp(PyObject
*me
, PyObject
*arg
)
1279 return mexp_common(me
, arg
, sizeof(mp_expfactor
),
1280 mp_mexp_id
, mp_mexp_fill
, mm_mexp
, mp_mexp_drop
);
1283 #define mmmeth_ext mmmeth_reduce
1284 static PyObject
*mmmeth_reduce(PyObject
*me
, PyObject
*arg
)
1289 if (!PyArg_ParseTuple(arg
, "O&", convmp
, &yy
)) goto end
;
1290 z
= mp_pywrap(mpmont_reduce(MPMONT_PY(me
), MP_NEW
, yy
));
1295 static void mpmont_pydealloc(PyObject
*me
)
1297 mpmont_destroy(MPMONT_PY(me
));
1301 static PyObject
*mpmont_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1303 mpmont_pyobj
*mm
= 0;
1304 static const char *const kwlist
[] = { "m", 0 };
1307 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", KWLIST
, convmp
, &xx
))
1309 if (!MP_POSP(xx
) || !MP_ODDP(xx
)) VALERR("m must be positive and odd");
1310 mm
= (mpmont_pyobj
*)ty
->tp_alloc(ty
, 0);
1311 mpmont_create(&mm
->mm
, xx
);
1313 if (xx
) MP_DROP(xx
);
1314 return ((PyObject
*)mm
);
1317 static PyObject
*mmget_m(PyObject
*me
, void *hunoz
)
1318 { return (mp_pywrap(MP_COPY(MPMONT_PY(me
)->m
))); }
1320 static PyObject
*mmget_r(PyObject
*me
, void *hunoz
)
1321 { return (mp_pywrap(MP_COPY(MPMONT_PY(me
)->r
))); }
1323 static PyObject
*mmget_r2(PyObject
*me
, void *hunoz
)
1324 { return (mp_pywrap(MP_COPY(MPMONT_PY(me
)->r2
))); }
1326 static PyGetSetDef mpmont_pygetset
[] = {
1327 #define GETSETNAME(op, name) mm##op##_##name
1328 GET (m
, "M.m -> modulus for reduction")
1329 GET (r
, "M.r -> multiplicative identity")
1330 GET (r2
, "M.r2 -> M.r^2, Montgomerization factor")
1335 static PyMethodDef mpmont_pymethods
[] = {
1336 #define METHNAME(name) mmmeth_##name
1337 METH (int, "M.int(X) -> XR")
1338 METH (mul
, "M.mul(XR, YR) -> ZR where Z = X Y")
1339 METH (expr
, "M.expr(XR, N) -> ZR where Z = X^N mod M.m")
1341 M.mexpr([(XR0, N0), (XR1, N1), ...]) = ZR where Z = X0^N0 X1^N1 ... mod M.m\n\
1342 \t(the list may be flattened if this more convenient.)")
1343 METH (reduce
, "M.reduce(XR) -> X")
1344 METH (ext
, "M.ext(XR) -> X")
1345 METH (exp
, "M.exp(X, N) -> X^N mod M.m")
1347 M.mexp([(X0, N0), (X1, N1), ...]) = X0^N0 X1^N1 ... mod M.m\n\
1348 \t(the list may be flattened if this more convenient.)")
1353 static PyTypeObject
*mpmont_pytype
, mpmont_pytype_skel
= {
1354 PyObject_HEAD_INIT(0) 0, /* Header */
1355 "MPMont", /* @tp_name@ */
1356 sizeof(mpmont_pyobj
), /* @tp_basicsize@ */
1357 0, /* @tp_itemsize@ */
1359 mpmont_pydealloc
, /* @tp_dealloc@ */
1361 0, /* @tp_getattr@ */
1362 0, /* @tp_setattr@ */
1363 0, /* @tp_compare@ */
1365 0, /* @tp_as_number@ */
1366 0, /* @tp_as_sequence@ */
1367 0, /* @tp_as_mapping@ */
1371 0, /* @tp_getattro@ */
1372 0, /* @tp_setattro@ */
1373 0, /* @tp_as_buffer@ */
1374 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1375 Py_TPFLAGS_BASETYPE
,
1378 "MPMont(N): a Montgomery reduction context.",
1380 0, /* @tp_traverse@ */
1382 0, /* @tp_richcompare@ */
1383 0, /* @tp_weaklistoffset@ */
1385 0, /* @tp_iternext@ */
1386 mpmont_pymethods
, /* @tp_methods@ */
1387 0, /* @tp_members@ */
1388 mpmont_pygetset
, /* @tp_getset@ */
1391 0, /* @tp_descr_get@ */
1392 0, /* @tp_descr_set@ */
1393 0, /* @tp_dictoffset@ */
1395 PyType_GenericAlloc
, /* @tp_alloc@ */
1396 mpmont_pynew
, /* @tp_new@ */
1401 /*----- Barrett reduction -------------------------------------------------*/
1403 typedef struct mpbarrett_pyobj
{
1408 #define MPBARRETT_PY(o) (&((mpbarrett_pyobj *)(o))->mb)
1410 static PyObject
*mbmeth_exp(PyObject
*me
, PyObject
*arg
)
1413 mp
*yy
= 0, *zz
= 0;
1415 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convmp
, &yy
, convmp
, &zz
))
1418 if ((yy
= mp_modinv_checked(yy
, yy
, MPBARRETT_PY(me
)->m
)) == 0) goto end
;
1419 zz
= mp_neg(zz
, zz
);
1421 rc
= mp_pywrap(mpbarrett_exp(MPBARRETT_PY(me
), MP_NEW
, yy
, zz
));
1423 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1427 static PyObject
*mb_mexp(PyObject
*me
, void *v
, int n
)
1428 { return mp_pywrap(mpbarrett_mexp(MPBARRETT_PY(me
), MP_NEW
, v
, n
)); }
1430 static PyObject
*mbmeth_mexp(PyObject
*me
, PyObject
*arg
)
1432 return mexp_common(me
, arg
, sizeof(mp_expfactor
),
1433 mp_mexp_id
, mp_mexp_fill
, mb_mexp
, mp_mexp_drop
);
1436 static PyObject
*mbmeth_reduce(PyObject
*me
, PyObject
*arg
)
1441 if (!PyArg_ParseTuple(arg
, "O&:reduce", convmp
, &yy
))
1443 z
= mp_pywrap(mpbarrett_reduce(MPBARRETT_PY(me
), MP_NEW
, yy
));
1448 static void mpbarrett_pydealloc(PyObject
*me
)
1450 mpbarrett_destroy(MPBARRETT_PY(me
));
1454 static PyObject
*mpbarrett_pynew(PyTypeObject
*ty
,
1455 PyObject
*arg
, PyObject
*kw
)
1457 mpbarrett_pyobj
*mb
= 0;
1458 static const char *const kwlist
[] = { "m", 0 };
1461 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", KWLIST
, convmp
, &xx
))
1463 if (!MP_POSP(xx
)) VALERR("m must be positive");
1464 mb
= (mpbarrett_pyobj
*)ty
->tp_alloc(ty
, 0);
1465 mpbarrett_create(&mb
->mb
, xx
);
1467 if (xx
) MP_DROP(xx
);
1468 return ((PyObject
*)mb
);
1471 static PyObject
*mbget_m(PyObject
*me
, void *hunoz
)
1472 { return (mp_pywrap(MP_COPY(MPBARRETT_PY(me
)->m
))); }
1474 static PyGetSetDef mpbarrett_pygetset
[] = {
1475 #define GETSETNAME(op, name) mb##op##_##name
1476 GET (m
, "B.m -> modulus for reduction")
1481 static PyMethodDef mpbarrett_pymethods
[] = {
1482 #define METHNAME(name) mbmeth_##name
1483 METH (reduce
, "B.reduce(X) -> X mod B.m")
1484 METH (exp
, "B.exp(X, N) -> X^N mod B.m")
1486 B.mexp([(X0, N0), (X1, N1), ...]) = X0^N0 X1^N1 ... mod B.m\n\
1487 \t(the list may be flattened if this more convenient.)")
1492 static PyTypeObject
*mpbarrett_pytype
, mpbarrett_pytype_skel
= {
1493 PyObject_HEAD_INIT(0) 0, /* Header */
1494 "MPBarrett", /* @tp_name@ */
1495 sizeof(mpbarrett_pyobj
), /* @tp_basicsize@ */
1496 0, /* @tp_itemsize@ */
1498 mpbarrett_pydealloc
, /* @tp_dealloc@ */
1500 0, /* @tp_getattr@ */
1501 0, /* @tp_setattr@ */
1502 0, /* @tp_compare@ */
1504 0, /* @tp_as_number@ */
1505 0, /* @tp_as_sequence@ */
1506 0, /* @tp_as_mapping@ */
1510 0, /* @tp_getattro@ */
1511 0, /* @tp_setattro@ */
1512 0, /* @tp_as_buffer@ */
1513 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1514 Py_TPFLAGS_BASETYPE
,
1517 "MPBarrett(N): a Barrett reduction context.",
1519 0, /* @tp_traverse@ */
1521 0, /* @tp_richcompare@ */
1522 0, /* @tp_weaklistoffset@ */
1524 0, /* @tp_iternext@ */
1525 mpbarrett_pymethods
, /* @tp_methods@ */
1526 0, /* @tp_members@ */
1527 mpbarrett_pygetset
, /* @tp_getset@ */
1530 0, /* @tp_descr_get@ */
1531 0, /* @tp_descr_set@ */
1532 0, /* @tp_dictoffset@ */
1534 PyType_GenericAlloc
, /* @tp_alloc@ */
1535 mpbarrett_pynew
, /* @tp_new@ */
1540 /*----- Nice prime reduction ----------------------------------------------*/
1542 typedef struct mpreduce_pyobj
{
1547 #define MPREDUCE_PY(o) (&((mpreduce_pyobj *)(o))->mr)
1549 static PyObject
*mrmeth_exp(PyObject
*me
, PyObject
*arg
)
1552 mp
*yy
= 0, *zz
= 0;
1554 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convmp
, &yy
, convmp
, &zz
))
1557 if ((yy
= mp_modinv_checked(yy
, yy
, MPREDUCE_PY(me
)->p
)) == 0) goto end
;
1558 zz
= mp_neg(zz
, zz
);
1560 rc
= mp_pywrap(mpreduce_exp(MPREDUCE_PY(me
), MP_NEW
, yy
, zz
));
1562 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1566 static PyObject
*mrmeth_reduce(PyObject
*me
, PyObject
*arg
)
1571 if (!PyArg_ParseTuple(arg
, "O&:reduce", convmp
, &yy
)) goto end
;
1572 z
= mp_pywrap(mpreduce_do(MPREDUCE_PY(me
), MP_NEW
, yy
));
1577 static void mpreduce_pydealloc(PyObject
*me
)
1579 mpreduce_destroy(MPREDUCE_PY(me
));
1583 static PyObject
*mpreduce_pynew(PyTypeObject
*ty
,
1584 PyObject
*arg
, PyObject
*kw
)
1586 mpreduce_pyobj
*mr
= 0;
1588 static const char *const kwlist
[] = { "m", 0 };
1591 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", KWLIST
, convmp
, &xx
))
1593 if (!MP_POSP(xx
)) VALERR("m must be positive");
1594 if (mpreduce_create(&r
, xx
)) VALERR("bad modulus (must be 2^k - ...)");
1595 mr
= (mpreduce_pyobj
*)ty
->tp_alloc(ty
, 0);
1598 if (xx
) MP_DROP(xx
);
1599 return ((PyObject
*)mr
);
1602 static PyObject
*mrget_m(PyObject
*me
, void *hunoz
)
1603 { return (mp_pywrap(MP_COPY(MPREDUCE_PY(me
)->p
))); }
1605 static PyGetSetDef mpreduce_pygetset
[] = {
1606 #define GETSETNAME(op, name) mr##op##_##name
1607 GET (m
, "R.m -> modulus for reduction")
1612 static PyMethodDef mpreduce_pymethods
[] = {
1613 #define METHNAME(name) mrmeth_##name
1614 METH (reduce
, "R.reduce(X) -> X mod B.m")
1615 METH (exp
, "R.exp(X, N) -> X^N mod B.m")
1620 static PyTypeObject
*mpreduce_pytype
, mpreduce_pytype_skel
= {
1621 PyObject_HEAD_INIT(0) 0, /* Header */
1622 "MPReduce", /* @tp_name@ */
1623 sizeof(mpreduce_pyobj
), /* @tp_basicsize@ */
1624 0, /* @tp_itemsize@ */
1626 mpreduce_pydealloc
, /* @tp_dealloc@ */
1628 0, /* @tp_getattr@ */
1629 0, /* @tp_setattr@ */
1630 0, /* @tp_compare@ */
1632 0, /* @tp_as_number@ */
1633 0, /* @tp_as_sequence@ */
1634 0, /* @tp_as_mapping@ */
1638 0, /* @tp_getattro@ */
1639 0, /* @tp_setattro@ */
1640 0, /* @tp_as_buffer@ */
1641 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1642 Py_TPFLAGS_BASETYPE
,
1645 "MPReduce(N): a reduction context for reduction modulo Solinas primes.",
1647 0, /* @tp_traverse@ */
1649 0, /* @tp_richcompare@ */
1650 0, /* @tp_weaklistoffset@ */
1652 0, /* @tp_iternext@ */
1653 mpreduce_pymethods
, /* @tp_methods@ */
1654 0, /* @tp_members@ */
1655 mpreduce_pygetset
, /* @tp_getset@ */
1658 0, /* @tp_descr_get@ */
1659 0, /* @tp_descr_set@ */
1660 0, /* @tp_dictoffset@ */
1662 PyType_GenericAlloc
, /* @tp_alloc@ */
1663 mpreduce_pynew
, /* @tp_new@ */
1668 /*----- Chinese Remainder Theorem solution --------------------------------*/
1670 typedef struct mpcrt_pyobj
{
1675 #define MPCRT_PY(o) (&((mpcrt_pyobj *)(o))->c)
1677 static PyObject
*mcmeth_solve(PyObject
*me
, PyObject
*arg
)
1679 mpcrt
*c
= MPCRT_PY(me
);
1680 PyObject
*q
= 0, *x
, *z
= 0;
1683 Py_ssize_t i
= 0, n
= c
->k
;
1686 if (PyTuple_Size(arg
) == n
)
1688 else if (!PyArg_ParseTuple(arg
, "O:solve", &q
))
1691 if (!PySequence_Check(q
)) TYERR("want a sequence of residues");
1692 i
= PySequence_Size(q
); if (i
< 0) goto end
;
1693 if (i
!= n
) VALERR("residue count mismatch");
1694 v
= xmalloc(n
* sizeof(*v
));
1695 for (i
= 0; i
< n
; i
++) {
1696 if ((x
= PySequence_GetItem(q
, i
)) == 0) goto end
;
1697 xx
= getmp(x
); Py_DECREF(x
); if (!xx
) goto end
;
1700 z
= mp_pywrap(mpcrt_solve(c
, MP_NEW
, v
));
1704 for (i
= 0; i
< n
; i
++)
1713 static void mpcrt_pydealloc(PyObject
*me
)
1715 mpcrt
*c
= MPCRT_PY(me
);
1720 static PyObject
*mpcrt_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1723 Py_ssize_t n
, i
= 0, j
;
1724 static const char *const kwlist
[] = { "mv", 0 };
1725 PyObject
*q
= 0, *x
;
1726 mp
*xx
= MP_NEW
, *y
= MP_NEW
, *g
= MP_NEW
;
1730 if (PyTuple_Size(arg
) > 1)
1732 else if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O:new", KWLIST
, &q
))
1735 if (!PySequence_Check(q
)) TYERR("want a sequence of moduli");
1736 n
= PySequence_Size(q
); if (n
< 0) goto end
;
1737 if (!n
) VALERR("want at least one modulus");
1738 v
= xmalloc(n
* sizeof(*v
));
1739 for (i
= 0; i
< n
; i
++) {
1740 if ((x
= PySequence_GetItem(q
, i
)) == 0) goto end
;
1741 xx
= getmp(x
); Py_DECREF(x
); if (!xx
) goto end
;
1742 if (MP_CMP(xx
, <=, MP_ZERO
)) VALERR("moduli must be positive");
1743 v
[i
].m
= xx
; v
[i
].n
= 0; v
[i
].ni
= 0; v
[i
].nni
= 0; xx
= MP_NEW
;
1746 for (j
= 0; j
< i
; j
++) mpmul_add(&mm
, v
[j
].m
);
1747 xx
= mpmul_done(&mm
);
1748 for (j
= 0; j
< i
; j
++) {
1749 mp_div(&y
, 0, xx
, v
[j
].m
);
1750 mp_gcd(&g
, 0, 0, y
, v
[j
].m
);
1751 if (!MP_EQ(g
, MP_ONE
)) VALERR("moduli must be pairwise coprime");
1754 c
= (mpcrt_pyobj
*)ty
->tp_alloc(ty
, 0);
1755 mpcrt_create(&c
->c
, v
, n
, 0);
1757 mp_drop(xx
); mp_drop(y
); mp_drop(g
);
1758 return ((PyObject
*)c
);
1763 for (i
= 0; i
< n
; i
++)
1768 mp_drop(xx
); mp_drop(y
); mp_drop(g
);
1772 static PyObject
*mcget_product(PyObject
*me
, void *hunoz
)
1773 { return (mp_pywrap(MP_COPY(MPCRT_PY(me
)->mb
.m
))); }
1775 static PyObject
*mcget_moduli(PyObject
*me
, void *hunoz
)
1779 mpcrt
*c
= MPCRT_PY(me
);
1781 if ((q
= PyList_New(c
->k
)) == 0) return (0);
1782 for (i
= 0; i
< c
->k
; i
++)
1783 PyList_SetItem(q
, i
, mp_pywrap(c
->v
[i
].m
));
1787 static PyGetSetDef mpcrt_pygetset
[] = {
1788 #define GETSETNAME(op, name) mc##op##_##name
1789 GET (product
, "C.product -> product of moduli")
1790 GET (moduli
, "C.moduli -> list of individual moduli")
1795 static PyMethodDef mpcrt_pymethods
[] = {
1796 #define METHNAME(name) mcmeth_##name
1797 METH (solve
, "C.solve([R0, R1]) -> X mod C.product")
1802 static PyTypeObject
*mpcrt_pytype
, mpcrt_pytype_skel
= {
1803 PyObject_HEAD_INIT(0) 0, /* Header */
1804 "MPCRT", /* @tp_name@ */
1805 sizeof(mpcrt_pyobj
), /* @tp_basicsize@ */
1806 0, /* @tp_itemsize@ */
1808 mpcrt_pydealloc
, /* @tp_dealloc@ */
1810 0, /* @tp_getattr@ */
1811 0, /* @tp_setattr@ */
1812 0, /* @tp_compare@ */
1814 0, /* @tp_as_number@ */
1815 0, /* @tp_as_sequence@ */
1816 0, /* @tp_as_mapping@ */
1820 0, /* @tp_getattro@ */
1821 0, /* @tp_setattro@ */
1822 0, /* @tp_as_buffer@ */
1823 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1824 Py_TPFLAGS_BASETYPE
,
1827 "MPCRT(SEQ): a context for solving Chinese Remainder Theorem problems.",
1829 0, /* @tp_traverse@ */
1831 0, /* @tp_richcompare@ */
1832 0, /* @tp_weaklistoffset@ */
1834 0, /* @tp_iternext@ */
1835 mpcrt_pymethods
, /* @tp_methods@ */
1836 0, /* @tp_members@ */
1837 mpcrt_pygetset
, /* @tp_getset@ */
1840 0, /* @tp_descr_get@ */
1841 0, /* @tp_descr_set@ */
1842 0, /* @tp_dictoffset@ */
1844 PyType_GenericAlloc
, /* @tp_alloc@ */
1845 mpcrt_pynew
, /* @tp_new@ */
1850 /*----- Binary polynomials ------------------------------------------------*/
1852 static PyObject
*gf_pyrepr(PyObject
*o
)
1853 { return mp_topystring(MP_X(o
), 16, "GF(", "0x", "L)"); }
1855 static PyObject
*gf_pyrichcompare(PyObject
*x
, PyObject
*y
, int op
)
1861 if (gfbinop(x
, y
, &xx
, &yy
)) RETURN_NOTIMPL
;
1863 case Py_EQ
: b
= MP_EQ(xx
, yy
); break;
1864 case Py_NE
: b
= !MP_EQ(xx
, yy
); break;
1869 case Py_LT
: b
= xl
< yl
; break;
1870 case Py_LE
: b
= xl
<= yl
; break;
1871 case Py_GT
: b
= xl
> yl
; break;
1872 case Py_GE
: b
= xl
>= yl
; break;
1877 MP_DROP(xx
); MP_DROP(yy
);
1878 return (getbool(b
));
1881 static PyObject
*gf_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1887 static const char *const kwlist
[] = { "x", "radix", 0 };
1889 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O|i:gf", KWLIST
, &x
, &radix
))
1891 if (GF_PYCHECK(x
)) RETURN_OBJ(x
);
1892 if (!good_radix_p(radix
, 1)) VALERR("radix out of range");
1893 if ((z
= mp_frompyobject(x
, radix
)) == 0) {
1894 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to gf",
1895 x
->ob_type
->tp_name
);
1900 VALERR("gf cannot be negative");
1902 zz
= (mp_pyobj
*)ty
->tp_alloc(ty
, 0);
1905 return ((PyObject
*)zz
);
1908 static PyObject
*gf_pyexp(PyObject
*x
, PyObject
*y
, PyObject
*z
)
1910 mp
*xx
= 0, *yy
= 0, *zz
= 0;
1914 if ((xx
= tomp(x
)) == 0 || (yy
= tomp(y
)) == 0 ||
1915 (z
&& z
!= Py_None
&& (zz
= tomp(z
)) == 0)) {
1916 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
1919 if (!z
|| z
== Py_None
) {
1920 if (MP_NEGP(yy
)) VALERR("negative exponent");
1921 r
= gf_exp(MP_NEW
, xx
, yy
);
1924 if (MP_ZEROP(zz
)) ZDIVERR("zero modulus");
1926 if ((xx
= gf_modinv_checked(xx
, xx
, zz
)) == 0) goto end
;
1927 yy
= mp_neg(yy
, yy
);
1929 gfreduce_create(&gr
, zz
);
1930 r
= gfreduce_exp(&gr
, MP_NEW
, xx
, yy
);
1931 gfreduce_destroy(&gr
);
1935 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
1939 static PyObject
*gfmeth_sqr(PyObject
*me
, PyObject
*arg
)
1941 if (!PyArg_ParseTuple(arg
, ":sqr")) return (0);
1942 return (gf_pywrap(gf_sqr(MP_NEW
, MP_X(me
))));
1945 static PyObject
*gfmeth_gcd(PyObject
*me
, PyObject
*arg
)
1948 mp
*yy
= 0, *zz
= MP_NEW
;
1950 if (!PyArg_ParseTuple(arg
, "O&:gcd", convgf
, &yy
)) goto end
;
1951 gf_gcd(&zz
, 0, 0, MP_X(me
), yy
);
1954 if (yy
) MP_DROP(yy
);
1958 static PyObject
*gfmeth_gcdx(PyObject
*me
, PyObject
*arg
)
1961 mp
*yy
= 0, *zz
= MP_NEW
, *uu
= MP_NEW
, *vv
= MP_NEW
;
1963 if (!PyArg_ParseTuple(arg
, "O&:gcdx", convgf
, &yy
))
1965 gf_gcd(&zz
, &uu
, &vv
, MP_X(me
), yy
);
1966 z
= Py_BuildValue("(NNN)",
1967 gf_pywrap(zz
), gf_pywrap(uu
), gf_pywrap(vv
));
1969 if (yy
) MP_DROP(yy
);
1973 static PyObject
*gfmeth_modinv(PyObject
*me
, PyObject
*arg
)
1976 mp
*yy
= 0, *zz
= MP_NEW
;
1978 if (!PyArg_ParseTuple(arg
, "O&:modinv", convgf
, &yy
) ||
1979 (zz
= gf_modinv_checked(MP_NEW
, yy
, MP_X(me
))) == 0)
1983 if (yy
) MP_DROP(yy
);
1987 static PyObject
*gfmeth_irreduciblep(PyObject
*me
, PyObject
*arg
)
1989 if (!PyArg_ParseTuple(arg
, ":irreduciblep")) return (0);
1990 return getbool(gf_irreduciblep(MP_X(me
)));
1993 static PyObject
*gfget_degree(PyObject
*me
, void *hunoz
)
1994 { return (PyInt_FromLong(mp_bits(MP_X(me
)) - 1)); }
1996 static PyGetSetDef gf_pygetset
[] = {
1997 #define GETSETNAME(op, name) gf##op##_##name
1998 GET (degree
, "X.degree -> polynomial degree of X")
2000 #define GETSETNAME(op, name) mp##op##_##name
2001 GET (nbits
, "X.nbits -> bit length of X")
2002 GET (noctets
, "X.noctets -> octet length of X")
2007 static PyMethodDef gf_pymethods
[] = {
2008 #define METHNAME(func) gfmeth_##func
2009 METH (setbit
, "X.setbit(N) -> X with bit N set")
2010 METH (clearbit
, "X.clearbit(N) -> X with bit N clear")
2011 METH (testbit
, "X.testbit(N) -> true/false if bit N set/clear in X")
2012 METH (sqr
, "X.sqr() -> X^2")
2013 METH (gcd
, "X.gcd(Y) -> gcd(X, Y)")
2015 "X.gcdx(Y) -> (gcd(X, Y), U, V) with X U + Y V = gcd(X, Y)")
2016 METH (modinv
, "X.modinv(Y) -> multiplicative inverse of Y mod X")
2017 METH (irreduciblep
, "X.irreduciblep() -> true/false")
2019 #define METHNAME(func) mpmeth_##func
2020 KWMETH(tostring
, "X.tostring([radix = 10]) -> STR")
2021 KWMETH(storel
, "X.storel([len = -1]) -> little-endian bytes")
2022 KWMETH(storeb
, "X.storeb([len = -1]) -> big-endian bytes")
2024 "X.storel2c([len = -1]) -> little-endian bytes, two's complement")
2026 "X.storeb2c([len = -1]) -> big-endian bytes, two's complement")
2027 METH (tobuf
, "X.tobuf() -> buffer format")
2032 static PyNumberMethods gf_pynumber
= {
2033 gf_pyadd
, /* @nb_add@ */
2034 gf_pysub
, /* @nb_subtract@ */
2035 gf_pymul
, /* @nb_multiply@ */
2036 0, /* @nb_divide@ */
2037 gf_pymod
, /* @nb_remainder@ */
2038 gf_pydivmod
, /* @nb_divmod@ */
2039 gf_pyexp
, /* @nb_power@ */
2040 mp_pyid
, /* @nb_negative@ */
2041 mp_pyid
, /* @nb_positive@ */
2042 mp_pyid
, /* @nb_absolute@ */
2043 mp_pynonzerop
, /* @nb_nonzero@ */
2044 0 /* doesn't make any sense */, /* @nb_invert@ */
2045 gf_pylsl
, /* @nb_lshift@ */
2046 gf_pylsr
, /* @nb_rshift@ */
2047 gf_pyand
, /* @nb_and@ */
2048 gf_pyxor
, /* @nb_xor@ */
2049 gf_pyor
, /* @nb_or@ */
2050 gf_pycoerce
, /* @nb_coerce@ */
2051 mp_pyint
, /* @nb_int@ */
2052 mp_pylong
, /* @nb_long@ */
2053 0 /* doesn't make any sense */, /* @nb_float@ */
2054 mp_pyoct
, /* @nb_oct@ */
2055 mp_pyhex
, /* @nb_hex@ */
2057 0, /* @nb_inplace_add@ */
2058 0, /* @nb_inplace_subtract@ */
2059 0, /* @nb_inplace_multiply@ */
2060 0, /* @nb_inplace_divide@ */
2061 0, /* @nb_inplace_remainder@ */
2062 0, /* @nb_inplace_power@ */
2063 0, /* @nb_inplace_lshift@ */
2064 0, /* @nb_inplace_rshift@ */
2065 0, /* @nb_inplace_and@ */
2066 0, /* @nb_inplace_xor@ */
2067 0, /* @nb_inplace_or@ */
2069 gf_pydiv
, /* @nb_floor_divide@ */
2070 0, /* @nb_true_divide@ */
2071 0, /* @nb_inplace_floor_divide@ */
2072 0, /* @nb_inplace_true_divide@ */
2075 static PyTypeObject gf_pytype_skel
= {
2076 PyObject_HEAD_INIT(0) 0, /* Header */
2077 "GF", /* @tp_name@ */
2078 sizeof(mp_pyobj
), /* @tp_basicsize@ */
2079 0, /* @tp_itemsize@ */
2081 mp_pydealloc
, /* @tp_dealloc@ */
2083 0, /* @tp_getattr@ */
2084 0, /* @tp_setattr@ */
2085 0, /* @tp_compare@ */
2086 gf_pyrepr
, /* @tp_repr@ */
2087 &gf_pynumber
, /* @tp_as_number@ */
2088 0, /* @tp_as_sequence@ */
2089 0, /* @tp_as_mapping@ */
2090 mp_pyhash
, /* @tp_hash@ */
2092 mp_pyhex
, /* @tp_str@ */
2093 0, /* @tp_getattro@ */
2094 0, /* @tp_setattro@ */
2095 0, /* @tp_as_buffer@ */
2096 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
2097 Py_TPFLAGS_CHECKTYPES
|
2098 Py_TPFLAGS_BASETYPE
,
2101 "Binary polynomials. Support almost all the standard arithmetic\n\
2104 Constructor GF(X, [radix = R]) attempts to convert X to a `GF'. If\n\
2105 X is a string, it's read in radix-R form, or we look for a prefix\n\
2106 if R = 0. Other acceptable things are field elements, elliptic curve\n\
2107 points, group elements, Python `int' and `long' objects, and anything\n\
2108 with an integer conversion.\n\
2110 The name is hopelessly wrong from a technical point of view, but\n\
2111 but it's much easier to type than `p2' or `c2' or whatever.\n\
2115 * Use `//' for Euclidean division: `/' gives exact rational division.",
2117 0, /* @tp_traverse@ */
2119 gf_pyrichcompare
, /* @tp_richcompare@ */
2120 0, /* @tp_weaklistoffset@ */
2122 0, /* @tp_iternext@ */
2123 gf_pymethods
, /* @tp_methods@ */
2124 0, /* @tp_members@ */
2125 gf_pygetset
, /* @tp_getset@ */
2128 0, /* @tp_descr_get@ */
2129 0, /* @tp_descr_set@ */
2130 0, /* @tp_dictoffset@ */
2132 PyType_GenericAlloc
, /* @tp_alloc@ */
2133 gf_pynew
, /* @tp_new@ */
2138 static PyObject
*meth__GF_fromstring(PyObject
*me
,
2139 PyObject
*arg
, PyObject
*kw
)
2146 mptext_stringctx sc
;
2147 static const char *const kwlist
[] = { "class", "x", "radix", 0 };
2149 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "Os#|i:fromstring",
2150 KWLIST
, &me
, &p
, &len
, &r
))
2152 if (!good_radix_p(r
, 1)) VALERR("bad radix");
2153 sc
.buf
= p
; sc
.lim
= p
+ len
;
2154 if ((zz
= mp_read(MP_NEW
, r
, &mptext_stringops
, &sc
)) == 0 ||
2156 if (zz
) MP_DROP(zz
);
2157 VALERR("bad binary polynomial");
2159 z
= Py_BuildValue("(Ns#)", gf_pywrap(zz
),
2160 sc
.buf
, (Py_ssize_t
)(sc
.lim
- sc
.buf
));
2165 /*----- Sparse poly reduction ---------------------------------------------*/
2167 typedef struct gfreduce_pyobj
{
2172 #define GFREDUCE_PY(o) (&((gfreduce_pyobj *)(o))->mr)
2174 static PyObject
*grmeth_exp(PyObject
*me
, PyObject
*arg
)
2177 mp
*yy
= 0, *zz
= 0;
2179 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convgf
, &yy
, convgf
, &zz
))
2182 if ((yy
= gf_modinv_checked(yy
, yy
, GFREDUCE_PY(me
)->p
)) == 0) goto end
;
2183 zz
= mp_neg(zz
, zz
);
2185 rc
= gf_pywrap(gfreduce_exp(GFREDUCE_PY(me
), MP_NEW
, yy
, zz
));
2187 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
2191 static PyObject
*grmeth_trace(PyObject
*me
, PyObject
*arg
)
2196 if (!PyArg_ParseTuple(arg
, "O&:trace", convgf
, &xx
)) goto end
;
2197 rc
= PyInt_FromLong(gfreduce_trace(GFREDUCE_PY(me
), xx
));
2199 if (xx
) MP_DROP(xx
);
2203 static PyObject
*grmeth_halftrace(PyObject
*me
, PyObject
*arg
)
2208 if (!PyArg_ParseTuple(arg
, "O&:halftrace", convgf
, &xx
)) goto end
;
2209 rc
= gf_pywrap(gfreduce_halftrace(GFREDUCE_PY(me
), MP_NEW
, xx
));
2211 if (xx
) MP_DROP(xx
);
2215 static PyObject
*grmeth_sqrt(PyObject
*me
, PyObject
*arg
)
2220 if (!PyArg_ParseTuple(arg
, "O&:sqrt", convgf
, &xx
)) goto end
;
2221 if ((yy
= gfreduce_sqrt(GFREDUCE_PY(me
), MP_NEW
, xx
)) == 0)
2222 VALERR("no modular square root");
2225 if (xx
) MP_DROP(xx
);
2229 static PyObject
*grmeth_quadsolve(PyObject
*me
, PyObject
*arg
)
2234 if (!PyArg_ParseTuple(arg
, "O&:quadsolve", convgf
, &xx
)) goto end
;
2235 if ((yy
= gfreduce_quadsolve(GFREDUCE_PY(me
), MP_NEW
, xx
)) == 0)
2236 VALERR("no solution found");
2239 if (xx
) MP_DROP(xx
);
2243 static PyObject
*grmeth_reduce(PyObject
*me
, PyObject
*arg
)
2248 if (!PyArg_ParseTuple(arg
, "O&:reduce", convgf
, &yy
)) goto end
;
2249 z
= gf_pywrap(gfreduce_do(GFREDUCE_PY(me
), MP_NEW
, yy
));
2254 static void gfreduce_pydealloc(PyObject
*me
)
2256 gfreduce_destroy(GFREDUCE_PY(me
));
2260 static PyObject
*gfreduce_pynew(PyTypeObject
*ty
,
2261 PyObject
*arg
, PyObject
*kw
)
2263 gfreduce_pyobj
*mr
= 0;
2265 static const char *const kwlist
[] = { "m", 0 };
2268 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", KWLIST
, convgf
, &xx
))
2270 if (MP_ZEROP(xx
)) ZDIVERR("modulus is zero!");
2271 gfreduce_create(&r
, xx
);
2272 mr
= (gfreduce_pyobj
*)ty
->tp_alloc(ty
, 0);
2275 if (xx
) MP_DROP(xx
);
2276 return ((PyObject
*)mr
);
2279 static PyObject
*grget_m(PyObject
*me
, void *hunoz
)
2280 { return (gf_pywrap(MP_COPY(GFREDUCE_PY(me
)->p
))); }
2282 static PyGetSetDef gfreduce_pygetset
[] = {
2283 #define GETSETNAME(op, name) gr##op##_##name
2284 GET (m
, "R.m -> reduction polynomial")
2289 static PyMethodDef gfreduce_pymethods
[] = {
2290 #define METHNAME(name) grmeth_##name
2291 METH (reduce
, "R.reduce(X) -> X mod B.m")
2292 METH (trace
, "R.trace(X) -> Tr(X) = x + x^2 + ... + x^{2^{m - 1}}")
2293 METH (halftrace
, "R.halftrace(X) -> x + x^{2^2} + ... + x^{2^{m - 1}}")
2294 METH (sqrt
, "R.sqrt(X) -> Y where Y^2 = X mod R")
2295 METH (quadsolve
, "R.quadsolve(X) -> Y where Y^2 + Y = X mod R")
2296 METH (exp
, "R.exp(X, N) -> X^N mod B.m")
2301 static PyTypeObject
*gfreduce_pytype
, gfreduce_pytype_skel
= {
2302 PyObject_HEAD_INIT(0) 0, /* Header */
2303 "GFReduce", /* @tp_name@ */
2304 sizeof(gfreduce_pyobj
), /* @tp_basicsize@ */
2305 0, /* @tp_itemsize@ */
2307 gfreduce_pydealloc
, /* @tp_dealloc@ */
2309 0, /* @tp_getattr@ */
2310 0, /* @tp_setattr@ */
2311 0, /* @tp_compare@ */
2313 0, /* @tp_as_number@ */
2314 0, /* @tp_as_sequence@ */
2315 0, /* @tp_as_mapping@ */
2319 0, /* @tp_getattro@ */
2320 0, /* @tp_setattro@ */
2321 0, /* @tp_as_buffer@ */
2322 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
2323 Py_TPFLAGS_BASETYPE
,
2326 "GFReduce(N): a context for reduction modulo sparse polynomials.",
2328 0, /* @tp_traverse@ */
2330 0, /* @tp_richcompare@ */
2331 0, /* @tp_weaklistoffset@ */
2333 0, /* @tp_iternext@ */
2334 gfreduce_pymethods
, /* @tp_methods@ */
2335 0, /* @tp_members@ */
2336 gfreduce_pygetset
, /* @tp_getset@ */
2339 0, /* @tp_descr_get@ */
2340 0, /* @tp_descr_set@ */
2341 0, /* @tp_dictoffset@ */
2343 PyType_GenericAlloc
, /* @tp_alloc@ */
2344 gfreduce_pynew
, /* @tp_new@ */
2349 /*----- Normal/poly transformation ----------------------------------------*/
2351 typedef struct gfn_pyobj
{
2357 static PyTypeObject
*gfn_pytype
, gfn_pytype_skel
;
2359 #define GFN_P(o) (((gfn_pyobj *)(o))->p)
2360 #define GFN_PTON(o) (&((gfn_pyobj *)(o))->pton)
2361 #define GFN_NTOP(o) (&((gfn_pyobj *)(o))->ntop)
2363 static PyObject
*gfn_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
2365 mp
*p
= 0, *beta
= 0;
2367 static const char *const kwlist
[] = { "p", "beta", 0 };
2369 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&O&:new", KWLIST
,
2370 convgf
, &p
, convgf
, &beta
))
2372 gg
= PyObject_New(gfn_pyobj
, ty
);
2374 if (gfn_create(p
, beta
, &gg
->ntop
, &gg
->pton
)) {
2377 VALERR("can't invert transformation matrix");
2383 return ((PyObject
*)gg
);
2386 static PyObject
*gfnget_p(PyObject
*me
, void *hunoz
)
2387 { return (gf_pywrap(MP_COPY(GFN_P(me
)))); }
2389 static PyObject
*gfnget_beta(PyObject
*me
, void *hunoz
)
2391 gfn
*n
= GFN_NTOP(me
);
2392 mp
*x
= n
->r
[n
->n
- 1];
2393 return (gf_pywrap(MP_COPY(x
)));
2396 #define XFORMOP(name, NAME) \
2397 static PyObject *gfnmeth_##name(PyObject *me, PyObject *arg) \
2402 if (!PyArg_ParseTuple(arg, "O&:" #name, convgf, &xx)) goto end; \
2403 z = gfn_transform(GFN_##NAME(me), MP_NEW, xx); \
2406 if (!z) return (0); \
2407 return (gf_pywrap(z)); \
2413 static void gfn_pydealloc(PyObject
*me
)
2417 gfn_destroy(GFN_PTON(me
));
2418 gfn_destroy(GFN_NTOP(me
));
2423 static PyGetSetDef gfn_pygetset
[] = {
2424 #define GETSETNAME(op, name) gfn##op##_##name
2425 GET (p
, "X.p -> polynomial basis, as polynomial")
2426 GET (beta
, "X.beta -> normal basis element, in poly form")
2431 static PyMethodDef gfn_pymethods
[] = {
2432 #define METHNAME(name) gfnmeth_##name
2433 METH (pton
, "X.pton(A) -> normal-basis representation of A")
2434 METH (ntop
, "X.ntop(A) -> polynomial-basis representation of A")
2439 static PyTypeObject gfn_pytype_skel
= {
2440 PyObject_HEAD_INIT(0) 0, /* Header */
2441 "GFN", /* @tp_name@ */
2442 sizeof(gfn_pyobj
), /* @tp_basicsize@ */
2443 0, /* @tp_itemsize@ */
2445 gfn_pydealloc
, /* @tp_dealloc@ */
2447 0, /* @tp_getattr@ */
2448 0, /* @tp_setattr@ */
2449 0, /* @tp_compare@ */
2451 0, /* @tp_as_number@ */
2452 0, /* @tp_as_sequence@ */
2453 0, /* @tp_as_mapping@ */
2457 0, /* @tp_getattro@ */
2458 0, /* @tp_setattro@ */
2459 0, /* @tp_as_buffer@ */
2460 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
2461 Py_TPFLAGS_BASETYPE
,
2464 "GFN(P, BETA): an object for transforming elements of binary fields\n\
2465 between polynomial and normal basis representations.",
2467 0, /* @tp_traverse@ */
2469 0, /* @tp_richcompare@ */
2470 0, /* @tp_weaklistoffset@ */
2472 0, /* @tp_iternext@ */
2473 gfn_pymethods
, /* @tp_methods@ */
2474 0, /* @tp_members@ */
2475 gfn_pygetset
, /* @tp_getset@ */
2478 0, /* @tp_descr_get@ */
2479 0, /* @tp_descr_set@ */
2480 0, /* @tp_dictoffset@ */
2482 PyType_GenericAlloc
, /* @tp_alloc@ */
2483 gfn_pynew
, /* @tp_new@ */
2488 /*----- Glue --------------------------------------------------------------*/
2490 static PyMethodDef methods
[] = {
2491 #define METHNAME(func) meth_##func
2492 KWMETH(_MP_fromstring
, "\
2493 fromstring(STR, [radix = 0]) -> (X, REST)\n\
2495 Parse STR as a large integer, according to radix. If radix is zero,\n\
2496 read a prefix from STR to decide radix: allow `0' for octal, `0x' for hex\n\
2497 or `R_' for other radix R.")
2498 KWMETH(_GF_fromstring
, "\
2499 fromstring(STR, [radix = 0]) -> (X, REST)\n\
2501 Parse STR as a binary polynomial, according to radix. If radix is zero,\n\
2502 read a prefix from STR to decide radix: allow `0' for octal, `0x' for hex\n\
2503 or `R_' for other radix R.")
2504 METH (_MP_factorial
, "\
2505 factorial(I) -> I!: compute factorial")
2506 METH (_MP_fibonacci
, "\
2507 fibonacci(I) -> F(I): compute Fibonacci number")
2509 loadl(STR) -> X: read little-endian bytes")
2511 loadb(STR) -> X: read big-endian bytes")
2512 METH (_MP_loadl2c
, "\
2513 loadl2c(STR) -> X: read little-endian bytes, two's complement")
2514 METH (_MP_loadb2c
, "\
2515 loadb2c(STR) -> X: read big-endian bytes, two's complement")
2516 METH (_MP_frombuf
, "\
2517 frombuf(STR) -> (X, REST): read buffer format")
2519 loadl(STR) -> X: read little-endian bytes")
2521 loadb(STR) -> X: read big-endian bytes")
2522 METH (_GF_frombuf
, "\
2523 frombuf(STR) -> (X, REST): read buffer format")
2528 void mp_pyinit(void)
2532 INITTYPE(mpmul
, root
);
2533 INITTYPE(mpmont
, root
);
2534 INITTYPE(mpbarrett
, root
);
2535 INITTYPE(mpreduce
, root
);
2536 INITTYPE(mpcrt
, root
);
2537 INITTYPE(gfreduce
, root
);
2538 INITTYPE(gfn
, root
);
2539 addmethods(methods
);
2542 void mp_pyinsert(PyObject
*mod
)
2544 INSERT("MP", mp_pytype
);
2545 INSERT("MPMul", mpmul_pytype
);
2546 INSERT("MPMont", mpmont_pytype
);
2547 INSERT("MPBarrett", mpbarrett_pytype
);
2548 INSERT("MPReduce", mpreduce_pytype
);
2549 INSERT("MPCRT", mpcrt_pytype
);
2550 INSERT("GF", gf_pytype
);
2551 INSERT("GFReduce", gfreduce_pytype
);
2552 INSERT("GFN", gfn_pytype
);
2555 /*----- That's all, folks -------------------------------------------------*/