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
)) {
218 } else if (GE_PYCHECK(o
)) {
219 if ((x
= G_TOINT(GE_G(o
), MP_NEW
, GE_X(o
))) == 0)
222 } else if (PyInt_Check(o
))
223 return (mp_fromlong(MP_NEW
, PyInt_AS_LONG(o
)));
224 else if ((l
= PyNumber_Long(o
)) != 0) {
225 x
= mp_frompylong(l
);
234 mp
*getmp(PyObject
*o
)
238 if ((x
= tomp(o
)) == 0) {
239 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to mp",
240 o
->ob_type
->tp_name
);
245 int convmp(PyObject
*o
, void *p
)
248 if ((x
= getmp(o
)) == 0) return (0);
253 mp
*getgf(PyObject
*o
)
257 if ((x
= tomp(o
)) == 0) {
258 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to gf",
259 o
->ob_type
->tp_name
);
264 int convgf(PyObject
*o
, void *p
)
267 if ((x
= getgf(o
)) == 0) return (0);
272 static mp
*implicitmp(PyObject
*o
)
283 static mp
*implicitgf(PyObject
*o
)
294 static int mpbinop(PyObject
*x
, PyObject
*y
, mp
**xx
, mp
**yy
)
296 if ((*xx
= implicitmp(x
)) == 0)
298 if ((*yy
= implicitmp(y
)) == 0) {
305 static int gfbinop(PyObject
*x
, PyObject
*y
, mp
**xx
, mp
**yy
)
307 if ((*xx
= implicitgf(x
)) == 0)
309 if ((*yy
= implicitgf(y
)) == 0) {
316 #define gf_and mp_and
318 #define gf_xor mp_xor
319 #define BINOP(pre, name) \
320 static PyObject *pre##_py##name(PyObject *x, PyObject *y) { \
322 if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL; \
323 zz = pre##_##name(MP_NEW, xx, yy); \
324 MP_DROP(xx); MP_DROP(yy); \
325 return (pre##_pywrap(zz)); \
341 static mp
*mp_abs(mp
*d
, mp
*x
)
344 return (mp_neg(d
, x
));
350 #define UNOP(pre, name) \
351 static PyObject *pre##_py##name(PyObject *x) \
352 { return mp_pywrap(pre##_##name(MP_NEW, MP_X(x))); }
358 static PyObject
*mp_pyid(PyObject
*x
) { RETURN_OBJ(x
); }
360 #define gf_lsr mp_lsr
361 #define SHIFTOP(pre, name, rname) \
362 static PyObject *pre##_py##name(PyObject *x, PyObject *y) { \
366 if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL; \
367 if (mp_tolong_checked(yy, &n, 1)) goto end; \
369 z = pre##_pywrap(mp_##rname(MP_NEW, xx, -n)); \
371 z = pre##_pywrap(mp_##name(MP_NEW, xx, n)); \
373 MP_DROP(xx); MP_DROP(yy); \
376 SHIFTOP(mp
, lsl2c
, lsr2c
)
377 SHIFTOP(mp
, lsr2c
, lsl2c
)
378 SHIFTOP(gf
, lsl
, lsr
)
379 SHIFTOP(gf
, lsr
, lsl
)
382 #define DIVOP(pre, name, qq, rr, gather) \
383 static PyObject *pre##_py##name(PyObject *x, PyObject *y) { \
386 INIT_##qq(q) INIT_##rr(r) \
387 if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL; \
389 ZDIVERR("division by zero"); \
390 pre##_div(ARG_##qq(q), ARG_##rr(r), xx, yy); \
393 MP_DROP(xx); MP_DROP(yy); \
396 #define INIT_YES(p) mp *p = MP_NEW;
398 #define ARG_YES(p) &p
400 DIVOP(mp
, divmod
, YES
, YES
,
401 Py_BuildValue("(NN)", mp_pywrap(q
), mp_pywrap(r
)))
402 DIVOP(mp
, div
, YES
, NO
, mp_pywrap(q
))
403 DIVOP(mp
, mod
, NO
, YES
, mp_pywrap(r
))
404 DIVOP(gf
, divmod
, YES
, YES
,
405 Py_BuildValue("(NN)", gf_pywrap(q
), gf_pywrap(r
)))
406 DIVOP(gf
, div
, YES
, NO
, gf_pywrap(q
))
407 DIVOP(gf
, mod
, NO
, YES
, gf_pywrap(r
))
414 static mp
*mp_modinv_checked(mp
*d
, mp
*x
, mp
*p
)
417 mp_gcd(&g
, 0, &d
, p
, x
);
418 if (!MP_EQ(g
, MP_ONE
)) {
419 MP_DROP(g
); MP_DROP(d
);
420 PyErr_SetString(PyExc_ZeroDivisionError
, "no modular inverse");
423 MP_DROP(g
); return (d
);
426 static PyObject
*mp_pyexp(PyObject
*x
, PyObject
*y
, PyObject
*z
)
428 mp
*xx
= 0, *yy
= 0, *zz
= 0;
432 if ((xx
= implicitmp(x
)) == 0 || (yy
= implicitmp(y
)) == 0 ||
433 (z
&& z
!= Py_None
&& (zz
= tomp(z
)) == 0)) {
434 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
437 if (!z
|| z
== Py_None
) {
438 if (MP_NEGP(yy
)) VALERR("negative exponent");
439 r
= mp_exp(MP_NEW
, xx
, yy
);
441 if (!MP_POSP(zz
)) VALERR("modulus must be positive");
443 if ((xx
= mp_modinv_checked(xx
, xx
, zz
)) == 0) goto end
;
448 mpmont_create(&mm
, zz
);
449 r
= mpmont_exp(&mm
, MP_NEW
, xx
, yy
);
453 mpbarrett_create(&mb
, zz
);
454 r
= mpbarrett_exp(&mb
, MP_NEW
, xx
, yy
);
455 mpbarrett_destroy(&mb
);
460 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
464 static mp
*gf_modinv_checked(mp
*d
, mp
*x
, mp
*p
)
467 gf_gcd(&g
, 0, &d
, p
, x
);
468 if (!MP_EQ(g
, MP_ONE
)) {
469 MP_DROP(g
); MP_DROP(d
);
470 PyErr_SetString(PyExc_ZeroDivisionError
, "no modular inverse");
473 MP_DROP(g
); return (d
);
476 #define BASEOP(name, radix, pre) \
477 static PyObject *mp_py##name(PyObject *x) \
478 { return mp_topystring(MP_X(x), radix, 0, pre, 0); }
480 BASEOP(hex
, 16, "0x");
483 static int mp_pynonzerop(PyObject
*x
) { return !MP_ZEROP(MP_X(x
)); }
485 static PyObject
*mp_pyint(PyObject
*x
)
488 if (!mp_tolong_checked(MP_X(x
), &l
, 0)) return (PyInt_FromLong(l
));
489 else return mp_topylong(MP_X(x
));
491 static PyObject
*mp_pylong(PyObject
*x
)
492 { return (mp_topylong(MP_X(x
))); }
493 static PyObject
*mp_pyfloat(PyObject
*x
)
495 PyObject
*l
= mp_topylong(MP_X(x
));
496 double f
= PyLong_AsDouble(l
);
498 return (PyFloat_FromDouble(f
));
501 #define COERCE(pre, PRE) \
502 static int pre##_pycoerce(PyObject **x, PyObject **y) \
506 if (PRE##_PYCHECK(*y)) { \
507 Py_INCREF(*x); Py_INCREF(*y); \
510 if ((z = tomp(*y)) != 0) { \
512 *y = pre##_pywrap(z); \
521 static int mp_pycompare(PyObject
*x
, PyObject
*y
)
522 { return mp_cmp(MP_X(x
), MP_X(y
)); }
524 static PyObject
*mp_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
530 char *kwlist
[] = { "x", "radix", 0 };
532 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O|i:new", kwlist
, &x
, &radix
))
534 if (MP_PYCHECK(x
)) RETURN_OBJ(x
);
535 if (!good_radix_p(radix
, 1)) VALERR("bad radix");
536 if ((z
= mp_frompyobject(x
, radix
)) == 0) {
537 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to mp",
538 x
->ob_type
->tp_name
);
541 zz
= (mp_pyobj
*)ty
->tp_alloc(ty
, 0);
544 return ((PyObject
*)zz
);
549 PyObject
*l
= mp_topylong(x
);
550 long h
= PyObject_Hash(l
);
551 Py_DECREF(l
); return (h
);
554 static long mp_pyhash(PyObject
*me
) { return (mphash(MP_X(me
))); }
556 static PyObject
*mpmeth_jacobi(PyObject
*me
, PyObject
*arg
)
561 if (!PyArg_ParseTuple(arg
, "O&:jacobi", convmp
, &y
)) goto end
;
562 z
= PyInt_FromLong(mp_jacobi(y
, MP_X(me
)));
568 #define BITOP(pre, name, c) \
569 static PyObject *pre##meth_##name(PyObject *me, PyObject *arg) \
572 if (!PyArg_ParseTuple(arg, "O&:" #name, convulong, &i)) return (0); \
573 return (pre##_pywrap(mp_##name##c(MP_NEW, MP_X(me), i))); \
575 BITOP(mp
, setbit
, 2c
);
576 BITOP(mp
, clearbit
, 2c
);
578 BITOP(gf
, clearbit
, );
581 static PyObject
*mpmeth_testbit(PyObject
*me
, PyObject
*arg
)
584 if (!PyArg_ParseTuple(arg
, "O&:testbit", convulong
, &i
)) return (0);
585 return (getbool(mp_testbit2c(MP_X(me
), i
)));
588 static PyObject
*gfmeth_testbit(PyObject
*me
, PyObject
*arg
)
591 if (!PyArg_ParseTuple(arg
, "O&:testbit", convulong
, &i
)) return (0);
592 return (getbool(mp_testbit(MP_X(me
), i
)));
595 static PyObject
*mpmeth_odd(PyObject
*me
, PyObject
*arg
)
600 if (!PyArg_ParseTuple(arg
, ":odd")) return (0);
601 t
= mp_odd(MP_NEW
, MP_X(me
), &s
);
602 return (Py_BuildValue("(lN)", (long)s
, mp_pywrap(t
)));
605 static PyObject
*mpmeth_sqr(PyObject
*me
, PyObject
*arg
)
607 if (!PyArg_ParseTuple(arg
, ":sqr")) return (0);
608 return (mp_pywrap(mp_sqr(MP_NEW
, MP_X(me
))));
611 static PyObject
*mpmeth_sqrt(PyObject
*me
, PyObject
*arg
)
613 if (!PyArg_ParseTuple(arg
, ":sqrt")) return (0);
614 if (MP_NEGP(MP_X(me
))) VALERR("negative root");
615 return (mp_pywrap(mp_sqrt(MP_NEW
, MP_X(me
))));
620 static PyObject
*mpmeth_gcd(PyObject
*me
, PyObject
*arg
)
622 mp
*y
= 0, *zz
= MP_NEW
;
625 if (!PyArg_ParseTuple(arg
, "O&:gcd", convmp
, &y
)) goto end
;
626 mp_gcd(&zz
, 0, 0, MP_X(me
), y
);
633 static PyObject
*mpmeth_gcdx(PyObject
*me
, PyObject
*arg
)
636 mp
*yy
= 0, *zz
= MP_NEW
, *uu
= MP_NEW
, *vv
= MP_NEW
;
638 if (!PyArg_ParseTuple(arg
, "O&:gcdx", convmp
, &yy
)) goto end
;
639 mp_gcd(&zz
, &uu
, &vv
, MP_X(me
), yy
);
640 z
= Py_BuildValue("(NNN)",
641 mp_pywrap(zz
), mp_pywrap(uu
), mp_pywrap(vv
));
647 static PyObject
*mpmeth_modinv(PyObject
*me
, PyObject
*arg
)
650 mp
*yy
= 0, *zz
= MP_NEW
;
652 if (!PyArg_ParseTuple(arg
, "O&:modinv", convmp
, &yy
) ||
653 (zz
= mp_modinv_checked(MP_NEW
, yy
, MP_X(me
))) == 0)
661 static PyObject
*mpmeth_tostring(PyObject
*me
, PyObject
*arg
, PyObject
*kw
)
664 char *kwlist
[] = { "radix", 0 };
665 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "|i:tostring", kwlist
, &radix
))
667 if (!good_radix_p(radix
, 0)) VALERR("bad radix");
668 return (mp_topystring(MP_X(me
), radix
, 0, 0, 0));
673 static PyObject
*mpmeth_modsqrt(PyObject
*me
, PyObject
*arg
)
676 mp
*yy
= 0, *zz
= MP_NEW
;
678 if (!PyArg_ParseTuple(arg
, "O&:modsqrt", convmp
, &yy
)) goto end
;
679 if ((zz
= mp_modsqrt(MP_NEW
, yy
, MP_X(me
))) == 0)
680 VALERR("no modular square root");
687 static PyObject
*mpmeth_leastcongruent(PyObject
*me
, PyObject
*arg
)
692 if (!PyArg_ParseTuple(arg
, "O&O&:leastcongruent", convmp
, &b
, convmp
, &m
))
694 z
= mp_leastcongruent(MP_NEW
, b
, MP_X(me
), m
);
700 #define STOREOP(name, c) \
701 static PyObject *mpmeth_##name(PyObject *me, \
702 PyObject *arg, PyObject *kw) \
705 char *kwlist[] = { "len", 0 }; \
708 if (!PyArg_ParseTupleAndKeywords(arg, kw, "|l:" #name, \
712 len = mp_octets##c(MP_X(me)); \
715 rc = bytestring_pywrap(0, len); \
716 mp_##name(MP_X(me), PyString_AS_STRING(rc), len); \
722 STOREOP(storel2c
, 2c
)
723 STOREOP(storeb2c
, 2c
)
726 #define BUFOP(ty, pyty) \
727 static PyObject *meth__##pyty##_frombuf(PyObject *me, PyObject *arg) \
735 if (!PyArg_ParseTuple(arg, "Os#:frombuf", &me, &p, &sz)) goto end; \
736 buf_init(&b, p, sz); \
737 if ((x = buf_getmp(&b)) == 0) VALERR("malformed data"); \
738 rc = Py_BuildValue("(NN)", ty##_pywrap(x), \
739 bytestring_pywrapbuf(&b)); \
747 static PyObject
*mpmeth_tobuf(PyObject
*me
, PyObject
*arg
)
754 if (!PyArg_ParseTuple(arg
, ":tobuf")) return (0);
756 n
= mp_octets(x
) + 3;
757 rc
= bytestring_pywrap(0, n
);
758 buf_init(&b
, PyString_AS_STRING(rc
), n
);
761 _PyString_Resize(&rc
, BLEN(&b
));
765 static PyObject
*mpmeth_primep(PyObject
*me
, PyObject
*arg
, PyObject
*kw
)
767 grand
*r
= &rand_global
;
768 char *kwlist
[] = { "rng", 0 };
771 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "|O&", kwlist
, convgrand
, &r
))
773 rc
= getbool(pgen_primep(MP_X(me
), r
));
778 static PyObject
*mpget_nbits(PyObject
*me
, void *hunoz
)
779 { return (PyInt_FromLong(mp_bits(MP_X(me
)))); }
781 static PyObject
*mpget_noctets(PyObject
*me
, void *hunoz
)
782 { return (PyInt_FromLong(mp_octets(MP_X(me
)))); }
784 static PyObject
*mpget_noctets2c(PyObject
*me
, void *hunoz
)
785 { return (PyInt_FromLong(mp_octets2c(MP_X(me
)))); }
787 static PyGetSetDef mp_pygetset
[] = {
788 #define GETSETNAME(op, func) mp##op##_##func
789 GET (nbits
, "X.nbits -> bit length of X")
790 GET (noctets
, "X.noctets -> octet length of X")
791 GET (noctets2c
, "X.noctets2c -> two's complement octet length of X")
796 static PyMethodDef mp_pymethods
[] = {
797 #define METHNAME(func) mpmeth_##func
798 METH (jacobi
, "X.jacobi(Y) -> Jacobi symbol (Y|X) (NB inversion!)")
799 METH (setbit
, "X.setbit(N) -> X with bit N set")
800 METH (clearbit
, "X.clearbit(N) -> X with bit N clear")
801 METH (testbit
, "X.testbit(N) -> true/false if bit N set/clear in X")
802 METH (odd
, "X.odd() -> S, T where X = 2^S T with T odd")
803 METH (sqr
, "X.sqr() -> X^2")
804 METH (sqrt
, "X.sqrt() -> largest integer <= sqrt(X)")
805 METH (gcd
, "X.gcd(Y) -> gcd(X, Y)")
807 "X.gcdx(Y) -> (gcd(X, Y), U, V) with X U + Y V = gcd(X, Y)")
808 METH (modinv
, "X.modinv(Y) -> multiplicative inverse of Y mod X")
809 METH (modsqrt
, "X.modsqrt(Y) -> square root of Y mod X, if X prime")
810 METH (leastcongruent
,
811 "X.leastcongruent(B, M) -> smallest Z >= B with Z == X (mod M)")
812 KWMETH(primep
, "X.primep([rng = rand]) -> true/false if X is prime")
813 KWMETH(tostring
, "X.tostring([radix = 10]) -> STR")
814 KWMETH(storel
, "X.storel([len = -1]) -> little-endian bytes")
815 KWMETH(storeb
, "X.storeb([len = -1]) -> big-endian bytes")
817 "X.storel2c([len = -1]) -> little-endian bytes, two's complement")
819 "X.storeb2c([len = -1]) -> big-endian bytes, two's complement")
820 METH (tobuf
, "X.tobuf() -> buffer format")
825 static PyNumberMethods mp_pynumber
= {
826 mp_pyadd
, /* @nb_add@ */
827 mp_pysub
, /* @nb_subtract@ */
828 mp_pymul
, /* @nb_multiply@ */
830 mp_pymod
, /* @nb_remainder@ */
831 mp_pydivmod
, /* @nb_divmod@ */
832 mp_pyexp
, /* @nb_power@ */
833 mp_pyneg
, /* @nb_negative@ */
834 mp_pyid
, /* @nb_positive@ */
835 mp_pyabs
, /* @nb_absolute@ */
836 mp_pynonzerop
, /* @nb_nonzero@ */
837 mp_pynot2c
, /* @nb_invert@ */
838 mp_pylsl2c
, /* @nb_lshift@ */
839 mp_pylsr2c
, /* @nb_rshift@ */
840 mp_pyand2c
, /* @nb_and@ */
841 mp_pyxor2c
, /* @nb_xor@ */
842 mp_pyor2c
, /* @nb_or@ */
843 mp_pycoerce
, /* @nb_coerce@ */
844 mp_pyint
, /* @nb_int@ */
845 mp_pylong
, /* @nb_long@ */
846 mp_pyfloat
, /* @nb_float@ */
847 mp_pyoct
, /* @nb_oct@ */
848 mp_pyhex
, /* @nb_hex@ */
850 0, /* @nb_inplace_add@ */
851 0, /* @nb_inplace_subtract@ */
852 0, /* @nb_inplace_multiply@ */
853 0, /* @nb_inplace_divide@ */
854 0, /* @nb_inplace_remainder@ */
855 0, /* @nb_inplace_power@ */
856 0, /* @nb_inplace_lshift@ */
857 0, /* @nb_inplace_rshift@ */
858 0, /* @nb_inplace_and@ */
859 0, /* @nb_inplace_xor@ */
860 0, /* @nb_inplace_or@ */
862 mp_pydiv
, /* @nb_floor_divide@ */
863 0, /* @nb_true_divide@ */
864 0, /* @nb_inplace_floor_divide@ */
865 0, /* @nb_inplace_true_divide@ */
868 static PyTypeObject mp_pytype_skel
= {
869 PyObject_HEAD_INIT(0) 0, /* Header */
870 "MP", /* @tp_name@ */
871 sizeof(mp_pyobj
), /* @tp_basicsize@ */
872 0, /* @tp_itemsize@ */
874 mp_pydealloc
, /* @tp_dealloc@ */
876 0, /* @tp_getattr@ */
877 0, /* @tp_setattr@ */
878 mp_pycompare
, /* @tp_compare@ */
879 mp_pyrepr
, /* @tp_repr@ */
880 &mp_pynumber
, /* @tp_as_number@ */
881 0, /* @tp_as_sequence@ */
882 0, /* @tp_as_mapping@ */
883 mp_pyhash
, /* @tp_hash@ */
885 mp_pystr
, /* @tp_str@ */
886 0, /* @tp_getattro@ */
887 0, /* @tp_setattro@ */
888 0, /* @tp_as_buffer@ */
889 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
890 Py_TPFLAGS_CHECKTYPES
|
894 "Multiprecision integers, similar to `long' but more efficient and\n\
895 versatile. Support all the standard arithmetic operations, with\n\
896 implicit conversions from `PrimeFilter', and other objects which\n\
897 convert to `long'.\n\
899 Constructor MP(X, [radix = R]) attempts to convert X to an `MP'. If\n\
900 X is a string, it's read in radix-R form, or we look for a prefix\n\
901 if R = 0. Other acceptable things are field elements, elliptic curve\n\
902 points, group elements, Python `int' and `long' objects, and anything\n\
903 with an integer conversion.\n\
907 * Use `//' for division. MPs don't have `/' division.",
909 0, /* @tp_traverse@ */
911 0, /* @tp_richcompare@ */
912 0, /* @tp_weaklistoffset@ */
914 0, /* @tp_iternext@ */
915 mp_pymethods
, /* @tp_methods@ */
916 0, /* @tp_members@ */
917 mp_pygetset
, /* @tp_getset@ */
920 0, /* @tp_descr_get@ */
921 0, /* @tp_descr_set@ */
922 0, /* @tp_dictoffset@ */
924 PyType_GenericAlloc
, /* @tp_alloc@ */
925 mp_pynew
, /* @tp_new@ */
930 static PyObject
*meth__MP_fromstring(PyObject
*me
,
931 PyObject
*arg
, PyObject
*kw
)
939 char *kwlist
[] = { "class", "x", "radix", 0 };
941 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "Os#|i:fromstring",
942 kwlist
, &me
, &p
, &len
, &r
))
944 if (!good_radix_p(r
, 1)) VALERR("bad radix");
945 sc
.buf
= p
; sc
.lim
= p
+ len
;
946 if ((zz
= mp_read(MP_NEW
, r
, &mptext_stringops
, &sc
)) == 0)
947 VALERR("bad integer");
948 z
= Py_BuildValue("(Ns#)", mp_pywrap(zz
),
949 sc
.buf
, (Py_ssize_t
)(sc
.lim
- sc
.buf
));
954 static PyObject
*meth__MP_factorial(PyObject
*me
, PyObject
*arg
)
958 if (!PyArg_ParseTuple(arg
, "OO&:factorial", &me
, convulong
, &i
))
964 static PyObject
*meth__MP_fibonacci(PyObject
*me
, PyObject
*arg
)
968 if (!PyArg_ParseTuple(arg
, "Ol:fibonacci", &me
, &i
)) return (0);
973 #define LOADOP(pre, py, name) \
974 static PyObject *meth__##py##_##name(PyObject *me, PyObject *arg) \
978 if (!PyArg_ParseTuple(arg, "Os#:" #name, &me, &p, &len)) return (0); \
979 return (pre##_pywrap(mp_##name(MP_NEW, p, len))); \
981 LOADOP(mp
, MP
, loadl
)
982 LOADOP(mp
, MP
, loadb
)
983 LOADOP(mp
, MP
, loadl2c
)
984 LOADOP(mp
, MP
, loadb2c
)
985 LOADOP(gf
, GF
, loadl
)
986 LOADOP(gf
, GF
, loadb
)
989 /*----- Products of small integers ----------------------------------------*/
991 typedef struct mpmul_pyobj
{
997 #define MPMUL_LIVEP(o) (((mpmul_pyobj *)(o))->livep)
998 #define MPMUL_PY(o) (&((mpmul_pyobj *)(o))->mm)
1000 static void mpmul_pydealloc(PyObject
*me
)
1002 if (MPMUL_LIVEP(me
))
1003 mp_drop(mpmul_done(MPMUL_PY(me
)));
1007 static PyObject
*mmmeth_factor(PyObject
*me
, PyObject
*arg
)
1012 if (!MPMUL_LIVEP(me
)) VALERR("MPMul object invalid");
1013 if (PyTuple_Size(arg
) != 1)
1014 i
= PyObject_GetIter(arg
);
1016 if ((q
= PyTuple_GetItem(arg
, 0)) == 0) goto end
;
1017 if ((i
= PyObject_GetIter(q
)) == 0) {
1018 PyErr_Clear(); /* that's ok */
1019 i
= PyObject_GetIter(arg
);
1023 while ((q
= PyIter_Next(i
)) != 0) {
1024 x
= getmp(q
); Py_DECREF(q
); if (!x
) {
1028 mpmul_add(MPMUL_PY(me
), x
);
1037 static PyObject
*mmmeth_done(PyObject
*me
, PyObject
*arg
)
1041 if (!PyArg_ParseTuple(arg
, ":done")) goto end
;
1042 if (!MPMUL_LIVEP(me
)) VALERR("MPMul object invalid");
1043 x
= mpmul_done(MPMUL_PY(me
));
1044 MPMUL_LIVEP(me
) = 0;
1045 return (mp_pywrap(x
));
1050 static PyObject
*mpmul_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1054 if (kw
) TYERR("keyword arguments not allowed here");
1055 mm
= (mpmul_pyobj
*)ty
->tp_alloc(ty
, 0);
1056 mpmul_init(&mm
->mm
);
1058 if (mmmeth_factor((PyObject
*)mm
, arg
) == 0) {
1062 return ((PyObject
*)mm
);
1067 static PyObject
*mmget_livep(PyObject
*me
, void *hunoz
)
1068 { return (getbool(MPMUL_LIVEP(me
))); }
1070 static PyGetSetDef mpmul_pygetset
[] = {
1071 #define GETSETNAME(op, name) mm##op##_##name
1072 GET (livep
, "MM.livep -> flag: object still valid?")
1077 static PyMethodDef mpmul_pymethods
[] = {
1078 #define METHNAME(name) mmmeth_##name
1079 METH (factor
, "MM.factor(ITERABLE) or MM.factor(I, ...)")
1080 METH (done
, "MM.done() -> PRODUCT")
1085 static PyTypeObject
*mpmul_pytype
, mpmul_pytype_skel
= {
1086 PyObject_HEAD_INIT(0) 0, /* Header */
1087 "MPMul", /* @tp_name@ */
1088 sizeof(mpmul_pyobj
), /* @tp_basicsize@ */
1089 0, /* @tp_itemsize@ */
1091 mpmul_pydealloc
, /* @tp_dealloc@ */
1093 0, /* @tp_getattr@ */
1094 0, /* @tp_setattr@ */
1095 0, /* @tp_compare@ */
1097 0, /* @tp_as_number@ */
1098 0, /* @tp_as_sequence@ */
1099 0, /* @tp_as_mapping@ */
1103 0, /* @tp_getattro@ */
1104 0, /* @tp_setattro@ */
1105 0, /* @tp_as_buffer@ */
1106 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1107 Py_TPFLAGS_BASETYPE
,
1110 "An object for multiplying many small integers.",
1112 0, /* @tp_traverse@ */
1114 0, /* @tp_richcompare@ */
1115 0, /* @tp_weaklistoffset@ */
1117 0, /* @tp_iternext@ */
1118 mpmul_pymethods
, /* @tp_methods@ */
1119 0, /* @tp_members@ */
1120 mpmul_pygetset
, /* @tp_getset@ */
1123 0, /* @tp_descr_get@ */
1124 0, /* @tp_descr_set@ */
1125 0, /* @tp_dictoffset@ */
1127 PyType_GenericAlloc
, /* @tp_alloc@ */
1128 mpmul_pynew
, /* @tp_new@ */
1133 /*----- Montgomery reduction ----------------------------------------------*/
1135 typedef struct mpmont_pyobj
{
1140 #define MPMONT_PY(o) (&((mpmont_pyobj *)(o))->mm)
1142 static PyObject
*mmmeth_int(PyObject
*me
, PyObject
*arg
)
1146 mpmont
*mm
= MPMONT_PY(me
);
1148 if (!PyArg_ParseTuple(arg
, "O&:in", convmp
, &yy
))
1150 mp_div(0, &yy
, yy
, mm
->m
);
1151 z
= mp_pywrap(mpmont_mul(mm
, MP_NEW
, yy
, mm
->r2
));
1153 if (yy
) MP_DROP(yy
);
1157 static PyObject
*mmmeth_mul(PyObject
*me
, PyObject
*arg
)
1160 mp
*yy
= 0, *zz
= 0;
1162 if (!PyArg_ParseTuple(arg
, "O&O&:mul", convmp
, &yy
, convmp
, &zz
))
1164 rc
= mp_pywrap(mpmont_mul(MPMONT_PY(me
), MP_NEW
, yy
, zz
));
1166 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1170 static PyObject
*mmmeth_exp(PyObject
*me
, PyObject
*arg
)
1173 mp
*yy
= 0, *zz
= 0;
1175 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convmp
, &yy
, convmp
, &zz
))
1178 if ((yy
= mp_modinv_checked(yy
, yy
, MPMONT_PY(me
)->m
)) == 0) goto end
;
1179 zz
= mp_neg(zz
, zz
);
1181 rc
= mp_pywrap(mpmont_exp(MPMONT_PY(me
), MP_NEW
, yy
, zz
));
1183 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1187 static PyObject
*mmmeth_expr(PyObject
*me
, PyObject
*arg
)
1190 mp
*yy
= 0, *zz
= 0;
1192 if (!PyArg_ParseTuple(arg
, "O&O&:expr", convmp
, &yy
, convmp
, &zz
))
1195 yy
= mpmont_reduce(MPMONT_PY(me
), yy
, yy
);
1196 if ((yy
= mp_modinv_checked(yy
, yy
, MPMONT_PY(me
)->m
)) == 0) goto end
;
1197 yy
= mpmont_mul(MPMONT_PY(me
), yy
, yy
, MPMONT_PY(me
)->r2
);
1198 zz
= mp_neg(zz
, zz
);
1200 rc
= mp_pywrap(mpmont_expr(MPMONT_PY(me
), MP_NEW
, yy
, zz
));
1202 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1206 static PyObject
*mm_mexpr_id(PyObject
*me
)
1207 { return mp_pywrap(MP_COPY(MPMONT_PY(me
)->r
)); }
1209 static int mm_mexpr_fill(void *p
, PyObject
*me
, PyObject
*x
, PyObject
*y
)
1211 mp
*xx
= 0, *yy
= 0;
1212 mp_expfactor
*f
= p
;
1213 mpmont
*mm
= MPMONT_PY(me
);
1215 if ((xx
= getmp(x
)) == 0 || (yy
= getmp(y
)) == 0)
1218 xx
= mpmont_reduce(mm
, xx
, xx
);
1219 if ((xx
= mp_modinv_checked(xx
, xx
, yy
)) == 0)
1221 xx
= mpmont_mul(mm
, xx
, xx
, mm
->r2
);
1222 yy
= mp_neg(yy
, yy
);
1229 mp_drop(xx
); mp_drop(yy
);
1233 static PyObject
*mm_mexpr(PyObject
*me
, void *v
, int n
)
1234 { return mp_pywrap(mpmont_mexpr(MPMONT_PY(me
), MP_NEW
, v
, n
)); }
1236 static void mp_mexp_drop(void *p
)
1238 mp_expfactor
*f
= p
;
1243 static PyObject
*mmmeth_mexpr(PyObject
*me
, PyObject
*arg
)
1245 return mexp_common(me
, arg
, sizeof(mp_expfactor
),
1246 mm_mexpr_id
, mm_mexpr_fill
, mm_mexpr
, mp_mexp_drop
);
1249 static PyObject
*mp_mexp_id(PyObject
*me
)
1250 { return mp_pywrap(MP_ONE
); }
1252 static int mp_mexp_fill(void *p
, PyObject
*me
, PyObject
*x
, PyObject
*y
)
1254 mp
*xx
= 0, *yy
= 0;
1255 mp_expfactor
*f
= p
;
1257 if ((xx
= getmp(x
)) == 0 || (yy
= getmp(y
)) == 0)
1260 if ((xx
= mp_modinv_checked(xx
, xx
, yy
)) == 0)
1262 yy
= mp_neg(yy
, yy
);
1269 mp_drop(xx
); mp_drop(yy
);
1273 static PyObject
*mm_mexp(PyObject
*me
, void *v
, int n
)
1274 { return mp_pywrap(mpmont_mexp(MPMONT_PY(me
), MP_NEW
, v
, n
)); }
1276 static PyObject
*mmmeth_mexp(PyObject
*me
, PyObject
*arg
)
1278 return mexp_common(me
, arg
, sizeof(mp_expfactor
),
1279 mp_mexp_id
, mp_mexp_fill
, mm_mexp
, mp_mexp_drop
);
1282 #define mmmeth_ext mmmeth_reduce
1283 static PyObject
*mmmeth_reduce(PyObject
*me
, PyObject
*arg
)
1288 if (!PyArg_ParseTuple(arg
, "O&", convmp
, &yy
)) goto end
;
1289 z
= mp_pywrap(mpmont_reduce(MPMONT_PY(me
), MP_NEW
, yy
));
1294 static void mpmont_pydealloc(PyObject
*me
)
1296 mpmont_destroy(MPMONT_PY(me
));
1300 static PyObject
*mpmont_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1302 mpmont_pyobj
*mm
= 0;
1303 char *kwlist
[] = { "m", 0 };
1306 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", kwlist
, convmp
, &xx
))
1308 if (!MP_POSP(xx
) || !MP_ODDP(xx
)) VALERR("m must be positive and odd");
1309 mm
= (mpmont_pyobj
*)ty
->tp_alloc(ty
, 0);
1310 mpmont_create(&mm
->mm
, xx
);
1312 if (xx
) MP_DROP(xx
);
1313 return ((PyObject
*)mm
);
1316 static PyObject
*mmget_m(PyObject
*me
, void *hunoz
)
1317 { return (mp_pywrap(MP_COPY(MPMONT_PY(me
)->m
))); }
1319 static PyObject
*mmget_r(PyObject
*me
, void *hunoz
)
1320 { return (mp_pywrap(MP_COPY(MPMONT_PY(me
)->r
))); }
1322 static PyObject
*mmget_r2(PyObject
*me
, void *hunoz
)
1323 { return (mp_pywrap(MP_COPY(MPMONT_PY(me
)->r2
))); }
1325 static PyGetSetDef mpmont_pygetset
[] = {
1326 #define GETSETNAME(op, name) mm##op##_##name
1327 GET (m
, "M.m -> modulus for reduction")
1328 GET (r
, "M.r -> multiplicative identity")
1329 GET (r2
, "M.r2 -> M.r^2, Montgomerization factor")
1334 static PyMethodDef mpmont_pymethods
[] = {
1335 #define METHNAME(name) mmmeth_##name
1336 METH (int, "M.int(X) -> XR")
1337 METH (mul
, "M.mul(XR, YR) -> ZR where Z = X Y")
1338 METH (expr
, "M.expr(XR, N) -> ZR where Z = X^N mod M.m")
1340 M.mexpr([(XR0, N0), (XR1, N1), ...]) = ZR where Z = X0^N0 X1^N1 ... mod M.m\n\
1341 \t(the list may be flattened if this more convenient.)")
1342 METH (reduce
, "M.reduce(XR) -> X")
1343 METH (ext
, "M.ext(XR) -> X")
1344 METH (exp
, "M.exp(X, N) -> X^N mod M.m")
1346 M.mexp([(X0, N0), (X1, N1), ...]) = X0^N0 X1^N1 ... mod M.m\n\
1347 \t(the list may be flattened if this more convenient.)")
1352 static PyTypeObject
*mpmont_pytype
, mpmont_pytype_skel
= {
1353 PyObject_HEAD_INIT(0) 0, /* Header */
1354 "MPMont", /* @tp_name@ */
1355 sizeof(mpmont_pyobj
), /* @tp_basicsize@ */
1356 0, /* @tp_itemsize@ */
1358 mpmont_pydealloc
, /* @tp_dealloc@ */
1360 0, /* @tp_getattr@ */
1361 0, /* @tp_setattr@ */
1362 0, /* @tp_compare@ */
1364 0, /* @tp_as_number@ */
1365 0, /* @tp_as_sequence@ */
1366 0, /* @tp_as_mapping@ */
1370 0, /* @tp_getattro@ */
1371 0, /* @tp_setattro@ */
1372 0, /* @tp_as_buffer@ */
1373 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1374 Py_TPFLAGS_BASETYPE
,
1377 "A Montgomery reduction context.",
1379 0, /* @tp_traverse@ */
1381 0, /* @tp_richcompare@ */
1382 0, /* @tp_weaklistoffset@ */
1384 0, /* @tp_iternext@ */
1385 mpmont_pymethods
, /* @tp_methods@ */
1386 0, /* @tp_members@ */
1387 mpmont_pygetset
, /* @tp_getset@ */
1390 0, /* @tp_descr_get@ */
1391 0, /* @tp_descr_set@ */
1392 0, /* @tp_dictoffset@ */
1394 PyType_GenericAlloc
, /* @tp_alloc@ */
1395 mpmont_pynew
, /* @tp_new@ */
1400 /*----- Barrett reduction -------------------------------------------------*/
1402 typedef struct mpbarrett_pyobj
{
1407 #define MPBARRETT_PY(o) (&((mpbarrett_pyobj *)(o))->mb)
1409 static PyObject
*mbmeth_exp(PyObject
*me
, PyObject
*arg
)
1412 mp
*yy
= 0, *zz
= 0;
1414 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convmp
, &yy
, convmp
, &zz
))
1417 if ((yy
= mp_modinv_checked(yy
, yy
, MPBARRETT_PY(me
)->m
)) == 0) goto end
;
1418 zz
= mp_neg(zz
, zz
);
1420 rc
= mp_pywrap(mpbarrett_exp(MPBARRETT_PY(me
), MP_NEW
, yy
, zz
));
1422 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1426 static PyObject
*mb_mexp(PyObject
*me
, void *v
, int n
)
1427 { return mp_pywrap(mpbarrett_mexp(MPBARRETT_PY(me
), MP_NEW
, v
, n
)); }
1429 static PyObject
*mbmeth_mexp(PyObject
*me
, PyObject
*arg
)
1431 return mexp_common(me
, arg
, sizeof(mp_expfactor
),
1432 mp_mexp_id
, mp_mexp_fill
, mb_mexp
, mp_mexp_drop
);
1435 static PyObject
*mbmeth_reduce(PyObject
*me
, PyObject
*arg
)
1440 if (!PyArg_ParseTuple(arg
, "O&:reduce", convmp
, &yy
))
1442 z
= mp_pywrap(mpbarrett_reduce(MPBARRETT_PY(me
), MP_NEW
, yy
));
1447 static void mpbarrett_pydealloc(PyObject
*me
)
1449 mpbarrett_destroy(MPBARRETT_PY(me
));
1453 static PyObject
*mpbarrett_pynew(PyTypeObject
*ty
,
1454 PyObject
*arg
, PyObject
*kw
)
1456 mpbarrett_pyobj
*mb
= 0;
1457 char *kwlist
[] = { "m", 0 };
1460 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", kwlist
, convmp
, &xx
))
1462 if (!MP_POSP(xx
)) VALERR("m must be positive");
1463 mb
= (mpbarrett_pyobj
*)ty
->tp_alloc(ty
, 0);
1464 mpbarrett_create(&mb
->mb
, xx
);
1466 if (xx
) MP_DROP(xx
);
1467 return ((PyObject
*)mb
);
1470 static PyObject
*mbget_m(PyObject
*me
, void *hunoz
)
1471 { return (mp_pywrap(MP_COPY(MPBARRETT_PY(me
)->m
))); }
1473 static PyGetSetDef mpbarrett_pygetset
[] = {
1474 #define GETSETNAME(op, name) mb##op##_##name
1475 GET (m
, "B.m -> modulus for reduction")
1480 static PyMethodDef mpbarrett_pymethods
[] = {
1481 #define METHNAME(name) mbmeth_##name
1482 METH (reduce
, "B.reduce(X) -> X mod B.m")
1483 METH (exp
, "B.exp(X, N) -> X^N mod B.m")
1485 B.mexp([(X0, N0), (X1, N1), ...]) = X0^N0 X1^N1 ... mod B.m\n\
1486 \t(the list may be flattened if this more convenient.)")
1491 static PyTypeObject
*mpbarrett_pytype
, mpbarrett_pytype_skel
= {
1492 PyObject_HEAD_INIT(0) 0, /* Header */
1493 "MPBarrett", /* @tp_name@ */
1494 sizeof(mpbarrett_pyobj
), /* @tp_basicsize@ */
1495 0, /* @tp_itemsize@ */
1497 mpbarrett_pydealloc
, /* @tp_dealloc@ */
1499 0, /* @tp_getattr@ */
1500 0, /* @tp_setattr@ */
1501 0, /* @tp_compare@ */
1503 0, /* @tp_as_number@ */
1504 0, /* @tp_as_sequence@ */
1505 0, /* @tp_as_mapping@ */
1509 0, /* @tp_getattro@ */
1510 0, /* @tp_setattro@ */
1511 0, /* @tp_as_buffer@ */
1512 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1513 Py_TPFLAGS_BASETYPE
,
1516 "A Barrett reduction context.",
1518 0, /* @tp_traverse@ */
1520 0, /* @tp_richcompare@ */
1521 0, /* @tp_weaklistoffset@ */
1523 0, /* @tp_iternext@ */
1524 mpbarrett_pymethods
, /* @tp_methods@ */
1525 0, /* @tp_members@ */
1526 mpbarrett_pygetset
, /* @tp_getset@ */
1529 0, /* @tp_descr_get@ */
1530 0, /* @tp_descr_set@ */
1531 0, /* @tp_dictoffset@ */
1533 PyType_GenericAlloc
, /* @tp_alloc@ */
1534 mpbarrett_pynew
, /* @tp_new@ */
1539 /*----- Nice prime reduction ----------------------------------------------*/
1541 typedef struct mpreduce_pyobj
{
1546 #define MPREDUCE_PY(o) (&((mpreduce_pyobj *)(o))->mr)
1548 static PyObject
*mrmeth_exp(PyObject
*me
, PyObject
*arg
)
1551 mp
*yy
= 0, *zz
= 0;
1553 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convmp
, &yy
, convmp
, &zz
))
1556 if ((yy
= mp_modinv_checked(yy
, yy
, MPREDUCE_PY(me
)->p
)) == 0) goto end
;
1557 zz
= mp_neg(zz
, zz
);
1559 rc
= mp_pywrap(mpreduce_exp(MPREDUCE_PY(me
), MP_NEW
, yy
, zz
));
1561 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1565 static PyObject
*mrmeth_reduce(PyObject
*me
, PyObject
*arg
)
1570 if (!PyArg_ParseTuple(arg
, "O&:reduce", convmp
, &yy
)) goto end
;
1571 z
= mp_pywrap(mpreduce_do(MPREDUCE_PY(me
), MP_NEW
, yy
));
1576 static void mpreduce_pydealloc(PyObject
*me
)
1578 mpreduce_destroy(MPREDUCE_PY(me
));
1582 static PyObject
*mpreduce_pynew(PyTypeObject
*ty
,
1583 PyObject
*arg
, PyObject
*kw
)
1585 mpreduce_pyobj
*mr
= 0;
1587 char *kwlist
[] = { "m", 0 };
1590 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", kwlist
, convmp
, &xx
))
1592 if (!MP_POSP(xx
)) VALERR("m must be positive");
1593 if (mpreduce_create(&r
, xx
)) VALERR("bad modulus (must be 2^k - ...)");
1594 mr
= (mpreduce_pyobj
*)ty
->tp_alloc(ty
, 0);
1597 if (xx
) MP_DROP(xx
);
1598 return ((PyObject
*)mr
);
1601 static PyObject
*mrget_m(PyObject
*me
, void *hunoz
)
1602 { return (mp_pywrap(MP_COPY(MPREDUCE_PY(me
)->p
))); }
1604 static PyGetSetDef mpreduce_pygetset
[] = {
1605 #define GETSETNAME(op, name) mr##op##_##name
1606 GET (m
, "R.m -> modulus for reduction")
1611 static PyMethodDef mpreduce_pymethods
[] = {
1612 #define METHNAME(name) mrmeth_##name
1613 METH (reduce
, "R.reduce(X) -> X mod B.m")
1614 METH (exp
, "R.exp(X, N) -> X^N mod B.m")
1619 static PyTypeObject
*mpreduce_pytype
, mpreduce_pytype_skel
= {
1620 PyObject_HEAD_INIT(0) 0, /* Header */
1621 "MPReduce", /* @tp_name@ */
1622 sizeof(mpreduce_pyobj
), /* @tp_basicsize@ */
1623 0, /* @tp_itemsize@ */
1625 mpreduce_pydealloc
, /* @tp_dealloc@ */
1627 0, /* @tp_getattr@ */
1628 0, /* @tp_setattr@ */
1629 0, /* @tp_compare@ */
1631 0, /* @tp_as_number@ */
1632 0, /* @tp_as_sequence@ */
1633 0, /* @tp_as_mapping@ */
1637 0, /* @tp_getattro@ */
1638 0, /* @tp_setattro@ */
1639 0, /* @tp_as_buffer@ */
1640 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1641 Py_TPFLAGS_BASETYPE
,
1644 "A reduction context for reduction modulo primes of special form.",
1646 0, /* @tp_traverse@ */
1648 0, /* @tp_richcompare@ */
1649 0, /* @tp_weaklistoffset@ */
1651 0, /* @tp_iternext@ */
1652 mpreduce_pymethods
, /* @tp_methods@ */
1653 0, /* @tp_members@ */
1654 mpreduce_pygetset
, /* @tp_getset@ */
1657 0, /* @tp_descr_get@ */
1658 0, /* @tp_descr_set@ */
1659 0, /* @tp_dictoffset@ */
1661 PyType_GenericAlloc
, /* @tp_alloc@ */
1662 mpreduce_pynew
, /* @tp_new@ */
1667 /*----- Chinese Remainder Theorem solution --------------------------------*/
1669 typedef struct mpcrt_pyobj
{
1674 #define MPCRT_PY(o) (&((mpcrt_pyobj *)(o))->c)
1676 static PyObject
*mcmeth_solve(PyObject
*me
, PyObject
*arg
)
1678 mpcrt
*c
= MPCRT_PY(me
);
1679 PyObject
*q
= 0, *x
, *z
= 0;
1682 int i
= 0, n
= c
->k
;
1685 if (PyTuple_Size(arg
) == n
)
1687 else if (!PyArg_ParseTuple(arg
, "O:solve", &q
))
1690 if (!PySequence_Check(q
)) TYERR("want a sequence of residues");
1691 if (PySequence_Size(q
) != n
) VALERR("residue count mismatch");
1692 v
= xmalloc(n
* sizeof(*v
));
1693 for (i
= 0; i
< n
; i
++) {
1694 if ((x
= PySequence_GetItem(q
, i
)) == 0) goto end
;
1695 xx
= getmp(x
); Py_DECREF(x
); if (!xx
) goto end
;
1698 z
= mp_pywrap(mpcrt_solve(c
, MP_NEW
, v
));
1702 for (i
= 0; i
< n
; i
++)
1711 static void mpcrt_pydealloc(PyObject
*me
)
1713 mpcrt
*c
= MPCRT_PY(me
);
1718 static PyObject
*mpcrt_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1722 char *kwlist
[] = { "mv", 0 };
1723 PyObject
*q
= 0, *x
;
1724 mp
*xx
= MP_NEW
, *y
= MP_NEW
, *g
= MP_NEW
;
1728 if (PyTuple_Size(arg
) > 1)
1730 else if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O:new", kwlist
, &q
))
1733 if (!PySequence_Check(q
)) TYERR("want a sequence of moduli");
1734 n
= PySequence_Size(q
);
1735 if (PyErr_Occurred()) goto end
;
1736 if (!n
) VALERR("want at least one modulus");
1737 v
= xmalloc(n
* sizeof(*v
));
1738 for (i
= 0; i
< n
; i
++) {
1739 if ((x
= PySequence_GetItem(q
, i
)) == 0) goto end
;
1740 xx
= getmp(x
); Py_DECREF(x
); if (!xx
) goto end
;
1741 if (MP_CMP(xx
, <=, MP_ZERO
)) VALERR("moduli must be positive");
1742 v
[i
].m
= xx
; v
[i
].n
= 0; v
[i
].ni
= 0; v
[i
].nni
= 0; xx
= MP_NEW
;
1745 for (j
= 0; j
< i
; j
++) mpmul_add(&mm
, v
[j
].m
);
1746 xx
= mpmul_done(&mm
);
1747 for (j
= 0; j
< i
; j
++) {
1748 mp_div(&y
, 0, xx
, v
[j
].m
);
1749 mp_gcd(&g
, 0, 0, y
, v
[j
].m
);
1750 if (!MP_EQ(g
, MP_ONE
)) VALERR("moduli must be pairwise coprime");
1753 c
= (mpcrt_pyobj
*)ty
->tp_alloc(ty
, 0);
1754 mpcrt_create(&c
->c
, v
, n
, 0);
1756 mp_drop(xx
); mp_drop(y
); mp_drop(g
);
1757 return ((PyObject
*)c
);
1762 for (i
= 0; i
< n
; i
++)
1767 mp_drop(xx
); mp_drop(y
); mp_drop(g
);
1771 static PyObject
*mcget_product(PyObject
*me
, void *hunoz
)
1772 { return (mp_pywrap(MP_COPY(MPCRT_PY(me
)->mb
.m
))); }
1774 static PyObject
*mcget_moduli(PyObject
*me
, void *hunoz
)
1778 mpcrt
*c
= MPCRT_PY(me
);
1780 if ((q
= PyList_New(c
->k
)) == 0) return (0);
1781 for (i
= 0; i
< c
->k
; i
++)
1782 PyList_SetItem(q
, i
, mp_pywrap(c
->v
[i
].m
));
1786 static PyGetSetDef mpcrt_pygetset
[] = {
1787 #define GETSETNAME(op, name) mc##op##_##name
1788 GET (product
, "C.product -> product of moduli")
1789 GET (moduli
, "C.moduli -> list of individual moduli")
1794 static PyMethodDef mpcrt_pymethods
[] = {
1795 #define METHNAME(name) mcmeth_##name
1796 METH (solve
, "C.solve([R0, R1]) -> X mod C.product")
1801 static PyTypeObject
*mpcrt_pytype
, mpcrt_pytype_skel
= {
1802 PyObject_HEAD_INIT(0) 0, /* Header */
1803 "MPCRT", /* @tp_name@ */
1804 sizeof(mpcrt_pyobj
), /* @tp_basicsize@ */
1805 0, /* @tp_itemsize@ */
1807 mpcrt_pydealloc
, /* @tp_dealloc@ */
1809 0, /* @tp_getattr@ */
1810 0, /* @tp_setattr@ */
1811 0, /* @tp_compare@ */
1813 0, /* @tp_as_number@ */
1814 0, /* @tp_as_sequence@ */
1815 0, /* @tp_as_mapping@ */
1819 0, /* @tp_getattro@ */
1820 0, /* @tp_setattro@ */
1821 0, /* @tp_as_buffer@ */
1822 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1823 Py_TPFLAGS_BASETYPE
,
1826 "A context for the solution of Chinese Remainder Theorem problems.",
1828 0, /* @tp_traverse@ */
1830 0, /* @tp_richcompare@ */
1831 0, /* @tp_weaklistoffset@ */
1833 0, /* @tp_iternext@ */
1834 mpcrt_pymethods
, /* @tp_methods@ */
1835 0, /* @tp_members@ */
1836 mpcrt_pygetset
, /* @tp_getset@ */
1839 0, /* @tp_descr_get@ */
1840 0, /* @tp_descr_set@ */
1841 0, /* @tp_dictoffset@ */
1843 PyType_GenericAlloc
, /* @tp_alloc@ */
1844 mpcrt_pynew
, /* @tp_new@ */
1849 /*----- Binary polynomials ------------------------------------------------*/
1851 static PyObject
*gf_pyrepr(PyObject
*o
)
1852 { return mp_topystring(MP_X(o
), 16, "GF(", "0x", "L)"); }
1854 static PyObject
*gf_pyrichcompare(PyObject
*x
, PyObject
*y
, int op
)
1860 if (gfbinop(x
, y
, &xx
, &yy
)) RETURN_NOTIMPL
;
1862 case Py_EQ
: b
= MP_EQ(xx
, yy
); break;
1863 case Py_NE
: b
= !MP_EQ(xx
, yy
); break;
1868 case Py_LT
: b
= xl
< yl
; break;
1869 case Py_LE
: b
= xl
<= yl
; break;
1870 case Py_GT
: b
= xl
> yl
; break;
1871 case Py_GE
: b
= xl
>= yl
; break;
1876 MP_DROP(xx
); MP_DROP(yy
);
1877 return (getbool(b
));
1880 static PyObject
*gf_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1886 char *kwlist
[] = { "x", "radix", 0 };
1888 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O|i:gf", kwlist
, &x
, &radix
))
1890 if (GF_PYCHECK(x
)) RETURN_OBJ(x
);
1891 if (!good_radix_p(radix
, 1)) VALERR("radix out of range");
1892 if ((z
= mp_frompyobject(x
, radix
)) == 0) {
1893 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to gf",
1894 x
->ob_type
->tp_name
);
1899 VALERR("gf cannot be negative");
1901 zz
= (mp_pyobj
*)ty
->tp_alloc(ty
, 0);
1904 return ((PyObject
*)zz
);
1907 static PyObject
*gf_pyexp(PyObject
*x
, PyObject
*y
, PyObject
*z
)
1909 mp
*xx
= 0, *yy
= 0, *zz
= 0;
1913 if ((xx
= tomp(x
)) == 0 || (yy
= tomp(y
)) == 0 ||
1914 (z
&& z
!= Py_None
&& (zz
= tomp(z
)) == 0)) {
1915 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
1918 if (!z
|| z
== Py_None
) {
1919 if (MP_NEGP(yy
)) VALERR("negative exponent");
1920 r
= gf_exp(MP_NEW
, xx
, yy
);
1923 if (MP_ZEROP(zz
)) ZDIVERR("zero modulus");
1925 if ((xx
= gf_modinv_checked(xx
, xx
, zz
)) == 0) goto end
;
1926 yy
= mp_neg(yy
, yy
);
1928 gfreduce_create(&gr
, zz
);
1929 r
= gfreduce_exp(&gr
, MP_NEW
, xx
, yy
);
1930 gfreduce_destroy(&gr
);
1934 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
1938 static PyObject
*gfmeth_sqr(PyObject
*me
, PyObject
*arg
)
1940 if (!PyArg_ParseTuple(arg
, ":sqr")) return (0);
1941 return (gf_pywrap(gf_sqr(MP_NEW
, MP_X(me
))));
1944 static PyObject
*gfmeth_gcd(PyObject
*me
, PyObject
*arg
)
1947 mp
*yy
= 0, *zz
= MP_NEW
;
1949 if (!PyArg_ParseTuple(arg
, "O&:gcd", convgf
, &yy
)) goto end
;
1950 gf_gcd(&zz
, 0, 0, MP_X(me
), yy
);
1953 if (yy
) MP_DROP(yy
);
1957 static PyObject
*gfmeth_gcdx(PyObject
*me
, PyObject
*arg
)
1960 mp
*yy
= 0, *zz
= MP_NEW
, *uu
= MP_NEW
, *vv
= MP_NEW
;
1962 if (!PyArg_ParseTuple(arg
, "O&:gcdx", convgf
, &yy
))
1964 gf_gcd(&zz
, &uu
, &vv
, MP_X(me
), yy
);
1965 z
= Py_BuildValue("(NNN)",
1966 gf_pywrap(zz
), gf_pywrap(uu
), gf_pywrap(vv
));
1968 if (yy
) MP_DROP(yy
);
1972 static PyObject
*gfmeth_modinv(PyObject
*me
, PyObject
*arg
)
1975 mp
*yy
= 0, *zz
= MP_NEW
;
1977 if (!PyArg_ParseTuple(arg
, "O&:modinv", convgf
, &yy
) ||
1978 (zz
= gf_modinv_checked(MP_NEW
, yy
, MP_X(me
))) == 0)
1982 if (yy
) MP_DROP(yy
);
1986 static PyObject
*gfmeth_irreduciblep(PyObject
*me
, PyObject
*arg
)
1988 if (!PyArg_ParseTuple(arg
, ":irreduciblep")) return (0);
1989 return getbool(gf_irreduciblep(MP_X(me
)));
1992 static PyObject
*gfget_degree(PyObject
*me
, void *hunoz
)
1993 { return (PyInt_FromLong(mp_bits(MP_X(me
)) - 1)); }
1995 static PyGetSetDef gf_pygetset
[] = {
1996 #define GETSETNAME(op, name) gf##op##_##name
1997 GET (degree
, "X.degree -> polynomial degree of X")
1999 #define GETSETNAME(op, name) mp##op##_##name
2000 GET (nbits
, "X.nbits -> bit length of X")
2001 GET (noctets
, "X.noctets -> octet length of X")
2006 static PyMethodDef gf_pymethods
[] = {
2007 #define METHNAME(func) gfmeth_##func
2008 METH (setbit
, "X.setbit(N) -> X with bit N set")
2009 METH (clearbit
, "X.clearbit(N) -> X with bit N clear")
2010 METH (testbit
, "X.testbit(N) -> true/false if bit N set/clear in X")
2011 METH (sqr
, "X.sqr() -> X^2")
2012 METH (gcd
, "X.gcd(Y) -> gcd(X, Y)")
2014 "X.gcdx(Y) -> (gcd(X, Y), U, V) with X U + Y V = gcd(X, Y)")
2015 METH (modinv
, "X.modinv(Y) -> multiplicative inverse of Y mod X")
2016 METH (irreduciblep
, "X.irreduciblep() -> true/false")
2018 #define METHNAME(func) mpmeth_##func
2019 KWMETH(tostring
, "X.tostring([radix = 10]) -> STR")
2020 KWMETH(storel
, "X.storel([len = -1]) -> little-endian bytes")
2021 KWMETH(storeb
, "X.storeb([len = -1]) -> big-endian bytes")
2023 "X.storel2c([len = -1]) -> little-endian bytes, two's complement")
2025 "X.storeb2c([len = -1]) -> big-endian bytes, two's complement")
2026 METH (tobuf
, "X.tobuf() -> buffer format")
2031 static PyNumberMethods gf_pynumber
= {
2032 gf_pyadd
, /* @nb_add@ */
2033 gf_pysub
, /* @nb_subtract@ */
2034 gf_pymul
, /* @nb_multiply@ */
2035 0, /* @nb_divide@ */
2036 gf_pymod
, /* @nb_remainder@ */
2037 gf_pydivmod
, /* @nb_divmod@ */
2038 gf_pyexp
, /* @nb_power@ */
2039 mp_pyid
, /* @nb_negative@ */
2040 mp_pyid
, /* @nb_positive@ */
2041 mp_pyid
, /* @nb_absolute@ */
2042 mp_pynonzerop
, /* @nb_nonzero@ */
2043 0 /* doesn't make any sense */, /* @nb_invert@ */
2044 gf_pylsl
, /* @nb_lshift@ */
2045 gf_pylsr
, /* @nb_rshift@ */
2046 gf_pyand
, /* @nb_and@ */
2047 gf_pyxor
, /* @nb_xor@ */
2048 gf_pyor
, /* @nb_or@ */
2049 gf_pycoerce
, /* @nb_coerce@ */
2050 mp_pyint
, /* @nb_int@ */
2051 mp_pylong
, /* @nb_long@ */
2052 0 /* doesn't make any sense */, /* @nb_float@ */
2053 mp_pyoct
, /* @nb_oct@ */
2054 mp_pyhex
, /* @nb_hex@ */
2056 0, /* @nb_inplace_add@ */
2057 0, /* @nb_inplace_subtract@ */
2058 0, /* @nb_inplace_multiply@ */
2059 0, /* @nb_inplace_divide@ */
2060 0, /* @nb_inplace_remainder@ */
2061 0, /* @nb_inplace_power@ */
2062 0, /* @nb_inplace_lshift@ */
2063 0, /* @nb_inplace_rshift@ */
2064 0, /* @nb_inplace_and@ */
2065 0, /* @nb_inplace_xor@ */
2066 0, /* @nb_inplace_or@ */
2068 gf_pydiv
, /* @nb_floor_divide@ */
2069 0, /* @nb_true_divide@ */
2070 0, /* @nb_inplace_floor_divide@ */
2071 0, /* @nb_inplace_true_divide@ */
2074 static PyTypeObject gf_pytype_skel
= {
2075 PyObject_HEAD_INIT(0) 0, /* Header */
2076 "GF", /* @tp_name@ */
2077 sizeof(mp_pyobj
), /* @tp_basicsize@ */
2078 0, /* @tp_itemsize@ */
2080 mp_pydealloc
, /* @tp_dealloc@ */
2082 0, /* @tp_getattr@ */
2083 0, /* @tp_setattr@ */
2084 0, /* @tp_compare@ */
2085 gf_pyrepr
, /* @tp_repr@ */
2086 &gf_pynumber
, /* @tp_as_number@ */
2087 0, /* @tp_as_sequence@ */
2088 0, /* @tp_as_mapping@ */
2089 mp_pyhash
, /* @tp_hash@ */
2091 mp_pyhex
, /* @tp_str@ */
2092 0, /* @tp_getattro@ */
2093 0, /* @tp_setattro@ */
2094 0, /* @tp_as_buffer@ */
2095 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
2096 Py_TPFLAGS_CHECKTYPES
|
2097 Py_TPFLAGS_BASETYPE
,
2100 "Binary polynomials. Support almost all the standard arithmetic\n\
2103 Constructor GF(X, [radix = R]) attempts to convert X to a `GF'. If\n\
2104 X is a string, it's read in radix-R form, or we look for a prefix\n\
2105 if R = 0. Other acceptable things are field elements, elliptic curve\n\
2106 points, group elements, Python `int' and `long' objects, and anything\n\
2107 with an integer conversion.\n\
2109 The name is hopelessly wrong from a technical point of view, but\n\
2110 but it's much easier to type than `p2' or `c2' or whatever.\n\
2114 * Use `//' for division. GFs don't have `/' division.",
2116 0, /* @tp_traverse@ */
2118 gf_pyrichcompare
, /* @tp_richcompare@ */
2119 0, /* @tp_weaklistoffset@ */
2121 0, /* @tp_iternext@ */
2122 gf_pymethods
, /* @tp_methods@ */
2123 0, /* @tp_members@ */
2124 gf_pygetset
, /* @tp_getset@ */
2127 0, /* @tp_descr_get@ */
2128 0, /* @tp_descr_set@ */
2129 0, /* @tp_dictoffset@ */
2131 PyType_GenericAlloc
, /* @tp_alloc@ */
2132 gf_pynew
, /* @tp_new@ */
2137 static PyObject
*meth__GF_fromstring(PyObject
*me
,
2138 PyObject
*arg
, PyObject
*kw
)
2145 mptext_stringctx sc
;
2146 char *kwlist
[] = { "class", "x", "radix", 0 };
2148 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "Os#|i:fromstring",
2149 kwlist
, &me
, &p
, &len
, &r
))
2151 if (!good_radix_p(r
, 1)) VALERR("bad radix");
2152 sc
.buf
= p
; sc
.lim
= p
+ len
;
2153 if ((zz
= mp_read(MP_NEW
, r
, &mptext_stringops
, &sc
)) == 0 ||
2155 if (zz
) MP_DROP(zz
);
2156 VALERR("bad binary polynomial");
2158 z
= Py_BuildValue("(Ns#)", gf_pywrap(zz
),
2159 sc
.buf
, (Py_ssize_t
)(sc
.lim
- sc
.buf
));
2164 /*----- Sparse poly reduction ---------------------------------------------*/
2166 typedef struct gfreduce_pyobj
{
2171 #define GFREDUCE_PY(o) (&((gfreduce_pyobj *)(o))->mr)
2173 static PyObject
*grmeth_exp(PyObject
*me
, PyObject
*arg
)
2176 mp
*yy
= 0, *zz
= 0;
2178 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convgf
, &yy
, convgf
, &zz
))
2181 if ((yy
= gf_modinv_checked(yy
, yy
, GFREDUCE_PY(me
)->p
)) == 0) goto end
;
2182 zz
= mp_neg(zz
, zz
);
2184 rc
= gf_pywrap(gfreduce_exp(GFREDUCE_PY(me
), MP_NEW
, yy
, zz
));
2186 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
2190 static PyObject
*grmeth_trace(PyObject
*me
, PyObject
*arg
)
2195 if (!PyArg_ParseTuple(arg
, "O&:trace", convgf
, &xx
)) goto end
;
2196 rc
= PyInt_FromLong(gfreduce_trace(GFREDUCE_PY(me
), xx
));
2198 if (xx
) MP_DROP(xx
);
2202 static PyObject
*grmeth_halftrace(PyObject
*me
, PyObject
*arg
)
2207 if (!PyArg_ParseTuple(arg
, "O&:halftrace", convgf
, &xx
)) goto end
;
2208 rc
= gf_pywrap(gfreduce_halftrace(GFREDUCE_PY(me
), MP_NEW
, xx
));
2210 if (xx
) MP_DROP(xx
);
2214 static PyObject
*grmeth_sqrt(PyObject
*me
, PyObject
*arg
)
2219 if (!PyArg_ParseTuple(arg
, "O&:sqrt", convgf
, &xx
)) goto end
;
2220 if ((yy
= gfreduce_sqrt(GFREDUCE_PY(me
), MP_NEW
, xx
)) == 0)
2221 VALERR("no modular square root");
2224 if (xx
) MP_DROP(xx
);
2228 static PyObject
*grmeth_quadsolve(PyObject
*me
, PyObject
*arg
)
2233 if (!PyArg_ParseTuple(arg
, "O&:quadsolve", convgf
, &xx
)) goto end
;
2234 if ((yy
= gfreduce_quadsolve(GFREDUCE_PY(me
), MP_NEW
, xx
)) == 0)
2235 VALERR("no solution found");
2238 if (xx
) MP_DROP(xx
);
2242 static PyObject
*grmeth_reduce(PyObject
*me
, PyObject
*arg
)
2247 if (!PyArg_ParseTuple(arg
, "O&:reduce", convgf
, &yy
)) goto end
;
2248 z
= gf_pywrap(gfreduce_do(GFREDUCE_PY(me
), MP_NEW
, yy
));
2253 static void gfreduce_pydealloc(PyObject
*me
)
2255 gfreduce_destroy(GFREDUCE_PY(me
));
2259 static PyObject
*gfreduce_pynew(PyTypeObject
*ty
,
2260 PyObject
*arg
, PyObject
*kw
)
2262 gfreduce_pyobj
*mr
= 0;
2264 char *kwlist
[] = { "m", 0 };
2267 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", kwlist
, convgf
, &xx
))
2269 if (MP_ZEROP(xx
)) ZDIVERR("modulus is zero!");
2270 gfreduce_create(&r
, xx
);
2271 mr
= (gfreduce_pyobj
*)ty
->tp_alloc(ty
, 0);
2274 if (xx
) MP_DROP(xx
);
2275 return ((PyObject
*)mr
);
2278 static PyObject
*grget_m(PyObject
*me
, void *hunoz
)
2279 { return (gf_pywrap(MP_COPY(GFREDUCE_PY(me
)->p
))); }
2281 static PyGetSetDef gfreduce_pygetset
[] = {
2282 #define GETSETNAME(op, name) gr##op##_##name
2283 GET (m
, "R.m -> reduction polynomial")
2288 static PyMethodDef gfreduce_pymethods
[] = {
2289 #define METHNAME(name) grmeth_##name
2290 METH (reduce
, "R.reduce(X) -> X mod B.m")
2291 METH (trace
, "R.trace(X) -> Tr(X) = x + x^2 + ... + x^{2^{m - 1}}")
2292 METH (halftrace
, "R.halftrace(X) -> x + x^{2^2} + ... + x^{2^{m - 1}}")
2293 METH (sqrt
, "R.sqrt(X) -> Y where Y^2 = X mod R")
2294 METH (quadsolve
, "R.quadsolve(X) -> Y where Y^2 + Y = X mod R")
2295 METH (exp
, "R.exp(X, N) -> X^N mod B.m")
2300 static PyTypeObject
*gfreduce_pytype
, gfreduce_pytype_skel
= {
2301 PyObject_HEAD_INIT(0) 0, /* Header */
2302 "GFReduce", /* @tp_name@ */
2303 sizeof(gfreduce_pyobj
), /* @tp_basicsize@ */
2304 0, /* @tp_itemsize@ */
2306 gfreduce_pydealloc
, /* @tp_dealloc@ */
2308 0, /* @tp_getattr@ */
2309 0, /* @tp_setattr@ */
2310 0, /* @tp_compare@ */
2312 0, /* @tp_as_number@ */
2313 0, /* @tp_as_sequence@ */
2314 0, /* @tp_as_mapping@ */
2318 0, /* @tp_getattro@ */
2319 0, /* @tp_setattro@ */
2320 0, /* @tp_as_buffer@ */
2321 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
2322 Py_TPFLAGS_BASETYPE
,
2325 "A reduction context for reduction modulo sparse irreducible polynomials.",
2327 0, /* @tp_traverse@ */
2329 0, /* @tp_richcompare@ */
2330 0, /* @tp_weaklistoffset@ */
2332 0, /* @tp_iternext@ */
2333 gfreduce_pymethods
, /* @tp_methods@ */
2334 0, /* @tp_members@ */
2335 gfreduce_pygetset
, /* @tp_getset@ */
2338 0, /* @tp_descr_get@ */
2339 0, /* @tp_descr_set@ */
2340 0, /* @tp_dictoffset@ */
2342 PyType_GenericAlloc
, /* @tp_alloc@ */
2343 gfreduce_pynew
, /* @tp_new@ */
2348 /*----- Normal/poly transformation ----------------------------------------*/
2350 typedef struct gfn_pyobj
{
2356 static PyTypeObject
*gfn_pytype
, gfn_pytype_skel
;
2358 #define GFN_P(o) (((gfn_pyobj *)(o))->p)
2359 #define GFN_PTON(o) (&((gfn_pyobj *)(o))->pton)
2360 #define GFN_NTOP(o) (&((gfn_pyobj *)(o))->ntop)
2362 static PyObject
*gfn_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
2364 mp
*p
= 0, *beta
= 0;
2366 char *kwlist
[] = { "p", "beta", 0 };
2368 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&O&:new", kwlist
,
2369 convgf
, &p
, convgf
, &beta
))
2371 gg
= PyObject_New(gfn_pyobj
, ty
);
2373 if (gfn_create(p
, beta
, &gg
->ntop
, &gg
->pton
)) {
2376 VALERR("can't invert transformation matrix");
2382 return ((PyObject
*)gg
);
2385 static PyObject
*gfnget_p(PyObject
*me
, void *hunoz
)
2386 { return (gf_pywrap(MP_COPY(GFN_P(me
)))); }
2388 static PyObject
*gfnget_beta(PyObject
*me
, void *hunoz
)
2390 gfn
*n
= GFN_NTOP(me
);
2391 mp
*x
= n
->r
[n
->n
- 1];
2392 return (gf_pywrap(MP_COPY(x
)));
2395 #define XFORMOP(name, NAME) \
2396 static PyObject *gfnmeth_##name(PyObject *me, PyObject *arg) \
2401 if (!PyArg_ParseTuple(arg, "O&:" #name, convgf, &xx)) goto end; \
2402 z = gfn_transform(GFN_##NAME(me), MP_NEW, xx); \
2405 if (!z) return (0); \
2406 return (gf_pywrap(z)); \
2412 static void gfn_pydealloc(PyObject
*me
)
2416 gfn_destroy(GFN_PTON(me
));
2417 gfn_destroy(GFN_NTOP(me
));
2422 static PyGetSetDef gfn_pygetset
[] = {
2423 #define GETSETNAME(op, name) gfn##op##_##name
2424 GET (p
, "X.p -> polynomial basis, as polynomial")
2425 GET (beta
, "X.beta -> normal basis element, in poly form")
2430 static PyMethodDef gfn_pymethods
[] = {
2431 #define METHNAME(name) gfnmeth_##name
2432 METH (pton
, "X.pton(A) -> normal-basis representation of A")
2433 METH (ntop
, "X.ntop(A) -> polynomial-basis representation of A")
2438 static PyTypeObject gfn_pytype_skel
= {
2439 PyObject_HEAD_INIT(0) 0, /* Header */
2440 "GFN", /* @tp_name@ */
2441 sizeof(gfn_pyobj
), /* @tp_basicsize@ */
2442 0, /* @tp_itemsize@ */
2444 gfn_pydealloc
, /* @tp_dealloc@ */
2446 0, /* @tp_getattr@ */
2447 0, /* @tp_setattr@ */
2448 0, /* @tp_compare@ */
2450 0, /* @tp_as_number@ */
2451 0, /* @tp_as_sequence@ */
2452 0, /* @tp_as_mapping@ */
2456 0, /* @tp_getattro@ */
2457 0, /* @tp_setattro@ */
2458 0, /* @tp_as_buffer@ */
2459 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
2460 Py_TPFLAGS_BASETYPE
,
2463 "An object for transforming elements of binary fields between polynomial\n\
2464 and normal basis representations.",
2466 0, /* @tp_traverse@ */
2468 0, /* @tp_richcompare@ */
2469 0, /* @tp_weaklistoffset@ */
2471 0, /* @tp_iternext@ */
2472 gfn_pymethods
, /* @tp_methods@ */
2473 0, /* @tp_members@ */
2474 gfn_pygetset
, /* @tp_getset@ */
2477 0, /* @tp_descr_get@ */
2478 0, /* @tp_descr_set@ */
2479 0, /* @tp_dictoffset@ */
2481 PyType_GenericAlloc
, /* @tp_alloc@ */
2482 gfn_pynew
, /* @tp_new@ */
2487 /*----- Glue --------------------------------------------------------------*/
2489 static PyMethodDef methods
[] = {
2490 #define METHNAME(func) meth_##func
2491 KWMETH(_MP_fromstring
, "\
2492 fromstring(STR, [radix = 0]) -> (X, REST)\n\
2494 Parse STR as a large integer, according to radix. If radix is zero,\n\
2495 read a prefix from STR to decide radix: allow `0' for octal, `0x' for hex\n\
2496 or `R_' for other radix R.")
2497 KWMETH(_GF_fromstring
, "\
2498 fromstring(STR, [radix = 0]) -> (X, REST)\n\
2500 Parse STR as a binary polynomial, according to radix. If radix is zero,\n\
2501 read a prefix from STR to decide radix: allow `0' for octal, `0x' for hex\n\
2502 or `R_' for other radix R.")
2503 METH (_MP_factorial
, "\
2504 factorial(I) -> I!: compute factorial")
2505 METH (_MP_fibonacci
, "\
2506 fibonacci(I) -> F(I): compute Fibonacci number")
2508 loadl(STR) -> X: read little-endian bytes")
2510 loadb(STR) -> X: read big-endian bytes")
2511 METH (_MP_loadl2c
, "\
2512 loadl2c(STR) -> X: read little-endian bytes, two's complement")
2513 METH (_MP_loadb2c
, "\
2514 loadb2c(STR) -> X: read big-endian bytes, two's complement")
2515 METH (_MP_frombuf
, "\
2516 frombuf(STR) -> (X, REST): read buffer format")
2518 loadl(STR) -> X: read little-endian bytes")
2520 loadb(STR) -> X: read big-endian bytes")
2521 METH (_GF_frombuf
, "\
2522 frombuf(STR) -> (X, REST): read buffer format")
2527 void mp_pyinit(void)
2531 INITTYPE(mpmul
, root
);
2532 INITTYPE(mpmont
, root
);
2533 INITTYPE(mpbarrett
, root
);
2534 INITTYPE(mpreduce
, root
);
2535 INITTYPE(mpcrt
, root
);
2536 INITTYPE(gfreduce
, root
);
2537 INITTYPE(gfn
, root
);
2538 addmethods(methods
);
2541 void mp_pyinsert(PyObject
*mod
)
2543 INSERT("MP", mp_pytype
);
2544 INSERT("MPMul", mpmul_pytype
);
2545 INSERT("MPMont", mpmont_pytype
);
2546 INSERT("MPBarrett", mpbarrett_pytype
);
2547 INSERT("MPReduce", mpreduce_pytype
);
2548 INSERT("MPCRT", mpcrt_pytype
);
2549 INSERT("GF", gf_pytype
);
2550 INSERT("GFReduce", gfreduce_pytype
);
2551 INSERT("GFN", gfn_pytype
);
2554 /*----- That's all, folks -------------------------------------------------*/