3 * Multiprecision arithmetic
5 * (c) 2004 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of the Python interface to Catacomb.
12 * Catacomb/Python is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU General Public License as published by
14 * the Free Software Foundation; either version 2 of the License, or
15 * (at your option) any later version.
17 * Catacomb/Python is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU General Public License for more details.
22 * You should have received a copy of the GNU General Public License
23 * along with Catacomb/Python; if not, write to the Free Software Foundation,
24 * Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
27 /*----- Header files ------------------------------------------------------*/
29 #include "catacomb-python.h"
31 /*----- General utilities -------------------------------------------------*/
33 PyTypeObject
*mp_pytype
= 0;
34 PyTypeObject
*gf_pytype
= 0;
37 # define PyLong_SHIFT SHIFT
41 # define PyLong_MASK MASK
44 STATIC_ASSERT(MPW_BITS
>= PyLong_SHIFT
,
45 "Catacomb's limbs are now narrower than than Python's!");
47 mp
*mp_frompylong(PyObject
*obj
)
50 PyLongObject
*l
= (PyLongObject
*)obj
;
61 long j
= PyLong_AsLongAndOverflow(obj
, &ov
);
62 if (!ov
) return mp_fromlong(MP_NEW
, j
);
67 bits
= (unsigned long)sz
* PyLong_SHIFT
;
68 w
= (bits
+ MPW_BITS
- 1)/MPW_BITS
;
69 x
= mp_new(w
, Py_SIZE(l
) < 0 ? MP_NEG
: 0);
71 for (i
= 0; i
< sz
; i
++) {
72 r
|= (mpd
)l
->ob_digit
[i
] << b
;
74 while (b
>= MPW_BITS
) {
89 PyObject
*mp_topylong(mp
*x
)
91 unsigned long bits
= mp_bits(x
);
92 int sz
= (bits
+ PyLong_SHIFT
- 1)/PyLong_SHIFT
;
93 PyLongObject
*l
= _PyLong_New(sz
);
99 while (i
< sz
&& p
< x
->vl
) {
102 while (i
< sz
&& b
>= PyLong_SHIFT
) {
103 l
->ob_digit
[i
++] = r
& PyLong_MASK
;
108 while (i
< sz
&& r
) {
109 l
->ob_digit
[i
++] = r
& PyLong_MASK
;
112 Py_SIZE(l
) = (x
->f
& MP_NEG
) ?
-sz
: sz
;
113 return ((PyObject
*)l
);
116 mp
*mp_frompyobject(PyObject
*o
, int radix
)
124 TEXT_PTRLEN(o
, sc
.buf
, sz
); sc
.lim
= sc
.buf
+ sz
;
125 x
= mp_read(MP_NEW
, radix
, &mptext_stringops
, &sc
);
127 if (sc
.buf
< sc
.lim
) { MP_DROP(x
); return (0); }
130 if ((x
= tomp(o
)) != 0)
135 PyObject
*mp_topystring(mp
*x
, int radix
, const char *xpre
,
136 const char *pre
, const char *post
)
138 int len
= mptext_len(x
, radix
) + 1;
141 size_t xprelen
= xpre ?
strlen(xpre
) : 0;
142 size_t prelen
= pre ?
strlen(pre
) : 0;
143 size_t postlen
= post ?
strlen(post
) : 0;
146 TEXT_PREPAREWRITE(o
, p
, len
+ 1 + xprelen
+ prelen
+ postlen
);
148 if (xpre
) { memcpy(sc
.buf
, xpre
, xprelen
); sc
.buf
+= xprelen
; }
149 if (MP_NEGP(x
)) { *sc
.buf
++ = '-'; x
= mp_neg(x
, x
); }
150 if (pre
) { memcpy(sc
.buf
, pre
, prelen
); sc
.buf
+= prelen
; }
151 sc
.lim
= sc
.buf
+ len
;
152 mp_write(x
, radix
, &mptext_stringops
, &sc
);
153 if (post
) { memcpy(sc
.buf
, post
, postlen
); sc
.buf
+= postlen
; }
155 TEXT_DONEWRITE(o
, sc
.buf
- p
);
159 static int good_radix_p(int r
, int readp
)
161 return ((r
>= -255 && r
<= -2) ||
163 (r
>= 2 && r
<= 62));
166 PyObject
*mp_pywrap(mp
*x
)
168 mp_pyobj
*z
= PyObject_New(mp_pyobj
, mp_pytype
);
170 return ((PyObject
*)z
);
173 PyObject
*gf_pywrap(mp
*x
)
175 mp_pyobj
*z
= PyObject_New(mp_pyobj
, gf_pytype
);
177 return ((PyObject
*)z
);
180 int mp_tolong_checked(mp
*x
, long *l
, int must
)
182 static mp
*longmin
= 0, *longmax
= 0;
186 longmin
= mp_fromlong(MP_NEW
, LONG_MIN
);
187 longmax
= mp_fromlong(MP_NEW
, LONG_MAX
);
189 if (MP_CMP(x
, <, longmin
) || MP_CMP(x
, >, longmax
)) {
190 if (must
) VALERR("mp out of range for int");
199 /*----- Python interface --------------------------------------------------*/
201 static void mp_pydealloc(PyObject
*o
)
207 static PyObject
*mp_pyrepr(PyObject
*o
)
208 { return mp_topystring(MP_X(o
), 10, "MP(", 0, ")"); }
210 static PyObject
*mp_pystr(PyObject
*o
)
211 { return mp_topystring(MP_X(o
), 10, 0, 0, 0); }
213 mp
*tomp(PyObject
*o
)
218 if (!o
|| PyFloat_Check(o
))
220 else if (MP_PYCHECK(o
) || GF_PYCHECK(o
))
221 return (MP_COPY(MP_X(o
)));
222 else if (FE_PYCHECK(o
))
223 return (F_OUT(FE_F(o
), MP_NEW
, FE_X(o
)));
224 else if (PFILT_PYCHECK(o
))
225 return (MP_COPY(PFILT_F(o
)->m
));
226 else if (ECPT_PYCHECK(o
)) {
228 if (EC_ATINF(ECPT_P(o
))) return (0);
233 } else if (GE_PYCHECK(o
)) {
234 if ((x
= G_TOINT(GE_G(o
), MP_NEW
, GE_X(o
))) == 0)
239 else if (PyInt_Check(o
))
240 return (mp_fromlong(MP_NEW
, PyInt_AS_LONG(o
)));
242 else if ((l
= PyNumber_Long(o
)) != 0) {
243 x
= mp_frompylong(l
);
252 mp
*getmp(PyObject
*o
)
256 if ((x
= tomp(o
)) == 0) {
257 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to mp",
258 Py_TYPE(o
)->tp_name
);
263 int convmp(PyObject
*o
, void *p
)
266 if ((x
= getmp(o
)) == 0) return (0);
271 mp
*getgf(PyObject
*o
)
275 if ((x
= tomp(o
)) == 0) {
276 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to gf",
277 Py_TYPE(o
)->tp_name
);
282 int convgf(PyObject
*o
, void *p
)
285 if ((x
= getgf(o
)) == 0) return (0);
290 mp
*implicitmp(PyObject
*o
)
294 if (!o
|| GF_PYCHECK(o
) || FE_PYCHECK(o
)) return (0);
295 else if (MP_PYCHECK(o
)) return (MP_COPY(MP_X(o
)));
296 else if (PFILT_PYCHECK(o
)) return (MP_COPY(PFILT_F(o
)->m
));
298 else if (PyInt_Check(o
)) return (mp_fromlong(MP_NEW
, PyInt_AS_LONG(o
)));
300 else if ((l
= PyNumber_Index(o
)) != 0) {
302 if (PyInt_Check(o
)) return (mp_fromlong(MP_NEW
, PyInt_AS_LONG(o
)));
304 if (PyLong_Check(o
)) return (mp_frompylong(o
));
306 PyErr_Clear(); return (0);
309 mp
*implicitgf(PyObject
*o
)
311 if (GF_PYCHECK(o
)) return (MP_COPY(MP_X(o
)));
315 static int mpbinop(PyObject
*x
, PyObject
*y
, mp
**xx
, mp
**yy
)
317 if ((*xx
= implicitmp(x
)) == 0)
319 if ((*yy
= implicitmp(y
)) == 0) {
326 static int gfbinop(PyObject
*x
, PyObject
*y
, mp
**xx
, mp
**yy
)
328 if ((*xx
= implicitgf(x
)) == 0)
330 if ((*yy
= implicitgf(y
)) == 0) {
337 #define FPBINOP(name, pyop) \
338 static PyObject *mp_py##name(PyObject *x, PyObject *y) { \
341 if (PyFloat_Check(x)) { \
342 l = mp_topylong(MP_X(y)); rc = PyNumber_##pyop(x, l); \
343 Py_DECREF(l); return (rc); \
344 } else if (PyFloat_Check(y)) { \
345 l = mp_topylong(MP_X(x)); rc = PyNumber_##pyop(l, y); \
346 Py_DECREF(l); return (rc); \
348 if (mpbinop(x, y, &xx, &yy)) RETURN_NOTIMPL; \
349 zz = mp_##name(MP_NEW, xx, yy); \
350 MP_DROP(xx); MP_DROP(yy); \
351 return (mp_pywrap(zz)); \
354 FPBINOP(sub
, Subtract
)
355 FPBINOP(mul
, Multiply
)
357 #define gf_and mp_and
359 #define gf_xor mp_xor
360 #define BINOP(pre, name) \
361 static PyObject *pre##_py##name(PyObject *x, PyObject *y) { \
363 if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL; \
364 zz = pre##_##name(MP_NEW, xx, yy); \
365 MP_DROP(xx); MP_DROP(yy); \
366 return (pre##_pywrap(zz)); \
379 static mp
*mp_abs(mp
*d
, mp
*x
)
382 return (mp_neg(d
, x
));
388 #define UNOP(pre, name) \
389 static PyObject *pre##_py##name(PyObject *x) \
390 { return mp_pywrap(pre##_##name(MP_NEW, MP_X(x))); }
396 static PyObject
*mp_pyid(PyObject
*x
) { RETURN_OBJ(x
); }
398 #define gf_lsr mp_lsr
399 #define SHIFTOP(pre, PRE, name, rname) \
400 static PyObject *pre##_py##name(PyObject *x, PyObject *y) { \
404 if (!PRE##_PYCHECK(x)) RETURN_NOTIMPL; \
405 if (GF_PYCHECK(y) || FE_PYCHECK(y)) RETURN_NOTIMPL; \
406 yix = PyNumber_Index(y); if (!yix) { PyErr_Clear(); RETURN_NOTIMPL; } \
407 n = PyInt_AsLong(yix); Py_DECREF(yix); \
408 if (n == -1 && PyErr_Occurred()) { PyErr_Clear(); RETURN_NOTIMPL; } \
409 if (n < 0) z = pre##_pywrap(mp_##rname(MP_NEW, MP_X(x), -n)); \
410 else z = pre##_pywrap(mp_##name(MP_NEW, MP_X(x), n)); \
413 SHIFTOP(mp
, MP
, lsl2c
, lsr2c
)
414 SHIFTOP(mp
, MP
, lsr2c
, lsl2c
)
415 SHIFTOP(gf
, GF
, lsl
, lsr
)
416 SHIFTOP(gf
, GF
, lsr
, lsl
)
419 #define DIVOP(pre, name, qq, rr, gather) \
420 static PyObject *pre##_py##name(PyObject *x, PyObject *y) { \
423 INIT_##qq(q) INIT_##rr(r) \
424 if (pre##binop(x, y, &xx, &yy)) RETURN_NOTIMPL; \
426 ZDIVERR("division by zero"); \
427 pre##_div(ARG_##qq(q), ARG_##rr(r), xx, yy); \
430 MP_DROP(xx); MP_DROP(yy); \
433 #define INIT_YES(p) mp *p = MP_NEW;
435 #define ARG_YES(p) &p
437 DIVOP(mp
, divmod
, YES
, YES
,
438 Py_BuildValue("(NN)", mp_pywrap(q
), mp_pywrap(r
)))
439 DIVOP(mp
, div
, YES
, NO
, mp_pywrap(q
))
440 DIVOP(mp
, mod
, NO
, YES
, mp_pywrap(r
))
441 DIVOP(gf
, divmod
, YES
, YES
,
442 Py_BuildValue("(NN)", gf_pywrap(q
), gf_pywrap(r
)))
443 DIVOP(gf
, div
, YES
, NO
, gf_pywrap(q
))
444 DIVOP(gf
, mod
, NO
, YES
, gf_pywrap(r
))
451 static mp
*mp_modinv_checked(mp
*d
, mp
*x
, mp
*p
)
454 mp_gcd(&g
, 0, &d
, p
, x
);
455 if (!MP_EQ(g
, MP_ONE
)) {
456 MP_DROP(g
); MP_DROP(d
);
457 PyErr_SetString(PyExc_ZeroDivisionError
, "no modular inverse");
460 MP_DROP(g
); return (d
);
463 static PyObject
*mp_pyexp(PyObject
*x
, PyObject
*y
, PyObject
*z
)
465 mp
*xx
= 0, *yy
= 0, *zz
= 0;
469 if ((xx
= implicitmp(x
)) == 0 || (yy
= implicitmp(y
)) == 0 ||
470 (z
&& z
!= Py_None
&& (zz
= implicitmp(z
)) == 0)) {
471 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
474 if (!z
|| z
== Py_None
) {
475 if (MP_NEGP(yy
)) VALERR("negative exponent");
476 r
= mp_exp(MP_NEW
, xx
, yy
);
478 if (!MP_POSP(zz
)) VALERR("modulus must be positive");
480 if ((xx
= mp_modinv_checked(xx
, xx
, zz
)) == 0) goto end
;
485 mpmont_create(&mm
, zz
);
486 r
= mpmont_exp(&mm
, MP_NEW
, xx
, yy
);
490 mpbarrett_create(&mb
, zz
);
491 r
= mpbarrett_exp(&mb
, MP_NEW
, xx
, yy
);
492 mpbarrett_destroy(&mb
);
497 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
501 static mp
*gf_modinv_checked(mp
*d
, mp
*x
, mp
*p
)
504 gf_gcd(&g
, 0, &d
, p
, x
);
505 if (!MP_EQ(g
, MP_ONE
)) {
506 MP_DROP(g
); MP_DROP(d
);
507 PyErr_SetString(PyExc_ZeroDivisionError
, "no modular inverse");
510 MP_DROP(g
); return (d
);
513 #define BASEOP(name, radix, pre) \
514 static PyObject *mp_py##name(PyObject *x) \
515 { return mp_topystring(MP_X(x), radix, 0, pre, 0); }
519 BASEOP(hex
, 16, "0x");
522 static int mp_pynonzerop(PyObject
*x
) { return !MP_ZEROP(MP_X(x
)); }
524 static PyObject
*mp_pyint(PyObject
*x
)
527 if (!mp_tolong_checked(MP_X(x
), &l
, 0)) return (PyInt_FromLong(l
));
528 else return mp_topylong(MP_X(x
));
531 static PyObject
*mp_pylong(PyObject
*x
)
532 { return (mp_topylong(MP_X(x
))); }
534 static PyObject
*mp_pyfloat(PyObject
*x
)
536 PyObject
*l
= mp_topylong(MP_X(x
));
537 double f
= PyLong_AsDouble(l
);
539 return (PyFloat_FromDouble(f
));
543 #define COERCE(pre, PRE) \
544 static int pre##_pycoerce(PyObject **x, PyObject **y) \
548 if (PRE##_PYCHECK(*y)) { \
549 Py_INCREF(*x); Py_INCREF(*y); \
552 if ((z = implicit##pre(*y)) != 0) { \
554 *y = pre##_pywrap(z); \
564 static PyObject
*mp_pyrichcompare(PyObject
*x
, PyObject
*y
, int op
)
568 if (PyFloat_Check(y
)) {
569 l
= mp_topylong(MP_X(x
)); rc
= PyObject_RichCompare(l
, y
, op
);
570 Py_DECREF(l
); return (rc
);
572 if (mpbinop(x
, y
, &xx
, &yy
)) RETURN_NOTIMPL
;
573 rc
= enrich_compare(op
, mp_cmp(xx
, yy
));
574 MP_DROP(xx
); MP_DROP(yy
);
579 static int mp_pycompare(PyObject
*x
, PyObject
*y
)
580 { return mp_cmp(MP_X(x
), MP_X(y
)); }
583 static PyObject
*mp_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
589 static const char *const kwlist
[] = { "x", "radix", 0 };
591 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O|i:new", KWLIST
, &x
, &radix
))
593 if (MP_PYCHECK(x
)) RETURN_OBJ(x
);
594 if (!good_radix_p(radix
, 1)) VALERR("bad radix");
595 if ((z
= mp_frompyobject(x
, radix
)) == 0) {
596 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to mp",
597 Py_TYPE(x
)->tp_name
);
600 zz
= (mp_pyobj
*)ty
->tp_alloc(ty
, 0);
603 return ((PyObject
*)zz
);
606 Py_hash_t
mphash(mp
*x
)
608 PyObject
*l
= mp_topylong(x
);
609 Py_hash_t h
= PyObject_Hash(l
);
610 Py_DECREF(l
); return (h
);
613 static Py_hash_t
mp_pyhash(PyObject
*me
) { return (mphash(MP_X(me
))); }
615 static PyObject
*mpmeth_jacobi(PyObject
*me
, PyObject
*arg
)
620 if (!PyArg_ParseTuple(arg
, "O&:jacobi", convmp
, &y
)) goto end
;
621 z
= PyInt_FromLong(mp_jacobi(y
, MP_X(me
)));
627 #define BITOP(pre, name, c) \
628 static PyObject *pre##meth_##name(PyObject *me, PyObject *arg) \
631 if (!PyArg_ParseTuple(arg, "O&:" #name, convulong, &i)) return (0); \
632 return (pre##_pywrap(mp_##name##c(MP_NEW, MP_X(me), i))); \
634 BITOP(mp
, setbit
, 2c
);
635 BITOP(mp
, clearbit
, 2c
);
637 BITOP(gf
, clearbit
, );
640 static PyObject
*mpmeth_testbit(PyObject
*me
, PyObject
*arg
)
643 if (!PyArg_ParseTuple(arg
, "O&:testbit", convulong
, &i
)) return (0);
644 return (getbool(mp_testbit2c(MP_X(me
), i
)));
647 static PyObject
*gfmeth_testbit(PyObject
*me
, PyObject
*arg
)
650 if (!PyArg_ParseTuple(arg
, "O&:testbit", convulong
, &i
)) return (0);
651 return (getbool(mp_testbit(MP_X(me
), i
)));
654 static PyObject
*mpmeth_odd(PyObject
*me
)
659 t
= mp_odd(MP_NEW
, MP_X(me
), &s
);
660 return (Py_BuildValue("(lN)", (long)s
, mp_pywrap(t
)));
663 static PyObject
*mpmeth_sqr(PyObject
*me
)
664 { return (mp_pywrap(mp_sqr(MP_NEW
, MP_X(me
)))); }
666 static PyObject
*mpmeth_sqrt(PyObject
*me
)
668 if (MP_NEGP(MP_X(me
))) VALERR("negative root");
669 return (mp_pywrap(mp_sqrt(MP_NEW
, MP_X(me
))));
674 static PyObject
*mpmeth_gcd(PyObject
*me
, PyObject
*arg
)
676 mp
*y
= 0, *zz
= MP_NEW
;
679 if (!PyArg_ParseTuple(arg
, "O&:gcd", convmp
, &y
)) goto end
;
680 mp_gcd(&zz
, 0, 0, MP_X(me
), y
);
687 static PyObject
*mpmeth_gcdx(PyObject
*me
, PyObject
*arg
)
690 mp
*yy
= 0, *zz
= MP_NEW
, *uu
= MP_NEW
, *vv
= MP_NEW
;
692 if (!PyArg_ParseTuple(arg
, "O&:gcdx", convmp
, &yy
)) goto end
;
693 mp_gcd(&zz
, &uu
, &vv
, MP_X(me
), yy
);
694 z
= Py_BuildValue("(NNN)",
695 mp_pywrap(zz
), mp_pywrap(uu
), mp_pywrap(vv
));
701 static PyObject
*mpmeth_modinv(PyObject
*me
, PyObject
*arg
)
704 mp
*yy
= 0, *zz
= MP_NEW
;
706 if (!PyArg_ParseTuple(arg
, "O&:modinv", convmp
, &yy
) ||
707 (zz
= mp_modinv_checked(MP_NEW
, yy
, MP_X(me
))) == 0)
715 static PyObject
*mpmeth_tostring(PyObject
*me
, PyObject
*arg
, PyObject
*kw
)
718 static const char *const kwlist
[] = { "radix", 0 };
719 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "|i:tostring", KWLIST
, &radix
))
721 if (!good_radix_p(radix
, 0)) VALERR("bad radix");
722 return (mp_topystring(MP_X(me
), radix
, 0, 0, 0));
727 static PyObject
*mpmeth_modsqrt(PyObject
*me
, PyObject
*arg
)
730 mp
*yy
= 0, *zz
= MP_NEW
;
732 if (!PyArg_ParseTuple(arg
, "O&:modsqrt", convmp
, &yy
)) goto end
;
733 if ((zz
= mp_modsqrt(MP_NEW
, yy
, MP_X(me
))) == 0)
734 VALERR("no modular square root");
741 static PyObject
*mpmeth_leastcongruent(PyObject
*me
, PyObject
*arg
)
746 if (!PyArg_ParseTuple(arg
, "O&O&:leastcongruent", convmp
, &b
, convmp
, &m
))
748 z
= mp_leastcongruent(MP_NEW
, b
, MP_X(me
), m
);
754 #define STOREOP(name, c) \
755 static PyObject *mpmeth_##name(PyObject *me, \
756 PyObject *arg, PyObject *kw) \
759 static const char *const kwlist[] = { "len", 0 }; \
762 if (!PyArg_ParseTupleAndKeywords(arg, kw, "|l:" #name, \
766 len = mp_octets##c(MP_X(me)); \
769 rc = bytestring_pywrap(0, len); \
770 mp_##name(MP_X(me), BIN_PTR(rc), len); \
776 STOREOP(storel2c
, 2c
)
777 STOREOP(storeb2c
, 2c
)
781 static PyObject *ty##meth_frombuf(PyObject *me, PyObject *arg) \
788 if (!PyArg_ParseTuple(arg, "O&:frombuf", convbin, &in)) goto end; \
789 buf_init(&b, (/*unconst*/ void *)in.p, in.sz); \
790 if ((x = buf_getmp(&b)) == 0) VALERR("malformed data"); \
791 rc = Py_BuildValue("(NN)", ty##_pywrap(x), \
792 bytestring_pywrapbuf(&b)); \
800 static PyObject
*mpmeth_tobuf(PyObject
*me
)
808 n
= mp_octets(x
) + 3;
809 rc
= bytestring_pywrap(0, n
);
810 buf_init(&b
, BIN_PTR(rc
), n
);
813 BIN_SETLEN(rc
, BLEN(&b
));
817 static PyObject
*mpmeth_primep(PyObject
*me
, PyObject
*arg
, PyObject
*kw
)
819 grand
*r
= &rand_global
;
820 static const char *const kwlist
[] = { "rng", 0 };
823 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "|O&", KWLIST
, convgrand
, &r
))
825 rc
= getbool(pgen_primep(MP_X(me
), r
));
830 static PyObject
*mpmeth_fromstring(PyObject
*me
,
831 PyObject
*arg
, PyObject
*kw
)
839 static const char *const kwlist
[] = { "x", "radix", 0 };
841 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "s#|i:fromstring", KWLIST
,
844 if (!good_radix_p(r
, 1)) VALERR("bad radix");
845 sc
.buf
= p
; sc
.lim
= p
+ len
;
846 if ((zz
= mp_read(MP_NEW
, r
, &mptext_stringops
, &sc
)) == 0)
847 VALERR("bad integer");
848 z
= Py_BuildValue("(Ns#)", mp_pywrap(zz
),
849 sc
.buf
, (Py_ssize_t
)(sc
.lim
- sc
.buf
));
854 static PyObject
*mpmeth_factorial(PyObject
*me
, PyObject
*arg
)
858 if (!PyArg_ParseTuple(arg
, "O&:factorial", convulong
, &i
)) return (0);
863 static PyObject
*mpmeth_fibonacci(PyObject
*me
, PyObject
*arg
)
867 if (!PyArg_ParseTuple(arg
, "l:fibonacci", &i
)) return (0);
872 #define LOADOP(pre, name) \
873 static PyObject *pre##meth_##name(PyObject *me, PyObject *arg) \
876 if (!PyArg_ParseTuple(arg, "O&:" #name, convbin, &in)) return (0); \
877 return (pre##_pywrap(mp_##name(MP_NEW, in.p, in.sz))); \
887 static PyObject
*mpget_nbits(PyObject
*me
, void *hunoz
)
888 { return (PyInt_FromLong(mp_bits(MP_X(me
)))); }
890 static PyObject
*mpget_noctets(PyObject
*me
, void *hunoz
)
891 { return (PyInt_FromLong(mp_octets(MP_X(me
)))); }
893 static PyObject
*mpget_noctets2c(PyObject
*me
, void *hunoz
)
894 { return (PyInt_FromLong(mp_octets2c(MP_X(me
)))); }
896 static const PyGetSetDef mp_pygetset
[] = {
897 #define GETSETNAME(op, func) mp##op##_##func
898 GET (nbits
, "X.nbits -> bit length of X")
899 GET (noctets
, "X.noctets -> octet length of X")
900 GET (noctets2c
, "X.noctets2c -> two's complement octet length of X")
905 static const PyMethodDef mp_pymethods
[] = {
906 #define METHNAME(func) mpmeth_##func
907 METH (jacobi
, "X.jacobi(Y) -> Jacobi symbol (Y|X) (NB inversion!)")
908 METH (setbit
, "X.setbit(N) -> X with bit N set")
909 METH (clearbit
, "X.clearbit(N) -> X with bit N clear")
910 METH (testbit
, "X.testbit(N) -> true/false if bit N set/clear in X")
911 NAMETH(odd
, "X.odd() -> S, T where X = 2^S T with T odd")
912 NAMETH(sqr
, "X.sqr() -> X^2")
913 NAMETH(sqrt
, "X.sqrt() -> largest integer <= sqrt(X)")
914 METH (gcd
, "X.gcd(Y) -> gcd(X, Y)")
915 METH (gcdx
, "X.gcdx(Y) -> (gcd(X, Y), U, V) "
916 "with X U + Y V = gcd(X, Y)")
917 METH (modinv
, "X.modinv(Y) -> multiplicative inverse of Y mod X")
918 METH (modsqrt
, "X.modsqrt(Y) -> square root of Y mod X, if X prime")
919 METH (leastcongruent
, "X.leastcongruent(B, M) -> "
920 "smallest Z >= B with Z == X (mod M)")
921 KWMETH(primep
, "X.primep([rng = rand]) -> X is prime?")
922 KWMETH(tostring
, "X.tostring([radix = 10]) -> STR")
923 KWMETH(storel
, "X.storel([len = -1]) -> little-endian bytes")
924 KWMETH(storeb
, "X.storeb([len = -1]) -> big-endian bytes")
925 KWMETH(storel2c
, "X.storel2c([len = -1]) -> "
926 "little-endian bytes, two's complement")
927 KWMETH(storeb2c
, "X.storeb2c([len = -1]) -> "
928 "big-endian bytes, two's complement")
929 NAMETH(tobuf
, "X.tobuf() -> buffer format")
930 KWSMTH(fromstring
, "fromstring(STR, [radix = 0]) -> (X, REST)\n"
931 " Parse STR as a large integer, according to RADIX. If RADIX is\n"
932 " zero, read a prefix from STR to decide radix: allow `0b' for binary,\n"
933 " `0' or `0o' for octal, `0x' for hex, or `R_' for other radix R.")
934 SMTH (factorial
, "factorial(I) -> I!: compute factorial")
935 SMTH (fibonacci
, "fibonacci(I) -> F(I): compute Fibonacci number")
936 SMTH (loadl
, "loadl(STR) -> X: read little-endian bytes")
937 SMTH (loadb
, "loadb(STR) -> X: read big-endian bytes")
938 SMTH (loadl2c
, "loadl2c(STR) -> X: "
939 "read little-endian bytes, two's complement")
940 SMTH (loadb2c
, "loadb2c(STR) -> X: "
941 "read big-endian bytes, two's complement")
942 SMTH (frombuf
, "frombuf(STR) -> (X, REST): read buffer format")
947 static const PyNumberMethods mp_pynumber
= {
948 mp_pyadd
, /* @nb_add@ */
949 mp_pysub
, /* @nb_subtract@ */
950 mp_pymul
, /* @nb_multiply@ */
954 mp_pymod
, /* @nb_remainder@ */
955 mp_pydivmod
, /* @nb_divmod@ */
956 mp_pyexp
, /* @nb_power@ */
957 mp_pyneg
, /* @nb_negative@ */
958 mp_pyid
, /* @nb_positive@ */
959 mp_pyabs
, /* @nb_absolute@ */
960 mp_pynonzerop
, /* @nb_nonzero@ */
961 mp_pynot2c
, /* @nb_invert@ */
962 mp_pylsl2c
, /* @nb_lshift@ */
963 mp_pylsr2c
, /* @nb_rshift@ */
964 mp_pyand2c
, /* @nb_and@ */
965 mp_pyxor2c
, /* @nb_xor@ */
966 mp_pyor2c
, /* @nb_or@ */
968 mp_pycoerce
, /* @nb_coerce@ */
970 mp_pyint
, /* @nb_int@ */
971 PY23(mp_pylong
, 0), /* @nb_long@ */
972 mp_pyfloat
, /* @nb_float@ */
974 mp_pyoct
, /* @nb_oct@ */
975 mp_pyhex
, /* @nb_hex@ */
978 0, /* @nb_inplace_add@ */
979 0, /* @nb_inplace_subtract@ */
980 0, /* @nb_inplace_multiply@ */
982 0, /* @nb_inplace_divide@ */
984 0, /* @nb_inplace_remainder@ */
985 0, /* @nb_inplace_power@ */
986 0, /* @nb_inplace_lshift@ */
987 0, /* @nb_inplace_rshift@ */
988 0, /* @nb_inplace_and@ */
989 0, /* @nb_inplace_xor@ */
990 0, /* @nb_inplace_or@ */
992 mp_pydiv
, /* @nb_floor_divide@ */
993 0, /* @nb_true_divide@ */
994 0, /* @nb_inplace_floor_divide@ */
995 0, /* @nb_inplace_true_divide@ */
997 mp_pyint
, /* @nb_index@ */
1000 static const PyTypeObject mp_pytype_skel
= {
1001 PyVarObject_HEAD_INIT(0, 0) /* Header */
1002 "MP", /* @tp_name@ */
1003 sizeof(mp_pyobj
), /* @tp_basicsize@ */
1004 0, /* @tp_itemsize@ */
1006 mp_pydealloc
, /* @tp_dealloc@ */
1008 0, /* @tp_getattr@ */
1009 0, /* @tp_setattr@ */
1010 PY23(mp_pycompare
, 0), /* @tp_compare@/@tp_as_async@ */
1011 mp_pyrepr
, /* @tp_repr@ */
1012 PYNUMBER(mp
), /* @tp_as_number@ */
1013 0, /* @tp_as_sequence@ */
1014 0, /* @tp_as_mapping@ */
1015 mp_pyhash
, /* @tp_hash@ */
1017 mp_pystr
, /* @tp_str@ */
1018 0, /* @tp_getattro@ */
1019 0, /* @tp_setattro@ */
1020 0, /* @tp_as_buffer@ */
1021 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1022 Py_TPFLAGS_CHECKTYPES
|
1023 Py_TPFLAGS_BASETYPE
,
1026 "Multiprecision integers, similar to `long' but more efficient and\n"
1027 "versatile. Support all the standard arithmetic operations, with\n"
1028 "implicit conversions from `PrimeFilter', and other objects which\n"
1029 "convert to `" PY23("long", "int") "'.\n"
1031 "Constructor MP(X, [radix = R]) attempts to convert X to an `MP'. If\n"
1032 "X is a string, it's read in radix-R form, or we look for a prefix\n"
1033 "if R = 0. Other acceptable things are field elements, elliptic curve\n"
1035 "points, group elements, Python `int' and `long' objects, and anything\n"
1036 "with an integer conversion.\n",
1037 "points, group elements, Python `int' objects, and anything with an\n"
1038 "integer conversion.\n")
1042 " * Use `//' for integer division: `/' gives exact rational division.",
1044 0, /* @tp_traverse@ */
1046 mp_pyrichcompare
, /* @tp_richcompare@ */
1047 0, /* @tp_weaklistoffset@ */
1049 0, /* @tp_iternext@ */
1050 PYMETHODS(mp
), /* @tp_methods@ */
1051 0, /* @tp_members@ */
1052 PYGETSET(mp
), /* @tp_getset@ */
1055 0, /* @tp_descr_get@ */
1056 0, /* @tp_descr_set@ */
1057 0, /* @tp_dictoffset@ */
1059 PyType_GenericAlloc
, /* @tp_alloc@ */
1060 mp_pynew
, /* @tp_new@ */
1065 /*----- Products of small integers ----------------------------------------*/
1067 static PyTypeObject
*mpmul_pytype
;
1069 typedef struct mpmul_pyobj
{
1075 #define MPMUL_LIVEP(o) (((mpmul_pyobj *)(o))->livep)
1076 #define MPMUL_PY(o) (&((mpmul_pyobj *)(o))->mm)
1078 static void mpmul_pydealloc(PyObject
*me
)
1080 if (MPMUL_LIVEP(me
))
1081 mp_drop(mpmul_done(MPMUL_PY(me
)));
1085 static PyObject
*mmmeth_factor(PyObject
*me
, PyObject
*arg
)
1090 if (!MPMUL_LIVEP(me
)) VALERR("MPMul object invalid");
1091 if (PyTuple_GET_SIZE(arg
) != 1)
1092 i
= PyObject_GetIter(arg
);
1094 if ((q
= PyTuple_GET_ITEM(arg
, 0)) == 0) goto end
;
1095 if ((i
= PyObject_GetIter(q
)) == 0) {
1096 PyErr_Clear(); /* that's ok */
1097 i
= PyObject_GetIter(arg
);
1101 while ((q
= PyIter_Next(i
)) != 0) {
1102 x
= getmp(q
); Py_DECREF(q
); if (!x
) {
1106 mpmul_add(MPMUL_PY(me
), x
);
1115 static PyObject
*mmmeth_done(PyObject
*me
)
1119 if (!MPMUL_LIVEP(me
)) VALERR("MPMul object invalid");
1120 x
= mpmul_done(MPMUL_PY(me
));
1121 MPMUL_LIVEP(me
) = 0;
1122 return (mp_pywrap(x
));
1127 static PyObject
*mpmul_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1131 if (kw
) TYERR("keyword arguments not allowed here");
1132 mm
= (mpmul_pyobj
*)ty
->tp_alloc(ty
, 0);
1133 mpmul_init(&mm
->mm
);
1135 if (mmmeth_factor((PyObject
*)mm
, arg
) == 0) {
1139 return ((PyObject
*)mm
);
1144 static PyObject
*mmget_livep(PyObject
*me
, void *hunoz
)
1145 { return (getbool(MPMUL_LIVEP(me
))); }
1147 static const PyGetSetDef mpmul_pygetset
[] = {
1148 #define GETSETNAME(op, name) mm##op##_##name
1149 GET (livep
, "MM.livep -> flag: object still valid?")
1154 static const PyMethodDef mpmul_pymethods
[] = {
1155 #define METHNAME(name) mmmeth_##name
1156 METH (factor
, "MM.factor(ITERABLE) or MM.factor(I, ...)")
1157 NAMETH(done
, "MM.done() -> PRODUCT")
1162 static const PyTypeObject mpmul_pytype_skel
= {
1163 PyVarObject_HEAD_INIT(0, 0) /* Header */
1164 "MPMul", /* @tp_name@ */
1165 sizeof(mpmul_pyobj
), /* @tp_basicsize@ */
1166 0, /* @tp_itemsize@ */
1168 mpmul_pydealloc
, /* @tp_dealloc@ */
1170 0, /* @tp_getattr@ */
1171 0, /* @tp_setattr@ */
1172 0, /* @tp_compare@ */
1174 0, /* @tp_as_number@ */
1175 0, /* @tp_as_sequence@ */
1176 0, /* @tp_as_mapping@ */
1180 0, /* @tp_getattro@ */
1181 0, /* @tp_setattro@ */
1182 0, /* @tp_as_buffer@ */
1183 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1184 Py_TPFLAGS_BASETYPE
,
1187 "MPMul(N_0, N_1, ....): an object for multiplying many small integers.",
1189 0, /* @tp_traverse@ */
1191 0, /* @tp_richcompare@ */
1192 0, /* @tp_weaklistoffset@ */
1194 0, /* @tp_iternext@ */
1195 PYMETHODS(mpmul
), /* @tp_methods@ */
1196 0, /* @tp_members@ */
1197 PYGETSET(mpmul
), /* @tp_getset@ */
1200 0, /* @tp_descr_get@ */
1201 0, /* @tp_descr_set@ */
1202 0, /* @tp_dictoffset@ */
1204 PyType_GenericAlloc
, /* @tp_alloc@ */
1205 mpmul_pynew
, /* @tp_new@ */
1210 /*----- Montgomery reduction ----------------------------------------------*/
1212 static PyTypeObject
*mpmont_pytype
;
1214 typedef struct mpmont_pyobj
{
1219 #define MPMONT_PY(o) (&((mpmont_pyobj *)(o))->mm)
1221 static PyObject
*mmmeth_int(PyObject
*me
, PyObject
*arg
)
1225 mpmont
*mm
= MPMONT_PY(me
);
1227 if (!PyArg_ParseTuple(arg
, "O&:in", convmp
, &yy
))
1229 mp_div(0, &yy
, yy
, mm
->m
);
1230 z
= mp_pywrap(mpmont_mul(mm
, MP_NEW
, yy
, mm
->r2
));
1232 if (yy
) MP_DROP(yy
);
1236 static PyObject
*mmmeth_mul(PyObject
*me
, PyObject
*arg
)
1239 mp
*yy
= 0, *zz
= 0;
1241 if (!PyArg_ParseTuple(arg
, "O&O&:mul", convmp
, &yy
, convmp
, &zz
))
1243 rc
= mp_pywrap(mpmont_mul(MPMONT_PY(me
), MP_NEW
, yy
, zz
));
1245 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1249 static PyObject
*mmmeth_exp(PyObject
*me
, PyObject
*arg
)
1252 mp
*yy
= 0, *zz
= 0;
1254 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convmp
, &yy
, convmp
, &zz
))
1257 if ((yy
= mp_modinv_checked(yy
, yy
, MPMONT_PY(me
)->m
)) == 0) goto end
;
1258 zz
= mp_neg(zz
, zz
);
1260 rc
= mp_pywrap(mpmont_exp(MPMONT_PY(me
), MP_NEW
, yy
, zz
));
1262 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1266 static PyObject
*mmmeth_expr(PyObject
*me
, PyObject
*arg
)
1269 mp
*yy
= 0, *zz
= 0;
1271 if (!PyArg_ParseTuple(arg
, "O&O&:expr", convmp
, &yy
, convmp
, &zz
))
1274 yy
= mpmont_reduce(MPMONT_PY(me
), yy
, yy
);
1275 if ((yy
= mp_modinv_checked(yy
, yy
, MPMONT_PY(me
)->m
)) == 0) goto end
;
1276 yy
= mpmont_mul(MPMONT_PY(me
), yy
, yy
, MPMONT_PY(me
)->r2
);
1277 zz
= mp_neg(zz
, zz
);
1279 rc
= mp_pywrap(mpmont_expr(MPMONT_PY(me
), MP_NEW
, yy
, zz
));
1281 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1285 static PyObject
*mm_mexpr_id(PyObject
*me
)
1286 { return mp_pywrap(MP_COPY(MPMONT_PY(me
)->r
)); }
1288 static int mm_mexpr_fill(void *p
, PyObject
*me
, PyObject
*x
, PyObject
*y
)
1290 mp
*xx
= 0, *yy
= 0;
1291 mp_expfactor
*f
= p
;
1292 mpmont
*mm
= MPMONT_PY(me
);
1294 if ((xx
= getmp(x
)) == 0 || (yy
= getmp(y
)) == 0)
1297 xx
= mpmont_reduce(mm
, xx
, xx
);
1298 if ((xx
= mp_modinv_checked(xx
, xx
, yy
)) == 0)
1300 xx
= mpmont_mul(mm
, xx
, xx
, mm
->r2
);
1301 yy
= mp_neg(yy
, yy
);
1308 mp_drop(xx
); mp_drop(yy
);
1312 static PyObject
*mm_mexpr(PyObject
*me
, void *v
, int n
)
1313 { return mp_pywrap(mpmont_mexpr(MPMONT_PY(me
), MP_NEW
, v
, n
)); }
1315 static void mp_mexp_drop(void *p
)
1317 mp_expfactor
*f
= p
;
1322 static PyObject
*mmmeth_mexpr(PyObject
*me
, PyObject
*arg
)
1324 return mexp_common(me
, arg
, sizeof(mp_expfactor
),
1325 mm_mexpr_id
, mm_mexpr_fill
, mm_mexpr
, mp_mexp_drop
);
1328 static PyObject
*mp_mexp_id(PyObject
*me
)
1329 { return mp_pywrap(MP_ONE
); }
1331 static int mp_mexp_fill(void *p
, PyObject
*me
, PyObject
*x
, PyObject
*y
)
1333 mp
*xx
= 0, *yy
= 0;
1334 mp_expfactor
*f
= p
;
1336 if ((xx
= getmp(x
)) == 0 || (yy
= getmp(y
)) == 0)
1339 if ((xx
= mp_modinv_checked(xx
, xx
, yy
)) == 0)
1341 yy
= mp_neg(yy
, yy
);
1348 mp_drop(xx
); mp_drop(yy
);
1352 static PyObject
*mm_mexp(PyObject
*me
, void *v
, int n
)
1353 { return mp_pywrap(mpmont_mexp(MPMONT_PY(me
), MP_NEW
, v
, n
)); }
1355 static PyObject
*mmmeth_mexp(PyObject
*me
, PyObject
*arg
)
1357 return mexp_common(me
, arg
, sizeof(mp_expfactor
),
1358 mp_mexp_id
, mp_mexp_fill
, mm_mexp
, mp_mexp_drop
);
1361 #define mmmeth_ext mmmeth_reduce
1362 static PyObject
*mmmeth_reduce(PyObject
*me
, PyObject
*arg
)
1367 if (!PyArg_ParseTuple(arg
, "O&", convmp
, &yy
)) goto end
;
1368 z
= mp_pywrap(mpmont_reduce(MPMONT_PY(me
), MP_NEW
, yy
));
1373 static void mpmont_pydealloc(PyObject
*me
)
1375 mpmont_destroy(MPMONT_PY(me
));
1379 static PyObject
*mpmont_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1381 mpmont_pyobj
*mm
= 0;
1382 static const char *const kwlist
[] = { "m", 0 };
1385 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", KWLIST
, convmp
, &xx
))
1387 if (!MP_POSP(xx
) || !MP_ODDP(xx
)) VALERR("m must be positive and odd");
1388 mm
= (mpmont_pyobj
*)ty
->tp_alloc(ty
, 0);
1389 mpmont_create(&mm
->mm
, xx
);
1391 if (xx
) MP_DROP(xx
);
1392 return ((PyObject
*)mm
);
1395 static PyObject
*mmget_m(PyObject
*me
, void *hunoz
)
1396 { return (mp_pywrap(MP_COPY(MPMONT_PY(me
)->m
))); }
1398 static PyObject
*mmget_r(PyObject
*me
, void *hunoz
)
1399 { return (mp_pywrap(MP_COPY(MPMONT_PY(me
)->r
))); }
1401 static PyObject
*mmget_r2(PyObject
*me
, void *hunoz
)
1402 { return (mp_pywrap(MP_COPY(MPMONT_PY(me
)->r2
))); }
1404 static const PyGetSetDef mpmont_pygetset
[] = {
1405 #define GETSETNAME(op, name) mm##op##_##name
1406 GET (m
, "M.m -> modulus for reduction")
1407 GET (r
, "M.r -> multiplicative identity")
1408 GET (r2
, "M.r2 -> M.r^2, Montgomerization factor")
1413 static const PyMethodDef mpmont_pymethods
[] = {
1414 #define METHNAME(name) mmmeth_##name
1415 METH (int, "M.int(X) -> XR")
1416 METH (mul
, "M.mul(XR, YR) -> ZR where Z = X Y")
1417 METH (expr
, "M.expr(XR, N) -> ZR where Z = X^N mod M.m")
1418 METH (mexpr
, "M.mexpr([(XR0, N0), (XR1, N1), ...]) = ZR "
1419 "where Z = X0^N0 X1^N1 ... mod M.m\n"
1420 "\t(the list may be flattened if this more convenient.)")
1421 METH (reduce
, "M.reduce(XR) -> X")
1422 METH (ext
, "M.ext(XR) -> X")
1423 METH (exp
, "M.exp(X, N) -> X^N mod M.m")
1424 METH (mexp
, "M.mexp([(X0, N0), (X1, N1), ...]) = "
1425 "X0^N0 X1^N1 ... mod M.m\n"
1426 "\t(the list may be flattened if this more convenient.)")
1431 static const PyTypeObject mpmont_pytype_skel
= {
1432 PyVarObject_HEAD_INIT(0, 0) /* Header */
1433 "MPMont", /* @tp_name@ */
1434 sizeof(mpmont_pyobj
), /* @tp_basicsize@ */
1435 0, /* @tp_itemsize@ */
1437 mpmont_pydealloc
, /* @tp_dealloc@ */
1439 0, /* @tp_getattr@ */
1440 0, /* @tp_setattr@ */
1441 0, /* @tp_compare@ */
1443 0, /* @tp_as_number@ */
1444 0, /* @tp_as_sequence@ */
1445 0, /* @tp_as_mapping@ */
1449 0, /* @tp_getattro@ */
1450 0, /* @tp_setattro@ */
1451 0, /* @tp_as_buffer@ */
1452 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1453 Py_TPFLAGS_BASETYPE
,
1456 "MPMont(N): a Montgomery reduction context.",
1458 0, /* @tp_traverse@ */
1460 0, /* @tp_richcompare@ */
1461 0, /* @tp_weaklistoffset@ */
1463 0, /* @tp_iternext@ */
1464 PYMETHODS(mpmont
), /* @tp_methods@ */
1465 0, /* @tp_members@ */
1466 PYGETSET(mpmont
), /* @tp_getset@ */
1469 0, /* @tp_descr_get@ */
1470 0, /* @tp_descr_set@ */
1471 0, /* @tp_dictoffset@ */
1473 PyType_GenericAlloc
, /* @tp_alloc@ */
1474 mpmont_pynew
, /* @tp_new@ */
1479 /*----- Barrett reduction -------------------------------------------------*/
1481 static PyTypeObject
*mpbarrett_pytype
;
1483 typedef struct mpbarrett_pyobj
{
1488 #define MPBARRETT_PY(o) (&((mpbarrett_pyobj *)(o))->mb)
1490 static PyObject
*mbmeth_exp(PyObject
*me
, PyObject
*arg
)
1493 mp
*yy
= 0, *zz
= 0;
1495 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convmp
, &yy
, convmp
, &zz
))
1498 if ((yy
= mp_modinv_checked(yy
, yy
, MPBARRETT_PY(me
)->m
)) == 0) goto end
;
1499 zz
= mp_neg(zz
, zz
);
1501 rc
= mp_pywrap(mpbarrett_exp(MPBARRETT_PY(me
), MP_NEW
, yy
, zz
));
1503 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1507 static PyObject
*mb_mexp(PyObject
*me
, void *v
, int n
)
1508 { return mp_pywrap(mpbarrett_mexp(MPBARRETT_PY(me
), MP_NEW
, v
, n
)); }
1510 static PyObject
*mbmeth_mexp(PyObject
*me
, PyObject
*arg
)
1512 return mexp_common(me
, arg
, sizeof(mp_expfactor
),
1513 mp_mexp_id
, mp_mexp_fill
, mb_mexp
, mp_mexp_drop
);
1516 static PyObject
*mbmeth_reduce(PyObject
*me
, PyObject
*arg
)
1521 if (!PyArg_ParseTuple(arg
, "O&:reduce", convmp
, &yy
))
1523 z
= mp_pywrap(mpbarrett_reduce(MPBARRETT_PY(me
), MP_NEW
, yy
));
1528 static void mpbarrett_pydealloc(PyObject
*me
)
1530 mpbarrett_destroy(MPBARRETT_PY(me
));
1534 static PyObject
*mpbarrett_pynew(PyTypeObject
*ty
,
1535 PyObject
*arg
, PyObject
*kw
)
1537 mpbarrett_pyobj
*mb
= 0;
1538 static const char *const kwlist
[] = { "m", 0 };
1541 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", KWLIST
, convmp
, &xx
))
1543 if (!MP_POSP(xx
)) VALERR("m must be positive");
1544 mb
= (mpbarrett_pyobj
*)ty
->tp_alloc(ty
, 0);
1545 mpbarrett_create(&mb
->mb
, xx
);
1547 if (xx
) MP_DROP(xx
);
1548 return ((PyObject
*)mb
);
1551 static PyObject
*mbget_m(PyObject
*me
, void *hunoz
)
1552 { return (mp_pywrap(MP_COPY(MPBARRETT_PY(me
)->m
))); }
1554 static const PyGetSetDef mpbarrett_pygetset
[] = {
1555 #define GETSETNAME(op, name) mb##op##_##name
1556 GET (m
, "B.m -> modulus for reduction")
1561 static const PyMethodDef mpbarrett_pymethods
[] = {
1562 #define METHNAME(name) mbmeth_##name
1563 METH (reduce
, "B.reduce(X) -> X mod B.m")
1564 METH (exp
, "B.exp(X, N) -> X^N mod B.m")
1565 METH (mexp
, "B.mexp([(X0, N0), (X1, N1), ...]) = "
1566 "X0^N0 X1^N1 ... mod B.m\n"
1567 "\t(the list may be flattened if this more convenient.)")
1572 static const PyTypeObject mpbarrett_pytype_skel
= {
1573 PyVarObject_HEAD_INIT(0, 0) /* Header */
1574 "MPBarrett", /* @tp_name@ */
1575 sizeof(mpbarrett_pyobj
), /* @tp_basicsize@ */
1576 0, /* @tp_itemsize@ */
1578 mpbarrett_pydealloc
, /* @tp_dealloc@ */
1580 0, /* @tp_getattr@ */
1581 0, /* @tp_setattr@ */
1582 0, /* @tp_compare@ */
1584 0, /* @tp_as_number@ */
1585 0, /* @tp_as_sequence@ */
1586 0, /* @tp_as_mapping@ */
1590 0, /* @tp_getattro@ */
1591 0, /* @tp_setattro@ */
1592 0, /* @tp_as_buffer@ */
1593 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1594 Py_TPFLAGS_BASETYPE
,
1597 "MPBarrett(N): a Barrett reduction context.",
1599 0, /* @tp_traverse@ */
1601 0, /* @tp_richcompare@ */
1602 0, /* @tp_weaklistoffset@ */
1604 0, /* @tp_iternext@ */
1605 PYMETHODS(mpbarrett
), /* @tp_methods@ */
1606 0, /* @tp_members@ */
1607 PYGETSET(mpbarrett
), /* @tp_getset@ */
1610 0, /* @tp_descr_get@ */
1611 0, /* @tp_descr_set@ */
1612 0, /* @tp_dictoffset@ */
1614 PyType_GenericAlloc
, /* @tp_alloc@ */
1615 mpbarrett_pynew
, /* @tp_new@ */
1620 /*----- Nice prime reduction ----------------------------------------------*/
1622 static PyTypeObject
*mpreduce_pytype
;
1624 typedef struct mpreduce_pyobj
{
1629 #define MPREDUCE_PY(o) (&((mpreduce_pyobj *)(o))->mr)
1631 static PyObject
*mrmeth_exp(PyObject
*me
, PyObject
*arg
)
1634 mp
*yy
= 0, *zz
= 0;
1636 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convmp
, &yy
, convmp
, &zz
))
1639 if ((yy
= mp_modinv_checked(yy
, yy
, MPREDUCE_PY(me
)->p
)) == 0) goto end
;
1640 zz
= mp_neg(zz
, zz
);
1642 rc
= mp_pywrap(mpreduce_exp(MPREDUCE_PY(me
), MP_NEW
, yy
, zz
));
1644 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
1648 static PyObject
*mrmeth_reduce(PyObject
*me
, PyObject
*arg
)
1653 if (!PyArg_ParseTuple(arg
, "O&:reduce", convmp
, &yy
)) goto end
;
1654 z
= mp_pywrap(mpreduce_do(MPREDUCE_PY(me
), MP_NEW
, yy
));
1659 static void mpreduce_pydealloc(PyObject
*me
)
1661 mpreduce_destroy(MPREDUCE_PY(me
));
1665 static PyObject
*mpreduce_pynew(PyTypeObject
*ty
,
1666 PyObject
*arg
, PyObject
*kw
)
1668 mpreduce_pyobj
*mr
= 0;
1670 static const char *const kwlist
[] = { "m", 0 };
1673 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", KWLIST
, convmp
, &xx
))
1675 if (!MP_POSP(xx
)) VALERR("m must be positive");
1676 if (mpreduce_create(&r
, xx
)) VALERR("bad modulus (must be 2^k - ...)");
1677 mr
= (mpreduce_pyobj
*)ty
->tp_alloc(ty
, 0);
1680 if (xx
) MP_DROP(xx
);
1681 return ((PyObject
*)mr
);
1684 static PyObject
*mrget_m(PyObject
*me
, void *hunoz
)
1685 { return (mp_pywrap(MP_COPY(MPREDUCE_PY(me
)->p
))); }
1687 static const PyGetSetDef mpreduce_pygetset
[] = {
1688 #define GETSETNAME(op, name) mr##op##_##name
1689 GET (m
, "R.m -> modulus for reduction")
1694 static const const PyMethodDef mpreduce_pymethods
[] = {
1695 #define METHNAME(name) mrmeth_##name
1696 METH (reduce
, "R.reduce(X) -> X mod B.m")
1697 METH (exp
, "R.exp(X, N) -> X^N mod B.m")
1702 static const PyTypeObject mpreduce_pytype_skel
= {
1703 PyVarObject_HEAD_INIT(0, 0) /* Header */
1704 "MPReduce", /* @tp_name@ */
1705 sizeof(mpreduce_pyobj
), /* @tp_basicsize@ */
1706 0, /* @tp_itemsize@ */
1708 mpreduce_pydealloc
, /* @tp_dealloc@ */
1710 0, /* @tp_getattr@ */
1711 0, /* @tp_setattr@ */
1712 0, /* @tp_compare@ */
1714 0, /* @tp_as_number@ */
1715 0, /* @tp_as_sequence@ */
1716 0, /* @tp_as_mapping@ */
1720 0, /* @tp_getattro@ */
1721 0, /* @tp_setattro@ */
1722 0, /* @tp_as_buffer@ */
1723 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1724 Py_TPFLAGS_BASETYPE
,
1727 "MPReduce(N): a reduction context for reduction modulo Solinas primes.",
1729 0, /* @tp_traverse@ */
1731 0, /* @tp_richcompare@ */
1732 0, /* @tp_weaklistoffset@ */
1734 0, /* @tp_iternext@ */
1735 PYMETHODS(mpreduce
), /* @tp_methods@ */
1736 0, /* @tp_members@ */
1737 PYGETSET(mpreduce
), /* @tp_getset@ */
1740 0, /* @tp_descr_get@ */
1741 0, /* @tp_descr_set@ */
1742 0, /* @tp_dictoffset@ */
1744 PyType_GenericAlloc
, /* @tp_alloc@ */
1745 mpreduce_pynew
, /* @tp_new@ */
1750 /*----- Chinese Remainder Theorem solution --------------------------------*/
1752 static PyTypeObject
*mpcrt_pytype
;
1754 typedef struct mpcrt_pyobj
{
1759 #define MPCRT_PY(o) (&((mpcrt_pyobj *)(o))->c)
1761 static PyObject
*mcmeth_solve(PyObject
*me
, PyObject
*arg
)
1763 mpcrt
*c
= MPCRT_PY(me
);
1764 PyObject
*q
= 0, *x
, *z
= 0;
1767 Py_ssize_t i
= 0, n
= c
->k
;
1770 if (PyTuple_GET_SIZE(arg
) == n
)
1772 else if (!PyArg_ParseTuple(arg
, "O:solve", &q
))
1775 if (!PySequence_Check(q
)) TYERR("want a sequence of residues");
1776 i
= PySequence_Size(q
); if (i
< 0) goto end
;
1777 if (i
!= n
) VALERR("residue count mismatch");
1778 v
= xmalloc(n
* sizeof(*v
));
1779 for (i
= 0; i
< n
; i
++) {
1780 if ((x
= PySequence_GetItem(q
, i
)) == 0) goto end
;
1781 xx
= getmp(x
); Py_DECREF(x
); if (!xx
) goto end
;
1784 z
= mp_pywrap(mpcrt_solve(c
, MP_NEW
, v
));
1788 for (i
= 0; i
< n
; i
++)
1797 static void mpcrt_pydealloc(PyObject
*me
)
1799 mpcrt
*c
= MPCRT_PY(me
);
1804 static PyObject
*mpcrt_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1807 Py_ssize_t n
, i
= 0, j
;
1808 static const char *const kwlist
[] = { "mv", 0 };
1809 PyObject
*q
= 0, *x
;
1810 mp
*xx
= MP_NEW
, *y
= MP_NEW
, *g
= MP_NEW
;
1814 if (PyTuple_GET_SIZE(arg
) > 1)
1816 else if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O:new", KWLIST
, &q
))
1819 if (!PySequence_Check(q
)) TYERR("want a sequence of moduli");
1820 n
= PySequence_Size(q
); if (n
< 0) goto end
;
1821 if (!n
) VALERR("want at least one modulus");
1822 v
= xmalloc(n
* sizeof(*v
));
1823 for (i
= 0; i
< n
; i
++) {
1824 if ((x
= PySequence_GetItem(q
, i
)) == 0) goto end
;
1825 xx
= getmp(x
); Py_DECREF(x
); if (!xx
) goto end
;
1826 if (MP_CMP(xx
, <=, MP_ZERO
)) VALERR("moduli must be positive");
1827 v
[i
].m
= xx
; v
[i
].n
= 0; v
[i
].ni
= 0; v
[i
].nni
= 0; xx
= MP_NEW
;
1830 for (j
= 0; j
< i
; j
++) mpmul_add(&mm
, v
[j
].m
);
1831 xx
= mpmul_done(&mm
);
1832 for (j
= 0; j
< i
; j
++) {
1833 mp_div(&y
, 0, xx
, v
[j
].m
);
1834 mp_gcd(&g
, 0, 0, y
, v
[j
].m
);
1835 if (!MP_EQ(g
, MP_ONE
)) VALERR("moduli must be pairwise coprime");
1838 c
= (mpcrt_pyobj
*)ty
->tp_alloc(ty
, 0);
1839 mpcrt_create(&c
->c
, v
, n
, 0);
1841 mp_drop(xx
); mp_drop(y
); mp_drop(g
);
1842 return ((PyObject
*)c
);
1847 for (i
= 0; i
< n
; i
++)
1852 mp_drop(xx
); mp_drop(y
); mp_drop(g
);
1856 static PyObject
*mcget_product(PyObject
*me
, void *hunoz
)
1857 { return (mp_pywrap(MP_COPY(MPCRT_PY(me
)->mb
.m
))); }
1859 static PyObject
*mcget_moduli(PyObject
*me
, void *hunoz
)
1863 mpcrt
*c
= MPCRT_PY(me
);
1865 if ((q
= PyList_New(c
->k
)) == 0) return (0);
1866 for (i
= 0; i
< c
->k
; i
++)
1867 PyList_SET_ITEM(q
, i
, mp_pywrap(c
->v
[i
].m
));
1871 static const PyGetSetDef mpcrt_pygetset
[] = {
1872 #define GETSETNAME(op, name) mc##op##_##name
1873 GET (product
, "C.product -> product of moduli")
1874 GET (moduli
, "C.moduli -> list of individual moduli")
1879 static const PyMethodDef mpcrt_pymethods
[] = {
1880 #define METHNAME(name) mcmeth_##name
1881 METH (solve
, "C.solve([R0, R1]) -> X mod C.product")
1886 static const PyTypeObject mpcrt_pytype_skel
= {
1887 PyVarObject_HEAD_INIT(0, 0) /* Header */
1888 "MPCRT", /* @tp_name@ */
1889 sizeof(mpcrt_pyobj
), /* @tp_basicsize@ */
1890 0, /* @tp_itemsize@ */
1892 mpcrt_pydealloc
, /* @tp_dealloc@ */
1894 0, /* @tp_getattr@ */
1895 0, /* @tp_setattr@ */
1896 0, /* @tp_compare@ */
1898 0, /* @tp_as_number@ */
1899 0, /* @tp_as_sequence@ */
1900 0, /* @tp_as_mapping@ */
1904 0, /* @tp_getattro@ */
1905 0, /* @tp_setattro@ */
1906 0, /* @tp_as_buffer@ */
1907 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
1908 Py_TPFLAGS_BASETYPE
,
1911 "MPCRT(SEQ): a context for solving Chinese Remainder Theorem problems.",
1913 0, /* @tp_traverse@ */
1915 0, /* @tp_richcompare@ */
1916 0, /* @tp_weaklistoffset@ */
1918 0, /* @tp_iternext@ */
1919 PYMETHODS(mpcrt
), /* @tp_methods@ */
1920 0, /* @tp_members@ */
1921 PYGETSET(mpcrt
), /* @tp_getset@ */
1924 0, /* @tp_descr_get@ */
1925 0, /* @tp_descr_set@ */
1926 0, /* @tp_dictoffset@ */
1928 PyType_GenericAlloc
, /* @tp_alloc@ */
1929 mpcrt_pynew
, /* @tp_new@ */
1934 /*----- Binary polynomials ------------------------------------------------*/
1936 static PyObject
*gf_pyrepr(PyObject
*o
)
1937 { return mp_topystring(MP_X(o
), 16, "GF(", "0x", ")"); }
1939 static PyObject
*gf_pyrichcompare(PyObject
*x
, PyObject
*y
, int op
)
1945 if (gfbinop(x
, y
, &xx
, &yy
)) RETURN_NOTIMPL
;
1947 case Py_EQ
: b
= MP_EQ(xx
, yy
); break;
1948 case Py_NE
: b
= !MP_EQ(xx
, yy
); break;
1953 case Py_LT
: b
= xl
< yl
; break;
1954 case Py_LE
: b
= xl
<= yl
; break;
1955 case Py_GT
: b
= xl
> yl
; break;
1956 case Py_GE
: b
= xl
>= yl
; break;
1961 MP_DROP(xx
); MP_DROP(yy
);
1962 return (getbool(b
));
1965 static PyObject
*gf_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
1971 static const char *const kwlist
[] = { "x", "radix", 0 };
1973 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O|i:gf", KWLIST
, &x
, &radix
))
1975 if (GF_PYCHECK(x
)) RETURN_OBJ(x
);
1976 if (!good_radix_p(radix
, 1)) VALERR("radix out of range");
1977 if ((z
= mp_frompyobject(x
, radix
)) == 0) {
1978 PyErr_Format(PyExc_TypeError
, "can't convert %.100s to gf",
1979 Py_TYPE(x
)->tp_name
);
1984 VALERR("gf cannot be negative");
1986 zz
= (mp_pyobj
*)ty
->tp_alloc(ty
, 0);
1989 return ((PyObject
*)zz
);
1992 static PyObject
*gf_pyexp(PyObject
*x
, PyObject
*y
, PyObject
*z
)
1994 mp
*xx
= 0, *yy
= 0, *zz
= 0;
1998 if ((xx
= implicitgf(x
)) == 0 || (yy
= implicitmp(y
)) == 0 ||
1999 (z
&& z
!= Py_None
&& (zz
= implicitgf(z
)) == 0)) {
2000 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
2003 if (!z
|| z
== Py_None
) {
2004 if (MP_NEGP(yy
)) VALERR("negative exponent");
2005 r
= gf_exp(MP_NEW
, xx
, yy
);
2008 if (MP_ZEROP(zz
)) ZDIVERR("zero modulus");
2010 if ((xx
= gf_modinv_checked(xx
, xx
, zz
)) == 0) goto end
;
2011 yy
= mp_neg(yy
, yy
);
2013 gfreduce_create(&gr
, zz
);
2014 r
= gfreduce_exp(&gr
, MP_NEW
, xx
, yy
);
2015 gfreduce_destroy(&gr
);
2019 mp_drop(xx
); mp_drop(yy
); mp_drop(zz
);
2023 static PyObject
*gfmeth_sqr(PyObject
*me
)
2024 { return (gf_pywrap(gf_sqr(MP_NEW
, MP_X(me
)))); }
2026 static PyObject
*gfmeth_gcd(PyObject
*me
, PyObject
*arg
)
2029 mp
*yy
= 0, *zz
= MP_NEW
;
2031 if (!PyArg_ParseTuple(arg
, "O&:gcd", convgf
, &yy
)) goto end
;
2032 gf_gcd(&zz
, 0, 0, MP_X(me
), yy
);
2035 if (yy
) MP_DROP(yy
);
2039 static PyObject
*gfmeth_gcdx(PyObject
*me
, PyObject
*arg
)
2042 mp
*yy
= 0, *zz
= MP_NEW
, *uu
= MP_NEW
, *vv
= MP_NEW
;
2044 if (!PyArg_ParseTuple(arg
, "O&:gcdx", convgf
, &yy
))
2046 gf_gcd(&zz
, &uu
, &vv
, MP_X(me
), yy
);
2047 z
= Py_BuildValue("(NNN)",
2048 gf_pywrap(zz
), gf_pywrap(uu
), gf_pywrap(vv
));
2050 if (yy
) MP_DROP(yy
);
2054 static PyObject
*gfmeth_modinv(PyObject
*me
, PyObject
*arg
)
2057 mp
*yy
= 0, *zz
= MP_NEW
;
2059 if (!PyArg_ParseTuple(arg
, "O&:modinv", convgf
, &yy
) ||
2060 (zz
= gf_modinv_checked(MP_NEW
, yy
, MP_X(me
))) == 0)
2064 if (yy
) MP_DROP(yy
);
2068 static PyObject
*gfmeth_fromstring(PyObject
*me
,
2069 PyObject
*arg
, PyObject
*kw
)
2076 mptext_stringctx sc
;
2077 static const char *const kwlist
[] = { "x", "radix", 0 };
2079 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "s#|i:fromstring", KWLIST
,
2082 if (!good_radix_p(r
, 1)) VALERR("bad radix");
2083 sc
.buf
= p
; sc
.lim
= p
+ len
;
2084 if ((zz
= mp_read(MP_NEW
, r
, &mptext_stringops
, &sc
)) == 0 ||
2086 if (zz
) MP_DROP(zz
);
2087 VALERR("bad binary polynomial");
2089 z
= Py_BuildValue("(Ns#)", gf_pywrap(zz
),
2090 sc
.buf
, (Py_ssize_t
)(sc
.lim
- sc
.buf
));
2095 static PyObject
*gfmeth_irreduciblep(PyObject
*me
)
2096 { return getbool(gf_irreduciblep(MP_X(me
))); }
2098 static PyObject
*gfget_degree(PyObject
*me
, void *hunoz
)
2099 { return (PyInt_FromLong(mp_bits(MP_X(me
)) - 1)); }
2101 static const PyGetSetDef gf_pygetset
[] = {
2102 #define GETSETNAME(op, name) gf##op##_##name
2103 GET (degree
, "X.degree -> polynomial degree of X")
2105 #define GETSETNAME(op, name) mp##op##_##name
2106 GET (nbits
, "X.nbits -> bit length of X")
2107 GET (noctets
, "X.noctets -> octet length of X")
2112 static const PyMethodDef gf_pymethods
[] = {
2113 #define METHNAME(func) gfmeth_##func
2114 METH (setbit
, "X.setbit(N) -> X with bit N set")
2115 METH (clearbit
, "X.clearbit(N) -> X with bit N clear")
2116 METH (testbit
, "X.testbit(N) -> true/false if bit N set/clear in X")
2117 NAMETH(sqr
, "X.sqr() -> X^2")
2118 METH (gcd
, "X.gcd(Y) -> gcd(X, Y)")
2119 METH (gcdx
, "X.gcdx(Y) -> (gcd(X, Y), U, V) with X U + Y V = gcd(X, Y)")
2120 METH (modinv
, "X.modinv(Y) -> multiplicative inverse of Y mod X")
2121 NAMETH(irreduciblep
, "X.irreduciblep() -> true/false")
2122 KWSMTH(fromstring
, "fromstring(STR, [radix = 0]) -> (X, REST)\n"
2123 " Parse STR as a binary polynomial, according to RADIX. If RADIX is\n"
2124 " zero, read a prefix from STR to decide radix: allow `0b' for binary,\n"
2125 " `0' or `0o' for octal, `0x' for hex, or `R_' for other radix R.")
2126 SMTH (loadl
, "loadl(STR) -> X: read little-endian bytes")
2127 SMTH (loadb
, "loadb(STR) -> X: read big-endian bytes")
2128 SMTH (frombuf
, "frombuf(STR) -> (X, REST): read buffer format")
2130 #define METHNAME(func) mpmeth_##func
2131 KWMETH(tostring
, "X.tostring([radix = 10]) -> STR")
2132 KWMETH(storel
, "X.storel([len = -1]) -> little-endian bytes")
2133 KWMETH(storeb
, "X.storeb([len = -1]) -> big-endian bytes")
2134 KWMETH(storel2c
, "X.storel2c([len = -1]) -> "
2135 "little-endian bytes, two's complement")
2136 KWMETH(storeb2c
, "X.storeb2c([len = -1]) -> "
2137 "big-endian bytes, two's complement")
2138 NAMETH(tobuf
, "X.tobuf() -> buffer format")
2143 static const PyNumberMethods gf_pynumber
= {
2144 gf_pyadd
, /* @nb_add@ */
2145 gf_pysub
, /* @nb_subtract@ */
2146 gf_pymul
, /* @nb_multiply@ */
2148 0, /* @nb_divide@ */
2150 gf_pymod
, /* @nb_remainder@ */
2151 gf_pydivmod
, /* @nb_divmod@ */
2152 gf_pyexp
, /* @nb_power@ */
2153 mp_pyid
, /* @nb_negative@ */
2154 mp_pyid
, /* @nb_positive@ */
2155 mp_pyid
, /* @nb_absolute@ */
2156 mp_pynonzerop
, /* @nb_nonzero@ */
2157 0 /* doesn't make any sense */, /* @nb_invert@ */
2158 gf_pylsl
, /* @nb_lshift@ */
2159 gf_pylsr
, /* @nb_rshift@ */
2160 gf_pyand
, /* @nb_and@ */
2161 gf_pyxor
, /* @nb_xor@ */
2162 gf_pyor
, /* @nb_or@ */
2164 gf_pycoerce
, /* @nb_coerce@ */
2166 mp_pyint
, /* @nb_int@ */
2167 PY23(mp_pylong
, 0), /* @nb_long@ */
2168 0 /* doesn't make any sense */, /* @nb_float@ */
2170 mp_pyoct
, /* @nb_oct@ */
2171 mp_pyhex
, /* @nb_hex@ */
2174 0, /* @nb_inplace_add@ */
2175 0, /* @nb_inplace_subtract@ */
2176 0, /* @nb_inplace_multiply@ */
2178 0, /* @nb_inplace_divide@ */
2180 0, /* @nb_inplace_remainder@ */
2181 0, /* @nb_inplace_power@ */
2182 0, /* @nb_inplace_lshift@ */
2183 0, /* @nb_inplace_rshift@ */
2184 0, /* @nb_inplace_and@ */
2185 0, /* @nb_inplace_xor@ */
2186 0, /* @nb_inplace_or@ */
2188 gf_pydiv
, /* @nb_floor_divide@ */
2189 0, /* @nb_true_divide@ */
2190 0, /* @nb_inplace_floor_divide@ */
2191 0, /* @nb_inplace_true_divide@ */
2193 mp_pyint
, /* @nb_index@ */
2196 static const PyTypeObject gf_pytype_skel
= {
2197 PyVarObject_HEAD_INIT(0, 0) /* Header */
2198 "GF", /* @tp_name@ */
2199 sizeof(mp_pyobj
), /* @tp_basicsize@ */
2200 0, /* @tp_itemsize@ */
2202 mp_pydealloc
, /* @tp_dealloc@ */
2204 0, /* @tp_getattr@ */
2205 0, /* @tp_setattr@ */
2206 0, /* @tp_compare@ */
2207 gf_pyrepr
, /* @tp_repr@ */
2208 PYNUMBER(gf
), /* @tp_as_number@ */
2209 0, /* @tp_as_sequence@ */
2210 0, /* @tp_as_mapping@ */
2211 mp_pyhash
, /* @tp_hash@ */
2213 mp_pyhex
, /* @tp_str@ */
2214 0, /* @tp_getattro@ */
2215 0, /* @tp_setattro@ */
2216 0, /* @tp_as_buffer@ */
2217 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
2218 Py_TPFLAGS_CHECKTYPES
|
2219 Py_TPFLAGS_BASETYPE
,
2222 "Binary polynomials. Support almost all the standard arithmetic\n"
2225 "Constructor GF(X, [radix = R]) attempts to convert X to a `GF'. If\n"
2226 "X is a string, it's read in radix-R form, or we look for a prefix\n"
2227 "if R = 0. Other acceptable things are field elements, elliptic curve\n"
2229 "points, group elements, Python `int' and `long' objects, and anything\n"
2230 "with an integer conversion.\n",
2231 "points, group elements, Python `int' objects, and anything with an\n"
2232 "integer conversion.\n")
2234 "The name is hopelessly wrong from a technical point of view, but\n"
2235 "but it's much easier to type than `p2' or `c2' or whatever.\n"
2239 " * Use `//' for Euclidean division: `/' gives exact rational division.",
2241 0, /* @tp_traverse@ */
2243 gf_pyrichcompare
, /* @tp_richcompare@ */
2244 0, /* @tp_weaklistoffset@ */
2246 0, /* @tp_iternext@ */
2247 PYMETHODS(gf
), /* @tp_methods@ */
2248 0, /* @tp_members@ */
2249 PYGETSET(gf
), /* @tp_getset@ */
2252 0, /* @tp_descr_get@ */
2253 0, /* @tp_descr_set@ */
2254 0, /* @tp_dictoffset@ */
2256 PyType_GenericAlloc
, /* @tp_alloc@ */
2257 gf_pynew
, /* @tp_new@ */
2262 /*----- Sparse poly reduction ---------------------------------------------*/
2264 static PyTypeObject
*gfreduce_pytype
;
2266 typedef struct gfreduce_pyobj
{
2271 #define GFREDUCE_PY(o) (&((gfreduce_pyobj *)(o))->mr)
2273 static PyObject
*grmeth_exp(PyObject
*me
, PyObject
*arg
)
2276 mp
*yy
= 0, *zz
= 0;
2278 if (!PyArg_ParseTuple(arg
, "O&O&:exp", convgf
, &yy
, convgf
, &zz
))
2281 if ((yy
= gf_modinv_checked(yy
, yy
, GFREDUCE_PY(me
)->p
)) == 0) goto end
;
2282 zz
= mp_neg(zz
, zz
);
2284 rc
= gf_pywrap(gfreduce_exp(GFREDUCE_PY(me
), MP_NEW
, yy
, zz
));
2286 if (yy
) MP_DROP(yy
); if (zz
) MP_DROP(zz
);
2290 static PyObject
*grmeth_trace(PyObject
*me
, PyObject
*arg
)
2295 if (!PyArg_ParseTuple(arg
, "O&:trace", convgf
, &xx
)) goto end
;
2296 rc
= PyInt_FromLong(gfreduce_trace(GFREDUCE_PY(me
), xx
));
2298 if (xx
) MP_DROP(xx
);
2302 static PyObject
*grmeth_halftrace(PyObject
*me
, PyObject
*arg
)
2307 if (!PyArg_ParseTuple(arg
, "O&:halftrace", convgf
, &xx
)) goto end
;
2308 rc
= gf_pywrap(gfreduce_halftrace(GFREDUCE_PY(me
), MP_NEW
, xx
));
2310 if (xx
) MP_DROP(xx
);
2314 static PyObject
*grmeth_sqrt(PyObject
*me
, PyObject
*arg
)
2319 if (!PyArg_ParseTuple(arg
, "O&:sqrt", convgf
, &xx
)) goto end
;
2320 if ((yy
= gfreduce_sqrt(GFREDUCE_PY(me
), MP_NEW
, xx
)) == 0)
2321 VALERR("no modular square root");
2324 if (xx
) MP_DROP(xx
);
2328 static PyObject
*grmeth_quadsolve(PyObject
*me
, PyObject
*arg
)
2333 if (!PyArg_ParseTuple(arg
, "O&:quadsolve", convgf
, &xx
)) goto end
;
2334 if ((yy
= gfreduce_quadsolve(GFREDUCE_PY(me
), MP_NEW
, xx
)) == 0)
2335 VALERR("no solution found");
2338 if (xx
) MP_DROP(xx
);
2342 static PyObject
*grmeth_reduce(PyObject
*me
, PyObject
*arg
)
2347 if (!PyArg_ParseTuple(arg
, "O&:reduce", convgf
, &yy
)) goto end
;
2348 z
= gf_pywrap(gfreduce_do(GFREDUCE_PY(me
), MP_NEW
, yy
));
2353 static void gfreduce_pydealloc(PyObject
*me
)
2355 gfreduce_destroy(GFREDUCE_PY(me
));
2359 static PyObject
*gfreduce_pynew(PyTypeObject
*ty
,
2360 PyObject
*arg
, PyObject
*kw
)
2362 gfreduce_pyobj
*mr
= 0;
2364 static const char *const kwlist
[] = { "m", 0 };
2367 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&:new", KWLIST
, convgf
, &xx
))
2369 if (MP_ZEROP(xx
)) ZDIVERR("modulus is zero!");
2370 gfreduce_create(&r
, xx
);
2371 mr
= (gfreduce_pyobj
*)ty
->tp_alloc(ty
, 0);
2374 if (xx
) MP_DROP(xx
);
2375 return ((PyObject
*)mr
);
2378 static PyObject
*grget_m(PyObject
*me
, void *hunoz
)
2379 { return (gf_pywrap(MP_COPY(GFREDUCE_PY(me
)->p
))); }
2381 static const PyGetSetDef gfreduce_pygetset
[] = {
2382 #define GETSETNAME(op, name) gr##op##_##name
2383 GET (m
, "R.m -> reduction polynomial")
2388 static const PyMethodDef gfreduce_pymethods
[] = {
2389 #define METHNAME(name) grmeth_##name
2390 METH (reduce
, "R.reduce(X) -> X mod B.m")
2391 METH (trace
, "R.trace(X) -> Tr(X) = x + x^2 + ... + x^{2^{m - 1}}")
2392 METH (halftrace
, "R.halftrace(X) -> x + x^{2^2} + ... + x^{2^{m - 1}}")
2393 METH (sqrt
, "R.sqrt(X) -> Y where Y^2 = X mod R")
2394 METH (quadsolve
, "R.quadsolve(X) -> Y where Y^2 + Y = X mod R")
2395 METH (exp
, "R.exp(X, N) -> X^N mod B.m")
2400 static const PyTypeObject gfreduce_pytype_skel
= {
2401 PyVarObject_HEAD_INIT(0, 0) /* Header */
2402 "GFReduce", /* @tp_name@ */
2403 sizeof(gfreduce_pyobj
), /* @tp_basicsize@ */
2404 0, /* @tp_itemsize@ */
2406 gfreduce_pydealloc
, /* @tp_dealloc@ */
2408 0, /* @tp_getattr@ */
2409 0, /* @tp_setattr@ */
2410 0, /* @tp_compare@ */
2412 0, /* @tp_as_number@ */
2413 0, /* @tp_as_sequence@ */
2414 0, /* @tp_as_mapping@ */
2418 0, /* @tp_getattro@ */
2419 0, /* @tp_setattro@ */
2420 0, /* @tp_as_buffer@ */
2421 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
2422 Py_TPFLAGS_BASETYPE
,
2425 "GFReduce(N): a context for reduction modulo sparse polynomials.",
2427 0, /* @tp_traverse@ */
2429 0, /* @tp_richcompare@ */
2430 0, /* @tp_weaklistoffset@ */
2432 0, /* @tp_iternext@ */
2433 PYMETHODS(gfreduce
), /* @tp_methods@ */
2434 0, /* @tp_members@ */
2435 PYGETSET(gfreduce
), /* @tp_getset@ */
2438 0, /* @tp_descr_get@ */
2439 0, /* @tp_descr_set@ */
2440 0, /* @tp_dictoffset@ */
2442 PyType_GenericAlloc
, /* @tp_alloc@ */
2443 gfreduce_pynew
, /* @tp_new@ */
2448 /*----- Normal/poly transformation ----------------------------------------*/
2450 static PyTypeObject
*gfn_pytype
;
2452 typedef struct gfn_pyobj
{
2458 #define GFN_P(o) (((gfn_pyobj *)(o))->p)
2459 #define GFN_PTON(o) (&((gfn_pyobj *)(o))->pton)
2460 #define GFN_NTOP(o) (&((gfn_pyobj *)(o))->ntop)
2462 static PyObject
*gfn_pynew(PyTypeObject
*ty
, PyObject
*arg
, PyObject
*kw
)
2464 mp
*p
= 0, *beta
= 0;
2466 static const char *const kwlist
[] = { "p", "beta", 0 };
2468 if (!PyArg_ParseTupleAndKeywords(arg
, kw
, "O&O&:new", KWLIST
,
2469 convgf
, &p
, convgf
, &beta
))
2471 gg
= PyObject_New(gfn_pyobj
, ty
);
2473 if (gfn_create(p
, beta
, &gg
->ntop
, &gg
->pton
)) {
2476 VALERR("can't invert transformation matrix");
2482 return ((PyObject
*)gg
);
2485 static PyObject
*gfnget_p(PyObject
*me
, void *hunoz
)
2486 { return (gf_pywrap(MP_COPY(GFN_P(me
)))); }
2488 static PyObject
*gfnget_beta(PyObject
*me
, void *hunoz
)
2490 gfn
*n
= GFN_NTOP(me
);
2491 mp
*x
= n
->r
[n
->n
- 1];
2492 return (gf_pywrap(MP_COPY(x
)));
2495 #define XFORMOP(name, NAME) \
2496 static PyObject *gfnmeth_##name(PyObject *me, PyObject *arg) \
2501 if (!PyArg_ParseTuple(arg, "O&:" #name, convgf, &xx)) goto end; \
2502 z = gfn_transform(GFN_##NAME(me), MP_NEW, xx); \
2505 if (!z) return (0); \
2506 return (gf_pywrap(z)); \
2512 static void gfn_pydealloc(PyObject
*me
)
2516 gfn_destroy(GFN_PTON(me
));
2517 gfn_destroy(GFN_NTOP(me
));
2522 static const PyGetSetDef gfn_pygetset
[] = {
2523 #define GETSETNAME(op, name) gfn##op##_##name
2524 GET (p
, "X.p -> polynomial basis, as polynomial")
2525 GET (beta
, "X.beta -> normal basis element, in poly form")
2530 static const PyMethodDef gfn_pymethods
[] = {
2531 #define METHNAME(name) gfnmeth_##name
2532 METH (pton
, "X.pton(A) -> normal-basis representation of A")
2533 METH (ntop
, "X.ntop(A) -> polynomial-basis representation of A")
2538 static const PyTypeObject gfn_pytype_skel
= {
2539 PyVarObject_HEAD_INIT(0, 0) /* Header */
2540 "GFN", /* @tp_name@ */
2541 sizeof(gfn_pyobj
), /* @tp_basicsize@ */
2542 0, /* @tp_itemsize@ */
2544 gfn_pydealloc
, /* @tp_dealloc@ */
2546 0, /* @tp_getattr@ */
2547 0, /* @tp_setattr@ */
2548 0, /* @tp_compare@ */
2550 0, /* @tp_as_number@ */
2551 0, /* @tp_as_sequence@ */
2552 0, /* @tp_as_mapping@ */
2556 0, /* @tp_getattro@ */
2557 0, /* @tp_setattro@ */
2558 0, /* @tp_as_buffer@ */
2559 Py_TPFLAGS_DEFAULT
| /* @tp_flags@ */
2560 Py_TPFLAGS_BASETYPE
,
2563 "GFN(P, BETA): an object for transforming elements of binary fields\n"
2564 " between polynomial and normal basis representations.",
2566 0, /* @tp_traverse@ */
2568 0, /* @tp_richcompare@ */
2569 0, /* @tp_weaklistoffset@ */
2571 0, /* @tp_iternext@ */
2572 PYMETHODS(gfn
), /* @tp_methods@ */
2573 0, /* @tp_members@ */
2574 PYGETSET(gfn
), /* @tp_getset@ */
2577 0, /* @tp_descr_get@ */
2578 0, /* @tp_descr_set@ */
2579 0, /* @tp_dictoffset@ */
2581 PyType_GenericAlloc
, /* @tp_alloc@ */
2582 gfn_pynew
, /* @tp_new@ */
2587 /*----- Glue --------------------------------------------------------------*/
2589 static const struct nameval consts
[] = {
2594 void mp_pyinit(void)
2598 INITTYPE(mpmul
, root
);
2599 INITTYPE(mpmont
, root
);
2600 INITTYPE(mpbarrett
, root
);
2601 INITTYPE(mpreduce
, root
);
2602 INITTYPE(mpcrt
, root
);
2603 INITTYPE(gfreduce
, root
);
2604 INITTYPE(gfn
, root
);
2607 void mp_pyinsert(PyObject
*mod
)
2609 INSERT("MP", mp_pytype
);
2610 INSERT("MPMul", mpmul_pytype
);
2611 INSERT("MPMont", mpmont_pytype
);
2612 INSERT("MPBarrett", mpbarrett_pytype
);
2613 INSERT("MPReduce", mpreduce_pytype
);
2614 INSERT("MPCRT", mpcrt_pytype
);
2615 INSERT("GF", gf_pytype
);
2616 INSERT("GFReduce", gfreduce_pytype
);
2617 INSERT("GFN", gfn_pytype
);
2618 setconstants(mod
, consts
);
2621 /*----- That's all, folks -------------------------------------------------*/