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1.4 noro 1: /*
2: * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
3: * All rights reserved.
4: *
5: * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
6: * non-exclusive and royalty-free license to use, copy, modify and
7: * redistribute, solely for non-commercial and non-profit purposes, the
8: * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
9: * conditions of this Agreement. For the avoidance of doubt, you acquire
10: * only a limited right to use the SOFTWARE hereunder, and FLL or any
11: * third party developer retains all rights, including but not limited to
12: * copyrights, in and to the SOFTWARE.
13: *
14: * (1) FLL does not grant you a license in any way for commercial
15: * purposes. You may use the SOFTWARE only for non-commercial and
16: * non-profit purposes only, such as academic, research and internal
17: * business use.
18: * (2) The SOFTWARE is protected by the Copyright Law of Japan and
19: * international copyright treaties. If you make copies of the SOFTWARE,
20: * with or without modification, as permitted hereunder, you shall affix
21: * to all such copies of the SOFTWARE the above copyright notice.
22: * (3) An explicit reference to this SOFTWARE and its copyright owner
23: * shall be made on your publication or presentation in any form of the
24: * results obtained by use of the SOFTWARE.
25: * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
1.5 noro 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.4 noro 27: * for such modification or the source code of the modified part of the
28: * SOFTWARE.
29: *
30: * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
31: * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
32: * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
33: * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
34: * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
35: * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
36: * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
37: * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
38: * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
39: * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
40: * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
41: * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
42: * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
43: * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
44: * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
45: * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
46: * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
47: *
1.11 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/builtin/int.c,v 1.10 2001/10/09 01:36:06 noro Exp $
1.4 noro 49: */
1.1 noro 50: #include "ca.h"
51: #include "parse.h"
52: #include "base.h"
53:
54: void Pidiv(), Pirem(), Pigcd(), Pilcm(), Pfac(), Prandom(), Pinv();
55: void Pup2_inv(),Pgf2nton(), Pntogf2n();
56: void Pup2_init_eg(), Pup2_show_eg();
57: void Piqr(), Pprime(), Plprime(), Pinttorat();
58: void Piand(), Pior(), Pixor(), Pishift();
59: void Pisqrt();
60: void Plrandom();
61: void Pset_upkara(), Pset_uptkara(), Pset_up2kara(), Pset_upfft();
62: void Pmt_save(), Pmt_load();
63: void Psmall_jacobi();
64: void Pdp_set_mpi();
1.2 noro 65: void Pntoint32(),Pint32ton();
1.1 noro 66:
67: void Pigcdbin(), Pigcdbmod(), PigcdEuc(), Pigcdacc(), Pigcdcntl();
68:
69: void Pihex();
70: void Pimaxrsh(), Pilen();
71: void Ptype_t_NB();
72:
73: struct ftab int_tab[] = {
74: {"dp_set_mpi",Pdp_set_mpi,-1},
75: {"isqrt",Pisqrt,1},
76: {"idiv",Pidiv,2},
77: {"irem",Pirem,2},
78: {"iqr",Piqr,2},
79: {"igcd",Pigcd,-2},
80: {"ilcm",Pilcm,2},
81: {"up2_inv",Pup2_inv,2},
82: {"up2_init_eg",Pup2_init_eg,0},
83: {"up2_show_eg",Pup2_show_eg,0},
84: {"type_t_NB",Ptype_t_NB,2},
85: {"gf2nton",Pgf2nton,1},
86: {"ntogf2n",Pntogf2n,1},
87: {"set_upkara",Pset_upkara,-1},
88: {"set_uptkara",Pset_uptkara,-1},
89: {"set_up2kara",Pset_up2kara,-1},
90: {"set_upfft",Pset_upfft,-1},
91: {"inv",Pinv,2},
92: {"inttorat",Pinttorat,3},
93: {"fac",Pfac,1},
94: {"prime",Pprime,1},
95: {"lprime",Plprime,1},
96: {"random",Prandom,-1},
97: {"lrandom",Plrandom,1},
98: {"iand",Piand,2},
99: {"ior",Pior,2},
100: {"ixor",Pixor,2},
101: {"ishift",Pishift,2},
102: {"small_jacobi",Psmall_jacobi,2},
1.8 murao 103:
1.1 noro 104: {"igcdbin",Pigcdbin,2}, /* HM@CCUT extension */
105: {"igcdbmod",Pigcdbmod,2}, /* HM@CCUT extension */
106: {"igcdeuc",PigcdEuc,2}, /* HM@CCUT extension */
107: {"igcdacc",Pigcdacc,2}, /* HM@CCUT extension */
108: {"igcdcntl",Pigcdcntl,-1}, /* HM@CCUT extension */
1.8 murao 109:
1.1 noro 110: {"mt_save",Pmt_save,1},
111: {"mt_load",Pmt_load,1},
1.2 noro 112: {"ntoint32",Pntoint32,1},
113: {"int32ton",Pint32ton,1},
1.1 noro 114: {0,0,0},
115: };
116:
117: static int is_prime_small(unsigned int);
118: static unsigned int gcd_small(unsigned int,unsigned int);
119: int TypeT_NB_check(unsigned int, unsigned int);
120: int mpi_mag;
1.2 noro 121:
1.10 noro 122: void Pntoint32(NODE arg,USINT *rp)
1.2 noro 123: {
124: Q q;
1.3 noro 125: unsigned int t;
1.2 noro 126:
127: asir_assert(ARG0(arg),O_N,"ntoint32");
128: q = (Q)ARG0(arg);
129: if ( !q ) {
130: MKUSINT(*rp,0);
131: return;
132: }
1.3 noro 133: if ( NID(q)!=N_Q || !INT(q) || PL(NM(q))>1 )
1.2 noro 134: error("ntoint32 : invalid argument");
1.3 noro 135: t = BD(NM(q))[0];
136: if ( SGN(q) < 0 )
1.10 noro 137: t = -(int)t;
1.3 noro 138: MKUSINT(*rp,t);
1.2 noro 139: }
140:
1.10 noro 141: void Pint32ton(NODE arg,Q *rp)
1.2 noro 142: {
1.3 noro 143: int t;
1.2 noro 144:
145: asir_assert(ARG0(arg),O_USINT,"int32ton");
1.3 noro 146: t = (int)BDY((USINT)ARG0(arg));
147: STOQ(t,*rp);
1.2 noro 148: }
1.1 noro 149:
1.10 noro 150: void Pdp_set_mpi(NODE arg,Q *rp)
1.1 noro 151: {
152: if ( arg ) {
153: asir_assert(ARG0(arg),O_N,"dp_set_mpi");
154: mpi_mag = QTOS((Q)ARG0(arg));
155: }
156: STOQ(mpi_mag,*rp);
157: }
158:
1.10 noro 159: void Psmall_jacobi(NODE arg,Q *rp)
1.1 noro 160: {
161: Q a,m;
162: int a0,m0,s;
163:
164: a = (Q)ARG0(arg);
165: m = (Q)ARG1(arg);
166: asir_assert(a,O_N,"small_jacobi");
167: asir_assert(m,O_N,"small_jacobi");
168: if ( !a )
169: *rp = ONE;
170: else if ( !m || !INT(m) || !INT(a)
171: || PL(NM(m))>1 || PL(NM(a))>1 || SGN(m) < 0 || EVENN(NM(m)) )
172: error("small_jacobi : invalid input");
173: else {
174: a0 = QTOS(a); m0 = QTOS(m);
175: s = small_jacobi(a0,m0);
176: STOQ(s,*rp);
177: }
178: }
179:
1.10 noro 180: int small_jacobi(int a,int m)
1.1 noro 181: {
182: int m4,m8,a4,j1,i,s;
183:
184: a %= m;
185: if ( a == 0 || a == 1 )
186: return 1;
187: else if ( a < 0 ) {
188: j1 = small_jacobi(-a,m);
189: m4 = m%4;
190: return m4==1?j1:-j1;
191: } else {
192: for ( i = 0; a && !(a&1); i++, a >>= 1 );
193: if ( i&1 ) {
194: m8 = m%8;
195: s = (m8==1||m8==7) ? 1 : -1;
196: } else
197: s = 1;
198: /* a, m are odd */
199: j1 = small_jacobi(m%a,a);
200: m4 = m%4; a4 = a%4;
201: s *= (m4==1||a4==1) ? 1 : -1;
202: return j1*s;
203: }
204: }
205:
1.10 noro 206: void Ptype_t_NB(NODE arg,Q *rp)
1.1 noro 207: {
208: if ( TypeT_NB_check(QTOS((Q)ARG0(arg)),QTOS((Q)ARG1(arg))))
209: *rp = ONE;
210: else
211: *rp = 0;
212: }
213:
214: int TypeT_NB_check(unsigned int m, unsigned int t)
215: {
216: unsigned int p,k,u,h,d;
217:
218: if ( !(m%8) )
219: return 0;
220: p = t*m+1;
221: if ( !is_prime_small(p) )
222: return 0;
223: for ( k = 1, u = 2%p; ; k++ )
224: if ( u == 1 )
225: break;
226: else
227: u = (2*u)%p;
228: h = t*m/k;
229: d = gcd_small(h,m);
230: return d == 1 ? 1 : 0;
231: }
232:
233: /*
234: * a simple prime checker
235: * return value: 1 --- prime number
236: * 0 --- composite number
237: */
238:
239: static int is_prime_small(unsigned int a)
240: {
241: unsigned int b,t,i;
242:
243: if ( !(a%2) ) return 0;
244: for ( t = a, i = 0; t; i++, t >>= 1 );
245: /* b >= sqrt(a) */
246: b = 1<<((i+1)/2);
247:
248: /* divisibility test by all odd numbers <= b */
249: for ( i = 3; i <= b; i += 2 )
250: if ( !(a%i) )
251: return 0;
252: return 1;
253: }
254:
255: /*
256: * gcd for unsigned int as integers
257: * return value: GCD(a,b)
258: *
259: */
260:
261:
262: static unsigned int gcd_small(unsigned int a,unsigned int b)
263: {
264: unsigned int t;
265:
266: if ( b > a ) {
267: t = a; a = b; b = t;
268: }
269: /* Euclid's algorithm */
270: while ( 1 )
271: if ( !(t = a%b) ) return b;
272: else {
273: a = b; b = t;
274: }
275: }
276:
1.10 noro 277: void Pmt_save(NODE arg,Q *rp)
1.1 noro 278: {
279: int ret;
280:
281: ret = mt_save(BDY((STRING)ARG0(arg)));
282: STOQ(ret,*rp);
283: }
284:
1.10 noro 285: void Pmt_load(NODE arg,Q *rp)
1.1 noro 286: {
287: int ret;
288:
289: ret = mt_load(BDY((STRING)ARG0(arg)));
290: STOQ(ret,*rp);
291: }
292:
1.10 noro 293: void Pisqrt(NODE arg,Q *rp)
1.1 noro 294: {
295: Q a;
296: N r;
297:
298: a = (Q)ARG0(arg);
299: asir_assert(a,O_N,"isqrt");
300: if ( !a )
301: *rp = 0;
302: else if ( SGN(a) < 0 )
303: error("isqrt : negative argument");
304: else {
305: isqrt(NM(a),&r);
306: NTOQ(r,1,*rp);
307: }
308: }
309:
1.10 noro 310: void Pidiv(NODE arg,Obj *rp)
1.1 noro 311: {
312: N q,r;
313: Q a;
314: Q dnd,dvr;
315:
316: dnd = (Q)ARG0(arg); dvr = (Q)ARG1(arg);
317: asir_assert(dnd,O_N,"idiv");
318: asir_assert(dvr,O_N,"idiv");
319: if ( !dvr )
320: error("idiv: division by 0");
321: else if ( !dnd )
322: *rp = 0;
323: else {
324: divn(NM(dnd),NM(dvr),&q,&r);
325: NTOQ(q,SGN(dnd)*SGN(dvr),a); *rp = (Obj)a;
326: }
327: }
328:
1.10 noro 329: void Pirem(NODE arg,Obj *rp)
1.1 noro 330: {
331: N q,r;
332: Q a;
333: Q dnd,dvr;
334:
335: dnd = (Q)ARG0(arg); dvr = (Q)ARG1(arg);
336: asir_assert(dnd,O_N,"irem");
337: asir_assert(dvr,O_N,"irem");
338: if ( !dvr )
339: error("irem: division by 0");
340: else if ( !dnd )
341: *rp = 0;
342: else {
343: divn(NM(dnd),NM(dvr),&q,&r);
344: NTOQ(r,SGN(dnd),a); *rp = (Obj)a;
345: }
346: }
347:
1.10 noro 348: void Piqr(NODE arg,LIST *rp)
1.1 noro 349: {
350: N q,r;
351: Q a,b;
352: Q dnd,dvr;
353: NODE node1,node2;
354:
355: dnd = (Q)ARG0(arg); dvr = (Q)ARG1(arg);
356: if ( !dvr )
357: error("iqr: division by 0");
358: else if ( !dnd )
359: a = b = 0;
360: else if ( OID(dnd) == O_VECT ) {
361: iqrv((VECT)dnd,dvr,rp); return;
362: } else {
363: asir_assert(dnd,O_N,"iqr");
364: asir_assert(dvr,O_N,"iqr");
365: divn(NM(dnd),NM(dvr),&q,&r);
366: NTOQ(q,SGN(dnd)*SGN(dvr),a);
367: NTOQ(r,SGN(dnd),b);
368: }
369: MKNODE(node2,b,0); MKNODE(node1,a,node2); MKLIST(*rp,node1);
370: }
371:
1.10 noro 372: void Pinttorat(NODE arg,LIST *rp)
1.1 noro 373: {
374: Q cq,qq,t,u1,v1,r1,nm;
375: N m,b,q,r,c,u2,v2,r2;
376: NODE node1,node2;
377: P p;
378:
379: asir_assert(ARG0(arg),O_N,"inttorat");
380: asir_assert(ARG1(arg),O_N,"inttorat");
381: asir_assert(ARG2(arg),O_N,"inttorat");
382: cq = (Q)ARG0(arg); m = NM((Q)ARG1(arg)); b = NM((Q)ARG2(arg));
383: if ( !cq ) {
384: MKNODE(node2,(pointer)ONE,0); MKNODE(node1,0,node2); MKLIST(*rp,node1);
385: return;
386: }
387: divn(NM(cq),m,&q,&r);
388: if ( !r ) {
389: MKNODE(node2,(pointer)ONE,0); MKNODE(node1,0,node2); MKLIST(*rp,node1);
390: return;
391: } else if ( SGN(cq) < 0 ) {
392: subn(m,r,&c);
393: } else
394: c = r;
395: u1 = 0; v1 = ONE; u2 = m; v2 = c;
396: while ( cmpn(v2,b) >= 0 ) {
397: divn(u2,v2,&q,&r2); u2 = v2; v2 = r2;
398: NTOQ(q,1,qq); mulq(qq,v1,&t); subq(u1,t,&r1); u1 = v1; v1 = r1;
399: }
400: if ( cmpn(NM(v1),b) >= 0 )
401: *rp = 0;
402: else {
403: if ( SGN(v1) < 0 ) {
404: chsgnp((P)v1,&p); v1 = (Q)p; NTOQ(v2,-1,nm);
405: } else
406: NTOQ(v2,1,nm);
407: MKNODE(node2,v1,0); MKNODE(node1,nm,node2); MKLIST(*rp,node1);
408: }
409: }
410:
1.10 noro 411: void Pigcd(NODE arg,Q *rp)
1.1 noro 412: {
413: N g;
414: Q n1,n2,a;
415:
416: if ( argc(arg) == 1 ) {
417: igcdv((VECT)ARG0(arg),rp);
418: return;
419: }
420: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
421: asir_assert(n1,O_N,"igcd");
422: asir_assert(n2,O_N,"igcd");
423: if ( !n1 )
424: *rp = n2;
425: else if ( !n2 )
426: *rp = n1;
427: else {
428: gcdn(NM(n1),NM(n2),&g);
429: NTOQ(g,1,a); *rp = a;
430: }
431: }
432:
1.10 noro 433: int comp_n(N *a,N *b)
1.1 noro 434: {
435: return cmpn(*a,*b);
436: }
437:
1.10 noro 438: void iqrv(VECT a,Q dvr,LIST *rp)
1.1 noro 439: {
440: int i,n;
441: VECT q,r;
442: Q dnd,qi,ri;
443: Q *b;
444: N qn,rn;
445: NODE n0,n1;
446:
447: if ( !dvr )
448: error("iqrv: division by 0");
449: n = a->len; b = (Q *)BDY(a);
450: MKVECT(q,n); MKVECT(r,n);
451: for ( i = 0; i < n; i++ ) {
452: dnd = b[i];
453: if ( !dnd ) {
454: qi = ri = 0;
455: } else {
456: divn(NM(dnd),NM(dvr),&qn,&rn);
457: NTOQ(qn,SGN(dnd)*SGN(dvr),qi);
458: NTOQ(rn,SGN(dnd),ri);
459: }
460: BDY(q)[i] = (pointer)qi; BDY(r)[i] = (pointer)ri;
461: }
462: MKNODE(n1,r,0); MKNODE(n0,q,n1); MKLIST(*rp,n0);
1.7 noro 463: }
464:
465: /*
466: * gcd = GCD(a,b), ca = a/g, cb = b/g
467: */
468:
1.10 noro 469: void igcd_cofactor(Q a,Q b,Q *gcd,Q *ca,Q *cb)
1.7 noro 470: {
471: N gn,tn;
472:
473: if ( !a ) {
474: if ( !b )
475: error("igcd_cofactor : invalid input");
476: else {
477: *ca = 0;
478: *cb = ONE;
479: *gcd = b;
480: }
481: } else if ( !b ) {
482: *ca = ONE;
483: *cb = 0;
484: *gcd = a;
485: } else {
486: gcdn(NM(a),NM(b),&gn); NTOQ(gn,1,*gcd);
487: divsn(NM(a),gn,&tn); NTOQ(tn,SGN(a),*ca);
488: divsn(NM(b),gn,&tn); NTOQ(tn,SGN(b),*cb);
489: }
1.1 noro 490: }
491:
1.10 noro 492: void igcdv(VECT a,Q *rp)
1.1 noro 493: {
494: int i,j,n,nz;
495: N g,gt,q,r;
496: N *c;
497:
498: n = a->len;
499: c = (N *)ALLOCA(n*sizeof(N));
500: for ( i = 0; i < n; i++ )
501: c[i] = BDY(a)[i]?NM((Q)(BDY(a)[i])):0;
502: qsort(c,n,sizeof(N),(int (*) (const void *,const void *))comp_n);
503: for ( ; n && ! *c; n--, c++ );
504:
505: if ( !n ) {
506: *rp = 0; return;
507: } else if ( n == 1 ) {
508: NTOQ(*c,1,*rp); return;
509: }
510: gcdn(c[0],c[1],&g);
1.11 ! noro 511: #if 0
1.1 noro 512: for ( i = 2; i < n; i++ ) {
513: divn(c[i],g,&q,&r);
514: gcdn(g,r,>);
515: if ( !cmpn(g,gt) ) {
516: for ( j = i+1, nz = 0; j < n; j++ ) {
517: divn(c[j],g,&q,&r); c[j] = r;
518: if ( r )
519: nz = 1;
520: }
521: } else
522: g = gt;
523: }
1.11 ! noro 524: #else
! 525: for ( i = 2; i < n; i++ ) {
! 526: gcdn(g,c[i],>); g = gt;
! 527: }
! 528: #endif
1.1 noro 529: NTOQ(g,1,*rp);
530: }
531:
1.10 noro 532: void igcdv_estimate(VECT a,Q *rp)
1.1 noro 533: {
534: int n,i,m;
535: N s,t,u,g;
536: Q *q;
537:
538: n = a->len; q = (Q *)a->body;
539: if ( n == 1 ) {
540: NTOQ(NM(q[0]),1,*rp); return;
541: }
542:
543: m = n/2;
544: for ( i = 0 , s = 0; i < m; i++ ) {
545: addn(s,NM(q[i]),&u); s = u;
546: }
547: for ( t = 0; i < n; i++ ) {
548: addn(t,NM(q[i]),&u); t = u;
549: }
550: gcdn(s,t,&g); NTOQ(g,1,*rp);
551: }
552:
1.10 noro 553: void Pilcm(NODE arg,Obj *rp)
1.1 noro 554: {
555: N g,q,r,l;
556: Q n1,n2,a;
557:
558: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
559: asir_assert(n1,O_N,"ilcm");
560: asir_assert(n2,O_N,"ilcm");
561: if ( !n1 || !n2 )
562: *rp = 0;
563: else {
564: gcdn(NM(n1),NM(n2),&g); divn(NM(n1),g,&q,&r);
565: muln(q,NM(n2),&l); NTOQ(l,1,a); *rp = (Obj)a;
566: }
567: }
568:
1.10 noro 569: void Piand(NODE arg,Q *rp)
1.1 noro 570: {
571: N g;
572: Q n1,n2,a;
573:
574: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
575: asir_assert(n1,O_N,"iand");
576: asir_assert(n2,O_N,"iand");
577: if ( !n1 || !n2 )
578: *rp = 0;
579: else {
580: iand(NM(n1),NM(n2),&g);
581: NTOQ(g,1,a); *rp = a;
582: }
583: }
584:
1.10 noro 585: void Pior(NODE arg,Q *rp)
1.1 noro 586: {
587: N g;
588: Q n1,n2,a;
589:
590: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
591: asir_assert(n1,O_N,"ior");
592: asir_assert(n2,O_N,"ior");
593: if ( !n1 )
594: *rp = n2;
595: else if ( !n2 )
596: *rp = n1;
597: else {
598: ior(NM(n1),NM(n2),&g);
599: NTOQ(g,1,a); *rp = a;
600: }
601: }
602:
1.10 noro 603: void Pixor(NODE arg,Q *rp)
1.1 noro 604: {
605: N g;
606: Q n1,n2,a;
607:
608: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
609: asir_assert(n1,O_N,"ixor");
610: asir_assert(n2,O_N,"ixor");
611: if ( !n1 )
612: *rp = n2;
613: else if ( !n2 )
614: *rp = n1;
615: else {
616: ixor(NM(n1),NM(n2),&g);
617: NTOQ(g,1,a); *rp = a;
618: }
619: }
620:
1.10 noro 621: void Pishift(NODE arg,Q *rp)
1.1 noro 622: {
623: N g;
624: Q n1,s,a;
625:
626: n1 = (Q)ARG0(arg); s = (Q)ARG1(arg);
627: asir_assert(n1,O_N,"ixor");
628: asir_assert(s,O_N,"ixor");
629: if ( !n1 )
630: *rp = 0;
631: else if ( !s )
632: *rp = n1;
633: else {
634: bshiftn(NM(n1),QTOS(s),&g);
635: NTOQ(g,1,a); *rp = a;
636: }
637: }
638:
1.10 noro 639: void isqrt(N a,N *r)
1.1 noro 640: {
641: int k;
642: N x,t,x2,xh,quo,rem;
643:
644: if ( !a )
645: *r = 0;
646: else if ( UNIN(a) )
647: *r = ONEN;
648: else {
649: k = n_bits(a); /* a <= 2^k-1 */
650: bshiftn(ONEN,-((k>>1)+(k&1)),&x); /* a <= x^2 */
651: while ( 1 ) {
652: pwrn(x,2,&t);
653: if ( cmpn(t,a) <= 0 ) {
654: *r = x; return;
655: } else {
656: if ( BD(x)[0] & 1 )
657: addn(x,a,&t);
658: else
659: t = a;
660: bshiftn(x,-1,&x2); divn(t,x2,&quo,&rem);
661: bshiftn(x,1,&xh); addn(quo,xh,&x);
662: }
663: }
664: }
665: }
666:
1.10 noro 667: void iand(N n1,N n2,N *r)
1.1 noro 668: {
669: int d1,d2,d,i;
670: N nr;
671: int *p1,*p2,*pr;
672:
673: d1 = PL(n1); d2 = PL(n2);
674: d = MIN(d1,d2);
675: nr = NALLOC(d);
676: for ( i = 0, p1 = BD(n1), p2 = BD(n2), pr = BD(nr); i < d; i++ )
677: pr[i] = p1[i] & p2[i];
678: for ( i = d-1; i >= 0 && !pr[i]; i-- );
679: if ( i < 0 )
680: *r = 0;
681: else {
682: PL(nr) = i+1; *r = nr;
683: }
684: }
685:
1.10 noro 686: void ior(N n1,N n2,N *r)
1.1 noro 687: {
688: int d1,d2,i;
689: N nr;
690: int *p1,*p2,*pr;
691:
692: if ( PL(n1) < PL(n2) ) {
693: nr = n1; n1 = n2; n2 = nr;
694: }
695: d1 = PL(n1); d2 = PL(n2);
696: *r = nr = NALLOC(d1);
697: for ( i = 0, p1 = BD(n1), p2 = BD(n2), pr = BD(nr); i < d2; i++ )
698: pr[i] = p1[i] | p2[i];
699: for ( ; i < d1; i++ )
700: pr[i] = p1[i];
701: for ( i = d1-1; i >= 0 && !pr[i]; i-- );
702: if ( i < 0 )
703: *r = 0;
704: else {
705: PL(nr) = i+1; *r = nr;
706: }
707: }
708:
1.10 noro 709: void ixor(N n1,N n2,N *r)
1.1 noro 710: {
711: int d1,d2,i;
712: N nr;
713: int *p1,*p2,*pr;
714:
715: if ( PL(n1) < PL(n2) ) {
716: nr = n1; n1 = n2; n2 = nr;
717: }
718: d1 = PL(n1); d2 = PL(n2);
719: *r = nr = NALLOC(d1);
720: for ( i = 0, p1 = BD(n1), p2 = BD(n2), pr = BD(nr); i < d2; i++ )
721: pr[i] = p1[i] ^ p2[i];
722: for ( ; i < d1; i++ )
723: pr[i] = p1[i];
724: for ( i = d1-1; i >= 0 && !pr[i]; i-- );
725: if ( i < 0 )
726: *r = 0;
727: else {
728: PL(nr) = i+1; *r = nr;
729: }
730: }
731:
1.10 noro 732: void Pup2_init_eg(Obj *rp)
1.1 noro 733: {
734: up2_init_eg();
735: *rp = 0;
736: }
737:
1.10 noro 738: void Pup2_show_eg(Obj *rp)
1.1 noro 739: {
740: up2_show_eg();
741: *rp = 0;
742: }
743:
1.10 noro 744: void Pgf2nton(NODE arg,Q *rp)
1.1 noro 745: {
746: if ( !ARG0(arg) )
747: *rp = 0;
748: else
749: up2ton(((GF2N)ARG0(arg))->body,rp);
750: }
751:
1.10 noro 752: void Pntogf2n(NODE arg,GF2N *rp)
1.1 noro 753: {
754: UP2 t;
755:
756: ntoup2(ARG0(arg),&t);
757: MKGF2N(t,*rp);
758: }
759:
1.10 noro 760: void Pup2_inv(NODE arg,P *rp)
1.1 noro 761: {
762: UP2 a,b,t;
763:
764: ptoup2(ARG0(arg),&a);
765: ptoup2(ARG1(arg),&b);
766: invup2(a,b,&t);
767: up2top(t,rp);
768: }
769:
1.10 noro 770: void Pinv(NODE arg,Num *rp)
1.1 noro 771: {
772: Num n;
773: Q mod;
774: MQ r;
775: int inv;
776:
777: n = (Num)ARG0(arg); mod = (Q)ARG1(arg);
778: asir_assert(n,O_N,"inv");
779: asir_assert(mod,O_N,"inv");
780: if ( !n || !mod )
781: error("inv: invalid input");
782: else
783: switch ( NID(n) ) {
784: case N_Q:
785: invl((Q)n,mod,(Q *)rp);
786: break;
787: case N_M:
788: inv = invm(CONT((MQ)n),QTOS(mod));
789: STOMQ(inv,r);
790: *rp = (Num)r;
791: break;
792: default:
793: error("inv: invalid input");
794: }
795: }
796:
1.10 noro 797: void Pfac(NODE arg,Q *rp)
1.1 noro 798: {
799: asir_assert(ARG0(arg),O_N,"fac");
800: factorial(QTOS((Q)ARG0(arg)),rp);
801: }
802:
1.10 noro 803: void Plrandom(NODE arg,Q *rp)
1.1 noro 804: {
805: N r;
806:
807: asir_assert(ARG0(arg),O_N,"lrandom");
808: randomn(QTOS((Q)ARG0(arg)),&r);
809: NTOQ(r,1,*rp);
810: }
811:
1.10 noro 812: void Prandom(NODE arg,Q *rp)
1.1 noro 813: {
814: unsigned int r;
815:
816: #if 0
817: #if defined(_PA_RISC1_1)
818: r = mrand48()&BMASK;
819: #else
820: if ( arg )
821: srandom(QTOS((Q)ARG0(arg)));
822: r = random()&BMASK;
823: #endif
824: #endif
825: if ( arg )
826: mt_sgenrand(QTOS((Q)ARG0(arg)));
827: r = mt_genrand();
828: UTOQ(r,*rp);
829: }
830:
1.6 noro 831: #if defined(VISUAL)
1.1 noro 832: void srandom(unsigned int);
833:
834: static unsigned int R_Next;
835:
836: unsigned int random() {
837: if ( !R_Next )
838: R_Next = 1;
839: return R_Next = (R_Next * 1103515245 + 12345);
840: }
841:
1.10 noro 842: void srandom(unsigned int s)
1.1 noro 843: {
844: if ( s )
845: R_Next = s;
846: else if ( !R_Next )
847: R_Next = 1;
848: }
849: #endif
850:
1.10 noro 851: void Pprime(NODE arg,Q *rp)
1.1 noro 852: {
853: int i;
854:
855: asir_assert(ARG0(arg),O_N,"prime");
856: i = QTOS((Q)ARG0(arg));
857: if ( i < 0 || i >= 1900 )
858: *rp = 0;
859: else
860: STOQ(sprime[i],*rp);
861: }
862:
1.10 noro 863: void Plprime(NODE arg,Q *rp)
1.1 noro 864: {
1.9 noro 865: int i,p;
1.1 noro 866:
867: asir_assert(ARG0(arg),O_N,"lprime");
868: i = QTOS((Q)ARG0(arg));
1.9 noro 869: if ( i < 0 )
1.1 noro 870: *rp = 0;
1.9 noro 871: else
872: p = get_lprime(i);
873: STOQ(p,*rp);
1.1 noro 874: }
875:
876: extern int up_kara_mag, up_tkara_mag, up_fft_mag;
877:
1.10 noro 878: void Pset_upfft(NODE arg,Q *rp)
1.1 noro 879: {
880: if ( arg ) {
881: asir_assert(ARG0(arg),O_N,"set_upfft");
882: up_fft_mag = QTOS((Q)ARG0(arg));
883: }
884: STOQ(up_fft_mag,*rp);
885: }
886:
1.10 noro 887: void Pset_upkara(NODE arg,Q *rp)
1.1 noro 888: {
889: if ( arg ) {
890: asir_assert(ARG0(arg),O_N,"set_upkara");
891: up_kara_mag = QTOS((Q)ARG0(arg));
892: }
893: STOQ(up_kara_mag,*rp);
894: }
895:
1.10 noro 896: void Pset_uptkara(NODE arg,Q *rp)
1.1 noro 897: {
898: if ( arg ) {
899: asir_assert(ARG0(arg),O_N,"set_uptkara");
900: up_tkara_mag = QTOS((Q)ARG0(arg));
901: }
902: STOQ(up_tkara_mag,*rp);
903: }
904:
905: extern int up2_kara_mag;
906:
1.10 noro 907: void Pset_up2kara(NODE arg,Q *rp)
1.1 noro 908: {
909: if ( arg ) {
910: asir_assert(ARG0(arg),O_N,"set_up2kara");
911: up2_kara_mag = QTOS((Q)ARG0(arg));
912: }
913: STOQ(up2_kara_mag,*rp);
914: }
915:
1.10 noro 916: void Pigcdbin(NODE arg,Obj *rp)
1.1 noro 917: {
918: N g;
919: Q n1,n2,a;
920:
921: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
922: asir_assert(n1,O_N,"igcd");
923: asir_assert(n2,O_N,"igcd");
924: if ( !n1 )
925: *rp = (Obj)n2;
926: else if ( !n2 )
927: *rp = (Obj)n1;
928: else {
929: gcdbinn(NM(n1),NM(n2),&g);
930: NTOQ(g,1,a); *rp = (Obj)a;
931: }
932: }
933:
1.10 noro 934: void Pigcdbmod(NODE arg,Obj *rp)
1.1 noro 935: {
936: N g;
937: Q n1,n2,a;
938:
939: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
940: asir_assert(n1,O_N,"igcdbmod");
941: asir_assert(n2,O_N,"igcdbmod");
942: if ( !n1 )
943: *rp = (Obj)n2;
944: else if ( !n2 )
945: *rp = (Obj)n1;
946: else {
947: gcdbmodn(NM(n1),NM(n2),&g);
948: NTOQ(g,1,a); *rp = (Obj)a;
949: }
950: }
951:
1.10 noro 952: void Pigcdacc(NODE arg,Obj *rp)
1.1 noro 953: {
954: N g;
955: Q n1,n2,a;
956:
957: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
958: asir_assert(n1,O_N,"igcdacc");
959: asir_assert(n2,O_N,"igcdacc");
960: if ( !n1 )
961: *rp = (Obj)n2;
962: else if ( !n2 )
963: *rp = (Obj)n1;
964: else {
965: gcdaccn(NM(n1),NM(n2),&g);
966: NTOQ(g,1,a); *rp = (Obj)a;
967: }
968: }
969:
1.10 noro 970: void PigcdEuc(NODE arg,Obj *rp)
1.1 noro 971: {
972: N g;
973: Q n1,n2,a;
974:
975: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
976: asir_assert(n1,O_N,"igcdbmod");
977: asir_assert(n2,O_N,"igcdbmod");
978: if ( !n1 )
979: *rp = (Obj)n2;
980: else if ( !n2 )
981: *rp = (Obj)n1;
982: else {
983: gcdEuclidn(NM(n1),NM(n2),&g);
984: NTOQ(g,1,a); *rp = (Obj)a;
985: }
986: }
987:
988: extern int igcd_algorithm;
989: /* == 0 : Euclid,
990: * == 1 : binary,
991: * == 2 : bmod,
992: * >= 3 : (Weber's accelerated)/(Jebelean's generalized binary) algorithm,
993: */
994: extern int igcd_thre_inidiv;
995: /*
996: * In the non-Euclidean algorithms, if the ratio of the lengths (number
997: * of words) of two integers is >= igcd_thre_inidiv, we first perform
998: * remainder calculation.
999: * If == 0, this remainder calculation is not performed.
1000: */
1001: extern int igcdacc_thre;
1002: /*
1003: * In the accelerated algorithm, if the bit-lengths of two integers is
1004: * > igcdacc_thre, "bmod" reduction is done.
1005: */
1006:
1.10 noro 1007: void Pigcdcntl(NODE arg,Obj *rp)
1.1 noro 1008: {
1009: Obj p;
1010: Q a;
1011: int k, m;
1012:
1013: if ( arg ) {
1014: p = (Obj)ARG0(arg);
1015: if ( !p ) {
1016: igcd_algorithm = 0;
1017: *rp = p;
1018: return;
1019: } else if ( OID(p) == O_N ) {
1020: k = QTOS((Q)p);
1021: a = (Q)p;
1022: if ( k >= 0 ) igcd_algorithm = k;
1023: else if ( k == -1 ) {
1024: ret_thre:
1025: k = - igcd_thre_inidiv - igcdacc_thre*10000;
1026: STOQ(k,a);
1027: *rp = (Obj)a;
1028: return;
1029: } else {
1030: if ( (m = (-k)%10000) != 0 ) igcd_thre_inidiv = m;
1031: if ( (m = -k/10000) != 0 ) igcdacc_thre = m;
1032: goto ret_thre;
1033: }
1034: } else if ( OID(p) == O_STR ) {
1035: char *n = BDY((STRING) p);
1036:
1037: if ( !strcmp( n, "binary" ) || !strcmp( n, "Binary" )
1038: || !strcmp( n, "bin" ) || !strcmp( n, "Bin" ) )
1039: k = igcd_algorithm = 1;
1040: else if ( !strcmp( n, "bmod" ) || !strcmp( n, "Bmod" ) )
1041: igcd_algorithm = 2;
1042: else if ( !strcmp( n, "euc" ) || !strcmp( n, "Euc" )
1043: || !strcmp( n, "euclid" ) || !strcmp( n, "Euclid" ) )
1044: igcd_algorithm = 0;
1045: else if ( !strcmp( n, "acc" ) || !strcmp( n, "Acc" )
1046: || !strcmp( n, "gen" ) || !strcmp( n, "Gen" )
1047: || !strcmp( n, "genbin" ) || !strcmp( n, "GenBin" ) )
1048: igcd_algorithm = 3;
1049: else error( "igcdhow : invalid algorithm specification" );
1050: }
1051: }
1052: STOQ(igcd_algorithm,a);
1053: *rp = (Obj)a;
1054: return;
1055: }