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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: *
1.5 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/builtin/int.c,v 1.4 2000/08/21 08:31:20 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 iand(), ior(), ixor();
61: void isqrt();
62: void Plrandom();
63: void Pset_upkara(), Pset_uptkara(), Pset_up2kara(), Pset_upfft();
64: void Pmt_save(), Pmt_load();
65: void Psmall_jacobi();
66: void Pdp_set_mpi();
1.2 noro 67: void Pntoint32(),Pint32ton();
1.1 noro 68:
69: #ifdef HMEXT
70: void Pigcdbin(), Pigcdbmod(), PigcdEuc(), Pigcdacc(), Pigcdcntl();
71:
72: void Pihex();
73: void Pimaxrsh(), Pilen();
74: void Ptype_t_NB();
75:
76: #endif /* HMEXT */
77:
78: struct ftab int_tab[] = {
79: {"dp_set_mpi",Pdp_set_mpi,-1},
80: {"isqrt",Pisqrt,1},
81: {"idiv",Pidiv,2},
82: {"irem",Pirem,2},
83: {"iqr",Piqr,2},
84: {"igcd",Pigcd,-2},
85: {"ilcm",Pilcm,2},
86: {"up2_inv",Pup2_inv,2},
87: {"up2_init_eg",Pup2_init_eg,0},
88: {"up2_show_eg",Pup2_show_eg,0},
89: {"type_t_NB",Ptype_t_NB,2},
90: {"gf2nton",Pgf2nton,1},
91: {"ntogf2n",Pntogf2n,1},
92: {"set_upkara",Pset_upkara,-1},
93: {"set_uptkara",Pset_uptkara,-1},
94: {"set_up2kara",Pset_up2kara,-1},
95: {"set_upfft",Pset_upfft,-1},
96: {"inv",Pinv,2},
97: {"inttorat",Pinttorat,3},
98: {"fac",Pfac,1},
99: {"prime",Pprime,1},
100: {"lprime",Plprime,1},
101: {"random",Prandom,-1},
102: {"lrandom",Plrandom,1},
103: {"iand",Piand,2},
104: {"ior",Pior,2},
105: {"ixor",Pixor,2},
106: {"ishift",Pishift,2},
107: {"small_jacobi",Psmall_jacobi,2},
108: #ifdef HMEXT
109: {"igcdbin",Pigcdbin,2}, /* HM@CCUT extension */
110: {"igcdbmod",Pigcdbmod,2}, /* HM@CCUT extension */
111: {"igcdeuc",PigcdEuc,2}, /* HM@CCUT extension */
112: {"igcdacc",Pigcdacc,2}, /* HM@CCUT extension */
113: {"igcdcntl",Pigcdcntl,-1}, /* HM@CCUT extension */
114: {"ihex",Pihex,1}, /* HM@CCUT extension */
115: {"imaxrsh",Pimaxrsh,1}, /* HM@CCUT extension */
116: {"ilen",Pilen,1}, /* HM@CCUT extension */
117: #endif /* HMEXT */
118: {"mt_save",Pmt_save,1},
119: {"mt_load",Pmt_load,1},
1.2 noro 120: {"ntoint32",Pntoint32,1},
121: {"int32ton",Pint32ton,1},
1.1 noro 122: {0,0,0},
123: };
124:
125: static int is_prime_small(unsigned int);
126: static unsigned int gcd_small(unsigned int,unsigned int);
127: int TypeT_NB_check(unsigned int, unsigned int);
128: int mpi_mag;
1.2 noro 129:
130: void Pntoint32(arg,rp)
131: NODE arg;
132: USINT *rp;
133: {
134: Q q;
1.3 noro 135: unsigned int t;
1.2 noro 136:
137: asir_assert(ARG0(arg),O_N,"ntoint32");
138: q = (Q)ARG0(arg);
139: if ( !q ) {
140: MKUSINT(*rp,0);
141: return;
142: }
1.3 noro 143: if ( NID(q)!=N_Q || !INT(q) || PL(NM(q))>1 )
1.2 noro 144: error("ntoint32 : invalid argument");
1.3 noro 145: t = BD(NM(q))[0];
146: if ( SGN(q) < 0 )
147: t = -t;
148: MKUSINT(*rp,t);
1.2 noro 149: }
150:
151: void Pint32ton(arg,rp)
152: NODE arg;
153: Q *rp;
154: {
1.3 noro 155: int t;
1.2 noro 156:
157: asir_assert(ARG0(arg),O_USINT,"int32ton");
1.3 noro 158: t = (int)BDY((USINT)ARG0(arg));
159: STOQ(t,*rp);
1.2 noro 160: }
1.1 noro 161:
162: void Pdp_set_mpi(arg,rp)
163: NODE arg;
164: Q *rp;
165: {
166: if ( arg ) {
167: asir_assert(ARG0(arg),O_N,"dp_set_mpi");
168: mpi_mag = QTOS((Q)ARG0(arg));
169: }
170: STOQ(mpi_mag,*rp);
171: }
172:
173: void Psmall_jacobi(arg,rp)
174: NODE arg;
175: Q *rp;
176: {
177: Q a,m;
178: int a0,m0,s;
179:
180: a = (Q)ARG0(arg);
181: m = (Q)ARG1(arg);
182: asir_assert(a,O_N,"small_jacobi");
183: asir_assert(m,O_N,"small_jacobi");
184: if ( !a )
185: *rp = ONE;
186: else if ( !m || !INT(m) || !INT(a)
187: || PL(NM(m))>1 || PL(NM(a))>1 || SGN(m) < 0 || EVENN(NM(m)) )
188: error("small_jacobi : invalid input");
189: else {
190: a0 = QTOS(a); m0 = QTOS(m);
191: s = small_jacobi(a0,m0);
192: STOQ(s,*rp);
193: }
194: }
195:
196: int small_jacobi(a,m)
197: int a,m;
198: {
199: int m4,m8,a4,j1,i,s;
200:
201: a %= m;
202: if ( a == 0 || a == 1 )
203: return 1;
204: else if ( a < 0 ) {
205: j1 = small_jacobi(-a,m);
206: m4 = m%4;
207: return m4==1?j1:-j1;
208: } else {
209: for ( i = 0; a && !(a&1); i++, a >>= 1 );
210: if ( i&1 ) {
211: m8 = m%8;
212: s = (m8==1||m8==7) ? 1 : -1;
213: } else
214: s = 1;
215: /* a, m are odd */
216: j1 = small_jacobi(m%a,a);
217: m4 = m%4; a4 = a%4;
218: s *= (m4==1||a4==1) ? 1 : -1;
219: return j1*s;
220: }
221: }
222:
223: void Ptype_t_NB(arg,rp)
224: NODE arg;
225: Q *rp;
226: {
227: if ( TypeT_NB_check(QTOS((Q)ARG0(arg)),QTOS((Q)ARG1(arg))))
228: *rp = ONE;
229: else
230: *rp = 0;
231: }
232:
233: int TypeT_NB_check(unsigned int m, unsigned int t)
234: {
235: unsigned int p,k,u,h,d;
236:
237: if ( !(m%8) )
238: return 0;
239: p = t*m+1;
240: if ( !is_prime_small(p) )
241: return 0;
242: for ( k = 1, u = 2%p; ; k++ )
243: if ( u == 1 )
244: break;
245: else
246: u = (2*u)%p;
247: h = t*m/k;
248: d = gcd_small(h,m);
249: return d == 1 ? 1 : 0;
250: }
251:
252: /*
253: * a simple prime checker
254: * return value: 1 --- prime number
255: * 0 --- composite number
256: */
257:
258: static int is_prime_small(unsigned int a)
259: {
260: unsigned int b,t,i;
261:
262: if ( !(a%2) ) return 0;
263: for ( t = a, i = 0; t; i++, t >>= 1 );
264: /* b >= sqrt(a) */
265: b = 1<<((i+1)/2);
266:
267: /* divisibility test by all odd numbers <= b */
268: for ( i = 3; i <= b; i += 2 )
269: if ( !(a%i) )
270: return 0;
271: return 1;
272: }
273:
274: /*
275: * gcd for unsigned int as integers
276: * return value: GCD(a,b)
277: *
278: */
279:
280:
281: static unsigned int gcd_small(unsigned int a,unsigned int b)
282: {
283: unsigned int t;
284:
285: if ( b > a ) {
286: t = a; a = b; b = t;
287: }
288: /* Euclid's algorithm */
289: while ( 1 )
290: if ( !(t = a%b) ) return b;
291: else {
292: a = b; b = t;
293: }
294: }
295:
296: void Pmt_save(arg,rp)
297: NODE arg;
298: Q *rp;
299: {
300: int ret;
301:
302: ret = mt_save(BDY((STRING)ARG0(arg)));
303: STOQ(ret,*rp);
304: }
305:
306: void Pmt_load(arg,rp)
307: NODE arg;
308: Q *rp;
309: {
310: int ret;
311:
312: ret = mt_load(BDY((STRING)ARG0(arg)));
313: STOQ(ret,*rp);
314: }
315:
316: void Pisqrt(arg,rp)
317: NODE arg;
318: Q *rp;
319: {
320: Q a;
321: N r;
322:
323: a = (Q)ARG0(arg);
324: asir_assert(a,O_N,"isqrt");
325: if ( !a )
326: *rp = 0;
327: else if ( SGN(a) < 0 )
328: error("isqrt : negative argument");
329: else {
330: isqrt(NM(a),&r);
331: NTOQ(r,1,*rp);
332: }
333: }
334:
335: void Pidiv(arg,rp)
336: NODE arg;
337: Obj *rp;
338: {
339: N q,r;
340: Q a;
341: Q dnd,dvr;
342:
343: dnd = (Q)ARG0(arg); dvr = (Q)ARG1(arg);
344: asir_assert(dnd,O_N,"idiv");
345: asir_assert(dvr,O_N,"idiv");
346: if ( !dvr )
347: error("idiv: division by 0");
348: else if ( !dnd )
349: *rp = 0;
350: else {
351: divn(NM(dnd),NM(dvr),&q,&r);
352: NTOQ(q,SGN(dnd)*SGN(dvr),a); *rp = (Obj)a;
353: }
354: }
355:
356: void Pirem(arg,rp)
357: NODE arg;
358: Obj *rp;
359: {
360: N q,r;
361: Q a;
362: Q dnd,dvr;
363:
364: dnd = (Q)ARG0(arg); dvr = (Q)ARG1(arg);
365: asir_assert(dnd,O_N,"irem");
366: asir_assert(dvr,O_N,"irem");
367: if ( !dvr )
368: error("irem: division by 0");
369: else if ( !dnd )
370: *rp = 0;
371: else {
372: divn(NM(dnd),NM(dvr),&q,&r);
373: NTOQ(r,SGN(dnd),a); *rp = (Obj)a;
374: }
375: }
376:
377: void Piqr(arg,rp)
378: NODE arg;
379: LIST *rp;
380: {
381: N q,r;
382: Q a,b;
383: Q dnd,dvr;
384: NODE node1,node2;
385:
386: dnd = (Q)ARG0(arg); dvr = (Q)ARG1(arg);
387: if ( !dvr )
388: error("iqr: division by 0");
389: else if ( !dnd )
390: a = b = 0;
391: else if ( OID(dnd) == O_VECT ) {
392: iqrv((VECT)dnd,dvr,rp); return;
393: } else {
394: asir_assert(dnd,O_N,"iqr");
395: asir_assert(dvr,O_N,"iqr");
396: divn(NM(dnd),NM(dvr),&q,&r);
397: NTOQ(q,SGN(dnd)*SGN(dvr),a);
398: NTOQ(r,SGN(dnd),b);
399: }
400: MKNODE(node2,b,0); MKNODE(node1,a,node2); MKLIST(*rp,node1);
401: }
402:
403: void Pinttorat(arg,rp)
404: NODE arg;
405: LIST *rp;
406: {
407: Q cq,qq,t,u1,v1,r1,nm;
408: N m,b,q,r,c,u2,v2,r2;
409: NODE node1,node2;
410: P p;
411:
412: asir_assert(ARG0(arg),O_N,"inttorat");
413: asir_assert(ARG1(arg),O_N,"inttorat");
414: asir_assert(ARG2(arg),O_N,"inttorat");
415: cq = (Q)ARG0(arg); m = NM((Q)ARG1(arg)); b = NM((Q)ARG2(arg));
416: if ( !cq ) {
417: MKNODE(node2,(pointer)ONE,0); MKNODE(node1,0,node2); MKLIST(*rp,node1);
418: return;
419: }
420: divn(NM(cq),m,&q,&r);
421: if ( !r ) {
422: MKNODE(node2,(pointer)ONE,0); MKNODE(node1,0,node2); MKLIST(*rp,node1);
423: return;
424: } else if ( SGN(cq) < 0 ) {
425: subn(m,r,&c);
426: } else
427: c = r;
428: u1 = 0; v1 = ONE; u2 = m; v2 = c;
429: while ( cmpn(v2,b) >= 0 ) {
430: divn(u2,v2,&q,&r2); u2 = v2; v2 = r2;
431: NTOQ(q,1,qq); mulq(qq,v1,&t); subq(u1,t,&r1); u1 = v1; v1 = r1;
432: }
433: if ( cmpn(NM(v1),b) >= 0 )
434: *rp = 0;
435: else {
436: if ( SGN(v1) < 0 ) {
437: chsgnp((P)v1,&p); v1 = (Q)p; NTOQ(v2,-1,nm);
438: } else
439: NTOQ(v2,1,nm);
440: MKNODE(node2,v1,0); MKNODE(node1,nm,node2); MKLIST(*rp,node1);
441: }
442: }
443:
444: void Pigcd(arg,rp)
445: NODE arg;
446: Q *rp;
447: {
448: N g;
449: Q n1,n2,a;
450:
451: if ( argc(arg) == 1 ) {
452: igcdv((VECT)ARG0(arg),rp);
453: return;
454: }
455: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
456: asir_assert(n1,O_N,"igcd");
457: asir_assert(n2,O_N,"igcd");
458: if ( !n1 )
459: *rp = n2;
460: else if ( !n2 )
461: *rp = n1;
462: else {
463: gcdn(NM(n1),NM(n2),&g);
464: NTOQ(g,1,a); *rp = a;
465: }
466: }
467:
468: int comp_n(a,b)
469: N *a,*b;
470: {
471: return cmpn(*a,*b);
472: }
473:
474: void iqrv(a,dvr,rp)
475: VECT a;
476: Q dvr;
477: LIST *rp;
478: {
479: int i,n;
480: VECT q,r;
481: Q dnd,qi,ri;
482: Q *b;
483: N qn,rn;
484: NODE n0,n1;
485:
486: if ( !dvr )
487: error("iqrv: division by 0");
488: n = a->len; b = (Q *)BDY(a);
489: MKVECT(q,n); MKVECT(r,n);
490: for ( i = 0; i < n; i++ ) {
491: dnd = b[i];
492: if ( !dnd ) {
493: qi = ri = 0;
494: } else {
495: divn(NM(dnd),NM(dvr),&qn,&rn);
496: NTOQ(qn,SGN(dnd)*SGN(dvr),qi);
497: NTOQ(rn,SGN(dnd),ri);
498: }
499: BDY(q)[i] = (pointer)qi; BDY(r)[i] = (pointer)ri;
500: }
501: MKNODE(n1,r,0); MKNODE(n0,q,n1); MKLIST(*rp,n0);
502: }
503:
504: void igcdv(a,rp)
505: VECT a;
506: Q *rp;
507: {
508: int i,j,n,nz;
509: N g,gt,q,r;
510: N *c;
511:
512: n = a->len;
513: c = (N *)ALLOCA(n*sizeof(N));
514: for ( i = 0; i < n; i++ )
515: c[i] = BDY(a)[i]?NM((Q)(BDY(a)[i])):0;
516: qsort(c,n,sizeof(N),(int (*) (const void *,const void *))comp_n);
517: for ( ; n && ! *c; n--, c++ );
518:
519: if ( !n ) {
520: *rp = 0; return;
521: } else if ( n == 1 ) {
522: NTOQ(*c,1,*rp); return;
523: }
524: gcdn(c[0],c[1],&g);
525: for ( i = 2; i < n; i++ ) {
526: divn(c[i],g,&q,&r);
527: gcdn(g,r,>);
528: if ( !cmpn(g,gt) ) {
529: for ( j = i+1, nz = 0; j < n; j++ ) {
530: divn(c[j],g,&q,&r); c[j] = r;
531: if ( r )
532: nz = 1;
533: }
534: } else
535: g = gt;
536: }
537: NTOQ(g,1,*rp);
538: }
539:
540: void igcdv_estimate(a,rp)
541: VECT a;
542: Q *rp;
543: {
544: int n,i,m;
545: N s,t,u,g;
546: Q *q;
547:
548: n = a->len; q = (Q *)a->body;
549: if ( n == 1 ) {
550: NTOQ(NM(q[0]),1,*rp); return;
551: }
552:
553: m = n/2;
554: for ( i = 0 , s = 0; i < m; i++ ) {
555: addn(s,NM(q[i]),&u); s = u;
556: }
557: for ( t = 0; i < n; i++ ) {
558: addn(t,NM(q[i]),&u); t = u;
559: }
560: gcdn(s,t,&g); NTOQ(g,1,*rp);
561: }
562:
563: void Pilcm(arg,rp)
564: NODE arg;
565: Obj *rp;
566: {
567: N g,q,r,l;
568: Q n1,n2,a;
569:
570: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
571: asir_assert(n1,O_N,"ilcm");
572: asir_assert(n2,O_N,"ilcm");
573: if ( !n1 || !n2 )
574: *rp = 0;
575: else {
576: gcdn(NM(n1),NM(n2),&g); divn(NM(n1),g,&q,&r);
577: muln(q,NM(n2),&l); NTOQ(l,1,a); *rp = (Obj)a;
578: }
579: }
580:
581: void Piand(arg,rp)
582: NODE arg;
583: Q *rp;
584: {
585: N g;
586: Q n1,n2,a;
587:
588: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
589: asir_assert(n1,O_N,"iand");
590: asir_assert(n2,O_N,"iand");
591: if ( !n1 || !n2 )
592: *rp = 0;
593: else {
594: iand(NM(n1),NM(n2),&g);
595: NTOQ(g,1,a); *rp = a;
596: }
597: }
598:
599: void Pior(arg,rp)
600: NODE arg;
601: Q *rp;
602: {
603: N g;
604: Q n1,n2,a;
605:
606: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
607: asir_assert(n1,O_N,"ior");
608: asir_assert(n2,O_N,"ior");
609: if ( !n1 )
610: *rp = n2;
611: else if ( !n2 )
612: *rp = n1;
613: else {
614: ior(NM(n1),NM(n2),&g);
615: NTOQ(g,1,a); *rp = a;
616: }
617: }
618:
619: void Pixor(arg,rp)
620: NODE arg;
621: Q *rp;
622: {
623: N g;
624: Q n1,n2,a;
625:
626: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
627: asir_assert(n1,O_N,"ixor");
628: asir_assert(n2,O_N,"ixor");
629: if ( !n1 )
630: *rp = n2;
631: else if ( !n2 )
632: *rp = n1;
633: else {
634: ixor(NM(n1),NM(n2),&g);
635: NTOQ(g,1,a); *rp = a;
636: }
637: }
638:
639: void Pishift(arg,rp)
640: NODE arg;
641: Q *rp;
642: {
643: N g;
644: Q n1,s,a;
645:
646: n1 = (Q)ARG0(arg); s = (Q)ARG1(arg);
647: asir_assert(n1,O_N,"ixor");
648: asir_assert(s,O_N,"ixor");
649: if ( !n1 )
650: *rp = 0;
651: else if ( !s )
652: *rp = n1;
653: else {
654: bshiftn(NM(n1),QTOS(s),&g);
655: NTOQ(g,1,a); *rp = a;
656: }
657: }
658:
659: void isqrt(a,r)
660: N a,*r;
661: {
662: int k;
663: N x,t,x2,xh,quo,rem;
664:
665: if ( !a )
666: *r = 0;
667: else if ( UNIN(a) )
668: *r = ONEN;
669: else {
670: k = n_bits(a); /* a <= 2^k-1 */
671: bshiftn(ONEN,-((k>>1)+(k&1)),&x); /* a <= x^2 */
672: while ( 1 ) {
673: pwrn(x,2,&t);
674: if ( cmpn(t,a) <= 0 ) {
675: *r = x; return;
676: } else {
677: if ( BD(x)[0] & 1 )
678: addn(x,a,&t);
679: else
680: t = a;
681: bshiftn(x,-1,&x2); divn(t,x2,&quo,&rem);
682: bshiftn(x,1,&xh); addn(quo,xh,&x);
683: }
684: }
685: }
686: }
687:
688: void iand(n1,n2,r)
689: N n1,n2,*r;
690: {
691: int d1,d2,d,i;
692: N nr;
693: int *p1,*p2,*pr;
694:
695: d1 = PL(n1); d2 = PL(n2);
696: d = MIN(d1,d2);
697: nr = NALLOC(d);
698: for ( i = 0, p1 = BD(n1), p2 = BD(n2), pr = BD(nr); i < d; i++ )
699: pr[i] = p1[i] & p2[i];
700: for ( i = d-1; i >= 0 && !pr[i]; i-- );
701: if ( i < 0 )
702: *r = 0;
703: else {
704: PL(nr) = i+1; *r = nr;
705: }
706: }
707:
708: void ior(n1,n2,r)
709: N n1,n2,*r;
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:
732: void ixor(n1,n2,r)
733: N n1,n2,*r;
734: {
735: int d1,d2,i;
736: N nr;
737: int *p1,*p2,*pr;
738:
739: if ( PL(n1) < PL(n2) ) {
740: nr = n1; n1 = n2; n2 = nr;
741: }
742: d1 = PL(n1); d2 = PL(n2);
743: *r = nr = NALLOC(d1);
744: for ( i = 0, p1 = BD(n1), p2 = BD(n2), pr = BD(nr); i < d2; i++ )
745: pr[i] = p1[i] ^ p2[i];
746: for ( ; i < d1; i++ )
747: pr[i] = p1[i];
748: for ( i = d1-1; i >= 0 && !pr[i]; i-- );
749: if ( i < 0 )
750: *r = 0;
751: else {
752: PL(nr) = i+1; *r = nr;
753: }
754: }
755:
756: void Pup2_init_eg(rp)
757: Obj *rp;
758: {
759: up2_init_eg();
760: *rp = 0;
761: }
762:
763: void Pup2_show_eg(rp)
764: Obj *rp;
765: {
766: up2_show_eg();
767: *rp = 0;
768: }
769:
770: void Pgf2nton(arg,rp)
771: NODE arg;
772: Q *rp;
773: {
774: if ( !ARG0(arg) )
775: *rp = 0;
776: else
777: up2ton(((GF2N)ARG0(arg))->body,rp);
778: }
779:
780: void Pntogf2n(arg,rp)
781: NODE arg;
782: GF2N *rp;
783: {
784: UP2 t;
785:
786: ntoup2(ARG0(arg),&t);
787: MKGF2N(t,*rp);
788: }
789:
790: void Pup2_inv(arg,rp)
791: NODE arg;
792: P *rp;
793: {
794: UP2 a,b,t;
795:
796: ptoup2(ARG0(arg),&a);
797: ptoup2(ARG1(arg),&b);
798: invup2(a,b,&t);
799: up2top(t,rp);
800: }
801:
802: void Pinv(arg,rp)
803: NODE arg;
804: Num *rp;
805: {
806: Num n;
807: Q mod;
808: MQ r;
809: int inv;
810:
811: n = (Num)ARG0(arg); mod = (Q)ARG1(arg);
812: asir_assert(n,O_N,"inv");
813: asir_assert(mod,O_N,"inv");
814: if ( !n || !mod )
815: error("inv: invalid input");
816: else
817: switch ( NID(n) ) {
818: case N_Q:
819: invl((Q)n,mod,(Q *)rp);
820: break;
821: case N_M:
822: inv = invm(CONT((MQ)n),QTOS(mod));
823: STOMQ(inv,r);
824: *rp = (Num)r;
825: break;
826: default:
827: error("inv: invalid input");
828: }
829: }
830:
831: void Pfac(arg,rp)
832: NODE arg;
833: Q *rp;
834: {
835: asir_assert(ARG0(arg),O_N,"fac");
836: factorial(QTOS((Q)ARG0(arg)),rp);
837: }
838:
839: void Plrandom(arg,rp)
840: NODE arg;
841: Q *rp;
842: {
843: N r;
844:
845: asir_assert(ARG0(arg),O_N,"lrandom");
846: randomn(QTOS((Q)ARG0(arg)),&r);
847: NTOQ(r,1,*rp);
848: }
849:
850: void Prandom(arg,rp)
851: NODE arg;
852: Q *rp;
853: {
854: unsigned int r;
855:
856: #if 0
857: #if defined(_PA_RISC1_1)
858: r = mrand48()&BMASK;
859: #else
860: if ( arg )
861: srandom(QTOS((Q)ARG0(arg)));
862: r = random()&BMASK;
863: #endif
864: #endif
865: if ( arg )
866: mt_sgenrand(QTOS((Q)ARG0(arg)));
867: r = mt_genrand();
868: UTOQ(r,*rp);
869: }
870:
871: #if defined(VISUAL) || defined(THINK_C)
872: void srandom(unsigned int);
873:
874: static unsigned int R_Next;
875:
876: unsigned int random() {
877: if ( !R_Next )
878: R_Next = 1;
879: return R_Next = (R_Next * 1103515245 + 12345);
880: }
881:
882: void srandom(s)
883: unsigned int s;
884: {
885: if ( s )
886: R_Next = s;
887: else if ( !R_Next )
888: R_Next = 1;
889: }
890: #endif
891:
892: void Pprime(arg,rp)
893: NODE arg;
894: Q *rp;
895: {
896: int i;
897:
898: asir_assert(ARG0(arg),O_N,"prime");
899: i = QTOS((Q)ARG0(arg));
900: if ( i < 0 || i >= 1900 )
901: *rp = 0;
902: else
903: STOQ(sprime[i],*rp);
904: }
905:
906: void Plprime(arg,rp)
907: NODE arg;
908: Q *rp;
909: {
910: int i;
911:
912: asir_assert(ARG0(arg),O_N,"lprime");
913: i = QTOS((Q)ARG0(arg));
914: if ( i < 0 || i >= 1000 )
915: *rp = 0;
916: else
917: STOQ(lprime[i],*rp);
918: }
919:
920: extern int up_kara_mag, up_tkara_mag, up_fft_mag;
921:
922: void Pset_upfft(arg,rp)
923: NODE arg;
924: Q *rp;
925: {
926: if ( arg ) {
927: asir_assert(ARG0(arg),O_N,"set_upfft");
928: up_fft_mag = QTOS((Q)ARG0(arg));
929: }
930: STOQ(up_fft_mag,*rp);
931: }
932:
933: void Pset_upkara(arg,rp)
934: NODE arg;
935: Q *rp;
936: {
937: if ( arg ) {
938: asir_assert(ARG0(arg),O_N,"set_upkara");
939: up_kara_mag = QTOS((Q)ARG0(arg));
940: }
941: STOQ(up_kara_mag,*rp);
942: }
943:
944: void Pset_uptkara(arg,rp)
945: NODE arg;
946: Q *rp;
947: {
948: if ( arg ) {
949: asir_assert(ARG0(arg),O_N,"set_uptkara");
950: up_tkara_mag = QTOS((Q)ARG0(arg));
951: }
952: STOQ(up_tkara_mag,*rp);
953: }
954:
955: extern int up2_kara_mag;
956:
957: void Pset_up2kara(arg,rp)
958: NODE arg;
959: Q *rp;
960: {
961: if ( arg ) {
962: asir_assert(ARG0(arg),O_N,"set_up2kara");
963: up2_kara_mag = QTOS((Q)ARG0(arg));
964: }
965: STOQ(up2_kara_mag,*rp);
966: }
967:
968: #ifdef HMEXT
969: void Pigcdbin(arg,rp)
970: NODE arg;
971: Obj *rp;
972: {
973: N g;
974: Q n1,n2,a;
975:
976: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
977: asir_assert(n1,O_N,"igcd");
978: asir_assert(n2,O_N,"igcd");
979: if ( !n1 )
980: *rp = (Obj)n2;
981: else if ( !n2 )
982: *rp = (Obj)n1;
983: else {
984: gcdbinn(NM(n1),NM(n2),&g);
985: NTOQ(g,1,a); *rp = (Obj)a;
986: }
987: }
988:
989: void Pigcdbmod(arg,rp)
990: NODE arg;
991: Obj *rp;
992: {
993: N g;
994: Q n1,n2,a;
995:
996: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
997: asir_assert(n1,O_N,"igcdbmod");
998: asir_assert(n2,O_N,"igcdbmod");
999: if ( !n1 )
1000: *rp = (Obj)n2;
1001: else if ( !n2 )
1002: *rp = (Obj)n1;
1003: else {
1004: gcdbmodn(NM(n1),NM(n2),&g);
1005: NTOQ(g,1,a); *rp = (Obj)a;
1006: }
1007: }
1008:
1009: void Pigcdacc(arg,rp)
1010: NODE arg;
1011: Obj *rp;
1012: {
1013: N g;
1014: Q n1,n2,a;
1015:
1016: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
1017: asir_assert(n1,O_N,"igcdacc");
1018: asir_assert(n2,O_N,"igcdacc");
1019: if ( !n1 )
1020: *rp = (Obj)n2;
1021: else if ( !n2 )
1022: *rp = (Obj)n1;
1023: else {
1024: gcdaccn(NM(n1),NM(n2),&g);
1025: NTOQ(g,1,a); *rp = (Obj)a;
1026: }
1027: }
1028:
1029: void PigcdEuc(arg,rp)
1030: NODE arg;
1031: Obj *rp;
1032: {
1033: N g;
1034: Q n1,n2,a;
1035:
1036: n1 = (Q)ARG0(arg); n2 = (Q)ARG1(arg);
1037: asir_assert(n1,O_N,"igcdbmod");
1038: asir_assert(n2,O_N,"igcdbmod");
1039: if ( !n1 )
1040: *rp = (Obj)n2;
1041: else if ( !n2 )
1042: *rp = (Obj)n1;
1043: else {
1044: gcdEuclidn(NM(n1),NM(n2),&g);
1045: NTOQ(g,1,a); *rp = (Obj)a;
1046: }
1047: }
1048:
1049: extern int igcd_algorithm;
1050: /* == 0 : Euclid,
1051: * == 1 : binary,
1052: * == 2 : bmod,
1053: * >= 3 : (Weber's accelerated)/(Jebelean's generalized binary) algorithm,
1054: */
1055: extern int igcd_thre_inidiv;
1056: /*
1057: * In the non-Euclidean algorithms, if the ratio of the lengths (number
1058: * of words) of two integers is >= igcd_thre_inidiv, we first perform
1059: * remainder calculation.
1060: * If == 0, this remainder calculation is not performed.
1061: */
1062: extern int igcdacc_thre;
1063: /*
1064: * In the accelerated algorithm, if the bit-lengths of two integers is
1065: * > igcdacc_thre, "bmod" reduction is done.
1066: */
1067:
1068: void Pigcdcntl(arg,rp)
1069: NODE arg;
1070: Obj *rp;
1071: {
1072: Obj p;
1073: Q a;
1074: int k, m;
1075:
1076: if ( arg ) {
1077: p = (Obj)ARG0(arg);
1078: if ( !p ) {
1079: igcd_algorithm = 0;
1080: *rp = p;
1081: return;
1082: } else if ( OID(p) == O_N ) {
1083: k = QTOS((Q)p);
1084: a = (Q)p;
1085: if ( k >= 0 ) igcd_algorithm = k;
1086: else if ( k == -1 ) {
1087: ret_thre:
1088: k = - igcd_thre_inidiv - igcdacc_thre*10000;
1089: STOQ(k,a);
1090: *rp = (Obj)a;
1091: return;
1092: } else {
1093: if ( (m = (-k)%10000) != 0 ) igcd_thre_inidiv = m;
1094: if ( (m = -k/10000) != 0 ) igcdacc_thre = m;
1095: goto ret_thre;
1096: }
1097: } else if ( OID(p) == O_STR ) {
1098: char *n = BDY((STRING) p);
1099:
1100: if ( !strcmp( n, "binary" ) || !strcmp( n, "Binary" )
1101: || !strcmp( n, "bin" ) || !strcmp( n, "Bin" ) )
1102: k = igcd_algorithm = 1;
1103: else if ( !strcmp( n, "bmod" ) || !strcmp( n, "Bmod" ) )
1104: igcd_algorithm = 2;
1105: else if ( !strcmp( n, "euc" ) || !strcmp( n, "Euc" )
1106: || !strcmp( n, "euclid" ) || !strcmp( n, "Euclid" ) )
1107: igcd_algorithm = 0;
1108: else if ( !strcmp( n, "acc" ) || !strcmp( n, "Acc" )
1109: || !strcmp( n, "gen" ) || !strcmp( n, "Gen" )
1110: || !strcmp( n, "genbin" ) || !strcmp( n, "GenBin" ) )
1111: igcd_algorithm = 3;
1112: else error( "igcdhow : invalid algorithm specification" );
1113: }
1114: }
1115: STOQ(igcd_algorithm,a);
1116: *rp = (Obj)a;
1117: return;
1118: }
1119:
1120:
1121: void Pimaxrsh(arg,rp)
1122: NODE arg;
1123: LIST *rp;
1124: {
1125: N n1, n2;
1126: Q q;
1127: NODE node1, node2;
1128: int bits;
1129: N maxrshn();
1130:
1131: q = (Q)ARG0(arg);
1132: asir_assert(q,O_N,"imaxrsh");
1133: if ( !q ) n1 = n2 = 0;
1134: else {
1135: n1 = maxrshn( NM(q), &bits );
1136: STON( bits, n2 );
1137: }
1138: NTOQ( n2, 1, q );
1139: MKNODE( node2, q, 0 );
1140: NTOQ( n1, 1, q );
1141: MKNODE( node1, q, node2 );
1142: MKLIST( *rp, node1 );
1143: }
1144: void Pilen(arg,rp)
1145: NODE arg;
1146: Obj *rp;
1147: {
1148: Q q;
1149: int l;
1150:
1151: q = (Q)ARG0(arg);
1152: asir_assert(q,O_N,"ilenh");
1153: if ( !q ) l = 0;
1154: else l = PL(NM(q));
1155: STOQ(l,q);
1156: *rp = (Obj)q;
1157: }
1158:
1159: void Pihex(arg,rp)
1160: NODE arg;
1161: Obj *rp;
1162: {
1163: Q n1;
1164:
1165: n1 = (Q)ARG0(arg);
1166: asir_assert(n1,O_N,"ihex");
1167: if ( n1 ) {
1168: int i, l = PL(NM(n1)), *p = BD(NM(n1));
1169:
1170: for ( i = 0; i < l; i++ ) printf( " 0x%08x", p[i] );
1171: printf( "\n" );
1172: } else printf( " 0x%08x\n", 0 );
1173: *rp = (Obj)n1;
1174: }
1175: #endif /* HMEXT */