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1.1 murao 1: /*
1.3 ! noro 2: * $OpenXM: OpenXM_contrib2/asir2000/engine/Ngcd.c,v 1.2 2000/12/21 02:56:31 murao Exp $
1.1 murao 3: */
4: /*
5: #include "ca.h"
6: #include "base.h"
7: */
8:
9: #undef CALL
10:
11: /**** Machine specific ****/
12: #define BIT_WIDTH_OF_INT 32
13:
14:
15: #if BSH == BIT_WIDTH_OF_INT
1.3 ! noro 16: #if defined(BMASK)
! 17: #undef BMASK
! 18: #endif
1.1 murao 19: #define BMask ((unsigned)(-1))
20: #define BMASK BMask
21: #endif
22:
23:
24: int igcd_algorithm = 0;
25: /* == 0 : Euclid,
26: * == 1 : binary,
27: * == 2 : bmod,
28: * >= 3 : (Weber's accelerated)/(Jebelean's generalized binary) algorithm,
29: */
30: int igcd_thre_inidiv = 50;
31: /*
32: * In the non-Euclidean algorithms, if the ratio of the lengths (number
33: * of words) of two integers is >= igcd_thre_inidiv, we first perform
34: * remainder calculation.
35: * If == 0, this remainder calculation is not performed.
36: */
37: int igcdacc_thre = 10;
38: /*
39: * In the accelerated algorithm, if the bit-lengths of two integers is
40: * > igcdacc_thre, "bmod" reduction is done.
41: */
42:
43: #include "inline.h"
44:
45: #define TRAILINGZEROS(t,cntr) for(cntr=0;(t&1)==0;t>>=1)cntr++;
46:
47: #define W_NALLOC(d) ((N)ALLOCA(TRUESIZE(oN,(d)-1,int)))
48:
49: #define ShouldCompRemInit(n1,n2) (igcd_thre_inidiv != 0 && PL(n1) >= igcd_thre_inidiv*PL(n2))
50:
51: #define IniDiv(n1,n2) \
52: if ( ShouldCompRemInit(n1,n2) ) {\
53: N q, r; int w, b; \
54: divn(n1,n2,&q,&r); \
55: if ( !r ) return(n2); \
56: b = trailingzerosn( r, &w ); \
57: q = n1; n1 = n2; n2 = q; \
58: rshiftn( r, w, b, n2 ); \
59: }
60:
61: /*
62: * Binary GCD algorithm by J.Stein
63: * [J. Comp. Phys. Vol. 1 (1967), pp. 397-405)]:
64: * The right-shift binary algorithm is used.
65: */
66:
67:
68: /*
69: * subsidiary routines for gcdbinn below.
70: */
71: static int /* number of bits */ trailingzeros_nbd( /* BD of N */ nbd, pnw )
72: int *nbd, *pnw /* number of zero words */;
73: {
74: #if BSH == BIT_WIDTH_OF_INT
75: unsigned
76: #endif
77: int nw, nb, w;
78:
79: for ( nw = 0; (w = *nbd) == 0; nbd++ ) nw++;
80: TRAILINGZEROS(w,nb);
81: *pnw = nw;
82: return nb;
83: }
84:
85: #define trailingzerosn(n,pnw) trailingzeros_nbd(BD(n),pnw)
86:
87: static int /* PL of N */ rshift_nbd( /* BD of N */ nbd, /* PL of N */ nl,
88: /* # words */ shw, /* # bits */ shb, /* BD of N */ p )
89: #if BSH == BIT_WIDTH_OF_INT
90: unsigned
91: #endif
92: int *nbd, nl, shw, shb, *p;
93: {
94: unsigned int i, v, w, lshb; /* <---- */
95:
96: nbd += shw, i = (nl -= shw);
97: if ( shb == 0 ) {
98: for ( ; nl > 0; nl-- ) *p++ = *nbd++;
99: return i;
100: } else if ( nl < 2 ) {
101: *p = (*nbd) >> shb;
102: return 1;
103: }
104: for ( lshb = BSH - shb, v = *nbd++; --nl > 0; v = w ) {
105: w = *nbd++;
106: #if BSH == BIT_WIDTH_OF_INT
107: *p++ = (v >> shb) | (w << lshb); /********/
108: #else
109: *p++ = (v >> shb) | ((w << lshb)&BMASK);
110: #endif
111: }
112: if ( (v >>= shb) == 0 ) return( i-1 );
113: *p = v;
114: return i;
115: }
116:
117: #define rshiftn(ns,shw,shb,nd) (PL(nd)=rshift_nbd(BD(ns),PL(ns),shw,shb,BD(nd)))
118: /* nd <= ns << (shb + shw*BSH), returns PL of the result */
119:
120: #ifdef FULLSET
121: static N N_of_i_lshifted_by_wb( i, gw, gb )
122: int i, gw, gb;
123: /*
124: * returns pointer to a new struct (N)(((int)i) >> (gb + gw*BSH))
125: */
126: {
127: unsigned int j, l, *p; /* <---- */
128: N n;
129:
130: j = i >> (BSH - gb);
131: #if BSH == BIT_WIDTH_OF_INT
132: i = (i << gb); /********/
133: #else
134: i = (i << gb)&BMASK;
135: #endif
136: l = j != 0 ? gw + 2 : gw + 1;
137: n = NALLOC(l);
138: PL(n) = l;
139: for ( p = BD(n); gw-- > 0; ) *p++ = 0;
140: *p++ = i;
141: if ( j != 0 ) *p = j;
142: return n;
143: }
144: #endif /* FULLSET */
145:
146: /*
147: * routines to make a new struct
148: * (N)(((BD of N)(b[0],...,b[lb-1])) << (gb + gw*BSH))
149: */
150: static N N_of_nbd_lshifted_by_wb( /* BD of N */ b, /* PL of N */ lb, gw, gb )
151: int *b, lb, gw, gb;
152: /*
153: * returns pointer to a new struct
154: * (N)(((BD of N)(b[0],...,b[lb-1])) << (gb + gw*BSH))
155: */
156: {
157: unsigned int rsh, s, t, *p, l; /* <---- */
158: N n;
159:
160: l = lb + gw;
161: if ( gb == 0 ) {
162: n = NALLOC(l);
163: PL(n) = l;
164: for ( p = BD(n); gw-- > 0; ) *p++ = 0;
165: while ( lb-- > 0 ) *p++ = *b++;
166: return n;
167: }
168: rsh = BSH - gb; s = b[lb-1];
169: if ( (t = s >> rsh) != 0 ) {
170: n = NALLOC(l+1);
171: PL(n) = l+1;
172: (p = BD(n))[l] = t;
173: } else {
174: n = NALLOC(l);
175: PL(n) = l;
176: p = BD(n);
177: }
178: while ( gw-- > 0 ) *p++ = 0;
179: #if BSH == BIT_WIDTH_OF_INT
180: *p++ = (t = *b++) << gb; /********/
181: for ( ; --lb > 0; t = s )
182: *p++ = (t >> rsh) | ((s = *b++) << gb); /********/
183: #else
184: *p++ = ((t = *b++) << gb)&BMASK;
185: for ( ; --lb > 0; t = s )
186: *p++ = (t >> rsh) | (((s = *b++) << gb)&BMASK);
187: #endif
188: return n;
189: }
190:
191: #define N_of_n_lshifted_by_wb(a,gw,gb) N_of_nbd_lshifted_by_wb(BD(a),PL(a),gw,gb)
192:
193: #define SWAP(a,b,Type) { Type temp=a;a=b;b=temp;}
194: #define SIGNED_VAL(a,s) ((s)>0?(a):-(a))
195:
196:
197: #ifdef CALL
198: static int bw_int32( n )
199: unsigned int n; /* <---- */
200: {
201: int w;
202:
203: w = 0;
204: #if BSH > 32
205: if ( n > 0xffffffff ) w += 32, n >>= 32;
206: #endif
207: if ( n >= 0x10000 ) w += 16, n >>= 16;
208: if ( n >= 0x100 ) w += 8, n >>= 8;
209: if ( n >= 0x10 ) w += 4, n >>= 4;
210: if ( n >= 0x4 ) w += 2, n >>= 2;
211: if ( n >= 0x2 ) w += 1, n >>= 1;
212: if ( n != 0 ) ++w;
213: return w;
214: }
215: #define BitWidth(n,bw) bw = bw_int32( n )
216: #else
217:
218: #if BSH > 32
219: #define BitWidth(n,bw) {\
220: unsigned int k = (n); \
221: bw = 0; \
222: if ( k > 0xffffffff ) bw += 32, k >>= 32; \
223: if ( k >= 0x10000 ) bw += 16, k >>= 16; \
224: if ( k >= 0x100 ) bw += 8, k >>= 8; \
225: if ( k >= 0x10 ) bw += 4, k >>= 4; \
226: if ( k >= 0x4 ) bw += 2, k >>= 2; \
227: if ( k >= 0x2 ) bw += 1, k >>= 1; \
228: if ( k != 0 ) bw++; \
229: }
230: #else
231: #define BitWidth(n,bw) {\
232: unsigned int k = (n); \
233: bw = 0; \
234: if ( k >= 0x10000 ) bw += 16, k >>= 16; \
235: if ( k >= 0x100 ) bw += 8, k >>= 8; \
236: if ( k >= 0x10 ) bw += 4, k >>= 4; \
237: if ( k >= 0x4 ) bw += 2, k >>= 2; \
238: if ( k >= 0x2 ) bw += 1, k >>= 1; \
239: if ( k != 0 ) bw++; \
240: }
241: #endif
242: #endif
243:
244: #include "igcdhack.c"
245:
246: /*
247: * Implementation of the binary GCD algorithm for two oN structs
248: * (big-integers) in risa.
249: *
250: * The major operations in the following algorithms are the binary-shifts
251: * and the updates of (u, v) by (min(u,v), |u-v|), and are to be open-coded
252: * without using routines for oN structures just as in addn() or subn().
253: */
254:
255: static int igcd_binary_2w( u, lu, v, lv, pans )
256: #if BSH == BIT_WIDTH_OF_INT
257: unsigned
258: #endif
259: int *u, lu, *v, lv, *pans; /* <---- */
260: /* both u[0:lu-1] and v[0:lv-1] are assumed to be odd */
261: {
262: #if BSH == BIT_WIDTH_OF_INT
263: unsigned
264: #endif
265: int i, h1, l1, h2, l2; /* <---- */
266:
267: l1 = u[0], l2 = v[0];
268: h1 = lu <= 1 ? 0 : u[1];
269: h2 = lv <= 1 ? 0 : v[1];
270: /**/
271: loop: if ( h1 == 0 ) {
272: no_hi1: if ( h2 == 0 ) goto one_word;
273: no_hi1n:if ( l1 == 1 ) return 0;
274: #if BSH == BIT_WIDTH_OF_INT
275: if ( l2 == l1 ) {
276: for ( l2 = h2; (l2&1) == 0; l2 >>= 1 ) ;
277: goto one_word;
278: } else if ( l2 < l1 ) {
279: l2 -= l1, h2--;
280: } else l2 -= l1;
281: i = 0; do { l2 >>= 1, i++; } while ( (l2&1) == 0 );
282: l2 |= (h2 << (BSH - i));
283: #else
284: if ( (l2 -= l1) == 0 ) {
285: for ( l2 = h2; (l2&1) == 0; l2 >>= 1 ) ;
286: goto one_word;
287: } else if ( l2 < 0 ) h2--, l2 += BASE;
288: i = 0; do { l2 >>= 1, i++; } while ( (l2&1) == 0 );
289: l2 |= ((h2 << (BSH - i)) & BMASK);
290: #endif
291: h2 >>= i;
292: goto no_hi1;
293: } else if ( h2 == 0 ) {
294: no_hi2: if ( l2 == 1 ) return 0;
295: #if BSH == BIT_WIDTH_OF_INT
296: if ( l1 == l2 ) {
297: for ( l1 = h1; (l1&1) == 0; l1 >>= 1 ) ;
298: goto one_word;
299: } else if ( l1 < l2 ) {
300: l1 -= l2, h1--;
301: } else l1 -= l2;
302: i = 0; do { l1 >>= 1, i++; } while ( (l1&1) == 0 );
303: l1 |= (h1 << (BSH - i));
304: #else
305: if ( (l1 -= l2) == 0 ) {
306: for ( l1 = h1; (l1&1) == 0; l1 >>= 1 ) ;
307: goto one_word;
308: } else if ( l1 < 0 ) h1--, l1 += BASE;
309: i = 0; do { l1 >>= 1, i++; } while ( (l1&1) == 0 );
310: l1 |= ((h1 << (BSH - i)) & BMASK);
311: #endif
312: if ( (h1 >>= i) == 0 ) goto one_word;
313: goto no_hi2;
314: } else if ( l1 == l2 ) {
315: if ( h1 == h2 ) {
316: pans[0] = l1, pans[1] = h1;
317: return 2;
318: } else if ( h1 > h2 ) {
319: for ( l1 = h1 - h2; (l1&1) == 0; l1 >>= 1 ) ;
320: goto no_hi1n;
321: } else {
322: for ( l2 = h2 - h1; (l2&1) == 0; l2 >>= 1 ) ;
323: goto no_hi2;
324: }
325: } else if ( h1 == h2 ) {
326: if ( l1 > l2 ) {
327: for ( l1 -= l2; (l1&1) == 0; l1 >>= 1 ) ;
328: goto no_hi1n;
329: } else {
330: for ( l2 -= l1; (l2&1) == 0; l2 >>= 1 ) ;
331: goto no_hi2;
332: }
333: } else if ( h1 > h2 ) {
334: h1 -= h2;
335: #if BSH == BIT_WIDTH_OF_INT
336: if ( l1 < l2 ) l1 -= l2, h1--;
337: else l1 -= l2;
338: i = 0; do { l1 >>= 1, i++; } while ( (l1&1) == 0 );
339: l1 |= (h1 << (BSH - i));
340: #else
341: if ( (l1 -= l2) < 0 ) h1--, l1 += BASE;
342: i = 0; do { l1 >>= 1, i++; } while ( (l1&1) == 0 );
343: l1 |= ((h1 << (BSH - i)) & BMASK);
344: #endif
345: h1 >>= i;
346: } else {
347: h2 -= h1;
348: #if BSH == BIT_WIDTH_OF_INT
349: if ( l2 < l1 ) l2 -= l1, h2--;
350: else l2 -= l1;
351: i = 0; do { l2 >>= 1, i++; } while ( (l2&1) == 0 );
352: l2 |= (h2 << (BSH - i));
353: #else
354: if ( (l2 -= l1) < 0 ) h2--, l2 += BASE;
355: i = 0; do { l2 >>= 1, i++; } while ( (l2&1) == 0 );
356: l2 |= ((h2 << (BSH - i)) & BMASK);
357: #endif
358: h2 >>= i;
359: }
360: goto loop;
361: one_word:
362: if ( l1 == 1 || l2 == 1 ) return 0;
363: else if ( l1 == l2 ) {
364: pans[0] = l1;
365: return 1;
366: }
367: one_word_neq:
368: if ( l1 > l2 ) {
369: l1 -= l2;
370: do { l1 >>= 1; } while ( (l1&1) == 0 );
371: goto one_word;
372: } else {
373: l2 -= l1;
374: do { l2 >>= 1; } while ( (l2&1) == 0 );
375: goto one_word;
376: }
377: }
378:
379: static N igcd_binary( n1, n2, nt )
380: N n1, n2, nt;
381: /* both n1 and n2 are assumed to be odd */
382: {
383: int l1, *b1, l2, *b2, *bt = BD(nt);
384: int l;
385:
386: if ( (l = cmpn( n1, n2 )) == 0 ) return n1;
387: else if ( l < 0 ) { SWAP( n1, n2, N ); }
388: IniDiv( n1, n2 );
389: if ( UNIN(n2) ) return 0;
390: l1 = PL(n1), b1 = BD(n1), l2 = PL(n2), b2 = BD(n2);
391: loop:
392: #if 0000
393: {
394: int i, b, w;
395:
396: printf( "===============\n" );
397: for ( i = 0; i < l1; i++ ) printf( "0x%08x ", b1[i] );
398: printf( "\n" );
399: for ( i = 0; i < l2; i++ ) printf( "0x%08x ", b2[i] );
400: printf( "\n" );
401: }
402: #endif
403: if ( l1 <= 2 && l2 <= 2 ) {
404: l = igcd_binary_2w( b1, l1, b2, l2, bt );
405: if ( l == 0 ) return 0;
406: PL(nt) = l;
407: return nt;
408: }
409: /**/
410: l = abs_U_V_maxrshift( b1, l1, b2, l2, bt );
411: /**/
412: if ( l == 0 ) {
413: PL(n1) = l1;
414: return n1;
415: } else if ( l > 0 ) {
416: l1 = l;
417: SWAP( b1, bt, int * ); SWAP( n1, nt, N );
418: } else {
419: l2 = -l;
420: SWAP( b2, bt, int * ); SWAP( n2, nt, N );
421: }
422: goto loop;
423: }
424:
425: #define RetTrueGCD(p,gw,gb,nr,l0) \
426: if (p==0) { l0: if (gw==0&&gb==0) { *(nr)=ONEN; return; } else p=ONEN; } \
427: *(nr) = N_of_n_lshifted_by_wb(p,gw,gb); \
428: return;
429:
430: void gcdbinn( n1, n2, nr )
431: N n1, n2, *nr;
432: {
433: int s1, s2, gw, gb, t1, t2;
434: int w1, w2;
435: N tn1, tn2, tnt, p;
436:
437: if ( !n1 ) {
438: *nr = n2;
439: return;
440: } else if ( !n2 ) {
441: *nr = n1;
442: return;
443: }
444: s1 = trailingzerosn( n1, &w1 );
445: s2 = trailingzerosn( n2, &w2 );
446: if ( w1 == w2 ) gw = w1, gb = s1 <= s2 ? s1 : s2;
447: else if ( w1 < w2 ) gw = w1, gb = s1;
448: else gw = w2, gb = s2;
449: /*
450: * true GCD must be multiplied by 2^{gw*BSH+gb}.
451: */
452: t1 = PL(n1) - w1;
453: t2 = PL(n2) - w2;
454: if ( t1 < t2 ) t1 = t2;
455: tn1 = W_NALLOC(t1); tn2 = W_NALLOC(t1); tnt = W_NALLOC(t1);
456: rshiftn( n1, w1, s1, tn1 );
457: rshiftn( n2, w2, s2, tn2 );
458: p = igcd_binary( tn1, tn2, tnt );
459: RetTrueGCD( p, gw, gb, nr, L0 )
460: }
461:
462:
463: /*
464: * The bmod gcd algorithm stated briefly in K.Weber's paper
465: * [ACM TOMS, Vol.21, No. 1 (1995), pp. 111-122].
466: * It replaces the subtraction (n1 - n2) in the binary algorithm
467: * by (n1 - S*n2) with such an S that (n1 - S*n2) \equiv 0 \bmod 2^BSH,
468: * which should improve the efficiency when n1 \gg n2.
469: */
470:
471: /* subsidiary routines */
472: #if BSH == BIT_WIDTH_OF_INT
473: #ifdef CALL
474: static int u_div_v_mod_2toBSH( u, v )
475: unsigned int u, v;
476: /*
477: * u/v mod 2^BSH.
478: */
479: {
480: unsigned int i, lsh_i, m;
481:
482: lsh_i = (sizeof(int) << 3) - 1;
483: m = i = 0;
484: do {
485: if ( u == 0 ) break;
486: if ( (u << lsh_i) != 0 ) {
487: m += (1 << i);
488: u -= (v << i);
489: }
490: lsh_i--;
491: } while ( ++i != BSH );
492: return m;
493: }
494:
495: #define Comp_U_div_V_mod_BASE(U,V,R) R = u_div_v_mod_2toBSH(U,V)
496: #else /* CALL */
497: #define Comp_U_div_V_mod_BASE(U,V,R) {\
498: unsigned int u = (U), v = (V), i, lsh; \
499: /* U and V are assumed to be odd */ \
500: i = R = 1, lsh = (sizeof(int) << 3) - 2; u = (u - v); \
501: do { if ( u == 0 ) break; \
502: if ( (u << lsh) != 0 ) R += (1 << i), u = (u - (v << i)); \
503: i++, lsh--; \
504: } while ( i < BSH ); \
505: }
506: #endif /* CALL */
507: #else
508: #ifdef CALL
509: static int u_div_v_mod_2tos( u, v, s )
510: int u, v, s;
511: /*
512: * u/v mod 2^s.
513: */
514: {
515: int i, lsh_i, mask, m;
516:
517: mask = (1 << s) - 1;
518: lsh_i = (sizeof(int) << 3) - 1;
519: m = i = 0;
520: u &= mask, v &= mask;
521: do {
522: if ( u == 0 ) break;
523: if ( (u << lsh_i) != 0 ) {
524: m += (1 << i);
525: u -= (v << i);
526: u &= mask;
527: }
528: lsh_i--;
529: } while ( ++i != s );
530: return m;
531: }
532:
533: #define Comp_U_div_V_mod_BASE(U,V,R) R = u_div_v_mod_2tos(U,V,BSH)
534: #else
535: #define Comp_U_div_V_mod_BASE(U,V,R) {\
536: int u = (U), v = (V), i, lsh; \
537: /* U and V are assumed to be odd */ \
538: i = R = 1, lsh = (sizeof(int) << 3) - 2; u = (u - v) & BMASK; \
539: do { if ( u == 0 ) break; \
540: if ( (u << lsh) != 0 ) R += (1 << i), u = (u - (v << i)) & BMASK; \
541: i++, lsh--; \
542: } while ( i < BSH ); \
543: }
544: #endif
545: #endif
546:
547:
548: static int bmod_n( nu, nv, na )
549: N nu, nv, na;
550: /*
551: * Computes (u[] \bmod v[]) >> (as much as possible) in r[].
552: */
553: {
554: #if BSH == BIT_WIDTH_OF_INT
555: unsigned int *u = BD(nu), *v = BD(nv), *r = BD(na);
556: unsigned int *p, a, t, l, v0, vh, bv, v0r;
557: int lu = PL(nu), lv = PL(nv), z;
558: #else
559: int *u = BD(nu), lu = PL(nu), *v = BD(nv), lv = PL(nv),
560: *r = BD(na);
561: int *p, a, t, l, z, v0, vh, bv, v0r;
562: #endif
563:
564: v0 = v[0];
565: if ( lv == 1 ) {
566: if ( lu == 1 ) a = u[0] % v0;
567: else {
568: p = &u[--lu];
569: #if BSH == BIT_WIDTH_OF_INT
570: a = (*p) % v0, t = (unsigned)(-((int)v0)) % v0;
571: #else
572: a = (*p) % v0, t = BASE % v0;
573: #endif
574: for ( ; --lu >= 0; a = l ) {
575: --p;
576: DMAR(a,t,*p,v0,l);
577: /* l <= (a*t + p[0])%v0 */
578: }
579: }
580: if ( a == 0 ) return 0;
581: while ( (a&1) == 0 ) a >>= 1;
582: *r = a;
583: return( PL(na) = 1 );
584: }
585: Comp_U_div_V_mod_BASE( 1, v0, v0r );
586: vh = v[lv -1];
587: BitWidth( vh, bv );
588: bv--;
589: t = 1 << bv;
590: l = lv + 1;
591: for ( z = -1; lu > l || lu == l && u[lu-1] >= t; z = -z ) {
592: #if BSH == BIT_WIDTH_OF_INT
593: a = (v0r*u[0]);
594: #else
595: a = (v0r*u[0])&BMASK;
596: #endif
597: /**/
598: #if 0000
599: {
600: int i;
601: for ( i = 0; i < lu; i++ ) printf( "0x%08x ", u[i] );
602: printf( "\n- a=0x%08x, %u*\n", a, a );
603: for ( i = 0; i < lv; i++ ) printf( "0x%08x ", v[i] );
604: printf( "\n=>\n" );
605: }
606: #endif
607: lu = abs_U_aV_maxrshift( u, lu, a, v, lv, r );
608: /**/
609: #if 0000
610: printf( "***lu=%d\n", lu );
611: if ( lu != 0 ) {
612: int i;
613: for ( i = 0; i < lu; i++ ) printf( "0x%08x ", r[i] );
614: printf( "\n" );
615: }
616: #endif
617: if ( lu == 0 ) return 0;
618: p = r;
619: r = u;
620: u = p;
621: }
622: if ( lu < lv ) goto ret;
623: t = u[lu-1];
624: if ( lu > lv ) l = BSH;
625: else if ( t < vh ) goto ret;
626: else l = 0;
627: BitWidth( t, a );
628: l += (a - bv);
629: #if BSH == BIT_WIDTH_OF_INT
630: a = (v0r*u[0])&((unsigned)(-1) >> (BSH - l));
631: #else
632: a = (v0r*u[0])&(BMASK >> (BSH - l));
633: #endif
634: #if 0000
635: {
636: int i;
637: for ( i = 0; i < lu; i++ ) printf( "0x%08x ", u[i] );
638: printf( "\n - a=0x%08x, %u*\n", a, a );
639: for ( i = 0; i < lv; i++ ) printf( "0x%08x ", v[i] );
640: printf( "\n =>\n" );
641: }
642: #endif
643: /**/
644: lu = abs_U_aV_maxrshift( u, lu, a, v, lv, r );
645: /**/
646: #if 0000
647: printf( "::: lu=%d\n", lu );
648: if ( lu != 0 ) {
649: int i;
650: for ( i = 0; i < lu; i++ ) printf( "0x%08x ", r[i] );
651: printf( "\n" );
652: }
653: #endif
654: if ( lu == 0 ) return 0;
655: z = -z;
656: ret: if ( z > 0 ) return( PL(na) = lu );
657: PL(nu) = lu;
658: return( -lu );
659: }
660:
661:
662: static N igcd_bmod( n1, n2, nt )
663: N n1, n2, nt;
664: /* both n1 and n2 are assumed to be odd */
665: {
666: int l1, l2;
667: int l;
668:
669: if ( (l = cmpn( n1, n2 )) == 0 ) return n1;
670: else if ( l < 0 ) { SWAP( n1, n2, N ); }
671: IniDiv( n1, n2 );
672: if ( UNIN(n2) ) return 0;
673: loop: if ( (l1 = PL(n1)) <= 2 && (l2 = PL(n2)) <= 2 ) {
674: l = igcd_binary_2w( BD(n1), l1, BD(n2), l2, BD(nt) );
675: if ( l == 0 ) return 0;
676: PL(nt) = l;
677: return nt;
678: }
679: /**/
680: l = bmod_n( n1, n2, nt );
681: /**/
682: if ( l == 0 ) return n2;
683: else if ( l > 0 ) {
684: N tmp = n1;
685:
686: n1 = n2;
687: n2 = nt;
688: nt = tmp;
689: } else SWAP( n1, n2, N );
690: goto loop;
691: }
692:
693: void gcdbmodn( n1, n2, nr )
694: N n1, n2, *nr;
695: {
696: int s1, s2, gw, gb, t1, t2;
697: int w1, w2;
698: N tn1, tn2, tnt, p;
699:
700: if ( !n1 ) {
701: *nr = n2;
702: return;
703: } else if ( !n2 ) {
704: *nr = n1;
705: return;
706: }
707: s1 = trailingzerosn( n1, &w1 );
708: s2 = trailingzerosn( n2, &w2 );
709: if ( w1 == w2 ) gw = w1, gb = s1 <= s2 ? s1 : s2;
710: else if ( w1 < w2 ) gw = w1, gb = s1;
711: else gw = w2, gb = s2;
712: /*
713: * true GCD must be multiplied by 2^{gw*BSH+gs}.
714: */
715: t1 = PL(n1) - w1;
716: t2 = PL(n2) - w2;
717: if ( t1 < t2 ) t1 = t2;
718: tn1 = W_NALLOC(t1); tn2 = W_NALLOC(t1); tnt = W_NALLOC(t1);
719: rshiftn( n1, w1, s1, tn1 );
720: rshiftn( n2, w2, s2, tn2 );
721: p = igcd_bmod( tn1, tn2, tnt );
722: RetTrueGCD( p, gw, gb, nr, L0 )
723: }
724:
725: /*
726: * The accelerated integer GCD algorithm by K.Weber
727: * [ACM TOMS, Vol.21, No. 1 (1995), pp. 111-122]:
728: */
729:
730: static int ReducedRatMod( x, y, pn, pd )
731: N x, y;
732: #if BSH == BIT_WIDTH_OF_INT
733: unsigned
734: #endif
735: int *pn, *pd;
736: /*
737: * Let m = 2^{2*BSH} = 2*BASE. We assume x, y > 0 and \gcd(x,m)
738: * = \gcd(y,m) = 1. This routine computes n and d (resp. returned
739: * in *pn and *pd) such that 0 < n, |d| < \sqrt{m} and
740: * n*y \equiv x*d \bmod m.
741: */
742: {
743: #if BSH == BIT_WIDTH_OF_INT
744: unsigned int n1h, n1l, d1h, d1l, n2h, n2l, d2h, d2l;
745: unsigned int th, tl, l1, l2, i, ir;
746: int s1, s2;
747: #else
748: int n1h, n1l, d1h, d1l, n2h, n2l, d2h, d2l;
749: int th, tl, l1, l2, i, ir;
750: int s1, s2;
751: #endif
752:
753: {
754: #if BSH == BIT_WIDTH_OF_INT
755: unsigned
756: #endif
757: int xh, xl, yh, yl, lsh_i;
758:
759: xl = BD(x)[0];
760: xh = PL(x) > 1 ? BD(x)[1] : 0;
761: yl = BD(y)[0];
762: yh = PL(y) > 1 ? BD(y)[1] : 0;
763: #if 0000
764: printf( "*** RedRatMod: (0x%08x:0x%08x=%u*2^%d+%u)\n /(0x%08x:0x%08x=%u*2^%d+%u) mod 2^%d\n",
765: xh,xl, xh,BSH,xl, yh,yl, yh,BSH,yl, BSH );
766: #endif
767: Comp_U_div_V_mod_BASE( xl, yl, n2l );
768: DM(n2l,yl,th,tl) /* n2l*yl = tl+th*BASE, where tl==xl. */;
769: #if BSH == BIT_WIDTH_OF_INT
770: xh -= th;
771: #else
772: if ( xh > th ) xh -= th;
773: else xh += (BASE - th);
774: #endif
775: DM(n2l,yh,th,tl) /* n2l*yh = tl+th*BASE. */;
776: #if BSH == BIT_WIDTH_OF_INT
777: xh -= tl;
778: #else
779: if ( xh > tl ) xh -= tl;
780: else xh += (BASE - tl);
781: #endif
782: /* n2h = i = 0, lsh_i = 31;*/
783: n2h = i = 0, lsh_i = BIT_WIDTH_OF_INT -1;
784: do {
785: if ( xh == 0 ) break;
786: if ( (xh << lsh_i) != 0 ) {
787: n2h += (1 << i);
788: #if BSH == BIT_WIDTH_OF_INT
789: tl = yl << i;
790: xh -= tl;
791: #else
792: tl = (yl << i)&BMASK;
793: if ( xh > tl ) xh -= tl;
794: else xh += (BASE - tl);
795: #endif
796: }
797: lsh_i--;
798: } while ( ++i != BSH );
799: }
800: /*
801: * n2l + n2h*BASE = x/y mod 2^{2*BSH}.
802: */
803: #if 0000
804: printf( "=====> 0x%08x(%u) + 2^%d*0x%08x(%u)\n", n2l, n2l, BSH, n2h, n2h );
805: #endif
806: d2h = 0, d2l = 1, s2 = 1;
807: #if BSH == BIT_WIDTH_OF_INT
808: if ( n2h == 0 ) goto done;
809: BitWidth( n2h, l2 );
810: if ( l2 == BSH ) {
811: d1h = 0, d1l = 1, s1 = -1;
812: th = n2h, tl = n2l;
813: } else {
814: i = BSH - l2;
815: d1h = 0, d1l = 1 << i, s1 = -1;
816: th = (n2h << i) | (n2l >> l2);
817: tl = n2l << i;
818: }
819: if ( tl == 0 ) n1h = - th, n1l = 0;
820: else n1h = BMASK - th, n1l = - tl;
821: /**/
822: if ( n1h < n2h || (n1h == n2h && n1l < n2l) ) goto swap12;
823: BitWidth( n1h, l1 );
824: goto sub12;
825: #else
826: n1h = BASE, n1l = 0, l1 = BSH,
827: d1h = d1l = 0, s1 = 0;
828: #endif
829: /**/
830: while ( n2h != 0 ) {
831: BitWidth( n2h, l2 );
832: sub12: ir = BSH - (i = l1 - l2);
833: do {
834: if ( i == 0 ) th = n2h, tl = n2l;
835: else
836: th = (n2h << i) | (n2l >> ir),
837: #if BSH == BIT_WIDTH_OF_INT
838: tl = n2l << i;
839: #else
840: tl = (n2l << i) & BMASK;
841: #endif
842: if ( th > n1h || (th == n1h && tl > n1l) ) goto next_i;
843: #if BSH == BIT_WIDTH_OF_INT
844: if ( tl > n1l ) n1h--;
845: n1l -= tl;
846: #else
847: if ( tl <= n1l ) n1l -= tl;
848: else n1l += (BASE - tl), n1h--;
849: #endif
850: n1h -= th;
851: /* (s1:d1h,d1l) -= ((s2:d2h,d2l) << i); */
852: if ( s2 != 0 ) {
853: if ( i == 0 ) th = d2h, tl = d2l;
854: else
855: #if BSH == BIT_WIDTH_OF_INT
856: th = (d2h << i) | (d2l >> ir),
857: tl = (d2l << i);
858: #else
859: th = (d2h << i)&BMASK | (d2l >> ir),
860: tl = (d2l << i)&BMASK;
861: #endif
862: if ( s1 == 0 )
863: s1 = -s2, d1h = th, d1l = tl;
864: else if ( s1 != s2 ) {
865: #if BSH == BIT_WIDTH_OF_INT
866: d1l += tl,
867: d1h += th;
868: if ( d1l < tl ) d1h++;
869: #else
870: tl += d1l;
871: d1l = tl&BMASK;
872: d1h = (d1h + th + (tl >> BSH))&BMASK;
873: #endif
874: if ( d1h == 0 && d1l == 0 ) s1 = 0;
875: } else if ( d1h > th ) {
876: #if BSH == BIT_WIDTH_OF_INT
877: if ( d1l < tl ) d1h--;
878: d1l -= tl;
879: #else
880: if ( d1l >= tl ) d1l -= tl;
881: else d1l += (BASE - tl), d1h--;
882: #endif
883: d1h -= th;
884: } else if ( d1h == th ) {
885: d1h = 0;
886: if ( d1l == tl ) s1 = d2h = 0;
887: else if ( d1l > tl ) d1l -= tl;
888: else d1l = tl - d1l, s1 = -s1;
889: } else {
890: #if BSH == BIT_WIDTH_OF_INT
891: if ( tl < d1l ) th--;
892: d1l = tl - d1l;
893: #else
894: if ( tl >= d1l ) d1l = tl - d1l;
895: else d1l = tl + (BASE - d1l), th--;
896: #endif
897: d1h = th - d1h;
898: s1 = -s1;
899: }
900: }
901: next_i: i--, ir++;
902: } while ( n1h > n2h || (n1h == n2h && n1l >= n2l) );
903: swap12: /* swap 1 and 2 */
904: th = n1h, tl = n1l;
905: n1h = n2h, n1l = n2l;
906: n2h = th, n2l = tl;
907: l1 = l2;
908: th = d1h, tl = d1l, i = s1;
909: d1h = d2h, d1l = d2l, s1 = s2;
910: d2h = th, d2l = tl, s2 = i;
911: }
912: /**/
913: done: *pn = n2l, *pd = d2l;
914: return s2;
915: }
916:
917: static int igcd_spurious_factor;
918:
919: #define SaveN(s,d) {\
920: int i, l; \
921: for ( l = PL(d) = PL(s), i = 0; i < l; i++ ) BD(d)[i] = BD(s)[i]; \
922: }
923:
924: static N igcd_acc( n1, n2, nt )
925: N n1, n2, nt;
926: /* both n1 and n2 are assumed to be odd */
927: {
928: int l1, l2, *b1, *b2, bw1, bw2;
929: int l;
930: int n, d;
931: N p, s1, s2;
932:
933: if ( (l = cmpn( n1, n2 )) == 0 ) return n1;
934: else if ( l < 0 ) { SWAP( n1, n2, N ); }
935: if ( ShouldCompRemInit(n1,n2) ) {
936: int w, b;
937:
938: divn( n1, n2, &s1, &s2 );
939: if ( !s2 ) return n2;
940: b = trailingzerosn( s2, &w );
941: p = n1; n1 = n2; n2 = p;
942: rshiftn( s2, w, b, n2 );
943: if ( UNIN(n2) ) return 0;
944: l1 = PL(n1);
945: if ( !s1 || PL(s1) < l1 ) s1 = NALLOC(l1);
946: } else if ( UNIN(n2) ) return 0;
947: else {
948: s1 = NALLOC(PL(n1));
949: s2 = NALLOC(PL(n2));
950: }
951: SaveN( n1, s1 );
952: SaveN( n2, s2 );
953: igcd_spurious_factor = 0;
954: loop: l1 = PL(n1), l2 = PL(n2);
955: if ( l1 <= 2 && l2 <= 2 ) {
956: l = igcd_binary_2w( BD(n1), l1, BD(n2), l2, BD(nt) );
957: if ( l == 0 ) return 0;
958: PL(nt) = l;
959: SWAP( n2, nt, N );
960: goto ret;
961: }
962: /**/
963: b1 = BD(n1), b2 = BD(n2);
964: BitWidth( b1[l1 -1], bw1 );
965: BitWidth( b2[l2 -1], bw2 );
966: if ( (l1*BSH + bw1) - (l2*BSH + bw2) <= igcdacc_thre ) {
967: l = ReducedRatMod( n1, n2, &n, &d );
968: l = l < 0 ? aUplusbV_maxrshift( n, b2, l2, d, b1, l1, BD(nt) ) :
969: abs_axU_bxV_maxrshift( n, b2, l2, d, b1, l1, BD(nt) );
970: igcd_spurious_factor++;
971: if ( l == 0 ) goto ret;
972: PL(nt) = l;
973: } else {
974: l = bmod_n( n1, n2, nt );
975: if ( l == 0 ) goto ret;
976: else if ( l < 0 ) {
977: SWAP( n1, n2, N );
978: goto loop;
979: }
980: }
981: p = n1;
982: n1 = n2;
983: n2 = nt;
984: nt = p;
985: goto loop;
986: /**/
987: ret: if ( igcd_spurious_factor != 0 && !UNIN(n2) ) {
988: if ( (p = igcd_bmod( n2, s1, n1 )) == 0 ) return 0;
989: if ( (p = igcd_bmod( p, s2, nt )) == 0 ) return 0;
990: return p;
991: } else return n2;
992: }
993:
994: void gcdaccn( n1, n2, nr )
995: N n1, n2, *nr;
996: {
997: int s1, s2, gw, gb, t1, t2;
998: int w1, w2;
999: N tn1, tn2, tnt, p;
1000:
1001: if ( !n1 ) {
1002: *nr = n2;
1003: return;
1004: } else if ( !n2 ) {
1005: *nr = n1;
1006: return;
1007: }
1008: s1 = trailingzerosn( n1, &w1 );
1009: s2 = trailingzerosn( n2, &w2 );
1010: if ( w1 == w2 ) gw = w1, gb = s1 <= s2 ? s1 : s2;
1011: else if ( w1 < w2 ) gw = w1, gb = s1;
1012: else gw = w2, gb = s2;
1013: /*
1014: * true GCD must be multiplied by 2^{gw*BSH+gs}.
1015: */
1016: t1 = PL(n1) - w1;
1017: t2 = PL(n2) - w2;
1018: if ( t1 < t2 ) t1 = t2;
1019: tn1 = W_NALLOC(t1); tn2 = W_NALLOC(t1); tnt = W_NALLOC(t1);
1020: rshiftn( n1, w1, s1, tn1 );
1021: rshiftn( n2, w2, s2, tn2 );
1022: /**/
1023: p = igcd_acc( tn1, tn2, tnt );
1024: /**/
1025: if ( p == 0 ) goto L0;
1026: RetTrueGCD( p, gw, gb, nr, L0 )
1027: }
1028:
1029:
1030: /********************************/
1031:
1032: void gcdn_HMEXT( n1, n2, nr )
1033: N n1, n2, *nr;
1034: {
1035: int b1, b2, w1, w2, gw, gb;
1036: int l1, l2;
1037: N tn1, tn2, tnt, a;
1038:
1039: if ( !n1 ) {
1040: *nr = n2; return;
1041: } else if ( !n2 ) {
1042: *nr = n1; return;
1043: }
1044: b1 = trailingzerosn( n1, &w1 );
1045: b2 = trailingzerosn( n2, &w2 );
1046: if ( w1 == w2 ) gw = w1, gb = b1 <= b2 ? b1 : b2;
1047: else if ( w1 < w2 ) gw = w1, gb = b1;
1048: else gw = w2, gb = b2;
1049: /*
1050: * true GCD must be multiplied by 2^{gw*BSH+gb}.
1051: */
1052: l1 = PL(n1) - w1;
1053: l2 = PL(n2) - w2;
1054: if ( l1 < l2 ) l1 = l2;
1055: tn1 = W_NALLOC( l1 ); tn2 = W_NALLOC( l1 ); tnt = W_NALLOC( l1 );
1056: rshiftn( n1, w1, b1, tn1 );
1057: rshiftn( n2, w2, b2, tn2 );
1058: /**/
1059: if ( igcd_algorithm == 1 ) {
1060: a = igcd_binary( tn1, tn2, tnt );
1061: } else if ( igcd_algorithm == 2 ) {
1062: a = igcd_bmod( tn1, tn2, tnt );
1063: } else {
1064: a = igcd_acc( tn1, tn2, tnt );
1065: if ( igcd_spurious_factor != 0 ) {
1066: }
1067: }
1068: RetTrueGCD( a, gw, gb, nr, L0 )
1069: }
1070:
1071:
1072: /**************************/
1073: #if 111
1074: N maxrshn( n, p )
1075: N n;
1076: int *p;
1077: {
1078: int nw, nb, c, l;
1079: N new;
1080:
1081: nb = trailingzerosn( n, &nw );
1082: l = PL(n);
1083: c = BD(n)[l -1];
1084: l -= nw;
1085: if ( (c >> nb) == 0 ) l--;
1086: new = NALLOC(l);
1087: rshiftn( n, nw, nb, new );
1088: *p = nb + nw*BSH;
1089: return new;
1090: }
1091: #endif