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1.1 noro 1: /* $OpenXM: OpenXM/src/asir99/engine-27/N-27.c,v 1.1.1.1 1999/11/10 08:12:27 noro Exp $ */
2: #include "ca-27.h"
3: #include "base.h"
4:
5: #ifndef HMEXT
6: #define HMEXT
7: #endif
8:
9: #ifdef HMEXT
10: #undef FULLSET
11: #undef CALL
12: #undef DIVISION
13:
14: int igcd_algorithm = 0;
15: /* == 0 : Euclid,
16: * == 1 : binary,
17: * == 2 : bmod,
18: * >= 3 : (Weber's accelerated)/(Jebelean's generalized binary) algorithm,
19: */
20: int igcd_thre_inidiv = 50;
21: /*
22: * In the non-Euclidean algorithms, if the ratio of the lengths (number
23: * of words) of two integers is >= igcd_thre_inidiv, we first perform
24: * remainder calculation.
25: * If == 0, this remainder calculation is not performed.
26: */
27: int igcdacc_thre = 10;
28: /*
29: * In the accelerated algorithm, if the bit-lengths of two integers is
30: * > igcdacc_thre, "bmod" reduction is done.
31: */
32:
33: #include "inline.h"
34:
35: #define TRAILINGZEROS(t,cntr) for(cntr=0;(t&1)==0;t>>=1)cntr++;
36:
37: #define W_NALLOC(d) ((N)ALLOCA(TRUESIZE(oN,(d)-1,int)))
38:
39: #define ShouldCompRemInit(n1,n2) (igcd_thre_inidiv != 0 && PL(n1) >= igcd_thre_inidiv*PL(n2))
40:
41: #define IniDiv(n1,n2) \
42: if ( ShouldCompRemInit(n1,n2) ) {\
43: N q, r; int w, b; \
44: divn_27(n1,n2,&q,&r); \
45: if ( !r ) return(n2); \
46: b = trailingzerosn( r, &w ); \
47: q = n1; n1 = n2; n2 = q; \
48: rshiftn( r, w, b, n2 ); \
49: }
50:
51: /*
52: * Binary GCD algorithm by J.Stein
53: * [J. Comp. Phys. Vol. 1 (1967), pp. 397-405)]:
54: * The right-shift binary algorithm is used.
55: */
56:
57:
58: /*
59: * subsidiary routines for gcdbinn below.
60: */
61: static int /* number of bits */ trailingzeros_nbd( /* BD of N */ nbd, pnw )
62: int *nbd, *pnw /* number of zero words */;
63: {
64: int nw, nb, w;
65:
66: for ( nw = 0; (w = *nbd) == 0; nbd++ ) nw++;
67: TRAILINGZEROS(w,nb);
68: *pnw = nw;
69: return nb;
70: }
71:
72: #define trailingzerosn(n,pnw) trailingzeros_nbd(BD(n),pnw)
73:
74: static int /* PL of N */ rshift_nbd( /* BD of N */ nbd, /* PL of N */ nl,
75: /* # words */ shw, /* # bits */ shb, /* BD of N */ p )
76: int *nbd, nl, shw, shb, *p;
77: {
78: int i, v, w, lshb;
79:
80: nbd += shw, i = (nl -= shw);
81: if ( shb == 0 ) {
82: for ( ; nl > 0; nl-- ) *p++ = *nbd++;
83: return i;
84: } else if ( nl < 2 ) {
85: *p = (*nbd) >> shb;
86: return 1;
87: }
88: for ( lshb = BSH27 - shb, v = *nbd++; --nl > 0; v = w ) {
89: w = *nbd++;
90: *p++ = (v >> shb) | ((w << lshb)&BMASK27);
91: }
92: if ( (v >>= shb) == 0 ) return( i-1 );
93: *p = v;
94: return i;
95: }
96:
97: #define rshiftn(ns,shw,shb,nd) (PL(nd)=rshift_nbd(BD(ns),PL(ns),shw,shb,BD(nd)))
98: /* nd <= ns << (shb + shw*BSH27), returns PL of the result */
99:
100: #ifdef FULLSET
101: static N N_of_i_lshifted_by_wb( i, gw, gb )
102: int i, gw, gb;
103: /*
104: * returns pointer to a new struct (N)(((int)i) >> (gb + gw*BSH27))
105: */
106: {
107: int j, l, *p;
108: N n;
109:
110: j = i >> (BSH27 - gb);
111: i = (i << gb)&BMASK27;
112: l = j != 0 ? gw + 2 : gw + 1;
113: n = NALLOC(l);
114: PL(n) = l;
115: for ( p = BD(n); gw-- > 0; ) *p++ = 0;
116: *p++ = i;
117: if ( j != 0 ) *p = j;
118: return n;
119: }
120: #endif /* FULLSET */
121:
122: /*
123: * routines to make a new struct
124: * (N)(((BD of N)(b[0],...,b[lb-1])) << (gb + gw*BSH27))
125: */
126: static N N_of_nbd_lshifted_by_wb( /* BD of N */ b, /* PL of N */ lb, gw, gb )
127: int *b, lb, gw, gb;
128: /*
129: * returns pointer to a new struct
130: * (N)(((BD of N)(b[0],...,b[lb-1])) << (gb + gw*BSH27))
131: */
132: {
133: int rsh, s, t, *p, l;
134: N n;
135:
136: l = lb + gw;
137: if ( gb == 0 ) {
138: n = NALLOC(l);
139: PL(n) = l;
140: for ( p = BD(n); gw-- > 0; ) *p++ = 0;
141: while ( lb-- > 0 ) *p++ = *b++;
142: return n;
143: }
144: rsh = BSH27 - gb; s = b[lb-1];
145: if ( (t = s >> rsh) != 0 ) {
146: n = NALLOC(l+1);
147: PL(n) = l+1;
148: (p = BD(n))[l] = t;
149: } else {
150: n = NALLOC(l);
151: PL(n) = l;
152: p = BD(n);
153: }
154: while ( gw-- > 0 ) *p++ = 0;
155: *p++ = ((t = *b++) << gb)&BMASK27;
156: for ( ; --lb > 0; t = s )
157: *p++ = (t >> rsh) | (((s = *b++) << gb)&BMASK27);
158: return n;
159: }
160:
161: #define N_of_n_lshifted_by_wb(a,gw,gb) N_of_nbd_lshifted_by_wb(BD(a),PL(a),gw,gb)
162:
163: #define SWAP(a,b,Type) { Type temp=a;a=b;b=temp;}
164: #define SIGNED_VAL(a,s) ((s)>0?(a):-(a))
165:
166:
167: #ifdef CALL
168: static int bw_int32( n )
169: int n;
170: {
171: int w;
172:
173: w = 0;
174: #if BSH27 >= 32
175: if ( n > 0xffffffff ) w += 32, n >>= 32;
176: #endif
177: if ( n >= 0x10000 ) w += 16, n >>= 16;
178: if ( n >= 0x100 ) w += 8, n >>= 8;
179: if ( n >= 0x10 ) w += 4, n >>= 4;
180: if ( n >= 0x4 ) w += 2, n >>= 2;
181: if ( n >= 0x2 ) w += 1, n >>= 1;
182: if ( n != 0 ) ++w;
183: return w;
184: }
185: #define BitWidth(n,bw) bw = bw_int32( n )
186: #else
187:
188: #if BSH27 >= 32
189: #define BitWidth(n,bw) {\
190: int k = (n); \
191: bw = 0; \
192: if ( BSH27 >= 32 ) if ( k > 0xffffffff ) bw += 32, k >>= 32; \
193: if ( k >= 0x10000 ) bw += 16, k >>= 16; \
194: if ( k >= 0x100 ) bw += 8, k >>= 8; \
195: if ( k >= 0x10 ) bw += 4, k >>= 4; \
196: if ( k >= 0x4 ) bw += 2, k >>= 2; \
197: if ( k >= 0x2 ) bw += 1, k >>= 1; \
198: if ( k != 0 ) bw++; \
199: }
200: #else
201: #define BitWidth(n,bw) {\
202: int k = (n); \
203: bw = 0; \
204: if ( k >= 0x10000 ) bw += 16, k >>= 16; \
205: if ( k >= 0x100 ) bw += 8, k >>= 8; \
206: if ( k >= 0x10 ) bw += 4, k >>= 4; \
207: if ( k >= 0x4 ) bw += 2, k >>= 2; \
208: if ( k >= 0x2 ) bw += 1, k >>= 1; \
209: if ( k != 0 ) bw++; \
210: }
211: #endif
212: #endif
213:
214: #include "igcdhack.c"
215:
216: /*
217: * Implementation of the binary GCD algorithm for two oN structs
218: * (big-integers) in risa.
219: *
220: * The major operations in the following algorithms are the binary-shifts
221: * and the updates of (u, v) by (min(u,v), |u-v|), and are to be open-coded
222: * without using routines for oN structures just as in addn() or subn().
223: */
224:
225: static int igcd_binary_2w( u, lu, v, lv, pans )
226: int *u, lu, *v, lv, *pans;
227: /* both u[0:lu-1] and v[0:lv-1] are assumed to be odd */
228: {
229: int i, h1, l1, h2, l2;
230:
231: l1 = u[0], l2 = v[0];
232: h1 = lu <= 1 ? 0 : u[1];
233: h2 = lv <= 1 ? 0 : v[1];
234: /**/
235: loop: if ( h1 == 0 ) {
236: no_hi1: if ( h2 == 0 ) goto one_word;
237: no_hi1n:if ( l1 == 1 ) return 0;
238: if ( (l2 -= l1) == 0 ) {
239: for ( l2 = h2; (l2&1) == 0; l2 >>= 1 ) ;
240: goto one_word;
241: } else if ( l2 < 0 ) h2--, l2 += BASE27;
242: i = 0; do { l2 >>= 1, i++; } while ( (l2&1) == 0 );
243: l2 |= ((h2 << (BSH27 - i)) & BMASK27);
244: h2 >>= i;
245: goto no_hi1;
246: } else if ( h2 == 0 ) {
247: no_hi2: if ( l2 == 1 ) return 0;
248: if ( (l1 -= l2) == 0 ) {
249: for ( l1 = h1; (l1&1) == 0; l1 >>= 1 ) ;
250: goto one_word;
251: } else if ( l1 < 0 ) h1--, l1 += BASE27;
252: i = 0; do { l1 >>= 1, i++; } while ( (l1&1) == 0 );
253: l1 |= ((h1 << (BSH27 - i)) & BMASK27);
254: if ( (h1 >>= i) == 0 ) goto one_word;
255: goto no_hi2;
256: } else if ( l1 == l2 ) {
257: if ( h1 == h2 ) {
258: pans[0] = l1, pans[1] = h1;
259: return 2;
260: } else if ( h1 > h2 ) {
261: for ( l1 = h1 - h2; (l1&1) == 0; l1 >>= 1 ) ;
262: goto no_hi1n;
263: } else {
264: for ( l2 = h2 - h1; (l2&1) == 0; l2 >>= 1 ) ;
265: goto no_hi2;
266: }
267: } else if ( h1 == h2 ) {
268: if ( l1 > l2 ) {
269: for ( l1 -= l2; (l1&1) == 0; l1 >>= 1 ) ;
270: goto no_hi1n;
271: } else {
272: for ( l2 -= l1; (l2&1) == 0; l2 >>= 1 ) ;
273: goto no_hi2;
274: }
275: } else if ( h1 > h2 ) {
276: h1 -= h2;
277: if ( (l1 -= l2) < 0 ) h1--, l1 += BASE27;
278: i = 0; do { l1 >>= 1, i++; } while ( (l1&1) == 0 );
279: l1 |= ((h1 << (BSH27 - i)) & BMASK27);
280: h1 >>= i;
281: } else {
282: h2 -= h1;
283: if ( (l2 -= l1) < 0 ) h2--, l2 += BASE27;
284: i = 0; do { l2 >>= 1, i++; } while ( (l2&1) == 0 );
285: l2 |= ((h2 << (BSH27 - i)) & BMASK27);
286: h2 >>= i;
287: }
288: goto loop;
289: one_word:
290: if ( l1 == 1 || l2 == 1 ) return 0;
291: else if ( l1 == l2 ) {
292: pans[0] = l1;
293: return 1;
294: }
295: one_word_neq:
296: if ( l1 > l2 ) {
297: l1 -= l2;
298: do { l1 >>= 1; } while ( (l1&1) == 0 );
299: goto one_word;
300: } else {
301: l2 -= l1;
302: do { l2 >>= 1; } while ( (l2&1) == 0 );
303: goto one_word;
304: }
305: }
306:
307: static N igcd_binary( n1, n2, nt )
308: N n1, n2, nt;
309: /* both n1 and n2 are assumed to be odd */
310: {
311: int l1, *b1, l2, *b2, *bt = BD(nt);
312: int l;
313:
314: if ( (l = cmpn( n1, n2 )) == 0 ) return n1;
315: else if ( l < 0 ) { SWAP( n1, n2, N ); }
316: IniDiv( n1, n2 );
317: if ( UNIN(n2) ) return 0;
318: l1 = PL(n1), b1 = BD(n1), l2 = PL(n2), b2 = BD(n2);
319: loop: if ( l1 <= 2 && l2 <= 2 ) {
320: l = igcd_binary_2w( b1, l1, b2, l2, bt );
321: if ( l == 0 ) return 0;
322: PL(nt) = l;
323: return nt;
324: }
325: /**/
326: l = abs_U_V_maxrshift( b1, l1, b2, l2, bt );
327: /**/
328: if ( l == 0 ) {
329: PL(n1) = l1;
330: return n1;
331: } else if ( l > 0 ) {
332: l1 = l;
333: SWAP( b1, bt, int * ); SWAP( n1, nt, N );
334: } else {
335: l2 = -l;
336: SWAP( b2, bt, int * ); SWAP( n2, nt, N );
337: }
338: goto loop;
339: }
340:
341: #define RetTrueGCD(p,gw,gb,nr,l0) \
342: if (p==0) { l0: if (gw==0&&gb==0) { *(nr)=ONEN; return; } else p=ONEN; } \
343: *(nr) = N_of_n_lshifted_by_wb(p,gw,gb); \
344: return;
345:
346: void gcdbinn( n1, n2, nr )
347: N n1, n2, *nr;
348: {
349: int s1, s2, gw, gb, t1, t2;
350: int w1, w2;
351: N tn1, tn2, tnt, p;
352:
353: if ( !n1 ) {
354: *nr = n2;
355: return;
356: } else if ( !n2 ) {
357: *nr = n1;
358: return;
359: }
360: s1 = trailingzerosn( n1, &w1 );
361: s2 = trailingzerosn( n2, &w2 );
362: if ( w1 == w2 ) gw = w1, gb = s1 <= s2 ? s1 : s2;
363: else if ( w1 < w2 ) gw = w1, gb = s1;
364: else gw = w2, gb = s2;
365: /*
366: * true GCD must be multiplied by 2^{gw*BSH27+gb}.
367: */
368: t1 = PL(n1) - w1;
369: t2 = PL(n2) - w2;
370: if ( t1 < t2 ) t1 = t2;
371: tn1 = W_NALLOC(t1); tn2 = W_NALLOC(t1); tnt = W_NALLOC(t1);
372: rshiftn( n1, w1, s1, tn1 );
373: rshiftn( n2, w2, s2, tn2 );
374: p = igcd_binary( tn1, tn2, tnt );
375: RetTrueGCD( p, gw, gb, nr, L0 )
376: }
377:
378:
379: /*
380: * The bmod gcd algorithm stated briefly in K.Weber's paper
381: * [ACM TOMS, Vol.21, No. 1 (1995), pp. 111-122].
382: * It replaces the subtraction (n1 - n2) in the binary algorithm
383: * by (n1 - S*n2) with such an S that (n1 - S*n2) \equiv 0 \bmod 2^BSH27,
384: * which should improve the efficiency when n1 \gg n2.
385: */
386:
387: /* subsidiary routines */
388: #ifdef CALL
389: #ifndef DIVISION
390: static int u_div_v_mod_2tos( u, v, s )
391: int u, v, s;
392: /*
393: * u/v mod 2^s.
394: */
395: {
396: int i,lsh_i, mask, m, two_to_s;
397:
398: mask = (two_to_s = 1 << s) - 1;
399: lsh_i = (sizeof(int) << 3) - 1;
400: m = i = 0;
401: u &= mask, v &= mask;
402: do {
403: if ( u == 0 ) break;
404: if ( (u << lsh_i) != 0 ) {
405: m += (1 << i);
406: u -= (v << i);
407: u &= mask;
408: }
409: lsh_i--;
410: } while ( ++i != s );
411: return m;
412: }
413: #else
414: static int u_div_v_mod_2tos( u, v, s )
415: int u, v, s;
416: {
417: int f1 = 1 << s, f2 = u, q, r, c1 = 0, c2 = v, m;
418:
419: m = f1 - 1;
420: do { q = f1 / f2;
421: r = f1 - q*f2; f1 = f2; f2 = r;
422: r = c1 - q*c2; c1 = c2; c2 = r;
423: } while ( f2 != 1 );
424: return( c2 & m );
425: }
426: #endif /* DIVISION */
427:
428: #define Comp_U_div_V_mod_BASE27(U,V,R) R = u_div_v_mod_2tos(U,V,BSH27)
429: #else
430: #ifndef DIVISION
431: #define Comp_U_div_V_mod_BASE27(U,V,R) {\
432: int u = (U), v = (V), i, lsh; \
433: /* U and V are assumed to be odd */ \
434: i = R = 1, lsh = (sizeof(int) << 3) - 2; u = (u - v) & BMASK27; \
435: do { if ( u == 0 ) break; \
436: if ( (u << lsh) != 0 ) R += (1 << i), u = (u - (v << i)) & BMASK27; \
437: i++, lsh--; \
438: } while ( i < BSH27 ); \
439: }
440: #else
441: #define Comp_U_div_V_mod_BASE27(U,V,R) {\
442: int f1 = BASE27, f2 = (V), q, r, c1 = 0, c2 = (U); \
443: do { q = f1 / f2; \
444: r = f1 - q*f2; f1 = f2; f2 = r; \
445: r = c1 - q*c2; c1 = c2; c2 = r; \
446: } while ( f2 != 1 ); \
447: R = c2 & BMASK27; \
448: }
449: #endif /* DIVISION */
450: #endif
451:
452:
453: static int bmod_n( nu, nv, na )
454: N nu, nv, na;
455: /*
456: * Computes (u[] \bmod v[]) >> (as much as possible) in r[].
457: */
458: {
459: int *u = BD(nu), lu = PL(nu), *v = BD(nv), lv = PL(nv),
460: *r = BD(na);
461: int *p, a, t, l, z, v0, vh, bv, v0r;
462:
463: v0 = v[0];
464: if ( lv == 1 ) {
465: if ( lu == 1 ) a = u[0] % v0;
466: else {
467: p = &u[--lu];
468: a = (*p) % v0, t = BASE27 % v0;
469: for ( ; --lu >= 0; a = l ) {
470: --p;
471: DMAR(a,t,*p,v0,l)
472: /* l <= (a*t + p[0])%v0 */
473: }
474: }
475: if ( a == 0 ) return 0;
476: while ( (a&1) == 0 ) a >>= 1;
477: *r = a;
478: return( PL(na) = 1 );
479: }
480: Comp_U_div_V_mod_BASE27( 1, v0, v0r );
481: vh = v[lv -1];
482: BitWidth( vh, bv );
483: bv--;
484: t = 1 << bv;
485: l = lv + 1;
486: for ( z = -1; lu > l || lu == l && u[lu-1] >= t; z = -z ) {
487: a = (v0r*u[0])&BMASK27;
488: /**/
489: lu = abs_U_aV_maxrshift( u, lu, a, v, lv, r );
490: /**/
491: if ( lu == 0 ) return 0;
492: p = r;
493: r = u;
494: u = p;
495: }
496: if ( lu < lv ) goto ret;
497: t = u[lu-1];
498: if ( lu > lv ) l = BSH27;
499: else if ( t < vh ) goto ret;
500: else l = 0;
501: BitWidth( t, a );
502: l += (a - bv);
503: a = (v0r*u[0])&(BMASK27 >> (BSH27 - l));
504: /**/
505: lu = abs_U_aV_maxrshift( u, lu, a, v, lv, r );
506: /**/
507: if ( lu == 0 ) return 0;
508: z = -z;
509: ret: if ( z > 0 ) return( PL(na) = lu );
510: PL(nu) = lu;
511: return( -lu );
512: }
513:
514:
515: static N igcd_bmod( n1, n2, nt )
516: N n1, n2, nt;
517: /* both n1 and n2 are assumed to be odd */
518: {
519: int l1, l2;
520: int l;
521:
522: if ( (l = cmpn( n1, n2 )) == 0 ) return n1;
523: else if ( l < 0 ) { SWAP( n1, n2, N ); }
524: IniDiv( n1, n2 );
525: if ( UNIN(n2) ) return 0;
526: loop: if ( (l1 = PL(n1)) <= 2 && (l2 = PL(n2)) <= 2 ) {
527: l = igcd_binary_2w( BD(n1), l1, BD(n2), l2, BD(nt) );
528: if ( l == 0 ) return 0;
529: PL(nt) = l;
530: return nt;
531: }
532: /**/
533: l = bmod_n( n1, n2, nt );
534: /**/
535: if ( l == 0 ) return n2;
536: else if ( l > 0 ) {
537: N tmp = n1;
538:
539: n1 = n2;
540: n2 = nt;
541: nt = tmp;
542: } else SWAP( n1, n2, N );
543: goto loop;
544: }
545:
546: void gcdbmodn( n1, n2, nr )
547: N n1, n2, *nr;
548: {
549: int s1, s2, gw, gb, t1, t2;
550: int w1, w2;
551: N tn1, tn2, tnt, p;
552:
553: if ( !n1 ) {
554: *nr = n2;
555: return;
556: } else if ( !n2 ) {
557: *nr = n1;
558: return;
559: }
560: s1 = trailingzerosn( n1, &w1 );
561: s2 = trailingzerosn( n2, &w2 );
562: if ( w1 == w2 ) gw = w1, gb = s1 <= s2 ? s1 : s2;
563: else if ( w1 < w2 ) gw = w1, gb = s1;
564: else gw = w2, gb = s2;
565: /*
566: * true GCD must be multiplied by 2^{gw*BSH27+gs}.
567: */
568: t1 = PL(n1) - w1;
569: t2 = PL(n2) - w2;
570: if ( t1 < t2 ) t1 = t2;
571: tn1 = W_NALLOC(t1); tn2 = W_NALLOC(t1); tnt = W_NALLOC(t1);
572: rshiftn( n1, w1, s1, tn1 );
573: rshiftn( n2, w2, s2, tn2 );
574: p = igcd_bmod( tn1, tn2, tnt );
575: RetTrueGCD( p, gw, gb, nr, L0 )
576: }
577:
578: /*
579: * The accelerated integer GCD algorithm by K.Weber
580: * [ACM TOMS, Vol.21, No. 1 (1995), pp. 111-122]:
581: */
582:
583: static int ReducedRatMod( x, y, pn, pd )
584: N x, y;
585: int *pn, *pd;
586: /*
587: * Let m = 2^{2*BSH27} = 2*BASE27. We assume x, y > 0 and \gcd(x,m)
588: * = \gcd(y,m) = 1. This routine computes n and d (resp. returned
589: * in *pn and *pd) such that 0 < n, |d| < \sqrt{m} and
590: * n*y \equiv x*d \bmod m.
591: */
592: {
593: int n1h, n1l, d1h, d1l, n2h, n2l, d2h, d2l;
594: int s1, s2, l1, l2;
595:
596:
597: {
598: int xh, xl, yh, yl, tl, i, lsh_i;
599: int th;
600:
601: xl = BD(x)[0];
602: xh = PL(x) > 1 ? BD(x)[1] : 0;
603: yl = BD(y)[0];
604: yh = PL(y) > 1 ? BD(y)[1] : 0;
605: Comp_U_div_V_mod_BASE27( xl, yl, n2l );
606: DM27(n2l,yl,th,tl) /* n2l*yl = tl+th*BASE27, where tl==xl. */;
607: if ( xh > th ) xh -= th;
608: else xh += (BASE27 - th);
609: DM27(n2l,yh,th,tl) /* n2l*yh = tl+th*BASE27. */;
610: if ( xh > tl ) xh -= tl;
611: else xh += (BASE27 - tl);
612: n2h = i = 0, lsh_i = 31;
613: do {
614: if ( xh == 0 ) break;
615: if ( (xh << lsh_i) != 0 ) {
616: n2h += (1 << i);
617: tl = (yl << i)&BMASK27;
618: if ( xh > tl ) xh -= tl;
619: else xh += (BASE27 - tl);
620: }
621: lsh_i--;
622: } while ( ++i != BSH27 );
623: }
624: /*
625: * n2l + n2h*BASE27 = x/y mod 2^{2*BSH27}.
626: */
627: n1h = BASE27, n1l = 0, l1 = BSH27,
628: d1h = d1l = 0, s1 = 0,
629: d2h = 0, d2l = 1, s2 = 1;
630: /**/
631: while ( n2h != 0 ) {
632: int i, ir, th, tl;
633:
634: BitWidth( n2h, l2 );
635: ir = BSH27 - (i = l1 - l2);
636: do {
637: if ( i == 0 ) th = n2h, tl = n2l;
638: else
639: th = (n2h << i) | (n2l >> ir),
640: tl = (n2l << i) & BMASK27;
641: if ( th > n1h || (th == n1h && tl > n1l) ) goto next_i;
642: if ( tl <= n1l ) n1l -= tl;
643: else n1l += (BASE27 - tl), n1h--;
644: n1h -= th;
645: /* (s1:d1h,d1l) -= ((s2:d2h,d2l) << i); */
646: if ( s2 != 0 ) {
647: if ( i == 0 ) th = d2h, tl = d2l;
648: else
649: th = (d2h << i)&BMASK27 | (d2l >> ir),
650: tl = (d2l << i)&BMASK27;
651: if ( s1 == 0 )
652: s1 = -s2, d1h = th, d1l = tl;
653: else if ( s1 != s2 ) {
654: tl += d1l;
655: d1l = tl&BMASK27;
656: d1h = (th + (tl >> BSH27))&BMASK27;
657: if ( d1h == 0 && d1l == 0 ) s1 = 0;
658: } else if ( d1h > th ) {
659: if ( d1l >= tl ) d1l -= tl;
660: else d1l += (BASE27 - tl), d1h--;
661: d1h -= th;
662: } else if ( d1h == th ) {
663: d1h = 0;
664: if ( d1l == tl ) s1 = d2h = 0;
665: else if ( d1l > tl ) d1l -= tl;
666: else d1l = tl - d1l, s1 = -s1;
667: } else {
668: if ( tl >= d1l ) d1l = tl - d1l;
669: else d1l = tl + (BASE27 - d1l), th--;
670: d1h = th - d1h;
671: s1 = -s1;
672: }
673: }
674: next_i: i--, ir++;
675: } while ( n1h > n2h || (n1h == n2h && n1l >= n2l) );
676: /* swap 1 and 2 */
677: th = n1h, tl = n1l;
678: n1h = n2h, n1l = n2l;
679: n2h = th, n2l = tl;
680: l1 = l2;
681: th = d1h, tl = d1l, i = s1;
682: d1h = d2h, d1l = d2l, s1 = s2;
683: d2h = th, d2l = tl, s2 = i;
684: }
685: /**/
686: *pn = n2l, *pd = d2l;
687: return s2;
688: }
689:
690: static int igcd_spurious_factor;
691:
692: #define SaveN(s,d) {\
693: int i, l; \
694: for ( l = PL(d) = PL(s), i = 0; i < l; i++ ) BD(d)[i] = BD(s)[i]; \
695: }
696:
697: static N igcd_acc( n1, n2, nt )
698: N n1, n2, nt;
699: /* both n1 and n2 are assumed to be odd */
700: {
701: int l1, l2, *b1, *b2, bw1, bw2;
702: int l;
703: int n, d;
704: N p, s1, s2;
705:
706: if ( (l = cmpn( n1, n2 )) == 0 ) return n1;
707: else if ( l < 0 ) { SWAP( n1, n2, N ); }
708: if ( ShouldCompRemInit(n1,n2) ) {
709: int w, b;
710:
711: divn_27( n1, n2, &s1, &s2 );
712: if ( !s2 ) return n2;
713: b = trailingzerosn( s2, &w );
714: p = n1; n1 = n2; n2 = p;
715: rshiftn( s2, w, b, n2 );
716: if ( UNIN(n2) ) return 0;
717: l1 = PL(n1);
718: if ( !s1 || PL(s1) < l1 ) s1 = NALLOC(l1);
719: } else if ( UNIN(n2) ) return 0;
720: else {
721: s1 = NALLOC(PL(n1));
722: s2 = NALLOC(PL(n2));
723: }
724: SaveN( n1, s1 );
725: SaveN( n2, s2 );
726: igcd_spurious_factor = 0;
727: loop: l1 = PL(n1), l2 = PL(n2);
728: if ( l1 <= 2 && l2 <= 2 ) {
729: l = igcd_binary_2w( BD(n1), l1, BD(n2), l2, BD(nt) );
730: if ( l == 0 ) return 0;
731: PL(nt) = l;
732: SWAP( n2, nt, N );
733: goto ret;
734: }
735: /**/
736: b1 = BD(n1), b2 = BD(n2);
737: BitWidth( b1[l1 -1], bw1 );
738: BitWidth( b2[l2 -1], bw2 );
739: if ( (l1*BSH27 + bw1) - (l2*BSH27 + bw2) <= igcdacc_thre ) {
740: l = ReducedRatMod( n1, n2, &n, &d );
741: l = l < 0 ? aUplusbV_maxrshift( n, b2, l2, d, b1, l1, BD(nt) ) :
742: abs_axU_bxV_maxrshift( n, b2, l2, d, b1, l1, BD(nt) );
743: igcd_spurious_factor++;
744: if ( l == 0 ) goto ret;
745: PL(nt) = l;
746: } else {
747: l = bmod_n( n1, n2, nt );
748: if ( l == 0 ) goto ret;
749: else if ( l < 0 ) {
750: SWAP( n1, n2, N );
751: goto loop;
752: }
753: }
754: p = n1;
755: n1 = n2;
756: n2 = nt;
757: nt = p;
758: goto loop;
759: /**/
760: ret: if ( igcd_spurious_factor != 0 && !UNIN(n2) ) {
761: if ( (p = igcd_bmod( n2, s1, n1 )) == 0 ) return 0;
762: if ( (p = igcd_bmod( p, s2, nt )) == 0 ) return 0;
763: return p;
764: } else return n2;
765: }
766:
767: void gcdaccn( n1, n2, nr )
768: N n1, n2, *nr;
769: {
770: int s1, s2, gw, gb, t1, t2;
771: int w1, w2;
772: N tn1, tn2, tnt, p;
773:
774: if ( !n1 ) {
775: *nr = n2;
776: return;
777: } else if ( !n2 ) {
778: *nr = n1;
779: return;
780: }
781: s1 = trailingzerosn( n1, &w1 );
782: s2 = trailingzerosn( n2, &w2 );
783: if ( w1 == w2 ) gw = w1, gb = s1 <= s2 ? s1 : s2;
784: else if ( w1 < w2 ) gw = w1, gb = s1;
785: else gw = w2, gb = s2;
786: /*
787: * true GCD must be multiplied by 2^{gw*BSH27+gs}.
788: */
789: t1 = PL(n1) - w1;
790: t2 = PL(n2) - w2;
791: if ( t1 < t2 ) t1 = t2;
792: tn1 = W_NALLOC(t1); tn2 = W_NALLOC(t1); tnt = W_NALLOC(t1);
793: rshiftn( n1, w1, s1, tn1 );
794: rshiftn( n2, w2, s2, tn2 );
795: /**/
796: p = igcd_acc( tn1, tn2, tnt );
797: /**/
798: if ( p == 0 ) goto L0;
799: RetTrueGCD( p, gw, gb, nr, L0 )
800: }
801:
802:
803: /********************************/
804:
805: void gcdBinary_27n( n1, n2, nr )
806: N n1, n2, *nr;
807: {
808: int b1, b2, w1, w2, gw, gb;
809: int l1, l2;
810: N tn1, tn2, tnt, a;
811:
812: if ( !n1 ) {
813: *nr = n2; return;
814: } else if ( !n2 ) {
815: *nr = n1; return;
816: }
817: b1 = trailingzerosn( n1, &w1 );
818: b2 = trailingzerosn( n2, &w2 );
819: if ( w1 == w2 ) gw = w1, gb = b1 <= b2 ? b1 : b2;
820: else if ( w1 < w2 ) gw = w1, gb = b1;
821: else gw = w2, gb = b2;
822: /*
823: * true GCD must be multiplied by 2^{gw*BSH27+gb}.
824: */
825: l1 = PL(n1) - w1;
826: l2 = PL(n2) - w2;
827: if ( l1 < l2 ) l1 = l2;
828: tn1 = W_NALLOC( l1 ); tn2 = W_NALLOC( l1 ); tnt = W_NALLOC( l1 );
829: rshiftn( n1, w1, b1, tn1 );
830: rshiftn( n2, w2, b2, tn2 );
831: /**/
832: if ( igcd_algorithm == 1 ) {
833: a = igcd_binary( tn1, tn2, tnt );
834: } else if ( igcd_algorithm == 2 ) {
835: a = igcd_bmod( tn1, tn2, tnt );
836: } else {
837: a = igcd_acc( tn1, tn2, tnt, -igcd_algorithm );
838: if ( igcd_spurious_factor != 0 ) {
839: }
840: }
841: RetTrueGCD( a, gw, gb, nr, L0 )
842: }
843:
844: /**************************/
845: N maxrshn( n, p )
846: N n;
847: int *p;
848: {
849: int nw, nb, c, l;
850: N new;
851:
852: nb = trailingzerosn( n, &nw );
853: l = PL(n);
854: c = BD(n)[l -1];
855: l -= nw;
856: if ( (c >> nb) == 0 ) l--;
857: new = NALLOC(l);
858: rshiftn( n, nw, nb, new );
859: *p = nb + nw*BSH27;
860: return new;
861: }
862: #endif /* HMEXT */