Line data Source code
1 : /* Copyright (C) 2000-2010 The PARI group.
2 :
3 : This file is part of the PARI/GP package.
4 :
5 : PARI/GP is free software; you can redistribute it and/or modify it under the
6 : terms of the GNU General Public License as published by the Free Software
7 : Foundation. It is distributed in the hope that it will be useful, but WITHOUT
8 : ANY WARRANTY WHATSOEVER.
9 :
10 : Check the License for details. You should have received a copy of it, along
11 : with the package; see the file 'COPYING'. If not, write to the Free Software
12 : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
13 :
14 : /*******************************************************************/
15 : /* */
16 : /* CONSTRUCTORS */
17 : /* */
18 : /*******************************************************************/
19 : #define retmkfrac(x,y)\
20 : do { GEN _v = cgetg(3, t_FRAC);\
21 : gel(_v,1) = (x);\
22 : gel(_v,2) = (y); return _v; } while(0)
23 : #define retmkrfrac(x,y)\
24 : do { GEN _v = cgetg(3, t_RFRAC);\
25 : gel(_v,1) = (x);\
26 : gel(_v,2) = (y); return _v; } while(0)
27 : #define retmkintmod(x,y)\
28 : do { GEN _v = cgetg(3, t_INTMOD);\
29 : gel(_v,1) = (y);\
30 : gel(_v,2) = (x); return _v; } while(0)
31 : #define retmkcomplex(x,y)\
32 : do { GEN _v = cgetg(3, t_COMPLEX);\
33 : gel(_v,1) = (x);\
34 : gel(_v,2) = (y); return _v; } while(0)
35 : #define retmkpolmod(x,y)\
36 : do { GEN _v = cgetg(3, t_POLMOD);\
37 : gel(_v,1) = (y);\
38 : gel(_v,2) = (x); return _v; } while(0)
39 : #define retmkvec(x)\
40 : do { GEN _v = cgetg(2, t_VEC);\
41 : gel(_v,1) = (x); return _v; } while(0)
42 : #define retmkvec2(x,y)\
43 : do { GEN _v = cgetg(3, t_VEC);\
44 : gel(_v,1) = (x);\
45 : gel(_v,2) = (y); return _v; } while(0)
46 : #define retmkvec3(x,y,z)\
47 : do { GEN _v = cgetg(4, t_VEC);\
48 : gel(_v,1) = (x);\
49 : gel(_v,2) = (y);\
50 : gel(_v,3) = (z); return _v; } while(0)
51 : #define retmkqfi(x,y,z)\
52 : do { GEN _v = cgetg(4, t_QFI);\
53 : gel(_v,1) = (x);\
54 : gel(_v,2) = (y);\
55 : gel(_v,3) = (z); return _v; } while(0)
56 : #define retmkqfr(x,y,z,d)\
57 : do { GEN _v = cgetg(5, t_QFR);\
58 : gel(_v,1) = (x);\
59 : gel(_v,2) = (y);\
60 : gel(_v,3) = (z);\
61 : gel(_v,4) = (d); return _v; } while(0)
62 : #define retmkquad(x,y,z)\
63 : do { GEN _v = cgetg(4, t_QUAD);\
64 : gel(_v,1) = (x);\
65 : gel(_v,2) = (y);\
66 : gel(_v,3) = (z); return _v; } while(0)
67 : #define retmkvec4(x,y,z,t)\
68 : do { GEN _v = cgetg(5, t_VEC);\
69 : gel(_v,1) = (x);\
70 : gel(_v,2) = (y);\
71 : gel(_v,3) = (z);\
72 : gel(_v,4) = (t); return _v; } while(0)
73 : #define retmkvec5(x,y,z,t,u)\
74 : do { GEN _v = cgetg(6, t_VEC);\
75 : gel(_v,1) = (x);\
76 : gel(_v,2) = (y);\
77 : gel(_v,3) = (z);\
78 : gel(_v,4) = (t);\
79 : gel(_v,5) = (u); return _v; } while(0)
80 : #define retmkcol(x)\
81 : do { GEN _v = cgetg(2, t_COL);\
82 : gel(_v,1) = (x); return _v; } while(0)
83 : #define retmkcol2(x,y)\
84 : do { GEN _v = cgetg(3, t_COL);\
85 : gel(_v,1) = (x);\
86 : gel(_v,2) = (y); return _v; } while(0)
87 : #define retmkcol3(x,y,z)\
88 : do { GEN _v = cgetg(4, t_COL);\
89 : gel(_v,1) = (x);\
90 : gel(_v,2) = (y);\
91 : gel(_v,3) = (z); return _v; } while(0)
92 : #define retmkcol4(x,y,z,t)\
93 : do { GEN _v = cgetg(5, t_COL);\
94 : gel(_v,1) = (x);\
95 : gel(_v,2) = (y);\
96 : gel(_v,3) = (z);\
97 : gel(_v,4) = (t); return _v; } while(0)
98 : #define retmkcol5(x,y,z,t,u)\
99 : do { GEN _v = cgetg(6, t_COL);\
100 : gel(_v,1) = (x);\
101 : gel(_v,2) = (y);\
102 : gel(_v,3) = (z);\
103 : gel(_v,4) = (t);\
104 : gel(_v,5) = (u); return _v; } while(0)
105 : #define retmkcol6(x,y,z,t,u,v)\
106 : do { GEN _v = cgetg(7, t_COL);\
107 : gel(_v,1) = (x);\
108 : gel(_v,2) = (y);\
109 : gel(_v,3) = (z);\
110 : gel(_v,4) = (t);\
111 : gel(_v,5) = (u);\
112 : gel(_v,6) = (v); return _v; } while(0)
113 : #define retmkmat(x)\
114 : do { GEN _v = cgetg(2, t_MAT);\
115 : gel(_v,1) = (x); return _v; } while(0)
116 : #define retmkmat2(x,y)\
117 : do { GEN _v = cgetg(3, t_MAT);\
118 : gel(_v,1) = (x);\
119 : gel(_v,2) = (y); return _v; } while(0)
120 : #define retmkmat3(x,y,z)\
121 : do { GEN _v = cgetg(4, t_MAT);\
122 : gel(_v,1) = (x);\
123 : gel(_v,2) = (y);\
124 : gel(_v,3) = (z); return _v; } while(0)
125 : #define retmkmat4(x,y,z,t)\
126 : do { GEN _v = cgetg(5, t_MAT);\
127 : gel(_v,1) = (x);\
128 : gel(_v,2) = (y);\
129 : gel(_v,3) = (z);\
130 : gel(_v,4) = (t); return _v; } while(0)
131 : #define retmkmat5(x,y,z,t,u)\
132 : do { GEN _v = cgetg(6, t_MAT);\
133 : gel(_v,1) = (x);\
134 : gel(_v,2) = (y);\
135 : gel(_v,3) = (z);\
136 : gel(_v,4) = (t);\
137 : gel(_v,5) = (u); return _v; } while(0)
138 :
139 : INLINE GEN
140 2156105 : mkintmod(GEN x, GEN y) { retmkintmod(x,y); }
141 : INLINE GEN
142 3794 : mkintmodu(ulong x, ulong y) {
143 3794 : GEN v = cgetg(3,t_INTMOD);
144 3794 : gel(v,1) = utoipos(y);
145 3794 : gel(v,2) = utoi(x); return v;
146 : }
147 : INLINE GEN
148 1429277 : mkpolmod(GEN x, GEN y) { retmkpolmod(x,y); }
149 : INLINE GEN
150 2397809 : mkfrac(GEN x, GEN y) { retmkfrac(x,y); }
151 : INLINE GEN
152 336 : mkfracss(long x, long y) { retmkfrac(stoi(x),stoi(y)); }
153 : /* q = n/d a t_FRAC or t_INT; recover (n,d) */
154 : INLINE void
155 0 : Qtoss(GEN q, long *n, long *d)
156 : {
157 0 : if (typ(q) == t_INT) { *n = itos(q); *d = 1; }
158 0 : else { *n = itos(gel(q,1)); *d = itou(gel(q,2)); }
159 0 : }
160 : INLINE GEN
161 18067 : sstoQ(long n, long d)
162 : {
163 : long g, r, q;
164 18067 : if (d == 1) return stoi(n);
165 17878 : q = sdivss_rem(n,d,&r);
166 17878 : if (!r) return stoi(q);
167 11235 : g = cgcd(d,r); /* gcd(n,d) */
168 11235 : if (g != 1) { n /= g; d /= g; }
169 11235 : if (d < 0) { d = -d; n = -n; }
170 11235 : retmkfrac(stoi(n), utoi(d));
171 : }
172 :
173 : INLINE GEN
174 5437859 : mkfraccopy(GEN x, GEN y) { retmkfrac(icopy(x), icopy(y)); }
175 : INLINE GEN
176 7 : mkrfrac(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
177 7 : gel(v,1) = x; gel(v,2) = y; return v; }
178 : INLINE GEN
179 7 : mkrfraccopy(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
180 7 : gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
181 : INLINE GEN
182 3163536 : mkcomplex(GEN x, GEN y) { retmkcomplex(x,y); }
183 : INLINE GEN
184 436032 : gen_I(void) { return mkcomplex(gen_0, gen_1); }
185 : INLINE GEN
186 203084 : cgetc(long l) { retmkcomplex(cgetr(l), cgetr(l)); }
187 : INLINE GEN
188 42 : mkquad(GEN n, GEN x, GEN y) { GEN v = cgetg(4, t_QUAD);
189 42 : gel(v,1) = n; gel(v,2) = x; gel(v,3) = y; return v; }
190 : /* vecsmall */
191 : INLINE GEN
192 55101431 : mkvecsmall(long x) { GEN v = cgetg(2, t_VECSMALL); v[1] = x; return v; }
193 : INLINE GEN
194 110495410 : mkvecsmall2(long x,long y) { GEN v = cgetg(3, t_VECSMALL);
195 110489432 : v[1]=x; v[2]=y; return v; }
196 : INLINE GEN
197 65047289 : mkvecsmall3(long x,long y,long z) { GEN v = cgetg(4, t_VECSMALL);
198 65044608 : v[1]=x; v[2]=y; v[3]=z; return v; }
199 : INLINE GEN
200 23739110 : mkvecsmall4(long x,long y,long z,long t) { GEN v = cgetg(5, t_VECSMALL);
201 23729454 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; return v; }
202 : INLINE GEN
203 702726 : mkvecsmall5(long x,long y,long z,long t,long u) { GEN v = cgetg(6, t_VECSMALL);
204 702726 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; v[5]=u; return v; }
205 :
206 : INLINE GEN
207 158123 : mkqfi(GEN x, GEN y, GEN z) { retmkqfi(x,y,z); }
208 : /* vec */
209 : INLINE GEN
210 12576478 : mkvec(GEN x) { retmkvec(x); }
211 : INLINE GEN
212 132253402 : mkvec2(GEN x, GEN y) { retmkvec2(x,y); }
213 : INLINE GEN
214 73870634 : mkvec3(GEN x, GEN y, GEN z) { retmkvec3(x,y,z); }
215 : INLINE GEN
216 7750003 : mkvec4(GEN x, GEN y, GEN z, GEN t) { retmkvec4(x,y,z,t); }
217 : INLINE GEN
218 11954697 : mkvec5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkvec5(x,y,z,t,u); }
219 : INLINE GEN
220 7 : mkvecs(long x) { retmkvec(stoi(x)); }
221 : INLINE GEN
222 20046 : mkvec2s(long x, long y) { retmkvec2(stoi(x),stoi(y)); }
223 : INLINE GEN
224 492702 : mkvec3s(long x, long y, long z) { retmkvec3(stoi(x),stoi(y),stoi(z)); }
225 : INLINE GEN
226 0 : mkvec4s(long x, long y, long z, long t) { retmkvec4(stoi(x),stoi(y),stoi(z),stoi(t)); }
227 : INLINE GEN
228 33460 : mkveccopy(GEN x) { GEN v = cgetg(2, t_VEC); gel(v,1) = gcopy(x); return v; }
229 : INLINE GEN
230 108962 : mkvec2copy(GEN x, GEN y) {
231 108962 : GEN v = cgetg(3,t_VEC); gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
232 : /* col */
233 : INLINE GEN
234 2222778 : mkcol(GEN x) { retmkcol(x); }
235 : INLINE GEN
236 14953083 : mkcol2(GEN x, GEN y) { retmkcol2(x,y); }
237 : INLINE GEN
238 41615 : mkcol3(GEN x, GEN y, GEN z) { retmkcol3(x,y,z); }
239 : INLINE GEN
240 0 : mkcol4(GEN x, GEN y, GEN z, GEN t) { retmkcol4(x,y,z,t); }
241 : INLINE GEN
242 0 : mkcol5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkcol5(x,y,z,t,u); }
243 : INLINE GEN
244 4208 : mkcol6(GEN x, GEN y, GEN z, GEN t, GEN u, GEN v) { retmkcol6(x,y,z,t,u,v); }
245 : INLINE GEN
246 735 : mkcols(long x) { retmkcol(stoi(x)); }
247 : INLINE GEN
248 1181376 : mkcol2s(long x, long y) { retmkcol2(stoi(x),stoi(y)); }
249 : INLINE GEN
250 0 : mkcol3s(long x, long y, long z) { retmkcol3(stoi(x),stoi(y),stoi(z)); }
251 : INLINE GEN
252 0 : mkcol4s(long x, long y, long z, long t) { retmkcol4(stoi(x),stoi(y),stoi(z),stoi(t)); }
253 : INLINE GEN
254 28872 : mkcolcopy(GEN x) { GEN v = cgetg(2, t_COL); gel(v,1) = gcopy(x); return v; }
255 : /* mat */
256 : INLINE GEN
257 730701 : mkmat(GEN x) { retmkmat(x); }
258 : INLINE GEN
259 16241926 : mkmat2(GEN x, GEN y) { retmkmat2(x,y); }
260 : INLINE GEN
261 2352 : mkmat3(GEN x, GEN y, GEN z) { retmkmat3(x,y,z); }
262 : INLINE GEN
263 0 : mkmat4(GEN x, GEN y, GEN z, GEN t) { retmkmat4(x,y,z,t); }
264 : INLINE GEN
265 0 : mkmat5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkmat5(x,y,z,t,u); }
266 : INLINE GEN
267 7445 : mkmatcopy(GEN x) { GEN v = cgetg(2, t_MAT); gel(v,1) = gcopy(x); return v; }
268 : INLINE GEN
269 0 : mkerr(long x) { GEN v = cgetg(2, t_ERROR); v[1] = x; return v; }
270 : INLINE GEN
271 24416 : mkoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
272 : INLINE GEN
273 13979 : mkmoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
274 : INLINE long
275 47776 : inf_get_sign(GEN x) { return signe(gel(x,1)); }
276 : /* pol */
277 : INLINE GEN
278 735925 : pol_x(long v) {
279 735925 : GEN p = cgetg(4, t_POL);
280 735925 : p[1] = evalsigne(1)|evalvarn(v);
281 735925 : gel(p,2) = gen_0;
282 735925 : gel(p,3) = gen_1; return p;
283 : }
284 : /* x^n, assume n >= 0 */
285 : INLINE GEN
286 2489881 : pol_xn(long n, long v) {
287 2489881 : long i, a = n+2;
288 2489881 : GEN p = cgetg(a+1, t_POL);
289 2489881 : p[1] = evalsigne(1)|evalvarn(v);
290 2489881 : for (i = 2; i < a; i++) gel(p,i) = gen_0;
291 2489881 : gel(p,a) = gen_1; return p;
292 : }
293 : /* x^n, no assumption on n */
294 : INLINE GEN
295 42 : pol_xnall(long n, long v)
296 : {
297 42 : if (n < 0) retmkrfrac(gen_1, pol_xn(-n,v));
298 42 : return pol_xn(n, v);
299 : }
300 : INLINE GEN
301 1271267 : pol_1(long v) {
302 1271267 : GEN p = cgetg(3, t_POL);
303 1271271 : p[1] = evalsigne(1)|evalvarn(v);
304 1271271 : gel(p,2) = gen_1; return p;
305 : }
306 : INLINE GEN
307 18717699 : pol_0(long v)
308 : {
309 18717699 : GEN x = cgetg(2,t_POL);
310 18717699 : x[1] = evalvarn(v); return x;
311 : }
312 : #define retconst_vec(n,x)\
313 : do { long _i, _n = (n);\
314 : GEN _v = cgetg(_n+1, t_VEC), _x = (x);\
315 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
316 : return _v; } while(0)
317 : INLINE GEN
318 7572769 : const_vec(long n, GEN x) { retconst_vec(n, x); }
319 : #define retconst_col(n,x)\
320 : do { long _i, _n = (n);\
321 : GEN _v = cgetg(_n+1, t_COL), _x = (x);\
322 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
323 : return _v; } while(0)
324 : INLINE GEN
325 84785 : const_col(long n, GEN x) { retconst_col(n, x); }
326 : INLINE GEN
327 4687403 : const_vecsmall(long n, long c)
328 : {
329 : long i;
330 4687403 : GEN V = cgetg(n+1,t_VECSMALL);
331 4687405 : for(i=1;i<=n;i++) V[i] = c;
332 4687405 : return V;
333 : }
334 :
335 : /*** ZERO ***/
336 : /* O(p^e) */
337 : INLINE GEN
338 303174 : zeropadic(GEN p, long e)
339 : {
340 303174 : GEN y = cgetg(5,t_PADIC);
341 303174 : gel(y,4) = gen_0;
342 303174 : gel(y,3) = gen_1;
343 303174 : gel(y,2) = icopy(p);
344 303174 : y[1] = evalvalp(e) | _evalprecp(0);
345 303174 : return y;
346 : }
347 : INLINE GEN
348 532 : zeropadic_shallow(GEN p, long e)
349 : {
350 532 : GEN y = cgetg(5,t_PADIC);
351 532 : gel(y,4) = gen_0;
352 532 : gel(y,3) = gen_1;
353 532 : gel(y,2) = p;
354 532 : y[1] = evalvalp(e) | _evalprecp(0);
355 532 : return y;
356 : }
357 : /* O(pol_x(v)^e) */
358 : INLINE GEN
359 14532 : zeroser(long v, long e)
360 : {
361 14532 : GEN x = cgetg(2, t_SER);
362 14532 : x[1] = evalvalp(e) | evalvarn(v); return x;
363 : }
364 : INLINE int
365 3700017 : ser_isexactzero(GEN x)
366 : {
367 3700017 : if (!signe(x)) switch(lg(x))
368 : {
369 12761 : case 2: return 1;
370 840 : case 3: return isexactzero(gel(x,2));
371 : }
372 3686416 : return 0;
373 : }
374 : /* 0 * pol_x(v) */
375 : INLINE GEN
376 6422783 : zeropol(long v) { return pol_0(v); }
377 : /* vector(n) */
378 : INLINE GEN
379 28313448 : zerocol(long n)
380 : {
381 28313448 : GEN y = cgetg(n+1,t_COL);
382 28313448 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
383 28313448 : return y;
384 : }
385 : /* vectorv(n) */
386 : INLINE GEN
387 18225336 : zerovec(long n)
388 : {
389 18225336 : GEN y = cgetg(n+1,t_VEC);
390 18225333 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
391 18225333 : return y;
392 : }
393 : /* matrix(m, n) */
394 : INLINE GEN
395 15498 : zeromat(long m, long n)
396 : {
397 15498 : GEN y = cgetg(n+1,t_MAT);
398 15498 : GEN v = zerocol(m);
399 15498 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
400 15498 : return y;
401 : }
402 : /* = zero_zx, sv is a evalvarn()*/
403 : INLINE GEN
404 792542 : zero_Flx(long sv) { return pol0_Flx(sv); }
405 : INLINE GEN
406 32308484 : zero_Flv(long n)
407 : {
408 32308484 : GEN y = cgetg(n+1,t_VECSMALL);
409 32308640 : long i; for (i=1; i<=n; i++) y[i] = 0;
410 32308640 : return y;
411 : }
412 : /* matrix(m, n) */
413 : INLINE GEN
414 882112 : zero_Flm(long m, long n)
415 : {
416 882112 : GEN y = cgetg(n+1,t_MAT);
417 882112 : GEN v = zero_Flv(m);
418 882112 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
419 882112 : return y;
420 : }
421 : /* matrix(m, n) */
422 : INLINE GEN
423 93238 : zero_Flm_copy(long m, long n)
424 : {
425 93238 : GEN y = cgetg(n+1,t_MAT);
426 93249 : long i; for (i=1; i<=n; i++) gel(y,i) = zero_Flv(m);
427 93243 : return y;
428 : }
429 :
430 : INLINE GEN
431 789520 : zero_F2v(long m)
432 : {
433 789520 : long l = nbits2nlong(m);
434 789520 : GEN v = zero_Flv(l+1);
435 789520 : v[1] = m;
436 789520 : return v;
437 : }
438 :
439 : INLINE GEN
440 0 : zero_F2m(long m, long n)
441 : {
442 : long i;
443 0 : GEN M = cgetg(n+1, t_MAT);
444 0 : GEN v = zero_F2v(m);
445 0 : for (i = 1; i <= n; i++)
446 0 : gel(M,i) = v;
447 0 : return M;
448 : }
449 :
450 :
451 : INLINE GEN
452 280225 : zero_F2m_copy(long m, long n)
453 : {
454 : long i;
455 280225 : GEN M = cgetg(n+1, t_MAT);
456 859181 : for (i = 1; i <= n; i++)
457 578956 : gel(M,i)= zero_F2v(m);
458 280225 : return M;
459 : }
460 :
461 : /* matrix(m, n) */
462 : INLINE GEN
463 2001482 : zeromatcopy(long m, long n)
464 : {
465 2001482 : GEN y = cgetg(n+1,t_MAT);
466 2001482 : long i; for (i=1; i<=n; i++) gel(y,i) = zerocol(m);
467 2001482 : return y;
468 : }
469 :
470 : INLINE GEN
471 16919 : zerovec_block(long len)
472 : {
473 : long i;
474 16919 : GEN blk = cgetg_block(len + 1, t_VEC);
475 558327 : for (i = 1; i <= len; ++i)
476 541408 : gel(blk, i) = gen_0;
477 16919 : return blk;
478 : }
479 :
480 : /* i-th vector in the standard basis */
481 : INLINE GEN
482 1389431 : col_ei(long n, long i) { GEN e = zerocol(n); gel(e,i) = gen_1; return e; }
483 : INLINE GEN
484 337212 : vec_ei(long n, long i) { GEN e = zerovec(n); gel(e,i) = gen_1; return e; }
485 : INLINE GEN
486 7 : F2v_ei(long n, long i) { GEN e = zero_F2v(n); F2v_set(e,i); return e; }
487 : INLINE GEN
488 68825 : vecsmall_ei(long n, long i) { GEN e = zero_zv(n); e[i] = 1; return e; }
489 : INLINE GEN
490 1170157 : Rg_col_ei(GEN x, long n, long i) { GEN e = zerocol(n); gel(e,i) = x; return e; }
491 :
492 : INLINE GEN
493 2653456 : shallowcopy(GEN x)
494 2653456 : { return typ(x) == t_MAT ? RgM_shallowcopy(x): leafcopy(x); }
495 :
496 : /* routines for naive growarrays */
497 : INLINE GEN
498 12711125 : vectrunc_init(long l)
499 : {
500 12711125 : GEN z = new_chunk(l);
501 12711482 : z[0] = evaltyp(t_VEC) | _evallg(1); return z;
502 : }
503 : INLINE void
504 507093123 : lg_increase(GEN x) { x[0]++; }
505 : INLINE void
506 49284454 : vectrunc_append(GEN x, GEN t) { gel(x, lg(x)) = t; lg_increase(x); }
507 : INLINE void
508 0 : vectrunc_append_batch(GEN x, GEN y)
509 : {
510 0 : long i, l = lg(x), ly = lg(y);
511 0 : GEN z = x + l-1;
512 0 : for (i = 1; i < ly; i++) gel(z,i) = gel(y,i);
513 0 : setlg(x, l+ly-1);
514 0 : }
515 : INLINE GEN
516 168349369 : vecsmalltrunc_init(long l)
517 : {
518 168349369 : GEN z = new_chunk(l);
519 168349369 : z[0] = evaltyp(t_VECSMALL) | _evallg(1); return z;
520 : }
521 : INLINE void
522 25858660 : vecsmalltrunc_append(GEN x, long t) { x[ lg(x) ] = t; lg_increase(x); }
523 :
524 : /*******************************************************************/
525 : /* */
526 : /* VEC / COL / VECSMALL */
527 : /* */
528 : /*******************************************************************/
529 : /* shallow*/
530 : INLINE GEN
531 0 : vec_shorten(GEN v, long n)
532 : {
533 : long i;
534 0 : GEN V = cgetg(n+1,t_VEC);
535 0 : for(i=1;i<=n;i++) gel(V,i) = gel(v,i);
536 0 : return V;
537 : }
538 : /* shallow*/
539 : INLINE GEN
540 10969 : vec_lengthen(GEN v, long n)
541 : {
542 : long i;
543 10969 : long l=lg(v);
544 10969 : GEN V = cgetg(n+1,t_VEC);
545 10969 : for(i=1;i<l;i++) gel(V,i) = gel(v,i);
546 10969 : return V;
547 : }
548 : /* shallow*/
549 : INLINE GEN
550 59332 : vec_append(GEN V, GEN s)
551 : {
552 59332 : long i, l2 = lg(V);
553 59332 : GEN res = cgetg(l2+1, typ(V));
554 59332 : for (i = 1; i < l2; ++i) gel(res, i) = gel(V,i);
555 59332 : gel(res,l2) = s; return res;
556 : }
557 : /* shallow*/
558 : INLINE GEN
559 49 : vec_prepend(GEN v, GEN s)
560 : {
561 49 : long i, l = lg(v);
562 49 : GEN w = cgetg(l+1, typ(v));
563 49 : gel(w,1) = s;
564 49 : for (i = 2; i <= l; ++i) gel(w,i) = gel(v,i-1);
565 49 : return w;
566 : }
567 : /* shallow*/
568 : INLINE GEN
569 0 : vec_setconst(GEN v, GEN x)
570 : {
571 0 : long i, l = lg(v);
572 0 : for (i = 1; i < l; i++) gel(v,i) = x;
573 0 : return v;
574 : }
575 : INLINE GEN
576 178946 : vecsmall_shorten(GEN v, long n)
577 : {
578 : long i;
579 178946 : GEN V = cgetg(n+1,t_VECSMALL);
580 178949 : for(i=1;i<=n;i++) V[i] = v[i];
581 178949 : return V;
582 : }
583 : INLINE GEN
584 21 : vecsmall_lengthen(GEN v, long n)
585 : {
586 21 : long i, l = lg(v);
587 21 : GEN V = cgetg(n+1,t_VECSMALL);
588 21 : for(i=1;i<l;i++) V[i] = v[i];
589 21 : return V;
590 : }
591 :
592 : INLINE GEN
593 410163 : vec_to_vecsmall(GEN z)
594 : {
595 410163 : long i, l = lg(z);
596 410163 : GEN x = cgetg(l, t_VECSMALL);
597 410163 : for (i=1; i<l; i++) x[i] = itos(gel(z,i));
598 410163 : return x;
599 : }
600 : INLINE GEN
601 71232 : vecsmall_to_vec(GEN z)
602 : {
603 71232 : long i, l = lg(z);
604 71232 : GEN x = cgetg(l,t_VEC);
605 71232 : for (i=1; i<l; i++) gel(x,i) = stoi(z[i]);
606 71232 : return x;
607 : }
608 : INLINE GEN
609 938 : vecsmall_to_vec_inplace(GEN z)
610 : {
611 938 : long i, l = lg(z);
612 938 : for (i=1; i<l; i++) gel(z,i) = stoi(z[i]);
613 938 : settyp(z, t_VEC); return z;
614 : }
615 : INLINE GEN
616 1301803 : vecsmall_to_col(GEN z)
617 : {
618 1301803 : long i, l = lg(z);
619 1301803 : GEN x = cgetg(l,t_COL);
620 1301803 : for (i=1; i<l; i++) gel(x,i) = stoi(z[i]);
621 1301803 : return x;
622 : }
623 :
624 : INLINE int
625 9456409 : vecsmall_lexcmp(GEN x, GEN y)
626 : {
627 : long lx,ly,l,i;
628 9456409 : lx = lg(x);
629 9456409 : ly = lg(y); l = minss(lx,ly);
630 56689382 : for (i=1; i<l; i++)
631 54634408 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
632 2054974 : if (lx == ly) return 0;
633 14 : return (lx < ly)? -1 : 1;
634 : }
635 :
636 : INLINE int
637 47066978 : vecsmall_prefixcmp(GEN x, GEN y)
638 : {
639 47066978 : long i, lx = lg(x), ly = lg(y), l = minss(lx,ly);
640 148811348 : for (i=1; i<l; i++)
641 134951817 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
642 13859531 : return 0;
643 : }
644 :
645 : /*Can be used on t_VEC, but coeffs not gcopy-ed*/
646 : INLINE GEN
647 12663 : vecsmall_prepend(GEN V, long s)
648 : {
649 12663 : long i, l2 = lg(V);
650 12663 : GEN res = cgetg(l2+1, typ(V));
651 12663 : res[1] = s;
652 12663 : for (i = 2; i <= l2; ++i) res[i] = V[i - 1];
653 12663 : return res;
654 : }
655 :
656 : INLINE GEN
657 3765602 : vecsmall_append(GEN V, long s)
658 : {
659 3765602 : long i, l2 = lg(V);
660 3765602 : GEN res = cgetg(l2+1, t_VECSMALL);
661 3765602 : for (i = 1; i < l2; ++i) res[i] = V[i];
662 3765602 : res[l2] = s; return res;
663 : }
664 :
665 : INLINE GEN
666 774688 : vecsmall_concat(GEN u, GEN v)
667 : {
668 774688 : long i, l1 = lg(u)-1, l2 = lg(v)-1;
669 774688 : GEN res = cgetg(l1+l2+1, t_VECSMALL);
670 774688 : for (i = 1; i <= l1; ++i) res[i] = u[i];
671 774688 : for (i = 1; i <= l2; ++i) res[i+l1] = v[i];
672 774688 : return res;
673 : }
674 :
675 : /* return the number of indices where u and v are equal */
676 : INLINE long
677 0 : vecsmall_coincidence(GEN u, GEN v)
678 : {
679 0 : long i, s = 0, l = minss(lg(u),lg(v));
680 0 : for(i=1; i<l; i++)
681 0 : if(u[i] == v[i]) s++;
682 0 : return s;
683 : }
684 :
685 : /* returns the first index i<=n such that x=v[i] if it exists, 0 otherwise */
686 : INLINE long
687 0 : vecsmall_isin(GEN v, long x)
688 : {
689 0 : long i, l = lg(v);
690 0 : for (i = 1; i < l; i++)
691 0 : if (v[i] == x) return i;
692 0 : return 0;
693 : }
694 :
695 : INLINE long
696 84 : vecsmall_pack(GEN V, long base, long mod)
697 : {
698 84 : long i, s = 0;
699 84 : for(i=1; i<lg(V); i++) s = (base*s + V[i]) % mod;
700 84 : return s;
701 : }
702 :
703 : INLINE long
704 14 : vecsmall_indexmax(GEN x)
705 : {
706 14 : long i, i0 = 1, t = x[1], lx = lg(x);
707 56 : for (i=2; i<lx; i++)
708 42 : if (x[i] > t) t = x[i0=i];
709 14 : return i0;
710 : }
711 :
712 : INLINE long
713 42799 : vecsmall_max(GEN x)
714 : {
715 42799 : long i, t = x[1], lx = lg(x);
716 78161 : for (i=2; i<lx; i++)
717 35362 : if (x[i] > t) t = x[i];
718 42799 : return t;
719 : }
720 :
721 : INLINE long
722 14 : vecsmall_indexmin(GEN x)
723 : {
724 14 : long i, i0 = 1, t = x[1], lx =lg(x);
725 56 : for (i=2; i<lx; i++)
726 42 : if (x[i] < t) t = x[i0=i];
727 14 : return i0;
728 : }
729 :
730 : INLINE long
731 0 : vecsmall_min(GEN x)
732 : {
733 0 : long i, t = x[1], lx =lg(x);
734 0 : for (i=2; i<lx; i++)
735 0 : if (x[i] < t) t = x[i];
736 0 : return t;
737 : }
738 :
739 : INLINE int
740 2123118 : ZV_isscalar(GEN x)
741 : {
742 2123118 : long l = lg(x);
743 7471640 : while (--l > 1)
744 4967399 : if (signe(gel(x, l))) return 0;
745 381123 : return 1;
746 : }
747 : INLINE int
748 17394262 : QV_isscalar(GEN x)
749 : {
750 17394262 : long lx = lg(x),i;
751 18858504 : for (i=2; i<lx; i++)
752 18331322 : if (!isintzero(gel(x, i))) return 0;
753 527182 : return 1;
754 : }
755 : INLINE int
756 3864 : RgV_isscalar(GEN x)
757 : {
758 3864 : long lx = lg(x),i;
759 7340 : for (i=2; i<lx; i++)
760 6241 : if (!gequal0(gel(x, i))) return 0;
761 1099 : return 1;
762 : }
763 : INLINE int
764 0 : RgX_isscalar(GEN x)
765 : {
766 : long i;
767 0 : for (i=lg(x)-1; i>2; i--)
768 0 : if (!gequal0(gel(x, i))) return 0;
769 0 : return 1;
770 : }
771 : INLINE long
772 23335040 : RgX_equal_var(GEN x, GEN y) { return varn(x) == varn(y) && RgX_equal(x,y); }
773 :
774 : INLINE int
775 5293 : RgX_is_rational(GEN x)
776 : {
777 : long i;
778 23499 : for (i = lg(x)-1; i > 1; i--)
779 22140 : if (!is_rational_t(typ(gel(x,i)))) return 0;
780 1359 : return 1;
781 : }
782 : INLINE int
783 3503162 : RgX_is_ZX(GEN x)
784 : {
785 : long i;
786 15184762 : for (i = lg(x)-1; i > 1; i--)
787 11690217 : if (typ(gel(x,i)) != t_INT) return 0;
788 3494545 : return 1;
789 : }
790 : INLINE int
791 121275 : RgX_is_QX(GEN x)
792 : {
793 121275 : long k = lg(x)-1;
794 447419 : for ( ; k>1; k--)
795 327152 : if (!is_rational_t(typ(gel(x,k)))) return 0;
796 120267 : return 1;
797 : }
798 : INLINE int
799 15518388 : RgX_is_monomial(GEN x)
800 : {
801 : long i;
802 15518388 : if (!signe(x)) return 0;
803 25658844 : for (i=lg(x)-2; i>1; i--)
804 17734511 : if (!isexactzero(gel(x,i))) return 0;
805 7924333 : return 1;
806 : }
807 : INLINE int
808 18293926 : RgV_is_ZV(GEN x)
809 : {
810 : long i;
811 74712292 : for (i = lg(x)-1; i > 0; i--)
812 56419479 : if (typ(gel(x,i)) != t_INT) return 0;
813 18292813 : return 1;
814 : }
815 : INLINE int
816 4200 : RgV_is_QV(GEN x)
817 : {
818 : long i;
819 96334 : for (i = lg(x)-1; i > 0; i--)
820 94759 : if (!is_rational_t(typ(gel(x,i)))) return 0;
821 1575 : return 1;
822 : }
823 :
824 : /********************************************************************/
825 : /** **/
826 : /** Dynamic arrays implementation **/
827 : /** **/
828 : /********************************************************************/
829 : INLINE void **
830 407891221 : pari_stack_base(pari_stack *s) { return s->data; }
831 :
832 : INLINE void
833 923677 : pari_stack_init(pari_stack *s, size_t size, void **data)
834 : {
835 923677 : s->data = data;
836 923677 : *data = NULL;
837 923677 : s->n = 0;
838 923677 : s->alloc = 0;
839 923677 : s->size = size;
840 923677 : }
841 :
842 : INLINE void
843 406966929 : pari_stack_alloc(pari_stack *s, long nb)
844 : {
845 406966929 : void **sdat = pari_stack_base(s);
846 407258663 : long alloc = s->alloc;
847 814518577 : if (s->n+nb <= alloc) return;
848 391424 : if (!alloc)
849 343107 : alloc = nb;
850 : else
851 : {
852 48317 : while (s->n+nb > alloc) alloc <<= 1;
853 : }
854 391424 : *sdat = pari_realloc(*sdat,alloc*s->size);
855 392675 : s->alloc = alloc;
856 : }
857 :
858 : INLINE long
859 339025766 : pari_stack_new(pari_stack *s) { pari_stack_alloc(s, 1); return s->n++; }
860 :
861 : INLINE void
862 794974 : pari_stack_delete(pari_stack *s)
863 : {
864 794974 : void **sdat = pari_stack_base(s);
865 794561 : if (*sdat) pari_free(*sdat);
866 794860 : }
867 :
868 : INLINE void
869 4671 : pari_stack_pushp(pari_stack *s, void *u)
870 : {
871 4671 : long n = pari_stack_new(s);
872 4671 : void **sdat =(void**) *pari_stack_base(s);
873 4671 : sdat[n] = u;
874 4671 : }
875 :
876 : /*******************************************************************/
877 : /* */
878 : /* EXTRACT */
879 : /* */
880 : /*******************************************************************/
881 : INLINE GEN
882 201912299 : vecslice(GEN A, long y1, long y2)
883 : {
884 201912299 : long i,lB = y2 - y1 + 2;
885 201912299 : GEN B = cgetg(lB, typ(A));
886 201912299 : for (i=1; i<lB; i++) B[i] = A[y1-1+i];
887 201912299 : return B;
888 : }
889 : INLINE GEN
890 733774 : vecslicepermute(GEN A, GEN p, long y1, long y2)
891 : {
892 733774 : long i,lB = y2 - y1 + 2;
893 733774 : GEN B = cgetg(lB, typ(A));
894 733774 : for (i=1; i<lB; i++) B[i] = A[p[y1-1+i]];
895 733774 : return B;
896 : }
897 : /* rowslice(rowpermute(A,p), x1, x2) */
898 : INLINE GEN
899 34342 : rowslicepermute(GEN A, GEN p, long x1, long x2)
900 : {
901 34342 : long i, lB = lg(A);
902 34342 : GEN B = cgetg(lB, typ(A));
903 34342 : for (i=1; i<lB; i++) gel(B,i) = vecslicepermute(gel(A,i),p,x1,x2);
904 34342 : return B;
905 : }
906 : INLINE GEN
907 20248028 : rowslice(GEN A, long x1, long x2)
908 : {
909 20248028 : long i, lB = lg(A);
910 20248028 : GEN B = cgetg(lB, typ(A));
911 20248028 : for (i=1; i<lB; i++) gel(B,i) = vecslice(gel(A,i),x1,x2);
912 20248028 : return B;
913 : }
914 :
915 : INLINE GEN
916 212362 : matslice(GEN A, long x1, long x2, long y1, long y2)
917 : {
918 212362 : return rowslice(vecslice(A, y1, y2), x1, x2);
919 : }
920 :
921 : /* shallow, remove coeff of index j */
922 : INLINE GEN
923 133 : rowsplice(GEN a, long j)
924 : {
925 : long i, l;
926 133 : GEN b = cgetg_copy(a,&l);
927 133 : for (i = 1; i < l; i++) gel(b,i) = vecsplice(gel(a,i), j);
928 133 : return b;
929 : }
930 : /* shallow, remove coeff of index j */
931 : INLINE GEN
932 45164 : vecsplice(GEN a, long j)
933 : {
934 45164 : long i, k, l = lg(a);
935 : GEN b;
936 45164 : if (l == 1) pari_err(e_MISC, "incorrect component in vecsplice");
937 45164 : b = cgetg(l-1, typ(a));
938 190323 : for (i = k = 1; i < l; i++)
939 145159 : if (i != j) gel(b, k++) = gel(a,i);
940 45164 : return b;
941 : }
942 : /* shallow */
943 : INLINE GEN
944 756 : RgM_minor(GEN a, long i, long j)
945 : {
946 756 : GEN b = vecsplice(a, j);
947 756 : long k, l = lg(b);
948 756 : for (k = 1; k < l; k++) gel(b,k) = vecsplice(gel(b,k), i);
949 756 : return b;
950 : }
951 :
952 : /* A[x0,] */
953 : INLINE GEN
954 178650 : row(GEN A, long x0)
955 : {
956 178650 : long i, lB = lg(A);
957 178650 : GEN B = cgetg(lB, t_VEC);
958 178650 : for (i=1; i<lB; i++) gel(B, i) = gcoeff(A, x0, i);
959 178650 : return B;
960 : }
961 : INLINE GEN
962 4481672 : Flm_row(GEN A, long x0)
963 : {
964 4481672 : long i, lB = lg(A);
965 4481672 : GEN B = cgetg(lB, t_VECSMALL);
966 4481669 : for (i=1; i<lB; i++) B[i] = coeff(A, x0, i);
967 4481669 : return B;
968 : }
969 : /* A[x0,] */
970 : INLINE GEN
971 56 : rowcopy(GEN A, long x0)
972 : {
973 56 : long i, lB = lg(A);
974 56 : GEN B = cgetg(lB, t_VEC);
975 56 : for (i=1; i<lB; i++) gel(B, i) = gcopy(gcoeff(A, x0, i));
976 56 : return B;
977 : }
978 : /* A[x0, x1..x2] */
979 : INLINE GEN
980 2177 : row_i(GEN A, long x0, long x1, long x2)
981 : {
982 2177 : long i, lB = x2 - x1 + 2;
983 2177 : GEN B = cgetg(lB, t_VEC);
984 2177 : for (i=x1; i<=x2; i++) gel(B, i) = gcoeff(A, x0, i);
985 2177 : return B;
986 : }
987 :
988 : INLINE GEN
989 5491550 : vecreverse(GEN A)
990 : {
991 : long i, l;
992 5491550 : GEN B = cgetg_copy(A, &l);
993 5491550 : for (i=1; i<l; i++) gel(B, i) = gel(A, l-i);
994 5491550 : return B;
995 : }
996 :
997 : INLINE GEN
998 252 : vecsmall_reverse(GEN A)
999 : {
1000 : long i, l;
1001 252 : GEN B = cgetg_copy(A, &l);
1002 252 : for (i=1; i<l; i++) B[i] = A[l-i];
1003 252 : return B;
1004 : }
1005 :
1006 : INLINE void
1007 232 : vecreverse_inplace(GEN y)
1008 : {
1009 232 : long ly = lg(y), lim = ly>>1, i;
1010 640 : for (i = 1; i <= lim; i++)
1011 : {
1012 408 : GEN z = gel(y,i);
1013 408 : gel(y,i) = gel(y,ly-i);
1014 408 : gel(y,ly-i) = z;
1015 : }
1016 232 : }
1017 :
1018 : INLINE GEN
1019 44970616 : vecsmallpermute(GEN A, GEN p) { return perm_mul(A, p); }
1020 :
1021 : INLINE GEN
1022 5389204 : vecpermute(GEN A, GEN p)
1023 : {
1024 5389204 : long i,lB = lg(p);
1025 5389204 : GEN B = cgetg(lB, typ(A));
1026 5389204 : for (i=1; i<lB; i++) gel(B, i) = gel(A, p[i]);
1027 5389204 : return B;
1028 : }
1029 : INLINE GEN
1030 2839820 : rowpermute(GEN A, GEN p)
1031 : {
1032 2839820 : long i, lB = lg(A);
1033 2839820 : GEN B = cgetg(lB, typ(A));
1034 28591108 : for (i=1; i<lB; i++)
1035 27181166 : gel(B, i) = typ(gel(A,i)) == t_VECSMALL ? vecsmallpermute(gel(A, i), p):
1036 1429878 : vecpermute(gel(A, i), p);
1037 2839820 : return B;
1038 : }
1039 : /*******************************************************************/
1040 : /* */
1041 : /* PERMUTATIONS */
1042 : /* */
1043 : /*******************************************************************/
1044 : /* identity permutation */
1045 : INLINE GEN
1046 609288 : identity_perm(long n)
1047 : {
1048 609288 : GEN perm = cgetg(n+1, t_VECSMALL);
1049 : long i;
1050 609288 : for (i = 1; i <= n; i++) perm[i] = i;
1051 609288 : return perm;
1052 : }
1053 :
1054 : /* assume d <= n */
1055 : INLINE GEN
1056 0 : cyclic_perm(long n, long d)
1057 : {
1058 0 : GEN perm = cgetg(n+1, t_VECSMALL);
1059 : long i;
1060 0 : for (i = 1; i <= n-d; i++) perm[i] = i+d;
1061 0 : for ( ; i <= n; i++) perm[i] = i-n+d;
1062 0 : return perm;
1063 : }
1064 :
1065 : /* Multiply (compose) two permutations */
1066 : INLINE GEN
1067 46601352 : perm_mul(GEN s, GEN t)
1068 : {
1069 : GEN u;
1070 46601352 : long i, l = lg(t);
1071 46601352 : u = cgetg(l, t_VECSMALL);
1072 46601352 : for (i = 1; i < l; i++) u[i] = s[ t[i] ];
1073 46601352 : return u;
1074 : }
1075 : /* Compute the inverse (reciprocal) of a permutation. */
1076 : INLINE GEN
1077 594800 : perm_inv(GEN x)
1078 : {
1079 : long i, lx;
1080 594800 : GEN y = cgetg_copy(x, &lx);
1081 594800 : for (i=1; i<lx; i++) y[ x[i] ] = i;
1082 594800 : return y;
1083 : }
1084 : /* Return s*t*s^-1 */
1085 : INLINE GEN
1086 506639 : perm_conj(GEN s, GEN t)
1087 : {
1088 : long i, l;
1089 506639 : GEN v = cgetg_copy(s, &l);
1090 506639 : for (i = 1; i < l; i++) v[ s[i] ] = s[ t[i] ];
1091 506639 : return v;
1092 : }
1093 :
1094 : /*********************************************************************/
1095 : /* MALLOC/FREE WRAPPERS */
1096 : /*********************************************************************/
1097 : #define BLOCK_SIGALRM_START \
1098 : { \
1099 : int block=PARI_SIGINT_block; \
1100 : PARI_SIGINT_block = 2; \
1101 : MT_SIGINT_BLOCK(block);
1102 :
1103 : #define BLOCK_SIGINT_START \
1104 : { \
1105 : int block=PARI_SIGINT_block; \
1106 : PARI_SIGINT_block = 1; \
1107 : MT_SIGINT_BLOCK(block);
1108 :
1109 : #define BLOCK_SIGINT_END \
1110 : PARI_SIGINT_block = block; \
1111 : MT_SIGINT_UNBLOCK(block); \
1112 : if (!block && PARI_SIGINT_pending) \
1113 : { \
1114 : int sig = PARI_SIGINT_pending; \
1115 : PARI_SIGINT_pending = 0; \
1116 : raise(sig); \
1117 : } \
1118 : }
1119 :
1120 : INLINE void
1121 53679409 : pari_free(void *pointer)
1122 : {
1123 53679409 : BLOCK_SIGINT_START;
1124 53681110 : free(pointer);
1125 53681110 : BLOCK_SIGINT_END;
1126 53680534 : }
1127 : INLINE void*
1128 234559160 : pari_malloc(size_t size)
1129 : {
1130 234559160 : if (size)
1131 : {
1132 : char *tmp;
1133 234559160 : BLOCK_SIGINT_START;
1134 234561505 : tmp = (char*)malloc(size);
1135 234561505 : BLOCK_SIGINT_END;
1136 234561359 : if (!tmp) pari_err(e_MEM);
1137 234561359 : return tmp;
1138 : }
1139 0 : if (DEBUGMEM) pari_warn(warner,"mallocing NULL object");
1140 0 : return NULL;
1141 : }
1142 : INLINE void*
1143 403387 : pari_realloc(void *pointer, size_t size)
1144 : {
1145 : char *tmp;
1146 :
1147 403387 : BLOCK_SIGINT_START;
1148 405110 : if (!pointer) tmp = (char *) malloc(size);
1149 51944 : else tmp = (char *) realloc(pointer,size);
1150 405110 : BLOCK_SIGINT_END;
1151 404514 : if (!tmp) pari_err(e_MEM);
1152 404514 : return tmp;
1153 : }
1154 : INLINE void*
1155 32596 : pari_calloc(size_t size)
1156 : {
1157 32596 : void *t = pari_malloc(size);
1158 32596 : memset(t, 0, size); return t;
1159 : }
1160 : INLINE GEN
1161 4194 : cgetalloc(long t, size_t l)
1162 : {
1163 4194 : GEN x = (GEN)pari_malloc(l * sizeof(long));
1164 4194 : x[0] = evaltyp(t) | evallg(l); return x;
1165 : }
1166 :
1167 : /*******************************************************************/
1168 : /* */
1169 : /* GARBAGE COLLECTION */
1170 : /* */
1171 : /*******************************************************************/
1172 : /* copy integer x as if we had avma = av */
1173 : INLINE GEN
1174 3660537989 : icopy_avma(GEN x, pari_sp av)
1175 : {
1176 3660537989 : long i = lgefint(x), lx = i;
1177 3660537989 : GEN y = ((GEN)av) - i;
1178 3660537989 : while (--i > 0) y[i] = x[i];
1179 3660537989 : y[0] = evaltyp(t_INT)|evallg(lx);
1180 3660297273 : return y;
1181 : }
1182 : /* copy leaf x as if we had avma = av */
1183 : INLINE GEN
1184 156144455 : leafcopy_avma(GEN x, pari_sp av)
1185 : {
1186 156144455 : long i = lg(x);
1187 156144455 : GEN y = ((GEN)av) - i;
1188 156144455 : while (--i > 0) y[i] = x[i];
1189 156144455 : y[0] = x[0] & (~CLONEBIT);
1190 156144455 : return y;
1191 : }
1192 : INLINE GEN
1193 603517003 : gerepileuptoleaf(pari_sp av, GEN x)
1194 : {
1195 : long lx;
1196 : GEN q;
1197 :
1198 603517003 : if (!isonstack(x) || (GEN)av<=x) { avma = av; return x; }
1199 604515928 : lx = lg(x);
1200 604515928 : q = ((GEN)av) - lx;
1201 604515928 : avma = (pari_sp)q;
1202 604515928 : while (--lx >= 0) q[lx] = x[lx];
1203 604515928 : return q;
1204 : }
1205 : INLINE GEN
1206 1219552471 : gerepileuptoint(pari_sp av, GEN x)
1207 : {
1208 1219552471 : if (!isonstack(x) || (GEN)av<=x) { avma = av; return x; }
1209 1074755796 : avma = (pari_sp)icopy_avma(x, av);
1210 1075502873 : return (GEN)avma;
1211 : }
1212 : INLINE GEN
1213 733693950 : gerepileupto(pari_sp av, GEN x)
1214 : {
1215 733693950 : if (!isonstack(x) || (GEN)av<=x) { avma = av; return x; }
1216 632689046 : switch(typ(x))
1217 : { /* non-default = !is_recursive_t(tq) */
1218 212082287 : case t_INT: return gerepileuptoint(av, x);
1219 : case t_REAL:
1220 : case t_STR:
1221 125990759 : case t_VECSMALL: return gerepileuptoleaf(av,x);
1222 : default:
1223 : /* NB: x+i --> ((long)x) + i*sizeof(long) */
1224 294616000 : return gerepile(av, (pari_sp) (x+lg(x)), x);
1225 : }
1226 : }
1227 :
1228 : /* gerepileupto(av, gcopy(x)) */
1229 : INLINE GEN
1230 40794399 : gerepilecopy(pari_sp av, GEN x)
1231 : {
1232 40794399 : if (is_recursive_t(typ(x)))
1233 : {
1234 33265861 : GENbin *p = copy_bin(x);
1235 33265879 : avma = av; return bin_copy(p);
1236 : }
1237 : else
1238 : {
1239 7528543 : avma = av;
1240 7528543 : if (x < (GEN)av) {
1241 6111689 : if (x < (GEN)pari_mainstack->bot) new_chunk(lg(x));
1242 6111689 : x = leafcopy_avma(x, av);
1243 6111695 : avma = (pari_sp)x;
1244 : } else
1245 1416854 : x = leafcopy(x);
1246 7528552 : return x;
1247 : }
1248 : }
1249 :
1250 : /* Takes an array of pointers to GENs, of length n. Copies all
1251 : * objects to contiguous locations and cleans up the stack between
1252 : * av and avma. */
1253 : INLINE void
1254 136927 : gerepilemany(pari_sp av, GEN* gptr[], int n)
1255 : {
1256 : int i;
1257 136927 : for (i=0; i<n; i++) *gptr[i] = (GEN)copy_bin(*gptr[i]);
1258 136927 : avma = av;
1259 136927 : for (i=0; i<n; i++) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1260 136927 : }
1261 :
1262 : INLINE void
1263 5701704 : gerepileall(pari_sp av, int n, ...)
1264 : {
1265 : int i;
1266 5701704 : va_list a; va_start(a, n);
1267 5701704 : if (n < 10)
1268 : {
1269 : GEN *gptr[10];
1270 17322562 : for (i=0; i<n; i++)
1271 11620866 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1272 5701696 : avma = av;
1273 5701696 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1274 :
1275 : }
1276 : else
1277 : {
1278 0 : GEN **gptr = (GEN**) pari_malloc(n*sizeof(GEN*));
1279 0 : for (i=0; i<n; i++)
1280 0 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1281 0 : avma = av;
1282 0 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1283 0 : pari_free(gptr);
1284 : }
1285 5701707 : va_end(a);
1286 5701707 : }
1287 :
1288 : INLINE void
1289 8 : gerepilecoeffs(pari_sp av, GEN x, int n)
1290 : {
1291 : int i;
1292 8 : for (i=0; i<n; i++) gel(x,i) = (GEN)copy_bin(gel(x,i));
1293 8 : avma = av;
1294 8 : for (i=0; i<n; i++) gel(x,i) = bin_copy((GENbin*)x[i]);
1295 8 : }
1296 :
1297 : /* p from copy_bin. Copy p->x back to stack, then destroy p */
1298 : INLINE GEN
1299 45294433 : bin_copy(GENbin *p)
1300 : {
1301 : GEN x, y, base;
1302 : long dx, len;
1303 :
1304 45294433 : x = p->x; if (!x) { pari_free(p); return gen_0; }
1305 45287606 : len = p->len;
1306 45287606 : base= p->base; dx = x - base;
1307 45287606 : y = (GEN)memcpy((void*)new_chunk(len), (void*)GENbinbase(p), len*sizeof(long));
1308 45287631 : y += dx;
1309 45287631 : p->rebase(y, ((ulong)y-(ulong)x));
1310 45287606 : pari_free(p); return y;
1311 : }
1312 :
1313 : INLINE GEN
1314 90582124 : GENbinbase(GENbin *p) { return (GEN)(p + 1); }
1315 :
1316 : INLINE void
1317 27360019 : cgiv(GEN x)
1318 : {
1319 27360019 : pari_sp av = (pari_sp)(x+lg(x));
1320 27360019 : if (isonstack((GEN)av)) avma = av;
1321 27359616 : }
1322 :
1323 : INLINE void
1324 1184411 : killblock(GEN x) { gunclone(x); }
1325 :
1326 : INLINE int
1327 17745784 : is_universal_constant(GEN x) { return (x >= gen_0 && x <= ghalf); }
1328 :
1329 : /*******************************************************************/
1330 : /* */
1331 : /* CONVERSION / ASSIGNMENT */
1332 : /* */
1333 : /*******************************************************************/
1334 : /* z is a type which may be a t_COMPLEX component (not a t_QUAD) */
1335 : INLINE GEN
1336 2680902 : cxcompotor(GEN z, long prec)
1337 : {
1338 2680902 : switch(typ(z))
1339 : {
1340 1470514 : case t_INT: return itor(z, prec);
1341 134120 : case t_FRAC: return fractor(z, prec);
1342 1076268 : case t_REAL: return rtor(z, prec);
1343 0 : default: pari_err_TYPE("cxcompotor",z);
1344 : return NULL; /* LCOV_EXCL_LINE */
1345 : }
1346 : }
1347 : INLINE GEN
1348 1333002 : cxtofp(GEN x, long prec)
1349 1333002 : { retmkcomplex(cxcompotor(gel(x,1),prec), cxcompotor(gel(x,2),prec)); }
1350 :
1351 : INLINE double
1352 17290174 : gtodouble(GEN x)
1353 : {
1354 17290174 : if (typ(x)!=t_REAL) {
1355 3209414 : pari_sp av = avma;
1356 3209414 : x = gtofp(x, DEFAULTPREC);
1357 3209414 : if (typ(x)!=t_REAL) pari_err_TYPE("gtodouble [t_REAL expected]", x);
1358 3209414 : avma = av;
1359 : }
1360 17290174 : return rtodbl(x);
1361 : }
1362 : INLINE long
1363 67227352 : gtos(GEN x) {
1364 67227352 : if (typ(x) != t_INT) pari_err_TYPE("gtos [integer expected]",x);
1365 67227345 : return itos(x);
1366 : }
1367 :
1368 : INLINE ulong
1369 136677 : gtou(GEN x) {
1370 136677 : if (typ(x) != t_INT || signe(x)<0)
1371 0 : pari_err_TYPE("gtou [integer >=0 expected]",x);
1372 136959 : return itou(x);
1373 : }
1374 :
1375 : INLINE GEN
1376 10348562 : absfrac(GEN x)
1377 : {
1378 10348562 : GEN y = cgetg(3, t_FRAC);
1379 10348562 : gel(y,1) = absi(gel(x,1));
1380 10348562 : gel(y,2) = icopy(gel(x,2)); return y;
1381 : }
1382 : INLINE GEN
1383 32308 : absfrac_shallow(GEN x)
1384 32308 : { return signe(gel(x,1))>0? x: mkfrac(negi(gel(x,1)), gel(x,2)); }
1385 : INLINE GEN
1386 1492246 : Q_abs(GEN x) { return (typ(x) == t_INT)? absi(x): absfrac(x); }
1387 : INLINE GEN
1388 106034 : Q_abs_shallow(GEN x)
1389 106034 : { return (typ(x) == t_INT)? absi_shallow(x): absfrac_shallow(x); }
1390 : INLINE GEN
1391 322 : R_abs_shallow(GEN x)
1392 322 : { return (typ(x) == t_FRAC)? absfrac_shallow(x): mpabs_shallow(x); }
1393 : INLINE GEN
1394 0 : R_abs(GEN x)
1395 0 : { return (typ(x) == t_FRAC)? absfrac(x): mpabs(x); }
1396 :
1397 : /* Force z to be of type real/complex with floating point components */
1398 : INLINE GEN
1399 18138963 : gtofp(GEN z, long prec)
1400 : {
1401 18138963 : switch(typ(z))
1402 : {
1403 8273274 : case t_INT: return itor(z, prec);
1404 4257450 : case t_FRAC: return fractor(z, prec);
1405 4458975 : case t_REAL: return rtor(z, prec);
1406 : case t_COMPLEX: {
1407 1149264 : GEN a = gel(z,1), b = gel(z,2);
1408 1149264 : if (isintzero(b)) return cxcompotor(a, prec);
1409 1147193 : if (isintzero(a)) {
1410 1865 : GEN y = cgetg(3, t_COMPLEX);
1411 1865 : b = cxcompotor(b, prec);
1412 1865 : gel(y,1) = real_0_bit(expo(b) - prec2nbits(prec));
1413 1865 : gel(y,2) = b; return y;
1414 : }
1415 1145328 : return cxtofp(z, prec);
1416 : }
1417 0 : case t_QUAD: return quadtofp(z, prec);
1418 0 : default: pari_err_TYPE("gtofp",z);
1419 : return NULL; /* LCOV_EXCL_LINE */
1420 : }
1421 : }
1422 : /* Force z to be of type real / int */
1423 : INLINE GEN
1424 22400 : gtomp(GEN z, long prec)
1425 : {
1426 22400 : switch(typ(z))
1427 : {
1428 14 : case t_INT: return z;
1429 22386 : case t_FRAC: return fractor(z, prec);
1430 0 : case t_REAL: return rtor(z, prec);
1431 0 : case t_QUAD: z = quadtofp(z, prec);
1432 0 : if (typ(z) == t_REAL) return z;
1433 0 : default: pari_err_TYPE("gtomp",z);
1434 : return NULL; /* LCOV_EXCL_LINE */
1435 : }
1436 : }
1437 :
1438 : INLINE GEN
1439 636407 : RgX_gtofp(GEN x, long prec)
1440 : {
1441 : long l;
1442 636407 : GEN y = cgetg_copy(x, &l);
1443 636407 : while (--l > 1) gel(y,l) = gtofp(gel(x,l), prec);
1444 636407 : y[1] = x[1]; return y;
1445 : }
1446 : INLINE GEN
1447 292709 : RgC_gtofp(GEN x, long prec)
1448 : {
1449 292709 : long l = lg(x);
1450 292709 : GEN y = cgetg(l, t_COL);
1451 292709 : while (--l > 0) gel(y,l) = gtofp(gel(x,l), prec);
1452 292709 : return y;
1453 : }
1454 : INLINE GEN
1455 42 : RgV_gtofp(GEN x, long prec)
1456 : {
1457 42 : long l = lg(x);
1458 42 : GEN y = cgetg(l, t_VEC);
1459 42 : while (--l > 0) gel(y,l) = gtofp(gel(x,l), prec);
1460 42 : return y;
1461 : }
1462 : INLINE GEN
1463 20553 : RgM_gtofp(GEN x, long prec)
1464 : {
1465 : long l;
1466 20553 : GEN y = cgetg_copy(x, &l);
1467 20553 : while (--l > 0) gel(y,l) = RgC_gtofp(gel(x,l), prec);
1468 20553 : return y;
1469 : }
1470 : INLINE GEN
1471 560 : RgC_gtomp(GEN x, long prec)
1472 : {
1473 560 : long l = lg(x);
1474 560 : GEN y = cgetg(l, t_COL);
1475 560 : while (--l > 0) gel(y,l) = gtomp(gel(x,l), prec);
1476 560 : return y;
1477 : }
1478 : INLINE GEN
1479 14 : RgM_gtomp(GEN x, long prec)
1480 : {
1481 : long l;
1482 14 : GEN y = cgetg_copy(x, &l);
1483 14 : while (--l > 0) gel(y,l) = RgC_gtomp(gel(x,l), prec);
1484 14 : return y;
1485 : }
1486 :
1487 : INLINE GEN
1488 8562 : RgX_fpnorml2(GEN x, long prec)
1489 : {
1490 8562 : pari_sp av = avma;
1491 8562 : return gerepileupto(av, gnorml2(RgX_gtofp(x, prec)));
1492 : }
1493 : INLINE GEN
1494 155156 : RgC_fpnorml2(GEN x, long prec)
1495 : {
1496 155156 : pari_sp av = avma;
1497 155156 : return gerepileupto(av, gnorml2(RgC_gtofp(x, prec)));
1498 : }
1499 : INLINE GEN
1500 3201 : RgM_fpnorml2(GEN x, long prec)
1501 : {
1502 3201 : pari_sp av = avma;
1503 3201 : return gerepileupto(av, gnorml2(RgM_gtofp(x, prec)));
1504 : }
1505 :
1506 : /* y a t_REAL */
1507 : INLINE void
1508 190202 : affgr(GEN x, GEN y)
1509 : {
1510 : pari_sp av;
1511 190202 : switch(typ(x)) {
1512 5992 : case t_INT: affir(x,y); break;
1513 184210 : case t_REAL: affrr(x,y); break;
1514 0 : case t_FRAC: rdiviiz(gel(x,1),gel(x,2), y); break;
1515 0 : case t_QUAD: av = avma; affgr(quadtofp(x,realprec(y)), y); avma = av; break;
1516 0 : default: pari_err_TYPE2("=",x,y);
1517 : }
1518 190202 : }
1519 :
1520 : INLINE GEN
1521 185736 : affc_fixlg(GEN x, GEN res)
1522 : {
1523 185736 : if (typ(x) == t_COMPLEX)
1524 : {
1525 175616 : affrr_fixlg(gel(x,1), gel(res,1));
1526 175616 : affrr_fixlg(gel(x,2), gel(res,2));
1527 : }
1528 : else
1529 : {
1530 10120 : avma = (pari_sp)(res+3);
1531 10120 : res = cgetr(realprec(gel(res,1)));
1532 10120 : affrr_fixlg(x, res);
1533 : }
1534 185736 : return res;
1535 : }
1536 :
1537 : INLINE GEN
1538 0 : trunc_safe(GEN x) { long e; return gcvtoi(x,&e); }
1539 :
1540 : /*******************************************************************/
1541 : /* */
1542 : /* LENGTH CONVERSIONS */
1543 : /* */
1544 : /*******************************************************************/
1545 : INLINE long
1546 24545 : ndec2nlong(long x) { return 1 + (long)((x)*(LOG2_10/BITS_IN_LONG)); }
1547 : INLINE long
1548 24067 : ndec2prec(long x) { return 2 + ndec2nlong(x); }
1549 : INLINE long
1550 478 : ndec2nbits(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1551 : /* Fast implementation of ceil(x / (8*sizeof(long))); typecast to (ulong)
1552 : * to avoid overflow. Faster than 1 + ((x-1)>>TWOPOTBITS_IN_LONG)) :
1553 : * addl, shrl instead of subl, sarl, addl */
1554 : INLINE long
1555 1134574 : nbits2nlong(long x) {
1556 1134574 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1557 : }
1558 :
1559 : INLINE long
1560 243786212 : nbits2extraprec(long x) {
1561 243786212 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1562 : }
1563 :
1564 : /* Fast implementation of 2 + nbits2nlong(x) */
1565 : INLINE long
1566 78423393 : nbits2prec(long x) {
1567 78423393 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1568 : }
1569 : INLINE long
1570 6562411 : nbits2lg(long x) {
1571 6562411 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1572 : }
1573 : /* ceil(x / sizeof(long)) */
1574 : INLINE long
1575 8282115 : nchar2nlong(long x) {
1576 8282115 : return (long)(((ulong)x+sizeof(long)-1) >> (TWOPOTBITS_IN_LONG-3L));
1577 : }
1578 : INLINE long
1579 1056703552 : prec2nbits(long x) { return (x-2) * BITS_IN_LONG; }
1580 : INLINE double
1581 448573 : bit_accuracy_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1582 : INLINE double
1583 229883 : prec2nbits_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1584 : INLINE long
1585 25963855 : bit_prec(GEN x) { return prec2nbits(realprec(x)); }
1586 : INLINE long
1587 974194274 : bit_accuracy(long x) { return prec2nbits(x); }
1588 : INLINE long
1589 12071 : prec2ndec(long x) { return (long)prec2nbits_mul(x, LOG10_2); }
1590 : INLINE long
1591 179 : nbits2ndec(long x) { return (long)(x * LOG10_2); }
1592 : INLINE long
1593 1651 : precdbl(long x) {return (x - 1) << 1;}
1594 : INLINE long
1595 3078927665 : divsBIL(long n) { return n >> TWOPOTBITS_IN_LONG; }
1596 : INLINE long
1597 3044533009 : remsBIL(long n) { return n & (BITS_IN_LONG-1); }
1598 :
1599 : /*********************************************************************/
1600 : /** **/
1601 : /** OPERATIONS MODULO m **/
1602 : /** **/
1603 : /*********************************************************************/
1604 : /* Assume m > 0, more efficient if 0 <= a, b < m */
1605 :
1606 : INLINE GEN
1607 2439563 : Fp_red(GEN a, GEN m) { return modii(a, m); }
1608 : INLINE GEN
1609 87093436 : Fp_add(GEN a, GEN b, GEN m)
1610 : {
1611 87093436 : pari_sp av=avma;
1612 87093436 : GEN p = addii(a,b);
1613 87107893 : long s = signe(p);
1614 87107893 : if (!s) return p; /* = gen_0 */
1615 76392563 : if (s > 0) /* general case */
1616 : {
1617 76169395 : GEN t = subii(p, m);
1618 76238735 : s = signe(t);
1619 76238735 : if (!s) { avma = av; return gen_0; }
1620 70758006 : if (s < 0) { avma = (pari_sp)p; return p; }
1621 31062821 : if (cmpii(t, m) < 0) return gerepileuptoint(av, t); /* general case ! */
1622 1122054 : p = remii(t, m);
1623 : }
1624 : else
1625 223168 : p = modii(p, m);
1626 1345222 : return gerepileuptoint(av, p);
1627 : }
1628 : INLINE GEN
1629 75898193 : Fp_sub(GEN a, GEN b, GEN m)
1630 : {
1631 75898193 : pari_sp av=avma;
1632 75898193 : GEN p = subii(a,b);
1633 76202340 : long s = signe(p);
1634 76202340 : if (!s) return p; /* = gen_0 */
1635 68333799 : if (s > 0)
1636 : {
1637 32996331 : if (cmpii(p, m) < 0) return p; /* general case ! */
1638 1315908 : p = remii(p, m);
1639 : }
1640 : else
1641 : {
1642 35337468 : GEN t = addii(p, m);
1643 35320175 : if (!s) { avma = av; return gen_0; }
1644 35320175 : if (s > 0) return gerepileuptoint(av, t); /* general case ! */
1645 35320175 : p = modii(t, m);
1646 : }
1647 36651898 : return gerepileuptoint(av, p);
1648 : }
1649 : INLINE GEN
1650 10979353 : Fp_neg(GEN b, GEN m)
1651 : {
1652 10979353 : pari_sp av = avma;
1653 10979353 : long s = signe(b);
1654 : GEN p;
1655 10979353 : if (!s) return gen_0;
1656 7580908 : if (s > 0)
1657 : {
1658 7378650 : p = subii(m, b);
1659 7378392 : if (signe(p) >= 0) return p; /* general case ! */
1660 92460 : p = modii(p, m);
1661 : } else
1662 202258 : p = remii(negi(b), m);
1663 294718 : return gerepileuptoint(av, p);
1664 : }
1665 :
1666 : INLINE GEN
1667 19996 : Fp_halve(GEN a, GEN p)
1668 : {
1669 19996 : if (mpodd(a)) a = addii(a,p);
1670 19996 : return shifti(a,-1);
1671 : }
1672 :
1673 : /* assume 0 <= u < p and ps2 = p>>1 */
1674 : INLINE GEN
1675 5861107 : Fp_center(GEN u, GEN p, GEN ps2)
1676 5861107 : { return abscmpii(u,ps2)<=0? icopy(u): subii(u,p); }
1677 :
1678 : /* x + y*z mod p */
1679 : INLINE GEN
1680 7875652 : Fp_addmul(GEN x, GEN y, GEN z, GEN p)
1681 : {
1682 : pari_sp av;
1683 7875652 : if (!signe(y) || !signe(z)) return Fp_red(x, p);
1684 7452070 : if (!signe(x)) return Fp_mul(z,y, p);
1685 7151191 : av = avma;
1686 7151191 : return gerepileuptoint(av, modii(addii(x, mulii(y,z)), p));
1687 : }
1688 :
1689 : INLINE GEN
1690 64343929 : Fp_mul(GEN a, GEN b, GEN m)
1691 : {
1692 64343929 : pari_sp av=avma;
1693 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1694 64343929 : (void)new_chunk(lg(a)+lg(b)+(lg(m)<<1));
1695 64354438 : p = mulii(a,b);
1696 64351824 : avma = av; return modii(p,m);
1697 : }
1698 : INLINE GEN
1699 61921229 : Fp_sqr(GEN a, GEN m)
1700 : {
1701 61921229 : pari_sp av=avma;
1702 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1703 61921229 : (void)new_chunk((lg(a)+lg(m))<<1);
1704 62180921 : p = sqri(a);
1705 62462176 : avma = av; return remii(p,m); /*Use remii: p >= 0 */
1706 : }
1707 : INLINE GEN
1708 80184742 : Fp_mulu(GEN a, ulong b, GEN m)
1709 : {
1710 80184742 : long l = lgefint(m);
1711 80184742 : if (l == 3)
1712 : {
1713 42993581 : ulong mm = m[2];
1714 42993581 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1715 : } else {
1716 37191161 : pari_sp av = avma;
1717 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1718 37191161 : (void)new_chunk(lg(a)+1+(l<<1));
1719 37244085 : p = muliu(a,b);
1720 36927424 : avma = av; return modii(p,m);
1721 : }
1722 : }
1723 : INLINE GEN
1724 0 : Fp_muls(GEN a, long b, GEN m)
1725 : {
1726 0 : long l = lgefint(m);
1727 0 : if (l == 3)
1728 : {
1729 0 : ulong mm = m[2];
1730 0 : if (b < 0)
1731 : {
1732 0 : ulong t = Fl_mul(umodiu(a, mm), -b, mm);
1733 0 : return t? utoipos(mm - t): gen_0;
1734 : }
1735 : else
1736 0 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1737 : } else {
1738 0 : pari_sp av = avma;
1739 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1740 0 : (void)new_chunk(lg(a)+1+(l<<1));
1741 0 : p = mulis(a,b);
1742 0 : avma = av; return modii(p,m);
1743 : }
1744 : }
1745 :
1746 : INLINE GEN
1747 8456506 : Fp_inv(GEN a, GEN m)
1748 : {
1749 : GEN res;
1750 8456506 : if (! invmod(a,m,&res)) pari_err_INV("Fp_inv", mkintmod(res,m));
1751 8456402 : return res;
1752 : }
1753 : INLINE GEN
1754 296687 : Fp_invsafe(GEN a, GEN m)
1755 : {
1756 : GEN res;
1757 296687 : if (! invmod(a,m,&res)) return NULL;
1758 296687 : return res;
1759 : }
1760 : INLINE GEN
1761 2296180 : Fp_div(GEN a, GEN b, GEN m)
1762 : {
1763 2296180 : pari_sp av=avma;
1764 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1765 2296180 : (void)new_chunk(lg(a)+(lg(m)<<1));
1766 2296180 : p = mulii(a, Fp_inv(b,m));
1767 2296180 : avma = av; return modii(p,m);
1768 : }
1769 :
1770 : INLINE GEN
1771 682452 : Flx_mulu(GEN x, ulong a, ulong p) { return Flx_Fl_mul(x,a%p,p); }
1772 :
1773 : INLINE GEN
1774 0 : get_F2x_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1775 :
1776 : INLINE long
1777 448057 : get_F2x_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1778 :
1779 : INLINE long
1780 121401 : get_F2x_degree(GEN T) { return typ(T)==t_VEC? F2x_degree(gel(T,2)): F2x_degree(T); }
1781 :
1782 : INLINE GEN
1783 280 : get_F2xqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1784 :
1785 : INLINE long
1786 376425 : get_F2xqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1787 :
1788 : INLINE long
1789 201418 : get_F2xqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1790 :
1791 : INLINE GEN
1792 5975752 : get_Flx_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1793 :
1794 : INLINE long
1795 16091047 : get_Flx_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1796 :
1797 : INLINE long
1798 30066043 : get_Flx_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1799 :
1800 : INLINE GEN
1801 996 : get_FlxqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1802 :
1803 : INLINE long
1804 354401 : get_FlxqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1805 :
1806 : INLINE long
1807 89578 : get_FlxqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1808 :
1809 : INLINE GEN
1810 406085 : get_FpX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1811 :
1812 : INLINE long
1813 1489150 : get_FpX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1814 :
1815 : INLINE long
1816 1543568 : get_FpX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1817 :
1818 : INLINE GEN
1819 142588 : get_FpXQX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1820 :
1821 : INLINE long
1822 52012 : get_FpXQX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1823 :
1824 : INLINE long
1825 1806 : get_FpXQX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1826 :
1827 : /*******************************************************************/
1828 : /* */
1829 : /* ADDMULII / SUBMULII */
1830 : /* */
1831 : /*******************************************************************/
1832 : /* x - y*z */
1833 : INLINE GEN
1834 13208462 : submulii(GEN x, GEN y, GEN z)
1835 : {
1836 13208462 : long lx = lgefint(x), ly, lz;
1837 : pari_sp av;
1838 : GEN t;
1839 13208462 : if (lx == 2) { t = mulii(z,y); togglesign(t); return t; }
1840 11421470 : ly = lgefint(y);
1841 11421470 : if (ly == 2) return icopy(x);
1842 10420286 : lz = lgefint(z);
1843 10420286 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1844 10420286 : t = mulii(z, y);
1845 10420286 : avma = av; return subii(x,t);
1846 : }
1847 : /* y*z - x */
1848 : INLINE GEN
1849 3674306 : mulsubii(GEN y, GEN z, GEN x)
1850 : {
1851 3674306 : long lx = lgefint(x), ly, lz;
1852 : pari_sp av;
1853 : GEN t;
1854 3674306 : if (lx == 2) return mulii(z,y);
1855 2197528 : ly = lgefint(y);
1856 2197528 : if (ly == 2) return negi(x);
1857 1464640 : lz = lgefint(z);
1858 1464640 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1859 1464640 : t = mulii(z, y);
1860 1464640 : avma = av; return subii(t,x);
1861 : }
1862 :
1863 : /* x - u*y */
1864 : INLINE GEN
1865 7371 : submuliu(GEN x, GEN y, ulong u)
1866 : {
1867 : pari_sp av;
1868 7371 : long ly = lgefint(y);
1869 7371 : if (ly == 2) return icopy(x);
1870 7371 : av = avma;
1871 7371 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1872 7371 : y = mului(u,y);
1873 7371 : avma = av; return subii(x, y);
1874 : }
1875 : /* x + u*y */
1876 : INLINE GEN
1877 7371 : addmuliu(GEN x, GEN y, ulong u)
1878 : {
1879 : pari_sp av;
1880 7371 : long ly = lgefint(y);
1881 7371 : if (ly == 2) return icopy(x);
1882 7371 : av = avma;
1883 7371 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1884 7371 : y = mului(u,y);
1885 7371 : avma = av; return addii(x, y);
1886 : }
1887 : /* x - u*y */
1888 : INLINE GEN
1889 112742270 : submuliu_inplace(GEN x, GEN y, ulong u)
1890 : {
1891 : pari_sp av;
1892 112742270 : long ly = lgefint(y);
1893 112742270 : if (ly == 2) return x;
1894 89715555 : av = avma;
1895 89715555 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1896 89715555 : y = mului(u,y);
1897 89715555 : avma = av; return subii(x, y);
1898 : }
1899 : /* x + u*y */
1900 : INLINE GEN
1901 111349124 : addmuliu_inplace(GEN x, GEN y, ulong u)
1902 : {
1903 : pari_sp av;
1904 111349124 : long ly = lgefint(y);
1905 111349124 : if (ly == 2) return x;
1906 89316496 : av = avma;
1907 89316496 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1908 89316496 : y = mului(u,y);
1909 89316496 : avma = av; return addii(x, y);
1910 : }
1911 : /* ux + vy */
1912 : INLINE GEN
1913 41113440 : lincombii(GEN u, GEN v, GEN x, GEN y)
1914 : {
1915 41113440 : long lx = lgefint(x), ly;
1916 : GEN p1, p2;
1917 : pari_sp av;
1918 41113440 : if (lx == 2) return mulii(v,y);
1919 20885530 : ly = lgefint(y);
1920 20885530 : if (ly == 2) return mulii(u,x);
1921 17895789 : av = avma; (void)new_chunk(lx+ly+lgefint(u)+lgefint(v)); /* HACK */
1922 17895789 : p1 = mulii(u,x);
1923 17895789 : p2 = mulii(v,y);
1924 17895789 : avma = av; return addii(p1,p2);
1925 : }
1926 :
1927 : /*******************************************************************/
1928 : /* */
1929 : /* GEN SUBTYPES */
1930 : /* */
1931 : /*******************************************************************/
1932 :
1933 : INLINE int
1934 1272075224 : is_const_t(long t) { return (t < t_POLMOD); }
1935 : INLINE int
1936 5283 : is_extscalar_t(long t) { return (t <= t_POL); }
1937 : INLINE int
1938 1021108 : is_intreal_t(long t) { return (t <= t_REAL); }
1939 : INLINE int
1940 378013262 : is_matvec_t(long t) { return (t >= t_VEC && t <= t_MAT); }
1941 : INLINE int
1942 50320404 : is_noncalc_t(long tx) { return (tx) >= t_LIST; }
1943 : INLINE int
1944 754018 : is_rational_t(long t) { return (t == t_INT || t == t_FRAC); }
1945 : INLINE int
1946 276325 : is_real_t(long t) { return (t == t_INT || t == t_REAL || t == t_FRAC); }
1947 : INLINE int
1948 2807189801 : is_recursive_t(long t) { return lontyp[t]; }
1949 : INLINE int
1950 171408050 : is_scalar_t(long t) { return (t < t_POL); }
1951 : INLINE int
1952 862213 : is_vec_t(long t) { return (t == t_VEC || t == t_COL); }
1953 :
1954 : /*******************************************************************/
1955 : /* */
1956 : /* TRANSCENDENTAL */
1957 : /* */
1958 : /*******************************************************************/
1959 : INLINE GEN
1960 16559684 : sqrtr(GEN x) {
1961 16559684 : long s = signe(x);
1962 16559684 : if (s == 0) return real_0_bit(expo(x) >> 1);
1963 16525997 : if (s >= 0) return sqrtr_abs(x);
1964 26939 : retmkcomplex(gen_0, sqrtr_abs(x));
1965 : }
1966 : INLINE GEN
1967 0 : cbrtr_abs(GEN x) { return sqrtnr_abs(x, 3); }
1968 : INLINE GEN
1969 0 : cbrtr(GEN x) {
1970 0 : long s = signe(x);
1971 : GEN r;
1972 0 : if (s == 0) return real_0_bit(expo(x) / 3);
1973 0 : r = cbrtr_abs(x);
1974 0 : if (s < 0) togglesign(r);
1975 0 : return r;
1976 : }
1977 : INLINE GEN
1978 283401 : sqrtnr(GEN x, long n) {
1979 283401 : long s = signe(x);
1980 : GEN r;
1981 283401 : if (s == 0) return real_0_bit(expo(x) / n);
1982 283401 : r = sqrtnr_abs(x, n);
1983 283401 : if (s < 0) pari_err_IMPL("sqrtnr for x < 0");
1984 283401 : return r;
1985 : }
1986 : INLINE long
1987 211344 : logint(GEN B, GEN y) { return logintall(B,y,NULL); }
1988 : INLINE ulong
1989 8269363 : ulogint(ulong B, ulong y)
1990 : {
1991 : ulong r;
1992 : long e;
1993 8269363 : if (y == 2) return expu(B);
1994 8192379 : r = y;
1995 27488328 : for (e=1;; e++)
1996 : { /* here, r = y^e, r2 = y^(e-1) */
1997 27488328 : if (r >= B) return r == B? e: e-1;
1998 19295949 : r = umuluu_or_0(y, r);
1999 19295949 : if (!r) return e;
2000 19295949 : }
2001 : }
2002 :
2003 : /*******************************************************************/
2004 : /* */
2005 : /* MISCELLANEOUS */
2006 : /* */
2007 : /*******************************************************************/
2008 1021031 : INLINE int ismpzero(GEN x) { return is_intreal_t(typ(x)) && !signe(x); }
2009 520101186 : INLINE int isintzero(GEN x) { return typ(x) == t_INT && !signe(x); }
2010 10060720 : INLINE int isint1(GEN x) { return typ(x)==t_INT && equali1(x); }
2011 5103 : INLINE int isintm1(GEN x){ return typ(x)==t_INT && equalim1(x);}
2012 287160214 : INLINE int equali1(GEN n)
2013 287160214 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(1)) && n[2] == 1; }
2014 51604775 : INLINE int equalim1(GEN n)
2015 51604775 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(-1)) && n[2] == 1; }
2016 : /* works only for POSITIVE integers */
2017 1563258962 : INLINE int is_pm1(GEN n)
2018 1563258962 : { return lgefint(n) == 3 && n[2] == 1; }
2019 581765327 : INLINE int is_bigint(GEN n)
2020 581765327 : { long l = lgefint(n); return l > 3 || (l == 3 && (n[2] & HIGHBIT)); }
2021 :
2022 2121414711 : INLINE int odd(long x) { return x & 1; }
2023 28994165 : INLINE int both_odd(long x, long y) { return x & y & 1; }
2024 :
2025 : INLINE int
2026 2584380476 : isonstack(GEN x)
2027 5168760952 : { return ((pari_sp)x >= pari_mainstack->bot
2028 2584380476 : && (pari_sp)x < pari_mainstack->top); }
2029 :
2030 : /* assume x != 0 and x t_REAL, return an approximation to log2(|x|) */
2031 : INLINE double
2032 17883518 : dbllog2r(GEN x)
2033 17883518 : { return log2((double)(ulong)x[2]) + (double)(expo(x) - (BITS_IN_LONG-1)); }
2034 :
2035 : INLINE GEN
2036 279694 : mul_content(GEN cx, GEN cy)
2037 : {
2038 279694 : if (!cx) return cy;
2039 95228 : if (!cy) return cx;
2040 70411 : return gmul(cx,cy);
2041 : }
2042 : INLINE GEN
2043 1536886 : mul_denom(GEN dx, GEN dy)
2044 : {
2045 1536886 : if (!dx) return dy;
2046 1018896 : if (!dy) return dx;
2047 315931 : return mulii(dx,dy);
2048 : }
2049 :
2050 : /* POLYNOMIALS */
2051 : INLINE GEN
2052 17565372 : constant_coeff(GEN x) { return signe(x)? gel(x,2): gen_0; }
2053 : INLINE GEN
2054 78621592 : leading_coeff(GEN x) { return lg(x) == 2? gen_0: gel(x,lg(x)-1); }
2055 : INLINE ulong
2056 412643 : Flx_lead(GEN x) { return lg(x) == 2? 0: x[lg(x)-1]; }
2057 : INLINE long
2058 2781882802 : degpol(GEN x) { return lg(x)-3; }
2059 : INLINE long
2060 1371454463 : lgpol(GEN x) { return lg(x)-2; }
2061 : INLINE long
2062 98705966 : lgcols(GEN x) { return lg(gel(x,1)); }
2063 : INLINE long
2064 20822561 : nbrows(GEN x) { return lg(gel(x,1))-1; }
2065 : INLINE GEN
2066 0 : truecoeff(GEN x, long n) { return polcoeff0(x,n,-1); }
2067 :
2068 : INLINE GEN
2069 432776 : RgXQ_mul(GEN y, GEN x, GEN T) { return RgX_rem(RgX_mul(y, x), T); }
2070 : INLINE GEN
2071 281360 : RgXQ_sqr(GEN x, GEN T) { return RgX_rem(RgX_sqr(x), T); }
2072 :
2073 : INLINE GEN
2074 143451 : ZXQ_mul(GEN y, GEN x, GEN T) { return ZX_rem(ZX_mul(y, x), T); }
2075 : INLINE GEN
2076 35161 : ZXQ_sqr(GEN x, GEN T) { return ZX_rem(ZX_sqr(x), T); }
2077 :
2078 : INLINE GEN
2079 85006234 : RgX_copy(GEN x)
2080 : {
2081 : long lx, i;
2082 85006234 : GEN y = cgetg_copy(x, &lx); y[1] = x[1];
2083 85006233 : for (i = 2; i<lx; i++) gel(y,i) = gcopy(gel(x,i));
2084 85006232 : return y;
2085 : }
2086 : /* have to use ulong to avoid silly warnings from gcc "assuming signed
2087 : * overflow does not occur" */
2088 : INLINE GEN
2089 2224202 : RgX_coeff(GEN x, long n)
2090 : {
2091 2224202 : ulong l = lg(x);
2092 2224202 : return (n < 0 || ((ulong)n+3) > l)? gen_0: gel(x,n+2);
2093 : }
2094 : INLINE GEN
2095 315497 : RgX_renormalize(GEN x) { return RgX_renormalize_lg(x, lg(x)); }
2096 : INLINE GEN
2097 6489392 : RgX_div(GEN x, GEN y) { return RgX_divrem(x,y,NULL); }
2098 : INLINE GEN
2099 1792 : RgXQX_div(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,NULL); }
2100 : INLINE GEN
2101 52061 : RgXQX_rem(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,ONLY_REM); }
2102 : INLINE GEN
2103 827318 : FpX_div(GEN x, GEN y, GEN p) { return FpX_divrem(x,y,p, NULL); }
2104 : INLINE GEN
2105 3632187 : Flx_div(GEN x, GEN y, ulong p) { return Flx_divrem(x,y,p, NULL); }
2106 : INLINE GEN
2107 2990369 : F2x_div(GEN x, GEN y) { return F2x_divrem(x,y, NULL); }
2108 : INLINE GEN
2109 0 : FpV_FpC_mul(GEN x, GEN y, GEN p) { return FpV_dotproduct(x,y,p); }
2110 : INLINE GEN
2111 44890697 : pol0_Flx(long sv) { return mkvecsmall(sv); }
2112 : INLINE GEN
2113 18528522 : pol1_Flx(long sv) { return mkvecsmall2(sv, 1); }
2114 : INLINE GEN
2115 18101624 : polx_Flx(long sv) { return mkvecsmall3(sv, 0, 1); }
2116 : INLINE GEN
2117 0 : zero_zx(long sv) { return zero_Flx(sv); }
2118 : INLINE GEN
2119 0 : polx_zx(long sv) { return polx_Flx(sv); }
2120 : INLINE GEN
2121 0 : zx_shift(GEN x, long n) { return Flx_shift(x,n); }
2122 : INLINE GEN
2123 0 : zx_renormalize(GEN x, long l) { return Flx_renormalize(x,l); }
2124 : INLINE GEN
2125 1383 : zero_F2x(long sv) { return zero_Flx(sv); }
2126 : INLINE GEN
2127 11373102 : pol0_F2x(long sv) { return pol0_Flx(sv); }
2128 : INLINE GEN
2129 2801730 : pol1_F2x(long sv) { return pol1_Flx(sv); }
2130 : INLINE GEN
2131 671804 : polx_F2x(long sv) { return mkvecsmall2(sv, 2); }
2132 : INLINE int
2133 815743 : F2x_equal1(GEN x) { return Flx_equal1(x); }
2134 : INLINE int
2135 3547127 : F2x_equal(GEN V, GEN W) { return Flx_equal(V,W); }
2136 : INLINE GEN
2137 69615247 : F2x_copy(GEN x) { return leafcopy(x); }
2138 : INLINE GEN
2139 0 : F2v_copy(GEN x) { return leafcopy(x); }
2140 : INLINE GEN
2141 2347064 : Flv_copy(GEN x) { return leafcopy(x); }
2142 : INLINE GEN
2143 74703769 : Flx_copy(GEN x) { return leafcopy(x); }
2144 : INLINE GEN
2145 1658252 : vecsmall_copy(GEN x) { return leafcopy(x); }
2146 : INLINE int
2147 4742377 : Flx_equal1(GEN x) { return degpol(x)==0 && x[2] == 1; }
2148 : INLINE int
2149 17635 : ZX_equal1(GEN x) { return degpol(x)==0 && equali1(gel(x,2)); }
2150 :
2151 : INLINE GEN
2152 43242149 : ZX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2153 : INLINE GEN
2154 54367100 : FpX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2155 : INLINE GEN
2156 961806 : FpXX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2157 : INLINE GEN
2158 993815 : FpXQX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2159 : INLINE GEN
2160 122784710 : F2x_renormalize(GEN x, long lx) { return Flx_renormalize(x,lx); }
2161 : INLINE GEN
2162 8744 : F2v_to_F2x(GEN x, long sv) {
2163 8744 : GEN y = leafcopy(x);
2164 8744 : y[1] = sv; F2x_renormalize(y, lg(y)); return y;
2165 : }
2166 :
2167 : INLINE long
2168 455 : sturm(GEN x) { return sturmpart(x, NULL, NULL); }
2169 :
2170 : INLINE long
2171 2429 : gval(GEN x, long v) {
2172 2429 : pari_sp av = avma;
2173 2429 : long n = gvaluation(x, pol_x(v));
2174 2429 : avma = av; return n;
2175 : }
2176 :
2177 : INLINE void
2178 485426 : RgX_shift_inplace_init(long v)
2179 485426 : { if (v) (void)cgetg(v, t_VECSMALL); }
2180 : /* shift polynomial in place. assume v free cells have been left before x */
2181 : INLINE GEN
2182 485426 : RgX_shift_inplace(GEN x, long v)
2183 : {
2184 : long i, lx;
2185 : GEN y, z;
2186 485426 : if (!v) return x;
2187 253272 : lx = lg(x);
2188 253272 : if (lx == 2) return x;
2189 253272 : y = x + v;
2190 253272 : z = x + lx;
2191 : /* stackdummy from normalizepol: move it up */
2192 253272 : if (lg(z) != v) x[lx + v] = z[0];
2193 253272 : for (i = lx-1; i >= 2; i--) gel(y,i) = gel(x,i);
2194 253272 : for (i = v+1; i >= 2; i--) gel(x,i) = gen_0;
2195 : /* leave x[1] alone: it is correct */
2196 253272 : x[0] = evaltyp(t_POL) | evallg(lx+v); return x;
2197 : }
2198 :
2199 :
2200 : /* LINEAR ALGEBRA */
2201 : INLINE GEN
2202 68075 : zv_to_ZV(GEN x) { return vecsmall_to_vec(x); }
2203 : INLINE GEN
2204 1282798 : zc_to_ZC(GEN x) { return vecsmall_to_col(x); }
2205 : INLINE GEN
2206 392124 : ZV_to_zv(GEN x) { return vec_to_vecsmall(x); }
2207 : INLINE GEN
2208 0 : zx_to_zv(GEN x, long N) { return Flx_to_Flv(x,N); }
2209 : INLINE GEN
2210 0 : zv_to_zx(GEN x, long sv) { return Flv_to_Flx(x,sv); }
2211 : INLINE GEN
2212 0 : zm_to_zxV(GEN x, long sv) { return Flm_to_FlxV(x,sv); }
2213 : INLINE GEN
2214 0 : zero_zm(long x, long y) { return zero_Flm(x,y); }
2215 : INLINE GEN
2216 18064670 : zero_zv(long x) { return zero_Flv(x); }
2217 : INLINE GEN
2218 168 : zm_transpose(GEN x) { return Flm_transpose(x); }
2219 : INLINE GEN
2220 0 : zm_copy(GEN x) { return Flm_copy(x); }
2221 : INLINE GEN
2222 2002568 : zv_copy(GEN x) { return Flv_copy(x); }
2223 : INLINE GEN
2224 0 : zm_row(GEN x, long i) { return Flm_row(x,i); }
2225 :
2226 : INLINE GEN
2227 840045 : ZC_hnfrem(GEN x, GEN y) { return ZC_hnfremdiv(x,y,NULL); }
2228 : INLINE GEN
2229 35604 : ZM_hnfrem(GEN x, GEN y) { return ZM_hnfdivrem(x,y,NULL); }
2230 : INLINE GEN
2231 1162823 : ZM_lll(GEN x, double D, long f) { return ZM_lll_norms(x,D,f,NULL); }
2232 : INLINE void
2233 191759 : RgM_dimensions(GEN x, long *m, long *n) { *n = lg(x)-1; *m = *n? nbrows(x): 0; }
2234 : INLINE GEN
2235 43912 : RgM_inv(GEN a) { return RgM_solve(a, NULL); }
2236 : INLINE GEN
2237 6776813 : RgM_shallowcopy(GEN x)
2238 : {
2239 : long l;
2240 6776813 : GEN y = cgetg_copy(x, &l);
2241 6776813 : while (--l > 0) gel(y,l) = leafcopy(gel(x,l));
2242 6776813 : return y;
2243 : }
2244 : INLINE GEN
2245 362 : F2m_copy(GEN x) { return RgM_shallowcopy(x); }
2246 :
2247 : INLINE GEN
2248 1383749 : Flm_copy(GEN x) { return RgM_shallowcopy(x); }
2249 :
2250 : /* divisibility: return 1 if y[i] | x[i] for all i, 0 otherwise. Assume
2251 : * x,y are ZV of the same length */
2252 : INLINE int
2253 23198 : ZV_dvd(GEN x, GEN y)
2254 : {
2255 23198 : long i, l = lg(x);
2256 36652 : for (i=1; i < l; i++)
2257 29519 : if ( ! dvdii( gel(x,i), gel(y,i) ) ) return 0;
2258 7133 : return 1;
2259 : }
2260 :
2261 : /* Fq */
2262 : INLINE GEN
2263 2223566 : Fq_red(GEN x, GEN T, GEN p)
2264 2223566 : { return typ(x)==t_INT? Fp_red(x,p): FpXQ_red(x,T,p); }
2265 : INLINE GEN
2266 11499 : Fq_to_FpXQ(GEN x, GEN T, GEN p /*unused*/)
2267 : {
2268 : (void) p;
2269 11499 : return typ(x)==t_INT ? scalarpol(x, get_FpX_var(T)): x;
2270 : }
2271 :
2272 : INLINE GEN
2273 833 : gener_Fq_local(GEN T, GEN p, GEN L)
2274 833 : { return T? gener_FpXQ_local(T,p, L)
2275 833 : : pgener_Fp_local(p, L); }
2276 :
2277 : /* FpXQX */
2278 : INLINE GEN
2279 1396 : FpXQX_div(GEN x, GEN y, GEN T, GEN p) { return FpXQX_divrem(x, y, T, p, NULL); }
2280 : INLINE GEN
2281 33186 : FlxqX_div(GEN x, GEN y, GEN T, ulong p) { return FlxqX_divrem(x, y, T, p, NULL); }
2282 : INLINE GEN
2283 30779 : F2xqX_div(GEN x, GEN y, GEN T) { return F2xqX_divrem(x, y, T, NULL); }
2284 :
2285 : /* FqX */
2286 : INLINE GEN
2287 27419 : FqX_red(GEN z, GEN T, GEN p) { return T? FpXQX_red(z, T, p): FpX_red(z, p); }
2288 : INLINE GEN
2289 903749 : FqX_add(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2290 : INLINE GEN
2291 16438 : FqX_neg(GEN x,GEN T,GEN p) { return T? FpXX_neg(x,p): FpX_neg(x,p); }
2292 : INLINE GEN
2293 2380 : FqX_sub(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2294 : INLINE GEN
2295 617158 : FqX_Fp_mul(GEN P, GEN u, GEN T, GEN p)
2296 617158 : { return T? FpXX_Fp_mul(P, u, p): FpX_Fp_mul(P, u, p); }
2297 : INLINE GEN
2298 552395 : FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
2299 552395 : { return typ(U)==t_INT ? FqX_Fp_mul(P, U, T, p): FpXQX_FpXQ_mul(P, U, T, p); }
2300 : INLINE GEN
2301 87634 : FqX_mul(GEN x, GEN y, GEN T, GEN p)
2302 87634 : { return T? FpXQX_mul(x, y, T, p): FpX_mul(x, y, p); }
2303 : INLINE GEN
2304 459889 : FqX_mulu(GEN x, ulong y, GEN T, GEN p)
2305 459889 : { return T? FpXX_mulu(x, y, p): FpX_mulu(x, y, p); }
2306 : INLINE GEN
2307 4760 : FqX_sqr(GEN x, GEN T, GEN p)
2308 4760 : { return T? FpXQX_sqr(x, T, p): FpX_sqr(x, p); }
2309 : INLINE GEN
2310 1428 : FqX_powu(GEN x, ulong n, GEN T, GEN p)
2311 1428 : { return T? FpXQX_powu(x, n, T, p): FpX_powu(x, n, p); }
2312 : INLINE GEN
2313 5145 : FqX_div(GEN x, GEN y, GEN T, GEN p)
2314 5145 : { return T? FpXQX_divrem(x,y,T,p,NULL): FpX_divrem(x,y,p,NULL); }
2315 : INLINE GEN
2316 5605 : FqX_get_red(GEN S, GEN T, GEN p)
2317 5605 : { return T? FpXQX_get_red(S,T,p): FpX_get_red(S,p); }
2318 : INLINE GEN
2319 47767 : FqX_rem(GEN x, GEN y, GEN T, GEN p)
2320 47767 : { return T? FpXQX_rem(x,y,T,p): FpX_rem(x,y,p); }
2321 : INLINE GEN
2322 329 : FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
2323 329 : { return T? FpXQX_divrem(x,y,T,p,z): FpX_divrem(x,y,p,z); }
2324 : INLINE GEN
2325 5957 : FqX_div_by_X_x(GEN x, GEN y, GEN T, GEN p, GEN *z)
2326 5957 : { return T? FpXQX_div_by_X_x(x,y,T,p,z): FpX_div_by_X_x(x,y,p,z); }
2327 : INLINE GEN
2328 0 : FqX_halfgcd(GEN P,GEN Q,GEN T,GEN p)
2329 0 : {return T? FpXQX_halfgcd(P,Q,T,p): FpX_halfgcd(P,Q,p);}
2330 : INLINE GEN
2331 257866 : FqX_gcd(GEN P,GEN Q,GEN T,GEN p)
2332 257866 : {return T? FpXQX_gcd(P,Q,T,p): FpX_gcd(P,Q,p);}
2333 : INLINE GEN
2334 85302 : FqX_extgcd(GEN P,GEN Q,GEN T,GEN p, GEN *U, GEN *V)
2335 85302 : { return T? FpXQX_extgcd(P,Q,T,p,U,V): FpX_extgcd(P,Q,p,U,V); }
2336 : INLINE GEN
2337 3122 : FqX_normalize(GEN z, GEN T, GEN p) { return T? FpXQX_normalize(z, T, p): FpX_normalize(z, p); }
2338 : INLINE GEN
2339 270081 : FqX_deriv(GEN f, /*unused*/GEN T, GEN p) { (void)T; return FpXX_deriv(f, p); }
2340 : INLINE GEN
2341 72961 : FqX_factor(GEN f, GEN T, GEN p) { return T?FpXQX_factor(f, T, p): FpX_factor(f, p); }
2342 : INLINE GEN
2343 6391 : FqX_roots(GEN f, GEN T, GEN p) { return T?FpXQX_roots(f, T, p): FpX_roots(f, p); }
2344 :
2345 : /*FqXQ*/
2346 : INLINE GEN
2347 0 : FqXQ_add(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2348 0 : { (void)S; return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2349 : INLINE GEN
2350 0 : FqXQ_sub(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2351 0 : { (void)S; return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2352 : INLINE GEN
2353 0 : FqXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
2354 0 : { return T? FpXQXQ_div(x,y,S,T,p): FpXQ_div(x,y,S,p); }
2355 : INLINE GEN
2356 0 : FqXQ_inv(GEN x, GEN S, GEN T, GEN p)
2357 0 : { return T? FpXQXQ_inv(x,S,T,p): FpXQ_inv(x,S,p); }
2358 : INLINE GEN
2359 0 : FqXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
2360 0 : { return T? FpXQXQ_invsafe(x,S,T,p): FpXQ_inv(x,S,p); }
2361 : INLINE GEN
2362 21018 : FqXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
2363 21018 : { return T? FpXQXQ_mul(x,y,S,T,p): FpXQ_mul(x,y,S,p); }
2364 : INLINE GEN
2365 0 : FqXQ_sqr(GEN x, GEN S, GEN T, GEN p)
2366 0 : { return T? FpXQXQ_sqr(x,S,T,p): FpXQ_sqr(x,S,p); }
2367 : INLINE GEN
2368 0 : FqXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
2369 0 : { return T? FpXQXQ_pow(x,n,S,T,p): FpXQ_pow(x,n,S,p); }
2370 :
2371 : /*FpXQ*/
2372 : INLINE GEN
2373 0 : FpXQ_add(GEN x,GEN y,GEN T/*unused*/,GEN p)
2374 0 : { (void)T; return FpX_add(x,y,p); }
2375 : INLINE GEN
2376 0 : FpXQ_sub(GEN x,GEN y,GEN T/*unused*/,GEN p)
2377 0 : { (void)T; return FpX_sub(x,y,p); }
2378 :
2379 : /*Flxq*/
2380 : INLINE GEN
2381 0 : Flxq_add(GEN x,GEN y,GEN T/*unused*/,ulong p)
2382 0 : { (void)T; return Flx_add(x,y,p); }
2383 : INLINE GEN
2384 0 : Flxq_sub(GEN x,GEN y,GEN T/*unused*/,ulong p)
2385 0 : { (void)T; return Flx_sub(x,y,p); }
2386 :
2387 : /* F2x */
2388 :
2389 : INLINE ulong
2390 168914536 : F2x_coeff(GEN x,long v)
2391 : {
2392 168914536 : ulong u=(ulong)x[2+divsBIL(v)];
2393 168914436 : return (u>>remsBIL(v))&1UL;
2394 : }
2395 :
2396 : INLINE void
2397 4180114 : F2x_clear(GEN x,long v)
2398 : {
2399 4180114 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2400 4180114 : *u&=~(1UL<<remsBIL(v));
2401 4180114 : }
2402 :
2403 : INLINE void
2404 38818428 : F2x_set(GEN x,long v)
2405 : {
2406 38818428 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2407 38820087 : *u|=1UL<<remsBIL(v);
2408 38822519 : }
2409 :
2410 : INLINE void
2411 1360015 : F2x_flip(GEN x,long v)
2412 : {
2413 1360015 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2414 1360015 : *u^=1UL<<remsBIL(v);
2415 1360015 : }
2416 :
2417 : /* F2v */
2418 :
2419 : INLINE ulong
2420 162414928 : F2v_coeff(GEN x,long v) { return F2x_coeff(x,v-1); }
2421 :
2422 : INLINE void
2423 4180114 : F2v_clear(GEN x,long v) { F2x_clear(x,v-1); }
2424 :
2425 : INLINE void
2426 12561215 : F2v_set(GEN x,long v) { F2x_set(x,v-1); }
2427 :
2428 : INLINE void
2429 1360015 : F2v_flip(GEN x,long v) { F2x_flip(x,v-1); }
2430 :
2431 : /* F2m */
2432 :
2433 : INLINE ulong
2434 19319262 : F2m_coeff(GEN x, long a, long b) { return F2v_coeff(gel(x,b), a); }
2435 :
2436 : INLINE void
2437 0 : F2m_clear(GEN x, long a, long b) { F2v_clear(gel(x,b), a); }
2438 :
2439 : INLINE void
2440 2352087 : F2m_set(GEN x, long a, long b) { F2v_set(gel(x,b), a); }
2441 :
2442 : INLINE void
2443 1360015 : F2m_flip(GEN x, long a, long b) { F2v_flip(gel(x,b), a); }
2444 :
2445 : /* ARITHMETIC */
2446 : INLINE GEN
2447 1029 : matpascal(long n) { return matqpascal(n, NULL); }
2448 : INLINE long
2449 2225428 : Z_issquare(GEN x) { return Z_issquareall(x, NULL); }
2450 : INLINE long
2451 14 : Z_ispower(GEN x, ulong k) { return Z_ispowerall(x, k, NULL); }
2452 : INLINE GEN
2453 5425298 : sqrti(GEN x) { return sqrtremi(x,NULL); }
2454 : INLINE GEN
2455 7403535 : gaddgs(GEN y, long s) { return gaddsg(s,y); }
2456 : INLINE int
2457 23890 : gcmpgs(GEN y, long s) { return -gcmpsg(s,y); }
2458 : INLINE int
2459 24367 : gequalgs(GEN y, long s) { return gequalsg(s,y); }
2460 : INLINE GEN
2461 0 : gmaxsg(long s, GEN y) { return gmaxgs(y,s); }
2462 : INLINE GEN
2463 0 : gminsg(long s, GEN y) { return gmings(y,s); }
2464 : INLINE GEN
2465 13262836 : gmulgs(GEN y, long s) { return gmulsg(s,y); }
2466 : INLINE GEN
2467 558170 : gsubgs(GEN y, long s) { return gaddgs(y, -s); }
2468 : INLINE GEN
2469 462774 : gdivsg(long s, GEN y) { return gdiv(stoi(s), y); }
2470 :
2471 : /* x t_COMPLEX */
2472 : INLINE GEN
2473 9741721 : cxnorm(GEN x) { return gadd(gsqr(gel(x,1)), gsqr(gel(x,2))); }
2474 : /* q t_QUAD */
2475 : INLINE GEN
2476 623 : quadnorm(GEN q)
2477 : {
2478 623 : GEN X = gel(q,1), b = gel(X,3), c = gel(X,2);
2479 623 : GEN z, u = gel(q,3), v = gel(q,2);
2480 623 : if (typ(u) == t_INT && typ(v) == t_INT) /* generic case */
2481 : {
2482 308 : z = signe(b)? mulii(v, addii(u,v)): sqri(v);
2483 308 : return addii(z, mulii(c, sqri(u)));
2484 : }
2485 : else
2486 : {
2487 315 : z = signe(b)? gmul(v, gadd(u,v)): gsqr(v);
2488 315 : return gadd(z, gmul(c, gsqr(u)));
2489 : }
2490 : }
2491 : /* x a t_QUAD, return the attached discriminant */
2492 : INLINE GEN
2493 252 : quad_disc(GEN x)
2494 : {
2495 252 : GEN Q = gel(x,1), b = gel(Q,3), c = gel(Q,2), c4;
2496 252 : if (is_pm1(b))
2497 : {
2498 196 : pari_sp av = avma; (void)new_chunk(lgefint(c) + 1);
2499 196 : c4 = shifti(c,2); avma = av; return subsi(1, c4);
2500 : }
2501 56 : c4 = shifti(c,2); togglesign_safe(&c4); return c4;
2502 : }
2503 : INLINE GEN
2504 6345364 : qfb_disc3(GEN x, GEN y, GEN z) { return subii(sqri(y), shifti(mulii(x,z),2)); }
2505 : INLINE GEN
2506 6264528 : qfb_disc(GEN x) { return qfb_disc3(gel(x,1), gel(x,2), gel(x,3)); }
2507 :
2508 : INLINE GEN
2509 1245037 : sqrfrac(GEN x)
2510 : {
2511 1245037 : GEN z = cgetg(3,t_FRAC);
2512 1245037 : gel(z,1) = sqri(gel(x,1));
2513 1245037 : gel(z,2) = sqri(gel(x,2)); return z;
2514 : }
2515 :
2516 : INLINE void
2517 17521003 : normalize_frac(GEN z) {
2518 17521003 : if (signe(gel(z,2)) < 0) { togglesign(gel(z,1)); setabssign(gel(z,2)); }
2519 17521003 : }
2520 :
2521 : INLINE GEN
2522 231714 : powii(GEN x, GEN n)
2523 : {
2524 231714 : long ln = lgefint(n);
2525 231714 : if (ln == 3) {
2526 : GEN z;
2527 228501 : if (signe(n) > 0) return powiu(x, n[2]);
2528 4956 : z = cgetg(3, t_FRAC);
2529 4956 : gel(z,1) = gen_1;
2530 4956 : gel(z,2) = powiu(x, n[2]);
2531 4956 : return z;
2532 : }
2533 3213 : if (ln == 2) return gen_1; /* rare */
2534 : /* should never happen */
2535 0 : return powgi(x, n); /* overflow unless x = 0, 1, -1 */
2536 : }
2537 : INLINE GEN
2538 1477 : powIs(long n) {
2539 1477 : switch(n & 3)
2540 : {
2541 7 : case 1: return mkcomplex(gen_0,gen_1);
2542 364 : case 2: return gen_m1;
2543 455 : case 3: return mkcomplex(gen_0,gen_m1);
2544 : }
2545 651 : return gen_1;
2546 : }
2547 :
2548 : /*******************************************************************/
2549 : /* */
2550 : /* ASSIGNMENTS */
2551 : /* */
2552 : /*******************************************************************/
2553 0 : INLINE void mpexpz(GEN x, GEN z)
2554 0 : { pari_sp av = avma; gaffect(mpexp(x), z); avma = av; }
2555 0 : INLINE void mplogz(GEN x, GEN z)
2556 0 : { pari_sp av = avma; gaffect(mplog(x), z); avma = av; }
2557 0 : INLINE void mpcosz(GEN x, GEN z)
2558 0 : { pari_sp av = avma; gaffect(mpcos(x), z); avma = av; }
2559 0 : INLINE void mpsinz(GEN x, GEN z)
2560 0 : { pari_sp av = avma; gaffect(mpsin(x), z); avma = av; }
2561 0 : INLINE void gnegz(GEN x, GEN z)
2562 0 : { pari_sp av = avma; gaffect(gneg(x), z); avma = av; }
2563 0 : INLINE void gabsz(GEN x, long prec, GEN z)
2564 0 : { pari_sp av = avma; gaffect(gabs(x,prec), z); avma = av; }
2565 23318 : INLINE void gaddz(GEN x, GEN y, GEN z)
2566 23318 : { pari_sp av = avma; gaffect(gadd(x,y), z); avma = av; }
2567 0 : INLINE void gsubz(GEN x, GEN y, GEN z)
2568 0 : { pari_sp av = avma; gaffect(gsub(x,y), z); avma = av; }
2569 11673 : INLINE void gmulz(GEN x, GEN y, GEN z)
2570 11673 : { pari_sp av = avma; gaffect(gmul(x,y), z); avma = av; }
2571 0 : INLINE void gdivz(GEN x, GEN y, GEN z)
2572 0 : { pari_sp av = avma; gaffect(gdiv(x,y), z); avma = av; }
2573 0 : INLINE void gdiventz(GEN x, GEN y, GEN z)
2574 0 : { pari_sp av = avma; gaffect(gdivent(x,y), z); avma = av; }
2575 0 : INLINE void gmodz(GEN x, GEN y, GEN z)
2576 0 : { pari_sp av = avma; gaffect(gmod(x,y), z); avma = av; }
2577 0 : INLINE void gmul2nz(GEN x, long s, GEN z)
2578 0 : { pari_sp av = avma; gaffect(gmul2n(x,s), z); avma = av; }
2579 0 : INLINE void gshiftz(GEN x, long s, GEN z)
2580 0 : { pari_sp av = avma; gaffect(gshift(x,s), z); avma = av; }
2581 :
2582 : /*******************************************************************/
2583 : /* */
2584 : /* ELLIPTIC CURVES */
2585 : /* */
2586 : /*******************************************************************/
2587 5287715 : INLINE GEN ell_get_a1(GEN e) { return gel(e,1); }
2588 3095171 : INLINE GEN ell_get_a2(GEN e) { return gel(e,2); }
2589 4515902 : INLINE GEN ell_get_a3(GEN e) { return gel(e,3); }
2590 3888005 : INLINE GEN ell_get_a4(GEN e) { return gel(e,4); }
2591 4704352 : INLINE GEN ell_get_a6(GEN e) { return gel(e,5); }
2592 3968891 : INLINE GEN ell_get_b2(GEN e) { return gel(e,6); }
2593 1021637 : INLINE GEN ell_get_b4(GEN e) { return gel(e,7); }
2594 1627613 : INLINE GEN ell_get_b6(GEN e) { return gel(e,8); }
2595 1464204 : INLINE GEN ell_get_b8(GEN e) { return gel(e,9); }
2596 5899340 : INLINE GEN ell_get_c4(GEN e) { return gel(e,10); }
2597 7931182 : INLINE GEN ell_get_c6(GEN e) { return gel(e,11); }
2598 9365459 : INLINE GEN ell_get_disc(GEN e) { return gel(e,12); }
2599 1027341 : INLINE GEN ell_get_j(GEN e) { return gel(e,13); }
2600 7907941 : INLINE long ell_get_type(GEN e) { return mael(e,14,1); }
2601 1561498 : INLINE GEN ellff_get_field(GEN x) { return gmael(x, 15, 1); }
2602 678312 : INLINE GEN ellff_get_a4a6(GEN x) { return gmael(x, 15, 2); }
2603 917 : INLINE GEN ellQp_get_zero(GEN x) { return gmael(x, 15, 1); }
2604 287 : INLINE long ellQp_get_prec(GEN E) { GEN z = ellQp_get_zero(E); return valp(z); }
2605 623 : INLINE GEN ellQp_get_p(GEN E) { GEN z = ellQp_get_zero(E); return gel(z,2); }
2606 36960 : INLINE long ellR_get_prec(GEN x) { return nbits2prec(mael3(x, 15, 1, 1)); }
2607 8262 : INLINE long ellR_get_sign(GEN x) { return mael3(x, 15, 1, 2); }
2608 501578 : INLINE GEN ellnf_get_nf(GEN x) { return checknf_i(gmael(x,15,1)); }
2609 49 : INLINE GEN ellnf_get_bnf(GEN x) { return checkbnf_i(gmael(x,15,1)); }
2610 :
2611 21510996 : INLINE int ell_is_inf(GEN z) { return lg(z) == 2; }
2612 787451 : INLINE GEN ellinf(void) { return mkvec(gen_0); }
2613 :
2614 : /*******************************************************************/
2615 : /* */
2616 : /* ALGEBRAIC NUMBER THEORY */
2617 : /* */
2618 : /*******************************************************************/
2619 8123314 : INLINE GEN modpr_get_pr(GEN x) { return gel(x,3); }
2620 609923 : INLINE GEN modpr_get_p(GEN x) { return pr_get_p(modpr_get_pr(x)); }
2621 2520010 : INLINE GEN modpr_get_T(GEN x) { return lg(x) == 4? NULL: gel(x,4); }
2622 :
2623 18283531 : INLINE GEN pr_get_p(GEN pr) { return gel(pr,1); }
2624 4838271 : INLINE GEN pr_get_gen(GEN pr){ return gel(pr,2); }
2625 : /* .[2] instead of itos works: e and f are small positive integers */
2626 2226406 : INLINE long pr_get_e(GEN pr) { return gel(pr,3)[2]; }
2627 7775032 : INLINE long pr_get_f(GEN pr) { return gel(pr,4)[2]; }
2628 5792168 : INLINE GEN pr_get_tau(GEN pr){ return gel(pr,5); }
2629 : INLINE int
2630 2344286 : pr_is_inert(GEN P) { return pr_get_f(P) == lg(pr_get_gen(P))-1; }
2631 : INLINE GEN
2632 206850 : pr_norm(GEN pr) { return powiu(pr_get_p(pr), pr_get_f(pr)); }
2633 : INLINE ulong
2634 40873 : upr_norm(GEN pr) { return upowuu(pr_get_p(pr)[2], pr_get_f(pr)); }
2635 :
2636 : /* assume nf a genuine nf */
2637 : INLINE long
2638 4185 : nf_get_varn(GEN nf) { return varn(gel(nf,1)); }
2639 : INLINE GEN
2640 27095341 : nf_get_pol(GEN nf) { return gel(nf,1); }
2641 : INLINE long
2642 21248968 : nf_get_degree(GEN nf) { return degpol( nf_get_pol(nf) ); }
2643 : INLINE long
2644 1274407 : nf_get_r1(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,1)); }
2645 : INLINE long
2646 8197 : nf_get_r2(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,2)); }
2647 : INLINE GEN
2648 46797 : nf_get_disc(GEN nf) { return gel(nf,3); }
2649 : INLINE GEN
2650 751940 : nf_get_index(GEN nf) { return gel(nf,4); }
2651 : INLINE GEN
2652 1215467 : nf_get_M(GEN nf) { return gmael(nf,5,1); }
2653 : INLINE GEN
2654 60567 : nf_get_G(GEN nf) { return gmael(nf,5,2); }
2655 : INLINE GEN
2656 440320 : nf_get_roundG(GEN nf) { return gmael(nf,5,3); }
2657 : INLINE GEN
2658 24339 : nf_get_Tr(GEN nf) { return gmael(nf,5,4); }
2659 : INLINE GEN
2660 2191 : nf_get_diff(GEN nf) { return gmael(nf,5,5); }
2661 : INLINE GEN
2662 28 : nf_get_ramified_primes(GEN nf) { return gmael(nf,5,8); }
2663 : INLINE GEN
2664 158004 : nf_get_roots(GEN nf) { return gel(nf,6); }
2665 : INLINE GEN
2666 77 : nf_get_zk(GEN nf)
2667 : {
2668 77 : GEN y = gel(nf,7), D = nf_get_zkden(nf);
2669 77 : if (!equali1(D)) y = gdiv(y, D);
2670 77 : return y;
2671 : }
2672 : INLINE GEN
2673 219876 : nf_get_zkprimpart(GEN nf)
2674 : {
2675 219876 : GEN y = gel(nf,7);
2676 : /* test for old format of nf.zk: non normalized */
2677 219876 : if (!equali1(gel(nf,4)) && gequal1(gel(y,1))) y = Q_remove_denom(y,NULL);
2678 219876 : return y;
2679 : }
2680 : INLINE GEN
2681 222473 : nf_get_zkden(GEN nf)
2682 : {
2683 222473 : GEN y = gel(nf,7), D = gel(y,1);
2684 222473 : if (typ(D) == t_POL) D = gel(D,2);
2685 : /* test for old format of nf.zk: non normalized */
2686 222473 : if (!equali1(gel(nf,4)) && equali1(D)) D = Q_denom(y);
2687 222473 : return D;
2688 : }
2689 : INLINE GEN
2690 2176443 : nf_get_invzk(GEN nf) { return gel(nf,8); }
2691 : INLINE void
2692 13734 : nf_get_sign(GEN nf, long *r1, long *r2)
2693 : {
2694 13734 : GEN x = gel(nf,2);
2695 13734 : *r1 = itou(gel(x,1));
2696 13734 : *r2 = itou(gel(x,2));
2697 13734 : }
2698 :
2699 : INLINE GEN
2700 49616 : abgrp_get_no(GEN x) { return gel(x,1); }
2701 : INLINE GEN
2702 2033778 : abgrp_get_cyc(GEN x) { return gel(x,2); }
2703 : INLINE GEN
2704 396461 : abgrp_get_gen(GEN x) { return gel(x,3); }
2705 : INLINE GEN
2706 2064067 : bnf_get_nf(GEN bnf) { return gel(bnf,7); }
2707 : INLINE GEN
2708 806355 : bnf_get_clgp(GEN bnf) { return gmael(bnf,8,1); }
2709 : INLINE GEN
2710 4536 : bnf_get_no(GEN bnf) { return abgrp_get_no(bnf_get_clgp(bnf)); }
2711 : INLINE GEN
2712 434282 : bnf_get_cyc(GEN bnf) { return abgrp_get_cyc(bnf_get_clgp(bnf)); }
2713 : INLINE GEN
2714 367208 : bnf_get_gen(GEN bnf) { return abgrp_get_gen(bnf_get_clgp(bnf)); }
2715 : INLINE GEN
2716 860 : bnf_get_reg(GEN bnf) { return gmael(bnf,8,2); }
2717 : INLINE GEN
2718 482141 : bnf_get_logfu(GEN bnf) { return gel(bnf,3); }
2719 : INLINE GEN
2720 5867 : bnf_get_tuU(GEN bnf) { return gmael3(bnf,8,4,2); }
2721 : INLINE long
2722 24535 : bnf_get_tuN(GEN bnf) { return gmael3(bnf,8,4,1)[2]; }
2723 : INLINE GEN
2724 1806 : bnf_get_fu(GEN bnf) {
2725 1806 : GEN fu = bnf_get_fu_nocheck(bnf);
2726 1806 : if (typ(fu) == t_MAT) pari_err(e_MISC,"missing units in bnf");
2727 1806 : return fu;
2728 : }
2729 : INLINE GEN
2730 7134 : bnf_get_fu_nocheck(GEN bnf) { return gmael(bnf,8,5); }
2731 :
2732 : INLINE GEN
2733 747465 : bnr_get_bnf(GEN bnr) { return gel(bnr,1); }
2734 : INLINE GEN
2735 384509 : bnr_get_bid(GEN bnr) { return gel(bnr,2); }
2736 : INLINE GEN
2737 18102 : bnr_get_mod(GEN bnr) { return gmael(bnr,2,1); }
2738 : INLINE GEN
2739 27104 : bnr_get_nf(GEN bnr) { return gmael(bnr,1,7); }
2740 : INLINE GEN
2741 520568 : bnr_get_clgp(GEN bnr) { return gel(bnr,5); }
2742 : INLINE GEN
2743 45080 : bnr_get_no(GEN bnr) { return abgrp_get_no(bnr_get_clgp(bnr)); }
2744 : INLINE GEN
2745 463560 : bnr_get_cyc(GEN bnr) { return abgrp_get_cyc(bnr_get_clgp(bnr)); }
2746 : INLINE GEN
2747 70 : bnr_get_gen_nocheck(GEN bnr) { return abgrp_get_gen(bnr_get_clgp(bnr)); }
2748 : INLINE GEN
2749 11025 : bnr_get_gen(GEN bnr) {
2750 11025 : GEN G = bnr_get_clgp(bnr);
2751 11025 : if (lg(G) != 4)
2752 0 : pari_err(e_MISC,"missing bnr generators: please use bnrinit(,,1)");
2753 11025 : return gel(G,3);
2754 : }
2755 :
2756 : INLINE GEN
2757 302504 : bid_get_mod(GEN bid) { return gel(bid,1); }
2758 : INLINE GEN
2759 44681 : bid_get_ideal(GEN bid) { return gmael(bid,1,1); }
2760 : INLINE GEN
2761 448 : bid_get_arch(GEN bid) { return gmael(bid,1,2); }
2762 : INLINE GEN
2763 1061330 : bid_get_grp(GEN bid) { return gel(bid,2); }
2764 : INLINE GEN
2765 395912 : bid_get_fact(GEN bid) { return gmael(bid,3,1); }
2766 : INLINE GEN
2767 354612 : bid_get_fact2(GEN bid) { return gmael(bid,3,2); }
2768 : INLINE GEN
2769 354682 : bid_get_sprk(GEN bid) { return gmael(bid,4,1); }
2770 : INLINE GEN
2771 29813 : bid_get_sarch(GEN bid) { return gmael(bid,4,2); }
2772 : INLINE GEN
2773 375262 : bid_get_archp(GEN bid) { return gmael3(bid,4,2,2); }
2774 : INLINE GEN
2775 657396 : bid_get_U(GEN bid) { return gel(bid,5); }
2776 : INLINE GEN
2777 0 : bid_get_no(GEN bid) { return abgrp_get_no(bid_get_grp(bid)); }
2778 : INLINE GEN
2779 1033043 : bid_get_cyc(GEN bid) { return abgrp_get_cyc(bid_get_grp(bid)); }
2780 : INLINE GEN
2781 0 : bid_get_gen_nocheck(GEN bid) { return abgrp_get_gen(bid_get_grp(bid)); }
2782 : INLINE GEN
2783 27692 : bid_get_gen(GEN bid) {
2784 27692 : GEN G = bid_get_grp(bid);
2785 27692 : if (lg(G) != 4) pari_err(e_MISC,"missing bid generators. Use idealstar(,,2)");
2786 27692 : return abgrp_get_gen(G);
2787 : }
2788 :
2789 : INLINE GEN
2790 2519832 : znstar_get_N(GEN G) { return gmael(G,1,1); }
2791 : INLINE GEN
2792 2800315 : znstar_get_faN(GEN G) { return gel(G,3); }
2793 : INLINE GEN
2794 0 : znstar_get_no(GEN G) { return abgrp_get_no(gel(G,2)); }
2795 : INLINE GEN
2796 101479 : znstar_get_cyc(GEN G) { return abgrp_get_cyc(gel(G,2)); }
2797 : INLINE GEN
2798 0 : znstar_get_gen(GEN G) { return abgrp_get_gen(gel(G,2)); }
2799 : INLINE GEN
2800 2735887 : znstar_get_conreycyc(GEN G) { return gmael(G,4,5); }
2801 : INLINE GEN
2802 1260686 : znstar_get_conreygen(GEN G) { return gmael(G,4,4); }
2803 : INLINE GEN
2804 40103 : znstar_get_Ui(GEN G) { return gmael(G,4,3); }
2805 : INLINE GEN
2806 28322 : znstar_get_U(GEN G) { return gel(G,5); }
2807 : INLINE GEN
2808 1223516 : znstar_get_pe(GEN G) { return gmael(G,4,1); }
2809 : INLINE GEN
2810 19152 : gal_get_pol(GEN gal) { return gel(gal,1); }
2811 : INLINE GEN
2812 1225 : gal_get_p(GEN gal) { return gmael(gal,2,1); }
2813 : INLINE GEN
2814 63 : gal_get_e(GEN gal) { return gmael(gal,2,2); }
2815 : INLINE GEN
2816 15631 : gal_get_mod(GEN gal) { return gmael(gal,2,3); }
2817 : INLINE GEN
2818 16009 : gal_get_roots(GEN gal) { return gel(gal,3); }
2819 : INLINE GEN
2820 15631 : gal_get_invvdm(GEN gal) { return gel(gal,4); }
2821 : INLINE GEN
2822 15631 : gal_get_den(GEN gal) { return gel(gal,5); }
2823 : INLINE GEN
2824 61516 : gal_get_group(GEN gal) { return gel(gal,6); }
2825 : INLINE GEN
2826 3927 : gal_get_gen(GEN gal) { return gel(gal,7); }
2827 : INLINE GEN
2828 3577 : gal_get_orders(GEN gal) { return gel(gal,8); }
2829 :
2830 : /* assume rnf a genuine rnf */
2831 : INLINE long
2832 944804 : rnf_get_degree(GEN rnf) { return degpol(rnf_get_pol(rnf)); }
2833 : INLINE long
2834 15274 : rnf_get_nfdegree(GEN rnf) { return degpol(nf_get_pol(rnf_get_nf(rnf))); }
2835 : INLINE long
2836 763693 : rnf_get_absdegree(GEN rnf) { return degpol(gmael(rnf,11,1)); }
2837 : INLINE GEN
2838 462 : rnf_get_idealdisc(GEN rnf) { return gmael(rnf,3,1); }
2839 : INLINE GEN
2840 448 : rnf_get_k(GEN rnf) { return gmael(rnf,11,3); }
2841 : INLINE GEN
2842 448 : rnf_get_alpha(GEN rnf) { return gmael(rnf, 11, 2); }
2843 : INLINE GEN
2844 128744 : rnf_get_nf(GEN rnf) { return gel(rnf,10); }
2845 : INLINE void
2846 2485 : rnf_get_nfzk(GEN rnf, GEN *b, GEN *cb) {*b=gmael(rnf,2,1); *cb=gmael(rnf,2,2);}
2847 : INLINE GEN
2848 97384 : rnf_get_polabs(GEN rnf) { return gmael(rnf,11,1); }
2849 : INLINE GEN
2850 1099035 : rnf_get_pol(GEN rnf) { return gel(rnf,1); }
2851 : INLINE GEN
2852 63 : rnf_get_disc(GEN rnf) { return gel(rnf,3); }
2853 : INLINE GEN
2854 105 : rnf_get_index(GEN rnf) { return gel(rnf,4); }
2855 : INLINE long
2856 0 : rnf_get_varn(GEN rnf) { return varn(gel(rnf,1)); }
2857 : INLINE GEN
2858 108150 : rnf_get_nfpol(GEN rnf) { return gmael(rnf,10,1); }
2859 : INLINE long
2860 595 : rnf_get_nfvarn(GEN rnf) { return varn(gmael(rnf,10,1)); }
2861 : INLINE GEN
2862 2856 : rnf_get_zk(GEN rnf) { return gel(rnf,7); }
2863 : INLINE GEN
2864 35287 : rnf_get_map(GEN rnf) { return gel(rnf,11); }
2865 : INLINE GEN
2866 1190 : rnf_get_invzk(GEN rnf) { return gel(rnf,8); }
2867 :
2868 : /* I integral ZM (not HNF), G ZM, rounded Cholesky form of a weighted
2869 : * T2 matrix. Reduce I wrt G */
2870 : INLINE GEN
2871 13132 : idealpseudored(GEN I, GEN G)
2872 13132 : { return ZM_mul(I, ZM_lll(ZM_mul(G, I), 0.99, LLL_IM)); }
2873 :
2874 : /* I integral (not necessarily HNF), G ZM, rounded Cholesky form of a weighted
2875 : * T2 matrix. Return m in I with T2(m) small */
2876 : INLINE GEN
2877 157002 : idealpseudomin(GEN I, GEN G)
2878 : {
2879 157002 : GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
2880 157002 : return ZM_ZC_mul(I, gel(u,1));
2881 : }
2882 : /* I, G as in idealpseudomin. Return an irrational m in I with T2(m) small */
2883 : INLINE GEN
2884 300506 : idealpseudomin_nonscalar(GEN I, GEN G)
2885 : {
2886 300506 : GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
2887 300506 : GEN m = ZM_ZC_mul(I, gel(u,1));
2888 300506 : if (ZV_isscalar(m) && lg(u) > 2) m = ZM_ZC_mul(I, gel(u,2));
2889 300506 : return m;
2890 : }
2891 :
2892 : INLINE GEN
2893 0 : idealred_elt(GEN nf, GEN I) {
2894 0 : pari_sp av = avma;
2895 0 : GEN u = idealpseudomin(I, nf_get_roundG(nf));
2896 0 : return gerepileupto(av, u);
2897 : }
2898 : INLINE GEN
2899 162736 : idealred(GEN nf, GEN I) { return idealred0(nf, I, NULL); }
2900 :
2901 : INLINE GEN
2902 1302 : idealchineseinit(GEN nf, GEN x)
2903 1302 : { return idealchinese(nf,x,NULL); }
2904 :
2905 : /*******************************************************************/
2906 : /* */
2907 : /* CLOSURES */
2908 : /* */
2909 : /*******************************************************************/
2910 248959670 : INLINE long closure_arity(GEN C) { return ((ulong)C[1])&ARITYBITS; }
2911 34811355 : INLINE long closure_is_variadic(GEN C) { return !!(((ulong)C[1])&VARARGBITS); }
2912 213839418 : INLINE const char *closure_codestr(GEN C) { return GSTR(gel(C,2))-1; }
2913 0 : INLINE GEN closure_get_code(GEN C) { return gel(C,2); }
2914 213847586 : INLINE GEN closure_get_oper(GEN C) { return gel(C,3); }
2915 213832646 : INLINE GEN closure_get_data(GEN C) { return gel(C,4); }
2916 8413 : INLINE GEN closure_get_dbg(GEN C) { return gel(C,5); }
2917 20375 : INLINE GEN closure_get_text(GEN C) { return gel(C,6); }
2918 813154 : INLINE GEN closure_get_frame(GEN C) { return gel(C,7); }
2919 :
2920 : /*******************************************************************/
2921 : /* */
2922 : /* ERRORS */
2923 : /* */
2924 : /*******************************************************************/
2925 : INLINE long
2926 30463 : err_get_num(GEN e) { return e[1]; }
2927 : INLINE GEN
2928 70 : err_get_compo(GEN e, long i) { return gel(e, i+1); }
2929 :
2930 : INLINE void
2931 14 : pari_err_BUG(const char *f) { pari_err(e_BUG,f); }
2932 : INLINE void
2933 7 : pari_err_CONSTPOL(const char *f) { pari_err(e_CONSTPOL, f); }
2934 : INLINE void
2935 63 : pari_err_COPRIME(const char *f, GEN x, GEN y) { pari_err(e_COPRIME, f,x,y); }
2936 : INLINE void
2937 445 : pari_err_DIM(const char *f) { pari_err(e_DIM, f); }
2938 : INLINE void
2939 0 : pari_err_FILE(const char *f, const char *g) { pari_err(e_FILE, f,g); }
2940 : INLINE void
2941 28 : pari_err_FLAG(const char *f) { pari_err(e_FLAG,f); }
2942 : INLINE void
2943 357 : pari_err_IMPL(const char *f) { pari_err(e_IMPL,f); }
2944 : INLINE void
2945 705 : pari_err_INV(const char *f, GEN x) { pari_err(e_INV,f,x); }
2946 : INLINE void
2947 21 : pari_err_IRREDPOL(const char *f, GEN x) { pari_err(e_IRREDPOL, f,x); }
2948 : INLINE void
2949 1688 : pari_err_DOMAIN(const char *f, const char *v, const char *op, GEN l, GEN x) { pari_err(e_DOMAIN, f,v,op,l,x); }
2950 : INLINE void
2951 245 : pari_err_COMPONENT(const char *f, const char *op, GEN l, GEN x) { pari_err(e_COMPONENT, f,op,l,x); }
2952 : INLINE void
2953 0 : pari_err_MAXPRIME(ulong c) { pari_err(e_MAXPRIME, c); }
2954 : INLINE void
2955 287 : pari_err_OP(const char *f, GEN x, GEN y) { pari_err(e_OP, f,x,y); }
2956 : INLINE void
2957 84 : pari_err_OVERFLOW(const char *f) { pari_err(e_OVERFLOW, f); }
2958 : INLINE void
2959 219 : pari_err_PREC(const char *f) { pari_err(e_PREC,f); }
2960 : INLINE void
2961 0 : pari_err_PACKAGE(const char *f) { pari_err(e_PACKAGE,f); }
2962 : INLINE void
2963 56 : pari_err_PRIME(const char *f, GEN x) { pari_err(e_PRIME, f,x); }
2964 : INLINE void
2965 735 : pari_err_MODULUS(const char *f, GEN x, GEN y) { pari_err(e_MODULUS, f,x,y); }
2966 : INLINE void
2967 42 : pari_err_ROOTS0(const char *f) { pari_err(e_ROOTS0, f); }
2968 : INLINE void
2969 77 : pari_err_SQRTN(const char *f, GEN x) { pari_err(e_SQRTN, f,x); }
2970 : INLINE void
2971 11383 : pari_err_TYPE(const char *f, GEN x) { pari_err(e_TYPE, f,x); }
2972 : INLINE void
2973 3045 : pari_err_TYPE2(const char *f, GEN x, GEN y) { pari_err(e_TYPE2, f,x,y); }
2974 : INLINE void
2975 203 : pari_err_VAR(const char *f, GEN x, GEN y) { pari_err(e_VAR, f,x,y); }
2976 : INLINE void
2977 147 : pari_err_PRIORITY(const char *f, GEN x, const char *op, long v)
2978 147 : { pari_err(e_PRIORITY, f,x,op,v); }
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