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; either version 2 of the License, or (at your option) any later
8 : version. It is distributed in the hope that it will be useful, but WITHOUT
9 : ANY WARRANTY WHATSOEVER.
10 :
11 : Check the License for details. You should have received a copy of it, along
12 : with the package; see the file 'COPYING'. If not, write to the Free Software
13 : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
14 :
15 :
16 : /*********************************************************************/
17 : /* MALLOC/FREE WRAPPERS */
18 : /*********************************************************************/
19 : #define BLOCK_SIGALRM_START \
20 : { \
21 : int block=PARI_SIGINT_block; \
22 : PARI_SIGINT_block = 2; \
23 : MT_SIGINT_BLOCK(block);
24 :
25 : #define BLOCK_SIGINT_START \
26 : { \
27 : int block=PARI_SIGINT_block; \
28 : PARI_SIGINT_block = 1; \
29 : MT_SIGINT_BLOCK(block);
30 :
31 : #define BLOCK_SIGINT_END \
32 : PARI_SIGINT_block = block; \
33 : MT_SIGINT_UNBLOCK(block); \
34 : if (!block && PARI_SIGINT_pending) \
35 : { \
36 : int sig = PARI_SIGINT_pending; \
37 : PARI_SIGINT_pending = 0; \
38 : raise(sig); \
39 : } \
40 : }
41 :
42 : /*******************************************************************/
43 : /* */
44 : /* CONSTRUCTORS */
45 : /* */
46 : /*******************************************************************/
47 : #define retmkfrac(x,y)\
48 : do { GEN _v = cgetg(3, t_FRAC);\
49 : gel(_v,1) = (x);\
50 : gel(_v,2) = (y); return _v; } while(0)
51 : #define retmkrfrac(x,y)\
52 : do { GEN _v = cgetg(3, t_RFRAC);\
53 : gel(_v,1) = (x);\
54 : gel(_v,2) = (y); return _v; } while(0)
55 : #define retmkintmod(x,y)\
56 : do { GEN _v = cgetg(3, t_INTMOD);\
57 : gel(_v,1) = (y);\
58 : gel(_v,2) = (x); return _v; } while(0)
59 : #define retmkcomplex(x,y)\
60 : do { GEN _v = cgetg(3, t_COMPLEX);\
61 : gel(_v,1) = (x);\
62 : gel(_v,2) = (y); return _v; } while(0)
63 : #define retmkpolmod(x,y)\
64 : do { GEN _v = cgetg(3, t_POLMOD);\
65 : gel(_v,1) = (y);\
66 : gel(_v,2) = (x); return _v; } while(0)
67 : #define retmkvec(x)\
68 : do { GEN _v = cgetg(2, t_VEC);\
69 : gel(_v,1) = (x); return _v; } while(0)
70 : #define retmkvec2(x,y)\
71 : do { GEN _v = cgetg(3, t_VEC);\
72 : gel(_v,1) = (x);\
73 : gel(_v,2) = (y); return _v; } while(0)
74 : #define retmkvec3(x,y,z)\
75 : do { GEN _v = cgetg(4, t_VEC);\
76 : gel(_v,1) = (x);\
77 : gel(_v,2) = (y);\
78 : gel(_v,3) = (z); return _v; } while(0)
79 : #define retmkpadic(x,p,pd,e,d)\
80 : do { GEN _v = cgetg(5, t_PADIC);\
81 : _v[1] = evalvalp(e) | evalprecp(d);\
82 : gel(_v,2) = (p);\
83 : gel(_v,3) = (pd);\
84 : gel(_v,4) = (x); return _v; } while(0)
85 : /* x allowed to contain _pd */
86 : #define retmkpadic_i(x,p,pd,e,d)\
87 : do { GEN _v = cgetg(5, t_PADIC), _pd = (pd);\
88 : _v[1] = evalvalp(e) | evalprecp(d);\
89 : gel(_v,2) = (p);\
90 : gel(_v,3) = (_pd);\
91 : gel(_v,4) = (x); return _v; } while(0)
92 : #define retmkqfb(x,y,z,d)\
93 : do { GEN _v = cgetg(5, t_QFB);\
94 : gel(_v,1) = (x);\
95 : gel(_v,2) = (y);\
96 : gel(_v,3) = (z);\
97 : gel(_v,4) = (d); return _v; } while(0)
98 : #define retmkquad(x,y,z)\
99 : do { GEN _v = cgetg(4, t_QUAD);\
100 : gel(_v,1) = (x);\
101 : gel(_v,2) = (y);\
102 : gel(_v,3) = (z); return _v; } while(0)
103 : #define retmkvec4(x,y,z,t)\
104 : do { GEN _v = cgetg(5, t_VEC);\
105 : gel(_v,1) = (x);\
106 : gel(_v,2) = (y);\
107 : gel(_v,3) = (z);\
108 : gel(_v,4) = (t); return _v; } while(0)
109 : #define retmkvec5(x,y,z,t,u)\
110 : do { GEN _v = cgetg(6, t_VEC);\
111 : gel(_v,1) = (x);\
112 : gel(_v,2) = (y);\
113 : gel(_v,3) = (z);\
114 : gel(_v,4) = (t);\
115 : gel(_v,5) = (u); return _v; } while(0)
116 : #define retmkcol(x)\
117 : do { GEN _v = cgetg(2, t_COL);\
118 : gel(_v,1) = (x); return _v; } while(0)
119 : #define retmkcol2(x,y)\
120 : do { GEN _v = cgetg(3, t_COL);\
121 : gel(_v,1) = (x);\
122 : gel(_v,2) = (y); return _v; } while(0)
123 : #define retmkcol3(x,y,z)\
124 : do { GEN _v = cgetg(4, t_COL);\
125 : gel(_v,1) = (x);\
126 : gel(_v,2) = (y);\
127 : gel(_v,3) = (z); return _v; } while(0)
128 : #define retmkcol4(x,y,z,t)\
129 : do { GEN _v = cgetg(5, t_COL);\
130 : gel(_v,1) = (x);\
131 : gel(_v,2) = (y);\
132 : gel(_v,3) = (z);\
133 : gel(_v,4) = (t); return _v; } while(0)
134 : #define retmkcol5(x,y,z,t,u)\
135 : do { GEN _v = cgetg(6, t_COL);\
136 : gel(_v,1) = (x);\
137 : gel(_v,2) = (y);\
138 : gel(_v,3) = (z);\
139 : gel(_v,4) = (t);\
140 : gel(_v,5) = (u); return _v; } while(0)
141 : #define retmkcol6(x,y,z,t,u,v)\
142 : do { GEN _v = cgetg(7, t_COL);\
143 : gel(_v,1) = (x);\
144 : gel(_v,2) = (y);\
145 : gel(_v,3) = (z);\
146 : gel(_v,4) = (t);\
147 : gel(_v,5) = (u);\
148 : gel(_v,6) = (v); return _v; } while(0)
149 : #define retmkmat(x)\
150 : do { GEN _v = cgetg(2, t_MAT);\
151 : gel(_v,1) = (x); return _v; } while(0)
152 : #define retmkmat2(x,y)\
153 : do { GEN _v = cgetg(3, t_MAT);\
154 : gel(_v,1) = (x);\
155 : gel(_v,2) = (y); return _v; } while(0)
156 : #define retmkmat3(x,y,z)\
157 : do { GEN _v = cgetg(4, t_MAT);\
158 : gel(_v,1) = (x);\
159 : gel(_v,2) = (y);\
160 : gel(_v,3) = (z); return _v; } while(0)
161 : #define retmkmat4(x,y,z,t)\
162 : do { GEN _v = cgetg(5, t_MAT);\
163 : gel(_v,1) = (x);\
164 : gel(_v,2) = (y);\
165 : gel(_v,3) = (z);\
166 : gel(_v,4) = (t); return _v; } while(0)
167 : #define retmkmat5(x,y,z,t,u)\
168 : do { GEN _v = cgetg(6, t_MAT);\
169 : gel(_v,1) = (x);\
170 : gel(_v,2) = (y);\
171 : gel(_v,3) = (z);\
172 : gel(_v,4) = (t);\
173 : gel(_v,5) = (u); return _v; } while(0)
174 : #define retmkmat22(a,b,c,d)\
175 : do { GEN _v = cgetg(3, t_MAT);\
176 : gel(_v,1) = mkcol2(a,c);\
177 : gel(_v,2) = mkcol2(b,d); return _v; } while(0)
178 : INLINE GEN
179 8025468 : mkintmod(GEN x, GEN y) { retmkintmod(x,y); }
180 : INLINE GEN
181 1813 : mkintmodu(ulong x, ulong y) {
182 1813 : GEN v = cgetg(3,t_INTMOD);
183 1813 : gel(v,1) = utoipos(y);
184 1813 : gel(v,2) = utoi(x); return v;
185 : }
186 : INLINE GEN
187 0 : mkpadic(GEN x, GEN p, GEN pd, long e, long d) { retmkpadic(x,p,pd,e,d); }
188 : INLINE GEN
189 3018050 : mkpolmod(GEN x, GEN y) { retmkpolmod(x,y); }
190 : INLINE GEN
191 41018729 : mkfrac(GEN x, GEN y) { retmkfrac(x,y); }
192 : INLINE GEN
193 1209626 : mkfracss(long x, long y) { retmkfrac(stoi(x),utoipos(y)); }
194 : /* q = n/d a t_FRAC or t_INT; recover (n,d) */
195 : INLINE void
196 19922 : Qtoss(GEN q, long *n, long *d)
197 : {
198 19922 : if (typ(q) == t_INT) { *n = itos(q); *d = 1; }
199 5796 : else { *n = itos(gel(q,1)); *d = itou(gel(q,2)); }
200 19922 : }
201 : INLINE GEN
202 1074164 : sstoQ(long n, long d)
203 : {
204 : ulong r;
205 : long g, q;
206 1074164 : if (!n)
207 : {
208 95095 : if (!d) pari_err_INV("sstoQ",gen_0);
209 95095 : return gen_0;
210 : }
211 979069 : if (d < 0) { d = -d; n = -n; }
212 979069 : if (d == 1) return stoi(n);
213 959756 : r = labs(n);
214 959756 : if (r == 1) retmkfrac(n > 0? gen_1: gen_m1, utoipos(d));
215 909748 : q = udivuu_rem(r, d, &r);
216 909748 : if (!r) return n > 0? utoipos(q): utoineg(q);
217 854875 : g = ugcd(d,r); /* gcd(n,d) */
218 854875 : if (g != 1) { n /= g; d /= g; }
219 854875 : retmkfrac(stoi(n), utoipos(d));
220 : }
221 :
222 : INLINE GEN
223 158072807 : uutoQ(ulong n, ulong d)
224 : {
225 : ulong r;
226 : long g, q;
227 158072807 : if (!n)
228 : {
229 38108 : if (!d) pari_err_INV("uutoQ",gen_0);
230 38108 : return gen_0;
231 : }
232 158034699 : if (d == 1) return utoipos(n);
233 158023597 : if (n == 1) retmkfrac(gen_1, utoipos(d));
234 157934621 : q = udivuu_rem(n,d,&r);
235 157934621 : if (!r) return utoipos(q);
236 5180040 : g = ugcd(d,r); /* gcd(n,d) */
237 5180040 : if (g != 1) { n /= g; d /= g; }
238 5180040 : retmkfrac(utoipos(n), utoipos(d));
239 : }
240 :
241 : INLINE GEN
242 4844525 : mkfraccopy(GEN x, GEN y) { retmkfrac(icopy(x), icopy(y)); }
243 : INLINE GEN
244 698131 : mkrfrac(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
245 698131 : gel(v,1) = x; gel(v,2) = y; return v; }
246 : INLINE GEN
247 14 : mkrfraccopy(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
248 14 : gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
249 : INLINE GEN
250 90152877 : mkcomplex(GEN x, GEN y) { retmkcomplex(x,y); }
251 : INLINE GEN
252 1269300 : gen_I(void) { return mkcomplex(gen_0, gen_1); }
253 : INLINE GEN
254 968280 : cgetc(long l) { retmkcomplex(cgetr(l), cgetr(l)); }
255 : INLINE GEN
256 69118 : mkquad(GEN n, GEN x, GEN y) { GEN v = cgetg(4, t_QUAD);
257 69118 : gel(v,1) = n; gel(v,2) = x; gel(v,3) = y; return v; }
258 : /* vecsmall */
259 : INLINE GEN
260 129152182 : mkvecsmall(long x) { GEN v = cgetg(2, t_VECSMALL); v[1] = x; return v; }
261 : INLINE GEN
262 223649321 : mkvecsmall2(long x,long y) { GEN v = cgetg(3, t_VECSMALL);
263 223667367 : v[1]=x; v[2]=y; return v; }
264 : INLINE GEN
265 100294677 : mkvecsmall3(long x,long y,long z) { GEN v = cgetg(4, t_VECSMALL);
266 100290644 : v[1]=x; v[2]=y; v[3]=z; return v; }
267 : INLINE GEN
268 15454358 : mkvecsmall4(long x,long y,long z,long t) { GEN v = cgetg(5, t_VECSMALL);
269 15455102 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; return v; }
270 : INLINE GEN
271 691954 : mkvecsmall5(long x,long y,long z,long t,long u) { GEN v = cgetg(6, t_VECSMALL);
272 691955 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; v[5]=u; return v; }
273 :
274 : INLINE GEN
275 27798682 : mkqfb(GEN x, GEN y, GEN z, GEN d) { retmkqfb(x,y,z,d); }
276 : /* vec */
277 : INLINE GEN
278 68026718 : mkvec(GEN x) { retmkvec(x); }
279 : INLINE GEN
280 182648099 : mkvec2(GEN x, GEN y) { retmkvec2(x,y); }
281 : INLINE GEN
282 115279395 : mkvec3(GEN x, GEN y, GEN z) { retmkvec3(x,y,z); }
283 : INLINE GEN
284 6637562 : mkvec4(GEN x, GEN y, GEN z, GEN t) { retmkvec4(x,y,z,t); }
285 : INLINE GEN
286 14486807 : mkvec5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkvec5(x,y,z,t,u); }
287 : INLINE GEN
288 168 : mkvecs(long x) { retmkvec(stoi(x)); }
289 : INLINE GEN
290 219950 : mkvec2s(long x, long y) { retmkvec2(stoi(x),stoi(y)); }
291 : INLINE GEN
292 524441 : mkvec3s(long x, long y, long z) { retmkvec3(stoi(x),stoi(y),stoi(z)); }
293 : INLINE GEN
294 21 : mkvec4s(long x, long y, long z, long t) { retmkvec4(stoi(x),stoi(y),stoi(z),stoi(t)); }
295 : INLINE GEN
296 122507 : mkveccopy(GEN x) { GEN v = cgetg(2, t_VEC); gel(v,1) = gcopy(x); return v; }
297 : INLINE GEN
298 114445 : mkvec2copy(GEN x, GEN y) {
299 114445 : GEN v = cgetg(3,t_VEC); gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
300 : /* col */
301 : INLINE GEN
302 10180159 : mkcol(GEN x) { retmkcol(x); }
303 : INLINE GEN
304 156650163 : mkcol2(GEN x, GEN y) { retmkcol2(x,y); }
305 : INLINE GEN
306 88314 : mkcol3(GEN x, GEN y, GEN z) { retmkcol3(x,y,z); }
307 : INLINE GEN
308 103467 : mkcol4(GEN x, GEN y, GEN z, GEN t) { retmkcol4(x,y,z,t); }
309 : INLINE GEN
310 94 : mkcol5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkcol5(x,y,z,t,u); }
311 : INLINE GEN
312 232344 : mkcol6(GEN x, GEN y, GEN z, GEN t, GEN u, GEN v) { retmkcol6(x,y,z,t,u,v); }
313 : INLINE GEN
314 40411 : mkcols(long x) { retmkcol(stoi(x)); }
315 : INLINE GEN
316 4415390 : mkcol2s(long x, long y) { retmkcol2(stoi(x),stoi(y)); }
317 : INLINE GEN
318 315 : mkcol3s(long x, long y, long z) { retmkcol3(stoi(x),stoi(y),stoi(z)); }
319 : INLINE GEN
320 0 : mkcol4s(long x, long y, long z, long t) { retmkcol4(stoi(x),stoi(y),stoi(z),stoi(t)); }
321 : INLINE GEN
322 33493 : mkcolcopy(GEN x) { GEN v = cgetg(2, t_COL); gel(v,1) = gcopy(x); return v; }
323 : /* mat */
324 : INLINE GEN
325 4610224 : mkmat(GEN x) { retmkmat(x); }
326 : INLINE GEN
327 32592912 : mkmat2(GEN x, GEN y) { retmkmat2(x,y); }
328 : INLINE GEN
329 17001 : mkmat3(GEN x, GEN y, GEN z) { retmkmat3(x,y,z); }
330 : INLINE GEN
331 84 : mkmat4(GEN x, GEN y, GEN z, GEN t) { retmkmat4(x,y,z,t); }
332 : INLINE GEN
333 0 : mkmat5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkmat5(x,y,z,t,u); }
334 : INLINE GEN
335 121048 : mkmatcopy(GEN x) { GEN v = cgetg(2, t_MAT); gel(v,1) = gcopy(x); return v; }
336 : INLINE GEN
337 0 : mkerr(long x) { GEN v = cgetg(2, t_ERROR); v[1] = x; return v; }
338 : INLINE GEN
339 1077520 : mkoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
340 : INLINE GEN
341 105907 : mkmoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
342 : INLINE long
343 1195695 : inf_get_sign(GEN x) { return signe(gel(x,1)); }
344 : INLINE GEN
345 207501 : mkmat22s(long a, long b, long c, long d) {retmkmat2(mkcol2s(a,c),mkcol2s(b,d));}
346 : INLINE GEN
347 50594279 : mkmat22(GEN a, GEN b, GEN c, GEN d) { retmkmat2(mkcol2(a,c),mkcol2(b,d)); }
348 :
349 : /* pol */
350 : INLINE GEN
351 3565072 : pol_x(long v) {
352 3565072 : GEN p = cgetg(4, t_POL);
353 3565058 : p[1] = evalsigne(1)|evalvarn(v);
354 3565058 : gel(p,2) = gen_0;
355 3565058 : gel(p,3) = gen_1; return p;
356 : }
357 : /* x^n, assume n >= 0 */
358 : INLINE GEN
359 2231886 : pol_xn(long n, long v) {
360 2231886 : long i, a = n+2;
361 2231886 : GEN p = cgetg(a+1, t_POL);
362 2231886 : p[1] = evalsigne(1)|evalvarn(v);
363 5382840 : for (i = 2; i < a; i++) gel(p,i) = gen_0;
364 2231886 : gel(p,a) = gen_1; return p;
365 : }
366 : /* x^n, no assumption on n */
367 : INLINE GEN
368 294 : pol_xnall(long n, long v)
369 : {
370 294 : if (n < 0) retmkrfrac(gen_1, pol_xn(-n,v));
371 287 : return pol_xn(n, v);
372 : }
373 : /* x^n, assume n >= 0 */
374 : INLINE GEN
375 371 : polxn_Flx(long n, long sv) {
376 371 : long i, a = n+2;
377 371 : GEN p = cgetg(a+1, t_VECSMALL);
378 371 : p[1] = sv;
379 1806 : for (i = 2; i < a; i++) p[i] = 0;
380 371 : p[a] = 1; return p;
381 : }
382 : INLINE GEN
383 4459461 : pol_1(long v) {
384 4459461 : GEN p = cgetg(3, t_POL);
385 4459461 : p[1] = evalsigne(1)|evalvarn(v);
386 4459461 : gel(p,2) = gen_1; return p;
387 : }
388 : INLINE GEN
389 82482882 : pol_0(long v)
390 : {
391 82482882 : GEN x = cgetg(2,t_POL);
392 82482871 : x[1] = evalvarn(v); return x;
393 : }
394 : #define retconst_vec(n,x)\
395 : do { long _i, _n = (n);\
396 : GEN _v = cgetg(_n+1, t_VEC), _x = (x);\
397 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
398 : return _v; } while(0)
399 : INLINE GEN
400 233984780 : const_vec(long n, GEN x) { retconst_vec(n, x); }
401 : #define retconst_col(n,x)\
402 : do { long _i, _n = (n);\
403 : GEN _v = cgetg(_n+1, t_COL), _x = (x);\
404 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
405 : return _v; } while(0)
406 : INLINE GEN
407 39271288 : const_col(long n, GEN x) { retconst_col(n, x); }
408 : INLINE GEN
409 19055708 : const_vecsmall(long n, long c)
410 : {
411 : long i;
412 19055708 : GEN V = cgetg(n+1,t_VECSMALL);
413 752922538 : for(i=1;i<=n;i++) V[i] = c;
414 19056491 : return V;
415 : }
416 :
417 : /*** ZERO ***/
418 : /* O(p^e) */
419 : INLINE GEN
420 855758 : zeropadic(GEN p, long e) { retmkpadic(gen_0, icopy(p), gen_1, e, 0); }
421 : INLINE GEN
422 17010 : zeropadic_shallow(GEN p, long e) { retmkpadic(gen_0, icopy(p), gen_1, e, 0); }
423 : /* O(pol_x(v)^e) */
424 : INLINE GEN
425 138698 : zeroser(long v, long e)
426 : {
427 138698 : GEN x = cgetg(2, t_SER);
428 138698 : x[1] = evalvalser(e) | evalvarn(v); return x;
429 : }
430 : INLINE int
431 10079052 : ser_isexactzero(GEN x)
432 : {
433 10079052 : if (!signe(x)) switch(lg(x))
434 : {
435 132741 : case 2: return 1;
436 4648 : case 3: return isexactzero(gel(x,2));
437 : }
438 9941663 : return 0;
439 : }
440 : /* 0 * pol_x(v) */
441 : INLINE GEN
442 42303292 : zeropol(long v) { return pol_0(v); }
443 : /* vector(n) */
444 : INLINE GEN
445 118820980 : zerocol(long n)
446 : {
447 118820980 : GEN y = cgetg(n+1,t_COL);
448 803781590 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
449 118822118 : return y;
450 : }
451 : /* vectorv(n) */
452 : INLINE GEN
453 26629559 : zerovec(long n)
454 : {
455 26629559 : GEN y = cgetg(n+1,t_VEC);
456 391579656 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
457 26629543 : return y;
458 : }
459 : /* matrix(m, n) */
460 : INLINE GEN
461 109084 : zeromat(long m, long n)
462 : {
463 109084 : GEN y = cgetg(n+1,t_MAT);
464 109085 : GEN v = zerocol(m);
465 403707 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
466 109086 : return y;
467 : }
468 : /* = zero_zx, sv is a evalvarn()*/
469 : INLINE GEN
470 1426037 : zero_Flx(long sv) { return pol0_Flx(sv); }
471 : INLINE GEN
472 58741256 : zero_Flv(long n)
473 : {
474 58741256 : GEN y = cgetg(n+1,t_VECSMALL);
475 946087291 : long i; for (i=1; i<=n; i++) y[i] = 0;
476 58741481 : return y;
477 : }
478 : /* matrix(m, n) */
479 : INLINE GEN
480 2783237 : zero_Flm(long m, long n)
481 : {
482 2783237 : GEN y = cgetg(n+1,t_MAT);
483 2783222 : GEN v = zero_Flv(m);
484 17701554 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
485 2783222 : return y;
486 : }
487 : /* matrix(m, n) */
488 : INLINE GEN
489 232089 : zero_Flm_copy(long m, long n)
490 : {
491 232089 : GEN y = cgetg(n+1,t_MAT);
492 2397157 : long i; for (i=1; i<=n; i++) gel(y,i) = zero_Flv(m);
493 232086 : return y;
494 : }
495 :
496 : INLINE GEN
497 3627967 : zero_F2v(long m)
498 : {
499 3627967 : long l = nbits2nlong(m);
500 3627961 : GEN v = zero_Flv(l+1);
501 3627935 : v[1] = m;
502 3627935 : return v;
503 : }
504 :
505 : INLINE GEN
506 0 : zero_F2m(long m, long n)
507 : {
508 : long i;
509 0 : GEN M = cgetg(n+1, t_MAT);
510 0 : GEN v = zero_F2v(m);
511 0 : for (i = 1; i <= n; i++)
512 0 : gel(M,i) = v;
513 0 : return M;
514 : }
515 :
516 :
517 : INLINE GEN
518 840091 : zero_F2m_copy(long m, long n)
519 : {
520 : long i;
521 840091 : GEN M = cgetg(n+1, t_MAT);
522 2006777 : for (i = 1; i <= n; i++)
523 1166691 : gel(M,i)= zero_F2v(m);
524 840086 : return M;
525 : }
526 :
527 : /* matrix(m, n) */
528 : INLINE GEN
529 14024263 : zeromatcopy(long m, long n)
530 : {
531 14024263 : GEN y = cgetg(n+1,t_MAT);
532 70988274 : long i; for (i=1; i<=n; i++) gel(y,i) = zerocol(m);
533 14024264 : return y;
534 : }
535 :
536 : INLINE GEN
537 28009 : zerovec_block(long len)
538 : {
539 : long i;
540 28009 : GEN blk = cgetg_block(len + 1, t_VEC);
541 924297 : for (i = 1; i <= len; ++i)
542 896288 : gel(blk, i) = gen_0;
543 28009 : return blk;
544 : }
545 :
546 : /* i-th vector in the standard basis */
547 : INLINE GEN
548 5679229 : col_ei(long n, long i) { GEN e = zerocol(n); gel(e,i) = gen_1; return e; }
549 : INLINE GEN
550 1711378 : vec_ei(long n, long i) { GEN e = zerovec(n); gel(e,i) = gen_1; return e; }
551 : INLINE GEN
552 42 : F2v_ei(long n, long i) { GEN e = zero_F2v(n); F2v_set(e,i); return e; }
553 : INLINE GEN
554 494381 : vecsmall_ei(long n, long i) { GEN e = zero_zv(n); e[i] = 1; return e; }
555 : INLINE GEN
556 1293451 : Rg_col_ei(GEN x, long n, long i) { GEN e = zerocol(n); gel(e,i) = x; return e; }
557 :
558 : INLINE GEN
559 25866274 : shallowcopy(GEN x)
560 25866274 : { return typ(x) == t_MAT ? RgM_shallowcopy(x): leafcopy(x); }
561 :
562 : /* routines for naive growarrays */
563 : INLINE GEN
564 11683067 : vectrunc_init(long l)
565 : {
566 11683067 : GEN z = new_chunk(l);
567 11682883 : z[0] = evaltyp(t_VEC) | _evallg(1); return z;
568 : }
569 : INLINE GEN
570 393680 : coltrunc_init(long l)
571 : {
572 393680 : GEN z = new_chunk(l);
573 393680 : z[0] = evaltyp(t_COL) | _evallg(1); return z;
574 : }
575 : INLINE void
576 313088682 : lg_increase(GEN x) { x[0]++; }
577 : INLINE void
578 15216584 : vectrunc_append(GEN x, GEN t) { gel(x, lg(x)) = t; lg_increase(x); }
579 : INLINE void
580 9821 : vectrunc_append_batch(GEN x, GEN y)
581 : {
582 9821 : long i, l = lg(x), ly = lg(y);
583 9821 : GEN z = x + l-1;
584 33229 : for (i = 1; i < ly; i++) gel(z,i) = gel(y,i);
585 9821 : setlg(x, l+ly-1);
586 9821 : }
587 : INLINE GEN
588 187989914 : vecsmalltrunc_init(long l)
589 : {
590 187989914 : GEN z = new_chunk(l);
591 188067575 : z[0] = evaltyp(t_VECSMALL) | _evallg(1); return z;
592 : }
593 : INLINE void
594 99615262 : vecsmalltrunc_append(GEN x, long t) { x[ lg(x) ] = t; lg_increase(x); }
595 :
596 : /*******************************************************************/
597 : /* */
598 : /* STRING HASH FUNCTIONS */
599 : /* */
600 : /*******************************************************************/
601 : INLINE ulong
602 2737312 : hash_str(const char *str)
603 : {
604 2737312 : ulong hash = 5381UL, c;
605 28449371 : while ( (c = (ulong)*str++) )
606 25712059 : hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
607 2737312 : return hash;
608 : }
609 : INLINE ulong
610 18203083 : hash_str_len(const char *str, long len)
611 : {
612 18203083 : ulong hash = 5381UL;
613 : long i;
614 166334077 : for (i = 0; i < len; i++)
615 : {
616 148130994 : ulong c = (ulong)*str++;
617 148130994 : hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
618 : }
619 18203083 : return hash;
620 : }
621 :
622 : /*******************************************************************/
623 : /* */
624 : /* VEC / COL / VECSMALL */
625 : /* */
626 : /*******************************************************************/
627 : /* shallow*/
628 : INLINE GEN
629 11550 : vec_shorten(GEN v, long n)
630 : {
631 11550 : GEN V = cgetg(n+1, t_VEC);
632 : long i;
633 13006 : for(i = 1; i <= n; i++) gel(V,i) = gel(v,i);
634 11550 : return V;
635 : }
636 : /* shallow*/
637 : INLINE GEN
638 18941 : vec_lengthen(GEN v, long n)
639 : {
640 18941 : GEN V = cgetg(n+1, t_VEC);
641 18941 : long i, l = lg(v);
642 1935639 : for(i = 1; i < l; i++) gel(V,i) = gel(v,i);
643 18941 : return V;
644 : }
645 : /* shallow*/
646 : INLINE GEN
647 3431760 : vec_append(GEN V, GEN s)
648 : {
649 3431760 : long i, l2 = lg(V);
650 3431760 : GEN res = cgetg(l2+1, typ(V));
651 10736409 : for (i = 1; i < l2; i++) gel(res, i) = gel(V,i);
652 3431759 : gel(res,l2) = s; return res;
653 : }
654 : /* shallow*/
655 : INLINE GEN
656 300961 : vec_prepend(GEN v, GEN s)
657 : {
658 300961 : long i, l = lg(v);
659 300961 : GEN w = cgetg(l+1, typ(v));
660 300963 : gel(w,1) = s;
661 769567 : for (i = 2; i <= l; i++) gel(w,i) = gel(v,i-1);
662 300963 : return w;
663 : }
664 : /* shallow*/
665 : INLINE GEN
666 0 : vec_setconst(GEN v, GEN x)
667 : {
668 0 : long i, l = lg(v);
669 0 : for (i = 1; i < l; i++) gel(v,i) = x;
670 0 : return v;
671 : }
672 : INLINE GEN
673 72686 : vecsmall_shorten(GEN v, long n)
674 : {
675 72686 : GEN V = cgetg(n+1,t_VECSMALL);
676 : long i;
677 892249 : for(i = 1; i <= n; i++) V[i] = v[i];
678 72685 : return V;
679 : }
680 : INLINE GEN
681 526 : vecsmall_lengthen(GEN v, long n)
682 : {
683 526 : long i, l = lg(v);
684 526 : GEN V = cgetg(n+1,t_VECSMALL);
685 46315 : for(i = 1; i < l; i++) V[i] = v[i];
686 526 : return V;
687 : }
688 :
689 : INLINE GEN
690 4015855 : vec_to_vecsmall(GEN x)
691 18860289 : { pari_APPLY_long(itos(gel(x,i))) }
692 : INLINE GEN
693 511088 : vecsmall_to_vec(GEN x)
694 7069105 : { pari_APPLY_type(t_VEC, stoi(x[i])) }
695 : INLINE GEN
696 3304 : vecsmall_to_vec_inplace(GEN z)
697 : {
698 3304 : long i, l = lg(z);
699 79604 : for (i=1; i<l; i++) gel(z,i) = stoi(z[i]);
700 3304 : settyp(z, t_VEC); return z;
701 : }
702 : INLINE GEN
703 7761525 : vecsmall_to_col(GEN x)
704 59564368 : { pari_APPLY_type(t_COL, stoi(x[i])) }
705 :
706 : INLINE int
707 7209139 : vecsmall_lexcmp(GEN x, GEN y)
708 : {
709 : long lx,ly,l,i;
710 7209139 : lx = lg(x);
711 7209139 : ly = lg(y); l = minss(lx,ly);
712 30649306 : for (i=1; i<l; i++)
713 29021866 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
714 1627440 : if (lx == ly) return 0;
715 30578 : return (lx < ly)? -1 : 1;
716 : }
717 :
718 : INLINE int
719 108088071 : vecsmall_prefixcmp(GEN x, GEN y)
720 : {
721 108088071 : long i, lx = lg(x), ly = lg(y), l = minss(lx,ly);
722 542691324 : for (i=1; i<l; i++)
723 519806035 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
724 22885289 : return 0;
725 : }
726 :
727 : /*Can be used on t_VEC, but coeffs not gcopy-ed*/
728 : INLINE GEN
729 186753 : vecsmall_prepend(GEN V, long s)
730 : {
731 186753 : long i, l2 = lg(V);
732 186753 : GEN res = cgetg(l2+1, typ(V));
733 186753 : res[1] = s;
734 624853 : for (i = 2; i <= l2; ++i) res[i] = V[i - 1];
735 186753 : return res;
736 : }
737 :
738 : INLINE GEN
739 4071287 : vecsmall_append(GEN V, long s)
740 : {
741 4071287 : long i, l2 = lg(V);
742 4071287 : GEN res = cgetg(l2+1, t_VECSMALL);
743 5982615 : for (i = 1; i < l2; ++i) res[i] = V[i];
744 4071289 : res[l2] = s; return res;
745 : }
746 :
747 : INLINE GEN
748 1464160 : vecsmall_concat(GEN u, GEN v)
749 : {
750 1464160 : long i, l1 = lg(u)-1, l2 = lg(v)-1;
751 1464160 : GEN res = cgetg(l1+l2+1, t_VECSMALL);
752 11616724 : for (i = 1; i <= l1; ++i) res[i] = u[i];
753 15218166 : for (i = 1; i <= l2; ++i) res[i+l1] = v[i];
754 1464157 : return res;
755 : }
756 :
757 : /* return the number of indices where u and v are equal */
758 : INLINE long
759 0 : vecsmall_coincidence(GEN u, GEN v)
760 : {
761 0 : long i, s = 0, l = minss(lg(u),lg(v));
762 0 : for(i=1; i<l; i++)
763 0 : if(u[i] == v[i]) s++;
764 0 : return s;
765 : }
766 :
767 : /* returns the first index i<=n such that x=v[i] if it exists, 0 otherwise */
768 : INLINE long
769 84 : vecsmall_isin(GEN v, long x)
770 : {
771 84 : long i, l = lg(v);
772 124 : for (i = 1; i < l; i++)
773 80 : if (v[i] == x) return i;
774 44 : return 0;
775 : }
776 :
777 : INLINE long
778 84 : vecsmall_pack(GEN V, long base, long mod)
779 : {
780 84 : long i, s = 0;
781 273 : for(i=1; i<lg(V); i++) s = (base*s + V[i]) % mod;
782 84 : return s;
783 : }
784 :
785 : INLINE long
786 21 : vecsmall_indexmax(GEN x)
787 : {
788 21 : long i, i0 = 1, t = x[1], lx = lg(x);
789 84 : for (i=2; i<lx; i++)
790 63 : if (x[i] > t) t = x[i0=i];
791 21 : return i0;
792 : }
793 :
794 : INLINE long
795 1011232 : vecsmall_max(GEN x)
796 : {
797 1011232 : long i, t = x[1], lx = lg(x);
798 2825334 : for (i=2; i<lx; i++)
799 1814102 : if (x[i] > t) t = x[i];
800 1011232 : return t;
801 : }
802 :
803 : INLINE long
804 21 : vecsmall_indexmin(GEN x)
805 : {
806 21 : long i, i0 = 1, t = x[1], lx =lg(x);
807 84 : for (i=2; i<lx; i++)
808 63 : if (x[i] < t) t = x[i0=i];
809 21 : return i0;
810 : }
811 :
812 : INLINE long
813 2324 : vecsmall_min(GEN x)
814 : {
815 2324 : long i, t = x[1], lx =lg(x);
816 16268 : for (i=2; i<lx; i++)
817 13944 : if (x[i] < t) t = x[i];
818 2324 : return t;
819 : }
820 :
821 : INLINE int
822 22760807 : ZV_isscalar(GEN x)
823 : {
824 22760807 : long l = lg(x);
825 54254999 : while (--l > 1)
826 53860917 : if (signe(gel(x, l))) return 0;
827 394082 : return 1;
828 : }
829 : INLINE int
830 52360320 : QV_isscalar(GEN x)
831 : {
832 52360320 : long lx = lg(x),i;
833 68049086 : for (i=2; i<lx; i++)
834 64331787 : if (!isintzero(gel(x, i))) return 0;
835 3717299 : return 1;
836 : }
837 : INLINE int
838 1140179 : RgV_isscalar(GEN x)
839 : {
840 1140179 : long lx = lg(x),i;
841 1166343 : for (i=2; i<lx; i++)
842 1162637 : if (!gequal0(gel(x, i))) return 0;
843 3706 : return 1;
844 : }
845 : INLINE int
846 0 : RgX_isscalar(GEN x)
847 : {
848 : long i;
849 0 : for (i=lg(x)-1; i>2; i--)
850 0 : if (!gequal0(gel(x, i))) return 0;
851 0 : return 1;
852 : }
853 : INLINE long
854 26877609 : RgX_equal_var(GEN x, GEN y) { return varn(x) == varn(y) && RgX_equal(x,y); }
855 : INLINE GEN
856 140 : RgX_to_RgV(GEN x, long N) { x = RgX_to_RgC(x, N); settyp(x, t_VEC); return x; }
857 :
858 : #define RgX_type_code(t1,t2) ((t1 << 6) | t2)
859 :
860 : INLINE int
861 67689 : RgX_is_rational(GEN x)
862 : {
863 : long i;
864 308229 : for (i = lg(x)-1; i > 1; i--)
865 292434 : if (!is_rational_t(typ(gel(x,i)))) return 0;
866 15795 : return 1;
867 : }
868 : INLINE int
869 15293117 : RgX_is_ZX(GEN x)
870 : {
871 : long i;
872 65349068 : for (i = lg(x)-1; i > 1; i--)
873 50120293 : if (typ(gel(x,i)) != t_INT) return 0;
874 15228775 : return 1;
875 : }
876 : INLINE int
877 395594 : RgX_is_QX(GEN x)
878 : {
879 395594 : long k = lg(x)-1;
880 1482268 : for ( ; k>1; k--)
881 1086955 : if (!is_rational_t(typ(gel(x,k)))) return 0;
882 395313 : return 1;
883 : }
884 : INLINE int
885 3111057 : RgX_is_monomial(GEN x)
886 : {
887 : long i;
888 3111057 : if (!signe(x)) return 0;
889 7119066 : for (i=lg(x)-2; i>1; i--)
890 4721146 : if (!isexactzero(gel(x,i))) return 0;
891 2397920 : return 1;
892 : }
893 : INLINE int
894 31358318 : RgV_is_ZV(GEN x)
895 : {
896 : long i;
897 124665765 : for (i = lg(x)-1; i > 0; i--)
898 93339878 : if (typ(gel(x,i)) != t_INT) return 0;
899 31325887 : return 1;
900 : }
901 : INLINE int
902 140073 : RgV_is_QV(GEN x)
903 : {
904 : long i;
905 619646 : for (i = lg(x)-1; i > 0; i--)
906 482527 : if (!is_rational_t(typ(gel(x,i)))) return 0;
907 137119 : return 1;
908 : }
909 : INLINE long
910 110130 : RgV_isin_i(GEN v, GEN x, long n)
911 : {
912 : long i;
913 1033437 : for (i = 1; i <= n; i++)
914 1026703 : if (gequal(gel(v,i), x)) return i;
915 6734 : return 0;
916 : }
917 : INLINE long
918 110130 : RgV_isin(GEN v, GEN x) { return RgV_isin_i(v, x, lg(v)-1); }
919 :
920 : /********************************************************************/
921 : /** **/
922 : /** Dynamic arrays implementation **/
923 : /** **/
924 : /********************************************************************/
925 : INLINE void **
926 703903966 : pari_stack_base(pari_stack *s) { return s->data; }
927 :
928 : INLINE void
929 5738133 : pari_stack_init(pari_stack *s, size_t size, void **data)
930 : {
931 5738133 : s->data = data;
932 5738133 : *data = NULL;
933 5738133 : s->n = 0;
934 5738133 : s->alloc = 0;
935 5738133 : s->size = size;
936 5738133 : }
937 :
938 : INLINE void
939 698615912 : pari_stack_alloc(pari_stack *s, long nb)
940 : {
941 698615912 : void **sdat = pari_stack_base(s);
942 698534371 : long alloc = s->alloc;
943 698534371 : if (s->n+nb <= alloc) return;
944 2138270 : if (!alloc)
945 2041303 : alloc = nb;
946 : else
947 : {
948 197792 : while (s->n+nb > alloc) alloc <<= 1;
949 : }
950 2138270 : pari_realloc_ip(sdat,alloc*s->size);
951 2139955 : s->alloc = alloc;
952 : }
953 :
954 : INLINE long
955 605578815 : pari_stack_new(pari_stack *s) { pari_stack_alloc(s, 1); return s->n++; }
956 :
957 : INLINE void
958 5316568 : pari_stack_delete(pari_stack *s)
959 : {
960 5316568 : void **sdat = pari_stack_base(s);
961 5308136 : if (*sdat) pari_free(*sdat);
962 5331599 : }
963 :
964 : INLINE void
965 5830 : pari_stack_pushp(pari_stack *s, void *u)
966 : {
967 5830 : long n = pari_stack_new(s);
968 5830 : void **sdat =(void**) *pari_stack_base(s);
969 5830 : sdat[n] = u;
970 5830 : }
971 :
972 : /*******************************************************************/
973 : /* */
974 : /* EXTRACT */
975 : /* */
976 : /*******************************************************************/
977 : INLINE GEN
978 641298225 : vecslice(GEN A, long y1, long y2)
979 : {
980 641298225 : long i,lB = y2 - y1 + 2;
981 641298225 : GEN B = cgetg(lB, typ(A));
982 2855024107 : for (i=1; i<lB; i++) B[i] = A[y1-1+i];
983 641302034 : return B;
984 : }
985 : INLINE GEN
986 2645210 : vecslicepermute(GEN A, GEN p, long y1, long y2)
987 : {
988 2645210 : long i,lB = y2 - y1 + 2;
989 2645210 : GEN B = cgetg(lB, typ(A));
990 29932059 : for (i=1; i<lB; i++) B[i] = A[p[y1-1+i]];
991 2645202 : return B;
992 : }
993 : /* rowslice(rowpermute(A,p), x1, x2) */
994 : INLINE GEN
995 182774 : rowslicepermute(GEN x, GEN p, long j1, long j2)
996 771451 : { pari_APPLY_same(vecslicepermute(gel(x,i),p,j1,j2)) }
997 :
998 : INLINE GEN
999 78325946 : rowslice(GEN x, long j1, long j2)
1000 657232633 : { pari_APPLY_same(vecslice(gel(x,i), j1, j2)) }
1001 :
1002 : INLINE GEN
1003 16594795 : matslice(GEN A, long x1, long x2, long y1, long y2)
1004 16594795 : { return rowslice(vecslice(A, y1, y2), x1, x2); }
1005 :
1006 : /* shallow, remove coeff of index j */
1007 : INLINE GEN
1008 273 : rowsplice(GEN x, long j)
1009 1225 : { pari_APPLY_same(vecsplice(gel(x,i), j)) }
1010 :
1011 : /* shallow, remove coeff of index j */
1012 : INLINE GEN
1013 354683 : vecsplice(GEN a, long j)
1014 : {
1015 354683 : long i, k, l = lg(a);
1016 : GEN b;
1017 354683 : if (l == 1) pari_err(e_MISC, "incorrect component in vecsplice");
1018 354683 : b = cgetg(l-1, typ(a));
1019 1503108 : for (i = k = 1; i < l; i++)
1020 1148432 : if (i != j) gel(b, k++) = gel(a,i);
1021 354676 : return b;
1022 : }
1023 : /* shallow */
1024 : INLINE GEN
1025 1036 : RgM_minor(GEN a, long i, long j)
1026 : {
1027 1036 : GEN b = vecsplice(a, j);
1028 1036 : long k, l = lg(b);
1029 4242 : for (k = 1; k < l; k++) gel(b,k) = vecsplice(gel(b,k), i);
1030 1036 : return b;
1031 : }
1032 :
1033 : /* A[x0,] */
1034 : INLINE GEN
1035 762810 : row(GEN x, long j)
1036 6687288 : { pari_APPLY_type(t_VEC, gcoeff(x, j, i)) }
1037 : INLINE GEN
1038 8741175 : Flm_row(GEN x, long j)
1039 231878249 : { pari_APPLY_ulong((ulong)coeff(x, j, i)) }
1040 : /* A[x0,] */
1041 : INLINE GEN
1042 204988 : rowcopy(GEN x, long j)
1043 2105509 : { pari_APPLY_type(t_VEC, gcopy(gcoeff(x, j, i))) }
1044 : /* A[x0, x1..x2] */
1045 : INLINE GEN
1046 987 : row_i(GEN A, long x0, long x1, long x2)
1047 : {
1048 987 : long i, lB = x2 - x1 + 2;
1049 987 : GEN B = cgetg(lB, t_VEC);
1050 2989 : for (i=x1; i<=x2; i++) gel(B, i) = gcoeff(A, x0, i);
1051 987 : return B;
1052 : }
1053 :
1054 : INLINE GEN
1055 697039 : vecreverse(GEN A)
1056 : {
1057 : long i, l;
1058 697039 : GEN B = cgetg_copy(A, &l);
1059 2407783 : for (i=1; i<l; i++) gel(B, i) = gel(A, l-i);
1060 697039 : return B;
1061 : }
1062 :
1063 : INLINE GEN
1064 3052 : vecsmall_reverse(GEN A)
1065 : {
1066 : long i, l;
1067 3052 : GEN B = cgetg_copy(A, &l);
1068 12698 : for (i=1; i<l; i++) B[i] = A[l-i];
1069 3052 : return B;
1070 : }
1071 :
1072 : INLINE void
1073 2570 : vecreverse_inplace(GEN y)
1074 : {
1075 2570 : long l = lg(y), lim = l>>1, i;
1076 8242 : for (i = 1; i <= lim; i++)
1077 : {
1078 5672 : GEN z = gel(y,i);
1079 5672 : gel(y,i) = gel(y,l-i);
1080 5672 : gel(y,l-i) = z;
1081 : }
1082 2570 : }
1083 :
1084 : INLINE GEN
1085 77947701 : vecsmallpermute(GEN A, GEN p) { return perm_mul(A, p); }
1086 :
1087 : INLINE GEN
1088 19831911 : vecpermute(GEN A, GEN x)
1089 112457516 : { pari_APPLY_type(typ(A), gel(A, x[i])) }
1090 :
1091 : INLINE GEN
1092 6933198 : veclast(GEN A) { return gel(A, lg(A)-1); }
1093 :
1094 : INLINE GEN
1095 14413312 : rowpermute(GEN x, GEN p)
1096 100757856 : { pari_APPLY_same(typ(gel(x,i)) == t_VECSMALL ? vecsmallpermute(gel(x, i), p)
1097 : : vecpermute(gel(x, i), p))
1098 : }
1099 : /*******************************************************************/
1100 : /* */
1101 : /* PERMUTATIONS */
1102 : /* */
1103 : /*******************************************************************/
1104 : INLINE GEN
1105 3149326 : identity_zv(long n)
1106 : {
1107 3149326 : GEN v = cgetg(n+1, t_VECSMALL);
1108 : long i;
1109 32212504 : for (i = 1; i <= n; i++) v[i] = i;
1110 3149311 : return v;
1111 : }
1112 : INLINE GEN
1113 4333 : identity_ZV(long n)
1114 : {
1115 4333 : GEN v = cgetg(n+1, t_VEC);
1116 : long i;
1117 51898 : for (i = 1; i <= n; i++) gel(v,i) = utoipos(i);
1118 4333 : return v;
1119 : }
1120 : /* identity permutation */
1121 : INLINE GEN
1122 3124983 : identity_perm(long n) { return identity_zv(n); }
1123 :
1124 : /* assume d <= n */
1125 : INLINE GEN
1126 99911 : cyclic_perm(long n, long d)
1127 : {
1128 99911 : GEN perm = cgetg(n+1, t_VECSMALL);
1129 : long i;
1130 520240 : for (i = 1; i <= n-d; i++) perm[i] = i+d;
1131 226702 : for ( ; i <= n; i++) perm[i] = i-n+d;
1132 99911 : return perm;
1133 : }
1134 :
1135 : /* Multiply (compose) two permutations */
1136 : INLINE GEN
1137 80141928 : perm_mul(GEN s, GEN x)
1138 1014085538 : { pari_APPLY_long(s[x[i]]) }
1139 :
1140 : INLINE GEN
1141 728 : perm_sqr(GEN x)
1142 18284 : { pari_APPLY_long(x[x[i]]) }
1143 :
1144 : /* Compute the inverse (reciprocal) of a permutation. */
1145 : INLINE GEN
1146 2778237 : perm_inv(GEN x)
1147 : {
1148 : long i, lx;
1149 2778237 : GEN y = cgetg_copy(x, &lx);
1150 39054910 : for (i=1; i<lx; i++) y[ x[i] ] = i;
1151 2778225 : return y;
1152 : }
1153 : /* Return s*t*s^-1 */
1154 : INLINE GEN
1155 418299 : perm_conj(GEN s, GEN t)
1156 : {
1157 : long i, l;
1158 418299 : GEN v = cgetg_copy(s, &l);
1159 6857893 : for (i = 1; i < l; i++) v[ s[i] ] = s[ t[i] ];
1160 418299 : return v;
1161 : }
1162 :
1163 : INLINE void
1164 490272678 : pari_free(void *pointer)
1165 : {
1166 490272678 : BLOCK_SIGINT_START;
1167 490321302 : free(pointer);
1168 490321302 : BLOCK_SIGINT_END;
1169 490319619 : }
1170 : INLINE void*
1171 720596287 : pari_malloc(size_t size)
1172 : {
1173 720596287 : if (size)
1174 : {
1175 : char *tmp;
1176 720597049 : BLOCK_SIGINT_START;
1177 720666608 : tmp = (char*)malloc(size);
1178 720666608 : BLOCK_SIGINT_END;
1179 720663087 : if (!tmp) pari_err(e_MEM);
1180 720673603 : return tmp;
1181 : }
1182 0 : return NULL;
1183 : }
1184 : INLINE void*
1185 1883 : pari_realloc(void *pointer, size_t size)
1186 : {
1187 : char *tmp;
1188 :
1189 1883 : BLOCK_SIGINT_START;
1190 1883 : if (!pointer) tmp = (char *) malloc(size);
1191 1883 : else tmp = (char *) realloc(pointer,size);
1192 1883 : BLOCK_SIGINT_END;
1193 1883 : if (!tmp) pari_err(e_MEM);
1194 1883 : return tmp;
1195 : }
1196 : INLINE void
1197 2142170 : pari_realloc_ip(void **pointer, size_t size)
1198 : {
1199 : char *tmp;
1200 2142170 : BLOCK_SIGINT_START;
1201 2141815 : if (!*pointer) tmp = (char *) malloc(size);
1202 101123 : else tmp = (char *) realloc(*pointer,size);
1203 2141815 : if (!tmp) pari_err(e_MEM);
1204 2141815 : *pointer = tmp;
1205 2141815 : BLOCK_SIGINT_END;
1206 2141531 : }
1207 :
1208 : INLINE void*
1209 47377 : pari_calloc(size_t size)
1210 : {
1211 47377 : void *t = pari_malloc(size);
1212 47377 : memset(t, 0, size); return t;
1213 : }
1214 : INLINE GEN
1215 10138 : cgetalloc(size_t l, long t)
1216 : { /* evallg may raise e_OVERFLOW, which would leak x */
1217 10138 : ulong x0 = evaltyp(t) | evallg(l);
1218 10138 : GEN x = (GEN)pari_malloc(l * sizeof(long));
1219 10138 : x[0] = x0; return x;
1220 : }
1221 :
1222 : /*******************************************************************/
1223 : /* */
1224 : /* GARBAGE COLLECTION */
1225 : /* */
1226 : /*******************************************************************/
1227 : /* copy integer x as if we had set_avma(av) */
1228 : INLINE GEN
1229 7893037831 : icopy_avma(GEN x, pari_sp av)
1230 : {
1231 7893037831 : long i = lgefint(x), lx = i;
1232 7893037831 : GEN y = ((GEN)av) - i;
1233 57832132996 : while (--i > 0) y[i] = x[i];
1234 7893037831 : y[0] = evaltyp(t_INT)|evallg(lx);
1235 7896219252 : return y;
1236 : }
1237 : /* copy leaf x as if we had set_avma(av) */
1238 : INLINE GEN
1239 548500010 : leafcopy_avma(GEN x, pari_sp av)
1240 : {
1241 548500010 : long i = lg(x);
1242 548500010 : GEN y = ((GEN)av) - i;
1243 2983750989 : while (--i > 0) y[i] = x[i];
1244 548500010 : y[0] = x[0] & (~CLONEBIT);
1245 548500010 : return y;
1246 : }
1247 : INLINE GEN
1248 1072812101 : gerepileuptoleaf(pari_sp av, GEN x)
1249 : {
1250 : long lx;
1251 : GEN q;
1252 :
1253 1072812101 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1254 1071512887 : lx = lg(x);
1255 1071512887 : q = ((GEN)av) - lx;
1256 1071512887 : set_avma((pari_sp)q);
1257 10804180098 : while (--lx >= 0) q[lx] = x[lx];
1258 1071099661 : return q;
1259 : }
1260 : INLINE GEN
1261 4035044433 : gc_INT(pari_sp av, GEN x)
1262 : {
1263 4035044433 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1264 3599317257 : set_avma((pari_sp)icopy_avma(x, av));
1265 3602751740 : return (GEN)avma;
1266 : }
1267 : INLINE GEN
1268 1860579891 : gerepileupto(pari_sp av, GEN x)
1269 : {
1270 1860579891 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1271 1677417403 : switch(typ(x))
1272 : { /* non-default = !is_recursive_t(tq) */
1273 480691692 : case t_INT: return gc_INT(av, x);
1274 338210630 : case t_REAL:
1275 : case t_STR:
1276 338210630 : case t_VECSMALL: return gerepileuptoleaf(av,x);
1277 858516674 : default:
1278 : /* NB: x+i --> ((long)x) + i*sizeof(long) */
1279 858516674 : return gerepile(av, (pari_sp) (x+lg(x)), x);
1280 : }
1281 : }
1282 :
1283 : /* gerepileupto(av, gcopy(x)) */
1284 : INLINE GEN
1285 227238039 : gc_GEN(pari_sp av, GEN x)
1286 : {
1287 227238039 : if (is_recursive_t(typ(x)))
1288 : {
1289 207811978 : GENbin *p = copy_bin(x);
1290 207831799 : set_avma(av); return bin_copy(p);
1291 : }
1292 : else
1293 : {
1294 19425910 : set_avma(av);
1295 19426100 : if (x < (GEN)av) {
1296 19218324 : if (x < (GEN)pari_mainstack->bot) new_chunk(lg(x));
1297 19218331 : x = leafcopy_avma(x, av);
1298 19218356 : set_avma((pari_sp)x);
1299 : } else
1300 207780 : x = leafcopy(x);
1301 19426131 : return x;
1302 : }
1303 : }
1304 :
1305 : INLINE void
1306 47774524 : guncloneNULL(GEN x) { if (x) gunclone(x); }
1307 : INLINE void
1308 1365120 : guncloneNULL_deep(GEN x) { if (x) gunclone_deep(x); }
1309 :
1310 : /* Takes an array of pointers to GENs, of length n. Copies all
1311 : * objects to contiguous locations and cleans up the stack between
1312 : * av and avma. */
1313 : INLINE void
1314 984774 : gerepilemany(pari_sp av, GEN* gptr[], int n)
1315 : {
1316 : int i;
1317 3912389 : for (i=0; i<n; i++) *gptr[i] = (GEN)copy_bin(*gptr[i]);
1318 984703 : set_avma(av);
1319 3912917 : for (i=0; i<n; i++) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1320 984949 : }
1321 :
1322 : INLINE void
1323 19230516 : gerepileall(pari_sp av, int n, ...)
1324 : {
1325 : int i;
1326 19230516 : va_list a; va_start(a, n);
1327 19230516 : if (n < 10)
1328 : {
1329 : GEN *gptr[10];
1330 58313122 : for (i=0; i<n; i++)
1331 39081894 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1332 19231228 : set_avma(av);
1333 58314194 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1334 :
1335 : }
1336 : else
1337 : {
1338 1 : GEN **gptr = (GEN**) pari_malloc(n*sizeof(GEN*));
1339 0 : for (i=0; i<n; i++)
1340 0 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1341 0 : set_avma(av);
1342 0 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1343 0 : pari_free(gptr);
1344 : }
1345 19231907 : va_end(a);
1346 19231907 : }
1347 :
1348 : /* assume 1 <= n < 10 */
1349 : INLINE GEN
1350 86046084 : gc_all(pari_sp av, int n, ...)
1351 : {
1352 : int i;
1353 : GEN *v[10];
1354 86046084 : va_list a; va_start(a, n);
1355 289117908 : for (i=0; i<n; i++) { v[i] = va_arg(a,GEN*); *v[i] = (GEN)copy_bin(*v[i]); }
1356 86046390 : set_avma(av);
1357 289118803 : for (i=0; i<n; i++) *v[i] = bin_copy((GENbin*)*v[i]);
1358 86046595 : return *v[0];
1359 : }
1360 :
1361 : INLINE void
1362 2202151 : gerepilecoeffs(pari_sp av, GEN x, int n)
1363 : {
1364 : int i;
1365 26224665 : for (i=0; i<n; i++) gel(x,i) = (GEN)copy_bin(gel(x,i));
1366 2202693 : set_avma(av);
1367 26226051 : for (i=0; i<n; i++) gel(x,i) = bin_copy((GENbin*)x[i]);
1368 2202338 : }
1369 :
1370 : /* p from copy_bin. Copy p->x back to stack, then destroy p */
1371 : INLINE GEN
1372 476984412 : bin_copy(GENbin *p)
1373 : {
1374 : GEN x, y, base;
1375 : long dx, len;
1376 :
1377 476984412 : x = p->x; if (!x) { pari_free(p); return gen_0; }
1378 447986551 : len = p->len;
1379 447986551 : base= p->base; dx = x - base;
1380 447986551 : y = (GEN)memcpy((void*)new_chunk(len), (void*)GENbinbase(p), len*sizeof(long));
1381 447980052 : y += dx;
1382 447980052 : p->rebase(y, ((ulong)y-(ulong)x));
1383 447984407 : pari_free(p); return y;
1384 : }
1385 :
1386 : INLINE GEN
1387 924965187 : GENbinbase(GENbin *p) { return (GEN)(p + 1); }
1388 :
1389 : INLINE void
1390 117687099 : cgiv(GEN x)
1391 : {
1392 117687099 : pari_sp av = (pari_sp)(x+lg(x));
1393 117687099 : if (isonstack((GEN)av)) set_avma(av);
1394 117700634 : }
1395 :
1396 : INLINE void
1397 1881569 : killblock(GEN x) { gunclone(x); }
1398 :
1399 : INLINE int
1400 291184252 : is_universal_constant(GEN x) { return (x >= gen_0 && x <= ghalf); }
1401 :
1402 : /*******************************************************************/
1403 : /* */
1404 : /* CONVERSION / ASSIGNMENT */
1405 : /* */
1406 : /*******************************************************************/
1407 : /* z is a type which may be a t_COMPLEX component (not a t_QUAD) */
1408 : INLINE GEN
1409 17937234 : cxcompotor(GEN z, long prec)
1410 : {
1411 17937234 : switch(typ(z))
1412 : {
1413 11784734 : case t_INT: return itor(z, prec);
1414 293293 : case t_FRAC: return fractor(z, prec);
1415 5859426 : case t_REAL: return rtor(z, prec);
1416 0 : default: pari_err_TYPE("cxcompotor",z);
1417 : return NULL; /* LCOV_EXCL_LINE */
1418 : }
1419 : }
1420 : INLINE GEN
1421 8951920 : cxtofp(GEN x, long prec)
1422 8951920 : { retmkcomplex(cxcompotor(gel(x,1),prec), cxcompotor(gel(x,2),prec)); }
1423 :
1424 : INLINE GEN
1425 389553 : cxtoreal(GEN q)
1426 389553 : { return (typ(q) == t_COMPLEX && gequal0(gel(q,2)))? gel(q,1): q; }
1427 :
1428 : INLINE double
1429 60616712 : gtodouble(GEN x)
1430 : {
1431 60616712 : if (typ(x)!=t_REAL) {
1432 8160439 : pari_sp av = avma;
1433 8160439 : x = gtofp(x, DEFAULTPREC);
1434 8159896 : if (typ(x)!=t_REAL) pari_err_TYPE("gtodouble [t_REAL expected]", x);
1435 8159896 : set_avma(av);
1436 : }
1437 60616067 : return rtodbl(x);
1438 : }
1439 :
1440 : INLINE int
1441 2966925 : gisdouble(GEN x, double *g)
1442 : {
1443 2966925 : if (typ(x)!=t_REAL) {
1444 41899 : pari_sp av = avma;
1445 41899 : x = gtofp(x, DEFAULTPREC);
1446 41899 : if (typ(x)!=t_REAL) pari_err_TYPE("gisdouble [t_REAL expected]", x);
1447 41899 : set_avma(av);
1448 : }
1449 2966926 : if (expo(x) >= 0x3ff) return 0;
1450 2966926 : *g = rtodbl(x); return 1;
1451 : }
1452 :
1453 : INLINE long
1454 85802303 : gtos(GEN x) {
1455 85802303 : if (typ(x) != t_INT) pari_err_TYPE("gtos [integer expected]",x);
1456 85802289 : return itos(x);
1457 : }
1458 :
1459 : INLINE ulong
1460 102549 : gtou(GEN x) {
1461 102549 : if (typ(x) != t_INT || signe(x)<0)
1462 7 : pari_err_TYPE("gtou [integer >=0 expected]",x);
1463 102542 : return itou(x);
1464 : }
1465 :
1466 : INLINE GEN
1467 45562176 : absfrac(GEN x)
1468 : {
1469 45562176 : GEN y = cgetg(3, t_FRAC);
1470 45562204 : gel(y,1) = absi(gel(x,1));
1471 45562227 : gel(y,2) = icopy(gel(x,2)); return y;
1472 : }
1473 : INLINE GEN
1474 27313 : absfrac_shallow(GEN x)
1475 27313 : { return signe(gel(x,1))>0? x: mkfrac(negi(gel(x,1)), gel(x,2)); }
1476 : INLINE GEN
1477 7911649 : Q_abs(GEN x) { return (typ(x) == t_INT)? absi(x): absfrac(x); }
1478 : INLINE GEN
1479 118528 : Q_abs_shallow(GEN x)
1480 118528 : { return (typ(x) == t_INT)? absi_shallow(x): absfrac_shallow(x); }
1481 : INLINE GEN
1482 13083 : R_abs_shallow(GEN x)
1483 13083 : { return (typ(x) == t_FRAC)? absfrac_shallow(x): mpabs_shallow(x); }
1484 : INLINE GEN
1485 0 : R_abs(GEN x)
1486 0 : { return (typ(x) == t_FRAC)? absfrac(x): mpabs(x); }
1487 :
1488 : /* Force z to be of type real/complex with floating point components */
1489 : INLINE GEN
1490 252435105 : gtofp(GEN z, long prec)
1491 : {
1492 252435105 : switch(typ(z))
1493 : {
1494 213698920 : case t_INT: return itor(z, prec);
1495 4097489 : case t_FRAC: return fractor(z, prec);
1496 25947259 : case t_REAL: return rtor(z, prec);
1497 8698867 : case t_COMPLEX: {
1498 8698867 : GEN a = gel(z,1), b = gel(z,2);
1499 8698867 : if (isintzero(b)) return cxcompotor(a, prec);
1500 8698871 : if (isintzero(a)) {
1501 9198 : GEN y = cgetg(3, t_COMPLEX);
1502 9198 : b = cxcompotor(b, prec);
1503 9198 : gel(y,1) = real_0_bit(expo(b) - prec);
1504 9198 : gel(y,2) = b; return y;
1505 : }
1506 8689651 : return cxtofp(z, prec);
1507 : }
1508 0 : case t_QUAD: return quadtofp(z, prec);
1509 0 : default: pari_err_TYPE("gtofp",z);
1510 : return NULL; /* LCOV_EXCL_LINE */
1511 : }
1512 : }
1513 : /* Force z to be of type real / int */
1514 : INLINE GEN
1515 22428 : gtomp(GEN z, long prec)
1516 : {
1517 22428 : switch(typ(z))
1518 : {
1519 42 : case t_INT: return z;
1520 22386 : case t_FRAC: return fractor(z, prec);
1521 0 : case t_REAL: return rtor(z, prec);
1522 0 : case t_QUAD: z = quadtofp(z, prec);
1523 0 : if (typ(z) == t_REAL) return z;
1524 0 : default: pari_err_TYPE("gtomp",z);
1525 : return NULL; /* LCOV_EXCL_LINE */
1526 : }
1527 : }
1528 :
1529 : INLINE GEN
1530 7131748 : RgX_gtofp(GEN x, long prec)
1531 37206870 : { pari_APPLY_pol_normalized(gtofp(gel(x,i), prec)); }
1532 :
1533 : INLINE GEN
1534 33705734 : RgC_gtofp(GEN x, long prec)
1535 217354335 : { pari_APPLY_type(t_COL, gtofp(gel(x,i), prec)) }
1536 :
1537 : INLINE GEN
1538 56 : RgV_gtofp(GEN x, long prec)
1539 4781 : { pari_APPLY_type(t_VEC, gtofp(gel(x,i), prec)) }
1540 :
1541 : INLINE GEN
1542 8177993 : RgM_gtofp(GEN x, long prec)
1543 41255041 : { pari_APPLY_same(RgC_gtofp(gel(x,i), prec)) }
1544 :
1545 : INLINE GEN
1546 574 : RgC_gtomp(GEN x, long prec)
1547 23002 : { pari_APPLY_type(t_COL, gtomp(gel(x,i), prec)) }
1548 :
1549 : INLINE GEN
1550 21 : RgM_gtomp(GEN x, long prec)
1551 595 : { pari_APPLY_same(RgC_gtomp(gel(x,i), prec)) }
1552 :
1553 : INLINE GEN
1554 60522 : RgX_fpnorml2(GEN x, long prec)
1555 : {
1556 60522 : pari_sp av = avma;
1557 60522 : return gerepileupto(av, gnorml2(RgX_gtofp(x, prec)));
1558 : }
1559 : INLINE GEN
1560 617599 : RgC_fpnorml2(GEN x, long prec)
1561 : {
1562 617599 : pari_sp av = avma;
1563 617599 : return gerepileupto(av, gnorml2(RgC_gtofp(x, prec)));
1564 : }
1565 : INLINE GEN
1566 22374 : RgM_fpnorml2(GEN x, long prec)
1567 : {
1568 22374 : pari_sp av = avma;
1569 22374 : return gerepileupto(av, gnorml2(RgM_gtofp(x, prec)));
1570 : }
1571 :
1572 : /* y a t_REAL */
1573 : INLINE void
1574 220535 : affgr(GEN x, GEN y)
1575 : {
1576 : pari_sp av;
1577 220535 : switch(typ(x)) {
1578 5999 : case t_INT: affir(x,y); break;
1579 214536 : case t_REAL: affrr(x,y); break;
1580 0 : case t_FRAC: rdiviiz(gel(x,1),gel(x,2), y); break;
1581 0 : case t_QUAD: av = avma; affgr(quadtofp(x,realprec(y)), y); set_avma(av); break;
1582 0 : default: pari_err_TYPE2("=",x,y);
1583 : }
1584 220535 : }
1585 :
1586 : INLINE GEN
1587 244489 : affc_fixlg(GEN x, GEN res)
1588 : {
1589 244489 : if (typ(x) == t_COMPLEX)
1590 : {
1591 206878 : affrr_fixlg(gel(x,1), gel(res,1));
1592 206878 : affrr_fixlg(gel(x,2), gel(res,2));
1593 : }
1594 : else
1595 : {
1596 37611 : set_avma((pari_sp)(res+3));
1597 37611 : res = cgetr(realprec(gel(res,1)));
1598 37612 : affrr_fixlg(x, res);
1599 : }
1600 244491 : return res;
1601 : }
1602 :
1603 : INLINE GEN
1604 0 : trunc_safe(GEN x) { long e; return gcvtoi(x,&e); }
1605 :
1606 : /*******************************************************************/
1607 : /* */
1608 : /* LENGTH CONVERSIONS */
1609 : /* */
1610 : /*******************************************************************/
1611 : INLINE long
1612 41486 : ndec2nlong(long x) { return 1 + (long)((x)*(LOG2_10/BITS_IN_LONG)); }
1613 : INLINE long
1614 33216 : ndec2prec(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1615 : INLINE long
1616 8270 : ndec2nbits(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1617 : /* Fast implementation of ceil(x / (8*sizeof(long))); typecast to (ulong)
1618 : * to avoid overflow. Faster than 1 + ((x-1)>>TWOPOTBITS_IN_LONG)) :
1619 : * addl, shrl instead of subl, sarl, addl */
1620 : INLINE long
1621 12567211 : nbits2nlong(long x) {
1622 12567211 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1623 : }
1624 :
1625 : INLINE long
1626 1477211232 : nbits2extraprec(long x) {
1627 1477211232 : return (((ulong)x+BITS_IN_LONG-1)>>TWOPOTBITS_IN_LONG) << TWOPOTBITS_IN_LONG;
1628 : }
1629 :
1630 : INLINE long
1631 185619154 : nbits2prec(long x) {
1632 185619154 : return (((ulong)x+BITS_IN_LONG-1)>>TWOPOTBITS_IN_LONG) << TWOPOTBITS_IN_LONG;
1633 : }
1634 :
1635 : INLINE long
1636 4461938250 : prec2lg(long x) {
1637 4461938250 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1638 : }
1639 : /* ceil(x / sizeof(long)) */
1640 : INLINE long
1641 120799880 : nchar2nlong(long x) {
1642 120799880 : return (long)(((ulong)x+sizeof(long)-1) >> (TWOPOTBITS_IN_LONG-3L));
1643 : }
1644 : INLINE long
1645 104446311 : prec2nbits(long x) { return x; }
1646 : INLINE double
1647 3175234 : bit_accuracy_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1648 : INLINE double
1649 575818 : prec2nbits_mul(long x, double y) { return x * y; }
1650 : INLINE long
1651 141500056 : bit_prec(GEN x) { return realprec(x); }
1652 : INLINE long
1653 3118621709 : bit_accuracy(long x) { return (x-2) * BITS_IN_LONG; }
1654 : INLINE long
1655 9778 : prec2ndec(long x) { return (long)(x * LOG10_2); }
1656 : INLINE long
1657 228 : nbits2ndec(long x) { return prec2ndec(x); }
1658 : INLINE long
1659 475317 : precdbl(long x) {return x << 1;}
1660 : INLINE long
1661 8066387155 : divsBIL(long n) { return n >> TWOPOTBITS_IN_LONG; }
1662 : INLINE long
1663 7976537454 : remsBIL(long n) { return n & (BITS_IN_LONG-1); }
1664 :
1665 : /*********************************************************************/
1666 : /** **/
1667 : /** OPERATIONS MODULO m **/
1668 : /** **/
1669 : /*********************************************************************/
1670 : /* Assume m > 0, more efficient if 0 <= a, b < m */
1671 :
1672 : INLINE GEN
1673 80582557 : Fp_red(GEN a, GEN m) { return modii(a, m); }
1674 : INLINE GEN
1675 173385515 : Fp_add(GEN a, GEN b, GEN m)
1676 : {
1677 173385515 : pari_sp av=avma;
1678 173385515 : GEN p = addii(a,b);
1679 172834240 : long s = signe(p);
1680 172834240 : if (!s) return p; /* = gen_0 */
1681 160013330 : if (s > 0) /* general case */
1682 : {
1683 159757379 : GEN t = subii(p, m);
1684 159645342 : s = signe(t);
1685 159645342 : if (!s) return gc_const(av, gen_0);
1686 151371030 : if (s < 0) return gc_const((pari_sp)p, p);
1687 72305730 : if (cmpii(t, m) < 0) return gc_INT(av, t); /* general case ! */
1688 3289324 : p = remii(t, m);
1689 : }
1690 : else
1691 260352 : p = modii(p, m);
1692 3549782 : return gc_INT(av, p);
1693 : }
1694 : INLINE GEN
1695 21206150 : Fp_double(GEN x, GEN N)
1696 : {
1697 21206150 : GEN z = shifti(x, 1);
1698 20844327 : return cmpii(z, N) >= 0? subii(z, N): z;
1699 : }
1700 : INLINE GEN
1701 203118348 : Fp_sub(GEN a, GEN b, GEN m)
1702 : {
1703 203118348 : pari_sp av=avma;
1704 203118348 : GEN p = subii(a,b);
1705 201554517 : long s = signe(p);
1706 201554517 : if (!s) return p; /* = gen_0 */
1707 185881925 : if (s > 0)
1708 : {
1709 93200919 : if (cmpii(p, m) < 0) return p; /* general case ! */
1710 1449965 : p = remii(p, m);
1711 : }
1712 : else
1713 : {
1714 92681006 : GEN t = addii(p, m);
1715 94198436 : if (!s) return gc_const(av, gen_0);
1716 94196219 : if (s > 0) return gc_INT(av, t); /* general case ! */
1717 94196219 : p = modii(t, m);
1718 : }
1719 95992013 : return gc_INT(av, p);
1720 : }
1721 : INLINE GEN
1722 28821907 : Fp_neg(GEN b, GEN m)
1723 : {
1724 28821907 : pari_sp av = avma;
1725 28821907 : long s = signe(b);
1726 : GEN p;
1727 28821907 : if (!s) return gen_0;
1728 24388134 : if (s > 0)
1729 : {
1730 23262065 : p = subii(m, b);
1731 23261810 : if (signe(p) >= 0) return p; /* general case ! */
1732 387034 : p = modii(p, m);
1733 : } else
1734 1126513 : p = remii(negi(b), m);
1735 1513795 : return gc_INT(av, p);
1736 : }
1737 :
1738 : INLINE GEN
1739 246991 : Fp_halve(GEN a, GEN p)
1740 : {
1741 246991 : if (mpodd(a)) a = addii(a,p);
1742 246991 : return shifti(a,-1);
1743 : }
1744 :
1745 : /* assume 0 <= u < p and ps2 = p>>1 */
1746 : INLINE GEN
1747 75601471 : Fp_center(GEN u, GEN p, GEN ps2)
1748 75601471 : { return abscmpii(u,ps2)<=0? icopy(u): subii(u,p); }
1749 : /* same without copy */
1750 : INLINE GEN
1751 14147564 : Fp_center_i(GEN u, GEN p, GEN ps2)
1752 14147564 : { return abscmpii(u,ps2)<=0? u: subii(u,p); }
1753 :
1754 : /* x + y*z mod p */
1755 : INLINE GEN
1756 11285183 : Fp_addmul(GEN x, GEN y, GEN z, GEN p)
1757 : {
1758 : pari_sp av;
1759 11285183 : if (!signe(y) || !signe(z)) return Fp_red(x, p);
1760 10794483 : if (!signe(x)) return Fp_mul(z,y, p);
1761 9796593 : av = avma;
1762 9796593 : return gc_INT(av, modii(addii(x, mulii(y,z)), p));
1763 : }
1764 :
1765 : INLINE GEN
1766 199594861 : Fp_mul(GEN a, GEN b, GEN m)
1767 : {
1768 199594861 : pari_sp av=avma;
1769 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1770 199594861 : (void)new_chunk(lg(a)+lg(b)+(lg(m)<<1));
1771 199661328 : p = mulii(a,b);
1772 199489401 : set_avma(av); return modii(p,m);
1773 : }
1774 : INLINE GEN
1775 63968445 : Fp_sqr(GEN a, GEN m)
1776 : {
1777 63968445 : pari_sp av=avma;
1778 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1779 63968445 : (void)new_chunk((lg(a)+lg(m))<<1);
1780 64332302 : p = sqri(a);
1781 62625304 : set_avma(av); return remii(p,m); /*Use remii: p >= 0 */
1782 : }
1783 : INLINE GEN
1784 67061090 : Fp_mulu(GEN a, ulong b, GEN m)
1785 : {
1786 67061090 : long l = lgefint(m);
1787 67061090 : if (l == 3)
1788 : {
1789 45423855 : ulong mm = m[2];
1790 45423855 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1791 : } else {
1792 21637235 : pari_sp av = avma;
1793 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1794 21637235 : (void)new_chunk(lg(a)+1+(l<<1));
1795 21602762 : p = muliu(a,b);
1796 21394497 : set_avma(av); return modii(p,m);
1797 : }
1798 : }
1799 : INLINE GEN
1800 17780 : Fp_muls(GEN a, long b, GEN m)
1801 : {
1802 17780 : long l = lgefint(m);
1803 17780 : if (l == 3)
1804 : {
1805 3578 : ulong mm = m[2];
1806 3578 : if (b < 0)
1807 : {
1808 3578 : ulong t = Fl_mul(umodiu(a, mm), -b, mm);
1809 3578 : return t? utoipos(mm - t): gen_0;
1810 : }
1811 : else
1812 0 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1813 : } else {
1814 14202 : pari_sp av = avma;
1815 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1816 14202 : (void)new_chunk(lg(a)+1+(l<<1));
1817 14202 : p = mulis(a,b);
1818 14202 : set_avma(av); return modii(p,m);
1819 : }
1820 : }
1821 :
1822 : INLINE GEN
1823 23211728 : Fp_inv(GEN a, GEN m)
1824 : {
1825 : GEN res;
1826 23211728 : if (! invmod(a,m,&res)) pari_err_INV("Fp_inv", mkintmod(res,m));
1827 23211406 : return res;
1828 : }
1829 : INLINE GEN
1830 1099929 : Fp_invsafe(GEN a, GEN m)
1831 : {
1832 : GEN res;
1833 1099929 : if (! invmod(a,m,&res)) return NULL;
1834 1099873 : return res;
1835 : }
1836 : INLINE GEN
1837 14986634 : Fp_div(GEN a, GEN b, GEN m)
1838 : {
1839 14986634 : pari_sp av = avma;
1840 : GEN p;
1841 14986634 : if (lgefint(b) == 3)
1842 : {
1843 13842100 : a = Fp_divu(a, b[2], m);
1844 13843184 : if (signe(b) < 0) a = Fp_neg(a, m);
1845 13843187 : return a;
1846 : }
1847 : /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1848 1144534 : (void)new_chunk(lg(a)+(lg(m)<<1));
1849 1144538 : p = mulii(a, Fp_inv(b,m));
1850 1144538 : set_avma(av); return modii(p,m);
1851 : }
1852 : INLINE GEN
1853 15086494 : Fp_divu(GEN x, ulong a, GEN p)
1854 : {
1855 15086494 : pari_sp av = avma;
1856 : ulong b;
1857 15086494 : if (lgefint(p) == 3)
1858 : {
1859 14553535 : ulong pp = p[2], xp = umodiu(x, pp);
1860 14554224 : return xp? utoipos(Fl_div(xp, a % pp, pp)): gen_0;
1861 : }
1862 532959 : x = Fp_red(x, p);
1863 532964 : b = Fl_neg(Fl_div(umodiu(x,a), umodiu(p,a), a), a); /* x + pb = 0 (mod a) */
1864 532966 : return gc_INT(av, diviuexact(addmuliu(x, p, b), a));
1865 : }
1866 :
1867 : INLINE GEN
1868 1094713 : Flx_mulu(GEN x, ulong a, ulong p) { return Flx_Fl_mul(x,a%p,p); }
1869 :
1870 : INLINE GEN
1871 2498998 : get_F2x_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1872 :
1873 : INLINE long
1874 2532657 : get_F2x_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1875 :
1876 : INLINE long
1877 1929017 : get_F2x_degree(GEN T) { return typ(T)==t_VEC? F2x_degree(gel(T,2)): F2x_degree(T); }
1878 :
1879 : INLINE GEN
1880 343 : get_F2xqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1881 :
1882 : INLINE long
1883 375375 : get_F2xqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1884 :
1885 : INLINE long
1886 200851 : get_F2xqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1887 :
1888 : INLINE GEN
1889 25406564 : get_Flx_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1890 :
1891 : INLINE long
1892 67620910 : get_Flx_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1893 :
1894 : INLINE long
1895 81658337 : get_Flx_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1896 :
1897 : INLINE GEN
1898 8033 : get_FlxqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1899 :
1900 : INLINE long
1901 264420 : get_FlxqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1902 :
1903 : INLINE long
1904 317565 : get_FlxqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1905 :
1906 : INLINE GEN
1907 3393079 : get_FpX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1908 :
1909 : INLINE long
1910 7237097 : get_FpX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1911 :
1912 : INLINE long
1913 6005786 : get_FpX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1914 :
1915 : INLINE GEN
1916 146583 : get_FpXQX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1917 :
1918 : INLINE long
1919 51630 : get_FpXQX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1920 :
1921 : INLINE long
1922 3589 : get_FpXQX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1923 :
1924 : /*******************************************************************/
1925 : /* */
1926 : /* ADDMULII / SUBMULII */
1927 : /* */
1928 : /*******************************************************************/
1929 : /* x - y*z */
1930 : INLINE GEN
1931 32800182 : submulii(GEN x, GEN y, GEN z)
1932 : {
1933 32800182 : long lx = lgefint(x), ly, lz;
1934 : pari_sp av;
1935 : GEN t;
1936 32800182 : if (lx == 2) { t = mulii(z,y); togglesign(t); return t; }
1937 30268074 : ly = lgefint(y);
1938 30268074 : if (ly == 2) return icopy(x);
1939 28999820 : lz = lgefint(z);
1940 28999820 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1941 28999820 : t = mulii(z, y);
1942 28999820 : set_avma(av); return subii(x,t);
1943 : }
1944 : /* y*z - x */
1945 : INLINE GEN
1946 3848399 : mulsubii(GEN y, GEN z, GEN x)
1947 : {
1948 3848399 : long lx = lgefint(x), ly, lz;
1949 : pari_sp av;
1950 : GEN t;
1951 3848399 : if (lx == 2) return mulii(z,y);
1952 2429388 : ly = lgefint(y);
1953 2429388 : if (ly == 2) return negi(x);
1954 2151859 : lz = lgefint(z);
1955 2151859 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1956 2151899 : t = mulii(z, y);
1957 2151869 : set_avma(av); return subii(t,x);
1958 : }
1959 :
1960 : /* x - u*y */
1961 : INLINE GEN
1962 7728 : submuliu(GEN x, GEN y, ulong u)
1963 : {
1964 : pari_sp av;
1965 7728 : long ly = lgefint(y);
1966 7728 : if (ly == 2) return icopy(x);
1967 7728 : av = avma;
1968 7728 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1969 7728 : y = mului(u,y);
1970 7728 : set_avma(av); return subii(x, y);
1971 : }
1972 : /* x + u*y */
1973 : INLINE GEN
1974 541069 : addmuliu(GEN x, GEN y, ulong u)
1975 : {
1976 : pari_sp av;
1977 541069 : long ly = lgefint(y);
1978 541069 : if (ly == 2) return icopy(x);
1979 541069 : av = avma;
1980 541069 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1981 541069 : y = mului(u,y);
1982 541069 : set_avma(av); return addii(x, y);
1983 : }
1984 : /* x - u*y */
1985 : INLINE GEN
1986 59968220 : submuliu_inplace(GEN x, GEN y, ulong u)
1987 : {
1988 : pari_sp av;
1989 59968220 : long ly = lgefint(y);
1990 59968220 : if (ly == 2) return x;
1991 38006405 : av = avma;
1992 38006405 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1993 38011107 : y = mului(u,y);
1994 38010878 : set_avma(av); return subii(x, y);
1995 : }
1996 : /* x + u*y */
1997 : INLINE GEN
1998 59471813 : addmuliu_inplace(GEN x, GEN y, ulong u)
1999 : {
2000 : pari_sp av;
2001 59471813 : long ly = lgefint(y);
2002 59471813 : if (ly == 2) return x;
2003 37913895 : av = avma;
2004 37913895 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
2005 37918197 : y = mului(u,y);
2006 37918027 : set_avma(av); return addii(x, y);
2007 : }
2008 : /* ux + vy */
2009 : INLINE GEN
2010 37826392 : lincombii(GEN u, GEN v, GEN x, GEN y)
2011 : {
2012 37826392 : long lx = lgefint(x), ly;
2013 : GEN p1, p2;
2014 : pari_sp av;
2015 37826392 : if (lx == 2) return mulii(v,y);
2016 23784506 : ly = lgefint(y);
2017 23784506 : if (ly == 2) return mulii(u,x);
2018 21102068 : av = avma; (void)new_chunk(lx+ly+lgefint(u)+lgefint(v)); /* HACK */
2019 21105449 : p1 = mulii(u,x);
2020 21103985 : p2 = mulii(v,y);
2021 21103647 : set_avma(av); return addii(p1,p2);
2022 : }
2023 :
2024 : /*******************************************************************/
2025 : /* */
2026 : /* GEN SUBTYPES */
2027 : /* */
2028 : /*******************************************************************/
2029 :
2030 : INLINE int
2031 4884635619 : is_const_t(long t) { return (t < t_POLMOD); }
2032 : INLINE int
2033 6960 : is_extscalar_t(long t) { return (t <= t_POL); }
2034 : INLINE int
2035 9575203 : is_intreal_t(long t) { return (t <= t_REAL); }
2036 : INLINE int
2037 655725046 : is_matvec_t(long t) { return (t >= t_VEC && t <= t_MAT); }
2038 : INLINE int
2039 90576695 : is_noncalc_t(long tx) { return (tx) >= t_LIST; }
2040 : INLINE int
2041 0 : is_qfb_t(long t) { return (t == t_QFB); }
2042 : INLINE int
2043 5015518 : is_rational_t(long t) { return (t == t_INT || t == t_FRAC); }
2044 : INLINE int
2045 62560882 : is_real_t(long t) { return (t == t_INT || t == t_REAL || t == t_FRAC); }
2046 : INLINE int
2047 9165269587 : is_recursive_t(long t) { return lontyp[t]; }
2048 : INLINE int
2049 368258204 : is_scalar_t(long t) { return (t < t_POL); }
2050 : INLINE int
2051 43381486 : is_vec_t(long t) { return (t == t_VEC || t == t_COL); }
2052 :
2053 : INLINE int
2054 67776646 : qfb_is_qfi(GEN q) { return signe(gel(q,4)) < 0; }
2055 :
2056 : /*******************************************************************/
2057 : /* */
2058 : /* TRANSCENDENTAL */
2059 : /* */
2060 : /*******************************************************************/
2061 : INLINE GEN
2062 79919054 : sqrtr(GEN x) {
2063 79919054 : long s = signe(x);
2064 79919054 : if (s == 0) return real_0_bit(expo(x) >> 1);
2065 79885939 : if (s >= 0) return sqrtr_abs(x);
2066 433258 : retmkcomplex(gen_0, sqrtr_abs(x));
2067 : }
2068 : INLINE GEN
2069 0 : cbrtr_abs(GEN x) { return sqrtnr_abs(x, 3); }
2070 : INLINE GEN
2071 0 : cbrtr(GEN x) {
2072 0 : long s = signe(x);
2073 : GEN r;
2074 0 : if (s == 0) return real_0_bit(expo(x) / 3);
2075 0 : r = cbrtr_abs(x);
2076 0 : if (s < 0) togglesign(r);
2077 0 : return r;
2078 : }
2079 : INLINE GEN
2080 2795010 : sqrtnr(GEN x, long n) {
2081 2795010 : long s = signe(x);
2082 : GEN r;
2083 2795010 : if (s == 0) return real_0_bit(expo(x) / n);
2084 2795010 : r = sqrtnr_abs(x, n);
2085 2795004 : if (s < 0) pari_err_IMPL("sqrtnr for x < 0");
2086 2795004 : return r;
2087 : }
2088 : INLINE long
2089 752104 : logint(GEN B, GEN y) { return logintall(B,y,NULL); }
2090 : INLINE ulong
2091 1720600 : ulogint(ulong B, ulong y)
2092 : {
2093 : ulong r;
2094 : long e;
2095 1720600 : if (y == 2) return expu(B);
2096 1672586 : r = y;
2097 5054448 : for (e=1;; e++)
2098 : { /* here, r = y^e, r2 = y^(e-1) */
2099 5054448 : if (r >= B) return r == B? e: e-1;
2100 3383383 : r = umuluu_or_0(y, r);
2101 3383388 : if (!r) return e;
2102 : }
2103 : }
2104 :
2105 : /*******************************************************************/
2106 : /* */
2107 : /* MISCELLANEOUS */
2108 : /* */
2109 : /*******************************************************************/
2110 9575086 : INLINE int ismpzero(GEN x) { return is_intreal_t(typ(x)) && !signe(x); }
2111 2800365333 : INLINE int isintzero(GEN x) { return typ(x) == t_INT && !signe(x); }
2112 17004663 : INLINE int isint1(GEN x) { return typ(x)==t_INT && equali1(x); }
2113 5701421 : INLINE int isintm1(GEN x){ return typ(x)==t_INT && equalim1(x);}
2114 1275573774 : INLINE int equali1(GEN n)
2115 1275573774 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(1)) && n[2] == 1; }
2116 139008666 : INLINE int equalim1(GEN n)
2117 139008666 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(-1)) && n[2] == 1; }
2118 : /* works only for POSITIVE integers */
2119 2187674121 : INLINE int is_pm1(GEN n)
2120 2187674121 : { return lgefint(n) == 3 && n[2] == 1; }
2121 557522330 : INLINE int is_bigint(GEN n)
2122 557522330 : { long l = lgefint(n); return l > 3 || (l == 3 && (n[2] & HIGHBIT)); }
2123 :
2124 2052988062 : INLINE int odd(long x) { return x & 1; }
2125 116881651 : INLINE int both_odd(long x, long y) { return x & y & 1; }
2126 :
2127 : INLINE int
2128 8047723351 : isonstack(GEN x)
2129 8047723351 : { return ((pari_sp)x >= pari_mainstack->bot
2130 8047723351 : && (pari_sp)x < pari_mainstack->top); }
2131 :
2132 : /* assume x != 0 and x t_REAL, return an approximation to log2(|x|) */
2133 : INLINE double
2134 92961347 : dbllog2r(GEN x)
2135 92961347 : { return log2((double)(ulong)x[2]) + (double)(expo(x) - (BITS_IN_LONG-1)); }
2136 :
2137 : INLINE GEN
2138 2512240 : mul_content(GEN cx, GEN cy)
2139 : {
2140 2512240 : if (!cx) return cy;
2141 520054 : if (!cy) return cx;
2142 332827 : return gmul(cx,cy);
2143 : }
2144 : INLINE GEN
2145 0 : inv_content(GEN c) { return c? ginv(c): NULL; }
2146 : INLINE GEN
2147 57950 : div_content(GEN cx, GEN cy)
2148 : {
2149 57950 : if (!cy) return cx;
2150 56816 : if (!cx) return ginv(cy);
2151 25758 : return gdiv(cx,cy);
2152 : }
2153 : INLINE GEN
2154 10293926 : mul_denom(GEN dx, GEN dy)
2155 : {
2156 10293926 : if (!dx) return dy;
2157 1835896 : if (!dy) return dx;
2158 1368163 : return mulii(dx,dy);
2159 : }
2160 :
2161 : /* POLYNOMIALS */
2162 : INLINE GEN
2163 1439404 : constant_coeff(GEN x) { return signe(x)? gel(x,2): gen_0; }
2164 : INLINE GEN
2165 168979493 : leading_coeff(GEN x) { return lg(x) == 2? gen_0: gel(x,lg(x)-1); }
2166 : INLINE ulong
2167 969165 : Flx_lead(GEN x) { return lg(x) == 2? 0: x[lg(x)-1]; }
2168 : INLINE ulong
2169 330286 : Flx_constant(GEN x) { return lg(x) == 2? 0: x[2]; }
2170 : INLINE long
2171 5330354391 : degpol(GEN x) { return lg(x)-3; }
2172 : INLINE long
2173 2618430416 : lgpol(GEN x) { return lg(x)-2; }
2174 : INLINE long
2175 341316842 : lgcols(GEN x) { return lg(gel(x,1)); }
2176 : INLINE long
2177 153659891 : nbrows(GEN x) { return lg(gel(x,1))-1; }
2178 : INLINE GEN
2179 0 : truecoef(GEN x, long n) { return polcoef(x,n,-1); }
2180 :
2181 : INLINE GEN
2182 2128025 : ZXQ_mul(GEN y, GEN x, GEN T) { return ZX_rem(ZX_mul(y, x), T); }
2183 : INLINE GEN
2184 950775 : ZXQ_sqr(GEN x, GEN T) { return ZX_rem(ZX_sqr(x), T); }
2185 :
2186 : INLINE GEN
2187 103468855 : RgX_copy(GEN x)
2188 376960853 : { pari_APPLY_pol_normalized(gcopy(gel(x,i))); }
2189 : /* have to use ulong to avoid silly warnings from gcc "assuming signed
2190 : * overflow does not occur" */
2191 : INLINE GEN
2192 2551519 : RgX_coeff(GEN x, long n)
2193 : {
2194 2551519 : ulong l = lg(x);
2195 2551519 : return (n < 0 || ((ulong)n+3) > l)? gen_0: gel(x,n+2);
2196 : }
2197 : INLINE GEN
2198 349345 : RgX_renormalize(GEN x) { return RgX_renormalize_lg(x, lg(x)); }
2199 : INLINE GEN
2200 7053359 : RgX_div(GEN x, GEN y) { return RgX_divrem(x,y,NULL); }
2201 : INLINE GEN
2202 1904 : RgXQX_div(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,NULL); }
2203 : INLINE GEN
2204 125476 : RgXQX_rem(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,ONLY_REM); }
2205 : INLINE GEN
2206 5437055 : FpX_div(GEN x, GEN y, GEN p) { return FpX_divrem(x,y,p, NULL); }
2207 : INLINE GEN
2208 1995667 : Flx_div(GEN x, GEN y, ulong p) { return Flx_divrem(x,y,p, NULL); }
2209 : INLINE GEN
2210 21395522 : Flx_div_pre(GEN x, GEN y, ulong p, ulong pi)
2211 21395522 : { return Flx_divrem_pre(x,y,p,pi, NULL); }
2212 : INLINE GEN
2213 1552381 : F2x_div(GEN x, GEN y) { return F2x_divrem(x,y, NULL); }
2214 : INLINE GEN
2215 0 : FpV_FpC_mul(GEN x, GEN y, GEN p) { return FpV_dotproduct(x,y,p); }
2216 : INLINE GEN
2217 101696857 : pol0_Flx(long sv) { return mkvecsmall(sv); }
2218 : INLINE GEN
2219 54570600 : pol1_Flx(long sv) { return mkvecsmall2(sv, 1); }
2220 : INLINE GEN
2221 37590216 : polx_Flx(long sv) { return mkvecsmall3(sv, 0, 1); }
2222 : INLINE GEN
2223 0 : zero_zx(long sv) { return zero_Flx(sv); }
2224 : INLINE GEN
2225 0 : polx_zx(long sv) { return polx_Flx(sv); }
2226 : INLINE GEN
2227 0 : zx_shift(GEN x, long n) { return Flx_shift(x,n); }
2228 : INLINE GEN
2229 14049 : zx_renormalize(GEN x, long l) { return Flx_renormalize(x,l); }
2230 : INLINE GEN
2231 1350 : zero_F2x(long sv) { return zero_Flx(sv); }
2232 : INLINE GEN
2233 13186673 : pol0_F2x(long sv) { return pol0_Flx(sv); }
2234 : INLINE GEN
2235 3954137 : pol1_F2x(long sv) { return pol1_Flx(sv); }
2236 : INLINE GEN
2237 1070496 : polx_F2x(long sv) { return mkvecsmall2(sv, 2); }
2238 : INLINE int
2239 2873469 : F2x_equal1(GEN x) { return Flx_equal1(x); }
2240 : INLINE int
2241 4598280 : F2x_equal(GEN V, GEN W) { return Flx_equal(V,W); }
2242 : INLINE GEN
2243 59606511 : F2x_copy(GEN x) { return leafcopy(x); }
2244 : INLINE GEN
2245 4487 : F2v_copy(GEN x) { return leafcopy(x); }
2246 : INLINE GEN
2247 2545331 : Flv_copy(GEN x) { return leafcopy(x); }
2248 : INLINE GEN
2249 172063458 : Flx_copy(GEN x) { return leafcopy(x); }
2250 : INLINE GEN
2251 4366143 : vecsmall_copy(GEN x) { return leafcopy(x); }
2252 : INLINE int
2253 8318111 : Flx_equal1(GEN x) { return degpol(x)==0 && x[2] == 1; }
2254 : INLINE int
2255 12549 : ZX_equal1(GEN x) { return degpol(x)==0 && equali1(gel(x,2)); }
2256 : INLINE int
2257 7266145 : ZX_is_monic(GEN x) { return equali1(leading_coeff(x)); }
2258 :
2259 : INLINE GEN
2260 154331543 : ZX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2261 : INLINE GEN
2262 144996437 : FpX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2263 : INLINE GEN
2264 849896 : FpXX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2265 : INLINE GEN
2266 4693783 : FpXQX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2267 : INLINE GEN
2268 114209830 : F2x_renormalize(GEN x, long lx) { return Flx_renormalize(x,lx); }
2269 :
2270 : INLINE GEN
2271 0 : F2xX_shift(GEN a, long n, long vs) { return FlxX_shift(a, n, vs); }
2272 :
2273 : INLINE GEN
2274 37585 : F2v_to_F2x(GEN x, long sv) {
2275 37585 : GEN y = leafcopy(x);
2276 37585 : y[1] = sv; F2x_renormalize(y, lg(y)); return y;
2277 : }
2278 :
2279 : INLINE long
2280 385 : sturm(GEN x) { return sturmpart(x, NULL, NULL); }
2281 :
2282 : INLINE long
2283 5796 : gval(GEN x, long v)
2284 5796 : { pari_sp av = avma; return gc_long(av, gvaluation(x, pol_x(v))); }
2285 :
2286 : INLINE void
2287 480682 : RgX_shift_inplace_init(long v)
2288 480682 : { if (v) (void)cgetg(v, t_VECSMALL); }
2289 : /* shift polynomial in place. assume v free cells have been left before x */
2290 : INLINE GEN
2291 480682 : RgX_shift_inplace(GEN x, long v)
2292 : {
2293 : long i, lx;
2294 : GEN z;
2295 480682 : if (!v) return x;
2296 253169 : lx = lg(x);
2297 253169 : if (lx == 2) return x;
2298 253169 : z = x + lx;
2299 : /* stackdummy's from normalizepol */
2300 253169 : while (lg(z) != v) z += lg(z);
2301 253169 : z += v;
2302 4654514 : for (i = lx-1; i >= 2; i--) gel(--z,0) = gel(x,i);
2303 675895 : for (i = 0; i < v; i++) gel(--z,0) = gen_0;
2304 253169 : z -= 2;
2305 253169 : z[1] = x[1];
2306 253169 : z[0] = evaltyp(t_POL) | evallg(lx+v);
2307 253169 : stackdummy((pari_sp)z, (pari_sp)x); return z;
2308 : }
2309 :
2310 :
2311 : /* LINEAR ALGEBRA */
2312 : INLINE GEN
2313 502527 : zv_to_ZV(GEN x) { return vecsmall_to_vec(x); }
2314 : INLINE GEN
2315 7747345 : zc_to_ZC(GEN x) { return vecsmall_to_col(x); }
2316 : INLINE GEN
2317 3190968 : ZV_to_zv(GEN x) { return vec_to_vecsmall(x); }
2318 : INLINE GEN
2319 0 : zx_to_zv(GEN x, long N) { return Flx_to_Flv(x,N); }
2320 : INLINE GEN
2321 104146 : zv_to_zx(GEN x, long sv) { return Flv_to_Flx(x,sv); }
2322 : INLINE GEN
2323 0 : zm_to_zxV(GEN x, long sv) { return Flm_to_FlxV(x,sv); }
2324 : INLINE GEN
2325 0 : zero_zm(long x, long y) { return zero_Flm(x,y); }
2326 : INLINE GEN
2327 36150200 : zero_zv(long x) { return zero_Flv(x); }
2328 : INLINE GEN
2329 266 : zm_transpose(GEN x) { return Flm_transpose(x); }
2330 : INLINE GEN
2331 0 : zm_copy(GEN x) { return Flm_copy(x); }
2332 : INLINE GEN
2333 2183634 : zv_copy(GEN x) { return Flv_copy(x); }
2334 : INLINE GEN
2335 0 : zm_row(GEN x, long i) { return Flm_row(x,i); }
2336 :
2337 : INLINE GEN
2338 10191821 : ZC_hnfrem(GEN x, GEN y) { return ZC_hnfdivrem(x,y,NULL); }
2339 : INLINE GEN
2340 326773 : ZM_hnfrem(GEN x, GEN y) { return ZM_hnfdivrem(x,y,NULL); }
2341 : INLINE GEN
2342 6933424 : ZM_lll(GEN x, double D, long f) { return ZM_lll_norms(x,D,f,NULL); }
2343 : INLINE void
2344 9404898 : RgM_dimensions(GEN x, long *m, long *n) { *n = lg(x)-1; *m = *n? nbrows(x): 0; }
2345 : INLINE GEN
2346 21440427 : RgM_shallowcopy(GEN x)
2347 93322866 : { pari_APPLY_same(leafcopy(gel(x,i))); }
2348 : INLINE GEN
2349 198008 : F2m_copy(GEN x) { return RgM_shallowcopy(x); }
2350 :
2351 : INLINE GEN
2352 0 : F3m_copy(GEN x) { return RgM_shallowcopy(x); }
2353 :
2354 : INLINE GEN
2355 6275279 : Flm_copy(GEN x) { return RgM_shallowcopy(x); }
2356 :
2357 : /* divisibility: return 1 if y[i] | x[i] for all i, 0 otherwise. Assume
2358 : * x,y are ZV of the same length */
2359 : INLINE int
2360 23485 : ZV_dvd(GEN x, GEN y)
2361 : {
2362 23485 : long i, l = lg(x);
2363 37856 : for (i=1; i < l; i++)
2364 30464 : if ( ! dvdii( gel(x,i), gel(y,i) ) ) return 0;
2365 7392 : return 1;
2366 : }
2367 : INLINE GEN
2368 539090 : ZM_ZV_mod(GEN x, GEN y)
2369 1537888 : { pari_APPLY_same(ZV_ZV_mod(gel(x,i), y)) }
2370 : INLINE GEN
2371 7322904 : ZV_ZV_mod(GEN x, GEN y)
2372 18920474 : { pari_APPLY_same(modii(gel(x,i), gel(y,i))) }
2373 : INLINE GEN
2374 0 : vecmodii(GEN x, GEN y) { return ZV_ZV_mod(x,y); }
2375 : INLINE GEN
2376 174881 : vecmoduu(GEN x, GEN y) { pari_APPLY_ulong(((ulong*)x)[i] % ((ulong*)y)[i]) }
2377 :
2378 : /* Fq */
2379 : INLINE GEN
2380 3106428 : Fq_red(GEN x, GEN T, GEN p)
2381 3106428 : { return typ(x)==t_INT? Fp_red(x,p): FpXQ_red(x,T,p); }
2382 : INLINE GEN
2383 73792 : Fq_to_FpXQ(GEN x, GEN T, GEN p /*unused*/)
2384 : {
2385 : (void) p;
2386 73792 : return typ(x)==t_INT ? scalarpol(x, get_FpX_var(T)): x;
2387 : }
2388 : INLINE GEN
2389 756 : Rg_to_Fq(GEN x, GEN T, GEN p) { return T? Rg_to_FpXQ(x,T,p): Rg_to_Fp(x,p); }
2390 :
2391 : INLINE GEN
2392 14594 : gener_Fq_local(GEN T, GEN p, GEN L)
2393 0 : { return T? gener_FpXQ_local(T,p, L)
2394 14594 : : pgener_Fp_local(p, L); }
2395 :
2396 : INLINE GEN
2397 0 : random_Fq(GEN T, GEN p)
2398 0 : { return T ? random_FpX(get_FpX_degree(T), get_FpX_var(T), p): randomi(p); }
2399 :
2400 : /* FpXQX */
2401 : INLINE GEN
2402 4526 : FpXQX_div(GEN x, GEN y, GEN T, GEN p) { return FpXQX_divrem(x, y, T, p, NULL); }
2403 : INLINE GEN
2404 0 : FlxqX_div(GEN x, GEN y, GEN T, ulong p) { return FlxqX_divrem(x, y, T, p, NULL); }
2405 : INLINE GEN
2406 165407 : FlxqX_div_pre(GEN x, GEN y, GEN T, ulong p, ulong pi) { return FlxqX_divrem_pre(x, y, T, p, pi, NULL); }
2407 : INLINE GEN
2408 33173 : F2xqX_div(GEN x, GEN y, GEN T) { return F2xqX_divrem(x, y, T, NULL); }
2409 :
2410 : INLINE GEN
2411 20587 : FpXY_Fq_evaly(GEN Q, GEN y, GEN T, GEN p, long vx)
2412 20587 : { return T ? FpXY_FpXQ_evaly(Q, y, T, p, vx): FpXY_evaly(Q, y, p, vx); }
2413 :
2414 : /* FqX */
2415 : INLINE GEN
2416 25354 : FqX_red(GEN z, GEN T, GEN p) { return T? FpXQX_red(z, T, p): FpX_red(z, p); }
2417 : INLINE GEN
2418 127694 : FqX_add(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2419 : INLINE GEN
2420 24956 : FqX_neg(GEN x,GEN T,GEN p) { return T? FpXX_neg(x,p): FpX_neg(x,p); }
2421 : INLINE GEN
2422 68607 : FqX_sub(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2423 : INLINE GEN
2424 567980 : FqX_Fp_mul(GEN P, GEN u, GEN T, GEN p)
2425 567980 : { return T? FpXX_Fp_mul(P, u, p): FpX_Fp_mul(P, u, p); }
2426 : INLINE GEN
2427 427291 : FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
2428 427291 : { return typ(U)==t_INT ? FqX_Fp_mul(P, U, T, p): FpXQX_FpXQ_mul(P, U, T, p); }
2429 : INLINE GEN
2430 367095 : FqX_mul(GEN x, GEN y, GEN T, GEN p)
2431 367095 : { return T? FpXQX_mul(x, y, T, p): FpX_mul(x, y, p); }
2432 : INLINE GEN
2433 21942 : FqX_mulu(GEN x, ulong y, GEN T, GEN p)
2434 21942 : { return T? FpXX_mulu(x, y, p): FpX_mulu(x, y, p); }
2435 : INLINE GEN
2436 71855 : FqX_sqr(GEN x, GEN T, GEN p)
2437 71855 : { return T? FpXQX_sqr(x, T, p): FpX_sqr(x, p); }
2438 : INLINE GEN
2439 1295 : FqX_powu(GEN x, ulong n, GEN T, GEN p)
2440 1295 : { return T? FpXQX_powu(x, n, T, p): FpX_powu(x, n, p); }
2441 : INLINE GEN
2442 19411 : FqX_halve(GEN x, GEN T, GEN p)
2443 19411 : { return T? FpXX_halve(x, p): FpX_halve(x, p); }
2444 : INLINE GEN
2445 38450 : FqX_div(GEN x, GEN y, GEN T, GEN p)
2446 38450 : { return T? FpXQX_divrem(x,y,T,p,NULL): FpX_divrem(x,y,p,NULL); }
2447 : INLINE GEN
2448 6090 : FqX_get_red(GEN S, GEN T, GEN p)
2449 6090 : { return T? FpXQX_get_red(S,T,p): FpX_get_red(S,p); }
2450 : INLINE GEN
2451 37743 : FqX_rem(GEN x, GEN y, GEN T, GEN p)
2452 37743 : { return T? FpXQX_rem(x,y,T,p): FpX_rem(x,y,p); }
2453 : INLINE GEN
2454 0 : FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
2455 0 : { return T? FpXQX_divrem(x,y,T,p,z): FpX_divrem(x,y,p,z); }
2456 : INLINE GEN
2457 69629 : FqX_div_by_X_x(GEN x, GEN y, GEN T, GEN p, GEN *z)
2458 69629 : { return T? FpXQX_div_by_X_x(x,y,T,p,z): FpX_div_by_X_x(x,y,p,z); }
2459 : INLINE GEN
2460 0 : FqX_halfgcd(GEN P,GEN Q,GEN T,GEN p)
2461 0 : {return T? FpXQX_halfgcd(P,Q,T,p): FpX_halfgcd(P,Q,p);}
2462 : INLINE GEN
2463 8106 : FqX_gcd(GEN P,GEN Q,GEN T,GEN p)
2464 8106 : {return T? FpXQX_gcd(P,Q,T,p): FpX_gcd(P,Q,p);}
2465 : INLINE GEN
2466 442840 : FqX_extgcd(GEN P,GEN Q,GEN T,GEN p, GEN *U, GEN *V)
2467 442840 : { return T? FpXQX_extgcd(P,Q,T,p,U,V): FpX_extgcd(P,Q,p,U,V); }
2468 : INLINE GEN
2469 4053 : FqX_normalize(GEN z, GEN T, GEN p)
2470 4053 : { return T? FpXQX_normalize(z, T, p): FpX_normalize(z, p); }
2471 : INLINE GEN
2472 40061 : FqX_deriv(GEN f, GEN T, GEN p) { return T? FpXX_deriv(f, p): FpX_deriv(f, p); }
2473 : INLINE long
2474 683802 : FqX_is_squarefree(GEN P, GEN T, GEN p)
2475 683802 : { return T ? FpXQX_is_squarefree(P, T, p): FpX_is_squarefree(P, p); }
2476 : INLINE GEN
2477 0 : FqX_integ(GEN f, GEN T, GEN p) { return T? FpXX_integ(f, p): FpX_integ(f, p); }
2478 : INLINE GEN
2479 140834 : FqX_factor(GEN f, GEN T, GEN p)
2480 140834 : { return T?FpXQX_factor(f, T, p): FpX_factor(f, p); }
2481 : INLINE GEN
2482 7 : FqX_factor_squarefree(GEN f, GEN T, GEN p)
2483 7 : { return T ? FpXQX_factor_squarefree(f, T, p): FpX_factor_squarefree(f, p); }
2484 : INLINE GEN
2485 7 : FqX_ddf(GEN f, GEN T, GEN p)
2486 7 : { return T ? FpXQX_ddf(f, T, p): FpX_ddf(f, p); }
2487 : INLINE GEN
2488 47786 : FqX_degfact(GEN f, GEN T, GEN p)
2489 47786 : { return T?FpXQX_degfact(f, T, p): FpX_degfact(f, p); }
2490 : INLINE GEN
2491 7273 : FqX_roots(GEN f, GEN T, GEN p)
2492 7273 : { return T?FpXQX_roots(f, T, p): FpX_roots(f, p); }
2493 : INLINE GEN
2494 175 : FqX_to_mod(GEN f, GEN T, GEN p)
2495 175 : { return T?FpXQX_to_mod(f, T, p): FpX_to_mod(f, p); }
2496 :
2497 : /*FqXQ*/
2498 : INLINE GEN
2499 0 : FqXQ_add(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2500 0 : { (void)S; return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2501 : INLINE GEN
2502 0 : FqXQ_sub(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2503 0 : { (void)S; return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2504 : INLINE GEN
2505 0 : FqXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
2506 0 : { return T? FpXQXQ_div(x,y,S,T,p): FpXQ_div(x,y,S,p); }
2507 : INLINE GEN
2508 0 : FqXQ_inv(GEN x, GEN S, GEN T, GEN p)
2509 0 : { return T? FpXQXQ_inv(x,S,T,p): FpXQ_inv(x,S,p); }
2510 : INLINE GEN
2511 0 : FqXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
2512 0 : { return T? FpXQXQ_invsafe(x,S,T,p): FpXQ_inv(x,S,p); }
2513 : INLINE GEN
2514 22766 : FqXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
2515 22766 : { return T? FpXQXQ_mul(x,y,S,T,p): FpXQ_mul(x,y,S,p); }
2516 : INLINE GEN
2517 0 : FqXQ_sqr(GEN x, GEN S, GEN T, GEN p)
2518 0 : { return T? FpXQXQ_sqr(x,S,T,p): FpXQ_sqr(x,S,p); }
2519 : INLINE GEN
2520 0 : FqXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
2521 0 : { return T? FpXQXQ_pow(x,n,S,T,p): FpXQ_pow(x,n,S,p); }
2522 :
2523 : /*FqXn*/
2524 : INLINE GEN
2525 6590 : FqXn_expint(GEN x, long n, GEN T, GEN p)
2526 6590 : { return T? FpXQXn_expint(x,n,T,p): FpXn_expint(x,n,p); }
2527 : INLINE GEN
2528 0 : FqXn_exp(GEN x, long n, GEN T, GEN p)
2529 0 : { return T? FpXQXn_exp(x,n,T,p): FpXn_exp(x,n,p); }
2530 : INLINE GEN
2531 7126 : FqXn_inv(GEN x, long n, GEN T, GEN p)
2532 7126 : { return T? FpXQXn_inv(x,n,T,p): FpXn_inv(x,n,p); }
2533 : INLINE GEN
2534 263403 : FqXn_mul(GEN x, GEN y, long n, GEN T, GEN p)
2535 263403 : { return T? FpXQXn_mul(x, y, n, T, p): FpXn_mul(x, y, n, p); }
2536 : INLINE GEN
2537 0 : FqXn_sqr(GEN x, long n, GEN T, GEN p)
2538 0 : { return T? FpXQXn_sqr(x,n,T,p): FpXn_sqr(x,n,p); }
2539 :
2540 : /*FpXQ*/
2541 : INLINE GEN
2542 0 : FpXQ_add(GEN x,GEN y,GEN T/*unused*/,GEN p)
2543 0 : { (void)T; return FpX_add(x,y,p); }
2544 : INLINE GEN
2545 0 : FpXQ_sub(GEN x,GEN y,GEN T/*unused*/,GEN p)
2546 0 : { (void)T; return FpX_sub(x,y,p); }
2547 :
2548 : /*Flxq*/
2549 : INLINE GEN
2550 0 : Flxq_add(GEN x,GEN y,GEN T/*unused*/,ulong p)
2551 0 : { (void)T; return Flx_add(x,y,p); }
2552 : INLINE GEN
2553 0 : Flxq_sub(GEN x,GEN y,GEN T/*unused*/,ulong p)
2554 0 : { (void)T; return Flx_sub(x,y,p); }
2555 :
2556 : /* F2x */
2557 :
2558 : INLINE ulong
2559 667530066 : F2x_coeff(GEN x,long v)
2560 : {
2561 667530066 : ulong u=(ulong)x[2+divsBIL(v)];
2562 667529923 : return (u>>remsBIL(v))&1UL;
2563 : }
2564 :
2565 : INLINE void
2566 12263289 : F2x_clear(GEN x,long v)
2567 : {
2568 12263289 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2569 12263247 : *u&=~(1UL<<remsBIL(v));
2570 12263227 : }
2571 :
2572 : INLINE void
2573 124446185 : F2x_set(GEN x,long v)
2574 : {
2575 124446185 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2576 124444656 : *u|=1UL<<remsBIL(v);
2577 124443679 : }
2578 :
2579 : INLINE void
2580 1553274 : F2x_flip(GEN x,long v)
2581 : {
2582 1553274 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2583 1553274 : *u^=1UL<<remsBIL(v);
2584 1553274 : }
2585 :
2586 : /* F2v */
2587 :
2588 : INLINE ulong
2589 660967309 : F2v_coeff(GEN x,long v) { return F2x_coeff(x,v-1); }
2590 :
2591 : INLINE void
2592 12263294 : F2v_clear(GEN x,long v) { F2x_clear(x,v-1); }
2593 :
2594 : INLINE void
2595 101337123 : F2v_set(GEN x,long v) { F2x_set(x,v-1); }
2596 :
2597 : INLINE void
2598 1553274 : F2v_flip(GEN x,long v) { F2x_flip(x,v-1); }
2599 :
2600 : /* F2m */
2601 :
2602 : INLINE ulong
2603 8019135 : F2m_coeff(GEN x, long a, long b) { return F2v_coeff(gel(x,b), a); }
2604 :
2605 : INLINE void
2606 0 : F2m_clear(GEN x, long a, long b) { F2v_clear(gel(x,b), a); }
2607 :
2608 : INLINE void
2609 798 : F2m_set(GEN x, long a, long b) { F2v_set(gel(x,b), a); }
2610 :
2611 : INLINE void
2612 1553274 : F2m_flip(GEN x, long a, long b) { F2v_flip(gel(x,b), a); }
2613 :
2614 : /* F3m */
2615 :
2616 : INLINE ulong
2617 3247859 : F3m_coeff(GEN x, long a, long b) { return F3v_coeff(gel(x,b), a); }
2618 :
2619 : INLINE void
2620 0 : F3m_set(GEN x, long a, long b, ulong c) { F3v_set(gel(x,b), a, c); }
2621 :
2622 : /* ARITHMETIC */
2623 : INLINE GEN
2624 3885 : matpascal(long n) { return matqpascal(n, NULL); }
2625 : INLINE long
2626 458538 : Z_issquare(GEN x) { return Z_issquareall(x, NULL); }
2627 : INLINE long
2628 98 : Z_ispower(GEN x, ulong k) { return Z_ispowerall(x, k, NULL); }
2629 : INLINE GEN
2630 6590415 : sqrti(GEN x) { return sqrtremi(x,NULL); }
2631 : INLINE GEN
2632 123157930 : gaddgs(GEN y, long s) { return gaddsg(s,y); }
2633 : INLINE int
2634 785658 : gcmpgs(GEN y, long s) { return -gcmpsg(s,y); }
2635 : INLINE int
2636 29176 : gequalgs(GEN y, long s) { return gequalsg(s,y); }
2637 : INLINE GEN
2638 0 : gmaxsg(long s, GEN y) { return gmaxgs(y,s); }
2639 : INLINE GEN
2640 0 : gminsg(long s, GEN y) { return gmings(y,s); }
2641 : INLINE GEN
2642 21998398 : gmulgs(GEN y, long s) { return gmulsg(s,y); }
2643 : INLINE GEN
2644 124174680 : gmulgu(GEN y, ulong s) { return gmulug(s,y); }
2645 : INLINE GEN
2646 1707262 : gsubgs(GEN y, long s) { return gaddgs(y, -s); }
2647 : INLINE GEN
2648 529180 : gdivsg(long s, GEN y) { return gdiv(stoi(s), y); }
2649 :
2650 : INLINE GEN
2651 13509989 : gmax_shallow(GEN x, GEN y) { return gcmp(x,y)<0? y: x; }
2652 : INLINE GEN
2653 874938 : gmin_shallow(GEN x, GEN y) { return gcmp(x,y)<0? x: y; }
2654 :
2655 : /* x t_COMPLEX */
2656 : INLINE GEN
2657 90768114 : cxnorm(GEN x) { return gadd(gsqr(gel(x,1)), gsqr(gel(x,2))); }
2658 : /* q t_QUAD */
2659 : INLINE GEN
2660 69860 : quadnorm(GEN q)
2661 : {
2662 69860 : GEN X = gel(q,1), b = gel(X,3), c = gel(X,2);
2663 69860 : GEN z, u = gel(q,3), v = gel(q,2);
2664 69860 : if (typ(u) == t_INT && typ(v) == t_INT) /* generic case */
2665 : {
2666 69671 : z = signe(b)? mulii(v, addii(u,v)): sqri(v);
2667 69671 : return addii(z, mulii(c, sqri(u)));
2668 : }
2669 : else
2670 : {
2671 189 : z = signe(b)? gmul(v, gadd(u,v)): gsqr(v);
2672 189 : return gadd(z, gmul(c, gsqr(u)));
2673 : }
2674 : }
2675 : /* x a t_QUAD, return the attached discriminant */
2676 : INLINE GEN
2677 1078 : quad_disc(GEN x)
2678 : {
2679 1078 : GEN Q = gel(x,1), b = gel(Q,3), c = gel(Q,2), c4 = shifti(c,2);
2680 1078 : if (is_pm1(b)) return subsi(1, c4);
2681 154 : togglesign_safe(&c4); return c4;
2682 : }
2683 : INLINE GEN
2684 4848289 : qfb_disc3(GEN x, GEN y, GEN z) { return subii(sqri(y), shifti(mulii(x,z),2)); }
2685 : INLINE GEN
2686 18470593 : qfb_disc(GEN x) { return gel(x,4); }
2687 :
2688 : INLINE GEN
2689 4137470 : sqrfrac(GEN x)
2690 : {
2691 4137470 : GEN z = cgetg(3,t_FRAC);
2692 4137468 : gel(z,1) = sqri(gel(x,1));
2693 4137436 : gel(z,2) = sqri(gel(x,2)); return z;
2694 : }
2695 :
2696 : INLINE void
2697 16753948 : normalize_frac(GEN z) {
2698 16753948 : if (signe(gel(z,2)) < 0) { togglesign(gel(z,1)); setabssign(gel(z,2)); }
2699 16753948 : }
2700 :
2701 : INLINE GEN
2702 42892007 : powii(GEN x, GEN n)
2703 : {
2704 42892007 : long ln = lgefint(n);
2705 42892007 : if (ln == 3) {
2706 : GEN z;
2707 42869042 : if (signe(n) > 0) return powiu(x, n[2]);
2708 74807 : z = cgetg(3, t_FRAC);
2709 74829 : gel(z,1) = gen_1;
2710 74829 : gel(z,2) = powiu(x, n[2]);
2711 74829 : return z;
2712 : }
2713 22965 : if (ln == 2) return gen_1; /* rare */
2714 : /* should never happen */
2715 0 : return powgi(x, n); /* overflow unless x = 0, 1, -1 */
2716 : }
2717 : INLINE GEN
2718 1561 : powIs(long n) {
2719 1561 : switch(n & 3)
2720 : {
2721 63 : case 1: return mkcomplex(gen_0,gen_1);
2722 385 : case 2: return gen_m1;
2723 707 : case 3: return mkcomplex(gen_0,gen_m1);
2724 : }
2725 406 : return gen_1;
2726 : }
2727 :
2728 : /*******************************************************************/
2729 : /* */
2730 : /* ASSIGNMENTS */
2731 : /* */
2732 : /*******************************************************************/
2733 0 : INLINE void mpexpz(GEN x, GEN z)
2734 0 : { pari_sp av = avma; gaffect(mpexp(x), z); set_avma(av); }
2735 0 : INLINE void mplogz(GEN x, GEN z)
2736 0 : { pari_sp av = avma; gaffect(mplog(x), z); set_avma(av); }
2737 0 : INLINE void mpcosz(GEN x, GEN z)
2738 0 : { pari_sp av = avma; gaffect(mpcos(x), z); set_avma(av); }
2739 0 : INLINE void mpsinz(GEN x, GEN z)
2740 0 : { pari_sp av = avma; gaffect(mpsin(x), z); set_avma(av); }
2741 0 : INLINE void gnegz(GEN x, GEN z)
2742 0 : { pari_sp av = avma; gaffect(gneg(x), z); set_avma(av); }
2743 0 : INLINE void gabsz(GEN x, long prec, GEN z)
2744 0 : { pari_sp av = avma; gaffect(gabs(x,prec), z); set_avma(av); }
2745 0 : INLINE void gaddz(GEN x, GEN y, GEN z)
2746 0 : { pari_sp av = avma; gaffect(gadd(x,y), z); set_avma(av); }
2747 0 : INLINE void gsubz(GEN x, GEN y, GEN z)
2748 0 : { pari_sp av = avma; gaffect(gsub(x,y), z); set_avma(av); }
2749 0 : INLINE void gmulz(GEN x, GEN y, GEN z)
2750 0 : { pari_sp av = avma; gaffect(gmul(x,y), z); set_avma(av); }
2751 0 : INLINE void gdivz(GEN x, GEN y, GEN z)
2752 0 : { pari_sp av = avma; gaffect(gdiv(x,y), z); set_avma(av); }
2753 0 : INLINE void gdiventz(GEN x, GEN y, GEN z)
2754 0 : { pari_sp av = avma; gaffect(gdivent(x,y), z); set_avma(av); }
2755 0 : INLINE void gmodz(GEN x, GEN y, GEN z)
2756 0 : { pari_sp av = avma; gaffect(gmod(x,y), z); set_avma(av); }
2757 0 : INLINE void gmul2nz(GEN x, long s, GEN z)
2758 0 : { pari_sp av = avma; gaffect(gmul2n(x,s), z); set_avma(av); }
2759 0 : INLINE void gshiftz(GEN x, long s, GEN z)
2760 0 : { pari_sp av = avma; gaffect(gshift(x,s), z); set_avma(av); }
2761 :
2762 : /*******************************************************************/
2763 : /* */
2764 : /* ELLIPTIC CURVES */
2765 : /* */
2766 : /*******************************************************************/
2767 7116195 : INLINE GEN ell_get_a1(GEN e) { return gel(e,1); }
2768 5709704 : INLINE GEN ell_get_a2(GEN e) { return gel(e,2); }
2769 6912842 : INLINE GEN ell_get_a3(GEN e) { return gel(e,3); }
2770 6522705 : INLINE GEN ell_get_a4(GEN e) { return gel(e,4); }
2771 7961478 : INLINE GEN ell_get_a6(GEN e) { return gel(e,5); }
2772 5432777 : INLINE GEN ell_get_b2(GEN e) { return gel(e,6); }
2773 2135641 : INLINE GEN ell_get_b4(GEN e) { return gel(e,7); }
2774 3055105 : INLINE GEN ell_get_b6(GEN e) { return gel(e,8); }
2775 2608978 : INLINE GEN ell_get_b8(GEN e) { return gel(e,9); }
2776 8021709 : INLINE GEN ell_get_c4(GEN e) { return gel(e,10); }
2777 8850348 : INLINE GEN ell_get_c6(GEN e) { return gel(e,11); }
2778 11279869 : INLINE GEN ell_get_disc(GEN e) { return gel(e,12); }
2779 1295726 : INLINE GEN ell_get_j(GEN e) { return gel(e,13); }
2780 11588331 : INLINE long ell_get_type(GEN e) { return mael(e,14,1); }
2781 2036746 : INLINE GEN ellff_get_field(GEN x) { return gmael(x, 15, 1); }
2782 800034 : INLINE GEN ellff_get_a4a6(GEN x) { return gmael(x, 15, 2); }
2783 1463 : INLINE GEN ellQp_get_zero(GEN x) { return gmael(x, 15, 1); }
2784 308 : INLINE long ellQp_get_prec(GEN E) { return valp(ellQp_get_zero(E)); }
2785 1134 : INLINE GEN ellQp_get_p(GEN E) { return padic_p(ellQp_get_zero(E)); }
2786 232582 : INLINE long ellR_get_prec(GEN x) { return nbits2prec(mael3(x, 15, 1, 1)); }
2787 371325 : INLINE long ellR_get_sign(GEN x) { return mael3(x, 15, 1, 2); }
2788 2027603 : INLINE GEN ellnf_get_nf(GEN x) { return checknf_i(gmael(x,15,1)); }
2789 126 : INLINE GEN ellnf_get_bnf(GEN x) { return checkbnf_i(gmael(x,15,1)); }
2790 :
2791 4677492 : INLINE int checkell_i(GEN e) { return typ(e) == t_VEC && lg(e) == 17; }
2792 51072998 : INLINE int ell_is_inf(GEN z) { return lg(z) == 2; }
2793 1868493 : INLINE GEN ellinf(void) { return mkvec(gen_0); }
2794 :
2795 : /*******************************************************************/
2796 : /* */
2797 : /* ALGEBRAIC NUMBER THEORY */
2798 : /* */
2799 : /*******************************************************************/
2800 30052504 : INLINE GEN modpr_get_pr(GEN x) { return gel(x,3); }
2801 1888446 : INLINE GEN modpr_get_p(GEN x) { return pr_get_p(modpr_get_pr(x)); }
2802 13187471 : INLINE GEN modpr_get_T(GEN x) { return lg(x) == 4? NULL: gel(x,4); }
2803 :
2804 89368727 : INLINE GEN pr_get_p(GEN pr) { return gel(pr,1); }
2805 11508177 : INLINE GEN pr_get_gen(GEN pr){ return gel(pr,2); }
2806 : /* .[2] instead of itos works: e and f are small positive integers */
2807 15718247 : INLINE long pr_get_e(GEN pr) { return gel(pr,3)[2]; }
2808 25341018 : INLINE long pr_get_f(GEN pr) { return gel(pr,4)[2]; }
2809 47842516 : INLINE GEN pr_get_tau(GEN pr){ return gel(pr,5); }
2810 : INLINE int
2811 16399400 : pr_is_inert(GEN P) { return typ(pr_get_tau(P)) == t_INT; }
2812 : INLINE GEN
2813 1066910 : pr_norm(GEN pr) { return powiu(pr_get_p(pr), pr_get_f(pr)); }
2814 : INLINE ulong
2815 343931 : upr_norm(GEN pr) { return upowuu(pr_get_p(pr)[2], pr_get_f(pr)); }
2816 :
2817 : /* assume nf a genuine nf */
2818 : INLINE long
2819 1167335 : nf_get_varn(GEN nf) { return varn(gel(nf,1)); }
2820 : INLINE GEN
2821 94431081 : nf_get_pol(GEN nf) { return gel(nf,1); }
2822 : INLINE long
2823 68810677 : nf_get_degree(GEN nf) { return degpol( nf_get_pol(nf) ); }
2824 : INLINE long
2825 22160779 : nf_get_r1(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,1)); }
2826 : INLINE long
2827 4140 : nf_get_r2(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,2)); }
2828 : INLINE GEN
2829 456897 : nf_get_disc(GEN nf) { return gel(nf,3); }
2830 : INLINE GEN
2831 3580215 : nf_get_index(GEN nf) { return gel(nf,4); }
2832 : INLINE GEN
2833 20766678 : nf_get_M(GEN nf) { return gmael(nf,5,1); }
2834 : INLINE GEN
2835 301274 : nf_get_G(GEN nf) { return gmael(nf,5,2); }
2836 : INLINE GEN
2837 1685995 : nf_get_roundG(GEN nf) { return gmael(nf,5,3); }
2838 : INLINE GEN
2839 22081 : nf_get_Tr(GEN nf) { return gmael(nf,5,4); }
2840 : INLINE GEN
2841 4438 : nf_get_diff(GEN nf) { return gmael(nf,5,5); }
2842 : INLINE GEN
2843 59381 : nf_get_ramified_primes(GEN nf) { return gmael(nf,5,8); }
2844 : INLINE GEN
2845 1531127 : nf_get_roots(GEN nf) { return gel(nf,6); }
2846 : INLINE GEN
2847 4382 : nf_get_zk(GEN nf)
2848 : {
2849 4382 : GEN y = gel(nf,7), D = gel(y, 1);
2850 4382 : if (typ(D) == t_POL) D = gel(D, 2);
2851 4382 : if (!equali1(D)) y = gdiv(y, D);
2852 4382 : return y;
2853 : }
2854 : INLINE GEN
2855 5021316 : nf_get_zkprimpart(GEN nf)
2856 : {
2857 5021316 : GEN y = gel(nf,7);
2858 : /* test for old format of nf.zk: non normalized */
2859 5021316 : if (!equali1(gel(nf,4)) && gequal1(gel(y,1))) y = Q_remove_denom(y,NULL);
2860 5021309 : return y;
2861 : }
2862 : INLINE GEN
2863 5067159 : nf_get_zkden(GEN nf)
2864 : {
2865 5067159 : GEN y = gel(nf,7), D = gel(y,1);
2866 5067159 : if (typ(D) == t_POL) D = gel(D,2);
2867 : /* test for old format of nf.zk: non normalized */
2868 5067159 : if (!equali1(gel(nf,4)) && equali1(D)) D = Q_denom(y);
2869 5067162 : return D;
2870 : }
2871 : INLINE GEN
2872 9487042 : nf_get_invzk(GEN nf) { return gel(nf,8); }
2873 : INLINE void
2874 516827 : nf_get_sign(GEN nf, long *r1, long *r2)
2875 : {
2876 516827 : GEN x = gel(nf,2);
2877 516827 : *r1 = itou(gel(x,1));
2878 516827 : *r2 = itou(gel(x,2));
2879 516827 : }
2880 :
2881 : INLINE GEN
2882 2521140 : cyc_get_expo(GEN c) { return lg(c) == 1? gen_1: gel(c,1); }
2883 : INLINE GEN
2884 391887 : abgrp_get_no(GEN x) { return gel(x,1); }
2885 : INLINE GEN
2886 11549156 : abgrp_get_cyc(GEN x) { return gel(x,2); }
2887 : INLINE GEN
2888 1653645 : abgrp_get_gen(GEN x) { return gel(x,3); }
2889 : INLINE GEN
2890 9425782 : bnf_get_nf(GEN bnf) { return gel(bnf,7); }
2891 : INLINE GEN
2892 5097423 : bnf_get_clgp(GEN bnf) { return gmael(bnf,8,1); }
2893 : INLINE GEN
2894 8358 : bnf_get_no(GEN bnf) { return abgrp_get_no(bnf_get_clgp(bnf)); }
2895 : INLINE GEN
2896 3509044 : bnf_get_cyc(GEN bnf) { return abgrp_get_cyc(bnf_get_clgp(bnf)); }
2897 : INLINE GEN
2898 1579856 : bnf_get_gen(GEN bnf) { return abgrp_get_gen(bnf_get_clgp(bnf)); }
2899 : INLINE GEN
2900 641 : bnf_get_reg(GEN bnf) { return gmael(bnf,8,2); }
2901 : INLINE GEN
2902 2702040 : bnf_get_logfu(GEN bnf) { return gel(bnf,3); }
2903 : INLINE GEN
2904 1278295 : bnf_get_sunits(GEN bnf)
2905 1278295 : { GEN s = gmael(bnf,8,3); return typ(s) == t_INT? NULL: s; }
2906 : INLINE GEN
2907 290535 : bnf_get_tuU(GEN bnf) { return gmael3(bnf,8,4,2); }
2908 : INLINE long
2909 265194 : bnf_get_tuN(GEN bnf) { return gmael3(bnf,8,4,1)[2]; }
2910 : INLINE GEN
2911 288187 : bnf_get_fu_nocheck(GEN bnf) { return gmael(bnf,8,5); }
2912 : INLINE GEN
2913 26293 : nfV_to_scalar_or_alg(GEN nf, GEN x)
2914 63435 : { pari_APPLY_same(nf_to_scalar_or_alg(nf, gel(x,i))) }
2915 : INLINE GEN
2916 25852 : bnf_get_fu(GEN bnf) {
2917 25852 : GEN fu = bnf_build_units(bnf), nf = bnf_get_nf(bnf);
2918 25852 : if (typ(fu) == t_MAT) pari_err(e_MISC,"missing units in bnf");
2919 25852 : return nfV_to_scalar_or_alg(nf, vecslice(fu, 2, lg(fu)-1));
2920 : }
2921 :
2922 : INLINE GEN
2923 3632291 : bnr_get_bnf(GEN bnr) { return gel(bnr,1); }
2924 : INLINE GEN
2925 1936927 : bnr_get_bid(GEN bnr) { return gel(bnr,2); }
2926 : INLINE GEN
2927 140998 : bnr_get_mod(GEN bnr) { return gmael(bnr,2,1); }
2928 : INLINE GEN
2929 1260065 : bnr_get_nf(GEN bnr) { return gmael(bnr,1,7); }
2930 : INLINE GEN
2931 2728627 : bnr_get_clgp(GEN bnr) { return gel(bnr,5); }
2932 : INLINE GEN
2933 314572 : bnr_get_no(GEN bnr) { return abgrp_get_no(bnr_get_clgp(bnr)); }
2934 : INLINE GEN
2935 2396450 : bnr_get_cyc(GEN bnr) { return abgrp_get_cyc(bnr_get_clgp(bnr)); }
2936 : INLINE GEN
2937 70 : bnr_get_gen_nocheck(GEN bnr) { return abgrp_get_gen(bnr_get_clgp(bnr)); }
2938 : INLINE GEN
2939 7847 : bnr_get_gen(GEN bnr) {
2940 7847 : GEN G = bnr_get_clgp(bnr);
2941 7847 : if (lg(G) != 4)
2942 0 : pari_err(e_MISC,"missing bnr generators: please use bnrinit(,,1)");
2943 7847 : return gel(G,3);
2944 : }
2945 :
2946 : /* localstar, used in gchar */
2947 : INLINE GEN
2948 51955 : locs_get_cyc(GEN locs) { return gel(locs,1); }
2949 : INLINE GEN
2950 191695 : locs_get_Lsprk(GEN locs) { return gel(locs,2); }
2951 : INLINE GEN
2952 1260 : locs_get_Lgenfil(GEN locs) { return gel(locs,3); }
2953 : INLINE GEN
2954 8225 : locs_get_mod(GEN locs) { return gel(locs,4); }
2955 : /* pr dividing the modulus N of locs, 0 <= i < v_pr(N)
2956 : * return a t_MAT whose columns are the logs
2957 : * of generators of U_i(pr)/U_{i+1}(pr). */
2958 : INLINE GEN
2959 1260 : locs_get_famod(GEN locs) { return gmael(locs,4,1); }
2960 : INLINE GEN
2961 207235 : locs_get_m_infty(GEN locs) { return gmael(locs,4,2); }
2962 :
2963 : /* G a grossenchar group */
2964 : INLINE GEN
2965 32639 : gchar_get_basis(GEN gc) { return gel(gc, 1); }
2966 : INLINE GEN
2967 203105 : gchar_get_bnf(GEN gc) { return gel(gc, 2); }
2968 : INLINE GEN
2969 241501 : gchar_get_nf(GEN gc) { return gel(gc, 3); }
2970 : INLINE GEN
2971 279434 : gchar_get_zm(GEN gc) { return gel(gc, 4); }
2972 : INLINE GEN
2973 8225 : gchar_get_mod(GEN gc) { return locs_get_mod(gchar_get_zm(gc)); }
2974 : INLINE GEN
2975 4095 : gchar_get_modP(GEN gc) { return gmael(gchar_get_mod(gc),1,1); }
2976 : INLINE GEN
2977 36865 : gchar_get_S(GEN gc) { return gel(gc, 5); }
2978 : INLINE GEN
2979 188468 : gchar_get_DLdata(GEN gc) { return gel(gc, 6); }
2980 : INLINE GEN
2981 1748 : gchar_get_sfu(GEN gc) { return gel(gc, 7); }
2982 : INLINE GEN
2983 16168 : gchar_get_cyc(GEN gc) { return gel(gc, 9); }
2984 : INLINE GEN
2985 0 : gchar_get_hnf(GEN gc) { return gmael(gc, 10, 1); }
2986 : INLINE GEN
2987 0 : gchar_get_U(GEN gc) { return gmael(gc, 10, 2); }
2988 : INLINE GEN
2989 10969 : gchar_get_Ui(GEN gc) { return gmael(gc, 10, 3); }
2990 : INLINE GEN
2991 3321 : gchar_get_m0(GEN gc) { return gel(gc, 11); }
2992 : INLINE GEN
2993 4267 : gchar_get_u0(GEN gc) { return gel(gc, 12); }
2994 : INLINE long
2995 17416 : gchar_get_r1(GEN gc) { return nf_get_r1(gchar_get_nf(gc)); }
2996 : INLINE long
2997 623 : gchar_get_r2(GEN gc) { return nf_get_r2(gchar_get_nf(gc)); }
2998 : INLINE GEN
2999 50347 : gchar_get_loccyc(GEN gc) { return locs_get_cyc(gchar_get_zm(gc)); }
3000 : INLINE long
3001 37131 : gchar_get_nc(GEN gc) { return lg(gchar_get_loccyc(gc))-1; }
3002 : INLINE long
3003 36865 : gchar_get_ns(GEN gc) { return lg(gchar_get_S(gc))-1; }
3004 : INLINE long
3005 1841 : gchar_get_nm(GEN gc) { return lg(gchar_get_basis(gc))-1; }
3006 : INLINE long
3007 4011 : gchar_get_evalprec(GEN gc) { return gmael(gc, 8, 1)[1]; }
3008 : INLINE long
3009 18732 : gchar_get_prec(GEN gc) { return gmael(gc, 8, 1)[2]; }
3010 : INLINE long
3011 13419 : gchar_get_nfprec(GEN gc) { return gmael(gc, 8, 1)[3]; }
3012 : INLINE void
3013 1785 : gchar_set_evalprec(GEN gc, long prec) { gmael(gc, 8, 1)[1] = prec; }
3014 : INLINE void
3015 1202 : gchar_set_prec(GEN gc, long prec) { gmael(gc, 8, 1)[2] = prec; }
3016 : INLINE void
3017 1202 : gchar_copy_precs(GEN gc, GEN gc2)
3018 : {
3019 1202 : gel(gc2, 8) = shallowcopy(gel(gc,8));
3020 1202 : gmael(gc2, 8, 1) = shallowcopy(gmael(gc, 8, 1));
3021 1202 : }
3022 : INLINE void
3023 2950 : gchar_set_nfprec(GEN gc, long prec) { gmael(gc, 8, 1)[3] = prec; }
3024 : INLINE long
3025 322 : gchar_get_ntors(GEN gc) { return gmael(gc, 8, 2)[1]; }
3026 : INLINE long
3027 322 : gchar_get_nfree(GEN gc) { return gmael(gc, 8, 2)[2]; }
3028 : INLINE long
3029 2042 : gchar_get_nalg(GEN gc) { return gmael(gc, 8, 2)[3]; }
3030 : INLINE void
3031 1573 : gchar_set_basis(GEN gc, GEN m_inv) { gel(gc, 1) = m_inv; }
3032 : INLINE void
3033 2077 : gchar_set_nf(GEN gc, GEN nf) { gel(gc, 3) = nf; }
3034 : INLINE void
3035 623 : gchar_set_ntors(GEN gc, long n) { gmael(gc, 8, 2)[1] = n; }
3036 : INLINE void
3037 623 : gchar_set_nfree(GEN gc, long n) { gmael(gc, 8, 2)[2] = n; }
3038 : INLINE void
3039 623 : gchar_set_nalg(GEN gc, long n) { gmael(gc, 8, 2)[3] = n; }
3040 : INLINE void
3041 1573 : gchar_set_cyc(GEN gc, GEN cyc) { gel(gc, 9) = cyc; }
3042 : INLINE void
3043 623 : gchar_set_HUUi(GEN gc, GEN hnf, GEN U, GEN Ui) { gel(gc, 10) = mkvec3(hnf, U, Ui); }
3044 : INLINE void
3045 950 : gchar_set_m0(GEN gc, GEN m0) { gel(gc, 11) = m0; }
3046 : INLINE void
3047 2093 : gchar_set_u0(GEN gc, GEN u0) { gel(gc, 12) = u0; }
3048 :
3049 : INLINE GEN
3050 1386556 : bid_get_mod(GEN bid) { return gel(bid,1); }
3051 : INLINE GEN
3052 78295 : bid_get_ideal(GEN bid) { return gmael(bid,1,1); }
3053 : INLINE GEN
3054 35098 : bid_get_arch(GEN bid) { return gmael(bid,1,2); }
3055 : INLINE GEN
3056 5415498 : bid_get_grp(GEN bid) { return gel(bid,2); }
3057 : INLINE GEN
3058 2313944 : bid_get_fact(GEN bid) { return gmael(bid,3,1); }
3059 : INLINE GEN
3060 2025283 : bid_get_fact2(GEN bid) { return gmael(bid,3,2); }
3061 : INLINE GEN
3062 1990743 : bid_get_MOD(GEN bid) { GEN y = gel(bid,4); return lg(y) == 4? gel(y,3): NULL; }
3063 : INLINE GEN
3064 1991473 : bid_get_sprk(GEN bid) { return gmael(bid,4,1); }
3065 : INLINE GEN
3066 51226 : bid_get_sarch(GEN bid) { return gmael(bid,4,2); }
3067 : INLINE GEN
3068 2217789 : bid_get_archp(GEN bid) { return gmael3(bid,4,2,2); }
3069 : INLINE GEN
3070 3378355 : bid_get_U(GEN bid) { return gel(bid,5); }
3071 : INLINE GEN
3072 0 : bid_get_no(GEN bid) { return abgrp_get_no(bid_get_grp(bid)); }
3073 : INLINE GEN
3074 5361588 : bid_get_cyc(GEN bid) { return abgrp_get_cyc(bid_get_grp(bid)); }
3075 : INLINE GEN
3076 0 : bid_get_gen_nocheck(GEN bid) { return abgrp_get_gen(bid_get_grp(bid)); }
3077 : INLINE GEN
3078 53333 : bid_get_gen(GEN bid) {
3079 53333 : GEN G = bid_get_grp(bid);
3080 53333 : if (lg(G) != 4) pari_err(e_MISC,"missing bid generators. Use idealstar(,,2)");
3081 53333 : return abgrp_get_gen(G);
3082 : }
3083 :
3084 : INLINE GEN
3085 34544862 : znstar_get_N(GEN G) { return gmael(G,1,1); }
3086 : INLINE GEN
3087 7211010 : znstar_get_faN(GEN G) { return gel(G,3); }
3088 : INLINE GEN
3089 14 : znstar_get_no(GEN G) { return abgrp_get_no(gel(G,2)); }
3090 : INLINE GEN
3091 261976 : znstar_get_cyc(GEN G) { return abgrp_get_cyc(gel(G,2)); }
3092 : INLINE GEN
3093 16150 : znstar_get_gen(GEN G) { return abgrp_get_gen(gel(G,2)); }
3094 : INLINE GEN
3095 7824104 : znstar_get_conreycyc(GEN G) { return gmael(G,4,5); }
3096 : INLINE GEN
3097 3221821 : znstar_get_conreygen(GEN G) { return gmael(G,4,4); }
3098 : INLINE GEN
3099 46788 : znstar_get_Ui(GEN G) { return gmael(G,4,3); }
3100 : INLINE GEN
3101 176051 : znstar_get_U(GEN G) { return gel(G,5); }
3102 : INLINE GEN
3103 2820777 : znstar_get_pe(GEN G) { return gmael(G,4,1); }
3104 : INLINE GEN
3105 36112 : gal_get_pol(GEN gal) { return gel(gal,1); }
3106 : INLINE GEN
3107 6020 : gal_get_p(GEN gal) { return gmael(gal,2,1); }
3108 : INLINE GEN
3109 91 : gal_get_e(GEN gal) { return gmael(gal,2,2); }
3110 : INLINE GEN
3111 23772 : gal_get_mod(GEN gal) { return gmael(gal,2,3); }
3112 : INLINE GEN
3113 32528 : gal_get_roots(GEN gal) { return gel(gal,3); }
3114 : INLINE GEN
3115 27656 : gal_get_invvdm(GEN gal) { return gel(gal,4); }
3116 : INLINE GEN
3117 27650 : gal_get_den(GEN gal) { return gel(gal,5); }
3118 : INLINE GEN
3119 80170 : gal_get_group(GEN gal) { return gel(gal,6); }
3120 : INLINE GEN
3121 15435 : gal_get_gen(GEN gal) { return gel(gal,7); }
3122 : INLINE GEN
3123 6664 : gal_get_orders(GEN gal) { return gel(gal,8); }
3124 :
3125 : /* assume rnf a genuine rnf */
3126 : INLINE long
3127 2506083 : rnf_get_degree(GEN rnf) { return degpol(rnf_get_pol(rnf)); }
3128 : INLINE long
3129 21217 : rnf_get_nfdegree(GEN rnf) { return degpol(nf_get_pol(rnf_get_nf(rnf))); }
3130 : INLINE long
3131 1392746 : rnf_get_absdegree(GEN rnf) { return degpol(gmael(rnf,11,1)); }
3132 : INLINE GEN
3133 1386 : rnf_get_idealdisc(GEN rnf) { return gmael(rnf,3,1); }
3134 : INLINE GEN
3135 1225 : rnf_get_k(GEN rnf) { return gmael(rnf,11,3); }
3136 : INLINE GEN
3137 1204 : rnf_get_alpha(GEN rnf) { return gmael(rnf, 11, 2); }
3138 : INLINE GEN
3139 733698 : rnf_get_nf(GEN rnf) { return gel(rnf,10); }
3140 : INLINE GEN
3141 6559 : rnf_get_nfzk(GEN rnf) { return gel(rnf,2); }
3142 : INLINE GEN
3143 314482 : rnf_get_polabs(GEN rnf) { return gmael(rnf,11,1); }
3144 : INLINE GEN
3145 2844933 : rnf_get_pol(GEN rnf) { return gel(rnf,1); }
3146 : INLINE GEN
3147 350 : rnf_get_disc(GEN rnf) { return gel(rnf,3); }
3148 : INLINE GEN
3149 105 : rnf_get_index(GEN rnf) { return gel(rnf,4); }
3150 : INLINE GEN
3151 2611 : rnf_get_ramified_primes(GEN rnf) { return gel(rnf,5); }
3152 : INLINE long
3153 574 : rnf_get_varn(GEN rnf) { return varn(gel(rnf,1)); }
3154 : INLINE GEN
3155 255354 : rnf_get_nfpol(GEN rnf) { return gmael(rnf,10,1); }
3156 : INLINE long
3157 4886 : rnf_get_nfvarn(GEN rnf) { return varn(gmael(rnf,10,1)); }
3158 : INLINE GEN
3159 4592 : rnf_get_zk(GEN rnf) { return gel(rnf,7); }
3160 : INLINE GEN
3161 135183 : rnf_get_map(GEN rnf) { return gel(rnf,11); }
3162 : INLINE GEN
3163 1225 : rnf_get_invzk(GEN rnf) { return gel(rnf,8); }
3164 :
3165 : INLINE GEN
3166 138519 : idealred(GEN nf, GEN id) { return idealred0(nf, id, NULL); }
3167 :
3168 : INLINE GEN
3169 5427 : idealchineseinit(GEN nf, GEN x)
3170 5427 : { return idealchinese(nf,x,NULL); }
3171 :
3172 : /*******************************************************************/
3173 : /* */
3174 : /* CLOSURES */
3175 : /* */
3176 : /*******************************************************************/
3177 368052919 : INLINE long closure_arity(GEN C) { return ((ulong)C[1])&ARITYBITS; }
3178 40098206 : INLINE long closure_is_variadic(GEN C) { return !!(((ulong)C[1])&VARARGBITS); }
3179 319336337 : INLINE const char *closure_codestr(GEN C) { return GSTR(gel(C,2))-1; }
3180 0 : INLINE GEN closure_get_code(GEN C) { return gel(C,2); }
3181 319310213 : INLINE GEN closure_get_oper(GEN C) { return gel(C,3); }
3182 319280756 : INLINE GEN closure_get_data(GEN C) { return gel(C,4); }
3183 13523 : INLINE GEN closure_get_dbg(GEN C) { return gel(C,5); }
3184 36855 : INLINE GEN closure_get_text(GEN C) { return gel(C,6); }
3185 13052221 : INLINE GEN closure_get_frame(GEN C) { return gel(C,7); }
3186 :
3187 : /*******************************************************************/
3188 : /* */
3189 : /* ERRORS */
3190 : /* */
3191 : /*******************************************************************/
3192 : INLINE long
3193 62334 : err_get_num(GEN e) { return e[1]; }
3194 : INLINE GEN
3195 294 : err_get_compo(GEN e, long i) { return gel(e, i+1); }
3196 :
3197 : INLINE void
3198 14 : pari_err_BUG(const char *f) { pari_err(e_BUG,f); }
3199 : INLINE void
3200 21 : pari_err_CONSTPOL(const char *f) { pari_err(e_CONSTPOL, f); }
3201 : INLINE void
3202 84 : pari_err_COPRIME(const char *f, GEN x, GEN y) { pari_err(e_COPRIME, f,x,y); }
3203 : INLINE void
3204 718 : pari_err_DIM(const char *f) { pari_err(e_DIM, f); }
3205 : INLINE void
3206 0 : pari_err_FILE(const char *f, const char *g) { pari_err(e_FILE, f,g); }
3207 : INLINE void
3208 36 : pari_err_FILEDESC(const char *f, long n) { pari_err(e_FILEDESC, f,n); }
3209 : INLINE void
3210 98 : pari_err_FLAG(const char *f) { pari_err(e_FLAG,f); }
3211 : INLINE void
3212 539 : pari_err_IMPL(const char *f) { pari_err(e_IMPL,f); }
3213 : INLINE void
3214 20018 : pari_err_INV(const char *f, GEN x) { pari_err(e_INV,f,x); }
3215 : INLINE void
3216 63 : pari_err_IRREDPOL(const char *f, GEN x) { pari_err(e_IRREDPOL, f,x); }
3217 : INLINE void
3218 2771 : 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); }
3219 : INLINE void
3220 214 : pari_err_COMPONENT(const char *f, const char *op, GEN l, GEN x) { pari_err(e_COMPONENT, f,op,l,x); }
3221 : INLINE void
3222 0 : pari_err_MAXPRIME(ulong c) { pari_err(e_MAXPRIME, c); }
3223 : INLINE void
3224 406 : pari_err_OP(const char *f, GEN x, GEN y) { pari_err(e_OP, f,x,y); }
3225 : INLINE void
3226 156 : pari_err_OVERFLOW(const char *f) { pari_err(e_OVERFLOW, f); }
3227 : INLINE void
3228 238 : pari_err_PREC(const char *f) { pari_err(e_PREC,f); }
3229 : INLINE void
3230 0 : pari_err_PACKAGE(const char *f) { pari_err(e_PACKAGE,f); }
3231 : INLINE void
3232 98 : pari_err_PRIME(const char *f, GEN x) { pari_err(e_PRIME, f,x); }
3233 : INLINE void
3234 1316 : pari_err_MODULUS(const char *f, GEN x, GEN y) { pari_err(e_MODULUS, f,x,y); }
3235 : INLINE void
3236 63 : pari_err_ROOTS0(const char *f) { pari_err(e_ROOTS0, f); }
3237 : INLINE void
3238 7084 : pari_err_SQRTN(const char *f, GEN x) { pari_err(e_SQRTN, f,x); }
3239 : INLINE void
3240 15384 : pari_err_TYPE(const char *f, GEN x) { pari_err(e_TYPE, f,x); }
3241 : INLINE void
3242 3493 : pari_err_TYPE2(const char *f, GEN x, GEN y) { pari_err(e_TYPE2, f,x,y); }
3243 : INLINE void
3244 371 : pari_err_VAR(const char *f, GEN x, GEN y) { pari_err(e_VAR, f,x,y); }
3245 : INLINE void
3246 238 : pari_err_PRIORITY(const char *f, GEN x, const char *op, long v)
3247 238 : { pari_err(e_PRIORITY, f,x,op,v); }
3248 :
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