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 retmkqfb(x,y,z,d)\
80 : do { GEN _v = cgetg(5, t_QFB);\
81 : gel(_v,1) = (x);\
82 : gel(_v,2) = (y);\
83 : gel(_v,3) = (z);\
84 : gel(_v,4) = (d); return _v; } while(0)
85 : #define retmkquad(x,y,z)\
86 : do { GEN _v = cgetg(4, t_QUAD);\
87 : gel(_v,1) = (x);\
88 : gel(_v,2) = (y);\
89 : gel(_v,3) = (z); return _v; } while(0)
90 : #define retmkvec4(x,y,z,t)\
91 : do { GEN _v = cgetg(5, t_VEC);\
92 : gel(_v,1) = (x);\
93 : gel(_v,2) = (y);\
94 : gel(_v,3) = (z);\
95 : gel(_v,4) = (t); return _v; } while(0)
96 : #define retmkvec5(x,y,z,t,u)\
97 : do { GEN _v = cgetg(6, t_VEC);\
98 : gel(_v,1) = (x);\
99 : gel(_v,2) = (y);\
100 : gel(_v,3) = (z);\
101 : gel(_v,4) = (t);\
102 : gel(_v,5) = (u); return _v; } while(0)
103 : #define retmkcol(x)\
104 : do { GEN _v = cgetg(2, t_COL);\
105 : gel(_v,1) = (x); return _v; } while(0)
106 : #define retmkcol2(x,y)\
107 : do { GEN _v = cgetg(3, t_COL);\
108 : gel(_v,1) = (x);\
109 : gel(_v,2) = (y); return _v; } while(0)
110 : #define retmkcol3(x,y,z)\
111 : do { GEN _v = cgetg(4, t_COL);\
112 : gel(_v,1) = (x);\
113 : gel(_v,2) = (y);\
114 : gel(_v,3) = (z); return _v; } while(0)
115 : #define retmkcol4(x,y,z,t)\
116 : do { GEN _v = cgetg(5, t_COL);\
117 : gel(_v,1) = (x);\
118 : gel(_v,2) = (y);\
119 : gel(_v,3) = (z);\
120 : gel(_v,4) = (t); return _v; } while(0)
121 : #define retmkcol5(x,y,z,t,u)\
122 : do { GEN _v = cgetg(6, t_COL);\
123 : gel(_v,1) = (x);\
124 : gel(_v,2) = (y);\
125 : gel(_v,3) = (z);\
126 : gel(_v,4) = (t);\
127 : gel(_v,5) = (u); return _v; } while(0)
128 : #define retmkcol6(x,y,z,t,u,v)\
129 : do { GEN _v = cgetg(7, t_COL);\
130 : gel(_v,1) = (x);\
131 : gel(_v,2) = (y);\
132 : gel(_v,3) = (z);\
133 : gel(_v,4) = (t);\
134 : gel(_v,5) = (u);\
135 : gel(_v,6) = (v); return _v; } while(0)
136 : #define retmkmat(x)\
137 : do { GEN _v = cgetg(2, t_MAT);\
138 : gel(_v,1) = (x); return _v; } while(0)
139 : #define retmkmat2(x,y)\
140 : do { GEN _v = cgetg(3, t_MAT);\
141 : gel(_v,1) = (x);\
142 : gel(_v,2) = (y); return _v; } while(0)
143 : #define retmkmat3(x,y,z)\
144 : do { GEN _v = cgetg(4, t_MAT);\
145 : gel(_v,1) = (x);\
146 : gel(_v,2) = (y);\
147 : gel(_v,3) = (z); return _v; } while(0)
148 : #define retmkmat4(x,y,z,t)\
149 : do { GEN _v = cgetg(5, t_MAT);\
150 : gel(_v,1) = (x);\
151 : gel(_v,2) = (y);\
152 : gel(_v,3) = (z);\
153 : gel(_v,4) = (t); return _v; } while(0)
154 : #define retmkmat5(x,y,z,t,u)\
155 : do { GEN _v = cgetg(6, t_MAT);\
156 : gel(_v,1) = (x);\
157 : gel(_v,2) = (y);\
158 : gel(_v,3) = (z);\
159 : gel(_v,4) = (t);\
160 : gel(_v,5) = (u); return _v; } while(0)
161 : #define retmkmat22(a,b,c,d)\
162 : do { GEN _v = cgetg(3, t_MAT);\
163 : gel(_v,1) = mkcol2(a,c);\
164 : gel(_v,2) = mkcol2(b,d); return _v; } while(0)
165 : INLINE GEN
166 8201267 : mkintmod(GEN x, GEN y) { retmkintmod(x,y); }
167 : INLINE GEN
168 1806 : mkintmodu(ulong x, ulong y) {
169 1806 : GEN v = cgetg(3,t_INTMOD);
170 1806 : gel(v,1) = utoipos(y);
171 1806 : gel(v,2) = utoi(x); return v;
172 : }
173 : INLINE GEN
174 2813524 : mkpolmod(GEN x, GEN y) { retmkpolmod(x,y); }
175 : INLINE GEN
176 33274801 : mkfrac(GEN x, GEN y) { retmkfrac(x,y); }
177 : INLINE GEN
178 1209507 : mkfracss(long x, long y) { retmkfrac(stoi(x),utoipos(y)); }
179 : /* q = n/d a t_FRAC or t_INT; recover (n,d) */
180 : INLINE void
181 19313 : Qtoss(GEN q, long *n, long *d)
182 : {
183 19313 : if (typ(q) == t_INT) { *n = itos(q); *d = 1; }
184 5761 : else { *n = itos(gel(q,1)); *d = itou(gel(q,2)); }
185 19313 : }
186 : INLINE GEN
187 1073513 : sstoQ(long n, long d)
188 : {
189 : ulong r;
190 : long g, q;
191 1073513 : if (!n)
192 : {
193 94318 : if (!d) pari_err_INV("sstoQ",gen_0);
194 94318 : return gen_0;
195 : }
196 979195 : if (d < 0) { d = -d; n = -n; }
197 979195 : if (d == 1) return stoi(n);
198 959882 : r = labs(n);
199 959882 : if (r == 1) retmkfrac(n > 0? gen_1: gen_m1, utoipos(d));
200 910161 : q = udivuu_rem(r, d, &r);
201 910161 : if (!r) return n > 0? utoipos(q): utoineg(q);
202 855274 : g = ugcd(d,r); /* gcd(n,d) */
203 855274 : if (g != 1) { n /= g; d /= g; }
204 855274 : retmkfrac(stoi(n), utoipos(d));
205 : }
206 :
207 : INLINE GEN
208 158054726 : uutoQ(ulong n, ulong d)
209 : {
210 : ulong r;
211 : long g, q;
212 158054726 : if (!n)
213 : {
214 38108 : if (!d) pari_err_INV("uutoQ",gen_0);
215 38108 : return gen_0;
216 : }
217 158016618 : if (d == 1) return utoipos(n);
218 158005516 : if (n == 1) retmkfrac(gen_1, utoipos(d));
219 157916589 : q = udivuu_rem(n,d,&r);
220 157916589 : if (!r) return utoipos(q);
221 5178542 : g = ugcd(d,r); /* gcd(n,d) */
222 5178542 : if (g != 1) { n /= g; d /= g; }
223 5178542 : retmkfrac(utoipos(n), utoipos(d));
224 : }
225 :
226 : INLINE GEN
227 4739651 : mkfraccopy(GEN x, GEN y) { retmkfrac(icopy(x), icopy(y)); }
228 : INLINE GEN
229 698138 : mkrfrac(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
230 698138 : gel(v,1) = x; gel(v,2) = y; return v; }
231 : INLINE GEN
232 14 : mkrfraccopy(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
233 14 : gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
234 : INLINE GEN
235 89876402 : mkcomplex(GEN x, GEN y) { retmkcomplex(x,y); }
236 : INLINE GEN
237 1266804 : gen_I(void) { return mkcomplex(gen_0, gen_1); }
238 : INLINE GEN
239 981723 : cgetc(long l) { retmkcomplex(cgetr(l), cgetr(l)); }
240 : INLINE GEN
241 69132 : mkquad(GEN n, GEN x, GEN y) { GEN v = cgetg(4, t_QUAD);
242 69132 : gel(v,1) = n; gel(v,2) = x; gel(v,3) = y; return v; }
243 : /* vecsmall */
244 : INLINE GEN
245 126159869 : mkvecsmall(long x) { GEN v = cgetg(2, t_VECSMALL); v[1] = x; return v; }
246 : INLINE GEN
247 221358913 : mkvecsmall2(long x,long y) { GEN v = cgetg(3, t_VECSMALL);
248 221375311 : v[1]=x; v[2]=y; return v; }
249 : INLINE GEN
250 94463444 : mkvecsmall3(long x,long y,long z) { GEN v = cgetg(4, t_VECSMALL);
251 94462652 : v[1]=x; v[2]=y; v[3]=z; return v; }
252 : INLINE GEN
253 15292911 : mkvecsmall4(long x,long y,long z,long t) { GEN v = cgetg(5, t_VECSMALL);
254 15296984 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; return v; }
255 : INLINE GEN
256 669638 : mkvecsmall5(long x,long y,long z,long t,long u) { GEN v = cgetg(6, t_VECSMALL);
257 669638 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; v[5]=u; return v; }
258 :
259 : INLINE GEN
260 27654902 : mkqfb(GEN x, GEN y, GEN z, GEN d) { retmkqfb(x,y,z,d); }
261 : /* vec */
262 : INLINE GEN
263 64865031 : mkvec(GEN x) { retmkvec(x); }
264 : INLINE GEN
265 180524569 : mkvec2(GEN x, GEN y) { retmkvec2(x,y); }
266 : INLINE GEN
267 126941791 : mkvec3(GEN x, GEN y, GEN z) { retmkvec3(x,y,z); }
268 : INLINE GEN
269 6553302 : mkvec4(GEN x, GEN y, GEN z, GEN t) { retmkvec4(x,y,z,t); }
270 : INLINE GEN
271 14158519 : mkvec5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkvec5(x,y,z,t,u); }
272 : INLINE GEN
273 161 : mkvecs(long x) { retmkvec(stoi(x)); }
274 : INLINE GEN
275 213248 : mkvec2s(long x, long y) { retmkvec2(stoi(x),stoi(y)); }
276 : INLINE GEN
277 524441 : mkvec3s(long x, long y, long z) { retmkvec3(stoi(x),stoi(y),stoi(z)); }
278 : INLINE GEN
279 21 : mkvec4s(long x, long y, long z, long t) { retmkvec4(stoi(x),stoi(y),stoi(z),stoi(t)); }
280 : INLINE GEN
281 121947 : mkveccopy(GEN x) { GEN v = cgetg(2, t_VEC); gel(v,1) = gcopy(x); return v; }
282 : INLINE GEN
283 119997 : mkvec2copy(GEN x, GEN y) {
284 119997 : GEN v = cgetg(3,t_VEC); gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
285 : /* col */
286 : INLINE GEN
287 10159913 : mkcol(GEN x) { retmkcol(x); }
288 : INLINE GEN
289 154321325 : mkcol2(GEN x, GEN y) { retmkcol2(x,y); }
290 : INLINE GEN
291 87642 : mkcol3(GEN x, GEN y, GEN z) { retmkcol3(x,y,z); }
292 : INLINE GEN
293 102935 : mkcol4(GEN x, GEN y, GEN z, GEN t) { retmkcol4(x,y,z,t); }
294 : INLINE GEN
295 101 : mkcol5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkcol5(x,y,z,t,u); }
296 : INLINE GEN
297 232050 : mkcol6(GEN x, GEN y, GEN z, GEN t, GEN u, GEN v) { retmkcol6(x,y,z,t,u,v); }
298 : INLINE GEN
299 40411 : mkcols(long x) { retmkcol(stoi(x)); }
300 : INLINE GEN
301 4414032 : mkcol2s(long x, long y) { retmkcol2(stoi(x),stoi(y)); }
302 : INLINE GEN
303 308 : mkcol3s(long x, long y, long z) { retmkcol3(stoi(x),stoi(y),stoi(z)); }
304 : INLINE GEN
305 0 : mkcol4s(long x, long y, long z, long t) { retmkcol4(stoi(x),stoi(y),stoi(z),stoi(t)); }
306 : INLINE GEN
307 29494 : mkcolcopy(GEN x) { GEN v = cgetg(2, t_COL); gel(v,1) = gcopy(x); return v; }
308 : /* mat */
309 : INLINE GEN
310 4575240 : mkmat(GEN x) { retmkmat(x); }
311 : INLINE GEN
312 31639572 : mkmat2(GEN x, GEN y) { retmkmat2(x,y); }
313 : INLINE GEN
314 16777 : mkmat3(GEN x, GEN y, GEN z) { retmkmat3(x,y,z); }
315 : INLINE GEN
316 0 : mkmat4(GEN x, GEN y, GEN z, GEN t) { retmkmat4(x,y,z,t); }
317 : INLINE GEN
318 0 : mkmat5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkmat5(x,y,z,t,u); }
319 : INLINE GEN
320 112276 : mkmatcopy(GEN x) { GEN v = cgetg(2, t_MAT); gel(v,1) = gcopy(x); return v; }
321 : INLINE GEN
322 0 : mkerr(long x) { GEN v = cgetg(2, t_ERROR); v[1] = x; return v; }
323 : INLINE GEN
324 200959 : mkoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
325 : INLINE GEN
326 103548 : mkmoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
327 : INLINE long
328 316822 : inf_get_sign(GEN x) { return signe(gel(x,1)); }
329 : INLINE GEN
330 206822 : mkmat22s(long a, long b, long c, long d) {retmkmat2(mkcol2s(a,c),mkcol2s(b,d));}
331 : INLINE GEN
332 50571970 : mkmat22(GEN a, GEN b, GEN c, GEN d) { retmkmat2(mkcol2(a,c),mkcol2(b,d)); }
333 :
334 : /* pol */
335 : INLINE GEN
336 2688492 : pol_x(long v) {
337 2688492 : GEN p = cgetg(4, t_POL);
338 2688489 : p[1] = evalsigne(1)|evalvarn(v);
339 2688489 : gel(p,2) = gen_0;
340 2688489 : gel(p,3) = gen_1; return p;
341 : }
342 : /* x^n, assume n >= 0 */
343 : INLINE GEN
344 2222628 : pol_xn(long n, long v) {
345 2222628 : long i, a = n+2;
346 2222628 : GEN p = cgetg(a+1, t_POL);
347 2222630 : p[1] = evalsigne(1)|evalvarn(v);
348 5324123 : for (i = 2; i < a; i++) gel(p,i) = gen_0;
349 2222630 : gel(p,a) = gen_1; return p;
350 : }
351 : /* x^n, no assumption on n */
352 : INLINE GEN
353 294 : pol_xnall(long n, long v)
354 : {
355 294 : if (n < 0) retmkrfrac(gen_1, pol_xn(-n,v));
356 287 : return pol_xn(n, v);
357 : }
358 : /* x^n, assume n >= 0 */
359 : INLINE GEN
360 371 : polxn_Flx(long n, long sv) {
361 371 : long i, a = n+2;
362 371 : GEN p = cgetg(a+1, t_VECSMALL);
363 371 : p[1] = sv;
364 1806 : for (i = 2; i < a; i++) p[i] = 0;
365 371 : p[a] = 1; return p;
366 : }
367 : INLINE GEN
368 4465986 : pol_1(long v) {
369 4465986 : GEN p = cgetg(3, t_POL);
370 4465982 : p[1] = evalsigne(1)|evalvarn(v);
371 4465982 : gel(p,2) = gen_1; return p;
372 : }
373 : INLINE GEN
374 35204392 : pol_0(long v)
375 : {
376 35204392 : GEN x = cgetg(2,t_POL);
377 35204399 : x[1] = evalvarn(v); return x;
378 : }
379 : #define retconst_vec(n,x)\
380 : do { long _i, _n = (n);\
381 : GEN _v = cgetg(_n+1, t_VEC), _x = (x);\
382 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
383 : return _v; } while(0)
384 : INLINE GEN
385 231141726 : const_vec(long n, GEN x) { retconst_vec(n, x); }
386 : #define retconst_col(n,x)\
387 : do { long _i, _n = (n);\
388 : GEN _v = cgetg(_n+1, t_COL), _x = (x);\
389 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
390 : return _v; } while(0)
391 : INLINE GEN
392 37239843 : const_col(long n, GEN x) { retconst_col(n, x); }
393 : INLINE GEN
394 18636914 : const_vecsmall(long n, long c)
395 : {
396 : long i;
397 18636914 : GEN V = cgetg(n+1,t_VECSMALL);
398 751436468 : for(i=1;i<=n;i++) V[i] = c;
399 18637496 : return V;
400 : }
401 :
402 : /*** ZERO ***/
403 : /* O(p^e) */
404 : INLINE GEN
405 856055 : zeropadic(GEN p, long e)
406 : {
407 856055 : GEN y = cgetg(5,t_PADIC);
408 856057 : gel(y,4) = gen_0;
409 856057 : gel(y,3) = gen_1;
410 856057 : gel(y,2) = icopy(p);
411 855959 : y[1] = evalvalp(e) | _evalprecp(0);
412 855957 : return y;
413 : }
414 : INLINE GEN
415 15337 : zeropadic_shallow(GEN p, long e)
416 : {
417 15337 : GEN y = cgetg(5,t_PADIC);
418 15337 : gel(y,4) = gen_0;
419 15337 : gel(y,3) = gen_1;
420 15337 : gel(y,2) = p;
421 15337 : y[1] = evalvalp(e) | _evalprecp(0);
422 15337 : return y;
423 : }
424 : /* O(pol_x(v)^e) */
425 : INLINE GEN
426 138796 : zeroser(long v, long e)
427 : {
428 138796 : GEN x = cgetg(2, t_SER);
429 138796 : x[1] = evalvalser(e) | evalvarn(v); return x;
430 : }
431 : INLINE int
432 10128087 : ser_isexactzero(GEN x)
433 : {
434 10128087 : if (!signe(x)) switch(lg(x))
435 : {
436 132853 : case 2: return 1;
437 4641 : case 3: return isexactzero(gel(x,2));
438 : }
439 9990593 : return 0;
440 : }
441 : /* 0 * pol_x(v) */
442 : INLINE GEN
443 14735393 : zeropol(long v) { return pol_0(v); }
444 : /* vector(n) */
445 : INLINE GEN
446 118689445 : zerocol(long n)
447 : {
448 118689445 : GEN y = cgetg(n+1,t_COL);
449 795253461 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
450 118690278 : return y;
451 : }
452 : /* vectorv(n) */
453 : INLINE GEN
454 25905342 : zerovec(long n)
455 : {
456 25905342 : GEN y = cgetg(n+1,t_VEC);
457 344819804 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
458 25905325 : return y;
459 : }
460 : /* matrix(m, n) */
461 : INLINE GEN
462 92530 : zeromat(long m, long n)
463 : {
464 92530 : GEN y = cgetg(n+1,t_MAT);
465 92529 : GEN v = zerocol(m);
466 315484 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
467 92534 : return y;
468 : }
469 : /* = zero_zx, sv is a evalvarn()*/
470 : INLINE GEN
471 1334647 : zero_Flx(long sv) { return pol0_Flx(sv); }
472 : INLINE GEN
473 60688967 : zero_Flv(long n)
474 : {
475 60688967 : GEN y = cgetg(n+1,t_VECSMALL);
476 951003614 : long i; for (i=1; i<=n; i++) y[i] = 0;
477 60689189 : return y;
478 : }
479 : /* matrix(m, n) */
480 : INLINE GEN
481 2684934 : zero_Flm(long m, long n)
482 : {
483 2684934 : GEN y = cgetg(n+1,t_MAT);
484 2684922 : GEN v = zero_Flv(m);
485 17066448 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
486 2684918 : return y;
487 : }
488 : /* matrix(m, n) */
489 : INLINE GEN
490 231825 : zero_Flm_copy(long m, long n)
491 : {
492 231825 : GEN y = cgetg(n+1,t_MAT);
493 2396352 : long i; for (i=1; i<=n; i++) gel(y,i) = zero_Flv(m);
494 231833 : return y;
495 : }
496 :
497 : INLINE GEN
498 3517702 : zero_F2v(long m)
499 : {
500 3517702 : long l = nbits2nlong(m);
501 3517689 : GEN v = zero_Flv(l+1);
502 3517681 : v[1] = m;
503 3517681 : return v;
504 : }
505 :
506 : INLINE GEN
507 0 : zero_F2m(long m, long n)
508 : {
509 : long i;
510 0 : GEN M = cgetg(n+1, t_MAT);
511 0 : GEN v = zero_F2v(m);
512 0 : for (i = 1; i <= n; i++)
513 0 : gel(M,i) = v;
514 0 : return M;
515 : }
516 :
517 :
518 : INLINE GEN
519 833997 : zero_F2m_copy(long m, long n)
520 : {
521 : long i;
522 833997 : GEN M = cgetg(n+1, t_MAT);
523 1983061 : for (i = 1; i <= n; i++)
524 1149070 : gel(M,i)= zero_F2v(m);
525 833991 : return M;
526 : }
527 :
528 : /* matrix(m, n) */
529 : INLINE GEN
530 13878380 : zeromatcopy(long m, long n)
531 : {
532 13878380 : GEN y = cgetg(n+1,t_MAT);
533 70229299 : long i; for (i=1; i<=n; i++) gel(y,i) = zerocol(m);
534 13878416 : return y;
535 : }
536 :
537 : INLINE GEN
538 24429 : zerovec_block(long len)
539 : {
540 : long i;
541 24429 : GEN blk = cgetg_block(len + 1, t_VEC);
542 806157 : for (i = 1; i <= len; ++i)
543 781728 : gel(blk, i) = gen_0;
544 24429 : return blk;
545 : }
546 :
547 : /* i-th vector in the standard basis */
548 : INLINE GEN
549 5625012 : col_ei(long n, long i) { GEN e = zerocol(n); gel(e,i) = gen_1; return e; }
550 : INLINE GEN
551 1699595 : vec_ei(long n, long i) { GEN e = zerovec(n); gel(e,i) = gen_1; return e; }
552 : INLINE GEN
553 42 : F2v_ei(long n, long i) { GEN e = zero_F2v(n); F2v_set(e,i); return e; }
554 : INLINE GEN
555 50058 : vecsmall_ei(long n, long i) { GEN e = zero_zv(n); e[i] = 1; return e; }
556 : INLINE GEN
557 1243338 : Rg_col_ei(GEN x, long n, long i) { GEN e = zerocol(n); gel(e,i) = x; return e; }
558 :
559 : INLINE GEN
560 19514680 : shallowcopy(GEN x)
561 19514680 : { return typ(x) == t_MAT ? RgM_shallowcopy(x): leafcopy(x); }
562 :
563 : /* routines for naive growarrays */
564 : INLINE GEN
565 11707343 : vectrunc_init(long l)
566 : {
567 11707343 : GEN z = new_chunk(l);
568 11707113 : z[0] = evaltyp(t_VEC) | _evallg(1); return z;
569 : }
570 : INLINE GEN
571 391664 : coltrunc_init(long l)
572 : {
573 391664 : GEN z = new_chunk(l);
574 391664 : z[0] = evaltyp(t_COL) | _evallg(1); return z;
575 : }
576 : INLINE void
577 316872936 : lg_increase(GEN x) { x[0]++; }
578 : INLINE void
579 15233045 : vectrunc_append(GEN x, GEN t) { gel(x, lg(x)) = t; lg_increase(x); }
580 : INLINE void
581 10864 : vectrunc_append_batch(GEN x, GEN y)
582 : {
583 10864 : long i, l = lg(x), ly = lg(y);
584 10864 : GEN z = x + l-1;
585 36358 : for (i = 1; i < ly; i++) gel(z,i) = gel(y,i);
586 10864 : setlg(x, l+ly-1);
587 10864 : }
588 : INLINE GEN
589 189720970 : vecsmalltrunc_init(long l)
590 : {
591 189720970 : GEN z = new_chunk(l);
592 189753894 : z[0] = evaltyp(t_VECSMALL) | _evallg(1); return z;
593 : }
594 : INLINE void
595 99940235 : vecsmalltrunc_append(GEN x, long t) { x[ lg(x) ] = t; lg_increase(x); }
596 :
597 : /*******************************************************************/
598 : /* */
599 : /* STRING HASH FUNCTIONS */
600 : /* */
601 : /*******************************************************************/
602 : INLINE ulong
603 2641954 : hash_str(const char *str)
604 : {
605 2641954 : ulong hash = 5381UL, c;
606 27347397 : while ( (c = (ulong)*str++) )
607 24705443 : hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
608 2641954 : return hash;
609 : }
610 : INLINE ulong
611 18162283 : hash_str_len(const char *str, long len)
612 : {
613 18162283 : ulong hash = 5381UL;
614 : long i;
615 164929453 : for (i = 0; i < len; i++)
616 : {
617 146767170 : ulong c = (ulong)*str++;
618 146767170 : hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
619 : }
620 18162283 : return hash;
621 : }
622 :
623 : /*******************************************************************/
624 : /* */
625 : /* VEC / COL / VECSMALL */
626 : /* */
627 : /*******************************************************************/
628 : /* shallow*/
629 : INLINE GEN
630 11543 : vec_shorten(GEN v, long n)
631 : {
632 11543 : GEN V = cgetg(n+1, t_VEC);
633 : long i;
634 12999 : for(i = 1; i <= n; i++) gel(V,i) = gel(v,i);
635 11543 : return V;
636 : }
637 : /* shallow*/
638 : INLINE GEN
639 18927 : vec_lengthen(GEN v, long n)
640 : {
641 18927 : GEN V = cgetg(n+1, t_VEC);
642 18927 : long i, l = lg(v);
643 1935611 : for(i = 1; i < l; i++) gel(V,i) = gel(v,i);
644 18927 : return V;
645 : }
646 : /* shallow*/
647 : INLINE GEN
648 3426720 : vec_append(GEN V, GEN s)
649 : {
650 3426720 : long i, l2 = lg(V);
651 3426720 : GEN res = cgetg(l2+1, typ(V));
652 10712670 : for (i = 1; i < l2; i++) gel(res, i) = gel(V,i);
653 3426704 : gel(res,l2) = s; return res;
654 : }
655 : /* shallow*/
656 : INLINE GEN
657 300769 : vec_prepend(GEN v, GEN s)
658 : {
659 300769 : long i, l = lg(v);
660 300769 : GEN w = cgetg(l+1, typ(v));
661 300767 : gel(w,1) = s;
662 768503 : for (i = 2; i <= l; i++) gel(w,i) = gel(v,i-1);
663 300767 : return w;
664 : }
665 : /* shallow*/
666 : INLINE GEN
667 0 : vec_setconst(GEN v, GEN x)
668 : {
669 0 : long i, l = lg(v);
670 0 : for (i = 1; i < l; i++) gel(v,i) = x;
671 0 : return v;
672 : }
673 : INLINE GEN
674 72479 : vecsmall_shorten(GEN v, long n)
675 : {
676 72479 : GEN V = cgetg(n+1,t_VECSMALL);
677 : long i;
678 889648 : for(i = 1; i <= n; i++) V[i] = v[i];
679 72478 : return V;
680 : }
681 : INLINE GEN
682 505 : vecsmall_lengthen(GEN v, long n)
683 : {
684 505 : long i, l = lg(v);
685 505 : GEN V = cgetg(n+1,t_VECSMALL);
686 46147 : for(i = 1; i < l; i++) V[i] = v[i];
687 505 : return V;
688 : }
689 :
690 : INLINE GEN
691 4013224 : vec_to_vecsmall(GEN x)
692 18852131 : { pari_APPLY_long(itos(gel(x,i))) }
693 : INLINE GEN
694 509066 : vecsmall_to_vec(GEN x)
695 7065210 : { pari_APPLY_type(t_VEC, stoi(x[i])) }
696 : INLINE GEN
697 3262 : vecsmall_to_vec_inplace(GEN z)
698 : {
699 3262 : long i, l = lg(z);
700 79436 : for (i=1; i<l; i++) gel(z,i) = stoi(z[i]);
701 3262 : settyp(z, t_VEC); return z;
702 : }
703 : INLINE GEN
704 7687512 : vecsmall_to_col(GEN x)
705 59425439 : { pari_APPLY_type(t_COL, stoi(x[i])) }
706 :
707 : INLINE int
708 7208553 : vecsmall_lexcmp(GEN x, GEN y)
709 : {
710 : long lx,ly,l,i;
711 7208553 : lx = lg(x);
712 7208553 : ly = lg(y); l = minss(lx,ly);
713 30644488 : for (i=1; i<l; i++)
714 29017624 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
715 1626864 : if (lx == ly) return 0;
716 30578 : return (lx < ly)? -1 : 1;
717 : }
718 :
719 : INLINE int
720 108088071 : vecsmall_prefixcmp(GEN x, GEN y)
721 : {
722 108088071 : long i, lx = lg(x), ly = lg(y), l = minss(lx,ly);
723 542691324 : for (i=1; i<l; i++)
724 519806035 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
725 22885289 : return 0;
726 : }
727 :
728 : /*Can be used on t_VEC, but coeffs not gcopy-ed*/
729 : INLINE GEN
730 184938 : vecsmall_prepend(GEN V, long s)
731 : {
732 184938 : long i, l2 = lg(V);
733 184938 : GEN res = cgetg(l2+1, typ(V));
734 184938 : res[1] = s;
735 619564 : for (i = 2; i <= l2; ++i) res[i] = V[i - 1];
736 184938 : return res;
737 : }
738 :
739 : INLINE GEN
740 4059688 : vecsmall_append(GEN V, long s)
741 : {
742 4059688 : long i, l2 = lg(V);
743 4059688 : GEN res = cgetg(l2+1, t_VECSMALL);
744 5968369 : for (i = 1; i < l2; ++i) res[i] = V[i];
745 4059688 : res[l2] = s; return res;
746 : }
747 :
748 : INLINE GEN
749 1440607 : vecsmall_concat(GEN u, GEN v)
750 : {
751 1440607 : long i, l1 = lg(u)-1, l2 = lg(v)-1;
752 1440607 : GEN res = cgetg(l1+l2+1, t_VECSMALL);
753 11399039 : for (i = 1; i <= l1; ++i) res[i] = u[i];
754 14913126 : for (i = 1; i <= l2; ++i) res[i+l1] = v[i];
755 1440607 : return res;
756 : }
757 :
758 : /* return the number of indices where u and v are equal */
759 : INLINE long
760 0 : vecsmall_coincidence(GEN u, GEN v)
761 : {
762 0 : long i, s = 0, l = minss(lg(u),lg(v));
763 0 : for(i=1; i<l; i++)
764 0 : if(u[i] == v[i]) s++;
765 0 : return s;
766 : }
767 :
768 : /* returns the first index i<=n such that x=v[i] if it exists, 0 otherwise */
769 : INLINE long
770 84 : vecsmall_isin(GEN v, long x)
771 : {
772 84 : long i, l = lg(v);
773 125 : for (i = 1; i < l; i++)
774 82 : if (v[i] == x) return i;
775 43 : return 0;
776 : }
777 :
778 : INLINE long
779 84 : vecsmall_pack(GEN V, long base, long mod)
780 : {
781 84 : long i, s = 0;
782 273 : for(i=1; i<lg(V); i++) s = (base*s + V[i]) % mod;
783 84 : return s;
784 : }
785 :
786 : INLINE long
787 21 : vecsmall_indexmax(GEN x)
788 : {
789 21 : long i, i0 = 1, t = x[1], lx = lg(x);
790 84 : for (i=2; i<lx; i++)
791 63 : if (x[i] > t) t = x[i0=i];
792 21 : return i0;
793 : }
794 :
795 : INLINE long
796 927773 : vecsmall_max(GEN x)
797 : {
798 927773 : long i, t = x[1], lx = lg(x);
799 2547775 : for (i=2; i<lx; i++)
800 1620002 : if (x[i] > t) t = x[i];
801 927773 : return t;
802 : }
803 :
804 : INLINE long
805 21 : vecsmall_indexmin(GEN x)
806 : {
807 21 : long i, i0 = 1, t = x[1], lx =lg(x);
808 84 : for (i=2; i<lx; i++)
809 63 : if (x[i] < t) t = x[i0=i];
810 21 : return i0;
811 : }
812 :
813 : INLINE long
814 1442 : vecsmall_min(GEN x)
815 : {
816 1442 : long i, t = x[1], lx =lg(x);
817 10094 : for (i=2; i<lx; i++)
818 8652 : if (x[i] < t) t = x[i];
819 1442 : return t;
820 : }
821 :
822 : INLINE int
823 24491943 : ZV_isscalar(GEN x)
824 : {
825 24491943 : long l = lg(x);
826 56021675 : while (--l > 1)
827 55598216 : if (signe(gel(x, l))) return 0;
828 423459 : return 1;
829 : }
830 : INLINE int
831 63373777 : QV_isscalar(GEN x)
832 : {
833 63373777 : long lx = lg(x),i;
834 79234856 : for (i=2; i<lx; i++)
835 75350567 : if (!isintzero(gel(x, i))) return 0;
836 3884289 : return 1;
837 : }
838 : INLINE int
839 1140310 : RgV_isscalar(GEN x)
840 : {
841 1140310 : long lx = lg(x),i;
842 1166498 : for (i=2; i<lx; i++)
843 1162783 : if (!gequal0(gel(x, i))) return 0;
844 3715 : return 1;
845 : }
846 : INLINE int
847 0 : RgX_isscalar(GEN x)
848 : {
849 : long i;
850 0 : for (i=lg(x)-1; i>2; i--)
851 0 : if (!gequal0(gel(x, i))) return 0;
852 0 : return 1;
853 : }
854 : INLINE long
855 26748801 : RgX_equal_var(GEN x, GEN y) { return varn(x) == varn(y) && RgX_equal(x,y); }
856 : INLINE GEN
857 140 : RgX_to_RgV(GEN x, long N) { x = RgX_to_RgC(x, N); settyp(x, t_VEC); return x; }
858 :
859 : INLINE int
860 66834 : RgX_is_rational(GEN x)
861 : {
862 : long i;
863 305353 : for (i = lg(x)-1; i > 1; i--)
864 289985 : if (!is_rational_t(typ(gel(x,i)))) return 0;
865 15368 : return 1;
866 : }
867 : INLINE int
868 14593266 : RgX_is_ZX(GEN x)
869 : {
870 : long i;
871 60940879 : for (i = lg(x)-1; i > 1; i--)
872 46409525 : if (typ(gel(x,i)) != t_INT) return 0;
873 14531354 : return 1;
874 : }
875 : INLINE int
876 362077 : RgX_is_QX(GEN x)
877 : {
878 362077 : long k = lg(x)-1;
879 1378870 : for ( ; k>1; k--)
880 1017080 : if (!is_rational_t(typ(gel(x,k)))) return 0;
881 361790 : return 1;
882 : }
883 : INLINE int
884 2943737 : RgX_is_monomial(GEN x)
885 : {
886 : long i;
887 2943737 : if (!signe(x)) return 0;
888 6920698 : for (i=lg(x)-2; i>1; i--)
889 4551800 : if (!isexactzero(gel(x,i))) return 0;
890 2368898 : return 1;
891 : }
892 : INLINE int
893 31331752 : RgV_is_ZV(GEN x)
894 : {
895 : long i;
896 124570368 : for (i = lg(x)-1; i > 0; i--)
897 93270319 : if (typ(gel(x,i)) != t_INT) return 0;
898 31300049 : return 1;
899 : }
900 : INLINE int
901 139424 : RgV_is_QV(GEN x)
902 : {
903 : long i;
904 615851 : for (i = lg(x)-1; i > 0; i--)
905 479381 : if (!is_rational_t(typ(gel(x,i)))) return 0;
906 136470 : return 1;
907 : }
908 : INLINE long
909 109073 : RgV_isin_i(GEN v, GEN x, long n)
910 : {
911 : long i;
912 1031386 : for (i = 1; i <= n; i++)
913 1025597 : if (gequal(gel(v,i), x)) return i;
914 5789 : return 0;
915 : }
916 : INLINE long
917 109073 : RgV_isin(GEN v, GEN x) { return RgV_isin_i(v, x, lg(v)-1); }
918 :
919 : /********************************************************************/
920 : /** **/
921 : /** Dynamic arrays implementation **/
922 : /** **/
923 : /********************************************************************/
924 : INLINE void **
925 694110737 : pari_stack_base(pari_stack *s) { return s->data; }
926 :
927 : INLINE void
928 5522186 : pari_stack_init(pari_stack *s, size_t size, void **data)
929 : {
930 5522186 : s->data = data;
931 5522186 : *data = NULL;
932 5522186 : s->n = 0;
933 5522186 : s->alloc = 0;
934 5522186 : s->size = size;
935 5522186 : }
936 :
937 : INLINE void
938 689029754 : pari_stack_alloc(pari_stack *s, long nb)
939 : {
940 689029754 : void **sdat = pari_stack_base(s);
941 689034721 : long alloc = s->alloc;
942 689034721 : if (s->n+nb <= alloc) return;
943 2058685 : if (!alloc)
944 1964498 : alloc = nb;
945 : else
946 : {
947 193341 : while (s->n+nb > alloc) alloc <<= 1;
948 : }
949 2058685 : pari_realloc_ip(sdat,alloc*s->size);
950 2061423 : s->alloc = alloc;
951 : }
952 :
953 : INLINE long
954 596167114 : pari_stack_new(pari_stack *s) { pari_stack_alloc(s, 1); return s->n++; }
955 :
956 : INLINE void
957 5075322 : pari_stack_delete(pari_stack *s)
958 : {
959 5075322 : void **sdat = pari_stack_base(s);
960 5061534 : if (*sdat) pari_free(*sdat);
961 5095181 : }
962 :
963 : INLINE void
964 5704 : pari_stack_pushp(pari_stack *s, void *u)
965 : {
966 5704 : long n = pari_stack_new(s);
967 5704 : void **sdat =(void**) *pari_stack_base(s);
968 5704 : sdat[n] = u;
969 5704 : }
970 :
971 : /*******************************************************************/
972 : /* */
973 : /* EXTRACT */
974 : /* */
975 : /*******************************************************************/
976 : INLINE GEN
977 590428412 : vecslice(GEN A, long y1, long y2)
978 : {
979 590428412 : long i,lB = y2 - y1 + 2;
980 590428412 : GEN B = cgetg(lB, typ(A));
981 2630319691 : for (i=1; i<lB; i++) B[i] = A[y1-1+i];
982 590420358 : return B;
983 : }
984 : INLINE GEN
985 2423333 : vecslicepermute(GEN A, GEN p, long y1, long y2)
986 : {
987 2423333 : long i,lB = y2 - y1 + 2;
988 2423333 : GEN B = cgetg(lB, typ(A));
989 28195989 : for (i=1; i<lB; i++) B[i] = A[p[y1-1+i]];
990 2423329 : return B;
991 : }
992 : /* rowslice(rowpermute(A,p), x1, x2) */
993 : INLINE GEN
994 129518 : rowslicepermute(GEN x, GEN p, long j1, long j2)
995 576568 : { pari_APPLY_same(vecslicepermute(gel(x,i),p,j1,j2)) }
996 :
997 : INLINE GEN
998 75771841 : rowslice(GEN x, long j1, long j2)
999 605847218 : { pari_APPLY_same(vecslice(gel(x,i), j1, j2)) }
1000 :
1001 : INLINE GEN
1002 16159429 : matslice(GEN A, long x1, long x2, long y1, long y2)
1003 16159429 : { return rowslice(vecslice(A, y1, y2), x1, x2); }
1004 :
1005 : /* shallow, remove coeff of index j */
1006 : INLINE GEN
1007 210 : rowsplice(GEN x, long j)
1008 1036 : { pari_APPLY_same(vecsplice(gel(x,i), j)) }
1009 :
1010 : /* shallow, remove coeff of index j */
1011 : INLINE GEN
1012 354188 : vecsplice(GEN a, long j)
1013 : {
1014 354188 : long i, k, l = lg(a);
1015 : GEN b;
1016 354188 : if (l == 1) pari_err(e_MISC, "incorrect component in vecsplice");
1017 354188 : b = cgetg(l-1, typ(a));
1018 1499192 : for (i = k = 1; i < l; i++)
1019 1145008 : if (i != j) gel(b, k++) = gel(a,i);
1020 354184 : return b;
1021 : }
1022 : /* shallow */
1023 : INLINE GEN
1024 1036 : RgM_minor(GEN a, long i, long j)
1025 : {
1026 1036 : GEN b = vecsplice(a, j);
1027 1036 : long k, l = lg(b);
1028 4242 : for (k = 1; k < l; k++) gel(b,k) = vecsplice(gel(b,k), i);
1029 1036 : return b;
1030 : }
1031 :
1032 : /* A[x0,] */
1033 : INLINE GEN
1034 759809 : row(GEN x, long j)
1035 6676187 : { pari_APPLY_type(t_VEC, gcoeff(x, j, i)) }
1036 : INLINE GEN
1037 7818581 : Flm_row(GEN x, long j)
1038 203691470 : { pari_APPLY_ulong((ulong)coeff(x, j, i)) }
1039 : /* A[x0,] */
1040 : INLINE GEN
1041 204988 : rowcopy(GEN x, long j)
1042 2105509 : { pari_APPLY_type(t_VEC, gcopy(gcoeff(x, j, i))) }
1043 : /* A[x0, x1..x2] */
1044 : INLINE GEN
1045 987 : row_i(GEN A, long x0, long x1, long x2)
1046 : {
1047 987 : long i, lB = x2 - x1 + 2;
1048 987 : GEN B = cgetg(lB, t_VEC);
1049 2989 : for (i=x1; i<=x2; i++) gel(B, i) = gcoeff(A, x0, i);
1050 987 : return B;
1051 : }
1052 :
1053 : INLINE GEN
1054 697018 : vecreverse(GEN A)
1055 : {
1056 : long i, l;
1057 697018 : GEN B = cgetg_copy(A, &l);
1058 2407741 : for (i=1; i<l; i++) gel(B, i) = gel(A, l-i);
1059 697018 : return B;
1060 : }
1061 :
1062 : INLINE GEN
1063 3003 : vecsmall_reverse(GEN A)
1064 : {
1065 : long i, l;
1066 3003 : GEN B = cgetg_copy(A, &l);
1067 12523 : for (i=1; i<l; i++) B[i] = A[l-i];
1068 3003 : return B;
1069 : }
1070 :
1071 : INLINE void
1072 2570 : vecreverse_inplace(GEN y)
1073 : {
1074 2570 : long l = lg(y), lim = l>>1, i;
1075 8242 : for (i = 1; i <= lim; i++)
1076 : {
1077 5672 : GEN z = gel(y,i);
1078 5672 : gel(y,i) = gel(y,l-i);
1079 5672 : gel(y,l-i) = z;
1080 : }
1081 2570 : }
1082 :
1083 : INLINE GEN
1084 74204189 : vecsmallpermute(GEN A, GEN p) { return perm_mul(A, p); }
1085 :
1086 : INLINE GEN
1087 18758648 : vecpermute(GEN A, GEN x)
1088 106052753 : { pari_APPLY_type(typ(A), gel(A, x[i])) }
1089 :
1090 : INLINE GEN
1091 6925688 : veclast(GEN A) { return gel(A, lg(A)-1); }
1092 :
1093 : INLINE GEN
1094 13856464 : rowpermute(GEN x, GEN p)
1095 95890342 : { pari_APPLY_same(typ(gel(x,i)) == t_VECSMALL ? vecsmallpermute(gel(x, i), p)
1096 : : vecpermute(gel(x, i), p))
1097 : }
1098 : /*******************************************************************/
1099 : /* */
1100 : /* PERMUTATIONS */
1101 : /* */
1102 : /*******************************************************************/
1103 : INLINE GEN
1104 2763518 : identity_zv(long n)
1105 : {
1106 2763518 : GEN v = cgetg(n+1, t_VECSMALL);
1107 : long i;
1108 30114303 : for (i = 1; i <= n; i++) v[i] = i;
1109 2763495 : return v;
1110 : }
1111 : INLINE GEN
1112 4249 : identity_ZV(long n)
1113 : {
1114 4249 : GEN v = cgetg(n+1, t_VEC);
1115 : long i;
1116 51569 : for (i = 1; i <= n; i++) gel(v,i) = utoipos(i);
1117 4249 : return v;
1118 : }
1119 : /* identity permutation */
1120 : INLINE GEN
1121 2739182 : identity_perm(long n) { return identity_zv(n); }
1122 :
1123 : /* assume d <= n */
1124 : INLINE GEN
1125 99547 : cyclic_perm(long n, long d)
1126 : {
1127 99547 : GEN perm = cgetg(n+1, t_VECSMALL);
1128 : long i;
1129 507640 : for (i = 1; i <= n-d; i++) perm[i] = i+d;
1130 226338 : for ( ; i <= n; i++) perm[i] = i-n+d;
1131 99547 : return perm;
1132 : }
1133 :
1134 : /* Multiply (compose) two permutations */
1135 : INLINE GEN
1136 76383583 : perm_mul(GEN s, GEN x)
1137 960076361 : { pari_APPLY_long(s[x[i]]) }
1138 :
1139 : INLINE GEN
1140 728 : perm_sqr(GEN x)
1141 18284 : { pari_APPLY_long(x[x[i]]) }
1142 :
1143 : /* Compute the inverse (reciprocal) of a permutation. */
1144 : INLINE GEN
1145 2722458 : perm_inv(GEN x)
1146 : {
1147 : long i, lx;
1148 2722458 : GEN y = cgetg_copy(x, &lx);
1149 37564872 : for (i=1; i<lx; i++) y[ x[i] ] = i;
1150 2722452 : return y;
1151 : }
1152 : /* Return s*t*s^-1 */
1153 : INLINE GEN
1154 418299 : perm_conj(GEN s, GEN t)
1155 : {
1156 : long i, l;
1157 418299 : GEN v = cgetg_copy(s, &l);
1158 6857893 : for (i = 1; i < l; i++) v[ s[i] ] = s[ t[i] ];
1159 418299 : return v;
1160 : }
1161 :
1162 : INLINE void
1163 461952990 : pari_free(void *pointer)
1164 : {
1165 461952990 : BLOCK_SIGINT_START;
1166 462017121 : free(pointer);
1167 462017121 : BLOCK_SIGINT_END;
1168 462012146 : }
1169 : INLINE void*
1170 692247890 : pari_malloc(size_t size)
1171 : {
1172 692247890 : if (size)
1173 : {
1174 : char *tmp;
1175 692252230 : BLOCK_SIGINT_START;
1176 692313254 : tmp = (char*)malloc(size);
1177 692313254 : BLOCK_SIGINT_END;
1178 692315488 : if (!tmp) pari_err(e_MEM);
1179 692322089 : return tmp;
1180 : }
1181 0 : return NULL;
1182 : }
1183 : INLINE void*
1184 1841 : pari_realloc(void *pointer, size_t size)
1185 : {
1186 : char *tmp;
1187 :
1188 1841 : BLOCK_SIGINT_START;
1189 1841 : if (!pointer) tmp = (char *) malloc(size);
1190 1841 : else tmp = (char *) realloc(pointer,size);
1191 1841 : BLOCK_SIGINT_END;
1192 1841 : if (!tmp) pari_err(e_MEM);
1193 1841 : return tmp;
1194 : }
1195 : INLINE void
1196 2063600 : pari_realloc_ip(void **pointer, size_t size)
1197 : {
1198 : char *tmp;
1199 2063600 : BLOCK_SIGINT_START;
1200 2063588 : if (!*pointer) tmp = (char *) malloc(size);
1201 99527 : else tmp = (char *) realloc(*pointer,size);
1202 2063588 : if (!tmp) pari_err(e_MEM);
1203 2063588 : *pointer = tmp;
1204 2063588 : BLOCK_SIGINT_END;
1205 2063233 : }
1206 :
1207 : INLINE void*
1208 45557 : pari_calloc(size_t size)
1209 : {
1210 45557 : void *t = pari_malloc(size);
1211 45557 : memset(t, 0, size); return t;
1212 : }
1213 : INLINE GEN
1214 8171 : cgetalloc(size_t l, long t)
1215 : { /* evallg may raise e_OVERFLOW, which would leak x */
1216 8171 : ulong x0 = evaltyp(t) | evallg(l);
1217 8171 : GEN x = (GEN)pari_malloc(l * sizeof(long));
1218 8171 : x[0] = x0; return x;
1219 : }
1220 :
1221 : /*******************************************************************/
1222 : /* */
1223 : /* GARBAGE COLLECTION */
1224 : /* */
1225 : /*******************************************************************/
1226 : /* copy integer x as if we had set_avma(av) */
1227 : INLINE GEN
1228 7656725777 : icopy_avma(GEN x, pari_sp av)
1229 : {
1230 7656725777 : long i = lgefint(x), lx = i;
1231 7656725777 : GEN y = ((GEN)av) - i;
1232 52437906788 : while (--i > 0) y[i] = x[i];
1233 7656725777 : y[0] = evaltyp(t_INT)|evallg(lx);
1234 7659687811 : return y;
1235 : }
1236 : /* copy leaf x as if we had set_avma(av) */
1237 : INLINE GEN
1238 531426597 : leafcopy_avma(GEN x, pari_sp av)
1239 : {
1240 531426597 : long i = lg(x);
1241 531426597 : GEN y = ((GEN)av) - i;
1242 2915824468 : while (--i > 0) y[i] = x[i];
1243 531426597 : y[0] = x[0] & (~CLONEBIT);
1244 531426597 : return y;
1245 : }
1246 : INLINE GEN
1247 1079286799 : gerepileuptoleaf(pari_sp av, GEN x)
1248 : {
1249 : long lx;
1250 : GEN q;
1251 :
1252 1079286799 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1253 1078065482 : lx = lg(x);
1254 1078065482 : q = ((GEN)av) - lx;
1255 1078065482 : set_avma((pari_sp)q);
1256 10898162007 : while (--lx >= 0) q[lx] = x[lx];
1257 1077823498 : return q;
1258 : }
1259 : INLINE GEN
1260 3868356203 : gerepileuptoint(pari_sp av, GEN x)
1261 : {
1262 3868356203 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1263 3465034713 : set_avma((pari_sp)icopy_avma(x, av));
1264 3468219924 : return (GEN)avma;
1265 : }
1266 : INLINE GEN
1267 1788619077 : gerepileupto(pari_sp av, GEN x)
1268 : {
1269 1788619077 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1270 1615298896 : switch(typ(x))
1271 : { /* non-default = !is_recursive_t(tq) */
1272 473239296 : case t_INT: return gerepileuptoint(av, x);
1273 333363480 : case t_REAL:
1274 : case t_STR:
1275 333363480 : case t_VECSMALL: return gerepileuptoleaf(av,x);
1276 808697253 : default:
1277 : /* NB: x+i --> ((long)x) + i*sizeof(long) */
1278 808697253 : return gerepile(av, (pari_sp) (x+lg(x)), x);
1279 : }
1280 : }
1281 :
1282 : /* gerepileupto(av, gcopy(x)) */
1283 : INLINE GEN
1284 204253743 : gerepilecopy(pari_sp av, GEN x)
1285 : {
1286 204253743 : if (is_recursive_t(typ(x)))
1287 : {
1288 194272283 : GENbin *p = copy_bin(x);
1289 194286498 : set_avma(av); return bin_copy(p);
1290 : }
1291 : else
1292 : {
1293 9980681 : set_avma(av);
1294 9980840 : if (x < (GEN)av) {
1295 8054872 : if (x < (GEN)pari_mainstack->bot) new_chunk(lg(x));
1296 8054876 : x = leafcopy_avma(x, av);
1297 8054893 : set_avma((pari_sp)x);
1298 : } else
1299 1925968 : x = leafcopy(x);
1300 9980859 : return x;
1301 : }
1302 : }
1303 :
1304 : INLINE void
1305 48988692 : guncloneNULL(GEN x) { if (x) gunclone(x); }
1306 : INLINE void
1307 1304161 : guncloneNULL_deep(GEN x) { if (x) gunclone_deep(x); }
1308 :
1309 : /* Takes an array of pointers to GENs, of length n. Copies all
1310 : * objects to contiguous locations and cleans up the stack between
1311 : * av and avma. */
1312 : INLINE void
1313 983900 : gerepilemany(pari_sp av, GEN* gptr[], int n)
1314 : {
1315 : int i;
1316 3909341 : for (i=0; i<n; i++) *gptr[i] = (GEN)copy_bin(*gptr[i]);
1317 983712 : set_avma(av);
1318 3909860 : for (i=0; i<n; i++) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1319 984119 : }
1320 :
1321 : INLINE void
1322 19534793 : gerepileall(pari_sp av, int n, ...)
1323 : {
1324 : int i;
1325 19534793 : va_list a; va_start(a, n);
1326 19534793 : if (n < 10)
1327 : {
1328 : GEN *gptr[10];
1329 59222959 : for (i=0; i<n; i++)
1330 39687425 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1331 19535534 : set_avma(av);
1332 59223908 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1333 :
1334 : }
1335 : else
1336 : {
1337 0 : GEN **gptr = (GEN**) pari_malloc(n*sizeof(GEN*));
1338 0 : for (i=0; i<n; i++)
1339 0 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1340 0 : set_avma(av);
1341 0 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1342 0 : pari_free(gptr);
1343 : }
1344 19536035 : va_end(a);
1345 19536035 : }
1346 :
1347 : /* assume 1 <= n < 10 */
1348 : INLINE GEN
1349 79459003 : gc_all(pari_sp av, int n, ...)
1350 : {
1351 : int i;
1352 : GEN *v[10];
1353 79459003 : va_list a; va_start(a, n);
1354 267489503 : for (i=0; i<n; i++) { v[i] = va_arg(a,GEN*); *v[i] = (GEN)copy_bin(*v[i]); }
1355 79459247 : set_avma(av);
1356 267490089 : for (i=0; i<n; i++) *v[i] = bin_copy((GENbin*)*v[i]);
1357 79459392 : return *v[0];
1358 : }
1359 :
1360 : INLINE void
1361 2185776 : gerepilecoeffs(pari_sp av, GEN x, int n)
1362 : {
1363 : int i;
1364 26041995 : for (i=0; i<n; i++) gel(x,i) = (GEN)copy_bin(gel(x,i));
1365 2186128 : set_avma(av);
1366 26043056 : for (i=0; i<n; i++) gel(x,i) = bin_copy((GENbin*)x[i]);
1367 2185924 : }
1368 :
1369 : /* p from copy_bin. Copy p->x back to stack, then destroy p */
1370 : INLINE GEN
1371 448827251 : bin_copy(GENbin *p)
1372 : {
1373 : GEN x, y, base;
1374 : long dx, len;
1375 :
1376 448827251 : x = p->x; if (!x) { pari_free(p); return gen_0; }
1377 422787717 : len = p->len;
1378 422787717 : base= p->base; dx = x - base;
1379 422787717 : y = (GEN)memcpy((void*)new_chunk(len), (void*)GENbinbase(p), len*sizeof(long));
1380 422782061 : y += dx;
1381 422782061 : p->rebase(y, ((ulong)y-(ulong)x));
1382 422781376 : pari_free(p); return y;
1383 : }
1384 :
1385 : INLINE GEN
1386 871613747 : GENbinbase(GENbin *p) { return (GEN)(p + 1); }
1387 :
1388 : INLINE void
1389 117919968 : cgiv(GEN x)
1390 : {
1391 117919968 : pari_sp av = (pari_sp)(x+lg(x));
1392 117919968 : if (isonstack((GEN)av)) set_avma(av);
1393 117930862 : }
1394 :
1395 : INLINE void
1396 1848679 : killblock(GEN x) { gunclone(x); }
1397 :
1398 : INLINE int
1399 290522751 : is_universal_constant(GEN x) { return (x >= gen_0 && x <= ghalf); }
1400 :
1401 : /*******************************************************************/
1402 : /* */
1403 : /* CONVERSION / ASSIGNMENT */
1404 : /* */
1405 : /*******************************************************************/
1406 : /* z is a type which may be a t_COMPLEX component (not a t_QUAD) */
1407 : INLINE GEN
1408 17900388 : cxcompotor(GEN z, long prec)
1409 : {
1410 17900388 : switch(typ(z))
1411 : {
1412 11754981 : case t_INT: return itor(z, prec);
1413 293104 : case t_FRAC: return fractor(z, prec);
1414 5852534 : case t_REAL: return rtor(z, prec);
1415 0 : default: pari_err_TYPE("cxcompotor",z);
1416 : return NULL; /* LCOV_EXCL_LINE */
1417 : }
1418 : }
1419 : INLINE GEN
1420 8934251 : cxtofp(GEN x, long prec)
1421 8934251 : { retmkcomplex(cxcompotor(gel(x,1),prec), cxcompotor(gel(x,2),prec)); }
1422 :
1423 : INLINE GEN
1424 384533 : cxtoreal(GEN q)
1425 384533 : { return (typ(q) == t_COMPLEX && gequal0(gel(q,2)))? gel(q,1): q; }
1426 :
1427 : INLINE double
1428 60251930 : gtodouble(GEN x)
1429 : {
1430 60251930 : if (typ(x)!=t_REAL) {
1431 8155958 : pari_sp av = avma;
1432 8155958 : x = gtofp(x, DEFAULTPREC);
1433 8155342 : if (typ(x)!=t_REAL) pari_err_TYPE("gtodouble [t_REAL expected]", x);
1434 8155342 : set_avma(av);
1435 : }
1436 60251203 : return rtodbl(x);
1437 : }
1438 :
1439 : INLINE int
1440 2714315 : gisdouble(GEN x, double *g)
1441 : {
1442 2714315 : if (typ(x)!=t_REAL) {
1443 56051 : pari_sp av = avma;
1444 56051 : x = gtofp(x, DEFAULTPREC);
1445 56051 : if (typ(x)!=t_REAL) pari_err_TYPE("gisdouble [t_REAL expected]", x);
1446 56051 : set_avma(av);
1447 : }
1448 2714314 : if (expo(x) >= 0x3ff) return 0;
1449 2714314 : *g = rtodbl(x); return 1;
1450 : }
1451 :
1452 : INLINE long
1453 85736902 : gtos(GEN x) {
1454 85736902 : if (typ(x) != t_INT) pari_err_TYPE("gtos [integer expected]",x);
1455 85736888 : return itos(x);
1456 : }
1457 :
1458 : INLINE ulong
1459 107444 : gtou(GEN x) {
1460 107444 : if (typ(x) != t_INT || signe(x)<0)
1461 7 : pari_err_TYPE("gtou [integer >=0 expected]",x);
1462 107437 : return itou(x);
1463 : }
1464 :
1465 : INLINE GEN
1466 44011871 : absfrac(GEN x)
1467 : {
1468 44011871 : GEN y = cgetg(3, t_FRAC);
1469 44011907 : gel(y,1) = absi(gel(x,1));
1470 44011903 : gel(y,2) = icopy(gel(x,2)); return y;
1471 : }
1472 : INLINE GEN
1473 46738 : absfrac_shallow(GEN x)
1474 46738 : { return signe(gel(x,1))>0? x: mkfrac(negi(gel(x,1)), gel(x,2)); }
1475 : INLINE GEN
1476 7514025 : Q_abs(GEN x) { return (typ(x) == t_INT)? absi(x): absfrac(x); }
1477 : INLINE GEN
1478 169264 : Q_abs_shallow(GEN x)
1479 169264 : { return (typ(x) == t_INT)? absi_shallow(x): absfrac_shallow(x); }
1480 : INLINE GEN
1481 13083 : R_abs_shallow(GEN x)
1482 13083 : { return (typ(x) == t_FRAC)? absfrac_shallow(x): mpabs_shallow(x); }
1483 : INLINE GEN
1484 0 : R_abs(GEN x)
1485 0 : { return (typ(x) == t_FRAC)? absfrac(x): mpabs(x); }
1486 :
1487 : /* Force z to be of type real/complex with floating point components */
1488 : INLINE GEN
1489 250478103 : gtofp(GEN z, long prec)
1490 : {
1491 250478103 : switch(typ(z))
1492 : {
1493 211858280 : case t_INT: return itor(z, prec);
1494 4097391 : case t_FRAC: return fractor(z, prec);
1495 25847885 : case t_REAL: return rtor(z, prec);
1496 8681542 : case t_COMPLEX: {
1497 8681542 : GEN a = gel(z,1), b = gel(z,2);
1498 8681542 : if (isintzero(b)) return cxcompotor(a, prec);
1499 8681535 : if (isintzero(a)) {
1500 9117 : GEN y = cgetg(3, t_COMPLEX);
1501 9117 : b = cxcompotor(b, prec);
1502 9117 : gel(y,1) = real_0_bit(expo(b) - prec);
1503 9117 : gel(y,2) = b; return y;
1504 : }
1505 8672385 : return cxtofp(z, prec);
1506 : }
1507 0 : case t_QUAD: return quadtofp(z, prec);
1508 0 : default: pari_err_TYPE("gtofp",z);
1509 : return NULL; /* LCOV_EXCL_LINE */
1510 : }
1511 : }
1512 : /* Force z to be of type real / int */
1513 : INLINE GEN
1514 22428 : gtomp(GEN z, long prec)
1515 : {
1516 22428 : switch(typ(z))
1517 : {
1518 42 : case t_INT: return z;
1519 22386 : case t_FRAC: return fractor(z, prec);
1520 0 : case t_REAL: return rtor(z, prec);
1521 0 : case t_QUAD: z = quadtofp(z, prec);
1522 0 : if (typ(z) == t_REAL) return z;
1523 0 : default: pari_err_TYPE("gtomp",z);
1524 : return NULL; /* LCOV_EXCL_LINE */
1525 : }
1526 : }
1527 :
1528 : INLINE GEN
1529 7088939 : RgX_gtofp(GEN x, long prec)
1530 : {
1531 : long l;
1532 7088939 : GEN y = cgetg_copy(x, &l);
1533 36971963 : while (--l > 1) gel(y,l) = gtofp(gel(x,l), prec);
1534 7088235 : y[1] = x[1]; return y;
1535 : }
1536 : INLINE GEN
1537 33565406 : RgC_gtofp(GEN x, long prec)
1538 215515611 : { pari_APPLY_type(t_COL, gtofp(gel(x,i), prec)) }
1539 :
1540 : INLINE GEN
1541 56 : RgV_gtofp(GEN x, long prec)
1542 4781 : { pari_APPLY_type(t_VEC, gtofp(gel(x,i), prec)) }
1543 :
1544 : INLINE GEN
1545 8155552 : RgM_gtofp(GEN x, long prec)
1546 41093098 : { pari_APPLY_same(RgC_gtofp(gel(x,i), prec)) }
1547 :
1548 : INLINE GEN
1549 574 : RgC_gtomp(GEN x, long prec)
1550 23002 : { pari_APPLY_type(t_COL, gtomp(gel(x,i), prec)) }
1551 :
1552 : INLINE GEN
1553 21 : RgM_gtomp(GEN x, long prec)
1554 595 : { pari_APPLY_same(RgC_gtomp(gel(x,i), prec)) }
1555 :
1556 : INLINE GEN
1557 60021 : RgX_fpnorml2(GEN x, long prec)
1558 : {
1559 60021 : pari_sp av = avma;
1560 60021 : return gerepileupto(av, gnorml2(RgX_gtofp(x, prec)));
1561 : }
1562 : INLINE GEN
1563 616887 : RgC_fpnorml2(GEN x, long prec)
1564 : {
1565 616887 : pari_sp av = avma;
1566 616887 : return gerepileupto(av, gnorml2(RgC_gtofp(x, prec)));
1567 : }
1568 : INLINE GEN
1569 21647 : RgM_fpnorml2(GEN x, long prec)
1570 : {
1571 21647 : pari_sp av = avma;
1572 21647 : return gerepileupto(av, gnorml2(RgM_gtofp(x, prec)));
1573 : }
1574 :
1575 : /* y a t_REAL */
1576 : INLINE void
1577 220528 : affgr(GEN x, GEN y)
1578 : {
1579 : pari_sp av;
1580 220528 : switch(typ(x)) {
1581 5992 : case t_INT: affir(x,y); break;
1582 214536 : case t_REAL: affrr(x,y); break;
1583 0 : case t_FRAC: rdiviiz(gel(x,1),gel(x,2), y); break;
1584 0 : case t_QUAD: av = avma; affgr(quadtofp(x,realprec(y)), y); set_avma(av); break;
1585 0 : default: pari_err_TYPE2("=",x,y);
1586 : }
1587 220528 : }
1588 :
1589 : INLINE GEN
1590 239493 : affc_fixlg(GEN x, GEN res)
1591 : {
1592 239493 : if (typ(x) == t_COMPLEX)
1593 : {
1594 206773 : affrr_fixlg(gel(x,1), gel(res,1));
1595 206773 : affrr_fixlg(gel(x,2), gel(res,2));
1596 : }
1597 : else
1598 : {
1599 32720 : set_avma((pari_sp)(res+3));
1600 32720 : res = cgetr(realprec(gel(res,1)));
1601 32720 : affrr_fixlg(x, res);
1602 : }
1603 239493 : return res;
1604 : }
1605 :
1606 : INLINE GEN
1607 0 : trunc_safe(GEN x) { long e; return gcvtoi(x,&e); }
1608 :
1609 : /*******************************************************************/
1610 : /* */
1611 : /* LENGTH CONVERSIONS */
1612 : /* */
1613 : /*******************************************************************/
1614 : INLINE long
1615 40982 : ndec2nlong(long x) { return 1 + (long)((x)*(LOG2_10/BITS_IN_LONG)); }
1616 : INLINE long
1617 32726 : ndec2prec(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1618 : INLINE long
1619 8256 : ndec2nbits(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1620 : /* Fast implementation of ceil(x / (8*sizeof(long))); typecast to (ulong)
1621 : * to avoid overflow. Faster than 1 + ((x-1)>>TWOPOTBITS_IN_LONG)) :
1622 : * addl, shrl instead of subl, sarl, addl */
1623 : INLINE long
1624 12172305 : nbits2nlong(long x) {
1625 12172305 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1626 : }
1627 :
1628 : INLINE long
1629 1474284830 : nbits2extraprec(long x) {
1630 1474284830 : return (((ulong)x+BITS_IN_LONG-1)>>TWOPOTBITS_IN_LONG) << TWOPOTBITS_IN_LONG;
1631 : }
1632 :
1633 : INLINE long
1634 185383628 : nbits2prec(long x) {
1635 185383628 : return (((ulong)x+BITS_IN_LONG-1)>>TWOPOTBITS_IN_LONG) << TWOPOTBITS_IN_LONG;
1636 : }
1637 :
1638 : INLINE long
1639 4437131612 : prec2lg(long x) {
1640 4437131612 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1641 : }
1642 : /* ceil(x / sizeof(long)) */
1643 : INLINE long
1644 119092749 : nchar2nlong(long x) {
1645 119092749 : return (long)(((ulong)x+sizeof(long)-1) >> (TWOPOTBITS_IN_LONG-3L));
1646 : }
1647 : INLINE long
1648 104403919 : prec2nbits(long x) { return x; }
1649 : INLINE double
1650 3178118 : bit_accuracy_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1651 : INLINE double
1652 570819 : prec2nbits_mul(long x, double y) { return x * y; }
1653 : INLINE long
1654 141200379 : bit_prec(GEN x) { return realprec(x); }
1655 : INLINE long
1656 2776362889 : bit_accuracy(long x) { return (x-2) * BITS_IN_LONG; }
1657 : INLINE long
1658 9750 : prec2ndec(long x) { return (long)(x * LOG10_2); }
1659 : INLINE long
1660 214 : nbits2ndec(long x) { return prec2ndec(x); }
1661 : INLINE long
1662 472933 : precdbl(long x) {return x << 1;}
1663 : INLINE long
1664 8013622729 : divsBIL(long n) { return n >> TWOPOTBITS_IN_LONG; }
1665 : INLINE long
1666 7928118654 : remsBIL(long n) { return n & (BITS_IN_LONG-1); }
1667 :
1668 : /*********************************************************************/
1669 : /** **/
1670 : /** OPERATIONS MODULO m **/
1671 : /** **/
1672 : /*********************************************************************/
1673 : /* Assume m > 0, more efficient if 0 <= a, b < m */
1674 :
1675 : INLINE GEN
1676 74913238 : Fp_red(GEN a, GEN m) { return modii(a, m); }
1677 : INLINE GEN
1678 170517095 : Fp_add(GEN a, GEN b, GEN m)
1679 : {
1680 170517095 : pari_sp av=avma;
1681 170517095 : GEN p = addii(a,b);
1682 170131593 : long s = signe(p);
1683 170131593 : if (!s) return p; /* = gen_0 */
1684 158639729 : if (s > 0) /* general case */
1685 : {
1686 158395170 : GEN t = subii(p, m);
1687 158281384 : s = signe(t);
1688 158281384 : if (!s) return gc_const(av, gen_0);
1689 150173867 : if (s < 0) return gc_const((pari_sp)p, p);
1690 72417134 : if (cmpii(t, m) < 0) return gerepileuptoint(av, t); /* general case ! */
1691 3299475 : p = remii(t, m);
1692 : }
1693 : else
1694 262607 : p = modii(p, m);
1695 3562169 : return gerepileuptoint(av, p);
1696 : }
1697 : INLINE GEN
1698 21084533 : Fp_double(GEN x, GEN N)
1699 : {
1700 21084533 : GEN z = shifti(x, 1);
1701 20837200 : return cmpii(z, N) >= 0? subii(z, N): z;
1702 : }
1703 : INLINE GEN
1704 136284641 : Fp_sub(GEN a, GEN b, GEN m)
1705 : {
1706 136284641 : pari_sp av=avma;
1707 136284641 : GEN p = subii(a,b);
1708 135245198 : long s = signe(p);
1709 135245198 : if (!s) return p; /* = gen_0 */
1710 125596239 : if (s > 0)
1711 : {
1712 62958154 : if (cmpii(p, m) < 0) return p; /* general case ! */
1713 1456626 : p = remii(p, m);
1714 : }
1715 : else
1716 : {
1717 62638085 : GEN t = addii(p, m);
1718 63999194 : if (!s) return gc_const(av, gen_0);
1719 64004520 : if (s > 0) return gerepileuptoint(av, t); /* general case ! */
1720 64004520 : p = modii(t, m);
1721 : }
1722 65675235 : return gerepileuptoint(av, p);
1723 : }
1724 : INLINE GEN
1725 28267723 : Fp_neg(GEN b, GEN m)
1726 : {
1727 28267723 : pari_sp av = avma;
1728 28267723 : long s = signe(b);
1729 : GEN p;
1730 28267723 : if (!s) return gen_0;
1731 23837676 : if (s > 0)
1732 : {
1733 22715254 : p = subii(m, b);
1734 22715016 : if (signe(p) >= 0) return p; /* general case ! */
1735 385327 : p = modii(p, m);
1736 : } else
1737 1122775 : p = remii(negi(b), m);
1738 1508292 : return gerepileuptoint(av, p);
1739 : }
1740 :
1741 : INLINE GEN
1742 252540 : Fp_halve(GEN a, GEN p)
1743 : {
1744 252540 : if (mpodd(a)) a = addii(a,p);
1745 252540 : return shifti(a,-1);
1746 : }
1747 :
1748 : /* assume 0 <= u < p and ps2 = p>>1 */
1749 : INLINE GEN
1750 73221887 : Fp_center(GEN u, GEN p, GEN ps2)
1751 73221887 : { return abscmpii(u,ps2)<=0? icopy(u): subii(u,p); }
1752 : /* same without copy */
1753 : INLINE GEN
1754 13555780 : Fp_center_i(GEN u, GEN p, GEN ps2)
1755 13555780 : { return abscmpii(u,ps2)<=0? u: subii(u,p); }
1756 :
1757 : /* x + y*z mod p */
1758 : INLINE GEN
1759 11247587 : Fp_addmul(GEN x, GEN y, GEN z, GEN p)
1760 : {
1761 : pari_sp av;
1762 11247587 : if (!signe(y) || !signe(z)) return Fp_red(x, p);
1763 10899770 : if (!signe(x)) return Fp_mul(z,y, p);
1764 9900060 : av = avma;
1765 9900060 : return gerepileuptoint(av, modii(addii(x, mulii(y,z)), p));
1766 : }
1767 :
1768 : INLINE GEN
1769 177095944 : Fp_mul(GEN a, GEN b, GEN m)
1770 : {
1771 177095944 : pari_sp av=avma;
1772 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1773 177095944 : (void)new_chunk(lg(a)+lg(b)+(lg(m)<<1));
1774 177149949 : p = mulii(a,b);
1775 177045934 : set_avma(av); return modii(p,m);
1776 : }
1777 : INLINE GEN
1778 64731843 : Fp_sqr(GEN a, GEN m)
1779 : {
1780 64731843 : pari_sp av=avma;
1781 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1782 64731843 : (void)new_chunk((lg(a)+lg(m))<<1);
1783 65007566 : p = sqri(a);
1784 63686394 : set_avma(av); return remii(p,m); /*Use remii: p >= 0 */
1785 : }
1786 : INLINE GEN
1787 75522196 : Fp_mulu(GEN a, ulong b, GEN m)
1788 : {
1789 75522196 : long l = lgefint(m);
1790 75522196 : if (l == 3)
1791 : {
1792 55444209 : ulong mm = m[2];
1793 55444209 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1794 : } else {
1795 20077987 : pari_sp av = avma;
1796 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1797 20077987 : (void)new_chunk(lg(a)+1+(l<<1));
1798 20056746 : p = muliu(a,b);
1799 19912225 : set_avma(av); return modii(p,m);
1800 : }
1801 : }
1802 : INLINE GEN
1803 17780 : Fp_muls(GEN a, long b, GEN m)
1804 : {
1805 17780 : long l = lgefint(m);
1806 17780 : if (l == 3)
1807 : {
1808 3578 : ulong mm = m[2];
1809 3578 : if (b < 0)
1810 : {
1811 3578 : ulong t = Fl_mul(umodiu(a, mm), -b, mm);
1812 3578 : return t? utoipos(mm - t): gen_0;
1813 : }
1814 : else
1815 0 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1816 : } else {
1817 14202 : pari_sp av = avma;
1818 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1819 14202 : (void)new_chunk(lg(a)+1+(l<<1));
1820 14202 : p = mulis(a,b);
1821 14202 : set_avma(av); return modii(p,m);
1822 : }
1823 : }
1824 :
1825 : INLINE GEN
1826 36420062 : Fp_inv(GEN a, GEN m)
1827 : {
1828 : GEN res;
1829 36420062 : if (! invmod(a,m,&res)) pari_err_INV("Fp_inv", mkintmod(res,m));
1830 36421324 : return res;
1831 : }
1832 : INLINE GEN
1833 1181936 : Fp_invsafe(GEN a, GEN m)
1834 : {
1835 : GEN res;
1836 1181936 : if (! invmod(a,m,&res)) return NULL;
1837 1181884 : return res;
1838 : }
1839 : INLINE GEN
1840 1614030 : Fp_div(GEN a, GEN b, GEN m)
1841 : {
1842 1614030 : pari_sp av = avma;
1843 : GEN p;
1844 1614030 : if (lgefint(b) == 3)
1845 : {
1846 659614 : a = Fp_divu(a, b[2], m);
1847 659614 : if (signe(b) < 0) a = Fp_neg(a, m);
1848 659614 : return a;
1849 : }
1850 : /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1851 954416 : (void)new_chunk(lg(a)+(lg(m)<<1));
1852 954416 : p = mulii(a, Fp_inv(b,m));
1853 954416 : set_avma(av); return modii(p,m);
1854 : }
1855 : INLINE GEN
1856 1898036 : Fp_divu(GEN x, ulong a, GEN p)
1857 : {
1858 1898036 : pari_sp av = avma;
1859 : ulong b;
1860 1898036 : if (lgefint(p) == 3)
1861 : {
1862 1501353 : ulong pp = p[2], xp = umodiu(x, pp);
1863 1501353 : return xp? utoipos(Fl_div(xp, a % pp, pp)): gen_0;
1864 : }
1865 396683 : x = Fp_red(x, p);
1866 396683 : b = Fl_neg(Fl_div(umodiu(x,a), umodiu(p,a), a), a); /* x + pb = 0 (mod a) */
1867 396683 : return gerepileuptoint(av, diviuexact(addmuliu(x, p, b), a));
1868 : }
1869 :
1870 : INLINE GEN
1871 1086049 : Flx_mulu(GEN x, ulong a, ulong p) { return Flx_Fl_mul(x,a%p,p); }
1872 :
1873 : INLINE GEN
1874 2518014 : get_F2x_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1875 :
1876 : INLINE long
1877 2533672 : get_F2x_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1878 :
1879 : INLINE long
1880 1933592 : get_F2x_degree(GEN T) { return typ(T)==t_VEC? F2x_degree(gel(T,2)): F2x_degree(T); }
1881 :
1882 : INLINE GEN
1883 399 : get_F2xqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1884 :
1885 : INLINE long
1886 376978 : get_F2xqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1887 :
1888 : INLINE long
1889 201663 : get_F2xqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1890 :
1891 : INLINE GEN
1892 25860676 : get_Flx_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1893 :
1894 : INLINE long
1895 67363621 : get_Flx_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1896 :
1897 : INLINE long
1898 89168123 : get_Flx_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1899 :
1900 : INLINE GEN
1901 8040 : get_FlxqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1902 :
1903 : INLINE long
1904 265620 : get_FlxqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1905 :
1906 : INLINE long
1907 318850 : get_FlxqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1908 :
1909 : INLINE GEN
1910 3473607 : get_FpX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1911 :
1912 : INLINE long
1913 7019978 : get_FpX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1914 :
1915 : INLINE long
1916 5775856 : get_FpX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1917 :
1918 : INLINE GEN
1919 146583 : get_FpXQX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1920 :
1921 : INLINE long
1922 51837 : get_FpXQX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1923 :
1924 : INLINE long
1925 3686 : get_FpXQX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1926 :
1927 : /*******************************************************************/
1928 : /* */
1929 : /* ADDMULII / SUBMULII */
1930 : /* */
1931 : /*******************************************************************/
1932 : /* x - y*z */
1933 : INLINE GEN
1934 32717233 : submulii(GEN x, GEN y, GEN z)
1935 : {
1936 32717233 : long lx = lgefint(x), ly, lz;
1937 : pari_sp av;
1938 : GEN t;
1939 32717233 : if (lx == 2) { t = mulii(z,y); togglesign(t); return t; }
1940 30242753 : ly = lgefint(y);
1941 30242753 : if (ly == 2) return icopy(x);
1942 28977682 : lz = lgefint(z);
1943 28977682 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1944 28977682 : t = mulii(z, y);
1945 28977682 : set_avma(av); return subii(x,t);
1946 : }
1947 : /* y*z - x */
1948 : INLINE GEN
1949 3799748 : mulsubii(GEN y, GEN z, GEN x)
1950 : {
1951 3799748 : long lx = lgefint(x), ly, lz;
1952 : pari_sp av;
1953 : GEN t;
1954 3799748 : if (lx == 2) return mulii(z,y);
1955 2402635 : ly = lgefint(y);
1956 2402635 : if (ly == 2) return negi(x);
1957 2129503 : lz = lgefint(z);
1958 2129503 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1959 2129541 : t = mulii(z, y);
1960 2129518 : set_avma(av); return subii(t,x);
1961 : }
1962 :
1963 : /* x - u*y */
1964 : INLINE GEN
1965 7693 : submuliu(GEN x, GEN y, ulong u)
1966 : {
1967 : pari_sp av;
1968 7693 : long ly = lgefint(y);
1969 7693 : if (ly == 2) return icopy(x);
1970 7693 : av = avma;
1971 7693 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1972 7693 : y = mului(u,y);
1973 7693 : set_avma(av); return subii(x, y);
1974 : }
1975 : /* x + u*y */
1976 : INLINE GEN
1977 404751 : addmuliu(GEN x, GEN y, ulong u)
1978 : {
1979 : pari_sp av;
1980 404751 : long ly = lgefint(y);
1981 404751 : if (ly == 2) return icopy(x);
1982 404751 : av = avma;
1983 404751 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1984 404751 : y = mului(u,y);
1985 404751 : set_avma(av); return addii(x, y);
1986 : }
1987 : /* x - u*y */
1988 : INLINE GEN
1989 59684295 : submuliu_inplace(GEN x, GEN y, ulong u)
1990 : {
1991 : pari_sp av;
1992 59684295 : long ly = lgefint(y);
1993 59684295 : if (ly == 2) return x;
1994 37838953 : av = avma;
1995 37838953 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1996 37842288 : y = mului(u,y);
1997 37842205 : set_avma(av); return subii(x, y);
1998 : }
1999 : /* x + u*y */
2000 : INLINE GEN
2001 59177647 : addmuliu_inplace(GEN x, GEN y, ulong u)
2002 : {
2003 : pari_sp av;
2004 59177647 : long ly = lgefint(y);
2005 59177647 : if (ly == 2) return x;
2006 37748116 : av = avma;
2007 37748116 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
2008 37751647 : y = mului(u,y);
2009 37751509 : set_avma(av); return addii(x, y);
2010 : }
2011 : /* ux + vy */
2012 : INLINE GEN
2013 36927275 : lincombii(GEN u, GEN v, GEN x, GEN y)
2014 : {
2015 36927275 : long lx = lgefint(x), ly;
2016 : GEN p1, p2;
2017 : pari_sp av;
2018 36927275 : if (lx == 2) return mulii(v,y);
2019 23177781 : ly = lgefint(y);
2020 23177781 : if (ly == 2) return mulii(u,x);
2021 20557942 : av = avma; (void)new_chunk(lx+ly+lgefint(u)+lgefint(v)); /* HACK */
2022 20560504 : p1 = mulii(u,x);
2023 20559719 : p2 = mulii(v,y);
2024 20559660 : set_avma(av); return addii(p1,p2);
2025 : }
2026 :
2027 : /*******************************************************************/
2028 : /* */
2029 : /* GEN SUBTYPES */
2030 : /* */
2031 : /*******************************************************************/
2032 :
2033 : INLINE int
2034 4731819456 : is_const_t(long t) { return (t < t_POLMOD); }
2035 : INLINE int
2036 6946 : is_extscalar_t(long t) { return (t <= t_POL); }
2037 : INLINE int
2038 9600788 : is_intreal_t(long t) { return (t <= t_REAL); }
2039 : INLINE int
2040 601667603 : is_matvec_t(long t) { return (t >= t_VEC && t <= t_MAT); }
2041 : INLINE int
2042 94578833 : is_noncalc_t(long tx) { return (tx) >= t_LIST; }
2043 : INLINE int
2044 0 : is_qfb_t(long t) { return (t == t_QFB); }
2045 : INLINE int
2046 5028848 : is_rational_t(long t) { return (t == t_INT || t == t_FRAC); }
2047 : INLINE int
2048 62699701 : is_real_t(long t) { return (t == t_INT || t == t_REAL || t == t_FRAC); }
2049 : INLINE int
2050 8229478203 : is_recursive_t(long t) { return lontyp[t]; }
2051 : INLINE int
2052 303870319 : is_scalar_t(long t) { return (t < t_POL); }
2053 : INLINE int
2054 18105694 : is_vec_t(long t) { return (t == t_VEC || t == t_COL); }
2055 :
2056 : INLINE int
2057 59610324 : qfb_is_qfi(GEN q) { return signe(gel(q,4)) < 0; }
2058 :
2059 : /*******************************************************************/
2060 : /* */
2061 : /* TRANSCENDENTAL */
2062 : /* */
2063 : /*******************************************************************/
2064 : INLINE GEN
2065 79688242 : sqrtr(GEN x) {
2066 79688242 : long s = signe(x);
2067 79688242 : if (s == 0) return real_0_bit(expo(x) >> 1);
2068 79655134 : if (s >= 0) return sqrtr_abs(x);
2069 429792 : retmkcomplex(gen_0, sqrtr_abs(x));
2070 : }
2071 : INLINE GEN
2072 0 : cbrtr_abs(GEN x) { return sqrtnr_abs(x, 3); }
2073 : INLINE GEN
2074 0 : cbrtr(GEN x) {
2075 0 : long s = signe(x);
2076 : GEN r;
2077 0 : if (s == 0) return real_0_bit(expo(x) / 3);
2078 0 : r = cbrtr_abs(x);
2079 0 : if (s < 0) togglesign(r);
2080 0 : return r;
2081 : }
2082 : INLINE GEN
2083 2725929 : sqrtnr(GEN x, long n) {
2084 2725929 : long s = signe(x);
2085 : GEN r;
2086 2725929 : if (s == 0) return real_0_bit(expo(x) / n);
2087 2725929 : r = sqrtnr_abs(x, n);
2088 2725938 : if (s < 0) pari_err_IMPL("sqrtnr for x < 0");
2089 2725938 : return r;
2090 : }
2091 : INLINE long
2092 747863 : logint(GEN B, GEN y) { return logintall(B,y,NULL); }
2093 : INLINE ulong
2094 1724684 : ulogint(ulong B, ulong y)
2095 : {
2096 : ulong r;
2097 : long e;
2098 1724684 : if (y == 2) return expu(B);
2099 1676705 : r = y;
2100 5069652 : for (e=1;; e++)
2101 : { /* here, r = y^e, r2 = y^(e-1) */
2102 5069652 : if (r >= B) return r == B? e: e-1;
2103 3394479 : r = umuluu_or_0(y, r);
2104 3394484 : if (!r) return e;
2105 : }
2106 : }
2107 :
2108 : /*******************************************************************/
2109 : /* */
2110 : /* MISCELLANEOUS */
2111 : /* */
2112 : /*******************************************************************/
2113 9600679 : INLINE int ismpzero(GEN x) { return is_intreal_t(typ(x)) && !signe(x); }
2114 2813545280 : INLINE int isintzero(GEN x) { return typ(x) == t_INT && !signe(x); }
2115 16092118 : INLINE int isint1(GEN x) { return typ(x)==t_INT && equali1(x); }
2116 5944961 : INLINE int isintm1(GEN x){ return typ(x)==t_INT && equalim1(x);}
2117 1165039651 : INLINE int equali1(GEN n)
2118 1165039651 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(1)) && n[2] == 1; }
2119 138649525 : INLINE int equalim1(GEN n)
2120 138649525 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(-1)) && n[2] == 1; }
2121 : /* works only for POSITIVE integers */
2122 2171693388 : INLINE int is_pm1(GEN n)
2123 2171693388 : { return lgefint(n) == 3 && n[2] == 1; }
2124 554922311 : INLINE int is_bigint(GEN n)
2125 554922311 : { long l = lgefint(n); return l > 3 || (l == 3 && (n[2] & HIGHBIT)); }
2126 :
2127 2021223436 : INLINE int odd(long x) { return x & 1; }
2128 66432761 : INLINE int both_odd(long x, long y) { return x & y & 1; }
2129 :
2130 : INLINE int
2131 7788059685 : isonstack(GEN x)
2132 7788059685 : { return ((pari_sp)x >= pari_mainstack->bot
2133 7788059685 : && (pari_sp)x < pari_mainstack->top); }
2134 :
2135 : /* assume x != 0 and x t_REAL, return an approximation to log2(|x|) */
2136 : INLINE double
2137 90499617 : dbllog2r(GEN x)
2138 90499617 : { return log2((double)(ulong)x[2]) + (double)(expo(x) - (BITS_IN_LONG-1)); }
2139 :
2140 : INLINE GEN
2141 2462259 : mul_content(GEN cx, GEN cy)
2142 : {
2143 2462259 : if (!cx) return cy;
2144 519597 : if (!cy) return cx;
2145 336725 : return gmul(cx,cy);
2146 : }
2147 : INLINE GEN
2148 0 : inv_content(GEN c) { return c? ginv(c): NULL; }
2149 : INLINE GEN
2150 56394 : div_content(GEN cx, GEN cy)
2151 : {
2152 56394 : if (!cy) return cx;
2153 55302 : if (!cx) return ginv(cy);
2154 25387 : return gdiv(cx,cy);
2155 : }
2156 : INLINE GEN
2157 10331664 : mul_denom(GEN dx, GEN dy)
2158 : {
2159 10331664 : if (!dx) return dy;
2160 2560743 : if (!dy) return dx;
2161 1543778 : return mulii(dx,dy);
2162 : }
2163 :
2164 : /* POLYNOMIALS */
2165 : INLINE GEN
2166 1433046 : constant_coeff(GEN x) { return signe(x)? gel(x,2): gen_0; }
2167 : INLINE GEN
2168 162548015 : leading_coeff(GEN x) { return lg(x) == 2? gen_0: gel(x,lg(x)-1); }
2169 : INLINE ulong
2170 772740 : Flx_lead(GEN x) { return lg(x) == 2? 0: x[lg(x)-1]; }
2171 : INLINE ulong
2172 137782 : Flx_constant(GEN x) { return lg(x) == 2? 0: x[2]; }
2173 : INLINE long
2174 4992388914 : degpol(GEN x) { return lg(x)-3; }
2175 : INLINE long
2176 2540540994 : lgpol(GEN x) { return lg(x)-2; }
2177 : INLINE long
2178 338053883 : lgcols(GEN x) { return lg(gel(x,1)); }
2179 : INLINE long
2180 151755580 : nbrows(GEN x) { return lg(gel(x,1))-1; }
2181 : INLINE GEN
2182 0 : truecoef(GEN x, long n) { return polcoef(x,n,-1); }
2183 :
2184 : INLINE GEN
2185 2139840 : ZXQ_mul(GEN y, GEN x, GEN T) { return ZX_rem(ZX_mul(y, x), T); }
2186 : INLINE GEN
2187 959329 : ZXQ_sqr(GEN x, GEN T) { return ZX_rem(ZX_sqr(x), T); }
2188 :
2189 : INLINE GEN
2190 103033176 : RgX_copy(GEN x)
2191 : {
2192 : long lx, i;
2193 103033176 : GEN y = cgetg_copy(x, &lx); y[1] = x[1];
2194 375573526 : for (i = 2; i<lx; i++) gel(y,i) = gcopy(gel(x,i));
2195 103033199 : return y;
2196 : }
2197 : /* have to use ulong to avoid silly warnings from gcc "assuming signed
2198 : * overflow does not occur" */
2199 : INLINE GEN
2200 2543693 : RgX_coeff(GEN x, long n)
2201 : {
2202 2543693 : ulong l = lg(x);
2203 2543693 : return (n < 0 || ((ulong)n+3) > l)? gen_0: gel(x,n+2);
2204 : }
2205 : INLINE GEN
2206 347497 : RgX_renormalize(GEN x) { return RgX_renormalize_lg(x, lg(x)); }
2207 : INLINE GEN
2208 6917097 : RgX_div(GEN x, GEN y) { return RgX_divrem(x,y,NULL); }
2209 : INLINE GEN
2210 1904 : RgXQX_div(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,NULL); }
2211 : INLINE GEN
2212 107489 : RgXQX_rem(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,ONLY_REM); }
2213 : INLINE GEN
2214 5412703 : FpX_div(GEN x, GEN y, GEN p) { return FpX_divrem(x,y,p, NULL); }
2215 : INLINE GEN
2216 1985558 : Flx_div(GEN x, GEN y, ulong p) { return Flx_divrem(x,y,p, NULL); }
2217 : INLINE GEN
2218 21248551 : Flx_div_pre(GEN x, GEN y, ulong p, ulong pi)
2219 21248551 : { return Flx_divrem_pre(x,y,p,pi, NULL); }
2220 : INLINE GEN
2221 1562370 : F2x_div(GEN x, GEN y) { return F2x_divrem(x,y, NULL); }
2222 : INLINE GEN
2223 0 : FpV_FpC_mul(GEN x, GEN y, GEN p) { return FpV_dotproduct(x,y,p); }
2224 : INLINE GEN
2225 99020906 : pol0_Flx(long sv) { return mkvecsmall(sv); }
2226 : INLINE GEN
2227 55349543 : pol1_Flx(long sv) { return mkvecsmall2(sv, 1); }
2228 : INLINE GEN
2229 35882771 : polx_Flx(long sv) { return mkvecsmall3(sv, 0, 1); }
2230 : INLINE GEN
2231 0 : zero_zx(long sv) { return zero_Flx(sv); }
2232 : INLINE GEN
2233 0 : polx_zx(long sv) { return polx_Flx(sv); }
2234 : INLINE GEN
2235 0 : zx_shift(GEN x, long n) { return Flx_shift(x,n); }
2236 : INLINE GEN
2237 14049 : zx_renormalize(GEN x, long l) { return Flx_renormalize(x,l); }
2238 : INLINE GEN
2239 1350 : zero_F2x(long sv) { return zero_Flx(sv); }
2240 : INLINE GEN
2241 13260030 : pol0_F2x(long sv) { return pol0_Flx(sv); }
2242 : INLINE GEN
2243 3967980 : pol1_F2x(long sv) { return pol1_Flx(sv); }
2244 : INLINE GEN
2245 1077096 : polx_F2x(long sv) { return mkvecsmall2(sv, 2); }
2246 : INLINE int
2247 2870018 : F2x_equal1(GEN x) { return Flx_equal1(x); }
2248 : INLINE int
2249 4702374 : F2x_equal(GEN V, GEN W) { return Flx_equal(V,W); }
2250 : INLINE GEN
2251 62606121 : F2x_copy(GEN x) { return leafcopy(x); }
2252 : INLINE GEN
2253 4487 : F2v_copy(GEN x) { return leafcopy(x); }
2254 : INLINE GEN
2255 2385050 : Flv_copy(GEN x) { return leafcopy(x); }
2256 : INLINE GEN
2257 171367709 : Flx_copy(GEN x) { return leafcopy(x); }
2258 : INLINE GEN
2259 3949687 : vecsmall_copy(GEN x) { return leafcopy(x); }
2260 : INLINE int
2261 9975400 : Flx_equal1(GEN x) { return degpol(x)==0 && x[2] == 1; }
2262 : INLINE int
2263 14133 : ZX_equal1(GEN x) { return degpol(x)==0 && equali1(gel(x,2)); }
2264 : INLINE int
2265 6952466 : ZX_is_monic(GEN x) { return equali1(leading_coeff(x)); }
2266 :
2267 : INLINE GEN
2268 149766274 : ZX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2269 : INLINE GEN
2270 143380307 : FpX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2271 : INLINE GEN
2272 853110 : FpXX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2273 : INLINE GEN
2274 4703870 : FpXQX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2275 : INLINE GEN
2276 122452585 : F2x_renormalize(GEN x, long lx) { return Flx_renormalize(x,lx); }
2277 :
2278 : INLINE GEN
2279 0 : F2xX_shift(GEN a, long n, long vs) { return FlxX_shift(a, n, vs); }
2280 :
2281 : INLINE GEN
2282 38033 : F2v_to_F2x(GEN x, long sv) {
2283 38033 : GEN y = leafcopy(x);
2284 38033 : y[1] = sv; F2x_renormalize(y, lg(y)); return y;
2285 : }
2286 :
2287 : INLINE long
2288 385 : sturm(GEN x) { return sturmpart(x, NULL, NULL); }
2289 :
2290 : INLINE long
2291 5782 : gval(GEN x, long v)
2292 5782 : { pari_sp av = avma; return gc_long(av, gvaluation(x, pol_x(v))); }
2293 :
2294 : INLINE void
2295 480503 : RgX_shift_inplace_init(long v)
2296 480503 : { if (v) (void)cgetg(v, t_VECSMALL); }
2297 : /* shift polynomial in place. assume v free cells have been left before x */
2298 : INLINE GEN
2299 480503 : RgX_shift_inplace(GEN x, long v)
2300 : {
2301 : long i, lx;
2302 : GEN z;
2303 480503 : if (!v) return x;
2304 253169 : lx = lg(x);
2305 253169 : if (lx == 2) return x;
2306 253169 : z = x + lx;
2307 : /* stackdummy's from normalizepol */
2308 253169 : while (lg(z) != v) z += lg(z);
2309 253169 : z += v;
2310 4654514 : for (i = lx-1; i >= 2; i--) gel(--z,0) = gel(x,i);
2311 675895 : for (i = 0; i < v; i++) gel(--z,0) = gen_0;
2312 253169 : z -= 2;
2313 253169 : z[1] = x[1];
2314 253169 : z[0] = evaltyp(t_POL) | evallg(lx+v);
2315 253169 : stackdummy((pari_sp)z, (pari_sp)x); return z;
2316 : }
2317 :
2318 :
2319 : /* LINEAR ALGEBRA */
2320 : INLINE GEN
2321 500505 : zv_to_ZV(GEN x) { return vecsmall_to_vec(x); }
2322 : INLINE GEN
2323 7673415 : zc_to_ZC(GEN x) { return vecsmall_to_col(x); }
2324 : INLINE GEN
2325 3189433 : ZV_to_zv(GEN x) { return vec_to_vecsmall(x); }
2326 : INLINE GEN
2327 0 : zx_to_zv(GEN x, long N) { return Flx_to_Flv(x,N); }
2328 : INLINE GEN
2329 104146 : zv_to_zx(GEN x, long sv) { return Flv_to_Flx(x,sv); }
2330 : INLINE GEN
2331 0 : zm_to_zxV(GEN x, long sv) { return Flm_to_FlxV(x,sv); }
2332 : INLINE GEN
2333 0 : zero_zm(long x, long y) { return zero_Flm(x,y); }
2334 : INLINE GEN
2335 37006236 : zero_zv(long x) { return zero_Flv(x); }
2336 : INLINE GEN
2337 266 : zm_transpose(GEN x) { return Flm_transpose(x); }
2338 : INLINE GEN
2339 0 : zm_copy(GEN x) { return Flm_copy(x); }
2340 : INLINE GEN
2341 2157784 : zv_copy(GEN x) { return Flv_copy(x); }
2342 : INLINE GEN
2343 0 : zm_row(GEN x, long i) { return Flm_row(x,i); }
2344 :
2345 : INLINE GEN
2346 10630424 : ZC_hnfrem(GEN x, GEN y) { return ZC_hnfremdiv(x,y,NULL); }
2347 : INLINE GEN
2348 326512 : ZM_hnfrem(GEN x, GEN y) { return ZM_hnfdivrem(x,y,NULL); }
2349 : INLINE GEN
2350 6857561 : ZM_lll(GEN x, double D, long f) { return ZM_lll_norms(x,D,f,NULL); }
2351 : INLINE void
2352 9244009 : RgM_dimensions(GEN x, long *m, long *n) { *n = lg(x)-1; *m = *n? nbrows(x): 0; }
2353 : INLINE GEN
2354 20545306 : RgM_shallowcopy(GEN x)
2355 : {
2356 : long l;
2357 20545306 : GEN y = cgetg_copy(x, &l);
2358 89197939 : while (--l > 0) gel(y,l) = leafcopy(gel(x,l));
2359 20544950 : return y;
2360 : }
2361 : INLINE GEN
2362 195756 : F2m_copy(GEN x) { return RgM_shallowcopy(x); }
2363 :
2364 : INLINE GEN
2365 0 : F3m_copy(GEN x) { return RgM_shallowcopy(x); }
2366 :
2367 : INLINE GEN
2368 6179716 : Flm_copy(GEN x) { return RgM_shallowcopy(x); }
2369 :
2370 : /* divisibility: return 1 if y[i] | x[i] for all i, 0 otherwise. Assume
2371 : * x,y are ZV of the same length */
2372 : INLINE int
2373 23485 : ZV_dvd(GEN x, GEN y)
2374 : {
2375 23485 : long i, l = lg(x);
2376 37856 : for (i=1; i < l; i++)
2377 30464 : if ( ! dvdii( gel(x,i), gel(y,i) ) ) return 0;
2378 7392 : return 1;
2379 : }
2380 : INLINE GEN
2381 538692 : ZM_ZV_mod(GEN x, GEN y)
2382 1536735 : { pari_APPLY_same(ZV_ZV_mod(gel(x,i), y)) }
2383 : INLINE GEN
2384 7319788 : ZV_ZV_mod(GEN x, GEN y)
2385 18911011 : { pari_APPLY_same(modii(gel(x,i), gel(y,i))) }
2386 : INLINE GEN
2387 0 : vecmodii(GEN x, GEN y) { return ZV_ZV_mod(x,y); }
2388 : INLINE GEN
2389 174881 : vecmoduu(GEN x, GEN y) { pari_APPLY_ulong(((ulong*)x)[i] % ((ulong*)y)[i]) }
2390 :
2391 : /* Fq */
2392 : INLINE GEN
2393 3413221 : Fq_red(GEN x, GEN T, GEN p)
2394 3413221 : { return typ(x)==t_INT? Fp_red(x,p): FpXQ_red(x,T,p); }
2395 : INLINE GEN
2396 110255 : Fq_to_FpXQ(GEN x, GEN T, GEN p /*unused*/)
2397 : {
2398 : (void) p;
2399 110255 : return typ(x)==t_INT ? scalarpol(x, get_FpX_var(T)): x;
2400 : }
2401 : INLINE GEN
2402 756 : Rg_to_Fq(GEN x, GEN T, GEN p) { return T? Rg_to_FpXQ(x,T,p): Rg_to_Fp(x,p); }
2403 :
2404 : INLINE GEN
2405 14581 : gener_Fq_local(GEN T, GEN p, GEN L)
2406 0 : { return T? gener_FpXQ_local(T,p, L)
2407 14581 : : pgener_Fp_local(p, L); }
2408 :
2409 : INLINE GEN
2410 0 : random_Fq(GEN T, GEN p)
2411 0 : { return T ? random_FpX(get_FpX_degree(T), get_FpX_var(T), p): randomi(p); }
2412 :
2413 : /* FpXQX */
2414 : INLINE GEN
2415 4546 : FpXQX_div(GEN x, GEN y, GEN T, GEN p) { return FpXQX_divrem(x, y, T, p, NULL); }
2416 : INLINE GEN
2417 0 : FlxqX_div(GEN x, GEN y, GEN T, ulong p) { return FlxqX_divrem(x, y, T, p, NULL); }
2418 : INLINE GEN
2419 165310 : FlxqX_div_pre(GEN x, GEN y, GEN T, ulong p, ulong pi) { return FlxqX_divrem_pre(x, y, T, p, pi, NULL); }
2420 : INLINE GEN
2421 33243 : F2xqX_div(GEN x, GEN y, GEN T) { return F2xqX_divrem(x, y, T, NULL); }
2422 :
2423 : INLINE GEN
2424 20587 : FpXY_Fq_evaly(GEN Q, GEN y, GEN T, GEN p, long vx)
2425 20587 : { return T ? FpXY_FpXQ_evaly(Q, y, T, p, vx): FpXY_evaly(Q, y, p, vx); }
2426 :
2427 : /* FqX */
2428 : INLINE GEN
2429 25354 : FqX_red(GEN z, GEN T, GEN p) { return T? FpXQX_red(z, T, p): FpX_red(z, p); }
2430 : INLINE GEN
2431 127694 : FqX_add(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2432 : INLINE GEN
2433 24956 : FqX_neg(GEN x,GEN T,GEN p) { return T? FpXX_neg(x,p): FpX_neg(x,p); }
2434 : INLINE GEN
2435 68607 : FqX_sub(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2436 : INLINE GEN
2437 565080 : FqX_Fp_mul(GEN P, GEN u, GEN T, GEN p)
2438 565080 : { return T? FpXX_Fp_mul(P, u, p): FpX_Fp_mul(P, u, p); }
2439 : INLINE GEN
2440 426808 : FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
2441 426808 : { return typ(U)==t_INT ? FqX_Fp_mul(P, U, T, p): FpXQX_FpXQ_mul(P, U, T, p); }
2442 : INLINE GEN
2443 367883 : FqX_mul(GEN x, GEN y, GEN T, GEN p)
2444 367883 : { return T? FpXQX_mul(x, y, T, p): FpX_mul(x, y, p); }
2445 : INLINE GEN
2446 21942 : FqX_mulu(GEN x, ulong y, GEN T, GEN p)
2447 21942 : { return T? FpXX_mulu(x, y, p): FpX_mulu(x, y, p); }
2448 : INLINE GEN
2449 71855 : FqX_sqr(GEN x, GEN T, GEN p)
2450 71855 : { return T? FpXQX_sqr(x, T, p): FpX_sqr(x, p); }
2451 : INLINE GEN
2452 1295 : FqX_powu(GEN x, ulong n, GEN T, GEN p)
2453 1295 : { return T? FpXQX_powu(x, n, T, p): FpX_powu(x, n, p); }
2454 : INLINE GEN
2455 19411 : FqX_halve(GEN x, GEN T, GEN p)
2456 19411 : { return T? FpXX_halve(x, p): FpX_halve(x, p); }
2457 : INLINE GEN
2458 39756 : FqX_div(GEN x, GEN y, GEN T, GEN p)
2459 39756 : { return T? FpXQX_divrem(x,y,T,p,NULL): FpX_divrem(x,y,p,NULL); }
2460 : INLINE GEN
2461 6090 : FqX_get_red(GEN S, GEN T, GEN p)
2462 6090 : { return T? FpXQX_get_red(S,T,p): FpX_get_red(S,p); }
2463 : INLINE GEN
2464 37743 : FqX_rem(GEN x, GEN y, GEN T, GEN p)
2465 37743 : { return T? FpXQX_rem(x,y,T,p): FpX_rem(x,y,p); }
2466 : INLINE GEN
2467 0 : FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
2468 0 : { return T? FpXQX_divrem(x,y,T,p,z): FpX_divrem(x,y,p,z); }
2469 : INLINE GEN
2470 71939 : FqX_div_by_X_x(GEN x, GEN y, GEN T, GEN p, GEN *z)
2471 71939 : { return T? FpXQX_div_by_X_x(x,y,T,p,z): FpX_div_by_X_x(x,y,p,z); }
2472 : INLINE GEN
2473 0 : FqX_halfgcd(GEN P,GEN Q,GEN T,GEN p)
2474 0 : {return T? FpXQX_halfgcd(P,Q,T,p): FpX_halfgcd(P,Q,p);}
2475 : INLINE GEN
2476 692594 : FqX_gcd(GEN P,GEN Q,GEN T,GEN p)
2477 692594 : {return T? FpXQX_gcd(P,Q,T,p): FpX_gcd(P,Q,p);}
2478 : INLINE GEN
2479 440609 : FqX_extgcd(GEN P,GEN Q,GEN T,GEN p, GEN *U, GEN *V)
2480 440609 : { return T? FpXQX_extgcd(P,Q,T,p,U,V): FpX_extgcd(P,Q,p,U,V); }
2481 : INLINE GEN
2482 4487 : FqX_normalize(GEN z, GEN T, GEN p)
2483 4487 : { return T? FpXQX_normalize(z, T, p): FpX_normalize(z, p); }
2484 : INLINE GEN
2485 723681 : FqX_deriv(GEN f, GEN T, GEN p) { return T? FpXX_deriv(f, p): FpX_deriv(f, p); }
2486 : INLINE GEN
2487 0 : FqX_integ(GEN f, GEN T, GEN p) { return T? FpXX_integ(f, p): FpX_integ(f, p); }
2488 : INLINE GEN
2489 141254 : FqX_factor(GEN f, GEN T, GEN p)
2490 141254 : { return T?FpXQX_factor(f, T, p): FpX_factor(f, p); }
2491 : INLINE GEN
2492 7 : FqX_factor_squarefree(GEN f, GEN T, GEN p)
2493 7 : { return T ? FpXQX_factor_squarefree(f, T, p): FpX_factor_squarefree(f, p); }
2494 : INLINE GEN
2495 7 : FqX_ddf(GEN f, GEN T, GEN p)
2496 7 : { return T ? FpXQX_ddf(f, T, p): FpX_ddf(f, p); }
2497 : INLINE GEN
2498 47786 : FqX_degfact(GEN f, GEN T, GEN p)
2499 47786 : { return T?FpXQX_degfact(f, T, p): FpX_degfact(f, p); }
2500 : INLINE GEN
2501 7273 : FqX_roots(GEN f, GEN T, GEN p)
2502 7273 : { return T?FpXQX_roots(f, T, p): FpX_roots(f, p); }
2503 : INLINE GEN
2504 175 : FqX_to_mod(GEN f, GEN T, GEN p)
2505 175 : { return T?FpXQX_to_mod(f, T, p): FpX_to_mod(f, p); }
2506 :
2507 : /*FqXQ*/
2508 : INLINE GEN
2509 0 : FqXQ_add(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2510 0 : { (void)S; return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2511 : INLINE GEN
2512 0 : FqXQ_sub(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2513 0 : { (void)S; return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2514 : INLINE GEN
2515 0 : FqXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
2516 0 : { return T? FpXQXQ_div(x,y,S,T,p): FpXQ_div(x,y,S,p); }
2517 : INLINE GEN
2518 0 : FqXQ_inv(GEN x, GEN S, GEN T, GEN p)
2519 0 : { return T? FpXQXQ_inv(x,S,T,p): FpXQ_inv(x,S,p); }
2520 : INLINE GEN
2521 0 : FqXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
2522 0 : { return T? FpXQXQ_invsafe(x,S,T,p): FpXQ_inv(x,S,p); }
2523 : INLINE GEN
2524 22766 : FqXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
2525 22766 : { return T? FpXQXQ_mul(x,y,S,T,p): FpXQ_mul(x,y,S,p); }
2526 : INLINE GEN
2527 0 : FqXQ_sqr(GEN x, GEN S, GEN T, GEN p)
2528 0 : { return T? FpXQXQ_sqr(x,S,T,p): FpXQ_sqr(x,S,p); }
2529 : INLINE GEN
2530 0 : FqXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
2531 0 : { return T? FpXQXQ_pow(x,n,S,T,p): FpXQ_pow(x,n,S,p); }
2532 :
2533 : /*FqXn*/
2534 : INLINE GEN
2535 6590 : FqXn_expint(GEN x, long n, GEN T, GEN p)
2536 6590 : { return T? FpXQXn_expint(x,n,T,p): FpXn_expint(x,n,p); }
2537 : INLINE GEN
2538 0 : FqXn_exp(GEN x, long n, GEN T, GEN p)
2539 0 : { return T? FpXQXn_exp(x,n,T,p): FpXn_exp(x,n,p); }
2540 : INLINE GEN
2541 7126 : FqXn_inv(GEN x, long n, GEN T, GEN p)
2542 7126 : { return T? FpXQXn_inv(x,n,T,p): FpXn_inv(x,n,p); }
2543 : INLINE GEN
2544 263403 : FqXn_mul(GEN x, GEN y, long n, GEN T, GEN p)
2545 263403 : { return T? FpXQXn_mul(x, y, n, T, p): FpXn_mul(x, y, n, p); }
2546 : INLINE GEN
2547 0 : FqXn_sqr(GEN x, long n, GEN T, GEN p)
2548 0 : { return T? FpXQXn_sqr(x,n,T,p): FpXn_sqr(x,n,p); }
2549 :
2550 : /*FpXQ*/
2551 : INLINE GEN
2552 0 : FpXQ_add(GEN x,GEN y,GEN T/*unused*/,GEN p)
2553 0 : { (void)T; return FpX_add(x,y,p); }
2554 : INLINE GEN
2555 0 : FpXQ_sub(GEN x,GEN y,GEN T/*unused*/,GEN p)
2556 0 : { (void)T; return FpX_sub(x,y,p); }
2557 :
2558 : /*Flxq*/
2559 : INLINE GEN
2560 0 : Flxq_add(GEN x,GEN y,GEN T/*unused*/,ulong p)
2561 0 : { (void)T; return Flx_add(x,y,p); }
2562 : INLINE GEN
2563 0 : Flxq_sub(GEN x,GEN y,GEN T/*unused*/,ulong p)
2564 0 : { (void)T; return Flx_sub(x,y,p); }
2565 :
2566 : /* F2x */
2567 :
2568 : INLINE ulong
2569 652320341 : F2x_coeff(GEN x,long v)
2570 : {
2571 652320341 : ulong u=(ulong)x[2+divsBIL(v)];
2572 652320318 : return (u>>remsBIL(v))&1UL;
2573 : }
2574 :
2575 : INLINE void
2576 11711555 : F2x_clear(GEN x,long v)
2577 : {
2578 11711555 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2579 11711488 : *u&=~(1UL<<remsBIL(v));
2580 11711482 : }
2581 :
2582 : INLINE void
2583 128283588 : F2x_set(GEN x,long v)
2584 : {
2585 128283588 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2586 128280125 : *u|=1UL<<remsBIL(v);
2587 128281338 : }
2588 :
2589 : INLINE void
2590 1557175 : F2x_flip(GEN x,long v)
2591 : {
2592 1557175 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2593 1557175 : *u^=1UL<<remsBIL(v);
2594 1557175 : }
2595 :
2596 : /* F2v */
2597 :
2598 : INLINE ulong
2599 645698224 : F2v_coeff(GEN x,long v) { return F2x_coeff(x,v-1); }
2600 :
2601 : INLINE void
2602 11711567 : F2v_clear(GEN x,long v) { F2x_clear(x,v-1); }
2603 :
2604 : INLINE void
2605 101328292 : F2v_set(GEN x,long v) { F2x_set(x,v-1); }
2606 :
2607 : INLINE void
2608 1557175 : F2v_flip(GEN x,long v) { F2x_flip(x,v-1); }
2609 :
2610 : /* F2m */
2611 :
2612 : INLINE ulong
2613 7545865 : F2m_coeff(GEN x, long a, long b) { return F2v_coeff(gel(x,b), a); }
2614 :
2615 : INLINE void
2616 0 : F2m_clear(GEN x, long a, long b) { F2v_clear(gel(x,b), a); }
2617 :
2618 : INLINE void
2619 686 : F2m_set(GEN x, long a, long b) { F2v_set(gel(x,b), a); }
2620 :
2621 : INLINE void
2622 1557175 : F2m_flip(GEN x, long a, long b) { F2v_flip(gel(x,b), a); }
2623 :
2624 : /* F3m */
2625 :
2626 : INLINE ulong
2627 1807370 : F3m_coeff(GEN x, long a, long b) { return F3v_coeff(gel(x,b), a); }
2628 :
2629 : INLINE void
2630 0 : F3m_set(GEN x, long a, long b, ulong c) { F3v_set(gel(x,b), a, c); }
2631 :
2632 : /* ARITHMETIC */
2633 : INLINE GEN
2634 35811 : matpascal(long n) { return matqpascal(n, NULL); }
2635 : INLINE long
2636 458590 : Z_issquare(GEN x) { return Z_issquareall(x, NULL); }
2637 : INLINE long
2638 98 : Z_ispower(GEN x, ulong k) { return Z_ispowerall(x, k, NULL); }
2639 : INLINE GEN
2640 6567659 : sqrti(GEN x) { return sqrtremi(x,NULL); }
2641 : INLINE GEN
2642 123149650 : gaddgs(GEN y, long s) { return gaddsg(s,y); }
2643 : INLINE int
2644 616064 : gcmpgs(GEN y, long s) { return -gcmpsg(s,y); }
2645 : INLINE int
2646 29176 : gequalgs(GEN y, long s) { return gequalsg(s,y); }
2647 : INLINE GEN
2648 0 : gmaxsg(long s, GEN y) { return gmaxgs(y,s); }
2649 : INLINE GEN
2650 0 : gminsg(long s, GEN y) { return gmings(y,s); }
2651 : INLINE GEN
2652 20426357 : gmulgs(GEN y, long s) { return gmulsg(s,y); }
2653 : INLINE GEN
2654 124149795 : gmulgu(GEN y, ulong s) { return gmulug(s,y); }
2655 : INLINE GEN
2656 1712019 : gsubgs(GEN y, long s) { return gaddgs(y, -s); }
2657 : INLINE GEN
2658 522388 : gdivsg(long s, GEN y) { return gdiv(stoi(s), y); }
2659 :
2660 : INLINE GEN
2661 13509610 : gmax_shallow(GEN x, GEN y) { return gcmp(x,y)<0? y: x; }
2662 : INLINE GEN
2663 893400 : gmin_shallow(GEN x, GEN y) { return gcmp(x,y)<0? x: y; }
2664 :
2665 : /* x t_COMPLEX */
2666 : INLINE GEN
2667 91913316 : cxnorm(GEN x) { return gadd(gsqr(gel(x,1)), gsqr(gel(x,2))); }
2668 : /* q t_QUAD */
2669 : INLINE GEN
2670 69860 : quadnorm(GEN q)
2671 : {
2672 69860 : GEN X = gel(q,1), b = gel(X,3), c = gel(X,2);
2673 69860 : GEN z, u = gel(q,3), v = gel(q,2);
2674 69860 : if (typ(u) == t_INT && typ(v) == t_INT) /* generic case */
2675 : {
2676 69671 : z = signe(b)? mulii(v, addii(u,v)): sqri(v);
2677 69671 : return addii(z, mulii(c, sqri(u)));
2678 : }
2679 : else
2680 : {
2681 189 : z = signe(b)? gmul(v, gadd(u,v)): gsqr(v);
2682 189 : return gadd(z, gmul(c, gsqr(u)));
2683 : }
2684 : }
2685 : /* x a t_QUAD, return the attached discriminant */
2686 : INLINE GEN
2687 1078 : quad_disc(GEN x)
2688 : {
2689 1078 : GEN Q = gel(x,1), b = gel(Q,3), c = gel(Q,2), c4 = shifti(c,2);
2690 1078 : if (is_pm1(b)) return subsi(1, c4);
2691 154 : togglesign_safe(&c4); return c4;
2692 : }
2693 : INLINE GEN
2694 4777764 : qfb_disc3(GEN x, GEN y, GEN z) { return subii(sqri(y), shifti(mulii(x,z),2)); }
2695 : INLINE GEN
2696 18474869 : qfb_disc(GEN x) { return gel(x,4); }
2697 :
2698 : INLINE GEN
2699 4009304 : sqrfrac(GEN x)
2700 : {
2701 4009304 : GEN z = cgetg(3,t_FRAC);
2702 4009304 : gel(z,1) = sqri(gel(x,1));
2703 4009304 : gel(z,2) = sqri(gel(x,2)); return z;
2704 : }
2705 :
2706 : INLINE void
2707 16522936 : normalize_frac(GEN z) {
2708 16522936 : if (signe(gel(z,2)) < 0) { togglesign(gel(z,1)); setabssign(gel(z,2)); }
2709 16522936 : }
2710 :
2711 : INLINE GEN
2712 37985681 : powii(GEN x, GEN n)
2713 : {
2714 37985681 : long ln = lgefint(n);
2715 37985681 : if (ln == 3) {
2716 : GEN z;
2717 37962936 : if (signe(n) > 0) return powiu(x, n[2]);
2718 73707 : z = cgetg(3, t_FRAC);
2719 73711 : gel(z,1) = gen_1;
2720 73711 : gel(z,2) = powiu(x, n[2]);
2721 73711 : return z;
2722 : }
2723 22745 : if (ln == 2) return gen_1; /* rare */
2724 : /* should never happen */
2725 0 : return powgi(x, n); /* overflow unless x = 0, 1, -1 */
2726 : }
2727 : INLINE GEN
2728 1561 : powIs(long n) {
2729 1561 : switch(n & 3)
2730 : {
2731 63 : case 1: return mkcomplex(gen_0,gen_1);
2732 385 : case 2: return gen_m1;
2733 707 : case 3: return mkcomplex(gen_0,gen_m1);
2734 : }
2735 406 : return gen_1;
2736 : }
2737 :
2738 : /*******************************************************************/
2739 : /* */
2740 : /* ASSIGNMENTS */
2741 : /* */
2742 : /*******************************************************************/
2743 0 : INLINE void mpexpz(GEN x, GEN z)
2744 0 : { pari_sp av = avma; gaffect(mpexp(x), z); set_avma(av); }
2745 0 : INLINE void mplogz(GEN x, GEN z)
2746 0 : { pari_sp av = avma; gaffect(mplog(x), z); set_avma(av); }
2747 0 : INLINE void mpcosz(GEN x, GEN z)
2748 0 : { pari_sp av = avma; gaffect(mpcos(x), z); set_avma(av); }
2749 0 : INLINE void mpsinz(GEN x, GEN z)
2750 0 : { pari_sp av = avma; gaffect(mpsin(x), z); set_avma(av); }
2751 0 : INLINE void gnegz(GEN x, GEN z)
2752 0 : { pari_sp av = avma; gaffect(gneg(x), z); set_avma(av); }
2753 0 : INLINE void gabsz(GEN x, long prec, GEN z)
2754 0 : { pari_sp av = avma; gaffect(gabs(x,prec), z); set_avma(av); }
2755 0 : INLINE void gaddz(GEN x, GEN y, GEN z)
2756 0 : { pari_sp av = avma; gaffect(gadd(x,y), z); set_avma(av); }
2757 0 : INLINE void gsubz(GEN x, GEN y, GEN z)
2758 0 : { pari_sp av = avma; gaffect(gsub(x,y), z); set_avma(av); }
2759 0 : INLINE void gmulz(GEN x, GEN y, GEN z)
2760 0 : { pari_sp av = avma; gaffect(gmul(x,y), z); set_avma(av); }
2761 0 : INLINE void gdivz(GEN x, GEN y, GEN z)
2762 0 : { pari_sp av = avma; gaffect(gdiv(x,y), z); set_avma(av); }
2763 0 : INLINE void gdiventz(GEN x, GEN y, GEN z)
2764 0 : { pari_sp av = avma; gaffect(gdivent(x,y), z); set_avma(av); }
2765 0 : INLINE void gmodz(GEN x, GEN y, GEN z)
2766 0 : { pari_sp av = avma; gaffect(gmod(x,y), z); set_avma(av); }
2767 0 : INLINE void gmul2nz(GEN x, long s, GEN z)
2768 0 : { pari_sp av = avma; gaffect(gmul2n(x,s), z); set_avma(av); }
2769 0 : INLINE void gshiftz(GEN x, long s, GEN z)
2770 0 : { pari_sp av = avma; gaffect(gshift(x,s), z); set_avma(av); }
2771 :
2772 : /*******************************************************************/
2773 : /* */
2774 : /* ELLIPTIC CURVES */
2775 : /* */
2776 : /*******************************************************************/
2777 7133470 : INLINE GEN ell_get_a1(GEN e) { return gel(e,1); }
2778 5716415 : INLINE GEN ell_get_a2(GEN e) { return gel(e,2); }
2779 6922277 : INLINE GEN ell_get_a3(GEN e) { return gel(e,3); }
2780 6525928 : INLINE GEN ell_get_a4(GEN e) { return gel(e,4); }
2781 7959542 : INLINE GEN ell_get_a6(GEN e) { return gel(e,5); }
2782 5432029 : INLINE GEN ell_get_b2(GEN e) { return gel(e,6); }
2783 2135394 : INLINE GEN ell_get_b4(GEN e) { return gel(e,7); }
2784 3054676 : INLINE GEN ell_get_b6(GEN e) { return gel(e,8); }
2785 2608971 : INLINE GEN ell_get_b8(GEN e) { return gel(e,9); }
2786 8020889 : INLINE GEN ell_get_c4(GEN e) { return gel(e,10); }
2787 8849788 : INLINE GEN ell_get_c6(GEN e) { return gel(e,11); }
2788 11280211 : INLINE GEN ell_get_disc(GEN e) { return gel(e,12); }
2789 1296342 : INLINE GEN ell_get_j(GEN e) { return gel(e,13); }
2790 11379583 : INLINE long ell_get_type(GEN e) { return mael(e,14,1); }
2791 2037198 : INLINE GEN ellff_get_field(GEN x) { return gmael(x, 15, 1); }
2792 800245 : INLINE GEN ellff_get_a4a6(GEN x) { return gmael(x, 15, 2); }
2793 1484 : INLINE GEN ellQp_get_zero(GEN x) { return gmael(x, 15, 1); }
2794 315 : INLINE long ellQp_get_prec(GEN E) { GEN z = ellQp_get_zero(E); return valp(z); }
2795 1134 : INLINE GEN ellQp_get_p(GEN E) { GEN z = ellQp_get_zero(E); return gel(z,2); }
2796 249641 : INLINE long ellR_get_prec(GEN x) { return nbits2prec(mael3(x, 15, 1, 1)); }
2797 370840 : INLINE long ellR_get_sign(GEN x) { return mael3(x, 15, 1, 2); }
2798 1888750 : INLINE GEN ellnf_get_nf(GEN x) { return checknf_i(gmael(x,15,1)); }
2799 126 : INLINE GEN ellnf_get_bnf(GEN x) { return checkbnf_i(gmael(x,15,1)); }
2800 :
2801 4682625 : INLINE int checkell_i(GEN e) { return typ(e) == t_VEC && lg(e) == 17; }
2802 47615159 : INLINE int ell_is_inf(GEN z) { return lg(z) == 2; }
2803 1232341 : INLINE GEN ellinf(void) { return mkvec(gen_0); }
2804 :
2805 : /*******************************************************************/
2806 : /* */
2807 : /* ALGEBRAIC NUMBER THEORY */
2808 : /* */
2809 : /*******************************************************************/
2810 32021576 : INLINE GEN modpr_get_pr(GEN x) { return gel(x,3); }
2811 1887276 : INLINE GEN modpr_get_p(GEN x) { return pr_get_p(modpr_get_pr(x)); }
2812 13884940 : INLINE GEN modpr_get_T(GEN x) { return lg(x) == 4? NULL: gel(x,4); }
2813 :
2814 91249632 : INLINE GEN pr_get_p(GEN pr) { return gel(pr,1); }
2815 11411764 : INLINE GEN pr_get_gen(GEN pr){ return gel(pr,2); }
2816 : /* .[2] instead of itos works: e and f are small positive integers */
2817 15510422 : INLINE long pr_get_e(GEN pr) { return gel(pr,3)[2]; }
2818 25207830 : INLINE long pr_get_f(GEN pr) { return gel(pr,4)[2]; }
2819 47890293 : INLINE GEN pr_get_tau(GEN pr){ return gel(pr,5); }
2820 : INLINE int
2821 16409593 : pr_is_inert(GEN P) { return typ(pr_get_tau(P)) == t_INT; }
2822 : INLINE GEN
2823 1000386 : pr_norm(GEN pr) { return powiu(pr_get_p(pr), pr_get_f(pr)); }
2824 : INLINE ulong
2825 343931 : upr_norm(GEN pr) { return upowuu(pr_get_p(pr)[2], pr_get_f(pr)); }
2826 :
2827 : /* assume nf a genuine nf */
2828 : INLINE long
2829 1163584 : nf_get_varn(GEN nf) { return varn(gel(nf,1)); }
2830 : INLINE GEN
2831 106066427 : nf_get_pol(GEN nf) { return gel(nf,1); }
2832 : INLINE long
2833 80178456 : nf_get_degree(GEN nf) { return degpol( nf_get_pol(nf) ); }
2834 : INLINE long
2835 22516319 : nf_get_r1(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,1)); }
2836 : INLINE long
2837 4147 : nf_get_r2(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,2)); }
2838 : INLINE GEN
2839 452808 : nf_get_disc(GEN nf) { return gel(nf,3); }
2840 : INLINE GEN
2841 3569479 : nf_get_index(GEN nf) { return gel(nf,4); }
2842 : INLINE GEN
2843 22663429 : nf_get_M(GEN nf) { return gmael(nf,5,1); }
2844 : INLINE GEN
2845 238334 : nf_get_G(GEN nf) { return gmael(nf,5,2); }
2846 : INLINE GEN
2847 1618859 : nf_get_roundG(GEN nf) { return gmael(nf,5,3); }
2848 : INLINE GEN
2849 22084 : nf_get_Tr(GEN nf) { return gmael(nf,5,4); }
2850 : INLINE GEN
2851 4444 : nf_get_diff(GEN nf) { return gmael(nf,5,5); }
2852 : INLINE GEN
2853 58049 : nf_get_ramified_primes(GEN nf) { return gmael(nf,5,8); }
2854 : INLINE GEN
2855 1398978 : nf_get_roots(GEN nf) { return gel(nf,6); }
2856 : INLINE GEN
2857 1848 : nf_get_zk(GEN nf)
2858 : {
2859 1848 : GEN y = gel(nf,7), D = gel(y, 1);
2860 1848 : if (typ(D) == t_POL) D = gel(D, 2);
2861 1848 : if (!equali1(D)) y = gdiv(y, D);
2862 1848 : return y;
2863 : }
2864 : INLINE GEN
2865 4080308 : nf_get_zkprimpart(GEN nf)
2866 : {
2867 4080308 : GEN y = gel(nf,7);
2868 : /* test for old format of nf.zk: non normalized */
2869 4080308 : if (!equali1(gel(nf,4)) && gequal1(gel(y,1))) y = Q_remove_denom(y,NULL);
2870 4080307 : return y;
2871 : }
2872 : INLINE GEN
2873 4126708 : nf_get_zkden(GEN nf)
2874 : {
2875 4126708 : GEN y = gel(nf,7), D = gel(y,1);
2876 4126708 : if (typ(D) == t_POL) D = gel(D,2);
2877 : /* test for old format of nf.zk: non normalized */
2878 4126708 : if (!equali1(gel(nf,4)) && equali1(D)) D = Q_denom(y);
2879 4126695 : return D;
2880 : }
2881 : INLINE GEN
2882 9831326 : nf_get_invzk(GEN nf) { return gel(nf,8); }
2883 : INLINE void
2884 516227 : nf_get_sign(GEN nf, long *r1, long *r2)
2885 : {
2886 516227 : GEN x = gel(nf,2);
2887 516227 : *r1 = itou(gel(x,1));
2888 516225 : *r2 = itou(gel(x,2));
2889 516225 : }
2890 :
2891 : INLINE GEN
2892 2521277 : cyc_get_expo(GEN c) { return lg(c) == 1? gen_1: gel(c,1); }
2893 : INLINE GEN
2894 391805 : abgrp_get_no(GEN x) { return gel(x,1); }
2895 : INLINE GEN
2896 11548337 : abgrp_get_cyc(GEN x) { return gel(x,2); }
2897 : INLINE GEN
2898 1653401 : abgrp_get_gen(GEN x) { return gel(x,3); }
2899 : INLINE GEN
2900 9424663 : bnf_get_nf(GEN bnf) { return gel(bnf,7); }
2901 : INLINE GEN
2902 5097119 : bnf_get_clgp(GEN bnf) { return gmael(bnf,8,1); }
2903 : INLINE GEN
2904 8379 : bnf_get_no(GEN bnf) { return abgrp_get_no(bnf_get_clgp(bnf)); }
2905 : INLINE GEN
2906 3508921 : bnf_get_cyc(GEN bnf) { return abgrp_get_cyc(bnf_get_clgp(bnf)); }
2907 : INLINE GEN
2908 1579655 : bnf_get_gen(GEN bnf) { return abgrp_get_gen(bnf_get_clgp(bnf)); }
2909 : INLINE GEN
2910 641 : bnf_get_reg(GEN bnf) { return gmael(bnf,8,2); }
2911 : INLINE GEN
2912 2702003 : bnf_get_logfu(GEN bnf) { return gel(bnf,3); }
2913 : INLINE GEN
2914 1278258 : bnf_get_sunits(GEN bnf)
2915 1278258 : { GEN s = gmael(bnf,8,3); return typ(s) == t_INT? NULL: s; }
2916 : INLINE GEN
2917 290319 : bnf_get_tuU(GEN bnf) { return gmael3(bnf,8,4,2); }
2918 : INLINE long
2919 264984 : bnf_get_tuN(GEN bnf) { return gmael3(bnf,8,4,1)[2]; }
2920 : INLINE GEN
2921 287986 : bnf_get_fu_nocheck(GEN bnf) { return gmael(bnf,8,5); }
2922 : INLINE GEN
2923 26279 : nfV_to_scalar_or_alg(GEN nf, GEN x)
2924 63407 : { pari_APPLY_same(nf_to_scalar_or_alg(nf, gel(x,i))) }
2925 : INLINE GEN
2926 25838 : bnf_get_fu(GEN bnf) {
2927 25838 : GEN fu = bnf_build_units(bnf), nf = bnf_get_nf(bnf);
2928 25838 : if (typ(fu) == t_MAT) pari_err(e_MISC,"missing units in bnf");
2929 25838 : return nfV_to_scalar_or_alg(nf, vecslice(fu, 2, lg(fu)-1));
2930 : }
2931 :
2932 : INLINE GEN
2933 3631900 : bnr_get_bnf(GEN bnr) { return gel(bnr,1); }
2934 : INLINE GEN
2935 1936782 : bnr_get_bid(GEN bnr) { return gel(bnr,2); }
2936 : INLINE GEN
2937 140826 : bnr_get_mod(GEN bnr) { return gmael(bnr,2,1); }
2938 : INLINE GEN
2939 1259717 : bnr_get_nf(GEN bnr) { return gmael(bnr,1,7); }
2940 : INLINE GEN
2941 2728074 : bnr_get_clgp(GEN bnr) { return gel(bnr,5); }
2942 : INLINE GEN
2943 314409 : bnr_get_no(GEN bnr) { return abgrp_get_no(bnr_get_clgp(bnr)); }
2944 : INLINE GEN
2945 2396057 : bnr_get_cyc(GEN bnr) { return abgrp_get_cyc(bnr_get_clgp(bnr)); }
2946 : INLINE GEN
2947 70 : bnr_get_gen_nocheck(GEN bnr) { return abgrp_get_gen(bnr_get_clgp(bnr)); }
2948 : INLINE GEN
2949 7847 : bnr_get_gen(GEN bnr) {
2950 7847 : GEN G = bnr_get_clgp(bnr);
2951 7847 : if (lg(G) != 4)
2952 0 : pari_err(e_MISC,"missing bnr generators: please use bnrinit(,,1)");
2953 7847 : return gel(G,3);
2954 : }
2955 :
2956 : /* localstar, used in gchar */
2957 : INLINE GEN
2958 51956 : locs_get_cyc(GEN locs) { return gel(locs,1); }
2959 : INLINE GEN
2960 191695 : locs_get_Lsprk(GEN locs) { return gel(locs,2); }
2961 : INLINE GEN
2962 1260 : locs_get_Lgenfil(GEN locs) { return gel(locs,3); }
2963 : INLINE GEN
2964 8225 : locs_get_mod(GEN locs) { return gel(locs,4); }
2965 : /* pr dividing the modulus N of locs, 0 <= i < v_pr(N)
2966 : * return a t_MAT whose columns are the logs
2967 : * of generators of U_i(pr)/U_{i+1}(pr). */
2968 : INLINE GEN
2969 1260 : locs_get_famod(GEN locs) { return gmael(locs,4,1); }
2970 : INLINE GEN
2971 207235 : locs_get_m_infty(GEN locs) { return gmael(locs,4,2); }
2972 :
2973 : /* G a grossenchar group */
2974 : INLINE GEN
2975 32639 : gchar_get_basis(GEN gc) { return gel(gc, 1); }
2976 : INLINE GEN
2977 203105 : gchar_get_bnf(GEN gc) { return gel(gc, 2); }
2978 : INLINE GEN
2979 241405 : gchar_get_nf(GEN gc) { return gel(gc, 3); }
2980 : INLINE GEN
2981 279435 : gchar_get_zm(GEN gc) { return gel(gc, 4); }
2982 : INLINE GEN
2983 8225 : gchar_get_mod(GEN gc) { return locs_get_mod(gchar_get_zm(gc)); }
2984 : INLINE GEN
2985 4095 : gchar_get_modP(GEN gc) { return gmael(gchar_get_mod(gc),1,1); }
2986 : INLINE GEN
2987 36866 : gchar_get_S(GEN gc) { return gel(gc, 5); }
2988 : INLINE GEN
2989 188468 : gchar_get_DLdata(GEN gc) { return gel(gc, 6); }
2990 : INLINE GEN
2991 1749 : gchar_get_sfu(GEN gc) { return gel(gc, 7); }
2992 : INLINE GEN
2993 16168 : gchar_get_cyc(GEN gc) { return gel(gc, 9); }
2994 : INLINE GEN
2995 0 : gchar_get_hnf(GEN gc) { return gmael(gc, 10, 1); }
2996 : INLINE GEN
2997 0 : gchar_get_U(GEN gc) { return gmael(gc, 10, 2); }
2998 : INLINE GEN
2999 10969 : gchar_get_Ui(GEN gc) { return gmael(gc, 10, 3); }
3000 : INLINE GEN
3001 3322 : gchar_get_m0(GEN gc) { return gel(gc, 11); }
3002 : INLINE GEN
3003 4272 : gchar_get_u0(GEN gc) { return gel(gc, 12); }
3004 : INLINE long
3005 17416 : gchar_get_r1(GEN gc) { return nf_get_r1(gchar_get_nf(gc)); }
3006 : INLINE long
3007 623 : gchar_get_r2(GEN gc) { return nf_get_r2(gchar_get_nf(gc)); }
3008 : INLINE GEN
3009 50348 : gchar_get_loccyc(GEN gc) { return locs_get_cyc(gchar_get_zm(gc)); }
3010 : INLINE long
3011 37132 : gchar_get_nc(GEN gc) { return lg(gchar_get_loccyc(gc))-1; }
3012 : INLINE long
3013 36866 : gchar_get_ns(GEN gc) { return lg(gchar_get_S(gc))-1; }
3014 : INLINE long
3015 1841 : gchar_get_nm(GEN gc) { return lg(gchar_get_basis(gc))-1; }
3016 : INLINE long
3017 4011 : gchar_get_evalprec(GEN gc) { return gmael(gc, 8, 1)[1]; }
3018 : INLINE long
3019 18732 : gchar_get_prec(GEN gc) { return gmael(gc, 8, 1)[2]; }
3020 : INLINE long
3021 13419 : gchar_get_nfprec(GEN gc) { return gmael(gc, 8, 1)[3]; }
3022 : INLINE void
3023 1785 : gchar_set_evalprec(GEN gc, long prec) { gmael(gc, 8, 1)[1] = prec; }
3024 : INLINE void
3025 1202 : gchar_set_prec(GEN gc, long prec) { gmael(gc, 8, 1)[2] = prec; }
3026 : INLINE void
3027 1202 : gchar_copy_precs(GEN gc, GEN gc2)
3028 : {
3029 1202 : gel(gc2, 8) = shallowcopy(gel(gc,8));
3030 1202 : gmael(gc2, 8, 1) = shallowcopy(gmael(gc, 8, 1));
3031 1202 : }
3032 : INLINE void
3033 2951 : gchar_set_nfprec(GEN gc, long prec) { gmael(gc, 8, 1)[3] = prec; }
3034 : INLINE long
3035 322 : gchar_get_ntors(GEN gc) { return gmael(gc, 8, 2)[1]; }
3036 : INLINE long
3037 322 : gchar_get_nfree(GEN gc) { return gmael(gc, 8, 2)[2]; }
3038 : INLINE long
3039 2042 : gchar_get_nalg(GEN gc) { return gmael(gc, 8, 2)[3]; }
3040 : INLINE void
3041 1573 : gchar_set_basis(GEN gc, GEN m_inv) { gel(gc, 1) = m_inv; }
3042 : INLINE void
3043 2078 : gchar_set_nf(GEN gc, GEN nf) { gel(gc, 3) = nf; }
3044 : INLINE void
3045 623 : gchar_set_ntors(GEN gc, long n) { gmael(gc, 8, 2)[1] = n; }
3046 : INLINE void
3047 623 : gchar_set_nfree(GEN gc, long n) { gmael(gc, 8, 2)[2] = n; }
3048 : INLINE void
3049 623 : gchar_set_nalg(GEN gc, long n) { gmael(gc, 8, 2)[3] = n; }
3050 : INLINE void
3051 1573 : gchar_set_cyc(GEN gc, GEN cyc) { gel(gc, 9) = cyc; }
3052 : INLINE void
3053 623 : gchar_set_HUUi(GEN gc, GEN hnf, GEN U, GEN Ui) { gel(gc, 10) = mkvec3(hnf, U, Ui); }
3054 : INLINE void
3055 950 : gchar_set_m0(GEN gc, GEN m0) { gel(gc, 11) = m0; }
3056 : INLINE void
3057 2093 : gchar_set_u0(GEN gc, GEN u0) { gel(gc, 12) = u0; }
3058 :
3059 : INLINE GEN
3060 1386658 : bid_get_mod(GEN bid) { return gel(bid,1); }
3061 : INLINE GEN
3062 78295 : bid_get_ideal(GEN bid) { return gmael(bid,1,1); }
3063 : INLINE GEN
3064 35091 : bid_get_arch(GEN bid) { return gmael(bid,1,2); }
3065 : INLINE GEN
3066 5415218 : bid_get_grp(GEN bid) { return gel(bid,2); }
3067 : INLINE GEN
3068 2313541 : bid_get_fact(GEN bid) { return gmael(bid,3,1); }
3069 : INLINE GEN
3070 2025062 : bid_get_fact2(GEN bid) { return gmael(bid,3,2); }
3071 : INLINE GEN
3072 1990533 : bid_get_MOD(GEN bid) { GEN y = gel(bid,4); return lg(y) == 4? gel(y,3): NULL; }
3073 : INLINE GEN
3074 1991258 : bid_get_sprk(GEN bid) { return gmael(bid,4,1); }
3075 : INLINE GEN
3076 51226 : bid_get_sarch(GEN bid) { return gmael(bid,4,2); }
3077 : INLINE GEN
3078 2217457 : bid_get_archp(GEN bid) { return gmael3(bid,4,2,2); }
3079 : INLINE GEN
3080 3378246 : bid_get_U(GEN bid) { return gel(bid,5); }
3081 : INLINE GEN
3082 0 : bid_get_no(GEN bid) { return abgrp_get_no(bid_get_grp(bid)); }
3083 : INLINE GEN
3084 5361317 : bid_get_cyc(GEN bid) { return abgrp_get_cyc(bid_get_grp(bid)); }
3085 : INLINE GEN
3086 0 : bid_get_gen_nocheck(GEN bid) { return abgrp_get_gen(bid_get_grp(bid)); }
3087 : INLINE GEN
3088 53326 : bid_get_gen(GEN bid) {
3089 53326 : GEN G = bid_get_grp(bid);
3090 53326 : if (lg(G) != 4) pari_err(e_MISC,"missing bid generators. Use idealstar(,,2)");
3091 53326 : return abgrp_get_gen(G);
3092 : }
3093 :
3094 : INLINE GEN
3095 33820236 : znstar_get_N(GEN G) { return gmael(G,1,1); }
3096 : INLINE GEN
3097 7205872 : znstar_get_faN(GEN G) { return gel(G,3); }
3098 : INLINE GEN
3099 14 : znstar_get_no(GEN G) { return abgrp_get_no(gel(G,2)); }
3100 : INLINE GEN
3101 261920 : znstar_get_cyc(GEN G) { return abgrp_get_cyc(gel(G,2)); }
3102 : INLINE GEN
3103 16150 : znstar_get_gen(GEN G) { return abgrp_get_gen(gel(G,2)); }
3104 : INLINE GEN
3105 7818252 : znstar_get_conreycyc(GEN G) { return gmael(G,4,5); }
3106 : INLINE GEN
3107 3219560 : znstar_get_conreygen(GEN G) { return gmael(G,4,4); }
3108 : INLINE GEN
3109 46788 : znstar_get_Ui(GEN G) { return gmael(G,4,3); }
3110 : INLINE GEN
3111 176051 : znstar_get_U(GEN G) { return gel(G,5); }
3112 : INLINE GEN
3113 2819363 : znstar_get_pe(GEN G) { return gmael(G,4,1); }
3114 : INLINE GEN
3115 35875 : gal_get_pol(GEN gal) { return gel(gal,1); }
3116 : INLINE GEN
3117 6006 : gal_get_p(GEN gal) { return gmael(gal,2,1); }
3118 : INLINE GEN
3119 91 : gal_get_e(GEN gal) { return gmael(gal,2,2); }
3120 : INLINE GEN
3121 23660 : gal_get_mod(GEN gal) { return gmael(gal,2,3); }
3122 : INLINE GEN
3123 32319 : gal_get_roots(GEN gal) { return gel(gal,3); }
3124 : INLINE GEN
3125 27461 : gal_get_invvdm(GEN gal) { return gel(gal,4); }
3126 : INLINE GEN
3127 27454 : gal_get_den(GEN gal) { return gel(gal,5); }
3128 : INLINE GEN
3129 79518 : gal_get_group(GEN gal) { return gel(gal,6); }
3130 : INLINE GEN
3131 14889 : gal_get_gen(GEN gal) { return gel(gal,7); }
3132 : INLINE GEN
3133 6629 : gal_get_orders(GEN gal) { return gel(gal,8); }
3134 :
3135 : /* assume rnf a genuine rnf */
3136 : INLINE long
3137 1224663 : rnf_get_degree(GEN rnf) { return degpol(rnf_get_pol(rnf)); }
3138 : INLINE long
3139 17493 : rnf_get_nfdegree(GEN rnf) { return degpol(nf_get_pol(rnf_get_nf(rnf))); }
3140 : INLINE long
3141 768035 : rnf_get_absdegree(GEN rnf) { return degpol(gmael(rnf,11,1)); }
3142 : INLINE GEN
3143 819 : rnf_get_idealdisc(GEN rnf) { return gmael(rnf,3,1); }
3144 : INLINE GEN
3145 805 : rnf_get_k(GEN rnf) { return gmael(rnf,11,3); }
3146 : INLINE GEN
3147 903 : rnf_get_alpha(GEN rnf) { return gmael(rnf, 11, 2); }
3148 : INLINE GEN
3149 459753 : rnf_get_nf(GEN rnf) { return gel(rnf,10); }
3150 : INLINE GEN
3151 4760 : rnf_get_nfzk(GEN rnf) { return gel(rnf,2); }
3152 : INLINE GEN
3153 227315 : rnf_get_polabs(GEN rnf) { return gmael(rnf,11,1); }
3154 : INLINE GEN
3155 1486912 : rnf_get_pol(GEN rnf) { return gel(rnf,1); }
3156 : INLINE GEN
3157 280 : rnf_get_disc(GEN rnf) { return gel(rnf,3); }
3158 : INLINE GEN
3159 105 : rnf_get_index(GEN rnf) { return gel(rnf,4); }
3160 : INLINE GEN
3161 1904 : rnf_get_ramified_primes(GEN rnf) { return gel(rnf,5); }
3162 : INLINE long
3163 574 : rnf_get_varn(GEN rnf) { return varn(gel(rnf,1)); }
3164 : INLINE GEN
3165 199417 : rnf_get_nfpol(GEN rnf) { return gmael(rnf,10,1); }
3166 : INLINE long
3167 3388 : rnf_get_nfvarn(GEN rnf) { return varn(gmael(rnf,10,1)); }
3168 : INLINE GEN
3169 3885 : rnf_get_zk(GEN rnf) { return gel(rnf,7); }
3170 : INLINE GEN
3171 107826 : rnf_get_map(GEN rnf) { return gel(rnf,11); }
3172 : INLINE GEN
3173 1225 : rnf_get_invzk(GEN rnf) { return gel(rnf,8); }
3174 :
3175 : INLINE GEN
3176 138542 : idealred(GEN nf, GEN I) { return idealred0(nf, I, NULL); }
3177 :
3178 : INLINE GEN
3179 3415 : idealchineseinit(GEN nf, GEN x)
3180 3415 : { return idealchinese(nf,x,NULL); }
3181 :
3182 : /*******************************************************************/
3183 : /* */
3184 : /* CLOSURES */
3185 : /* */
3186 : /*******************************************************************/
3187 360403007 : INLINE long closure_arity(GEN C) { return ((ulong)C[1])&ARITYBITS; }
3188 40008212 : INLINE long closure_is_variadic(GEN C) { return !!(((ulong)C[1])&VARARGBITS); }
3189 311773866 : INLINE const char *closure_codestr(GEN C) { return GSTR(gel(C,2))-1; }
3190 0 : INLINE GEN closure_get_code(GEN C) { return gel(C,2); }
3191 311744900 : INLINE GEN closure_get_oper(GEN C) { return gel(C,3); }
3192 311725389 : INLINE GEN closure_get_data(GEN C) { return gel(C,4); }
3193 12865 : INLINE GEN closure_get_dbg(GEN C) { return gel(C,5); }
3194 35546 : INLINE GEN closure_get_text(GEN C) { return gel(C,6); }
3195 12948071 : INLINE GEN closure_get_frame(GEN C) { return gel(C,7); }
3196 :
3197 : /*******************************************************************/
3198 : /* */
3199 : /* ERRORS */
3200 : /* */
3201 : /*******************************************************************/
3202 : INLINE long
3203 61010 : err_get_num(GEN e) { return e[1]; }
3204 : INLINE GEN
3205 273 : err_get_compo(GEN e, long i) { return gel(e, i+1); }
3206 :
3207 : INLINE void
3208 14 : pari_err_BUG(const char *f) { pari_err(e_BUG,f); }
3209 : INLINE void
3210 21 : pari_err_CONSTPOL(const char *f) { pari_err(e_CONSTPOL, f); }
3211 : INLINE void
3212 84 : pari_err_COPRIME(const char *f, GEN x, GEN y) { pari_err(e_COPRIME, f,x,y); }
3213 : INLINE void
3214 690 : pari_err_DIM(const char *f) { pari_err(e_DIM, f); }
3215 : INLINE void
3216 0 : pari_err_FILE(const char *f, const char *g) { pari_err(e_FILE, f,g); }
3217 : INLINE void
3218 36 : pari_err_FILEDESC(const char *f, long n) { pari_err(e_FILEDESC, f,n); }
3219 : INLINE void
3220 98 : pari_err_FLAG(const char *f) { pari_err(e_FLAG,f); }
3221 : INLINE void
3222 518 : pari_err_IMPL(const char *f) { pari_err(e_IMPL,f); }
3223 : INLINE void
3224 19997 : pari_err_INV(const char *f, GEN x) { pari_err(e_INV,f,x); }
3225 : INLINE void
3226 63 : pari_err_IRREDPOL(const char *f, GEN x) { pari_err(e_IRREDPOL, f,x); }
3227 : INLINE void
3228 2736 : 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); }
3229 : INLINE void
3230 214 : pari_err_COMPONENT(const char *f, const char *op, GEN l, GEN x) { pari_err(e_COMPONENT, f,op,l,x); }
3231 : INLINE void
3232 0 : pari_err_MAXPRIME(ulong c) { pari_err(e_MAXPRIME, c); }
3233 : INLINE void
3234 406 : pari_err_OP(const char *f, GEN x, GEN y) { pari_err(e_OP, f,x,y); }
3235 : INLINE void
3236 156 : pari_err_OVERFLOW(const char *f) { pari_err(e_OVERFLOW, f); }
3237 : INLINE void
3238 238 : pari_err_PREC(const char *f) { pari_err(e_PREC,f); }
3239 : INLINE void
3240 0 : pari_err_PACKAGE(const char *f) { pari_err(e_PACKAGE,f); }
3241 : INLINE void
3242 98 : pari_err_PRIME(const char *f, GEN x) { pari_err(e_PRIME, f,x); }
3243 : INLINE void
3244 1316 : pari_err_MODULUS(const char *f, GEN x, GEN y) { pari_err(e_MODULUS, f,x,y); }
3245 : INLINE void
3246 63 : pari_err_ROOTS0(const char *f) { pari_err(e_ROOTS0, f); }
3247 : INLINE void
3248 84 : pari_err_SQRTN(const char *f, GEN x) { pari_err(e_SQRTN, f,x); }
3249 : INLINE void
3250 14796 : pari_err_TYPE(const char *f, GEN x) { pari_err(e_TYPE, f,x); }
3251 : INLINE void
3252 3500 : pari_err_TYPE2(const char *f, GEN x, GEN y) { pari_err(e_TYPE2, f,x,y); }
3253 : INLINE void
3254 364 : pari_err_VAR(const char *f, GEN x, GEN y) { pari_err(e_VAR, f,x,y); }
3255 : INLINE void
3256 245 : pari_err_PRIORITY(const char *f, GEN x, const char *op, long v)
3257 245 : { pari_err(e_PRIORITY, f,x,op,v); }
3258 :
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