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 8024631 : mkintmod(GEN x, GEN y) { retmkintmod(x,y); }
167 : INLINE GEN
168 1813 : mkintmodu(ulong x, ulong y) {
169 1813 : GEN v = cgetg(3,t_INTMOD);
170 1813 : gel(v,1) = utoipos(y);
171 1813 : gel(v,2) = utoi(x); return v;
172 : }
173 : INLINE GEN
174 2973560 : mkpolmod(GEN x, GEN y) { retmkpolmod(x,y); }
175 : INLINE GEN
176 33747737 : mkfrac(GEN x, GEN y) { retmkfrac(x,y); }
177 : INLINE GEN
178 1209528 : 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 19838 : Qtoss(GEN q, long *n, long *d)
182 : {
183 19838 : if (typ(q) == t_INT) { *n = itos(q); *d = 1; }
184 5796 : else { *n = itos(gel(q,1)); *d = itou(gel(q,2)); }
185 19838 : }
186 : INLINE GEN
187 1074486 : sstoQ(long n, long d)
188 : {
189 : ulong r;
190 : long g, q;
191 1074486 : if (!n)
192 : {
193 95095 : if (!d) pari_err_INV("sstoQ",gen_0);
194 95095 : return gen_0;
195 : }
196 979391 : if (d < 0) { d = -d; n = -n; }
197 979391 : if (d == 1) return stoi(n);
198 960078 : r = labs(n);
199 960078 : if (r == 1) retmkfrac(n > 0? gen_1: gen_m1, utoipos(d));
200 910168 : q = udivuu_rem(r, d, &r);
201 910168 : if (!r) return n > 0? utoipos(q): utoineg(q);
202 855281 : g = ugcd(d,r); /* gcd(n,d) */
203 855281 : if (g != 1) { n /= g; d /= g; }
204 855281 : retmkfrac(stoi(n), utoipos(d));
205 : }
206 :
207 : INLINE GEN
208 158074130 : uutoQ(ulong n, ulong d)
209 : {
210 : ulong r;
211 : long g, q;
212 158074130 : if (!n)
213 : {
214 38108 : if (!d) pari_err_INV("uutoQ",gen_0);
215 38108 : return gen_0;
216 : }
217 158036022 : if (d == 1) return utoipos(n);
218 158024920 : if (n == 1) retmkfrac(gen_1, utoipos(d));
219 157935993 : q = udivuu_rem(n,d,&r);
220 157935993 : if (!r) return utoipos(q);
221 5180964 : g = ugcd(d,r); /* gcd(n,d) */
222 5180964 : if (g != 1) { n /= g; d /= g; }
223 5180964 : retmkfrac(utoipos(n), utoipos(d));
224 : }
225 :
226 : INLINE GEN
227 4795479 : mkfraccopy(GEN x, GEN y) { retmkfrac(icopy(x), icopy(y)); }
228 : INLINE GEN
229 698145 : mkrfrac(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
230 698145 : 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 89952211 : mkcomplex(GEN x, GEN y) { retmkcomplex(x,y); }
236 : INLINE GEN
237 1267750 : gen_I(void) { return mkcomplex(gen_0, gen_1); }
238 : INLINE GEN
239 963392 : cgetc(long l) { retmkcomplex(cgetr(l), cgetr(l)); }
240 : INLINE GEN
241 69118 : mkquad(GEN n, GEN x, GEN y) { GEN v = cgetg(4, t_QUAD);
242 69118 : gel(v,1) = n; gel(v,2) = x; gel(v,3) = y; return v; }
243 : /* vecsmall */
244 : INLINE GEN
245 129392920 : mkvecsmall(long x) { GEN v = cgetg(2, t_VECSMALL); v[1] = x; return v; }
246 : INLINE GEN
247 224061936 : mkvecsmall2(long x,long y) { GEN v = cgetg(3, t_VECSMALL);
248 224075830 : v[1]=x; v[2]=y; return v; }
249 : INLINE GEN
250 100371741 : mkvecsmall3(long x,long y,long z) { GEN v = cgetg(4, t_VECSMALL);
251 100369046 : v[1]=x; v[2]=y; v[3]=z; return v; }
252 : INLINE GEN
253 15488460 : mkvecsmall4(long x,long y,long z,long t) { GEN v = cgetg(5, t_VECSMALL);
254 15492963 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; return v; }
255 : INLINE GEN
256 688700 : mkvecsmall5(long x,long y,long z,long t,long u) { GEN v = cgetg(6, t_VECSMALL);
257 688700 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; v[5]=u; return v; }
258 :
259 : INLINE GEN
260 27798145 : mkqfb(GEN x, GEN y, GEN z, GEN d) { retmkqfb(x,y,z,d); }
261 : /* vec */
262 : INLINE GEN
263 67484838 : mkvec(GEN x) { retmkvec(x); }
264 : INLINE GEN
265 182850952 : mkvec2(GEN x, GEN y) { retmkvec2(x,y); }
266 : INLINE GEN
267 120507062 : mkvec3(GEN x, GEN y, GEN z) { retmkvec3(x,y,z); }
268 : INLINE GEN
269 6589142 : mkvec4(GEN x, GEN y, GEN z, GEN t) { retmkvec4(x,y,z,t); }
270 : INLINE GEN
271 14485991 : 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 219599 : 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 122507 : mkveccopy(GEN x) { GEN v = cgetg(2, t_VEC); gel(v,1) = gcopy(x); return v; }
282 : INLINE GEN
283 123183 : mkvec2copy(GEN x, GEN y) {
284 123183 : GEN v = cgetg(3,t_VEC); gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
285 : /* col */
286 : INLINE GEN
287 10174280 : mkcol(GEN x) { retmkcol(x); }
288 : INLINE GEN
289 155871813 : mkcol2(GEN x, GEN y) { retmkcol2(x,y); }
290 : INLINE GEN
291 88314 : mkcol3(GEN x, GEN y, GEN z) { retmkcol3(x,y,z); }
292 : INLINE GEN
293 103320 : mkcol4(GEN x, GEN y, GEN z, GEN t) { retmkcol4(x,y,z,t); }
294 : INLINE GEN
295 94 : mkcol5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkcol5(x,y,z,t,u); }
296 : INLINE GEN
297 232043 : 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 4415292 : mkcol2s(long x, long y) { retmkcol2(stoi(x),stoi(y)); }
302 : INLINE GEN
303 315 : 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 33534 : mkcolcopy(GEN x) { GEN v = cgetg(2, t_COL); gel(v,1) = gcopy(x); return v; }
308 : /* mat */
309 : INLINE GEN
310 4640629 : mkmat(GEN x) { retmkmat(x); }
311 : INLINE GEN
312 32544448 : mkmat2(GEN x, GEN y) { retmkmat2(x,y); }
313 : INLINE GEN
314 17001 : mkmat3(GEN x, GEN y, GEN z) { retmkmat3(x,y,z); }
315 : INLINE GEN
316 63 : 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 121019 : 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 1075302 : mkoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
325 : INLINE GEN
326 105721 : mkmoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
327 : INLINE long
328 1193293 : inf_get_sign(GEN x) { return signe(gel(x,1)); }
329 : INLINE GEN
330 207452 : mkmat22s(long a, long b, long c, long d) {retmkmat2(mkcol2s(a,c),mkcol2s(b,d));}
331 : INLINE GEN
332 50319532 : mkmat22(GEN a, GEN b, GEN c, GEN d) { retmkmat2(mkcol2(a,c),mkcol2(b,d)); }
333 :
334 : /* pol */
335 : INLINE GEN
336 3537730 : pol_x(long v) {
337 3537730 : GEN p = cgetg(4, t_POL);
338 3537727 : p[1] = evalsigne(1)|evalvarn(v);
339 3537727 : gel(p,2) = gen_0;
340 3537727 : gel(p,3) = gen_1; return p;
341 : }
342 : /* x^n, assume n >= 0 */
343 : INLINE GEN
344 2221296 : pol_xn(long n, long v) {
345 2221296 : long i, a = n+2;
346 2221296 : GEN p = cgetg(a+1, t_POL);
347 2221299 : p[1] = evalsigne(1)|evalvarn(v);
348 5302965 : for (i = 2; i < a; i++) gel(p,i) = gen_0;
349 2221299 : 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 4372911 : pol_1(long v) {
369 4372911 : GEN p = cgetg(3, t_POL);
370 4372904 : p[1] = evalsigne(1)|evalvarn(v);
371 4372904 : gel(p,2) = gen_1; return p;
372 : }
373 : INLINE GEN
374 34998483 : pol_0(long v)
375 : {
376 34998483 : GEN x = cgetg(2,t_POL);
377 34998485 : 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 233827635 : 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 39300093 : const_col(long n, GEN x) { retconst_col(n, x); }
393 : INLINE GEN
394 19082343 : const_vecsmall(long n, long c)
395 : {
396 : long i;
397 19082343 : GEN V = cgetg(n+1,t_VECSMALL);
398 753407541 : for(i=1;i<=n;i++) V[i] = c;
399 19082886 : return V;
400 : }
401 :
402 : /*** ZERO ***/
403 : /* O(p^e) */
404 : INLINE GEN
405 855591 : zeropadic(GEN p, long e)
406 : {
407 855591 : GEN y = cgetg(5,t_PADIC);
408 855552 : gel(y,4) = gen_0;
409 855552 : gel(y,3) = gen_1;
410 855552 : gel(y,2) = icopy(p);
411 855455 : y[1] = evalvalp(e) | _evalprecp(0);
412 855443 : return y;
413 : }
414 : INLINE GEN
415 15358 : zeropadic_shallow(GEN p, long e)
416 : {
417 15358 : GEN y = cgetg(5,t_PADIC);
418 15358 : gel(y,4) = gen_0;
419 15358 : gel(y,3) = gen_1;
420 15358 : gel(y,2) = p;
421 15358 : y[1] = evalvalp(e) | _evalprecp(0);
422 15358 : return y;
423 : }
424 : /* O(pol_x(v)^e) */
425 : INLINE GEN
426 138698 : zeroser(long v, long e)
427 : {
428 138698 : GEN x = cgetg(2, t_SER);
429 138698 : x[1] = evalvalser(e) | evalvarn(v); return x;
430 : }
431 : INLINE int
432 10079024 : ser_isexactzero(GEN x)
433 : {
434 10079024 : if (!signe(x)) switch(lg(x))
435 : {
436 132741 : case 2: return 1;
437 4648 : case 3: return isexactzero(gel(x,2));
438 : }
439 9941635 : return 0;
440 : }
441 : /* 0 * pol_x(v) */
442 : INLINE GEN
443 14736361 : zeropol(long v) { return pol_0(v); }
444 : /* vector(n) */
445 : INLINE GEN
446 118964375 : zerocol(long n)
447 : {
448 118964375 : GEN y = cgetg(n+1,t_COL);
449 802725513 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
450 118965294 : return y;
451 : }
452 : /* vectorv(n) */
453 : INLINE GEN
454 26622869 : zerovec(long n)
455 : {
456 26622869 : GEN y = cgetg(n+1,t_VEC);
457 391731927 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
458 26622870 : return y;
459 : }
460 : /* matrix(m, n) */
461 : INLINE GEN
462 108859 : zeromat(long m, long n)
463 : {
464 108859 : GEN y = cgetg(n+1,t_MAT);
465 108860 : GEN v = zerocol(m);
466 401473 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
467 108862 : return y;
468 : }
469 : /* = zero_zx, sv is a evalvarn()*/
470 : INLINE GEN
471 1428886 : zero_Flx(long sv) { return pol0_Flx(sv); }
472 : INLINE GEN
473 58627933 : zero_Flv(long n)
474 : {
475 58627933 : GEN y = cgetg(n+1,t_VECSMALL);
476 946420853 : long i; for (i=1; i<=n; i++) y[i] = 0;
477 58628172 : return y;
478 : }
479 : /* matrix(m, n) */
480 : INLINE GEN
481 2750937 : zero_Flm(long m, long n)
482 : {
483 2750937 : GEN y = cgetg(n+1,t_MAT);
484 2750930 : GEN v = zero_Flv(m);
485 17519916 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
486 2750928 : return y;
487 : }
488 : /* matrix(m, n) */
489 : INLINE GEN
490 232072 : zero_Flm_copy(long m, long n)
491 : {
492 232072 : GEN y = cgetg(n+1,t_MAT);
493 2397519 : long i; for (i=1; i<=n; i++) gel(y,i) = zero_Flv(m);
494 232069 : return y;
495 : }
496 :
497 : INLINE GEN
498 3616951 : zero_F2v(long m)
499 : {
500 3616951 : long l = nbits2nlong(m);
501 3616940 : GEN v = zero_Flv(l+1);
502 3616916 : v[1] = m;
503 3616916 : 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 841298 : zero_F2m_copy(long m, long n)
520 : {
521 : long i;
522 841298 : GEN M = cgetg(n+1, t_MAT);
523 2008912 : for (i = 1; i <= n; i++)
524 1167620 : gel(M,i)= zero_F2v(m);
525 841292 : return M;
526 : }
527 :
528 : /* matrix(m, n) */
529 : INLINE GEN
530 14017391 : zeromatcopy(long m, long n)
531 : {
532 14017391 : GEN y = cgetg(n+1,t_MAT);
533 70921370 : long i; for (i=1; i<=n; i++) gel(y,i) = zerocol(m);
534 14017424 : 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 5700472 : col_ei(long n, long i) { GEN e = zerocol(n); gel(e,i) = gen_1; return e; }
550 : INLINE GEN
551 1703546 : 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 495147 : vecsmall_ei(long n, long i) { GEN e = zero_zv(n); e[i] = 1; return e; }
556 : INLINE GEN
557 1288284 : Rg_col_ei(GEN x, long n, long i) { GEN e = zerocol(n); gel(e,i) = x; return e; }
558 :
559 : INLINE GEN
560 25842790 : shallowcopy(GEN x)
561 25842790 : { return typ(x) == t_MAT ? RgM_shallowcopy(x): leafcopy(x); }
562 :
563 : /* routines for naive growarrays */
564 : INLINE GEN
565 11714814 : vectrunc_init(long l)
566 : {
567 11714814 : GEN z = new_chunk(l);
568 11714557 : z[0] = evaltyp(t_VEC) | _evallg(1); return z;
569 : }
570 : INLINE GEN
571 393680 : coltrunc_init(long l)
572 : {
573 393680 : GEN z = new_chunk(l);
574 393680 : z[0] = evaltyp(t_COL) | _evallg(1); return z;
575 : }
576 : INLINE void
577 317182772 : lg_increase(GEN x) { x[0]++; }
578 : INLINE void
579 15248301 : 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 189120468 : vecsmalltrunc_init(long l)
590 : {
591 189120468 : GEN z = new_chunk(l);
592 189118191 : z[0] = evaltyp(t_VECSMALL) | _evallg(1); return z;
593 : }
594 : INLINE void
595 99941921 : 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 2688625 : hash_str(const char *str)
604 : {
605 2688625 : ulong hash = 5381UL, c;
606 27919480 : while ( (c = (ulong)*str++) )
607 25230855 : hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
608 2688625 : return hash;
609 : }
610 : INLINE ulong
611 18259633 : hash_str_len(const char *str, long len)
612 : {
613 18259633 : ulong hash = 5381UL;
614 : long i;
615 166194619 : for (i = 0; i < len; i++)
616 : {
617 147934986 : ulong c = (ulong)*str++;
618 147934986 : hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
619 : }
620 18259633 : return hash;
621 : }
622 :
623 : /*******************************************************************/
624 : /* */
625 : /* VEC / COL / VECSMALL */
626 : /* */
627 : /*******************************************************************/
628 : /* shallow*/
629 : INLINE GEN
630 11550 : vec_shorten(GEN v, long n)
631 : {
632 11550 : GEN V = cgetg(n+1, t_VEC);
633 : long i;
634 13006 : for(i = 1; i <= n; i++) gel(V,i) = gel(v,i);
635 11550 : return V;
636 : }
637 : /* shallow*/
638 : INLINE GEN
639 18941 : vec_lengthen(GEN v, long n)
640 : {
641 18941 : GEN V = cgetg(n+1, t_VEC);
642 18941 : long i, l = lg(v);
643 1935639 : for(i = 1; i < l; i++) gel(V,i) = gel(v,i);
644 18941 : return V;
645 : }
646 : /* shallow*/
647 : INLINE GEN
648 3430115 : vec_append(GEN V, GEN s)
649 : {
650 3430115 : long i, l2 = lg(V);
651 3430115 : GEN res = cgetg(l2+1, typ(V));
652 10730723 : for (i = 1; i < l2; i++) gel(res, i) = gel(V,i);
653 3430115 : gel(res,l2) = s; return res;
654 : }
655 : /* shallow*/
656 : INLINE GEN
657 300927 : vec_prepend(GEN v, GEN s)
658 : {
659 300927 : long i, l = lg(v);
660 300927 : GEN w = cgetg(l+1, typ(v));
661 300927 : gel(w,1) = s;
662 769397 : for (i = 2; i <= l; i++) gel(w,i) = gel(v,i-1);
663 300927 : 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 72590 : vecsmall_shorten(GEN v, long n)
675 : {
676 72590 : GEN V = cgetg(n+1,t_VECSMALL);
677 : long i;
678 889715 : for(i = 1; i <= n; i++) V[i] = v[i];
679 72589 : 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 4014919 : vec_to_vecsmall(GEN x)
692 18857055 : { pari_APPLY_long(itos(gel(x,i))) }
693 : INLINE GEN
694 510059 : vecsmall_to_vec(GEN x)
695 7066741 : { pari_APPLY_type(t_VEC, stoi(x[i])) }
696 : INLINE GEN
697 3304 : vecsmall_to_vec_inplace(GEN z)
698 : {
699 3304 : long i, l = lg(z);
700 79604 : for (i=1; i<l; i++) gel(z,i) = stoi(z[i]);
701 3304 : settyp(z, t_VEC); return z;
702 : }
703 : INLINE GEN
704 7760786 : vecsmall_to_col(GEN x)
705 59563326 : { pari_APPLY_type(t_COL, stoi(x[i])) }
706 :
707 : INLINE int
708 7208565 : vecsmall_lexcmp(GEN x, GEN y)
709 : {
710 : long lx,ly,l,i;
711 7208565 : lx = lg(x);
712 7208565 : ly = lg(y); l = minss(lx,ly);
713 30644497 : for (i=1; i<l; i++)
714 29017633 : 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 186789 : vecsmall_prepend(GEN V, long s)
731 : {
732 186789 : long i, l2 = lg(V);
733 186789 : GEN res = cgetg(l2+1, typ(V));
734 186789 : res[1] = s;
735 624925 : for (i = 2; i <= l2; ++i) res[i] = V[i - 1];
736 186789 : return res;
737 : }
738 :
739 : INLINE GEN
740 4065086 : vecsmall_append(GEN V, long s)
741 : {
742 4065086 : long i, l2 = lg(V);
743 4065086 : GEN res = cgetg(l2+1, t_VECSMALL);
744 5975387 : for (i = 1; i < l2; ++i) res[i] = V[i];
745 4065086 : res[l2] = s; return res;
746 : }
747 :
748 : INLINE GEN
749 1456754 : vecsmall_concat(GEN u, GEN v)
750 : {
751 1456754 : long i, l1 = lg(u)-1, l2 = lg(v)-1;
752 1456754 : GEN res = cgetg(l1+l2+1, t_VECSMALL);
753 11548049 : for (i = 1; i <= l1; ++i) res[i] = u[i];
754 15157563 : for (i = 1; i <= l2; ++i) res[i+l1] = v[i];
755 1456753 : 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);
773 124 : for (i = 1; i < l; i++)
774 80 : if (v[i] == x) return i;
775 44 : 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 1007805 : vecsmall_max(GEN x)
797 : {
798 1007805 : long i, t = x[1], lx = lg(x);
799 2807584 : for (i=2; i<lx; i++)
800 1799779 : if (x[i] > t) t = x[i];
801 1007805 : 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 22780538 : ZV_isscalar(GEN x)
824 : {
825 22780538 : long l = lg(x);
826 54293918 : while (--l > 1)
827 53894551 : if (signe(gel(x, l))) return 0;
828 399367 : return 1;
829 : }
830 : INLINE int
831 64684432 : QV_isscalar(GEN x)
832 : {
833 64684432 : long lx = lg(x),i;
834 80646686 : for (i=2; i<lx; i++)
835 76734008 : if (!isintzero(gel(x, i))) return 0;
836 3912678 : return 1;
837 : }
838 : INLINE int
839 1140305 : RgV_isscalar(GEN x)
840 : {
841 1140305 : long lx = lg(x),i;
842 1166509 : for (i=2; i<lx; i++)
843 1162786 : if (!gequal0(gel(x, i))) return 0;
844 3723 : 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 26766290 : 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 67464 : RgX_is_rational(GEN x)
861 : {
862 : long i;
863 307821 : for (i = lg(x)-1; i > 1; i--)
864 292108 : if (!is_rational_t(typ(gel(x,i)))) return 0;
865 15713 : return 1;
866 : }
867 : INLINE int
868 15648146 : RgX_is_ZX(GEN x)
869 : {
870 : long i;
871 66311179 : for (i = lg(x)-1; i > 1; i--)
872 50727327 : if (typ(gel(x,i)) != t_INT) return 0;
873 15583852 : return 1;
874 : }
875 : INLINE int
876 378583 : RgX_is_QX(GEN x)
877 : {
878 378583 : long k = lg(x)-1;
879 1421865 : for ( ; k>1; k--)
880 1043562 : if (!is_rational_t(typ(gel(x,k)))) return 0;
881 378303 : return 1;
882 : }
883 : INLINE int
884 3079291 : RgX_is_monomial(GEN x)
885 : {
886 : long i;
887 3079291 : if (!signe(x)) return 0;
888 7056395 : for (i=lg(x)-2; i>1; i--)
889 4688743 : if (!isexactzero(gel(x,i))) return 0;
890 2367652 : return 1;
891 : }
892 : INLINE int
893 31340385 : RgV_is_ZV(GEN x)
894 : {
895 : long i;
896 124631697 : for (i = lg(x)-1; i > 0; i--)
897 93323414 : if (typ(gel(x,i)) != t_INT) return 0;
898 31308283 : return 1;
899 : }
900 : INLINE int
901 139963 : RgV_is_QV(GEN x)
902 : {
903 : long i;
904 619104 : for (i = lg(x)-1; i > 0; i--)
905 482095 : if (!is_rational_t(typ(gel(x,i)))) return 0;
906 137009 : return 1;
907 : }
908 : INLINE long
909 109213 : RgV_isin_i(GEN v, GEN x, long n)
910 : {
911 : long i;
912 1031582 : for (i = 1; i <= n; i++)
913 1025758 : if (gequal(gel(v,i), x)) return i;
914 5824 : return 0;
915 : }
916 : INLINE long
917 109213 : 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 695681666 : pari_stack_base(pari_stack *s) { return s->data; }
926 :
927 : INLINE void
928 5553291 : pari_stack_init(pari_stack *s, size_t size, void **data)
929 : {
930 5553291 : s->data = data;
931 5553291 : *data = NULL;
932 5553291 : s->n = 0;
933 5553291 : s->alloc = 0;
934 5553291 : s->size = size;
935 5553291 : }
936 :
937 : INLINE void
938 690600540 : pari_stack_alloc(pari_stack *s, long nb)
939 : {
940 690600540 : void **sdat = pari_stack_base(s);
941 690460948 : long alloc = s->alloc;
942 690460948 : if (s->n+nb <= alloc) return;
943 2071422 : if (!alloc)
944 1975550 : alloc = nb;
945 : else
946 : {
947 195803 : while (s->n+nb > alloc) alloc <<= 1;
948 : }
949 2071422 : pari_realloc_ip(sdat,alloc*s->size);
950 2073620 : s->alloc = alloc;
951 : }
952 :
953 : INLINE long
954 597680432 : pari_stack_new(pari_stack *s) { pari_stack_alloc(s, 1); return s->n++; }
955 :
956 : INLINE void
957 5135239 : pari_stack_delete(pari_stack *s)
958 : {
959 5135239 : void **sdat = pari_stack_base(s);
960 5125616 : if (*sdat) pari_free(*sdat);
961 5152401 : }
962 :
963 : INLINE void
964 5767 : pari_stack_pushp(pari_stack *s, void *u)
965 : {
966 5767 : long n = pari_stack_new(s);
967 5767 : void **sdat =(void**) *pari_stack_base(s);
968 5767 : sdat[n] = u;
969 5767 : }
970 :
971 : /*******************************************************************/
972 : /* */
973 : /* EXTRACT */
974 : /* */
975 : /*******************************************************************/
976 : INLINE GEN
977 633937722 : vecslice(GEN A, long y1, long y2)
978 : {
979 633937722 : long i,lB = y2 - y1 + 2;
980 633937722 : GEN B = cgetg(lB, typ(A));
981 2827558370 : for (i=1; i<lB; i++) B[i] = A[y1-1+i];
982 633920857 : return B;
983 : }
984 : INLINE GEN
985 2618012 : vecslicepermute(GEN A, GEN p, long y1, long y2)
986 : {
987 2618012 : long i,lB = y2 - y1 + 2;
988 2618012 : GEN B = cgetg(lB, typ(A));
989 29737813 : for (i=1; i<lB; i++) B[i] = A[p[y1-1+i]];
990 2618012 : return B;
991 : }
992 : /* rowslice(rowpermute(A,p), x1, x2) */
993 : INLINE GEN
994 182156 : rowslicepermute(GEN x, GEN p, long j1, long j2)
995 770167 : { pari_APPLY_same(vecslicepermute(gel(x,i),p,j1,j2)) }
996 :
997 : INLINE GEN
998 77527793 : rowslice(GEN x, long j1, long j2)
999 649573646 : { pari_APPLY_same(vecslice(gel(x,i), j1, j2)) }
1000 :
1001 : INLINE GEN
1002 16470741 : matslice(GEN A, long x1, long x2, long y1, long y2)
1003 16470741 : { return rowslice(vecslice(A, y1, y2), x1, x2); }
1004 :
1005 : /* shallow, remove coeff of index j */
1006 : INLINE GEN
1007 273 : rowsplice(GEN x, long j)
1008 1225 : { pari_APPLY_same(vecsplice(gel(x,i), j)) }
1009 :
1010 : /* shallow, remove coeff of index j */
1011 : INLINE GEN
1012 354715 : vecsplice(GEN a, long j)
1013 : {
1014 354715 : long i, k, l = lg(a);
1015 : GEN b;
1016 354715 : if (l == 1) pari_err(e_MISC, "incorrect component in vecsplice");
1017 354715 : b = cgetg(l-1, typ(a));
1018 1503236 : for (i = k = 1; i < l; i++)
1019 1148519 : if (i != j) gel(b, k++) = gel(a,i);
1020 354717 : 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 762515 : row(GEN x, long j)
1035 6685725 : { pari_APPLY_type(t_VEC, gcoeff(x, j, i)) }
1036 : INLINE GEN
1037 8463889 : Flm_row(GEN x, long j)
1038 226575915 : { 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 697025 : vecreverse(GEN A)
1055 : {
1056 : long i, l;
1057 697025 : GEN B = cgetg_copy(A, &l);
1058 2407755 : for (i=1; i<l; i++) gel(B, i) = gel(A, l-i);
1059 697025 : return B;
1060 : }
1061 :
1062 : INLINE GEN
1063 3052 : vecsmall_reverse(GEN A)
1064 : {
1065 : long i, l;
1066 3052 : GEN B = cgetg_copy(A, &l);
1067 12698 : for (i=1; i<l; i++) B[i] = A[l-i];
1068 3052 : 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 77037197 : vecsmallpermute(GEN A, GEN p) { return perm_mul(A, p); }
1085 :
1086 : INLINE GEN
1087 20009772 : vecpermute(GEN A, GEN x)
1088 113003472 : { pari_APPLY_type(typ(A), gel(A, x[i])) }
1089 :
1090 : INLINE GEN
1091 6905039 : veclast(GEN A) { return gel(A, lg(A)-1); }
1092 :
1093 : INLINE GEN
1094 14407607 : rowpermute(GEN x, GEN p)
1095 100134099 : { 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 3126970 : identity_zv(long n)
1105 : {
1106 3126970 : GEN v = cgetg(n+1, t_VECSMALL);
1107 : long i;
1108 31981283 : for (i = 1; i <= n; i++) v[i] = i;
1109 3126964 : return v;
1110 : }
1111 : INLINE GEN
1112 4333 : identity_ZV(long n)
1113 : {
1114 4333 : GEN v = cgetg(n+1, t_VEC);
1115 : long i;
1116 51898 : for (i = 1; i <= n; i++) gel(v,i) = utoipos(i);
1117 4333 : return v;
1118 : }
1119 : /* identity permutation */
1120 : INLINE GEN
1121 3102625 : identity_perm(long n) { return identity_zv(n); }
1122 :
1123 : /* assume d <= n */
1124 : INLINE GEN
1125 99911 : cyclic_perm(long n, long d)
1126 : {
1127 99911 : GEN perm = cgetg(n+1, t_VECSMALL);
1128 : long i;
1129 520240 : for (i = 1; i <= n-d; i++) perm[i] = i+d;
1130 226702 : for ( ; i <= n; i++) perm[i] = i-n+d;
1131 99911 : return perm;
1132 : }
1133 :
1134 : /* Multiply (compose) two permutations */
1135 : INLINE GEN
1136 79227117 : perm_mul(GEN s, GEN x)
1137 1004961472 : { 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 2763377 : perm_inv(GEN x)
1146 : {
1147 : long i, lx;
1148 2763377 : GEN y = cgetg_copy(x, &lx);
1149 38846005 : for (i=1; i<lx; i++) y[ x[i] ] = i;
1150 2763377 : 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 489776525 : pari_free(void *pointer)
1164 : {
1165 489776525 : BLOCK_SIGINT_START;
1166 489830026 : free(pointer);
1167 489830026 : BLOCK_SIGINT_END;
1168 489825897 : }
1169 : INLINE void*
1170 720112955 : pari_malloc(size_t size)
1171 : {
1172 720112955 : if (size)
1173 : {
1174 : char *tmp;
1175 720119503 : BLOCK_SIGINT_START;
1176 720172787 : tmp = (char*)malloc(size);
1177 720172787 : BLOCK_SIGINT_END;
1178 720176463 : if (!tmp) pari_err(e_MEM);
1179 720185915 : return tmp;
1180 : }
1181 0 : return NULL;
1182 : }
1183 : INLINE void*
1184 1862 : pari_realloc(void *pointer, size_t size)
1185 : {
1186 : char *tmp;
1187 :
1188 1862 : BLOCK_SIGINT_START;
1189 1862 : if (!pointer) tmp = (char *) malloc(size);
1190 1862 : else tmp = (char *) realloc(pointer,size);
1191 1862 : BLOCK_SIGINT_END;
1192 1862 : if (!tmp) pari_err(e_MEM);
1193 1862 : return tmp;
1194 : }
1195 : INLINE void
1196 2075588 : pari_realloc_ip(void **pointer, size_t size)
1197 : {
1198 : char *tmp;
1199 2075588 : BLOCK_SIGINT_START;
1200 2075408 : if (!*pointer) tmp = (char *) malloc(size);
1201 100234 : else tmp = (char *) realloc(*pointer,size);
1202 2075408 : if (!tmp) pari_err(e_MEM);
1203 2075408 : *pointer = tmp;
1204 2075408 : BLOCK_SIGINT_END;
1205 2074888 : }
1206 :
1207 : INLINE void*
1208 46684 : pari_calloc(size_t size)
1209 : {
1210 46684 : void *t = pari_malloc(size);
1211 46684 : memset(t, 0, size); return t;
1212 : }
1213 : INLINE GEN
1214 8213 : cgetalloc(size_t l, long t)
1215 : { /* evallg may raise e_OVERFLOW, which would leak x */
1216 8213 : ulong x0 = evaltyp(t) | evallg(l);
1217 8213 : GEN x = (GEN)pari_malloc(l * sizeof(long));
1218 8213 : 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 7810371207 : icopy_avma(GEN x, pari_sp av)
1229 : {
1230 7810371207 : long i = lgefint(x), lx = i;
1231 7810371207 : GEN y = ((GEN)av) - i;
1232 53408966379 : while (--i > 0) y[i] = x[i];
1233 7810371207 : y[0] = evaltyp(t_INT)|evallg(lx);
1234 7813616750 : return y;
1235 : }
1236 : /* copy leaf x as if we had set_avma(av) */
1237 : INLINE GEN
1238 550380319 : leafcopy_avma(GEN x, pari_sp av)
1239 : {
1240 550380319 : long i = lg(x);
1241 550380319 : GEN y = ((GEN)av) - i;
1242 2991782271 : while (--i > 0) y[i] = x[i];
1243 550380319 : y[0] = x[0] & (~CLONEBIT);
1244 550380319 : return y;
1245 : }
1246 : INLINE GEN
1247 1081772481 : gerepileuptoleaf(pari_sp av, GEN x)
1248 : {
1249 : long lx;
1250 : GEN q;
1251 :
1252 1081772481 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1253 1080534862 : lx = lg(x);
1254 1080534862 : q = ((GEN)av) - lx;
1255 1080534862 : set_avma((pari_sp)q);
1256 10859119007 : while (--lx >= 0) q[lx] = x[lx];
1257 1080145380 : return q;
1258 : }
1259 : INLINE GEN
1260 3953553358 : gerepileuptoint(pari_sp av, GEN x)
1261 : {
1262 3953553358 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1263 3519891518 : set_avma((pari_sp)icopy_avma(x, av));
1264 3523425049 : return (GEN)avma;
1265 : }
1266 : INLINE GEN
1267 1808643956 : gerepileupto(pari_sp av, GEN x)
1268 : {
1269 1808643956 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1270 1634875333 : switch(typ(x))
1271 : { /* non-default = !is_recursive_t(tq) */
1272 482629718 : case t_INT: return gerepileuptoint(av, x);
1273 337957789 : case t_REAL:
1274 : case t_STR:
1275 337957789 : case t_VECSMALL: return gerepileuptoleaf(av,x);
1276 814289520 : default:
1277 : /* NB: x+i --> ((long)x) + i*sizeof(long) */
1278 814289520 : return gerepile(av, (pari_sp) (x+lg(x)), x);
1279 : }
1280 : }
1281 :
1282 : /* gerepileupto(av, gcopy(x)) */
1283 : INLINE GEN
1284 227092177 : gerepilecopy(pari_sp av, GEN x)
1285 : {
1286 227092177 : if (is_recursive_t(typ(x)))
1287 : {
1288 207566712 : GENbin *p = copy_bin(x);
1289 207584515 : set_avma(av); return bin_copy(p);
1290 : }
1291 : else
1292 : {
1293 19524941 : set_avma(av);
1294 19525106 : if (x < (GEN)av) {
1295 19317323 : if (x < (GEN)pari_mainstack->bot) new_chunk(lg(x));
1296 19317326 : x = leafcopy_avma(x, av);
1297 19317357 : set_avma((pari_sp)x);
1298 : } else
1299 207787 : x = leafcopy(x);
1300 19525134 : return x;
1301 : }
1302 : }
1303 :
1304 : INLINE void
1305 48394240 : guncloneNULL(GEN x) { if (x) gunclone(x); }
1306 : INLINE void
1307 1320571 : 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 984829 : gerepilemany(pari_sp av, GEN* gptr[], int n)
1314 : {
1315 : int i;
1316 3912772 : for (i=0; i<n; i++) *gptr[i] = (GEN)copy_bin(*gptr[i]);
1317 984682 : set_avma(av);
1318 3913253 : for (i=0; i<n; i++) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1319 984976 : }
1320 :
1321 : INLINE void
1322 19027782 : gerepileall(pari_sp av, int n, ...)
1323 : {
1324 : int i;
1325 19027782 : va_list a; va_start(a, n);
1326 19027782 : if (n < 10)
1327 : {
1328 : GEN *gptr[10];
1329 57735268 : for (i=0; i<n; i++)
1330 38706752 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1331 19028516 : set_avma(av);
1332 57736193 : 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 19029009 : va_end(a);
1345 19029009 : }
1346 :
1347 : /* assume 1 <= n < 10 */
1348 : INLINE GEN
1349 86193232 : gc_all(pari_sp av, int n, ...)
1350 : {
1351 : int i;
1352 : GEN *v[10];
1353 86193232 : va_list a; va_start(a, n);
1354 289571190 : for (i=0; i<n; i++) { v[i] = va_arg(a,GEN*); *v[i] = (GEN)copy_bin(*v[i]); }
1355 86193532 : set_avma(av);
1356 289571925 : for (i=0; i<n; i++) *v[i] = bin_copy((GENbin*)*v[i]);
1357 86193680 : return *v[0];
1358 : }
1359 :
1360 : INLINE void
1361 2196013 : gerepilecoeffs(pari_sp av, GEN x, int n)
1362 : {
1363 : int i;
1364 26159530 : for (i=0; i<n; i++) gel(x,i) = (GEN)copy_bin(gel(x,i));
1365 2196590 : set_avma(av);
1366 26160907 : for (i=0; i<n; i++) gel(x,i) = bin_copy((GENbin*)x[i]);
1367 2196199 : }
1368 :
1369 : /* p from copy_bin. Copy p->x back to stack, then destroy p */
1370 : INLINE GEN
1371 476601498 : bin_copy(GENbin *p)
1372 : {
1373 : GEN x, y, base;
1374 : long dx, len;
1375 :
1376 476601498 : x = p->x; if (!x) { pari_free(p); return gen_0; }
1377 447589723 : len = p->len;
1378 447589723 : base= p->base; dx = x - base;
1379 447589723 : y = (GEN)memcpy((void*)new_chunk(len), (void*)GENbinbase(p), len*sizeof(long));
1380 447583013 : y += dx;
1381 447583013 : p->rebase(y, ((ulong)y-(ulong)x));
1382 447587034 : pari_free(p); return y;
1383 : }
1384 :
1385 : INLINE GEN
1386 924190431 : GENbinbase(GENbin *p) { return (GEN)(p + 1); }
1387 :
1388 : INLINE void
1389 117512033 : cgiv(GEN x)
1390 : {
1391 117512033 : pari_sp av = (pari_sp)(x+lg(x));
1392 117512033 : if (isonstack((GEN)av)) set_avma(av);
1393 117526978 : }
1394 :
1395 : INLINE void
1396 1859186 : killblock(GEN x) { gunclone(x); }
1397 :
1398 : INLINE int
1399 291123151 : 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 17885369 : cxcompotor(GEN z, long prec)
1409 : {
1410 17885369 : switch(typ(z))
1411 : {
1412 11743826 : case t_INT: return itor(z, prec);
1413 293174 : case t_FRAC: return fractor(z, prec);
1414 5848629 : 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 8926808 : cxtofp(GEN x, long prec)
1421 8926808 : { retmkcomplex(cxcompotor(gel(x,1),prec), cxcompotor(gel(x,2),prec)); }
1422 :
1423 : INLINE GEN
1424 384629 : cxtoreal(GEN q)
1425 384629 : { return (typ(q) == t_COMPLEX && gequal0(gel(q,2)))? gel(q,1): q; }
1426 :
1427 : INLINE double
1428 60500212 : gtodouble(GEN x)
1429 : {
1430 60500212 : if (typ(x)!=t_REAL) {
1431 8159395 : pari_sp av = avma;
1432 8159395 : x = gtofp(x, DEFAULTPREC);
1433 8158871 : if (typ(x)!=t_REAL) pari_err_TYPE("gtodouble [t_REAL expected]", x);
1434 8158871 : set_avma(av);
1435 : }
1436 60499599 : return rtodbl(x);
1437 : }
1438 :
1439 : INLINE int
1440 2967776 : gisdouble(GEN x, double *g)
1441 : {
1442 2967776 : if (typ(x)!=t_REAL) {
1443 41893 : pari_sp av = avma;
1444 41893 : x = gtofp(x, DEFAULTPREC);
1445 41893 : if (typ(x)!=t_REAL) pari_err_TYPE("gisdouble [t_REAL expected]", x);
1446 41893 : set_avma(av);
1447 : }
1448 2967777 : if (expo(x) >= 0x3ff) return 0;
1449 2967777 : *g = rtodbl(x); return 1;
1450 : }
1451 :
1452 : INLINE long
1453 85800707 : gtos(GEN x) {
1454 85800707 : if (typ(x) != t_INT) pari_err_TYPE("gtos [integer expected]",x);
1455 85800693 : return itos(x);
1456 : }
1457 :
1458 : INLINE ulong
1459 102638 : gtou(GEN x) {
1460 102638 : if (typ(x) != t_INT || signe(x)<0)
1461 7 : pari_err_TYPE("gtou [integer >=0 expected]",x);
1462 102631 : return itou(x);
1463 : }
1464 :
1465 : INLINE GEN
1466 45168315 : absfrac(GEN x)
1467 : {
1468 45168315 : GEN y = cgetg(3, t_FRAC);
1469 45168353 : gel(y,1) = absi(gel(x,1));
1470 45168351 : gel(y,2) = icopy(gel(x,2)); return y;
1471 : }
1472 : INLINE GEN
1473 47277 : absfrac_shallow(GEN x)
1474 47277 : { return signe(gel(x,1))>0? x: mkfrac(negi(gel(x,1)), gel(x,2)); }
1475 : INLINE GEN
1476 7793142 : Q_abs(GEN x) { return (typ(x) == t_INT)? absi(x): absfrac(x); }
1477 : INLINE GEN
1478 171571 : Q_abs_shallow(GEN x)
1479 171571 : { 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 251847826 : gtofp(GEN z, long prec)
1490 : {
1491 251847826 : switch(typ(z))
1492 : {
1493 213183625 : case t_INT: return itor(z, prec);
1494 4097405 : case t_FRAC: return fractor(z, prec);
1495 25900754 : case t_REAL: return rtor(z, prec);
1496 8673710 : case t_COMPLEX: {
1497 8673710 : GEN a = gel(z,1), b = gel(z,2);
1498 8673710 : if (isintzero(b)) return cxcompotor(a, prec);
1499 8673700 : if (isintzero(a)) {
1500 9102 : GEN y = cgetg(3, t_COMPLEX);
1501 9102 : b = cxcompotor(b, prec);
1502 9102 : gel(y,1) = real_0_bit(expo(b) - prec);
1503 9102 : gel(y,2) = b; return y;
1504 : }
1505 8664595 : 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 7114819 : RgX_gtofp(GEN x, long prec)
1530 37116453 : { pari_APPLY_pol_normalized(gtofp(gel(x,i), prec)); }
1531 :
1532 : INLINE GEN
1533 33675851 : RgC_gtofp(GEN x, long prec)
1534 216852292 : { pari_APPLY_type(t_COL, gtofp(gel(x,i), prec)) }
1535 :
1536 : INLINE GEN
1537 56 : RgV_gtofp(GEN x, long prec)
1538 4781 : { pari_APPLY_type(t_VEC, gtofp(gel(x,i), prec)) }
1539 :
1540 : INLINE GEN
1541 8175250 : RgM_gtofp(GEN x, long prec)
1542 41221377 : { pari_APPLY_same(RgC_gtofp(gel(x,i), prec)) }
1543 :
1544 : INLINE GEN
1545 574 : RgC_gtomp(GEN x, long prec)
1546 23002 : { pari_APPLY_type(t_COL, gtomp(gel(x,i), prec)) }
1547 :
1548 : INLINE GEN
1549 21 : RgM_gtomp(GEN x, long prec)
1550 595 : { pari_APPLY_same(RgC_gtomp(gel(x,i), prec)) }
1551 :
1552 : INLINE GEN
1553 60444 : RgX_fpnorml2(GEN x, long prec)
1554 : {
1555 60444 : pari_sp av = avma;
1556 60444 : return gerepileupto(av, gnorml2(RgX_gtofp(x, prec)));
1557 : }
1558 : INLINE GEN
1559 618672 : RgC_fpnorml2(GEN x, long prec)
1560 : {
1561 618672 : pari_sp av = avma;
1562 618672 : return gerepileupto(av, gnorml2(RgC_gtofp(x, prec)));
1563 : }
1564 : INLINE GEN
1565 22172 : RgM_fpnorml2(GEN x, long prec)
1566 : {
1567 22172 : pari_sp av = avma;
1568 22172 : return gerepileupto(av, gnorml2(RgM_gtofp(x, prec)));
1569 : }
1570 :
1571 : /* y a t_REAL */
1572 : INLINE void
1573 220535 : affgr(GEN x, GEN y)
1574 : {
1575 : pari_sp av;
1576 220535 : switch(typ(x)) {
1577 5999 : case t_INT: affir(x,y); break;
1578 214536 : case t_REAL: affrr(x,y); break;
1579 0 : case t_FRAC: rdiviiz(gel(x,1),gel(x,2), y); break;
1580 0 : case t_QUAD: av = avma; affgr(quadtofp(x,realprec(y)), y); set_avma(av); break;
1581 0 : default: pari_err_TYPE2("=",x,y);
1582 : }
1583 220535 : }
1584 :
1585 : INLINE GEN
1586 239591 : affc_fixlg(GEN x, GEN res)
1587 : {
1588 239591 : if (typ(x) == t_COMPLEX)
1589 : {
1590 206871 : affrr_fixlg(gel(x,1), gel(res,1));
1591 206871 : affrr_fixlg(gel(x,2), gel(res,2));
1592 : }
1593 : else
1594 : {
1595 32720 : set_avma((pari_sp)(res+3));
1596 32721 : res = cgetr(realprec(gel(res,1)));
1597 32721 : affrr_fixlg(x, res);
1598 : }
1599 239593 : return res;
1600 : }
1601 :
1602 : INLINE GEN
1603 0 : trunc_safe(GEN x) { long e; return gcvtoi(x,&e); }
1604 :
1605 : /*******************************************************************/
1606 : /* */
1607 : /* LENGTH CONVERSIONS */
1608 : /* */
1609 : /*******************************************************************/
1610 : INLINE long
1611 41087 : ndec2nlong(long x) { return 1 + (long)((x)*(LOG2_10/BITS_IN_LONG)); }
1612 : INLINE long
1613 32831 : ndec2prec(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1614 : INLINE long
1615 8256 : ndec2nbits(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1616 : /* Fast implementation of ceil(x / (8*sizeof(long))); typecast to (ulong)
1617 : * to avoid overflow. Faster than 1 + ((x-1)>>TWOPOTBITS_IN_LONG)) :
1618 : * addl, shrl instead of subl, sarl, addl */
1619 : INLINE long
1620 12568925 : nbits2nlong(long x) {
1621 12568925 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1622 : }
1623 :
1624 : INLINE long
1625 1474512397 : nbits2extraprec(long x) {
1626 1474512397 : return (((ulong)x+BITS_IN_LONG-1)>>TWOPOTBITS_IN_LONG) << TWOPOTBITS_IN_LONG;
1627 : }
1628 :
1629 : INLINE long
1630 185222516 : nbits2prec(long x) {
1631 185222516 : return (((ulong)x+BITS_IN_LONG-1)>>TWOPOTBITS_IN_LONG) << TWOPOTBITS_IN_LONG;
1632 : }
1633 :
1634 : INLINE long
1635 4452889887 : prec2lg(long x) {
1636 4452889887 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1637 : }
1638 : /* ceil(x / sizeof(long)) */
1639 : INLINE long
1640 120774415 : nchar2nlong(long x) {
1641 120774415 : return (long)(((ulong)x+sizeof(long)-1) >> (TWOPOTBITS_IN_LONG-3L));
1642 : }
1643 : INLINE long
1644 104209797 : prec2nbits(long x) { return x; }
1645 : INLINE double
1646 3178219 : bit_accuracy_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1647 : INLINE double
1648 570919 : prec2nbits_mul(long x, double y) { return x * y; }
1649 : INLINE long
1650 141324145 : bit_prec(GEN x) { return realprec(x); }
1651 : INLINE long
1652 2834623624 : bit_accuracy(long x) { return (x-2) * BITS_IN_LONG; }
1653 : INLINE long
1654 9750 : prec2ndec(long x) { return (long)(x * LOG10_2); }
1655 : INLINE long
1656 214 : nbits2ndec(long x) { return prec2ndec(x); }
1657 : INLINE long
1658 474213 : precdbl(long x) {return x << 1;}
1659 : INLINE long
1660 8058333901 : divsBIL(long n) { return n >> TWOPOTBITS_IN_LONG; }
1661 : INLINE long
1662 7970302399 : remsBIL(long n) { return n & (BITS_IN_LONG-1); }
1663 :
1664 : /*********************************************************************/
1665 : /** **/
1666 : /** OPERATIONS MODULO m **/
1667 : /** **/
1668 : /*********************************************************************/
1669 : /* Assume m > 0, more efficient if 0 <= a, b < m */
1670 :
1671 : INLINE GEN
1672 80054526 : Fp_red(GEN a, GEN m) { return modii(a, m); }
1673 : INLINE GEN
1674 174305990 : Fp_add(GEN a, GEN b, GEN m)
1675 : {
1676 174305990 : pari_sp av=avma;
1677 174305990 : GEN p = addii(a,b);
1678 173824891 : long s = signe(p);
1679 173824891 : if (!s) return p; /* = gen_0 */
1680 161012435 : if (s > 0) /* general case */
1681 : {
1682 160752377 : GEN t = subii(p, m);
1683 160679114 : s = signe(t);
1684 160679114 : if (!s) return gc_const(av, gen_0);
1685 152351970 : if (s < 0) return gc_const((pari_sp)p, p);
1686 72859432 : if (cmpii(t, m) < 0) return gerepileuptoint(av, t); /* general case ! */
1687 3301154 : p = remii(t, m);
1688 : }
1689 : else
1690 262453 : p = modii(p, m);
1691 3563689 : return gerepileuptoint(av, p);
1692 : }
1693 : INLINE GEN
1694 20878860 : Fp_double(GEN x, GEN N)
1695 : {
1696 20878860 : GEN z = shifti(x, 1);
1697 20579074 : return cmpii(z, N) >= 0? subii(z, N): z;
1698 : }
1699 : INLINE GEN
1700 147341653 : Fp_sub(GEN a, GEN b, GEN m)
1701 : {
1702 147341653 : pari_sp av=avma;
1703 147341653 : GEN p = subii(a,b);
1704 146218171 : long s = signe(p);
1705 146218171 : if (!s) return p; /* = gen_0 */
1706 130572803 : if (s > 0)
1707 : {
1708 65572650 : if (cmpii(p, m) < 0) return p; /* general case ! */
1709 1450808 : p = remii(p, m);
1710 : }
1711 : else
1712 : {
1713 65000153 : GEN t = addii(p, m);
1714 66566781 : if (!s) return gc_const(av, gen_0);
1715 66567350 : if (s > 0) return gerepileuptoint(av, t); /* general case ! */
1716 66567350 : p = modii(t, m);
1717 : }
1718 68324431 : return gerepileuptoint(av, p);
1719 : }
1720 : INLINE GEN
1721 28711043 : Fp_neg(GEN b, GEN m)
1722 : {
1723 28711043 : pari_sp av = avma;
1724 28711043 : long s = signe(b);
1725 : GEN p;
1726 28711043 : if (!s) return gen_0;
1727 24281730 : if (s > 0)
1728 : {
1729 23149735 : p = subii(m, b);
1730 23149316 : if (signe(p) >= 0) return p; /* general case ! */
1731 386954 : p = modii(p, m);
1732 : } else
1733 1132656 : p = remii(negi(b), m);
1734 1519826 : return gerepileuptoint(av, p);
1735 : }
1736 :
1737 : INLINE GEN
1738 252335 : Fp_halve(GEN a, GEN p)
1739 : {
1740 252335 : if (mpodd(a)) a = addii(a,p);
1741 252335 : return shifti(a,-1);
1742 : }
1743 :
1744 : /* assume 0 <= u < p and ps2 = p>>1 */
1745 : INLINE GEN
1746 74997636 : Fp_center(GEN u, GEN p, GEN ps2)
1747 74997636 : { return abscmpii(u,ps2)<=0? icopy(u): subii(u,p); }
1748 : /* same without copy */
1749 : INLINE GEN
1750 13855860 : Fp_center_i(GEN u, GEN p, GEN ps2)
1751 13855860 : { return abscmpii(u,ps2)<=0? u: subii(u,p); }
1752 :
1753 : /* x + y*z mod p */
1754 : INLINE GEN
1755 11230521 : Fp_addmul(GEN x, GEN y, GEN z, GEN p)
1756 : {
1757 : pari_sp av;
1758 11230521 : if (!signe(y) || !signe(z)) return Fp_red(x, p);
1759 10884441 : if (!signe(x)) return Fp_mul(z,y, p);
1760 9884671 : av = avma;
1761 9884671 : return gerepileuptoint(av, modii(addii(x, mulii(y,z)), p));
1762 : }
1763 :
1764 : INLINE GEN
1765 181803527 : Fp_mul(GEN a, GEN b, GEN m)
1766 : {
1767 181803527 : pari_sp av=avma;
1768 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1769 181803527 : (void)new_chunk(lg(a)+lg(b)+(lg(m)<<1));
1770 181875646 : p = mulii(a,b);
1771 181734359 : set_avma(av); return modii(p,m);
1772 : }
1773 : INLINE GEN
1774 63580642 : Fp_sqr(GEN a, GEN m)
1775 : {
1776 63580642 : pari_sp av=avma;
1777 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1778 63580642 : (void)new_chunk((lg(a)+lg(m))<<1);
1779 63872601 : p = sqri(a);
1780 62455568 : set_avma(av); return remii(p,m); /*Use remii: p >= 0 */
1781 : }
1782 : INLINE GEN
1783 70595787 : Fp_mulu(GEN a, ulong b, GEN m)
1784 : {
1785 70595787 : long l = lgefint(m);
1786 70595787 : if (l == 3)
1787 : {
1788 51021615 : ulong mm = m[2];
1789 51021615 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1790 : } else {
1791 19574172 : pari_sp av = avma;
1792 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1793 19574172 : (void)new_chunk(lg(a)+1+(l<<1));
1794 19546223 : p = muliu(a,b);
1795 19376401 : set_avma(av); return modii(p,m);
1796 : }
1797 : }
1798 : INLINE GEN
1799 17780 : Fp_muls(GEN a, long b, GEN m)
1800 : {
1801 17780 : long l = lgefint(m);
1802 17780 : if (l == 3)
1803 : {
1804 3578 : ulong mm = m[2];
1805 3578 : if (b < 0)
1806 : {
1807 3578 : ulong t = Fl_mul(umodiu(a, mm), -b, mm);
1808 3578 : return t? utoipos(mm - t): gen_0;
1809 : }
1810 : else
1811 0 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1812 : } else {
1813 14202 : pari_sp av = avma;
1814 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1815 14202 : (void)new_chunk(lg(a)+1+(l<<1));
1816 14202 : p = mulis(a,b);
1817 14202 : set_avma(av); return modii(p,m);
1818 : }
1819 : }
1820 :
1821 : INLINE GEN
1822 36330704 : Fp_inv(GEN a, GEN m)
1823 : {
1824 : GEN res;
1825 36330704 : if (! invmod(a,m,&res)) pari_err_INV("Fp_inv", mkintmod(res,m));
1826 36331265 : return res;
1827 : }
1828 : INLINE GEN
1829 1095789 : Fp_invsafe(GEN a, GEN m)
1830 : {
1831 : GEN res;
1832 1095789 : if (! invmod(a,m,&res)) return NULL;
1833 1095727 : return res;
1834 : }
1835 : INLINE GEN
1836 1614856 : Fp_div(GEN a, GEN b, GEN m)
1837 : {
1838 1614856 : pari_sp av = avma;
1839 : GEN p;
1840 1614856 : if (lgefint(b) == 3)
1841 : {
1842 660507 : a = Fp_divu(a, b[2], m);
1843 660507 : if (signe(b) < 0) a = Fp_neg(a, m);
1844 660507 : return a;
1845 : }
1846 : /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1847 954349 : (void)new_chunk(lg(a)+(lg(m)<<1));
1848 954349 : p = mulii(a, Fp_inv(b,m));
1849 954349 : set_avma(av); return modii(p,m);
1850 : }
1851 : INLINE GEN
1852 1898892 : Fp_divu(GEN x, ulong a, GEN p)
1853 : {
1854 1898892 : pari_sp av = avma;
1855 : ulong b;
1856 1898892 : if (lgefint(p) == 3)
1857 : {
1858 1502393 : ulong pp = p[2], xp = umodiu(x, pp);
1859 1502393 : return xp? utoipos(Fl_div(xp, a % pp, pp)): gen_0;
1860 : }
1861 396499 : x = Fp_red(x, p);
1862 396499 : b = Fl_neg(Fl_div(umodiu(x,a), umodiu(p,a), a), a); /* x + pb = 0 (mod a) */
1863 396498 : return gerepileuptoint(av, diviuexact(addmuliu(x, p, b), a));
1864 : }
1865 :
1866 : INLINE GEN
1867 1086723 : Flx_mulu(GEN x, ulong a, ulong p) { return Flx_Fl_mul(x,a%p,p); }
1868 :
1869 : INLINE GEN
1870 2498826 : get_F2x_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1871 :
1872 : INLINE long
1873 2529925 : get_F2x_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1874 :
1875 : INLINE long
1876 1928534 : get_F2x_degree(GEN T) { return typ(T)==t_VEC? F2x_degree(gel(T,2)): F2x_degree(T); }
1877 :
1878 : INLINE GEN
1879 399 : get_F2xqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1880 :
1881 : INLINE long
1882 375795 : get_F2xqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1883 :
1884 : INLINE long
1885 201201 : get_F2xqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1886 :
1887 : INLINE GEN
1888 25490224 : get_Flx_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1889 :
1890 : INLINE long
1891 67528254 : get_Flx_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1892 :
1893 : INLINE long
1894 83947698 : get_Flx_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1895 :
1896 : INLINE GEN
1897 8047 : get_FlxqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1898 :
1899 : INLINE long
1900 264625 : get_FlxqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1901 :
1902 : INLINE long
1903 317862 : get_FlxqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1904 :
1905 : INLINE GEN
1906 3388354 : get_FpX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1907 :
1908 : INLINE long
1909 7217213 : get_FpX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1910 :
1911 : INLINE long
1912 5989472 : get_FpX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1913 :
1914 : INLINE GEN
1915 146583 : get_FpXQX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1916 :
1917 : INLINE long
1918 51784 : get_FpXQX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1919 :
1920 : INLINE long
1921 3640 : get_FpXQX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1922 :
1923 : /*******************************************************************/
1924 : /* */
1925 : /* ADDMULII / SUBMULII */
1926 : /* */
1927 : /*******************************************************************/
1928 : /* x - y*z */
1929 : INLINE GEN
1930 32707271 : submulii(GEN x, GEN y, GEN z)
1931 : {
1932 32707271 : long lx = lgefint(x), ly, lz;
1933 : pari_sp av;
1934 : GEN t;
1935 32707271 : if (lx == 2) { t = mulii(z,y); togglesign(t); return t; }
1936 30259167 : ly = lgefint(y);
1937 30259167 : if (ly == 2) return icopy(x);
1938 28993179 : lz = lgefint(z);
1939 28993179 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1940 28993179 : t = mulii(z, y);
1941 28993179 : set_avma(av); return subii(x,t);
1942 : }
1943 : /* y*z - x */
1944 : INLINE GEN
1945 3823996 : mulsubii(GEN y, GEN z, GEN x)
1946 : {
1947 3823996 : long lx = lgefint(x), ly, lz;
1948 : pari_sp av;
1949 : GEN t;
1950 3823996 : if (lx == 2) return mulii(z,y);
1951 2415107 : ly = lgefint(y);
1952 2415107 : if (ly == 2) return negi(x);
1953 2141560 : lz = lgefint(z);
1954 2141560 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1955 2141589 : t = mulii(z, y);
1956 2141575 : set_avma(av); return subii(t,x);
1957 : }
1958 :
1959 : /* x - u*y */
1960 : INLINE GEN
1961 7693 : submuliu(GEN x, GEN y, ulong u)
1962 : {
1963 : pari_sp av;
1964 7693 : long ly = lgefint(y);
1965 7693 : if (ly == 2) return icopy(x);
1966 7693 : av = avma;
1967 7693 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1968 7693 : y = mului(u,y);
1969 7693 : set_avma(av); return subii(x, y);
1970 : }
1971 : /* x + u*y */
1972 : INLINE GEN
1973 404566 : addmuliu(GEN x, GEN y, ulong u)
1974 : {
1975 : pari_sp av;
1976 404566 : long ly = lgefint(y);
1977 404566 : if (ly == 2) return icopy(x);
1978 404566 : av = avma;
1979 404566 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1980 404566 : y = mului(u,y);
1981 404566 : set_avma(av); return addii(x, y);
1982 : }
1983 : /* x - u*y */
1984 : INLINE GEN
1985 59732190 : submuliu_inplace(GEN x, GEN y, ulong u)
1986 : {
1987 : pari_sp av;
1988 59732190 : long ly = lgefint(y);
1989 59732190 : if (ly == 2) return x;
1990 37865191 : av = avma;
1991 37865191 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1992 37869125 : y = mului(u,y);
1993 37868940 : set_avma(av); return subii(x, y);
1994 : }
1995 : /* x + u*y */
1996 : INLINE GEN
1997 59178150 : addmuliu_inplace(GEN x, GEN y, ulong u)
1998 : {
1999 : pari_sp av;
2000 59178150 : long ly = lgefint(y);
2001 59178150 : if (ly == 2) return x;
2002 37772793 : av = avma;
2003 37772793 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
2004 37776665 : y = mului(u,y);
2005 37776434 : set_avma(av); return addii(x, y);
2006 : }
2007 : /* ux + vy */
2008 : INLINE GEN
2009 37686023 : lincombii(GEN u, GEN v, GEN x, GEN y)
2010 : {
2011 37686023 : long lx = lgefint(x), ly;
2012 : GEN p1, p2;
2013 : pari_sp av;
2014 37686023 : if (lx == 2) return mulii(v,y);
2015 23722196 : ly = lgefint(y);
2016 23722196 : if (ly == 2) return mulii(u,x);
2017 21053600 : av = avma; (void)new_chunk(lx+ly+lgefint(u)+lgefint(v)); /* HACK */
2018 21056554 : p1 = mulii(u,x);
2019 21055442 : p2 = mulii(v,y);
2020 21055226 : set_avma(av); return addii(p1,p2);
2021 : }
2022 :
2023 : /*******************************************************************/
2024 : /* */
2025 : /* GEN SUBTYPES */
2026 : /* */
2027 : /*******************************************************************/
2028 :
2029 : INLINE int
2030 4751422013 : is_const_t(long t) { return (t < t_POLMOD); }
2031 : INLINE int
2032 6946 : is_extscalar_t(long t) { return (t <= t_POL); }
2033 : INLINE int
2034 9579869 : is_intreal_t(long t) { return (t <= t_REAL); }
2035 : INLINE int
2036 603528776 : is_matvec_t(long t) { return (t >= t_VEC && t <= t_MAT); }
2037 : INLINE int
2038 93662981 : is_noncalc_t(long tx) { return (tx) >= t_LIST; }
2039 : INLINE int
2040 0 : is_qfb_t(long t) { return (t == t_QFB); }
2041 : INLINE int
2042 5127007 : is_rational_t(long t) { return (t == t_INT || t == t_FRAC); }
2043 : INLINE int
2044 62552929 : is_real_t(long t) { return (t == t_INT || t == t_REAL || t == t_FRAC); }
2045 : INLINE int
2046 8425054155 : is_recursive_t(long t) { return lontyp[t]; }
2047 : INLINE int
2048 314465041 : is_scalar_t(long t) { return (t < t_POL); }
2049 : INLINE int
2050 43372540 : is_vec_t(long t) { return (t == t_VEC || t == t_COL); }
2051 :
2052 : INLINE int
2053 68060239 : qfb_is_qfi(GEN q) { return signe(gel(q,4)) < 0; }
2054 :
2055 : /*******************************************************************/
2056 : /* */
2057 : /* TRANSCENDENTAL */
2058 : /* */
2059 : /*******************************************************************/
2060 : INLINE GEN
2061 79825784 : sqrtr(GEN x) {
2062 79825784 : long s = signe(x);
2063 79825784 : if (s == 0) return real_0_bit(expo(x) >> 1);
2064 79792676 : if (s >= 0) return sqrtr_abs(x);
2065 432772 : retmkcomplex(gen_0, sqrtr_abs(x));
2066 : }
2067 : INLINE GEN
2068 0 : cbrtr_abs(GEN x) { return sqrtnr_abs(x, 3); }
2069 : INLINE GEN
2070 0 : cbrtr(GEN x) {
2071 0 : long s = signe(x);
2072 : GEN r;
2073 0 : if (s == 0) return real_0_bit(expo(x) / 3);
2074 0 : r = cbrtr_abs(x);
2075 0 : if (s < 0) togglesign(r);
2076 0 : return r;
2077 : }
2078 : INLINE GEN
2079 2791983 : sqrtnr(GEN x, long n) {
2080 2791983 : long s = signe(x);
2081 : GEN r;
2082 2791983 : if (s == 0) return real_0_bit(expo(x) / n);
2083 2791983 : r = sqrtnr_abs(x, n);
2084 2791993 : if (s < 0) pari_err_IMPL("sqrtnr for x < 0");
2085 2791993 : return r;
2086 : }
2087 : INLINE long
2088 751937 : logint(GEN B, GEN y) { return logintall(B,y,NULL); }
2089 : INLINE ulong
2090 1726671 : ulogint(ulong B, ulong y)
2091 : {
2092 : ulong r;
2093 : long e;
2094 1726671 : if (y == 2) return expu(B);
2095 1678685 : r = y;
2096 5075118 : for (e=1;; e++)
2097 : { /* here, r = y^e, r2 = y^(e-1) */
2098 5075118 : if (r >= B) return r == B? e: e-1;
2099 3397952 : r = umuluu_or_0(y, r);
2100 3397966 : if (!r) return e;
2101 : }
2102 : }
2103 :
2104 : /*******************************************************************/
2105 : /* */
2106 : /* MISCELLANEOUS */
2107 : /* */
2108 : /*******************************************************************/
2109 9579758 : INLINE int ismpzero(GEN x) { return is_intreal_t(typ(x)) && !signe(x); }
2110 2812679011 : INLINE int isintzero(GEN x) { return typ(x) == t_INT && !signe(x); }
2111 17290044 : INLINE int isint1(GEN x) { return typ(x)==t_INT && equali1(x); }
2112 5954045 : INLINE int isintm1(GEN x){ return typ(x)==t_INT && equalim1(x);}
2113 1218477529 : INLINE int equali1(GEN n)
2114 1218477529 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(1)) && n[2] == 1; }
2115 139002908 : INLINE int equalim1(GEN n)
2116 139002908 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(-1)) && n[2] == 1; }
2117 : /* works only for POSITIVE integers */
2118 2185282560 : INLINE int is_pm1(GEN n)
2119 2185282560 : { return lgefint(n) == 3 && n[2] == 1; }
2120 556645219 : INLINE int is_bigint(GEN n)
2121 556645219 : { long l = lgefint(n); return l > 3 || (l == 3 && (n[2] & HIGHBIT)); }
2122 :
2123 2028986315 : INLINE int odd(long x) { return x & 1; }
2124 116543393 : INLINE int both_odd(long x, long y) { return x & y & 1; }
2125 :
2126 : INLINE int
2127 7909203534 : isonstack(GEN x)
2128 7909203534 : { return ((pari_sp)x >= pari_mainstack->bot
2129 7909203534 : && (pari_sp)x < pari_mainstack->top); }
2130 :
2131 : /* assume x != 0 and x t_REAL, return an approximation to log2(|x|) */
2132 : INLINE double
2133 92793367 : dbllog2r(GEN x)
2134 92793367 : { return log2((double)(ulong)x[2]) + (double)(expo(x) - (BITS_IN_LONG-1)); }
2135 :
2136 : INLINE GEN
2137 2508992 : mul_content(GEN cx, GEN cy)
2138 : {
2139 2508992 : if (!cx) return cy;
2140 526610 : if (!cy) return cx;
2141 338897 : return gmul(cx,cy);
2142 : }
2143 : INLINE GEN
2144 0 : inv_content(GEN c) { return c? ginv(c): NULL; }
2145 : INLINE GEN
2146 57571 : div_content(GEN cx, GEN cy)
2147 : {
2148 57571 : if (!cy) return cx;
2149 56451 : if (!cx) return ginv(cy);
2150 25653 : return gdiv(cx,cy);
2151 : }
2152 : INLINE GEN
2153 11277324 : mul_denom(GEN dx, GEN dy)
2154 : {
2155 11277324 : if (!dx) return dy;
2156 2570787 : if (!dy) return dx;
2157 1549386 : return mulii(dx,dy);
2158 : }
2159 :
2160 : /* POLYNOMIALS */
2161 : INLINE GEN
2162 1435439 : constant_coeff(GEN x) { return signe(x)? gel(x,2): gen_0; }
2163 : INLINE GEN
2164 169441733 : leading_coeff(GEN x) { return lg(x) == 2? gen_0: gel(x,lg(x)-1); }
2165 : INLINE ulong
2166 968466 : Flx_lead(GEN x) { return lg(x) == 2? 0: x[lg(x)-1]; }
2167 : INLINE ulong
2168 294711 : Flx_constant(GEN x) { return lg(x) == 2? 0: x[2]; }
2169 : INLINE long
2170 5371555567 : degpol(GEN x) { return lg(x)-3; }
2171 : INLINE long
2172 2553466066 : lgpol(GEN x) { return lg(x)-2; }
2173 : INLINE long
2174 340361232 : lgcols(GEN x) { return lg(gel(x,1)); }
2175 : INLINE long
2176 154387113 : nbrows(GEN x) { return lg(gel(x,1))-1; }
2177 : INLINE GEN
2178 0 : truecoef(GEN x, long n) { return polcoef(x,n,-1); }
2179 :
2180 : INLINE GEN
2181 2124801 : ZXQ_mul(GEN y, GEN x, GEN T) { return ZX_rem(ZX_mul(y, x), T); }
2182 : INLINE GEN
2183 949847 : ZXQ_sqr(GEN x, GEN T) { return ZX_rem(ZX_sqr(x), T); }
2184 :
2185 : INLINE GEN
2186 103379528 : RgX_copy(GEN x)
2187 376669156 : { pari_APPLY_pol_normalized(gcopy(gel(x,i))); }
2188 : /* have to use ulong to avoid silly warnings from gcc "assuming signed
2189 : * overflow does not occur" */
2190 : INLINE GEN
2191 2544022 : RgX_coeff(GEN x, long n)
2192 : {
2193 2544022 : ulong l = lg(x);
2194 2544022 : return (n < 0 || ((ulong)n+3) > l)? gen_0: gel(x,n+2);
2195 : }
2196 : INLINE GEN
2197 347497 : RgX_renormalize(GEN x) { return RgX_renormalize_lg(x, lg(x)); }
2198 : INLINE GEN
2199 7051300 : RgX_div(GEN x, GEN y) { return RgX_divrem(x,y,NULL); }
2200 : INLINE GEN
2201 1904 : RgXQX_div(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,NULL); }
2202 : INLINE GEN
2203 114083 : RgXQX_rem(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,ONLY_REM); }
2204 : INLINE GEN
2205 5427165 : FpX_div(GEN x, GEN y, GEN p) { return FpX_divrem(x,y,p, NULL); }
2206 : INLINE GEN
2207 1989313 : Flx_div(GEN x, GEN y, ulong p) { return Flx_divrem(x,y,p, NULL); }
2208 : INLINE GEN
2209 21359844 : Flx_div_pre(GEN x, GEN y, ulong p, ulong pi)
2210 21359844 : { return Flx_divrem_pre(x,y,p,pi, NULL); }
2211 : INLINE GEN
2212 1568272 : F2x_div(GEN x, GEN y) { return F2x_divrem(x,y, NULL); }
2213 : INLINE GEN
2214 0 : FpV_FpC_mul(GEN x, GEN y, GEN p) { return FpV_dotproduct(x,y,p); }
2215 : INLINE GEN
2216 102090796 : pol0_Flx(long sv) { return mkvecsmall(sv); }
2217 : INLINE GEN
2218 54800433 : pol1_Flx(long sv) { return mkvecsmall2(sv, 1); }
2219 : INLINE GEN
2220 37603654 : polx_Flx(long sv) { return mkvecsmall3(sv, 0, 1); }
2221 : INLINE GEN
2222 0 : zero_zx(long sv) { return zero_Flx(sv); }
2223 : INLINE GEN
2224 0 : polx_zx(long sv) { return polx_Flx(sv); }
2225 : INLINE GEN
2226 0 : zx_shift(GEN x, long n) { return Flx_shift(x,n); }
2227 : INLINE GEN
2228 14049 : zx_renormalize(GEN x, long l) { return Flx_renormalize(x,l); }
2229 : INLINE GEN
2230 1350 : zero_F2x(long sv) { return zero_Flx(sv); }
2231 : INLINE GEN
2232 13269139 : pol0_F2x(long sv) { return pol0_Flx(sv); }
2233 : INLINE GEN
2234 3952604 : pol1_F2x(long sv) { return pol1_Flx(sv); }
2235 : INLINE GEN
2236 1075964 : polx_F2x(long sv) { return mkvecsmall2(sv, 2); }
2237 : INLINE int
2238 2872172 : F2x_equal1(GEN x) { return Flx_equal1(x); }
2239 : INLINE int
2240 4690716 : F2x_equal(GEN V, GEN W) { return Flx_equal(V,W); }
2241 : INLINE GEN
2242 60652578 : F2x_copy(GEN x) { return leafcopy(x); }
2243 : INLINE GEN
2244 4487 : F2v_copy(GEN x) { return leafcopy(x); }
2245 : INLINE GEN
2246 2505305 : Flv_copy(GEN x) { return leafcopy(x); }
2247 : INLINE GEN
2248 172271770 : Flx_copy(GEN x) { return leafcopy(x); }
2249 : INLINE GEN
2250 4293270 : vecsmall_copy(GEN x) { return leafcopy(x); }
2251 : INLINE int
2252 8581544 : Flx_equal1(GEN x) { return degpol(x)==0 && x[2] == 1; }
2253 : INLINE int
2254 12080 : ZX_equal1(GEN x) { return degpol(x)==0 && equali1(gel(x,2)); }
2255 : INLINE int
2256 7180525 : ZX_is_monic(GEN x) { return equali1(leading_coeff(x)); }
2257 :
2258 : INLINE GEN
2259 152326870 : ZX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2260 : INLINE GEN
2261 142407732 : FpX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2262 : INLINE GEN
2263 850077 : FpXX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2264 : INLINE GEN
2265 4698170 : FpXQX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2266 : INLINE GEN
2267 115529382 : F2x_renormalize(GEN x, long lx) { return Flx_renormalize(x,lx); }
2268 :
2269 : INLINE GEN
2270 0 : F2xX_shift(GEN a, long n, long vs) { return FlxX_shift(a, n, vs); }
2271 :
2272 : INLINE GEN
2273 38185 : F2v_to_F2x(GEN x, long sv) {
2274 38185 : GEN y = leafcopy(x);
2275 38184 : y[1] = sv; F2x_renormalize(y, lg(y)); return y;
2276 : }
2277 :
2278 : INLINE long
2279 385 : sturm(GEN x) { return sturmpart(x, NULL, NULL); }
2280 :
2281 : INLINE long
2282 5796 : gval(GEN x, long v)
2283 5796 : { pari_sp av = avma; return gc_long(av, gvaluation(x, pol_x(v))); }
2284 :
2285 : INLINE void
2286 480553 : RgX_shift_inplace_init(long v)
2287 480553 : { if (v) (void)cgetg(v, t_VECSMALL); }
2288 : /* shift polynomial in place. assume v free cells have been left before x */
2289 : INLINE GEN
2290 480553 : RgX_shift_inplace(GEN x, long v)
2291 : {
2292 : long i, lx;
2293 : GEN z;
2294 480553 : if (!v) return x;
2295 253169 : lx = lg(x);
2296 253169 : if (lx == 2) return x;
2297 253169 : z = x + lx;
2298 : /* stackdummy's from normalizepol */
2299 253169 : while (lg(z) != v) z += lg(z);
2300 253169 : z += v;
2301 4654514 : for (i = lx-1; i >= 2; i--) gel(--z,0) = gel(x,i);
2302 675895 : for (i = 0; i < v; i++) gel(--z,0) = gen_0;
2303 253169 : z -= 2;
2304 253169 : z[1] = x[1];
2305 253169 : z[0] = evaltyp(t_POL) | evallg(lx+v);
2306 253169 : stackdummy((pari_sp)z, (pari_sp)x); return z;
2307 : }
2308 :
2309 :
2310 : /* LINEAR ALGEBRA */
2311 : INLINE GEN
2312 501498 : zv_to_ZV(GEN x) { return vecsmall_to_vec(x); }
2313 : INLINE GEN
2314 7746604 : zc_to_ZC(GEN x) { return vecsmall_to_col(x); }
2315 : INLINE GEN
2316 3190421 : ZV_to_zv(GEN x) { return vec_to_vecsmall(x); }
2317 : INLINE GEN
2318 0 : zx_to_zv(GEN x, long N) { return Flx_to_Flv(x,N); }
2319 : INLINE GEN
2320 104146 : zv_to_zx(GEN x, long sv) { return Flv_to_Flx(x,sv); }
2321 : INLINE GEN
2322 0 : zm_to_zxV(GEN x, long sv) { return Flm_to_FlxV(x,sv); }
2323 : INLINE GEN
2324 0 : zero_zm(long x, long y) { return zero_Flm(x,y); }
2325 : INLINE GEN
2326 36080193 : zero_zv(long x) { return zero_Flv(x); }
2327 : INLINE GEN
2328 266 : zm_transpose(GEN x) { return Flm_transpose(x); }
2329 : INLINE GEN
2330 0 : zm_copy(GEN x) { return Flm_copy(x); }
2331 : INLINE GEN
2332 2183302 : zv_copy(GEN x) { return Flv_copy(x); }
2333 : INLINE GEN
2334 0 : zm_row(GEN x, long i) { return Flm_row(x,i); }
2335 :
2336 : INLINE GEN
2337 10675901 : ZC_hnfrem(GEN x, GEN y) { return ZC_hnfdivrem(x,y,NULL); }
2338 : INLINE GEN
2339 326809 : ZM_hnfrem(GEN x, GEN y) { return ZM_hnfdivrem(x,y,NULL); }
2340 : INLINE GEN
2341 6933683 : ZM_lll(GEN x, double D, long f) { return ZM_lll_norms(x,D,f,NULL); }
2342 : INLINE void
2343 9406532 : RgM_dimensions(GEN x, long *m, long *n) { *n = lg(x)-1; *m = *n? nbrows(x): 0; }
2344 : INLINE GEN
2345 21103235 : RgM_shallowcopy(GEN x)
2346 92407173 : { pari_APPLY_same(leafcopy(gel(x,i))); }
2347 : INLINE GEN
2348 197828 : F2m_copy(GEN x) { return RgM_shallowcopy(x); }
2349 :
2350 : INLINE GEN
2351 0 : F3m_copy(GEN x) { return RgM_shallowcopy(x); }
2352 :
2353 : INLINE GEN
2354 6245112 : Flm_copy(GEN x) { return RgM_shallowcopy(x); }
2355 :
2356 : /* divisibility: return 1 if y[i] | x[i] for all i, 0 otherwise. Assume
2357 : * x,y are ZV of the same length */
2358 : INLINE int
2359 23485 : ZV_dvd(GEN x, GEN y)
2360 : {
2361 23485 : long i, l = lg(x);
2362 37856 : for (i=1; i < l; i++)
2363 30464 : if ( ! dvdii( gel(x,i), gel(y,i) ) ) return 0;
2364 7392 : return 1;
2365 : }
2366 : INLINE GEN
2367 539086 : ZM_ZV_mod(GEN x, GEN y)
2368 1537833 : { pari_APPLY_same(ZV_ZV_mod(gel(x,i), y)) }
2369 : INLINE GEN
2370 7322829 : ZV_ZV_mod(GEN x, GEN y)
2371 18920849 : { pari_APPLY_same(modii(gel(x,i), gel(y,i))) }
2372 : INLINE GEN
2373 0 : vecmodii(GEN x, GEN y) { return ZV_ZV_mod(x,y); }
2374 : INLINE GEN
2375 174881 : vecmoduu(GEN x, GEN y) { pari_APPLY_ulong(((ulong*)x)[i] % ((ulong*)y)[i]) }
2376 :
2377 : /* Fq */
2378 : INLINE GEN
2379 3476647 : Fq_red(GEN x, GEN T, GEN p)
2380 3476647 : { return typ(x)==t_INT? Fp_red(x,p): FpXQ_red(x,T,p); }
2381 : INLINE GEN
2382 110255 : Fq_to_FpXQ(GEN x, GEN T, GEN p /*unused*/)
2383 : {
2384 : (void) p;
2385 110255 : return typ(x)==t_INT ? scalarpol(x, get_FpX_var(T)): x;
2386 : }
2387 : INLINE GEN
2388 756 : Rg_to_Fq(GEN x, GEN T, GEN p) { return T? Rg_to_FpXQ(x,T,p): Rg_to_Fp(x,p); }
2389 :
2390 : INLINE GEN
2391 14601 : gener_Fq_local(GEN T, GEN p, GEN L)
2392 0 : { return T? gener_FpXQ_local(T,p, L)
2393 14601 : : pgener_Fp_local(p, L); }
2394 :
2395 : INLINE GEN
2396 0 : random_Fq(GEN T, GEN p)
2397 0 : { return T ? random_FpX(get_FpX_degree(T), get_FpX_var(T), p): randomi(p); }
2398 :
2399 : /* FpXQX */
2400 : INLINE GEN
2401 4525 : FpXQX_div(GEN x, GEN y, GEN T, GEN p) { return FpXQX_divrem(x, y, T, p, NULL); }
2402 : INLINE GEN
2403 0 : FlxqX_div(GEN x, GEN y, GEN T, ulong p) { return FlxqX_divrem(x, y, T, p, NULL); }
2404 : INLINE GEN
2405 165453 : FlxqX_div_pre(GEN x, GEN y, GEN T, ulong p, ulong pi) { return FlxqX_divrem_pre(x, y, T, p, pi, NULL); }
2406 : INLINE GEN
2407 33243 : F2xqX_div(GEN x, GEN y, GEN T) { return F2xqX_divrem(x, y, T, NULL); }
2408 :
2409 : INLINE GEN
2410 20587 : FpXY_Fq_evaly(GEN Q, GEN y, GEN T, GEN p, long vx)
2411 20587 : { return T ? FpXY_FpXQ_evaly(Q, y, T, p, vx): FpXY_evaly(Q, y, p, vx); }
2412 :
2413 : /* FqX */
2414 : INLINE GEN
2415 25354 : FqX_red(GEN z, GEN T, GEN p) { return T? FpXQX_red(z, T, p): FpX_red(z, p); }
2416 : INLINE GEN
2417 127694 : FqX_add(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2418 : INLINE GEN
2419 24956 : FqX_neg(GEN x,GEN T,GEN p) { return T? FpXX_neg(x,p): FpX_neg(x,p); }
2420 : INLINE GEN
2421 68607 : FqX_sub(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2422 : INLINE GEN
2423 568082 : FqX_Fp_mul(GEN P, GEN u, GEN T, GEN p)
2424 568082 : { return T? FpXX_Fp_mul(P, u, p): FpX_Fp_mul(P, u, p); }
2425 : INLINE GEN
2426 427376 : FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
2427 427376 : { return typ(U)==t_INT ? FqX_Fp_mul(P, U, T, p): FpXQX_FpXQ_mul(P, U, T, p); }
2428 : INLINE GEN
2429 368601 : FqX_mul(GEN x, GEN y, GEN T, GEN p)
2430 368601 : { return T? FpXQX_mul(x, y, T, p): FpX_mul(x, y, p); }
2431 : INLINE GEN
2432 21942 : FqX_mulu(GEN x, ulong y, GEN T, GEN p)
2433 21942 : { return T? FpXX_mulu(x, y, p): FpX_mulu(x, y, p); }
2434 : INLINE GEN
2435 71855 : FqX_sqr(GEN x, GEN T, GEN p)
2436 71855 : { return T? FpXQX_sqr(x, T, p): FpX_sqr(x, p); }
2437 : INLINE GEN
2438 1295 : FqX_powu(GEN x, ulong n, GEN T, GEN p)
2439 1295 : { return T? FpXQX_powu(x, n, T, p): FpX_powu(x, n, p); }
2440 : INLINE GEN
2441 19411 : FqX_halve(GEN x, GEN T, GEN p)
2442 19411 : { return T? FpXX_halve(x, p): FpX_halve(x, p); }
2443 : INLINE GEN
2444 40283 : FqX_div(GEN x, GEN y, GEN T, GEN p)
2445 40283 : { return T? FpXQX_divrem(x,y,T,p,NULL): FpX_divrem(x,y,p,NULL); }
2446 : INLINE GEN
2447 6090 : FqX_get_red(GEN S, GEN T, GEN p)
2448 6090 : { return T? FpXQX_get_red(S,T,p): FpX_get_red(S,p); }
2449 : INLINE GEN
2450 37743 : FqX_rem(GEN x, GEN y, GEN T, GEN p)
2451 37743 : { return T? FpXQX_rem(x,y,T,p): FpX_rem(x,y,p); }
2452 : INLINE GEN
2453 0 : FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
2454 0 : { return T? FpXQX_divrem(x,y,T,p,z): FpX_divrem(x,y,p,z); }
2455 : INLINE GEN
2456 71939 : FqX_div_by_X_x(GEN x, GEN y, GEN T, GEN p, GEN *z)
2457 71939 : { return T? FpXQX_div_by_X_x(x,y,T,p,z): FpX_div_by_X_x(x,y,p,z); }
2458 : INLINE GEN
2459 0 : FqX_halfgcd(GEN P,GEN Q,GEN T,GEN p)
2460 0 : {return T? FpXQX_halfgcd(P,Q,T,p): FpX_halfgcd(P,Q,p);}
2461 : INLINE GEN
2462 693364 : FqX_gcd(GEN P,GEN Q,GEN T,GEN p)
2463 693364 : {return T? FpXQX_gcd(P,Q,T,p): FpX_gcd(P,Q,p);}
2464 : INLINE GEN
2465 442903 : FqX_extgcd(GEN P,GEN Q,GEN T,GEN p, GEN *U, GEN *V)
2466 442903 : { return T? FpXQX_extgcd(P,Q,T,p,U,V): FpX_extgcd(P,Q,p,U,V); }
2467 : INLINE GEN
2468 4872 : FqX_normalize(GEN z, GEN T, GEN p)
2469 4872 : { return T? FpXQX_normalize(z, T, p): FpX_normalize(z, p); }
2470 : INLINE GEN
2471 723681 : FqX_deriv(GEN f, GEN T, GEN p) { return T? FpXX_deriv(f, p): FpX_deriv(f, p); }
2472 : INLINE GEN
2473 0 : FqX_integ(GEN f, GEN T, GEN p) { return T? FpXX_integ(f, p): FpX_integ(f, p); }
2474 : INLINE GEN
2475 141723 : FqX_factor(GEN f, GEN T, GEN p)
2476 141723 : { return T?FpXQX_factor(f, T, p): FpX_factor(f, p); }
2477 : INLINE GEN
2478 7 : FqX_factor_squarefree(GEN f, GEN T, GEN p)
2479 7 : { return T ? FpXQX_factor_squarefree(f, T, p): FpX_factor_squarefree(f, p); }
2480 : INLINE GEN
2481 7 : FqX_ddf(GEN f, GEN T, GEN p)
2482 7 : { return T ? FpXQX_ddf(f, T, p): FpX_ddf(f, p); }
2483 : INLINE GEN
2484 47786 : FqX_degfact(GEN f, GEN T, GEN p)
2485 47786 : { return T?FpXQX_degfact(f, T, p): FpX_degfact(f, p); }
2486 : INLINE GEN
2487 7273 : FqX_roots(GEN f, GEN T, GEN p)
2488 7273 : { return T?FpXQX_roots(f, T, p): FpX_roots(f, p); }
2489 : INLINE GEN
2490 175 : FqX_to_mod(GEN f, GEN T, GEN p)
2491 175 : { return T?FpXQX_to_mod(f, T, p): FpX_to_mod(f, p); }
2492 :
2493 : /*FqXQ*/
2494 : INLINE GEN
2495 0 : FqXQ_add(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2496 0 : { (void)S; return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2497 : INLINE GEN
2498 0 : FqXQ_sub(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2499 0 : { (void)S; return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2500 : INLINE GEN
2501 0 : FqXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
2502 0 : { return T? FpXQXQ_div(x,y,S,T,p): FpXQ_div(x,y,S,p); }
2503 : INLINE GEN
2504 0 : FqXQ_inv(GEN x, GEN S, GEN T, GEN p)
2505 0 : { return T? FpXQXQ_inv(x,S,T,p): FpXQ_inv(x,S,p); }
2506 : INLINE GEN
2507 0 : FqXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
2508 0 : { return T? FpXQXQ_invsafe(x,S,T,p): FpXQ_inv(x,S,p); }
2509 : INLINE GEN
2510 22766 : FqXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
2511 22766 : { return T? FpXQXQ_mul(x,y,S,T,p): FpXQ_mul(x,y,S,p); }
2512 : INLINE GEN
2513 0 : FqXQ_sqr(GEN x, GEN S, GEN T, GEN p)
2514 0 : { return T? FpXQXQ_sqr(x,S,T,p): FpXQ_sqr(x,S,p); }
2515 : INLINE GEN
2516 0 : FqXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
2517 0 : { return T? FpXQXQ_pow(x,n,S,T,p): FpXQ_pow(x,n,S,p); }
2518 :
2519 : /*FqXn*/
2520 : INLINE GEN
2521 6590 : FqXn_expint(GEN x, long n, GEN T, GEN p)
2522 6590 : { return T? FpXQXn_expint(x,n,T,p): FpXn_expint(x,n,p); }
2523 : INLINE GEN
2524 0 : FqXn_exp(GEN x, long n, GEN T, GEN p)
2525 0 : { return T? FpXQXn_exp(x,n,T,p): FpXn_exp(x,n,p); }
2526 : INLINE GEN
2527 7126 : FqXn_inv(GEN x, long n, GEN T, GEN p)
2528 7126 : { return T? FpXQXn_inv(x,n,T,p): FpXn_inv(x,n,p); }
2529 : INLINE GEN
2530 263403 : FqXn_mul(GEN x, GEN y, long n, GEN T, GEN p)
2531 263403 : { return T? FpXQXn_mul(x, y, n, T, p): FpXn_mul(x, y, n, p); }
2532 : INLINE GEN
2533 0 : FqXn_sqr(GEN x, long n, GEN T, GEN p)
2534 0 : { return T? FpXQXn_sqr(x,n,T,p): FpXn_sqr(x,n,p); }
2535 :
2536 : /*FpXQ*/
2537 : INLINE GEN
2538 0 : FpXQ_add(GEN x,GEN y,GEN T/*unused*/,GEN p)
2539 0 : { (void)T; return FpX_add(x,y,p); }
2540 : INLINE GEN
2541 0 : FpXQ_sub(GEN x,GEN y,GEN T/*unused*/,GEN p)
2542 0 : { (void)T; return FpX_sub(x,y,p); }
2543 :
2544 : /*Flxq*/
2545 : INLINE GEN
2546 0 : Flxq_add(GEN x,GEN y,GEN T/*unused*/,ulong p)
2547 0 : { (void)T; return Flx_add(x,y,p); }
2548 : INLINE GEN
2549 0 : Flxq_sub(GEN x,GEN y,GEN T/*unused*/,ulong p)
2550 0 : { (void)T; return Flx_sub(x,y,p); }
2551 :
2552 : /* F2x */
2553 :
2554 : INLINE ulong
2555 666935695 : F2x_coeff(GEN x,long v)
2556 : {
2557 666935695 : ulong u=(ulong)x[2+divsBIL(v)];
2558 666935565 : return (u>>remsBIL(v))&1UL;
2559 : }
2560 :
2561 : INLINE void
2562 12143069 : F2x_clear(GEN x,long v)
2563 : {
2564 12143069 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2565 12143011 : *u&=~(1UL<<remsBIL(v));
2566 12142994 : }
2567 :
2568 : INLINE void
2569 124770438 : F2x_set(GEN x,long v)
2570 : {
2571 124770438 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2572 124766237 : *u|=1UL<<remsBIL(v);
2573 124765565 : }
2574 :
2575 : INLINE void
2576 1554457 : F2x_flip(GEN x,long v)
2577 : {
2578 1554457 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2579 1554457 : *u^=1UL<<remsBIL(v);
2580 1554457 : }
2581 :
2582 : /* F2v */
2583 :
2584 : INLINE ulong
2585 660358862 : F2v_coeff(GEN x,long v) { return F2x_coeff(x,v-1); }
2586 :
2587 : INLINE void
2588 12143065 : F2v_clear(GEN x,long v) { F2x_clear(x,v-1); }
2589 :
2590 : INLINE void
2591 101378241 : F2v_set(GEN x,long v) { F2x_set(x,v-1); }
2592 :
2593 : INLINE void
2594 1554457 : F2v_flip(GEN x,long v) { F2x_flip(x,v-1); }
2595 :
2596 : /* F2m */
2597 :
2598 : INLINE ulong
2599 8073360 : F2m_coeff(GEN x, long a, long b) { return F2v_coeff(gel(x,b), a); }
2600 :
2601 : INLINE void
2602 0 : F2m_clear(GEN x, long a, long b) { F2v_clear(gel(x,b), a); }
2603 :
2604 : INLINE void
2605 798 : F2m_set(GEN x, long a, long b) { F2v_set(gel(x,b), a); }
2606 :
2607 : INLINE void
2608 1554457 : F2m_flip(GEN x, long a, long b) { F2v_flip(gel(x,b), a); }
2609 :
2610 : /* F3m */
2611 :
2612 : INLINE ulong
2613 3206656 : F3m_coeff(GEN x, long a, long b) { return F3v_coeff(gel(x,b), a); }
2614 :
2615 : INLINE void
2616 0 : F3m_set(GEN x, long a, long b, ulong c) { F3v_set(gel(x,b), a, c); }
2617 :
2618 : /* ARITHMETIC */
2619 : INLINE GEN
2620 3885 : matpascal(long n) { return matqpascal(n, NULL); }
2621 : INLINE long
2622 458558 : Z_issquare(GEN x) { return Z_issquareall(x, NULL); }
2623 : INLINE long
2624 98 : Z_ispower(GEN x, ulong k) { return Z_ispowerall(x, k, NULL); }
2625 : INLINE GEN
2626 6589883 : sqrti(GEN x) { return sqrtremi(x,NULL); }
2627 : INLINE GEN
2628 123137211 : gaddgs(GEN y, long s) { return gaddsg(s,y); }
2629 : INLINE int
2630 780380 : gcmpgs(GEN y, long s) { return -gcmpsg(s,y); }
2631 : INLINE int
2632 29176 : gequalgs(GEN y, long s) { return gequalsg(s,y); }
2633 : INLINE GEN
2634 0 : gmaxsg(long s, GEN y) { return gmaxgs(y,s); }
2635 : INLINE GEN
2636 0 : gminsg(long s, GEN y) { return gmings(y,s); }
2637 : INLINE GEN
2638 22014867 : gmulgs(GEN y, long s) { return gmulsg(s,y); }
2639 : INLINE GEN
2640 124173007 : gmulgu(GEN y, ulong s) { return gmulug(s,y); }
2641 : INLINE GEN
2642 1691647 : gsubgs(GEN y, long s) { return gaddgs(y, -s); }
2643 : INLINE GEN
2644 528210 : gdivsg(long s, GEN y) { return gdiv(stoi(s), y); }
2645 :
2646 : INLINE GEN
2647 13509935 : gmax_shallow(GEN x, GEN y) { return gcmp(x,y)<0? y: x; }
2648 : INLINE GEN
2649 868577 : gmin_shallow(GEN x, GEN y) { return gcmp(x,y)<0? x: y; }
2650 :
2651 : /* x t_COMPLEX */
2652 : INLINE GEN
2653 90669546 : cxnorm(GEN x) { return gadd(gsqr(gel(x,1)), gsqr(gel(x,2))); }
2654 : /* q t_QUAD */
2655 : INLINE GEN
2656 69860 : quadnorm(GEN q)
2657 : {
2658 69860 : GEN X = gel(q,1), b = gel(X,3), c = gel(X,2);
2659 69860 : GEN z, u = gel(q,3), v = gel(q,2);
2660 69860 : if (typ(u) == t_INT && typ(v) == t_INT) /* generic case */
2661 : {
2662 69671 : z = signe(b)? mulii(v, addii(u,v)): sqri(v);
2663 69671 : return addii(z, mulii(c, sqri(u)));
2664 : }
2665 : else
2666 : {
2667 189 : z = signe(b)? gmul(v, gadd(u,v)): gsqr(v);
2668 189 : return gadd(z, gmul(c, gsqr(u)));
2669 : }
2670 : }
2671 : /* x a t_QUAD, return the attached discriminant */
2672 : INLINE GEN
2673 1078 : quad_disc(GEN x)
2674 : {
2675 1078 : GEN Q = gel(x,1), b = gel(Q,3), c = gel(Q,2), c4 = shifti(c,2);
2676 1078 : if (is_pm1(b)) return subsi(1, c4);
2677 154 : togglesign_safe(&c4); return c4;
2678 : }
2679 : INLINE GEN
2680 4848011 : qfb_disc3(GEN x, GEN y, GEN z) { return subii(sqri(y), shifti(mulii(x,z),2)); }
2681 : INLINE GEN
2682 18474990 : qfb_disc(GEN x) { return gel(x,4); }
2683 :
2684 : INLINE GEN
2685 4140310 : sqrfrac(GEN x)
2686 : {
2687 4140310 : GEN z = cgetg(3,t_FRAC);
2688 4140308 : gel(z,1) = sqri(gel(x,1));
2689 4140285 : gel(z,2) = sqri(gel(x,2)); return z;
2690 : }
2691 :
2692 : INLINE void
2693 16693566 : normalize_frac(GEN z) {
2694 16693566 : if (signe(gel(z,2)) < 0) { togglesign(gel(z,1)); setabssign(gel(z,2)); }
2695 16693566 : }
2696 :
2697 : INLINE GEN
2698 42911404 : powii(GEN x, GEN n)
2699 : {
2700 42911404 : long ln = lgefint(n);
2701 42911404 : if (ln == 3) {
2702 : GEN z;
2703 42888512 : if (signe(n) > 0) return powiu(x, n[2]);
2704 74539 : z = cgetg(3, t_FRAC);
2705 74551 : gel(z,1) = gen_1;
2706 74551 : gel(z,2) = powiu(x, n[2]);
2707 74551 : return z;
2708 : }
2709 22892 : if (ln == 2) return gen_1; /* rare */
2710 : /* should never happen */
2711 0 : return powgi(x, n); /* overflow unless x = 0, 1, -1 */
2712 : }
2713 : INLINE GEN
2714 1561 : powIs(long n) {
2715 1561 : switch(n & 3)
2716 : {
2717 63 : case 1: return mkcomplex(gen_0,gen_1);
2718 385 : case 2: return gen_m1;
2719 707 : case 3: return mkcomplex(gen_0,gen_m1);
2720 : }
2721 406 : return gen_1;
2722 : }
2723 :
2724 : /*******************************************************************/
2725 : /* */
2726 : /* ASSIGNMENTS */
2727 : /* */
2728 : /*******************************************************************/
2729 0 : INLINE void mpexpz(GEN x, GEN z)
2730 0 : { pari_sp av = avma; gaffect(mpexp(x), z); set_avma(av); }
2731 0 : INLINE void mplogz(GEN x, GEN z)
2732 0 : { pari_sp av = avma; gaffect(mplog(x), z); set_avma(av); }
2733 0 : INLINE void mpcosz(GEN x, GEN z)
2734 0 : { pari_sp av = avma; gaffect(mpcos(x), z); set_avma(av); }
2735 0 : INLINE void mpsinz(GEN x, GEN z)
2736 0 : { pari_sp av = avma; gaffect(mpsin(x), z); set_avma(av); }
2737 0 : INLINE void gnegz(GEN x, GEN z)
2738 0 : { pari_sp av = avma; gaffect(gneg(x), z); set_avma(av); }
2739 0 : INLINE void gabsz(GEN x, long prec, GEN z)
2740 0 : { pari_sp av = avma; gaffect(gabs(x,prec), z); set_avma(av); }
2741 0 : INLINE void gaddz(GEN x, GEN y, GEN z)
2742 0 : { pari_sp av = avma; gaffect(gadd(x,y), z); set_avma(av); }
2743 0 : INLINE void gsubz(GEN x, GEN y, GEN z)
2744 0 : { pari_sp av = avma; gaffect(gsub(x,y), z); set_avma(av); }
2745 0 : INLINE void gmulz(GEN x, GEN y, GEN z)
2746 0 : { pari_sp av = avma; gaffect(gmul(x,y), z); set_avma(av); }
2747 0 : INLINE void gdivz(GEN x, GEN y, GEN z)
2748 0 : { pari_sp av = avma; gaffect(gdiv(x,y), z); set_avma(av); }
2749 0 : INLINE void gdiventz(GEN x, GEN y, GEN z)
2750 0 : { pari_sp av = avma; gaffect(gdivent(x,y), z); set_avma(av); }
2751 0 : INLINE void gmodz(GEN x, GEN y, GEN z)
2752 0 : { pari_sp av = avma; gaffect(gmod(x,y), z); set_avma(av); }
2753 0 : INLINE void gmul2nz(GEN x, long s, GEN z)
2754 0 : { pari_sp av = avma; gaffect(gmul2n(x,s), z); set_avma(av); }
2755 0 : INLINE void gshiftz(GEN x, long s, GEN z)
2756 0 : { pari_sp av = avma; gaffect(gshift(x,s), z); set_avma(av); }
2757 :
2758 : /*******************************************************************/
2759 : /* */
2760 : /* ELLIPTIC CURVES */
2761 : /* */
2762 : /*******************************************************************/
2763 7133652 : INLINE GEN ell_get_a1(GEN e) { return gel(e,1); }
2764 5716571 : INLINE GEN ell_get_a2(GEN e) { return gel(e,2); }
2765 6922445 : INLINE GEN ell_get_a3(GEN e) { return gel(e,3); }
2766 6526084 : INLINE GEN ell_get_a4(GEN e) { return gel(e,4); }
2767 7959670 : INLINE GEN ell_get_a6(GEN e) { return gel(e,5); }
2768 5432104 : INLINE GEN ell_get_b2(GEN e) { return gel(e,6); }
2769 2135457 : INLINE GEN ell_get_b4(GEN e) { return gel(e,7); }
2770 3054739 : INLINE GEN ell_get_b6(GEN e) { return gel(e,8); }
2771 2608999 : INLINE GEN ell_get_b8(GEN e) { return gel(e,9); }
2772 8021739 : INLINE GEN ell_get_c4(GEN e) { return gel(e,10); }
2773 8850714 : INLINE GEN ell_get_c6(GEN e) { return gel(e,11); }
2774 11280238 : INLINE GEN ell_get_disc(GEN e) { return gel(e,12); }
2775 1296377 : INLINE GEN ell_get_j(GEN e) { return gel(e,13); }
2776 11591968 : INLINE long ell_get_type(GEN e) { return mael(e,14,1); }
2777 2036495 : INLINE GEN ellff_get_field(GEN x) { return gmael(x, 15, 1); }
2778 799916 : INLINE GEN ellff_get_a4a6(GEN x) { return gmael(x, 15, 2); }
2779 1463 : INLINE GEN ellQp_get_zero(GEN x) { return gmael(x, 15, 1); }
2780 308 : INLINE long ellQp_get_prec(GEN E) { GEN z = ellQp_get_zero(E); return valp(z); }
2781 1134 : INLINE GEN ellQp_get_p(GEN E) { GEN z = ellQp_get_zero(E); return gel(z,2); }
2782 232652 : INLINE long ellR_get_prec(GEN x) { return nbits2prec(mael3(x, 15, 1, 1)); }
2783 370819 : INLINE long ellR_get_sign(GEN x) { return mael3(x, 15, 1, 2); }
2784 2029444 : INLINE GEN ellnf_get_nf(GEN x) { return checknf_i(gmael(x,15,1)); }
2785 126 : INLINE GEN ellnf_get_bnf(GEN x) { return checkbnf_i(gmael(x,15,1)); }
2786 :
2787 4680653 : INLINE int checkell_i(GEN e) { return typ(e) == t_VEC && lg(e) == 17; }
2788 51344051 : INLINE int ell_is_inf(GEN z) { return lg(z) == 2; }
2789 1874410 : INLINE GEN ellinf(void) { return mkvec(gen_0); }
2790 :
2791 : /*******************************************************************/
2792 : /* */
2793 : /* ALGEBRAIC NUMBER THEORY */
2794 : /* */
2795 : /*******************************************************************/
2796 32093495 : INLINE GEN modpr_get_pr(GEN x) { return gel(x,3); }
2797 1888117 : INLINE GEN modpr_get_p(GEN x) { return pr_get_p(modpr_get_pr(x)); }
2798 13920852 : INLINE GEN modpr_get_T(GEN x) { return lg(x) == 4? NULL: gel(x,4); }
2799 :
2800 91458042 : INLINE GEN pr_get_p(GEN pr) { return gel(pr,1); }
2801 11508483 : INLINE GEN pr_get_gen(GEN pr){ return gel(pr,2); }
2802 : /* .[2] instead of itos works: e and f are small positive integers */
2803 15752638 : INLINE long pr_get_e(GEN pr) { return gel(pr,3)[2]; }
2804 25352398 : INLINE long pr_get_f(GEN pr) { return gel(pr,4)[2]; }
2805 47869462 : INLINE GEN pr_get_tau(GEN pr){ return gel(pr,5); }
2806 : INLINE int
2807 16405188 : pr_is_inert(GEN P) { return typ(pr_get_tau(P)) == t_INT; }
2808 : INLINE GEN
2809 1067255 : pr_norm(GEN pr) { return powiu(pr_get_p(pr), pr_get_f(pr)); }
2810 : INLINE ulong
2811 343930 : upr_norm(GEN pr) { return upowuu(pr_get_p(pr)[2], pr_get_f(pr)); }
2812 :
2813 : /* assume nf a genuine nf */
2814 : INLINE long
2815 1166920 : nf_get_varn(GEN nf) { return varn(gel(nf,1)); }
2816 : INLINE GEN
2817 109051617 : nf_get_pol(GEN nf) { return gel(nf,1); }
2818 : INLINE long
2819 81961001 : nf_get_degree(GEN nf) { return degpol( nf_get_pol(nf) ); }
2820 : INLINE long
2821 22158322 : nf_get_r1(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,1)); }
2822 : INLINE long
2823 4140 : nf_get_r2(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,2)); }
2824 : INLINE GEN
2825 456399 : nf_get_disc(GEN nf) { return gel(nf,3); }
2826 : INLINE GEN
2827 3580956 : nf_get_index(GEN nf) { return gel(nf,4); }
2828 : INLINE GEN
2829 20771923 : nf_get_M(GEN nf) { return gmael(nf,5,1); }
2830 : INLINE GEN
2831 301228 : nf_get_G(GEN nf) { return gmael(nf,5,2); }
2832 : INLINE GEN
2833 1685534 : nf_get_roundG(GEN nf) { return gmael(nf,5,3); }
2834 : INLINE GEN
2835 22084 : nf_get_Tr(GEN nf) { return gmael(nf,5,4); }
2836 : INLINE GEN
2837 4458 : nf_get_diff(GEN nf) { return gmael(nf,5,5); }
2838 : INLINE GEN
2839 59183 : nf_get_ramified_primes(GEN nf) { return gmael(nf,5,8); }
2840 : INLINE GEN
2841 1509032 : nf_get_roots(GEN nf) { return gel(nf,6); }
2842 : INLINE GEN
2843 4382 : nf_get_zk(GEN nf)
2844 : {
2845 4382 : GEN y = gel(nf,7), D = gel(y, 1);
2846 4382 : if (typ(D) == t_POL) D = gel(D, 2);
2847 4382 : if (!equali1(D)) y = gdiv(y, D);
2848 4382 : return y;
2849 : }
2850 : INLINE GEN
2851 5011385 : nf_get_zkprimpart(GEN nf)
2852 : {
2853 5011385 : GEN y = gel(nf,7);
2854 : /* test for old format of nf.zk: non normalized */
2855 5011385 : if (!equali1(gel(nf,4)) && gequal1(gel(y,1))) y = Q_remove_denom(y,NULL);
2856 5011396 : return y;
2857 : }
2858 : INLINE GEN
2859 5057508 : nf_get_zkden(GEN nf)
2860 : {
2861 5057508 : GEN y = gel(nf,7), D = gel(y,1);
2862 5057508 : if (typ(D) == t_POL) D = gel(D,2);
2863 : /* test for old format of nf.zk: non normalized */
2864 5057508 : if (!equali1(gel(nf,4)) && equali1(D)) D = Q_denom(y);
2865 5057491 : return D;
2866 : }
2867 : INLINE GEN
2868 9891074 : nf_get_invzk(GEN nf) { return gel(nf,8); }
2869 : INLINE void
2870 516469 : nf_get_sign(GEN nf, long *r1, long *r2)
2871 : {
2872 516469 : GEN x = gel(nf,2);
2873 516469 : *r1 = itou(gel(x,1));
2874 516469 : *r2 = itou(gel(x,2));
2875 516469 : }
2876 :
2877 : INLINE GEN
2878 2521805 : cyc_get_expo(GEN c) { return lg(c) == 1? gen_1: gel(c,1); }
2879 : INLINE GEN
2880 391986 : abgrp_get_no(GEN x) { return gel(x,1); }
2881 : INLINE GEN
2882 11549584 : abgrp_get_cyc(GEN x) { return gel(x,2); }
2883 : INLINE GEN
2884 1653756 : abgrp_get_gen(GEN x) { return gel(x,3); }
2885 : INLINE GEN
2886 9426230 : bnf_get_nf(GEN bnf) { return gel(bnf,7); }
2887 : INLINE GEN
2888 5097814 : bnf_get_clgp(GEN bnf) { return gmael(bnf,8,1); }
2889 : INLINE GEN
2890 8379 : bnf_get_no(GEN bnf) { return abgrp_get_no(bnf_get_clgp(bnf)); }
2891 : INLINE GEN
2892 3509290 : bnf_get_cyc(GEN bnf) { return abgrp_get_cyc(bnf_get_clgp(bnf)); }
2893 : INLINE GEN
2894 1579983 : bnf_get_gen(GEN bnf) { return abgrp_get_gen(bnf_get_clgp(bnf)); }
2895 : INLINE GEN
2896 641 : bnf_get_reg(GEN bnf) { return gmael(bnf,8,2); }
2897 : INLINE GEN
2898 2702244 : bnf_get_logfu(GEN bnf) { return gel(bnf,3); }
2899 : INLINE GEN
2900 1278422 : bnf_get_sunits(GEN bnf)
2901 1278422 : { GEN s = gmael(bnf,8,3); return typ(s) == t_INT? NULL: s; }
2902 : INLINE GEN
2903 290505 : bnf_get_tuU(GEN bnf) { return gmael3(bnf,8,4,2); }
2904 : INLINE long
2905 265161 : bnf_get_tuN(GEN bnf) { return gmael3(bnf,8,4,1)[2]; }
2906 : INLINE GEN
2907 288153 : bnf_get_fu_nocheck(GEN bnf) { return gmael(bnf,8,5); }
2908 : INLINE GEN
2909 26293 : nfV_to_scalar_or_alg(GEN nf, GEN x)
2910 63435 : { pari_APPLY_same(nf_to_scalar_or_alg(nf, gel(x,i))) }
2911 : INLINE GEN
2912 25852 : bnf_get_fu(GEN bnf) {
2913 25852 : GEN fu = bnf_build_units(bnf), nf = bnf_get_nf(bnf);
2914 25852 : if (typ(fu) == t_MAT) pari_err(e_MISC,"missing units in bnf");
2915 25852 : return nfV_to_scalar_or_alg(nf, vecslice(fu, 2, lg(fu)-1));
2916 : }
2917 :
2918 : INLINE GEN
2919 3632382 : bnr_get_bnf(GEN bnr) { return gel(bnr,1); }
2920 : INLINE GEN
2921 1937030 : bnr_get_bid(GEN bnr) { return gel(bnr,2); }
2922 : INLINE GEN
2923 141041 : bnr_get_mod(GEN bnr) { return gmael(bnr,2,1); }
2924 : INLINE GEN
2925 1260077 : bnr_get_nf(GEN bnr) { return gmael(bnr,1,7); }
2926 : INLINE GEN
2927 2728724 : bnr_get_clgp(GEN bnr) { return gel(bnr,5); }
2928 : INLINE GEN
2929 314588 : bnr_get_no(GEN bnr) { return abgrp_get_no(bnr_get_clgp(bnr)); }
2930 : INLINE GEN
2931 2396526 : bnr_get_cyc(GEN bnr) { return abgrp_get_cyc(bnr_get_clgp(bnr)); }
2932 : INLINE GEN
2933 70 : bnr_get_gen_nocheck(GEN bnr) { return abgrp_get_gen(bnr_get_clgp(bnr)); }
2934 : INLINE GEN
2935 7847 : bnr_get_gen(GEN bnr) {
2936 7847 : GEN G = bnr_get_clgp(bnr);
2937 7847 : if (lg(G) != 4)
2938 0 : pari_err(e_MISC,"missing bnr generators: please use bnrinit(,,1)");
2939 7847 : return gel(G,3);
2940 : }
2941 :
2942 : /* localstar, used in gchar */
2943 : INLINE GEN
2944 51954 : locs_get_cyc(GEN locs) { return gel(locs,1); }
2945 : INLINE GEN
2946 191695 : locs_get_Lsprk(GEN locs) { return gel(locs,2); }
2947 : INLINE GEN
2948 1260 : locs_get_Lgenfil(GEN locs) { return gel(locs,3); }
2949 : INLINE GEN
2950 8225 : locs_get_mod(GEN locs) { return gel(locs,4); }
2951 : /* pr dividing the modulus N of locs, 0 <= i < v_pr(N)
2952 : * return a t_MAT whose columns are the logs
2953 : * of generators of U_i(pr)/U_{i+1}(pr). */
2954 : INLINE GEN
2955 1260 : locs_get_famod(GEN locs) { return gmael(locs,4,1); }
2956 : INLINE GEN
2957 207235 : locs_get_m_infty(GEN locs) { return gmael(locs,4,2); }
2958 :
2959 : /* G a grossenchar group */
2960 : INLINE GEN
2961 32639 : gchar_get_basis(GEN gc) { return gel(gc, 1); }
2962 : INLINE GEN
2963 203105 : gchar_get_bnf(GEN gc) { return gel(gc, 2); }
2964 : INLINE GEN
2965 241464 : gchar_get_nf(GEN gc) { return gel(gc, 3); }
2966 : INLINE GEN
2967 279433 : gchar_get_zm(GEN gc) { return gel(gc, 4); }
2968 : INLINE GEN
2969 8225 : gchar_get_mod(GEN gc) { return locs_get_mod(gchar_get_zm(gc)); }
2970 : INLINE GEN
2971 4095 : gchar_get_modP(GEN gc) { return gmael(gchar_get_mod(gc),1,1); }
2972 : INLINE GEN
2973 36864 : gchar_get_S(GEN gc) { return gel(gc, 5); }
2974 : INLINE GEN
2975 188468 : gchar_get_DLdata(GEN gc) { return gel(gc, 6); }
2976 : INLINE GEN
2977 1747 : gchar_get_sfu(GEN gc) { return gel(gc, 7); }
2978 : INLINE GEN
2979 16168 : gchar_get_cyc(GEN gc) { return gel(gc, 9); }
2980 : INLINE GEN
2981 0 : gchar_get_hnf(GEN gc) { return gmael(gc, 10, 1); }
2982 : INLINE GEN
2983 0 : gchar_get_U(GEN gc) { return gmael(gc, 10, 2); }
2984 : INLINE GEN
2985 10969 : gchar_get_Ui(GEN gc) { return gmael(gc, 10, 3); }
2986 : INLINE GEN
2987 3320 : gchar_get_m0(GEN gc) { return gel(gc, 11); }
2988 : INLINE GEN
2989 4266 : gchar_get_u0(GEN gc) { return gel(gc, 12); }
2990 : INLINE long
2991 17416 : gchar_get_r1(GEN gc) { return nf_get_r1(gchar_get_nf(gc)); }
2992 : INLINE long
2993 623 : gchar_get_r2(GEN gc) { return nf_get_r2(gchar_get_nf(gc)); }
2994 : INLINE GEN
2995 50346 : gchar_get_loccyc(GEN gc) { return locs_get_cyc(gchar_get_zm(gc)); }
2996 : INLINE long
2997 37130 : gchar_get_nc(GEN gc) { return lg(gchar_get_loccyc(gc))-1; }
2998 : INLINE long
2999 36864 : gchar_get_ns(GEN gc) { return lg(gchar_get_S(gc))-1; }
3000 : INLINE long
3001 1841 : gchar_get_nm(GEN gc) { return lg(gchar_get_basis(gc))-1; }
3002 : INLINE long
3003 4011 : gchar_get_evalprec(GEN gc) { return gmael(gc, 8, 1)[1]; }
3004 : INLINE long
3005 18732 : gchar_get_prec(GEN gc) { return gmael(gc, 8, 1)[2]; }
3006 : INLINE long
3007 13419 : gchar_get_nfprec(GEN gc) { return gmael(gc, 8, 1)[3]; }
3008 : INLINE void
3009 1785 : gchar_set_evalprec(GEN gc, long prec) { gmael(gc, 8, 1)[1] = prec; }
3010 : INLINE void
3011 1202 : gchar_set_prec(GEN gc, long prec) { gmael(gc, 8, 1)[2] = prec; }
3012 : INLINE void
3013 1202 : gchar_copy_precs(GEN gc, GEN gc2)
3014 : {
3015 1202 : gel(gc2, 8) = shallowcopy(gel(gc,8));
3016 1202 : gmael(gc2, 8, 1) = shallowcopy(gmael(gc, 8, 1));
3017 1202 : }
3018 : INLINE void
3019 2949 : gchar_set_nfprec(GEN gc, long prec) { gmael(gc, 8, 1)[3] = prec; }
3020 : INLINE long
3021 322 : gchar_get_ntors(GEN gc) { return gmael(gc, 8, 2)[1]; }
3022 : INLINE long
3023 322 : gchar_get_nfree(GEN gc) { return gmael(gc, 8, 2)[2]; }
3024 : INLINE long
3025 2042 : gchar_get_nalg(GEN gc) { return gmael(gc, 8, 2)[3]; }
3026 : INLINE void
3027 1573 : gchar_set_basis(GEN gc, GEN m_inv) { gel(gc, 1) = m_inv; }
3028 : INLINE void
3029 2076 : gchar_set_nf(GEN gc, GEN nf) { gel(gc, 3) = nf; }
3030 : INLINE void
3031 623 : gchar_set_ntors(GEN gc, long n) { gmael(gc, 8, 2)[1] = n; }
3032 : INLINE void
3033 623 : gchar_set_nfree(GEN gc, long n) { gmael(gc, 8, 2)[2] = n; }
3034 : INLINE void
3035 623 : gchar_set_nalg(GEN gc, long n) { gmael(gc, 8, 2)[3] = n; }
3036 : INLINE void
3037 1573 : gchar_set_cyc(GEN gc, GEN cyc) { gel(gc, 9) = cyc; }
3038 : INLINE void
3039 623 : gchar_set_HUUi(GEN gc, GEN hnf, GEN U, GEN Ui) { gel(gc, 10) = mkvec3(hnf, U, Ui); }
3040 : INLINE void
3041 950 : gchar_set_m0(GEN gc, GEN m0) { gel(gc, 11) = m0; }
3042 : INLINE void
3043 2093 : gchar_set_u0(GEN gc, GEN u0) { gel(gc, 12) = u0; }
3044 :
3045 : INLINE GEN
3046 1386571 : bid_get_mod(GEN bid) { return gel(bid,1); }
3047 : INLINE GEN
3048 78295 : bid_get_ideal(GEN bid) { return gmael(bid,1,1); }
3049 : INLINE GEN
3050 35098 : bid_get_arch(GEN bid) { return gmael(bid,1,2); }
3051 : INLINE GEN
3052 5415578 : bid_get_grp(GEN bid) { return gel(bid,2); }
3053 : INLINE GEN
3054 2313955 : bid_get_fact(GEN bid) { return gmael(bid,3,1); }
3055 : INLINE GEN
3056 2025296 : bid_get_fact2(GEN bid) { return gmael(bid,3,2); }
3057 : INLINE GEN
3058 1990763 : bid_get_MOD(GEN bid) { GEN y = gel(bid,4); return lg(y) == 4? gel(y,3): NULL; }
3059 : INLINE GEN
3060 1991491 : bid_get_sprk(GEN bid) { return gmael(bid,4,1); }
3061 : INLINE GEN
3062 51226 : bid_get_sarch(GEN bid) { return gmael(bid,4,2); }
3063 : INLINE GEN
3064 2217807 : bid_get_archp(GEN bid) { return gmael3(bid,4,2,2); }
3065 : INLINE GEN
3066 3378387 : bid_get_U(GEN bid) { return gel(bid,5); }
3067 : INLINE GEN
3068 0 : bid_get_no(GEN bid) { return abgrp_get_no(bid_get_grp(bid)); }
3069 : INLINE GEN
3070 5361669 : bid_get_cyc(GEN bid) { return abgrp_get_cyc(bid_get_grp(bid)); }
3071 : INLINE GEN
3072 0 : bid_get_gen_nocheck(GEN bid) { return abgrp_get_gen(bid_get_grp(bid)); }
3073 : INLINE GEN
3074 53326 : bid_get_gen(GEN bid) {
3075 53326 : GEN G = bid_get_grp(bid);
3076 53326 : if (lg(G) != 4) pari_err(e_MISC,"missing bid generators. Use idealstar(,,2)");
3077 53326 : return abgrp_get_gen(G);
3078 : }
3079 :
3080 : INLINE GEN
3081 34543777 : znstar_get_N(GEN G) { return gmael(G,1,1); }
3082 : INLINE GEN
3083 7210394 : znstar_get_faN(GEN G) { return gel(G,3); }
3084 : INLINE GEN
3085 14 : znstar_get_no(GEN G) { return abgrp_get_no(gel(G,2)); }
3086 : INLINE GEN
3087 261948 : znstar_get_cyc(GEN G) { return abgrp_get_cyc(gel(G,2)); }
3088 : INLINE GEN
3089 16150 : znstar_get_gen(GEN G) { return abgrp_get_gen(gel(G,2)); }
3090 : INLINE GEN
3091 7823726 : znstar_get_conreycyc(GEN G) { return gmael(G,4,5); }
3092 : INLINE GEN
3093 3221793 : znstar_get_conreygen(GEN G) { return gmael(G,4,4); }
3094 : INLINE GEN
3095 46788 : znstar_get_Ui(GEN G) { return gmael(G,4,3); }
3096 : INLINE GEN
3097 176051 : znstar_get_U(GEN G) { return gel(G,5); }
3098 : INLINE GEN
3099 2820763 : znstar_get_pe(GEN G) { return gmael(G,4,1); }
3100 : INLINE GEN
3101 36050 : gal_get_pol(GEN gal) { return gel(gal,1); }
3102 : INLINE GEN
3103 6041 : gal_get_p(GEN gal) { return gmael(gal,2,1); }
3104 : INLINE GEN
3105 91 : gal_get_e(GEN gal) { return gmael(gal,2,2); }
3106 : INLINE GEN
3107 23744 : gal_get_mod(GEN gal) { return gmael(gal,2,3); }
3108 : INLINE GEN
3109 32487 : gal_get_roots(GEN gal) { return gel(gal,3); }
3110 : INLINE GEN
3111 27594 : gal_get_invvdm(GEN gal) { return gel(gal,4); }
3112 : INLINE GEN
3113 27587 : gal_get_den(GEN gal) { return gel(gal,5); }
3114 : INLINE GEN
3115 80134 : gal_get_group(GEN gal) { return gel(gal,6); }
3116 : INLINE GEN
3117 15456 : gal_get_gen(GEN gal) { return gel(gal,7); }
3118 : INLINE GEN
3119 6664 : gal_get_orders(GEN gal) { return gel(gal,8); }
3120 :
3121 : /* assume rnf a genuine rnf */
3122 : INLINE long
3123 2466302 : rnf_get_degree(GEN rnf) { return degpol(rnf_get_pol(rnf)); }
3124 : INLINE long
3125 19957 : rnf_get_nfdegree(GEN rnf) { return degpol(nf_get_pol(rnf_get_nf(rnf))); }
3126 : INLINE long
3127 1377518 : rnf_get_absdegree(GEN rnf) { return degpol(gmael(rnf,11,1)); }
3128 : INLINE GEN
3129 1127 : rnf_get_idealdisc(GEN rnf) { return gmael(rnf,3,1); }
3130 : INLINE GEN
3131 1015 : rnf_get_k(GEN rnf) { return gmael(rnf,11,3); }
3132 : INLINE GEN
3133 1043 : rnf_get_alpha(GEN rnf) { return gmael(rnf, 11, 2); }
3134 : INLINE GEN
3135 697213 : rnf_get_nf(GEN rnf) { return gel(rnf,10); }
3136 : INLINE GEN
3137 5516 : rnf_get_nfzk(GEN rnf) { return gel(rnf,2); }
3138 : INLINE GEN
3139 287402 : rnf_get_polabs(GEN rnf) { return gmael(rnf,11,1); }
3140 : INLINE GEN
3141 2776606 : rnf_get_pol(GEN rnf) { return gel(rnf,1); }
3142 : INLINE GEN
3143 315 : rnf_get_disc(GEN rnf) { return gel(rnf,3); }
3144 : INLINE GEN
3145 105 : rnf_get_index(GEN rnf) { return gel(rnf,4); }
3146 : INLINE GEN
3147 2282 : rnf_get_ramified_primes(GEN rnf) { return gel(rnf,5); }
3148 : INLINE long
3149 574 : rnf_get_varn(GEN rnf) { return varn(gel(rnf,1)); }
3150 : INLINE GEN
3151 235999 : rnf_get_nfpol(GEN rnf) { return gmael(rnf,10,1); }
3152 : INLINE long
3153 3724 : rnf_get_nfvarn(GEN rnf) { return varn(gmael(rnf,10,1)); }
3154 : INLINE GEN
3155 4263 : rnf_get_zk(GEN rnf) { return gel(rnf,7); }
3156 : INLINE GEN
3157 124550 : rnf_get_map(GEN rnf) { return gel(rnf,11); }
3158 : INLINE GEN
3159 1225 : rnf_get_invzk(GEN rnf) { return gel(rnf,8); }
3160 :
3161 : INLINE GEN
3162 138591 : idealred(GEN nf, GEN id) { return idealred0(nf, id, NULL); }
3163 :
3164 : INLINE GEN
3165 4514 : idealchineseinit(GEN nf, GEN x)
3166 4514 : { return idealchinese(nf,x,NULL); }
3167 :
3168 : /*******************************************************************/
3169 : /* */
3170 : /* CLOSURES */
3171 : /* */
3172 : /*******************************************************************/
3173 360857818 : INLINE long closure_arity(GEN C) { return ((ulong)C[1])&ARITYBITS; }
3174 39983683 : INLINE long closure_is_variadic(GEN C) { return !!(((ulong)C[1])&VARARGBITS); }
3175 312214824 : INLINE const char *closure_codestr(GEN C) { return GSTR(gel(C,2))-1; }
3176 0 : INLINE GEN closure_get_code(GEN C) { return gel(C,2); }
3177 312197267 : INLINE GEN closure_get_oper(GEN C) { return gel(C,3); }
3178 312175360 : INLINE GEN closure_get_data(GEN C) { return gel(C,4); }
3179 13327 : INLINE GEN closure_get_dbg(GEN C) { return gel(C,5); }
3180 36456 : INLINE GEN closure_get_text(GEN C) { return gel(C,6); }
3181 12952532 : INLINE GEN closure_get_frame(GEN C) { return gel(C,7); }
3182 :
3183 : /*******************************************************************/
3184 : /* */
3185 : /* ERRORS */
3186 : /* */
3187 : /*******************************************************************/
3188 : INLINE long
3189 61912 : err_get_num(GEN e) { return e[1]; }
3190 : INLINE GEN
3191 273 : err_get_compo(GEN e, long i) { return gel(e, i+1); }
3192 :
3193 : INLINE void
3194 14 : pari_err_BUG(const char *f) { pari_err(e_BUG,f); }
3195 : INLINE void
3196 21 : pari_err_CONSTPOL(const char *f) { pari_err(e_CONSTPOL, f); }
3197 : INLINE void
3198 84 : pari_err_COPRIME(const char *f, GEN x, GEN y) { pari_err(e_COPRIME, f,x,y); }
3199 : INLINE void
3200 711 : pari_err_DIM(const char *f) { pari_err(e_DIM, f); }
3201 : INLINE void
3202 0 : pari_err_FILE(const char *f, const char *g) { pari_err(e_FILE, f,g); }
3203 : INLINE void
3204 36 : pari_err_FILEDESC(const char *f, long n) { pari_err(e_FILEDESC, f,n); }
3205 : INLINE void
3206 98 : pari_err_FLAG(const char *f) { pari_err(e_FLAG,f); }
3207 : INLINE void
3208 525 : pari_err_IMPL(const char *f) { pari_err(e_IMPL,f); }
3209 : INLINE void
3210 19997 : pari_err_INV(const char *f, GEN x) { pari_err(e_INV,f,x); }
3211 : INLINE void
3212 63 : pari_err_IRREDPOL(const char *f, GEN x) { pari_err(e_IRREDPOL, f,x); }
3213 : INLINE void
3214 2750 : 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); }
3215 : INLINE void
3216 214 : pari_err_COMPONENT(const char *f, const char *op, GEN l, GEN x) { pari_err(e_COMPONENT, f,op,l,x); }
3217 : INLINE void
3218 0 : pari_err_MAXPRIME(ulong c) { pari_err(e_MAXPRIME, c); }
3219 : INLINE void
3220 406 : pari_err_OP(const char *f, GEN x, GEN y) { pari_err(e_OP, f,x,y); }
3221 : INLINE void
3222 156 : pari_err_OVERFLOW(const char *f) { pari_err(e_OVERFLOW, f); }
3223 : INLINE void
3224 238 : pari_err_PREC(const char *f) { pari_err(e_PREC,f); }
3225 : INLINE void
3226 0 : pari_err_PACKAGE(const char *f) { pari_err(e_PACKAGE,f); }
3227 : INLINE void
3228 98 : pari_err_PRIME(const char *f, GEN x) { pari_err(e_PRIME, f,x); }
3229 : INLINE void
3230 1316 : pari_err_MODULUS(const char *f, GEN x, GEN y) { pari_err(e_MODULUS, f,x,y); }
3231 : INLINE void
3232 63 : pari_err_ROOTS0(const char *f) { pari_err(e_ROOTS0, f); }
3233 : INLINE void
3234 84 : pari_err_SQRTN(const char *f, GEN x) { pari_err(e_SQRTN, f,x); }
3235 : INLINE void
3236 15251 : pari_err_TYPE(const char *f, GEN x) { pari_err(e_TYPE, f,x); }
3237 : INLINE void
3238 3493 : pari_err_TYPE2(const char *f, GEN x, GEN y) { pari_err(e_TYPE2, f,x,y); }
3239 : INLINE void
3240 371 : pari_err_VAR(const char *f, GEN x, GEN y) { pari_err(e_VAR, f,x,y); }
3241 : INLINE void
3242 245 : pari_err_PRIORITY(const char *f, GEN x, const char *op, long v)
3243 245 : { pari_err(e_PRIORITY, f,x,op,v); }
3244 :
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