Line data Source code
1 : /* Copyright (C) 2000-2010 The PARI group.
2 :
3 : This file is part of the PARI/GP package.
4 :
5 : PARI/GP is free software; you can redistribute it and/or modify it under the
6 : terms of the GNU General Public License as published by the Free Software
7 : Foundation; either version 2 of the License, or (at your option) any later
8 : version. It is distributed in the hope that it will be useful, but WITHOUT
9 : ANY WARRANTY WHATSOEVER.
10 :
11 : Check the License for details. You should have received a copy of it, along
12 : with the package; see the file 'COPYING'. If not, write to the Free Software
13 : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
14 :
15 :
16 : /*********************************************************************/
17 : /* MALLOC/FREE WRAPPERS */
18 : /*********************************************************************/
19 : #define BLOCK_SIGALRM_START \
20 : { \
21 : int block=PARI_SIGINT_block; \
22 : PARI_SIGINT_block = 2; \
23 : MT_SIGINT_BLOCK(block);
24 :
25 : #define BLOCK_SIGINT_START \
26 : { \
27 : int block=PARI_SIGINT_block; \
28 : PARI_SIGINT_block = 1; \
29 : MT_SIGINT_BLOCK(block);
30 :
31 : #define BLOCK_SIGINT_END \
32 : PARI_SIGINT_block = block; \
33 : MT_SIGINT_UNBLOCK(block); \
34 : if (!block && PARI_SIGINT_pending) \
35 : { \
36 : int sig = PARI_SIGINT_pending; \
37 : PARI_SIGINT_pending = 0; \
38 : raise(sig); \
39 : } \
40 : }
41 :
42 : /*******************************************************************/
43 : /* */
44 : /* CONSTRUCTORS */
45 : /* */
46 : /*******************************************************************/
47 : #define retmkfrac(x,y)\
48 : do { GEN _v = cgetg(3, t_FRAC);\
49 : gel(_v,1) = (x);\
50 : gel(_v,2) = (y); return _v; } while(0)
51 : #define retmkrfrac(x,y)\
52 : do { GEN _v = cgetg(3, t_RFRAC);\
53 : gel(_v,1) = (x);\
54 : gel(_v,2) = (y); return _v; } while(0)
55 : #define retmkintmod(x,y)\
56 : do { GEN _v = cgetg(3, t_INTMOD);\
57 : gel(_v,1) = (y);\
58 : gel(_v,2) = (x); return _v; } while(0)
59 : #define retmkcomplex(x,y)\
60 : do { GEN _v = cgetg(3, t_COMPLEX);\
61 : gel(_v,1) = (x);\
62 : gel(_v,2) = (y); return _v; } while(0)
63 : #define retmkpolmod(x,y)\
64 : do { GEN _v = cgetg(3, t_POLMOD);\
65 : gel(_v,1) = (y);\
66 : gel(_v,2) = (x); return _v; } while(0)
67 : #define retmkvec(x)\
68 : do { GEN _v = cgetg(2, t_VEC);\
69 : gel(_v,1) = (x); return _v; } while(0)
70 : #define retmkvec2(x,y)\
71 : do { GEN _v = cgetg(3, t_VEC);\
72 : gel(_v,1) = (x);\
73 : gel(_v,2) = (y); return _v; } while(0)
74 : #define retmkvec3(x,y,z)\
75 : do { GEN _v = cgetg(4, t_VEC);\
76 : gel(_v,1) = (x);\
77 : gel(_v,2) = (y);\
78 : gel(_v,3) = (z); return _v; } while(0)
79 : #define retmkpadic(x,p,pd,e,d)\
80 : do { GEN _v = cgetg(5, t_PADIC);\
81 : _v[1] = evalvalp(e) | evalprecp(d);\
82 : gel(_v,2) = (p);\
83 : gel(_v,3) = (pd);\
84 : gel(_v,4) = (x); return _v; } while(0)
85 : /* x allowed to contain _pd */
86 : #define retmkpadic_i(x,p,pd,e,d)\
87 : do { GEN _v = cgetg(5, t_PADIC), _pd = (pd);\
88 : _v[1] = evalvalp(e) | evalprecp(d);\
89 : gel(_v,2) = (p);\
90 : gel(_v,3) = (_pd);\
91 : gel(_v,4) = (x); return _v; } while(0)
92 : #define retmkqfb(x,y,z,d)\
93 : do { GEN _v = cgetg(5, t_QFB);\
94 : gel(_v,1) = (x);\
95 : gel(_v,2) = (y);\
96 : gel(_v,3) = (z);\
97 : gel(_v,4) = (d); return _v; } while(0)
98 : #define retmkquad(x,y,z)\
99 : do { GEN _v = cgetg(4, t_QUAD);\
100 : gel(_v,1) = (x);\
101 : gel(_v,2) = (y);\
102 : gel(_v,3) = (z); return _v; } while(0)
103 : #define retmkvec4(x,y,z,t)\
104 : do { GEN _v = cgetg(5, t_VEC);\
105 : gel(_v,1) = (x);\
106 : gel(_v,2) = (y);\
107 : gel(_v,3) = (z);\
108 : gel(_v,4) = (t); return _v; } while(0)
109 : #define retmkvec5(x,y,z,t,u)\
110 : do { GEN _v = cgetg(6, t_VEC);\
111 : gel(_v,1) = (x);\
112 : gel(_v,2) = (y);\
113 : gel(_v,3) = (z);\
114 : gel(_v,4) = (t);\
115 : gel(_v,5) = (u); return _v; } while(0)
116 : #define retmkcol(x)\
117 : do { GEN _v = cgetg(2, t_COL);\
118 : gel(_v,1) = (x); return _v; } while(0)
119 : #define retmkcol2(x,y)\
120 : do { GEN _v = cgetg(3, t_COL);\
121 : gel(_v,1) = (x);\
122 : gel(_v,2) = (y); return _v; } while(0)
123 : #define retmkcol3(x,y,z)\
124 : do { GEN _v = cgetg(4, t_COL);\
125 : gel(_v,1) = (x);\
126 : gel(_v,2) = (y);\
127 : gel(_v,3) = (z); return _v; } while(0)
128 : #define retmkcol4(x,y,z,t)\
129 : do { GEN _v = cgetg(5, t_COL);\
130 : gel(_v,1) = (x);\
131 : gel(_v,2) = (y);\
132 : gel(_v,3) = (z);\
133 : gel(_v,4) = (t); return _v; } while(0)
134 : #define retmkcol5(x,y,z,t,u)\
135 : do { GEN _v = cgetg(6, t_COL);\
136 : gel(_v,1) = (x);\
137 : gel(_v,2) = (y);\
138 : gel(_v,3) = (z);\
139 : gel(_v,4) = (t);\
140 : gel(_v,5) = (u); return _v; } while(0)
141 : #define retmkcol6(x,y,z,t,u,v)\
142 : do { GEN _v = cgetg(7, t_COL);\
143 : gel(_v,1) = (x);\
144 : gel(_v,2) = (y);\
145 : gel(_v,3) = (z);\
146 : gel(_v,4) = (t);\
147 : gel(_v,5) = (u);\
148 : gel(_v,6) = (v); return _v; } while(0)
149 : #define retmkmat(x)\
150 : do { GEN _v = cgetg(2, t_MAT);\
151 : gel(_v,1) = (x); return _v; } while(0)
152 : #define retmkmat2(x,y)\
153 : do { GEN _v = cgetg(3, t_MAT);\
154 : gel(_v,1) = (x);\
155 : gel(_v,2) = (y); return _v; } while(0)
156 : #define retmkmat3(x,y,z)\
157 : do { GEN _v = cgetg(4, t_MAT);\
158 : gel(_v,1) = (x);\
159 : gel(_v,2) = (y);\
160 : gel(_v,3) = (z); return _v; } while(0)
161 : #define retmkmat4(x,y,z,t)\
162 : do { GEN _v = cgetg(5, t_MAT);\
163 : gel(_v,1) = (x);\
164 : gel(_v,2) = (y);\
165 : gel(_v,3) = (z);\
166 : gel(_v,4) = (t); return _v; } while(0)
167 : #define retmkmat5(x,y,z,t,u)\
168 : do { GEN _v = cgetg(6, t_MAT);\
169 : gel(_v,1) = (x);\
170 : gel(_v,2) = (y);\
171 : gel(_v,3) = (z);\
172 : gel(_v,4) = (t);\
173 : gel(_v,5) = (u); return _v; } while(0)
174 : #define retmkmat22(a,b,c,d)\
175 : do { GEN _v = cgetg(3, t_MAT);\
176 : gel(_v,1) = mkcol2(a,c);\
177 : gel(_v,2) = mkcol2(b,d); return _v; } while(0)
178 : INLINE GEN
179 8025238 : mkintmod(GEN x, GEN y) { retmkintmod(x,y); }
180 : INLINE GEN
181 1813 : mkintmodu(ulong x, ulong y) {
182 1813 : GEN v = cgetg(3,t_INTMOD);
183 1813 : gel(v,1) = utoipos(y);
184 1813 : gel(v,2) = utoi(x); return v;
185 : }
186 : INLINE GEN
187 0 : mkpadic(GEN x, GEN p, GEN pd, long e, long d) { retmkpadic(x,p,pd,e,d); }
188 : INLINE GEN
189 3019855 : mkpolmod(GEN x, GEN y) { retmkpolmod(x,y); }
190 : INLINE GEN
191 34040875 : mkfrac(GEN x, GEN y) { retmkfrac(x,y); }
192 : INLINE GEN
193 1209535 : mkfracss(long x, long y) { retmkfrac(stoi(x),utoipos(y)); }
194 : /* q = n/d a t_FRAC or t_INT; recover (n,d) */
195 : INLINE void
196 19838 : Qtoss(GEN q, long *n, long *d)
197 : {
198 19838 : if (typ(q) == t_INT) { *n = itos(q); *d = 1; }
199 5796 : else { *n = itos(gel(q,1)); *d = itou(gel(q,2)); }
200 19838 : }
201 : INLINE GEN
202 1074073 : sstoQ(long n, long d)
203 : {
204 : ulong r;
205 : long g, q;
206 1074073 : if (!n)
207 : {
208 95095 : if (!d) pari_err_INV("sstoQ",gen_0);
209 95095 : return gen_0;
210 : }
211 978978 : if (d < 0) { d = -d; n = -n; }
212 978978 : if (d == 1) return stoi(n);
213 959665 : r = labs(n);
214 959665 : if (r == 1) retmkfrac(n > 0? gen_1: gen_m1, utoipos(d));
215 909748 : q = udivuu_rem(r, d, &r);
216 909748 : if (!r) return n > 0? utoipos(q): utoineg(q);
217 854875 : g = ugcd(d,r); /* gcd(n,d) */
218 854875 : if (g != 1) { n /= g; d /= g; }
219 854875 : retmkfrac(stoi(n), utoipos(d));
220 : }
221 :
222 : INLINE GEN
223 158072611 : uutoQ(ulong n, ulong d)
224 : {
225 : ulong r;
226 : long g, q;
227 158072611 : if (!n)
228 : {
229 38108 : if (!d) pari_err_INV("uutoQ",gen_0);
230 38108 : return gen_0;
231 : }
232 158034503 : if (d == 1) return utoipos(n);
233 158023401 : if (n == 1) retmkfrac(gen_1, utoipos(d));
234 157934474 : q = udivuu_rem(n,d,&r);
235 157934474 : if (!r) return utoipos(q);
236 5179921 : g = ugcd(d,r); /* gcd(n,d) */
237 5179921 : if (g != 1) { n /= g; d /= g; }
238 5179921 : retmkfrac(utoipos(n), utoipos(d));
239 : }
240 :
241 : INLINE GEN
242 4844366 : mkfraccopy(GEN x, GEN y) { retmkfrac(icopy(x), icopy(y)); }
243 : INLINE GEN
244 698089 : mkrfrac(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
245 698089 : gel(v,1) = x; gel(v,2) = y; return v; }
246 : INLINE GEN
247 14 : mkrfraccopy(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
248 14 : gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
249 : INLINE GEN
250 90194945 : mkcomplex(GEN x, GEN y) { retmkcomplex(x,y); }
251 : INLINE GEN
252 1269555 : gen_I(void) { return mkcomplex(gen_0, gen_1); }
253 : INLINE GEN
254 963395 : cgetc(long l) { retmkcomplex(cgetr(l), cgetr(l)); }
255 : INLINE GEN
256 69118 : mkquad(GEN n, GEN x, GEN y) { GEN v = cgetg(4, t_QUAD);
257 69118 : gel(v,1) = n; gel(v,2) = x; gel(v,3) = y; return v; }
258 : /* vecsmall */
259 : INLINE GEN
260 129281770 : mkvecsmall(long x) { GEN v = cgetg(2, t_VECSMALL); v[1] = x; return v; }
261 : INLINE GEN
262 223876444 : mkvecsmall2(long x,long y) { GEN v = cgetg(3, t_VECSMALL);
263 223901980 : v[1]=x; v[2]=y; return v; }
264 : INLINE GEN
265 100399072 : mkvecsmall3(long x,long y,long z) { GEN v = cgetg(4, t_VECSMALL);
266 100398612 : v[1]=x; v[2]=y; v[3]=z; return v; }
267 : INLINE GEN
268 15482275 : mkvecsmall4(long x,long y,long z,long t) { GEN v = cgetg(5, t_VECSMALL);
269 15483993 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; return v; }
270 : INLINE GEN
271 689652 : mkvecsmall5(long x,long y,long z,long t,long u) { GEN v = cgetg(6, t_VECSMALL);
272 689650 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; v[5]=u; return v; }
273 :
274 : INLINE GEN
275 27802533 : mkqfb(GEN x, GEN y, GEN z, GEN d) { retmkqfb(x,y,z,d); }
276 : /* vec */
277 : INLINE GEN
278 68068433 : mkvec(GEN x) { retmkvec(x); }
279 : INLINE GEN
280 182652351 : mkvec2(GEN x, GEN y) { retmkvec2(x,y); }
281 : INLINE GEN
282 116381200 : mkvec3(GEN x, GEN y, GEN z) { retmkvec3(x,y,z); }
283 : INLINE GEN
284 6640530 : mkvec4(GEN x, GEN y, GEN z, GEN t) { retmkvec4(x,y,z,t); }
285 : INLINE GEN
286 14493387 : mkvec5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkvec5(x,y,z,t,u); }
287 : INLINE GEN
288 161 : mkvecs(long x) { retmkvec(stoi(x)); }
289 : INLINE GEN
290 220133 : mkvec2s(long x, long y) { retmkvec2(stoi(x),stoi(y)); }
291 : INLINE GEN
292 524441 : mkvec3s(long x, long y, long z) { retmkvec3(stoi(x),stoi(y),stoi(z)); }
293 : INLINE GEN
294 21 : mkvec4s(long x, long y, long z, long t) { retmkvec4(stoi(x),stoi(y),stoi(z),stoi(t)); }
295 : INLINE GEN
296 122507 : mkveccopy(GEN x) { GEN v = cgetg(2, t_VEC); gel(v,1) = gcopy(x); return v; }
297 : INLINE GEN
298 114618 : mkvec2copy(GEN x, GEN y) {
299 114618 : GEN v = cgetg(3,t_VEC); gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
300 : /* col */
301 : INLINE GEN
302 10184914 : mkcol(GEN x) { retmkcol(x); }
303 : INLINE GEN
304 156699457 : mkcol2(GEN x, GEN y) { retmkcol2(x,y); }
305 : INLINE GEN
306 88314 : mkcol3(GEN x, GEN y, GEN z) { retmkcol3(x,y,z); }
307 : INLINE GEN
308 103467 : mkcol4(GEN x, GEN y, GEN z, GEN t) { retmkcol4(x,y,z,t); }
309 : INLINE GEN
310 94 : mkcol5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkcol5(x,y,z,t,u); }
311 : INLINE GEN
312 232379 : mkcol6(GEN x, GEN y, GEN z, GEN t, GEN u, GEN v) { retmkcol6(x,y,z,t,u,v); }
313 : INLINE GEN
314 40411 : mkcols(long x) { retmkcol(stoi(x)); }
315 : INLINE GEN
316 4415292 : mkcol2s(long x, long y) { retmkcol2(stoi(x),stoi(y)); }
317 : INLINE GEN
318 315 : mkcol3s(long x, long y, long z) { retmkcol3(stoi(x),stoi(y),stoi(z)); }
319 : INLINE GEN
320 0 : mkcol4s(long x, long y, long z, long t) { retmkcol4(stoi(x),stoi(y),stoi(z),stoi(t)); }
321 : INLINE GEN
322 33522 : mkcolcopy(GEN x) { GEN v = cgetg(2, t_COL); gel(v,1) = gcopy(x); return v; }
323 : /* mat */
324 : INLINE GEN
325 4609614 : mkmat(GEN x) { retmkmat(x); }
326 : INLINE GEN
327 32550355 : mkmat2(GEN x, GEN y) { retmkmat2(x,y); }
328 : INLINE GEN
329 17001 : mkmat3(GEN x, GEN y, GEN z) { retmkmat3(x,y,z); }
330 : INLINE GEN
331 84 : mkmat4(GEN x, GEN y, GEN z, GEN t) { retmkmat4(x,y,z,t); }
332 : INLINE GEN
333 0 : mkmat5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkmat5(x,y,z,t,u); }
334 : INLINE GEN
335 121186 : mkmatcopy(GEN x) { GEN v = cgetg(2, t_MAT); gel(v,1) = gcopy(x); return v; }
336 : INLINE GEN
337 0 : mkerr(long x) { GEN v = cgetg(2, t_ERROR); v[1] = x; return v; }
338 : INLINE GEN
339 1079859 : mkoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
340 : INLINE GEN
341 106014 : mkmoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
342 : INLINE long
343 1198145 : inf_get_sign(GEN x) { return signe(gel(x,1)); }
344 : INLINE GEN
345 207452 : mkmat22s(long a, long b, long c, long d) {retmkmat2(mkcol2s(a,c),mkcol2s(b,d));}
346 : INLINE GEN
347 50649379 : mkmat22(GEN a, GEN b, GEN c, GEN d) { retmkmat2(mkcol2(a,c),mkcol2(b,d)); }
348 :
349 : /* pol */
350 : INLINE GEN
351 3568029 : pol_x(long v) {
352 3568029 : GEN p = cgetg(4, t_POL);
353 3568025 : p[1] = evalsigne(1)|evalvarn(v);
354 3568025 : gel(p,2) = gen_0;
355 3568025 : gel(p,3) = gen_1; return p;
356 : }
357 : /* x^n, assume n >= 0 */
358 : INLINE GEN
359 2236202 : pol_xn(long n, long v) {
360 2236202 : long i, a = n+2;
361 2236202 : GEN p = cgetg(a+1, t_POL);
362 2236207 : p[1] = evalsigne(1)|evalvarn(v);
363 5391568 : for (i = 2; i < a; i++) gel(p,i) = gen_0;
364 2236207 : gel(p,a) = gen_1; return p;
365 : }
366 : /* x^n, no assumption on n */
367 : INLINE GEN
368 294 : pol_xnall(long n, long v)
369 : {
370 294 : if (n < 0) retmkrfrac(gen_1, pol_xn(-n,v));
371 287 : return pol_xn(n, v);
372 : }
373 : /* x^n, assume n >= 0 */
374 : INLINE GEN
375 371 : polxn_Flx(long n, long sv) {
376 371 : long i, a = n+2;
377 371 : GEN p = cgetg(a+1, t_VECSMALL);
378 371 : p[1] = sv;
379 1806 : for (i = 2; i < a; i++) p[i] = 0;
380 371 : p[a] = 1; return p;
381 : }
382 : INLINE GEN
383 4461812 : pol_1(long v) {
384 4461812 : GEN p = cgetg(3, t_POL);
385 4461809 : p[1] = evalsigne(1)|evalvarn(v);
386 4461809 : gel(p,2) = gen_1; return p;
387 : }
388 : INLINE GEN
389 82536561 : pol_0(long v)
390 : {
391 82536561 : GEN x = cgetg(2,t_POL);
392 82536557 : x[1] = evalvarn(v); return x;
393 : }
394 : #define retconst_vec(n,x)\
395 : do { long _i, _n = (n);\
396 : GEN _v = cgetg(_n+1, t_VEC), _x = (x);\
397 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
398 : return _v; } while(0)
399 : INLINE GEN
400 234093594 : const_vec(long n, GEN x) { retconst_vec(n, x); }
401 : #define retconst_col(n,x)\
402 : do { long _i, _n = (n);\
403 : GEN _v = cgetg(_n+1, t_COL), _x = (x);\
404 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
405 : return _v; } while(0)
406 : INLINE GEN
407 39280148 : const_col(long n, GEN x) { retconst_col(n, x); }
408 : INLINE GEN
409 19061633 : const_vecsmall(long n, long c)
410 : {
411 : long i;
412 19061633 : GEN V = cgetg(n+1,t_VECSMALL);
413 753207861 : for(i=1;i<=n;i++) V[i] = c;
414 19062326 : return V;
415 : }
416 :
417 : /*** ZERO ***/
418 : /* O(p^e) */
419 : INLINE GEN
420 855885 : zeropadic(GEN p, long e) { retmkpadic(gen_0, icopy(p), gen_1, e, 0); }
421 : INLINE GEN
422 17010 : zeropadic_shallow(GEN p, long e) { retmkpadic(gen_0, icopy(p), gen_1, e, 0); }
423 : /* O(pol_x(v)^e) */
424 : INLINE GEN
425 138698 : zeroser(long v, long e)
426 : {
427 138698 : GEN x = cgetg(2, t_SER);
428 138698 : x[1] = evalvalser(e) | evalvarn(v); return x;
429 : }
430 : INLINE int
431 10079052 : ser_isexactzero(GEN x)
432 : {
433 10079052 : if (!signe(x)) switch(lg(x))
434 : {
435 132741 : case 2: return 1;
436 4648 : case 3: return isexactzero(gel(x,2));
437 : }
438 9941663 : return 0;
439 : }
440 : /* 0 * pol_x(v) */
441 : INLINE GEN
442 42302957 : zeropol(long v) { return pol_0(v); }
443 : /* vector(n) */
444 : INLINE GEN
445 118901332 : zerocol(long n)
446 : {
447 118901332 : GEN y = cgetg(n+1,t_COL);
448 803564842 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
449 118903692 : return y;
450 : }
451 : /* vectorv(n) */
452 : INLINE GEN
453 26634564 : zerovec(long n)
454 : {
455 26634564 : GEN y = cgetg(n+1,t_VEC);
456 391822476 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
457 26634566 : return y;
458 : }
459 : /* matrix(m, n) */
460 : INLINE GEN
461 108942 : zeromat(long m, long n)
462 : {
463 108942 : GEN y = cgetg(n+1,t_MAT);
464 108941 : GEN v = zerocol(m);
465 401806 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
466 108942 : return y;
467 : }
468 : /* = zero_zx, sv is a evalvarn()*/
469 : INLINE GEN
470 1431944 : zero_Flx(long sv) { return pol0_Flx(sv); }
471 : INLINE GEN
472 58786169 : zero_Flv(long n)
473 : {
474 58786169 : GEN y = cgetg(n+1,t_VECSMALL);
475 947486057 : long i; for (i=1; i<=n; i++) y[i] = 0;
476 58786305 : return y;
477 : }
478 : /* matrix(m, n) */
479 : INLINE GEN
480 2786979 : zero_Flm(long m, long n)
481 : {
482 2786979 : GEN y = cgetg(n+1,t_MAT);
483 2786975 : GEN v = zero_Flv(m);
484 17722786 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
485 2786971 : return y;
486 : }
487 : /* matrix(m, n) */
488 : INLINE GEN
489 232107 : zero_Flm_copy(long m, long n)
490 : {
491 232107 : GEN y = cgetg(n+1,t_MAT);
492 2397509 : long i; for (i=1; i<=n; i++) gel(y,i) = zero_Flv(m);
493 232113 : return y;
494 : }
495 :
496 : INLINE GEN
497 3633833 : zero_F2v(long m)
498 : {
499 3633833 : long l = nbits2nlong(m);
500 3633828 : GEN v = zero_Flv(l+1);
501 3633800 : v[1] = m;
502 3633800 : return v;
503 : }
504 :
505 : INLINE GEN
506 0 : zero_F2m(long m, long n)
507 : {
508 : long i;
509 0 : GEN M = cgetg(n+1, t_MAT);
510 0 : GEN v = zero_F2v(m);
511 0 : for (i = 1; i <= n; i++)
512 0 : gel(M,i) = v;
513 0 : return M;
514 : }
515 :
516 :
517 : INLINE GEN
518 841614 : zero_F2m_copy(long m, long n)
519 : {
520 : long i;
521 841614 : GEN M = cgetg(n+1, t_MAT);
522 2010645 : for (i = 1; i <= n; i++)
523 1169036 : gel(M,i)= zero_F2v(m);
524 841609 : return M;
525 : }
526 :
527 : /* matrix(m, n) */
528 : INLINE GEN
529 14032430 : zeromatcopy(long m, long n)
530 : {
531 14032430 : GEN y = cgetg(n+1,t_MAT);
532 71039390 : long i; for (i=1; i<=n; i++) gel(y,i) = zerocol(m);
533 14032475 : return y;
534 : }
535 :
536 : INLINE GEN
537 24429 : zerovec_block(long len)
538 : {
539 : long i;
540 24429 : GEN blk = cgetg_block(len + 1, t_VEC);
541 806157 : for (i = 1; i <= len; ++i)
542 781728 : gel(blk, i) = gen_0;
543 24429 : return blk;
544 : }
545 :
546 : /* i-th vector in the standard basis */
547 : INLINE GEN
548 5684113 : col_ei(long n, long i) { GEN e = zerocol(n); gel(e,i) = gen_1; return e; }
549 : INLINE GEN
550 1711471 : vec_ei(long n, long i) { GEN e = zerovec(n); gel(e,i) = gen_1; return e; }
551 : INLINE GEN
552 42 : F2v_ei(long n, long i) { GEN e = zero_F2v(n); F2v_set(e,i); return e; }
553 : INLINE GEN
554 497064 : vecsmall_ei(long n, long i) { GEN e = zero_zv(n); e[i] = 1; return e; }
555 : INLINE GEN
556 1292390 : Rg_col_ei(GEN x, long n, long i) { GEN e = zerocol(n); gel(e,i) = x; return e; }
557 :
558 : INLINE GEN
559 25798808 : shallowcopy(GEN x)
560 25798808 : { return typ(x) == t_MAT ? RgM_shallowcopy(x): leafcopy(x); }
561 :
562 : /* routines for naive growarrays */
563 : INLINE GEN
564 11735013 : vectrunc_init(long l)
565 : {
566 11735013 : GEN z = new_chunk(l);
567 11734774 : z[0] = evaltyp(t_VEC) | _evallg(1); return z;
568 : }
569 : INLINE GEN
570 393680 : coltrunc_init(long l)
571 : {
572 393680 : GEN z = new_chunk(l);
573 393680 : z[0] = evaltyp(t_COL) | _evallg(1); return z;
574 : }
575 : INLINE void
576 315042832 : lg_increase(GEN x) { x[0]++; }
577 : INLINE void
578 15262450 : vectrunc_append(GEN x, GEN t) { gel(x, lg(x)) = t; lg_increase(x); }
579 : INLINE void
580 10864 : vectrunc_append_batch(GEN x, GEN y)
581 : {
582 10864 : long i, l = lg(x), ly = lg(y);
583 10864 : GEN z = x + l-1;
584 36358 : for (i = 1; i < ly; i++) gel(z,i) = gel(y,i);
585 10864 : setlg(x, l+ly-1);
586 10864 : }
587 : INLINE GEN
588 188498273 : vecsmalltrunc_init(long l)
589 : {
590 188498273 : GEN z = new_chunk(l);
591 188504421 : z[0] = evaltyp(t_VECSMALL) | _evallg(1); return z;
592 : }
593 : INLINE void
594 99971627 : vecsmalltrunc_append(GEN x, long t) { x[ lg(x) ] = t; lg_increase(x); }
595 :
596 : /*******************************************************************/
597 : /* */
598 : /* STRING HASH FUNCTIONS */
599 : /* */
600 : /*******************************************************************/
601 : INLINE ulong
602 2709825 : hash_str(const char *str)
603 : {
604 2709825 : ulong hash = 5381UL, c;
605 28156342 : while ( (c = (ulong)*str++) )
606 25446517 : hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
607 2709825 : return hash;
608 : }
609 : INLINE ulong
610 18201388 : hash_str_len(const char *str, long len)
611 : {
612 18201388 : ulong hash = 5381UL;
613 : long i;
614 166366184 : for (i = 0; i < len; i++)
615 : {
616 148164796 : ulong c = (ulong)*str++;
617 148164796 : hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
618 : }
619 18201388 : return hash;
620 : }
621 :
622 : /*******************************************************************/
623 : /* */
624 : /* VEC / COL / VECSMALL */
625 : /* */
626 : /*******************************************************************/
627 : /* shallow*/
628 : INLINE GEN
629 11550 : vec_shorten(GEN v, long n)
630 : {
631 11550 : GEN V = cgetg(n+1, t_VEC);
632 : long i;
633 13006 : for(i = 1; i <= n; i++) gel(V,i) = gel(v,i);
634 11550 : return V;
635 : }
636 : /* shallow*/
637 : INLINE GEN
638 18941 : vec_lengthen(GEN v, long n)
639 : {
640 18941 : GEN V = cgetg(n+1, t_VEC);
641 18941 : long i, l = lg(v);
642 1935639 : for(i = 1; i < l; i++) gel(V,i) = gel(v,i);
643 18941 : return V;
644 : }
645 : /* shallow*/
646 : INLINE GEN
647 3432388 : vec_append(GEN V, GEN s)
648 : {
649 3432388 : long i, l2 = lg(V);
650 3432388 : GEN res = cgetg(l2+1, typ(V));
651 10737632 : for (i = 1; i < l2; i++) gel(res, i) = gel(V,i);
652 3432392 : gel(res,l2) = s; return res;
653 : }
654 : /* shallow*/
655 : INLINE GEN
656 300942 : vec_prepend(GEN v, GEN s)
657 : {
658 300942 : long i, l = lg(v);
659 300942 : GEN w = cgetg(l+1, typ(v));
660 300945 : gel(w,1) = s;
661 769430 : for (i = 2; i <= l; i++) gel(w,i) = gel(v,i-1);
662 300945 : return w;
663 : }
664 : /* shallow*/
665 : INLINE GEN
666 0 : vec_setconst(GEN v, GEN x)
667 : {
668 0 : long i, l = lg(v);
669 0 : for (i = 1; i < l; i++) gel(v,i) = x;
670 0 : return v;
671 : }
672 : INLINE GEN
673 72596 : vecsmall_shorten(GEN v, long n)
674 : {
675 72596 : GEN V = cgetg(n+1,t_VECSMALL);
676 : long i;
677 889707 : for(i = 1; i <= n; i++) V[i] = v[i];
678 72597 : return V;
679 : }
680 : INLINE GEN
681 526 : vecsmall_lengthen(GEN v, long n)
682 : {
683 526 : long i, l = lg(v);
684 526 : GEN V = cgetg(n+1,t_VECSMALL);
685 46315 : for(i = 1; i < l; i++) V[i] = v[i];
686 526 : return V;
687 : }
688 :
689 : INLINE GEN
690 4016095 : vec_to_vecsmall(GEN x)
691 18861117 : { pari_APPLY_long(itos(gel(x,i))) }
692 : INLINE GEN
693 511220 : vecsmall_to_vec(GEN x)
694 7069327 : { pari_APPLY_type(t_VEC, stoi(x[i])) }
695 : INLINE GEN
696 3304 : vecsmall_to_vec_inplace(GEN z)
697 : {
698 3304 : long i, l = lg(z);
699 79604 : for (i=1; i<l; i++) gel(z,i) = stoi(z[i]);
700 3304 : settyp(z, t_VEC); return z;
701 : }
702 : INLINE GEN
703 7762016 : vecsmall_to_col(GEN x)
704 59564903 : { pari_APPLY_type(t_COL, stoi(x[i])) }
705 :
706 : INLINE int
707 7209171 : vecsmall_lexcmp(GEN x, GEN y)
708 : {
709 : long lx,ly,l,i;
710 7209171 : lx = lg(x);
711 7209171 : ly = lg(y); l = minss(lx,ly);
712 30649366 : for (i=1; i<l; i++)
713 29021896 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
714 1627470 : if (lx == ly) return 0;
715 30578 : return (lx < ly)? -1 : 1;
716 : }
717 :
718 : INLINE int
719 108088071 : vecsmall_prefixcmp(GEN x, GEN y)
720 : {
721 108088071 : long i, lx = lg(x), ly = lg(y), l = minss(lx,ly);
722 542691324 : for (i=1; i<l; i++)
723 519806035 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
724 22885289 : return 0;
725 : }
726 :
727 : /*Can be used on t_VEC, but coeffs not gcopy-ed*/
728 : INLINE GEN
729 186798 : vecsmall_prepend(GEN V, long s)
730 : {
731 186798 : long i, l2 = lg(V);
732 186798 : GEN res = cgetg(l2+1, typ(V));
733 186798 : res[1] = s;
734 624943 : for (i = 2; i <= l2; ++i) res[i] = V[i - 1];
735 186798 : return res;
736 : }
737 :
738 : INLINE GEN
739 4065039 : vecsmall_append(GEN V, long s)
740 : {
741 4065039 : long i, l2 = lg(V);
742 4065039 : GEN res = cgetg(l2+1, t_VECSMALL);
743 5975261 : for (i = 1; i < l2; ++i) res[i] = V[i];
744 4065039 : res[l2] = s; return res;
745 : }
746 :
747 : INLINE GEN
748 1465404 : vecsmall_concat(GEN u, GEN v)
749 : {
750 1465404 : long i, l1 = lg(u)-1, l2 = lg(v)-1;
751 1465404 : GEN res = cgetg(l1+l2+1, t_VECSMALL);
752 11628998 : for (i = 1; i <= l1; ++i) res[i] = u[i];
753 15225361 : for (i = 1; i <= l2; ++i) res[i+l1] = v[i];
754 1465404 : return res;
755 : }
756 :
757 : /* return the number of indices where u and v are equal */
758 : INLINE long
759 0 : vecsmall_coincidence(GEN u, GEN v)
760 : {
761 0 : long i, s = 0, l = minss(lg(u),lg(v));
762 0 : for(i=1; i<l; i++)
763 0 : if(u[i] == v[i]) s++;
764 0 : return s;
765 : }
766 :
767 : /* returns the first index i<=n such that x=v[i] if it exists, 0 otherwise */
768 : INLINE long
769 84 : vecsmall_isin(GEN v, long x)
770 : {
771 84 : long i, l = lg(v);
772 123 : for (i = 1; i < l; i++)
773 78 : if (v[i] == x) return i;
774 45 : return 0;
775 : }
776 :
777 : INLINE long
778 84 : vecsmall_pack(GEN V, long base, long mod)
779 : {
780 84 : long i, s = 0;
781 273 : for(i=1; i<lg(V); i++) s = (base*s + V[i]) % mod;
782 84 : return s;
783 : }
784 :
785 : INLINE long
786 21 : vecsmall_indexmax(GEN x)
787 : {
788 21 : long i, i0 = 1, t = x[1], lx = lg(x);
789 84 : for (i=2; i<lx; i++)
790 63 : if (x[i] > t) t = x[i0=i];
791 21 : return i0;
792 : }
793 :
794 : INLINE long
795 1011287 : vecsmall_max(GEN x)
796 : {
797 1011287 : long i, t = x[1], lx = lg(x);
798 2825464 : for (i=2; i<lx; i++)
799 1814177 : if (x[i] > t) t = x[i];
800 1011287 : return t;
801 : }
802 :
803 : INLINE long
804 21 : vecsmall_indexmin(GEN x)
805 : {
806 21 : long i, i0 = 1, t = x[1], lx =lg(x);
807 84 : for (i=2; i<lx; i++)
808 63 : if (x[i] < t) t = x[i0=i];
809 21 : return i0;
810 : }
811 :
812 : INLINE long
813 2324 : vecsmall_min(GEN x)
814 : {
815 2324 : long i, t = x[1], lx =lg(x);
816 16268 : for (i=2; i<lx; i++)
817 13944 : if (x[i] < t) t = x[i];
818 2324 : return t;
819 : }
820 :
821 : INLINE int
822 22771191 : ZV_isscalar(GEN x)
823 : {
824 22771191 : long l = lg(x);
825 54275479 : while (--l > 1)
826 53881059 : if (signe(gel(x, l))) return 0;
827 394420 : return 1;
828 : }
829 : INLINE int
830 52379370 : QV_isscalar(GEN x)
831 : {
832 52379370 : long lx = lg(x),i;
833 68076488 : for (i=2; i<lx; i++)
834 64355321 : if (!isintzero(gel(x, i))) return 0;
835 3721167 : return 1;
836 : }
837 : INLINE int
838 1140352 : RgV_isscalar(GEN x)
839 : {
840 1140352 : long lx = lg(x),i;
841 1166553 : for (i=2; i<lx; i++)
842 1162841 : if (!gequal0(gel(x, i))) return 0;
843 3712 : return 1;
844 : }
845 : INLINE int
846 0 : RgX_isscalar(GEN x)
847 : {
848 : long i;
849 0 : for (i=lg(x)-1; i>2; i--)
850 0 : if (!gequal0(gel(x, i))) return 0;
851 0 : return 1;
852 : }
853 : INLINE long
854 26879315 : RgX_equal_var(GEN x, GEN y) { return varn(x) == varn(y) && RgX_equal(x,y); }
855 : INLINE GEN
856 140 : RgX_to_RgV(GEN x, long N) { x = RgX_to_RgC(x, N); settyp(x, t_VEC); return x; }
857 :
858 : #define RgX_type_code(t1,t2) ((t1 << 6) | t2)
859 :
860 : INLINE int
861 67889 : RgX_is_rational(GEN x)
862 : {
863 : long i;
864 309349 : for (i = lg(x)-1; i > 1; i--)
865 293421 : if (!is_rational_t(typ(gel(x,i)))) return 0;
866 15928 : return 1;
867 : }
868 : INLINE int
869 15301276 : RgX_is_ZX(GEN x)
870 : {
871 : long i;
872 65379851 : for (i = lg(x)-1; i > 1; i--)
873 50142963 : if (typ(gel(x,i)) != t_INT) return 0;
874 15236888 : return 1;
875 : }
876 : INLINE int
877 395945 : RgX_is_QX(GEN x)
878 : {
879 395945 : long k = lg(x)-1;
880 1483353 : for ( ; k>1; k--)
881 1087688 : if (!is_rational_t(typ(gel(x,k)))) return 0;
882 395665 : return 1;
883 : }
884 : INLINE int
885 3113552 : RgX_is_monomial(GEN x)
886 : {
887 : long i;
888 3113552 : if (!signe(x)) return 0;
889 7121576 : for (i=lg(x)-2; i>1; i--)
890 4723641 : if (!isexactzero(gel(x,i))) return 0;
891 2397935 : return 1;
892 : }
893 : INLINE int
894 31362761 : RgV_is_ZV(GEN x)
895 : {
896 : long i;
897 124680563 : for (i = lg(x)-1; i > 0; i--)
898 93350233 : if (typ(gel(x,i)) != t_INT) return 0;
899 31330330 : return 1;
900 : }
901 : INLINE int
902 140156 : RgV_is_QV(GEN x)
903 : {
904 : long i;
905 620023 : for (i = lg(x)-1; i > 0; i--)
906 482821 : if (!is_rational_t(typ(gel(x,i)))) return 0;
907 137202 : return 1;
908 : }
909 : INLINE long
910 110130 : RgV_isin_i(GEN v, GEN x, long n)
911 : {
912 : long i;
913 1033437 : for (i = 1; i <= n; i++)
914 1026703 : if (gequal(gel(v,i), x)) return i;
915 6734 : return 0;
916 : }
917 : INLINE long
918 110130 : RgV_isin(GEN v, GEN x) { return RgV_isin_i(v, x, lg(v)-1); }
919 :
920 : /********************************************************************/
921 : /** **/
922 : /** Dynamic arrays implementation **/
923 : /** **/
924 : /********************************************************************/
925 : INLINE void **
926 697130461 : pari_stack_base(pari_stack *s) { return s->data; }
927 :
928 : INLINE void
929 5754002 : pari_stack_init(pari_stack *s, size_t size, void **data)
930 : {
931 5754002 : s->data = data;
932 5754002 : *data = NULL;
933 5754002 : s->n = 0;
934 5754002 : s->alloc = 0;
935 5754002 : s->size = size;
936 5754002 : }
937 :
938 : INLINE void
939 691829946 : pari_stack_alloc(pari_stack *s, long nb)
940 : {
941 691829946 : void **sdat = pari_stack_base(s);
942 691737578 : long alloc = s->alloc;
943 691737578 : if (s->n+nb <= alloc) return;
944 2142432 : if (!alloc)
945 2046455 : alloc = nb;
946 : else
947 : {
948 196479 : while (s->n+nb > alloc) alloc <<= 1;
949 : }
950 2142432 : pari_realloc_ip(sdat,alloc*s->size);
951 2144274 : s->alloc = alloc;
952 : }
953 :
954 : INLINE long
955 598789590 : pari_stack_new(pari_stack *s) { pari_stack_alloc(s, 1); return s->n++; }
956 :
957 : INLINE void
958 5335407 : pari_stack_delete(pari_stack *s)
959 : {
960 5335407 : void **sdat = pari_stack_base(s);
961 5325824 : if (*sdat) pari_free(*sdat);
962 5346563 : }
963 :
964 : INLINE void
965 5788 : pari_stack_pushp(pari_stack *s, void *u)
966 : {
967 5788 : long n = pari_stack_new(s);
968 5788 : void **sdat =(void**) *pari_stack_base(s);
969 5788 : sdat[n] = u;
970 5788 : }
971 :
972 : /*******************************************************************/
973 : /* */
974 : /* EXTRACT */
975 : /* */
976 : /*******************************************************************/
977 : INLINE GEN
978 642360493 : vecslice(GEN A, long y1, long y2)
979 : {
980 642360493 : long i,lB = y2 - y1 + 2;
981 642360493 : GEN B = cgetg(lB, typ(A));
982 2858657959 : for (i=1; i<lB; i++) B[i] = A[y1-1+i];
983 642353042 : return B;
984 : }
985 : INLINE GEN
986 2649050 : vecslicepermute(GEN A, GEN p, long y1, long y2)
987 : {
988 2649050 : long i,lB = y2 - y1 + 2;
989 2649050 : GEN B = cgetg(lB, typ(A));
990 29982181 : for (i=1; i<lB; i++) B[i] = A[p[y1-1+i]];
991 2649035 : return B;
992 : }
993 : /* rowslice(rowpermute(A,p), x1, x2) */
994 : INLINE GEN
995 182825 : rowslicepermute(GEN x, GEN p, long j1, long j2)
996 772142 : { pari_APPLY_same(vecslicepermute(gel(x,i),p,j1,j2)) }
997 :
998 : INLINE GEN
999 78449315 : rowslice(GEN x, long j1, long j2)
1000 658344306 : { pari_APPLY_same(vecslice(gel(x,i), j1, j2)) }
1001 :
1002 : INLINE GEN
1003 16613014 : matslice(GEN A, long x1, long x2, long y1, long y2)
1004 16613014 : { return rowslice(vecslice(A, y1, y2), x1, x2); }
1005 :
1006 : /* shallow, remove coeff of index j */
1007 : INLINE GEN
1008 273 : rowsplice(GEN x, long j)
1009 1225 : { pari_APPLY_same(vecsplice(gel(x,i), j)) }
1010 :
1011 : /* shallow, remove coeff of index j */
1012 : INLINE GEN
1013 354714 : vecsplice(GEN a, long j)
1014 : {
1015 354714 : long i, k, l = lg(a);
1016 : GEN b;
1017 354714 : if (l == 1) pari_err(e_MISC, "incorrect component in vecsplice");
1018 354714 : b = cgetg(l-1, typ(a));
1019 1503221 : for (i = k = 1; i < l; i++)
1020 1148508 : if (i != j) gel(b, k++) = gel(a,i);
1021 354713 : return b;
1022 : }
1023 : /* shallow */
1024 : INLINE GEN
1025 1036 : RgM_minor(GEN a, long i, long j)
1026 : {
1027 1036 : GEN b = vecsplice(a, j);
1028 1036 : long k, l = lg(b);
1029 4242 : for (k = 1; k < l; k++) gel(b,k) = vecsplice(gel(b,k), i);
1030 1036 : return b;
1031 : }
1032 :
1033 : /* A[x0,] */
1034 : INLINE GEN
1035 762864 : row(GEN x, long j)
1036 6687584 : { pari_APPLY_type(t_VEC, gcoeff(x, j, i)) }
1037 : INLINE GEN
1038 8757799 : Flm_row(GEN x, long j)
1039 232252740 : { pari_APPLY_ulong((ulong)coeff(x, j, i)) }
1040 : /* A[x0,] */
1041 : INLINE GEN
1042 204988 : rowcopy(GEN x, long j)
1043 2105509 : { pari_APPLY_type(t_VEC, gcopy(gcoeff(x, j, i))) }
1044 : /* A[x0, x1..x2] */
1045 : INLINE GEN
1046 987 : row_i(GEN A, long x0, long x1, long x2)
1047 : {
1048 987 : long i, lB = x2 - x1 + 2;
1049 987 : GEN B = cgetg(lB, t_VEC);
1050 2989 : for (i=x1; i<=x2; i++) gel(B, i) = gcoeff(A, x0, i);
1051 987 : return B;
1052 : }
1053 :
1054 : INLINE GEN
1055 697025 : vecreverse(GEN A)
1056 : {
1057 : long i, l;
1058 697025 : GEN B = cgetg_copy(A, &l);
1059 2407755 : for (i=1; i<l; i++) gel(B, i) = gel(A, l-i);
1060 697025 : return B;
1061 : }
1062 :
1063 : INLINE GEN
1064 3073 : vecsmall_reverse(GEN A)
1065 : {
1066 : long i, l;
1067 3073 : GEN B = cgetg_copy(A, &l);
1068 12761 : for (i=1; i<l; i++) B[i] = A[l-i];
1069 3073 : return B;
1070 : }
1071 :
1072 : INLINE void
1073 2570 : vecreverse_inplace(GEN y)
1074 : {
1075 2570 : long l = lg(y), lim = l>>1, i;
1076 8242 : for (i = 1; i <= lim; i++)
1077 : {
1078 5672 : GEN z = gel(y,i);
1079 5672 : gel(y,i) = gel(y,l-i);
1080 5672 : gel(y,l-i) = z;
1081 : }
1082 2570 : }
1083 :
1084 : INLINE GEN
1085 78052642 : vecsmallpermute(GEN A, GEN p) { return perm_mul(A, p); }
1086 :
1087 : INLINE GEN
1088 19846902 : vecpermute(GEN A, GEN x)
1089 112527216 : { pari_APPLY_type(typ(A), gel(A, x[i])) }
1090 :
1091 : INLINE GEN
1092 6937796 : veclast(GEN A) { return gel(A, lg(A)-1); }
1093 :
1094 : INLINE GEN
1095 14431796 : rowpermute(GEN x, GEN p)
1096 100895459 : { pari_APPLY_same(typ(gel(x,i)) == t_VECSMALL ? vecsmallpermute(gel(x, i), p)
1097 : : vecpermute(gel(x, i), p))
1098 : }
1099 : /*******************************************************************/
1100 : /* */
1101 : /* PERMUTATIONS */
1102 : /* */
1103 : /*******************************************************************/
1104 : INLINE GEN
1105 3155926 : identity_zv(long n)
1106 : {
1107 3155926 : GEN v = cgetg(n+1, t_VECSMALL);
1108 : long i;
1109 32251070 : for (i = 1; i <= n; i++) v[i] = i;
1110 3155925 : return v;
1111 : }
1112 : INLINE GEN
1113 4333 : identity_ZV(long n)
1114 : {
1115 4333 : GEN v = cgetg(n+1, t_VEC);
1116 : long i;
1117 51898 : for (i = 1; i <= n; i++) gel(v,i) = utoipos(i);
1118 4333 : return v;
1119 : }
1120 : /* identity permutation */
1121 : INLINE GEN
1122 3131580 : identity_perm(long n) { return identity_zv(n); }
1123 :
1124 : /* assume d <= n */
1125 : INLINE GEN
1126 99911 : cyclic_perm(long n, long d)
1127 : {
1128 99911 : GEN perm = cgetg(n+1, t_VECSMALL);
1129 : long i;
1130 520240 : for (i = 1; i <= n-d; i++) perm[i] = i+d;
1131 226702 : for ( ; i <= n; i++) perm[i] = i-n+d;
1132 99911 : return perm;
1133 : }
1134 :
1135 : /* Multiply (compose) two permutations */
1136 : INLINE GEN
1137 80247691 : perm_mul(GEN s, GEN x)
1138 1014859932 : { pari_APPLY_long(s[x[i]]) }
1139 :
1140 : INLINE GEN
1141 728 : perm_sqr(GEN x)
1142 18284 : { pari_APPLY_long(x[x[i]]) }
1143 :
1144 : /* Compute the inverse (reciprocal) of a permutation. */
1145 : INLINE GEN
1146 2780864 : perm_inv(GEN x)
1147 : {
1148 : long i, lx;
1149 2780864 : GEN y = cgetg_copy(x, &lx);
1150 39084125 : for (i=1; i<lx; i++) y[ x[i] ] = i;
1151 2780861 : return y;
1152 : }
1153 : /* Return s*t*s^-1 */
1154 : INLINE GEN
1155 418299 : perm_conj(GEN s, GEN t)
1156 : {
1157 : long i, l;
1158 418299 : GEN v = cgetg_copy(s, &l);
1159 6857893 : for (i = 1; i < l; i++) v[ s[i] ] = s[ t[i] ];
1160 418299 : return v;
1161 : }
1162 :
1163 : INLINE void
1164 490894085 : pari_free(void *pointer)
1165 : {
1166 490894085 : BLOCK_SIGINT_START;
1167 490941383 : free(pointer);
1168 490941383 : BLOCK_SIGINT_END;
1169 490935601 : }
1170 : INLINE void*
1171 721236302 : pari_malloc(size_t size)
1172 : {
1173 721236302 : if (size)
1174 : {
1175 : char *tmp;
1176 721236705 : BLOCK_SIGINT_START;
1177 721289313 : tmp = (char*)malloc(size);
1178 721289313 : BLOCK_SIGINT_END;
1179 721291084 : if (!tmp) pari_err(e_MEM);
1180 721299877 : return tmp;
1181 : }
1182 0 : return NULL;
1183 : }
1184 : INLINE void*
1185 1869 : pari_realloc(void *pointer, size_t size)
1186 : {
1187 : char *tmp;
1188 :
1189 1869 : BLOCK_SIGINT_START;
1190 1869 : if (!pointer) tmp = (char *) malloc(size);
1191 1869 : else tmp = (char *) realloc(pointer,size);
1192 1869 : BLOCK_SIGINT_END;
1193 1869 : if (!tmp) pari_err(e_MEM);
1194 1869 : return tmp;
1195 : }
1196 : INLINE void
1197 2147101 : pari_realloc_ip(void **pointer, size_t size)
1198 : {
1199 : char *tmp;
1200 2147101 : BLOCK_SIGINT_START;
1201 2146984 : if (!*pointer) tmp = (char *) malloc(size);
1202 100788 : else tmp = (char *) realloc(*pointer,size);
1203 2146984 : if (!tmp) pari_err(e_MEM);
1204 2146984 : *pointer = tmp;
1205 2146984 : BLOCK_SIGINT_END;
1206 2146837 : }
1207 :
1208 : INLINE void*
1209 47076 : pari_calloc(size_t size)
1210 : {
1211 47076 : void *t = pari_malloc(size);
1212 47076 : memset(t, 0, size); return t;
1213 : }
1214 : INLINE GEN
1215 10096 : cgetalloc(size_t l, long t)
1216 : { /* evallg may raise e_OVERFLOW, which would leak x */
1217 10096 : ulong x0 = evaltyp(t) | evallg(l);
1218 10096 : GEN x = (GEN)pari_malloc(l * sizeof(long));
1219 10096 : x[0] = x0; return x;
1220 : }
1221 :
1222 : /*******************************************************************/
1223 : /* */
1224 : /* GARBAGE COLLECTION */
1225 : /* */
1226 : /*******************************************************************/
1227 : /* copy integer x as if we had set_avma(av) */
1228 : INLINE GEN
1229 7851757489 : icopy_avma(GEN x, pari_sp av)
1230 : {
1231 7851757489 : long i = lgefint(x), lx = i;
1232 7851757489 : GEN y = ((GEN)av) - i;
1233 57729630178 : while (--i > 0) y[i] = x[i];
1234 7851757489 : y[0] = evaltyp(t_INT)|evallg(lx);
1235 7854973957 : return y;
1236 : }
1237 : /* copy leaf x as if we had set_avma(av) */
1238 : INLINE GEN
1239 547439685 : leafcopy_avma(GEN x, pari_sp av)
1240 : {
1241 547439685 : long i = lg(x);
1242 547439685 : GEN y = ((GEN)av) - i;
1243 2975263763 : while (--i > 0) y[i] = x[i];
1244 547439685 : y[0] = x[0] & (~CLONEBIT);
1245 547439685 : return y;
1246 : }
1247 : INLINE GEN
1248 1076156044 : gerepileuptoleaf(pari_sp av, GEN x)
1249 : {
1250 : long lx;
1251 : GEN q;
1252 :
1253 1076156044 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1254 1074850845 : lx = lg(x);
1255 1074850845 : q = ((GEN)av) - lx;
1256 1074850845 : set_avma((pari_sp)q);
1257 10848865793 : while (--lx >= 0) q[lx] = x[lx];
1258 1074566219 : return q;
1259 : }
1260 : INLINE GEN
1261 3990755934 : gerepileuptoint(pari_sp av, GEN x)
1262 : {
1263 3990755934 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1264 3555074251 : set_avma((pari_sp)icopy_avma(x, av));
1265 3558645939 : return (GEN)avma;
1266 : }
1267 : INLINE GEN
1268 1832910663 : gerepileupto(pari_sp av, GEN x)
1269 : {
1270 1832910663 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1271 1669155309 : switch(typ(x))
1272 : { /* non-default = !is_recursive_t(tq) */
1273 480835643 : case t_INT: return gerepileuptoint(av, x);
1274 338418130 : case t_REAL:
1275 : case t_STR:
1276 338418130 : case t_VECSMALL: return gerepileuptoleaf(av,x);
1277 849903517 : default:
1278 : /* NB: x+i --> ((long)x) + i*sizeof(long) */
1279 849903517 : return gerepile(av, (pari_sp) (x+lg(x)), x);
1280 : }
1281 : }
1282 :
1283 : /* gerepileupto(av, gcopy(x)) */
1284 : INLINE GEN
1285 227664568 : gerepilecopy(pari_sp av, GEN x)
1286 : {
1287 227664568 : if (is_recursive_t(typ(x)))
1288 : {
1289 208160863 : GENbin *p = copy_bin(x);
1290 208180385 : set_avma(av); return bin_copy(p);
1291 : }
1292 : else
1293 : {
1294 19503121 : set_avma(av);
1295 19503278 : if (x < (GEN)av) {
1296 19295494 : if (x < (GEN)pari_mainstack->bot) new_chunk(lg(x));
1297 19295499 : x = leafcopy_avma(x, av);
1298 19295532 : set_avma((pari_sp)x);
1299 : } else
1300 207787 : x = leafcopy(x);
1301 19503326 : return x;
1302 : }
1303 : }
1304 :
1305 : INLINE void
1306 47884485 : guncloneNULL(GEN x) { if (x) gunclone(x); }
1307 : INLINE void
1308 1371530 : guncloneNULL_deep(GEN x) { if (x) gunclone_deep(x); }
1309 :
1310 : /* Takes an array of pointers to GENs, of length n. Copies all
1311 : * objects to contiguous locations and cleans up the stack between
1312 : * av and avma. */
1313 : INLINE void
1314 984985 : gerepilemany(pari_sp av, GEN* gptr[], int n)
1315 : {
1316 : int i;
1317 3913358 : for (i=0; i<n; i++) *gptr[i] = (GEN)copy_bin(*gptr[i]);
1318 984872 : set_avma(av);
1319 3913886 : for (i=0; i<n; i++) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1320 985117 : }
1321 :
1322 : INLINE void
1323 19178159 : gerepileall(pari_sp av, int n, ...)
1324 : {
1325 : int i;
1326 19178159 : va_list a; va_start(a, n);
1327 19178159 : if (n < 10)
1328 : {
1329 : GEN *gptr[10];
1330 58156819 : for (i=0; i<n; i++)
1331 38977834 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1332 19178985 : set_avma(av);
1333 58157870 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1334 :
1335 : }
1336 : else
1337 : {
1338 0 : GEN **gptr = (GEN**) pari_malloc(n*sizeof(GEN*));
1339 0 : for (i=0; i<n; i++)
1340 0 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1341 0 : set_avma(av);
1342 0 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1343 0 : pari_free(gptr);
1344 : }
1345 19179522 : va_end(a);
1346 19179522 : }
1347 :
1348 : /* assume 1 <= n < 10 */
1349 : INLINE GEN
1350 86227674 : gc_all(pari_sp av, int n, ...)
1351 : {
1352 : int i;
1353 : GEN *v[10];
1354 86227674 : va_list a; va_start(a, n);
1355 289705791 : for (i=0; i<n; i++) { v[i] = va_arg(a,GEN*); *v[i] = (GEN)copy_bin(*v[i]); }
1356 86227941 : set_avma(av);
1357 289706409 : for (i=0; i<n; i++) *v[i] = bin_copy((GENbin*)*v[i]);
1358 86228065 : return *v[0];
1359 : }
1360 :
1361 : INLINE void
1362 2200355 : gerepilecoeffs(pari_sp av, GEN x, int n)
1363 : {
1364 : int i;
1365 26205004 : for (i=0; i<n; i++) gel(x,i) = (GEN)copy_bin(gel(x,i));
1366 2200924 : set_avma(av);
1367 26206123 : for (i=0; i<n; i++) gel(x,i) = bin_copy((GENbin*)x[i]);
1368 2200519 : }
1369 :
1370 : /* p from copy_bin. Copy p->x back to stack, then destroy p */
1371 : INLINE GEN
1372 477617244 : bin_copy(GENbin *p)
1373 : {
1374 : GEN x, y, base;
1375 : long dx, len;
1376 :
1377 477617244 : x = p->x; if (!x) { pari_free(p); return gen_0; }
1378 448568662 : len = p->len;
1379 448568662 : base= p->base; dx = x - base;
1380 448568662 : y = (GEN)memcpy((void*)new_chunk(len), (void*)GENbinbase(p), len*sizeof(long));
1381 448562019 : y += dx;
1382 448562019 : p->rebase(y, ((ulong)y-(ulong)x));
1383 448565516 : pari_free(p); return y;
1384 : }
1385 :
1386 : INLINE GEN
1387 926184449 : GENbinbase(GENbin *p) { return (GEN)(p + 1); }
1388 :
1389 : INLINE void
1390 117721061 : cgiv(GEN x)
1391 : {
1392 117721061 : pari_sp av = (pari_sp)(x+lg(x));
1393 117721061 : if (isonstack((GEN)av)) set_avma(av);
1394 117735132 : }
1395 :
1396 : INLINE void
1397 1886974 : killblock(GEN x) { gunclone(x); }
1398 :
1399 : INLINE int
1400 291184394 : is_universal_constant(GEN x) { return (x >= gen_0 && x <= ghalf); }
1401 :
1402 : /*******************************************************************/
1403 : /* */
1404 : /* CONVERSION / ASSIGNMENT */
1405 : /* */
1406 : /*******************************************************************/
1407 : /* z is a type which may be a t_COMPLEX component (not a t_QUAD) */
1408 : INLINE GEN
1409 17935384 : cxcompotor(GEN z, long prec)
1410 : {
1411 17935384 : switch(typ(z))
1412 : {
1413 11783125 : case t_INT: return itor(z, prec);
1414 293174 : case t_FRAC: return fractor(z, prec);
1415 5859308 : case t_REAL: return rtor(z, prec);
1416 0 : default: pari_err_TYPE("cxcompotor",z);
1417 : return NULL; /* LCOV_EXCL_LINE */
1418 : }
1419 : }
1420 : INLINE GEN
1421 8951032 : cxtofp(GEN x, long prec)
1422 8951032 : { retmkcomplex(cxcompotor(gel(x,1),prec), cxcompotor(gel(x,2),prec)); }
1423 :
1424 : INLINE GEN
1425 384632 : cxtoreal(GEN q)
1426 384632 : { return (typ(q) == t_COMPLEX && gequal0(gel(q,2)))? gel(q,1): q; }
1427 :
1428 : INLINE double
1429 60621255 : gtodouble(GEN x)
1430 : {
1431 60621255 : if (typ(x)!=t_REAL) {
1432 8161091 : pari_sp av = avma;
1433 8161091 : x = gtofp(x, DEFAULTPREC);
1434 8160521 : if (typ(x)!=t_REAL) pari_err_TYPE("gtodouble [t_REAL expected]", x);
1435 8160521 : set_avma(av);
1436 : }
1437 60620578 : return rtodbl(x);
1438 : }
1439 :
1440 : INLINE int
1441 2971837 : gisdouble(GEN x, double *g)
1442 : {
1443 2971837 : if (typ(x)!=t_REAL) {
1444 41923 : pari_sp av = avma;
1445 41923 : x = gtofp(x, DEFAULTPREC);
1446 41923 : if (typ(x)!=t_REAL) pari_err_TYPE("gisdouble [t_REAL expected]", x);
1447 41923 : set_avma(av);
1448 : }
1449 2971838 : if (expo(x) >= 0x3ff) return 0;
1450 2971838 : *g = rtodbl(x); return 1;
1451 : }
1452 :
1453 : INLINE long
1454 85800843 : gtos(GEN x) {
1455 85800843 : if (typ(x) != t_INT) pari_err_TYPE("gtos [integer expected]",x);
1456 85800829 : return itos(x);
1457 : }
1458 :
1459 : INLINE ulong
1460 102638 : gtou(GEN x) {
1461 102638 : if (typ(x) != t_INT || signe(x)<0)
1462 7 : pari_err_TYPE("gtou [integer >=0 expected]",x);
1463 102631 : return itou(x);
1464 : }
1465 :
1466 : INLINE GEN
1467 45575930 : absfrac(GEN x)
1468 : {
1469 45575930 : GEN y = cgetg(3, t_FRAC);
1470 45575971 : gel(y,1) = absi(gel(x,1));
1471 45576006 : gel(y,2) = icopy(gel(x,2)); return y;
1472 : }
1473 : INLINE GEN
1474 27254 : absfrac_shallow(GEN x)
1475 27254 : { return signe(gel(x,1))>0? x: mkfrac(negi(gel(x,1)), gel(x,2)); }
1476 : INLINE GEN
1477 7922114 : Q_abs(GEN x) { return (typ(x) == t_INT)? absi(x): absfrac(x); }
1478 : INLINE GEN
1479 118421 : Q_abs_shallow(GEN x)
1480 118421 : { return (typ(x) == t_INT)? absi_shallow(x): absfrac_shallow(x); }
1481 : INLINE GEN
1482 13083 : R_abs_shallow(GEN x)
1483 13083 : { return (typ(x) == t_FRAC)? absfrac_shallow(x): mpabs_shallow(x); }
1484 : INLINE GEN
1485 0 : R_abs(GEN x)
1486 0 : { return (typ(x) == t_FRAC)? absfrac(x): mpabs(x); }
1487 :
1488 : /* Force z to be of type real/complex with floating point components */
1489 : INLINE GEN
1490 252459467 : gtofp(GEN z, long prec)
1491 : {
1492 252459467 : switch(typ(z))
1493 : {
1494 213726500 : case t_INT: return itor(z, prec);
1495 4097405 : case t_FRAC: return fractor(z, prec);
1496 25944810 : case t_REAL: return rtor(z, prec);
1497 8697935 : case t_COMPLEX: {
1498 8697935 : GEN a = gel(z,1), b = gel(z,2);
1499 8697935 : if (isintzero(b)) return cxcompotor(a, prec);
1500 8697919 : if (isintzero(a)) {
1501 9103 : GEN y = cgetg(3, t_COMPLEX);
1502 9103 : b = cxcompotor(b, prec);
1503 9103 : gel(y,1) = real_0_bit(expo(b) - prec);
1504 9103 : gel(y,2) = b; return y;
1505 : }
1506 8688774 : return cxtofp(z, prec);
1507 : }
1508 0 : case t_QUAD: return quadtofp(z, prec);
1509 0 : default: pari_err_TYPE("gtofp",z);
1510 : return NULL; /* LCOV_EXCL_LINE */
1511 : }
1512 : }
1513 : /* Force z to be of type real / int */
1514 : INLINE GEN
1515 22428 : gtomp(GEN z, long prec)
1516 : {
1517 22428 : switch(typ(z))
1518 : {
1519 42 : case t_INT: return z;
1520 22386 : case t_FRAC: return fractor(z, prec);
1521 0 : case t_REAL: return rtor(z, prec);
1522 0 : case t_QUAD: z = quadtofp(z, prec);
1523 0 : if (typ(z) == t_REAL) return z;
1524 0 : default: pari_err_TYPE("gtomp",z);
1525 : return NULL; /* LCOV_EXCL_LINE */
1526 : }
1527 : }
1528 :
1529 : INLINE GEN
1530 7132561 : RgX_gtofp(GEN x, long prec)
1531 37210857 : { pari_APPLY_pol_normalized(gtofp(gel(x,i), prec)); }
1532 :
1533 : INLINE GEN
1534 33738298 : RgC_gtofp(GEN x, long prec)
1535 217411109 : { pari_APPLY_type(t_COL, gtofp(gel(x,i), prec)) }
1536 :
1537 : INLINE GEN
1538 56 : RgV_gtofp(GEN x, long prec)
1539 4781 : { pari_APPLY_type(t_VEC, gtofp(gel(x,i), prec)) }
1540 :
1541 : INLINE GEN
1542 8183566 : RgM_gtofp(GEN x, long prec)
1543 41291324 : { pari_APPLY_same(RgC_gtofp(gel(x,i), prec)) }
1544 :
1545 : INLINE GEN
1546 574 : RgC_gtomp(GEN x, long prec)
1547 23002 : { pari_APPLY_type(t_COL, gtomp(gel(x,i), prec)) }
1548 :
1549 : INLINE GEN
1550 21 : RgM_gtomp(GEN x, long prec)
1551 595 : { pari_APPLY_same(RgC_gtomp(gel(x,i), prec)) }
1552 :
1553 : INLINE GEN
1554 60610 : RgX_fpnorml2(GEN x, long prec)
1555 : {
1556 60610 : pari_sp av = avma;
1557 60610 : return gerepileupto(av, gnorml2(RgX_gtofp(x, prec)));
1558 : }
1559 : INLINE GEN
1560 619428 : RgC_fpnorml2(GEN x, long prec)
1561 : {
1562 619428 : pari_sp av = avma;
1563 619428 : return gerepileupto(av, gnorml2(RgC_gtofp(x, prec)));
1564 : }
1565 : INLINE GEN
1566 22534 : RgM_fpnorml2(GEN x, long prec)
1567 : {
1568 22534 : pari_sp av = avma;
1569 22534 : return gerepileupto(av, gnorml2(RgM_gtofp(x, prec)));
1570 : }
1571 :
1572 : /* y a t_REAL */
1573 : INLINE void
1574 220535 : affgr(GEN x, GEN y)
1575 : {
1576 : pari_sp av;
1577 220535 : switch(typ(x)) {
1578 5999 : case t_INT: affir(x,y); break;
1579 214536 : case t_REAL: affrr(x,y); break;
1580 0 : case t_FRAC: rdiviiz(gel(x,1),gel(x,2), y); break;
1581 0 : case t_QUAD: av = avma; affgr(quadtofp(x,realprec(y)), y); set_avma(av); break;
1582 0 : default: pari_err_TYPE2("=",x,y);
1583 : }
1584 220535 : }
1585 :
1586 : INLINE GEN
1587 239589 : affc_fixlg(GEN x, GEN res)
1588 : {
1589 239589 : if (typ(x) == t_COMPLEX)
1590 : {
1591 206871 : affrr_fixlg(gel(x,1), gel(res,1));
1592 206871 : affrr_fixlg(gel(x,2), gel(res,2));
1593 : }
1594 : else
1595 : {
1596 32718 : set_avma((pari_sp)(res+3));
1597 32718 : res = cgetr(realprec(gel(res,1)));
1598 32719 : affrr_fixlg(x, res);
1599 : }
1600 239591 : return res;
1601 : }
1602 :
1603 : INLINE GEN
1604 0 : trunc_safe(GEN x) { long e; return gcvtoi(x,&e); }
1605 :
1606 : /*******************************************************************/
1607 : /* */
1608 : /* LENGTH CONVERSIONS */
1609 : /* */
1610 : /*******************************************************************/
1611 : INLINE long
1612 41087 : ndec2nlong(long x) { return 1 + (long)((x)*(LOG2_10/BITS_IN_LONG)); }
1613 : INLINE long
1614 32831 : ndec2prec(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1615 : INLINE long
1616 8256 : ndec2nbits(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1617 : /* Fast implementation of ceil(x / (8*sizeof(long))); typecast to (ulong)
1618 : * to avoid overflow. Faster than 1 + ((x-1)>>TWOPOTBITS_IN_LONG)) :
1619 : * addl, shrl instead of subl, sarl, addl */
1620 : INLINE long
1621 12591451 : nbits2nlong(long x) {
1622 12591451 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1623 : }
1624 :
1625 : INLINE long
1626 1474871461 : nbits2extraprec(long x) {
1627 1474871461 : return (((ulong)x+BITS_IN_LONG-1)>>TWOPOTBITS_IN_LONG) << TWOPOTBITS_IN_LONG;
1628 : }
1629 :
1630 : INLINE long
1631 185704561 : nbits2prec(long x) {
1632 185704561 : return (((ulong)x+BITS_IN_LONG-1)>>TWOPOTBITS_IN_LONG) << TWOPOTBITS_IN_LONG;
1633 : }
1634 :
1635 : INLINE long
1636 4459646831 : prec2lg(long x) {
1637 4459646831 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1638 : }
1639 : /* ceil(x / sizeof(long)) */
1640 : INLINE long
1641 120860127 : nchar2nlong(long x) {
1642 120860127 : return (long)(((ulong)x+sizeof(long)-1) >> (TWOPOTBITS_IN_LONG-3L));
1643 : }
1644 : INLINE long
1645 104294207 : prec2nbits(long x) { return x; }
1646 : INLINE double
1647 3175075 : bit_accuracy_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1648 : INLINE double
1649 570916 : prec2nbits_mul(long x, double y) { return x * y; }
1650 : INLINE long
1651 141596466 : bit_prec(GEN x) { return realprec(x); }
1652 : INLINE long
1653 3126166208 : bit_accuracy(long x) { return (x-2) * BITS_IN_LONG; }
1654 : INLINE long
1655 9750 : prec2ndec(long x) { return (long)(x * LOG10_2); }
1656 : INLINE long
1657 214 : nbits2ndec(long x) { return prec2ndec(x); }
1658 : INLINE long
1659 475486 : precdbl(long x) {return x << 1;}
1660 : INLINE long
1661 8070346539 : divsBIL(long n) { return n >> TWOPOTBITS_IN_LONG; }
1662 : INLINE long
1663 7980732158 : remsBIL(long n) { return n & (BITS_IN_LONG-1); }
1664 :
1665 : /*********************************************************************/
1666 : /** **/
1667 : /** OPERATIONS MODULO m **/
1668 : /** **/
1669 : /*********************************************************************/
1670 : /* Assume m > 0, more efficient if 0 <= a, b < m */
1671 :
1672 : INLINE GEN
1673 79918365 : Fp_red(GEN a, GEN m) { return modii(a, m); }
1674 : INLINE GEN
1675 173798856 : Fp_add(GEN a, GEN b, GEN m)
1676 : {
1677 173798856 : pari_sp av=avma;
1678 173798856 : GEN p = addii(a,b);
1679 173249226 : long s = signe(p);
1680 173249226 : if (!s) return p; /* = gen_0 */
1681 160360482 : if (s > 0) /* general case */
1682 : {
1683 160104479 : GEN t = subii(p, m);
1684 160009649 : s = signe(t);
1685 160009649 : if (!s) return gc_const(av, gen_0);
1686 151721382 : if (s < 0) return gc_const((pari_sp)p, p);
1687 72440711 : if (cmpii(t, m) < 0) return gerepileuptoint(av, t); /* general case ! */
1688 3296435 : p = remii(t, m);
1689 : }
1690 : else
1691 261528 : p = modii(p, m);
1692 3558048 : return gerepileuptoint(av, p);
1693 : }
1694 : INLINE GEN
1695 20984059 : Fp_double(GEN x, GEN N)
1696 : {
1697 20984059 : GEN z = shifti(x, 1);
1698 20633368 : return cmpii(z, N) >= 0? subii(z, N): z;
1699 : }
1700 : INLINE GEN
1701 203463517 : Fp_sub(GEN a, GEN b, GEN m)
1702 : {
1703 203463517 : pari_sp av=avma;
1704 203463517 : GEN p = subii(a,b);
1705 201924545 : long s = signe(p);
1706 201924545 : if (!s) return p; /* = gen_0 */
1707 186038295 : if (s > 0)
1708 : {
1709 93289738 : if (cmpii(p, m) < 0) return p; /* general case ! */
1710 1452411 : p = remii(p, m);
1711 : }
1712 : else
1713 : {
1714 92748557 : GEN t = addii(p, m);
1715 94275581 : if (!s) return gc_const(av, gen_0);
1716 94274308 : if (s > 0) return gerepileuptoint(av, t); /* general case ! */
1717 94274308 : p = modii(t, m);
1718 : }
1719 96038924 : return gerepileuptoint(av, p);
1720 : }
1721 : INLINE GEN
1722 28806479 : Fp_neg(GEN b, GEN m)
1723 : {
1724 28806479 : pari_sp av = avma;
1725 28806479 : long s = signe(b);
1726 : GEN p;
1727 28806479 : if (!s) return gen_0;
1728 24374004 : if (s > 0)
1729 : {
1730 23245423 : p = subii(m, b);
1731 23245106 : if (signe(p) >= 0) return p; /* general case ! */
1732 386776 : p = modii(p, m);
1733 : } else
1734 1129178 : p = remii(negi(b), m);
1735 1516160 : return gerepileuptoint(av, p);
1736 : }
1737 :
1738 : INLINE GEN
1739 252299 : Fp_halve(GEN a, GEN p)
1740 : {
1741 252299 : if (mpodd(a)) a = addii(a,p);
1742 252299 : return shifti(a,-1);
1743 : }
1744 :
1745 : /* assume 0 <= u < p and ps2 = p>>1 */
1746 : INLINE GEN
1747 75647408 : Fp_center(GEN u, GEN p, GEN ps2)
1748 75647408 : { return abscmpii(u,ps2)<=0? icopy(u): subii(u,p); }
1749 : /* same without copy */
1750 : INLINE GEN
1751 14165781 : Fp_center_i(GEN u, GEN p, GEN ps2)
1752 14165781 : { return abscmpii(u,ps2)<=0? u: subii(u,p); }
1753 :
1754 : /* x + y*z mod p */
1755 : INLINE GEN
1756 11298187 : Fp_addmul(GEN x, GEN y, GEN z, GEN p)
1757 : {
1758 : pari_sp av;
1759 11298187 : if (!signe(y) || !signe(z)) return Fp_red(x, p);
1760 10951834 : if (!signe(x)) return Fp_mul(z,y, p);
1761 9951854 : av = avma;
1762 9951854 : return gerepileuptoint(av, modii(addii(x, mulii(y,z)), p));
1763 : }
1764 :
1765 : INLINE GEN
1766 200036748 : Fp_mul(GEN a, GEN b, GEN m)
1767 : {
1768 200036748 : pari_sp av=avma;
1769 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1770 200036748 : (void)new_chunk(lg(a)+lg(b)+(lg(m)<<1));
1771 200103642 : p = mulii(a,b);
1772 199929742 : set_avma(av); return modii(p,m);
1773 : }
1774 : INLINE GEN
1775 64070650 : Fp_sqr(GEN a, GEN m)
1776 : {
1777 64070650 : pari_sp av=avma;
1778 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1779 64070650 : (void)new_chunk((lg(a)+lg(m))<<1);
1780 64421725 : p = sqri(a);
1781 62677889 : set_avma(av); return remii(p,m); /*Use remii: p >= 0 */
1782 : }
1783 : INLINE GEN
1784 67786246 : Fp_mulu(GEN a, ulong b, GEN m)
1785 : {
1786 67786246 : long l = lgefint(m);
1787 67786246 : if (l == 3)
1788 : {
1789 46133867 : ulong mm = m[2];
1790 46133867 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1791 : } else {
1792 21652379 : pari_sp av = avma;
1793 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1794 21652379 : (void)new_chunk(lg(a)+1+(l<<1));
1795 21624041 : p = muliu(a,b);
1796 21419429 : set_avma(av); return modii(p,m);
1797 : }
1798 : }
1799 : INLINE GEN
1800 17780 : Fp_muls(GEN a, long b, GEN m)
1801 : {
1802 17780 : long l = lgefint(m);
1803 17780 : if (l == 3)
1804 : {
1805 3578 : ulong mm = m[2];
1806 3578 : if (b < 0)
1807 : {
1808 3578 : ulong t = Fl_mul(umodiu(a, mm), -b, mm);
1809 3578 : return t? utoipos(mm - t): gen_0;
1810 : }
1811 : else
1812 0 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1813 : } else {
1814 14202 : pari_sp av = avma;
1815 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1816 14202 : (void)new_chunk(lg(a)+1+(l<<1));
1817 14202 : p = mulis(a,b);
1818 14202 : set_avma(av); return modii(p,m);
1819 : }
1820 : }
1821 :
1822 : INLINE GEN
1823 23213811 : Fp_inv(GEN a, GEN m)
1824 : {
1825 : GEN res;
1826 23213811 : if (! invmod(a,m,&res)) pari_err_INV("Fp_inv", mkintmod(res,m));
1827 23213527 : return res;
1828 : }
1829 : INLINE GEN
1830 1098655 : Fp_invsafe(GEN a, GEN m)
1831 : {
1832 : GEN res;
1833 1098655 : if (! invmod(a,m,&res)) return NULL;
1834 1098606 : return res;
1835 : }
1836 : INLINE GEN
1837 14988533 : Fp_div(GEN a, GEN b, GEN m)
1838 : {
1839 14988533 : pari_sp av = avma;
1840 : GEN p;
1841 14988533 : if (lgefint(b) == 3)
1842 : {
1843 13843500 : a = Fp_divu(a, b[2], m);
1844 13844946 : if (signe(b) < 0) a = Fp_neg(a, m);
1845 13844955 : return a;
1846 : }
1847 : /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1848 1145033 : (void)new_chunk(lg(a)+(lg(m)<<1));
1849 1145035 : p = mulii(a, Fp_inv(b,m));
1850 1145035 : set_avma(av); return modii(p,m);
1851 : }
1852 : INLINE GEN
1853 15087784 : Fp_divu(GEN x, ulong a, GEN p)
1854 : {
1855 15087784 : pari_sp av = avma;
1856 : ulong b;
1857 15087784 : if (lgefint(p) == 3)
1858 : {
1859 14554457 : ulong pp = p[2], xp = umodiu(x, pp);
1860 14555268 : return xp? utoipos(Fl_div(xp, a % pp, pp)): gen_0;
1861 : }
1862 533327 : x = Fp_red(x, p);
1863 533330 : b = Fl_neg(Fl_div(umodiu(x,a), umodiu(p,a), a), a); /* x + pb = 0 (mod a) */
1864 533330 : return gerepileuptoint(av, diviuexact(addmuliu(x, p, b), a));
1865 : }
1866 :
1867 : INLINE GEN
1868 1095042 : Flx_mulu(GEN x, ulong a, ulong p) { return Flx_Fl_mul(x,a%p,p); }
1869 :
1870 : INLINE GEN
1871 2498398 : get_F2x_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1872 :
1873 : INLINE long
1874 2532923 : get_F2x_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1875 :
1876 : INLINE long
1877 1929009 : get_F2x_degree(GEN T) { return typ(T)==t_VEC? F2x_degree(gel(T,2)): F2x_degree(T); }
1878 :
1879 : INLINE GEN
1880 343 : get_F2xqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1881 :
1882 : INLINE long
1883 375375 : get_F2xqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1884 :
1885 : INLINE long
1886 200851 : get_F2xqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1887 :
1888 : INLINE GEN
1889 25431761 : get_Flx_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1890 :
1891 : INLINE long
1892 67692244 : get_Flx_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1893 :
1894 : INLINE long
1895 82064916 : get_Flx_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1896 :
1897 : INLINE GEN
1898 8033 : get_FlxqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1899 :
1900 : INLINE long
1901 264970 : get_FlxqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1902 :
1903 : INLINE long
1904 318193 : get_FlxqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1905 :
1906 : INLINE GEN
1907 3392226 : get_FpX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1908 :
1909 : INLINE long
1910 7241110 : get_FpX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1911 :
1912 : INLINE long
1913 6005685 : get_FpX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1914 :
1915 : INLINE GEN
1916 146583 : get_FpXQX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1917 :
1918 : INLINE long
1919 51621 : get_FpXQX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1920 :
1921 : INLINE long
1922 3586 : get_FpXQX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1923 :
1924 : /*******************************************************************/
1925 : /* */
1926 : /* ADDMULII / SUBMULII */
1927 : /* */
1928 : /*******************************************************************/
1929 : /* x - y*z */
1930 : INLINE GEN
1931 32772656 : submulii(GEN x, GEN y, GEN z)
1932 : {
1933 32772656 : long lx = lgefint(x), ly, lz;
1934 : pari_sp av;
1935 : GEN t;
1936 32772656 : if (lx == 2) { t = mulii(z,y); togglesign(t); return t; }
1937 30267181 : ly = lgefint(y);
1938 30267181 : if (ly == 2) return icopy(x);
1939 28999749 : lz = lgefint(z);
1940 28999749 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1941 28999749 : t = mulii(z, y);
1942 28999749 : set_avma(av); return subii(x,t);
1943 : }
1944 : /* y*z - x */
1945 : INLINE GEN
1946 3863369 : mulsubii(GEN y, GEN z, GEN x)
1947 : {
1948 3863369 : long lx = lgefint(x), ly, lz;
1949 : pari_sp av;
1950 : GEN t;
1951 3863369 : if (lx == 2) return mulii(z,y);
1952 2438525 : ly = lgefint(y);
1953 2438525 : if (ly == 2) return negi(x);
1954 2160412 : lz = lgefint(z);
1955 2160412 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1956 2160438 : t = mulii(z, y);
1957 2160413 : set_avma(av); return subii(t,x);
1958 : }
1959 :
1960 : /* x - u*y */
1961 : INLINE GEN
1962 7693 : submuliu(GEN x, GEN y, ulong u)
1963 : {
1964 : pari_sp av;
1965 7693 : long ly = lgefint(y);
1966 7693 : if (ly == 2) return icopy(x);
1967 7693 : av = avma;
1968 7693 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1969 7693 : y = mului(u,y);
1970 7693 : set_avma(av); return subii(x, y);
1971 : }
1972 : /* x + u*y */
1973 : INLINE GEN
1974 541398 : addmuliu(GEN x, GEN y, ulong u)
1975 : {
1976 : pari_sp av;
1977 541398 : long ly = lgefint(y);
1978 541398 : if (ly == 2) return icopy(x);
1979 541398 : av = avma;
1980 541398 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1981 541398 : y = mului(u,y);
1982 541399 : set_avma(av); return addii(x, y);
1983 : }
1984 : /* x - u*y */
1985 : INLINE GEN
1986 59546910 : submuliu_inplace(GEN x, GEN y, ulong u)
1987 : {
1988 : pari_sp av;
1989 59546910 : long ly = lgefint(y);
1990 59546910 : if (ly == 2) return x;
1991 38027640 : av = avma;
1992 38027640 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1993 38031987 : y = mului(u,y);
1994 38031776 : set_avma(av); return subii(x, y);
1995 : }
1996 : /* x + u*y */
1997 : INLINE GEN
1998 59003105 : addmuliu_inplace(GEN x, GEN y, ulong u)
1999 : {
2000 : pari_sp av;
2001 59003105 : long ly = lgefint(y);
2002 59003105 : if (ly == 2) return x;
2003 37932990 : av = avma;
2004 37932990 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
2005 37937304 : y = mului(u,y);
2006 37937140 : set_avma(av); return addii(x, y);
2007 : }
2008 : /* ux + vy */
2009 : INLINE GEN
2010 38088321 : lincombii(GEN u, GEN v, GEN x, GEN y)
2011 : {
2012 38088321 : long lx = lgefint(x), ly;
2013 : GEN p1, p2;
2014 : pari_sp av;
2015 38088321 : if (lx == 2) return mulii(v,y);
2016 23961528 : ly = lgefint(y);
2017 23961528 : if (ly == 2) return mulii(u,x);
2018 21276567 : av = avma; (void)new_chunk(lx+ly+lgefint(u)+lgefint(v)); /* HACK */
2019 21279711 : p1 = mulii(u,x);
2020 21278370 : p2 = mulii(v,y);
2021 21278065 : set_avma(av); return addii(p1,p2);
2022 : }
2023 :
2024 : /*******************************************************************/
2025 : /* */
2026 : /* GEN SUBTYPES */
2027 : /* */
2028 : /*******************************************************************/
2029 :
2030 : INLINE int
2031 4809641636 : is_const_t(long t) { return (t < t_POLMOD); }
2032 : INLINE int
2033 6960 : is_extscalar_t(long t) { return (t <= t_POL); }
2034 : INLINE int
2035 9575961 : is_intreal_t(long t) { return (t <= t_REAL); }
2036 : INLINE int
2037 656038357 : is_matvec_t(long t) { return (t >= t_VEC && t <= t_MAT); }
2038 : INLINE int
2039 90582654 : is_noncalc_t(long tx) { return (tx) >= t_LIST; }
2040 : INLINE int
2041 0 : is_qfb_t(long t) { return (t == t_QFB); }
2042 : INLINE int
2043 5017360 : is_rational_t(long t) { return (t == t_INT || t == t_FRAC); }
2044 : INLINE int
2045 62561340 : is_real_t(long t) { return (t == t_INT || t == t_REAL || t == t_FRAC); }
2046 : INLINE int
2047 9119144070 : is_recursive_t(long t) { return lontyp[t]; }
2048 : INLINE int
2049 361254820 : is_scalar_t(long t) { return (t < t_POL); }
2050 : INLINE int
2051 43393233 : is_vec_t(long t) { return (t == t_VEC || t == t_COL); }
2052 :
2053 : INLINE int
2054 68052805 : qfb_is_qfi(GEN q) { return signe(gel(q,4)) < 0; }
2055 :
2056 : /*******************************************************************/
2057 : /* */
2058 : /* TRANSCENDENTAL */
2059 : /* */
2060 : /*******************************************************************/
2061 : INLINE GEN
2062 79927518 : sqrtr(GEN x) {
2063 79927518 : long s = signe(x);
2064 79927518 : if (s == 0) return real_0_bit(expo(x) >> 1);
2065 79894403 : if (s >= 0) return sqrtr_abs(x);
2066 433606 : retmkcomplex(gen_0, sqrtr_abs(x));
2067 : }
2068 : INLINE GEN
2069 0 : cbrtr_abs(GEN x) { return sqrtnr_abs(x, 3); }
2070 : INLINE GEN
2071 0 : cbrtr(GEN x) {
2072 0 : long s = signe(x);
2073 : GEN r;
2074 0 : if (s == 0) return real_0_bit(expo(x) / 3);
2075 0 : r = cbrtr_abs(x);
2076 0 : if (s < 0) togglesign(r);
2077 0 : return r;
2078 : }
2079 : INLINE GEN
2080 2794100 : sqrtnr(GEN x, long n) {
2081 2794100 : long s = signe(x);
2082 : GEN r;
2083 2794100 : if (s == 0) return real_0_bit(expo(x) / n);
2084 2794100 : r = sqrtnr_abs(x, n);
2085 2794113 : if (s < 0) pari_err_IMPL("sqrtnr for x < 0");
2086 2794112 : return r;
2087 : }
2088 : INLINE long
2089 752242 : logint(GEN B, GEN y) { return logintall(B,y,NULL); }
2090 : INLINE ulong
2091 1723379 : ulogint(ulong B, ulong y)
2092 : {
2093 : ulong r;
2094 : long e;
2095 1723379 : if (y == 2) return expu(B);
2096 1675393 : r = y;
2097 5063875 : for (e=1;; e++)
2098 : { /* here, r = y^e, r2 = y^(e-1) */
2099 5063875 : if (r >= B) return r == B? e: e-1;
2100 3389992 : r = umuluu_or_0(y, r);
2101 3390023 : if (!r) return e;
2102 : }
2103 : }
2104 :
2105 : /*******************************************************************/
2106 : /* */
2107 : /* MISCELLANEOUS */
2108 : /* */
2109 : /*******************************************************************/
2110 9575840 : INLINE int ismpzero(GEN x) { return is_intreal_t(typ(x)) && !signe(x); }
2111 2797330486 : INLINE int isintzero(GEN x) { return typ(x) == t_INT && !signe(x); }
2112 17007588 : INLINE int isint1(GEN x) { return typ(x)==t_INT && equali1(x); }
2113 5702656 : INLINE int isintm1(GEN x){ return typ(x)==t_INT && equalim1(x);}
2114 1212968663 : INLINE int equali1(GEN n)
2115 1212968663 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(1)) && n[2] == 1; }
2116 139008323 : INLINE int equalim1(GEN n)
2117 139008323 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(-1)) && n[2] == 1; }
2118 : /* works only for POSITIVE integers */
2119 2189876918 : INLINE int is_pm1(GEN n)
2120 2189876918 : { return lgefint(n) == 3 && n[2] == 1; }
2121 557170077 : INLINE int is_bigint(GEN n)
2122 557170077 : { long l = lgefint(n); return l > 3 || (l == 3 && (n[2] & HIGHBIT)); }
2123 :
2124 2026313299 : INLINE int odd(long x) { return x & 1; }
2125 116946405 : INLINE int both_odd(long x, long y) { return x & y & 1; }
2126 :
2127 : INLINE int
2128 7965851785 : isonstack(GEN x)
2129 7965851785 : { return ((pari_sp)x >= pari_mainstack->bot
2130 7965851785 : && (pari_sp)x < pari_mainstack->top); }
2131 :
2132 : /* assume x != 0 and x t_REAL, return an approximation to log2(|x|) */
2133 : INLINE double
2134 92936758 : dbllog2r(GEN x)
2135 92936758 : { return log2((double)(ulong)x[2]) + (double)(expo(x) - (BITS_IN_LONG-1)); }
2136 :
2137 : INLINE GEN
2138 2514735 : mul_content(GEN cx, GEN cy)
2139 : {
2140 2514735 : if (!cx) return cy;
2141 520763 : if (!cy) return cx;
2142 332964 : return gmul(cx,cy);
2143 : }
2144 : INLINE GEN
2145 0 : inv_content(GEN c) { return c? ginv(c): NULL; }
2146 : INLINE GEN
2147 57990 : div_content(GEN cx, GEN cy)
2148 : {
2149 57990 : if (!cy) return cx;
2150 56856 : if (!cx) return ginv(cy);
2151 25795 : return gdiv(cx,cy);
2152 : }
2153 : INLINE GEN
2154 10300180 : mul_denom(GEN dx, GEN dy)
2155 : {
2156 10300180 : if (!dx) return dy;
2157 1836212 : if (!dy) return dx;
2158 1368371 : return mulii(dx,dy);
2159 : }
2160 :
2161 : /* POLYNOMIALS */
2162 : INLINE GEN
2163 1439828 : constant_coeff(GEN x) { return signe(x)? gel(x,2): gen_0; }
2164 : INLINE GEN
2165 169109962 : leading_coeff(GEN x) { return lg(x) == 2? gen_0: gel(x,lg(x)-1); }
2166 : INLINE ulong
2167 968933 : Flx_lead(GEN x) { return lg(x) == 2? 0: x[lg(x)-1]; }
2168 : INLINE ulong
2169 330388 : Flx_constant(GEN x) { return lg(x) == 2? 0: x[2]; }
2170 : INLINE long
2171 5342975441 : degpol(GEN x) { return lg(x)-3; }
2172 : INLINE long
2173 2626910406 : lgpol(GEN x) { return lg(x)-2; }
2174 : INLINE long
2175 341566811 : lgcols(GEN x) { return lg(gel(x,1)); }
2176 : INLINE long
2177 153813825 : nbrows(GEN x) { return lg(gel(x,1))-1; }
2178 : INLINE GEN
2179 0 : truecoef(GEN x, long n) { return polcoef(x,n,-1); }
2180 :
2181 : INLINE GEN
2182 2128418 : ZXQ_mul(GEN y, GEN x, GEN T) { return ZX_rem(ZX_mul(y, x), T); }
2183 : INLINE GEN
2184 951138 : ZXQ_sqr(GEN x, GEN T) { return ZX_rem(ZX_sqr(x), T); }
2185 :
2186 : INLINE GEN
2187 103474401 : RgX_copy(GEN x)
2188 376975764 : { pari_APPLY_pol_normalized(gcopy(gel(x,i))); }
2189 : /* have to use ulong to avoid silly warnings from gcc "assuming signed
2190 : * overflow does not occur" */
2191 : INLINE GEN
2192 2551365 : RgX_coeff(GEN x, long n)
2193 : {
2194 2551365 : ulong l = lg(x);
2195 2551365 : return (n < 0 || ((ulong)n+3) > l)? gen_0: gel(x,n+2);
2196 : }
2197 : INLINE GEN
2198 349345 : RgX_renormalize(GEN x) { return RgX_renormalize_lg(x, lg(x)); }
2199 : INLINE GEN
2200 7053519 : RgX_div(GEN x, GEN y) { return RgX_divrem(x,y,NULL); }
2201 : INLINE GEN
2202 1904 : RgXQX_div(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,NULL); }
2203 : INLINE GEN
2204 125497 : RgXQX_rem(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,ONLY_REM); }
2205 : INLINE GEN
2206 5440717 : FpX_div(GEN x, GEN y, GEN p) { return FpX_divrem(x,y,p, NULL); }
2207 : INLINE GEN
2208 1996024 : Flx_div(GEN x, GEN y, ulong p) { return Flx_divrem(x,y,p, NULL); }
2209 : INLINE GEN
2210 21460590 : Flx_div_pre(GEN x, GEN y, ulong p, ulong pi)
2211 21460590 : { return Flx_divrem_pre(x,y,p,pi, NULL); }
2212 : INLINE GEN
2213 1566236 : F2x_div(GEN x, GEN y) { return F2x_divrem(x,y, NULL); }
2214 : INLINE GEN
2215 0 : FpV_FpC_mul(GEN x, GEN y, GEN p) { return FpV_dotproduct(x,y,p); }
2216 : INLINE GEN
2217 101807655 : pol0_Flx(long sv) { return mkvecsmall(sv); }
2218 : INLINE GEN
2219 54626886 : pol1_Flx(long sv) { return mkvecsmall2(sv, 1); }
2220 : INLINE GEN
2221 37668393 : polx_Flx(long sv) { return mkvecsmall3(sv, 0, 1); }
2222 : INLINE GEN
2223 0 : zero_zx(long sv) { return zero_Flx(sv); }
2224 : INLINE GEN
2225 0 : polx_zx(long sv) { return polx_Flx(sv); }
2226 : INLINE GEN
2227 0 : zx_shift(GEN x, long n) { return Flx_shift(x,n); }
2228 : INLINE GEN
2229 14049 : zx_renormalize(GEN x, long l) { return Flx_renormalize(x,l); }
2230 : INLINE GEN
2231 1350 : zero_F2x(long sv) { return zero_Flx(sv); }
2232 : INLINE GEN
2233 13233905 : pol0_F2x(long sv) { return pol0_Flx(sv); }
2234 : INLINE GEN
2235 3953483 : pol1_F2x(long sv) { return pol1_Flx(sv); }
2236 : INLINE GEN
2237 1076080 : polx_F2x(long sv) { return mkvecsmall2(sv, 2); }
2238 : INLINE int
2239 2872207 : F2x_equal1(GEN x) { return Flx_equal1(x); }
2240 : INLINE int
2241 4653204 : F2x_equal(GEN V, GEN W) { return Flx_equal(V,W); }
2242 : INLINE GEN
2243 60402141 : F2x_copy(GEN x) { return leafcopy(x); }
2244 : INLINE GEN
2245 4487 : F2v_copy(GEN x) { return leafcopy(x); }
2246 : INLINE GEN
2247 2545781 : Flv_copy(GEN x) { return leafcopy(x); }
2248 : INLINE GEN
2249 172268008 : Flx_copy(GEN x) { return leafcopy(x); }
2250 : INLINE GEN
2251 4370368 : vecsmall_copy(GEN x) { return leafcopy(x); }
2252 : INLINE int
2253 8319425 : Flx_equal1(GEN x) { return degpol(x)==0 && x[2] == 1; }
2254 : INLINE int
2255 12633 : ZX_equal1(GEN x) { return degpol(x)==0 && equali1(gel(x,2)); }
2256 : INLINE int
2257 7268099 : ZX_is_monic(GEN x) { return equali1(leading_coeff(x)); }
2258 :
2259 : INLINE GEN
2260 154324608 : ZX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2261 : INLINE GEN
2262 145095638 : FpX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2263 : INLINE GEN
2264 849899 : FpXX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2265 : INLINE GEN
2266 4695314 : FpXQX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2267 : INLINE GEN
2268 115101126 : F2x_renormalize(GEN x, long lx) { return Flx_renormalize(x,lx); }
2269 :
2270 : INLINE GEN
2271 0 : F2xX_shift(GEN a, long n, long vs) { return FlxX_shift(a, n, vs); }
2272 :
2273 : INLINE GEN
2274 37865 : F2v_to_F2x(GEN x, long sv) {
2275 37865 : GEN y = leafcopy(x);
2276 37865 : y[1] = sv; F2x_renormalize(y, lg(y)); return y;
2277 : }
2278 :
2279 : INLINE long
2280 385 : sturm(GEN x) { return sturmpart(x, NULL, NULL); }
2281 :
2282 : INLINE long
2283 5796 : gval(GEN x, long v)
2284 5796 : { pari_sp av = avma; return gc_long(av, gvaluation(x, pol_x(v))); }
2285 :
2286 : INLINE void
2287 480509 : RgX_shift_inplace_init(long v)
2288 480509 : { if (v) (void)cgetg(v, t_VECSMALL); }
2289 : /* shift polynomial in place. assume v free cells have been left before x */
2290 : INLINE GEN
2291 480509 : RgX_shift_inplace(GEN x, long v)
2292 : {
2293 : long i, lx;
2294 : GEN z;
2295 480509 : if (!v) return x;
2296 253169 : lx = lg(x);
2297 253169 : if (lx == 2) return x;
2298 253169 : z = x + lx;
2299 : /* stackdummy's from normalizepol */
2300 253169 : while (lg(z) != v) z += lg(z);
2301 253169 : z += v;
2302 4654514 : for (i = lx-1; i >= 2; i--) gel(--z,0) = gel(x,i);
2303 675895 : for (i = 0; i < v; i++) gel(--z,0) = gen_0;
2304 253169 : z -= 2;
2305 253169 : z[1] = x[1];
2306 253169 : z[0] = evaltyp(t_POL) | evallg(lx+v);
2307 253169 : stackdummy((pari_sp)z, (pari_sp)x); return z;
2308 : }
2309 :
2310 :
2311 : /* LINEAR ALGEBRA */
2312 : INLINE GEN
2313 502659 : zv_to_ZV(GEN x) { return vecsmall_to_vec(x); }
2314 : INLINE GEN
2315 7747834 : zc_to_ZC(GEN x) { return vecsmall_to_col(x); }
2316 : INLINE GEN
2317 3190952 : ZV_to_zv(GEN x) { return vec_to_vecsmall(x); }
2318 : INLINE GEN
2319 0 : zx_to_zv(GEN x, long N) { return Flx_to_Flv(x,N); }
2320 : INLINE GEN
2321 104146 : zv_to_zx(GEN x, long sv) { return Flv_to_Flx(x,sv); }
2322 : INLINE GEN
2323 0 : zm_to_zxV(GEN x, long sv) { return Flm_to_FlxV(x,sv); }
2324 : INLINE GEN
2325 0 : zero_zm(long x, long y) { return zero_Flm(x,y); }
2326 : INLINE GEN
2327 36184078 : zero_zv(long x) { return zero_Flv(x); }
2328 : INLINE GEN
2329 266 : zm_transpose(GEN x) { return Flm_transpose(x); }
2330 : INLINE GEN
2331 0 : zm_copy(GEN x) { return Flm_copy(x); }
2332 : INLINE GEN
2333 2183260 : zv_copy(GEN x) { return Flv_copy(x); }
2334 : INLINE GEN
2335 0 : zm_row(GEN x, long i) { return Flm_row(x,i); }
2336 :
2337 : INLINE GEN
2338 10692183 : ZC_hnfrem(GEN x, GEN y) { return ZC_hnfdivrem(x,y,NULL); }
2339 : INLINE GEN
2340 326812 : ZM_hnfrem(GEN x, GEN y) { return ZM_hnfdivrem(x,y,NULL); }
2341 : INLINE GEN
2342 6937193 : ZM_lll(GEN x, double D, long f) { return ZM_lll_norms(x,D,f,NULL); }
2343 : INLINE void
2344 9402895 : RgM_dimensions(GEN x, long *m, long *n) { *n = lg(x)-1; *m = *n? nbrows(x): 0; }
2345 : INLINE GEN
2346 21451183 : RgM_shallowcopy(GEN x)
2347 93405494 : { pari_APPLY_same(leafcopy(gel(x,i))); }
2348 : INLINE GEN
2349 198567 : F2m_copy(GEN x) { return RgM_shallowcopy(x); }
2350 :
2351 : INLINE GEN
2352 0 : F3m_copy(GEN x) { return RgM_shallowcopy(x); }
2353 :
2354 : INLINE GEN
2355 6280935 : Flm_copy(GEN x) { return RgM_shallowcopy(x); }
2356 :
2357 : /* divisibility: return 1 if y[i] | x[i] for all i, 0 otherwise. Assume
2358 : * x,y are ZV of the same length */
2359 : INLINE int
2360 23485 : ZV_dvd(GEN x, GEN y)
2361 : {
2362 23485 : long i, l = lg(x);
2363 37856 : for (i=1; i < l; i++)
2364 30464 : if ( ! dvdii( gel(x,i), gel(y,i) ) ) return 0;
2365 7392 : return 1;
2366 : }
2367 : INLINE GEN
2368 539185 : ZM_ZV_mod(GEN x, GEN y)
2369 1538061 : { pari_APPLY_same(ZV_ZV_mod(gel(x,i), y)) }
2370 : INLINE GEN
2371 7323197 : ZV_ZV_mod(GEN x, GEN y)
2372 18922070 : { pari_APPLY_same(modii(gel(x,i), gel(y,i))) }
2373 : INLINE GEN
2374 0 : vecmodii(GEN x, GEN y) { return ZV_ZV_mod(x,y); }
2375 : INLINE GEN
2376 174881 : vecmoduu(GEN x, GEN y) { pari_APPLY_ulong(((ulong*)x)[i] % ((ulong*)y)[i]) }
2377 :
2378 : /* Fq */
2379 : INLINE GEN
2380 3106123 : Fq_red(GEN x, GEN T, GEN p)
2381 3106123 : { return typ(x)==t_INT? Fp_red(x,p): FpXQ_red(x,T,p); }
2382 : INLINE GEN
2383 73792 : Fq_to_FpXQ(GEN x, GEN T, GEN p /*unused*/)
2384 : {
2385 : (void) p;
2386 73792 : return typ(x)==t_INT ? scalarpol(x, get_FpX_var(T)): x;
2387 : }
2388 : INLINE GEN
2389 756 : Rg_to_Fq(GEN x, GEN T, GEN p) { return T? Rg_to_FpXQ(x,T,p): Rg_to_Fp(x,p); }
2390 :
2391 : INLINE GEN
2392 14602 : gener_Fq_local(GEN T, GEN p, GEN L)
2393 0 : { return T? gener_FpXQ_local(T,p, L)
2394 14602 : : pgener_Fp_local(p, L); }
2395 :
2396 : INLINE GEN
2397 0 : random_Fq(GEN T, GEN p)
2398 0 : { return T ? random_FpX(get_FpX_degree(T), get_FpX_var(T), p): randomi(p); }
2399 :
2400 : /* FpXQX */
2401 : INLINE GEN
2402 4526 : FpXQX_div(GEN x, GEN y, GEN T, GEN p) { return FpXQX_divrem(x, y, T, p, NULL); }
2403 : INLINE GEN
2404 0 : FlxqX_div(GEN x, GEN y, GEN T, ulong p) { return FlxqX_divrem(x, y, T, p, NULL); }
2405 : INLINE GEN
2406 165383 : FlxqX_div_pre(GEN x, GEN y, GEN T, ulong p, ulong pi) { return FlxqX_divrem_pre(x, y, T, p, pi, NULL); }
2407 : INLINE GEN
2408 33173 : F2xqX_div(GEN x, GEN y, GEN T) { return F2xqX_divrem(x, y, T, NULL); }
2409 :
2410 : INLINE GEN
2411 20587 : FpXY_Fq_evaly(GEN Q, GEN y, GEN T, GEN p, long vx)
2412 20587 : { return T ? FpXY_FpXQ_evaly(Q, y, T, p, vx): FpXY_evaly(Q, y, p, vx); }
2413 :
2414 : /* FqX */
2415 : INLINE GEN
2416 25354 : FqX_red(GEN z, GEN T, GEN p) { return T? FpXQX_red(z, T, p): FpX_red(z, p); }
2417 : INLINE GEN
2418 127694 : FqX_add(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2419 : INLINE GEN
2420 24956 : FqX_neg(GEN x,GEN T,GEN p) { return T? FpXX_neg(x,p): FpX_neg(x,p); }
2421 : INLINE GEN
2422 68607 : FqX_sub(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2423 : INLINE GEN
2424 568918 : FqX_Fp_mul(GEN P, GEN u, GEN T, GEN p)
2425 568918 : { return T? FpXX_Fp_mul(P, u, p): FpX_Fp_mul(P, u, p); }
2426 : INLINE GEN
2427 427291 : FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
2428 427291 : { return typ(U)==t_INT ? FqX_Fp_mul(P, U, T, p): FpXQX_FpXQ_mul(P, U, T, p); }
2429 : INLINE GEN
2430 367212 : FqX_mul(GEN x, GEN y, GEN T, GEN p)
2431 367212 : { return T? FpXQX_mul(x, y, T, p): FpX_mul(x, y, p); }
2432 : INLINE GEN
2433 21942 : FqX_mulu(GEN x, ulong y, GEN T, GEN p)
2434 21942 : { return T? FpXX_mulu(x, y, p): FpX_mulu(x, y, p); }
2435 : INLINE GEN
2436 71855 : FqX_sqr(GEN x, GEN T, GEN p)
2437 71855 : { return T? FpXQX_sqr(x, T, p): FpX_sqr(x, p); }
2438 : INLINE GEN
2439 1295 : FqX_powu(GEN x, ulong n, GEN T, GEN p)
2440 1295 : { return T? FpXQX_powu(x, n, T, p): FpX_powu(x, n, p); }
2441 : INLINE GEN
2442 19411 : FqX_halve(GEN x, GEN T, GEN p)
2443 19411 : { return T? FpXX_halve(x, p): FpX_halve(x, p); }
2444 : INLINE GEN
2445 38414 : FqX_div(GEN x, GEN y, GEN T, GEN p)
2446 38414 : { return T? FpXQX_divrem(x,y,T,p,NULL): FpX_divrem(x,y,p,NULL); }
2447 : INLINE GEN
2448 6090 : FqX_get_red(GEN S, GEN T, GEN p)
2449 6090 : { return T? FpXQX_get_red(S,T,p): FpX_get_red(S,p); }
2450 : INLINE GEN
2451 37743 : FqX_rem(GEN x, GEN y, GEN T, GEN p)
2452 37743 : { return T? FpXQX_rem(x,y,T,p): FpX_rem(x,y,p); }
2453 : INLINE GEN
2454 0 : FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
2455 0 : { return T? FpXQX_divrem(x,y,T,p,z): FpX_divrem(x,y,p,z); }
2456 : INLINE GEN
2457 71939 : FqX_div_by_X_x(GEN x, GEN y, GEN T, GEN p, GEN *z)
2458 71939 : { return T? FpXQX_div_by_X_x(x,y,T,p,z): FpX_div_by_X_x(x,y,p,z); }
2459 : INLINE GEN
2460 0 : FqX_halfgcd(GEN P,GEN Q,GEN T,GEN p)
2461 0 : {return T? FpXQX_halfgcd(P,Q,T,p): FpX_halfgcd(P,Q,p);}
2462 : INLINE GEN
2463 691866 : FqX_gcd(GEN P,GEN Q,GEN T,GEN p)
2464 691866 : {return T? FpXQX_gcd(P,Q,T,p): FpX_gcd(P,Q,p);}
2465 : INLINE GEN
2466 443270 : FqX_extgcd(GEN P,GEN Q,GEN T,GEN p, GEN *U, GEN *V)
2467 443270 : { return T? FpXQX_extgcd(P,Q,T,p,U,V): FpX_extgcd(P,Q,p,U,V); }
2468 : INLINE GEN
2469 4032 : FqX_normalize(GEN z, GEN T, GEN p)
2470 4032 : { return T? FpXQX_normalize(z, T, p): FpX_normalize(z, p); }
2471 : INLINE GEN
2472 723863 : FqX_deriv(GEN f, GEN T, GEN p) { return T? FpXX_deriv(f, p): FpX_deriv(f, p); }
2473 : INLINE GEN
2474 0 : FqX_integ(GEN f, GEN T, GEN p) { return T? FpXX_integ(f, p): FpX_integ(f, p); }
2475 : INLINE GEN
2476 140974 : FqX_factor(GEN f, GEN T, GEN p)
2477 140974 : { return T?FpXQX_factor(f, T, p): FpX_factor(f, p); }
2478 : INLINE GEN
2479 7 : FqX_factor_squarefree(GEN f, GEN T, GEN p)
2480 7 : { return T ? FpXQX_factor_squarefree(f, T, p): FpX_factor_squarefree(f, p); }
2481 : INLINE GEN
2482 7 : FqX_ddf(GEN f, GEN T, GEN p)
2483 7 : { return T ? FpXQX_ddf(f, T, p): FpX_ddf(f, p); }
2484 : INLINE GEN
2485 47786 : FqX_degfact(GEN f, GEN T, GEN p)
2486 47786 : { return T?FpXQX_degfact(f, T, p): FpX_degfact(f, p); }
2487 : INLINE GEN
2488 7273 : FqX_roots(GEN f, GEN T, GEN p)
2489 7273 : { return T?FpXQX_roots(f, T, p): FpX_roots(f, p); }
2490 : INLINE GEN
2491 175 : FqX_to_mod(GEN f, GEN T, GEN p)
2492 175 : { return T?FpXQX_to_mod(f, T, p): FpX_to_mod(f, p); }
2493 :
2494 : /*FqXQ*/
2495 : INLINE GEN
2496 0 : FqXQ_add(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2497 0 : { (void)S; return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2498 : INLINE GEN
2499 0 : FqXQ_sub(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2500 0 : { (void)S; return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2501 : INLINE GEN
2502 0 : FqXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
2503 0 : { return T? FpXQXQ_div(x,y,S,T,p): FpXQ_div(x,y,S,p); }
2504 : INLINE GEN
2505 0 : FqXQ_inv(GEN x, GEN S, GEN T, GEN p)
2506 0 : { return T? FpXQXQ_inv(x,S,T,p): FpXQ_inv(x,S,p); }
2507 : INLINE GEN
2508 0 : FqXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
2509 0 : { return T? FpXQXQ_invsafe(x,S,T,p): FpXQ_inv(x,S,p); }
2510 : INLINE GEN
2511 22766 : FqXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
2512 22766 : { return T? FpXQXQ_mul(x,y,S,T,p): FpXQ_mul(x,y,S,p); }
2513 : INLINE GEN
2514 0 : FqXQ_sqr(GEN x, GEN S, GEN T, GEN p)
2515 0 : { return T? FpXQXQ_sqr(x,S,T,p): FpXQ_sqr(x,S,p); }
2516 : INLINE GEN
2517 0 : FqXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
2518 0 : { return T? FpXQXQ_pow(x,n,S,T,p): FpXQ_pow(x,n,S,p); }
2519 :
2520 : /*FqXn*/
2521 : INLINE GEN
2522 6590 : FqXn_expint(GEN x, long n, GEN T, GEN p)
2523 6590 : { return T? FpXQXn_expint(x,n,T,p): FpXn_expint(x,n,p); }
2524 : INLINE GEN
2525 0 : FqXn_exp(GEN x, long n, GEN T, GEN p)
2526 0 : { return T? FpXQXn_exp(x,n,T,p): FpXn_exp(x,n,p); }
2527 : INLINE GEN
2528 7126 : FqXn_inv(GEN x, long n, GEN T, GEN p)
2529 7126 : { return T? FpXQXn_inv(x,n,T,p): FpXn_inv(x,n,p); }
2530 : INLINE GEN
2531 263403 : FqXn_mul(GEN x, GEN y, long n, GEN T, GEN p)
2532 263403 : { return T? FpXQXn_mul(x, y, n, T, p): FpXn_mul(x, y, n, p); }
2533 : INLINE GEN
2534 0 : FqXn_sqr(GEN x, long n, GEN T, GEN p)
2535 0 : { return T? FpXQXn_sqr(x,n,T,p): FpXn_sqr(x,n,p); }
2536 :
2537 : /*FpXQ*/
2538 : INLINE GEN
2539 0 : FpXQ_add(GEN x,GEN y,GEN T/*unused*/,GEN p)
2540 0 : { (void)T; return FpX_add(x,y,p); }
2541 : INLINE GEN
2542 0 : FpXQ_sub(GEN x,GEN y,GEN T/*unused*/,GEN p)
2543 0 : { (void)T; return FpX_sub(x,y,p); }
2544 :
2545 : /*Flxq*/
2546 : INLINE GEN
2547 0 : Flxq_add(GEN x,GEN y,GEN T/*unused*/,ulong p)
2548 0 : { (void)T; return Flx_add(x,y,p); }
2549 : INLINE GEN
2550 0 : Flxq_sub(GEN x,GEN y,GEN T/*unused*/,ulong p)
2551 0 : { (void)T; return Flx_sub(x,y,p); }
2552 :
2553 : /* F2x */
2554 :
2555 : INLINE ulong
2556 667574011 : F2x_coeff(GEN x,long v)
2557 : {
2558 667574011 : ulong u=(ulong)x[2+divsBIL(v)];
2559 667573691 : return (u>>remsBIL(v))&1UL;
2560 : }
2561 :
2562 : INLINE void
2563 12280110 : F2x_clear(GEN x,long v)
2564 : {
2565 12280110 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2566 12280065 : *u&=~(1UL<<remsBIL(v));
2567 12280042 : }
2568 :
2569 : INLINE void
2570 124634739 : F2x_set(GEN x,long v)
2571 : {
2572 124634739 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2573 124630704 : *u|=1UL<<remsBIL(v);
2574 124631671 : }
2575 :
2576 : INLINE void
2577 1553944 : F2x_flip(GEN x,long v)
2578 : {
2579 1553944 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2580 1553944 : *u^=1UL<<remsBIL(v);
2581 1553944 : }
2582 :
2583 : /* F2v */
2584 :
2585 : INLINE ulong
2586 661059730 : F2v_coeff(GEN x,long v) { return F2x_coeff(x,v-1); }
2587 :
2588 : INLINE void
2589 12280123 : F2v_clear(GEN x,long v) { F2x_clear(x,v-1); }
2590 :
2591 : INLINE void
2592 101346857 : F2v_set(GEN x,long v) { F2x_set(x,v-1); }
2593 :
2594 : INLINE void
2595 1553944 : F2v_flip(GEN x,long v) { F2x_flip(x,v-1); }
2596 :
2597 : /* F2m */
2598 :
2599 : INLINE ulong
2600 8033376 : F2m_coeff(GEN x, long a, long b) { return F2v_coeff(gel(x,b), a); }
2601 :
2602 : INLINE void
2603 0 : F2m_clear(GEN x, long a, long b) { F2v_clear(gel(x,b), a); }
2604 :
2605 : INLINE void
2606 798 : F2m_set(GEN x, long a, long b) { F2v_set(gel(x,b), a); }
2607 :
2608 : INLINE void
2609 1553944 : F2m_flip(GEN x, long a, long b) { F2v_flip(gel(x,b), a); }
2610 :
2611 : /* F3m */
2612 :
2613 : INLINE ulong
2614 3240628 : F3m_coeff(GEN x, long a, long b) { return F3v_coeff(gel(x,b), a); }
2615 :
2616 : INLINE void
2617 0 : F3m_set(GEN x, long a, long b, ulong c) { F3v_set(gel(x,b), a, c); }
2618 :
2619 : /* ARITHMETIC */
2620 : INLINE GEN
2621 3885 : matpascal(long n) { return matqpascal(n, NULL); }
2622 : INLINE long
2623 458607 : Z_issquare(GEN x) { return Z_issquareall(x, NULL); }
2624 : INLINE long
2625 98 : Z_ispower(GEN x, ulong k) { return Z_ispowerall(x, k, NULL); }
2626 : INLINE GEN
2627 6591387 : sqrti(GEN x) { return sqrtremi(x,NULL); }
2628 : INLINE GEN
2629 123138367 : gaddgs(GEN y, long s) { return gaddsg(s,y); }
2630 : INLINE int
2631 780379 : gcmpgs(GEN y, long s) { return -gcmpsg(s,y); }
2632 : INLINE int
2633 29176 : gequalgs(GEN y, long s) { return gequalsg(s,y); }
2634 : INLINE GEN
2635 0 : gmaxsg(long s, GEN y) { return gmaxgs(y,s); }
2636 : INLINE GEN
2637 0 : gminsg(long s, GEN y) { return gmings(y,s); }
2638 : INLINE GEN
2639 22347687 : gmulgs(GEN y, long s) { return gmulsg(s,y); }
2640 : INLINE GEN
2641 124174659 : gmulgu(GEN y, ulong s) { return gmulug(s,y); }
2642 : INLINE GEN
2643 1692556 : gsubgs(GEN y, long s) { return gaddgs(y, -s); }
2644 : INLINE GEN
2645 528371 : gdivsg(long s, GEN y) { return gdiv(stoi(s), y); }
2646 :
2647 : INLINE GEN
2648 13509971 : gmax_shallow(GEN x, GEN y) { return gcmp(x,y)<0? y: x; }
2649 : INLINE GEN
2650 876179 : gmin_shallow(GEN x, GEN y) { return gcmp(x,y)<0? x: y; }
2651 :
2652 : /* x t_COMPLEX */
2653 : INLINE GEN
2654 90802305 : cxnorm(GEN x) { return gadd(gsqr(gel(x,1)), gsqr(gel(x,2))); }
2655 : /* q t_QUAD */
2656 : INLINE GEN
2657 69860 : quadnorm(GEN q)
2658 : {
2659 69860 : GEN X = gel(q,1), b = gel(X,3), c = gel(X,2);
2660 69860 : GEN z, u = gel(q,3), v = gel(q,2);
2661 69860 : if (typ(u) == t_INT && typ(v) == t_INT) /* generic case */
2662 : {
2663 69671 : z = signe(b)? mulii(v, addii(u,v)): sqri(v);
2664 69671 : return addii(z, mulii(c, sqri(u)));
2665 : }
2666 : else
2667 : {
2668 189 : z = signe(b)? gmul(v, gadd(u,v)): gsqr(v);
2669 189 : return gadd(z, gmul(c, gsqr(u)));
2670 : }
2671 : }
2672 : /* x a t_QUAD, return the attached discriminant */
2673 : INLINE GEN
2674 1078 : quad_disc(GEN x)
2675 : {
2676 1078 : GEN Q = gel(x,1), b = gel(Q,3), c = gel(Q,2), c4 = shifti(c,2);
2677 1078 : if (is_pm1(b)) return subsi(1, c4);
2678 154 : togglesign_safe(&c4); return c4;
2679 : }
2680 : INLINE GEN
2681 4850203 : qfb_disc3(GEN x, GEN y, GEN z) { return subii(sqri(y), shifti(mulii(x,z),2)); }
2682 : INLINE GEN
2683 18474970 : qfb_disc(GEN x) { return gel(x,4); }
2684 :
2685 : INLINE GEN
2686 4135849 : sqrfrac(GEN x)
2687 : {
2688 4135849 : GEN z = cgetg(3,t_FRAC);
2689 4135847 : gel(z,1) = sqri(gel(x,1));
2690 4135824 : gel(z,2) = sqri(gel(x,2)); return z;
2691 : }
2692 :
2693 : INLINE void
2694 16754122 : normalize_frac(GEN z) {
2695 16754122 : if (signe(gel(z,2)) < 0) { togglesign(gel(z,1)); setabssign(gel(z,2)); }
2696 16754122 : }
2697 :
2698 : INLINE GEN
2699 42913879 : powii(GEN x, GEN n)
2700 : {
2701 42913879 : long ln = lgefint(n);
2702 42913879 : if (ln == 3) {
2703 : GEN z;
2704 42890931 : if (signe(n) > 0) return powiu(x, n[2]);
2705 74810 : z = cgetg(3, t_FRAC);
2706 74825 : gel(z,1) = gen_1;
2707 74825 : gel(z,2) = powiu(x, n[2]);
2708 74823 : return z;
2709 : }
2710 22948 : if (ln == 2) return gen_1; /* rare */
2711 : /* should never happen */
2712 0 : return powgi(x, n); /* overflow unless x = 0, 1, -1 */
2713 : }
2714 : INLINE GEN
2715 1561 : powIs(long n) {
2716 1561 : switch(n & 3)
2717 : {
2718 63 : case 1: return mkcomplex(gen_0,gen_1);
2719 385 : case 2: return gen_m1;
2720 707 : case 3: return mkcomplex(gen_0,gen_m1);
2721 : }
2722 406 : return gen_1;
2723 : }
2724 :
2725 : /*******************************************************************/
2726 : /* */
2727 : /* ASSIGNMENTS */
2728 : /* */
2729 : /*******************************************************************/
2730 0 : INLINE void mpexpz(GEN x, GEN z)
2731 0 : { pari_sp av = avma; gaffect(mpexp(x), z); set_avma(av); }
2732 0 : INLINE void mplogz(GEN x, GEN z)
2733 0 : { pari_sp av = avma; gaffect(mplog(x), z); set_avma(av); }
2734 0 : INLINE void mpcosz(GEN x, GEN z)
2735 0 : { pari_sp av = avma; gaffect(mpcos(x), z); set_avma(av); }
2736 0 : INLINE void mpsinz(GEN x, GEN z)
2737 0 : { pari_sp av = avma; gaffect(mpsin(x), z); set_avma(av); }
2738 0 : INLINE void gnegz(GEN x, GEN z)
2739 0 : { pari_sp av = avma; gaffect(gneg(x), z); set_avma(av); }
2740 0 : INLINE void gabsz(GEN x, long prec, GEN z)
2741 0 : { pari_sp av = avma; gaffect(gabs(x,prec), z); set_avma(av); }
2742 0 : INLINE void gaddz(GEN x, GEN y, GEN z)
2743 0 : { pari_sp av = avma; gaffect(gadd(x,y), z); set_avma(av); }
2744 0 : INLINE void gsubz(GEN x, GEN y, GEN z)
2745 0 : { pari_sp av = avma; gaffect(gsub(x,y), z); set_avma(av); }
2746 0 : INLINE void gmulz(GEN x, GEN y, GEN z)
2747 0 : { pari_sp av = avma; gaffect(gmul(x,y), z); set_avma(av); }
2748 0 : INLINE void gdivz(GEN x, GEN y, GEN z)
2749 0 : { pari_sp av = avma; gaffect(gdiv(x,y), z); set_avma(av); }
2750 0 : INLINE void gdiventz(GEN x, GEN y, GEN z)
2751 0 : { pari_sp av = avma; gaffect(gdivent(x,y), z); set_avma(av); }
2752 0 : INLINE void gmodz(GEN x, GEN y, GEN z)
2753 0 : { pari_sp av = avma; gaffect(gmod(x,y), z); set_avma(av); }
2754 0 : INLINE void gmul2nz(GEN x, long s, GEN z)
2755 0 : { pari_sp av = avma; gaffect(gmul2n(x,s), z); set_avma(av); }
2756 0 : INLINE void gshiftz(GEN x, long s, GEN z)
2757 0 : { pari_sp av = avma; gaffect(gshift(x,s), z); set_avma(av); }
2758 :
2759 : /*******************************************************************/
2760 : /* */
2761 : /* ELLIPTIC CURVES */
2762 : /* */
2763 : /*******************************************************************/
2764 7116195 : INLINE GEN ell_get_a1(GEN e) { return gel(e,1); }
2765 5709699 : INLINE GEN ell_get_a2(GEN e) { return gel(e,2); }
2766 6912842 : INLINE GEN ell_get_a3(GEN e) { return gel(e,3); }
2767 6522700 : INLINE GEN ell_get_a4(GEN e) { return gel(e,4); }
2768 7961473 : INLINE GEN ell_get_a6(GEN e) { return gel(e,5); }
2769 5432782 : INLINE GEN ell_get_b2(GEN e) { return gel(e,6); }
2770 2135641 : INLINE GEN ell_get_b4(GEN e) { return gel(e,7); }
2771 3055105 : INLINE GEN ell_get_b6(GEN e) { return gel(e,8); }
2772 2608978 : INLINE GEN ell_get_b8(GEN e) { return gel(e,9); }
2773 8021727 : INLINE GEN ell_get_c4(GEN e) { return gel(e,10); }
2774 8850368 : INLINE GEN ell_get_c6(GEN e) { return gel(e,11); }
2775 11279870 : INLINE GEN ell_get_disc(GEN e) { return gel(e,12); }
2776 1295726 : INLINE GEN ell_get_j(GEN e) { return gel(e,13); }
2777 11588371 : INLINE long ell_get_type(GEN e) { return mael(e,14,1); }
2778 2036736 : INLINE GEN ellff_get_field(GEN x) { return gmael(x, 15, 1); }
2779 800034 : INLINE GEN ellff_get_a4a6(GEN x) { return gmael(x, 15, 2); }
2780 1463 : INLINE GEN ellQp_get_zero(GEN x) { return gmael(x, 15, 1); }
2781 308 : INLINE long ellQp_get_prec(GEN E) { return valp(ellQp_get_zero(E)); }
2782 1134 : INLINE GEN ellQp_get_p(GEN E) { return padic_p(ellQp_get_zero(E)); }
2783 232582 : INLINE long ellR_get_prec(GEN x) { return nbits2prec(mael3(x, 15, 1, 1)); }
2784 371325 : INLINE long ellR_get_sign(GEN x) { return mael3(x, 15, 1, 2); }
2785 2027603 : INLINE GEN ellnf_get_nf(GEN x) { return checknf_i(gmael(x,15,1)); }
2786 126 : INLINE GEN ellnf_get_bnf(GEN x) { return checkbnf_i(gmael(x,15,1)); }
2787 :
2788 4677488 : INLINE int checkell_i(GEN e) { return typ(e) == t_VEC && lg(e) == 17; }
2789 51365180 : INLINE int ell_is_inf(GEN z) { return lg(z) == 2; }
2790 1875768 : INLINE GEN ellinf(void) { return mkvec(gen_0); }
2791 :
2792 : /*******************************************************************/
2793 : /* */
2794 : /* ALGEBRAIC NUMBER THEORY */
2795 : /* */
2796 : /*******************************************************************/
2797 30054958 : INLINE GEN modpr_get_pr(GEN x) { return gel(x,3); }
2798 1888768 : INLINE GEN modpr_get_p(GEN x) { return pr_get_p(modpr_get_pr(x)); }
2799 13188190 : INLINE GEN modpr_get_T(GEN x) { return lg(x) == 4? NULL: gel(x,4); }
2800 :
2801 89397417 : INLINE GEN pr_get_p(GEN pr) { return gel(pr,1); }
2802 11517886 : INLINE GEN pr_get_gen(GEN pr){ return gel(pr,2); }
2803 : /* .[2] instead of itos works: e and f are small positive integers */
2804 15726675 : INLINE long pr_get_e(GEN pr) { return gel(pr,3)[2]; }
2805 25357162 : INLINE long pr_get_f(GEN pr) { return gel(pr,4)[2]; }
2806 47864250 : INLINE GEN pr_get_tau(GEN pr){ return gel(pr,5); }
2807 : INLINE int
2808 16405300 : pr_is_inert(GEN P) { return typ(pr_get_tau(P)) == t_INT; }
2809 : INLINE GEN
2810 1067670 : pr_norm(GEN pr) { return powiu(pr_get_p(pr), pr_get_f(pr)); }
2811 : INLINE ulong
2812 343931 : upr_norm(GEN pr) { return upowuu(pr_get_p(pr)[2], pr_get_f(pr)); }
2813 :
2814 : /* assume nf a genuine nf */
2815 : INLINE long
2816 1167403 : nf_get_varn(GEN nf) { return varn(gel(nf,1)); }
2817 : INLINE GEN
2818 94477544 : nf_get_pol(GEN nf) { return gel(nf,1); }
2819 : INLINE long
2820 68840272 : nf_get_degree(GEN nf) { return degpol( nf_get_pol(nf) ); }
2821 : INLINE long
2822 22172435 : nf_get_r1(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,1)); }
2823 : INLINE long
2824 4140 : nf_get_r2(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,2)); }
2825 : INLINE GEN
2826 457800 : nf_get_disc(GEN nf) { return gel(nf,3); }
2827 : INLINE GEN
2828 3582805 : nf_get_index(GEN nf) { return gel(nf,4); }
2829 : INLINE GEN
2830 20779157 : nf_get_M(GEN nf) { return gmael(nf,5,1); }
2831 : INLINE GEN
2832 301779 : nf_get_G(GEN nf) { return gmael(nf,5,2); }
2833 : INLINE GEN
2834 1686960 : nf_get_roundG(GEN nf) { return gmael(nf,5,3); }
2835 : INLINE GEN
2836 22082 : nf_get_Tr(GEN nf) { return gmael(nf,5,4); }
2837 : INLINE GEN
2838 4459 : nf_get_diff(GEN nf) { return gmael(nf,5,5); }
2839 : INLINE GEN
2840 59584 : nf_get_ramified_primes(GEN nf) { return gmael(nf,5,8); }
2841 : INLINE GEN
2842 1532505 : nf_get_roots(GEN nf) { return gel(nf,6); }
2843 : INLINE GEN
2844 4382 : nf_get_zk(GEN nf)
2845 : {
2846 4382 : GEN y = gel(nf,7), D = gel(y, 1);
2847 4382 : if (typ(D) == t_POL) D = gel(D, 2);
2848 4382 : if (!equali1(D)) y = gdiv(y, D);
2849 4382 : return y;
2850 : }
2851 : INLINE GEN
2852 5025881 : nf_get_zkprimpart(GEN nf)
2853 : {
2854 5025881 : GEN y = gel(nf,7);
2855 : /* test for old format of nf.zk: non normalized */
2856 5025881 : if (!equali1(gel(nf,4)) && gequal1(gel(y,1))) y = Q_remove_denom(y,NULL);
2857 5025870 : return y;
2858 : }
2859 : INLINE GEN
2860 5071750 : nf_get_zkden(GEN nf)
2861 : {
2862 5071750 : GEN y = gel(nf,7), D = gel(y,1);
2863 5071750 : if (typ(D) == t_POL) D = gel(D,2);
2864 : /* test for old format of nf.zk: non normalized */
2865 5071750 : if (!equali1(gel(nf,4)) && equali1(D)) D = Q_denom(y);
2866 5071741 : return D;
2867 : }
2868 : INLINE GEN
2869 9493081 : nf_get_invzk(GEN nf) { return gel(nf,8); }
2870 : INLINE void
2871 516870 : nf_get_sign(GEN nf, long *r1, long *r2)
2872 : {
2873 516870 : GEN x = gel(nf,2);
2874 516870 : *r1 = itou(gel(x,1));
2875 516870 : *r2 = itou(gel(x,2));
2876 516870 : }
2877 :
2878 : INLINE GEN
2879 2521972 : cyc_get_expo(GEN c) { return lg(c) == 1? gen_1: gel(c,1); }
2880 : INLINE GEN
2881 392012 : abgrp_get_no(GEN x) { return gel(x,1); }
2882 : INLINE GEN
2883 11550141 : abgrp_get_cyc(GEN x) { return gel(x,2); }
2884 : INLINE GEN
2885 1653906 : abgrp_get_gen(GEN x) { return gel(x,3); }
2886 : INLINE GEN
2887 9426929 : bnf_get_nf(GEN bnf) { return gel(bnf,7); }
2888 : INLINE GEN
2889 5098134 : bnf_get_clgp(GEN bnf) { return gmael(bnf,8,1); }
2890 : INLINE GEN
2891 8379 : bnf_get_no(GEN bnf) { return abgrp_get_no(bnf_get_clgp(bnf)); }
2892 : INLINE GEN
2893 3509475 : bnf_get_cyc(GEN bnf) { return abgrp_get_cyc(bnf_get_clgp(bnf)); }
2894 : INLINE GEN
2895 1580120 : bnf_get_gen(GEN bnf) { return abgrp_get_gen(bnf_get_clgp(bnf)); }
2896 : INLINE GEN
2897 641 : bnf_get_reg(GEN bnf) { return gmael(bnf,8,2); }
2898 : INLINE GEN
2899 2702370 : bnf_get_logfu(GEN bnf) { return gel(bnf,3); }
2900 : INLINE GEN
2901 1278530 : bnf_get_sunits(GEN bnf)
2902 1278530 : { GEN s = gmael(bnf,8,3); return typ(s) == t_INT? NULL: s; }
2903 : INLINE GEN
2904 290540 : bnf_get_tuU(GEN bnf) { return gmael3(bnf,8,4,2); }
2905 : INLINE long
2906 265199 : bnf_get_tuN(GEN bnf) { return gmael3(bnf,8,4,1)[2]; }
2907 : INLINE GEN
2908 288195 : bnf_get_fu_nocheck(GEN bnf) { return gmael(bnf,8,5); }
2909 : INLINE GEN
2910 26293 : nfV_to_scalar_or_alg(GEN nf, GEN x)
2911 63435 : { pari_APPLY_same(nf_to_scalar_or_alg(nf, gel(x,i))) }
2912 : INLINE GEN
2913 25852 : bnf_get_fu(GEN bnf) {
2914 25852 : GEN fu = bnf_build_units(bnf), nf = bnf_get_nf(bnf);
2915 25852 : if (typ(fu) == t_MAT) pari_err(e_MISC,"missing units in bnf");
2916 25852 : return nfV_to_scalar_or_alg(nf, vecslice(fu, 2, lg(fu)-1));
2917 : }
2918 :
2919 : INLINE GEN
2920 3632609 : bnr_get_bnf(GEN bnr) { return gel(bnr,1); }
2921 : INLINE GEN
2922 1937120 : bnr_get_bid(GEN bnr) { return gel(bnr,2); }
2923 : INLINE GEN
2924 141127 : bnr_get_mod(GEN bnr) { return gmael(bnr,2,1); }
2925 : INLINE GEN
2926 1260192 : bnr_get_nf(GEN bnr) { return gmael(bnr,1,7); }
2927 : INLINE GEN
2928 2728937 : bnr_get_clgp(GEN bnr) { return gel(bnr,5); }
2929 : INLINE GEN
2930 314614 : bnr_get_no(GEN bnr) { return abgrp_get_no(bnr_get_clgp(bnr)); }
2931 : INLINE GEN
2932 2396704 : bnr_get_cyc(GEN bnr) { return abgrp_get_cyc(bnr_get_clgp(bnr)); }
2933 : INLINE GEN
2934 70 : bnr_get_gen_nocheck(GEN bnr) { return abgrp_get_gen(bnr_get_clgp(bnr)); }
2935 : INLINE GEN
2936 7847 : bnr_get_gen(GEN bnr) {
2937 7847 : GEN G = bnr_get_clgp(bnr);
2938 7847 : if (lg(G) != 4)
2939 0 : pari_err(e_MISC,"missing bnr generators: please use bnrinit(,,1)");
2940 7847 : return gel(G,3);
2941 : }
2942 :
2943 : /* localstar, used in gchar */
2944 : INLINE GEN
2945 51955 : locs_get_cyc(GEN locs) { return gel(locs,1); }
2946 : INLINE GEN
2947 191695 : locs_get_Lsprk(GEN locs) { return gel(locs,2); }
2948 : INLINE GEN
2949 1260 : locs_get_Lgenfil(GEN locs) { return gel(locs,3); }
2950 : INLINE GEN
2951 8225 : locs_get_mod(GEN locs) { return gel(locs,4); }
2952 : /* pr dividing the modulus N of locs, 0 <= i < v_pr(N)
2953 : * return a t_MAT whose columns are the logs
2954 : * of generators of U_i(pr)/U_{i+1}(pr). */
2955 : INLINE GEN
2956 1260 : locs_get_famod(GEN locs) { return gmael(locs,4,1); }
2957 : INLINE GEN
2958 207235 : locs_get_m_infty(GEN locs) { return gmael(locs,4,2); }
2959 :
2960 : /* G a grossenchar group */
2961 : INLINE GEN
2962 32639 : gchar_get_basis(GEN gc) { return gel(gc, 1); }
2963 : INLINE GEN
2964 203105 : gchar_get_bnf(GEN gc) { return gel(gc, 2); }
2965 : INLINE GEN
2966 241501 : gchar_get_nf(GEN gc) { return gel(gc, 3); }
2967 : INLINE GEN
2968 279434 : gchar_get_zm(GEN gc) { return gel(gc, 4); }
2969 : INLINE GEN
2970 8225 : gchar_get_mod(GEN gc) { return locs_get_mod(gchar_get_zm(gc)); }
2971 : INLINE GEN
2972 4095 : gchar_get_modP(GEN gc) { return gmael(gchar_get_mod(gc),1,1); }
2973 : INLINE GEN
2974 36865 : gchar_get_S(GEN gc) { return gel(gc, 5); }
2975 : INLINE GEN
2976 188468 : gchar_get_DLdata(GEN gc) { return gel(gc, 6); }
2977 : INLINE GEN
2978 1748 : gchar_get_sfu(GEN gc) { return gel(gc, 7); }
2979 : INLINE GEN
2980 16168 : gchar_get_cyc(GEN gc) { return gel(gc, 9); }
2981 : INLINE GEN
2982 0 : gchar_get_hnf(GEN gc) { return gmael(gc, 10, 1); }
2983 : INLINE GEN
2984 0 : gchar_get_U(GEN gc) { return gmael(gc, 10, 2); }
2985 : INLINE GEN
2986 10969 : gchar_get_Ui(GEN gc) { return gmael(gc, 10, 3); }
2987 : INLINE GEN
2988 3321 : gchar_get_m0(GEN gc) { return gel(gc, 11); }
2989 : INLINE GEN
2990 4267 : gchar_get_u0(GEN gc) { return gel(gc, 12); }
2991 : INLINE long
2992 17416 : gchar_get_r1(GEN gc) { return nf_get_r1(gchar_get_nf(gc)); }
2993 : INLINE long
2994 623 : gchar_get_r2(GEN gc) { return nf_get_r2(gchar_get_nf(gc)); }
2995 : INLINE GEN
2996 50347 : gchar_get_loccyc(GEN gc) { return locs_get_cyc(gchar_get_zm(gc)); }
2997 : INLINE long
2998 37131 : gchar_get_nc(GEN gc) { return lg(gchar_get_loccyc(gc))-1; }
2999 : INLINE long
3000 36865 : gchar_get_ns(GEN gc) { return lg(gchar_get_S(gc))-1; }
3001 : INLINE long
3002 1841 : gchar_get_nm(GEN gc) { return lg(gchar_get_basis(gc))-1; }
3003 : INLINE long
3004 4011 : gchar_get_evalprec(GEN gc) { return gmael(gc, 8, 1)[1]; }
3005 : INLINE long
3006 18732 : gchar_get_prec(GEN gc) { return gmael(gc, 8, 1)[2]; }
3007 : INLINE long
3008 13419 : gchar_get_nfprec(GEN gc) { return gmael(gc, 8, 1)[3]; }
3009 : INLINE void
3010 1785 : gchar_set_evalprec(GEN gc, long prec) { gmael(gc, 8, 1)[1] = prec; }
3011 : INLINE void
3012 1202 : gchar_set_prec(GEN gc, long prec) { gmael(gc, 8, 1)[2] = prec; }
3013 : INLINE void
3014 1202 : gchar_copy_precs(GEN gc, GEN gc2)
3015 : {
3016 1202 : gel(gc2, 8) = shallowcopy(gel(gc,8));
3017 1202 : gmael(gc2, 8, 1) = shallowcopy(gmael(gc, 8, 1));
3018 1202 : }
3019 : INLINE void
3020 2950 : gchar_set_nfprec(GEN gc, long prec) { gmael(gc, 8, 1)[3] = prec; }
3021 : INLINE long
3022 322 : gchar_get_ntors(GEN gc) { return gmael(gc, 8, 2)[1]; }
3023 : INLINE long
3024 322 : gchar_get_nfree(GEN gc) { return gmael(gc, 8, 2)[2]; }
3025 : INLINE long
3026 2042 : gchar_get_nalg(GEN gc) { return gmael(gc, 8, 2)[3]; }
3027 : INLINE void
3028 1573 : gchar_set_basis(GEN gc, GEN m_inv) { gel(gc, 1) = m_inv; }
3029 : INLINE void
3030 2077 : gchar_set_nf(GEN gc, GEN nf) { gel(gc, 3) = nf; }
3031 : INLINE void
3032 623 : gchar_set_ntors(GEN gc, long n) { gmael(gc, 8, 2)[1] = n; }
3033 : INLINE void
3034 623 : gchar_set_nfree(GEN gc, long n) { gmael(gc, 8, 2)[2] = n; }
3035 : INLINE void
3036 623 : gchar_set_nalg(GEN gc, long n) { gmael(gc, 8, 2)[3] = n; }
3037 : INLINE void
3038 1573 : gchar_set_cyc(GEN gc, GEN cyc) { gel(gc, 9) = cyc; }
3039 : INLINE void
3040 623 : gchar_set_HUUi(GEN gc, GEN hnf, GEN U, GEN Ui) { gel(gc, 10) = mkvec3(hnf, U, Ui); }
3041 : INLINE void
3042 950 : gchar_set_m0(GEN gc, GEN m0) { gel(gc, 11) = m0; }
3043 : INLINE void
3044 2093 : gchar_set_u0(GEN gc, GEN u0) { gel(gc, 12) = u0; }
3045 :
3046 : INLINE GEN
3047 1386618 : bid_get_mod(GEN bid) { return gel(bid,1); }
3048 : INLINE GEN
3049 78295 : bid_get_ideal(GEN bid) { return gmael(bid,1,1); }
3050 : INLINE GEN
3051 35098 : bid_get_arch(GEN bid) { return gmael(bid,1,2); }
3052 : INLINE GEN
3053 5415792 : bid_get_grp(GEN bid) { return gel(bid,2); }
3054 : INLINE GEN
3055 2314077 : bid_get_fact(GEN bid) { return gmael(bid,3,1); }
3056 : INLINE GEN
3057 2025387 : bid_get_fact2(GEN bid) { return gmael(bid,3,2); }
3058 : INLINE GEN
3059 1990848 : bid_get_MOD(GEN bid) { GEN y = gel(bid,4); return lg(y) == 4? gel(y,3): NULL; }
3060 : INLINE GEN
3061 1991579 : bid_get_sprk(GEN bid) { return gmael(bid,4,1); }
3062 : INLINE GEN
3063 51226 : bid_get_sarch(GEN bid) { return gmael(bid,4,2); }
3064 : INLINE GEN
3065 2217875 : bid_get_archp(GEN bid) { return gmael3(bid,4,2,2); }
3066 : INLINE GEN
3067 3378524 : bid_get_U(GEN bid) { return gel(bid,5); }
3068 : INLINE GEN
3069 0 : bid_get_no(GEN bid) { return abgrp_get_no(bid_get_grp(bid)); }
3070 : INLINE GEN
3071 5361884 : bid_get_cyc(GEN bid) { return abgrp_get_cyc(bid_get_grp(bid)); }
3072 : INLINE GEN
3073 0 : bid_get_gen_nocheck(GEN bid) { return abgrp_get_gen(bid_get_grp(bid)); }
3074 : INLINE GEN
3075 53326 : bid_get_gen(GEN bid) {
3076 53326 : GEN G = bid_get_grp(bid);
3077 53326 : if (lg(G) != 4) pari_err(e_MISC,"missing bid generators. Use idealstar(,,2)");
3078 53326 : return abgrp_get_gen(G);
3079 : }
3080 :
3081 : INLINE GEN
3082 34543777 : znstar_get_N(GEN G) { return gmael(G,1,1); }
3083 : INLINE GEN
3084 7210394 : znstar_get_faN(GEN G) { return gel(G,3); }
3085 : INLINE GEN
3086 14 : znstar_get_no(GEN G) { return abgrp_get_no(gel(G,2)); }
3087 : INLINE GEN
3088 261948 : znstar_get_cyc(GEN G) { return abgrp_get_cyc(gel(G,2)); }
3089 : INLINE GEN
3090 16150 : znstar_get_gen(GEN G) { return abgrp_get_gen(gel(G,2)); }
3091 : INLINE GEN
3092 7823726 : znstar_get_conreycyc(GEN G) { return gmael(G,4,5); }
3093 : INLINE GEN
3094 3221793 : znstar_get_conreygen(GEN G) { return gmael(G,4,4); }
3095 : INLINE GEN
3096 46788 : znstar_get_Ui(GEN G) { return gmael(G,4,3); }
3097 : INLINE GEN
3098 176051 : znstar_get_U(GEN G) { return gel(G,5); }
3099 : INLINE GEN
3100 2820763 : znstar_get_pe(GEN G) { return gmael(G,4,1); }
3101 : INLINE GEN
3102 36154 : gal_get_pol(GEN gal) { return gel(gal,1); }
3103 : INLINE GEN
3104 6041 : gal_get_p(GEN gal) { return gmael(gal,2,1); }
3105 : INLINE GEN
3106 91 : gal_get_e(GEN gal) { return gmael(gal,2,2); }
3107 : INLINE GEN
3108 23793 : gal_get_mod(GEN gal) { return gmael(gal,2,3); }
3109 : INLINE GEN
3110 32570 : gal_get_roots(GEN gal) { return gel(gal,3); }
3111 : INLINE GEN
3112 27677 : gal_get_invvdm(GEN gal) { return gel(gal,4); }
3113 : INLINE GEN
3114 27671 : gal_get_den(GEN gal) { return gel(gal,5); }
3115 : INLINE GEN
3116 80190 : gal_get_group(GEN gal) { return gel(gal,6); }
3117 : INLINE GEN
3118 15456 : gal_get_gen(GEN gal) { return gel(gal,7); }
3119 : INLINE GEN
3120 6664 : gal_get_orders(GEN gal) { return gel(gal,8); }
3121 :
3122 : /* assume rnf a genuine rnf */
3123 : INLINE long
3124 2507249 : rnf_get_degree(GEN rnf) { return degpol(rnf_get_pol(rnf)); }
3125 : INLINE long
3126 21217 : rnf_get_nfdegree(GEN rnf) { return degpol(nf_get_pol(rnf_get_nf(rnf))); }
3127 : INLINE long
3128 1393227 : rnf_get_absdegree(GEN rnf) { return degpol(gmael(rnf,11,1)); }
3129 : INLINE GEN
3130 1386 : rnf_get_idealdisc(GEN rnf) { return gmael(rnf,3,1); }
3131 : INLINE GEN
3132 1225 : rnf_get_k(GEN rnf) { return gmael(rnf,11,3); }
3133 : INLINE GEN
3134 1204 : rnf_get_alpha(GEN rnf) { return gmael(rnf, 11, 2); }
3135 : INLINE GEN
3136 734423 : rnf_get_nf(GEN rnf) { return gel(rnf,10); }
3137 : INLINE GEN
3138 6559 : rnf_get_nfzk(GEN rnf) { return gel(rnf,2); }
3139 : INLINE GEN
3140 315053 : rnf_get_polabs(GEN rnf) { return gmael(rnf,11,1); }
3141 : INLINE GEN
3142 2846441 : rnf_get_pol(GEN rnf) { return gel(rnf,1); }
3143 : INLINE GEN
3144 350 : rnf_get_disc(GEN rnf) { return gel(rnf,3); }
3145 : INLINE GEN
3146 105 : rnf_get_index(GEN rnf) { return gel(rnf,4); }
3147 : INLINE GEN
3148 2611 : rnf_get_ramified_primes(GEN rnf) { return gel(rnf,5); }
3149 : INLINE long
3150 574 : rnf_get_varn(GEN rnf) { return varn(gel(rnf,1)); }
3151 : INLINE GEN
3152 255696 : rnf_get_nfpol(GEN rnf) { return gmael(rnf,10,1); }
3153 : INLINE long
3154 4886 : rnf_get_nfvarn(GEN rnf) { return varn(gmael(rnf,10,1)); }
3155 : INLINE GEN
3156 4592 : rnf_get_zk(GEN rnf) { return gel(rnf,7); }
3157 : INLINE GEN
3158 135229 : rnf_get_map(GEN rnf) { return gel(rnf,11); }
3159 : INLINE GEN
3160 1225 : rnf_get_invzk(GEN rnf) { return gel(rnf,8); }
3161 :
3162 : INLINE GEN
3163 138615 : idealred(GEN nf, GEN id) { return idealred0(nf, id, NULL); }
3164 :
3165 : INLINE GEN
3166 5455 : idealchineseinit(GEN nf, GEN x)
3167 5455 : { return idealchinese(nf,x,NULL); }
3168 :
3169 : /*******************************************************************/
3170 : /* */
3171 : /* CLOSURES */
3172 : /* */
3173 : /*******************************************************************/
3174 361260405 : INLINE long closure_arity(GEN C) { return ((ulong)C[1])&ARITYBITS; }
3175 40099519 : INLINE long closure_is_variadic(GEN C) { return !!(((ulong)C[1])&VARARGBITS); }
3176 312515453 : INLINE const char *closure_codestr(GEN C) { return GSTR(gel(C,2))-1; }
3177 0 : INLINE GEN closure_get_code(GEN C) { return gel(C,2); }
3178 312499728 : INLINE GEN closure_get_oper(GEN C) { return gel(C,3); }
3179 312481274 : INLINE GEN closure_get_data(GEN C) { return gel(C,4); }
3180 13502 : INLINE GEN closure_get_dbg(GEN C) { return gel(C,5); }
3181 36806 : INLINE GEN closure_get_text(GEN C) { return gel(C,6); }
3182 13054133 : INLINE GEN closure_get_frame(GEN C) { return gel(C,7); }
3183 :
3184 : /*******************************************************************/
3185 : /* */
3186 : /* ERRORS */
3187 : /* */
3188 : /*******************************************************************/
3189 : INLINE long
3190 62291 : err_get_num(GEN e) { return e[1]; }
3191 : INLINE GEN
3192 294 : err_get_compo(GEN e, long i) { return gel(e, i+1); }
3193 :
3194 : INLINE void
3195 14 : pari_err_BUG(const char *f) { pari_err(e_BUG,f); }
3196 : INLINE void
3197 21 : pari_err_CONSTPOL(const char *f) { pari_err(e_CONSTPOL, f); }
3198 : INLINE void
3199 84 : pari_err_COPRIME(const char *f, GEN x, GEN y) { pari_err(e_COPRIME, f,x,y); }
3200 : INLINE void
3201 718 : pari_err_DIM(const char *f) { pari_err(e_DIM, f); }
3202 : INLINE void
3203 0 : pari_err_FILE(const char *f, const char *g) { pari_err(e_FILE, f,g); }
3204 : INLINE void
3205 36 : pari_err_FILEDESC(const char *f, long n) { pari_err(e_FILEDESC, f,n); }
3206 : INLINE void
3207 98 : pari_err_FLAG(const char *f) { pari_err(e_FLAG,f); }
3208 : INLINE void
3209 539 : pari_err_IMPL(const char *f) { pari_err(e_IMPL,f); }
3210 : INLINE void
3211 20018 : pari_err_INV(const char *f, GEN x) { pari_err(e_INV,f,x); }
3212 : INLINE void
3213 63 : pari_err_IRREDPOL(const char *f, GEN x) { pari_err(e_IRREDPOL, f,x); }
3214 : INLINE void
3215 2764 : 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); }
3216 : INLINE void
3217 214 : pari_err_COMPONENT(const char *f, const char *op, GEN l, GEN x) { pari_err(e_COMPONENT, f,op,l,x); }
3218 : INLINE void
3219 0 : pari_err_MAXPRIME(ulong c) { pari_err(e_MAXPRIME, c); }
3220 : INLINE void
3221 406 : pari_err_OP(const char *f, GEN x, GEN y) { pari_err(e_OP, f,x,y); }
3222 : INLINE void
3223 156 : pari_err_OVERFLOW(const char *f) { pari_err(e_OVERFLOW, f); }
3224 : INLINE void
3225 238 : pari_err_PREC(const char *f) { pari_err(e_PREC,f); }
3226 : INLINE void
3227 0 : pari_err_PACKAGE(const char *f) { pari_err(e_PACKAGE,f); }
3228 : INLINE void
3229 98 : pari_err_PRIME(const char *f, GEN x) { pari_err(e_PRIME, f,x); }
3230 : INLINE void
3231 1316 : pari_err_MODULUS(const char *f, GEN x, GEN y) { pari_err(e_MODULUS, f,x,y); }
3232 : INLINE void
3233 63 : pari_err_ROOTS0(const char *f) { pari_err(e_ROOTS0, f); }
3234 : INLINE void
3235 7084 : pari_err_SQRTN(const char *f, GEN x) { pari_err(e_SQRTN, f,x); }
3236 : INLINE void
3237 15377 : pari_err_TYPE(const char *f, GEN x) { pari_err(e_TYPE, f,x); }
3238 : INLINE void
3239 3493 : pari_err_TYPE2(const char *f, GEN x, GEN y) { pari_err(e_TYPE2, f,x,y); }
3240 : INLINE void
3241 371 : pari_err_VAR(const char *f, GEN x, GEN y) { pari_err(e_VAR, f,x,y); }
3242 : INLINE void
3243 238 : pari_err_PRIORITY(const char *f, GEN x, const char *op, long v)
3244 238 : { pari_err(e_PRIORITY, f,x,op,v); }
3245 :
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