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 : /* MALLOC/FREE WRAPPERS */
17 : /*********************************************************************/
18 : #define BLOCK_SIGALRM_START \
19 : { \
20 : int block=PARI_SIGINT_block; \
21 : PARI_SIGINT_block = 2; \
22 : MT_SIGINT_BLOCK(block);
23 :
24 : #define BLOCK_SIGINT_START \
25 : { \
26 : int block=PARI_SIGINT_block; \
27 : PARI_SIGINT_block = 1; \
28 : MT_SIGINT_BLOCK(block);
29 :
30 : #define BLOCK_SIGINT_END \
31 : PARI_SIGINT_block = block; \
32 : MT_SIGINT_UNBLOCK(block); \
33 : if (!block && PARI_SIGINT_pending) \
34 : { \
35 : int sig = PARI_SIGINT_pending; \
36 : PARI_SIGINT_pending = 0; \
37 : raise(sig); \
38 : } \
39 : }
40 :
41 : /*******************************************************************/
42 : /* */
43 : /* CONSTRUCTORS */
44 : /* */
45 : /*******************************************************************/
46 : #define retmkfrac(x,y)\
47 : do { GEN _v = cgetg(3, t_FRAC);\
48 : gel(_v,1) = (x);\
49 : gel(_v,2) = (y); return _v; } while(0)
50 : #define retmkrfrac(x,y)\
51 : do { GEN _v = cgetg(3, t_RFRAC);\
52 : gel(_v,1) = (x);\
53 : gel(_v,2) = (y); return _v; } while(0)
54 : #define retmkintmod(x,y)\
55 : do { GEN _v = cgetg(3, t_INTMOD);\
56 : gel(_v,1) = (y);\
57 : gel(_v,2) = (x); return _v; } while(0)
58 : #define retmkcomplex(x,y)\
59 : do { GEN _v = cgetg(3, t_COMPLEX);\
60 : gel(_v,1) = (x);\
61 : gel(_v,2) = (y); return _v; } while(0)
62 : #define retmkpolmod(x,y)\
63 : do { GEN _v = cgetg(3, t_POLMOD);\
64 : gel(_v,1) = (y);\
65 : gel(_v,2) = (x); return _v; } while(0)
66 : #define retmkvec(x)\
67 : do { GEN _v = cgetg(2, t_VEC);\
68 : gel(_v,1) = (x); return _v; } while(0)
69 : #define retmkvec2(x,y)\
70 : do { GEN _v = cgetg(3, t_VEC);\
71 : gel(_v,1) = (x);\
72 : gel(_v,2) = (y); return _v; } while(0)
73 : #define retmkvec3(x,y,z)\
74 : do { GEN _v = cgetg(4, t_VEC);\
75 : gel(_v,1) = (x);\
76 : gel(_v,2) = (y);\
77 : gel(_v,3) = (z); return _v; } while(0)
78 : #define retmkqfb(x,y,z,d)\
79 : do { GEN _v = cgetg(5, t_QFB);\
80 : gel(_v,1) = (x);\
81 : gel(_v,2) = (y);\
82 : gel(_v,3) = (z);\
83 : gel(_v,4) = (d); return _v; } while(0)
84 : #define retmkquad(x,y,z)\
85 : do { GEN _v = cgetg(4, t_QUAD);\
86 : gel(_v,1) = (x);\
87 : gel(_v,2) = (y);\
88 : gel(_v,3) = (z); return _v; } while(0)
89 : #define retmkvec4(x,y,z,t)\
90 : do { GEN _v = cgetg(5, t_VEC);\
91 : gel(_v,1) = (x);\
92 : gel(_v,2) = (y);\
93 : gel(_v,3) = (z);\
94 : gel(_v,4) = (t); return _v; } while(0)
95 : #define retmkvec5(x,y,z,t,u)\
96 : do { GEN _v = cgetg(6, t_VEC);\
97 : gel(_v,1) = (x);\
98 : gel(_v,2) = (y);\
99 : gel(_v,3) = (z);\
100 : gel(_v,4) = (t);\
101 : gel(_v,5) = (u); return _v; } while(0)
102 : #define retmkcol(x)\
103 : do { GEN _v = cgetg(2, t_COL);\
104 : gel(_v,1) = (x); return _v; } while(0)
105 : #define retmkcol2(x,y)\
106 : do { GEN _v = cgetg(3, t_COL);\
107 : gel(_v,1) = (x);\
108 : gel(_v,2) = (y); return _v; } while(0)
109 : #define retmkcol3(x,y,z)\
110 : do { GEN _v = cgetg(4, t_COL);\
111 : gel(_v,1) = (x);\
112 : gel(_v,2) = (y);\
113 : gel(_v,3) = (z); return _v; } while(0)
114 : #define retmkcol4(x,y,z,t)\
115 : do { GEN _v = cgetg(5, t_COL);\
116 : gel(_v,1) = (x);\
117 : gel(_v,2) = (y);\
118 : gel(_v,3) = (z);\
119 : gel(_v,4) = (t); return _v; } while(0)
120 : #define retmkcol5(x,y,z,t,u)\
121 : do { GEN _v = cgetg(6, t_COL);\
122 : gel(_v,1) = (x);\
123 : gel(_v,2) = (y);\
124 : gel(_v,3) = (z);\
125 : gel(_v,4) = (t);\
126 : gel(_v,5) = (u); return _v; } while(0)
127 : #define retmkcol6(x,y,z,t,u,v)\
128 : do { GEN _v = cgetg(7, t_COL);\
129 : gel(_v,1) = (x);\
130 : gel(_v,2) = (y);\
131 : gel(_v,3) = (z);\
132 : gel(_v,4) = (t);\
133 : gel(_v,5) = (u);\
134 : gel(_v,6) = (v); return _v; } while(0)
135 : #define retmkmat(x)\
136 : do { GEN _v = cgetg(2, t_MAT);\
137 : gel(_v,1) = (x); return _v; } while(0)
138 : #define retmkmat2(x,y)\
139 : do { GEN _v = cgetg(3, t_MAT);\
140 : gel(_v,1) = (x);\
141 : gel(_v,2) = (y); return _v; } while(0)
142 : #define retmkmat3(x,y,z)\
143 : do { GEN _v = cgetg(4, t_MAT);\
144 : gel(_v,1) = (x);\
145 : gel(_v,2) = (y);\
146 : gel(_v,3) = (z); return _v; } while(0)
147 : #define retmkmat4(x,y,z,t)\
148 : do { GEN _v = cgetg(5, t_MAT);\
149 : gel(_v,1) = (x);\
150 : gel(_v,2) = (y);\
151 : gel(_v,3) = (z);\
152 : gel(_v,4) = (t); return _v; } while(0)
153 : #define retmkmat5(x,y,z,t,u)\
154 : do { GEN _v = cgetg(6, t_MAT);\
155 : gel(_v,1) = (x);\
156 : gel(_v,2) = (y);\
157 : gel(_v,3) = (z);\
158 : gel(_v,4) = (t);\
159 : gel(_v,5) = (u); return _v; } while(0)
160 :
161 : INLINE GEN
162 6197080 : mkintmod(GEN x, GEN y) { retmkintmod(x,y); }
163 : INLINE GEN
164 1666 : mkintmodu(ulong x, ulong y) {
165 1666 : GEN v = cgetg(3,t_INTMOD);
166 1666 : gel(v,1) = utoipos(y);
167 1666 : gel(v,2) = utoi(x); return v;
168 : }
169 : INLINE GEN
170 2626614 : mkpolmod(GEN x, GEN y) { retmkpolmod(x,y); }
171 : INLINE GEN
172 29165944 : mkfrac(GEN x, GEN y) { retmkfrac(x,y); }
173 : INLINE GEN
174 32881 : mkfracss(long x, long y) { retmkfrac(stoi(x),utoipos(y)); }
175 : /* q = n/d a t_FRAC or t_INT; recover (n,d) */
176 : INLINE void
177 14161 : Qtoss(GEN q, long *n, long *d)
178 : {
179 14161 : if (typ(q) == t_INT) { *n = itos(q); *d = 1; }
180 2912 : else { *n = itos(gel(q,1)); *d = itou(gel(q,2)); }
181 14161 : }
182 : INLINE GEN
183 137650754 : sstoQ(long n, long d)
184 : {
185 : ulong r;
186 : long g, q;
187 137650754 : if (!n)
188 : {
189 100613 : if (!d) pari_err_INV("sstoQ",gen_0);
190 100613 : return gen_0;
191 : }
192 137550141 : if (d < 0) { d = -d; n = -n; }
193 137550141 : if (d == 1) return stoi(n);
194 137537786 : q = udivuu_rem(labs(n),d,&r);
195 137537786 : if (!r) return n > 0? utoipos(q): utoineg(q);
196 4932558 : g = ugcd(d,r); /* gcd(n,d) */
197 4932558 : if (g != 1) { n /= g; d /= g; }
198 4932558 : retmkfrac(stoi(n), utoi(d));
199 : }
200 :
201 : INLINE GEN
202 3695584 : mkfraccopy(GEN x, GEN y) { retmkfrac(icopy(x), icopy(y)); }
203 : INLINE GEN
204 9345 : mkrfrac(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
205 9345 : gel(v,1) = x; gel(v,2) = y; return v; }
206 : INLINE GEN
207 7 : mkrfraccopy(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
208 7 : gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
209 : INLINE GEN
210 84905300 : mkcomplex(GEN x, GEN y) { retmkcomplex(x,y); }
211 : INLINE GEN
212 854446 : gen_I(void) { return mkcomplex(gen_0, gen_1); }
213 : INLINE GEN
214 293378 : cgetc(long l) { retmkcomplex(cgetr(l), cgetr(l)); }
215 : INLINE GEN
216 86331 : mkquad(GEN n, GEN x, GEN y) { GEN v = cgetg(4, t_QUAD);
217 86331 : gel(v,1) = n; gel(v,2) = x; gel(v,3) = y; return v; }
218 : /* vecsmall */
219 : INLINE GEN
220 111015976 : mkvecsmall(long x) { GEN v = cgetg(2, t_VECSMALL); v[1] = x; return v; }
221 : INLINE GEN
222 515867513 : mkvecsmall2(long x,long y) { GEN v = cgetg(3, t_VECSMALL);
223 515845896 : v[1]=x; v[2]=y; return v; }
224 : INLINE GEN
225 229766348 : mkvecsmall3(long x,long y,long z) { GEN v = cgetg(4, t_VECSMALL);
226 229753063 : v[1]=x; v[2]=y; v[3]=z; return v; }
227 : INLINE GEN
228 13902141 : mkvecsmall4(long x,long y,long z,long t) { GEN v = cgetg(5, t_VECSMALL);
229 13888075 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; return v; }
230 : INLINE GEN
231 556102 : mkvecsmall5(long x,long y,long z,long t,long u) { GEN v = cgetg(6, t_VECSMALL);
232 556101 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; v[5]=u; return v; }
233 :
234 : INLINE GEN
235 16845548 : mkqfb(GEN x, GEN y, GEN z, GEN d) { retmkqfb(x,y,z,d); }
236 : /* vec */
237 : INLINE GEN
238 56457602 : mkvec(GEN x) { retmkvec(x); }
239 : INLINE GEN
240 162180134 : mkvec2(GEN x, GEN y) { retmkvec2(x,y); }
241 : INLINE GEN
242 92115251 : mkvec3(GEN x, GEN y, GEN z) { retmkvec3(x,y,z); }
243 : INLINE GEN
244 7947856 : mkvec4(GEN x, GEN y, GEN z, GEN t) { retmkvec4(x,y,z,t); }
245 : INLINE GEN
246 14306754 : mkvec5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkvec5(x,y,z,t,u); }
247 : INLINE GEN
248 105 : mkvecs(long x) { retmkvec(stoi(x)); }
249 : INLINE GEN
250 91900 : mkvec2s(long x, long y) { retmkvec2(stoi(x),stoi(y)); }
251 : INLINE GEN
252 488650 : mkvec3s(long x, long y, long z) { retmkvec3(stoi(x),stoi(y),stoi(z)); }
253 : INLINE GEN
254 21 : mkvec4s(long x, long y, long z, long t) { retmkvec4(stoi(x),stoi(y),stoi(z),stoi(t)); }
255 : INLINE GEN
256 35763 : mkveccopy(GEN x) { GEN v = cgetg(2, t_VEC); gel(v,1) = gcopy(x); return v; }
257 : INLINE GEN
258 114235 : mkvec2copy(GEN x, GEN y) {
259 114235 : GEN v = cgetg(3,t_VEC); gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
260 : /* col */
261 : INLINE GEN
262 4938207 : mkcol(GEN x) { retmkcol(x); }
263 : INLINE GEN
264 63681082 : mkcol2(GEN x, GEN y) { retmkcol2(x,y); }
265 : INLINE GEN
266 51943 : mkcol3(GEN x, GEN y, GEN z) { retmkcol3(x,y,z); }
267 : INLINE GEN
268 0 : mkcol4(GEN x, GEN y, GEN z, GEN t) { retmkcol4(x,y,z,t); }
269 : INLINE GEN
270 106 : mkcol5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkcol5(x,y,z,t,u); }
271 : INLINE GEN
272 11902 : mkcol6(GEN x, GEN y, GEN z, GEN t, GEN u, GEN v) { retmkcol6(x,y,z,t,u,v); }
273 : INLINE GEN
274 36589 : mkcols(long x) { retmkcol(stoi(x)); }
275 : INLINE GEN
276 2760800 : mkcol2s(long x, long y) { retmkcol2(stoi(x),stoi(y)); }
277 : INLINE GEN
278 0 : mkcol3s(long x, long y, long z) { retmkcol3(stoi(x),stoi(y),stoi(z)); }
279 : INLINE GEN
280 0 : mkcol4s(long x, long y, long z, long t) { retmkcol4(stoi(x),stoi(y),stoi(z),stoi(t)); }
281 : INLINE GEN
282 27627 : mkcolcopy(GEN x) { GEN v = cgetg(2, t_COL); gel(v,1) = gcopy(x); return v; }
283 : /* mat */
284 : INLINE GEN
285 3305011 : mkmat(GEN x) { retmkmat(x); }
286 : INLINE GEN
287 39527015 : mkmat2(GEN x, GEN y) { retmkmat2(x,y); }
288 : INLINE GEN
289 5341 : mkmat3(GEN x, GEN y, GEN z) { retmkmat3(x,y,z); }
290 : INLINE GEN
291 0 : mkmat4(GEN x, GEN y, GEN z, GEN t) { retmkmat4(x,y,z,t); }
292 : INLINE GEN
293 0 : mkmat5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkmat5(x,y,z,t,u); }
294 : INLINE GEN
295 118953 : mkmatcopy(GEN x) { GEN v = cgetg(2, t_MAT); gel(v,1) = gcopy(x); return v; }
296 : INLINE GEN
297 0 : mkerr(long x) { GEN v = cgetg(2, t_ERROR); v[1] = x; return v; }
298 : INLINE GEN
299 197270 : mkoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
300 : INLINE GEN
301 100905 : mkmoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
302 : INLINE long
303 310154 : inf_get_sign(GEN x) { return signe(gel(x,1)); }
304 : INLINE GEN
305 12432 : mkmat22s(long a, long b, long c, long d) {retmkmat2(mkcol2s(a,c),mkcol2s(b,d));}
306 : INLINE GEN
307 5355456 : mkmat22(GEN a, GEN b, GEN c, GEN d) { retmkmat2(mkcol2(a,c),mkcol2(b,d)); }
308 :
309 : /* pol */
310 : INLINE GEN
311 2458147 : pol_x(long v) {
312 2458147 : GEN p = cgetg(4, t_POL);
313 2458183 : p[1] = evalsigne(1)|evalvarn(v);
314 2458183 : gel(p,2) = gen_0;
315 2458183 : gel(p,3) = gen_1; return p;
316 : }
317 : /* x^n, assume n >= 0 */
318 : INLINE GEN
319 2140031 : pol_xn(long n, long v) {
320 2140031 : long i, a = n+2;
321 2140031 : GEN p = cgetg(a+1, t_POL);
322 2140035 : p[1] = evalsigne(1)|evalvarn(v);
323 5012733 : for (i = 2; i < a; i++) gel(p,i) = gen_0;
324 2140035 : gel(p,a) = gen_1; return p;
325 : }
326 : /* x^n, no assumption on n */
327 : INLINE GEN
328 287 : pol_xnall(long n, long v)
329 : {
330 287 : if (n < 0) retmkrfrac(gen_1, pol_xn(-n,v));
331 280 : return pol_xn(n, v);
332 : }
333 : /* x^n, assume n >= 0 */
334 : INLINE GEN
335 210 : polxn_Flx(long n, long sv) {
336 210 : long i, a = n+2;
337 210 : GEN p = cgetg(a+1, t_VECSMALL);
338 210 : p[1] = sv;
339 1022 : for (i = 2; i < a; i++) p[i] = 0;
340 210 : p[a] = 1; return p;
341 : }
342 : INLINE GEN
343 3108565 : pol_1(long v) {
344 3108565 : GEN p = cgetg(3, t_POL);
345 3108550 : p[1] = evalsigne(1)|evalvarn(v);
346 3108550 : gel(p,2) = gen_1; return p;
347 : }
348 : INLINE GEN
349 31942548 : pol_0(long v)
350 : {
351 31942548 : GEN x = cgetg(2,t_POL);
352 31942543 : x[1] = evalvarn(v); return x;
353 : }
354 : #define retconst_vec(n,x)\
355 : do { long _i, _n = (n);\
356 : GEN _v = cgetg(_n+1, t_VEC), _x = (x);\
357 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
358 : return _v; } while(0)
359 : INLINE GEN
360 238378363 : const_vec(long n, GEN x) { retconst_vec(n, x); }
361 : #define retconst_col(n,x)\
362 : do { long _i, _n = (n);\
363 : GEN _v = cgetg(_n+1, t_COL), _x = (x);\
364 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
365 : return _v; } while(0)
366 : INLINE GEN
367 37090604 : const_col(long n, GEN x) { retconst_col(n, x); }
368 : INLINE GEN
369 18236970 : const_vecsmall(long n, long c)
370 : {
371 : long i;
372 18236970 : GEN V = cgetg(n+1,t_VECSMALL);
373 453748828 : for(i=1;i<=n;i++) V[i] = c;
374 18237339 : return V;
375 : }
376 :
377 : /*** ZERO ***/
378 : /* O(p^e) */
379 : INLINE GEN
380 366877 : zeropadic(GEN p, long e)
381 : {
382 366877 : GEN y = cgetg(5,t_PADIC);
383 366877 : gel(y,4) = gen_0;
384 366877 : gel(y,3) = gen_1;
385 366877 : gel(y,2) = icopy(p);
386 366877 : y[1] = evalvalp(e) | _evalprecp(0);
387 366877 : return y;
388 : }
389 : INLINE GEN
390 973 : zeropadic_shallow(GEN p, long e)
391 : {
392 973 : GEN y = cgetg(5,t_PADIC);
393 973 : gel(y,4) = gen_0;
394 973 : gel(y,3) = gen_1;
395 973 : gel(y,2) = p;
396 973 : y[1] = evalvalp(e) | _evalprecp(0);
397 973 : return y;
398 : }
399 : /* O(pol_x(v)^e) */
400 : INLINE GEN
401 138446 : zeroser(long v, long e)
402 : {
403 138446 : GEN x = cgetg(2, t_SER);
404 138446 : x[1] = evalvalp(e) | evalvarn(v); return x;
405 : }
406 : INLINE int
407 7119170 : ser_isexactzero(GEN x)
408 : {
409 7119170 : if (!signe(x)) switch(lg(x))
410 : {
411 132566 : case 2: return 1;
412 1267 : case 3: return isexactzero(gel(x,2));
413 : }
414 6985337 : return 0;
415 : }
416 : /* 0 * pol_x(v) */
417 : INLINE GEN
418 14542355 : zeropol(long v) { return pol_0(v); }
419 : /* vector(n) */
420 : INLINE GEN
421 78089470 : zerocol(long n)
422 : {
423 78089470 : GEN y = cgetg(n+1,t_COL);
424 543680726 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
425 78089866 : return y;
426 : }
427 : /* vectorv(n) */
428 : INLINE GEN
429 19684367 : zerovec(long n)
430 : {
431 19684367 : GEN y = cgetg(n+1,t_VEC);
432 183232494 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
433 19684356 : return y;
434 : }
435 : /* matrix(m, n) */
436 : INLINE GEN
437 91171 : zeromat(long m, long n)
438 : {
439 91171 : GEN y = cgetg(n+1,t_MAT);
440 91170 : GEN v = zerocol(m);
441 291379 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
442 91170 : return y;
443 : }
444 : /* = zero_zx, sv is a evalvarn()*/
445 : INLINE GEN
446 1095273 : zero_Flx(long sv) { return pol0_Flx(sv); }
447 : INLINE GEN
448 47831370 : zero_Flv(long n)
449 : {
450 47831370 : GEN y = cgetg(n+1,t_VECSMALL);
451 962553391 : long i; for (i=1; i<=n; i++) y[i] = 0;
452 47831661 : return y;
453 : }
454 : /* matrix(m, n) */
455 : INLINE GEN
456 2188570 : zero_Flm(long m, long n)
457 : {
458 2188570 : GEN y = cgetg(n+1,t_MAT);
459 2188569 : GEN v = zero_Flv(m);
460 14278649 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
461 2188561 : return y;
462 : }
463 : /* matrix(m, n) */
464 : INLINE GEN
465 219270 : zero_Flm_copy(long m, long n)
466 : {
467 219270 : GEN y = cgetg(n+1,t_MAT);
468 2234028 : long i; for (i=1; i<=n; i++) gel(y,i) = zero_Flv(m);
469 219270 : return y;
470 : }
471 :
472 : INLINE GEN
473 2602965 : zero_F2v(long m)
474 : {
475 2602965 : long l = nbits2nlong(m);
476 2602942 : GEN v = zero_Flv(l+1);
477 2602944 : v[1] = m;
478 2602944 : return v;
479 : }
480 :
481 : INLINE GEN
482 0 : zero_F2m(long m, long n)
483 : {
484 : long i;
485 0 : GEN M = cgetg(n+1, t_MAT);
486 0 : GEN v = zero_F2v(m);
487 0 : for (i = 1; i <= n; i++)
488 0 : gel(M,i) = v;
489 0 : return M;
490 : }
491 :
492 :
493 : INLINE GEN
494 804494 : zero_F2m_copy(long m, long n)
495 : {
496 : long i;
497 804494 : GEN M = cgetg(n+1, t_MAT);
498 1881467 : for (i = 1; i <= n; i++)
499 1076976 : gel(M,i)= zero_F2v(m);
500 804491 : return M;
501 : }
502 :
503 : /* matrix(m, n) */
504 : INLINE GEN
505 8105053 : zeromatcopy(long m, long n)
506 : {
507 8105053 : GEN y = cgetg(n+1,t_MAT);
508 34624086 : long i; for (i=1; i<=n; i++) gel(y,i) = zerocol(m);
509 8105082 : return y;
510 : }
511 :
512 : INLINE GEN
513 18235 : zerovec_block(long len)
514 : {
515 : long i;
516 18235 : GEN blk = cgetg_block(len + 1, t_VEC);
517 601755 : for (i = 1; i <= len; ++i)
518 583520 : gel(blk, i) = gen_0;
519 18235 : return blk;
520 : }
521 :
522 : /* i-th vector in the standard basis */
523 : INLINE GEN
524 4060756 : col_ei(long n, long i) { GEN e = zerocol(n); gel(e,i) = gen_1; return e; }
525 : INLINE GEN
526 1250218 : vec_ei(long n, long i) { GEN e = zerovec(n); gel(e,i) = gen_1; return e; }
527 : INLINE GEN
528 42 : F2v_ei(long n, long i) { GEN e = zero_F2v(n); F2v_set(e,i); return e; }
529 : INLINE GEN
530 66220 : vecsmall_ei(long n, long i) { GEN e = zero_zv(n); e[i] = 1; return e; }
531 : INLINE GEN
532 1190664 : Rg_col_ei(GEN x, long n, long i) { GEN e = zerocol(n); gel(e,i) = x; return e; }
533 :
534 : INLINE GEN
535 23569370 : shallowcopy(GEN x)
536 23569370 : { return typ(x) == t_MAT ? RgM_shallowcopy(x): leafcopy(x); }
537 :
538 : /* routines for naive growarrays */
539 : INLINE GEN
540 13283595 : vectrunc_init(long l)
541 : {
542 13283595 : GEN z = new_chunk(l);
543 13283609 : z[0] = evaltyp(t_VEC) | _evallg(1); return z;
544 : }
545 : INLINE GEN
546 348180 : coltrunc_init(long l)
547 : {
548 348180 : GEN z = new_chunk(l);
549 348180 : z[0] = evaltyp(t_COL) | _evallg(1); return z;
550 : }
551 : INLINE void
552 355439634 : lg_increase(GEN x) { x[0]++; }
553 : INLINE void
554 54127611 : vectrunc_append(GEN x, GEN t) { gel(x, lg(x)) = t; lg_increase(x); }
555 : INLINE void
556 10864 : vectrunc_append_batch(GEN x, GEN y)
557 : {
558 10864 : long i, l = lg(x), ly = lg(y);
559 10864 : GEN z = x + l-1;
560 36358 : for (i = 1; i < ly; i++) gel(z,i) = gel(y,i);
561 10864 : setlg(x, l+ly-1);
562 10864 : }
563 : INLINE GEN
564 126195602 : vecsmalltrunc_init(long l)
565 : {
566 126195602 : GEN z = new_chunk(l);
567 126123460 : z[0] = evaltyp(t_VECSMALL) | _evallg(1); return z;
568 : }
569 : INLINE void
570 35183330 : vecsmalltrunc_append(GEN x, long t) { x[ lg(x) ] = t; lg_increase(x); }
571 :
572 : /*******************************************************************/
573 : /* */
574 : /* STRING HASH FUNCTIONS */
575 : /* */
576 : /*******************************************************************/
577 : INLINE ulong
578 2295680 : hash_str(const char *str)
579 : {
580 2295680 : ulong hash = 5381UL, c;
581 23521058 : while ( (c = (ulong)*str++) )
582 21225378 : hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
583 2295680 : return hash;
584 : }
585 : INLINE ulong
586 136452912 : hash_str_len(const char *str, long len)
587 : {
588 136452912 : ulong hash = 5381UL;
589 : long i;
590 568075687 : for (i = 0; i < len; i++)
591 : {
592 431622775 : ulong c = (ulong)*str++;
593 431622775 : hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
594 : }
595 136452912 : return hash;
596 : }
597 :
598 : /*******************************************************************/
599 : /* */
600 : /* VEC / COL / VECSMALL */
601 : /* */
602 : /*******************************************************************/
603 : /* shallow*/
604 : INLINE GEN
605 0 : vec_shorten(GEN v, long n)
606 : {
607 : long i;
608 0 : GEN V = cgetg(n+1,t_VEC);
609 0 : for(i=1;i<=n;i++) gel(V,i) = gel(v,i);
610 0 : return V;
611 : }
612 : /* shallow*/
613 : INLINE GEN
614 17674 : vec_lengthen(GEN v, long n)
615 : {
616 : long i;
617 17674 : long l=lg(v);
618 17674 : GEN V = cgetg(n+1,t_VEC);
619 7008650 : for(i=1;i<l;i++) gel(V,i) = gel(v,i);
620 17674 : return V;
621 : }
622 : /* shallow*/
623 : INLINE GEN
624 2538224 : vec_append(GEN V, GEN s)
625 : {
626 2538224 : long i, l2 = lg(V);
627 2538224 : GEN res = cgetg(l2+1, typ(V));
628 6160170 : for (i = 1; i < l2; ++i) gel(res, i) = gel(V,i);
629 2538227 : gel(res,l2) = s; return res;
630 : }
631 : /* shallow*/
632 : INLINE GEN
633 270076 : vec_prepend(GEN v, GEN s)
634 : {
635 270076 : long i, l = lg(v);
636 270076 : GEN w = cgetg(l+1, typ(v));
637 270082 : gel(w,1) = s;
638 529856 : for (i = 2; i <= l; ++i) gel(w,i) = gel(v,i-1);
639 270082 : return w;
640 : }
641 : /* shallow*/
642 : INLINE GEN
643 0 : vec_setconst(GEN v, GEN x)
644 : {
645 0 : long i, l = lg(v);
646 0 : for (i = 1; i < l; i++) gel(v,i) = x;
647 0 : return v;
648 : }
649 : INLINE GEN
650 51650 : vecsmall_shorten(GEN v, long n)
651 : {
652 : long i;
653 51650 : GEN V = cgetg(n+1,t_VECSMALL);
654 628295 : for(i=1;i<=n;i++) V[i] = v[i];
655 51650 : return V;
656 : }
657 : INLINE GEN
658 0 : vecsmall_lengthen(GEN v, long n)
659 : {
660 0 : long i, l = lg(v);
661 0 : GEN V = cgetg(n+1,t_VECSMALL);
662 0 : for(i=1;i<l;i++) V[i] = v[i];
663 0 : return V;
664 : }
665 :
666 : INLINE GEN
667 4220737 : vec_to_vecsmall(GEN x)
668 19510768 : { pari_APPLY_long(itos(gel(x,i))) }
669 : INLINE GEN
670 471310 : vecsmall_to_vec(GEN x)
671 6138923 : { pari_APPLY_type(t_VEC, stoi(x[i])) }
672 : INLINE GEN
673 2457 : vecsmall_to_vec_inplace(GEN z)
674 : {
675 2457 : long i, l = lg(z);
676 76587 : for (i=1; i<l; i++) gel(z,i) = stoi(z[i]);
677 2457 : settyp(z, t_VEC); return z;
678 : }
679 : INLINE GEN
680 6578206 : vecsmall_to_col(GEN x)
681 59184790 : { pari_APPLY_type(t_COL, stoi(x[i])) }
682 :
683 : INLINE int
684 6973952 : vecsmall_lexcmp(GEN x, GEN y)
685 : {
686 : long lx,ly,l,i;
687 6973952 : lx = lg(x);
688 6973952 : ly = lg(y); l = minss(lx,ly);
689 30387665 : for (i=1; i<l; i++)
690 28769406 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
691 1618259 : if (lx == ly) return 0;
692 30578 : return (lx < ly)? -1 : 1;
693 : }
694 :
695 : INLINE int
696 109454527 : vecsmall_prefixcmp(GEN x, GEN y)
697 : {
698 109454527 : long i, lx = lg(x), ly = lg(y), l = minss(lx,ly);
699 578736592 : for (i=1; i<l; i++)
700 556596383 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
701 22140209 : return 0;
702 : }
703 :
704 : /*Can be used on t_VEC, but coeffs not gcopy-ed*/
705 : INLINE GEN
706 179711 : vecsmall_prepend(GEN V, long s)
707 : {
708 179711 : long i, l2 = lg(V);
709 179711 : GEN res = cgetg(l2+1, typ(V));
710 179711 : res[1] = s;
711 602385 : for (i = 2; i <= l2; ++i) res[i] = V[i - 1];
712 179711 : return res;
713 : }
714 :
715 : INLINE GEN
716 3508773 : vecsmall_append(GEN V, long s)
717 : {
718 3508773 : long i, l2 = lg(V);
719 3508773 : GEN res = cgetg(l2+1, t_VECSMALL);
720 5256719 : for (i = 1; i < l2; ++i) res[i] = V[i];
721 3508773 : res[l2] = s; return res;
722 : }
723 :
724 : INLINE GEN
725 1605809 : vecsmall_concat(GEN u, GEN v)
726 : {
727 1605809 : long i, l1 = lg(u)-1, l2 = lg(v)-1;
728 1605809 : GEN res = cgetg(l1+l2+1, t_VECSMALL);
729 13287100 : for (i = 1; i <= l1; ++i) res[i] = u[i];
730 16563764 : for (i = 1; i <= l2; ++i) res[i+l1] = v[i];
731 1605809 : return res;
732 : }
733 :
734 : /* return the number of indices where u and v are equal */
735 : INLINE long
736 0 : vecsmall_coincidence(GEN u, GEN v)
737 : {
738 0 : long i, s = 0, l = minss(lg(u),lg(v));
739 0 : for(i=1; i<l; i++)
740 0 : if(u[i] == v[i]) s++;
741 0 : return s;
742 : }
743 :
744 : /* returns the first index i<=n such that x=v[i] if it exists, 0 otherwise */
745 : INLINE long
746 42 : vecsmall_isin(GEN v, long x)
747 : {
748 42 : long i, l = lg(v);
749 63 : for (i = 1; i < l; i++)
750 42 : if (v[i] == x) return i;
751 21 : return 0;
752 : }
753 :
754 : INLINE long
755 84 : vecsmall_pack(GEN V, long base, long mod)
756 : {
757 84 : long i, s = 0;
758 273 : for(i=1; i<lg(V); i++) s = (base*s + V[i]) % mod;
759 84 : return s;
760 : }
761 :
762 : INLINE long
763 14 : vecsmall_indexmax(GEN x)
764 : {
765 14 : long i, i0 = 1, t = x[1], lx = lg(x);
766 56 : for (i=2; i<lx; i++)
767 42 : if (x[i] > t) t = x[i0=i];
768 14 : return i0;
769 : }
770 :
771 : INLINE long
772 364152 : vecsmall_max(GEN x)
773 : {
774 364152 : long i, t = x[1], lx = lg(x);
775 889587 : for (i=2; i<lx; i++)
776 525435 : if (x[i] > t) t = x[i];
777 364152 : return t;
778 : }
779 :
780 : INLINE long
781 14 : vecsmall_indexmin(GEN x)
782 : {
783 14 : long i, i0 = 1, t = x[1], lx =lg(x);
784 56 : for (i=2; i<lx; i++)
785 42 : if (x[i] < t) t = x[i0=i];
786 14 : return i0;
787 : }
788 :
789 : INLINE long
790 1421 : vecsmall_min(GEN x)
791 : {
792 1421 : long i, t = x[1], lx =lg(x);
793 9947 : for (i=2; i<lx; i++)
794 8526 : if (x[i] < t) t = x[i];
795 1421 : return t;
796 : }
797 :
798 : INLINE int
799 10880785 : ZV_isscalar(GEN x)
800 : {
801 10880785 : long l = lg(x);
802 26512442 : while (--l > 1)
803 24785816 : if (signe(gel(x, l))) return 0;
804 1726626 : return 1;
805 : }
806 : INLINE int
807 34527145 : QV_isscalar(GEN x)
808 : {
809 34527145 : long lx = lg(x),i;
810 39450699 : for (i=2; i<lx; i++)
811 38249366 : if (!isintzero(gel(x, i))) return 0;
812 1201333 : return 1;
813 : }
814 : INLINE int
815 9578 : RgV_isscalar(GEN x)
816 : {
817 9578 : long lx = lg(x),i;
818 10306 : for (i=2; i<lx; i++)
819 10264 : if (!gequal0(gel(x, i))) return 0;
820 42 : return 1;
821 : }
822 : INLINE int
823 0 : RgX_isscalar(GEN x)
824 : {
825 : long i;
826 0 : for (i=lg(x)-1; i>2; i--)
827 0 : if (!gequal0(gel(x, i))) return 0;
828 0 : return 1;
829 : }
830 : INLINE long
831 25357229 : RgX_equal_var(GEN x, GEN y) { return varn(x) == varn(y) && RgX_equal(x,y); }
832 : INLINE GEN
833 140 : RgX_to_RgV(GEN x, long N) { x = RgX_to_RgC(x, N); settyp(x, t_VEC); return x; }
834 :
835 : INLINE int
836 63651 : RgX_is_rational(GEN x)
837 : {
838 : long i;
839 296284 : for (i = lg(x)-1; i > 1; i--)
840 281048 : if (!is_rational_t(typ(gel(x,i)))) return 0;
841 15236 : return 1;
842 : }
843 : INLINE int
844 10984813 : RgX_is_ZX(GEN x)
845 : {
846 : long i;
847 46881314 : for (i = lg(x)-1; i > 1; i--)
848 35953969 : if (typ(gel(x,i)) != t_INT) return 0;
849 10927345 : return 1;
850 : }
851 : INLINE int
852 333031 : RgX_is_QX(GEN x)
853 : {
854 333031 : long k = lg(x)-1;
855 1230523 : for ( ; k>1; k--)
856 897772 : if (!is_rational_t(typ(gel(x,k)))) return 0;
857 332751 : return 1;
858 : }
859 : INLINE int
860 17172521 : RgX_is_monomial(GEN x)
861 : {
862 : long i;
863 17172521 : if (!signe(x)) return 0;
864 35512387 : for (i=lg(x)-2; i>1; i--)
865 18397179 : if (!isexactzero(gel(x,i))) return 0;
866 17115208 : return 1;
867 : }
868 : INLINE int
869 30040345 : RgV_is_ZV(GEN x)
870 : {
871 : long i;
872 120096148 : for (i = lg(x)-1; i > 0; i--)
873 90084629 : if (typ(gel(x,i)) != t_INT) return 0;
874 30011519 : return 1;
875 : }
876 : INLINE int
877 107856 : RgV_is_QV(GEN x)
878 : {
879 : long i;
880 515960 : for (i = lg(x)-1; i > 0; i--)
881 411026 : if (!is_rational_t(typ(gel(x,i)))) return 0;
882 104934 : return 1;
883 : }
884 : INLINE long
885 194208 : RgV_isin_i(GEN v, GEN x, long n)
886 : {
887 : long i;
888 3765090 : for (i = 1; i <= n; i++)
889 3764558 : if (gequal(gel(v,i), x)) return i;
890 532 : return 0;
891 : }
892 : INLINE long
893 194208 : RgV_isin(GEN v, GEN x) { return RgV_isin_i(v, x, lg(v)-1); }
894 :
895 : /********************************************************************/
896 : /** **/
897 : /** Dynamic arrays implementation **/
898 : /** **/
899 : /********************************************************************/
900 : INLINE void **
901 994248097 : pari_stack_base(pari_stack *s) { return s->data; }
902 :
903 : INLINE void
904 3526149 : pari_stack_init(pari_stack *s, size_t size, void **data)
905 : {
906 3526149 : s->data = data;
907 3526149 : *data = NULL;
908 3526149 : s->n = 0;
909 3526149 : s->alloc = 0;
910 3526149 : s->size = size;
911 3526149 : }
912 :
913 : INLINE void
914 990958009 : pari_stack_alloc(pari_stack *s, long nb)
915 : {
916 990958009 : void **sdat = pari_stack_base(s);
917 990952070 : long alloc = s->alloc;
918 990952070 : if (s->n+nb <= alloc) return;
919 1363016 : if (!alloc)
920 1266661 : alloc = nb;
921 : else
922 : {
923 193304 : while (s->n+nb > alloc) alloc <<= 1;
924 : }
925 1363016 : pari_realloc_ip(sdat,alloc*s->size);
926 1365686 : s->alloc = alloc;
927 : }
928 :
929 : INLINE long
930 905476296 : pari_stack_new(pari_stack *s) { pari_stack_alloc(s, 1); return s->n++; }
931 :
932 : INLINE void
933 3291991 : pari_stack_delete(pari_stack *s)
934 : {
935 3291991 : void **sdat = pari_stack_base(s);
936 3287557 : if (*sdat) pari_free(*sdat);
937 3303289 : }
938 :
939 : INLINE void
940 5228 : pari_stack_pushp(pari_stack *s, void *u)
941 : {
942 5228 : long n = pari_stack_new(s);
943 5228 : void **sdat =(void**) *pari_stack_base(s);
944 5228 : sdat[n] = u;
945 5228 : }
946 :
947 : /*******************************************************************/
948 : /* */
949 : /* EXTRACT */
950 : /* */
951 : /*******************************************************************/
952 : INLINE GEN
953 559727947 : vecslice(GEN A, long y1, long y2)
954 : {
955 559727947 : long i,lB = y2 - y1 + 2;
956 559727947 : GEN B = cgetg(lB, typ(A));
957 2511520120 : for (i=1; i<lB; i++) B[i] = A[y1-1+i];
958 559721827 : return B;
959 : }
960 : INLINE GEN
961 2027271 : vecslicepermute(GEN A, GEN p, long y1, long y2)
962 : {
963 2027271 : long i,lB = y2 - y1 + 2;
964 2027271 : GEN B = cgetg(lB, typ(A));
965 35416107 : for (i=1; i<lB; i++) B[i] = A[p[y1-1+i]];
966 2027260 : return B;
967 : }
968 : /* rowslice(rowpermute(A,p), x1, x2) */
969 : INLINE GEN
970 193312 : rowslicepermute(GEN x, GEN p, long j1, long j2)
971 837708 : { pari_APPLY_same(vecslicepermute(gel(x,i),p,j1,j2)) }
972 :
973 : INLINE GEN
974 57861724 : rowslice(GEN x, long j1, long j2)
975 569314923 : { pari_APPLY_same(vecslice(gel(x,i), j1, j2)) }
976 :
977 : INLINE GEN
978 8589505 : matslice(GEN A, long x1, long x2, long y1, long y2)
979 8589505 : { return rowslice(vecslice(A, y1, y2), x1, x2); }
980 :
981 : /* shallow, remove coeff of index j */
982 : INLINE GEN
983 210 : rowsplice(GEN x, long j)
984 1036 : { pari_APPLY_same(vecsplice(gel(x,i), j)) }
985 :
986 : /* shallow, remove coeff of index j */
987 : INLINE GEN
988 349945 : vecsplice(GEN a, long j)
989 : {
990 349945 : long i, k, l = lg(a);
991 : GEN b;
992 349945 : if (l == 1) pari_err(e_MISC, "incorrect component in vecsplice");
993 349945 : b = cgetg(l-1, typ(a));
994 1471460 : for (i = k = 1; i < l; i++)
995 1121514 : if (i != j) gel(b, k++) = gel(a,i);
996 349946 : return b;
997 : }
998 : /* shallow */
999 : INLINE GEN
1000 1036 : RgM_minor(GEN a, long i, long j)
1001 : {
1002 1036 : GEN b = vecsplice(a, j);
1003 1036 : long k, l = lg(b);
1004 4242 : for (k = 1; k < l; k++) gel(b,k) = vecsplice(gel(b,k), i);
1005 1036 : return b;
1006 : }
1007 :
1008 : /* A[x0,] */
1009 : INLINE GEN
1010 418995 : row(GEN x, long j)
1011 4154441 : { pari_APPLY_type(t_VEC, gcoeff(x, j, i)) }
1012 : INLINE GEN
1013 9202760 : Flm_row(GEN x, long j)
1014 235616228 : { pari_APPLY_ulong((ulong)coeff(x, j, i)) }
1015 : /* A[x0,] */
1016 : INLINE GEN
1017 204834 : rowcopy(GEN x, long j)
1018 2097809 : { pari_APPLY_type(t_VEC, gcopy(gcoeff(x, j, i))) }
1019 : /* A[x0, x1..x2] */
1020 : INLINE GEN
1021 987 : row_i(GEN A, long x0, long x1, long x2)
1022 : {
1023 987 : long i, lB = x2 - x1 + 2;
1024 987 : GEN B = cgetg(lB, t_VEC);
1025 2989 : for (i=x1; i<=x2; i++) gel(B, i) = gcoeff(A, x0, i);
1026 987 : return B;
1027 : }
1028 :
1029 : INLINE GEN
1030 6101792 : vecreverse(GEN A)
1031 : {
1032 : long i, l;
1033 6101792 : GEN B = cgetg_copy(A, &l);
1034 14807657 : for (i=1; i<l; i++) gel(B, i) = gel(A, l-i);
1035 6101792 : return B;
1036 : }
1037 :
1038 : INLINE GEN
1039 2954 : vecsmall_reverse(GEN A)
1040 : {
1041 : long i, l;
1042 2954 : GEN B = cgetg_copy(A, &l);
1043 11648 : for (i=1; i<l; i++) B[i] = A[l-i];
1044 2954 : return B;
1045 : }
1046 :
1047 : INLINE void
1048 449 : vecreverse_inplace(GEN y)
1049 : {
1050 449 : long l = lg(y), lim = l>>1, i;
1051 1704 : for (i = 1; i <= lim; i++)
1052 : {
1053 1255 : GEN z = gel(y,i);
1054 1255 : gel(y,i) = gel(y,l-i);
1055 1255 : gel(y,l-i) = z;
1056 : }
1057 449 : }
1058 :
1059 : INLINE GEN
1060 70164952 : vecsmallpermute(GEN A, GEN p) { return perm_mul(A, p); }
1061 :
1062 : INLINE GEN
1063 11262279 : vecpermute(GEN A, GEN x)
1064 123927873 : { pari_APPLY_type(typ(A), gel(A, x[i])) }
1065 :
1066 : INLINE GEN
1067 8420734 : rowpermute(GEN x, GEN p)
1068 79619196 : { pari_APPLY_same(typ(gel(x,i)) == t_VECSMALL ? vecsmallpermute(gel(x, i), p)
1069 : : vecpermute(gel(x, i), p))
1070 : }
1071 : /*******************************************************************/
1072 : /* */
1073 : /* PERMUTATIONS */
1074 : /* */
1075 : /*******************************************************************/
1076 : INLINE GEN
1077 1773617 : identity_zv(long n)
1078 : {
1079 1773617 : GEN v = cgetg(n+1, t_VECSMALL);
1080 : long i;
1081 24258744 : for (i = 1; i <= n; i++) v[i] = i;
1082 1773605 : return v;
1083 : }
1084 : INLINE GEN
1085 4179 : identity_ZV(long n)
1086 : {
1087 4179 : GEN v = cgetg(n+1, t_VEC);
1088 : long i;
1089 51121 : for (i = 1; i <= n; i++) gel(v,i) = utoipos(i);
1090 4179 : return v;
1091 : }
1092 : /* identity permutation */
1093 : INLINE GEN
1094 1749522 : identity_perm(long n) { return identity_zv(n); }
1095 :
1096 : /* assume d <= n */
1097 : INLINE GEN
1098 98483 : cyclic_perm(long n, long d)
1099 : {
1100 98483 : GEN perm = cgetg(n+1, t_VECSMALL);
1101 : long i;
1102 504098 : for (i = 1; i <= n-d; i++) perm[i] = i+d;
1103 225029 : for ( ; i <= n; i++) perm[i] = i-n+d;
1104 98483 : return perm;
1105 : }
1106 :
1107 : /* Multiply (compose) two permutations */
1108 : INLINE GEN
1109 72213466 : perm_mul(GEN s, GEN x)
1110 959393538 : { pari_APPLY_long(s[x[i]]) }
1111 :
1112 : INLINE GEN
1113 749 : perm_sqr(GEN x)
1114 18725 : { pari_APPLY_long(x[x[i]]) }
1115 :
1116 : /* Compute the inverse (reciprocal) of a permutation. */
1117 : INLINE GEN
1118 2282545 : perm_inv(GEN x)
1119 : {
1120 : long i, lx;
1121 2282545 : GEN y = cgetg_copy(x, &lx);
1122 34382532 : for (i=1; i<lx; i++) y[ x[i] ] = i;
1123 2282541 : return y;
1124 : }
1125 : /* Return s*t*s^-1 */
1126 : INLINE GEN
1127 417816 : perm_conj(GEN s, GEN t)
1128 : {
1129 : long i, l;
1130 417816 : GEN v = cgetg_copy(s, &l);
1131 6853658 : for (i = 1; i < l; i++) v[ s[i] ] = s[ t[i] ];
1132 417816 : return v;
1133 : }
1134 :
1135 : INLINE void
1136 496105015 : pari_free(void *pointer)
1137 : {
1138 496105015 : BLOCK_SIGINT_START;
1139 496164906 : free(pointer);
1140 496164906 : BLOCK_SIGINT_END;
1141 496166588 : }
1142 : INLINE void*
1143 717884694 : pari_malloc(size_t size)
1144 : {
1145 717884694 : if (size)
1146 : {
1147 : char *tmp;
1148 717886865 : BLOCK_SIGINT_START;
1149 717962998 : tmp = (char*)malloc(size);
1150 717962998 : BLOCK_SIGINT_END;
1151 717967151 : if (!tmp) pari_err(e_MEM);
1152 717976446 : return tmp;
1153 : }
1154 0 : return NULL;
1155 : }
1156 : INLINE void*
1157 1689 : pari_realloc(void *pointer, size_t size)
1158 : {
1159 : char *tmp;
1160 :
1161 1689 : BLOCK_SIGINT_START;
1162 1689 : if (!pointer) tmp = (char *) malloc(size);
1163 1689 : else tmp = (char *) realloc(pointer,size);
1164 1689 : BLOCK_SIGINT_END;
1165 1689 : if (!tmp) pari_err(e_MEM);
1166 1689 : return tmp;
1167 : }
1168 : INLINE void
1169 1425994 : pari_realloc_ip(void **pointer, size_t size)
1170 : {
1171 : char *tmp;
1172 1425994 : BLOCK_SIGINT_START;
1173 1424521 : if (!*pointer) tmp = (char *) malloc(size);
1174 97558 : else tmp = (char *) realloc(*pointer,size);
1175 1424521 : if (!tmp) pari_err(e_MEM);
1176 1424521 : *pointer = tmp;
1177 1424521 : BLOCK_SIGINT_END;
1178 1420132 : }
1179 :
1180 : INLINE void*
1181 40602 : pari_calloc(size_t size)
1182 : {
1183 40602 : void *t = pari_malloc(size);
1184 40602 : memset(t, 0, size); return t;
1185 : }
1186 : INLINE GEN
1187 8001 : cgetalloc(long t, size_t l)
1188 : { /* evallg may raise e_OVERFLOW, which would leak x */
1189 8001 : ulong x0 = evaltyp(t) | evallg(l);
1190 8001 : GEN x = (GEN)pari_malloc(l * sizeof(long));
1191 8001 : x[0] = x0; return x;
1192 : }
1193 :
1194 : /*******************************************************************/
1195 : /* */
1196 : /* GARBAGE COLLECTION */
1197 : /* */
1198 : /*******************************************************************/
1199 : /* copy integer x as if we had set_avma(av) */
1200 : INLINE GEN
1201 6072431926 : icopy_avma(GEN x, pari_sp av)
1202 : {
1203 6072431926 : long i = lgefint(x), lx = i;
1204 6072431926 : GEN y = ((GEN)av) - i;
1205 33024117896 : while (--i > 0) y[i] = x[i];
1206 6072431926 : y[0] = evaltyp(t_INT)|evallg(lx);
1207 6075718729 : return y;
1208 : }
1209 : /* copy leaf x as if we had set_avma(av) */
1210 : INLINE GEN
1211 445890051 : leafcopy_avma(GEN x, pari_sp av)
1212 : {
1213 445890051 : long i = lg(x);
1214 445890051 : GEN y = ((GEN)av) - i;
1215 2912762216 : while (--i > 0) y[i] = x[i];
1216 445890051 : y[0] = x[0] & (~CLONEBIT);
1217 445890051 : return y;
1218 : }
1219 : INLINE GEN
1220 891215817 : gerepileuptoleaf(pari_sp av, GEN x)
1221 : {
1222 : long lx;
1223 : GEN q;
1224 :
1225 891215817 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1226 890643679 : lx = lg(x);
1227 890643679 : q = ((GEN)av) - lx;
1228 890643679 : set_avma((pari_sp)q);
1229 9078526801 : while (--lx >= 0) q[lx] = x[lx];
1230 890651244 : return q;
1231 : }
1232 : INLINE GEN
1233 2594106605 : gerepileuptoint(pari_sp av, GEN x)
1234 : {
1235 2594106605 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1236 2254926884 : set_avma((pari_sp)icopy_avma(x, av));
1237 2257491856 : return (GEN)avma;
1238 : }
1239 : INLINE GEN
1240 1327758846 : gerepileupto(pari_sp av, GEN x)
1241 : {
1242 1327758846 : if (!isonstack(x) || (GEN)av<=x) return gc_const(av,x);
1243 1198754919 : switch(typ(x))
1244 : { /* non-default = !is_recursive_t(tq) */
1245 318401008 : case t_INT: return gerepileuptoint(av, x);
1246 236551833 : case t_REAL:
1247 : case t_STR:
1248 236551833 : case t_VECSMALL: return gerepileuptoleaf(av,x);
1249 643803416 : default:
1250 : /* NB: x+i --> ((long)x) + i*sizeof(long) */
1251 643803416 : return gerepile(av, (pari_sp) (x+lg(x)), x);
1252 : }
1253 : }
1254 :
1255 : /* gerepileupto(av, gcopy(x)) */
1256 : INLINE GEN
1257 167861249 : gerepilecopy(pari_sp av, GEN x)
1258 : {
1259 167861249 : if (is_recursive_t(typ(x)))
1260 : {
1261 161704033 : GENbin *p = copy_bin(x);
1262 161717045 : set_avma(av); return bin_copy(p);
1263 : }
1264 : else
1265 : {
1266 6158007 : set_avma(av);
1267 6158029 : if (x < (GEN)av) {
1268 4427854 : if (x < (GEN)pari_mainstack->bot) new_chunk(lg(x));
1269 4427861 : x = leafcopy_avma(x, av);
1270 4427889 : set_avma((pari_sp)x);
1271 : } else
1272 1730175 : x = leafcopy(x);
1273 6158062 : return x;
1274 : }
1275 : }
1276 :
1277 : INLINE void
1278 27886197 : guncloneNULL(GEN x) { if (x) gunclone(x); }
1279 : INLINE void
1280 446734 : guncloneNULL_deep(GEN x) { if (x) gunclone_deep(x); }
1281 :
1282 : /* Takes an array of pointers to GENs, of length n. Copies all
1283 : * objects to contiguous locations and cleans up the stack between
1284 : * av and avma. */
1285 : INLINE void
1286 936464 : gerepilemany(pari_sp av, GEN* gptr[], int n)
1287 : {
1288 : int i;
1289 3737656 : for (i=0; i<n; i++) *gptr[i] = (GEN)copy_bin(*gptr[i]);
1290 935995 : set_avma(av);
1291 3738377 : for (i=0; i<n; i++) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1292 936754 : }
1293 :
1294 : INLINE void
1295 125411856 : gerepileall(pari_sp av, int n, ...)
1296 : {
1297 : int i;
1298 125411856 : va_list a; va_start(a, n);
1299 125411856 : if (n < 10)
1300 : {
1301 : GEN *gptr[10];
1302 416222507 : for (i=0; i<n; i++)
1303 290809998 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1304 125412509 : set_avma(av);
1305 416223422 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1306 :
1307 : }
1308 : else
1309 : {
1310 0 : GEN **gptr = (GEN**) pari_malloc(n*sizeof(GEN*));
1311 0 : for (i=0; i<n; i++)
1312 0 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1313 0 : set_avma(av);
1314 0 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1315 0 : pari_free(gptr);
1316 : }
1317 125413378 : va_end(a);
1318 125413378 : }
1319 :
1320 : INLINE void
1321 2745562 : gerepilecoeffs(pari_sp av, GEN x, int n)
1322 : {
1323 : int i;
1324 32466923 : for (i=0; i<n; i++) gel(x,i) = (GEN)copy_bin(gel(x,i));
1325 2746032 : set_avma(av);
1326 32468317 : for (i=0; i<n; i++) gel(x,i) = bin_copy((GENbin*)x[i]);
1327 2745729 : }
1328 :
1329 : /* p from copy_bin. Copy p->x back to stack, then destroy p */
1330 : INLINE GEN
1331 485105576 : bin_copy(GENbin *p)
1332 : {
1333 : GEN x, y, base;
1334 : long dx, len;
1335 :
1336 485105576 : x = p->x; if (!x) { pari_free(p); return gen_0; }
1337 449848568 : len = p->len;
1338 449848568 : base= p->base; dx = x - base;
1339 449848568 : y = (GEN)memcpy((void*)new_chunk(len), (void*)GENbinbase(p), len*sizeof(long));
1340 449845927 : y += dx;
1341 449845927 : p->rebase(y, ((ulong)y-(ulong)x));
1342 449843249 : pari_free(p); return y;
1343 : }
1344 :
1345 : INLINE GEN
1346 934951884 : GENbinbase(GENbin *p) { return (GEN)(p + 1); }
1347 :
1348 : INLINE void
1349 93266342 : cgiv(GEN x)
1350 : {
1351 93266342 : pari_sp av = (pari_sp)(x+lg(x));
1352 93266342 : if (isonstack((GEN)av)) set_avma(av);
1353 93267321 : }
1354 :
1355 : INLINE void
1356 6696465 : killblock(GEN x) { gunclone(x); }
1357 :
1358 : INLINE int
1359 247468042 : is_universal_constant(GEN x) { return (x >= gen_0 && x <= ghalf); }
1360 :
1361 : /*******************************************************************/
1362 : /* */
1363 : /* CONVERSION / ASSIGNMENT */
1364 : /* */
1365 : /*******************************************************************/
1366 : /* z is a type which may be a t_COMPLEX component (not a t_QUAD) */
1367 : INLINE GEN
1368 18133843 : cxcompotor(GEN z, long prec)
1369 : {
1370 18133843 : switch(typ(z))
1371 : {
1372 13670451 : case t_INT: return itor(z, prec);
1373 284074 : case t_FRAC: return fractor(z, prec);
1374 4179696 : case t_REAL: return rtor(z, prec);
1375 0 : default: pari_err_TYPE("cxcompotor",z);
1376 : return NULL; /* LCOV_EXCL_LINE */
1377 : }
1378 : }
1379 : INLINE GEN
1380 9051816 : cxtofp(GEN x, long prec)
1381 9051816 : { retmkcomplex(cxcompotor(gel(x,1),prec), cxcompotor(gel(x,2),prec)); }
1382 :
1383 : INLINE GEN
1384 273443 : cxtoreal(GEN q)
1385 273443 : { return (typ(q) == t_COMPLEX && gequal0(gel(q,2)))? gel(q,1): q; }
1386 :
1387 : INLINE double
1388 60819732 : gtodouble(GEN x)
1389 : {
1390 60819732 : if (typ(x)!=t_REAL) {
1391 5127255 : pari_sp av = avma;
1392 5127255 : x = gtofp(x, DEFAULTPREC);
1393 5126650 : if (typ(x)!=t_REAL) pari_err_TYPE("gtodouble [t_REAL expected]", x);
1394 5126650 : set_avma(av);
1395 : }
1396 60818988 : return rtodbl(x);
1397 : }
1398 :
1399 : INLINE int
1400 16046693 : gisdouble(GEN x, double *g)
1401 : {
1402 16046693 : if (typ(x)!=t_REAL) {
1403 1432105 : pari_sp av = avma;
1404 1432105 : x = gtofp(x, DEFAULTPREC);
1405 1432103 : if (typ(x)!=t_REAL) pari_err_TYPE("gisdouble [t_REAL expected]", x);
1406 1432103 : set_avma(av);
1407 : }
1408 16046675 : if (expo(x) >= 0x3ff) return 0;
1409 16046675 : *g = rtodbl(x); return 1;
1410 : }
1411 :
1412 : INLINE long
1413 73572053 : gtos(GEN x) {
1414 73572053 : if (typ(x) != t_INT) pari_err_TYPE("gtos [integer expected]",x);
1415 73572046 : return itos(x);
1416 : }
1417 :
1418 : INLINE ulong
1419 95950 : gtou(GEN x) {
1420 95950 : if (typ(x) != t_INT || signe(x)<0)
1421 7 : pari_err_TYPE("gtou [integer >=0 expected]",x);
1422 95943 : return itou(x);
1423 : }
1424 :
1425 : INLINE GEN
1426 37996030 : absfrac(GEN x)
1427 : {
1428 37996030 : GEN y = cgetg(3, t_FRAC);
1429 37996065 : gel(y,1) = absi(gel(x,1));
1430 37996059 : gel(y,2) = icopy(gel(x,2)); return y;
1431 : }
1432 : INLINE GEN
1433 41545 : absfrac_shallow(GEN x)
1434 41545 : { return signe(gel(x,1))>0? x: mkfrac(negi(gel(x,1)), gel(x,2)); }
1435 : INLINE GEN
1436 6768358 : Q_abs(GEN x) { return (typ(x) == t_INT)? absi(x): absfrac(x); }
1437 : INLINE GEN
1438 153601 : Q_abs_shallow(GEN x)
1439 153601 : { return (typ(x) == t_INT)? absi_shallow(x): absfrac_shallow(x); }
1440 : INLINE GEN
1441 12712 : R_abs_shallow(GEN x)
1442 12712 : { return (typ(x) == t_FRAC)? absfrac_shallow(x): mpabs_shallow(x); }
1443 : INLINE GEN
1444 0 : R_abs(GEN x)
1445 0 : { return (typ(x) == t_FRAC)? absfrac(x): mpabs(x); }
1446 :
1447 : /* Force z to be of type real/complex with floating point components */
1448 : INLINE GEN
1449 79084728 : gtofp(GEN z, long prec)
1450 : {
1451 79084728 : switch(typ(z))
1452 : {
1453 44375971 : case t_INT: return itor(z, prec);
1454 4355153 : case t_FRAC: return fractor(z, prec);
1455 21572699 : case t_REAL: return rtor(z, prec);
1456 8789270 : case t_COMPLEX: {
1457 8789270 : GEN a = gel(z,1), b = gel(z,2);
1458 8789270 : if (isintzero(b)) return cxcompotor(a, prec);
1459 8789318 : if (isintzero(a)) {
1460 9484 : GEN y = cgetg(3, t_COMPLEX);
1461 9484 : b = cxcompotor(b, prec);
1462 9484 : gel(y,1) = real_0_bit(expo(b) - prec2nbits(prec));
1463 9484 : gel(y,2) = b; return y;
1464 : }
1465 8779841 : return cxtofp(z, prec);
1466 : }
1467 0 : case t_QUAD: return quadtofp(z, prec);
1468 0 : default: pari_err_TYPE("gtofp",z);
1469 : return NULL; /* LCOV_EXCL_LINE */
1470 : }
1471 : }
1472 : /* Force z to be of type real / int */
1473 : INLINE GEN
1474 22428 : gtomp(GEN z, long prec)
1475 : {
1476 22428 : switch(typ(z))
1477 : {
1478 42 : case t_INT: return z;
1479 22386 : case t_FRAC: return fractor(z, prec);
1480 0 : case t_REAL: return rtor(z, prec);
1481 0 : case t_QUAD: z = quadtofp(z, prec);
1482 0 : if (typ(z) == t_REAL) return z;
1483 0 : default: pari_err_TYPE("gtomp",z);
1484 : return NULL; /* LCOV_EXCL_LINE */
1485 : }
1486 : }
1487 :
1488 : INLINE GEN
1489 5800537 : RgX_gtofp(GEN x, long prec)
1490 : {
1491 : long l;
1492 5800537 : GEN y = cgetg_copy(x, &l);
1493 33440775 : while (--l > 1) gel(y,l) = gtofp(gel(x,l), prec);
1494 5798527 : y[1] = x[1]; return y;
1495 : }
1496 : INLINE GEN
1497 2521138 : RgC_gtofp(GEN x, long prec)
1498 22862804 : { pari_APPLY_type(t_COL, gtofp(gel(x,i), prec)) }
1499 :
1500 : INLINE GEN
1501 49 : RgV_gtofp(GEN x, long prec)
1502 4746 : { pari_APPLY_type(t_VEC, gtofp(gel(x,i), prec)) }
1503 :
1504 : INLINE GEN
1505 396728 : RgM_gtofp(GEN x, long prec)
1506 2340247 : { pari_APPLY_same(RgC_gtofp(gel(x,i), prec)) }
1507 :
1508 : INLINE GEN
1509 574 : RgC_gtomp(GEN x, long prec)
1510 23002 : { pari_APPLY_type(t_COL, gtomp(gel(x,i), prec)) }
1511 :
1512 : INLINE GEN
1513 21 : RgM_gtomp(GEN x, long prec)
1514 595 : { pari_APPLY_same(RgC_gtomp(gel(x,i), prec)) }
1515 :
1516 : INLINE GEN
1517 96719 : RgX_fpnorml2(GEN x, long prec)
1518 : {
1519 96719 : pari_sp av = avma;
1520 96719 : return gerepileupto(av, gnorml2(RgX_gtofp(x, prec)));
1521 : }
1522 : INLINE GEN
1523 567732 : RgC_fpnorml2(GEN x, long prec)
1524 : {
1525 567732 : pari_sp av = avma;
1526 567732 : return gerepileupto(av, gnorml2(RgC_gtofp(x, prec)));
1527 : }
1528 : INLINE GEN
1529 18651 : RgM_fpnorml2(GEN x, long prec)
1530 : {
1531 18651 : pari_sp av = avma;
1532 18651 : return gerepileupto(av, gnorml2(RgM_gtofp(x, prec)));
1533 : }
1534 :
1535 : /* y a t_REAL */
1536 : INLINE void
1537 216244 : affgr(GEN x, GEN y)
1538 : {
1539 : pari_sp av;
1540 216244 : switch(typ(x)) {
1541 5992 : case t_INT: affir(x,y); break;
1542 210252 : case t_REAL: affrr(x,y); break;
1543 0 : case t_FRAC: rdiviiz(gel(x,1),gel(x,2), y); break;
1544 0 : case t_QUAD: av = avma; affgr(quadtofp(x,realprec(y)), y); set_avma(av); break;
1545 0 : default: pari_err_TYPE2("=",x,y);
1546 : }
1547 216244 : }
1548 :
1549 : INLINE GEN
1550 243089 : affc_fixlg(GEN x, GEN res)
1551 : {
1552 243089 : if (typ(x) == t_COMPLEX)
1553 : {
1554 210679 : affrr_fixlg(gel(x,1), gel(res,1));
1555 210679 : affrr_fixlg(gel(x,2), gel(res,2));
1556 : }
1557 : else
1558 : {
1559 32410 : set_avma((pari_sp)(res+3));
1560 32408 : res = cgetr(realprec(gel(res,1)));
1561 32412 : affrr_fixlg(x, res);
1562 : }
1563 243091 : return res;
1564 : }
1565 :
1566 : INLINE GEN
1567 0 : trunc_safe(GEN x) { long e; return gcvtoi(x,&e); }
1568 :
1569 : /*******************************************************************/
1570 : /* */
1571 : /* LENGTH CONVERSIONS */
1572 : /* */
1573 : /*******************************************************************/
1574 : INLINE long
1575 37286 : ndec2nlong(long x) { return 1 + (long)((x)*(LOG2_10/BITS_IN_LONG)); }
1576 : INLINE long
1577 28988 : ndec2prec(long x) { return 2 + ndec2nlong(x); }
1578 : INLINE long
1579 8298 : ndec2nbits(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1580 : /* Fast implementation of ceil(x / (8*sizeof(long))); typecast to (ulong)
1581 : * to avoid overflow. Faster than 1 + ((x-1)>>TWOPOTBITS_IN_LONG)) :
1582 : * addl, shrl instead of subl, sarl, addl */
1583 : INLINE long
1584 9990775 : nbits2nlong(long x) {
1585 9990775 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1586 : }
1587 :
1588 : INLINE long
1589 307360458 : nbits2extraprec(long x) {
1590 307360458 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1591 : }
1592 :
1593 : /* Fast implementation of 2 + nbits2nlong(x) */
1594 : INLINE long
1595 192342030 : nbits2prec(long x) {
1596 192342030 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1597 : }
1598 : INLINE long
1599 243419247 : nbits2lg(long x) {
1600 243419247 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1601 : }
1602 : /* ceil(x / sizeof(long)) */
1603 : INLINE long
1604 110684421 : nchar2nlong(long x) {
1605 110684421 : return (long)(((ulong)x+sizeof(long)-1) >> (TWOPOTBITS_IN_LONG-3L));
1606 : }
1607 : INLINE long
1608 2152201775 : prec2nbits(long x) { return (x-2) * BITS_IN_LONG; }
1609 : INLINE double
1610 2866304 : bit_accuracy_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1611 : INLINE double
1612 273060 : prec2nbits_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1613 : INLINE long
1614 118040230 : bit_prec(GEN x) { return prec2nbits(realprec(x)); }
1615 : INLINE long
1616 1916921354 : bit_accuracy(long x) { return prec2nbits(x); }
1617 : INLINE long
1618 12861 : prec2ndec(long x) { return (long)prec2nbits_mul(x, LOG10_2); }
1619 : INLINE long
1620 200 : nbits2ndec(long x) { return (long)(x * LOG10_2); }
1621 : INLINE long
1622 4461 : precdbl(long x) {return (x - 1) << 1;}
1623 : INLINE long
1624 5329915491 : divsBIL(long n) { return n >> TWOPOTBITS_IN_LONG; }
1625 : INLINE long
1626 5262160369 : remsBIL(long n) { return n & (BITS_IN_LONG-1); }
1627 :
1628 : /*********************************************************************/
1629 : /** **/
1630 : /** OPERATIONS MODULO m **/
1631 : /** **/
1632 : /*********************************************************************/
1633 : /* Assume m > 0, more efficient if 0 <= a, b < m */
1634 :
1635 : INLINE GEN
1636 45370681 : Fp_red(GEN a, GEN m) { return modii(a, m); }
1637 : INLINE GEN
1638 97336065 : Fp_add(GEN a, GEN b, GEN m)
1639 : {
1640 97336065 : pari_sp av=avma;
1641 97336065 : GEN p = addii(a,b);
1642 95696327 : long s = signe(p);
1643 95696327 : if (!s) return p; /* = gen_0 */
1644 84787934 : if (s > 0) /* general case */
1645 : {
1646 84838886 : GEN t = subii(p, m);
1647 84487151 : s = signe(t);
1648 84487151 : if (!s) return gc_const(av, gen_0);
1649 77043572 : if (s < 0) return gc_const((pari_sp)p, p);
1650 38869938 : if (cmpii(t, m) < 0) return gerepileuptoint(av, t); /* general case ! */
1651 3001534 : p = remii(t, m);
1652 : }
1653 : else
1654 226428 : p = modii(p, m);
1655 3228074 : return gerepileuptoint(av, p);
1656 : }
1657 : INLINE GEN
1658 73775689 : Fp_sub(GEN a, GEN b, GEN m)
1659 : {
1660 73775689 : pari_sp av=avma;
1661 73775689 : GEN p = subii(a,b);
1662 71325898 : long s = signe(p);
1663 71325898 : if (!s) return p; /* = gen_0 */
1664 61876204 : if (s > 0)
1665 : {
1666 26717557 : if (cmpii(p, m) < 0) return p; /* general case ! */
1667 1058980 : p = remii(p, m);
1668 : }
1669 : else
1670 : {
1671 35158647 : GEN t = addii(p, m);
1672 36911094 : if (!s) return gc_const(av, gen_0);
1673 36985709 : if (s > 0) return gerepileuptoint(av, t); /* general case ! */
1674 36985709 : p = modii(t, m);
1675 : }
1676 38401150 : return gerepileuptoint(av, p);
1677 : }
1678 : INLINE GEN
1679 15462550 : Fp_neg(GEN b, GEN m)
1680 : {
1681 15462550 : pari_sp av = avma;
1682 15462550 : long s = signe(b);
1683 : GEN p;
1684 15462550 : if (!s) return gen_0;
1685 11863278 : if (s > 0)
1686 : {
1687 11080103 : p = subii(m, b);
1688 11077843 : if (signe(p) >= 0) return p; /* general case ! */
1689 378955 : p = modii(p, m);
1690 : } else
1691 783999 : p = remii(negi(b), m);
1692 1163187 : return gerepileuptoint(av, p);
1693 : }
1694 :
1695 : INLINE GEN
1696 63819 : Fp_halve(GEN a, GEN p)
1697 : {
1698 63819 : if (mpodd(a)) a = addii(a,p);
1699 63819 : return shifti(a,-1);
1700 : }
1701 :
1702 : /* assume 0 <= u < p and ps2 = p>>1 */
1703 : INLINE GEN
1704 55133346 : Fp_center(GEN u, GEN p, GEN ps2)
1705 55133346 : { return abscmpii(u,ps2)<=0? icopy(u): subii(u,p); }
1706 : /* same without copy */
1707 : INLINE GEN
1708 11607235 : Fp_center_i(GEN u, GEN p, GEN ps2)
1709 11607235 : { return abscmpii(u,ps2)<=0? u: subii(u,p); }
1710 :
1711 : /* x + y*z mod p */
1712 : INLINE GEN
1713 7270523 : Fp_addmul(GEN x, GEN y, GEN z, GEN p)
1714 : {
1715 : pari_sp av;
1716 7270523 : if (!signe(y) || !signe(z)) return Fp_red(x, p);
1717 6956661 : if (!signe(x)) return Fp_mul(z,y, p);
1718 5997085 : av = avma;
1719 5997085 : return gerepileuptoint(av, modii(addii(x, mulii(y,z)), p));
1720 : }
1721 :
1722 : INLINE GEN
1723 121165484 : Fp_mul(GEN a, GEN b, GEN m)
1724 : {
1725 121165484 : pari_sp av=avma;
1726 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1727 121165484 : (void)new_chunk(lg(a)+lg(b)+(lg(m)<<1));
1728 121154079 : p = mulii(a,b);
1729 121279781 : set_avma(av); return modii(p,m);
1730 : }
1731 : INLINE GEN
1732 34872368 : Fp_sqr(GEN a, GEN m)
1733 : {
1734 34872368 : pari_sp av=avma;
1735 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1736 34872368 : (void)new_chunk((lg(a)+lg(m))<<1);
1737 34639728 : p = sqri(a);
1738 32070767 : set_avma(av); return remii(p,m); /*Use remii: p >= 0 */
1739 : }
1740 : INLINE GEN
1741 66837527 : Fp_mulu(GEN a, ulong b, GEN m)
1742 : {
1743 66837527 : long l = lgefint(m);
1744 66837527 : if (l == 3)
1745 : {
1746 44768308 : ulong mm = m[2];
1747 44768308 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1748 : } else {
1749 22069219 : pari_sp av = avma;
1750 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1751 22069219 : (void)new_chunk(lg(a)+1+(l<<1));
1752 21981205 : p = muliu(a,b);
1753 20173460 : set_avma(av); return modii(p,m);
1754 : }
1755 : }
1756 : INLINE GEN
1757 17290 : Fp_muls(GEN a, long b, GEN m)
1758 : {
1759 17290 : long l = lgefint(m);
1760 17290 : if (l == 3)
1761 : {
1762 3058 : ulong mm = m[2];
1763 3058 : if (b < 0)
1764 : {
1765 3058 : ulong t = Fl_mul(umodiu(a, mm), -b, mm);
1766 3058 : return t? utoipos(mm - t): gen_0;
1767 : }
1768 : else
1769 0 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1770 : } else {
1771 14232 : pari_sp av = avma;
1772 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1773 14232 : (void)new_chunk(lg(a)+1+(l<<1));
1774 14232 : p = mulis(a,b);
1775 14232 : set_avma(av); return modii(p,m);
1776 : }
1777 : }
1778 :
1779 : INLINE GEN
1780 24407878 : Fp_inv(GEN a, GEN m)
1781 : {
1782 : GEN res;
1783 24407878 : if (! invmod(a,m,&res)) pari_err_INV("Fp_inv", mkintmod(res,m));
1784 24406536 : return res;
1785 : }
1786 : INLINE GEN
1787 779965 : Fp_invsafe(GEN a, GEN m)
1788 : {
1789 : GEN res;
1790 779965 : if (! invmod(a,m,&res)) return NULL;
1791 779861 : return res;
1792 : }
1793 : INLINE GEN
1794 1458491 : Fp_div(GEN a, GEN b, GEN m)
1795 : {
1796 1458491 : pari_sp av = avma;
1797 : GEN p;
1798 1458491 : if (lgefint(b) == 3)
1799 : {
1800 485936 : a = Fp_divu(a, b[2], m);
1801 485936 : if (signe(b) < 0) a = Fp_neg(a, m);
1802 485936 : return a;
1803 : }
1804 : /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1805 972555 : (void)new_chunk(lg(a)+(lg(m)<<1));
1806 972555 : p = mulii(a, Fp_inv(b,m));
1807 972555 : set_avma(av); return modii(p,m);
1808 : }
1809 : INLINE GEN
1810 1648664 : Fp_divu(GEN x, ulong a, GEN p)
1811 : {
1812 1648664 : pari_sp av = avma;
1813 : ulong b;
1814 1648664 : if (lgefint(p) == 3)
1815 : {
1816 1353140 : ulong pp = p[2], xp = umodiu(x, pp);
1817 1353140 : return xp? utoipos(Fl_div(xp, a % pp, pp)): gen_0;
1818 : }
1819 295524 : x = Fp_red(x, p);
1820 295524 : b = Fl_neg(Fl_div(umodiu(x,a), umodiu(p,a), a), a); /* x + pb = 0 (mod a) */
1821 295524 : return gerepileuptoint(av, diviuexact(addmuliu(x, p, b), a));
1822 : }
1823 :
1824 : INLINE GEN
1825 1113326 : Flx_mulu(GEN x, ulong a, ulong p) { return Flx_Fl_mul(x,a%p,p); }
1826 :
1827 : INLINE GEN
1828 1774860 : get_F2x_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1829 :
1830 : INLINE long
1831 2462580 : get_F2x_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1832 :
1833 : INLINE long
1834 1924978 : get_F2x_degree(GEN T) { return typ(T)==t_VEC? F2x_degree(gel(T,2)): F2x_degree(T); }
1835 :
1836 : INLINE GEN
1837 406 : get_F2xqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1838 :
1839 : INLINE long
1840 376187 : get_F2xqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1841 :
1842 : INLINE long
1843 201481 : get_F2xqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1844 :
1845 : INLINE GEN
1846 23560253 : get_Flx_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1847 :
1848 : INLINE long
1849 64693127 : get_Flx_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1850 :
1851 : INLINE long
1852 81648718 : get_Flx_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1853 :
1854 : INLINE GEN
1855 6997 : get_FlxqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1856 :
1857 : INLINE long
1858 245078 : get_FlxqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1859 :
1860 : INLINE long
1861 300898 : get_FlxqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1862 :
1863 : INLINE GEN
1864 2528646 : get_FpX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1865 :
1866 : INLINE long
1867 6556226 : get_FpX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1868 :
1869 : INLINE long
1870 5258249 : get_FpX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1871 :
1872 : INLINE GEN
1873 146583 : get_FpXQX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1874 :
1875 : INLINE long
1876 34808 : get_FpXQX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1877 :
1878 : INLINE long
1879 2259 : get_FpXQX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1880 :
1881 : /*******************************************************************/
1882 : /* */
1883 : /* ADDMULII / SUBMULII */
1884 : /* */
1885 : /*******************************************************************/
1886 : /* x - y*z */
1887 : INLINE GEN
1888 24638458 : submulii(GEN x, GEN y, GEN z)
1889 : {
1890 24638458 : long lx = lgefint(x), ly, lz;
1891 : pari_sp av;
1892 : GEN t;
1893 24638458 : if (lx == 2) { t = mulii(z,y); togglesign(t); return t; }
1894 19926421 : ly = lgefint(y);
1895 19926421 : if (ly == 2) return icopy(x);
1896 17630014 : lz = lgefint(z);
1897 17630014 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1898 17630014 : t = mulii(z, y);
1899 17630014 : set_avma(av); return subii(x,t);
1900 : }
1901 : /* y*z - x */
1902 : INLINE GEN
1903 2381438 : mulsubii(GEN y, GEN z, GEN x)
1904 : {
1905 2381438 : long lx = lgefint(x), ly, lz;
1906 : pari_sp av;
1907 : GEN t;
1908 2381438 : if (lx == 2) return mulii(z,y);
1909 1466316 : ly = lgefint(y);
1910 1466316 : if (ly == 2) return negi(x);
1911 1295796 : lz = lgefint(z);
1912 1295796 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1913 1295836 : t = mulii(z, y);
1914 1295775 : set_avma(av); return subii(t,x);
1915 : }
1916 :
1917 : /* x - u*y */
1918 : INLINE GEN
1919 7693 : submuliu(GEN x, GEN y, ulong u)
1920 : {
1921 : pari_sp av;
1922 7693 : long ly = lgefint(y);
1923 7693 : if (ly == 2) return icopy(x);
1924 7693 : av = avma;
1925 7693 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1926 7693 : y = mului(u,y);
1927 7693 : set_avma(av); return subii(x, y);
1928 : }
1929 : /* x + u*y */
1930 : INLINE GEN
1931 303592 : addmuliu(GEN x, GEN y, ulong u)
1932 : {
1933 : pari_sp av;
1934 303592 : long ly = lgefint(y);
1935 303592 : if (ly == 2) return icopy(x);
1936 303592 : av = avma;
1937 303592 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1938 303592 : y = mului(u,y);
1939 303591 : set_avma(av); return addii(x, y);
1940 : }
1941 : /* x - u*y */
1942 : INLINE GEN
1943 180099567 : submuliu_inplace(GEN x, GEN y, ulong u)
1944 : {
1945 : pari_sp av;
1946 180099567 : long ly = lgefint(y);
1947 180099567 : if (ly == 2) return x;
1948 132972806 : av = avma;
1949 132972806 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1950 132979595 : y = mului(u,y);
1951 132976967 : set_avma(av); return subii(x, y);
1952 : }
1953 : /* x + u*y */
1954 : INLINE GEN
1955 178029024 : addmuliu_inplace(GEN x, GEN y, ulong u)
1956 : {
1957 : pari_sp av;
1958 178029024 : long ly = lgefint(y);
1959 178029024 : if (ly == 2) return x;
1960 132862666 : av = avma;
1961 132862666 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1962 132870000 : y = mului(u,y);
1963 132867652 : set_avma(av); return addii(x, y);
1964 : }
1965 : /* ux + vy */
1966 : INLINE GEN
1967 38784743 : lincombii(GEN u, GEN v, GEN x, GEN y)
1968 : {
1969 38784743 : long lx = lgefint(x), ly;
1970 : GEN p1, p2;
1971 : pari_sp av;
1972 38784743 : if (lx == 2) return mulii(v,y);
1973 25260952 : ly = lgefint(y);
1974 25260952 : if (ly == 2) return mulii(u,x);
1975 22832023 : av = avma; (void)new_chunk(lx+ly+lgefint(u)+lgefint(v)); /* HACK */
1976 22835667 : p1 = mulii(u,x);
1977 22833666 : p2 = mulii(v,y);
1978 22833564 : set_avma(av); return addii(p1,p2);
1979 : }
1980 :
1981 : /*******************************************************************/
1982 : /* */
1983 : /* GEN SUBTYPES */
1984 : /* */
1985 : /*******************************************************************/
1986 :
1987 : INLINE int
1988 3201279305 : is_const_t(long t) { return (t < t_POLMOD); }
1989 : INLINE int
1990 6841 : is_extscalar_t(long t) { return (t <= t_POL); }
1991 : INLINE int
1992 4889537 : is_intreal_t(long t) { return (t <= t_REAL); }
1993 : INLINE int
1994 737105628 : is_matvec_t(long t) { return (t >= t_VEC && t <= t_MAT); }
1995 : INLINE int
1996 76220353 : is_noncalc_t(long tx) { return (tx) >= t_LIST; }
1997 : INLINE int
1998 0 : is_qfb_t(long t) { return (t == t_QFB); }
1999 : INLINE int
2000 3442422 : is_rational_t(long t) { return (t == t_INT || t == t_FRAC); }
2001 : INLINE int
2002 1106404 : is_real_t(long t) { return (t == t_INT || t == t_REAL || t == t_FRAC); }
2003 : INLINE int
2004 7501149686 : is_recursive_t(long t) { return lontyp[t]; }
2005 : INLINE int
2006 242038416 : is_scalar_t(long t) { return (t < t_POL); }
2007 : INLINE int
2008 1123036 : is_vec_t(long t) { return (t == t_VEC || t == t_COL); }
2009 :
2010 : INLINE int
2011 144389554 : qfb_is_qfi(GEN q) { return signe(gel(q,4)) < 0; }
2012 :
2013 : /*******************************************************************/
2014 : /* */
2015 : /* TRANSCENDENTAL */
2016 : /* */
2017 : /*******************************************************************/
2018 : INLINE GEN
2019 49349618 : sqrtr(GEN x) {
2020 49349618 : long s = signe(x);
2021 49349618 : if (s == 0) return real_0_bit(expo(x) >> 1);
2022 49316528 : if (s >= 0) return sqrtr_abs(x);
2023 279841 : retmkcomplex(gen_0, sqrtr_abs(x));
2024 : }
2025 : INLINE GEN
2026 0 : cbrtr_abs(GEN x) { return sqrtnr_abs(x, 3); }
2027 : INLINE GEN
2028 0 : cbrtr(GEN x) {
2029 0 : long s = signe(x);
2030 : GEN r;
2031 0 : if (s == 0) return real_0_bit(expo(x) / 3);
2032 0 : r = cbrtr_abs(x);
2033 0 : if (s < 0) togglesign(r);
2034 0 : return r;
2035 : }
2036 : INLINE GEN
2037 1014162 : sqrtnr(GEN x, long n) {
2038 1014162 : long s = signe(x);
2039 : GEN r;
2040 1014162 : if (s == 0) return real_0_bit(expo(x) / n);
2041 1014162 : r = sqrtnr_abs(x, n);
2042 1014190 : if (s < 0) pari_err_IMPL("sqrtnr for x < 0");
2043 1014192 : return r;
2044 : }
2045 : INLINE long
2046 411535 : logint(GEN B, GEN y) { return logintall(B,y,NULL); }
2047 : INLINE ulong
2048 2222048 : ulogint(ulong B, ulong y)
2049 : {
2050 : ulong r;
2051 : long e;
2052 2222048 : if (y == 2) return expu(B);
2053 2198580 : r = y;
2054 2198580 : for (e=1;; e++)
2055 : { /* here, r = y^e, r2 = y^(e-1) */
2056 7112921 : if (r >= B) return r == B? e: e-1;
2057 4914259 : r = umuluu_or_0(y, r);
2058 4914346 : if (!r) return e;
2059 : }
2060 : }
2061 :
2062 : /*******************************************************************/
2063 : /* */
2064 : /* MISCELLANEOUS */
2065 : /* */
2066 : /*******************************************************************/
2067 4889461 : INLINE int ismpzero(GEN x) { return is_intreal_t(typ(x)) && !signe(x); }
2068 3167192078 : INLINE int isintzero(GEN x) { return typ(x) == t_INT && !signe(x); }
2069 15107321 : INLINE int isint1(GEN x) { return typ(x)==t_INT && equali1(x); }
2070 4028436 : INLINE int isintm1(GEN x){ return typ(x)==t_INT && equalim1(x);}
2071 903756157 : INLINE int equali1(GEN n)
2072 903756157 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(1)) && n[2] == 1; }
2073 62817317 : INLINE int equalim1(GEN n)
2074 62817317 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(-1)) && n[2] == 1; }
2075 : /* works only for POSITIVE integers */
2076 2201511418 : INLINE int is_pm1(GEN n)
2077 2201511418 : { return lgefint(n) == 3 && n[2] == 1; }
2078 321123724 : INLINE int is_bigint(GEN n)
2079 321123724 : { long l = lgefint(n); return l > 3 || (l == 3 && (n[2] & HIGHBIT)); }
2080 :
2081 2632529407 : INLINE int odd(long x) { return x & 1; }
2082 55118302 : INLINE int both_odd(long x, long y) { return x & y & 1; }
2083 :
2084 : INLINE int
2085 5263334462 : isonstack(GEN x)
2086 5263334462 : { return ((pari_sp)x >= pari_mainstack->bot
2087 5263334462 : && (pari_sp)x < pari_mainstack->top); }
2088 :
2089 : /* assume x != 0 and x t_REAL, return an approximation to log2(|x|) */
2090 : INLINE double
2091 60870836 : dbllog2r(GEN x)
2092 60870836 : { return log2((double)(ulong)x[2]) + (double)(expo(x) - (BITS_IN_LONG-1)); }
2093 :
2094 : INLINE GEN
2095 1373404 : mul_content(GEN cx, GEN cy)
2096 : {
2097 1373404 : if (!cx) return cy;
2098 567017 : if (!cy) return cx;
2099 372902 : return gmul(cx,cy);
2100 : }
2101 : INLINE GEN
2102 0 : inv_content(GEN c) { return c? ginv(c): NULL; }
2103 : INLINE GEN
2104 36274 : div_content(GEN cx, GEN cy)
2105 : {
2106 36274 : if (!cy) return cx;
2107 35224 : if (!cx) return ginv(cy);
2108 7223 : return gdiv(cx,cy);
2109 : }
2110 : INLINE GEN
2111 5061480 : mul_denom(GEN dx, GEN dy)
2112 : {
2113 5061480 : if (!dx) return dy;
2114 1566111 : if (!dy) return dx;
2115 686553 : return mulii(dx,dy);
2116 : }
2117 :
2118 : /* POLYNOMIALS */
2119 : INLINE GEN
2120 1284432 : constant_coeff(GEN x) { return signe(x)? gel(x,2): gen_0; }
2121 : INLINE GEN
2122 77137900 : leading_coeff(GEN x) { return lg(x) == 2? gen_0: gel(x,lg(x)-1); }
2123 : INLINE ulong
2124 681944 : Flx_lead(GEN x) { return lg(x) == 2? 0: x[lg(x)-1]; }
2125 : INLINE ulong
2126 34313 : Flx_constant(GEN x) { return lg(x) == 2? 0: x[2]; }
2127 : INLINE long
2128 4483261825 : degpol(GEN x) { return lg(x)-3; }
2129 : INLINE long
2130 2285119788 : lgpol(GEN x) { return lg(x)-2; }
2131 : INLINE long
2132 237621740 : lgcols(GEN x) { return lg(gel(x,1)); }
2133 : INLINE long
2134 142220678 : nbrows(GEN x) { return lg(gel(x,1))-1; }
2135 : INLINE GEN
2136 0 : truecoef(GEN x, long n) { return polcoef(x,n,-1); }
2137 :
2138 : INLINE GEN
2139 1240048 : ZXQ_mul(GEN y, GEN x, GEN T) { return ZX_rem(ZX_mul(y, x), T); }
2140 : INLINE GEN
2141 499217 : ZXQ_sqr(GEN x, GEN T) { return ZX_rem(ZX_sqr(x), T); }
2142 :
2143 : INLINE GEN
2144 96667030 : RgX_copy(GEN x)
2145 : {
2146 : long lx, i;
2147 96667030 : GEN y = cgetg_copy(x, &lx); y[1] = x[1];
2148 351712942 : for (i = 2; i<lx; i++) gel(y,i) = gcopy(gel(x,i));
2149 96667051 : return y;
2150 : }
2151 : /* have to use ulong to avoid silly warnings from gcc "assuming signed
2152 : * overflow does not occur" */
2153 : INLINE GEN
2154 1087093 : RgX_coeff(GEN x, long n)
2155 : {
2156 1087093 : ulong l = lg(x);
2157 1087093 : return (n < 0 || ((ulong)n+3) > l)? gen_0: gel(x,n+2);
2158 : }
2159 : INLINE GEN
2160 345299 : RgX_renormalize(GEN x) { return RgX_renormalize_lg(x, lg(x)); }
2161 : INLINE GEN
2162 6835527 : RgX_div(GEN x, GEN y) { return RgX_divrem(x,y,NULL); }
2163 : INLINE GEN
2164 1792 : RgXQX_div(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,NULL); }
2165 : INLINE GEN
2166 104526 : RgXQX_rem(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,ONLY_REM); }
2167 : INLINE GEN
2168 4299218 : FpX_div(GEN x, GEN y, GEN p) { return FpX_divrem(x,y,p, NULL); }
2169 : INLINE GEN
2170 22002411 : Flx_div(GEN x, GEN y, ulong p) { return Flx_divrem(x,y,p, NULL); }
2171 : INLINE GEN
2172 1248603 : F2x_div(GEN x, GEN y) { return F2x_divrem(x,y, NULL); }
2173 : INLINE GEN
2174 0 : FpV_FpC_mul(GEN x, GEN y, GEN p) { return FpV_dotproduct(x,y,p); }
2175 : INLINE GEN
2176 87092706 : pol0_Flx(long sv) { return mkvecsmall(sv); }
2177 : INLINE GEN
2178 49870360 : pol1_Flx(long sv) { return mkvecsmall2(sv, 1); }
2179 : INLINE GEN
2180 34866196 : polx_Flx(long sv) { return mkvecsmall3(sv, 0, 1); }
2181 : INLINE GEN
2182 0 : zero_zx(long sv) { return zero_Flx(sv); }
2183 : INLINE GEN
2184 0 : polx_zx(long sv) { return polx_Flx(sv); }
2185 : INLINE GEN
2186 0 : zx_shift(GEN x, long n) { return Flx_shift(x,n); }
2187 : INLINE GEN
2188 0 : zx_renormalize(GEN x, long l) { return Flx_renormalize(x,l); }
2189 : INLINE GEN
2190 1341 : zero_F2x(long sv) { return zero_Flx(sv); }
2191 : INLINE GEN
2192 11428112 : pol0_F2x(long sv) { return pol0_Flx(sv); }
2193 : INLINE GEN
2194 3118449 : pol1_F2x(long sv) { return pol1_Flx(sv); }
2195 : INLINE GEN
2196 1001742 : polx_F2x(long sv) { return mkvecsmall2(sv, 2); }
2197 : INLINE int
2198 604532 : F2x_equal1(GEN x) { return Flx_equal1(x); }
2199 : INLINE int
2200 3110009 : F2x_equal(GEN V, GEN W) { return Flx_equal(V,W); }
2201 : INLINE GEN
2202 56103773 : F2x_copy(GEN x) { return leafcopy(x); }
2203 : INLINE GEN
2204 4074 : F2v_copy(GEN x) { return leafcopy(x); }
2205 : INLINE GEN
2206 2584436 : Flv_copy(GEN x) { return leafcopy(x); }
2207 : INLINE GEN
2208 168072583 : Flx_copy(GEN x) { return leafcopy(x); }
2209 : INLINE GEN
2210 3917134 : vecsmall_copy(GEN x) { return leafcopy(x); }
2211 : INLINE int
2212 6423934 : Flx_equal1(GEN x) { return degpol(x)==0 && x[2] == 1; }
2213 : INLINE int
2214 19303 : ZX_equal1(GEN x) { return degpol(x)==0 && equali1(gel(x,2)); }
2215 : INLINE int
2216 5646328 : ZX_is_monic(GEN x) { return equali1(leading_coeff(x)); }
2217 :
2218 : INLINE GEN
2219 137216585 : ZX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2220 : INLINE GEN
2221 97919088 : FpX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2222 : INLINE GEN
2223 677721 : FpXX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2224 : INLINE GEN
2225 4246201 : FpXQX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2226 : INLINE GEN
2227 111946679 : F2x_renormalize(GEN x, long lx) { return Flx_renormalize(x,lx); }
2228 : INLINE GEN
2229 39795 : F2v_to_F2x(GEN x, long sv) {
2230 39795 : GEN y = leafcopy(x);
2231 39795 : y[1] = sv; F2x_renormalize(y, lg(y)); return y;
2232 : }
2233 :
2234 : INLINE long
2235 350 : sturm(GEN x) { return sturmpart(x, NULL, NULL); }
2236 :
2237 : INLINE long
2238 4893 : gval(GEN x, long v)
2239 4893 : { pari_sp av = avma; return gc_long(av, gvaluation(x, pol_x(v))); }
2240 :
2241 : INLINE void
2242 494596 : RgX_shift_inplace_init(long v)
2243 494596 : { if (v) (void)cgetg(v, t_VECSMALL); }
2244 : /* shift polynomial in place. assume v free cells have been left before x */
2245 : INLINE GEN
2246 494596 : RgX_shift_inplace(GEN x, long v)
2247 : {
2248 : long i, lx;
2249 : GEN z;
2250 494596 : if (!v) return x;
2251 253165 : lx = lg(x);
2252 253165 : if (lx == 2) return x;
2253 253165 : z = x + lx;
2254 : /* stackdummy's from normalizepol */
2255 253165 : while (lg(z) != v) z += lg(z);
2256 253165 : z += v;
2257 4654452 : for (i = lx-1; i >= 2; i--) gel(--z,0) = gel(x,i);
2258 675883 : for (i = 0; i < v; i++) gel(--z,0) = gen_0;
2259 253165 : z -= 2;
2260 253165 : z[1] = x[1];
2261 253165 : z[0] = evaltyp(t_POL) | evallg(lx+v);
2262 253165 : stackdummy((pari_sp)z, (pari_sp)x); return z;
2263 : }
2264 :
2265 :
2266 : /* LINEAR ALGEBRA */
2267 : INLINE GEN
2268 466326 : zv_to_ZV(GEN x) { return vecsmall_to_vec(x); }
2269 : INLINE GEN
2270 6564400 : zc_to_ZC(GEN x) { return vecsmall_to_col(x); }
2271 : INLINE GEN
2272 3408128 : ZV_to_zv(GEN x) { return vec_to_vecsmall(x); }
2273 : INLINE GEN
2274 0 : zx_to_zv(GEN x, long N) { return Flx_to_Flv(x,N); }
2275 : INLINE GEN
2276 0 : zv_to_zx(GEN x, long sv) { return Flv_to_Flx(x,sv); }
2277 : INLINE GEN
2278 0 : zm_to_zxV(GEN x, long sv) { return Flm_to_FlxV(x,sv); }
2279 : INLINE GEN
2280 0 : zero_zm(long x, long y) { return zero_Flm(x,y); }
2281 : INLINE GEN
2282 25250869 : zero_zv(long x) { return zero_Flv(x); }
2283 : INLINE GEN
2284 266 : zm_transpose(GEN x) { return Flm_transpose(x); }
2285 : INLINE GEN
2286 0 : zm_copy(GEN x) { return Flm_copy(x); }
2287 : INLINE GEN
2288 2112809 : zv_copy(GEN x) { return Flv_copy(x); }
2289 : INLINE GEN
2290 0 : zm_row(GEN x, long i) { return Flm_row(x,i); }
2291 :
2292 : INLINE GEN
2293 5269198 : ZC_hnfrem(GEN x, GEN y) { return ZC_hnfremdiv(x,y,NULL); }
2294 : INLINE GEN
2295 312674 : ZM_hnfrem(GEN x, GEN y) { return ZM_hnfdivrem(x,y,NULL); }
2296 : INLINE GEN
2297 3858534 : ZM_lll(GEN x, double D, long f) { return ZM_lll_norms(x,D,f,NULL); }
2298 : INLINE void
2299 8947979 : RgM_dimensions(GEN x, long *m, long *n) { *n = lg(x)-1; *m = *n? nbrows(x): 0; }
2300 : INLINE GEN
2301 20061867 : RgM_shallowcopy(GEN x)
2302 : {
2303 : long l;
2304 20061867 : GEN y = cgetg_copy(x, &l);
2305 101930476 : while (--l > 0) gel(y,l) = leafcopy(gel(x,l));
2306 20061430 : return y;
2307 : }
2308 : INLINE GEN
2309 188913 : F2m_copy(GEN x) { return RgM_shallowcopy(x); }
2310 :
2311 : INLINE GEN
2312 0 : F3m_copy(GEN x) { return RgM_shallowcopy(x); }
2313 :
2314 : INLINE GEN
2315 5241264 : Flm_copy(GEN x) { return RgM_shallowcopy(x); }
2316 :
2317 : /* divisibility: return 1 if y[i] | x[i] for all i, 0 otherwise. Assume
2318 : * x,y are ZV of the same length */
2319 : INLINE int
2320 23198 : ZV_dvd(GEN x, GEN y)
2321 : {
2322 23198 : long i, l = lg(x);
2323 36666 : for (i=1; i < l; i++)
2324 29533 : if ( ! dvdii( gel(x,i), gel(y,i) ) ) return 0;
2325 7133 : return 1;
2326 : }
2327 :
2328 : /* Fq */
2329 : INLINE GEN
2330 2562860 : Fq_red(GEN x, GEN T, GEN p)
2331 2562860 : { return typ(x)==t_INT? Fp_red(x,p): FpXQ_red(x,T,p); }
2332 : INLINE GEN
2333 100519 : Fq_to_FpXQ(GEN x, GEN T, GEN p /*unused*/)
2334 : {
2335 : (void) p;
2336 100519 : return typ(x)==t_INT ? scalarpol(x, get_FpX_var(T)): x;
2337 : }
2338 : INLINE GEN
2339 756 : Rg_to_Fq(GEN x, GEN T, GEN p) { return T? Rg_to_FpXQ(x,T,p): Rg_to_Fp(x,p); }
2340 :
2341 : INLINE GEN
2342 14538 : gener_Fq_local(GEN T, GEN p, GEN L)
2343 0 : { return T? gener_FpXQ_local(T,p, L)
2344 14538 : : pgener_Fp_local(p, L); }
2345 :
2346 : /* FpXQX */
2347 : INLINE GEN
2348 4431 : FpXQX_div(GEN x, GEN y, GEN T, GEN p) { return FpXQX_divrem(x, y, T, p, NULL); }
2349 : INLINE GEN
2350 165966 : FlxqX_div(GEN x, GEN y, GEN T, ulong p) { return FlxqX_divrem(x, y, T, p, NULL); }
2351 : INLINE GEN
2352 33376 : F2xqX_div(GEN x, GEN y, GEN T) { return F2xqX_divrem(x, y, T, NULL); }
2353 :
2354 : INLINE GEN
2355 20006 : FpXY_Fq_evaly(GEN Q, GEN y, GEN T, GEN p, long vx)
2356 20006 : { return T ? FpXY_FpXQ_evaly(Q, y, T, p, vx): FpXY_evaly(Q, y, p, vx); }
2357 :
2358 : /* FqX */
2359 : INLINE GEN
2360 25109 : FqX_red(GEN z, GEN T, GEN p) { return T? FpXQX_red(z, T, p): FpX_red(z, p); }
2361 : INLINE GEN
2362 105343 : FqX_add(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2363 : INLINE GEN
2364 24313 : FqX_neg(GEN x,GEN T,GEN p) { return T? FpXX_neg(x,p): FpX_neg(x,p); }
2365 : INLINE GEN
2366 66458 : FqX_sub(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2367 : INLINE GEN
2368 613521 : FqX_Fp_mul(GEN P, GEN u, GEN T, GEN p)
2369 613521 : { return T? FpXX_Fp_mul(P, u, p): FpX_Fp_mul(P, u, p); }
2370 : INLINE GEN
2371 408572 : FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
2372 408572 : { return typ(U)==t_INT ? FqX_Fp_mul(P, U, T, p): FpXQX_FpXQ_mul(P, U, T, p); }
2373 : INLINE GEN
2374 377243 : FqX_mul(GEN x, GEN y, GEN T, GEN p)
2375 377243 : { return T? FpXQX_mul(x, y, T, p): FpX_mul(x, y, p); }
2376 : INLINE GEN
2377 17510 : FqX_mulu(GEN x, ulong y, GEN T, GEN p)
2378 17510 : { return T? FpXX_mulu(x, y, p): FpX_mulu(x, y, p); }
2379 : INLINE GEN
2380 69678 : FqX_sqr(GEN x, GEN T, GEN p)
2381 69678 : { return T? FpXQX_sqr(x, T, p): FpX_sqr(x, p); }
2382 : INLINE GEN
2383 1281 : FqX_powu(GEN x, ulong n, GEN T, GEN p)
2384 1281 : { return T? FpXQX_powu(x, n, T, p): FpX_powu(x, n, p); }
2385 : INLINE GEN
2386 18774 : FqX_halve(GEN x, GEN T, GEN p)
2387 18774 : { return T? FpXX_halve(x, p): FpX_halve(x, p); }
2388 : INLINE GEN
2389 38659 : FqX_div(GEN x, GEN y, GEN T, GEN p)
2390 38659 : { return T? FpXQX_divrem(x,y,T,p,NULL): FpX_divrem(x,y,p,NULL); }
2391 : INLINE GEN
2392 6081 : FqX_get_red(GEN S, GEN T, GEN p)
2393 6081 : { return T? FpXQX_get_red(S,T,p): FpX_get_red(S,p); }
2394 : INLINE GEN
2395 31086 : FqX_rem(GEN x, GEN y, GEN T, GEN p)
2396 31086 : { return T? FpXQX_rem(x,y,T,p): FpX_rem(x,y,p); }
2397 : INLINE GEN
2398 0 : FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
2399 0 : { return T? FpXQX_divrem(x,y,T,p,z): FpX_divrem(x,y,p,z); }
2400 : INLINE GEN
2401 5936 : FqX_div_by_X_x(GEN x, GEN y, GEN T, GEN p, GEN *z)
2402 5936 : { return T? FpXQX_div_by_X_x(x,y,T,p,z): FpX_div_by_X_x(x,y,p,z); }
2403 : INLINE GEN
2404 0 : FqX_halfgcd(GEN P,GEN Q,GEN T,GEN p)
2405 0 : {return T? FpXQX_halfgcd(P,Q,T,p): FpX_halfgcd(P,Q,p);}
2406 : INLINE GEN
2407 260645 : FqX_gcd(GEN P,GEN Q,GEN T,GEN p)
2408 260645 : {return T? FpXQX_gcd(P,Q,T,p): FpX_gcd(P,Q,p);}
2409 : INLINE GEN
2410 470900 : FqX_extgcd(GEN P,GEN Q,GEN T,GEN p, GEN *U, GEN *V)
2411 470900 : { return T? FpXQX_extgcd(P,Q,T,p,U,V): FpX_extgcd(P,Q,p,U,V); }
2412 : INLINE GEN
2413 3836 : FqX_normalize(GEN z, GEN T, GEN p)
2414 3836 : { return T? FpXQX_normalize(z, T, p): FpX_normalize(z, p); }
2415 : INLINE GEN
2416 291893 : FqX_deriv(GEN f, GEN T, GEN p) { return T? FpXX_deriv(f, p): FpX_deriv(f, p); }
2417 : INLINE GEN
2418 0 : FqX_integ(GEN f, GEN T, GEN p) { return T? FpXX_integ(f, p): FpX_integ(f, p); }
2419 : INLINE GEN
2420 86058 : FqX_factor(GEN f, GEN T, GEN p)
2421 86058 : { return T?FpXQX_factor(f, T, p): FpX_factor(f, p); }
2422 : INLINE GEN
2423 7 : FqX_factor_squarefree(GEN f, GEN T, GEN p)
2424 7 : { return T ? FpXQX_factor_squarefree(f, T, p): FpX_factor_squarefree(f, p); }
2425 : INLINE GEN
2426 7 : FqX_ddf(GEN f, GEN T, GEN p)
2427 7 : { return T ? FpXQX_ddf(f, T, p): FpX_ddf(f, p); }
2428 : INLINE GEN
2429 2002 : FqX_degfact(GEN f, GEN T, GEN p)
2430 2002 : { return T?FpXQX_degfact(f, T, p): FpX_degfact(f, p); }
2431 : INLINE GEN
2432 7147 : FqX_roots(GEN f, GEN T, GEN p)
2433 7147 : { return T?FpXQX_roots(f, T, p): FpX_roots(f, p); }
2434 : INLINE GEN
2435 175 : FqX_to_mod(GEN f, GEN T, GEN p)
2436 175 : { return T?FpXQX_to_mod(f, T, p): FpX_to_mod(f, p); }
2437 :
2438 : /*FqXQ*/
2439 : INLINE GEN
2440 0 : FqXQ_add(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2441 0 : { (void)S; return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2442 : INLINE GEN
2443 0 : FqXQ_sub(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2444 0 : { (void)S; return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2445 : INLINE GEN
2446 0 : FqXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
2447 0 : { return T? FpXQXQ_div(x,y,S,T,p): FpXQ_div(x,y,S,p); }
2448 : INLINE GEN
2449 0 : FqXQ_inv(GEN x, GEN S, GEN T, GEN p)
2450 0 : { return T? FpXQXQ_inv(x,S,T,p): FpXQ_inv(x,S,p); }
2451 : INLINE GEN
2452 0 : FqXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
2453 0 : { return T? FpXQXQ_invsafe(x,S,T,p): FpXQ_inv(x,S,p); }
2454 : INLINE GEN
2455 22320 : FqXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
2456 22320 : { return T? FpXQXQ_mul(x,y,S,T,p): FpXQ_mul(x,y,S,p); }
2457 : INLINE GEN
2458 0 : FqXQ_sqr(GEN x, GEN S, GEN T, GEN p)
2459 0 : { return T? FpXQXQ_sqr(x,S,T,p): FpXQ_sqr(x,S,p); }
2460 : INLINE GEN
2461 0 : FqXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
2462 0 : { return T? FpXQXQ_pow(x,n,S,T,p): FpXQ_pow(x,n,S,p); }
2463 :
2464 : /*FqXn*/
2465 : INLINE GEN
2466 6610 : FqXn_expint(GEN x, long n, GEN T, GEN p)
2467 6610 : { return T? FpXQXn_expint(x,n,T,p): FpXn_expint(x,n,p); }
2468 : INLINE GEN
2469 0 : FqXn_exp(GEN x, long n, GEN T, GEN p)
2470 0 : { return T? FpXQXn_exp(x,n,T,p): FpXn_exp(x,n,p); }
2471 : INLINE GEN
2472 6916 : FqXn_inv(GEN x, long n, GEN T, GEN p)
2473 6916 : { return T? FpXQXn_inv(x,n,T,p): FpXn_inv(x,n,p); }
2474 : INLINE GEN
2475 254926 : FqXn_mul(GEN x, GEN y, long n, GEN T, GEN p)
2476 254926 : { return T? FpXQXn_mul(x, y, n, T, p): FpXn_mul(x, y, n, p); }
2477 : INLINE GEN
2478 0 : FqXn_sqr(GEN x, long n, GEN T, GEN p)
2479 0 : { return T? FpXQXn_sqr(x,n,T,p): FpXn_sqr(x,n,p); }
2480 :
2481 : /*FpXQ*/
2482 : INLINE GEN
2483 0 : FpXQ_add(GEN x,GEN y,GEN T/*unused*/,GEN p)
2484 0 : { (void)T; return FpX_add(x,y,p); }
2485 : INLINE GEN
2486 0 : FpXQ_sub(GEN x,GEN y,GEN T/*unused*/,GEN p)
2487 0 : { (void)T; return FpX_sub(x,y,p); }
2488 :
2489 : /*Flxq*/
2490 : INLINE GEN
2491 0 : Flxq_add(GEN x,GEN y,GEN T/*unused*/,ulong p)
2492 0 : { (void)T; return Flx_add(x,y,p); }
2493 : INLINE GEN
2494 0 : Flxq_sub(GEN x,GEN y,GEN T/*unused*/,ulong p)
2495 0 : { (void)T; return Flx_sub(x,y,p); }
2496 :
2497 : /* F2x */
2498 :
2499 : INLINE ulong
2500 84570871 : F2x_coeff(GEN x,long v)
2501 : {
2502 84570871 : ulong u=(ulong)x[2+divsBIL(v)];
2503 84569453 : return (u>>remsBIL(v))&1UL;
2504 : }
2505 :
2506 : INLINE void
2507 10931599 : F2x_clear(GEN x,long v)
2508 : {
2509 10931599 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2510 10931521 : *u&=~(1UL<<remsBIL(v));
2511 10931506 : }
2512 :
2513 : INLINE void
2514 42162704 : F2x_set(GEN x,long v)
2515 : {
2516 42162704 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2517 42162108 : *u|=1UL<<remsBIL(v);
2518 42159554 : }
2519 :
2520 : INLINE void
2521 1577797 : F2x_flip(GEN x,long v)
2522 : {
2523 1577797 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2524 1577797 : *u^=1UL<<remsBIL(v);
2525 1577797 : }
2526 :
2527 : /* F2v */
2528 :
2529 : INLINE ulong
2530 80473496 : F2v_coeff(GEN x,long v) { return F2x_coeff(x,v-1); }
2531 :
2532 : INLINE void
2533 10931610 : F2v_clear(GEN x,long v) { F2x_clear(x,v-1); }
2534 :
2535 : INLINE void
2536 17998481 : F2v_set(GEN x,long v) { F2x_set(x,v-1); }
2537 :
2538 : INLINE void
2539 1577797 : F2v_flip(GEN x,long v) { F2x_flip(x,v-1); }
2540 :
2541 : /* F2m */
2542 :
2543 : INLINE ulong
2544 5361197 : F2m_coeff(GEN x, long a, long b) { return F2v_coeff(gel(x,b), a); }
2545 :
2546 : INLINE void
2547 0 : F2m_clear(GEN x, long a, long b) { F2v_clear(gel(x,b), a); }
2548 :
2549 : INLINE void
2550 0 : F2m_set(GEN x, long a, long b) { F2v_set(gel(x,b), a); }
2551 :
2552 : INLINE void
2553 1577797 : F2m_flip(GEN x, long a, long b) { F2v_flip(gel(x,b), a); }
2554 :
2555 : /* F3m */
2556 :
2557 : INLINE ulong
2558 0 : F3m_coeff(GEN x, long a, long b) { return F3v_coeff(gel(x,b), a); }
2559 :
2560 : INLINE void
2561 0 : F3m_set(GEN x, long a, long b, ulong c) { F3v_set(gel(x,b), a, c); }
2562 :
2563 : /* ARITHMETIC */
2564 : INLINE GEN
2565 33935 : matpascal(long n) { return matqpascal(n, NULL); }
2566 : INLINE long
2567 2729825 : Z_issquare(GEN x) { return Z_issquareall(x, NULL); }
2568 : INLINE long
2569 14 : Z_ispower(GEN x, ulong k) { return Z_ispowerall(x, k, NULL); }
2570 : INLINE GEN
2571 6456923 : sqrti(GEN x) { return sqrtremi(x,NULL); }
2572 : INLINE GEN
2573 7347166 : gaddgs(GEN y, long s) { return gaddsg(s,y); }
2574 : INLINE int
2575 74900 : gcmpgs(GEN y, long s) { return -gcmpsg(s,y); }
2576 : INLINE int
2577 24843 : gequalgs(GEN y, long s) { return gequalsg(s,y); }
2578 : INLINE GEN
2579 0 : gmaxsg(long s, GEN y) { return gmaxgs(y,s); }
2580 : INLINE GEN
2581 0 : gminsg(long s, GEN y) { return gmings(y,s); }
2582 : INLINE GEN
2583 59552192 : gmulgs(GEN y, long s) { return gmulsg(s,y); }
2584 : INLINE GEN
2585 1112326 : gsubgs(GEN y, long s) { return gaddgs(y, -s); }
2586 : INLINE GEN
2587 211950 : gdivsg(long s, GEN y) { return gdiv(stoi(s), y); }
2588 :
2589 : INLINE GEN
2590 13510226 : gmax_shallow(GEN x, GEN y) { return gcmp(x,y)<0? y: x; }
2591 : INLINE GEN
2592 910800 : gmin_shallow(GEN x, GEN y) { return gcmp(x,y)<0? x: y; }
2593 :
2594 : /* x t_COMPLEX */
2595 : INLINE GEN
2596 55478895 : cxnorm(GEN x) { return gadd(gsqr(gel(x,1)), gsqr(gel(x,2))); }
2597 : /* q t_QUAD */
2598 : INLINE GEN
2599 138873 : quadnorm(GEN q)
2600 : {
2601 138873 : GEN X = gel(q,1), b = gel(X,3), c = gel(X,2);
2602 138873 : GEN z, u = gel(q,3), v = gel(q,2);
2603 138873 : if (typ(u) == t_INT && typ(v) == t_INT) /* generic case */
2604 : {
2605 138684 : z = signe(b)? mulii(v, addii(u,v)): sqri(v);
2606 138684 : return addii(z, mulii(c, sqri(u)));
2607 : }
2608 : else
2609 : {
2610 189 : z = signe(b)? gmul(v, gadd(u,v)): gsqr(v);
2611 189 : return gadd(z, gmul(c, gsqr(u)));
2612 : }
2613 : }
2614 : /* x a t_QUAD, return the attached discriminant */
2615 : INLINE GEN
2616 1015 : quad_disc(GEN x)
2617 : {
2618 1015 : GEN Q = gel(x,1), b = gel(Q,3), c = gel(Q,2), c4 = shifti(c,2);
2619 1015 : if (is_pm1(b)) return subsi(1, c4);
2620 154 : togglesign_safe(&c4); return c4;
2621 : }
2622 : INLINE GEN
2623 80514 : qfb_disc3(GEN x, GEN y, GEN z) { return subii(sqri(y), shifti(mulii(x,z),2)); }
2624 : INLINE GEN
2625 20386339 : qfb_disc(GEN x) { return gel(x,4); }
2626 :
2627 : INLINE GEN
2628 2775717 : sqrfrac(GEN x)
2629 : {
2630 2775717 : GEN z = cgetg(3,t_FRAC);
2631 2775717 : gel(z,1) = sqri(gel(x,1));
2632 2775717 : gel(z,2) = sqri(gel(x,2)); return z;
2633 : }
2634 :
2635 : INLINE void
2636 12054978 : normalize_frac(GEN z) {
2637 12054978 : if (signe(gel(z,2)) < 0) { togglesign(gel(z,1)); setabssign(gel(z,2)); }
2638 12054978 : }
2639 :
2640 : INLINE GEN
2641 673734 : powii(GEN x, GEN n)
2642 : {
2643 673734 : long ln = lgefint(n);
2644 673734 : if (ln == 3) {
2645 : GEN z;
2646 651471 : if (signe(n) > 0) return powiu(x, n[2]);
2647 69106 : z = cgetg(3, t_FRAC);
2648 69112 : gel(z,1) = gen_1;
2649 69112 : gel(z,2) = powiu(x, n[2]);
2650 69115 : return z;
2651 : }
2652 22263 : if (ln == 2) return gen_1; /* rare */
2653 : /* should never happen */
2654 0 : return powgi(x, n); /* overflow unless x = 0, 1, -1 */
2655 : }
2656 : INLINE GEN
2657 1533 : powIs(long n) {
2658 1533 : switch(n & 3)
2659 : {
2660 63 : case 1: return mkcomplex(gen_0,gen_1);
2661 385 : case 2: return gen_m1;
2662 721 : case 3: return mkcomplex(gen_0,gen_m1);
2663 : }
2664 364 : return gen_1;
2665 : }
2666 :
2667 : /*******************************************************************/
2668 : /* */
2669 : /* ASSIGNMENTS */
2670 : /* */
2671 : /*******************************************************************/
2672 0 : INLINE void mpexpz(GEN x, GEN z)
2673 0 : { pari_sp av = avma; gaffect(mpexp(x), z); set_avma(av); }
2674 0 : INLINE void mplogz(GEN x, GEN z)
2675 0 : { pari_sp av = avma; gaffect(mplog(x), z); set_avma(av); }
2676 0 : INLINE void mpcosz(GEN x, GEN z)
2677 0 : { pari_sp av = avma; gaffect(mpcos(x), z); set_avma(av); }
2678 0 : INLINE void mpsinz(GEN x, GEN z)
2679 0 : { pari_sp av = avma; gaffect(mpsin(x), z); set_avma(av); }
2680 0 : INLINE void gnegz(GEN x, GEN z)
2681 0 : { pari_sp av = avma; gaffect(gneg(x), z); set_avma(av); }
2682 0 : INLINE void gabsz(GEN x, long prec, GEN z)
2683 0 : { pari_sp av = avma; gaffect(gabs(x,prec), z); set_avma(av); }
2684 0 : INLINE void gaddz(GEN x, GEN y, GEN z)
2685 0 : { pari_sp av = avma; gaffect(gadd(x,y), z); set_avma(av); }
2686 0 : INLINE void gsubz(GEN x, GEN y, GEN z)
2687 0 : { pari_sp av = avma; gaffect(gsub(x,y), z); set_avma(av); }
2688 0 : INLINE void gmulz(GEN x, GEN y, GEN z)
2689 0 : { pari_sp av = avma; gaffect(gmul(x,y), z); set_avma(av); }
2690 0 : INLINE void gdivz(GEN x, GEN y, GEN z)
2691 0 : { pari_sp av = avma; gaffect(gdiv(x,y), z); set_avma(av); }
2692 0 : INLINE void gdiventz(GEN x, GEN y, GEN z)
2693 0 : { pari_sp av = avma; gaffect(gdivent(x,y), z); set_avma(av); }
2694 0 : INLINE void gmodz(GEN x, GEN y, GEN z)
2695 0 : { pari_sp av = avma; gaffect(gmod(x,y), z); set_avma(av); }
2696 0 : INLINE void gmul2nz(GEN x, long s, GEN z)
2697 0 : { pari_sp av = avma; gaffect(gmul2n(x,s), z); set_avma(av); }
2698 0 : INLINE void gshiftz(GEN x, long s, GEN z)
2699 0 : { pari_sp av = avma; gaffect(gshift(x,s), z); set_avma(av); }
2700 :
2701 : /*******************************************************************/
2702 : /* */
2703 : /* ELLIPTIC CURVES */
2704 : /* */
2705 : /*******************************************************************/
2706 4200133 : INLINE GEN ell_get_a1(GEN e) { return gel(e,1); }
2707 3201886 : INLINE GEN ell_get_a2(GEN e) { return gel(e,2); }
2708 4030033 : INLINE GEN ell_get_a3(GEN e) { return gel(e,3); }
2709 3972614 : INLINE GEN ell_get_a4(GEN e) { return gel(e,4); }
2710 4760436 : INLINE GEN ell_get_a6(GEN e) { return gel(e,5); }
2711 3384501 : INLINE GEN ell_get_b2(GEN e) { return gel(e,6); }
2712 1055162 : INLINE GEN ell_get_b4(GEN e) { return gel(e,7); }
2713 1661229 : INLINE GEN ell_get_b6(GEN e) { return gel(e,8); }
2714 1488466 : INLINE GEN ell_get_b8(GEN e) { return gel(e,9); }
2715 6056554 : INLINE GEN ell_get_c4(GEN e) { return gel(e,10); }
2716 7258989 : INLINE GEN ell_get_c6(GEN e) { return gel(e,11); }
2717 9214521 : INLINE GEN ell_get_disc(GEN e) { return gel(e,12); }
2718 1042106 : INLINE GEN ell_get_j(GEN e) { return gel(e,13); }
2719 9890733 : INLINE long ell_get_type(GEN e) { return mael(e,14,1); }
2720 1569888 : INLINE GEN ellff_get_field(GEN x) { return gmael(x, 15, 1); }
2721 682639 : INLINE GEN ellff_get_a4a6(GEN x) { return gmael(x, 15, 2); }
2722 1407 : INLINE GEN ellQp_get_zero(GEN x) { return gmael(x, 15, 1); }
2723 287 : INLINE long ellQp_get_prec(GEN E) { GEN z = ellQp_get_zero(E); return valp(z); }
2724 1085 : INLINE GEN ellQp_get_p(GEN E) { GEN z = ellQp_get_zero(E); return gel(z,2); }
2725 37478 : INLINE long ellR_get_prec(GEN x) { return nbits2prec(mael3(x, 15, 1, 1)); }
2726 17099 : INLINE long ellR_get_sign(GEN x) { return mael3(x, 15, 1, 2); }
2727 713840 : INLINE GEN ellnf_get_nf(GEN x) { return checknf_i(gmael(x,15,1)); }
2728 56 : INLINE GEN ellnf_get_bnf(GEN x) { return checkbnf_i(gmael(x,15,1)); }
2729 :
2730 4124622 : INLINE int checkell_i(GEN e) { return typ(e) == t_VEC && lg(e) == 17; }
2731 38033339 : INLINE int ell_is_inf(GEN z) { return lg(z) == 2; }
2732 918819 : INLINE GEN ellinf(void) { return mkvec(gen_0); }
2733 :
2734 : /*******************************************************************/
2735 : /* */
2736 : /* ALGEBRAIC NUMBER THEORY */
2737 : /* */
2738 : /*******************************************************************/
2739 14870773 : INLINE GEN modpr_get_pr(GEN x) { return gel(x,3); }
2740 725457 : INLINE GEN modpr_get_p(GEN x) { return pr_get_p(modpr_get_pr(x)); }
2741 6361791 : INLINE GEN modpr_get_T(GEN x) { return lg(x) == 4? NULL: gel(x,4); }
2742 :
2743 60893140 : INLINE GEN pr_get_p(GEN pr) { return gel(pr,1); }
2744 9264996 : INLINE GEN pr_get_gen(GEN pr){ return gel(pr,2); }
2745 : /* .[2] instead of itos works: e and f are small positive integers */
2746 7020634 : INLINE long pr_get_e(GEN pr) { return gel(pr,3)[2]; }
2747 22677245 : INLINE long pr_get_f(GEN pr) { return gel(pr,4)[2]; }
2748 38498932 : INLINE GEN pr_get_tau(GEN pr){ return gel(pr,5); }
2749 : INLINE int
2750 6756033 : pr_is_inert(GEN P) { return typ(pr_get_tau(P)) == t_INT; }
2751 : INLINE GEN
2752 3040074 : pr_norm(GEN pr) { return powiu(pr_get_p(pr), pr_get_f(pr)); }
2753 : INLINE ulong
2754 156280 : upr_norm(GEN pr) { return upowuu(pr_get_p(pr)[2], pr_get_f(pr)); }
2755 :
2756 : /* assume nf a genuine nf */
2757 : INLINE long
2758 814904 : nf_get_varn(GEN nf) { return varn(gel(nf,1)); }
2759 : INLINE GEN
2760 65308929 : nf_get_pol(GEN nf) { return gel(nf,1); }
2761 : INLINE long
2762 46295549 : nf_get_degree(GEN nf) { return degpol( nf_get_pol(nf) ); }
2763 : INLINE long
2764 6031595 : nf_get_r1(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,1)); }
2765 : INLINE long
2766 3032 : nf_get_r2(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,2)); }
2767 : INLINE GEN
2768 431532 : nf_get_disc(GEN nf) { return gel(nf,3); }
2769 : INLINE GEN
2770 2242421 : nf_get_index(GEN nf) { return gel(nf,4); }
2771 : INLINE GEN
2772 3869164 : nf_get_M(GEN nf) { return gmael(nf,5,1); }
2773 : INLINE GEN
2774 2374691 : nf_get_G(GEN nf) { return gmael(nf,5,2); }
2775 : INLINE GEN
2776 2929997 : nf_get_roundG(GEN nf) { return gmael(nf,5,3); }
2777 : INLINE GEN
2778 21535 : nf_get_Tr(GEN nf) { return gmael(nf,5,4); }
2779 : INLINE GEN
2780 5593 : nf_get_diff(GEN nf) { return gmael(nf,5,5); }
2781 : INLINE GEN
2782 39270 : nf_get_ramified_primes(GEN nf) { return gmael(nf,5,8); }
2783 : INLINE GEN
2784 1061111 : nf_get_roots(GEN nf) { return gel(nf,6); }
2785 : INLINE GEN
2786 1456 : nf_get_zk(GEN nf)
2787 : {
2788 1456 : GEN y = gel(nf,7), D = gel(y, 1);
2789 1456 : if (typ(D) == t_POL) D = gel(D, 2);
2790 1456 : if (!equali1(D)) y = gdiv(y, D);
2791 1456 : return y;
2792 : }
2793 : INLINE GEN
2794 2916423 : nf_get_zkprimpart(GEN nf)
2795 : {
2796 2916423 : GEN y = gel(nf,7);
2797 : /* test for old format of nf.zk: non normalized */
2798 2916423 : if (!equali1(gel(nf,4)) && gequal1(gel(y,1))) y = Q_remove_denom(y,NULL);
2799 2916440 : return y;
2800 : }
2801 : INLINE GEN
2802 2962722 : nf_get_zkden(GEN nf)
2803 : {
2804 2962722 : GEN y = gel(nf,7), D = gel(y,1);
2805 2962722 : if (typ(D) == t_POL) D = gel(D,2);
2806 : /* test for old format of nf.zk: non normalized */
2807 2962722 : if (!equali1(gel(nf,4)) && equali1(D)) D = Q_denom(y);
2808 2962715 : return D;
2809 : }
2810 : INLINE GEN
2811 7251742 : nf_get_invzk(GEN nf) { return gel(nf,8); }
2812 : INLINE void
2813 74595 : nf_get_sign(GEN nf, long *r1, long *r2)
2814 : {
2815 74595 : GEN x = gel(nf,2);
2816 74595 : *r1 = itou(gel(x,1));
2817 74595 : *r2 = itou(gel(x,2));
2818 74595 : }
2819 :
2820 : INLINE GEN
2821 1055620 : cyc_get_expo(GEN c) { return lg(c) == 1? gen_1: gel(c,1); }
2822 : INLINE GEN
2823 348343 : abgrp_get_no(GEN x) { return gel(x,1); }
2824 : INLINE GEN
2825 5355825 : abgrp_get_cyc(GEN x) { return gel(x,2); }
2826 : INLINE GEN
2827 818265 : abgrp_get_gen(GEN x) { return gel(x,3); }
2828 : INLINE GEN
2829 4110284 : bnf_get_nf(GEN bnf) { return gel(bnf,7); }
2830 : INLINE GEN
2831 2266846 : bnf_get_clgp(GEN bnf) { return gmael(bnf,8,1); }
2832 : INLINE GEN
2833 30246 : bnf_get_no(GEN bnf) { return abgrp_get_no(bnf_get_clgp(bnf)); }
2834 : INLINE GEN
2835 1474412 : bnf_get_cyc(GEN bnf) { return abgrp_get_cyc(bnf_get_clgp(bnf)); }
2836 : INLINE GEN
2837 762030 : bnf_get_gen(GEN bnf) { return abgrp_get_gen(bnf_get_clgp(bnf)); }
2838 : INLINE GEN
2839 608 : bnf_get_reg(GEN bnf) { return gmael(bnf,8,2); }
2840 : INLINE GEN
2841 1093598 : bnf_get_logfu(GEN bnf) { return gel(bnf,3); }
2842 : INLINE GEN
2843 457147 : bnf_get_sunits(GEN bnf)
2844 457147 : { GEN s = gmael(bnf,8,3); return typ(s) == t_INT? NULL: s; }
2845 : INLINE GEN
2846 287894 : bnf_get_tuU(GEN bnf) { return gmael3(bnf,8,4,2); }
2847 : INLINE long
2848 262891 : bnf_get_tuN(GEN bnf) { return gmael3(bnf,8,4,1)[2]; }
2849 : INLINE GEN
2850 286871 : bnf_get_fu_nocheck(GEN bnf) { return gmael(bnf,8,5); }
2851 : INLINE GEN
2852 25998 : nfV_to_scalar_or_alg(GEN nf, GEN x)
2853 62404 : { pari_APPLY_same(nf_to_scalar_or_alg(nf, gel(x,i))) }
2854 : INLINE GEN
2855 25626 : bnf_get_fu(GEN bnf) {
2856 25626 : GEN fu = bnf_build_units(bnf), nf = bnf_get_nf(bnf);
2857 25627 : if (typ(fu) == t_MAT) pari_err(e_MISC,"missing units in bnf");
2858 25627 : return nfV_to_scalar_or_alg(nf, vecslice(fu, 2, lg(fu)-1));
2859 : }
2860 :
2861 : INLINE GEN
2862 1589780 : bnr_get_bnf(GEN bnr) { return gel(bnr,1); }
2863 : INLINE GEN
2864 913780 : bnr_get_bid(GEN bnr) { return gel(bnr,2); }
2865 : INLINE GEN
2866 137231 : bnr_get_mod(GEN bnr) { return gmael(bnr,2,1); }
2867 : INLINE GEN
2868 564231 : bnr_get_nf(GEN bnr) { return gmael(bnr,1,7); }
2869 : INLINE GEN
2870 1696730 : bnr_get_clgp(GEN bnr) { return gel(bnr,5); }
2871 : INLINE GEN
2872 311248 : bnr_get_no(GEN bnr) { return abgrp_get_no(bnr_get_clgp(bnr)); }
2873 : INLINE GEN
2874 1368645 : bnr_get_cyc(GEN bnr) { return abgrp_get_cyc(bnr_get_clgp(bnr)); }
2875 : INLINE GEN
2876 70 : bnr_get_gen_nocheck(GEN bnr) { return abgrp_get_gen(bnr_get_clgp(bnr)); }
2877 : INLINE GEN
2878 7833 : bnr_get_gen(GEN bnr) {
2879 7833 : GEN G = bnr_get_clgp(bnr);
2880 7833 : if (lg(G) != 4)
2881 0 : pari_err(e_MISC,"missing bnr generators: please use bnrinit(,,1)");
2882 7833 : return gel(G,3);
2883 : }
2884 :
2885 : INLINE GEN
2886 369400 : bid_get_mod(GEN bid) { return gel(bid,1); }
2887 : INLINE GEN
2888 68418 : bid_get_ideal(GEN bid) { return gmael(bid,1,1); }
2889 : INLINE GEN
2890 33460 : bid_get_arch(GEN bid) { return gmael(bid,1,2); }
2891 : INLINE GEN
2892 2356334 : bid_get_grp(GEN bid) { return gel(bid,2); }
2893 : INLINE GEN
2894 1291090 : bid_get_fact(GEN bid) { return gmael(bid,3,1); }
2895 : INLINE GEN
2896 1004195 : bid_get_fact2(GEN bid) { return gmael(bid,3,2); }
2897 : INLINE GEN
2898 970459 : bid_get_sprk(GEN bid) { return gmael(bid,4,1); }
2899 : INLINE GEN
2900 50750 : bid_get_sarch(GEN bid) { return gmael(bid,4,2); }
2901 : INLINE GEN
2902 1195752 : bid_get_archp(GEN bid) { return gmael3(bid,4,2,2); }
2903 : INLINE GEN
2904 1340130 : bid_get_U(GEN bid) { return gel(bid,5); }
2905 : INLINE GEN
2906 0 : bid_get_no(GEN bid) { return abgrp_get_no(bid_get_grp(bid)); }
2907 : INLINE GEN
2908 2303704 : bid_get_cyc(GEN bid) { return abgrp_get_cyc(bid_get_grp(bid)); }
2909 : INLINE GEN
2910 0 : bid_get_gen_nocheck(GEN bid) { return abgrp_get_gen(bid_get_grp(bid)); }
2911 : INLINE GEN
2912 52038 : bid_get_gen(GEN bid) {
2913 52038 : GEN G = bid_get_grp(bid);
2914 52038 : if (lg(G) != 4) pari_err(e_MISC,"missing bid generators. Use idealstar(,,2)");
2915 52038 : return abgrp_get_gen(G);
2916 : }
2917 :
2918 : INLINE GEN
2919 29703604 : znstar_get_N(GEN G) { return gmael(G,1,1); }
2920 : INLINE GEN
2921 6897527 : znstar_get_faN(GEN G) { return gel(G,3); }
2922 : INLINE GEN
2923 7 : znstar_get_no(GEN G) { return abgrp_get_no(gel(G,2)); }
2924 : INLINE GEN
2925 193382 : znstar_get_cyc(GEN G) { return abgrp_get_cyc(gel(G,2)); }
2926 : INLINE GEN
2927 7 : znstar_get_gen(GEN G) { return abgrp_get_gen(gel(G,2)); }
2928 : INLINE GEN
2929 7574231 : znstar_get_conreycyc(GEN G) { return gmael(G,4,5); }
2930 : INLINE GEN
2931 3131926 : znstar_get_conreygen(GEN G) { return gmael(G,4,4); }
2932 : INLINE GEN
2933 46704 : znstar_get_Ui(GEN G) { return gmael(G,4,3); }
2934 : INLINE GEN
2935 120932 : znstar_get_U(GEN G) { return gel(G,5); }
2936 : INLINE GEN
2937 2735215 : znstar_get_pe(GEN G) { return gmael(G,4,1); }
2938 : INLINE GEN
2939 35542 : gal_get_pol(GEN gal) { return gel(gal,1); }
2940 : INLINE GEN
2941 5838 : gal_get_p(GEN gal) { return gmael(gal,2,1); }
2942 : INLINE GEN
2943 91 : gal_get_e(GEN gal) { return gmael(gal,2,2); }
2944 : INLINE GEN
2945 23271 : gal_get_mod(GEN gal) { return gmael(gal,2,3); }
2946 : INLINE GEN
2947 31769 : gal_get_roots(GEN gal) { return gel(gal,3); }
2948 : INLINE GEN
2949 26967 : gal_get_invvdm(GEN gal) { return gel(gal,4); }
2950 : INLINE GEN
2951 26967 : gal_get_den(GEN gal) { return gel(gal,5); }
2952 : INLINE GEN
2953 79078 : gal_get_group(GEN gal) { return gel(gal,6); }
2954 : INLINE GEN
2955 8841 : gal_get_gen(GEN gal) { return gel(gal,7); }
2956 : INLINE GEN
2957 6832 : gal_get_orders(GEN gal) { return gel(gal,8); }
2958 :
2959 : /* assume rnf a genuine rnf */
2960 : INLINE long
2961 1237180 : rnf_get_degree(GEN rnf) { return degpol(rnf_get_pol(rnf)); }
2962 : INLINE long
2963 16758 : rnf_get_nfdegree(GEN rnf) { return degpol(nf_get_pol(rnf_get_nf(rnf))); }
2964 : INLINE long
2965 777028 : rnf_get_absdegree(GEN rnf) { return degpol(gmael(rnf,11,1)); }
2966 : INLINE GEN
2967 700 : rnf_get_idealdisc(GEN rnf) { return gmael(rnf,3,1); }
2968 : INLINE GEN
2969 749 : rnf_get_k(GEN rnf) { return gmael(rnf,11,3); }
2970 : INLINE GEN
2971 861 : rnf_get_alpha(GEN rnf) { return gmael(rnf, 11, 2); }
2972 : INLINE GEN
2973 442330 : rnf_get_nf(GEN rnf) { return gel(rnf,10); }
2974 : INLINE GEN
2975 3997 : rnf_get_nfzk(GEN rnf) { return gel(rnf,2); }
2976 : INLINE GEN
2977 215460 : rnf_get_polabs(GEN rnf) { return gmael(rnf,11,1); }
2978 : INLINE GEN
2979 1484063 : rnf_get_pol(GEN rnf) { return gel(rnf,1); }
2980 : INLINE GEN
2981 175 : rnf_get_disc(GEN rnf) { return gel(rnf,3); }
2982 : INLINE GEN
2983 105 : rnf_get_index(GEN rnf) { return gel(rnf,4); }
2984 : INLINE GEN
2985 1631 : rnf_get_ramified_primes(GEN rnf) { return gel(rnf,5); }
2986 : INLINE long
2987 231 : rnf_get_varn(GEN rnf) { return varn(gel(rnf,1)); }
2988 : INLINE GEN
2989 189133 : rnf_get_nfpol(GEN rnf) { return gmael(rnf,10,1); }
2990 : INLINE long
2991 3332 : rnf_get_nfvarn(GEN rnf) { return varn(gmael(rnf,10,1)); }
2992 : INLINE GEN
2993 3577 : rnf_get_zk(GEN rnf) { return gel(rnf,7); }
2994 : INLINE GEN
2995 103257 : rnf_get_map(GEN rnf) { return gel(rnf,11); }
2996 : INLINE GEN
2997 1197 : rnf_get_invzk(GEN rnf) { return gel(rnf,8); }
2998 :
2999 : /* I integral ZM (not HNF), G ZM, rounded Cholesky form of a weighted
3000 : * T2 matrix. Reduce I wrt G */
3001 : INLINE GEN
3002 472074 : idealpseudored(GEN I, GEN G)
3003 472074 : { return ZM_mul(I, ZM_lll(ZM_mul(G, I), 0.99, LLL_IM)); }
3004 :
3005 : /* Same I, G; m in I with T2(m) small */
3006 : INLINE GEN
3007 126536 : idealpseudomin(GEN I, GEN G)
3008 : {
3009 126536 : GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
3010 126536 : return ZM_ZC_mul(I, gel(u,1));
3011 : }
3012 : /* Same I,G; irrational m in I with T2(m) small */
3013 : INLINE GEN
3014 0 : idealpseudomin_nonscalar(GEN I, GEN G)
3015 : {
3016 0 : GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
3017 0 : GEN m = ZM_ZC_mul(I, gel(u,1));
3018 0 : if (ZV_isscalar(m) && lg(u) > 2) m = ZM_ZC_mul(I, gel(u,2));
3019 0 : return m;
3020 : }
3021 : /* Same I,G; t_VEC of irrational m in I with T2(m) small */
3022 : INLINE GEN
3023 393879 : idealpseudominvec(GEN I, GEN G)
3024 : {
3025 393879 : long i, j, k, n = lg(I)-1;
3026 393879 : GEN x, L, b = idealpseudored(I, G);
3027 393878 : L = cgetg(1 + (n*(n+1))/2, t_VEC);
3028 1495620 : for (i = k = 1; i <= n; i++)
3029 : {
3030 1101742 : x = gel(b,i);
3031 1101742 : if (!ZV_isscalar(x)) gel(L,k++) = x;
3032 : }
3033 1101740 : for (i = 2; i <= n; i++)
3034 1894178 : for (j = 1; j < i; j++)
3035 : {
3036 1186316 : x = ZC_add(gel(b,i),gel(b,j));
3037 1186315 : if (!ZV_isscalar(x)) gel(L,k++) = x;
3038 : }
3039 393877 : setlg(L,k); return L;
3040 : }
3041 :
3042 : INLINE GEN
3043 13865 : idealred_elt(GEN nf, GEN I) {
3044 13865 : pari_sp av = avma;
3045 13865 : GEN u = idealpseudomin(I, nf_get_roundG(nf));
3046 13865 : return gerepileupto(av, u);
3047 : }
3048 : INLINE GEN
3049 121801 : idealred(GEN nf, GEN I) { return idealred0(nf, I, NULL); }
3050 :
3051 : INLINE GEN
3052 2142 : idealchineseinit(GEN nf, GEN x)
3053 2142 : { return idealchinese(nf,x,NULL); }
3054 :
3055 : /*******************************************************************/
3056 : /* */
3057 : /* CLOSURES */
3058 : /* */
3059 : /*******************************************************************/
3060 244963565 : INLINE long closure_arity(GEN C) { return ((ulong)C[1])&ARITYBITS; }
3061 36118675 : INLINE long closure_is_variadic(GEN C) { return !!(((ulong)C[1])&VARARGBITS); }
3062 202862717 : INLINE const char *closure_codestr(GEN C) { return GSTR(gel(C,2))-1; }
3063 0 : INLINE GEN closure_get_code(GEN C) { return gel(C,2); }
3064 202846565 : INLINE GEN closure_get_oper(GEN C) { return gel(C,3); }
3065 202830030 : INLINE GEN closure_get_data(GEN C) { return gel(C,4); }
3066 10780 : INLINE GEN closure_get_dbg(GEN C) { return gel(C,5); }
3067 25483 : INLINE GEN closure_get_text(GEN C) { return gel(C,6); }
3068 7343563 : INLINE GEN closure_get_frame(GEN C) { return gel(C,7); }
3069 :
3070 : /*******************************************************************/
3071 : /* */
3072 : /* ERRORS */
3073 : /* */
3074 : /*******************************************************************/
3075 : INLINE long
3076 55346 : err_get_num(GEN e) { return e[1]; }
3077 : INLINE GEN
3078 189 : err_get_compo(GEN e, long i) { return gel(e, i+1); }
3079 :
3080 : INLINE void
3081 14 : pari_err_BUG(const char *f) { pari_err(e_BUG,f); }
3082 : INLINE void
3083 7 : pari_err_CONSTPOL(const char *f) { pari_err(e_CONSTPOL, f); }
3084 : INLINE void
3085 70 : pari_err_COPRIME(const char *f, GEN x, GEN y) { pari_err(e_COPRIME, f,x,y); }
3086 : INLINE void
3087 529 : pari_err_DIM(const char *f) { pari_err(e_DIM, f); }
3088 : INLINE void
3089 0 : pari_err_FILE(const char *f, const char *g) { pari_err(e_FILE, f,g); }
3090 : INLINE void
3091 0 : pari_err_FILEDESC(const char *f, long n) { pari_err(e_FILEDESC, f,n); }
3092 : INLINE void
3093 91 : pari_err_FLAG(const char *f) { pari_err(e_FLAG,f); }
3094 : INLINE void
3095 441 : pari_err_IMPL(const char *f) { pari_err(e_IMPL,f); }
3096 : INLINE void
3097 19870 : pari_err_INV(const char *f, GEN x) { pari_err(e_INV,f,x); }
3098 : INLINE void
3099 63 : pari_err_IRREDPOL(const char *f, GEN x) { pari_err(e_IRREDPOL, f,x); }
3100 : INLINE void
3101 2260 : 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); }
3102 : INLINE void
3103 200 : pari_err_COMPONENT(const char *f, const char *op, GEN l, GEN x) { pari_err(e_COMPONENT, f,op,l,x); }
3104 : INLINE void
3105 0 : pari_err_MAXPRIME(ulong c) { pari_err(e_MAXPRIME, c); }
3106 : INLINE void
3107 378 : pari_err_OP(const char *f, GEN x, GEN y) { pari_err(e_OP, f,x,y); }
3108 : INLINE void
3109 114 : pari_err_OVERFLOW(const char *f) { pari_err(e_OVERFLOW, f); }
3110 : INLINE void
3111 225 : pari_err_PREC(const char *f) { pari_err(e_PREC,f); }
3112 : INLINE void
3113 0 : pari_err_PACKAGE(const char *f) { pari_err(e_PACKAGE,f); }
3114 : INLINE void
3115 77 : pari_err_PRIME(const char *f, GEN x) { pari_err(e_PRIME, f,x); }
3116 : INLINE void
3117 749 : pari_err_MODULUS(const char *f, GEN x, GEN y) { pari_err(e_MODULUS, f,x,y); }
3118 : INLINE void
3119 49 : pari_err_ROOTS0(const char *f) { pari_err(e_ROOTS0, f); }
3120 : INLINE void
3121 84 : pari_err_SQRTN(const char *f, GEN x) { pari_err(e_SQRTN, f,x); }
3122 : INLINE void
3123 13182 : pari_err_TYPE(const char *f, GEN x) { pari_err(e_TYPE, f,x); }
3124 : INLINE void
3125 3388 : pari_err_TYPE2(const char *f, GEN x, GEN y) { pari_err(e_TYPE2, f,x,y); }
3126 : INLINE void
3127 280 : pari_err_VAR(const char *f, GEN x, GEN y) { pari_err(e_VAR, f,x,y); }
3128 : INLINE void
3129 231 : pari_err_PRIORITY(const char *f, GEN x, const char *op, long v)
3130 231 : { pari_err(e_PRIORITY, f,x,op,v); }
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