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. It is distributed in the hope that it will be useful, but WITHOUT
8 : ANY WARRANTY WHATSOEVER.
9 :
10 : Check the License for details. You should have received a copy of it, along
11 : with the package; see the file 'COPYING'. If not, write to the Free Software
12 : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
13 :
14 : /*******************************************************************/
15 : /* */
16 : /* CONSTRUCTORS */
17 : /* */
18 : /*******************************************************************/
19 : #define retmkfrac(x,y)\
20 : do { GEN _v = cgetg(3, t_FRAC);\
21 : gel(_v,1) = (x);\
22 : gel(_v,2) = (y); return _v; } while(0)
23 : #define retmkrfrac(x,y)\
24 : do { GEN _v = cgetg(3, t_RFRAC);\
25 : gel(_v,1) = (x);\
26 : gel(_v,2) = (y); return _v; } while(0)
27 : #define retmkintmod(x,y)\
28 : do { GEN _v = cgetg(3, t_INTMOD);\
29 : gel(_v,1) = (y);\
30 : gel(_v,2) = (x); return _v; } while(0)
31 : #define retmkcomplex(x,y)\
32 : do { GEN _v = cgetg(3, t_COMPLEX);\
33 : gel(_v,1) = (x);\
34 : gel(_v,2) = (y); return _v; } while(0)
35 : #define retmkpolmod(x,y)\
36 : do { GEN _v = cgetg(3, t_POLMOD);\
37 : gel(_v,1) = (y);\
38 : gel(_v,2) = (x); return _v; } while(0)
39 : #define retmkvec(x)\
40 : do { GEN _v = cgetg(2, t_VEC);\
41 : gel(_v,1) = (x); return _v; } while(0)
42 : #define retmkvec2(x,y)\
43 : do { GEN _v = cgetg(3, t_VEC);\
44 : gel(_v,1) = (x);\
45 : gel(_v,2) = (y); return _v; } while(0)
46 : #define retmkvec3(x,y,z)\
47 : do { GEN _v = cgetg(4, t_VEC);\
48 : gel(_v,1) = (x);\
49 : gel(_v,2) = (y);\
50 : gel(_v,3) = (z); return _v; } while(0)
51 : #define retmkqfi(x,y,z)\
52 : do { GEN _v = cgetg(4, t_QFI);\
53 : gel(_v,1) = (x);\
54 : gel(_v,2) = (y);\
55 : gel(_v,3) = (z); return _v; } while(0)
56 : #define retmkqfr(x,y,z,d)\
57 : do { GEN _v = cgetg(5, t_QFR);\
58 : gel(_v,1) = (x);\
59 : gel(_v,2) = (y);\
60 : gel(_v,3) = (z);\
61 : gel(_v,4) = (d); return _v; } while(0)
62 : #define retmkquad(x,y,z)\
63 : do { GEN _v = cgetg(4, t_QUAD);\
64 : gel(_v,1) = (x);\
65 : gel(_v,2) = (y);\
66 : gel(_v,3) = (z); return _v; } while(0)
67 : #define retmkvec4(x,y,z,t)\
68 : do { GEN _v = cgetg(5, t_VEC);\
69 : gel(_v,1) = (x);\
70 : gel(_v,2) = (y);\
71 : gel(_v,3) = (z);\
72 : gel(_v,4) = (t); return _v; } while(0)
73 : #define retmkvec5(x,y,z,t,u)\
74 : do { GEN _v = cgetg(6, t_VEC);\
75 : gel(_v,1) = (x);\
76 : gel(_v,2) = (y);\
77 : gel(_v,3) = (z);\
78 : gel(_v,4) = (t);\
79 : gel(_v,5) = (u); return _v; } while(0)
80 : #define retmkcol(x)\
81 : do { GEN _v = cgetg(2, t_COL);\
82 : gel(_v,1) = (x); return _v; } while(0)
83 : #define retmkcol2(x,y)\
84 : do { GEN _v = cgetg(3, t_COL);\
85 : gel(_v,1) = (x);\
86 : gel(_v,2) = (y); return _v; } while(0)
87 : #define retmkcol3(x,y,z)\
88 : do { GEN _v = cgetg(4, t_COL);\
89 : gel(_v,1) = (x);\
90 : gel(_v,2) = (y);\
91 : gel(_v,3) = (z); return _v; } while(0)
92 : #define retmkcol4(x,y,z,t)\
93 : do { GEN _v = cgetg(5, t_COL);\
94 : gel(_v,1) = (x);\
95 : gel(_v,2) = (y);\
96 : gel(_v,3) = (z);\
97 : gel(_v,4) = (t); return _v; } while(0)
98 : #define retmkcol5(x,y,z,t,u)\
99 : do { GEN _v = cgetg(6, t_COL);\
100 : gel(_v,1) = (x);\
101 : gel(_v,2) = (y);\
102 : gel(_v,3) = (z);\
103 : gel(_v,4) = (t);\
104 : gel(_v,5) = (u); return _v; } while(0)
105 : #define retmkcol6(x,y,z,t,u,v)\
106 : do { GEN _v = cgetg(7, t_COL);\
107 : gel(_v,1) = (x);\
108 : gel(_v,2) = (y);\
109 : gel(_v,3) = (z);\
110 : gel(_v,4) = (t);\
111 : gel(_v,5) = (u);\
112 : gel(_v,6) = (v); return _v; } while(0)
113 : #define retmkmat(x)\
114 : do { GEN _v = cgetg(2, t_MAT);\
115 : gel(_v,1) = (x); return _v; } while(0)
116 : #define retmkmat2(x,y)\
117 : do { GEN _v = cgetg(3, t_MAT);\
118 : gel(_v,1) = (x);\
119 : gel(_v,2) = (y); return _v; } while(0)
120 : #define retmkmat3(x,y,z)\
121 : do { GEN _v = cgetg(4, t_MAT);\
122 : gel(_v,1) = (x);\
123 : gel(_v,2) = (y);\
124 : gel(_v,3) = (z); return _v; } while(0)
125 : #define retmkmat4(x,y,z,t)\
126 : do { GEN _v = cgetg(5, t_MAT);\
127 : gel(_v,1) = (x);\
128 : gel(_v,2) = (y);\
129 : gel(_v,3) = (z);\
130 : gel(_v,4) = (t); return _v; } while(0)
131 : #define retmkmat5(x,y,z,t,u)\
132 : do { GEN _v = cgetg(6, t_MAT);\
133 : gel(_v,1) = (x);\
134 : gel(_v,2) = (y);\
135 : gel(_v,3) = (z);\
136 : gel(_v,4) = (t);\
137 : gel(_v,5) = (u); return _v; } while(0)
138 :
139 : INLINE GEN
140 1453551 : mkintmod(GEN x, GEN y) { retmkintmod(x,y); }
141 : INLINE GEN
142 3794 : mkintmodu(ulong x, ulong y) {
143 3794 : GEN v = cgetg(3,t_INTMOD);
144 3794 : gel(v,1) = utoipos(y);
145 3794 : gel(v,2) = utoi(x); return v;
146 : }
147 : INLINE GEN
148 264318 : mkpolmod(GEN x, GEN y) { retmkpolmod(x,y); }
149 : INLINE GEN
150 2396675 : mkfrac(GEN x, GEN y) { retmkfrac(x,y); }
151 : INLINE GEN
152 3955098 : mkfraccopy(GEN x, GEN y) { retmkfrac(icopy(x), icopy(y)); }
153 : INLINE GEN
154 7 : mkrfrac(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
155 7 : gel(v,1) = x; gel(v,2) = y; return v; }
156 : INLINE GEN
157 7 : mkrfraccopy(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
158 7 : gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
159 : INLINE GEN
160 3091819 : mkcomplex(GEN x, GEN y) { retmkcomplex(x,y); }
161 : INLINE GEN
162 435535 : gen_I(void) { return mkcomplex(gen_0, gen_1); }
163 : INLINE GEN
164 204387 : cgetc(long l) { retmkcomplex(cgetr(l), cgetr(l)); }
165 : INLINE GEN
166 42 : mkquad(GEN n, GEN x, GEN y) { GEN v = cgetg(4, t_QUAD);
167 42 : gel(v,1) = n; gel(v,2) = x; gel(v,3) = y; return v; }
168 : /* vecsmall */
169 : INLINE GEN
170 54608936 : mkvecsmall(long x) { GEN v = cgetg(2, t_VECSMALL); v[1] = x; return v; }
171 : INLINE GEN
172 109614320 : mkvecsmall2(long x,long y) { GEN v = cgetg(3, t_VECSMALL);
173 109606825 : v[1]=x; v[2]=y; return v; }
174 : INLINE GEN
175 64947099 : mkvecsmall3(long x,long y,long z) { GEN v = cgetg(4, t_VECSMALL);
176 64944615 : v[1]=x; v[2]=y; v[3]=z; return v; }
177 : INLINE GEN
178 23713036 : mkvecsmall4(long x,long y,long z,long t) { GEN v = cgetg(5, t_VECSMALL);
179 23698931 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; return v; }
180 : INLINE GEN
181 702726 : mkvecsmall5(long x,long y,long z,long t,long u) { GEN v = cgetg(6, t_VECSMALL);
182 702726 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; v[5]=u; return v; }
183 :
184 : INLINE GEN
185 158123 : mkqfi(GEN x, GEN y, GEN z) { retmkqfi(x,y,z); }
186 : /* vec */
187 : INLINE GEN
188 3662334 : mkvec(GEN x) { retmkvec(x); }
189 : INLINE GEN
190 131690496 : mkvec2(GEN x, GEN y) { retmkvec2(x,y); }
191 : INLINE GEN
192 74449636 : mkvec3(GEN x, GEN y, GEN z) { retmkvec3(x,y,z); }
193 : INLINE GEN
194 7740271 : mkvec4(GEN x, GEN y, GEN z, GEN t) { retmkvec4(x,y,z,t); }
195 : INLINE GEN
196 11954197 : mkvec5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkvec5(x,y,z,t,u); }
197 : INLINE GEN
198 7 : mkvecs(long x) { retmkvec(stoi(x)); }
199 : INLINE GEN
200 19885 : mkvec2s(long x, long y) { retmkvec2(stoi(x),stoi(y)); }
201 : INLINE GEN
202 492702 : mkvec3s(long x, long y, long z) { retmkvec3(stoi(x),stoi(y),stoi(z)); }
203 : INLINE GEN
204 0 : mkvec4s(long x, long y, long z, long t) { retmkvec4(stoi(x),stoi(y),stoi(z),stoi(t)); }
205 : INLINE GEN
206 33460 : mkveccopy(GEN x) { GEN v = cgetg(2, t_VEC); gel(v,1) = gcopy(x); return v; }
207 : INLINE GEN
208 109129 : mkvec2copy(GEN x, GEN y) {
209 109129 : GEN v = cgetg(3,t_VEC); gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
210 : /* col */
211 : INLINE GEN
212 2203381 : mkcol(GEN x) { retmkcol(x); }
213 : INLINE GEN
214 14935339 : mkcol2(GEN x, GEN y) { retmkcol2(x,y); }
215 : INLINE GEN
216 41615 : mkcol3(GEN x, GEN y, GEN z) { retmkcol3(x,y,z); }
217 : INLINE GEN
218 0 : mkcol4(GEN x, GEN y, GEN z, GEN t) { retmkcol4(x,y,z,t); }
219 : INLINE GEN
220 0 : mkcol5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkcol5(x,y,z,t,u); }
221 : INLINE GEN
222 4208 : mkcol6(GEN x, GEN y, GEN z, GEN t, GEN u, GEN v) { retmkcol6(x,y,z,t,u,v); }
223 : INLINE GEN
224 728 : mkcols(long x) { retmkcol(stoi(x)); }
225 : INLINE GEN
226 1181376 : mkcol2s(long x, long y) { retmkcol2(stoi(x),stoi(y)); }
227 : INLINE GEN
228 0 : mkcol3s(long x, long y, long z) { retmkcol3(stoi(x),stoi(y),stoi(z)); }
229 : INLINE GEN
230 0 : mkcol4s(long x, long y, long z, long t) { retmkcol4(stoi(x),stoi(y),stoi(z),stoi(t)); }
231 : INLINE GEN
232 28804 : mkcolcopy(GEN x) { GEN v = cgetg(2, t_COL); gel(v,1) = gcopy(x); return v; }
233 : /* mat */
234 : INLINE GEN
235 730466 : mkmat(GEN x) { retmkmat(x); }
236 : INLINE GEN
237 16239402 : mkmat2(GEN x, GEN y) { retmkmat2(x,y); }
238 : INLINE GEN
239 2352 : mkmat3(GEN x, GEN y, GEN z) { retmkmat3(x,y,z); }
240 : INLINE GEN
241 0 : mkmat4(GEN x, GEN y, GEN z, GEN t) { retmkmat4(x,y,z,t); }
242 : INLINE GEN
243 0 : mkmat5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkmat5(x,y,z,t,u); }
244 : INLINE GEN
245 7404 : mkmatcopy(GEN x) { GEN v = cgetg(2, t_MAT); gel(v,1) = gcopy(x); return v; }
246 : INLINE GEN
247 0 : mkerr(long x) { GEN v = cgetg(2, t_ERROR); v[1] = x; return v; }
248 : INLINE GEN
249 24192 : mkoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
250 : INLINE GEN
251 13867 : mkmoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
252 : INLINE long
253 47286 : inf_get_sign(GEN x) { return signe(gel(x,1)); }
254 : /* pol */
255 : INLINE GEN
256 711142 : pol_x(long v) {
257 711142 : GEN p = cgetg(4, t_POL);
258 711142 : p[1] = evalsigne(1)|evalvarn(v);
259 711142 : gel(p,2) = gen_0;
260 711142 : gel(p,3) = gen_1; return p;
261 : }
262 : /* x^n, assume n >= 0 */
263 : INLINE GEN
264 2473669 : pol_xn(long n, long v) {
265 2473669 : long i, a = n+2;
266 2473669 : GEN p = cgetg(a+1, t_POL);
267 2473669 : p[1] = evalsigne(1)|evalvarn(v);
268 2473669 : for (i = 2; i < a; i++) gel(p,i) = gen_0;
269 2473669 : gel(p,a) = gen_1; return p;
270 : }
271 : /* x^n, no assumption on n */
272 : INLINE GEN
273 42 : pol_xnall(long n, long v)
274 : {
275 42 : if (n < 0) retmkrfrac(gen_1, pol_xn(-n,v));
276 42 : return pol_xn(n, v);
277 : }
278 : INLINE GEN
279 1199867 : pol_1(long v) {
280 1199867 : GEN p = cgetg(3, t_POL);
281 1199867 : p[1] = evalsigne(1)|evalvarn(v);
282 1199867 : gel(p,2) = gen_1; return p;
283 : }
284 : INLINE GEN
285 18065159 : pol_0(long v)
286 : {
287 18065159 : GEN x = cgetg(2,t_POL);
288 18065159 : x[1] = evalvarn(v); return x;
289 : }
290 : #define retconst_vec(n,x)\
291 : do { long _i, _n = (n);\
292 : GEN _v = cgetg(_n+1, t_VEC), _x = (x);\
293 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
294 : return _v; } while(0)
295 : INLINE GEN
296 7356325 : const_vec(long n, GEN x) { retconst_vec(n, x); }
297 : #define retconst_col(n,x)\
298 : do { long _i, _n = (n);\
299 : GEN _v = cgetg(_n+1, t_COL), _x = (x);\
300 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
301 : return _v; } while(0)
302 : INLINE GEN
303 93426 : const_col(long n, GEN x) { retconst_col(n, x); }
304 : INLINE GEN
305 4532924 : const_vecsmall(long n, long c)
306 : {
307 : long i;
308 4532924 : GEN V = cgetg(n+1,t_VECSMALL);
309 4532925 : for(i=1;i<=n;i++) V[i] = c;
310 4532925 : return V;
311 : }
312 :
313 : /*** ZERO ***/
314 : /* O(p^e) */
315 : INLINE GEN
316 301252 : zeropadic(GEN p, long e)
317 : {
318 301252 : GEN y = cgetg(5,t_PADIC);
319 301252 : gel(y,4) = gen_0;
320 301252 : gel(y,3) = gen_1;
321 301252 : gel(y,2) = icopy(p);
322 301252 : y[1] = evalvalp(e) | _evalprecp(0);
323 301252 : return y;
324 : }
325 : INLINE GEN
326 532 : zeropadic_shallow(GEN p, long e)
327 : {
328 532 : GEN y = cgetg(5,t_PADIC);
329 532 : gel(y,4) = gen_0;
330 532 : gel(y,3) = gen_1;
331 532 : gel(y,2) = p;
332 532 : y[1] = evalvalp(e) | _evalprecp(0);
333 532 : return y;
334 : }
335 : /* O(pol_x(v)^e) */
336 : INLINE GEN
337 14959 : zeroser(long v, long e)
338 : {
339 14959 : GEN x = cgetg(2, t_SER);
340 14959 : x[1] = evalvalp(e) | evalvarn(v); return x;
341 : }
342 : INLINE int
343 3702019 : ser_isexactzero(GEN x)
344 : {
345 3702019 : if (!signe(x)) switch(lg(x))
346 : {
347 13230 : case 2: return 1;
348 840 : case 3: return isexactzero(gel(x,2));
349 : }
350 3687949 : return 0;
351 : }
352 : /* 0 * pol_x(v) */
353 : INLINE GEN
354 7064698 : zeropol(long v) { return pol_0(v); }
355 : /* vector(n) */
356 : INLINE GEN
357 23679328 : zerocol(long n)
358 : {
359 23679328 : GEN y = cgetg(n+1,t_COL);
360 23679328 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
361 23679328 : return y;
362 : }
363 : /* vectorv(n) */
364 : INLINE GEN
365 18169806 : zerovec(long n)
366 : {
367 18169806 : GEN y = cgetg(n+1,t_VEC);
368 18169806 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
369 18169806 : return y;
370 : }
371 : /* matrix(m, n) */
372 : INLINE GEN
373 15470 : zeromat(long m, long n)
374 : {
375 15470 : GEN y = cgetg(n+1,t_MAT);
376 15470 : GEN v = zerocol(m);
377 15470 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
378 15470 : return y;
379 : }
380 : /* = zero_zx, sv is a evalvarn()*/
381 : INLINE GEN
382 798909 : zero_Flx(long sv) { return pol0_Flx(sv); }
383 : INLINE GEN
384 32052929 : zero_Flv(long n)
385 : {
386 32052929 : GEN y = cgetg(n+1,t_VECSMALL);
387 32053175 : long i; for (i=1; i<=n; i++) y[i] = 0;
388 32053175 : return y;
389 : }
390 : /* matrix(m, n) */
391 : INLINE GEN
392 890800 : zero_Flm(long m, long n)
393 : {
394 890800 : GEN y = cgetg(n+1,t_MAT);
395 890800 : GEN v = zero_Flv(m);
396 890800 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
397 890800 : return y;
398 : }
399 : /* matrix(m, n) */
400 : INLINE GEN
401 93242 : zero_Flm_copy(long m, long n)
402 : {
403 93242 : GEN y = cgetg(n+1,t_MAT);
404 93239 : long i; for (i=1; i<=n; i++) gel(y,i) = zero_Flv(m);
405 93242 : return y;
406 : }
407 :
408 : INLINE GEN
409 789149 : zero_F2v(long m)
410 : {
411 789149 : long l = nbits2nlong(m);
412 789149 : GEN v = zero_Flv(l+1);
413 789149 : v[1] = m;
414 789149 : return v;
415 : }
416 :
417 : INLINE GEN
418 0 : zero_F2m(long m, long n)
419 : {
420 : long i;
421 0 : GEN M = cgetg(n+1, t_MAT);
422 0 : GEN v = zero_F2v(m);
423 0 : for (i = 1; i <= n; i++)
424 0 : gel(M,i) = v;
425 0 : return M;
426 : }
427 :
428 :
429 : INLINE GEN
430 280015 : zero_F2m_copy(long m, long n)
431 : {
432 : long i;
433 280015 : GEN M = cgetg(n+1, t_MAT);
434 858705 : for (i = 1; i <= n; i++)
435 578690 : gel(M,i)= zero_F2v(m);
436 280015 : return M;
437 : }
438 :
439 : /* matrix(m, n) */
440 : INLINE GEN
441 1787013 : zeromatcopy(long m, long n)
442 : {
443 1787013 : GEN y = cgetg(n+1,t_MAT);
444 1787013 : long i; for (i=1; i<=n; i++) gel(y,i) = zerocol(m);
445 1787013 : return y;
446 : }
447 :
448 : INLINE GEN
449 16919 : zerovec_block(long len)
450 : {
451 : long i;
452 16919 : GEN blk = cgetg_block(len + 1, t_VEC);
453 558327 : for (i = 1; i <= len; ++i)
454 541408 : gel(blk, i) = gen_0;
455 16919 : return blk;
456 : }
457 :
458 : /* i-th vector in the standard basis */
459 : INLINE GEN
460 1388919 : col_ei(long n, long i) { GEN e = zerocol(n); gel(e,i) = gen_1; return e; }
461 : INLINE GEN
462 308540 : vec_ei(long n, long i) { GEN e = zerovec(n); gel(e,i) = gen_1; return e; }
463 : INLINE GEN
464 7 : F2v_ei(long n, long i) { GEN e = zero_F2v(n); F2v_set(e,i); return e; }
465 : INLINE GEN
466 69271 : vecsmall_ei(long n, long i) { GEN e = zero_zv(n); e[i] = 1; return e; }
467 : INLINE GEN
468 1168038 : Rg_col_ei(GEN x, long n, long i) { GEN e = zerocol(n); gel(e,i) = x; return e; }
469 :
470 : INLINE GEN
471 2637472 : shallowcopy(GEN x)
472 2637472 : { return typ(x) == t_MAT ? RgM_shallowcopy(x): leafcopy(x); }
473 :
474 : /* routines for naive growarrays */
475 : INLINE GEN
476 12707545 : vectrunc_init(long l)
477 : {
478 12707545 : GEN z = new_chunk(l);
479 12707937 : z[0] = evaltyp(t_VEC) | _evallg(1); return z;
480 : }
481 : INLINE void
482 507085710 : lg_increase(GEN x) { x[0]++; }
483 : INLINE void
484 49275809 : vectrunc_append(GEN x, GEN t) { gel(x, lg(x)) = t; lg_increase(x); }
485 : INLINE void
486 0 : vectrunc_append_batch(GEN x, GEN y)
487 : {
488 0 : long i, l = lg(x), ly = lg(y);
489 0 : GEN z = x + l-1;
490 0 : for (i = 1; i < ly; i++) gel(z,i) = gel(y,i);
491 0 : setlg(x, l+ly-1);
492 0 : }
493 : INLINE GEN
494 168349482 : vecsmalltrunc_init(long l)
495 : {
496 168349482 : GEN z = new_chunk(l);
497 168349482 : z[0] = evaltyp(t_VECSMALL) | _evallg(1); return z;
498 : }
499 : INLINE void
500 25859876 : vecsmalltrunc_append(GEN x, long t) { x[ lg(x) ] = t; lg_increase(x); }
501 :
502 : /*******************************************************************/
503 : /* */
504 : /* VEC / COL / VECSMALL */
505 : /* */
506 : /*******************************************************************/
507 : /* shallow*/
508 : INLINE GEN
509 0 : vec_shorten(GEN v, long n)
510 : {
511 : long i;
512 0 : GEN V = cgetg(n+1,t_VEC);
513 0 : for(i=1;i<=n;i++) gel(V,i) = gel(v,i);
514 0 : return V;
515 : }
516 : /* shallow*/
517 : INLINE GEN
518 10906 : vec_lengthen(GEN v, long n)
519 : {
520 : long i;
521 10906 : long l=lg(v);
522 10906 : GEN V = cgetg(n+1,t_VEC);
523 10906 : for(i=1;i<l;i++) gel(V,i) = gel(v,i);
524 10906 : return V;
525 : }
526 : /* shallow*/
527 : INLINE GEN
528 59332 : vec_append(GEN V, GEN s)
529 : {
530 59332 : long i, l2 = lg(V);
531 59332 : GEN res = cgetg(l2+1, typ(V));
532 59332 : for (i = 1; i < l2; ++i) gel(res, i) = gel(V,i);
533 59332 : gel(res,l2) = s; return res;
534 : }
535 : /* shallow*/
536 : INLINE GEN
537 0 : vec_setconst(GEN v, GEN x)
538 : {
539 0 : long i, l = lg(v);
540 0 : for (i = 1; i < l; i++) gel(v,i) = x;
541 0 : return v;
542 : }
543 : INLINE GEN
544 178028 : vecsmall_shorten(GEN v, long n)
545 : {
546 : long i;
547 178028 : GEN V = cgetg(n+1,t_VECSMALL);
548 178029 : for(i=1;i<=n;i++) V[i] = v[i];
549 178029 : return V;
550 : }
551 : INLINE GEN
552 21 : vecsmall_lengthen(GEN v, long n)
553 : {
554 21 : long i, l = lg(v);
555 21 : GEN V = cgetg(n+1,t_VECSMALL);
556 21 : for(i=1;i<l;i++) V[i] = v[i];
557 21 : return V;
558 : }
559 :
560 : INLINE GEN
561 410016 : vec_to_vecsmall(GEN z)
562 : {
563 410016 : long i, l = lg(z);
564 410016 : GEN x = cgetg(l, t_VECSMALL);
565 410016 : for (i=1; i<l; i++) x[i] = itos(gel(z,i));
566 410016 : return x;
567 : }
568 : INLINE GEN
569 71218 : vecsmall_to_vec(GEN z)
570 : {
571 71218 : long i, l = lg(z);
572 71218 : GEN x = cgetg(l,t_VEC);
573 71218 : for (i=1; i<l; i++) gel(x,i) = stoi(z[i]);
574 71218 : return x;
575 : }
576 : INLINE GEN
577 938 : vecsmall_to_vec_inplace(GEN z)
578 : {
579 938 : long i, l = lg(z);
580 938 : for (i=1; i<l; i++) gel(z,i) = stoi(z[i]);
581 938 : settyp(z, t_VEC); return z;
582 : }
583 : INLINE GEN
584 1302413 : vecsmall_to_col(GEN z)
585 : {
586 1302413 : long i, l = lg(z);
587 1302413 : GEN x = cgetg(l,t_COL);
588 1302413 : for (i=1; i<l; i++) gel(x,i) = stoi(z[i]);
589 1302413 : return x;
590 : }
591 :
592 : INLINE int
593 9456367 : vecsmall_lexcmp(GEN x, GEN y)
594 : {
595 : long lx,ly,l,i;
596 9456367 : lx = lg(x);
597 9456367 : ly = lg(y); l = minss(lx,ly);
598 56689298 : for (i=1; i<l; i++)
599 54634366 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
600 2054932 : if (lx == ly) return 0;
601 14 : return (lx < ly)? -1 : 1;
602 : }
603 :
604 : INLINE int
605 47066978 : vecsmall_prefixcmp(GEN x, GEN y)
606 : {
607 47066978 : long i, lx = lg(x), ly = lg(y), l = minss(lx,ly);
608 148811348 : for (i=1; i<l; i++)
609 134951817 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
610 13859531 : return 0;
611 : }
612 :
613 : /*Can be used on t_VEC, but coeffs not gcopy-ed*/
614 : INLINE GEN
615 12663 : vecsmall_prepend(GEN V, long s)
616 : {
617 12663 : long i, l2 = lg(V);
618 12663 : GEN res = cgetg(l2+1, typ(V));
619 12663 : res[1] = s;
620 12663 : for (i = 2; i <= l2; ++i) res[i] = V[i - 1];
621 12663 : return res;
622 : }
623 :
624 : INLINE GEN
625 3765602 : vecsmall_append(GEN V, long s)
626 : {
627 3765602 : long i, l2 = lg(V);
628 3765602 : GEN res = cgetg(l2+1, t_VECSMALL);
629 3765602 : for (i = 1; i < l2; ++i) res[i] = V[i];
630 3765602 : res[l2] = s; return res;
631 : }
632 :
633 : INLINE GEN
634 784810 : vecsmall_concat(GEN u, GEN v)
635 : {
636 784810 : long i, l1 = lg(u)-1, l2 = lg(v)-1;
637 784810 : GEN res = cgetg(l1+l2+1, t_VECSMALL);
638 784810 : for (i = 1; i <= l1; ++i) res[i] = u[i];
639 784810 : for (i = 1; i <= l2; ++i) res[i+l1] = v[i];
640 784810 : return res;
641 : }
642 :
643 : /* return the number of indices where u and v are equal */
644 : INLINE long
645 0 : vecsmall_coincidence(GEN u, GEN v)
646 : {
647 0 : long i, s = 0, l = minss(lg(u),lg(v));
648 0 : for(i=1; i<l; i++)
649 0 : if(u[i] == v[i]) s++;
650 0 : return s;
651 : }
652 :
653 : /* returns the first index i<=n such that x=v[i] if it exists, 0 otherwise */
654 : INLINE long
655 0 : vecsmall_isin(GEN v, long x)
656 : {
657 0 : long i, l = lg(v);
658 0 : for (i = 1; i < l; i++)
659 0 : if (v[i] == x) return i;
660 0 : return 0;
661 : }
662 :
663 : INLINE long
664 84 : vecsmall_pack(GEN V, long base, long mod)
665 : {
666 84 : long i, s = 0;
667 84 : for(i=1; i<lg(V); i++) s = (base*s + V[i]) % mod;
668 84 : return s;
669 : }
670 :
671 : INLINE long
672 14 : vecsmall_indexmax(GEN x)
673 : {
674 14 : long i, i0 = 1, t = x[1], lx = lg(x);
675 56 : for (i=2; i<lx; i++)
676 42 : if (x[i] > t) t = x[i0=i];
677 14 : return i0;
678 : }
679 :
680 : INLINE long
681 42799 : vecsmall_max(GEN x)
682 : {
683 42799 : long i, t = x[1], lx = lg(x);
684 78161 : for (i=2; i<lx; i++)
685 35362 : if (x[i] > t) t = x[i];
686 42799 : return t;
687 : }
688 :
689 : INLINE long
690 14 : vecsmall_indexmin(GEN x)
691 : {
692 14 : long i, i0 = 1, t = x[1], lx =lg(x);
693 56 : for (i=2; i<lx; i++)
694 42 : if (x[i] < t) t = x[i0=i];
695 14 : return i0;
696 : }
697 :
698 : INLINE long
699 0 : vecsmall_min(GEN x)
700 : {
701 0 : long i, t = x[1], lx =lg(x);
702 0 : for (i=2; i<lx; i++)
703 0 : if (x[i] < t) t = x[i];
704 0 : return t;
705 : }
706 :
707 : INLINE int
708 2127333 : ZV_isscalar(GEN x)
709 : {
710 2127333 : long l = lg(x);
711 7488398 : while (--l > 1)
712 4981062 : if (signe(gel(x, l))) return 0;
713 380003 : return 1;
714 : }
715 : INLINE int
716 17397561 : QV_isscalar(GEN x)
717 : {
718 17397561 : long lx = lg(x),i;
719 18863123 : for (i=2; i<lx; i++)
720 18336333 : if (!isintzero(gel(x, i))) return 0;
721 526790 : return 1;
722 : }
723 : INLINE int
724 3864 : RgV_isscalar(GEN x)
725 : {
726 3864 : long lx = lg(x),i;
727 7343 : for (i=2; i<lx; i++)
728 6244 : if (!gequal0(gel(x, i))) return 0;
729 1099 : return 1;
730 : }
731 : INLINE int
732 0 : RgX_isscalar(GEN x)
733 : {
734 : long i;
735 0 : for (i=lg(x)-1; i>2; i--)
736 0 : if (!gequal0(gel(x, i))) return 0;
737 0 : return 1;
738 : }
739 : INLINE long
740 25588414 : RgX_equal_var(GEN x, GEN y) { return varn(x) == varn(y) && RgX_equal(x,y); }
741 :
742 : INLINE int
743 3886 : RgX_is_rational(GEN x)
744 : {
745 : long i;
746 20097 : for (i = lg(x)-1; i > 1; i--)
747 18836 : if (!is_rational_t(typ(gel(x,i)))) return 0;
748 1261 : return 1;
749 : }
750 : INLINE int
751 64413290 : RgX_is_ZX(GEN x)
752 : {
753 : long i;
754 277135961 : for (i = lg(x)-1; i > 1; i--)
755 218261609 : if (typ(gel(x,i)) != t_INT) return 0;
756 58874352 : return 1;
757 : }
758 : INLINE int
759 116447 : RgX_is_QX(GEN x)
760 : {
761 116447 : long k = lg(x)-1;
762 437754 : for ( ; k>1; k--)
763 323008 : if (!is_rational_t(typ(gel(x,k)))) return 0;
764 114746 : return 1;
765 : }
766 : INLINE int
767 15307692 : RgX_is_monomial(GEN x)
768 : {
769 : long i;
770 15307692 : if (!signe(x)) return 0;
771 25389647 : for (i=lg(x)-2; i>1; i--)
772 17486448 : if (!isexactzero(gel(x,i))) return 0;
773 7903199 : return 1;
774 : }
775 : INLINE int
776 18293780 : RgV_is_ZV(GEN x)
777 : {
778 : long i;
779 74712063 : for (i = lg(x)-1; i > 0; i--)
780 56419347 : if (typ(gel(x,i)) != t_INT) return 0;
781 18292716 : return 1;
782 : }
783 : INLINE int
784 4200 : RgV_is_QV(GEN x)
785 : {
786 : long i;
787 96334 : for (i = lg(x)-1; i > 0; i--)
788 94759 : if (!is_rational_t(typ(gel(x,i)))) return 0;
789 1575 : return 1;
790 : }
791 :
792 : /********************************************************************/
793 : /** **/
794 : /** Dynamic arrays implementation **/
795 : /** **/
796 : /********************************************************************/
797 : INLINE void **
798 406271732 : pari_stack_base(pari_stack *s) { return s->data; }
799 :
800 : INLINE void
801 467026 : pari_stack_init(pari_stack *s, size_t size, void **data)
802 : {
803 467026 : s->data = data;
804 467026 : *data = NULL;
805 467026 : s->n = 0;
806 467026 : s->alloc = 0;
807 467026 : s->size = size;
808 467026 : }
809 :
810 : INLINE void
811 405771150 : pari_stack_alloc(pari_stack *s, long nb)
812 : {
813 405771150 : void **sdat = pari_stack_base(s);
814 405941962 : long alloc = s->alloc;
815 811885093 : if (s->n+nb <= alloc) return;
816 226455 : if (!alloc)
817 178412 : alloc = nb;
818 : else
819 : {
820 48043 : while (s->n+nb > alloc) alloc <<= 1;
821 : }
822 226455 : *sdat = pari_realloc(*sdat,alloc*s->size);
823 227624 : s->alloc = alloc;
824 : }
825 :
826 : INLINE long
827 338261517 : pari_stack_new(pari_stack *s) { pari_stack_alloc(s, 1); return s->n++; }
828 :
829 : INLINE void
830 402659 : pari_stack_delete(pari_stack *s)
831 : {
832 402659 : void **sdat = pari_stack_base(s);
833 402457 : if (*sdat) pari_free(*sdat);
834 402667 : }
835 :
836 : INLINE void
837 4649 : pari_stack_pushp(pari_stack *s, void *u)
838 : {
839 4649 : long n = pari_stack_new(s);
840 4649 : void **sdat =(void**) *pari_stack_base(s);
841 4649 : sdat[n] = u;
842 4649 : }
843 :
844 : /*******************************************************************/
845 : /* */
846 : /* EXTRACT */
847 : /* */
848 : /*******************************************************************/
849 : INLINE GEN
850 202557584 : vecslice(GEN A, long y1, long y2)
851 : {
852 202557584 : long i,lB = y2 - y1 + 2;
853 202557584 : GEN B = cgetg(lB, typ(A));
854 202557584 : for (i=1; i<lB; i++) B[i] = A[y1-1+i];
855 202557584 : return B;
856 : }
857 : INLINE GEN
858 738136 : vecslicepermute(GEN A, GEN p, long y1, long y2)
859 : {
860 738136 : long i,lB = y2 - y1 + 2;
861 738136 : GEN B = cgetg(lB, typ(A));
862 738136 : for (i=1; i<lB; i++) B[i] = A[p[y1-1+i]];
863 738136 : return B;
864 : }
865 : /* rowslice(rowpermute(A,p), x1, x2) */
866 : INLINE GEN
867 34472 : rowslicepermute(GEN A, GEN p, long x1, long x2)
868 : {
869 34472 : long i, lB = lg(A);
870 34472 : GEN B = cgetg(lB, typ(A));
871 34472 : for (i=1; i<lB; i++) gel(B,i) = vecslicepermute(gel(A,i),p,x1,x2);
872 34472 : return B;
873 : }
874 : INLINE GEN
875 20368958 : rowslice(GEN A, long x1, long x2)
876 : {
877 20368958 : long i, lB = lg(A);
878 20368958 : GEN B = cgetg(lB, typ(A));
879 20368958 : for (i=1; i<lB; i++) gel(B,i) = vecslice(gel(A,i),x1,x2);
880 20368958 : return B;
881 : }
882 :
883 : INLINE GEN
884 212458 : matslice(GEN A, long x1, long x2, long y1, long y2)
885 : {
886 212458 : return rowslice(vecslice(A, y1, y2), x1, x2);
887 : }
888 :
889 : /* shallow, remove coeff of index j */
890 : INLINE GEN
891 133 : rowsplice(GEN a, long j)
892 : {
893 : long i, l;
894 133 : GEN b = cgetg_copy(a,&l);
895 133 : for (i = 1; i < l; i++) gel(b,i) = vecsplice(gel(a,i), j);
896 133 : return b;
897 : }
898 : /* shallow, remove coeff of index j */
899 : INLINE GEN
900 45164 : vecsplice(GEN a, long j)
901 : {
902 45164 : long i, k, l = lg(a);
903 : GEN b;
904 45164 : if (l == 1) pari_err(e_MISC, "incorrect component in vecsplice");
905 45164 : b = cgetg(l-1, typ(a));
906 190323 : for (i = k = 1; i < l; i++)
907 145159 : if (i != j) gel(b, k++) = gel(a,i);
908 45164 : return b;
909 : }
910 : /* shallow */
911 : INLINE GEN
912 756 : RgM_minor(GEN a, long i, long j)
913 : {
914 756 : GEN b = vecsplice(a, j);
915 756 : long k, l = lg(b);
916 756 : for (k = 1; k < l; k++) gel(b,k) = vecsplice(gel(b,k), i);
917 756 : return b;
918 : }
919 :
920 : /* A[x0,] */
921 : INLINE GEN
922 178650 : row(GEN A, long x0)
923 : {
924 178650 : long i, lB = lg(A);
925 178650 : GEN B = cgetg(lB, t_VEC);
926 178650 : for (i=1; i<lB; i++) gel(B, i) = gcoeff(A, x0, i);
927 178650 : return B;
928 : }
929 : INLINE GEN
930 4531535 : Flm_row(GEN A, long x0)
931 : {
932 4531535 : long i, lB = lg(A);
933 4531535 : GEN B = cgetg(lB, t_VECSMALL);
934 4531540 : for (i=1; i<lB; i++) B[i] = coeff(A, x0, i);
935 4531540 : return B;
936 : }
937 : /* A[x0,] */
938 : INLINE GEN
939 56 : rowcopy(GEN A, long x0)
940 : {
941 56 : long i, lB = lg(A);
942 56 : GEN B = cgetg(lB, t_VEC);
943 56 : for (i=1; i<lB; i++) gel(B, i) = gcopy(gcoeff(A, x0, i));
944 56 : return B;
945 : }
946 : /* A[x0, x1..x2] */
947 : INLINE GEN
948 2177 : row_i(GEN A, long x0, long x1, long x2)
949 : {
950 2177 : long i, lB = x2 - x1 + 2;
951 2177 : GEN B = cgetg(lB, t_VEC);
952 2177 : for (i=x1; i<=x2; i++) gel(B, i) = gcoeff(A, x0, i);
953 2177 : return B;
954 : }
955 :
956 : INLINE GEN
957 5491522 : vecreverse(GEN A)
958 : {
959 : long i, l;
960 5491522 : GEN B = cgetg_copy(A, &l);
961 5491522 : for (i=1; i<l; i++) gel(B, i) = gel(A, l-i);
962 5491522 : return B;
963 : }
964 :
965 : INLINE GEN
966 252 : vecsmall_reverse(GEN A)
967 : {
968 : long i, l;
969 252 : GEN B = cgetg_copy(A, &l);
970 252 : for (i=1; i<l; i++) B[i] = A[l-i];
971 252 : return B;
972 : }
973 :
974 : INLINE void
975 232 : vecreverse_inplace(GEN y)
976 : {
977 232 : long ly = lg(y), lim = ly>>1, i;
978 640 : for (i = 1; i <= lim; i++)
979 : {
980 408 : GEN z = gel(y,i);
981 408 : gel(y,i) = gel(y,ly-i);
982 408 : gel(y,ly-i) = z;
983 : }
984 232 : }
985 :
986 : INLINE GEN
987 45223254 : vecsmallpermute(GEN A, GEN p) { return perm_mul(A, p); }
988 :
989 : INLINE GEN
990 5421882 : vecpermute(GEN A, GEN p)
991 : {
992 5421882 : long i,lB = lg(p);
993 5421882 : GEN B = cgetg(lB, typ(A));
994 5421882 : for (i=1; i<lB; i++) gel(B, i) = gel(A, p[i]);
995 5421882 : return B;
996 : }
997 : INLINE GEN
998 2880174 : rowpermute(GEN A, GEN p)
999 : {
1000 2880174 : long i, lB = lg(A);
1001 2880174 : GEN B = cgetg(lB, typ(A));
1002 28927671 : for (i=1; i<lB; i++)
1003 27519341 : gel(B, i) = typ(gel(A,i)) == t_VECSMALL ? vecsmallpermute(gel(A, i), p):
1004 1471844 : vecpermute(gel(A, i), p);
1005 2880174 : return B;
1006 : }
1007 : /*******************************************************************/
1008 : /* */
1009 : /* PERMUTATIONS */
1010 : /* */
1011 : /*******************************************************************/
1012 : /* identity permutation */
1013 : INLINE GEN
1014 611193 : identity_perm(long n)
1015 : {
1016 611193 : GEN perm = cgetg(n+1, t_VECSMALL);
1017 : long i;
1018 611193 : for (i = 1; i <= n; i++) perm[i] = i;
1019 611193 : return perm;
1020 : }
1021 :
1022 : /* assume d <= n */
1023 : INLINE GEN
1024 0 : cyclic_perm(long n, long d)
1025 : {
1026 0 : GEN perm = cgetg(n+1, t_VECSMALL);
1027 : long i;
1028 0 : for (i = 1; i <= n-d; i++) perm[i] = i+d;
1029 0 : for ( ; i <= n; i++) perm[i] = i-n+d;
1030 0 : return perm;
1031 : }
1032 :
1033 : /* Multiply (compose) two permutations */
1034 : INLINE GEN
1035 46860550 : perm_mul(GEN s, GEN t)
1036 : {
1037 : GEN u;
1038 46860550 : long i, l = lg(t);
1039 46860550 : u = cgetg(l, t_VECSMALL);
1040 46860550 : for (i = 1; i < l; i++) u[i] = s[ t[i] ];
1041 46860550 : return u;
1042 : }
1043 : /* Compute the inverse (reciprocal) of a permutation. */
1044 : INLINE GEN
1045 604063 : perm_inv(GEN x)
1046 : {
1047 : long i, lx;
1048 604063 : GEN y = cgetg_copy(x, &lx);
1049 604063 : for (i=1; i<lx; i++) y[ x[i] ] = i;
1050 604063 : return y;
1051 : }
1052 : /* Return s*t*s^-1 */
1053 : INLINE GEN
1054 506639 : perm_conj(GEN s, GEN t)
1055 : {
1056 : long i, l;
1057 506639 : GEN v = cgetg_copy(s, &l);
1058 506639 : for (i = 1; i < l; i++) v[ s[i] ] = s[ t[i] ];
1059 506639 : return v;
1060 : }
1061 :
1062 : /*********************************************************************/
1063 : /* MALLOC/FREE WRAPPERS */
1064 : /*********************************************************************/
1065 : #define BLOCK_SIGALRM_START \
1066 : { \
1067 : int block=PARI_SIGINT_block; \
1068 : PARI_SIGINT_block = 2; \
1069 : MT_SIGINT_BLOCK(block);
1070 :
1071 : #define BLOCK_SIGINT_START \
1072 : { \
1073 : int block=PARI_SIGINT_block; \
1074 : PARI_SIGINT_block = 1; \
1075 : MT_SIGINT_BLOCK(block);
1076 :
1077 : #define BLOCK_SIGINT_END \
1078 : PARI_SIGINT_block = block; \
1079 : MT_SIGINT_UNBLOCK(block); \
1080 : if (!block && PARI_SIGINT_pending) \
1081 : { \
1082 : int sig = PARI_SIGINT_pending; \
1083 : PARI_SIGINT_pending = 0; \
1084 : raise(sig); \
1085 : } \
1086 : }
1087 :
1088 : INLINE void
1089 50501832 : pari_free(void *pointer)
1090 : {
1091 50501832 : BLOCK_SIGINT_START;
1092 50502625 : free(pointer);
1093 50502625 : BLOCK_SIGINT_END;
1094 50502352 : }
1095 : INLINE void*
1096 230869474 : pari_malloc(size_t size)
1097 : {
1098 230869474 : if (size)
1099 : {
1100 : char *tmp;
1101 230869474 : BLOCK_SIGINT_START;
1102 230870948 : tmp = (char*)malloc(size);
1103 230870948 : BLOCK_SIGINT_END;
1104 230870887 : if (!tmp) pari_err(e_MEM);
1105 230870887 : return tmp;
1106 : }
1107 0 : if (DEBUGMEM) pari_warn(warner,"mallocing NULL object");
1108 0 : return NULL;
1109 : }
1110 : INLINE void*
1111 238217 : pari_realloc(void *pointer, size_t size)
1112 : {
1113 : char *tmp;
1114 :
1115 238217 : BLOCK_SIGINT_START;
1116 240019 : if (!pointer) tmp = (char *) malloc(size);
1117 51641 : else tmp = (char *) realloc(pointer,size);
1118 240019 : BLOCK_SIGINT_END;
1119 239307 : if (!tmp) pari_err(e_MEM);
1120 239307 : return tmp;
1121 : }
1122 : INLINE void*
1123 32106 : pari_calloc(size_t size)
1124 : {
1125 32106 : void *t = pari_malloc(size);
1126 32106 : memset(t, 0, size); return t;
1127 : }
1128 : INLINE GEN
1129 4186 : cgetalloc(long t, size_t l)
1130 : {
1131 4186 : GEN x = (GEN)pari_malloc(l * sizeof(long));
1132 4186 : x[0] = evaltyp(t) | evallg(l); return x;
1133 : }
1134 :
1135 : /*******************************************************************/
1136 : /* */
1137 : /* GARBAGE COLLECTION */
1138 : /* */
1139 : /*******************************************************************/
1140 : /* copy integer x as if we had avma = av */
1141 : INLINE GEN
1142 3526643158 : icopy_avma(GEN x, pari_sp av)
1143 : {
1144 3526643158 : long i = lgefint(x), lx = i;
1145 3526643158 : GEN y = ((GEN)av) - i;
1146 3526643158 : while (--i > 0) y[i] = x[i];
1147 3526643158 : y[0] = evaltyp(t_INT)|evallg(lx);
1148 3526484848 : return y;
1149 : }
1150 : /* copy leaf x as if we had avma = av */
1151 : INLINE GEN
1152 154412004 : leafcopy_avma(GEN x, pari_sp av)
1153 : {
1154 154412004 : long i = lg(x);
1155 154412004 : GEN y = ((GEN)av) - i;
1156 154412004 : while (--i > 0) y[i] = x[i];
1157 154412004 : y[0] = x[0] & (~CLONEBIT);
1158 154412004 : return y;
1159 : }
1160 : INLINE GEN
1161 563951679 : gerepileuptoleaf(pari_sp av, GEN x)
1162 : {
1163 : long lx;
1164 : GEN q;
1165 :
1166 563951679 : if (!isonstack(x) || (GEN)av<=x) { avma = av; return x; }
1167 564953756 : lx = lg(x);
1168 564953756 : q = ((GEN)av) - lx;
1169 564953756 : avma = (pari_sp)q;
1170 564953756 : while (--lx >= 0) q[lx] = x[lx];
1171 564953756 : return q;
1172 : }
1173 : INLINE GEN
1174 1139526395 : gerepileuptoint(pari_sp av, GEN x)
1175 : {
1176 1139526395 : if (!isonstack(x) || (GEN)av<=x) { avma = av; return x; }
1177 1005156901 : avma = (pari_sp)icopy_avma(x, av);
1178 1005806843 : return (GEN)avma;
1179 : }
1180 : INLINE GEN
1181 778619853 : gerepileupto(pari_sp av, GEN x)
1182 : {
1183 778619853 : if (!isonstack(x) || (GEN)av<=x) { avma = av; return x; }
1184 683684324 : switch(typ(x))
1185 : { /* non-default = !is_recursive_t(tq) */
1186 253593944 : case t_INT: return gerepileuptoint(av, x);
1187 : case t_REAL:
1188 : case t_STR:
1189 113772738 : case t_VECSMALL: return gerepileuptoleaf(av,x);
1190 : default:
1191 : /* NB: x+i --> ((long)x) + i*sizeof(long) */
1192 316317642 : return gerepile(av, (pari_sp) (x+lg(x)), x);
1193 : }
1194 : }
1195 :
1196 : /* gerepileupto(av, gcopy(x)) */
1197 : INLINE GEN
1198 38811737 : gerepilecopy(pari_sp av, GEN x)
1199 : {
1200 38811737 : if (is_recursive_t(typ(x)))
1201 : {
1202 31286434 : GENbin *p = copy_bin(x);
1203 31286441 : avma = av; return bin_copy(p);
1204 : }
1205 : else
1206 : {
1207 7525299 : avma = av;
1208 7525299 : if (x < (GEN)av) {
1209 6108600 : if (x < (GEN)pari_mainstack->bot) new_chunk(lg(x));
1210 6108600 : x = leafcopy_avma(x, av);
1211 6108611 : avma = (pari_sp)x;
1212 : } else
1213 1416699 : x = leafcopy(x);
1214 7525310 : return x;
1215 : }
1216 : }
1217 :
1218 : /* Takes an array of pointers to GENs, of length n. Copies all
1219 : * objects to contiguous locations and cleans up the stack between
1220 : * av and avma. */
1221 : INLINE void
1222 136899 : gerepilemany(pari_sp av, GEN* gptr[], int n)
1223 : {
1224 : int i;
1225 136899 : for (i=0; i<n; i++) *gptr[i] = (GEN)copy_bin(*gptr[i]);
1226 136899 : avma = av;
1227 136899 : for (i=0; i<n; i++) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1228 136899 : }
1229 :
1230 : INLINE void
1231 5188649 : gerepileall(pari_sp av, int n, ...)
1232 : {
1233 : int i;
1234 5188649 : va_list a; va_start(a, n);
1235 5188649 : if (n < 10)
1236 : {
1237 : GEN *gptr[10];
1238 15823707 : for (i=0; i<n; i++)
1239 10635084 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1240 5188623 : avma = av;
1241 5188623 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1242 :
1243 : }
1244 : else
1245 : {
1246 0 : GEN **gptr = (GEN**) pari_malloc(n*sizeof(GEN*));
1247 0 : for (i=0; i<n; i++)
1248 0 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1249 0 : avma = av;
1250 0 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1251 0 : pari_free(gptr);
1252 : }
1253 5188653 : va_end(a);
1254 5188653 : }
1255 :
1256 : INLINE void
1257 8 : gerepilecoeffs(pari_sp av, GEN x, int n)
1258 : {
1259 : int i;
1260 8 : for (i=0; i<n; i++) gel(x,i) = (GEN)copy_bin(gel(x,i));
1261 8 : avma = av;
1262 8 : for (i=0; i<n; i++) gel(x,i) = bin_copy((GENbin*)x[i]);
1263 8 : }
1264 :
1265 : /* p from copy_bin. Copy p->x back to stack, then destroy p */
1266 : INLINE GEN
1267 42329090 : bin_copy(GENbin *p)
1268 : {
1269 : GEN x, y, base;
1270 : long dx, len;
1271 :
1272 42329090 : x = p->x; if (!x) { pari_free(p); return gen_0; }
1273 42322264 : len = p->len;
1274 42322264 : base= p->base; dx = x - base;
1275 42322264 : y = (GEN)memcpy((void*)new_chunk(len), (void*)GENbinbase(p), len*sizeof(long));
1276 42322247 : y += dx;
1277 42322247 : p->rebase(y, ((ulong)y-(ulong)x));
1278 42322249 : pari_free(p); return y;
1279 : }
1280 :
1281 : INLINE GEN
1282 84651406 : GENbinbase(GENbin *p) { return (GEN)(p + 1); }
1283 :
1284 : INLINE void
1285 26695428 : cgiv(GEN x)
1286 : {
1287 26695428 : pari_sp av = (pari_sp)(x+lg(x));
1288 26695428 : if (isonstack((GEN)av)) avma = av;
1289 26695310 : }
1290 :
1291 : INLINE void
1292 1117889 : killblock(GEN x) { gunclone(x); }
1293 :
1294 : INLINE int
1295 16953803 : is_universal_constant(GEN x) { return (x >= gen_0 && x <= ghalf); }
1296 :
1297 : /*******************************************************************/
1298 : /* */
1299 : /* CONVERSION / ASSIGNMENT */
1300 : /* */
1301 : /*******************************************************************/
1302 : /* z is a type which may be a t_COMPLEX component (not a t_QUAD) */
1303 : INLINE GEN
1304 2537330 : cxcompotor(GEN z, long prec)
1305 : {
1306 2537330 : switch(typ(z))
1307 : {
1308 1344818 : case t_INT: return itor(z, prec);
1309 134120 : case t_FRAC: return fractor(z, prec);
1310 1058392 : case t_REAL: return rtor(z, prec);
1311 0 : default: pari_err_TYPE("cxcompotor",z);
1312 : return NULL; /* LCOV_EXCL_LINE */
1313 : }
1314 : }
1315 : INLINE GEN
1316 1261313 : cxtofp(GEN x, long prec)
1317 1261313 : { retmkcomplex(cxcompotor(gel(x,1),prec), cxcompotor(gel(x,2),prec)); }
1318 :
1319 : INLINE double
1320 16984787 : gtodouble(GEN x)
1321 : {
1322 16984787 : if (typ(x)!=t_REAL) {
1323 3205977 : pari_sp av = avma;
1324 3205977 : x = gtofp(x, DEFAULTPREC);
1325 3205977 : if (typ(x)!=t_REAL) pari_err_TYPE("gtodouble [t_REAL expected]", x);
1326 3205977 : avma = av;
1327 : }
1328 16984787 : return rtodbl(x);
1329 : }
1330 : INLINE long
1331 67160337 : gtos(GEN x) {
1332 67160337 : if (typ(x) != t_INT) pari_err_TYPE("gtos [integer expected]",x);
1333 67160330 : return itos(x);
1334 : }
1335 :
1336 : INLINE ulong
1337 117053 : gtou(GEN x) {
1338 117053 : if (typ(x) != t_INT || signe(x)<0)
1339 0 : pari_err_TYPE("gtou [integer >=0 expected]",x);
1340 117622 : return itou(x);
1341 : }
1342 :
1343 : INLINE GEN
1344 1348677 : absfrac(GEN x)
1345 : {
1346 1348677 : GEN y = cgetg(3, t_FRAC);
1347 1348677 : gel(y,1) = absi(gel(x,1));
1348 1348677 : gel(y,2) = icopy(gel(x,2)); return y;
1349 : }
1350 : INLINE GEN
1351 32378 : absfrac_shallow(GEN x)
1352 32378 : { return signe(gel(x,1))>0? x: mkfrac(negi(gel(x,1)), gel(x,2)); }
1353 : INLINE GEN
1354 487923 : Q_abs(GEN x) { return (typ(x) == t_INT)? absi(x): absfrac(x); }
1355 : INLINE GEN
1356 105943 : Q_abs_shallow(GEN x)
1357 105943 : { return (typ(x) == t_INT)? absi_shallow(x): absfrac_shallow(x); }
1358 : INLINE GEN
1359 322 : R_abs_shallow(GEN x)
1360 322 : { return (typ(x) == t_FRAC)? absfrac_shallow(x): mpabs_shallow(x); }
1361 : INLINE GEN
1362 0 : R_abs(GEN x)
1363 0 : { return (typ(x) == t_FRAC)? absfrac(x): mpabs(x); }
1364 :
1365 : /* Force z to be of type real/complex with floating point components */
1366 : INLINE GEN
1367 17772371 : gtofp(GEN z, long prec)
1368 : {
1369 17772371 : switch(typ(z))
1370 : {
1371 8138988 : case t_INT: return itor(z, prec);
1372 4257450 : case t_FRAC: return fractor(z, prec);
1373 4298184 : case t_REAL: return rtor(z, prec);
1374 : case t_COMPLEX: {
1375 1077749 : GEN a = gel(z,1), b = gel(z,2);
1376 1077749 : if (isintzero(b)) return cxcompotor(a, prec);
1377 1075845 : if (isintzero(a)) {
1378 1838 : GEN y = cgetg(3, t_COMPLEX);
1379 1838 : b = cxcompotor(b, prec);
1380 1838 : gel(y,1) = real_0_bit(expo(b) - prec2nbits(prec));
1381 1838 : gel(y,2) = b; return y;
1382 : }
1383 1074007 : return cxtofp(z, prec);
1384 : }
1385 0 : case t_QUAD: return quadtofp(z, prec);
1386 0 : default: pari_err_TYPE("gtofp",z);
1387 : return NULL; /* LCOV_EXCL_LINE */
1388 : }
1389 : }
1390 : /* Force z to be of type real / int */
1391 : INLINE GEN
1392 22400 : gtomp(GEN z, long prec)
1393 : {
1394 22400 : switch(typ(z))
1395 : {
1396 14 : case t_INT: return z;
1397 22386 : case t_FRAC: return fractor(z, prec);
1398 0 : case t_REAL: return rtor(z, prec);
1399 0 : case t_QUAD: z = quadtofp(z, prec);
1400 0 : if (typ(z) == t_REAL) return z;
1401 0 : default: pari_err_TYPE("gtomp",z);
1402 : return NULL; /* LCOV_EXCL_LINE */
1403 : }
1404 : }
1405 :
1406 : INLINE GEN
1407 595609 : RgX_gtofp(GEN x, long prec)
1408 : {
1409 : long l;
1410 595609 : GEN y = cgetg_copy(x, &l);
1411 595609 : while (--l > 1) gel(y,l) = gtofp(gel(x,l), prec);
1412 595609 : y[1] = x[1]; return y;
1413 : }
1414 : INLINE GEN
1415 289412 : RgC_gtofp(GEN x, long prec)
1416 : {
1417 289412 : long l = lg(x);
1418 289412 : GEN y = cgetg(l, t_COL);
1419 289412 : while (--l > 0) gel(y,l) = gtofp(gel(x,l), prec);
1420 289412 : return y;
1421 : }
1422 : INLINE GEN
1423 42 : RgV_gtofp(GEN x, long prec)
1424 : {
1425 42 : long l = lg(x);
1426 42 : GEN y = cgetg(l, t_VEC);
1427 42 : while (--l > 0) gel(y,l) = gtofp(gel(x,l), prec);
1428 42 : return y;
1429 : }
1430 : INLINE GEN
1431 19146 : RgM_gtofp(GEN x, long prec)
1432 : {
1433 : long l;
1434 19146 : GEN y = cgetg_copy(x, &l);
1435 19146 : while (--l > 0) gel(y,l) = RgC_gtofp(gel(x,l), prec);
1436 19146 : return y;
1437 : }
1438 : INLINE GEN
1439 560 : RgC_gtomp(GEN x, long prec)
1440 : {
1441 560 : long l = lg(x);
1442 560 : GEN y = cgetg(l, t_COL);
1443 560 : while (--l > 0) gel(y,l) = gtomp(gel(x,l), prec);
1444 560 : return y;
1445 : }
1446 : INLINE GEN
1447 14 : RgM_gtomp(GEN x, long prec)
1448 : {
1449 : long l;
1450 14 : GEN y = cgetg_copy(x, &l);
1451 14 : while (--l > 0) gel(y,l) = RgC_gtomp(gel(x,l), prec);
1452 14 : return y;
1453 : }
1454 :
1455 : INLINE GEN
1456 7701 : RgX_fpnorml2(GEN x, long prec)
1457 : {
1458 7701 : pari_sp av = avma;
1459 7701 : return gerepileupto(av, gnorml2(RgX_gtofp(x, prec)));
1460 : }
1461 : INLINE GEN
1462 154967 : RgC_fpnorml2(GEN x, long prec)
1463 : {
1464 154967 : pari_sp av = avma;
1465 154967 : return gerepileupto(av, gnorml2(RgC_gtofp(x, prec)));
1466 : }
1467 : INLINE GEN
1468 1843 : RgM_fpnorml2(GEN x, long prec)
1469 : {
1470 1843 : pari_sp av = avma;
1471 1843 : return gerepileupto(av, gnorml2(RgM_gtofp(x, prec)));
1472 : }
1473 :
1474 : /* y a t_REAL */
1475 : INLINE void
1476 190202 : affgr(GEN x, GEN y)
1477 : {
1478 : pari_sp av;
1479 190202 : switch(typ(x)) {
1480 5992 : case t_INT: affir(x,y); break;
1481 184210 : case t_REAL: affrr(x,y); break;
1482 0 : case t_FRAC: rdiviiz(gel(x,1),gel(x,2), y); break;
1483 0 : case t_QUAD: av = avma; affgr(quadtofp(x,realprec(y)), y); avma = av; break;
1484 0 : default: pari_err_TYPE2("=",x,y);
1485 : }
1486 190202 : }
1487 :
1488 : INLINE GEN
1489 186840 : affc_fixlg(GEN x, GEN res)
1490 : {
1491 186840 : if (typ(x) == t_COMPLEX)
1492 : {
1493 175616 : affrr_fixlg(gel(x,1), gel(res,1));
1494 175616 : affrr_fixlg(gel(x,2), gel(res,2));
1495 : }
1496 : else
1497 : {
1498 11224 : avma = (pari_sp)(res+3);
1499 11224 : res = cgetr(realprec(gel(res,1)));
1500 11224 : affrr_fixlg(x, res);
1501 : }
1502 186840 : return res;
1503 : }
1504 :
1505 : INLINE GEN
1506 0 : trunc_safe(GEN x) { long e; return gcvtoi(x,&e); }
1507 :
1508 : /*******************************************************************/
1509 : /* */
1510 : /* LENGTH CONVERSIONS */
1511 : /* */
1512 : /*******************************************************************/
1513 : INLINE long
1514 24496 : ndec2nlong(long x) { return 1 + (long)((x)*(LOG2_10/BITS_IN_LONG)); }
1515 : INLINE long
1516 24032 : ndec2prec(long x) { return 2 + ndec2nlong(x); }
1517 : INLINE long
1518 464 : ndec2nbits(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1519 : /* Fast implementation of ceil(x / (8*sizeof(long))); typecast to (ulong)
1520 : * to avoid overflow. Faster than 1 + ((x-1)>>TWOPOTBITS_IN_LONG)) :
1521 : * addl, shrl instead of subl, sarl, addl */
1522 : INLINE long
1523 1049791 : nbits2nlong(long x) {
1524 1049791 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1525 : }
1526 :
1527 : INLINE long
1528 241704909 : nbits2extraprec(long x) {
1529 241704909 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1530 : }
1531 :
1532 : /* Fast implementation of 2 + nbits2nlong(x) */
1533 : INLINE long
1534 78210696 : nbits2prec(long x) {
1535 78210696 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1536 : }
1537 : INLINE long
1538 4143707 : nbits2lg(long x) {
1539 4143707 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1540 : }
1541 : /* ceil(x / sizeof(long)) */
1542 : INLINE long
1543 8163193 : nchar2nlong(long x) {
1544 8163193 : return (long)(((ulong)x+sizeof(long)-1) >> (TWOPOTBITS_IN_LONG-3L));
1545 : }
1546 : INLINE long
1547 1233289971 : prec2nbits(long x) { return (x-2) * BITS_IN_LONG; }
1548 : INLINE double
1549 448414 : bit_accuracy_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1550 : INLINE double
1551 231036 : prec2nbits_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1552 : INLINE long
1553 25092911 : bit_prec(GEN x) { return prec2nbits(realprec(x)); }
1554 : INLINE long
1555 1152101750 : bit_accuracy(long x) { return prec2nbits(x); }
1556 : INLINE long
1557 12148 : prec2ndec(long x) { return (long)prec2nbits_mul(x, LOG10_2); }
1558 : INLINE long
1559 179 : nbits2ndec(long x) { return (long)(x * LOG10_2); }
1560 : INLINE long
1561 1651 : precdbl(long x) {return (x - 1) << 1;}
1562 : INLINE long
1563 3089576178 : divsBIL(long n) { return n >> TWOPOTBITS_IN_LONG; }
1564 : INLINE long
1565 3024736015 : remsBIL(long n) { return n & (BITS_IN_LONG-1); }
1566 :
1567 : /*********************************************************************/
1568 : /** **/
1569 : /** OPERATIONS MODULO m **/
1570 : /** **/
1571 : /*********************************************************************/
1572 : /* Assume m > 0, more efficient if 0 <= a, b < m */
1573 :
1574 : INLINE GEN
1575 2440035 : Fp_red(GEN a, GEN m) { return modii(a, m); }
1576 : INLINE GEN
1577 86280910 : Fp_add(GEN a, GEN b, GEN m)
1578 : {
1579 86280910 : pari_sp av=avma;
1580 86280910 : GEN p = addii(a,b);
1581 86299123 : long s = signe(p);
1582 86299123 : if (!s) return p; /* = gen_0 */
1583 75589056 : if (s > 0) /* general case */
1584 : {
1585 75365959 : GEN t = subii(p, m);
1586 75428311 : s = signe(t);
1587 75428311 : if (!s) { avma = av; return gen_0; }
1588 69961096 : if (s < 0) { avma = (pari_sp)p; return p; }
1589 30696918 : if (cmpii(t, m) < 0) return gerepileuptoint(av, t); /* general case ! */
1590 1115251 : p = remii(t, m);
1591 : }
1592 : else
1593 223097 : p = modii(p, m);
1594 1338348 : return gerepileuptoint(av, p);
1595 : }
1596 : INLINE GEN
1597 75418461 : Fp_sub(GEN a, GEN b, GEN m)
1598 : {
1599 75418461 : pari_sp av=avma;
1600 75418461 : GEN p = subii(a,b);
1601 75699071 : long s = signe(p);
1602 75699071 : if (!s) return p; /* = gen_0 */
1603 67837894 : if (s > 0)
1604 : {
1605 32757000 : if (cmpii(p, m) < 0) return p; /* general case ! */
1606 1316889 : p = remii(p, m);
1607 : }
1608 : else
1609 : {
1610 35080894 : GEN t = addii(p, m);
1611 35067289 : if (!s) { avma = av; return gen_0; }
1612 35067289 : if (s > 0) return gerepileuptoint(av, t); /* general case ! */
1613 35067289 : p = modii(t, m);
1614 : }
1615 36393864 : return gerepileuptoint(av, p);
1616 : }
1617 : INLINE GEN
1618 10848939 : Fp_neg(GEN b, GEN m)
1619 : {
1620 10848939 : pari_sp av = avma;
1621 10848939 : long s = signe(b);
1622 : GEN p;
1623 10848939 : if (!s) return gen_0;
1624 7451961 : if (s > 0)
1625 : {
1626 7250155 : p = subii(m, b);
1627 7249990 : if (signe(p) >= 0) return p; /* general case ! */
1628 92399 : p = modii(p, m);
1629 : } else
1630 201806 : p = remii(negi(b), m);
1631 294205 : return gerepileuptoint(av, p);
1632 : }
1633 :
1634 : INLINE GEN
1635 19996 : Fp_halve(GEN a, GEN p)
1636 : {
1637 19996 : if (mpodd(a)) a = addii(a,p);
1638 19996 : return shifti(a,-1);
1639 : }
1640 :
1641 : /* assume 0 <= u < p and ps2 = p>>1 */
1642 : INLINE GEN
1643 5791913 : Fp_center(GEN u, GEN p, GEN ps2)
1644 5791913 : { return abscmpii(u,ps2)<=0? icopy(u): subii(u,p); }
1645 :
1646 : /* x + y*z mod p */
1647 : INLINE GEN
1648 7889401 : Fp_addmul(GEN x, GEN y, GEN z, GEN p)
1649 : {
1650 : pari_sp av;
1651 7889401 : if (!signe(y) || !signe(z)) return Fp_red(x, p);
1652 7466420 : if (!signe(x)) return Fp_mul(z,y, p);
1653 7165548 : av = avma;
1654 7165548 : return gerepileuptoint(av, modii(addii(x, mulii(y,z)), p));
1655 : }
1656 :
1657 : INLINE GEN
1658 65115411 : Fp_mul(GEN a, GEN b, GEN m)
1659 : {
1660 65115411 : pari_sp av=avma;
1661 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1662 65115411 : (void)new_chunk(lg(a)+lg(b)+(lg(m)<<1));
1663 65127351 : p = mulii(a,b);
1664 65127011 : avma = av; return modii(p,m);
1665 : }
1666 : INLINE GEN
1667 62173763 : Fp_sqr(GEN a, GEN m)
1668 : {
1669 62173763 : pari_sp av=avma;
1670 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1671 62173763 : (void)new_chunk((lg(a)+lg(m))<<1);
1672 62421627 : p = sqri(a);
1673 62607686 : avma = av; return remii(p,m); /*Use remii: p >= 0 */
1674 : }
1675 : INLINE GEN
1676 80651388 : Fp_mulu(GEN a, ulong b, GEN m)
1677 : {
1678 80651388 : long l = lgefint(m);
1679 80651388 : if (l == 3)
1680 : {
1681 43406142 : ulong mm = m[2];
1682 43406142 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1683 : } else {
1684 37245246 : pari_sp av = avma;
1685 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1686 37245246 : (void)new_chunk(lg(a)+1+(l<<1));
1687 37254372 : p = muliu(a,b);
1688 36996498 : avma = av; return modii(p,m);
1689 : }
1690 : }
1691 : INLINE GEN
1692 0 : Fp_muls(GEN a, long b, GEN m)
1693 : {
1694 0 : long l = lgefint(m);
1695 0 : if (l == 3)
1696 : {
1697 0 : ulong mm = m[2];
1698 0 : if (b < 0)
1699 : {
1700 0 : ulong t = Fl_mul(umodiu(a, mm), -b, mm);
1701 0 : return t? utoipos(mm - t): gen_0;
1702 : }
1703 : else
1704 0 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1705 : } else {
1706 0 : pari_sp av = avma;
1707 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1708 0 : (void)new_chunk(lg(a)+1+(l<<1));
1709 0 : p = mulis(a,b);
1710 0 : avma = av; return modii(p,m);
1711 : }
1712 : }
1713 :
1714 : INLINE GEN
1715 8119520 : Fp_inv(GEN a, GEN m)
1716 : {
1717 : GEN res;
1718 8119520 : if (! invmod(a,m,&res)) pari_err_INV("Fp_inv", mkintmod(res,m));
1719 8119413 : return res;
1720 : }
1721 : INLINE GEN
1722 291868 : Fp_invsafe(GEN a, GEN m)
1723 : {
1724 : GEN res;
1725 291868 : if (! invmod(a,m,&res)) return NULL;
1726 291868 : return res;
1727 : }
1728 : INLINE GEN
1729 2296135 : Fp_div(GEN a, GEN b, GEN m)
1730 : {
1731 2296135 : pari_sp av=avma;
1732 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1733 2296135 : (void)new_chunk(lg(a)+(lg(m)<<1));
1734 2296135 : p = mulii(a, Fp_inv(b,m));
1735 2296135 : avma = av; return modii(p,m);
1736 : }
1737 :
1738 : INLINE GEN
1739 681892 : Flx_mulu(GEN x, ulong a, ulong p) { return Flx_Fl_mul(x,a%p,p); }
1740 :
1741 : /*******************************************************************/
1742 : /* */
1743 : /* ADDMULII / SUBMULII */
1744 : /* */
1745 : /*******************************************************************/
1746 : /* x - y*z */
1747 : INLINE GEN
1748 13177423 : submulii(GEN x, GEN y, GEN z)
1749 : {
1750 13177423 : long lx = lgefint(x), ly, lz;
1751 : pari_sp av;
1752 : GEN t;
1753 13177423 : if (lx == 2) { t = mulii(z,y); togglesign(t); return t; }
1754 11393637 : ly = lgefint(y);
1755 11393637 : if (ly == 2) return icopy(x);
1756 10402721 : lz = lgefint(z);
1757 10402721 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1758 10402721 : t = mulii(z, y);
1759 10402721 : avma = av; return subii(x,t);
1760 : }
1761 : /* y*z - x */
1762 : INLINE GEN
1763 1399990 : mulsubii(GEN y, GEN z, GEN x)
1764 : {
1765 1399990 : long lx = lgefint(x), ly, lz;
1766 : pari_sp av;
1767 : GEN t;
1768 1399990 : if (lx == 2) return mulii(z,y);
1769 873763 : ly = lgefint(y);
1770 873763 : if (ly == 2) return negi(x);
1771 838615 : lz = lgefint(z);
1772 838615 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1773 838615 : t = mulii(z, y);
1774 838615 : avma = av; return subii(t,x);
1775 : }
1776 :
1777 : /* x - u*y */
1778 : INLINE GEN
1779 7371 : submuliu(GEN x, GEN y, ulong u)
1780 : {
1781 : pari_sp av;
1782 7371 : long ly = lgefint(y);
1783 7371 : if (ly == 2) return icopy(x);
1784 7371 : av = avma;
1785 7371 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1786 7371 : y = mului(u,y);
1787 7371 : avma = av; return subii(x, y);
1788 : }
1789 : /* x + u*y */
1790 : INLINE GEN
1791 7371 : addmuliu(GEN x, GEN y, ulong u)
1792 : {
1793 : pari_sp av;
1794 7371 : long ly = lgefint(y);
1795 7371 : if (ly == 2) return icopy(x);
1796 7371 : av = avma;
1797 7371 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1798 7371 : y = mului(u,y);
1799 7371 : avma = av; return addii(x, y);
1800 : }
1801 : /* x - u*y */
1802 : INLINE GEN
1803 112298196 : submuliu_inplace(GEN x, GEN y, ulong u)
1804 : {
1805 : pari_sp av;
1806 112298196 : long ly = lgefint(y);
1807 112298196 : if (ly == 2) return x;
1808 89375975 : av = avma;
1809 89375975 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1810 89375975 : y = mului(u,y);
1811 89375975 : avma = av; return subii(x, y);
1812 : }
1813 : /* x + u*y */
1814 : INLINE GEN
1815 110943235 : addmuliu_inplace(GEN x, GEN y, ulong u)
1816 : {
1817 : pari_sp av;
1818 110943235 : long ly = lgefint(y);
1819 110943235 : if (ly == 2) return x;
1820 88991076 : av = avma;
1821 88991076 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1822 88991076 : y = mului(u,y);
1823 88991076 : avma = av; return addii(x, y);
1824 : }
1825 : /* ux + vy */
1826 : INLINE GEN
1827 19304068 : lincombii(GEN u, GEN v, GEN x, GEN y)
1828 : {
1829 19304068 : long lx = lgefint(x), ly;
1830 : GEN p1, p2;
1831 : pari_sp av;
1832 19304068 : if (lx == 2) return mulii(v,y);
1833 12274330 : ly = lgefint(y);
1834 12274330 : if (ly == 2) return mulii(u,x);
1835 11541559 : av = avma; (void)new_chunk(lx+ly+lgefint(u)+lgefint(v)); /* HACK */
1836 11541559 : p1 = mulii(u,x);
1837 11541559 : p2 = mulii(v,y);
1838 11541559 : avma = av; return addii(p1,p2);
1839 : }
1840 :
1841 : /*******************************************************************/
1842 : /* */
1843 : /* GEN SUBTYPES */
1844 : /* */
1845 : /*******************************************************************/
1846 :
1847 : INLINE int
1848 1090205017 : is_const_t(long t) { return (t < t_POLMOD); }
1849 : INLINE int
1850 51797 : is_extscalar_t(long t) { return (t <= t_POL); }
1851 : INLINE int
1852 1023598 : is_intreal_t(long t) { return (t <= t_REAL); }
1853 : INLINE int
1854 378994977 : is_matvec_t(long t) { return (t >= t_VEC && t <= t_MAT); }
1855 : INLINE int
1856 45072483 : is_noncalc_t(long tx) { return (tx) >= t_LIST; }
1857 : INLINE int
1858 744182 : is_rational_t(long t) { return (t == t_INT || t == t_FRAC); }
1859 : INLINE int
1860 277665 : is_real_t(long t) { return (t == t_INT || t == t_REAL || t == t_FRAC); }
1861 : INLINE int
1862 2818955882 : is_recursive_t(long t) { return lontyp[t]; }
1863 : INLINE int
1864 167851657 : is_scalar_t(long t) { return (t < t_POL); }
1865 : INLINE int
1866 864399 : is_vec_t(long t) { return (t == t_VEC || t == t_COL); }
1867 :
1868 : /*******************************************************************/
1869 : /* */
1870 : /* TRANSCENDENTAL */
1871 : /* */
1872 : /*******************************************************************/
1873 : INLINE GEN
1874 16302644 : sqrtr(GEN x) {
1875 16302644 : long s = signe(x);
1876 16302644 : if (s == 0) return real_0_bit(expo(x) >> 1);
1877 16268957 : if (s >= 0) return sqrtr_abs(x);
1878 25314 : retmkcomplex(gen_0, sqrtr_abs(x));
1879 : }
1880 : INLINE GEN
1881 0 : cbrtr_abs(GEN x) { return sqrtnr_abs(x, 3); }
1882 : INLINE GEN
1883 0 : cbrtr(GEN x) {
1884 0 : long s = signe(x);
1885 : GEN r;
1886 0 : if (s == 0) return real_0_bit(expo(x) / 3);
1887 0 : r = cbrtr_abs(x);
1888 0 : if (s < 0) togglesign(r);
1889 0 : return r;
1890 : }
1891 : INLINE GEN
1892 281522 : sqrtnr(GEN x, long n) {
1893 281522 : long s = signe(x);
1894 : GEN r;
1895 281522 : if (s == 0) return real_0_bit(expo(x) / n);
1896 281522 : r = sqrtnr_abs(x, n);
1897 281522 : if (s < 0) pari_err_IMPL("sqrtnr for x < 0");
1898 281522 : return r;
1899 : }
1900 : INLINE long
1901 211267 : logint(GEN B, GEN y) { return logintall(B,y,NULL); }
1902 : INLINE ulong
1903 8269363 : ulogint(ulong B, ulong y)
1904 : {
1905 : ulong r;
1906 : long e;
1907 8269363 : if (y == 2) return expu(B);
1908 8192379 : r = y;
1909 27488328 : for (e=1;; e++)
1910 : { /* here, r = y^e, r2 = y^(e-1) */
1911 27488328 : if (r >= B) return r == B? e: e-1;
1912 19295949 : r = umuluu_or_0(y, r);
1913 19295949 : if (!r) return e;
1914 19295949 : }
1915 : }
1916 :
1917 : /*******************************************************************/
1918 : /* */
1919 : /* MISCELLANEOUS */
1920 : /* */
1921 : /*******************************************************************/
1922 1023521 : INLINE int ismpzero(GEN x) { return is_intreal_t(typ(x)) && !signe(x); }
1923 514042056 : INLINE int isintzero(GEN x) { return typ(x) == t_INT && !signe(x); }
1924 11553982 : INLINE int isint1(GEN x) { return typ(x)==t_INT && equali1(x); }
1925 5082 : INLINE int isintm1(GEN x){ return typ(x)==t_INT && equalim1(x);}
1926 275175710 : INLINE int equali1(GEN n)
1927 275175710 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(1)) && n[2] == 1; }
1928 51589624 : INLINE int equalim1(GEN n)
1929 51589624 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(-1)) && n[2] == 1; }
1930 : /* works only for POSITIVE integers */
1931 1762685888 : INLINE int is_pm1(GEN n)
1932 1762685888 : { return lgefint(n) == 3 && n[2] == 1; }
1933 168187505 : INLINE int is_bigint(GEN n)
1934 168187505 : { long l = lgefint(n); return l > 3 || (l == 3 && (n[2] & HIGHBIT)); }
1935 :
1936 2102693318 : INLINE int odd(long x) { return x & 1; }
1937 7348800 : INLINE int both_odd(long x, long y) { return x & y & 1; }
1938 :
1939 : INLINE int
1940 2509046959 : isonstack(GEN x)
1941 5018093918 : { return ((pari_sp)x >= pari_mainstack->bot
1942 2509046959 : && (pari_sp)x < pari_mainstack->top); }
1943 :
1944 : /* assume x != 0 and x t_REAL, return an approximation to log2(|x|) */
1945 : INLINE double
1946 17623597 : dbllog2r(GEN x)
1947 17623597 : { return log2((double)(ulong)x[2]) + (double)(expo(x) - (BITS_IN_LONG-1)); }
1948 :
1949 : INLINE GEN
1950 276464 : mul_content(GEN cx, GEN cy)
1951 : {
1952 276464 : if (!cx) return cy;
1953 93072 : if (!cy) return cx;
1954 70215 : return gmul(cx,cy);
1955 : }
1956 : INLINE GEN
1957 1535429 : mul_denom(GEN dx, GEN dy)
1958 : {
1959 1535429 : if (!dx) return dy;
1960 1018868 : if (!dy) return dx;
1961 315868 : return mulii(dx,dy);
1962 : }
1963 :
1964 : /* POLYNOMIALS */
1965 : INLINE GEN
1966 17562838 : constant_coeff(GEN x) { return signe(x)? gel(x,2): gen_0; }
1967 : INLINE GEN
1968 73876959 : leading_coeff(GEN x) { return lg(x) == 2? gen_0: gel(x,lg(x)-1); }
1969 : INLINE ulong
1970 403099 : Flx_lead(GEN x) { return lg(x) == 2? 0: x[lg(x)-1]; }
1971 : INLINE long
1972 2668054581 : degpol(GEN x) { return lg(x)-3; }
1973 : INLINE long
1974 1385510550 : lgpol(GEN x) { return lg(x)-2; }
1975 : INLINE long
1976 96476655 : lgcols(GEN x) { return lg(gel(x,1)); }
1977 : INLINE long
1978 20403374 : nbrows(GEN x) { return lg(gel(x,1))-1; }
1979 : INLINE GEN
1980 0 : truecoeff(GEN x, long n) { return polcoeff0(x,n,-1); }
1981 :
1982 : INLINE GEN
1983 525009 : RgXQ_mul(GEN y, GEN x, GEN T) { return RgX_rem(RgX_mul(y, x), T); }
1984 : INLINE GEN
1985 273058 : RgXQ_sqr(GEN x, GEN T) { return RgX_rem(RgX_sqr(x), T); }
1986 :
1987 : INLINE GEN
1988 141771 : ZXQ_mul(GEN y, GEN x, GEN T) { return ZX_rem(ZX_mul(y, x), T); }
1989 : INLINE GEN
1990 34839 : ZXQ_sqr(GEN x, GEN T) { return ZX_rem(ZX_sqr(x), T); }
1991 :
1992 : INLINE GEN
1993 92334069 : RgX_copy(GEN x)
1994 : {
1995 : long lx, i;
1996 92334069 : GEN y = cgetg_copy(x, &lx); y[1] = x[1];
1997 92334081 : for (i = 2; i<lx; i++) gel(y,i) = gcopy(gel(x,i));
1998 92334074 : return y;
1999 : }
2000 : /* have to use ulong to avoid silly warnings from gcc "assuming signed
2001 : * overflow does not occur" */
2002 : INLINE GEN
2003 2220422 : RgX_coeff(GEN x, long n)
2004 : {
2005 2220422 : ulong l = lg(x);
2006 2220422 : return (n < 0 || ((ulong)n+3) > l)? gen_0: gel(x,n+2);
2007 : }
2008 : INLINE GEN
2009 315497 : RgX_renormalize(GEN x) { return RgX_renormalize_lg(x, lg(x)); }
2010 : INLINE GEN
2011 6424883 : RgX_div(GEN x, GEN y) { return RgX_divrem(x,y,NULL); }
2012 : INLINE GEN
2013 3641500 : RgX_rem(GEN x, GEN y) { return RgX_divrem(x,y,ONLY_REM); }
2014 : INLINE GEN
2015 7 : RgXQX_div(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,NULL); }
2016 : INLINE GEN
2017 17808 : RgXQX_rem(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,ONLY_REM); }
2018 : INLINE GEN
2019 827879 : FpX_div(GEN x, GEN y, GEN p) { return FpX_divrem(x,y,p, NULL); }
2020 : INLINE GEN
2021 3501057 : Flx_div(GEN x, GEN y, ulong p) { return Flx_divrem(x,y,p, NULL); }
2022 : INLINE GEN
2023 2989160 : F2x_div(GEN x, GEN y) { return F2x_divrem(x,y, NULL); }
2024 : INLINE GEN
2025 0 : FpV_FpC_mul(GEN x, GEN y, GEN p) { return FpV_dotproduct(x,y,p); }
2026 : INLINE GEN
2027 44757094 : pol0_Flx(long sv) { return mkvecsmall(sv); }
2028 : INLINE GEN
2029 18207180 : pol1_Flx(long sv) { return mkvecsmall2(sv, 1); }
2030 : INLINE GEN
2031 18074276 : polx_Flx(long sv) { return mkvecsmall3(sv, 0, 1); }
2032 : INLINE GEN
2033 0 : zero_zx(long sv) { return zero_Flx(sv); }
2034 : INLINE GEN
2035 0 : polx_zx(long sv) { return polx_Flx(sv); }
2036 : INLINE GEN
2037 0 : zx_shift(GEN x, long n) { return Flx_shift(x,n); }
2038 : INLINE GEN
2039 0 : zx_renormalize(GEN x, long l) { return Flx_renormalize(x,l); }
2040 : INLINE GEN
2041 35 : zero_F2x(long sv) { return zero_Flx(sv); }
2042 : INLINE GEN
2043 11373132 : pol0_F2x(long sv) { return pol0_Flx(sv); }
2044 : INLINE GEN
2045 2766878 : pol1_F2x(long sv) { return pol1_Flx(sv); }
2046 : INLINE GEN
2047 671530 : polx_F2x(long sv) { return mkvecsmall2(sv, 2); }
2048 : INLINE int
2049 816781 : F2x_equal1(GEN x) { return Flx_equal1(x); }
2050 : INLINE int
2051 3545521 : F2x_equal(GEN V, GEN W) { return Flx_equal(V,W); }
2052 : INLINE GEN
2053 69047767 : F2x_copy(GEN x) { return leafcopy(x); }
2054 : INLINE GEN
2055 0 : F2v_copy(GEN x) { return leafcopy(x); }
2056 : INLINE GEN
2057 2343946 : Flv_copy(GEN x) { return leafcopy(x); }
2058 : INLINE GEN
2059 78089286 : Flx_copy(GEN x) { return leafcopy(x); }
2060 : INLINE GEN
2061 1756115 : vecsmall_copy(GEN x) { return leafcopy(x); }
2062 : INLINE int
2063 4720636 : Flx_equal1(GEN x) { return degpol(x)==0 && x[2] == 1; }
2064 : INLINE int
2065 17509 : ZX_equal1(GEN x) { return degpol(x)==0 && equali1(gel(x,2)); }
2066 :
2067 : INLINE GEN
2068 74127239 : ZX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2069 : INLINE GEN
2070 88296189 : FpX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2071 : INLINE GEN
2072 949403 : FpXX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2073 : INLINE GEN
2074 973385 : FpXQX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2075 : INLINE GEN
2076 130725008 : F2x_renormalize(GEN x, long lx) { return Flx_renormalize(x,lx); }
2077 : INLINE GEN
2078 8758 : F2v_to_F2x(GEN x, long sv) {
2079 8758 : GEN y = leafcopy(x);
2080 8758 : y[1] = sv; F2x_renormalize(y, lg(y)); return y;
2081 : }
2082 :
2083 : INLINE GEN
2084 0 : ZX_ZXY_resultant(GEN a, GEN b) { return ZX_ZXY_rnfequation(a,b,NULL); }
2085 : INLINE long
2086 448 : sturm(GEN x) { return sturmpart(x, NULL, NULL); }
2087 : INLINE GEN
2088 36873 : resultant(GEN x, GEN y) { return resultant_all(x,y,NULL); }
2089 :
2090 : INLINE long
2091 2429 : gval(GEN x, long v) {
2092 2429 : pari_sp av = avma;
2093 2429 : long n = gvaluation(x, pol_x(v));
2094 2429 : avma = av; return n;
2095 : }
2096 :
2097 : INLINE void
2098 675412 : RgX_shift_inplace_init(long v)
2099 675412 : { if (v) (void)cgetg(v, t_VECSMALL); }
2100 : /* shift polynomial in place. assume v free cells have been left before x */
2101 : INLINE GEN
2102 675414 : RgX_shift_inplace(GEN x, long v)
2103 : {
2104 : long i, lx;
2105 : GEN y, z;
2106 675414 : if (!v) return x;
2107 261991 : lx = lg(x);
2108 261991 : if (lx == 2) return x;
2109 261991 : y = x + v;
2110 261991 : z = x + lx;
2111 : /* stackdummy from normalizepol: move it up */
2112 261991 : if (lg(z) != v) x[lx + v] = z[0];
2113 261991 : for (i = lx-1; i >= 2; i--) gel(y,i) = gel(x,i);
2114 261991 : for (i = v+1; i >= 2; i--) gel(x,i) = gen_0;
2115 : /* leave x[1] alone: it is correct */
2116 261991 : x[0] = evaltyp(t_POL) | evallg(lx+v); return x;
2117 : }
2118 :
2119 :
2120 : /* LINEAR ALGEBRA */
2121 : INLINE GEN
2122 68061 : zv_to_ZV(GEN x) { return vecsmall_to_vec(x); }
2123 : INLINE GEN
2124 1283408 : zc_to_ZC(GEN x) { return vecsmall_to_col(x); }
2125 : INLINE GEN
2126 392124 : ZV_to_zv(GEN x) { return vec_to_vecsmall(x); }
2127 : INLINE GEN
2128 0 : zx_to_zv(GEN x, long N) { return Flx_to_Flv(x,N); }
2129 : INLINE GEN
2130 0 : zv_to_zx(GEN x, long sv) { return Flv_to_Flx(x,sv); }
2131 : INLINE GEN
2132 0 : zm_to_zxV(GEN x, long sv) { return Flm_to_FlxV(x,sv); }
2133 : INLINE GEN
2134 0 : zero_zm(long x, long y) { return zero_Flm(x,y); }
2135 : INLINE GEN
2136 17821280 : zero_zv(long x) { return zero_Flv(x); }
2137 : INLINE GEN
2138 168 : zm_transpose(GEN x) { return Flm_transpose(x); }
2139 : INLINE GEN
2140 0 : zm_copy(GEN x) { return Flm_copy(x); }
2141 : INLINE GEN
2142 2002560 : zv_copy(GEN x) { return Flv_copy(x); }
2143 : INLINE GEN
2144 0 : zm_row(GEN x, long i) { return Flm_row(x,i); }
2145 :
2146 : INLINE GEN
2147 840091 : ZC_hnfrem(GEN x, GEN y) { return ZC_hnfremdiv(x,y,NULL); }
2148 : INLINE GEN
2149 35604 : ZM_hnfrem(GEN x, GEN y) { return ZM_hnfdivrem(x,y,NULL); }
2150 : INLINE GEN
2151 1162218 : ZM_lll(GEN x, double D, long f) { return ZM_lll_norms(x,D,f,NULL); }
2152 : INLINE void
2153 142980 : RgM_dimensions(GEN x, long *m, long *n) { *n = lg(x)-1; *m = *n? nbrows(x): 0; }
2154 : INLINE GEN
2155 35482 : RgM_inv(GEN a) { return RgM_solve(a, NULL); }
2156 : INLINE GEN
2157 6618833 : RgM_shallowcopy(GEN x)
2158 : {
2159 : long l;
2160 6618833 : GEN y = cgetg_copy(x, &l);
2161 6618833 : while (--l > 0) gel(y,l) = leafcopy(gel(x,l));
2162 6618833 : return y;
2163 : }
2164 : INLINE GEN
2165 362 : F2m_copy(GEN x) { return RgM_shallowcopy(x); }
2166 :
2167 : INLINE GEN
2168 1394047 : Flm_copy(GEN x) { return RgM_shallowcopy(x); }
2169 :
2170 : /* divisibility: return 1 if y[i] | x[i] for all i, 0 otherwise. Assume
2171 : * x,y are ZV of the same length */
2172 : INLINE int
2173 23198 : ZV_dvd(GEN x, GEN y)
2174 : {
2175 23198 : long i, l = lg(x);
2176 36652 : for (i=1; i < l; i++)
2177 29519 : if ( ! dvdii( gel(x,i), gel(y,i) ) ) return 0;
2178 7133 : return 1;
2179 : }
2180 :
2181 : /* Fq */
2182 : INLINE GEN
2183 2166408 : Fq_red(GEN x, GEN T, GEN p)
2184 2166408 : { return typ(x)==t_INT? Fp_red(x,p): FpXQ_red(x,T,p); }
2185 : INLINE GEN
2186 10855 : Fq_to_FpXQ(GEN x, GEN T, GEN p /*unused*/)
2187 : {
2188 : (void) p;
2189 10855 : return typ(x)==t_INT ? scalarpol(x, get_FpX_var(T)): x;
2190 : }
2191 :
2192 : INLINE GEN
2193 833 : gener_Fq_local(GEN T, GEN p, GEN L)
2194 833 : { return T? gener_FpXQ_local(T,p, L)
2195 833 : : pgener_Fp_local(p, L); }
2196 :
2197 : /* FpXQX */
2198 : INLINE GEN
2199 961 : FpXQX_div(GEN x, GEN y, GEN T, GEN p) { return FpXQX_divrem(x, y, T, p, NULL); }
2200 : INLINE GEN
2201 31785 : FlxqX_div(GEN x, GEN y, GEN T, ulong p) { return FlxqX_divrem(x, y, T, p, NULL); }
2202 : INLINE GEN
2203 30632 : F2xqX_div(GEN x, GEN y, GEN T) { return F2xqX_divrem(x, y, T, NULL); }
2204 :
2205 : /* FqX */
2206 : INLINE GEN
2207 27419 : FqX_red(GEN z, GEN T, GEN p) { return T? FpXQX_red(z, T, p): FpX_red(z, p); }
2208 : INLINE GEN
2209 903963 : FqX_add(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2210 : INLINE GEN
2211 16438 : FqX_neg(GEN x,GEN T,GEN p) { return T? FpXX_neg(x,p): FpX_neg(x,p); }
2212 : INLINE GEN
2213 2380 : FqX_sub(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2214 : INLINE GEN
2215 613238 : FqX_Fp_mul(GEN P, GEN u, GEN T, GEN p)
2216 613238 : { return T? FpXX_Fp_mul(P, u, p): FpX_Fp_mul(P, u, p); }
2217 : INLINE GEN
2218 552476 : FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
2219 552476 : { return typ(U)==t_INT ? FqX_Fp_mul(P, U, T, p): FpXQX_FpXQ_mul(P, U, T, p); }
2220 : INLINE GEN
2221 87431 : FqX_mul(GEN x, GEN y, GEN T, GEN p)
2222 87431 : { return T? FpXQX_mul(x, y, T, p): FpX_mul(x, y, p); }
2223 : INLINE GEN
2224 459889 : FqX_mulu(GEN x, ulong y, GEN T, GEN p)
2225 459889 : { return T? FpXX_mulu(x, y, p): FpX_mulu(x, y, p); }
2226 : INLINE GEN
2227 4760 : FqX_sqr(GEN x, GEN T, GEN p)
2228 4760 : { return T? FpXQX_sqr(x, T, p): FpX_sqr(x, p); }
2229 : INLINE GEN
2230 1428 : FqX_powu(GEN x, ulong n, GEN T, GEN p)
2231 1428 : { return T? FpXQX_powu(x, n, T, p): FpX_powu(x, n, p); }
2232 : INLINE GEN
2233 5126 : FqX_div(GEN x, GEN y, GEN T, GEN p)
2234 5126 : { return T? FpXQX_divrem(x,y,T,p,NULL): FpX_divrem(x,y,p,NULL); }
2235 : INLINE GEN
2236 5605 : FqX_get_red(GEN S, GEN T, GEN p)
2237 5605 : { return T? FpXQX_get_red(S,T,p): FpX_get_red(S,p); }
2238 : INLINE GEN
2239 47875 : FqX_rem(GEN x, GEN y, GEN T, GEN p)
2240 47875 : { return T? FpXQX_rem(x,y,T,p): FpX_rem(x,y,p); }
2241 : INLINE GEN
2242 329 : FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
2243 329 : { return T? FpXQX_divrem(x,y,T,p,z): FpX_divrem(x,y,p,z); }
2244 : INLINE GEN
2245 5957 : FqX_div_by_X_x(GEN x, GEN y, GEN T, GEN p, GEN *z)
2246 5957 : { return T? FpXQX_div_by_X_x(x,y,T,p,z): FpX_div_by_X_x(x,y,p,z); }
2247 : INLINE GEN
2248 0 : FqX_halfgcd(GEN P,GEN Q,GEN T,GEN p)
2249 0 : {return T? FpXQX_halfgcd(P,Q,T,p): FpX_halfgcd(P,Q,p);}
2250 : INLINE GEN
2251 257791 : FqX_gcd(GEN P,GEN Q,GEN T,GEN p)
2252 257791 : {return T? FpXQX_gcd(P,Q,T,p): FpX_gcd(P,Q,p);}
2253 : INLINE GEN
2254 82936 : FqX_extgcd(GEN P,GEN Q,GEN T,GEN p, GEN *U, GEN *V)
2255 82936 : { return T? FpXQX_extgcd(P,Q,T,p,U,V): FpX_extgcd(P,Q,p,U,V); }
2256 : INLINE GEN
2257 3066 : FqX_normalize(GEN z, GEN T, GEN p) { return T? FpXQX_normalize(z, T, p): FpX_normalize(z, p); }
2258 : INLINE GEN
2259 270081 : FqX_deriv(GEN f, /*unused*/GEN T, GEN p) { (void)T; return FpXX_deriv(f, p); }
2260 : INLINE GEN
2261 72891 : FqX_factor(GEN f, GEN T, GEN p) { return T?FpXQX_factor(f, T, p): FpX_factor(f, p); }
2262 : INLINE GEN
2263 5810 : FqX_roots(GEN f, GEN T, GEN p) { return T?FpXQX_roots(f, T, p): FpX_roots(f, p); }
2264 :
2265 : /*FqXQ*/
2266 : INLINE GEN
2267 0 : FqXQ_add(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2268 0 : { (void)S; return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2269 : INLINE GEN
2270 0 : FqXQ_sub(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2271 0 : { (void)S; return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2272 : INLINE GEN
2273 0 : FqXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
2274 0 : { return T? FpXQXQ_div(x,y,S,T,p): FpXQ_div(x,y,S,p); }
2275 : INLINE GEN
2276 0 : FqXQ_inv(GEN x, GEN S, GEN T, GEN p)
2277 0 : { return T? FpXQXQ_inv(x,S,T,p): FpXQ_inv(x,S,p); }
2278 : INLINE GEN
2279 0 : FqXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
2280 0 : { return T? FpXQXQ_invsafe(x,S,T,p): FpXQ_inv(x,S,p); }
2281 : INLINE GEN
2282 21018 : FqXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
2283 21018 : { return T? FpXQXQ_mul(x,y,S,T,p): FpXQ_mul(x,y,S,p); }
2284 : INLINE GEN
2285 0 : FqXQ_sqr(GEN x, GEN S, GEN T, GEN p)
2286 0 : { return T? FpXQXQ_sqr(x,S,T,p): FpXQ_sqr(x,S,p); }
2287 : INLINE GEN
2288 0 : FqXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
2289 0 : { return T? FpXQXQ_pow(x,n,S,T,p): FpXQ_pow(x,n,S,p); }
2290 :
2291 : /*FpXQ*/
2292 : INLINE GEN
2293 0 : FpXQ_add(GEN x,GEN y,GEN T/*unused*/,GEN p)
2294 0 : { (void)T; return FpX_add(x,y,p); }
2295 : INLINE GEN
2296 0 : FpXQ_sub(GEN x,GEN y,GEN T/*unused*/,GEN p)
2297 0 : { (void)T; return FpX_sub(x,y,p); }
2298 :
2299 : /*Flxq*/
2300 : INLINE GEN
2301 0 : Flxq_add(GEN x,GEN y,GEN T/*unused*/,ulong p)
2302 0 : { (void)T; return Flx_add(x,y,p); }
2303 : INLINE GEN
2304 264 : Flxq_sub(GEN x,GEN y,GEN T/*unused*/,ulong p)
2305 264 : { (void)T; return Flx_sub(x,y,p); }
2306 :
2307 : /* F2x */
2308 :
2309 : INLINE ulong
2310 168860493 : F2x_coeff(GEN x,long v)
2311 : {
2312 168860493 : ulong u=(ulong)x[2+divsBIL(v)];
2313 168859931 : return (u>>remsBIL(v))&1UL;
2314 : }
2315 :
2316 : INLINE void
2317 4180338 : F2x_clear(GEN x,long v)
2318 : {
2319 4180338 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2320 4180338 : *u&=~(1UL<<remsBIL(v));
2321 4180338 : }
2322 :
2323 : INLINE void
2324 38796801 : F2x_set(GEN x,long v)
2325 : {
2326 38796801 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2327 38798627 : *u|=1UL<<remsBIL(v);
2328 38801745 : }
2329 :
2330 : INLINE void
2331 1360407 : F2x_flip(GEN x,long v)
2332 : {
2333 1360407 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2334 1360407 : *u^=1UL<<remsBIL(v);
2335 1360407 : }
2336 :
2337 : /* F2v */
2338 :
2339 : INLINE ulong
2340 162409916 : F2v_coeff(GEN x,long v) { return F2x_coeff(x,v-1); }
2341 :
2342 : INLINE void
2343 4180338 : F2v_clear(GEN x,long v) { F2x_clear(x,v-1); }
2344 :
2345 : INLINE void
2346 12561299 : F2v_set(GEN x,long v) { F2x_set(x,v-1); }
2347 :
2348 : INLINE void
2349 1360407 : F2v_flip(GEN x,long v) { F2x_flip(x,v-1); }
2350 :
2351 : /* F2m */
2352 :
2353 : INLINE ulong
2354 19319885 : F2m_coeff(GEN x, long a, long b) { return F2v_coeff(gel(x,b), a); }
2355 :
2356 : INLINE void
2357 0 : F2m_clear(GEN x, long a, long b) { F2v_clear(gel(x,b), a); }
2358 :
2359 : INLINE void
2360 2352087 : F2m_set(GEN x, long a, long b) { F2v_set(gel(x,b), a); }
2361 :
2362 : INLINE void
2363 1360407 : F2m_flip(GEN x, long a, long b) { F2v_flip(gel(x,b), a); }
2364 :
2365 : /* ARITHMETIC */
2366 : INLINE GEN
2367 1029 : matpascal(long n) { return matqpascal(n, NULL); }
2368 : INLINE long
2369 2225428 : Z_issquare(GEN x) { return Z_issquareall(x, NULL); }
2370 : INLINE long
2371 14 : Z_ispower(GEN x, ulong k) { return Z_ispowerall(x, k, NULL); }
2372 : INLINE GEN
2373 5426576 : sqrti(GEN x) { return sqrtremi(x,NULL); }
2374 : INLINE GEN
2375 7478021 : gaddgs(GEN y, long s) { return gaddsg(s,y); }
2376 : INLINE int
2377 23890 : gcmpgs(GEN y, long s) { return -gcmpsg(s,y); }
2378 : INLINE int
2379 22841 : gequalgs(GEN y, long s) { return gequalsg(s,y); }
2380 : INLINE GEN
2381 0 : gmaxsg(long s, GEN y) { return gmaxgs(y,s); }
2382 : INLINE GEN
2383 0 : gminsg(long s, GEN y) { return gmings(y,s); }
2384 : INLINE GEN
2385 13266538 : gmulgs(GEN y, long s) { return gmulsg(s,y); }
2386 : INLINE GEN
2387 558103 : gsubgs(GEN y, long s) { return gaddgs(y, -s); }
2388 : INLINE GEN
2389 462973 : gdivsg(long s, GEN y) { return gdiv(stoi(s), y); }
2390 :
2391 : /* x t_COMPLEX */
2392 : INLINE GEN
2393 9529913 : cxnorm(GEN x) { return gadd(gsqr(gel(x,1)), gsqr(gel(x,2))); }
2394 : /* q t_QUAD */
2395 : INLINE GEN
2396 623 : quadnorm(GEN q)
2397 : {
2398 623 : GEN X = gel(q,1), b = gel(X,3), c = gel(X,2);
2399 623 : GEN z, u = gel(q,3), v = gel(q,2);
2400 623 : if (typ(u) == t_INT && typ(v) == t_INT) /* generic case */
2401 : {
2402 308 : z = signe(b)? mulii(v, addii(u,v)): sqri(v);
2403 308 : return addii(z, mulii(c, sqri(u)));
2404 : }
2405 : else
2406 : {
2407 315 : z = signe(b)? gmul(v, gadd(u,v)): gsqr(v);
2408 315 : return gadd(z, gmul(c, gsqr(u)));
2409 : }
2410 : }
2411 : /* x a t_QUAD, return the attached discriminant */
2412 : INLINE GEN
2413 252 : quad_disc(GEN x)
2414 : {
2415 252 : GEN Q = gel(x,1), b = gel(Q,3), c = gel(Q,2), c4;
2416 252 : if (is_pm1(b))
2417 : {
2418 196 : pari_sp av = avma; (void)new_chunk(lgefint(c) + 1);
2419 196 : c4 = shifti(c,2); avma = av; return subsi(1, c4);
2420 : }
2421 56 : c4 = shifti(c,2); togglesign_safe(&c4); return c4;
2422 : }
2423 : INLINE GEN
2424 6345364 : qfb_disc3(GEN x, GEN y, GEN z) { return subii(sqri(y), shifti(mulii(x,z),2)); }
2425 : INLINE GEN
2426 6264528 : qfb_disc(GEN x) { return qfb_disc3(gel(x,1), gel(x,2), gel(x,3)); }
2427 :
2428 : INLINE GEN
2429 1289120 : sqrfrac(GEN x)
2430 : {
2431 1289120 : GEN z = cgetg(3,t_FRAC);
2432 1289120 : gel(z,1) = sqri(gel(x,1));
2433 1289120 : gel(z,2) = sqri(gel(x,2)); return z;
2434 : }
2435 :
2436 : INLINE void
2437 12715818 : normalize_frac(GEN z) {
2438 12715818 : if (signe(gel(z,2)) < 0) { togglesign(gel(z,1)); setabssign(gel(z,2)); }
2439 12715818 : }
2440 :
2441 : INLINE GEN
2442 231460 : powii(GEN x, GEN n)
2443 : {
2444 231460 : long ln = lgefint(n);
2445 231460 : if (ln == 3) {
2446 : GEN z;
2447 228331 : if (signe(n) > 0) return powiu(x, n[2]);
2448 4935 : z = cgetg(3, t_FRAC);
2449 4935 : gel(z,1) = gen_1;
2450 4935 : gel(z,2) = powiu(x, n[2]);
2451 4935 : return z;
2452 : }
2453 3129 : if (ln == 2) return gen_1; /* rare */
2454 : /* should never happen */
2455 0 : return powgi(x, n); /* overflow unless x = 0, 1, -1 */
2456 : }
2457 : INLINE GEN
2458 840 : powIs(long n) {
2459 840 : switch(n & 3)
2460 : {
2461 7 : case 1: return mkcomplex(gen_0,gen_1);
2462 315 : case 2: return gen_m1;
2463 455 : case 3: return mkcomplex(gen_0,gen_m1);
2464 : }
2465 63 : return gen_1;
2466 : }
2467 :
2468 : /*******************************************************************/
2469 : /* */
2470 : /* ASSIGNMENTS */
2471 : /* */
2472 : /*******************************************************************/
2473 0 : INLINE void mpexpz(GEN x, GEN z)
2474 0 : { pari_sp av = avma; gaffect(mpexp(x), z); avma = av; }
2475 0 : INLINE void mplogz(GEN x, GEN z)
2476 0 : { pari_sp av = avma; gaffect(mplog(x), z); avma = av; }
2477 0 : INLINE void mpcosz(GEN x, GEN z)
2478 0 : { pari_sp av = avma; gaffect(mpcos(x), z); avma = av; }
2479 0 : INLINE void mpsinz(GEN x, GEN z)
2480 0 : { pari_sp av = avma; gaffect(mpsin(x), z); avma = av; }
2481 0 : INLINE void gnegz(GEN x, GEN z)
2482 0 : { pari_sp av = avma; gaffect(gneg(x), z); avma = av; }
2483 0 : INLINE void gabsz(GEN x, long prec, GEN z)
2484 0 : { pari_sp av = avma; gaffect(gabs(x,prec), z); avma = av; }
2485 23318 : INLINE void gaddz(GEN x, GEN y, GEN z)
2486 23318 : { pari_sp av = avma; gaffect(gadd(x,y), z); avma = av; }
2487 0 : INLINE void gsubz(GEN x, GEN y, GEN z)
2488 0 : { pari_sp av = avma; gaffect(gsub(x,y), z); avma = av; }
2489 11673 : INLINE void gmulz(GEN x, GEN y, GEN z)
2490 11673 : { pari_sp av = avma; gaffect(gmul(x,y), z); avma = av; }
2491 0 : INLINE void gdivz(GEN x, GEN y, GEN z)
2492 0 : { pari_sp av = avma; gaffect(gdiv(x,y), z); avma = av; }
2493 0 : INLINE void gdiventz(GEN x, GEN y, GEN z)
2494 0 : { pari_sp av = avma; gaffect(gdivent(x,y), z); avma = av; }
2495 0 : INLINE void gmodz(GEN x, GEN y, GEN z)
2496 0 : { pari_sp av = avma; gaffect(gmod(x,y), z); avma = av; }
2497 0 : INLINE void gmul2nz(GEN x, long s, GEN z)
2498 0 : { pari_sp av = avma; gaffect(gmul2n(x,s), z); avma = av; }
2499 0 : INLINE void gshiftz(GEN x, long s, GEN z)
2500 0 : { pari_sp av = avma; gaffect(gshift(x,s), z); avma = av; }
2501 :
2502 : /*******************************************************************/
2503 : /* */
2504 : /* ELLIPTIC CURVES */
2505 : /* */
2506 : /*******************************************************************/
2507 5284895 : INLINE GEN ell_get_a1(GEN e) { return gel(e,1); }
2508 3093263 : INLINE GEN ell_get_a2(GEN e) { return gel(e,2); }
2509 4513419 : INLINE GEN ell_get_a3(GEN e) { return gel(e,3); }
2510 3886097 : INLINE GEN ell_get_a4(GEN e) { return gel(e,4); }
2511 4702780 : INLINE GEN ell_get_a6(GEN e) { return gel(e,5); }
2512 3964637 : INLINE GEN ell_get_b2(GEN e) { return gel(e,6); }
2513 1018683 : INLINE GEN ell_get_b4(GEN e) { return gel(e,7); }
2514 1624869 : INLINE GEN ell_get_b6(GEN e) { return gel(e,8); }
2515 1464197 : INLINE GEN ell_get_b8(GEN e) { return gel(e,9); }
2516 5897304 : INLINE GEN ell_get_c4(GEN e) { return gel(e,10); }
2517 7929144 : INLINE GEN ell_get_c6(GEN e) { return gel(e,11); }
2518 9362792 : INLINE GEN ell_get_disc(GEN e) { return gel(e,12); }
2519 1026081 : INLINE GEN ell_get_j(GEN e) { return gel(e,13); }
2520 7906380 : INLINE long ell_get_type(GEN e) { return mael(e,14,1); }
2521 1561487 : INLINE GEN ellff_get_field(GEN x) { return gmael(x, 15, 1); }
2522 678309 : INLINE GEN ellff_get_a4a6(GEN x) { return gmael(x, 15, 2); }
2523 917 : INLINE GEN ellQp_get_zero(GEN x) { return gmael(x, 15, 1); }
2524 287 : INLINE long ellQp_get_prec(GEN E) { GEN z = ellQp_get_zero(E); return valp(z); }
2525 623 : INLINE GEN ellQp_get_p(GEN E) { GEN z = ellQp_get_zero(E); return gel(z,2); }
2526 36960 : INLINE long ellR_get_prec(GEN x) { return nbits2prec(mael3(x, 15, 1, 1)); }
2527 8262 : INLINE long ellR_get_sign(GEN x) { return mael3(x, 15, 1, 2); }
2528 500353 : INLINE GEN ellnf_get_nf(GEN x) { return checknf_i(gmael(x,15,1)); }
2529 49 : INLINE GEN ellnf_get_bnf(GEN x) { return checkbnf_i(gmael(x,15,1)); }
2530 :
2531 21499333 : INLINE int ell_is_inf(GEN z) { return lg(z) == 2; }
2532 787016 : INLINE GEN ellinf(void) { return mkvec(gen_0); }
2533 :
2534 : /*******************************************************************/
2535 : /* */
2536 : /* ALGEBRAIC NUMBER THEORY */
2537 : /* */
2538 : /*******************************************************************/
2539 8119836 : INLINE GEN modpr_get_pr(GEN x) { return gel(x,3); }
2540 609916 : INLINE GEN modpr_get_p(GEN x) { return pr_get_p(modpr_get_pr(x)); }
2541 2518408 : INLINE GEN modpr_get_T(GEN x) { return lg(x) == 4? NULL: gel(x,4); }
2542 :
2543 18290176 : INLINE GEN pr_get_p(GEN pr) { return gel(pr,1); }
2544 4846125 : INLINE GEN pr_get_gen(GEN pr){ return gel(pr,2); }
2545 : /* .[2] instead of itos works: e and f are small positive integers */
2546 2230750 : INLINE long pr_get_e(GEN pr) { return gel(pr,3)[2]; }
2547 7787651 : INLINE long pr_get_f(GEN pr) { return gel(pr,4)[2]; }
2548 5803107 : INLINE GEN pr_get_tau(GEN pr){ return gel(pr,5); }
2549 : INLINE int
2550 2346053 : pr_is_inert(GEN P) { return pr_get_f(P) == lg(pr_get_gen(P))-1; }
2551 : INLINE GEN
2552 204456 : pr_norm(GEN pr) { return powiu(pr_get_p(pr), pr_get_f(pr)); }
2553 : INLINE ulong
2554 40873 : upr_norm(GEN pr) { return upowuu(pr_get_p(pr)[2], pr_get_f(pr)); }
2555 :
2556 : /* assume nf a genuine nf */
2557 : INLINE long
2558 4178 : nf_get_varn(GEN nf) { return varn(gel(nf,1)); }
2559 : INLINE GEN
2560 27063798 : nf_get_pol(GEN nf) { return gel(nf,1); }
2561 : INLINE long
2562 21250278 : nf_get_degree(GEN nf) { return degpol( nf_get_pol(nf) ); }
2563 : INLINE long
2564 1279808 : nf_get_r1(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,1)); }
2565 : INLINE long
2566 8197 : nf_get_r2(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,2)); }
2567 : INLINE GEN
2568 43854 : nf_get_disc(GEN nf) { return gel(nf,3); }
2569 : INLINE GEN
2570 745236 : nf_get_index(GEN nf) { return gel(nf,4); }
2571 : INLINE GEN
2572 1221669 : nf_get_M(GEN nf) { return gmael(nf,5,1); }
2573 : INLINE GEN
2574 60449 : nf_get_G(GEN nf) { return gmael(nf,5,2); }
2575 : INLINE GEN
2576 440110 : nf_get_roundG(GEN nf) { return gmael(nf,5,3); }
2577 : INLINE GEN
2578 24339 : nf_get_Tr(GEN nf) { return gmael(nf,5,4); }
2579 : INLINE GEN
2580 2191 : nf_get_diff(GEN nf) { return gmael(nf,5,5); }
2581 : INLINE GEN
2582 28 : nf_get_ramified_primes(GEN nf) { return gmael(nf,5,8); }
2583 : INLINE GEN
2584 152833 : nf_get_roots(GEN nf) { return gel(nf,6); }
2585 : INLINE GEN
2586 77 : nf_get_zk(GEN nf)
2587 : {
2588 77 : GEN y = gel(nf,7), D = nf_get_zkden(nf);
2589 77 : if (!equali1(D)) y = gdiv(y, D);
2590 77 : return y;
2591 : }
2592 : INLINE GEN
2593 217523 : nf_get_zkprimpart(GEN nf)
2594 : {
2595 217523 : GEN y = gel(nf,7);
2596 : /* test for old format of nf.zk: non normalized */
2597 217523 : if (!equali1(gel(nf,4)) && gequal1(gel(y,1))) y = Q_remove_denom(y,NULL);
2598 217523 : return y;
2599 : }
2600 : INLINE GEN
2601 220120 : nf_get_zkden(GEN nf)
2602 : {
2603 220120 : GEN y = gel(nf,7), D = gel(y,1);
2604 220120 : if (typ(D) == t_POL) D = gel(D,2);
2605 : /* test for old format of nf.zk: non normalized */
2606 220120 : if (!equali1(gel(nf,4)) && equali1(D)) D = Q_denom(y);
2607 220120 : return D;
2608 : }
2609 : INLINE GEN
2610 2167517 : nf_get_invzk(GEN nf) { return gel(nf,8); }
2611 : INLINE void
2612 13734 : nf_get_sign(GEN nf, long *r1, long *r2)
2613 : {
2614 13734 : GEN x = gel(nf,2);
2615 13734 : *r1 = itou(gel(x,1));
2616 13734 : *r2 = itou(gel(x,2));
2617 13734 : }
2618 :
2619 : INLINE GEN
2620 49616 : abgrp_get_no(GEN x) { return gel(x,1); }
2621 : INLINE GEN
2622 2033639 : abgrp_get_cyc(GEN x) { return gel(x,2); }
2623 : INLINE GEN
2624 396427 : abgrp_get_gen(GEN x) { return gel(x,3); }
2625 : INLINE GEN
2626 2063935 : bnf_get_nf(GEN bnf) { return gel(bnf,7); }
2627 : INLINE GEN
2628 806287 : bnf_get_clgp(GEN bnf) { return gmael(bnf,8,1); }
2629 : INLINE GEN
2630 4536 : bnf_get_no(GEN bnf) { return abgrp_get_no(bnf_get_clgp(bnf)); }
2631 : INLINE GEN
2632 434248 : bnf_get_cyc(GEN bnf) { return abgrp_get_cyc(bnf_get_clgp(bnf)); }
2633 : INLINE GEN
2634 367174 : bnf_get_gen(GEN bnf) { return abgrp_get_gen(bnf_get_clgp(bnf)); }
2635 : INLINE GEN
2636 860 : bnf_get_reg(GEN bnf) { return gmael(bnf,8,2); }
2637 : INLINE GEN
2638 482157 : bnf_get_logfu(GEN bnf) { return gel(bnf,3); }
2639 : INLINE GEN
2640 5867 : bnf_get_tuU(GEN bnf) { return gmael3(bnf,8,4,2); }
2641 : INLINE long
2642 24535 : bnf_get_tuN(GEN bnf) { return gmael3(bnf,8,4,1)[2]; }
2643 : INLINE GEN
2644 1806 : bnf_get_fu(GEN bnf) {
2645 1806 : GEN fu = bnf_get_fu_nocheck(bnf);
2646 1806 : if (typ(fu) == t_MAT) pari_err(e_MISC,"missing units in bnf");
2647 1806 : return fu;
2648 : }
2649 : INLINE GEN
2650 7134 : bnf_get_fu_nocheck(GEN bnf) { return gmael(bnf,8,5); }
2651 :
2652 : INLINE GEN
2653 747381 : bnr_get_bnf(GEN bnr) { return gel(bnr,1); }
2654 : INLINE GEN
2655 384460 : bnr_get_bid(GEN bnr) { return gel(bnr,2); }
2656 : INLINE GEN
2657 18102 : bnr_get_mod(GEN bnr) { return gmael(bnr,2,1); }
2658 : INLINE GEN
2659 27097 : bnr_get_nf(GEN bnr) { return gmael(bnr,1,7); }
2660 : INLINE GEN
2661 520526 : bnr_get_clgp(GEN bnr) { return gel(bnr,5); }
2662 : INLINE GEN
2663 45080 : bnr_get_no(GEN bnr) { return abgrp_get_no(bnr_get_clgp(bnr)); }
2664 : INLINE GEN
2665 463518 : bnr_get_cyc(GEN bnr) { return abgrp_get_cyc(bnr_get_clgp(bnr)); }
2666 : INLINE GEN
2667 70 : bnr_get_gen_nocheck(GEN bnr) { return abgrp_get_gen(bnr_get_clgp(bnr)); }
2668 : INLINE GEN
2669 11025 : bnr_get_gen(GEN bnr) {
2670 11025 : GEN G = bnr_get_clgp(bnr);
2671 11025 : if (lg(G) != 4)
2672 0 : pari_err(e_MISC,"missing bnr generators: please use bnrinit(,,1)");
2673 11025 : return gel(G,3);
2674 : }
2675 :
2676 : INLINE GEN
2677 302497 : bid_get_mod(GEN bid) { return gel(bid,1); }
2678 : INLINE GEN
2679 44968 : bid_get_ideal(GEN bid) { return gmael(bid,1,1); }
2680 : INLINE GEN
2681 448 : bid_get_arch(GEN bid) { return gmael(bid,1,2); }
2682 : INLINE GEN
2683 1061274 : bid_get_grp(GEN bid) { return gel(bid,2); }
2684 : INLINE GEN
2685 395905 : bid_get_fact(GEN bid) { return gmael(bid,3,1); }
2686 : INLINE GEN
2687 354605 : bid_get_fact2(GEN bid) { return gmael(bid,3,2); }
2688 : INLINE GEN
2689 354675 : bid_get_sprk(GEN bid) { return gmael(bid,4,1); }
2690 : INLINE GEN
2691 29813 : bid_get_sarch(GEN bid) { return gmael(bid,4,2); }
2692 : INLINE GEN
2693 375255 : bid_get_archp(GEN bid) { return gmael3(bid,4,2,2); }
2694 : INLINE GEN
2695 657382 : bid_get_U(GEN bid) { return gel(bid,5); }
2696 : INLINE GEN
2697 0 : bid_get_no(GEN bid) { return abgrp_get_no(bid_get_grp(bid)); }
2698 : INLINE GEN
2699 1032987 : bid_get_cyc(GEN bid) { return abgrp_get_cyc(bid_get_grp(bid)); }
2700 : INLINE GEN
2701 0 : bid_get_gen_nocheck(GEN bid) { return abgrp_get_gen(bid_get_grp(bid)); }
2702 : INLINE GEN
2703 27692 : bid_get_gen(GEN bid) {
2704 27692 : GEN G = bid_get_grp(bid);
2705 27692 : if (lg(G) != 4) pari_err(e_MISC,"missing bid generators. Use idealstar(,,2)");
2706 27692 : return abgrp_get_gen(G);
2707 : }
2708 :
2709 : INLINE GEN
2710 2522030 : znstar_get_N(GEN G) { return gmael(G,1,1); }
2711 : INLINE GEN
2712 2805866 : znstar_get_faN(GEN G) { return gel(G,3); }
2713 : INLINE GEN
2714 0 : znstar_get_no(GEN G) { return abgrp_get_no(gel(G,2)); }
2715 : INLINE GEN
2716 101472 : znstar_get_cyc(GEN G) { return abgrp_get_cyc(gel(G,2)); }
2717 : INLINE GEN
2718 0 : znstar_get_gen(GEN G) { return abgrp_get_gen(gel(G,2)); }
2719 : INLINE GEN
2720 2738365 : znstar_get_conreycyc(GEN G) { return gmael(G,4,5); }
2721 : INLINE GEN
2722 1263185 : znstar_get_conreygen(GEN G) { return gmael(G,4,4); }
2723 : INLINE GEN
2724 40103 : znstar_get_Ui(GEN G) { return gmael(G,4,3); }
2725 : INLINE GEN
2726 28322 : znstar_get_U(GEN G) { return gel(G,5); }
2727 : INLINE GEN
2728 1226309 : znstar_get_pe(GEN G) { return gmael(G,4,1); }
2729 : INLINE GEN
2730 19152 : gal_get_pol(GEN gal) { return gel(gal,1); }
2731 : INLINE GEN
2732 1225 : gal_get_p(GEN gal) { return gmael(gal,2,1); }
2733 : INLINE GEN
2734 63 : gal_get_e(GEN gal) { return gmael(gal,2,2); }
2735 : INLINE GEN
2736 15631 : gal_get_mod(GEN gal) { return gmael(gal,2,3); }
2737 : INLINE GEN
2738 16009 : gal_get_roots(GEN gal) { return gel(gal,3); }
2739 : INLINE GEN
2740 15631 : gal_get_invvdm(GEN gal) { return gel(gal,4); }
2741 : INLINE GEN
2742 15631 : gal_get_den(GEN gal) { return gel(gal,5); }
2743 : INLINE GEN
2744 61516 : gal_get_group(GEN gal) { return gel(gal,6); }
2745 : INLINE GEN
2746 3927 : gal_get_gen(GEN gal) { return gel(gal,7); }
2747 : INLINE GEN
2748 3577 : gal_get_orders(GEN gal) { return gel(gal,8); }
2749 :
2750 : /* assume rnf a genuine rnf */
2751 : INLINE long
2752 311458 : rnf_get_degree(GEN rnf) { return degpol(rnf_get_pol(rnf)); }
2753 : INLINE long
2754 15169 : rnf_get_nfdegree(GEN rnf) { return degpol(nf_get_pol(rnf_get_nf(rnf))); }
2755 : INLINE long
2756 156499 : rnf_get_absdegree(GEN rnf) { return degpol(gmael(rnf,11,1)); }
2757 : INLINE GEN
2758 434 : rnf_get_idealdisc(GEN rnf) { return gmael(rnf,3,1); }
2759 : INLINE GEN
2760 448 : rnf_get_k(GEN rnf) { return gmael(rnf,11,3); }
2761 : INLINE GEN
2762 448 : rnf_get_alpha(GEN rnf) { return gmael(rnf, 11, 2); }
2763 : INLINE GEN
2764 126063 : rnf_get_nf(GEN rnf) { return gel(rnf,10); }
2765 : INLINE void
2766 2387 : rnf_get_nfzk(GEN rnf, GEN *b, GEN *cb) {*b=gmael(rnf,2,1); *cb=gmael(rnf,2,2);}
2767 : INLINE GEN
2768 95865 : rnf_get_polabs(GEN rnf) { return gmael(rnf,11,1); }
2769 : INLINE GEN
2770 463260 : rnf_get_pol(GEN rnf) { return gel(rnf,1); }
2771 : INLINE GEN
2772 63 : rnf_get_disc(GEN rnf) { return gel(rnf,3); }
2773 : INLINE GEN
2774 105 : rnf_get_index(GEN rnf) { return gel(rnf,4); }
2775 : INLINE long
2776 0 : rnf_get_varn(GEN rnf) { return varn(gel(rnf,1)); }
2777 : INLINE GEN
2778 106624 : rnf_get_nfpol(GEN rnf) { return gmael(rnf,10,1); }
2779 : INLINE long
2780 595 : rnf_get_nfvarn(GEN rnf) { return varn(gmael(rnf,10,1)); }
2781 : INLINE GEN
2782 2807 : rnf_get_zk(GEN rnf) { return gel(rnf,7); }
2783 : INLINE GEN
2784 34629 : rnf_get_map(GEN rnf) { return gel(rnf,11); }
2785 : INLINE GEN
2786 1190 : rnf_get_invzk(GEN rnf) { return gel(rnf,8); }
2787 :
2788 : /* I integral ZM (not HNF), G ZM, rounded Cholesky form of a weighted
2789 : * T2 matrix. Reduce I wrt G */
2790 : INLINE GEN
2791 13048 : idealpseudored(GEN I, GEN G)
2792 13048 : { return ZM_mul(I, ZM_lll(ZM_mul(G, I), 0.99, LLL_IM)); }
2793 :
2794 : /* I integral (not necessarily HNF), G ZM, rounded Cholesky form of a weighted
2795 : * T2 matrix. Return m in I with T2(m) small */
2796 : INLINE GEN
2797 156926 : idealpseudomin(GEN I, GEN G)
2798 : {
2799 156926 : GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
2800 156926 : return ZM_ZC_mul(I, gel(u,1));
2801 : }
2802 : /* I, G as in idealpseudomin. Return an irrational m in I with T2(m) small */
2803 : INLINE GEN
2804 300359 : idealpseudomin_nonscalar(GEN I, GEN G)
2805 : {
2806 300359 : GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
2807 300359 : GEN m = ZM_ZC_mul(I, gel(u,1));
2808 300359 : if (ZV_isscalar(m) && lg(u) > 2) m = ZM_ZC_mul(I, gel(u,2));
2809 300359 : return m;
2810 : }
2811 :
2812 : INLINE GEN
2813 0 : idealred_elt(GEN nf, GEN I) {
2814 0 : pari_sp av = avma;
2815 0 : GEN u = idealpseudomin(I, nf_get_roundG(nf));
2816 0 : return gerepileupto(av, u);
2817 : }
2818 : INLINE GEN
2819 162624 : idealred(GEN nf, GEN I) { return idealred0(nf, I, NULL); }
2820 :
2821 : INLINE GEN
2822 1218 : idealchineseinit(GEN nf, GEN x)
2823 1218 : { return idealchinese(nf,x,NULL); }
2824 :
2825 : /*******************************************************************/
2826 : /* */
2827 : /* CLOSURES */
2828 : /* */
2829 : /*******************************************************************/
2830 248142463 : INLINE long closure_arity(GEN C) { return ((ulong)C[1])&ARITYBITS; }
2831 34478829 : INLINE long closure_is_variadic(GEN C) { return !!(((ulong)C[1])&VARARGBITS); }
2832 213428454 : INLINE const char *closure_codestr(GEN C) { return GSTR(gel(C,2))-1; }
2833 0 : INLINE GEN closure_get_code(GEN C) { return gel(C,2); }
2834 213371144 : INLINE GEN closure_get_oper(GEN C) { return gel(C,3); }
2835 213355907 : INLINE GEN closure_get_data(GEN C) { return gel(C,4); }
2836 8343 : INLINE GEN closure_get_dbg(GEN C) { return gel(C,5); }
2837 20235 : INLINE GEN closure_get_text(GEN C) { return gel(C,6); }
2838 479858 : INLINE GEN closure_get_frame(GEN C) { return gel(C,7); }
2839 :
2840 : /*******************************************************************/
2841 : /* */
2842 : /* ERRORS */
2843 : /* */
2844 : /*******************************************************************/
2845 : INLINE long
2846 30302 : err_get_num(GEN e) { return e[1]; }
2847 : INLINE GEN
2848 70 : err_get_compo(GEN e, long i) { return gel(e, i+1); }
2849 :
2850 : INLINE void
2851 14 : pari_err_BUG(const char *f) { pari_err(e_BUG,f); }
2852 : INLINE void
2853 7 : pari_err_CONSTPOL(const char *f) { pari_err(e_CONSTPOL, f); }
2854 : INLINE void
2855 63 : pari_err_COPRIME(const char *f, GEN x, GEN y) { pari_err(e_COPRIME, f,x,y); }
2856 : INLINE void
2857 438 : pari_err_DIM(const char *f) { pari_err(e_DIM, f); }
2858 : INLINE void
2859 0 : pari_err_FILE(const char *f, const char *g) { pari_err(e_FILE, f,g); }
2860 : INLINE void
2861 28 : pari_err_FLAG(const char *f) { pari_err(e_FLAG,f); }
2862 : INLINE void
2863 371 : pari_err_IMPL(const char *f) { pari_err(e_IMPL,f); }
2864 : INLINE void
2865 698 : pari_err_INV(const char *f, GEN x) { pari_err(e_INV,f,x); }
2866 : INLINE void
2867 21 : pari_err_IRREDPOL(const char *f, GEN x) { pari_err(e_IRREDPOL, f,x); }
2868 : INLINE void
2869 1674 : 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); }
2870 : INLINE void
2871 245 : pari_err_COMPONENT(const char *f, const char *op, GEN l, GEN x) { pari_err(e_COMPONENT, f,op,l,x); }
2872 : INLINE void
2873 0 : pari_err_MAXPRIME(ulong c) { pari_err(e_MAXPRIME, c); }
2874 : INLINE void
2875 287 : pari_err_OP(const char *f, GEN x, GEN y) { pari_err(e_OP, f,x,y); }
2876 : INLINE void
2877 70 : pari_err_OVERFLOW(const char *f) { pari_err(e_OVERFLOW, f); }
2878 : INLINE void
2879 219 : pari_err_PREC(const char *f) { pari_err(e_PREC,f); }
2880 : INLINE void
2881 0 : pari_err_PACKAGE(const char *f) { pari_err(e_PACKAGE,f); }
2882 : INLINE void
2883 56 : pari_err_PRIME(const char *f, GEN x) { pari_err(e_PRIME, f,x); }
2884 : INLINE void
2885 735 : pari_err_MODULUS(const char *f, GEN x, GEN y) { pari_err(e_MODULUS, f,x,y); }
2886 : INLINE void
2887 42 : pari_err_ROOTS0(const char *f) { pari_err(e_ROOTS0, f); }
2888 : INLINE void
2889 77 : pari_err_SQRTN(const char *f, GEN x) { pari_err(e_SQRTN, f,x); }
2890 : INLINE void
2891 11334 : pari_err_TYPE(const char *f, GEN x) { pari_err(e_TYPE, f,x); }
2892 : INLINE void
2893 3045 : pari_err_TYPE2(const char *f, GEN x, GEN y) { pari_err(e_TYPE2, f,x,y); }
2894 : INLINE void
2895 203 : pari_err_VAR(const char *f, GEN x, GEN y) { pari_err(e_VAR, f,x,y); }
2896 : INLINE void
2897 126 : pari_err_PRIORITY(const char *f, GEN x, const char *op, long v)
2898 126 : { pari_err(e_PRIORITY, f,x,op,v); }
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