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 3281614 : mkintmod(GEN x, GEN y) { retmkintmod(x,y); }
141 : INLINE GEN
142 4074 : mkintmodu(ulong x, ulong y) {
143 4074 : GEN v = cgetg(3,t_INTMOD);
144 4074 : gel(v,1) = utoipos(y);
145 4074 : gel(v,2) = utoi(x); return v;
146 : }
147 : INLINE GEN
148 2927680 : mkpolmod(GEN x, GEN y) { retmkpolmod(x,y); }
149 : INLINE GEN
150 23176109 : mkfrac(GEN x, GEN y) { retmkfrac(x,y); }
151 : INLINE GEN
152 32137 : mkfracss(long x, long y) { retmkfrac(stoi(x),utoipos(y)); }
153 : /* q = n/d a t_FRAC or t_INT; recover (n,d) */
154 : INLINE void
155 12215 : Qtoss(GEN q, long *n, long *d)
156 : {
157 12215 : if (typ(q) == t_INT) { *n = itos(q); *d = 1; }
158 2443 : else { *n = itos(gel(q,1)); *d = itou(gel(q,2)); }
159 12215 : }
160 : INLINE GEN
161 71228362 : sstoQ(long n, long d)
162 : {
163 : ulong r;
164 : long g, q;
165 71228362 : if (!n)
166 : {
167 88781 : if (!d) pari_err_INV("sstoQ",gen_0);
168 88781 : return gen_0;
169 : }
170 71139581 : if (d < 0) { d = -d; n = -n; }
171 71139581 : if (d == 1) return stoi(n);
172 71127989 : q = udivuu_rem(labs(n),d,&r);
173 71127989 : if (!r) return n > 0? utoipos(q): utoineg(q);
174 3612352 : g = ugcd(d,r); /* gcd(n,d) */
175 3612352 : if (g != 1) { n /= g; d /= g; }
176 3612352 : retmkfrac(stoi(n), utoi(d));
177 : }
178 :
179 : INLINE GEN
180 6675220 : mkfraccopy(GEN x, GEN y) { retmkfrac(icopy(x), icopy(y)); }
181 : INLINE GEN
182 7 : mkrfrac(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
183 7 : gel(v,1) = x; gel(v,2) = y; return v; }
184 : INLINE GEN
185 7 : mkrfraccopy(GEN x, GEN y) { GEN v = cgetg(3, t_RFRAC);
186 7 : gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
187 : INLINE GEN
188 9073395 : mkcomplex(GEN x, GEN y) { retmkcomplex(x,y); }
189 : INLINE GEN
190 449472 : gen_I(void) { return mkcomplex(gen_0, gen_1); }
191 : INLINE GEN
192 298639 : cgetc(long l) { retmkcomplex(cgetr(l), cgetr(l)); }
193 : INLINE GEN
194 105 : mkquad(GEN n, GEN x, GEN y) { GEN v = cgetg(4, t_QUAD);
195 105 : gel(v,1) = n; gel(v,2) = x; gel(v,3) = y; return v; }
196 : /* vecsmall */
197 : INLINE GEN
198 63420102 : mkvecsmall(long x) { GEN v = cgetg(2, t_VECSMALL); v[1] = x; return v; }
199 : INLINE GEN
200 114070412 : mkvecsmall2(long x,long y) { GEN v = cgetg(3, t_VECSMALL);
201 114052629 : v[1]=x; v[2]=y; return v; }
202 : INLINE GEN
203 58020610 : mkvecsmall3(long x,long y,long z) { GEN v = cgetg(4, t_VECSMALL);
204 58014005 : v[1]=x; v[2]=y; v[3]=z; return v; }
205 : INLINE GEN
206 11951850 : mkvecsmall4(long x,long y,long z,long t) { GEN v = cgetg(5, t_VECSMALL);
207 11932693 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; return v; }
208 : INLINE GEN
209 466537 : mkvecsmall5(long x,long y,long z,long t,long u) { GEN v = cgetg(6, t_VECSMALL);
210 466538 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; v[5]=u; return v; }
211 :
212 : INLINE GEN
213 158123 : mkqfi(GEN x, GEN y, GEN z) { retmkqfi(x,y,z); }
214 : /* vec */
215 : INLINE GEN
216 15039432 : mkvec(GEN x) { retmkvec(x); }
217 : INLINE GEN
218 102019808 : mkvec2(GEN x, GEN y) { retmkvec2(x,y); }
219 : INLINE GEN
220 74664034 : mkvec3(GEN x, GEN y, GEN z) { retmkvec3(x,y,z); }
221 : INLINE GEN
222 7271787 : mkvec4(GEN x, GEN y, GEN z, GEN t) { retmkvec4(x,y,z,t); }
223 : INLINE GEN
224 12082191 : mkvec5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkvec5(x,y,z,t,u); }
225 : INLINE GEN
226 0 : mkvecs(long x) { retmkvec(stoi(x)); }
227 : INLINE GEN
228 23028 : mkvec2s(long x, long y) { retmkvec2(stoi(x),stoi(y)); }
229 : INLINE GEN
230 492724 : mkvec3s(long x, long y, long z) { retmkvec3(stoi(x),stoi(y),stoi(z)); }
231 : INLINE GEN
232 21 : mkvec4s(long x, long y, long z, long t) { retmkvec4(stoi(x),stoi(y),stoi(z),stoi(t)); }
233 : INLINE GEN
234 35091 : mkveccopy(GEN x) { GEN v = cgetg(2, t_VEC); gel(v,1) = gcopy(x); return v; }
235 : INLINE GEN
236 96861 : mkvec2copy(GEN x, GEN y) {
237 96861 : GEN v = cgetg(3,t_VEC); gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
238 : /* col */
239 : INLINE GEN
240 2534642 : mkcol(GEN x) { retmkcol(x); }
241 : INLINE GEN
242 25643557 : mkcol2(GEN x, GEN y) { retmkcol2(x,y); }
243 : INLINE GEN
244 42385 : mkcol3(GEN x, GEN y, GEN z) { retmkcol3(x,y,z); }
245 : INLINE GEN
246 0 : mkcol4(GEN x, GEN y, GEN z, GEN t) { retmkcol4(x,y,z,t); }
247 : INLINE GEN
248 0 : mkcol5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkcol5(x,y,z,t,u); }
249 : INLINE GEN
250 8716 : mkcol6(GEN x, GEN y, GEN z, GEN t, GEN u, GEN v) { retmkcol6(x,y,z,t,u,v); }
251 : INLINE GEN
252 273 : mkcols(long x) { retmkcol(stoi(x)); }
253 : INLINE GEN
254 2176216 : mkcol2s(long x, long y) { retmkcol2(stoi(x),stoi(y)); }
255 : INLINE GEN
256 0 : mkcol3s(long x, long y, long z) { retmkcol3(stoi(x),stoi(y),stoi(z)); }
257 : INLINE GEN
258 0 : mkcol4s(long x, long y, long z, long t) { retmkcol4(stoi(x),stoi(y),stoi(z),stoi(t)); }
259 : INLINE GEN
260 50553 : mkcolcopy(GEN x) { GEN v = cgetg(2, t_COL); gel(v,1) = gcopy(x); return v; }
261 : /* mat */
262 : INLINE GEN
263 2536125 : mkmat(GEN x) { retmkmat(x); }
264 : INLINE GEN
265 32199223 : mkmat2(GEN x, GEN y) { retmkmat2(x,y); }
266 : INLINE GEN
267 2331 : mkmat3(GEN x, GEN y, GEN z) { retmkmat3(x,y,z); }
268 : INLINE GEN
269 0 : mkmat4(GEN x, GEN y, GEN z, GEN t) { retmkmat4(x,y,z,t); }
270 : INLINE GEN
271 0 : mkmat5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkmat5(x,y,z,t,u); }
272 : INLINE GEN
273 22383 : mkmatcopy(GEN x) { GEN v = cgetg(2, t_MAT); gel(v,1) = gcopy(x); return v; }
274 : INLINE GEN
275 0 : mkerr(long x) { GEN v = cgetg(2, t_ERROR); v[1] = x; return v; }
276 : INLINE GEN
277 95999 : mkoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
278 : INLINE GEN
279 16919 : mkmoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
280 : INLINE long
281 132494 : inf_get_sign(GEN x) { return signe(gel(x,1)); }
282 : INLINE GEN
283 10696 : mkmat22s(long a, long b, long c, long d) {retmkmat2(mkcol2s(a,c),mkcol2s(b,d));}
284 : INLINE GEN
285 1533070 : mkmat22(GEN a, GEN b, GEN c, GEN d) { retmkmat2(mkcol2(a,c),mkcol2(b,d)); }
286 :
287 : /* pol */
288 : INLINE GEN
289 989071 : pol_x(long v) {
290 989071 : GEN p = cgetg(4, t_POL);
291 989071 : p[1] = evalsigne(1)|evalvarn(v);
292 989071 : gel(p,2) = gen_0;
293 989071 : gel(p,3) = gen_1; return p;
294 : }
295 : /* x^n, assume n >= 0 */
296 : INLINE GEN
297 2710533 : pol_xn(long n, long v) {
298 2710533 : long i, a = n+2;
299 2710533 : GEN p = cgetg(a+1, t_POL);
300 2710531 : p[1] = evalsigne(1)|evalvarn(v);
301 2710531 : for (i = 2; i < a; i++) gel(p,i) = gen_0;
302 2710531 : gel(p,a) = gen_1; return p;
303 : }
304 : /* x^n, no assumption on n */
305 : INLINE GEN
306 287 : pol_xnall(long n, long v)
307 : {
308 287 : if (n < 0) retmkrfrac(gen_1, pol_xn(-n,v));
309 280 : return pol_xn(n, v);
310 : }
311 : INLINE GEN
312 1507362 : pol_1(long v) {
313 1507362 : GEN p = cgetg(3, t_POL);
314 1507361 : p[1] = evalsigne(1)|evalvarn(v);
315 1507361 : gel(p,2) = gen_1; return p;
316 : }
317 : INLINE GEN
318 32857689 : pol_0(long v)
319 : {
320 32857689 : GEN x = cgetg(2,t_POL);
321 32857689 : x[1] = evalvarn(v); return x;
322 : }
323 : #define retconst_vec(n,x)\
324 : do { long _i, _n = (n);\
325 : GEN _v = cgetg(_n+1, t_VEC), _x = (x);\
326 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
327 : return _v; } while(0)
328 : INLINE GEN
329 8745964 : const_vec(long n, GEN x) { retconst_vec(n, x); }
330 : #define retconst_col(n,x)\
331 : do { long _i, _n = (n);\
332 : GEN _v = cgetg(_n+1, t_COL), _x = (x);\
333 : for (_i = 1; _i <= _n; _i++) gel(_v,_i) = _x;\
334 : return _v; } while(0)
335 : INLINE GEN
336 8679095 : const_col(long n, GEN x) { retconst_col(n, x); }
337 : INLINE GEN
338 8602091 : const_vecsmall(long n, long c)
339 : {
340 : long i;
341 8602091 : GEN V = cgetg(n+1,t_VECSMALL);
342 8602260 : for(i=1;i<=n;i++) V[i] = c;
343 8602260 : return V;
344 : }
345 :
346 : /*** ZERO ***/
347 : /* O(p^e) */
348 : INLINE GEN
349 302754 : zeropadic(GEN p, long e)
350 : {
351 302754 : GEN y = cgetg(5,t_PADIC);
352 302754 : gel(y,4) = gen_0;
353 302754 : gel(y,3) = gen_1;
354 302754 : gel(y,2) = icopy(p);
355 302754 : y[1] = evalvalp(e) | _evalprecp(0);
356 302754 : return y;
357 : }
358 : INLINE GEN
359 966 : zeropadic_shallow(GEN p, long e)
360 : {
361 966 : GEN y = cgetg(5,t_PADIC);
362 966 : gel(y,4) = gen_0;
363 966 : gel(y,3) = gen_1;
364 966 : gel(y,2) = p;
365 966 : y[1] = evalvalp(e) | _evalprecp(0);
366 966 : return y;
367 : }
368 : /* O(pol_x(v)^e) */
369 : INLINE GEN
370 143472 : zeroser(long v, long e)
371 : {
372 143472 : GEN x = cgetg(2, t_SER);
373 143472 : x[1] = evalvalp(e) | evalvarn(v); return x;
374 : }
375 : INLINE int
376 5745062 : ser_isexactzero(GEN x)
377 : {
378 5745062 : if (!signe(x)) switch(lg(x))
379 : {
380 136129 : case 2: return 1;
381 854 : case 3: return isexactzero(gel(x,2));
382 : }
383 5608079 : return 0;
384 : }
385 : /* 0 * pol_x(v) */
386 : INLINE GEN
387 15599147 : zeropol(long v) { return pol_0(v); }
388 : /* vector(n) */
389 : INLINE GEN
390 37588077 : zerocol(long n)
391 : {
392 37588077 : GEN y = cgetg(n+1,t_COL);
393 37588224 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
394 37588224 : return y;
395 : }
396 : /* vectorv(n) */
397 : INLINE GEN
398 21782928 : zerovec(long n)
399 : {
400 21782928 : GEN y = cgetg(n+1,t_VEC);
401 21782934 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
402 21782934 : return y;
403 : }
404 : /* matrix(m, n) */
405 : INLINE GEN
406 23548 : zeromat(long m, long n)
407 : {
408 23548 : GEN y = cgetg(n+1,t_MAT);
409 23548 : GEN v = zerocol(m);
410 23548 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
411 23548 : return y;
412 : }
413 : /* = zero_zx, sv is a evalvarn()*/
414 : INLINE GEN
415 931007 : zero_Flx(long sv) { return pol0_Flx(sv); }
416 : INLINE GEN
417 33638765 : zero_Flv(long n)
418 : {
419 33638765 : GEN y = cgetg(n+1,t_VECSMALL);
420 33640400 : long i; for (i=1; i<=n; i++) y[i] = 0;
421 33640400 : return y;
422 : }
423 : /* matrix(m, n) */
424 : INLINE GEN
425 923001 : zero_Flm(long m, long n)
426 : {
427 923001 : GEN y = cgetg(n+1,t_MAT);
428 922983 : GEN v = zero_Flv(m);
429 922998 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
430 922998 : return y;
431 : }
432 : /* matrix(m, n) */
433 : INLINE GEN
434 110202 : zero_Flm_copy(long m, long n)
435 : {
436 110202 : GEN y = cgetg(n+1,t_MAT);
437 110197 : long i; for (i=1; i<=n; i++) gel(y,i) = zero_Flv(m);
438 110205 : return y;
439 : }
440 :
441 : INLINE GEN
442 797111 : zero_F2v(long m)
443 : {
444 797111 : long l = nbits2nlong(m);
445 797111 : GEN v = zero_Flv(l+1);
446 797111 : v[1] = m;
447 797111 : return v;
448 : }
449 :
450 : INLINE GEN
451 0 : zero_F2m(long m, long n)
452 : {
453 : long i;
454 0 : GEN M = cgetg(n+1, t_MAT);
455 0 : GEN v = zero_F2v(m);
456 0 : for (i = 1; i <= n; i++)
457 0 : gel(M,i) = v;
458 0 : return M;
459 : }
460 :
461 :
462 : INLINE GEN
463 277574 : zero_F2m_copy(long m, long n)
464 : {
465 : long i;
466 277574 : GEN M = cgetg(n+1, t_MAT);
467 808236 : for (i = 1; i <= n; i++)
468 530662 : gel(M,i)= zero_F2v(m);
469 277574 : return M;
470 : }
471 :
472 : /* matrix(m, n) */
473 : INLINE GEN
474 4890129 : zeromatcopy(long m, long n)
475 : {
476 4890129 : GEN y = cgetg(n+1,t_MAT);
477 4890129 : long i; for (i=1; i<=n; i++) gel(y,i) = zerocol(m);
478 4890129 : return y;
479 : }
480 :
481 : INLINE GEN
482 17605 : zerovec_block(long len)
483 : {
484 : long i;
485 17605 : GEN blk = cgetg_block(len + 1, t_VEC);
486 580965 : for (i = 1; i <= len; ++i)
487 563360 : gel(blk, i) = gen_0;
488 17605 : return blk;
489 : }
490 :
491 : /* i-th vector in the standard basis */
492 : INLINE GEN
493 1422076 : col_ei(long n, long i) { GEN e = zerocol(n); gel(e,i) = gen_1; return e; }
494 : INLINE GEN
495 336187 : vec_ei(long n, long i) { GEN e = zerovec(n); gel(e,i) = gen_1; return e; }
496 : INLINE GEN
497 42 : F2v_ei(long n, long i) { GEN e = zero_F2v(n); F2v_set(e,i); return e; }
498 : INLINE GEN
499 71428 : vecsmall_ei(long n, long i) { GEN e = zero_zv(n); e[i] = 1; return e; }
500 : INLINE GEN
501 683087 : Rg_col_ei(GEN x, long n, long i) { GEN e = zerocol(n); gel(e,i) = x; return e; }
502 :
503 : INLINE GEN
504 12709139 : shallowcopy(GEN x)
505 12709139 : { return typ(x) == t_MAT ? RgM_shallowcopy(x): leafcopy(x); }
506 :
507 : /* routines for naive growarrays */
508 : INLINE GEN
509 12714563 : vectrunc_init(long l)
510 : {
511 12714563 : GEN z = new_chunk(l);
512 12714730 : z[0] = evaltyp(t_VEC) | _evallg(1); return z;
513 : }
514 : INLINE GEN
515 28 : coltrunc_init(long l)
516 : {
517 28 : GEN z = new_chunk(l);
518 28 : z[0] = evaltyp(t_COL) | _evallg(1); return z;
519 : }
520 : INLINE void
521 257578458 : lg_increase(GEN x) { x[0]++; }
522 : INLINE void
523 51326607 : vectrunc_append(GEN x, GEN t) { gel(x, lg(x)) = t; lg_increase(x); }
524 : INLINE void
525 10416 : vectrunc_append_batch(GEN x, GEN y)
526 : {
527 10416 : long i, l = lg(x), ly = lg(y);
528 10416 : GEN z = x + l-1;
529 10416 : for (i = 1; i < ly; i++) gel(z,i) = gel(y,i);
530 10416 : setlg(x, l+ly-1);
531 10416 : }
532 : INLINE GEN
533 84513454 : vecsmalltrunc_init(long l)
534 : {
535 84513454 : GEN z = new_chunk(l);
536 84513454 : z[0] = evaltyp(t_VECSMALL) | _evallg(1); return z;
537 : }
538 : INLINE void
539 33067344 : vecsmalltrunc_append(GEN x, long t) { x[ lg(x) ] = t; lg_increase(x); }
540 :
541 : /*******************************************************************/
542 : /* */
543 : /* STRING HASH FUNCTIONS */
544 : /* */
545 : /*******************************************************************/
546 : INLINE ulong
547 1931379 : hash_str(const char *str)
548 : {
549 1931379 : ulong hash = 5381UL, c;
550 20949064 : while ( (c = (ulong)*str++) )
551 17086306 : hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
552 1931379 : return hash;
553 : }
554 : INLINE ulong
555 6575201 : hash_str_len(const char *str, long len)
556 : {
557 6575201 : ulong hash = 5381UL;
558 : long i;
559 24847507 : for (i = 0; i < len; i++)
560 : {
561 18272306 : ulong c = (ulong)*str++;
562 18272306 : hash = ((hash << 5) + hash) + c; /* hash * 33 + c */
563 : }
564 6575201 : return hash;
565 : }
566 :
567 : /*******************************************************************/
568 : /* */
569 : /* VEC / COL / VECSMALL */
570 : /* */
571 : /*******************************************************************/
572 : /* shallow*/
573 : INLINE GEN
574 0 : vec_shorten(GEN v, long n)
575 : {
576 : long i;
577 0 : GEN V = cgetg(n+1,t_VEC);
578 0 : for(i=1;i<=n;i++) gel(V,i) = gel(v,i);
579 0 : return V;
580 : }
581 : /* shallow*/
582 : INLINE GEN
583 13710 : vec_lengthen(GEN v, long n)
584 : {
585 : long i;
586 13710 : long l=lg(v);
587 13710 : GEN V = cgetg(n+1,t_VEC);
588 13710 : for(i=1;i<l;i++) gel(V,i) = gel(v,i);
589 13710 : return V;
590 : }
591 : /* shallow*/
592 : INLINE GEN
593 62706 : vec_append(GEN V, GEN s)
594 : {
595 62706 : long i, l2 = lg(V);
596 62706 : GEN res = cgetg(l2+1, typ(V));
597 62706 : for (i = 1; i < l2; ++i) gel(res, i) = gel(V,i);
598 62706 : gel(res,l2) = s; return res;
599 : }
600 : /* shallow*/
601 : INLINE GEN
602 1785 : vec_prepend(GEN v, GEN s)
603 : {
604 1785 : long i, l = lg(v);
605 1785 : GEN w = cgetg(l+1, typ(v));
606 1785 : gel(w,1) = s;
607 1785 : for (i = 2; i <= l; ++i) gel(w,i) = gel(v,i-1);
608 1785 : return w;
609 : }
610 : /* shallow*/
611 : INLINE GEN
612 0 : vec_setconst(GEN v, GEN x)
613 : {
614 0 : long i, l = lg(v);
615 0 : for (i = 1; i < l; i++) gel(v,i) = x;
616 0 : return v;
617 : }
618 : INLINE GEN
619 750188 : vecsmall_shorten(GEN v, long n)
620 : {
621 : long i;
622 750188 : GEN V = cgetg(n+1,t_VECSMALL);
623 750096 : for(i=1;i<=n;i++) V[i] = v[i];
624 750096 : return V;
625 : }
626 : INLINE GEN
627 21 : vecsmall_lengthen(GEN v, long n)
628 : {
629 21 : long i, l = lg(v);
630 21 : GEN V = cgetg(n+1,t_VECSMALL);
631 21 : for(i=1;i<l;i++) V[i] = v[i];
632 21 : return V;
633 : }
634 :
635 : INLINE GEN
636 3365332 : vec_to_vecsmall(GEN x)
637 3365332 : { pari_APPLY_long(itos(gel(x,i))) }
638 : INLINE GEN
639 135172 : vecsmall_to_vec(GEN x)
640 135172 : { pari_APPLY_type(t_VEC, stoi(x[i])) }
641 : INLINE GEN
642 1617 : vecsmall_to_vec_inplace(GEN z)
643 : {
644 1617 : long i, l = lg(z);
645 1617 : for (i=1; i<l; i++) gel(z,i) = stoi(z[i]);
646 1617 : settyp(z, t_VEC); return z;
647 : }
648 : INLINE GEN
649 5227133 : vecsmall_to_col(GEN x)
650 5227133 : { pari_APPLY_type(t_COL, stoi(x[i])) }
651 :
652 : INLINE int
653 8141461 : vecsmall_lexcmp(GEN x, GEN y)
654 : {
655 : long lx,ly,l,i;
656 8141461 : lx = lg(x);
657 8141461 : ly = lg(y); l = minss(lx,ly);
658 39719125 : for (i=1; i<l; i++)
659 37847303 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
660 1871822 : if (lx == ly) return 0;
661 14 : return (lx < ly)? -1 : 1;
662 : }
663 :
664 : INLINE int
665 85155511 : vecsmall_prefixcmp(GEN x, GEN y)
666 : {
667 85155511 : long i, lx = lg(x), ly = lg(y), l = minss(lx,ly);
668 394027655 : for (i=1; i<l; i++)
669 374395014 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
670 19632641 : return 0;
671 : }
672 :
673 : /*Can be used on t_VEC, but coeffs not gcopy-ed*/
674 : INLINE GEN
675 21414 : vecsmall_prepend(GEN V, long s)
676 : {
677 21414 : long i, l2 = lg(V);
678 21414 : GEN res = cgetg(l2+1, typ(V));
679 21414 : res[1] = s;
680 21414 : for (i = 2; i <= l2; ++i) res[i] = V[i - 1];
681 21414 : return res;
682 : }
683 :
684 : INLINE GEN
685 3128712 : vecsmall_append(GEN V, long s)
686 : {
687 3128712 : long i, l2 = lg(V);
688 3128712 : GEN res = cgetg(l2+1, t_VECSMALL);
689 3128711 : for (i = 1; i < l2; ++i) res[i] = V[i];
690 3128711 : res[l2] = s; return res;
691 : }
692 :
693 : INLINE GEN
694 786495 : vecsmall_concat(GEN u, GEN v)
695 : {
696 786495 : long i, l1 = lg(u)-1, l2 = lg(v)-1;
697 786495 : GEN res = cgetg(l1+l2+1, t_VECSMALL);
698 786496 : for (i = 1; i <= l1; ++i) res[i] = u[i];
699 786496 : for (i = 1; i <= l2; ++i) res[i+l1] = v[i];
700 786496 : return res;
701 : }
702 :
703 : /* return the number of indices where u and v are equal */
704 : INLINE long
705 0 : vecsmall_coincidence(GEN u, GEN v)
706 : {
707 0 : long i, s = 0, l = minss(lg(u),lg(v));
708 0 : for(i=1; i<l; i++)
709 0 : if(u[i] == v[i]) s++;
710 0 : return s;
711 : }
712 :
713 : /* returns the first index i<=n such that x=v[i] if it exists, 0 otherwise */
714 : INLINE long
715 0 : vecsmall_isin(GEN v, long x)
716 : {
717 0 : long i, l = lg(v);
718 0 : for (i = 1; i < l; i++)
719 0 : if (v[i] == x) return i;
720 0 : return 0;
721 : }
722 :
723 : INLINE long
724 84 : vecsmall_pack(GEN V, long base, long mod)
725 : {
726 84 : long i, s = 0;
727 84 : for(i=1; i<lg(V); i++) s = (base*s + V[i]) % mod;
728 84 : return s;
729 : }
730 :
731 : INLINE long
732 14 : vecsmall_indexmax(GEN x)
733 : {
734 14 : long i, i0 = 1, t = x[1], lx = lg(x);
735 56 : for (i=2; i<lx; i++)
736 42 : if (x[i] > t) t = x[i0=i];
737 14 : return i0;
738 : }
739 :
740 : INLINE long
741 179196 : vecsmall_max(GEN x)
742 : {
743 179196 : long i, t = x[1], lx = lg(x);
744 641674 : for (i=2; i<lx; i++)
745 462478 : if (x[i] > t) t = x[i];
746 179196 : return t;
747 : }
748 :
749 : INLINE long
750 14 : vecsmall_indexmin(GEN x)
751 : {
752 14 : long i, i0 = 1, t = x[1], lx =lg(x);
753 56 : for (i=2; i<lx; i++)
754 42 : if (x[i] < t) t = x[i0=i];
755 14 : return i0;
756 : }
757 :
758 : INLINE long
759 1421 : vecsmall_min(GEN x)
760 : {
761 1421 : long i, t = x[1], lx =lg(x);
762 9947 : for (i=2; i<lx; i++)
763 8526 : if (x[i] < t) t = x[i];
764 1421 : return t;
765 : }
766 :
767 : INLINE int
768 5045407 : ZV_isscalar(GEN x)
769 : {
770 5045407 : long l = lg(x);
771 14375695 : while (--l > 1)
772 8216439 : if (signe(gel(x, l))) return 0;
773 1113849 : return 1;
774 : }
775 : INLINE int
776 19658249 : QV_isscalar(GEN x)
777 : {
778 19658249 : long lx = lg(x),i;
779 21251162 : for (i=2; i<lx; i++)
780 20637120 : if (!isintzero(gel(x, i))) return 0;
781 614042 : return 1;
782 : }
783 : INLINE int
784 7676 : RgV_isscalar(GEN x)
785 : {
786 7676 : long lx = lg(x),i;
787 11255 : for (i=2; i<lx; i++)
788 9998 : if (!gequal0(gel(x, i))) return 0;
789 1257 : return 1;
790 : }
791 : INLINE int
792 0 : RgX_isscalar(GEN x)
793 : {
794 : long i;
795 0 : for (i=lg(x)-1; i>2; i--)
796 0 : if (!gequal0(gel(x, i))) return 0;
797 0 : return 1;
798 : }
799 : INLINE long
800 28786089 : RgX_equal_var(GEN x, GEN y) { return varn(x) == varn(y) && RgX_equal(x,y); }
801 :
802 : INLINE int
803 6259 : RgX_is_rational(GEN x)
804 : {
805 : long i;
806 29883 : for (i = lg(x)-1; i > 1; i--)
807 27901 : if (!is_rational_t(typ(gel(x,i)))) return 0;
808 1982 : return 1;
809 : }
810 : INLINE int
811 4451436 : RgX_is_ZX(GEN x)
812 : {
813 : long i;
814 19084627 : for (i = lg(x)-1; i > 1; i--)
815 14685642 : if (typ(gel(x,i)) != t_INT) return 0;
816 4398985 : return 1;
817 : }
818 : INLINE int
819 262577 : RgX_is_QX(GEN x)
820 : {
821 262577 : long k = lg(x)-1;
822 928107 : for ( ; k>1; k--)
823 665775 : if (!is_rational_t(typ(gel(x,k)))) return 0;
824 262332 : return 1;
825 : }
826 : INLINE int
827 16173623 : RgX_is_monomial(GEN x)
828 : {
829 : long i;
830 16173623 : if (!signe(x)) return 0;
831 26721442 : for (i=lg(x)-2; i>1; i--)
832 18332722 : if (!isexactzero(gel(x,i))) return 0;
833 8388720 : return 1;
834 : }
835 : INLINE int
836 27445544 : RgV_is_ZV(GEN x)
837 : {
838 : long i;
839 112529688 : for (i = lg(x)-1; i > 0; i--)
840 85086405 : if (typ(gel(x,i)) != t_INT) return 0;
841 27443283 : return 1;
842 : }
843 : INLINE int
844 21109 : RgV_is_QV(GEN x)
845 : {
846 : long i;
847 84923 : for (i = lg(x)-1; i > 0; i--)
848 65417 : if (!is_rational_t(typ(gel(x,i)))) return 0;
849 19506 : return 1;
850 : }
851 :
852 : /********************************************************************/
853 : /** **/
854 : /** Dynamic arrays implementation **/
855 : /** **/
856 : /********************************************************************/
857 : INLINE void **
858 403392007 : pari_stack_base(pari_stack *s) { return s->data; }
859 :
860 : INLINE void
861 1788155 : pari_stack_init(pari_stack *s, size_t size, void **data)
862 : {
863 1788155 : s->data = data;
864 1788155 : *data = NULL;
865 1788155 : s->n = 0;
866 1788155 : s->alloc = 0;
867 1788155 : s->size = size;
868 1788155 : }
869 :
870 : INLINE void
871 401651149 : pari_stack_alloc(pari_stack *s, long nb)
872 : {
873 401651149 : void **sdat = pari_stack_base(s);
874 401667739 : long alloc = s->alloc;
875 401667739 : if (s->n+nb <= alloc) return;
876 659258 : if (!alloc)
877 606171 : alloc = nb;
878 : else
879 : {
880 53087 : while (s->n+nb > alloc) alloc <<= 1;
881 : }
882 659258 : *sdat = pari_realloc(*sdat,alloc*s->size);
883 660061 : s->alloc = alloc;
884 : }
885 :
886 : INLINE long
887 323963110 : pari_stack_new(pari_stack *s) { pari_stack_alloc(s, 1); return s->n++; }
888 :
889 : INLINE void
890 1730858 : pari_stack_delete(pari_stack *s)
891 : {
892 1730858 : void **sdat = pari_stack_base(s);
893 1727258 : if (*sdat) pari_free(*sdat);
894 1739605 : }
895 :
896 : INLINE void
897 4815 : pari_stack_pushp(pari_stack *s, void *u)
898 : {
899 4815 : long n = pari_stack_new(s);
900 4815 : void **sdat =(void**) *pari_stack_base(s);
901 4815 : sdat[n] = u;
902 4815 : }
903 :
904 : /*******************************************************************/
905 : /* */
906 : /* EXTRACT */
907 : /* */
908 : /*******************************************************************/
909 : INLINE GEN
910 202212497 : vecslice(GEN A, long y1, long y2)
911 : {
912 202212497 : long i,lB = y2 - y1 + 2;
913 202212497 : GEN B = cgetg(lB, typ(A));
914 202213166 : for (i=1; i<lB; i++) B[i] = A[y1-1+i];
915 202213166 : return B;
916 : }
917 : INLINE GEN
918 816388 : vecslicepermute(GEN A, GEN p, long y1, long y2)
919 : {
920 816388 : long i,lB = y2 - y1 + 2;
921 816388 : GEN B = cgetg(lB, typ(A));
922 816397 : for (i=1; i<lB; i++) B[i] = A[p[y1-1+i]];
923 816397 : return B;
924 : }
925 : /* rowslice(rowpermute(A,p), x1, x2) */
926 : INLINE GEN
927 40668 : rowslicepermute(GEN x, GEN p, long j1, long j2)
928 40668 : { pari_APPLY_same(vecslicepermute(gel(x,i),p,j1,j2)) }
929 :
930 : INLINE GEN
931 22366668 : rowslice(GEN x, long j1, long j2)
932 22366668 : { pari_APPLY_same(vecslice(gel(x,i), j1, j2)) }
933 :
934 : INLINE GEN
935 3703684 : matslice(GEN A, long x1, long x2, long y1, long y2)
936 3703684 : { return rowslice(vecslice(A, y1, y2), x1, x2); }
937 :
938 : /* shallow, remove coeff of index j */
939 : INLINE GEN
940 133 : rowsplice(GEN x, long j)
941 133 : { pari_APPLY_same(vecsplice(gel(x,i), j)) }
942 :
943 : /* shallow, remove coeff of index j */
944 : INLINE GEN
945 264453 : vecsplice(GEN a, long j)
946 : {
947 264453 : long i, k, l = lg(a);
948 : GEN b;
949 264453 : if (l == 1) pari_err(e_MISC, "incorrect component in vecsplice");
950 264453 : b = cgetg(l-1, typ(a));
951 1056062 : for (i = k = 1; i < l; i++)
952 791609 : if (i != j) gel(b, k++) = gel(a,i);
953 264453 : return b;
954 : }
955 : /* shallow */
956 : INLINE GEN
957 833 : RgM_minor(GEN a, long i, long j)
958 : {
959 833 : GEN b = vecsplice(a, j);
960 833 : long k, l = lg(b);
961 833 : for (k = 1; k < l; k++) gel(b,k) = vecsplice(gel(b,k), i);
962 833 : return b;
963 : }
964 :
965 : /* A[x0,] */
966 : INLINE GEN
967 390422 : row(GEN x, long j)
968 390422 : { pari_APPLY_type(t_VEC, gcoeff(x, j, i)) }
969 : INLINE GEN
970 3758949 : Flm_row(GEN x, long j)
971 3758949 : { pari_APPLY_ulong((ulong)coeff(x, j, i)) }
972 : /* A[x0,] */
973 : INLINE GEN
974 204820 : rowcopy(GEN x, long j)
975 204820 : { pari_APPLY_type(t_VEC, gcopy(gcoeff(x, j, i))) }
976 : /* A[x0, x1..x2] */
977 : INLINE GEN
978 2303 : row_i(GEN A, long x0, long x1, long x2)
979 : {
980 2303 : long i, lB = x2 - x1 + 2;
981 2303 : GEN B = cgetg(lB, t_VEC);
982 2303 : for (i=x1; i<=x2; i++) gel(B, i) = gcoeff(A, x0, i);
983 2303 : return B;
984 : }
985 :
986 : INLINE GEN
987 5830483 : vecreverse(GEN A)
988 : {
989 : long i, l;
990 5830483 : GEN B = cgetg_copy(A, &l);
991 5830483 : for (i=1; i<l; i++) gel(B, i) = gel(A, l-i);
992 5830483 : return B;
993 : }
994 :
995 : INLINE GEN
996 329 : vecsmall_reverse(GEN A)
997 : {
998 : long i, l;
999 329 : GEN B = cgetg_copy(A, &l);
1000 329 : for (i=1; i<l; i++) B[i] = A[l-i];
1001 329 : return B;
1002 : }
1003 :
1004 : INLINE void
1005 253 : vecreverse_inplace(GEN y)
1006 : {
1007 253 : long l = lg(y), lim = l>>1, i;
1008 717 : for (i = 1; i <= lim; i++)
1009 : {
1010 464 : GEN z = gel(y,i);
1011 464 : gel(y,i) = gel(y,l-i);
1012 464 : gel(y,l-i) = z;
1013 : }
1014 253 : }
1015 :
1016 : INLINE GEN
1017 45407301 : vecsmallpermute(GEN A, GEN p) { return perm_mul(A, p); }
1018 :
1019 : INLINE GEN
1020 6509599 : vecpermute(GEN A, GEN x)
1021 6509599 : { pari_APPLY_type(typ(A), gel(A, x[i])) }
1022 :
1023 : INLINE GEN
1024 3011018 : rowpermute(GEN x, GEN p)
1025 3011018 : { pari_APPLY_same(typ(gel(x,i)) == t_VECSMALL ? vecsmallpermute(gel(x, i), p)
1026 : : vecpermute(gel(x, i), p))
1027 : }
1028 : /*******************************************************************/
1029 : /* */
1030 : /* PERMUTATIONS */
1031 : /* */
1032 : /*******************************************************************/
1033 : /* identity permutation */
1034 : INLINE GEN
1035 728152 : identity_perm(long n)
1036 : {
1037 728152 : GEN perm = cgetg(n+1, t_VECSMALL);
1038 : long i;
1039 728148 : for (i = 1; i <= n; i++) perm[i] = i;
1040 728148 : return perm;
1041 : }
1042 :
1043 : /* assume d <= n */
1044 : INLINE GEN
1045 98434 : cyclic_perm(long n, long d)
1046 : {
1047 98434 : GEN perm = cgetg(n+1, t_VECSMALL);
1048 : long i;
1049 98434 : for (i = 1; i <= n-d; i++) perm[i] = i+d;
1050 98434 : for ( ; i <= n; i++) perm[i] = i-n+d;
1051 98434 : return perm;
1052 : }
1053 :
1054 : /* Multiply (compose) two permutations */
1055 : INLINE GEN
1056 46651212 : perm_mul(GEN s, GEN x)
1057 46651212 : { pari_APPLY_long(s[x[i]]) }
1058 :
1059 : /* Compute the inverse (reciprocal) of a permutation. */
1060 : INLINE GEN
1061 1161956 : perm_inv(GEN x)
1062 : {
1063 : long i, lx;
1064 1161956 : GEN y = cgetg_copy(x, &lx);
1065 1161955 : for (i=1; i<lx; i++) y[ x[i] ] = i;
1066 1161955 : return y;
1067 : }
1068 : /* Return s*t*s^-1 */
1069 : INLINE GEN
1070 416934 : perm_conj(GEN s, GEN t)
1071 : {
1072 : long i, l;
1073 416934 : GEN v = cgetg_copy(s, &l);
1074 416934 : for (i = 1; i < l; i++) v[ s[i] ] = s[ t[i] ];
1075 416934 : return v;
1076 : }
1077 :
1078 : /*********************************************************************/
1079 : /* MALLOC/FREE WRAPPERS */
1080 : /*********************************************************************/
1081 : #define BLOCK_SIGALRM_START \
1082 : { \
1083 : int block=PARI_SIGINT_block; \
1084 : PARI_SIGINT_block = 2; \
1085 : MT_SIGINT_BLOCK(block);
1086 :
1087 : #define BLOCK_SIGINT_START \
1088 : { \
1089 : int block=PARI_SIGINT_block; \
1090 : PARI_SIGINT_block = 1; \
1091 : MT_SIGINT_BLOCK(block);
1092 :
1093 : #define BLOCK_SIGINT_END \
1094 : PARI_SIGINT_block = block; \
1095 : MT_SIGINT_UNBLOCK(block); \
1096 : if (!block && PARI_SIGINT_pending) \
1097 : { \
1098 : int sig = PARI_SIGINT_pending; \
1099 : PARI_SIGINT_pending = 0; \
1100 : raise(sig); \
1101 : } \
1102 : }
1103 :
1104 : INLINE void
1105 72147809 : pari_free(void *pointer)
1106 : {
1107 72147809 : BLOCK_SIGINT_START;
1108 72168450 : free(pointer);
1109 72168450 : BLOCK_SIGINT_END;
1110 72163833 : }
1111 : INLINE void*
1112 279143828 : pari_malloc(size_t size)
1113 : {
1114 279143828 : if (size)
1115 : {
1116 : char *tmp;
1117 279143828 : BLOCK_SIGINT_START;
1118 279147321 : tmp = (char*)malloc(size);
1119 279147321 : BLOCK_SIGINT_END;
1120 279146939 : if (!tmp) pari_err(e_MEM);
1121 279146939 : return tmp;
1122 : }
1123 0 : return NULL;
1124 : }
1125 : INLINE void*
1126 673959 : pari_realloc(void *pointer, size_t size)
1127 : {
1128 : char *tmp;
1129 :
1130 673959 : BLOCK_SIGINT_START;
1131 675705 : if (!pointer) tmp = (char *) malloc(size);
1132 56864 : else tmp = (char *) realloc(pointer,size);
1133 675705 : BLOCK_SIGINT_END;
1134 675130 : if (!tmp) pari_err(e_MEM);
1135 675130 : return tmp;
1136 : }
1137 : INLINE void*
1138 35683 : pari_calloc(size_t size)
1139 : {
1140 35683 : void *t = pari_malloc(size);
1141 35683 : memset(t, 0, size); return t;
1142 : }
1143 : INLINE GEN
1144 5813 : cgetalloc(long t, size_t l)
1145 : {
1146 5813 : GEN x = (GEN)pari_malloc(l * sizeof(long));
1147 5813 : x[0] = evaltyp(t) | evallg(l); return x;
1148 : }
1149 :
1150 : /*******************************************************************/
1151 : /* */
1152 : /* GARBAGE COLLECTION */
1153 : /* */
1154 : /*******************************************************************/
1155 : /* copy integer x as if we had set_avma(av) */
1156 : INLINE GEN
1157 3812592563 : icopy_avma(GEN x, pari_sp av)
1158 : {
1159 3812592563 : long i = lgefint(x), lx = i;
1160 3812592563 : GEN y = ((GEN)av) - i;
1161 3812592563 : while (--i > 0) y[i] = x[i];
1162 3812592563 : y[0] = evaltyp(t_INT)|evallg(lx);
1163 3812364030 : return y;
1164 : }
1165 : /* copy leaf x as if we had set_avma(av) */
1166 : INLINE GEN
1167 177549511 : leafcopy_avma(GEN x, pari_sp av)
1168 : {
1169 177549511 : long i = lg(x);
1170 177549511 : GEN y = ((GEN)av) - i;
1171 177549511 : while (--i > 0) y[i] = x[i];
1172 177549511 : y[0] = x[0] & (~CLONEBIT);
1173 177549511 : return y;
1174 : }
1175 : INLINE GEN
1176 638319543 : gerepileuptoleaf(pari_sp av, GEN x)
1177 : {
1178 : long lx;
1179 : GEN q;
1180 :
1181 638319543 : if (!isonstack(x) || (GEN)av<=x) { set_avma(av); return x; }
1182 638222046 : lx = lg(x);
1183 638222046 : q = ((GEN)av) - lx;
1184 638222046 : set_avma((pari_sp)q);
1185 640063297 : while (--lx >= 0) q[lx] = x[lx];
1186 640063297 : return q;
1187 : }
1188 : INLINE GEN
1189 1285700157 : gerepileuptoint(pari_sp av, GEN x)
1190 : {
1191 1285700157 : if (!isonstack(x) || (GEN)av<=x) { set_avma(av); return x; }
1192 1137631537 : set_avma((pari_sp)icopy_avma(x, av));
1193 1139169756 : return (GEN)avma;
1194 : }
1195 : INLINE GEN
1196 812912162 : gerepileupto(pari_sp av, GEN x)
1197 : {
1198 812912162 : if (!isonstack(x) || (GEN)av<=x) { set_avma(av); return x; }
1199 723406932 : switch(typ(x))
1200 : { /* non-default = !is_recursive_t(tq) */
1201 258988041 : case t_INT: return gerepileuptoint(av, x);
1202 : case t_REAL:
1203 : case t_STR:
1204 145498528 : case t_VECSMALL: return gerepileuptoleaf(av,x);
1205 : default:
1206 : /* NB: x+i --> ((long)x) + i*sizeof(long) */
1207 318920363 : return gerepile(av, (pari_sp) (x+lg(x)), x);
1208 : }
1209 : }
1210 : INLINE double
1211 2269412 : gc_double(pari_sp av, double d) { set_avma(av); return d; }
1212 : INLINE long
1213 112961134 : gc_long(pari_sp av, long s) { set_avma(av); return s; }
1214 : INLINE ulong
1215 15269264 : gc_ulong(pari_sp av, ulong s) { set_avma(av); return s; }
1216 : INLINE int
1217 21966149 : gc_bool(pari_sp av, int s) { set_avma(av); return s; }
1218 : INLINE int
1219 3366387 : gc_int(pari_sp av, int s) { set_avma(av); return s; }
1220 : INLINE GEN
1221 1610927 : gc_NULL(pari_sp av) { set_avma(av); return NULL; }
1222 :
1223 : /* gerepileupto(av, gcopy(x)) */
1224 : INLINE GEN
1225 53160162 : gerepilecopy(pari_sp av, GEN x)
1226 : {
1227 53160162 : if (is_recursive_t(typ(x)))
1228 : {
1229 48544508 : GENbin *p = copy_bin(x);
1230 48545012 : set_avma(av); return bin_copy(p);
1231 : }
1232 : else
1233 : {
1234 4615641 : set_avma(av);
1235 4615647 : if (x < (GEN)av) {
1236 3128191 : if (x < (GEN)pari_mainstack->bot) new_chunk(lg(x));
1237 3128191 : x = leafcopy_avma(x, av);
1238 3128197 : set_avma((pari_sp)x);
1239 : } else
1240 1487456 : x = leafcopy(x);
1241 4615653 : return x;
1242 : }
1243 : }
1244 :
1245 : /* Takes an array of pointers to GENs, of length n. Copies all
1246 : * objects to contiguous locations and cleans up the stack between
1247 : * av and avma. */
1248 : INLINE void
1249 199411 : gerepilemany(pari_sp av, GEN* gptr[], int n)
1250 : {
1251 : int i;
1252 199411 : for (i=0; i<n; i++) *gptr[i] = (GEN)copy_bin(*gptr[i]);
1253 199411 : set_avma(av);
1254 199411 : for (i=0; i<n; i++) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1255 199411 : }
1256 :
1257 : INLINE void
1258 7560473 : gerepileall(pari_sp av, int n, ...)
1259 : {
1260 : int i;
1261 7560473 : va_list a; va_start(a, n);
1262 7560473 : if (n < 10)
1263 : {
1264 : GEN *gptr[10];
1265 21891819 : for (i=0; i<n; i++)
1266 14331313 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1267 7560506 : set_avma(av);
1268 7560416 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1269 :
1270 : }
1271 : else
1272 : {
1273 0 : GEN **gptr = (GEN**) pari_malloc(n*sizeof(GEN*));
1274 0 : for (i=0; i<n; i++)
1275 0 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1276 0 : set_avma(av);
1277 0 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1278 0 : pari_free(gptr);
1279 : }
1280 7560607 : va_end(a);
1281 7560607 : }
1282 :
1283 : INLINE void
1284 6 : gerepilecoeffs(pari_sp av, GEN x, int n)
1285 : {
1286 : int i;
1287 6 : for (i=0; i<n; i++) gel(x,i) = (GEN)copy_bin(gel(x,i));
1288 6 : set_avma(av);
1289 6 : for (i=0; i<n; i++) gel(x,i) = bin_copy((GENbin*)x[i]);
1290 6 : }
1291 :
1292 : /* p from copy_bin. Copy p->x back to stack, then destroy p */
1293 : INLINE GEN
1294 63489604 : bin_copy(GENbin *p)
1295 : {
1296 : GEN x, y, base;
1297 : long dx, len;
1298 :
1299 63489604 : x = p->x; if (!x) { pari_free(p); return gen_0; }
1300 63482407 : len = p->len;
1301 63482407 : base= p->base; dx = x - base;
1302 63482407 : y = (GEN)memcpy((void*)new_chunk(len), (void*)GENbinbase(p), len*sizeof(long));
1303 63482291 : y += dx;
1304 63482291 : p->rebase(y, ((ulong)y-(ulong)x));
1305 63482270 : pari_free(p); return y;
1306 : }
1307 :
1308 : INLINE GEN
1309 126972276 : GENbinbase(GENbin *p) { return (GEN)(p + 1); }
1310 :
1311 : INLINE void
1312 31940396 : cgiv(GEN x)
1313 : {
1314 31940396 : pari_sp av = (pari_sp)(x+lg(x));
1315 31940396 : if (isonstack((GEN)av)) set_avma(av);
1316 31939818 : }
1317 :
1318 : INLINE void
1319 1286320 : killblock(GEN x) { gunclone(x); }
1320 :
1321 : INLINE int
1322 25903131 : is_universal_constant(GEN x) { return (x >= gen_0 && x <= ghalf); }
1323 :
1324 : /*******************************************************************/
1325 : /* */
1326 : /* CONVERSION / ASSIGNMENT */
1327 : /* */
1328 : /*******************************************************************/
1329 : /* z is a type which may be a t_COMPLEX component (not a t_QUAD) */
1330 : INLINE GEN
1331 3422600 : cxcompotor(GEN z, long prec)
1332 : {
1333 3422600 : switch(typ(z))
1334 : {
1335 1867585 : case t_INT: return itor(z, prec);
1336 136234 : case t_FRAC: return fractor(z, prec);
1337 1418781 : case t_REAL: return rtor(z, prec);
1338 0 : default: pari_err_TYPE("cxcompotor",z);
1339 : return NULL; /* LCOV_EXCL_LINE */
1340 : }
1341 : }
1342 : INLINE GEN
1343 1697888 : cxtofp(GEN x, long prec)
1344 1697888 : { retmkcomplex(cxcompotor(gel(x,1),prec), cxcompotor(gel(x,2),prec)); }
1345 :
1346 : INLINE GEN
1347 291102 : cxtoreal(GEN q)
1348 291102 : { return (typ(q) == t_COMPLEX && gequal0(gel(q,2)))? gel(q,1): q; }
1349 :
1350 : INLINE double
1351 33825061 : gtodouble(GEN x)
1352 : {
1353 33825061 : if (typ(x)!=t_REAL) {
1354 7447611 : pari_sp av = avma;
1355 7447611 : x = gtofp(x, DEFAULTPREC);
1356 7447611 : if (typ(x)!=t_REAL) pari_err_TYPE("gtodouble [t_REAL expected]", x);
1357 7447611 : set_avma(av);
1358 : }
1359 33825061 : return rtodbl(x);
1360 : }
1361 : INLINE long
1362 73376507 : gtos(GEN x) {
1363 73376507 : if (typ(x) != t_INT) pari_err_TYPE("gtos [integer expected]",x);
1364 73376500 : return itos(x);
1365 : }
1366 :
1367 : INLINE ulong
1368 152303 : gtou(GEN x) {
1369 152303 : if (typ(x) != t_INT || signe(x)<0)
1370 0 : pari_err_TYPE("gtou [integer >=0 expected]",x);
1371 152313 : return itou(x);
1372 : }
1373 :
1374 : INLINE GEN
1375 23163898 : absfrac(GEN x)
1376 : {
1377 23163898 : GEN y = cgetg(3, t_FRAC);
1378 23163898 : gel(y,1) = absi(gel(x,1));
1379 23163898 : gel(y,2) = icopy(gel(x,2)); return y;
1380 : }
1381 : INLINE GEN
1382 32658 : absfrac_shallow(GEN x)
1383 32658 : { return signe(gel(x,1))>0? x: mkfrac(negi(gel(x,1)), gel(x,2)); }
1384 : INLINE GEN
1385 7733307 : Q_abs(GEN x) { return (typ(x) == t_INT)? absi(x): absfrac(x); }
1386 : INLINE GEN
1387 130744 : Q_abs_shallow(GEN x)
1388 130744 : { return (typ(x) == t_INT)? absi_shallow(x): absfrac_shallow(x); }
1389 : INLINE GEN
1390 322 : R_abs_shallow(GEN x)
1391 322 : { return (typ(x) == t_FRAC)? absfrac_shallow(x): mpabs_shallow(x); }
1392 : INLINE GEN
1393 0 : R_abs(GEN x)
1394 0 : { return (typ(x) == t_FRAC)? absfrac(x): mpabs(x); }
1395 :
1396 : /* Force z to be of type real/complex with floating point components */
1397 : INLINE GEN
1398 35750132 : gtofp(GEN z, long prec)
1399 : {
1400 35750132 : switch(typ(z))
1401 : {
1402 22450256 : case t_INT: return itor(z, prec);
1403 4310668 : case t_FRAC: return fractor(z, prec);
1404 7523099 : case t_REAL: return rtor(z, prec);
1405 : case t_COMPLEX: {
1406 1466109 : GEN a = gel(z,1), b = gel(z,2);
1407 1466109 : if (isintzero(b)) return cxcompotor(a, prec);
1408 1463593 : if (isintzero(a)) {
1409 2114 : GEN y = cgetg(3, t_COMPLEX);
1410 2114 : b = cxcompotor(b, prec);
1411 2114 : gel(y,1) = real_0_bit(expo(b) - prec2nbits(prec));
1412 2114 : gel(y,2) = b; return y;
1413 : }
1414 1461479 : return cxtofp(z, prec);
1415 : }
1416 0 : case t_QUAD: return quadtofp(z, prec);
1417 0 : default: pari_err_TYPE("gtofp",z);
1418 : return NULL; /* LCOV_EXCL_LINE */
1419 : }
1420 : }
1421 : /* Force z to be of type real / int */
1422 : INLINE GEN
1423 22400 : gtomp(GEN z, long prec)
1424 : {
1425 22400 : switch(typ(z))
1426 : {
1427 14 : case t_INT: return z;
1428 22386 : case t_FRAC: return fractor(z, prec);
1429 0 : case t_REAL: return rtor(z, prec);
1430 0 : case t_QUAD: z = quadtofp(z, prec);
1431 0 : if (typ(z) == t_REAL) return z;
1432 0 : default: pari_err_TYPE("gtomp",z);
1433 : return NULL; /* LCOV_EXCL_LINE */
1434 : }
1435 : }
1436 :
1437 : INLINE GEN
1438 757234 : RgX_gtofp(GEN x, long prec)
1439 : {
1440 : long l;
1441 757234 : GEN y = cgetg_copy(x, &l);
1442 757234 : while (--l > 1) gel(y,l) = gtofp(gel(x,l), prec);
1443 757234 : y[1] = x[1]; return y;
1444 : }
1445 : INLINE GEN
1446 1192113 : RgC_gtofp(GEN x, long prec)
1447 1192113 : { pari_APPLY_type(t_COL, gtofp(gel(x,i), prec)) }
1448 :
1449 : INLINE GEN
1450 42 : RgV_gtofp(GEN x, long prec)
1451 42 : { pari_APPLY_type(t_VEC, gtofp(gel(x,i), prec)) }
1452 :
1453 : INLINE GEN
1454 134571 : RgM_gtofp(GEN x, long prec)
1455 134571 : { pari_APPLY_same(RgC_gtofp(gel(x,i), prec)) }
1456 :
1457 : INLINE GEN
1458 560 : RgC_gtomp(GEN x, long prec)
1459 560 : { pari_APPLY_type(t_COL, gtomp(gel(x,i), prec)) }
1460 :
1461 : INLINE GEN
1462 14 : RgM_gtomp(GEN x, long prec)
1463 14 : { pari_APPLY_same(RgC_gtomp(gel(x,i), prec)) }
1464 :
1465 : INLINE GEN
1466 9304 : RgX_fpnorml2(GEN x, long prec)
1467 : {
1468 9304 : pari_sp av = avma;
1469 9304 : return gerepileupto(av, gnorml2(RgX_gtofp(x, prec)));
1470 : }
1471 : INLINE GEN
1472 187187 : RgC_fpnorml2(GEN x, long prec)
1473 : {
1474 187187 : pari_sp av = avma;
1475 187187 : return gerepileupto(av, gnorml2(RgC_gtofp(x, prec)));
1476 : }
1477 : INLINE GEN
1478 3846 : RgM_fpnorml2(GEN x, long prec)
1479 : {
1480 3846 : pari_sp av = avma;
1481 3846 : return gerepileupto(av, gnorml2(RgM_gtofp(x, prec)));
1482 : }
1483 :
1484 : /* y a t_REAL */
1485 : INLINE void
1486 216244 : affgr(GEN x, GEN y)
1487 : {
1488 : pari_sp av;
1489 216244 : switch(typ(x)) {
1490 5992 : case t_INT: affir(x,y); break;
1491 210252 : case t_REAL: affrr(x,y); break;
1492 0 : case t_FRAC: rdiviiz(gel(x,1),gel(x,2), y); break;
1493 0 : case t_QUAD: av = avma; affgr(quadtofp(x,realprec(y)), y); set_avma(av); break;
1494 0 : default: pari_err_TYPE2("=",x,y);
1495 : }
1496 216244 : }
1497 :
1498 : INLINE GEN
1499 260887 : affc_fixlg(GEN x, GEN res)
1500 : {
1501 260887 : if (typ(x) == t_COMPLEX)
1502 : {
1503 207515 : affrr_fixlg(gel(x,1), gel(res,1));
1504 207515 : affrr_fixlg(gel(x,2), gel(res,2));
1505 : }
1506 : else
1507 : {
1508 53372 : set_avma((pari_sp)(res+3));
1509 53372 : res = cgetr(realprec(gel(res,1)));
1510 53372 : affrr_fixlg(x, res);
1511 : }
1512 260887 : return res;
1513 : }
1514 :
1515 : INLINE GEN
1516 0 : trunc_safe(GEN x) { long e; return gcvtoi(x,&e); }
1517 :
1518 : /*******************************************************************/
1519 : /* */
1520 : /* LENGTH CONVERSIONS */
1521 : /* */
1522 : /*******************************************************************/
1523 : INLINE long
1524 28793 : ndec2nlong(long x) { return 1 + (long)((x)*(LOG2_10/BITS_IN_LONG)); }
1525 : INLINE long
1526 20336 : ndec2prec(long x) { return 2 + ndec2nlong(x); }
1527 : INLINE long
1528 8457 : ndec2nbits(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1529 : /* Fast implementation of ceil(x / (8*sizeof(long))); typecast to (ulong)
1530 : * to avoid overflow. Faster than 1 + ((x-1)>>TWOPOTBITS_IN_LONG)) :
1531 : * addl, shrl instead of subl, sarl, addl */
1532 : INLINE long
1533 1190948 : nbits2nlong(long x) {
1534 1190948 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1535 : }
1536 :
1537 : INLINE long
1538 317253660 : nbits2extraprec(long x) {
1539 317253660 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1540 : }
1541 :
1542 : /* Fast implementation of 2 + nbits2nlong(x) */
1543 : INLINE long
1544 109695768 : nbits2prec(long x) {
1545 109695768 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1546 : }
1547 : INLINE long
1548 7698469 : nbits2lg(long x) {
1549 7698469 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1550 : }
1551 : /* ceil(x / sizeof(long)) */
1552 : INLINE long
1553 8746994 : nchar2nlong(long x) {
1554 8746994 : return (long)(((ulong)x+sizeof(long)-1) >> (TWOPOTBITS_IN_LONG-3L));
1555 : }
1556 : INLINE long
1557 1162996978 : prec2nbits(long x) { return (x-2) * BITS_IN_LONG; }
1558 : INLINE double
1559 564469 : bit_accuracy_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1560 : INLINE double
1561 302019 : prec2nbits_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1562 : INLINE long
1563 32640826 : bit_prec(GEN x) { return prec2nbits(realprec(x)); }
1564 : INLINE long
1565 1049397402 : bit_accuracy(long x) { return prec2nbits(x); }
1566 : INLINE long
1567 12399 : prec2ndec(long x) { return (long)prec2nbits_mul(x, LOG10_2); }
1568 : INLINE long
1569 193 : nbits2ndec(long x) { return (long)(x * LOG10_2); }
1570 : INLINE long
1571 3108 : precdbl(long x) {return (x - 1) << 1;}
1572 : INLINE long
1573 3478264647 : divsBIL(long n) { return n >> TWOPOTBITS_IN_LONG; }
1574 : INLINE long
1575 3433518568 : remsBIL(long n) { return n & (BITS_IN_LONG-1); }
1576 :
1577 : /*********************************************************************/
1578 : /** **/
1579 : /** OPERATIONS MODULO m **/
1580 : /** **/
1581 : /*********************************************************************/
1582 : /* Assume m > 0, more efficient if 0 <= a, b < m */
1583 :
1584 : INLINE GEN
1585 35042505 : Fp_red(GEN a, GEN m) { return modii(a, m); }
1586 : INLINE GEN
1587 71731497 : Fp_add(GEN a, GEN b, GEN m)
1588 : {
1589 71731497 : pari_sp av=avma;
1590 71731497 : GEN p = addii(a,b);
1591 70457875 : long s = signe(p);
1592 70457875 : if (!s) return p; /* = gen_0 */
1593 62850073 : if (s > 0) /* general case */
1594 : {
1595 62623657 : GEN t = subii(p, m);
1596 63567174 : s = signe(t);
1597 63567174 : if (!s) { set_avma(av); return gen_0; }
1598 57783618 : if (s < 0) { set_avma((pari_sp)p); return p; }
1599 24393898 : if (cmpii(t, m) < 0) return gerepileuptoint(av, t); /* general case ! */
1600 1112584 : p = remii(t, m);
1601 : }
1602 : else
1603 226416 : p = modii(p, m);
1604 1339000 : return gerepileuptoint(av, p);
1605 : }
1606 : INLINE GEN
1607 56632143 : Fp_sub(GEN a, GEN b, GEN m)
1608 : {
1609 56632143 : pari_sp av=avma;
1610 56632143 : GEN p = subii(a,b);
1611 56225018 : long s = signe(p);
1612 56225018 : if (!s) return p; /* = gen_0 */
1613 49961976 : if (s > 0)
1614 : {
1615 24147142 : if (cmpii(p, m) < 0) return p; /* general case ! */
1616 1121338 : p = remii(p, m);
1617 : }
1618 : else
1619 : {
1620 25814834 : GEN t = addii(p, m);
1621 25759792 : if (!s) { set_avma(av); return gen_0; }
1622 25759792 : if (s > 0) return gerepileuptoint(av, t); /* general case ! */
1623 25759792 : p = modii(t, m);
1624 : }
1625 27632277 : return gerepileuptoint(av, p);
1626 : }
1627 : INLINE GEN
1628 13458883 : Fp_neg(GEN b, GEN m)
1629 : {
1630 13458883 : pari_sp av = avma;
1631 13458883 : long s = signe(b);
1632 : GEN p;
1633 13458883 : if (!s) return gen_0;
1634 9988031 : if (s > 0)
1635 : {
1636 9766073 : p = subii(m, b);
1637 9764126 : if (signe(p) >= 0) return p; /* general case ! */
1638 114617 : p = modii(p, m);
1639 : } else
1640 221958 : p = remii(negi(b), m);
1641 336575 : return gerepileuptoint(av, p);
1642 : }
1643 :
1644 : INLINE GEN
1645 23592 : Fp_halve(GEN a, GEN p)
1646 : {
1647 23592 : if (mpodd(a)) a = addii(a,p);
1648 23592 : return shifti(a,-1);
1649 : }
1650 :
1651 : /* assume 0 <= u < p and ps2 = p>>1 */
1652 : INLINE GEN
1653 16689613 : Fp_center(GEN u, GEN p, GEN ps2)
1654 16689613 : { return abscmpii(u,ps2)<=0? icopy(u): subii(u,p); }
1655 : /* same without copy */
1656 : INLINE GEN
1657 15262646 : Fp_center_i(GEN u, GEN p, GEN ps2)
1658 15262646 : { return abscmpii(u,ps2)<=0? u: subii(u,p); }
1659 :
1660 : /* x + y*z mod p */
1661 : INLINE GEN
1662 5063607 : Fp_addmul(GEN x, GEN y, GEN z, GEN p)
1663 : {
1664 : pari_sp av;
1665 5063607 : if (!signe(y) || !signe(z)) return Fp_red(x, p);
1666 4766331 : if (!signe(x)) return Fp_mul(z,y, p);
1667 4462885 : av = avma;
1668 4462885 : return gerepileuptoint(av, modii(addii(x, mulii(y,z)), p));
1669 : }
1670 :
1671 : INLINE GEN
1672 92042882 : Fp_mul(GEN a, GEN b, GEN m)
1673 : {
1674 92042882 : pari_sp av=avma;
1675 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1676 92042882 : (void)new_chunk(lg(a)+lg(b)+(lg(m)<<1));
1677 92046518 : p = mulii(a,b);
1678 92195967 : set_avma(av); return modii(p,m);
1679 : }
1680 : INLINE GEN
1681 33524688 : Fp_sqr(GEN a, GEN m)
1682 : {
1683 33524688 : pari_sp av=avma;
1684 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1685 33524688 : (void)new_chunk((lg(a)+lg(m))<<1);
1686 33551381 : p = sqri(a);
1687 30737889 : set_avma(av); return remii(p,m); /*Use remii: p >= 0 */
1688 : }
1689 : INLINE GEN
1690 64689291 : Fp_mulu(GEN a, ulong b, GEN m)
1691 : {
1692 64689291 : long l = lgefint(m);
1693 64689291 : if (l == 3)
1694 : {
1695 38795981 : ulong mm = m[2];
1696 38795981 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1697 : } else {
1698 25893310 : pari_sp av = avma;
1699 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1700 25893310 : (void)new_chunk(lg(a)+1+(l<<1));
1701 25941588 : p = muliu(a,b);
1702 24466085 : set_avma(av); return modii(p,m);
1703 : }
1704 : }
1705 : INLINE GEN
1706 0 : Fp_muls(GEN a, long b, GEN m)
1707 : {
1708 0 : long l = lgefint(m);
1709 0 : if (l == 3)
1710 : {
1711 0 : ulong mm = m[2];
1712 0 : if (b < 0)
1713 : {
1714 0 : ulong t = Fl_mul(umodiu(a, mm), -b, mm);
1715 0 : return t? utoipos(mm - t): gen_0;
1716 : }
1717 : else
1718 0 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1719 : } else {
1720 0 : pari_sp av = avma;
1721 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1722 0 : (void)new_chunk(lg(a)+1+(l<<1));
1723 0 : p = mulis(a,b);
1724 0 : set_avma(av); return modii(p,m);
1725 : }
1726 : }
1727 :
1728 : INLINE GEN
1729 10972867 : Fp_inv(GEN a, GEN m)
1730 : {
1731 : GEN res;
1732 10972867 : if (! invmod(a,m,&res)) pari_err_INV("Fp_inv", mkintmod(res,m));
1733 10972540 : return res;
1734 : }
1735 : INLINE GEN
1736 315415 : Fp_invsafe(GEN a, GEN m)
1737 : {
1738 : GEN res;
1739 315415 : if (! invmod(a,m,&res)) return NULL;
1740 315415 : return res;
1741 : }
1742 : INLINE GEN
1743 2367113 : Fp_div(GEN a, GEN b, GEN m)
1744 : {
1745 2367113 : pari_sp av=avma;
1746 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1747 2367113 : (void)new_chunk(lg(a)+(lg(m)<<1));
1748 2367113 : p = mulii(a, Fp_inv(b,m));
1749 2367110 : set_avma(av); return modii(p,m);
1750 : }
1751 :
1752 : INLINE GEN
1753 847298 : Flx_mulu(GEN x, ulong a, ulong p) { return Flx_Fl_mul(x,a%p,p); }
1754 :
1755 : INLINE GEN
1756 0 : get_F2x_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1757 :
1758 : INLINE long
1759 448517 : get_F2x_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1760 :
1761 : INLINE long
1762 121548 : get_F2x_degree(GEN T) { return typ(T)==t_VEC? F2x_degree(gel(T,2)): F2x_degree(T); }
1763 :
1764 : INLINE GEN
1765 378 : get_F2xqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1766 :
1767 : INLINE long
1768 376495 : get_F2xqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1769 :
1770 : INLINE long
1771 201684 : get_F2xqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1772 :
1773 : INLINE GEN
1774 7571148 : get_Flx_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1775 :
1776 : INLINE long
1777 16813533 : get_Flx_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1778 :
1779 : INLINE long
1780 35937010 : get_Flx_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1781 :
1782 : INLINE GEN
1783 2461 : get_FlxqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1784 :
1785 : INLINE long
1786 368931 : get_FlxqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1787 :
1788 : INLINE long
1789 155787 : get_FlxqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1790 :
1791 : INLINE GEN
1792 1614100 : get_FpX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1793 :
1794 : INLINE long
1795 2918202 : get_FpX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1796 :
1797 : INLINE long
1798 1891848 : get_FpX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1799 :
1800 : INLINE GEN
1801 142586 : get_FpXQX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1802 :
1803 : INLINE long
1804 57357 : get_FpXQX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1805 :
1806 : INLINE long
1807 2187 : get_FpXQX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1808 :
1809 : /*******************************************************************/
1810 : /* */
1811 : /* ADDMULII / SUBMULII */
1812 : /* */
1813 : /*******************************************************************/
1814 : /* x - y*z */
1815 : INLINE GEN
1816 13447814 : submulii(GEN x, GEN y, GEN z)
1817 : {
1818 13447814 : long lx = lgefint(x), ly, lz;
1819 : pari_sp av;
1820 : GEN t;
1821 13447814 : if (lx == 2) { t = mulii(z,y); togglesign(t); return t; }
1822 11634755 : ly = lgefint(y);
1823 11634755 : if (ly == 2) return icopy(x);
1824 10498508 : lz = lgefint(z);
1825 10498508 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1826 10498508 : t = mulii(z, y);
1827 10498508 : set_avma(av); return subii(x,t);
1828 : }
1829 : /* y*z - x */
1830 : INLINE GEN
1831 1238672 : mulsubii(GEN y, GEN z, GEN x)
1832 : {
1833 1238672 : long lx = lgefint(x), ly, lz;
1834 : pari_sp av;
1835 : GEN t;
1836 1238672 : if (lx == 2) return mulii(z,y);
1837 788797 : ly = lgefint(y);
1838 788797 : if (ly == 2) return negi(x);
1839 723511 : lz = lgefint(z);
1840 723511 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1841 723511 : t = mulii(z, y);
1842 723511 : set_avma(av); return subii(t,x);
1843 : }
1844 :
1845 : /* x - u*y */
1846 : INLINE GEN
1847 7595 : submuliu(GEN x, GEN y, ulong u)
1848 : {
1849 : pari_sp av;
1850 7595 : long ly = lgefint(y);
1851 7595 : if (ly == 2) return icopy(x);
1852 7595 : av = avma;
1853 7595 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1854 7595 : y = mului(u,y);
1855 7595 : set_avma(av); return subii(x, y);
1856 : }
1857 : /* x + u*y */
1858 : INLINE GEN
1859 7595 : addmuliu(GEN x, GEN y, ulong u)
1860 : {
1861 : pari_sp av;
1862 7595 : long ly = lgefint(y);
1863 7595 : if (ly == 2) return icopy(x);
1864 7595 : av = avma;
1865 7595 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1866 7595 : y = mului(u,y);
1867 7595 : set_avma(av); return addii(x, y);
1868 : }
1869 : /* x - u*y */
1870 : INLINE GEN
1871 122920241 : submuliu_inplace(GEN x, GEN y, ulong u)
1872 : {
1873 : pari_sp av;
1874 122920241 : long ly = lgefint(y);
1875 122920241 : if (ly == 2) return x;
1876 98460711 : av = avma;
1877 98460711 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1878 98460711 : y = mului(u,y);
1879 98460711 : set_avma(av); return subii(x, y);
1880 : }
1881 : /* x + u*y */
1882 : INLINE GEN
1883 121400177 : addmuliu_inplace(GEN x, GEN y, ulong u)
1884 : {
1885 : pari_sp av;
1886 121400177 : long ly = lgefint(y);
1887 121400177 : if (ly == 2) return x;
1888 98345046 : av = avma;
1889 98345046 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1890 98345046 : y = mului(u,y);
1891 98345046 : set_avma(av); return addii(x, y);
1892 : }
1893 : /* ux + vy */
1894 : INLINE GEN
1895 20674200 : lincombii(GEN u, GEN v, GEN x, GEN y)
1896 : {
1897 20674200 : long lx = lgefint(x), ly;
1898 : GEN p1, p2;
1899 : pari_sp av;
1900 20674200 : if (lx == 2) return mulii(v,y);
1901 14585905 : ly = lgefint(y);
1902 14585905 : if (ly == 2) return mulii(u,x);
1903 13360667 : av = avma; (void)new_chunk(lx+ly+lgefint(u)+lgefint(v)); /* HACK */
1904 13360669 : p1 = mulii(u,x);
1905 13360571 : p2 = mulii(v,y);
1906 13360564 : set_avma(av); return addii(p1,p2);
1907 : }
1908 :
1909 : /*******************************************************************/
1910 : /* */
1911 : /* GEN SUBTYPES */
1912 : /* */
1913 : /*******************************************************************/
1914 :
1915 : INLINE int
1916 1254970307 : is_const_t(long t) { return (t < t_POLMOD); }
1917 : INLINE int
1918 5437 : is_extscalar_t(long t) { return (t <= t_POL); }
1919 : INLINE int
1920 1224255 : is_intreal_t(long t) { return (t <= t_REAL); }
1921 : INLINE int
1922 423245398 : is_matvec_t(long t) { return (t >= t_VEC && t <= t_MAT); }
1923 : INLINE int
1924 60302785 : is_noncalc_t(long tx) { return (tx) >= t_LIST; }
1925 : INLINE int
1926 1206174 : is_rational_t(long t) { return (t == t_INT || t == t_FRAC); }
1927 : INLINE int
1928 504331 : is_real_t(long t) { return (t == t_INT || t == t_REAL || t == t_FRAC); }
1929 : INLINE int
1930 3056939267 : is_recursive_t(long t) { return lontyp[t]; }
1931 : INLINE int
1932 197150484 : is_scalar_t(long t) { return (t < t_POL); }
1933 : INLINE int
1934 1499382 : is_vec_t(long t) { return (t == t_VEC || t == t_COL); }
1935 :
1936 : /*******************************************************************/
1937 : /* */
1938 : /* TRANSCENDENTAL */
1939 : /* */
1940 : /*******************************************************************/
1941 : INLINE GEN
1942 22376861 : sqrtr(GEN x) {
1943 22376861 : long s = signe(x);
1944 22376861 : if (s == 0) return real_0_bit(expo(x) >> 1);
1945 22343194 : if (s >= 0) return sqrtr_abs(x);
1946 34597 : retmkcomplex(gen_0, sqrtr_abs(x));
1947 : }
1948 : INLINE GEN
1949 0 : cbrtr_abs(GEN x) { return sqrtnr_abs(x, 3); }
1950 : INLINE GEN
1951 0 : cbrtr(GEN x) {
1952 0 : long s = signe(x);
1953 : GEN r;
1954 0 : if (s == 0) return real_0_bit(expo(x) / 3);
1955 0 : r = cbrtr_abs(x);
1956 0 : if (s < 0) togglesign(r);
1957 0 : return r;
1958 : }
1959 : INLINE GEN
1960 462351 : sqrtnr(GEN x, long n) {
1961 462351 : long s = signe(x);
1962 : GEN r;
1963 462351 : if (s == 0) return real_0_bit(expo(x) / n);
1964 462351 : r = sqrtnr_abs(x, n);
1965 462351 : if (s < 0) pari_err_IMPL("sqrtnr for x < 0");
1966 462351 : return r;
1967 : }
1968 : INLINE long
1969 221034 : logint(GEN B, GEN y) { return logintall(B,y,NULL); }
1970 : INLINE ulong
1971 1997441 : ulogint(ulong B, ulong y)
1972 : {
1973 : ulong r;
1974 : long e;
1975 1997441 : if (y == 2) return expu(B);
1976 1979339 : r = y;
1977 6389368 : for (e=1;; e++)
1978 : { /* here, r = y^e, r2 = y^(e-1) */
1979 10799397 : if (r >= B) return r == B? e: e-1;
1980 4410036 : r = umuluu_or_0(y, r);
1981 4410029 : if (!r) return e;
1982 : }
1983 : }
1984 :
1985 : /*******************************************************************/
1986 : /* */
1987 : /* MISCELLANEOUS */
1988 : /* */
1989 : /*******************************************************************/
1990 1224178 : INLINE int ismpzero(GEN x) { return is_intreal_t(typ(x)) && !signe(x); }
1991 657604590 : INLINE int isintzero(GEN x) { return typ(x) == t_INT && !signe(x); }
1992 9112743 : INLINE int isint1(GEN x) { return typ(x)==t_INT && equali1(x); }
1993 4641 : INLINE int isintm1(GEN x){ return typ(x)==t_INT && equalim1(x);}
1994 713498396 : INLINE int equali1(GEN n)
1995 713498396 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(1)) && n[2] == 1; }
1996 61421475 : INLINE int equalim1(GEN n)
1997 61421475 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(-1)) && n[2] == 1; }
1998 : /* works only for POSITIVE integers */
1999 970439222 : INLINE int is_pm1(GEN n)
2000 970439222 : { return lgefint(n) == 3 && n[2] == 1; }
2001 241615551 : INLINE int is_bigint(GEN n)
2002 241615551 : { long l = lgefint(n); return l > 3 || (l == 3 && (n[2] & HIGHBIT)); }
2003 :
2004 2069730321 : INLINE int odd(long x) { return x & 1; }
2005 28858171 : INLINE int both_odd(long x, long y) { return x & y & 1; }
2006 :
2007 : INLINE int
2008 2768396167 : isonstack(GEN x)
2009 2768396167 : { return ((pari_sp)x >= pari_mainstack->bot
2010 2768396167 : && (pari_sp)x < pari_mainstack->top); }
2011 :
2012 : /* assume x != 0 and x t_REAL, return an approximation to log2(|x|) */
2013 : INLINE double
2014 23270947 : dbllog2r(GEN x)
2015 23270947 : { return log2((double)(ulong)x[2]) + (double)(expo(x) - (BITS_IN_LONG-1)); }
2016 :
2017 : INLINE GEN
2018 362897 : mul_content(GEN cx, GEN cy)
2019 : {
2020 362897 : if (!cx) return cy;
2021 132999 : if (!cy) return cx;
2022 91485 : return gmul(cx,cy);
2023 : }
2024 : INLINE GEN
2025 6034 : inv_content(GEN c) { return c? ginv(c): NULL; }
2026 : INLINE GEN
2027 1627337 : mul_denom(GEN dx, GEN dy)
2028 : {
2029 1627337 : if (!dx) return dy;
2030 1074042 : if (!dy) return dx;
2031 338492 : return mulii(dx,dy);
2032 : }
2033 :
2034 : /* POLYNOMIALS */
2035 : INLINE GEN
2036 17947377 : constant_coeff(GEN x) { return signe(x)? gel(x,2): gen_0; }
2037 : INLINE GEN
2038 81760353 : leading_coeff(GEN x) { return lg(x) == 2? gen_0: gel(x,lg(x)-1); }
2039 : INLINE ulong
2040 479520 : Flx_lead(GEN x) { return lg(x) == 2? 0: x[lg(x)-1]; }
2041 : INLINE ulong
2042 12298 : Flx_constant(GEN x) { return lg(x) == 2? 0: x[2]; }
2043 : INLINE long
2044 2805402346 : degpol(GEN x) { return lg(x)-3; }
2045 : INLINE long
2046 1388440996 : lgpol(GEN x) { return lg(x)-2; }
2047 : INLINE long
2048 122833823 : lgcols(GEN x) { return lg(gel(x,1)); }
2049 : INLINE long
2050 34540447 : nbrows(GEN x) { return lg(gel(x,1))-1; }
2051 : INLINE GEN
2052 0 : truecoef(GEN x, long n) { return polcoef(x,n,-1); }
2053 :
2054 : INLINE GEN
2055 557581 : ZXQ_mul(GEN y, GEN x, GEN T) { return ZX_rem(ZX_mul(y, x), T); }
2056 : INLINE GEN
2057 281752 : ZXQ_sqr(GEN x, GEN T) { return ZX_rem(ZX_sqr(x), T); }
2058 :
2059 : INLINE GEN
2060 81498010 : RgX_copy(GEN x)
2061 : {
2062 : long lx, i;
2063 81498010 : GEN y = cgetg_copy(x, &lx); y[1] = x[1];
2064 81498008 : for (i = 2; i<lx; i++) gel(y,i) = gcopy(gel(x,i));
2065 81498015 : return y;
2066 : }
2067 : /* have to use ulong to avoid silly warnings from gcc "assuming signed
2068 : * overflow does not occur" */
2069 : INLINE GEN
2070 2961743 : RgX_coeff(GEN x, long n)
2071 : {
2072 2961743 : ulong l = lg(x);
2073 2961743 : return (n < 0 || ((ulong)n+3) > l)? gen_0: gel(x,n+2);
2074 : }
2075 : INLINE GEN
2076 368654 : RgX_renormalize(GEN x) { return RgX_renormalize_lg(x, lg(x)); }
2077 : INLINE GEN
2078 6743898 : RgX_div(GEN x, GEN y) { return RgX_divrem(x,y,NULL); }
2079 : INLINE GEN
2080 1792 : RgXQX_div(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,NULL); }
2081 : INLINE GEN
2082 67619 : RgXQX_rem(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,ONLY_REM); }
2083 : INLINE GEN
2084 947693 : FpX_div(GEN x, GEN y, GEN p) { return FpX_divrem(x,y,p, NULL); }
2085 : INLINE GEN
2086 4486842 : Flx_div(GEN x, GEN y, ulong p) { return Flx_divrem(x,y,p, NULL); }
2087 : INLINE GEN
2088 2608052 : F2x_div(GEN x, GEN y) { return F2x_divrem(x,y, NULL); }
2089 : INLINE GEN
2090 0 : FpV_FpC_mul(GEN x, GEN y, GEN p) { return FpV_dotproduct(x,y,p); }
2091 : INLINE GEN
2092 48498087 : pol0_Flx(long sv) { return mkvecsmall(sv); }
2093 : INLINE GEN
2094 15094564 : pol1_Flx(long sv) { return mkvecsmall2(sv, 1); }
2095 : INLINE GEN
2096 17831321 : polx_Flx(long sv) { return mkvecsmall3(sv, 0, 1); }
2097 : INLINE GEN
2098 0 : zero_zx(long sv) { return zero_Flx(sv); }
2099 : INLINE GEN
2100 0 : polx_zx(long sv) { return polx_Flx(sv); }
2101 : INLINE GEN
2102 0 : zx_shift(GEN x, long n) { return Flx_shift(x,n); }
2103 : INLINE GEN
2104 0 : zx_renormalize(GEN x, long l) { return Flx_renormalize(x,l); }
2105 : INLINE GEN
2106 1474 : zero_F2x(long sv) { return zero_Flx(sv); }
2107 : INLINE GEN
2108 11169563 : pol0_F2x(long sv) { return pol0_Flx(sv); }
2109 : INLINE GEN
2110 2874681 : pol1_F2x(long sv) { return pol1_Flx(sv); }
2111 : INLINE GEN
2112 687301 : polx_F2x(long sv) { return mkvecsmall2(sv, 2); }
2113 : INLINE int
2114 826227 : F2x_equal1(GEN x) { return Flx_equal1(x); }
2115 : INLINE int
2116 3135431 : F2x_equal(GEN V, GEN W) { return Flx_equal(V,W); }
2117 : INLINE GEN
2118 59355348 : F2x_copy(GEN x) { return leafcopy(x); }
2119 : INLINE GEN
2120 0 : F2v_copy(GEN x) { return leafcopy(x); }
2121 : INLINE GEN
2122 2274954 : Flv_copy(GEN x) { return leafcopy(x); }
2123 : INLINE GEN
2124 74530475 : Flx_copy(GEN x) { return leafcopy(x); }
2125 : INLINE GEN
2126 1871354 : vecsmall_copy(GEN x) { return leafcopy(x); }
2127 : INLINE int
2128 4887966 : Flx_equal1(GEN x) { return degpol(x)==0 && x[2] == 1; }
2129 : INLINE int
2130 18205 : ZX_equal1(GEN x) { return degpol(x)==0 && equali1(gel(x,2)); }
2131 : INLINE int
2132 5435578 : ZX_is_monic(GEN x) { return equali1(leading_coeff(x)); }
2133 :
2134 : INLINE GEN
2135 51035752 : ZX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2136 : INLINE GEN
2137 67479958 : FpX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2138 : INLINE GEN
2139 771564 : FpXX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2140 : INLINE GEN
2141 1249023 : FpXQX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2142 : INLINE GEN
2143 111654665 : F2x_renormalize(GEN x, long lx) { return Flx_renormalize(x,lx); }
2144 : INLINE GEN
2145 32321 : F2v_to_F2x(GEN x, long sv) {
2146 32321 : GEN y = leafcopy(x);
2147 32321 : y[1] = sv; F2x_renormalize(y, lg(y)); return y;
2148 : }
2149 :
2150 : INLINE long
2151 0 : sturm(GEN x) { return sturmpart(x, NULL, NULL); }
2152 :
2153 : INLINE long
2154 7042 : gval(GEN x, long v) {
2155 7042 : pari_sp av = avma;
2156 7042 : long n = gvaluation(x, pol_x(v));
2157 7042 : set_avma(av); return n;
2158 : }
2159 :
2160 : INLINE void
2161 470874 : RgX_shift_inplace_init(long v)
2162 470874 : { if (v) (void)cgetg(v, t_VECSMALL); }
2163 : /* shift polynomial in place. assume v free cells have been left before x */
2164 : INLINE GEN
2165 470874 : RgX_shift_inplace(GEN x, long v)
2166 : {
2167 : long i, lx;
2168 : GEN y, z;
2169 470874 : if (!v) return x;
2170 253227 : lx = lg(x);
2171 253227 : if (lx == 2) return x;
2172 253227 : y = x + v;
2173 253227 : z = x + lx;
2174 : /* stackdummy from normalizepol: move it up */
2175 253227 : if (lg(z) != v) x[lx + v] = z[0];
2176 253227 : for (i = lx-1; i >= 2; i--) gel(y,i) = gel(x,i);
2177 253227 : for (i = v+1; i >= 2; i--) gel(x,i) = gen_0;
2178 : /* leave x[1] alone: it is correct */
2179 253227 : x[0] = evaltyp(t_POL) | evallg(lx+v); return x;
2180 : }
2181 :
2182 :
2183 : /* LINEAR ALGEBRA */
2184 : INLINE GEN
2185 131966 : zv_to_ZV(GEN x) { return vecsmall_to_vec(x); }
2186 : INLINE GEN
2187 5208100 : zc_to_ZC(GEN x) { return vecsmall_to_col(x); }
2188 : INLINE GEN
2189 3343009 : ZV_to_zv(GEN x) { return vec_to_vecsmall(x); }
2190 : INLINE GEN
2191 0 : zx_to_zv(GEN x, long N) { return Flx_to_Flv(x,N); }
2192 : INLINE GEN
2193 0 : zv_to_zx(GEN x, long sv) { return Flv_to_Flx(x,sv); }
2194 : INLINE GEN
2195 0 : zm_to_zxV(GEN x, long sv) { return Flm_to_FlxV(x,sv); }
2196 : INLINE GEN
2197 0 : zero_zm(long x, long y) { return zero_Flm(x,y); }
2198 : INLINE GEN
2199 17404991 : zero_zv(long x) { return zero_Flv(x); }
2200 : INLINE GEN
2201 210 : zm_transpose(GEN x) { return Flm_transpose(x); }
2202 : INLINE GEN
2203 0 : zm_copy(GEN x) { return Flm_copy(x); }
2204 : INLINE GEN
2205 1903177 : zv_copy(GEN x) { return Flv_copy(x); }
2206 : INLINE GEN
2207 0 : zm_row(GEN x, long i) { return Flm_row(x,i); }
2208 :
2209 : INLINE GEN
2210 901843 : ZC_hnfrem(GEN x, GEN y) { return ZC_hnfremdiv(x,y,NULL); }
2211 : INLINE GEN
2212 48866 : ZM_hnfrem(GEN x, GEN y) { return ZM_hnfdivrem(x,y,NULL); }
2213 : INLINE GEN
2214 2438929 : ZM_lll(GEN x, double D, long f) { return ZM_lll_norms(x,D,f,NULL); }
2215 : INLINE void
2216 5673623 : RgM_dimensions(GEN x, long *m, long *n) { *n = lg(x)-1; *m = *n? nbrows(x): 0; }
2217 : INLINE GEN
2218 10336894 : RgM_shallowcopy(GEN x)
2219 : {
2220 : long l;
2221 10336894 : GEN y = cgetg_copy(x, &l);
2222 10336907 : while (--l > 0) gel(y,l) = leafcopy(gel(x,l));
2223 10336908 : return y;
2224 : }
2225 : INLINE GEN
2226 303 : F2m_copy(GEN x) { return RgM_shallowcopy(x); }
2227 :
2228 : INLINE GEN
2229 1375002 : Flm_copy(GEN x) { return RgM_shallowcopy(x); }
2230 :
2231 : /* divisibility: return 1 if y[i] | x[i] for all i, 0 otherwise. Assume
2232 : * x,y are ZV of the same length */
2233 : INLINE int
2234 23198 : ZV_dvd(GEN x, GEN y)
2235 : {
2236 23198 : long i, l = lg(x);
2237 36652 : for (i=1; i < l; i++)
2238 29519 : if ( ! dvdii( gel(x,i), gel(y,i) ) ) return 0;
2239 7133 : return 1;
2240 : }
2241 :
2242 : /* Fq */
2243 : INLINE GEN
2244 2802247 : Fq_red(GEN x, GEN T, GEN p)
2245 2802247 : { return typ(x)==t_INT? Fp_red(x,p): FpXQ_red(x,T,p); }
2246 : INLINE GEN
2247 43439 : Fq_to_FpXQ(GEN x, GEN T, GEN p /*unused*/)
2248 : {
2249 : (void) p;
2250 43439 : return typ(x)==t_INT ? scalarpol(x, get_FpX_var(T)): x;
2251 : }
2252 : INLINE GEN
2253 756 : Rg_to_Fq(GEN x, GEN T, GEN p) { return T? Rg_to_FpXQ(x,T,p): Rg_to_Fp(x,p); }
2254 :
2255 : INLINE GEN
2256 1253 : gener_Fq_local(GEN T, GEN p, GEN L)
2257 : { return T? gener_FpXQ_local(T,p, L)
2258 1253 : : pgener_Fp_local(p, L); }
2259 :
2260 : /* FpXQX */
2261 : INLINE GEN
2262 4347 : FpXQX_div(GEN x, GEN y, GEN T, GEN p) { return FpXQX_divrem(x, y, T, p, NULL); }
2263 : INLINE GEN
2264 35055 : FlxqX_div(GEN x, GEN y, GEN T, ulong p) { return FlxqX_divrem(x, y, T, p, NULL); }
2265 : INLINE GEN
2266 33278 : F2xqX_div(GEN x, GEN y, GEN T) { return F2xqX_divrem(x, y, T, NULL); }
2267 :
2268 : /* FqX */
2269 : INLINE GEN
2270 25431 : FqX_red(GEN z, GEN T, GEN p) { return T? FpXQX_red(z, T, p): FpX_red(z, p); }
2271 : INLINE GEN
2272 957187 : FqX_add(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2273 : INLINE GEN
2274 17404 : FqX_neg(GEN x,GEN T,GEN p) { return T? FpXX_neg(x,p): FpX_neg(x,p); }
2275 : INLINE GEN
2276 3234 : FqX_sub(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2277 : INLINE GEN
2278 657480 : FqX_Fp_mul(GEN P, GEN u, GEN T, GEN p)
2279 657480 : { return T? FpXX_Fp_mul(P, u, p): FpX_Fp_mul(P, u, p); }
2280 : INLINE GEN
2281 588211 : FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
2282 588211 : { return typ(U)==t_INT ? FqX_Fp_mul(P, U, T, p): FpXQX_FpXQ_mul(P, U, T, p); }
2283 : INLINE GEN
2284 96748 : FqX_mul(GEN x, GEN y, GEN T, GEN p)
2285 96748 : { return T? FpXQX_mul(x, y, T, p): FpX_mul(x, y, p); }
2286 : INLINE GEN
2287 489744 : FqX_mulu(GEN x, ulong y, GEN T, GEN p)
2288 489744 : { return T? FpXX_mulu(x, y, p): FpX_mulu(x, y, p); }
2289 : INLINE GEN
2290 6468 : FqX_sqr(GEN x, GEN T, GEN p)
2291 6468 : { return T? FpXQX_sqr(x, T, p): FpX_sqr(x, p); }
2292 : INLINE GEN
2293 1288 : FqX_powu(GEN x, ulong n, GEN T, GEN p)
2294 1288 : { return T? FpXQX_powu(x, n, T, p): FpX_powu(x, n, p); }
2295 : INLINE GEN
2296 0 : FqX_halve(GEN x, GEN T, GEN p)
2297 0 : { return T? FpXX_halve(x, p): FpX_halve(x, p); }
2298 : INLINE GEN
2299 5586 : FqX_div(GEN x, GEN y, GEN T, GEN p)
2300 5586 : { return T? FpXQX_divrem(x,y,T,p,NULL): FpX_divrem(x,y,p,NULL); }
2301 : INLINE GEN
2302 6095 : FqX_get_red(GEN S, GEN T, GEN p)
2303 6095 : { return T? FpXQX_get_red(S,T,p): FpX_get_red(S,p); }
2304 : INLINE GEN
2305 53108 : FqX_rem(GEN x, GEN y, GEN T, GEN p)
2306 53108 : { return T? FpXQX_rem(x,y,T,p): FpX_rem(x,y,p); }
2307 : INLINE GEN
2308 0 : FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
2309 0 : { return T? FpXQX_divrem(x,y,T,p,z): FpX_divrem(x,y,p,z); }
2310 : INLINE GEN
2311 5936 : FqX_div_by_X_x(GEN x, GEN y, GEN T, GEN p, GEN *z)
2312 5936 : { return T? FpXQX_div_by_X_x(x,y,T,p,z): FpX_div_by_X_x(x,y,p,z); }
2313 : INLINE GEN
2314 0 : FqX_halfgcd(GEN P,GEN Q,GEN T,GEN p)
2315 0 : {return T? FpXQX_halfgcd(P,Q,T,p): FpX_halfgcd(P,Q,p);}
2316 : INLINE GEN
2317 259224 : FqX_gcd(GEN P,GEN Q,GEN T,GEN p)
2318 259224 : {return T? FpXQX_gcd(P,Q,T,p): FpX_gcd(P,Q,p);}
2319 : INLINE GEN
2320 88128 : FqX_extgcd(GEN P,GEN Q,GEN T,GEN p, GEN *U, GEN *V)
2321 88128 : { return T? FpXQX_extgcd(P,Q,T,p,U,V): FpX_extgcd(P,Q,p,U,V); }
2322 : INLINE GEN
2323 3241 : FqX_normalize(GEN z, GEN T, GEN p)
2324 3241 : { return T? FpXQX_normalize(z, T, p): FpX_normalize(z, p); }
2325 : INLINE GEN
2326 272895 : FqX_deriv(GEN f, GEN T, GEN p) { return T? FpXX_deriv(f, p): FpX_deriv(f, p); }
2327 : INLINE GEN
2328 0 : FqX_integ(GEN f, GEN T, GEN p) { return T? FpXX_integ(f, p): FpX_integ(f, p); }
2329 : INLINE GEN
2330 74536 : FqX_factor(GEN f, GEN T, GEN p)
2331 74536 : { return T?FpXQX_factor(f, T, p): FpX_factor(f, p); }
2332 : INLINE GEN
2333 7 : FqX_factor_squarefree(GEN f, GEN T, GEN p)
2334 7 : { return T ? FpXQX_factor_squarefree(f, T, p): FpX_factor_squarefree(f, p); }
2335 : INLINE GEN
2336 7 : FqX_ddf(GEN f, GEN T, GEN p)
2337 7 : { return T ? FpXQX_ddf(f, T, p): FpX_ddf(f, p); }
2338 : INLINE GEN
2339 42 : FqX_degfact(GEN f, GEN T, GEN p)
2340 42 : { return T?FpXQX_degfact(f, T, p): FpX_degfact(f, p); }
2341 : INLINE GEN
2342 7126 : FqX_roots(GEN f, GEN T, GEN p)
2343 7126 : { return T?FpXQX_roots(f, T, p): FpX_roots(f, p); }
2344 : INLINE GEN
2345 203 : FqX_to_mod(GEN f, GEN T, GEN p)
2346 203 : { return T?FpXQX_to_mod(f, T, p): FpX_to_mod(f, p); }
2347 :
2348 : /*FqXQ*/
2349 : INLINE GEN
2350 0 : FqXQ_add(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2351 0 : { (void)S; return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2352 : INLINE GEN
2353 0 : FqXQ_sub(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2354 0 : { (void)S; return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2355 : INLINE GEN
2356 0 : FqXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
2357 0 : { return T? FpXQXQ_div(x,y,S,T,p): FpXQ_div(x,y,S,p); }
2358 : INLINE GEN
2359 0 : FqXQ_inv(GEN x, GEN S, GEN T, GEN p)
2360 0 : { return T? FpXQXQ_inv(x,S,T,p): FpXQ_inv(x,S,p); }
2361 : INLINE GEN
2362 0 : FqXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
2363 0 : { return T? FpXQXQ_invsafe(x,S,T,p): FpXQ_inv(x,S,p); }
2364 : INLINE GEN
2365 22348 : FqXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
2366 22348 : { return T? FpXQXQ_mul(x,y,S,T,p): FpXQ_mul(x,y,S,p); }
2367 : INLINE GEN
2368 0 : FqXQ_sqr(GEN x, GEN S, GEN T, GEN p)
2369 0 : { return T? FpXQXQ_sqr(x,S,T,p): FpXQ_sqr(x,S,p); }
2370 : INLINE GEN
2371 0 : FqXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
2372 0 : { return T? FpXQXQ_pow(x,n,S,T,p): FpXQ_pow(x,n,S,p); }
2373 :
2374 : /*FqXn*/
2375 : INLINE GEN
2376 0 : FqXn_exp(GEN x, long n, GEN T, GEN p)
2377 0 : { return T? FpXQXn_exp(x,n,T,p): FpXn_exp(x,n,p); }
2378 : INLINE GEN
2379 0 : FqXn_inv(GEN x, long n, GEN T, GEN p)
2380 0 : { return T? FpXQXn_inv(x,n,T,p): FpXn_inv(x,n,p); }
2381 : INLINE GEN
2382 0 : FqXn_mul(GEN x, GEN y, long n, GEN T, GEN p)
2383 0 : { return T? FpXQXn_mul(x, y, n, T, p): FpXn_mul(x, y, n, p); }
2384 : INLINE GEN
2385 0 : FqXn_sqr(GEN x, long n, GEN T, GEN p)
2386 0 : { return T? FpXQXn_sqr(x,n,T,p): FpXn_sqr(x,n,p); }
2387 :
2388 : /*FpXQ*/
2389 : INLINE GEN
2390 0 : FpXQ_add(GEN x,GEN y,GEN T/*unused*/,GEN p)
2391 0 : { (void)T; return FpX_add(x,y,p); }
2392 : INLINE GEN
2393 0 : FpXQ_sub(GEN x,GEN y,GEN T/*unused*/,GEN p)
2394 0 : { (void)T; return FpX_sub(x,y,p); }
2395 :
2396 : /*Flxq*/
2397 : INLINE GEN
2398 0 : Flxq_add(GEN x,GEN y,GEN T/*unused*/,ulong p)
2399 0 : { (void)T; return Flx_add(x,y,p); }
2400 : INLINE GEN
2401 0 : Flxq_sub(GEN x,GEN y,GEN T/*unused*/,ulong p)
2402 0 : { (void)T; return Flx_sub(x,y,p); }
2403 :
2404 : /* F2x */
2405 :
2406 : INLINE ulong
2407 100485311 : F2x_coeff(GEN x,long v)
2408 : {
2409 100485311 : ulong u=(ulong)x[2+divsBIL(v)];
2410 100484838 : return (u>>remsBIL(v))&1UL;
2411 : }
2412 :
2413 : INLINE void
2414 4728488 : F2x_clear(GEN x,long v)
2415 : {
2416 4728488 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2417 4728488 : *u&=~(1UL<<remsBIL(v));
2418 4728487 : }
2419 :
2420 : INLINE void
2421 32741169 : F2x_set(GEN x,long v)
2422 : {
2423 32741169 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2424 32720655 : *u|=1UL<<remsBIL(v);
2425 32710513 : }
2426 :
2427 : INLINE void
2428 1501777 : F2x_flip(GEN x,long v)
2429 : {
2430 1501777 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2431 1501777 : *u^=1UL<<remsBIL(v);
2432 1501777 : }
2433 :
2434 : /* F2v */
2435 :
2436 : INLINE ulong
2437 95954011 : F2v_coeff(GEN x,long v) { return F2x_coeff(x,v-1); }
2438 :
2439 : INLINE void
2440 4728488 : F2v_clear(GEN x,long v) { F2x_clear(x,v-1); }
2441 :
2442 : INLINE void
2443 8964070 : F2v_set(GEN x,long v) { F2x_set(x,v-1); }
2444 :
2445 : INLINE void
2446 1501777 : F2v_flip(GEN x,long v) { F2x_flip(x,v-1); }
2447 :
2448 : /* F2m */
2449 :
2450 : INLINE ulong
2451 11672001 : F2m_coeff(GEN x, long a, long b) { return F2v_coeff(gel(x,b), a); }
2452 :
2453 : INLINE void
2454 0 : F2m_clear(GEN x, long a, long b) { F2v_clear(gel(x,b), a); }
2455 :
2456 : INLINE void
2457 1362615 : F2m_set(GEN x, long a, long b) { F2v_set(gel(x,b), a); }
2458 :
2459 : INLINE void
2460 1501777 : F2m_flip(GEN x, long a, long b) { F2v_flip(gel(x,b), a); }
2461 :
2462 : /* ARITHMETIC */
2463 : INLINE GEN
2464 1071 : matpascal(long n) { return matqpascal(n, NULL); }
2465 : INLINE long
2466 2334531 : Z_issquare(GEN x) { return Z_issquareall(x, NULL); }
2467 : INLINE long
2468 14 : Z_ispower(GEN x, ulong k) { return Z_ispowerall(x, k, NULL); }
2469 : INLINE GEN
2470 5868317 : sqrti(GEN x) { return sqrtremi(x,NULL); }
2471 : INLINE GEN
2472 6168550 : gaddgs(GEN y, long s) { return gaddsg(s,y); }
2473 : INLINE int
2474 48712 : gcmpgs(GEN y, long s) { return -gcmpsg(s,y); }
2475 : INLINE int
2476 24570 : gequalgs(GEN y, long s) { return gequalsg(s,y); }
2477 : INLINE GEN
2478 0 : gmaxsg(long s, GEN y) { return gmaxgs(y,s); }
2479 : INLINE GEN
2480 0 : gminsg(long s, GEN y) { return gmings(y,s); }
2481 : INLINE GEN
2482 15177317 : gmulgs(GEN y, long s) { return gmulsg(s,y); }
2483 : INLINE GEN
2484 1354063 : gsubgs(GEN y, long s) { return gaddgs(y, -s); }
2485 : INLINE GEN
2486 682458 : gdivsg(long s, GEN y) { return gdiv(stoi(s), y); }
2487 :
2488 : /* x t_COMPLEX */
2489 : INLINE GEN
2490 12986450 : cxnorm(GEN x) { return gadd(gsqr(gel(x,1)), gsqr(gel(x,2))); }
2491 : /* q t_QUAD */
2492 : INLINE GEN
2493 623 : quadnorm(GEN q)
2494 : {
2495 623 : GEN X = gel(q,1), b = gel(X,3), c = gel(X,2);
2496 623 : GEN z, u = gel(q,3), v = gel(q,2);
2497 623 : if (typ(u) == t_INT && typ(v) == t_INT) /* generic case */
2498 : {
2499 308 : z = signe(b)? mulii(v, addii(u,v)): sqri(v);
2500 308 : return addii(z, mulii(c, sqri(u)));
2501 : }
2502 : else
2503 : {
2504 315 : z = signe(b)? gmul(v, gadd(u,v)): gsqr(v);
2505 315 : return gadd(z, gmul(c, gsqr(u)));
2506 : }
2507 : }
2508 : /* x a t_QUAD, return the attached discriminant */
2509 : INLINE GEN
2510 273 : quad_disc(GEN x)
2511 : {
2512 273 : GEN Q = gel(x,1), b = gel(Q,3), c = gel(Q,2), c4;
2513 273 : if (is_pm1(b))
2514 : {
2515 217 : pari_sp av = avma; (void)new_chunk(lgefint(c) + 1);
2516 217 : c4 = shifti(c,2); set_avma(av); return subsi(1, c4);
2517 : }
2518 56 : c4 = shifti(c,2); togglesign_safe(&c4); return c4;
2519 : }
2520 : INLINE GEN
2521 6386709 : qfb_disc3(GEN x, GEN y, GEN z) { return subii(sqri(y), shifti(mulii(x,z),2)); }
2522 : INLINE GEN
2523 6305775 : qfb_disc(GEN x) { return qfb_disc3(gel(x,1), gel(x,2), gel(x,3)); }
2524 :
2525 : INLINE GEN
2526 1283958 : sqrfrac(GEN x)
2527 : {
2528 1283958 : GEN z = cgetg(3,t_FRAC);
2529 1283958 : gel(z,1) = sqri(gel(x,1));
2530 1283958 : gel(z,2) = sqri(gel(x,2)); return z;
2531 : }
2532 :
2533 : INLINE void
2534 21509780 : normalize_frac(GEN z) {
2535 21509780 : if (signe(gel(z,2)) < 0) { togglesign(gel(z,1)); setabssign(gel(z,2)); }
2536 21509780 : }
2537 :
2538 : INLINE GEN
2539 265482 : powii(GEN x, GEN n)
2540 : {
2541 265482 : long ln = lgefint(n);
2542 265482 : if (ln == 3) {
2543 : GEN z;
2544 261093 : if (signe(n) > 0) return powiu(x, n[2]);
2545 8078 : z = cgetg(3, t_FRAC);
2546 8078 : gel(z,1) = gen_1;
2547 8078 : gel(z,2) = powiu(x, n[2]);
2548 8078 : return z;
2549 : }
2550 4389 : if (ln == 2) return gen_1; /* rare */
2551 : /* should never happen */
2552 0 : return powgi(x, n); /* overflow unless x = 0, 1, -1 */
2553 : }
2554 : INLINE GEN
2555 1246 : powIs(long n) {
2556 1246 : switch(n & 3)
2557 : {
2558 28 : case 1: return mkcomplex(gen_0,gen_1);
2559 378 : case 2: return gen_m1;
2560 518 : case 3: return mkcomplex(gen_0,gen_m1);
2561 : }
2562 322 : return gen_1;
2563 : }
2564 :
2565 : /*******************************************************************/
2566 : /* */
2567 : /* ASSIGNMENTS */
2568 : /* */
2569 : /*******************************************************************/
2570 0 : INLINE void mpexpz(GEN x, GEN z)
2571 0 : { pari_sp av = avma; gaffect(mpexp(x), z); set_avma(av); }
2572 0 : INLINE void mplogz(GEN x, GEN z)
2573 0 : { pari_sp av = avma; gaffect(mplog(x), z); set_avma(av); }
2574 0 : INLINE void mpcosz(GEN x, GEN z)
2575 0 : { pari_sp av = avma; gaffect(mpcos(x), z); set_avma(av); }
2576 0 : INLINE void mpsinz(GEN x, GEN z)
2577 0 : { pari_sp av = avma; gaffect(mpsin(x), z); set_avma(av); }
2578 0 : INLINE void gnegz(GEN x, GEN z)
2579 0 : { pari_sp av = avma; gaffect(gneg(x), z); set_avma(av); }
2580 0 : INLINE void gabsz(GEN x, long prec, GEN z)
2581 0 : { pari_sp av = avma; gaffect(gabs(x,prec), z); set_avma(av); }
2582 0 : INLINE void gaddz(GEN x, GEN y, GEN z)
2583 0 : { pari_sp av = avma; gaffect(gadd(x,y), z); set_avma(av); }
2584 0 : INLINE void gsubz(GEN x, GEN y, GEN z)
2585 0 : { pari_sp av = avma; gaffect(gsub(x,y), z); set_avma(av); }
2586 0 : INLINE void gmulz(GEN x, GEN y, GEN z)
2587 0 : { pari_sp av = avma; gaffect(gmul(x,y), z); set_avma(av); }
2588 0 : INLINE void gdivz(GEN x, GEN y, GEN z)
2589 0 : { pari_sp av = avma; gaffect(gdiv(x,y), z); set_avma(av); }
2590 0 : INLINE void gdiventz(GEN x, GEN y, GEN z)
2591 0 : { pari_sp av = avma; gaffect(gdivent(x,y), z); set_avma(av); }
2592 0 : INLINE void gmodz(GEN x, GEN y, GEN z)
2593 0 : { pari_sp av = avma; gaffect(gmod(x,y), z); set_avma(av); }
2594 0 : INLINE void gmul2nz(GEN x, long s, GEN z)
2595 0 : { pari_sp av = avma; gaffect(gmul2n(x,s), z); set_avma(av); }
2596 0 : INLINE void gshiftz(GEN x, long s, GEN z)
2597 0 : { pari_sp av = avma; gaffect(gshift(x,s), z); set_avma(av); }
2598 :
2599 : /*******************************************************************/
2600 : /* */
2601 : /* ELLIPTIC CURVES */
2602 : /* */
2603 : /*******************************************************************/
2604 3979743 : INLINE GEN ell_get_a1(GEN e) { return gel(e,1); }
2605 3095790 : INLINE GEN ell_get_a2(GEN e) { return gel(e,2); }
2606 3861697 : INLINE GEN ell_get_a3(GEN e) { return gel(e,3); }
2607 3888736 : INLINE GEN ell_get_a4(GEN e) { return gel(e,4); }
2608 4704915 : INLINE GEN ell_get_a6(GEN e) { return gel(e,5); }
2609 3318531 : INLINE GEN ell_get_b2(GEN e) { return gel(e,6); }
2610 1024949 : INLINE GEN ell_get_b4(GEN e) { return gel(e,7); }
2611 1630617 : INLINE GEN ell_get_b6(GEN e) { return gel(e,8); }
2612 1464001 : INLINE GEN ell_get_b8(GEN e) { return gel(e,9); }
2613 6167072 : INLINE GEN ell_get_c4(GEN e) { return gel(e,10); }
2614 7403595 : INLINE GEN ell_get_c6(GEN e) { return gel(e,11); }
2615 9653761 : INLINE GEN ell_get_disc(GEN e) { return gel(e,12); }
2616 1028909 : INLINE GEN ell_get_j(GEN e) { return gel(e,13); }
2617 11455565 : INLINE long ell_get_type(GEN e) { return mael(e,14,1); }
2618 1570438 : INLINE GEN ellff_get_field(GEN x) { return gmael(x, 15, 1); }
2619 683125 : INLINE GEN ellff_get_a4a6(GEN x) { return gmael(x, 15, 2); }
2620 1407 : INLINE GEN ellQp_get_zero(GEN x) { return gmael(x, 15, 1); }
2621 287 : INLINE long ellQp_get_prec(GEN E) { GEN z = ellQp_get_zero(E); return valp(z); }
2622 1085 : INLINE GEN ellQp_get_p(GEN E) { GEN z = ellQp_get_zero(E); return gel(z,2); }
2623 37156 : INLINE long ellR_get_prec(GEN x) { return nbits2prec(mael3(x, 15, 1, 1)); }
2624 12106 : INLINE long ellR_get_sign(GEN x) { return mael3(x, 15, 1, 2); }
2625 699393 : INLINE GEN ellnf_get_nf(GEN x) { return checknf_i(gmael(x,15,1)); }
2626 56 : INLINE GEN ellnf_get_bnf(GEN x) { return checkbnf_i(gmael(x,15,1)); }
2627 :
2628 4624907 : INLINE int checkell_i(GEN e) { return typ(e) == t_VEC && lg(e) == 17; }
2629 33981036 : INLINE int ell_is_inf(GEN z) { return lg(z) == 2; }
2630 809822 : INLINE GEN ellinf(void) { return mkvec(gen_0); }
2631 :
2632 : /*******************************************************************/
2633 : /* */
2634 : /* ALGEBRAIC NUMBER THEORY */
2635 : /* */
2636 : /*******************************************************************/
2637 8420034 : INLINE GEN modpr_get_pr(GEN x) { return gel(x,3); }
2638 609506 : INLINE GEN modpr_get_p(GEN x) { return pr_get_p(modpr_get_pr(x)); }
2639 2681211 : INLINE GEN modpr_get_T(GEN x) { return lg(x) == 4? NULL: gel(x,4); }
2640 :
2641 20066568 : INLINE GEN pr_get_p(GEN pr) { return gel(pr,1); }
2642 6618028 : INLINE GEN pr_get_gen(GEN pr){ return gel(pr,2); }
2643 : /* .[2] instead of itos works: e and f are small positive integers */
2644 2376598 : INLINE long pr_get_e(GEN pr) { return gel(pr,3)[2]; }
2645 9158781 : INLINE long pr_get_f(GEN pr) { return gel(pr,4)[2]; }
2646 6300022 : INLINE GEN pr_get_tau(GEN pr){ return gel(pr,5); }
2647 : INLINE int
2648 3188919 : pr_is_inert(GEN P) { return pr_get_f(P) == lg(pr_get_gen(P))-1; }
2649 : INLINE GEN
2650 232221 : pr_norm(GEN pr) { return powiu(pr_get_p(pr), pr_get_f(pr)); }
2651 : INLINE ulong
2652 48083 : upr_norm(GEN pr) { return upowuu(pr_get_p(pr)[2], pr_get_f(pr)); }
2653 :
2654 : /* assume nf a genuine nf */
2655 : INLINE long
2656 4675 : nf_get_varn(GEN nf) { return varn(gel(nf,1)); }
2657 : INLINE GEN
2658 31827705 : nf_get_pol(GEN nf) { return gel(nf,1); }
2659 : INLINE long
2660 25311029 : nf_get_degree(GEN nf) { return degpol( nf_get_pol(nf) ); }
2661 : INLINE long
2662 4136913 : nf_get_r1(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,1)); }
2663 : INLINE long
2664 1673 : nf_get_r2(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,2)); }
2665 : INLINE GEN
2666 53137 : nf_get_disc(GEN nf) { return gel(nf,3); }
2667 : INLINE GEN
2668 828822 : nf_get_index(GEN nf) { return gel(nf,4); }
2669 : INLINE GEN
2670 2864897 : nf_get_M(GEN nf) { return gmael(nf,5,1); }
2671 : INLINE GEN
2672 81489 : nf_get_G(GEN nf) { return gmael(nf,5,2); }
2673 : INLINE GEN
2674 408060 : nf_get_roundG(GEN nf) { return gmael(nf,5,3); }
2675 : INLINE GEN
2676 24367 : nf_get_Tr(GEN nf) { return gmael(nf,5,4); }
2677 : INLINE GEN
2678 2324 : nf_get_diff(GEN nf) { return gmael(nf,5,5); }
2679 : INLINE GEN
2680 91 : nf_get_ramified_primes(GEN nf) { return gmael(nf,5,8); }
2681 : INLINE GEN
2682 332826 : nf_get_roots(GEN nf) { return gel(nf,6); }
2683 : INLINE GEN
2684 91 : nf_get_zk(GEN nf)
2685 : {
2686 91 : GEN y = gel(nf,7), D = gel(y, 1);
2687 91 : if (typ(D) == t_POL) D = gel(D, 2);
2688 91 : if (!equali1(D)) y = gdiv(y, D);
2689 91 : return y;
2690 : }
2691 : INLINE GEN
2692 278996 : nf_get_zkprimpart(GEN nf)
2693 : {
2694 278996 : GEN y = gel(nf,7);
2695 : /* test for old format of nf.zk: non normalized */
2696 278996 : if (!equali1(gel(nf,4)) && gequal1(gel(y,1))) y = Q_remove_denom(y,NULL);
2697 278995 : return y;
2698 : }
2699 : INLINE GEN
2700 280150 : nf_get_zkden(GEN nf)
2701 : {
2702 280150 : GEN y = gel(nf,7), D = gel(y,1);
2703 280150 : if (typ(D) == t_POL) D = gel(D,2);
2704 : /* test for old format of nf.zk: non normalized */
2705 280150 : if (!equali1(gel(nf,4)) && equali1(D)) D = Q_denom(y);
2706 280148 : return D;
2707 : }
2708 : INLINE GEN
2709 2486872 : nf_get_invzk(GEN nf) { return gel(nf,8); }
2710 : INLINE void
2711 22843 : nf_get_sign(GEN nf, long *r1, long *r2)
2712 : {
2713 22843 : GEN x = gel(nf,2);
2714 22843 : *r1 = itou(gel(x,1));
2715 22843 : *r2 = itou(gel(x,2));
2716 22843 : }
2717 :
2718 : INLINE GEN
2719 92758 : abgrp_get_no(GEN x) { return gel(x,1); }
2720 : INLINE GEN
2721 2600822 : abgrp_get_cyc(GEN x) { return gel(x,2); }
2722 : INLINE GEN
2723 437924 : abgrp_get_gen(GEN x) { return gel(x,3); }
2724 : INLINE GEN
2725 2315220 : bnf_get_nf(GEN bnf) { return gel(bnf,7); }
2726 : INLINE GEN
2727 896050 : bnf_get_clgp(GEN bnf) { return gmael(bnf,8,1); }
2728 : INLINE GEN
2729 6713 : bnf_get_no(GEN bnf) { return abgrp_get_no(bnf_get_clgp(bnf)); }
2730 : INLINE GEN
2731 498019 : bnf_get_cyc(GEN bnf) { return abgrp_get_cyc(bnf_get_clgp(bnf)); }
2732 : INLINE GEN
2733 390989 : bnf_get_gen(GEN bnf) { return abgrp_get_gen(bnf_get_clgp(bnf)); }
2734 : INLINE GEN
2735 846 : bnf_get_reg(GEN bnf) { return gmael(bnf,8,2); }
2736 : INLINE GEN
2737 502386 : bnf_get_logfu(GEN bnf) { return gel(bnf,3); }
2738 : INLINE GEN
2739 7443 : bnf_get_tuU(GEN bnf) { return gmael3(bnf,8,4,2); }
2740 : INLINE long
2741 40201 : bnf_get_tuN(GEN bnf) { return gmael3(bnf,8,4,1)[2]; }
2742 : INLINE GEN
2743 1778 : bnf_get_fu(GEN bnf) {
2744 1778 : GEN fu = bnf_get_fu_nocheck(bnf);
2745 1778 : if (typ(fu) == t_MAT) pari_err(e_MISC,"missing units in bnf");
2746 1778 : return fu;
2747 : }
2748 : INLINE GEN
2749 8878 : bnf_get_fu_nocheck(GEN bnf) { return gmael(bnf,8,5); }
2750 :
2751 : INLINE GEN
2752 927533 : bnr_get_bnf(GEN bnr) { return gel(bnr,1); }
2753 : INLINE GEN
2754 474711 : bnr_get_bid(GEN bnr) { return gel(bnr,2); }
2755 : INLINE GEN
2756 18648 : bnr_get_mod(GEN bnr) { return gmael(bnr,2,1); }
2757 : INLINE GEN
2758 32557 : bnr_get_nf(GEN bnr) { return gmael(bnr,1,7); }
2759 : INLINE GEN
2760 716428 : bnr_get_clgp(GEN bnr) { return gel(bnr,5); }
2761 : INLINE GEN
2762 82278 : bnr_get_no(GEN bnr) { return abgrp_get_no(bnr_get_clgp(bnr)); }
2763 : INLINE GEN
2764 618106 : bnr_get_cyc(GEN bnr) { return abgrp_get_cyc(bnr_get_clgp(bnr)); }
2765 : INLINE GEN
2766 70 : bnr_get_gen_nocheck(GEN bnr) { return abgrp_get_gen(bnr_get_clgp(bnr)); }
2767 : INLINE GEN
2768 14931 : bnr_get_gen(GEN bnr) {
2769 14931 : GEN G = bnr_get_clgp(bnr);
2770 14931 : if (lg(G) != 4)
2771 0 : pari_err(e_MISC,"missing bnr generators: please use bnrinit(,,1)");
2772 14931 : return gel(G,3);
2773 : }
2774 :
2775 : INLINE GEN
2776 361227 : bid_get_mod(GEN bid) { return gel(bid,1); }
2777 : INLINE GEN
2778 65947 : bid_get_ideal(GEN bid) { return gmael(bid,1,1); }
2779 : INLINE GEN
2780 707 : bid_get_arch(GEN bid) { return gmael(bid,1,2); }
2781 : INLINE GEN
2782 1330683 : bid_get_grp(GEN bid) { return gel(bid,2); }
2783 : INLINE GEN
2784 528282 : bid_get_fact(GEN bid) { return gmael(bid,3,1); }
2785 : INLINE GEN
2786 458373 : bid_get_fact2(GEN bid) { return gmael(bid,3,2); }
2787 : INLINE GEN
2788 458184 : bid_get_sprk(GEN bid) { return gmael(bid,4,1); }
2789 : INLINE GEN
2790 49203 : bid_get_sarch(GEN bid) { return gmael(bid,4,2); }
2791 : INLINE GEN
2792 493975 : bid_get_archp(GEN bid) { return gmael3(bid,4,2,2); }
2793 : INLINE GEN
2794 819621 : bid_get_U(GEN bid) { return gel(bid,5); }
2795 : INLINE GEN
2796 0 : bid_get_no(GEN bid) { return abgrp_get_no(bid_get_grp(bid)); }
2797 : INLINE GEN
2798 1284742 : bid_get_cyc(GEN bid) { return abgrp_get_cyc(bid_get_grp(bid)); }
2799 : INLINE GEN
2800 0 : bid_get_gen_nocheck(GEN bid) { return abgrp_get_gen(bid_get_grp(bid)); }
2801 : INLINE GEN
2802 45346 : bid_get_gen(GEN bid) {
2803 45346 : GEN G = bid_get_grp(bid);
2804 45346 : if (lg(G) != 4) pari_err(e_MISC,"missing bid generators. Use idealstar(,,2)");
2805 45346 : return abgrp_get_gen(G);
2806 : }
2807 :
2808 : INLINE GEN
2809 22263563 : znstar_get_N(GEN G) { return gmael(G,1,1); }
2810 : INLINE GEN
2811 2820783 : znstar_get_faN(GEN G) { return gel(G,3); }
2812 : INLINE GEN
2813 7 : znstar_get_no(GEN G) { return abgrp_get_no(gel(G,2)); }
2814 : INLINE GEN
2815 198534 : znstar_get_cyc(GEN G) { return abgrp_get_cyc(gel(G,2)); }
2816 : INLINE GEN
2817 7 : znstar_get_gen(GEN G) { return abgrp_get_gen(gel(G,2)); }
2818 : INLINE GEN
2819 3495527 : znstar_get_conreycyc(GEN G) { return gmael(G,4,5); }
2820 : INLINE GEN
2821 1201494 : znstar_get_conreygen(GEN G) { return gmael(G,4,4); }
2822 : INLINE GEN
2823 45920 : znstar_get_Ui(GEN G) { return gmael(G,4,3); }
2824 : INLINE GEN
2825 118160 : znstar_get_U(GEN G) { return gel(G,5); }
2826 : INLINE GEN
2827 799701 : znstar_get_pe(GEN G) { return gmael(G,4,1); }
2828 : INLINE GEN
2829 19894 : gal_get_pol(GEN gal) { return gel(gal,1); }
2830 : INLINE GEN
2831 1323 : gal_get_p(GEN gal) { return gmael(gal,2,1); }
2832 : INLINE GEN
2833 84 : gal_get_e(GEN gal) { return gmael(gal,2,2); }
2834 : INLINE GEN
2835 15960 : gal_get_mod(GEN gal) { return gmael(gal,2,3); }
2836 : INLINE GEN
2837 16338 : gal_get_roots(GEN gal) { return gel(gal,3); }
2838 : INLINE GEN
2839 15918 : gal_get_invvdm(GEN gal) { return gel(gal,4); }
2840 : INLINE GEN
2841 15918 : gal_get_den(GEN gal) { return gel(gal,5); }
2842 : INLINE GEN
2843 66990 : gal_get_group(GEN gal) { return gel(gal,6); }
2844 : INLINE GEN
2845 1743 : gal_get_gen(GEN gal) { return gel(gal,7); }
2846 : INLINE GEN
2847 1379 : gal_get_orders(GEN gal) { return gel(gal,8); }
2848 :
2849 : /* assume rnf a genuine rnf */
2850 : INLINE long
2851 1233344 : rnf_get_degree(GEN rnf) { return degpol(rnf_get_pol(rnf)); }
2852 : INLINE long
2853 16436 : rnf_get_nfdegree(GEN rnf) { return degpol(nf_get_pol(rnf_get_nf(rnf))); }
2854 : INLINE long
2855 775670 : rnf_get_absdegree(GEN rnf) { return degpol(gmael(rnf,11,1)); }
2856 : INLINE GEN
2857 700 : rnf_get_idealdisc(GEN rnf) { return gmael(rnf,3,1); }
2858 : INLINE GEN
2859 742 : rnf_get_k(GEN rnf) { return gmael(rnf,11,3); }
2860 : INLINE GEN
2861 609 : rnf_get_alpha(GEN rnf) { return gmael(rnf, 11, 2); }
2862 : INLINE GEN
2863 384125 : rnf_get_nf(GEN rnf) { return gel(rnf,10); }
2864 : INLINE GEN
2865 3171 : rnf_get_nfzk(GEN rnf) { return gel(rnf,2); }
2866 : INLINE GEN
2867 205107 : rnf_get_polabs(GEN rnf) { return gmael(rnf,11,1); }
2868 : INLINE GEN
2869 1478575 : rnf_get_pol(GEN rnf) { return gel(rnf,1); }
2870 : INLINE GEN
2871 63 : rnf_get_disc(GEN rnf) { return gel(rnf,3); }
2872 : INLINE GEN
2873 105 : rnf_get_index(GEN rnf) { return gel(rnf,4); }
2874 : INLINE long
2875 0 : rnf_get_varn(GEN rnf) { return varn(gel(rnf,1)); }
2876 : INLINE GEN
2877 188062 : rnf_get_nfpol(GEN rnf) { return gmael(rnf,10,1); }
2878 : INLINE long
2879 3325 : rnf_get_nfvarn(GEN rnf) { return varn(gmael(rnf,10,1)); }
2880 : INLINE GEN
2881 3283 : rnf_get_zk(GEN rnf) { return gel(rnf,7); }
2882 : INLINE GEN
2883 96922 : rnf_get_map(GEN rnf) { return gel(rnf,11); }
2884 : INLINE GEN
2885 1197 : rnf_get_invzk(GEN rnf) { return gel(rnf,8); }
2886 :
2887 : /* I integral ZM (not HNF), G ZM, rounded Cholesky form of a weighted
2888 : * T2 matrix. Reduce I wrt G */
2889 : INLINE GEN
2890 21784 : idealpseudored(GEN I, GEN G)
2891 21784 : { return ZM_mul(I, ZM_lll(ZM_mul(G, I), 0.99, LLL_IM)); }
2892 :
2893 : /* I integral (not necessarily HNF), G ZM, rounded Cholesky form of a weighted
2894 : * T2 matrix. Return m in I with T2(m) small */
2895 : INLINE GEN
2896 140667 : idealpseudomin(GEN I, GEN G)
2897 : {
2898 140667 : GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
2899 140667 : return ZM_ZC_mul(I, gel(u,1));
2900 : }
2901 : /* I, G as in idealpseudomin. Return an irrational m in I with T2(m) small */
2902 : INLINE GEN
2903 298542 : idealpseudomin_nonscalar(GEN I, GEN G)
2904 : {
2905 298542 : GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
2906 298542 : GEN m = ZM_ZC_mul(I, gel(u,1));
2907 298542 : if (ZV_isscalar(m) && lg(u) > 2) m = ZM_ZC_mul(I, gel(u,2));
2908 298542 : return m;
2909 : }
2910 :
2911 : INLINE GEN
2912 819 : idealred_elt(GEN nf, GEN I) {
2913 819 : pari_sp av = avma;
2914 819 : GEN u = idealpseudomin(I, nf_get_roundG(nf));
2915 819 : return gerepileupto(av, u);
2916 : }
2917 : INLINE GEN
2918 122877 : idealred(GEN nf, GEN I) { return idealred0(nf, I, NULL); }
2919 :
2920 : INLINE GEN
2921 2058 : idealchineseinit(GEN nf, GEN x)
2922 2058 : { return idealchinese(nf,x,NULL); }
2923 :
2924 : /*******************************************************************/
2925 : /* */
2926 : /* CLOSURES */
2927 : /* */
2928 : /*******************************************************************/
2929 226023266 : INLINE long closure_arity(GEN C) { return ((ulong)C[1])&ARITYBITS; }
2930 35495839 : INLINE long closure_is_variadic(GEN C) { return !!(((ulong)C[1])&VARARGBITS); }
2931 190240371 : INLINE const char *closure_codestr(GEN C) { return GSTR(gel(C,2))-1; }
2932 0 : INLINE GEN closure_get_code(GEN C) { return gel(C,2); }
2933 190198380 : INLINE GEN closure_get_oper(GEN C) { return gel(C,3); }
2934 190172792 : INLINE GEN closure_get_data(GEN C) { return gel(C,4); }
2935 9589 : INLINE GEN closure_get_dbg(GEN C) { return gel(C,5); }
2936 22930 : INLINE GEN closure_get_text(GEN C) { return gel(C,6); }
2937 1225868 : INLINE GEN closure_get_frame(GEN C) { return gel(C,7); }
2938 :
2939 : /*******************************************************************/
2940 : /* */
2941 : /* ERRORS */
2942 : /* */
2943 : /*******************************************************************/
2944 : INLINE long
2945 52597 : err_get_num(GEN e) { return e[1]; }
2946 : INLINE GEN
2947 77 : err_get_compo(GEN e, long i) { return gel(e, i+1); }
2948 :
2949 : INLINE void
2950 14 : pari_err_BUG(const char *f) { pari_err(e_BUG,f); }
2951 : INLINE void
2952 7 : pari_err_CONSTPOL(const char *f) { pari_err(e_CONSTPOL, f); }
2953 : INLINE void
2954 63 : pari_err_COPRIME(const char *f, GEN x, GEN y) { pari_err(e_COPRIME, f,x,y); }
2955 : INLINE void
2956 487 : pari_err_DIM(const char *f) { pari_err(e_DIM, f); }
2957 : INLINE void
2958 0 : pari_err_FILE(const char *f, const char *g) { pari_err(e_FILE, f,g); }
2959 : INLINE void
2960 0 : pari_err_FILEDESC(const char *f, long n) { pari_err(e_FILEDESC, f,n); }
2961 : INLINE void
2962 63 : pari_err_FLAG(const char *f) { pari_err(e_FLAG,f); }
2963 : INLINE void
2964 434 : pari_err_IMPL(const char *f) { pari_err(e_IMPL,f); }
2965 : INLINE void
2966 19716 : pari_err_INV(const char *f, GEN x) { pari_err(e_INV,f,x); }
2967 : INLINE void
2968 28 : pari_err_IRREDPOL(const char *f, GEN x) { pari_err(e_IRREDPOL, f,x); }
2969 : INLINE void
2970 2043 : 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); }
2971 : INLINE void
2972 203 : pari_err_COMPONENT(const char *f, const char *op, GEN l, GEN x) { pari_err(e_COMPONENT, f,op,l,x); }
2973 : INLINE void
2974 0 : pari_err_MAXPRIME(ulong c) { pari_err(e_MAXPRIME, c); }
2975 : INLINE void
2976 350 : pari_err_OP(const char *f, GEN x, GEN y) { pari_err(e_OP, f,x,y); }
2977 : INLINE void
2978 86 : pari_err_OVERFLOW(const char *f) { pari_err(e_OVERFLOW, f); }
2979 : INLINE void
2980 218 : pari_err_PREC(const char *f) { pari_err(e_PREC,f); }
2981 : INLINE void
2982 0 : pari_err_PACKAGE(const char *f) { pari_err(e_PACKAGE,f); }
2983 : INLINE void
2984 70 : pari_err_PRIME(const char *f, GEN x) { pari_err(e_PRIME, f,x); }
2985 : INLINE void
2986 749 : pari_err_MODULUS(const char *f, GEN x, GEN y) { pari_err(e_MODULUS, f,x,y); }
2987 : INLINE void
2988 49 : pari_err_ROOTS0(const char *f) { pari_err(e_ROOTS0, f); }
2989 : INLINE void
2990 77 : pari_err_SQRTN(const char *f, GEN x) { pari_err(e_SQRTN, f,x); }
2991 : INLINE void
2992 12650 : pari_err_TYPE(const char *f, GEN x) { pari_err(e_TYPE, f,x); }
2993 : INLINE void
2994 3073 : pari_err_TYPE2(const char *f, GEN x, GEN y) { pari_err(e_TYPE2, f,x,y); }
2995 : INLINE void
2996 203 : pari_err_VAR(const char *f, GEN x, GEN y) { pari_err(e_VAR, f,x,y); }
2997 : INLINE void
2998 175 : pari_err_PRIORITY(const char *f, GEN x, const char *op, long v)
2999 175 : { pari_err(e_PRIORITY, f,x,op,v); }
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