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 2740783 : mkintmod(GEN x, GEN y) { retmkintmod(x,y); }
141 : INLINE GEN
142 3948 : mkintmodu(ulong x, ulong y) {
143 3948 : GEN v = cgetg(3,t_INTMOD);
144 3948 : gel(v,1) = utoipos(y);
145 3948 : gel(v,2) = utoi(x); return v;
146 : }
147 : INLINE GEN
148 2541147 : mkpolmod(GEN x, GEN y) { retmkpolmod(x,y); }
149 : INLINE GEN
150 22980931 : mkfrac(GEN x, GEN y) { retmkfrac(x,y); }
151 : INLINE GEN
152 31822 : 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 37068493 : sstoQ(long n, long d)
162 : {
163 : ulong r;
164 : long g, q;
165 37068493 : if (!n)
166 : {
167 59276 : if (!d) pari_err_INV("sstoQ",gen_0);
168 59276 : return gen_0;
169 : }
170 37009217 : if (d < 0) { d = -d; n = -n; }
171 37009217 : if (d == 1) return stoi(n);
172 37006004 : q = udivuu_rem(labs(n),d,&r);
173 37006004 : if (!r) return n > 0? utoipos(q): utoineg(q);
174 1517831 : g = ugcd(d,r); /* gcd(n,d) */
175 1517831 : if (g != 1) { n /= g; d /= g; }
176 1517831 : retmkfrac(stoi(n), utoi(d));
177 : }
178 :
179 : INLINE GEN
180 6635608 : 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 8944820 : mkcomplex(GEN x, GEN y) { retmkcomplex(x,y); }
189 : INLINE GEN
190 448819 : gen_I(void) { return mkcomplex(gen_0, gen_1); }
191 : INLINE GEN
192 296268 : 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 62381783 : mkvecsmall(long x) { GEN v = cgetg(2, t_VECSMALL); v[1] = x; return v; }
199 : INLINE GEN
200 113050043 : mkvecsmall2(long x,long y) { GEN v = cgetg(3, t_VECSMALL);
201 113045892 : v[1]=x; v[2]=y; return v; }
202 : INLINE GEN
203 57698213 : mkvecsmall3(long x,long y,long z) { GEN v = cgetg(4, t_VECSMALL);
204 57695360 : v[1]=x; v[2]=y; v[3]=z; return v; }
205 : INLINE GEN
206 11930206 : mkvecsmall4(long x,long y,long z,long t) { GEN v = cgetg(5, t_VECSMALL);
207 11922714 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; return v; }
208 : INLINE GEN
209 466226 : mkvecsmall5(long x,long y,long z,long t,long u) { GEN v = cgetg(6, t_VECSMALL);
210 466226 : 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 14111823 : mkvec(GEN x) { retmkvec(x); }
217 : INLINE GEN
218 95714398 : mkvec2(GEN x, GEN y) { retmkvec2(x,y); }
219 : INLINE GEN
220 71785712 : mkvec3(GEN x, GEN y, GEN z) { retmkvec3(x,y,z); }
221 : INLINE GEN
222 7254867 : mkvec4(GEN x, GEN y, GEN z, GEN t) { retmkvec4(x,y,z,t); }
223 : INLINE GEN
224 11968294 : 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 19794 : 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 35084 : mkveccopy(GEN x) { GEN v = cgetg(2, t_VEC); gel(v,1) = gcopy(x); return v; }
235 : INLINE GEN
236 91324 : mkvec2copy(GEN x, GEN y) {
237 91324 : GEN v = cgetg(3,t_VEC); gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
238 : /* col */
239 : INLINE GEN
240 2417874 : mkcol(GEN x) { retmkcol(x); }
241 : INLINE GEN
242 23606124 : 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 2176146 : 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 46031 : mkcolcopy(GEN x) { GEN v = cgetg(2, t_COL); gel(v,1) = gcopy(x); return v; }
261 : /* mat */
262 : INLINE GEN
263 2513300 : mkmat(GEN x) { retmkmat(x); }
264 : INLINE GEN
265 28845235 : 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 21998 : 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 62364 : mkoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
278 : INLINE GEN
279 14098 : mkmoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
280 : INLINE long
281 88716 : inf_get_sign(GEN x) { return signe(gel(x,1)); }
282 : INLINE GEN
283 10661 : mkmat22s(long a, long b, long c, long d) {retmkmat2(mkcol2s(a,c),mkcol2s(b,d));}
284 : INLINE GEN
285 1533049 : mkmat22(GEN a, GEN b, GEN c, GEN d) { retmkmat2(mkcol2(a,c),mkcol2(b,d)); }
286 :
287 : /* pol */
288 : INLINE GEN
289 972236 : pol_x(long v) {
290 972236 : GEN p = cgetg(4, t_POL);
291 972236 : p[1] = evalsigne(1)|evalvarn(v);
292 972236 : gel(p,2) = gen_0;
293 972236 : gel(p,3) = gen_1; return p;
294 : }
295 : /* x^n, assume n >= 0 */
296 : INLINE GEN
297 2699935 : pol_xn(long n, long v) {
298 2699935 : long i, a = n+2;
299 2699935 : GEN p = cgetg(a+1, t_POL);
300 2699935 : p[1] = evalsigne(1)|evalvarn(v);
301 2699935 : for (i = 2; i < a; i++) gel(p,i) = gen_0;
302 2699935 : 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 1502064 : pol_1(long v) {
313 1502064 : GEN p = cgetg(3, t_POL);
314 1502064 : p[1] = evalsigne(1)|evalvarn(v);
315 1502064 : gel(p,2) = gen_1; return p;
316 : }
317 : INLINE GEN
318 29081756 : pol_0(long v)
319 : {
320 29081756 : GEN x = cgetg(2,t_POL);
321 29081756 : 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 8348885 : 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 8663086 : const_col(long n, GEN x) { retconst_col(n, x); }
337 : INLINE GEN
338 8242262 : const_vecsmall(long n, long c)
339 : {
340 : long i;
341 8242262 : GEN V = cgetg(n+1,t_VECSMALL);
342 8242272 : for(i=1;i<=n;i++) V[i] = c;
343 8242272 : return V;
344 : }
345 :
346 : /*** ZERO ***/
347 : /* O(p^e) */
348 : INLINE GEN
349 302747 : zeropadic(GEN p, long e)
350 : {
351 302747 : GEN y = cgetg(5,t_PADIC);
352 302747 : gel(y,4) = gen_0;
353 302747 : gel(y,3) = gen_1;
354 302747 : gel(y,2) = icopy(p);
355 302747 : y[1] = evalvalp(e) | _evalprecp(0);
356 302747 : 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 143493 : zeroser(long v, long e)
371 : {
372 143493 : GEN x = cgetg(2, t_SER);
373 143493 : x[1] = evalvalp(e) | evalvarn(v); return x;
374 : }
375 : INLINE int
376 5743466 : ser_isexactzero(GEN x)
377 : {
378 5743466 : if (!signe(x)) switch(lg(x))
379 : {
380 136136 : case 2: return 1;
381 854 : case 3: return isexactzero(gel(x,2));
382 : }
383 5606476 : return 0;
384 : }
385 : /* 0 * pol_x(v) */
386 : INLINE GEN
387 14102666 : zeropol(long v) { return pol_0(v); }
388 : /* vector(n) */
389 : INLINE GEN
390 35992180 : zerocol(long n)
391 : {
392 35992180 : GEN y = cgetg(n+1,t_COL);
393 35992180 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
394 35992180 : return y;
395 : }
396 : /* vectorv(n) */
397 : INLINE GEN
398 18812310 : zerovec(long n)
399 : {
400 18812310 : GEN y = cgetg(n+1,t_VEC);
401 18812316 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
402 18812316 : return y;
403 : }
404 : /* matrix(m, n) */
405 : INLINE GEN
406 16107 : zeromat(long m, long n)
407 : {
408 16107 : GEN y = cgetg(n+1,t_MAT);
409 16107 : GEN v = zerocol(m);
410 16107 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
411 16107 : return y;
412 : }
413 : /* = zero_zx, sv is a evalvarn()*/
414 : INLINE GEN
415 931135 : zero_Flx(long sv) { return pol0_Flx(sv); }
416 : INLINE GEN
417 33304087 : zero_Flv(long n)
418 : {
419 33304087 : GEN y = cgetg(n+1,t_VECSMALL);
420 33305671 : long i; for (i=1; i<=n; i++) y[i] = 0;
421 33305671 : return y;
422 : }
423 : /* matrix(m, n) */
424 : INLINE GEN
425 912953 : zero_Flm(long m, long n)
426 : {
427 912953 : GEN y = cgetg(n+1,t_MAT);
428 912942 : GEN v = zero_Flv(m);
429 912949 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
430 912949 : return y;
431 : }
432 : /* matrix(m, n) */
433 : INLINE GEN
434 104213 : zero_Flm_copy(long m, long n)
435 : {
436 104213 : GEN y = cgetg(n+1,t_MAT);
437 104208 : long i; for (i=1; i<=n; i++) gel(y,i) = zero_Flv(m);
438 104215 : return y;
439 : }
440 :
441 : INLINE GEN
442 793137 : zero_F2v(long m)
443 : {
444 793137 : long l = nbits2nlong(m);
445 793137 : GEN v = zero_Flv(l+1);
446 793137 : v[1] = m;
447 793137 : 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 276546 : zero_F2m_copy(long m, long n)
464 : {
465 : long i;
466 276546 : GEN M = cgetg(n+1, t_MAT);
467 806069 : for (i = 1; i <= n; i++)
468 529523 : gel(M,i)= zero_F2v(m);
469 276546 : return M;
470 : }
471 :
472 : /* matrix(m, n) */
473 : INLINE GEN
474 4751963 : zeromatcopy(long m, long n)
475 : {
476 4751963 : GEN y = cgetg(n+1,t_MAT);
477 4751963 : long i; for (i=1; i<=n; i++) gel(y,i) = zerocol(m);
478 4751963 : 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 1311348 : col_ei(long n, long i) { GEN e = zerocol(n); gel(e,i) = gen_1; return e; }
494 : INLINE GEN
495 326509 : 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 71379 : vecsmall_ei(long n, long i) { GEN e = zero_zv(n); e[i] = 1; return e; }
500 : INLINE GEN
501 657808 : Rg_col_ei(GEN x, long n, long i) { GEN e = zerocol(n); gel(e,i) = x; return e; }
502 :
503 : INLINE GEN
504 12488431 : shallowcopy(GEN x)
505 12488431 : { return typ(x) == t_MAT ? RgM_shallowcopy(x): leafcopy(x); }
506 :
507 : /* routines for naive growarrays */
508 : INLINE GEN
509 12698559 : vectrunc_init(long l)
510 : {
511 12698559 : GEN z = new_chunk(l);
512 12698829 : 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 253345192 : lg_increase(GEN x) { x[0]++; }
522 : INLINE void
523 51301072 : 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 82748119 : vecsmalltrunc_init(long l)
534 : {
535 82748119 : GEN z = new_chunk(l);
536 82748119 : z[0] = evaltyp(t_VECSMALL) | _evallg(1); return z;
537 : }
538 : INLINE void
539 33040635 : vecsmalltrunc_append(GEN x, long t) { x[ lg(x) ] = t; lg_increase(x); }
540 :
541 : /*******************************************************************/
542 : /* */
543 : /* VEC / COL / VECSMALL */
544 : /* */
545 : /*******************************************************************/
546 : /* shallow*/
547 : INLINE GEN
548 0 : vec_shorten(GEN v, long n)
549 : {
550 : long i;
551 0 : GEN V = cgetg(n+1,t_VEC);
552 0 : for(i=1;i<=n;i++) gel(V,i) = gel(v,i);
553 0 : return V;
554 : }
555 : /* shallow*/
556 : INLINE GEN
557 13710 : vec_lengthen(GEN v, long n)
558 : {
559 : long i;
560 13710 : long l=lg(v);
561 13710 : GEN V = cgetg(n+1,t_VEC);
562 13710 : for(i=1;i<l;i++) gel(V,i) = gel(v,i);
563 13710 : return V;
564 : }
565 : /* shallow*/
566 : INLINE GEN
567 61173 : vec_append(GEN V, GEN s)
568 : {
569 61173 : long i, l2 = lg(V);
570 61173 : GEN res = cgetg(l2+1, typ(V));
571 61173 : for (i = 1; i < l2; ++i) gel(res, i) = gel(V,i);
572 61173 : gel(res,l2) = s; return res;
573 : }
574 : /* shallow*/
575 : INLINE GEN
576 1785 : vec_prepend(GEN v, GEN s)
577 : {
578 1785 : long i, l = lg(v);
579 1785 : GEN w = cgetg(l+1, typ(v));
580 1785 : gel(w,1) = s;
581 1785 : for (i = 2; i <= l; ++i) gel(w,i) = gel(v,i-1);
582 1785 : return w;
583 : }
584 : /* shallow*/
585 : INLINE GEN
586 0 : vec_setconst(GEN v, GEN x)
587 : {
588 0 : long i, l = lg(v);
589 0 : for (i = 1; i < l; i++) gel(v,i) = x;
590 0 : return v;
591 : }
592 : INLINE GEN
593 732358 : vecsmall_shorten(GEN v, long n)
594 : {
595 : long i;
596 732358 : GEN V = cgetg(n+1,t_VECSMALL);
597 732362 : for(i=1;i<=n;i++) V[i] = v[i];
598 732362 : return V;
599 : }
600 : INLINE GEN
601 21 : vecsmall_lengthen(GEN v, long n)
602 : {
603 21 : long i, l = lg(v);
604 21 : GEN V = cgetg(n+1,t_VECSMALL);
605 21 : for(i=1;i<l;i++) V[i] = v[i];
606 21 : return V;
607 : }
608 :
609 : INLINE GEN
610 457763 : vec_to_vecsmall(GEN x)
611 457763 : { pari_APPLY_long(itos(gel(x,i))) }
612 : INLINE GEN
613 135396 : vecsmall_to_vec(GEN x)
614 135396 : { pari_APPLY_type(t_VEC, stoi(x[i])) }
615 : INLINE GEN
616 1617 : vecsmall_to_vec_inplace(GEN z)
617 : {
618 1617 : long i, l = lg(z);
619 1617 : for (i=1; i<l; i++) gel(z,i) = stoi(z[i]);
620 1617 : settyp(z, t_VEC); return z;
621 : }
622 : INLINE GEN
623 5210063 : vecsmall_to_col(GEN x)
624 5210063 : { pari_APPLY_type(t_COL, stoi(x[i])) }
625 :
626 : INLINE int
627 8065780 : vecsmall_lexcmp(GEN x, GEN y)
628 : {
629 : long lx,ly,l,i;
630 8065780 : lx = lg(x);
631 8065780 : ly = lg(y); l = minss(lx,ly);
632 39684887 : for (i=1; i<l; i++)
633 37752457 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
634 1932430 : if (lx == ly) return 0;
635 14 : return (lx < ly)? -1 : 1;
636 : }
637 :
638 : INLINE int
639 85155511 : vecsmall_prefixcmp(GEN x, GEN y)
640 : {
641 85155511 : long i, lx = lg(x), ly = lg(y), l = minss(lx,ly);
642 394027655 : for (i=1; i<l; i++)
643 374395014 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
644 19632641 : return 0;
645 : }
646 :
647 : /*Can be used on t_VEC, but coeffs not gcopy-ed*/
648 : INLINE GEN
649 14162 : vecsmall_prepend(GEN V, long s)
650 : {
651 14162 : long i, l2 = lg(V);
652 14162 : GEN res = cgetg(l2+1, typ(V));
653 14162 : res[1] = s;
654 14162 : for (i = 2; i <= l2; ++i) res[i] = V[i - 1];
655 14162 : return res;
656 : }
657 :
658 : INLINE GEN
659 2552995 : vecsmall_append(GEN V, long s)
660 : {
661 2552995 : long i, l2 = lg(V);
662 2552995 : GEN res = cgetg(l2+1, t_VECSMALL);
663 2552995 : for (i = 1; i < l2; ++i) res[i] = V[i];
664 2552995 : res[l2] = s; return res;
665 : }
666 :
667 : INLINE GEN
668 782116 : vecsmall_concat(GEN u, GEN v)
669 : {
670 782116 : long i, l1 = lg(u)-1, l2 = lg(v)-1;
671 782116 : GEN res = cgetg(l1+l2+1, t_VECSMALL);
672 782116 : for (i = 1; i <= l1; ++i) res[i] = u[i];
673 782116 : for (i = 1; i <= l2; ++i) res[i+l1] = v[i];
674 782116 : return res;
675 : }
676 :
677 : /* return the number of indices where u and v are equal */
678 : INLINE long
679 0 : vecsmall_coincidence(GEN u, GEN v)
680 : {
681 0 : long i, s = 0, l = minss(lg(u),lg(v));
682 0 : for(i=1; i<l; i++)
683 0 : if(u[i] == v[i]) s++;
684 0 : return s;
685 : }
686 :
687 : /* returns the first index i<=n such that x=v[i] if it exists, 0 otherwise */
688 : INLINE long
689 0 : vecsmall_isin(GEN v, long x)
690 : {
691 0 : long i, l = lg(v);
692 0 : for (i = 1; i < l; i++)
693 0 : if (v[i] == x) return i;
694 0 : return 0;
695 : }
696 :
697 : INLINE long
698 84 : vecsmall_pack(GEN V, long base, long mod)
699 : {
700 84 : long i, s = 0;
701 84 : for(i=1; i<lg(V); i++) s = (base*s + V[i]) % mod;
702 84 : return s;
703 : }
704 :
705 : INLINE long
706 14 : vecsmall_indexmax(GEN x)
707 : {
708 14 : long i, i0 = 1, t = x[1], lx = lg(x);
709 56 : for (i=2; i<lx; i++)
710 42 : if (x[i] > t) t = x[i0=i];
711 14 : return i0;
712 : }
713 :
714 : INLINE long
715 154223 : vecsmall_max(GEN x)
716 : {
717 154223 : long i, t = x[1], lx = lg(x);
718 559244 : for (i=2; i<lx; i++)
719 405021 : if (x[i] > t) t = x[i];
720 154223 : return t;
721 : }
722 :
723 : INLINE long
724 14 : vecsmall_indexmin(GEN x)
725 : {
726 14 : long i, i0 = 1, t = x[1], lx =lg(x);
727 56 : for (i=2; i<lx; i++)
728 42 : if (x[i] < t) t = x[i0=i];
729 14 : return i0;
730 : }
731 :
732 : INLINE long
733 1421 : vecsmall_min(GEN x)
734 : {
735 1421 : long i, t = x[1], lx =lg(x);
736 9947 : for (i=2; i<lx; i++)
737 8526 : if (x[i] < t) t = x[i];
738 1421 : return t;
739 : }
740 :
741 : INLINE int
742 4976051 : ZV_isscalar(GEN x)
743 : {
744 4976051 : long l = lg(x);
745 14205343 : while (--l > 1)
746 8140566 : if (signe(gel(x, l))) return 0;
747 1088726 : return 1;
748 : }
749 : INLINE int
750 19351595 : QV_isscalar(GEN x)
751 : {
752 19351595 : long lx = lg(x),i;
753 20867286 : for (i=2; i<lx; i++)
754 20320577 : if (!isintzero(gel(x, i))) return 0;
755 546709 : return 1;
756 : }
757 : INLINE int
758 7501 : RgV_isscalar(GEN x)
759 : {
760 7501 : long lx = lg(x),i;
761 10891 : for (i=2; i<lx; i++)
762 9809 : if (!gequal0(gel(x, i))) return 0;
763 1082 : return 1;
764 : }
765 : INLINE int
766 0 : RgX_isscalar(GEN x)
767 : {
768 : long i;
769 0 : for (i=lg(x)-1; i>2; i--)
770 0 : if (!gequal0(gel(x, i))) return 0;
771 0 : return 1;
772 : }
773 : INLINE long
774 4502657 : RgX_equal_var(GEN x, GEN y) { return varn(x) == varn(y) && RgX_equal(x,y); }
775 :
776 : INLINE int
777 5909 : RgX_is_rational(GEN x)
778 : {
779 : long i;
780 28875 : for (i = lg(x)-1; i > 1; i--)
781 26879 : if (!is_rational_t(typ(gel(x,i)))) return 0;
782 1996 : return 1;
783 : }
784 : INLINE int
785 4308706 : RgX_is_ZX(GEN x)
786 : {
787 : long i;
788 18652926 : for (i = lg(x)-1; i > 1; i--)
789 14396426 : if (typ(gel(x,i)) != t_INT) return 0;
790 4256500 : return 1;
791 : }
792 : INLINE int
793 262241 : RgX_is_QX(GEN x)
794 : {
795 262241 : long k = lg(x)-1;
796 926254 : for ( ; k>1; k--)
797 664258 : if (!is_rational_t(typ(gel(x,k)))) return 0;
798 261996 : return 1;
799 : }
800 : INLINE int
801 16160498 : RgX_is_monomial(GEN x)
802 : {
803 : long i;
804 16160498 : if (!signe(x)) return 0;
805 26705625 : for (i=lg(x)-2; i>1; i--)
806 18325823 : if (!isexactzero(gel(x,i))) return 0;
807 8379802 : return 1;
808 : }
809 : INLINE int
810 27032589 : RgV_is_ZV(GEN x)
811 : {
812 : long i;
813 111360440 : for (i = lg(x)-1; i > 0; i--)
814 84330056 : if (typ(gel(x,i)) != t_INT) return 0;
815 27030384 : return 1;
816 : }
817 : INLINE int
818 15677 : RgV_is_QV(GEN x)
819 : {
820 : long i;
821 69411 : for (i = lg(x)-1; i > 0; i--)
822 54406 : if (!is_rational_t(typ(gel(x,i)))) return 0;
823 15005 : return 1;
824 : }
825 :
826 : /********************************************************************/
827 : /** **/
828 : /** Dynamic arrays implementation **/
829 : /** **/
830 : /********************************************************************/
831 : INLINE void **
832 404190115 : pari_stack_base(pari_stack *s) { return s->data; }
833 :
834 : INLINE void
835 1709626 : pari_stack_init(pari_stack *s, size_t size, void **data)
836 : {
837 1709626 : s->data = data;
838 1709626 : *data = NULL;
839 1709626 : s->n = 0;
840 1709626 : s->alloc = 0;
841 1709626 : s->size = size;
842 1709626 : }
843 :
844 : INLINE void
845 402531854 : pari_stack_alloc(pari_stack *s, long nb)
846 : {
847 402531854 : void **sdat = pari_stack_base(s);
848 402535442 : long alloc = s->alloc;
849 402535442 : if (s->n+nb <= alloc) return;
850 632173 : if (!alloc)
851 580258 : alloc = nb;
852 : else
853 : {
854 51915 : while (s->n+nb > alloc) alloc <<= 1;
855 : }
856 632173 : *sdat = pari_realloc(*sdat,alloc*s->size);
857 632904 : s->alloc = alloc;
858 : }
859 :
860 : INLINE long
861 324736766 : pari_stack_new(pari_stack *s) { pari_stack_alloc(s, 1); return s->n++; }
862 :
863 : INLINE void
864 1654352 : pari_stack_delete(pari_stack *s)
865 : {
866 1654352 : void **sdat = pari_stack_base(s);
867 1651374 : if (*sdat) pari_free(*sdat);
868 1663561 : }
869 :
870 : INLINE void
871 4794 : pari_stack_pushp(pari_stack *s, void *u)
872 : {
873 4794 : long n = pari_stack_new(s);
874 4794 : void **sdat =(void**) *pari_stack_base(s);
875 4794 : sdat[n] = u;
876 4794 : }
877 :
878 : /*******************************************************************/
879 : /* */
880 : /* EXTRACT */
881 : /* */
882 : /*******************************************************************/
883 : INLINE GEN
884 198830884 : vecslice(GEN A, long y1, long y2)
885 : {
886 198830884 : long i,lB = y2 - y1 + 2;
887 198830884 : GEN B = cgetg(lB, typ(A));
888 198831803 : for (i=1; i<lB; i++) B[i] = A[y1-1+i];
889 198831803 : return B;
890 : }
891 : INLINE GEN
892 805083 : vecslicepermute(GEN A, GEN p, long y1, long y2)
893 : {
894 805083 : long i,lB = y2 - y1 + 2;
895 805083 : GEN B = cgetg(lB, typ(A));
896 805085 : for (i=1; i<lB; i++) B[i] = A[p[y1-1+i]];
897 805085 : return B;
898 : }
899 : /* rowslice(rowpermute(A,p), x1, x2) */
900 : INLINE GEN
901 38458 : rowslicepermute(GEN x, GEN p, long j1, long j2)
902 38458 : { pari_APPLY_same(vecslicepermute(gel(x,i),p,j1,j2)) }
903 :
904 : INLINE GEN
905 22007820 : rowslice(GEN x, long j1, long j2)
906 22007820 : { pari_APPLY_same(vecslice(gel(x,i), j1, j2)) }
907 :
908 : INLINE GEN
909 3627977 : matslice(GEN A, long x1, long x2, long y1, long y2)
910 3627977 : { return rowslice(vecslice(A, y1, y2), x1, x2); }
911 :
912 : /* shallow, remove coeff of index j */
913 : INLINE GEN
914 133 : rowsplice(GEN x, long j)
915 133 : { pari_APPLY_same(vecsplice(gel(x,i), j)) }
916 :
917 : /* shallow, remove coeff of index j */
918 : INLINE GEN
919 252938 : vecsplice(GEN a, long j)
920 : {
921 252938 : long i, k, l = lg(a);
922 : GEN b;
923 252938 : if (l == 1) pari_err(e_MISC, "incorrect component in vecsplice");
924 252938 : b = cgetg(l-1, typ(a));
925 1007489 : for (i = k = 1; i < l; i++)
926 754551 : if (i != j) gel(b, k++) = gel(a,i);
927 252938 : return b;
928 : }
929 : /* shallow */
930 : INLINE GEN
931 833 : RgM_minor(GEN a, long i, long j)
932 : {
933 833 : GEN b = vecsplice(a, j);
934 833 : long k, l = lg(b);
935 833 : for (k = 1; k < l; k++) gel(b,k) = vecsplice(gel(b,k), i);
936 833 : return b;
937 : }
938 :
939 : /* A[x0,] */
940 : INLINE GEN
941 390121 : row(GEN x, long j)
942 390121 : { pari_APPLY_type(t_VEC, gcoeff(x, j, i)) }
943 : INLINE GEN
944 3713290 : Flm_row(GEN x, long j)
945 3713290 : { pari_APPLY_ulong((ulong)coeff(x, j, i)) }
946 : /* A[x0,] */
947 : INLINE GEN
948 204820 : rowcopy(GEN x, long j)
949 204820 : { pari_APPLY_type(t_VEC, gcopy(gcoeff(x, j, i))) }
950 : /* A[x0, x1..x2] */
951 : INLINE GEN
952 2177 : row_i(GEN A, long x0, long x1, long x2)
953 : {
954 2177 : long i, lB = x2 - x1 + 2;
955 2177 : GEN B = cgetg(lB, t_VEC);
956 2177 : for (i=x1; i<=x2; i++) gel(B, i) = gcoeff(A, x0, i);
957 2177 : return B;
958 : }
959 :
960 : INLINE GEN
961 5830336 : vecreverse(GEN A)
962 : {
963 : long i, l;
964 5830336 : GEN B = cgetg_copy(A, &l);
965 5830336 : for (i=1; i<l; i++) gel(B, i) = gel(A, l-i);
966 5830336 : return B;
967 : }
968 :
969 : INLINE GEN
970 252 : vecsmall_reverse(GEN A)
971 : {
972 : long i, l;
973 252 : GEN B = cgetg_copy(A, &l);
974 252 : for (i=1; i<l; i++) B[i] = A[l-i];
975 252 : return B;
976 : }
977 :
978 : INLINE void
979 260 : vecreverse_inplace(GEN y)
980 : {
981 260 : long l = lg(y), lim = l>>1, i;
982 724 : for (i = 1; i <= lim; i++)
983 : {
984 464 : GEN z = gel(y,i);
985 464 : gel(y,i) = gel(y,l-i);
986 464 : gel(y,l-i) = z;
987 : }
988 260 : }
989 :
990 : INLINE GEN
991 44959825 : vecsmallpermute(GEN A, GEN p) { return perm_mul(A, p); }
992 :
993 : INLINE GEN
994 6215155 : vecpermute(GEN A, GEN x)
995 6215155 : { pari_APPLY_type(typ(A), gel(A, x[i])) }
996 :
997 : INLINE GEN
998 2965281 : rowpermute(GEN x, GEN p)
999 2965281 : { pari_APPLY_same(typ(gel(x,i)) == t_VECSMALL ? vecsmallpermute(gel(x, i), p)
1000 : : vecpermute(gel(x, i), p))
1001 : }
1002 : /*******************************************************************/
1003 : /* */
1004 : /* PERMUTATIONS */
1005 : /* */
1006 : /*******************************************************************/
1007 : /* identity permutation */
1008 : INLINE GEN
1009 721198 : identity_perm(long n)
1010 : {
1011 721198 : GEN perm = cgetg(n+1, t_VECSMALL);
1012 : long i;
1013 721191 : for (i = 1; i <= n; i++) perm[i] = i;
1014 721191 : return perm;
1015 : }
1016 :
1017 : /* assume d <= n */
1018 : INLINE GEN
1019 98434 : cyclic_perm(long n, long d)
1020 : {
1021 98434 : GEN perm = cgetg(n+1, t_VECSMALL);
1022 : long i;
1023 98434 : for (i = 1; i <= n-d; i++) perm[i] = i+d;
1024 98434 : for ( ; i <= n; i++) perm[i] = i-n+d;
1025 98434 : return perm;
1026 : }
1027 :
1028 : /* Multiply (compose) two permutations */
1029 : INLINE GEN
1030 46200117 : perm_mul(GEN s, GEN x)
1031 46200117 : { pari_APPLY_long(s[x[i]]) }
1032 :
1033 : /* Compute the inverse (reciprocal) of a permutation. */
1034 : INLINE GEN
1035 1155219 : perm_inv(GEN x)
1036 : {
1037 : long i, lx;
1038 1155219 : GEN y = cgetg_copy(x, &lx);
1039 1155218 : for (i=1; i<lx; i++) y[ x[i] ] = i;
1040 1155218 : return y;
1041 : }
1042 : /* Return s*t*s^-1 */
1043 : INLINE GEN
1044 416934 : perm_conj(GEN s, GEN t)
1045 : {
1046 : long i, l;
1047 416934 : GEN v = cgetg_copy(s, &l);
1048 416934 : for (i = 1; i < l; i++) v[ s[i] ] = s[ t[i] ];
1049 416934 : return v;
1050 : }
1051 :
1052 : /*********************************************************************/
1053 : /* MALLOC/FREE WRAPPERS */
1054 : /*********************************************************************/
1055 : #define BLOCK_SIGALRM_START \
1056 : { \
1057 : int block=PARI_SIGINT_block; \
1058 : PARI_SIGINT_block = 2; \
1059 : MT_SIGINT_BLOCK(block);
1060 :
1061 : #define BLOCK_SIGINT_START \
1062 : { \
1063 : int block=PARI_SIGINT_block; \
1064 : PARI_SIGINT_block = 1; \
1065 : MT_SIGINT_BLOCK(block);
1066 :
1067 : #define BLOCK_SIGINT_END \
1068 : PARI_SIGINT_block = block; \
1069 : MT_SIGINT_UNBLOCK(block); \
1070 : if (!block && PARI_SIGINT_pending) \
1071 : { \
1072 : int sig = PARI_SIGINT_pending; \
1073 : PARI_SIGINT_pending = 0; \
1074 : raise(sig); \
1075 : } \
1076 : }
1077 :
1078 : INLINE void
1079 65657799 : pari_free(void *pointer)
1080 : {
1081 65657799 : BLOCK_SIGINT_START;
1082 65676995 : free(pointer);
1083 65676995 : BLOCK_SIGINT_END;
1084 65673961 : }
1085 : INLINE void*
1086 277512392 : pari_malloc(size_t size)
1087 : {
1088 277512392 : if (size)
1089 : {
1090 : char *tmp;
1091 277512392 : BLOCK_SIGINT_START;
1092 277514839 : tmp = (char*)malloc(size);
1093 277514839 : BLOCK_SIGINT_END;
1094 277514663 : if (!tmp) pari_err(e_MEM);
1095 277514663 : return tmp;
1096 : }
1097 0 : return NULL;
1098 : }
1099 : INLINE void*
1100 643833 : pari_realloc(void *pointer, size_t size)
1101 : {
1102 : char *tmp;
1103 :
1104 643833 : BLOCK_SIGINT_START;
1105 645391 : if (!pointer) tmp = (char *) malloc(size);
1106 55708 : else tmp = (char *) realloc(pointer,size);
1107 645391 : BLOCK_SIGINT_END;
1108 644923 : if (!tmp) pari_err(e_MEM);
1109 644923 : return tmp;
1110 : }
1111 : INLINE void*
1112 35410 : pari_calloc(size_t size)
1113 : {
1114 35410 : void *t = pari_malloc(size);
1115 35410 : memset(t, 0, size); return t;
1116 : }
1117 : INLINE GEN
1118 5785 : cgetalloc(long t, size_t l)
1119 : {
1120 5785 : GEN x = (GEN)pari_malloc(l * sizeof(long));
1121 5785 : x[0] = evaltyp(t) | evallg(l); return x;
1122 : }
1123 :
1124 : /*******************************************************************/
1125 : /* */
1126 : /* GARBAGE COLLECTION */
1127 : /* */
1128 : /*******************************************************************/
1129 : /* copy integer x as if we had set_avma(av) */
1130 : INLINE GEN
1131 3728914173 : icopy_avma(GEN x, pari_sp av)
1132 : {
1133 3728914173 : long i = lgefint(x), lx = i;
1134 3728914173 : GEN y = ((GEN)av) - i;
1135 3728914173 : while (--i > 0) y[i] = x[i];
1136 3728914173 : y[0] = evaltyp(t_INT)|evallg(lx);
1137 3728612438 : return y;
1138 : }
1139 : /* copy leaf x as if we had set_avma(av) */
1140 : INLINE GEN
1141 172970703 : leafcopy_avma(GEN x, pari_sp av)
1142 : {
1143 172970703 : long i = lg(x);
1144 172970703 : GEN y = ((GEN)av) - i;
1145 172970703 : while (--i > 0) y[i] = x[i];
1146 172970703 : y[0] = x[0] & (~CLONEBIT);
1147 172970703 : return y;
1148 : }
1149 : INLINE GEN
1150 640552565 : gerepileuptoleaf(pari_sp av, GEN x)
1151 : {
1152 : long lx;
1153 : GEN q;
1154 :
1155 640552565 : if (!isonstack(x) || (GEN)av<=x) { set_avma(av); return x; }
1156 642295952 : lx = lg(x);
1157 642295952 : q = ((GEN)av) - lx;
1158 642295952 : avma = (pari_sp)q;
1159 642295952 : while (--lx >= 0) q[lx] = x[lx];
1160 642295952 : return q;
1161 : }
1162 : INLINE GEN
1163 1224973645 : gerepileuptoint(pari_sp av, GEN x)
1164 : {
1165 1224973645 : if (!isonstack(x) || (GEN)av<=x) { set_avma(av); return x; }
1166 1078964887 : avma = (pari_sp)icopy_avma(x, av);
1167 1080867596 : return (GEN)avma;
1168 : }
1169 : INLINE GEN
1170 770077237 : gerepileupto(pari_sp av, GEN x)
1171 : {
1172 770077237 : if (!isonstack(x) || (GEN)av<=x) { set_avma(av); return x; }
1173 680451972 : switch(typ(x))
1174 : { /* non-default = !is_recursive_t(tq) */
1175 223927053 : case t_INT: return gerepileuptoint(av, x);
1176 : case t_REAL:
1177 : case t_STR:
1178 148320837 : case t_VECSMALL: return gerepileuptoleaf(av,x);
1179 : default:
1180 : /* NB: x+i --> ((long)x) + i*sizeof(long) */
1181 308204082 : return gerepile(av, (pari_sp) (x+lg(x)), x);
1182 : }
1183 : }
1184 : INLINE double
1185 2184614 : gc_double(pari_sp av, double d) { set_avma(av); return d; }
1186 : INLINE long
1187 112609105 : gc_long(pari_sp av, long s) { set_avma(av); return s; }
1188 : INLINE ulong
1189 15130133 : gc_ulong(pari_sp av, ulong s) { set_avma(av); return s; }
1190 : INLINE int
1191 19002329 : gc_bool(pari_sp av, int s) { set_avma(av); return s; }
1192 : INLINE int
1193 389563 : gc_int(pari_sp av, int s) { set_avma(av); return s; }
1194 : INLINE GEN
1195 1089289 : gc_NULL(pari_sp av) { set_avma(av); return NULL; }
1196 :
1197 : /* gerepileupto(av, gcopy(x)) */
1198 : INLINE GEN
1199 47057732 : gerepilecopy(pari_sp av, GEN x)
1200 : {
1201 47057732 : if (is_recursive_t(typ(x)))
1202 : {
1203 42457490 : GENbin *p = copy_bin(x);
1204 42457503 : set_avma(av); return bin_copy(p);
1205 : }
1206 : else
1207 : {
1208 4600243 : set_avma(av);
1209 4600246 : if (x < (GEN)av) {
1210 3112795 : if (x < (GEN)pari_mainstack->bot) new_chunk(lg(x));
1211 3112795 : x = leafcopy_avma(x, av);
1212 3112796 : avma = (pari_sp)x;
1213 : } else
1214 1487451 : x = leafcopy(x);
1215 4600247 : return x;
1216 : }
1217 : }
1218 :
1219 : /* Takes an array of pointers to GENs, of length n. Copies all
1220 : * objects to contiguous locations and cleans up the stack between
1221 : * av and avma. */
1222 : INLINE void
1223 136131 : gerepilemany(pari_sp av, GEN* gptr[], int n)
1224 : {
1225 : int i;
1226 136131 : for (i=0; i<n; i++) *gptr[i] = (GEN)copy_bin(*gptr[i]);
1227 136131 : set_avma(av);
1228 136131 : for (i=0; i<n; i++) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1229 136131 : }
1230 :
1231 : INLINE void
1232 7487945 : gerepileall(pari_sp av, int n, ...)
1233 : {
1234 : int i;
1235 7487945 : va_list a; va_start(a, n);
1236 7487945 : if (n < 10)
1237 : {
1238 : GEN *gptr[10];
1239 21650229 : for (i=0; i<n; i++)
1240 14162303 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1241 7487926 : set_avma(av);
1242 7487819 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1243 :
1244 : }
1245 : else
1246 : {
1247 0 : GEN **gptr = (GEN**) pari_malloc(n*sizeof(GEN*));
1248 0 : for (i=0; i<n; i++)
1249 0 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1250 0 : set_avma(av);
1251 0 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1252 0 : pari_free(gptr);
1253 : }
1254 7488051 : va_end(a);
1255 7488051 : }
1256 :
1257 : INLINE void
1258 6 : gerepilecoeffs(pari_sp av, GEN x, int n)
1259 : {
1260 : int i;
1261 6 : for (i=0; i<n; i++) gel(x,i) = (GEN)copy_bin(gel(x,i));
1262 6 : set_avma(av);
1263 6 : for (i=0; i<n; i++) gel(x,i) = bin_copy((GENbin*)x[i]);
1264 6 : }
1265 :
1266 : /* p from copy_bin. Copy p->x back to stack, then destroy p */
1267 : INLINE GEN
1268 57043191 : bin_copy(GENbin *p)
1269 : {
1270 : GEN x, y, base;
1271 : long dx, len;
1272 :
1273 57043191 : x = p->x; if (!x) { pari_free(p); return gen_0; }
1274 57036069 : len = p->len;
1275 57036069 : base= p->base; dx = x - base;
1276 57036069 : y = (GEN)memcpy((void*)new_chunk(len), (void*)GENbinbase(p), len*sizeof(long));
1277 57036031 : y += dx;
1278 57036031 : p->rebase(y, ((ulong)y-(ulong)x));
1279 57035958 : pari_free(p); return y;
1280 : }
1281 :
1282 : INLINE GEN
1283 114079572 : GENbinbase(GENbin *p) { return (GEN)(p + 1); }
1284 :
1285 : INLINE void
1286 31508337 : cgiv(GEN x)
1287 : {
1288 31508337 : pari_sp av = (pari_sp)(x+lg(x));
1289 31508337 : if (isonstack((GEN)av)) set_avma(av);
1290 31507990 : }
1291 :
1292 : INLINE void
1293 1273841 : killblock(GEN x) { gunclone(x); }
1294 :
1295 : INLINE int
1296 24166091 : is_universal_constant(GEN x) { return (x >= gen_0 && x <= ghalf); }
1297 :
1298 : /*******************************************************************/
1299 : /* */
1300 : /* CONVERSION / ASSIGNMENT */
1301 : /* */
1302 : /*******************************************************************/
1303 : /* z is a type which may be a t_COMPLEX component (not a t_QUAD) */
1304 : INLINE GEN
1305 3351805 : cxcompotor(GEN z, long prec)
1306 : {
1307 3351805 : switch(typ(z))
1308 : {
1309 1813602 : case t_INT: return itor(z, prec);
1310 136164 : case t_FRAC: return fractor(z, prec);
1311 1402039 : case t_REAL: return rtor(z, prec);
1312 0 : default: pari_err_TYPE("cxcompotor",z);
1313 : return NULL; /* LCOV_EXCL_LINE */
1314 : }
1315 : }
1316 : INLINE GEN
1317 1662557 : cxtofp(GEN x, long prec)
1318 1662557 : { retmkcomplex(cxcompotor(gel(x,1),prec), cxcompotor(gel(x,2),prec)); }
1319 :
1320 : INLINE GEN
1321 289289 : cxtoreal(GEN q)
1322 289289 : { return (typ(q) == t_COMPLEX && gequal0(gel(q,2)))? gel(q,1): q; }
1323 :
1324 : INLINE double
1325 33616432 : gtodouble(GEN x)
1326 : {
1327 33616432 : if (typ(x)!=t_REAL) {
1328 7433443 : pari_sp av = avma;
1329 7433443 : x = gtofp(x, DEFAULTPREC);
1330 7433443 : if (typ(x)!=t_REAL) pari_err_TYPE("gtodouble [t_REAL expected]", x);
1331 7433443 : set_avma(av);
1332 : }
1333 33616432 : return rtodbl(x);
1334 : }
1335 : INLINE long
1336 73016791 : gtos(GEN x) {
1337 73016791 : if (typ(x) != t_INT) pari_err_TYPE("gtos [integer expected]",x);
1338 73016784 : return itos(x);
1339 : }
1340 :
1341 : INLINE ulong
1342 122987 : gtou(GEN x) {
1343 122987 : if (typ(x) != t_INT || signe(x)<0)
1344 0 : pari_err_TYPE("gtou [integer >=0 expected]",x);
1345 122999 : return itou(x);
1346 : }
1347 :
1348 : INLINE GEN
1349 21959129 : absfrac(GEN x)
1350 : {
1351 21959129 : GEN y = cgetg(3, t_FRAC);
1352 21959129 : gel(y,1) = absi(gel(x,1));
1353 21959129 : gel(y,2) = icopy(gel(x,2)); return y;
1354 : }
1355 : INLINE GEN
1356 32434 : absfrac_shallow(GEN x)
1357 32434 : { return signe(gel(x,1))>0? x: mkfrac(negi(gel(x,1)), gel(x,2)); }
1358 : INLINE GEN
1359 7547343 : Q_abs(GEN x) { return (typ(x) == t_INT)? absi(x): absfrac(x); }
1360 : INLINE GEN
1361 113706 : Q_abs_shallow(GEN x)
1362 113706 : { return (typ(x) == t_INT)? absi_shallow(x): absfrac_shallow(x); }
1363 : INLINE GEN
1364 322 : R_abs_shallow(GEN x)
1365 322 : { return (typ(x) == t_FRAC)? absfrac_shallow(x): mpabs_shallow(x); }
1366 : INLINE GEN
1367 0 : R_abs(GEN x)
1368 0 : { return (typ(x) == t_FRAC)? absfrac(x): mpabs(x); }
1369 :
1370 : /* Force z to be of type real/complex with floating point components */
1371 : INLINE GEN
1372 35308514 : gtofp(GEN z, long prec)
1373 : {
1374 35308514 : switch(typ(z))
1375 : {
1376 22128572 : case t_INT: return itor(z, prec);
1377 4306503 : case t_FRAC: return fractor(z, prec);
1378 7442638 : case t_REAL: return rtor(z, prec);
1379 : case t_COMPLEX: {
1380 1430801 : GEN a = gel(z,1), b = gel(z,2);
1381 1430801 : if (isintzero(b)) return cxcompotor(a, prec);
1382 1428390 : if (isintzero(a)) {
1383 2086 : GEN y = cgetg(3, t_COMPLEX);
1384 2086 : b = cxcompotor(b, prec);
1385 2086 : gel(y,1) = real_0_bit(expo(b) - prec2nbits(prec));
1386 2086 : gel(y,2) = b; return y;
1387 : }
1388 1426304 : return cxtofp(z, prec);
1389 : }
1390 0 : case t_QUAD: return quadtofp(z, prec);
1391 0 : default: pari_err_TYPE("gtofp",z);
1392 : return NULL; /* LCOV_EXCL_LINE */
1393 : }
1394 : }
1395 : /* Force z to be of type real / int */
1396 : INLINE GEN
1397 22400 : gtomp(GEN z, long prec)
1398 : {
1399 22400 : switch(typ(z))
1400 : {
1401 14 : case t_INT: return z;
1402 22386 : case t_FRAC: return fractor(z, prec);
1403 0 : case t_REAL: return rtor(z, prec);
1404 0 : case t_QUAD: z = quadtofp(z, prec);
1405 0 : if (typ(z) == t_REAL) return z;
1406 0 : default: pari_err_TYPE("gtomp",z);
1407 : return NULL; /* LCOV_EXCL_LINE */
1408 : }
1409 : }
1410 :
1411 : INLINE GEN
1412 732494 : RgX_gtofp(GEN x, long prec)
1413 : {
1414 : long l;
1415 732494 : GEN y = cgetg_copy(x, &l);
1416 732494 : while (--l > 1) gel(y,l) = gtofp(gel(x,l), prec);
1417 732494 : y[1] = x[1]; return y;
1418 : }
1419 : INLINE GEN
1420 1177203 : RgC_gtofp(GEN x, long prec)
1421 1177203 : { pari_APPLY_type(t_COL, gtofp(gel(x,i), prec)) }
1422 :
1423 : INLINE GEN
1424 42 : RgV_gtofp(GEN x, long prec)
1425 42 : { pari_APPLY_type(t_VEC, gtofp(gel(x,i), prec)) }
1426 :
1427 : INLINE GEN
1428 133962 : RgM_gtofp(GEN x, long prec)
1429 133962 : { pari_APPLY_same(RgC_gtofp(gel(x,i), prec)) }
1430 :
1431 : INLINE GEN
1432 560 : RgC_gtomp(GEN x, long prec)
1433 560 : { pari_APPLY_type(t_COL, gtomp(gel(x,i), prec)) }
1434 :
1435 : INLINE GEN
1436 14 : RgM_gtomp(GEN x, long prec)
1437 14 : { pari_APPLY_same(RgC_gtomp(gel(x,i), prec)) }
1438 :
1439 : INLINE GEN
1440 9150 : RgX_fpnorml2(GEN x, long prec)
1441 : {
1442 9150 : pari_sp av = avma;
1443 9150 : return gerepileupto(av, gnorml2(RgX_gtofp(x, prec)));
1444 : }
1445 : INLINE GEN
1446 177877 : RgC_fpnorml2(GEN x, long prec)
1447 : {
1448 177877 : pari_sp av = avma;
1449 177877 : return gerepileupto(av, gnorml2(RgC_gtofp(x, prec)));
1450 : }
1451 : INLINE GEN
1452 3804 : RgM_fpnorml2(GEN x, long prec)
1453 : {
1454 3804 : pari_sp av = avma;
1455 3804 : return gerepileupto(av, gnorml2(RgM_gtofp(x, prec)));
1456 : }
1457 :
1458 : /* y a t_REAL */
1459 : INLINE void
1460 216244 : affgr(GEN x, GEN y)
1461 : {
1462 : pari_sp av;
1463 216244 : switch(typ(x)) {
1464 5992 : case t_INT: affir(x,y); break;
1465 210252 : case t_REAL: affrr(x,y); break;
1466 0 : case t_FRAC: rdiviiz(gel(x,1),gel(x,2), y); break;
1467 0 : case t_QUAD: av = avma; affgr(quadtofp(x,realprec(y)), y); set_avma(av); break;
1468 0 : default: pari_err_TYPE2("=",x,y);
1469 : }
1470 216244 : }
1471 :
1472 : INLINE GEN
1473 259074 : affc_fixlg(GEN x, GEN res)
1474 : {
1475 259074 : if (typ(x) == t_COMPLEX)
1476 : {
1477 207515 : affrr_fixlg(gel(x,1), gel(res,1));
1478 207515 : affrr_fixlg(gel(x,2), gel(res,2));
1479 : }
1480 : else
1481 : {
1482 51559 : avma = (pari_sp)(res+3);
1483 51559 : res = cgetr(realprec(gel(res,1)));
1484 51559 : affrr_fixlg(x, res);
1485 : }
1486 259074 : return res;
1487 : }
1488 :
1489 : INLINE GEN
1490 0 : trunc_safe(GEN x) { long e; return gcvtoi(x,&e); }
1491 :
1492 : /*******************************************************************/
1493 : /* */
1494 : /* LENGTH CONVERSIONS */
1495 : /* */
1496 : /*******************************************************************/
1497 : INLINE long
1498 28576 : ndec2nlong(long x) { return 1 + (long)((x)*(LOG2_10/BITS_IN_LONG)); }
1499 : INLINE long
1500 28085 : ndec2prec(long x) { return 2 + ndec2nlong(x); }
1501 : INLINE long
1502 491 : ndec2nbits(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1503 : /* Fast implementation of ceil(x / (8*sizeof(long))); typecast to (ulong)
1504 : * to avoid overflow. Faster than 1 + ((x-1)>>TWOPOTBITS_IN_LONG)) :
1505 : * addl, shrl instead of subl, sarl, addl */
1506 : INLINE long
1507 1188724 : nbits2nlong(long x) {
1508 1188724 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1509 : }
1510 :
1511 : INLINE long
1512 312800393 : nbits2extraprec(long x) {
1513 312800393 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1514 : }
1515 :
1516 : /* Fast implementation of 2 + nbits2nlong(x) */
1517 : INLINE long
1518 108433380 : nbits2prec(long x) {
1519 108433380 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1520 : }
1521 : INLINE long
1522 7635716 : nbits2lg(long x) {
1523 7635716 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1524 : }
1525 : /* ceil(x / sizeof(long)) */
1526 : INLINE long
1527 8620846 : nchar2nlong(long x) {
1528 8620846 : return (long)(((ulong)x+sizeof(long)-1) >> (TWOPOTBITS_IN_LONG-3L));
1529 : }
1530 : INLINE long
1531 1148226792 : prec2nbits(long x) { return (x-2) * BITS_IN_LONG; }
1532 : INLINE double
1533 563943 : bit_accuracy_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1534 : INLINE double
1535 300131 : prec2nbits_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1536 : INLINE long
1537 32093944 : bit_prec(GEN x) { return prec2nbits(realprec(x)); }
1538 : INLINE long
1539 1035656051 : bit_accuracy(long x) { return prec2nbits(x); }
1540 : INLINE long
1541 12379 : prec2ndec(long x) { return (long)prec2nbits_mul(x, LOG10_2); }
1542 : INLINE long
1543 193 : nbits2ndec(long x) { return (long)(x * LOG10_2); }
1544 : INLINE long
1545 1771 : precdbl(long x) {return (x - 1) << 1;}
1546 : INLINE long
1547 3407850563 : divsBIL(long n) { return n >> TWOPOTBITS_IN_LONG; }
1548 : INLINE long
1549 3362541870 : remsBIL(long n) { return n & (BITS_IN_LONG-1); }
1550 :
1551 : /*********************************************************************/
1552 : /** **/
1553 : /** OPERATIONS MODULO m **/
1554 : /** **/
1555 : /*********************************************************************/
1556 : /* Assume m > 0, more efficient if 0 <= a, b < m */
1557 :
1558 : INLINE GEN
1559 33685459 : Fp_red(GEN a, GEN m) { return modii(a, m); }
1560 : INLINE GEN
1561 72430955 : Fp_add(GEN a, GEN b, GEN m)
1562 : {
1563 72430955 : pari_sp av=avma;
1564 72430955 : GEN p = addii(a,b);
1565 70627248 : long s = signe(p);
1566 70627248 : if (!s) return p; /* = gen_0 */
1567 63019565 : if (s > 0) /* general case */
1568 : {
1569 62793128 : GEN t = subii(p, m);
1570 63898720 : s = signe(t);
1571 63898720 : if (!s) { set_avma(av); return gen_0; }
1572 58115164 : if (s < 0) { avma = (pari_sp)p; return p; }
1573 24526294 : if (cmpii(t, m) < 0) return gerepileuptoint(av, t); /* general case ! */
1574 1106122 : p = remii(t, m);
1575 : }
1576 : else
1577 226437 : p = modii(p, m);
1578 1332559 : return gerepileuptoint(av, p);
1579 : }
1580 : INLINE GEN
1581 57560874 : Fp_sub(GEN a, GEN b, GEN m)
1582 : {
1583 57560874 : pari_sp av=avma;
1584 57560874 : GEN p = subii(a,b);
1585 56071588 : long s = signe(p);
1586 56071588 : if (!s) return p; /* = gen_0 */
1587 49809610 : if (s > 0)
1588 : {
1589 24076719 : if (cmpii(p, m) < 0) return p; /* general case ! */
1590 1129471 : p = remii(p, m);
1591 : }
1592 : else
1593 : {
1594 25732891 : GEN t = addii(p, m);
1595 25654681 : if (!s) { set_avma(av); return gen_0; }
1596 25654681 : if (s > 0) return gerepileuptoint(av, t); /* general case ! */
1597 25654681 : p = modii(t, m);
1598 : }
1599 27550991 : return gerepileuptoint(av, p);
1600 : }
1601 : INLINE GEN
1602 11621655 : Fp_neg(GEN b, GEN m)
1603 : {
1604 11621655 : pari_sp av = avma;
1605 11621655 : long s = signe(b);
1606 : GEN p;
1607 11621655 : if (!s) return gen_0;
1608 8189630 : if (s > 0)
1609 : {
1610 7989505 : p = subii(m, b);
1611 7987398 : if (signe(p) >= 0) return p; /* general case ! */
1612 92070 : p = modii(p, m);
1613 : } else
1614 200125 : p = remii(negi(b), m);
1615 292195 : return gerepileuptoint(av, p);
1616 : }
1617 :
1618 : INLINE GEN
1619 23592 : Fp_halve(GEN a, GEN p)
1620 : {
1621 23592 : if (mpodd(a)) a = addii(a,p);
1622 23592 : return shifti(a,-1);
1623 : }
1624 :
1625 : /* assume 0 <= u < p and ps2 = p>>1 */
1626 : INLINE GEN
1627 16435266 : Fp_center(GEN u, GEN p, GEN ps2)
1628 16435266 : { return abscmpii(u,ps2)<=0? icopy(u): subii(u,p); }
1629 : /* same without copy */
1630 : INLINE GEN
1631 14930479 : Fp_center_i(GEN u, GEN p, GEN ps2)
1632 14930479 : { return abscmpii(u,ps2)<=0? u: subii(u,p); }
1633 :
1634 : /* x + y*z mod p */
1635 : INLINE GEN
1636 5170825 : Fp_addmul(GEN x, GEN y, GEN z, GEN p)
1637 : {
1638 : pari_sp av;
1639 5170825 : if (!signe(y) || !signe(z)) return Fp_red(x, p);
1640 4876445 : if (!signe(x)) return Fp_mul(z,y, p);
1641 4575606 : av = avma;
1642 4575606 : return gerepileuptoint(av, modii(addii(x, mulii(y,z)), p));
1643 : }
1644 :
1645 : INLINE GEN
1646 91053384 : Fp_mul(GEN a, GEN b, GEN m)
1647 : {
1648 91053384 : pari_sp av=avma;
1649 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1650 91053384 : (void)new_chunk(lg(a)+lg(b)+(lg(m)<<1));
1651 91049160 : p = mulii(a,b);
1652 91169663 : set_avma(av); return modii(p,m);
1653 : }
1654 : INLINE GEN
1655 34908138 : Fp_sqr(GEN a, GEN m)
1656 : {
1657 34908138 : pari_sp av=avma;
1658 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1659 34908138 : (void)new_chunk((lg(a)+lg(m))<<1);
1660 34809673 : p = sqri(a);
1661 30974604 : set_avma(av); return remii(p,m); /*Use remii: p >= 0 */
1662 : }
1663 : INLINE GEN
1664 65560271 : Fp_mulu(GEN a, ulong b, GEN m)
1665 : {
1666 65560271 : long l = lgefint(m);
1667 65560271 : if (l == 3)
1668 : {
1669 39096578 : ulong mm = m[2];
1670 39096578 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1671 : } else {
1672 26463693 : pari_sp av = avma;
1673 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1674 26463693 : (void)new_chunk(lg(a)+1+(l<<1));
1675 26365790 : p = muliu(a,b);
1676 24549564 : set_avma(av); return modii(p,m);
1677 : }
1678 : }
1679 : INLINE GEN
1680 0 : Fp_muls(GEN a, long b, GEN m)
1681 : {
1682 0 : long l = lgefint(m);
1683 0 : if (l == 3)
1684 : {
1685 0 : ulong mm = m[2];
1686 0 : if (b < 0)
1687 : {
1688 0 : ulong t = Fl_mul(umodiu(a, mm), -b, mm);
1689 0 : return t? utoipos(mm - t): gen_0;
1690 : }
1691 : else
1692 0 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1693 : } else {
1694 0 : pari_sp av = avma;
1695 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1696 0 : (void)new_chunk(lg(a)+1+(l<<1));
1697 0 : p = mulis(a,b);
1698 0 : set_avma(av); return modii(p,m);
1699 : }
1700 : }
1701 :
1702 : INLINE GEN
1703 8717051 : Fp_inv(GEN a, GEN m)
1704 : {
1705 : GEN res;
1706 8717051 : if (! invmod(a,m,&res)) pari_err_INV("Fp_inv", mkintmod(res,m));
1707 8716892 : return res;
1708 : }
1709 : INLINE GEN
1710 313889 : Fp_invsafe(GEN a, GEN m)
1711 : {
1712 : GEN res;
1713 313889 : if (! invmod(a,m,&res)) return NULL;
1714 313889 : return res;
1715 : }
1716 : INLINE GEN
1717 2366859 : Fp_div(GEN a, GEN b, GEN m)
1718 : {
1719 2366859 : pari_sp av=avma;
1720 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1721 2366859 : (void)new_chunk(lg(a)+(lg(m)<<1));
1722 2366859 : p = mulii(a, Fp_inv(b,m));
1723 2366855 : set_avma(av); return modii(p,m);
1724 : }
1725 :
1726 : INLINE GEN
1727 842951 : Flx_mulu(GEN x, ulong a, ulong p) { return Flx_Fl_mul(x,a%p,p); }
1728 :
1729 : INLINE GEN
1730 0 : get_F2x_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1731 :
1732 : INLINE long
1733 448468 : get_F2x_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1734 :
1735 : INLINE long
1736 121548 : get_F2x_degree(GEN T) { return typ(T)==t_VEC? F2x_degree(gel(T,2)): F2x_degree(T); }
1737 :
1738 : INLINE GEN
1739 378 : get_F2xqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1740 :
1741 : INLINE long
1742 376495 : get_F2xqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1743 :
1744 : INLINE long
1745 201684 : get_F2xqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1746 :
1747 : INLINE GEN
1748 7447658 : get_Flx_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1749 :
1750 : INLINE long
1751 16390428 : get_Flx_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1752 :
1753 : INLINE long
1754 35654613 : get_Flx_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1755 :
1756 : INLINE GEN
1757 2258 : get_FlxqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1758 :
1759 : INLINE long
1760 368931 : get_FlxqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1761 :
1762 : INLINE long
1763 155787 : get_FlxqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1764 :
1765 : INLINE GEN
1766 1608414 : get_FpX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1767 :
1768 : INLINE long
1769 2891021 : get_FpX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1770 :
1771 : INLINE long
1772 1881815 : get_FpX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1773 :
1774 : INLINE GEN
1775 142586 : get_FpXQX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1776 :
1777 : INLINE long
1778 57357 : get_FpXQX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1779 :
1780 : INLINE long
1781 2187 : get_FpXQX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1782 :
1783 : /*******************************************************************/
1784 : /* */
1785 : /* ADDMULII / SUBMULII */
1786 : /* */
1787 : /*******************************************************************/
1788 : /* x - y*z */
1789 : INLINE GEN
1790 13409985 : submulii(GEN x, GEN y, GEN z)
1791 : {
1792 13409985 : long lx = lgefint(x), ly, lz;
1793 : pari_sp av;
1794 : GEN t;
1795 13409985 : if (lx == 2) { t = mulii(z,y); togglesign(t); return t; }
1796 11599849 : ly = lgefint(y);
1797 11599849 : if (ly == 2) return icopy(x);
1798 10471602 : lz = lgefint(z);
1799 10471602 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1800 10471602 : t = mulii(z, y);
1801 10471602 : set_avma(av); return subii(x,t);
1802 : }
1803 : /* y*z - x */
1804 : INLINE GEN
1805 1188646 : mulsubii(GEN y, GEN z, GEN x)
1806 : {
1807 1188646 : long lx = lgefint(x), ly, lz;
1808 : pari_sp av;
1809 : GEN t;
1810 1188646 : if (lx == 2) return mulii(z,y);
1811 759394 : ly = lgefint(y);
1812 759394 : if (ly == 2) return negi(x);
1813 703302 : lz = lgefint(z);
1814 703302 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1815 703302 : t = mulii(z, y);
1816 703302 : set_avma(av); return subii(t,x);
1817 : }
1818 :
1819 : /* x - u*y */
1820 : INLINE GEN
1821 7595 : submuliu(GEN x, GEN y, ulong u)
1822 : {
1823 : pari_sp av;
1824 7595 : long ly = lgefint(y);
1825 7595 : if (ly == 2) return icopy(x);
1826 7595 : av = avma;
1827 7595 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1828 7595 : y = mului(u,y);
1829 7595 : set_avma(av); return subii(x, y);
1830 : }
1831 : /* x + u*y */
1832 : INLINE GEN
1833 7595 : addmuliu(GEN x, GEN y, ulong u)
1834 : {
1835 : pari_sp av;
1836 7595 : long ly = lgefint(y);
1837 7595 : if (ly == 2) return icopy(x);
1838 7595 : av = avma;
1839 7595 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1840 7595 : y = mului(u,y);
1841 7595 : set_avma(av); return addii(x, y);
1842 : }
1843 : /* x - u*y */
1844 : INLINE GEN
1845 120901232 : submuliu_inplace(GEN x, GEN y, ulong u)
1846 : {
1847 : pari_sp av;
1848 120901232 : long ly = lgefint(y);
1849 120901232 : if (ly == 2) return x;
1850 96727077 : av = avma;
1851 96727077 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1852 96727077 : y = mului(u,y);
1853 96727077 : set_avma(av); return subii(x, y);
1854 : }
1855 : /* x + u*y */
1856 : INLINE GEN
1857 119298819 : addmuliu_inplace(GEN x, GEN y, ulong u)
1858 : {
1859 : pari_sp av;
1860 119298819 : long ly = lgefint(y);
1861 119298819 : if (ly == 2) return x;
1862 96551444 : av = avma;
1863 96551444 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1864 96551444 : y = mului(u,y);
1865 96551444 : set_avma(av); return addii(x, y);
1866 : }
1867 : /* ux + vy */
1868 : INLINE GEN
1869 20302930 : lincombii(GEN u, GEN v, GEN x, GEN y)
1870 : {
1871 20302930 : long lx = lgefint(x), ly;
1872 : GEN p1, p2;
1873 : pari_sp av;
1874 20302930 : if (lx == 2) return mulii(v,y);
1875 14352655 : ly = lgefint(y);
1876 14352655 : if (ly == 2) return mulii(u,x);
1877 13211514 : av = avma; (void)new_chunk(lx+ly+lgefint(u)+lgefint(v)); /* HACK */
1878 13211514 : p1 = mulii(u,x);
1879 13211514 : p2 = mulii(v,y);
1880 13211514 : set_avma(av); return addii(p1,p2);
1881 : }
1882 :
1883 : /*******************************************************************/
1884 : /* */
1885 : /* GEN SUBTYPES */
1886 : /* */
1887 : /*******************************************************************/
1888 :
1889 : INLINE int
1890 1226082059 : is_const_t(long t) { return (t < t_POLMOD); }
1891 : INLINE int
1892 5437 : is_extscalar_t(long t) { return (t <= t_POL); }
1893 : INLINE int
1894 1137343 : is_intreal_t(long t) { return (t <= t_REAL); }
1895 : INLINE int
1896 395920226 : is_matvec_t(long t) { return (t >= t_VEC && t <= t_MAT); }
1897 : INLINE int
1898 60235213 : is_noncalc_t(long tx) { return (tx) >= t_LIST; }
1899 : INLINE int
1900 1184512 : is_rational_t(long t) { return (t == t_INT || t == t_FRAC); }
1901 : INLINE int
1902 416587 : is_real_t(long t) { return (t == t_INT || t == t_REAL || t == t_FRAC); }
1903 : INLINE int
1904 2912125847 : is_recursive_t(long t) { return lontyp[t]; }
1905 : INLINE int
1906 184768853 : is_scalar_t(long t) { return (t < t_POL); }
1907 : INLINE int
1908 1187922 : is_vec_t(long t) { return (t == t_VEC || t == t_COL); }
1909 :
1910 : /*******************************************************************/
1911 : /* */
1912 : /* TRANSCENDENTAL */
1913 : /* */
1914 : /*******************************************************************/
1915 : INLINE GEN
1916 21888771 : sqrtr(GEN x) {
1917 21888771 : long s = signe(x);
1918 21888771 : if (s == 0) return real_0_bit(expo(x) >> 1);
1919 21855104 : if (s >= 0) return sqrtr_abs(x);
1920 29356 : retmkcomplex(gen_0, sqrtr_abs(x));
1921 : }
1922 : INLINE GEN
1923 0 : cbrtr_abs(GEN x) { return sqrtnr_abs(x, 3); }
1924 : INLINE GEN
1925 0 : cbrtr(GEN x) {
1926 0 : long s = signe(x);
1927 : GEN r;
1928 0 : if (s == 0) return real_0_bit(expo(x) / 3);
1929 0 : r = cbrtr_abs(x);
1930 0 : if (s < 0) togglesign(r);
1931 0 : return r;
1932 : }
1933 : INLINE GEN
1934 412022 : sqrtnr(GEN x, long n) {
1935 412022 : long s = signe(x);
1936 : GEN r;
1937 412022 : if (s == 0) return real_0_bit(expo(x) / n);
1938 412022 : r = sqrtnr_abs(x, n);
1939 412022 : if (s < 0) pari_err_IMPL("sqrtnr for x < 0");
1940 412022 : return r;
1941 : }
1942 : INLINE long
1943 212480 : logint(GEN B, GEN y) { return logintall(B,y,NULL); }
1944 : INLINE ulong
1945 1811262 : ulogint(ulong B, ulong y)
1946 : {
1947 : ulong r;
1948 : long e;
1949 1811262 : if (y == 2) return expu(B);
1950 1793167 : r = y;
1951 6012476 : for (e=1;; e++)
1952 : { /* here, r = y^e, r2 = y^(e-1) */
1953 10231785 : if (r >= B) return r == B? e: e-1;
1954 4219309 : r = umuluu_or_0(y, r);
1955 4219309 : if (!r) return e;
1956 : }
1957 : }
1958 :
1959 : /*******************************************************************/
1960 : /* */
1961 : /* MISCELLANEOUS */
1962 : /* */
1963 : /*******************************************************************/
1964 1137266 : INLINE int ismpzero(GEN x) { return is_intreal_t(typ(x)) && !signe(x); }
1965 641782657 : INLINE int isintzero(GEN x) { return typ(x) == t_INT && !signe(x); }
1966 7013084 : INLINE int isint1(GEN x) { return typ(x)==t_INT && equali1(x); }
1967 4613 : INLINE int isintm1(GEN x){ return typ(x)==t_INT && equalim1(x);}
1968 694934452 : INLINE int equali1(GEN n)
1969 694934452 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(1)) && n[2] == 1; }
1970 62133210 : INLINE int equalim1(GEN n)
1971 62133210 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(-1)) && n[2] == 1; }
1972 : /* works only for POSITIVE integers */
1973 950858481 : INLINE int is_pm1(GEN n)
1974 950858481 : { return lgefint(n) == 3 && n[2] == 1; }
1975 238507258 : INLINE int is_bigint(GEN n)
1976 238507258 : { long l = lgefint(n); return l > 3 || (l == 3 && (n[2] & HIGHBIT)); }
1977 :
1978 2055853465 : INLINE int odd(long x) { return x & 1; }
1979 29054384 : INLINE int both_odd(long x, long y) { return x & y & 1; }
1980 :
1981 : INLINE int
1982 2666793322 : isonstack(GEN x)
1983 2666793322 : { return ((pari_sp)x >= pari_mainstack->bot
1984 2666793322 : && (pari_sp)x < pari_mainstack->top); }
1985 :
1986 : /* assume x != 0 and x t_REAL, return an approximation to log2(|x|) */
1987 : INLINE double
1988 22913054 : dbllog2r(GEN x)
1989 22913054 : { return log2((double)(ulong)x[2]) + (double)(expo(x) - (BITS_IN_LONG-1)); }
1990 :
1991 : INLINE GEN
1992 308688 : mul_content(GEN cx, GEN cy)
1993 : {
1994 308688 : if (!cx) return cy;
1995 108114 : if (!cy) return cx;
1996 79214 : return gmul(cx,cy);
1997 : }
1998 : INLINE GEN
1999 5901 : inv_content(GEN c) { return c? ginv(c): NULL; }
2000 : INLINE GEN
2001 1603364 : mul_denom(GEN dx, GEN dy)
2002 : {
2003 1603364 : if (!dx) return dy;
2004 1060357 : if (!dy) return dx;
2005 334397 : return mulii(dx,dy);
2006 : }
2007 :
2008 : /* POLYNOMIALS */
2009 : INLINE GEN
2010 17566877 : constant_coeff(GEN x) { return signe(x)? gel(x,2): gen_0; }
2011 : INLINE GEN
2012 80735685 : leading_coeff(GEN x) { return lg(x) == 2? gen_0: gel(x,lg(x)-1); }
2013 : INLINE ulong
2014 477524 : Flx_lead(GEN x) { return lg(x) == 2? 0: x[lg(x)-1]; }
2015 : INLINE ulong
2016 12348 : Flx_constant(GEN x) { return lg(x) == 2? 0: x[2]; }
2017 : INLINE long
2018 2785770956 : degpol(GEN x) { return lg(x)-3; }
2019 : INLINE long
2020 1380477513 : lgpol(GEN x) { return lg(x)-2; }
2021 : INLINE long
2022 120102311 : lgcols(GEN x) { return lg(gel(x,1)); }
2023 : INLINE long
2024 33484003 : nbrows(GEN x) { return lg(gel(x,1))-1; }
2025 : INLINE GEN
2026 0 : truecoef(GEN x, long n) { return polcoef(x,n,-1); }
2027 :
2028 : INLINE GEN
2029 556213 : ZXQ_mul(GEN y, GEN x, GEN T) { return ZX_rem(ZX_mul(y, x), T); }
2030 : INLINE GEN
2031 278004 : ZXQ_sqr(GEN x, GEN T) { return ZX_rem(ZX_sqr(x), T); }
2032 :
2033 : INLINE GEN
2034 57835841 : RgX_copy(GEN x)
2035 : {
2036 : long lx, i;
2037 57835841 : GEN y = cgetg_copy(x, &lx); y[1] = x[1];
2038 57835841 : for (i = 2; i<lx; i++) gel(y,i) = gcopy(gel(x,i));
2039 57835841 : return y;
2040 : }
2041 : /* have to use ulong to avoid silly warnings from gcc "assuming signed
2042 : * overflow does not occur" */
2043 : INLINE GEN
2044 2957130 : RgX_coeff(GEN x, long n)
2045 : {
2046 2957130 : ulong l = lg(x);
2047 2957130 : return (n < 0 || ((ulong)n+3) > l)? gen_0: gel(x,n+2);
2048 : }
2049 : INLINE GEN
2050 353293 : RgX_renormalize(GEN x) { return RgX_renormalize_lg(x, lg(x)); }
2051 : INLINE GEN
2052 6740160 : RgX_div(GEN x, GEN y) { return RgX_divrem(x,y,NULL); }
2053 : INLINE GEN
2054 1792 : RgXQX_div(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,NULL); }
2055 : INLINE GEN
2056 65162 : RgXQX_rem(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,ONLY_REM); }
2057 : INLINE GEN
2058 884963 : FpX_div(GEN x, GEN y, GEN p) { return FpX_divrem(x,y,p, NULL); }
2059 : INLINE GEN
2060 4350414 : Flx_div(GEN x, GEN y, ulong p) { return Flx_divrem(x,y,p, NULL); }
2061 : INLINE GEN
2062 2593329 : F2x_div(GEN x, GEN y) { return F2x_divrem(x,y, NULL); }
2063 : INLINE GEN
2064 0 : FpV_FpC_mul(GEN x, GEN y, GEN p) { return FpV_dotproduct(x,y,p); }
2065 : INLINE GEN
2066 48247393 : pol0_Flx(long sv) { return mkvecsmall(sv); }
2067 : INLINE GEN
2068 14769000 : pol1_Flx(long sv) { return mkvecsmall2(sv, 1); }
2069 : INLINE GEN
2070 17653106 : polx_Flx(long sv) { return mkvecsmall3(sv, 0, 1); }
2071 : INLINE GEN
2072 0 : zero_zx(long sv) { return zero_Flx(sv); }
2073 : INLINE GEN
2074 0 : polx_zx(long sv) { return polx_Flx(sv); }
2075 : INLINE GEN
2076 0 : zx_shift(GEN x, long n) { return Flx_shift(x,n); }
2077 : INLINE GEN
2078 0 : zx_renormalize(GEN x, long l) { return Flx_renormalize(x,l); }
2079 : INLINE GEN
2080 1474 : zero_F2x(long sv) { return zero_Flx(sv); }
2081 : INLINE GEN
2082 11148215 : pol0_F2x(long sv) { return pol0_Flx(sv); }
2083 : INLINE GEN
2084 2868998 : pol1_F2x(long sv) { return pol1_Flx(sv); }
2085 : INLINE GEN
2086 683448 : polx_F2x(long sv) { return mkvecsmall2(sv, 2); }
2087 : INLINE int
2088 812381 : F2x_equal1(GEN x) { return Flx_equal1(x); }
2089 : INLINE int
2090 3106308 : F2x_equal(GEN V, GEN W) { return Flx_equal(V,W); }
2091 : INLINE GEN
2092 59236901 : F2x_copy(GEN x) { return leafcopy(x); }
2093 : INLINE GEN
2094 0 : F2v_copy(GEN x) { return leafcopy(x); }
2095 : INLINE GEN
2096 2273195 : Flv_copy(GEN x) { return leafcopy(x); }
2097 : INLINE GEN
2098 73971640 : Flx_copy(GEN x) { return leafcopy(x); }
2099 : INLINE GEN
2100 1863876 : vecsmall_copy(GEN x) { return leafcopy(x); }
2101 : INLINE int
2102 4854502 : Flx_equal1(GEN x) { return degpol(x)==0 && x[2] == 1; }
2103 : INLINE int
2104 18205 : ZX_equal1(GEN x) { return degpol(x)==0 && equali1(gel(x,2)); }
2105 : INLINE int
2106 4629094 : ZX_is_monic(GEN x) { return equali1(leading_coeff(x)); }
2107 :
2108 : INLINE GEN
2109 50603134 : ZX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2110 : INLINE GEN
2111 67225900 : FpX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2112 : INLINE GEN
2113 771228 : FpXX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2114 : INLINE GEN
2115 1237233 : FpXQX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2116 : INLINE GEN
2117 111322394 : F2x_renormalize(GEN x, long lx) { return Flx_renormalize(x,lx); }
2118 : INLINE GEN
2119 32315 : F2v_to_F2x(GEN x, long sv) {
2120 32315 : GEN y = leafcopy(x);
2121 32315 : y[1] = sv; F2x_renormalize(y, lg(y)); return y;
2122 : }
2123 :
2124 : INLINE long
2125 0 : sturm(GEN x) { return sturmpart(x, NULL, NULL); }
2126 :
2127 : INLINE long
2128 7042 : gval(GEN x, long v) {
2129 7042 : pari_sp av = avma;
2130 7042 : long n = gvaluation(x, pol_x(v));
2131 7042 : set_avma(av); return n;
2132 : }
2133 :
2134 : INLINE void
2135 469122 : RgX_shift_inplace_init(long v)
2136 469122 : { if (v) (void)cgetg(v, t_VECSMALL); }
2137 : /* shift polynomial in place. assume v free cells have been left before x */
2138 : INLINE GEN
2139 469122 : RgX_shift_inplace(GEN x, long v)
2140 : {
2141 : long i, lx;
2142 : GEN y, z;
2143 469122 : if (!v) return x;
2144 253227 : lx = lg(x);
2145 253227 : if (lx == 2) return x;
2146 253227 : y = x + v;
2147 253227 : z = x + lx;
2148 : /* stackdummy from normalizepol: move it up */
2149 253227 : if (lg(z) != v) x[lx + v] = z[0];
2150 253227 : for (i = lx-1; i >= 2; i--) gel(y,i) = gel(x,i);
2151 253227 : for (i = v+1; i >= 2; i--) gel(x,i) = gen_0;
2152 : /* leave x[1] alone: it is correct */
2153 253227 : x[0] = evaltyp(t_POL) | evallg(lx+v); return x;
2154 : }
2155 :
2156 :
2157 : /* LINEAR ALGEBRA */
2158 : INLINE GEN
2159 131784 : zv_to_ZV(GEN x) { return vecsmall_to_vec(x); }
2160 : INLINE GEN
2161 5191030 : zc_to_ZC(GEN x) { return vecsmall_to_col(x); }
2162 : INLINE GEN
2163 438842 : ZV_to_zv(GEN x) { return vec_to_vecsmall(x); }
2164 : INLINE GEN
2165 0 : zx_to_zv(GEN x, long N) { return Flx_to_Flv(x,N); }
2166 : INLINE GEN
2167 0 : zv_to_zx(GEN x, long sv) { return Flv_to_Flx(x,sv); }
2168 : INLINE GEN
2169 0 : zm_to_zxV(GEN x, long sv) { return Flm_to_FlxV(x,sv); }
2170 : INLINE GEN
2171 0 : zero_zm(long x, long y) { return zero_Flm(x,y); }
2172 : INLINE GEN
2173 17148979 : zero_zv(long x) { return zero_Flv(x); }
2174 : INLINE GEN
2175 210 : zm_transpose(GEN x) { return Flm_transpose(x); }
2176 : INLINE GEN
2177 0 : zm_copy(GEN x) { return Flm_copy(x); }
2178 : INLINE GEN
2179 1903271 : zv_copy(GEN x) { return Flv_copy(x); }
2180 : INLINE GEN
2181 0 : zm_row(GEN x, long i) { return Flm_row(x,i); }
2182 :
2183 : INLINE GEN
2184 843568 : ZC_hnfrem(GEN x, GEN y) { return ZC_hnfremdiv(x,y,NULL); }
2185 : INLINE GEN
2186 35594 : ZM_hnfrem(GEN x, GEN y) { return ZM_hnfdivrem(x,y,NULL); }
2187 : INLINE GEN
2188 2380888 : ZM_lll(GEN x, double D, long f) { return ZM_lll_norms(x,D,f,NULL); }
2189 : INLINE void
2190 5649816 : RgM_dimensions(GEN x, long *m, long *n) { *n = lg(x)-1; *m = *n? nbrows(x): 0; }
2191 : INLINE GEN
2192 9921975 : RgM_shallowcopy(GEN x)
2193 : {
2194 : long l;
2195 9921975 : GEN y = cgetg_copy(x, &l);
2196 9921975 : while (--l > 0) gel(y,l) = leafcopy(gel(x,l));
2197 9921975 : return y;
2198 : }
2199 : INLINE GEN
2200 302 : F2m_copy(GEN x) { return RgM_shallowcopy(x); }
2201 :
2202 : INLINE GEN
2203 1313793 : Flm_copy(GEN x) { return RgM_shallowcopy(x); }
2204 :
2205 : /* divisibility: return 1 if y[i] | x[i] for all i, 0 otherwise. Assume
2206 : * x,y are ZV of the same length */
2207 : INLINE int
2208 23198 : ZV_dvd(GEN x, GEN y)
2209 : {
2210 23198 : long i, l = lg(x);
2211 36652 : for (i=1; i < l; i++)
2212 29519 : if ( ! dvdii( gel(x,i), gel(y,i) ) ) return 0;
2213 7133 : return 1;
2214 : }
2215 :
2216 : /* Fq */
2217 : INLINE GEN
2218 2798419 : Fq_red(GEN x, GEN T, GEN p)
2219 2798419 : { return typ(x)==t_INT? Fp_red(x,p): FpXQ_red(x,T,p); }
2220 : INLINE GEN
2221 43439 : Fq_to_FpXQ(GEN x, GEN T, GEN p /*unused*/)
2222 : {
2223 : (void) p;
2224 43439 : return typ(x)==t_INT ? scalarpol(x, get_FpX_var(T)): x;
2225 : }
2226 : INLINE GEN
2227 756 : Rg_to_Fq(GEN x, GEN T, GEN p) { return T? Rg_to_FpXQ(x,T,p): Rg_to_Fp(x,p); }
2228 :
2229 : INLINE GEN
2230 903 : gener_Fq_local(GEN T, GEN p, GEN L)
2231 : { return T? gener_FpXQ_local(T,p, L)
2232 903 : : pgener_Fp_local(p, L); }
2233 :
2234 : /* FpXQX */
2235 : INLINE GEN
2236 4347 : FpXQX_div(GEN x, GEN y, GEN T, GEN p) { return FpXQX_divrem(x, y, T, p, NULL); }
2237 : INLINE GEN
2238 34803 : FlxqX_div(GEN x, GEN y, GEN T, ulong p) { return FlxqX_divrem(x, y, T, p, NULL); }
2239 : INLINE GEN
2240 33278 : F2xqX_div(GEN x, GEN y, GEN T) { return F2xqX_divrem(x, y, T, NULL); }
2241 :
2242 : /* FqX */
2243 : INLINE GEN
2244 25431 : FqX_red(GEN z, GEN T, GEN p) { return T? FpXQX_red(z, T, p): FpX_red(z, p); }
2245 : INLINE GEN
2246 957187 : FqX_add(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2247 : INLINE GEN
2248 17404 : FqX_neg(GEN x,GEN T,GEN p) { return T? FpXX_neg(x,p): FpX_neg(x,p); }
2249 : INLINE GEN
2250 3234 : FqX_sub(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2251 : INLINE GEN
2252 656080 : FqX_Fp_mul(GEN P, GEN u, GEN T, GEN p)
2253 656080 : { return T? FpXX_Fp_mul(P, u, p): FpX_Fp_mul(P, u, p); }
2254 : INLINE GEN
2255 587707 : FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
2256 587707 : { return typ(U)==t_INT ? FqX_Fp_mul(P, U, T, p): FpXQX_FpXQ_mul(P, U, T, p); }
2257 : INLINE GEN
2258 96027 : FqX_mul(GEN x, GEN y, GEN T, GEN p)
2259 96027 : { return T? FpXQX_mul(x, y, T, p): FpX_mul(x, y, p); }
2260 : INLINE GEN
2261 489744 : FqX_mulu(GEN x, ulong y, GEN T, GEN p)
2262 489744 : { return T? FpXX_mulu(x, y, p): FpX_mulu(x, y, p); }
2263 : INLINE GEN
2264 6468 : FqX_sqr(GEN x, GEN T, GEN p)
2265 6468 : { return T? FpXQX_sqr(x, T, p): FpX_sqr(x, p); }
2266 : INLINE GEN
2267 1288 : FqX_powu(GEN x, ulong n, GEN T, GEN p)
2268 1288 : { return T? FpXQX_powu(x, n, T, p): FpX_powu(x, n, p); }
2269 : INLINE GEN
2270 0 : FqX_halve(GEN x, GEN T, GEN p)
2271 0 : { return T? FpXX_halve(x, p): FpX_halve(x, p); }
2272 : INLINE GEN
2273 5523 : FqX_div(GEN x, GEN y, GEN T, GEN p)
2274 5523 : { return T? FpXQX_divrem(x,y,T,p,NULL): FpX_divrem(x,y,p,NULL); }
2275 : INLINE GEN
2276 6095 : FqX_get_red(GEN S, GEN T, GEN p)
2277 6095 : { return T? FpXQX_get_red(S,T,p): FpX_get_red(S,p); }
2278 : INLINE GEN
2279 53108 : FqX_rem(GEN x, GEN y, GEN T, GEN p)
2280 53108 : { return T? FpXQX_rem(x,y,T,p): FpX_rem(x,y,p); }
2281 : INLINE GEN
2282 0 : FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
2283 0 : { return T? FpXQX_divrem(x,y,T,p,z): FpX_divrem(x,y,p,z); }
2284 : INLINE GEN
2285 5936 : FqX_div_by_X_x(GEN x, GEN y, GEN T, GEN p, GEN *z)
2286 5936 : { return T? FpXQX_div_by_X_x(x,y,T,p,z): FpX_div_by_X_x(x,y,p,z); }
2287 : INLINE GEN
2288 0 : FqX_halfgcd(GEN P,GEN Q,GEN T,GEN p)
2289 0 : {return T? FpXQX_halfgcd(P,Q,T,p): FpX_halfgcd(P,Q,p);}
2290 : INLINE GEN
2291 259098 : FqX_gcd(GEN P,GEN Q,GEN T,GEN p)
2292 259098 : {return T? FpXQX_gcd(P,Q,T,p): FpX_gcd(P,Q,p);}
2293 : INLINE GEN
2294 87043 : FqX_extgcd(GEN P,GEN Q,GEN T,GEN p, GEN *U, GEN *V)
2295 87043 : { return T? FpXQX_extgcd(P,Q,T,p,U,V): FpX_extgcd(P,Q,p,U,V); }
2296 : INLINE GEN
2297 3178 : FqX_normalize(GEN z, GEN T, GEN p)
2298 3178 : { return T? FpXQX_normalize(z, T, p): FpX_normalize(z, p); }
2299 : INLINE GEN
2300 272895 : FqX_deriv(GEN f, GEN T, GEN p) { return T? FpXX_deriv(f, p): FpX_deriv(f, p); }
2301 : INLINE GEN
2302 0 : FqX_integ(GEN f, GEN T, GEN p) { return T? FpXX_integ(f, p): FpX_integ(f, p); }
2303 : INLINE GEN
2304 74459 : FqX_factor(GEN f, GEN T, GEN p)
2305 74459 : { return T?FpXQX_factor(f, T, p): FpX_factor(f, p); }
2306 : INLINE GEN
2307 7 : FqX_factor_squarefree(GEN f, GEN T, GEN p)
2308 7 : { return T ? FpXQX_factor_squarefree(f, T, p): FpX_factor_squarefree(f, p); }
2309 : INLINE GEN
2310 7 : FqX_ddf(GEN f, GEN T, GEN p)
2311 7 : { return T ? FpXQX_ddf(f, T, p): FpX_ddf(f, p); }
2312 : INLINE GEN
2313 42 : FqX_degfact(GEN f, GEN T, GEN p)
2314 42 : { return T?FpXQX_degfact(f, T, p): FpX_degfact(f, p); }
2315 : INLINE GEN
2316 7126 : FqX_roots(GEN f, GEN T, GEN p)
2317 7126 : { return T?FpXQX_roots(f, T, p): FpX_roots(f, p); }
2318 : INLINE GEN
2319 203 : FqX_to_mod(GEN f, GEN T, GEN p)
2320 203 : { return T?FpXQX_to_mod(f, T, p): FpX_to_mod(f, p); }
2321 :
2322 : /*FqXQ*/
2323 : INLINE GEN
2324 0 : FqXQ_add(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2325 0 : { (void)S; return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2326 : INLINE GEN
2327 0 : FqXQ_sub(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2328 0 : { (void)S; return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2329 : INLINE GEN
2330 0 : FqXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
2331 0 : { return T? FpXQXQ_div(x,y,S,T,p): FpXQ_div(x,y,S,p); }
2332 : INLINE GEN
2333 0 : FqXQ_inv(GEN x, GEN S, GEN T, GEN p)
2334 0 : { return T? FpXQXQ_inv(x,S,T,p): FpXQ_inv(x,S,p); }
2335 : INLINE GEN
2336 0 : FqXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
2337 0 : { return T? FpXQXQ_invsafe(x,S,T,p): FpXQ_inv(x,S,p); }
2338 : INLINE GEN
2339 22348 : FqXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
2340 22348 : { return T? FpXQXQ_mul(x,y,S,T,p): FpXQ_mul(x,y,S,p); }
2341 : INLINE GEN
2342 0 : FqXQ_sqr(GEN x, GEN S, GEN T, GEN p)
2343 0 : { return T? FpXQXQ_sqr(x,S,T,p): FpXQ_sqr(x,S,p); }
2344 : INLINE GEN
2345 0 : FqXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
2346 0 : { return T? FpXQXQ_pow(x,n,S,T,p): FpXQ_pow(x,n,S,p); }
2347 :
2348 : /*FqXn*/
2349 : INLINE GEN
2350 0 : FqXn_exp(GEN x, long n, GEN T, GEN p)
2351 0 : { return T? FpXQXn_exp(x,n,T,p): FpXn_exp(x,n,p); }
2352 : INLINE GEN
2353 0 : FqXn_inv(GEN x, long n, GEN T, GEN p)
2354 0 : { return T? FpXQXn_inv(x,n,T,p): FpXn_inv(x,n,p); }
2355 : INLINE GEN
2356 0 : FqXn_mul(GEN x, GEN y, long n, GEN T, GEN p)
2357 0 : { return T? FpXQXn_mul(x, y, n, T, p): FpXn_mul(x, y, n, p); }
2358 : INLINE GEN
2359 0 : FqXn_sqr(GEN x, long n, GEN T, GEN p)
2360 0 : { return T? FpXQXn_sqr(x,n,T,p): FpXn_sqr(x,n,p); }
2361 :
2362 : /*FpXQ*/
2363 : INLINE GEN
2364 0 : FpXQ_add(GEN x,GEN y,GEN T/*unused*/,GEN p)
2365 0 : { (void)T; return FpX_add(x,y,p); }
2366 : INLINE GEN
2367 0 : FpXQ_sub(GEN x,GEN y,GEN T/*unused*/,GEN p)
2368 0 : { (void)T; return FpX_sub(x,y,p); }
2369 :
2370 : /*Flxq*/
2371 : INLINE GEN
2372 0 : Flxq_add(GEN x,GEN y,GEN T/*unused*/,ulong p)
2373 0 : { (void)T; return Flx_add(x,y,p); }
2374 : INLINE GEN
2375 0 : Flxq_sub(GEN x,GEN y,GEN T/*unused*/,ulong p)
2376 0 : { (void)T; return Flx_sub(x,y,p); }
2377 :
2378 : /* F2x */
2379 :
2380 : INLINE ulong
2381 100443820 : F2x_coeff(GEN x,long v)
2382 : {
2383 100443820 : ulong u=(ulong)x[2+divsBIL(v)];
2384 100441550 : return (u>>remsBIL(v))&1UL;
2385 : }
2386 :
2387 : INLINE void
2388 4710245 : F2x_clear(GEN x,long v)
2389 : {
2390 4710245 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2391 4710245 : *u&=~(1UL<<remsBIL(v));
2392 4710245 : }
2393 :
2394 : INLINE void
2395 32715384 : F2x_set(GEN x,long v)
2396 : {
2397 32715384 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2398 32694750 : *u|=1UL<<remsBIL(v);
2399 32690295 : }
2400 :
2401 : INLINE void
2402 1501266 : F2x_flip(GEN x,long v)
2403 : {
2404 1501266 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2405 1501266 : *u^=1UL<<remsBIL(v);
2406 1501266 : }
2407 :
2408 : /* F2v */
2409 :
2410 : INLINE ulong
2411 95878532 : F2v_coeff(GEN x,long v) { return F2x_coeff(x,v-1); }
2412 :
2413 : INLINE void
2414 4710245 : F2v_clear(GEN x,long v) { F2x_clear(x,v-1); }
2415 :
2416 : INLINE void
2417 8950420 : F2v_set(GEN x,long v) { F2x_set(x,v-1); }
2418 :
2419 : INLINE void
2420 1501266 : F2v_flip(GEN x,long v) { F2x_flip(x,v-1); }
2421 :
2422 : /* F2m */
2423 :
2424 : INLINE ulong
2425 11668689 : F2m_coeff(GEN x, long a, long b) { return F2v_coeff(gel(x,b), a); }
2426 :
2427 : INLINE void
2428 0 : F2m_clear(GEN x, long a, long b) { F2v_clear(gel(x,b), a); }
2429 :
2430 : INLINE void
2431 1362615 : F2m_set(GEN x, long a, long b) { F2v_set(gel(x,b), a); }
2432 :
2433 : INLINE void
2434 1501266 : F2m_flip(GEN x, long a, long b) { F2v_flip(gel(x,b), a); }
2435 :
2436 : /* ARITHMETIC */
2437 : INLINE GEN
2438 1071 : matpascal(long n) { return matqpascal(n, NULL); }
2439 : INLINE long
2440 2330804 : Z_issquare(GEN x) { return Z_issquareall(x, NULL); }
2441 : INLINE long
2442 14 : Z_ispower(GEN x, ulong k) { return Z_ispowerall(x, k, NULL); }
2443 : INLINE GEN
2444 5678647 : sqrti(GEN x) { return sqrtremi(x,NULL); }
2445 : INLINE GEN
2446 4654827 : gaddgs(GEN y, long s) { return gaddsg(s,y); }
2447 : INLINE int
2448 41894 : gcmpgs(GEN y, long s) { return -gcmpsg(s,y); }
2449 : INLINE int
2450 24570 : gequalgs(GEN y, long s) { return gequalsg(s,y); }
2451 : INLINE GEN
2452 0 : gmaxsg(long s, GEN y) { return gmaxgs(y,s); }
2453 : INLINE GEN
2454 0 : gminsg(long s, GEN y) { return gmings(y,s); }
2455 : INLINE GEN
2456 13320314 : gmulgs(GEN y, long s) { return gmulsg(s,y); }
2457 : INLINE GEN
2458 1368594 : gsubgs(GEN y, long s) { return gaddgs(y, -s); }
2459 : INLINE GEN
2460 678134 : gdivsg(long s, GEN y) { return gdiv(stoi(s), y); }
2461 :
2462 : /* x t_COMPLEX */
2463 : INLINE GEN
2464 12564580 : cxnorm(GEN x) { return gadd(gsqr(gel(x,1)), gsqr(gel(x,2))); }
2465 : /* q t_QUAD */
2466 : INLINE GEN
2467 623 : quadnorm(GEN q)
2468 : {
2469 623 : GEN X = gel(q,1), b = gel(X,3), c = gel(X,2);
2470 623 : GEN z, u = gel(q,3), v = gel(q,2);
2471 623 : if (typ(u) == t_INT && typ(v) == t_INT) /* generic case */
2472 : {
2473 308 : z = signe(b)? mulii(v, addii(u,v)): sqri(v);
2474 308 : return addii(z, mulii(c, sqri(u)));
2475 : }
2476 : else
2477 : {
2478 315 : z = signe(b)? gmul(v, gadd(u,v)): gsqr(v);
2479 315 : return gadd(z, gmul(c, gsqr(u)));
2480 : }
2481 : }
2482 : /* x a t_QUAD, return the attached discriminant */
2483 : INLINE GEN
2484 273 : quad_disc(GEN x)
2485 : {
2486 273 : GEN Q = gel(x,1), b = gel(Q,3), c = gel(Q,2), c4;
2487 273 : if (is_pm1(b))
2488 : {
2489 217 : pari_sp av = avma; (void)new_chunk(lgefint(c) + 1);
2490 217 : c4 = shifti(c,2); set_avma(av); return subsi(1, c4);
2491 : }
2492 56 : c4 = shifti(c,2); togglesign_safe(&c4); return c4;
2493 : }
2494 : INLINE GEN
2495 6480663 : qfb_disc3(GEN x, GEN y, GEN z) { return subii(sqri(y), shifti(mulii(x,z),2)); }
2496 : INLINE GEN
2497 6399785 : qfb_disc(GEN x) { return qfb_disc3(gel(x,1), gel(x,2), gel(x,3)); }
2498 :
2499 : INLINE GEN
2500 1401789 : sqrfrac(GEN x)
2501 : {
2502 1401789 : GEN z = cgetg(3,t_FRAC);
2503 1401789 : gel(z,1) = sqri(gel(x,1));
2504 1401789 : gel(z,2) = sqri(gel(x,2)); return z;
2505 : }
2506 :
2507 : INLINE void
2508 21986742 : normalize_frac(GEN z) {
2509 21986742 : if (signe(gel(z,2)) < 0) { togglesign(gel(z,1)); setabssign(gel(z,2)); }
2510 21986742 : }
2511 :
2512 : INLINE GEN
2513 251224 : powii(GEN x, GEN n)
2514 : {
2515 251224 : long ln = lgefint(n);
2516 251224 : if (ln == 3) {
2517 : GEN z;
2518 248606 : if (signe(n) > 0) return powiu(x, n[2]);
2519 5852 : z = cgetg(3, t_FRAC);
2520 5852 : gel(z,1) = gen_1;
2521 5852 : gel(z,2) = powiu(x, n[2]);
2522 5852 : return z;
2523 : }
2524 2618 : if (ln == 2) return gen_1; /* rare */
2525 : /* should never happen */
2526 0 : return powgi(x, n); /* overflow unless x = 0, 1, -1 */
2527 : }
2528 : INLINE GEN
2529 1246 : powIs(long n) {
2530 1246 : switch(n & 3)
2531 : {
2532 28 : case 1: return mkcomplex(gen_0,gen_1);
2533 378 : case 2: return gen_m1;
2534 518 : case 3: return mkcomplex(gen_0,gen_m1);
2535 : }
2536 322 : return gen_1;
2537 : }
2538 :
2539 : /*******************************************************************/
2540 : /* */
2541 : /* ASSIGNMENTS */
2542 : /* */
2543 : /*******************************************************************/
2544 0 : INLINE void mpexpz(GEN x, GEN z)
2545 0 : { pari_sp av = avma; gaffect(mpexp(x), z); set_avma(av); }
2546 0 : INLINE void mplogz(GEN x, GEN z)
2547 0 : { pari_sp av = avma; gaffect(mplog(x), z); set_avma(av); }
2548 0 : INLINE void mpcosz(GEN x, GEN z)
2549 0 : { pari_sp av = avma; gaffect(mpcos(x), z); set_avma(av); }
2550 0 : INLINE void mpsinz(GEN x, GEN z)
2551 0 : { pari_sp av = avma; gaffect(mpsin(x), z); set_avma(av); }
2552 0 : INLINE void gnegz(GEN x, GEN z)
2553 0 : { pari_sp av = avma; gaffect(gneg(x), z); set_avma(av); }
2554 0 : INLINE void gabsz(GEN x, long prec, GEN z)
2555 0 : { pari_sp av = avma; gaffect(gabs(x,prec), z); set_avma(av); }
2556 0 : INLINE void gaddz(GEN x, GEN y, GEN z)
2557 0 : { pari_sp av = avma; gaffect(gadd(x,y), z); set_avma(av); }
2558 0 : INLINE void gsubz(GEN x, GEN y, GEN z)
2559 0 : { pari_sp av = avma; gaffect(gsub(x,y), z); set_avma(av); }
2560 0 : INLINE void gmulz(GEN x, GEN y, GEN z)
2561 0 : { pari_sp av = avma; gaffect(gmul(x,y), z); set_avma(av); }
2562 0 : INLINE void gdivz(GEN x, GEN y, GEN z)
2563 0 : { pari_sp av = avma; gaffect(gdiv(x,y), z); set_avma(av); }
2564 0 : INLINE void gdiventz(GEN x, GEN y, GEN z)
2565 0 : { pari_sp av = avma; gaffect(gdivent(x,y), z); set_avma(av); }
2566 0 : INLINE void gmodz(GEN x, GEN y, GEN z)
2567 0 : { pari_sp av = avma; gaffect(gmod(x,y), z); set_avma(av); }
2568 0 : INLINE void gmul2nz(GEN x, long s, GEN z)
2569 0 : { pari_sp av = avma; gaffect(gmul2n(x,s), z); set_avma(av); }
2570 0 : INLINE void gshiftz(GEN x, long s, GEN z)
2571 0 : { pari_sp av = avma; gaffect(gshift(x,s), z); set_avma(av); }
2572 :
2573 : /*******************************************************************/
2574 : /* */
2575 : /* ELLIPTIC CURVES */
2576 : /* */
2577 : /*******************************************************************/
2578 3979762 : INLINE GEN ell_get_a1(GEN e) { return gel(e,1); }
2579 3095796 : INLINE GEN ell_get_a2(GEN e) { return gel(e,2); }
2580 3861712 : INLINE GEN ell_get_a3(GEN e) { return gel(e,3); }
2581 3888741 : INLINE GEN ell_get_a4(GEN e) { return gel(e,4); }
2582 4704920 : INLINE GEN ell_get_a6(GEN e) { return gel(e,5); }
2583 3318542 : INLINE GEN ell_get_b2(GEN e) { return gel(e,6); }
2584 1024949 : INLINE GEN ell_get_b4(GEN e) { return gel(e,7); }
2585 1630617 : INLINE GEN ell_get_b6(GEN e) { return gel(e,8); }
2586 1464001 : INLINE GEN ell_get_b8(GEN e) { return gel(e,9); }
2587 6167392 : INLINE GEN ell_get_c4(GEN e) { return gel(e,10); }
2588 7403867 : INLINE GEN ell_get_c6(GEN e) { return gel(e,11); }
2589 9654117 : INLINE GEN ell_get_disc(GEN e) { return gel(e,12); }
2590 1028909 : INLINE GEN ell_get_j(GEN e) { return gel(e,13); }
2591 11456590 : INLINE long ell_get_type(GEN e) { return mael(e,14,1); }
2592 1570443 : INLINE GEN ellff_get_field(GEN x) { return gmael(x, 15, 1); }
2593 683132 : INLINE GEN ellff_get_a4a6(GEN x) { return gmael(x, 15, 2); }
2594 1407 : INLINE GEN ellQp_get_zero(GEN x) { return gmael(x, 15, 1); }
2595 287 : INLINE long ellQp_get_prec(GEN E) { GEN z = ellQp_get_zero(E); return valp(z); }
2596 1085 : INLINE GEN ellQp_get_p(GEN E) { GEN z = ellQp_get_zero(E); return gel(z,2); }
2597 37156 : INLINE long ellR_get_prec(GEN x) { return nbits2prec(mael3(x, 15, 1, 1)); }
2598 12106 : INLINE long ellR_get_sign(GEN x) { return mael3(x, 15, 1, 2); }
2599 699475 : INLINE GEN ellnf_get_nf(GEN x) { return checknf_i(gmael(x,15,1)); }
2600 56 : INLINE GEN ellnf_get_bnf(GEN x) { return checkbnf_i(gmael(x,15,1)); }
2601 :
2602 4625083 : INLINE int checkell_i(GEN e) { return typ(e) == t_VEC && lg(e) == 17; }
2603 33935288 : INLINE int ell_is_inf(GEN z) { return lg(z) == 2; }
2604 809800 : INLINE GEN ellinf(void) { return mkvec(gen_0); }
2605 :
2606 : /*******************************************************************/
2607 : /* */
2608 : /* ALGEBRAIC NUMBER THEORY */
2609 : /* */
2610 : /*******************************************************************/
2611 8126888 : INLINE GEN modpr_get_pr(GEN x) { return gel(x,3); }
2612 609537 : INLINE GEN modpr_get_p(GEN x) { return pr_get_p(modpr_get_pr(x)); }
2613 2520393 : INLINE GEN modpr_get_T(GEN x) { return lg(x) == 4? NULL: gel(x,4); }
2614 :
2615 19371035 : INLINE GEN pr_get_p(GEN pr) { return gel(pr,1); }
2616 6273244 : INLINE GEN pr_get_gen(GEN pr){ return gel(pr,2); }
2617 : /* .[2] instead of itos works: e and f are small positive integers */
2618 2266368 : INLINE long pr_get_e(GEN pr) { return gel(pr,3)[2]; }
2619 8716225 : INLINE long pr_get_f(GEN pr) { return gel(pr,4)[2]; }
2620 6141813 : INLINE GEN pr_get_tau(GEN pr){ return gel(pr,5); }
2621 : INLINE int
2622 3051851 : pr_is_inert(GEN P) { return pr_get_f(P) == lg(pr_get_gen(P))-1; }
2623 : INLINE GEN
2624 217505 : pr_norm(GEN pr) { return powiu(pr_get_p(pr), pr_get_f(pr)); }
2625 : INLINE ulong
2626 39487 : upr_norm(GEN pr) { return upowuu(pr_get_p(pr)[2], pr_get_f(pr)); }
2627 :
2628 : /* assume nf a genuine nf */
2629 : INLINE long
2630 4528 : nf_get_varn(GEN nf) { return varn(gel(nf,1)); }
2631 : INLINE GEN
2632 30918941 : nf_get_pol(GEN nf) { return gel(nf,1); }
2633 : INLINE long
2634 24711013 : nf_get_degree(GEN nf) { return degpol( nf_get_pol(nf) ); }
2635 : INLINE long
2636 4092354 : nf_get_r1(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,1)); }
2637 : INLINE long
2638 1673 : nf_get_r2(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,2)); }
2639 : INLINE GEN
2640 49826 : nf_get_disc(GEN nf) { return gel(nf,3); }
2641 : INLINE GEN
2642 765959 : nf_get_index(GEN nf) { return gel(nf,4); }
2643 : INLINE GEN
2644 2821420 : nf_get_M(GEN nf) { return gmael(nf,5,1); }
2645 : INLINE GEN
2646 73824 : nf_get_G(GEN nf) { return gmael(nf,5,2); }
2647 : INLINE GEN
2648 385499 : nf_get_roundG(GEN nf) { return gmael(nf,5,3); }
2649 : INLINE GEN
2650 24367 : nf_get_Tr(GEN nf) { return gmael(nf,5,4); }
2651 : INLINE GEN
2652 2324 : nf_get_diff(GEN nf) { return gmael(nf,5,5); }
2653 : INLINE GEN
2654 84 : nf_get_ramified_primes(GEN nf) { return gmael(nf,5,8); }
2655 : INLINE GEN
2656 291043 : nf_get_roots(GEN nf) { return gel(nf,6); }
2657 : INLINE GEN
2658 91 : nf_get_zk(GEN nf)
2659 : {
2660 91 : GEN y = gel(nf,7), D = gel(y, 1);
2661 91 : if (typ(D) == t_POL) D = gel(D, 2);
2662 91 : if (!equali1(D)) y = gdiv(y, D);
2663 91 : return y;
2664 : }
2665 : INLINE GEN
2666 247685 : nf_get_zkprimpart(GEN nf)
2667 : {
2668 247685 : GEN y = gel(nf,7);
2669 : /* test for old format of nf.zk: non normalized */
2670 247685 : if (!equali1(gel(nf,4)) && gequal1(gel(y,1))) y = Q_remove_denom(y,NULL);
2671 247685 : return y;
2672 : }
2673 : INLINE GEN
2674 248813 : nf_get_zkden(GEN nf)
2675 : {
2676 248813 : GEN y = gel(nf,7), D = gel(y,1);
2677 248813 : if (typ(D) == t_POL) D = gel(D,2);
2678 : /* test for old format of nf.zk: non normalized */
2679 248813 : if (!equali1(gel(nf,4)) && equali1(D)) D = Q_denom(y);
2680 248813 : return D;
2681 : }
2682 : INLINE GEN
2683 2337048 : nf_get_invzk(GEN nf) { return gel(nf,8); }
2684 : INLINE void
2685 19819 : nf_get_sign(GEN nf, long *r1, long *r2)
2686 : {
2687 19819 : GEN x = gel(nf,2);
2688 19819 : *r1 = itou(gel(x,1));
2689 19819 : *r2 = itou(gel(x,2));
2690 19819 : }
2691 :
2692 : INLINE GEN
2693 53411 : abgrp_get_no(GEN x) { return gel(x,1); }
2694 : INLINE GEN
2695 2094351 : abgrp_get_cyc(GEN x) { return gel(x,2); }
2696 : INLINE GEN
2697 396512 : abgrp_get_gen(GEN x) { return gel(x,3); }
2698 : INLINE GEN
2699 2062709 : bnf_get_nf(GEN bnf) { return gel(bnf,7); }
2700 : INLINE GEN
2701 806275 : bnf_get_clgp(GEN bnf) { return gmael(bnf,8,1); }
2702 : INLINE GEN
2703 4564 : bnf_get_no(GEN bnf) { return abgrp_get_no(bnf_get_clgp(bnf)); }
2704 : INLINE GEN
2705 434249 : bnf_get_cyc(GEN bnf) { return abgrp_get_cyc(bnf_get_clgp(bnf)); }
2706 : INLINE GEN
2707 367133 : bnf_get_gen(GEN bnf) { return abgrp_get_gen(bnf_get_clgp(bnf)); }
2708 : INLINE GEN
2709 846 : bnf_get_reg(GEN bnf) { return gmael(bnf,8,2); }
2710 : INLINE GEN
2711 481743 : bnf_get_logfu(GEN bnf) { return gel(bnf,3); }
2712 : INLINE GEN
2713 5868 : bnf_get_tuU(GEN bnf) { return gmael3(bnf,8,4,2); }
2714 : INLINE long
2715 24682 : bnf_get_tuN(GEN bnf) { return gmael3(bnf,8,4,1)[2]; }
2716 : INLINE GEN
2717 1778 : bnf_get_fu(GEN bnf) {
2718 1778 : GEN fu = bnf_get_fu_nocheck(bnf);
2719 1778 : if (typ(fu) == t_MAT) pari_err(e_MISC,"missing units in bnf");
2720 1778 : return fu;
2721 : }
2722 : INLINE GEN
2723 7170 : bnf_get_fu_nocheck(GEN bnf) { return gmael(bnf,8,5); }
2724 :
2725 : INLINE GEN
2726 746961 : bnr_get_bnf(GEN bnr) { return gel(bnr,1); }
2727 : INLINE GEN
2728 384712 : bnr_get_bid(GEN bnr) { return gel(bnr,2); }
2729 : INLINE GEN
2730 18130 : bnr_get_mod(GEN bnr) { return gmael(bnr,2,1); }
2731 : INLINE GEN
2732 27811 : bnr_get_nf(GEN bnr) { return gmael(bnr,1,7); }
2733 : INLINE GEN
2734 516571 : bnr_get_clgp(GEN bnr) { return gel(bnr,5); }
2735 : INLINE GEN
2736 45080 : bnr_get_no(GEN bnr) { return abgrp_get_no(bnr_get_clgp(bnr)); }
2737 : INLINE GEN
2738 459598 : bnr_get_cyc(GEN bnr) { return abgrp_get_cyc(bnr_get_clgp(bnr)); }
2739 : INLINE GEN
2740 70 : bnr_get_gen_nocheck(GEN bnr) { return abgrp_get_gen(bnr_get_clgp(bnr)); }
2741 : INLINE GEN
2742 11032 : bnr_get_gen(GEN bnr) {
2743 11032 : GEN G = bnr_get_clgp(bnr);
2744 11032 : if (lg(G) != 4)
2745 0 : pari_err(e_MISC,"missing bnr generators: please use bnrinit(,,1)");
2746 11032 : return gel(G,3);
2747 : }
2748 :
2749 : INLINE GEN
2750 301888 : bid_get_mod(GEN bid) { return gel(bid,1); }
2751 : INLINE GEN
2752 46361 : bid_get_ideal(GEN bid) { return gmael(bid,1,1); }
2753 : INLINE GEN
2754 518 : bid_get_arch(GEN bid) { return gmael(bid,1,2); }
2755 : INLINE GEN
2756 1059923 : bid_get_grp(GEN bid) { return gel(bid,2); }
2757 : INLINE GEN
2758 395527 : bid_get_fact(GEN bid) { return gmael(bid,3,1); }
2759 : INLINE GEN
2760 354031 : bid_get_fact2(GEN bid) { return gmael(bid,3,2); }
2761 : INLINE GEN
2762 354031 : bid_get_sprk(GEN bid) { return gmael(bid,4,1); }
2763 : INLINE GEN
2764 29939 : bid_get_sarch(GEN bid) { return gmael(bid,4,2); }
2765 : INLINE GEN
2766 374695 : bid_get_archp(GEN bid) { return gmael3(bid,4,2,2); }
2767 : INLINE GEN
2768 656129 : bid_get_U(GEN bid) { return gel(bid,5); }
2769 : INLINE GEN
2770 0 : bid_get_no(GEN bid) { return abgrp_get_no(bid_get_grp(bid)); }
2771 : INLINE GEN
2772 1031538 : bid_get_cyc(GEN bid) { return abgrp_get_cyc(bid_get_grp(bid)); }
2773 : INLINE GEN
2774 0 : bid_get_gen_nocheck(GEN bid) { return abgrp_get_gen(bid_get_grp(bid)); }
2775 : INLINE GEN
2776 27790 : bid_get_gen(GEN bid) {
2777 27790 : GEN G = bid_get_grp(bid);
2778 27790 : if (lg(G) != 4) pari_err(e_MISC,"missing bid generators. Use idealstar(,,2)");
2779 27790 : return abgrp_get_gen(G);
2780 : }
2781 :
2782 : INLINE GEN
2783 21723009 : znstar_get_N(GEN G) { return gmael(G,1,1); }
2784 : INLINE GEN
2785 2239825 : znstar_get_faN(GEN G) { return gel(G,3); }
2786 : INLINE GEN
2787 7 : znstar_get_no(GEN G) { return abgrp_get_no(gel(G,2)); }
2788 : INLINE GEN
2789 167545 : znstar_get_cyc(GEN G) { return abgrp_get_cyc(gel(G,2)); }
2790 : INLINE GEN
2791 7 : znstar_get_gen(GEN G) { return abgrp_get_gen(gel(G,2)); }
2792 : INLINE GEN
2793 2888921 : znstar_get_conreycyc(GEN G) { return gmael(G,4,5); }
2794 : INLINE GEN
2795 887698 : znstar_get_conreygen(GEN G) { return gmael(G,4,4); }
2796 : INLINE GEN
2797 28518 : znstar_get_Ui(GEN G) { return gmael(G,4,3); }
2798 : INLINE GEN
2799 118160 : znstar_get_U(GEN G) { return gel(G,5); }
2800 : INLINE GEN
2801 521612 : znstar_get_pe(GEN G) { return gmael(G,4,1); }
2802 : INLINE GEN
2803 19880 : gal_get_pol(GEN gal) { return gel(gal,1); }
2804 : INLINE GEN
2805 1309 : gal_get_p(GEN gal) { return gmael(gal,2,1); }
2806 : INLINE GEN
2807 84 : gal_get_e(GEN gal) { return gmael(gal,2,2); }
2808 : INLINE GEN
2809 15946 : gal_get_mod(GEN gal) { return gmael(gal,2,3); }
2810 : INLINE GEN
2811 16324 : gal_get_roots(GEN gal) { return gel(gal,3); }
2812 : INLINE GEN
2813 15904 : gal_get_invvdm(GEN gal) { return gel(gal,4); }
2814 : INLINE GEN
2815 15904 : gal_get_den(GEN gal) { return gel(gal,5); }
2816 : INLINE GEN
2817 66983 : gal_get_group(GEN gal) { return gel(gal,6); }
2818 : INLINE GEN
2819 1715 : gal_get_gen(GEN gal) { return gel(gal,7); }
2820 : INLINE GEN
2821 1365 : gal_get_orders(GEN gal) { return gel(gal,8); }
2822 :
2823 : /* assume rnf a genuine rnf */
2824 : INLINE long
2825 1233638 : rnf_get_degree(GEN rnf) { return degpol(rnf_get_pol(rnf)); }
2826 : INLINE long
2827 16394 : rnf_get_nfdegree(GEN rnf) { return degpol(nf_get_pol(rnf_get_nf(rnf))); }
2828 : INLINE long
2829 775698 : rnf_get_absdegree(GEN rnf) { return degpol(gmael(rnf,11,1)); }
2830 : INLINE GEN
2831 700 : rnf_get_idealdisc(GEN rnf) { return gmael(rnf,3,1); }
2832 : INLINE GEN
2833 742 : rnf_get_k(GEN rnf) { return gmael(rnf,11,3); }
2834 : INLINE GEN
2835 609 : rnf_get_alpha(GEN rnf) { return gmael(rnf, 11, 2); }
2836 : INLINE GEN
2837 384706 : rnf_get_nf(GEN rnf) { return gel(rnf,10); }
2838 : INLINE GEN
2839 3087 : rnf_get_nfzk(GEN rnf) { return gel(rnf,2); }
2840 : INLINE GEN
2841 205170 : rnf_get_polabs(GEN rnf) { return gmael(rnf,11,1); }
2842 : INLINE GEN
2843 1479849 : rnf_get_pol(GEN rnf) { return gel(rnf,1); }
2844 : INLINE GEN
2845 63 : rnf_get_disc(GEN rnf) { return gel(rnf,3); }
2846 : INLINE GEN
2847 105 : rnf_get_index(GEN rnf) { return gel(rnf,4); }
2848 : INLINE long
2849 0 : rnf_get_varn(GEN rnf) { return varn(gel(rnf,1)); }
2850 : INLINE GEN
2851 188580 : rnf_get_nfpol(GEN rnf) { return gmael(rnf,10,1); }
2852 : INLINE long
2853 3325 : rnf_get_nfvarn(GEN rnf) { return varn(gmael(rnf,10,1)); }
2854 : INLINE GEN
2855 3213 : rnf_get_zk(GEN rnf) { return gel(rnf,7); }
2856 : INLINE GEN
2857 96775 : rnf_get_map(GEN rnf) { return gel(rnf,11); }
2858 : INLINE GEN
2859 1197 : rnf_get_invzk(GEN rnf) { return gel(rnf,8); }
2860 :
2861 : /* I integral ZM (not HNF), G ZM, rounded Cholesky form of a weighted
2862 : * T2 matrix. Reduce I wrt G */
2863 : INLINE GEN
2864 14077 : idealpseudored(GEN I, GEN G)
2865 14077 : { return ZM_mul(I, ZM_lll(ZM_mul(G, I), 0.99, LLL_IM)); }
2866 :
2867 : /* I integral (not necessarily HNF), G ZM, rounded Cholesky form of a weighted
2868 : * T2 matrix. Return m in I with T2(m) small */
2869 : INLINE GEN
2870 127731 : idealpseudomin(GEN I, GEN G)
2871 : {
2872 127731 : GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
2873 127731 : return ZM_ZC_mul(I, gel(u,1));
2874 : }
2875 : /* I, G as in idealpseudomin. Return an irrational m in I with T2(m) small */
2876 : INLINE GEN
2877 297163 : idealpseudomin_nonscalar(GEN I, GEN G)
2878 : {
2879 297163 : GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
2880 297163 : GEN m = ZM_ZC_mul(I, gel(u,1));
2881 297163 : if (ZV_isscalar(m) && lg(u) > 2) m = ZM_ZC_mul(I, gel(u,2));
2882 297163 : return m;
2883 : }
2884 :
2885 : INLINE GEN
2886 770 : idealred_elt(GEN nf, GEN I) {
2887 770 : pari_sp av = avma;
2888 770 : GEN u = idealpseudomin(I, nf_get_roundG(nf));
2889 770 : return gerepileupto(av, u);
2890 : }
2891 : INLINE GEN
2892 109444 : idealred(GEN nf, GEN I) { return idealred0(nf, I, NULL); }
2893 :
2894 : INLINE GEN
2895 2058 : idealchineseinit(GEN nf, GEN x)
2896 2058 : { return idealchinese(nf,x,NULL); }
2897 :
2898 : /*******************************************************************/
2899 : /* */
2900 : /* CLOSURES */
2901 : /* */
2902 : /*******************************************************************/
2903 227680147 : INLINE long closure_arity(GEN C) { return ((ulong)C[1])&ARITYBITS; }
2904 35447916 : INLINE long closure_is_variadic(GEN C) { return !!(((ulong)C[1])&VARARGBITS); }
2905 191921202 : INLINE const char *closure_codestr(GEN C) { return GSTR(gel(C,2))-1; }
2906 0 : INLINE GEN closure_get_code(GEN C) { return gel(C,2); }
2907 191897602 : INLINE GEN closure_get_oper(GEN C) { return gel(C,3); }
2908 191885870 : INLINE GEN closure_get_data(GEN C) { return gel(C,4); }
2909 9393 : INLINE GEN closure_get_dbg(GEN C) { return gel(C,5); }
2910 22524 : INLINE GEN closure_get_text(GEN C) { return gel(C,6); }
2911 1171748 : INLINE GEN closure_get_frame(GEN C) { return gel(C,7); }
2912 :
2913 : /*******************************************************************/
2914 : /* */
2915 : /* ERRORS */
2916 : /* */
2917 : /*******************************************************************/
2918 : INLINE long
2919 52184 : err_get_num(GEN e) { return e[1]; }
2920 : INLINE GEN
2921 77 : err_get_compo(GEN e, long i) { return gel(e, i+1); }
2922 :
2923 : INLINE void
2924 14 : pari_err_BUG(const char *f) { pari_err(e_BUG,f); }
2925 : INLINE void
2926 7 : pari_err_CONSTPOL(const char *f) { pari_err(e_CONSTPOL, f); }
2927 : INLINE void
2928 63 : pari_err_COPRIME(const char *f, GEN x, GEN y) { pari_err(e_COPRIME, f,x,y); }
2929 : INLINE void
2930 487 : pari_err_DIM(const char *f) { pari_err(e_DIM, f); }
2931 : INLINE void
2932 0 : pari_err_FILE(const char *f, const char *g) { pari_err(e_FILE, f,g); }
2933 : INLINE void
2934 0 : pari_err_FILEDESC(const char *f, long n) { pari_err(e_FILEDESC, f,n); }
2935 : INLINE void
2936 42 : pari_err_FLAG(const char *f) { pari_err(e_FLAG,f); }
2937 : INLINE void
2938 434 : pari_err_IMPL(const char *f) { pari_err(e_IMPL,f); }
2939 : INLINE void
2940 19716 : pari_err_INV(const char *f, GEN x) { pari_err(e_INV,f,x); }
2941 : INLINE void
2942 28 : pari_err_IRREDPOL(const char *f, GEN x) { pari_err(e_IRREDPOL, f,x); }
2943 : INLINE void
2944 2003 : 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); }
2945 : INLINE void
2946 203 : pari_err_COMPONENT(const char *f, const char *op, GEN l, GEN x) { pari_err(e_COMPONENT, f,op,l,x); }
2947 : INLINE void
2948 0 : pari_err_MAXPRIME(ulong c) { pari_err(e_MAXPRIME, c); }
2949 : INLINE void
2950 350 : pari_err_OP(const char *f, GEN x, GEN y) { pari_err(e_OP, f,x,y); }
2951 : INLINE void
2952 84 : pari_err_OVERFLOW(const char *f) { pari_err(e_OVERFLOW, f); }
2953 : INLINE void
2954 218 : pari_err_PREC(const char *f) { pari_err(e_PREC,f); }
2955 : INLINE void
2956 0 : pari_err_PACKAGE(const char *f) { pari_err(e_PACKAGE,f); }
2957 : INLINE void
2958 70 : pari_err_PRIME(const char *f, GEN x) { pari_err(e_PRIME, f,x); }
2959 : INLINE void
2960 749 : pari_err_MODULUS(const char *f, GEN x, GEN y) { pari_err(e_MODULUS, f,x,y); }
2961 : INLINE void
2962 49 : pari_err_ROOTS0(const char *f) { pari_err(e_ROOTS0, f); }
2963 : INLINE void
2964 77 : pari_err_SQRTN(const char *f, GEN x) { pari_err(e_SQRTN, f,x); }
2965 : INLINE void
2966 12503 : pari_err_TYPE(const char *f, GEN x) { pari_err(e_TYPE, f,x); }
2967 : INLINE void
2968 3073 : pari_err_TYPE2(const char *f, GEN x, GEN y) { pari_err(e_TYPE2, f,x,y); }
2969 : INLINE void
2970 203 : pari_err_VAR(const char *f, GEN x, GEN y) { pari_err(e_VAR, f,x,y); }
2971 : INLINE void
2972 175 : pari_err_PRIORITY(const char *f, GEN x, const char *op, long v)
2973 175 : { pari_err(e_PRIORITY, f,x,op,v); }
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