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 2740759 : 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 2541336 : mkpolmod(GEN x, GEN y) { retmkpolmod(x,y); }
149 : INLINE GEN
150 13245547 : mkfrac(GEN x, GEN y) { retmkfrac(x,y); }
151 : INLINE GEN
152 511 : mkfracss(long x, long y) { retmkfrac(stoi(x),stoi(y)); }
153 : /* q = n/d a t_FRAC or t_INT; recover (n,d) */
154 : INLINE void
155 12173 : Qtoss(GEN q, long *n, long *d)
156 : {
157 12173 : if (typ(q) == t_INT) { *n = itos(q); *d = 1; }
158 2443 : else { *n = itos(gel(q,1)); *d = itou(gel(q,2)); }
159 12173 : }
160 : INLINE GEN
161 36039472 : sstoQ(long n, long d)
162 : {
163 : ulong r;
164 : long g, q;
165 36039472 : if (!n)
166 : {
167 59206 : if (!d) pari_err_INV("sstoQ",gen_0);
168 59206 : return gen_0;
169 : }
170 35980266 : if (d < 0) { d = -d; n = -n; }
171 35980266 : if (d == 1) return stoi(n);
172 35977053 : q = udivuu_rem(labs(n),d,&r);
173 35977053 : if (!r) return n > 0? utoipos(q): utoineg(q);
174 1475782 : g = ugcd(d,r); /* gcd(n,d) */
175 1475782 : if (g != 1) { n /= g; d /= g; }
176 1475782 : retmkfrac(stoi(n), utoi(d));
177 : }
178 :
179 : INLINE GEN
180 4627816 : 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 7669453 : mkcomplex(GEN x, GEN y) { retmkcomplex(x,y); }
189 : INLINE GEN
190 448448 : gen_I(void) { return mkcomplex(gen_0, gen_1); }
191 : INLINE GEN
192 204391 : 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 70988186 : mkvecsmall(long x) { GEN v = cgetg(2, t_VECSMALL); v[1] = x; return v; }
199 : INLINE GEN
200 121015125 : mkvecsmall2(long x,long y) { GEN v = cgetg(3, t_VECSMALL);
201 121008813 : v[1]=x; v[2]=y; return v; }
202 : INLINE GEN
203 58202217 : mkvecsmall3(long x,long y,long z) { GEN v = cgetg(4, t_VECSMALL);
204 58198764 : v[1]=x; v[2]=y; v[3]=z; return v; }
205 : INLINE GEN
206 11936693 : mkvecsmall4(long x,long y,long z,long t) { GEN v = cgetg(5, t_VECSMALL);
207 11926217 : v[1]=x; v[2]=y; v[3]=z; v[4]=t; return v; }
208 : INLINE GEN
209 466224 : mkvecsmall5(long x,long y,long z,long t,long u) { GEN v = cgetg(6, t_VECSMALL);
210 466224 : 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 14008322 : mkvec(GEN x) { retmkvec(x); }
217 : INLINE GEN
218 95606485 : mkvec2(GEN x, GEN y) { retmkvec2(x,y); }
219 : INLINE GEN
220 72986467 : mkvec3(GEN x, GEN y, GEN z) { retmkvec3(x,y,z); }
221 : INLINE GEN
222 7254213 : mkvec4(GEN x, GEN y, GEN z, GEN t) { retmkvec4(x,y,z,t); }
223 : INLINE GEN
224 11968001 : mkvec5(GEN x, GEN y, GEN z, GEN t, GEN u) { retmkvec5(x,y,z,t,u); }
225 : INLINE GEN
226 7 : mkvecs(long x) { retmkvec(stoi(x)); }
227 : INLINE GEN
228 19780 : 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 91317 : mkvec2copy(GEN x, GEN y) {
237 91317 : GEN v = cgetg(3,t_VEC); gel(v,1) = gcopy(x); gel(v,2) = gcopy(y); return v; }
238 : /* col */
239 : INLINE GEN
240 2417812 : mkcol(GEN x) { retmkcol(x); }
241 : INLINE GEN
242 23605060 : 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 2513272 : mkmat(GEN x) { retmkmat(x); }
264 : INLINE GEN
265 28845688 : 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 25236 : mkoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_1; return v; }
278 : INLINE GEN
279 13979 : mkmoo(void) { GEN v = cgetg(2, t_INFINITY); gel(v,1) = gen_m1; return v; }
280 : INLINE long
281 50223 : 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 972019 : pol_x(long v) {
290 972019 : GEN p = cgetg(4, t_POL);
291 972019 : p[1] = evalsigne(1)|evalvarn(v);
292 972019 : gel(p,2) = gen_0;
293 972019 : gel(p,3) = gen_1; return p;
294 : }
295 : /* x^n, assume n >= 0 */
296 : INLINE GEN
297 2626765 : pol_xn(long n, long v) {
298 2626765 : long i, a = n+2;
299 2626765 : GEN p = cgetg(a+1, t_POL);
300 2626765 : p[1] = evalsigne(1)|evalvarn(v);
301 2626765 : for (i = 2; i < a; i++) gel(p,i) = gen_0;
302 2626765 : 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 1501957 : pol_1(long v) {
313 1501957 : GEN p = cgetg(3, t_POL);
314 1501954 : p[1] = evalsigne(1)|evalvarn(v);
315 1501954 : gel(p,2) = gen_1; return p;
316 : }
317 : INLINE GEN
318 15290560 : pol_0(long v)
319 : {
320 15290560 : GEN x = cgetg(2,t_POL);
321 15290560 : 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 8318409 : 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 8626042 : const_col(long n, GEN x) { retconst_col(n, x); }
337 : INLINE GEN
338 8234895 : const_vecsmall(long n, long c)
339 : {
340 : long i;
341 8234895 : GEN V = cgetg(n+1,t_VECSMALL);
342 8234907 : for(i=1;i<=n;i++) V[i] = c;
343 8234907 : 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 143479 : zeroser(long v, long e)
371 : {
372 143479 : GEN x = cgetg(2, t_SER);
373 143479 : x[1] = evalvalp(e) | evalvarn(v); return x;
374 : }
375 : INLINE int
376 5743459 : ser_isexactzero(GEN x)
377 : {
378 5743459 : if (!signe(x)) switch(lg(x))
379 : {
380 136136 : case 2: return 1;
381 854 : case 3: return isexactzero(gel(x,2));
382 : }
383 5606469 : return 0;
384 : }
385 : /* 0 * pol_x(v) */
386 : INLINE GEN
387 5490630 : zeropol(long v) { return pol_0(v); }
388 : /* vector(n) */
389 : INLINE GEN
390 35947682 : zerocol(long n)
391 : {
392 35947682 : GEN y = cgetg(n+1,t_COL);
393 35947682 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
394 35947682 : return y;
395 : }
396 : /* vectorv(n) */
397 : INLINE GEN
398 18750338 : zerovec(long n)
399 : {
400 18750338 : GEN y = cgetg(n+1,t_VEC);
401 18750337 : long i; for (i=1; i<=n; i++) gel(y,i) = gen_0;
402 18750337 : return y;
403 : }
404 : /* matrix(m, n) */
405 : INLINE GEN
406 16100 : zeromat(long m, long n)
407 : {
408 16100 : GEN y = cgetg(n+1,t_MAT);
409 16100 : GEN v = zerocol(m);
410 16100 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
411 16100 : return y;
412 : }
413 : /* = zero_zx, sv is a evalvarn()*/
414 : INLINE GEN
415 923838 : zero_Flx(long sv) { return pol0_Flx(sv); }
416 : INLINE GEN
417 33277498 : zero_Flv(long n)
418 : {
419 33277498 : GEN y = cgetg(n+1,t_VECSMALL);
420 33278567 : long i; for (i=1; i<=n; i++) y[i] = 0;
421 33278567 : return y;
422 : }
423 : /* matrix(m, n) */
424 : INLINE GEN
425 907342 : zero_Flm(long m, long n)
426 : {
427 907342 : GEN y = cgetg(n+1,t_MAT);
428 907325 : GEN v = zero_Flv(m);
429 907337 : long i; for (i=1; i<=n; i++) gel(y,i) = v;
430 907337 : return y;
431 : }
432 : /* matrix(m, n) */
433 : INLINE GEN
434 104215 : zero_Flm_copy(long m, long n)
435 : {
436 104215 : GEN y = cgetg(n+1,t_MAT);
437 104208 : long i; for (i=1; i<=n; i++) gel(y,i) = zero_Flv(m);
438 104217 : return y;
439 : }
440 :
441 : INLINE GEN
442 793139 : zero_F2v(long m)
443 : {
444 793139 : long l = nbits2nlong(m);
445 793139 : GEN v = zero_Flv(l+1);
446 793139 : v[1] = m;
447 793139 : 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 276544 : zero_F2m_copy(long m, long n)
464 : {
465 : long i;
466 276544 : GEN M = cgetg(n+1, t_MAT);
467 806069 : for (i = 1; i <= n; i++)
468 529525 : gel(M,i)= zero_F2v(m);
469 276544 : return M;
470 : }
471 :
472 : /* matrix(m, n) */
473 : INLINE GEN
474 4751431 : zeromatcopy(long m, long n)
475 : {
476 4751431 : GEN y = cgetg(n+1,t_MAT);
477 4751431 : long i; for (i=1; i<=n; i++) gel(y,i) = zerocol(m);
478 4751431 : 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 1311271 : col_ei(long n, long i) { GEN e = zerocol(n); gel(e,i) = gen_1; return e; }
494 : INLINE GEN
495 326495 : 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 12406236 : shallowcopy(GEN x)
505 12406236 : { return typ(x) == t_MAT ? RgM_shallowcopy(x): leafcopy(x); }
506 :
507 : /* routines for naive growarrays */
508 : INLINE GEN
509 12698039 : vectrunc_init(long l)
510 : {
511 12698039 : GEN z = new_chunk(l);
512 12698077 : 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 253329177 : lg_increase(GEN x) { x[0]++; }
522 : INLINE void
523 51301111 : 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 82737087 : vecsmalltrunc_init(long l)
534 : {
535 82737087 : GEN z = new_chunk(l);
536 82737087 : 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 13328 : vec_lengthen(GEN v, long n)
558 : {
559 : long i;
560 13328 : long l=lg(v);
561 13328 : GEN V = cgetg(n+1,t_VEC);
562 13328 : for(i=1;i<l;i++) gel(V,i) = gel(v,i);
563 13328 : return V;
564 : }
565 : /* shallow*/
566 : INLINE GEN
567 61124 : vec_append(GEN V, GEN s)
568 : {
569 61124 : long i, l2 = lg(V);
570 61124 : GEN res = cgetg(l2+1, typ(V));
571 61124 : for (i = 1; i < l2; ++i) gel(res, i) = gel(V,i);
572 61124 : 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 732256 : vecsmall_shorten(GEN v, long n)
594 : {
595 : long i;
596 732256 : GEN V = cgetg(n+1,t_VECSMALL);
597 732263 : for(i=1;i<=n;i++) V[i] = v[i];
598 732263 : 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 457679 : vec_to_vecsmall(GEN x)
611 457679 : { 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 8065634 : vecsmall_lexcmp(GEN x, GEN y)
628 : {
629 : long lx,ly,l,i;
630 8065634 : lx = lg(x);
631 8065634 : ly = lg(y); l = minss(lx,ly);
632 39683347 : for (i=1; i<l; i++)
633 37751063 : if (x[i] != y[i]) return x[i]<y[i]? -1: 1;
634 1932284 : 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 14155 : vecsmall_prepend(GEN V, long s)
650 : {
651 14155 : long i, l2 = lg(V);
652 14155 : GEN res = cgetg(l2+1, typ(V));
653 14155 : res[1] = s;
654 14155 : for (i = 2; i <= l2; ++i) res[i] = V[i - 1];
655 14155 : return res;
656 : }
657 :
658 : INLINE GEN
659 2551508 : vecsmall_append(GEN V, long s)
660 : {
661 2551508 : long i, l2 = lg(V);
662 2551508 : GEN res = cgetg(l2+1, t_VECSMALL);
663 2551508 : for (i = 1; i < l2; ++i) res[i] = V[i];
664 2551508 : res[l2] = s; return res;
665 : }
666 :
667 : INLINE GEN
668 781896 : vecsmall_concat(GEN u, GEN v)
669 : {
670 781896 : long i, l1 = lg(u)-1, l2 = lg(v)-1;
671 781896 : GEN res = cgetg(l1+l2+1, t_VECSMALL);
672 781897 : for (i = 1; i <= l1; ++i) res[i] = u[i];
673 781897 : for (i = 1; i <= l2; ++i) res[i+l1] = v[i];
674 781897 : 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 154033 : vecsmall_max(GEN x)
716 : {
717 154033 : long i, t = x[1], lx = lg(x);
718 558745 : for (i=2; i<lx; i++)
719 404712 : if (x[i] > t) t = x[i];
720 154033 : 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 19351548 : QV_isscalar(GEN x)
751 : {
752 19351548 : long lx = lg(x),i;
753 20867214 : for (i=2; i<lx; i++)
754 20320505 : 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 4479158 : RgX_equal_var(GEN x, GEN y) { return varn(x) == varn(y) && RgX_equal(x,y); }
775 :
776 : INLINE int
777 5902 : RgX_is_rational(GEN x)
778 : {
779 : long i;
780 28861 : for (i = lg(x)-1; i > 1; i--)
781 26865 : if (!is_rational_t(typ(gel(x,i)))) return 0;
782 1996 : return 1;
783 : }
784 : INLINE int
785 4272063 : RgX_is_ZX(GEN x)
786 : {
787 : long i;
788 18613500 : for (i = lg(x)-1; i > 1; i--)
789 14357201 : if (typ(gel(x,i)) != t_INT) return 0;
790 4256299 : return 1;
791 : }
792 : INLINE int
793 262213 : RgX_is_QX(GEN x)
794 : {
795 262213 : long k = lg(x)-1;
796 926114 : for ( ; k>1; k--)
797 664146 : if (!is_rational_t(typ(gel(x,k)))) return 0;
798 261968 : return 1;
799 : }
800 : INLINE int
801 15894289 : RgX_is_monomial(GEN x)
802 : {
803 : long i;
804 15894289 : if (!signe(x)) return 0;
805 26439350 : for (i=lg(x)-2; i>1; i--)
806 18325757 : if (!isexactzero(gel(x,i))) return 0;
807 8113593 : return 1;
808 : }
809 : INLINE int
810 27032301 : RgV_is_ZV(GEN x)
811 : {
812 : long i;
813 111359948 : for (i = lg(x)-1; i > 0; i--)
814 84329852 : if (typ(gel(x,i)) != t_INT) return 0;
815 27030096 : return 1;
816 : }
817 : INLINE int
818 798 : RgV_is_QV(GEN x)
819 : {
820 : long i;
821 1211 : for (i = lg(x)-1; i > 0; i--)
822 1078 : if (!is_rational_t(typ(gel(x,i)))) return 0;
823 133 : return 1;
824 : }
825 :
826 : /********************************************************************/
827 : /** **/
828 : /** Dynamic arrays implementation **/
829 : /** **/
830 : /********************************************************************/
831 : INLINE void **
832 404155694 : pari_stack_base(pari_stack *s) { return s->data; }
833 :
834 : INLINE void
835 1698918 : pari_stack_init(pari_stack *s, size_t size, void **data)
836 : {
837 1698918 : s->data = data;
838 1698918 : *data = NULL;
839 1698918 : s->n = 0;
840 1698918 : s->alloc = 0;
841 1698918 : s->size = size;
842 1698918 : }
843 :
844 : INLINE void
845 402563648 : pari_stack_alloc(pari_stack *s, long nb)
846 : {
847 402563648 : void **sdat = pari_stack_base(s);
848 402426588 : long alloc = s->alloc;
849 402426588 : if (s->n+nb <= alloc) return;
850 627876 : if (!alloc)
851 576306 : alloc = nb;
852 : else
853 : {
854 51570 : while (s->n+nb > alloc) alloc <<= 1;
855 : }
856 627876 : *sdat = pari_realloc(*sdat,alloc*s->size);
857 628760 : s->alloc = alloc;
858 : }
859 :
860 : INLINE long
861 324711147 : pari_stack_new(pari_stack *s) { pari_stack_alloc(s, 1); return s->n++; }
862 :
863 : INLINE void
864 1644046 : pari_stack_delete(pari_stack *s)
865 : {
866 1644046 : void **sdat = pari_stack_base(s);
867 1641095 : if (*sdat) pari_free(*sdat);
868 1652618 : }
869 :
870 : INLINE void
871 4773 : pari_stack_pushp(pari_stack *s, void *u)
872 : {
873 4773 : long n = pari_stack_new(s);
874 4773 : void **sdat =(void**) *pari_stack_base(s);
875 4773 : sdat[n] = u;
876 4773 : }
877 :
878 : /*******************************************************************/
879 : /* */
880 : /* EXTRACT */
881 : /* */
882 : /*******************************************************************/
883 : INLINE GEN
884 197232667 : vecslice(GEN A, long y1, long y2)
885 : {
886 197232667 : long i,lB = y2 - y1 + 2;
887 197232667 : GEN B = cgetg(lB, typ(A));
888 197234111 : for (i=1; i<lB; i++) B[i] = A[y1-1+i];
889 197234111 : return B;
890 : }
891 : INLINE GEN
892 799603 : vecslicepermute(GEN A, GEN p, long y1, long y2)
893 : {
894 799603 : long i,lB = y2 - y1 + 2;
895 799603 : GEN B = cgetg(lB, typ(A));
896 799602 : for (i=1; i<lB; i++) B[i] = A[p[y1-1+i]];
897 799602 : 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 21830470 : rowslice(GEN x, long j1, long j2)
906 21830470 : { pari_APPLY_same(vecslice(gel(x,i), j1, j2)) }
907 :
908 : INLINE GEN
909 3596674 : matslice(GEN A, long x1, long x2, long y1, long y2)
910 3596674 : { 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 252462 : vecsplice(GEN a, long j)
920 : {
921 252462 : long i, k, l = lg(a);
922 : GEN b;
923 252462 : if (l == 1) pari_err(e_MISC, "incorrect component in vecsplice");
924 252462 : b = cgetg(l-1, typ(a));
925 1006285 : for (i = k = 1; i < l; i++)
926 753823 : if (i != j) gel(b, k++) = gel(a,i);
927 252462 : 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 3710454 : Flm_row(GEN x, long j)
945 3710454 : { 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 44847941 : vecsmallpermute(GEN A, GEN p) { return perm_mul(A, p); }
992 :
993 : INLINE GEN
994 6211220 : vecpermute(GEN A, GEN x)
995 6211220 : { pari_APPLY_type(typ(A), gel(A, x[i])) }
996 :
997 : INLINE GEN
998 2954533 : rowpermute(GEN x, GEN p)
999 2954533 : { 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 716760 : identity_perm(long n)
1010 : {
1011 716760 : GEN perm = cgetg(n+1, t_VECSMALL);
1012 : long i;
1013 716754 : for (i = 1; i <= n; i++) perm[i] = i;
1014 716754 : 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 46088200 : perm_mul(GEN s, GEN x)
1031 46088200 : { pari_APPLY_long(s[x[i]]) }
1032 :
1033 : /* Compute the inverse (reciprocal) of a permutation. */
1034 : INLINE GEN
1035 1153295 : perm_inv(GEN x)
1036 : {
1037 : long i, lx;
1038 1153295 : GEN y = cgetg_copy(x, &lx);
1039 1153295 : for (i=1; i<lx; i++) y[ x[i] ] = i;
1040 1153295 : 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 65565413 : pari_free(void *pointer)
1080 : {
1081 65565413 : BLOCK_SIGINT_START;
1082 65582921 : free(pointer);
1083 65582921 : BLOCK_SIGINT_END;
1084 65579532 : }
1085 : INLINE void*
1086 277403804 : pari_malloc(size_t size)
1087 : {
1088 277403804 : if (size)
1089 : {
1090 : char *tmp;
1091 277403804 : BLOCK_SIGINT_START;
1092 277406020 : tmp = (char*)malloc(size);
1093 277406020 : BLOCK_SIGINT_END;
1094 277405783 : if (!tmp) pari_err(e_MEM);
1095 277405783 : return tmp;
1096 : }
1097 0 : return NULL;
1098 : }
1099 : INLINE void*
1100 639573 : pari_realloc(void *pointer, size_t size)
1101 : {
1102 : char *tmp;
1103 :
1104 639573 : BLOCK_SIGINT_START;
1105 641235 : if (!pointer) tmp = (char *) malloc(size);
1106 55324 : else tmp = (char *) realloc(pointer,size);
1107 641235 : BLOCK_SIGINT_END;
1108 640785 : if (!tmp) pari_err(e_MEM);
1109 640785 : return tmp;
1110 : }
1111 : INLINE void*
1112 35158 : pari_calloc(size_t size)
1113 : {
1114 35158 : void *t = pari_malloc(size);
1115 35158 : memset(t, 0, size); return t;
1116 : }
1117 : INLINE GEN
1118 5771 : cgetalloc(long t, size_t l)
1119 : {
1120 5771 : GEN x = (GEN)pari_malloc(l * sizeof(long));
1121 5771 : 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 3717998722 : icopy_avma(GEN x, pari_sp av)
1132 : {
1133 3717998722 : long i = lgefint(x), lx = i;
1134 3717998722 : GEN y = ((GEN)av) - i;
1135 3717998722 : while (--i > 0) y[i] = x[i];
1136 3717998722 : y[0] = evaltyp(t_INT)|evallg(lx);
1137 3717712713 : return y;
1138 : }
1139 : /* copy leaf x as if we had set_avma(av) */
1140 : INLINE GEN
1141 172634013 : leafcopy_avma(GEN x, pari_sp av)
1142 : {
1143 172634013 : long i = lg(x);
1144 172634013 : GEN y = ((GEN)av) - i;
1145 172634013 : while (--i > 0) y[i] = x[i];
1146 172634013 : y[0] = x[0] & (~CLONEBIT);
1147 172634013 : return y;
1148 : }
1149 : INLINE GEN
1150 630451213 : gerepileuptoleaf(pari_sp av, GEN x)
1151 : {
1152 : long lx;
1153 : GEN q;
1154 :
1155 630451213 : if (!isonstack(x) || (GEN)av<=x) { set_avma(av); return x; }
1156 632553055 : lx = lg(x);
1157 632553055 : q = ((GEN)av) - lx;
1158 632553055 : avma = (pari_sp)q;
1159 632553055 : while (--lx >= 0) q[lx] = x[lx];
1160 632553055 : return q;
1161 : }
1162 : INLINE GEN
1163 1214587441 : gerepileuptoint(pari_sp av, GEN x)
1164 : {
1165 1214587441 : if (!isonstack(x) || (GEN)av<=x) { set_avma(av); return x; }
1166 1068524054 : avma = (pari_sp)icopy_avma(x, av);
1167 1070439688 : return (GEN)avma;
1168 : }
1169 : INLINE GEN
1170 759683481 : gerepileupto(pari_sp av, GEN x)
1171 : {
1172 759683481 : if (!isonstack(x) || (GEN)av<=x) { set_avma(av); return x; }
1173 663312643 : switch(typ(x))
1174 : { /* non-default = !is_recursive_t(tq) */
1175 220649514 : case t_INT: return gerepileuptoint(av, x);
1176 : case t_REAL:
1177 : case t_STR:
1178 148012234 : case t_VECSMALL: return gerepileuptoleaf(av,x);
1179 : default:
1180 : /* NB: x+i --> ((long)x) + i*sizeof(long) */
1181 294650895 : return gerepile(av, (pari_sp) (x+lg(x)), x);
1182 : }
1183 : }
1184 :
1185 : /* gerepileupto(av, gcopy(x)) */
1186 : INLINE GEN
1187 46968298 : gerepilecopy(pari_sp av, GEN x)
1188 : {
1189 46968298 : if (is_recursive_t(typ(x)))
1190 : {
1191 42384975 : GENbin *p = copy_bin(x);
1192 42385000 : set_avma(av); return bin_copy(p);
1193 : }
1194 : else
1195 : {
1196 4583323 : set_avma(av);
1197 4583321 : if (x < (GEN)av) {
1198 3095898 : if (x < (GEN)pari_mainstack->bot) new_chunk(lg(x));
1199 3095898 : x = leafcopy_avma(x, av);
1200 3095903 : avma = (pari_sp)x;
1201 : } else
1202 1487423 : x = leafcopy(x);
1203 4583327 : return x;
1204 : }
1205 : }
1206 :
1207 : /* Takes an array of pointers to GENs, of length n. Copies all
1208 : * objects to contiguous locations and cleans up the stack between
1209 : * av and avma. */
1210 : INLINE void
1211 136131 : gerepilemany(pari_sp av, GEN* gptr[], int n)
1212 : {
1213 : int i;
1214 136131 : for (i=0; i<n; i++) *gptr[i] = (GEN)copy_bin(*gptr[i]);
1215 136131 : set_avma(av);
1216 136131 : for (i=0; i<n; i++) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1217 136131 : }
1218 :
1219 : INLINE void
1220 7478659 : gerepileall(pari_sp av, int n, ...)
1221 : {
1222 : int i;
1223 7478659 : va_list a; va_start(a, n);
1224 7478659 : if (n < 10)
1225 : {
1226 : GEN *gptr[10];
1227 21621733 : for (i=0; i<n; i++)
1228 14142954 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1229 7478779 : set_avma(av);
1230 7478617 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1231 :
1232 : }
1233 : else
1234 : {
1235 0 : GEN **gptr = (GEN**) pari_malloc(n*sizeof(GEN*));
1236 0 : for (i=0; i<n; i++)
1237 0 : { gptr[i] = va_arg(a,GEN*); *gptr[i] = (GEN)copy_bin(*gptr[i]); }
1238 0 : set_avma(av);
1239 0 : for (--i; i>=0; i--) *gptr[i] = bin_copy((GENbin*)*gptr[i]);
1240 0 : pari_free(gptr);
1241 : }
1242 7478885 : va_end(a);
1243 7478885 : }
1244 :
1245 : INLINE void
1246 14 : gerepilecoeffs(pari_sp av, GEN x, int n)
1247 : {
1248 : int i;
1249 14 : for (i=0; i<n; i++) gel(x,i) = (GEN)copy_bin(gel(x,i));
1250 14 : set_avma(av);
1251 14 : for (i=0; i<n; i++) gel(x,i) = bin_copy((GENbin*)x[i]);
1252 14 : }
1253 :
1254 : /* p from copy_bin. Copy p->x back to stack, then destroy p */
1255 : INLINE GEN
1256 56954122 : bin_copy(GENbin *p)
1257 : {
1258 : GEN x, y, base;
1259 : long dx, len;
1260 :
1261 56954122 : x = p->x; if (!x) { pari_free(p); return gen_0; }
1262 56947000 : len = p->len;
1263 56947000 : base= p->base; dx = x - base;
1264 56947000 : y = (GEN)memcpy((void*)new_chunk(len), (void*)GENbinbase(p), len*sizeof(long));
1265 56946949 : y += dx;
1266 56946949 : p->rebase(y, ((ulong)y-(ulong)x));
1267 56946849 : pari_free(p); return y;
1268 : }
1269 :
1270 : INLINE GEN
1271 113901431 : GENbinbase(GENbin *p) { return (GEN)(p + 1); }
1272 :
1273 : INLINE void
1274 31464068 : cgiv(GEN x)
1275 : {
1276 31464068 : pari_sp av = (pari_sp)(x+lg(x));
1277 31464068 : if (isonstack((GEN)av)) set_avma(av);
1278 31463547 : }
1279 :
1280 : INLINE void
1281 1256258 : killblock(GEN x) { gunclone(x); }
1282 :
1283 : INLINE int
1284 24155809 : is_universal_constant(GEN x) { return (x >= gen_0 && x <= ghalf); }
1285 :
1286 : /*******************************************************************/
1287 : /* */
1288 : /* CONVERSION / ASSIGNMENT */
1289 : /* */
1290 : /*******************************************************************/
1291 : /* z is a type which may be a t_COMPLEX component (not a t_QUAD) */
1292 : INLINE GEN
1293 3288034 : cxcompotor(GEN z, long prec)
1294 : {
1295 3288034 : switch(typ(z))
1296 : {
1297 1752228 : case t_INT: return itor(z, prec);
1298 134155 : case t_FRAC: return fractor(z, prec);
1299 1401651 : case t_REAL: return rtor(z, prec);
1300 0 : default: pari_err_TYPE("cxcompotor",z);
1301 : return NULL; /* LCOV_EXCL_LINE */
1302 : }
1303 : }
1304 : INLINE GEN
1305 1630694 : cxtofp(GEN x, long prec)
1306 1630694 : { retmkcomplex(cxcompotor(gel(x,1),prec), cxcompotor(gel(x,2),prec)); }
1307 :
1308 : INLINE GEN
1309 217474 : cxtoreal(GEN q)
1310 217474 : { return (typ(q) == t_COMPLEX && gequal0(gel(q,2)))? gel(q,1): q; }
1311 :
1312 : INLINE double
1313 33565511 : gtodouble(GEN x)
1314 : {
1315 33565511 : if (typ(x)!=t_REAL) {
1316 7429543 : pari_sp av = avma;
1317 7429543 : x = gtofp(x, DEFAULTPREC);
1318 7429543 : if (typ(x)!=t_REAL) pari_err_TYPE("gtodouble [t_REAL expected]", x);
1319 7429543 : set_avma(av);
1320 : }
1321 33565511 : return rtodbl(x);
1322 : }
1323 : INLINE long
1324 73013120 : gtos(GEN x) {
1325 73013120 : if (typ(x) != t_INT) pari_err_TYPE("gtos [integer expected]",x);
1326 73013113 : return itos(x);
1327 : }
1328 :
1329 : INLINE ulong
1330 122947 : gtou(GEN x) {
1331 122947 : if (typ(x) != t_INT || signe(x)<0)
1332 0 : pari_err_TYPE("gtou [integer >=0 expected]",x);
1333 122953 : return itou(x);
1334 : }
1335 :
1336 : INLINE GEN
1337 21933443 : absfrac(GEN x)
1338 : {
1339 21933443 : GEN y = cgetg(3, t_FRAC);
1340 21933443 : gel(y,1) = absi(gel(x,1));
1341 21933443 : gel(y,2) = icopy(gel(x,2)); return y;
1342 : }
1343 : INLINE GEN
1344 32434 : absfrac_shallow(GEN x)
1345 32434 : { return signe(gel(x,1))>0? x: mkfrac(negi(gel(x,1)), gel(x,2)); }
1346 : INLINE GEN
1347 7545307 : Q_abs(GEN x) { return (typ(x) == t_INT)? absi(x): absfrac(x); }
1348 : INLINE GEN
1349 113706 : Q_abs_shallow(GEN x)
1350 113706 : { return (typ(x) == t_INT)? absi_shallow(x): absfrac_shallow(x); }
1351 : INLINE GEN
1352 322 : R_abs_shallow(GEN x)
1353 322 : { return (typ(x) == t_FRAC)? absfrac_shallow(x): mpabs_shallow(x); }
1354 : INLINE GEN
1355 0 : R_abs(GEN x)
1356 0 : { return (typ(x) == t_FRAC)? absfrac(x): mpabs(x); }
1357 :
1358 : /* Force z to be of type real/complex with floating point components */
1359 : INLINE GEN
1360 35271508 : gtofp(GEN z, long prec)
1361 : {
1362 35271508 : switch(typ(z))
1363 : {
1364 22132475 : case t_INT: return itor(z, prec);
1365 4309030 : case t_FRAC: return fractor(z, prec);
1366 7399318 : case t_REAL: return rtor(z, prec);
1367 : case t_COMPLEX: {
1368 1430685 : GEN a = gel(z,1), b = gel(z,2);
1369 1430685 : if (isintzero(b)) return cxcompotor(a, prec);
1370 1428274 : if (isintzero(a)) {
1371 2041 : GEN y = cgetg(3, t_COMPLEX);
1372 2041 : b = cxcompotor(b, prec);
1373 2041 : gel(y,1) = real_0_bit(expo(b) - prec2nbits(prec));
1374 2041 : gel(y,2) = b; return y;
1375 : }
1376 1426233 : return cxtofp(z, prec);
1377 : }
1378 0 : case t_QUAD: return quadtofp(z, prec);
1379 0 : default: pari_err_TYPE("gtofp",z);
1380 : return NULL; /* LCOV_EXCL_LINE */
1381 : }
1382 : }
1383 : /* Force z to be of type real / int */
1384 : INLINE GEN
1385 22400 : gtomp(GEN z, long prec)
1386 : {
1387 22400 : switch(typ(z))
1388 : {
1389 14 : case t_INT: return z;
1390 22386 : case t_FRAC: return fractor(z, prec);
1391 0 : case t_REAL: return rtor(z, prec);
1392 0 : case t_QUAD: z = quadtofp(z, prec);
1393 0 : if (typ(z) == t_REAL) return z;
1394 0 : default: pari_err_TYPE("gtomp",z);
1395 : return NULL; /* LCOV_EXCL_LINE */
1396 : }
1397 : }
1398 :
1399 : INLINE GEN
1400 732423 : RgX_gtofp(GEN x, long prec)
1401 : {
1402 : long l;
1403 732423 : GEN y = cgetg_copy(x, &l);
1404 732423 : while (--l > 1) gel(y,l) = gtofp(gel(x,l), prec);
1405 732423 : y[1] = x[1]; return y;
1406 : }
1407 : INLINE GEN
1408 1176608 : RgC_gtofp(GEN x, long prec)
1409 1176608 : { pari_APPLY_type(t_COL, gtofp(gel(x,i), prec)) }
1410 :
1411 : INLINE GEN
1412 42 : RgV_gtofp(GEN x, long prec)
1413 42 : { pari_APPLY_type(t_VEC, gtofp(gel(x,i), prec)) }
1414 :
1415 : INLINE GEN
1416 133885 : RgM_gtofp(GEN x, long prec)
1417 133885 : { pari_APPLY_same(RgC_gtofp(gel(x,i), prec)) }
1418 :
1419 : INLINE GEN
1420 560 : RgC_gtomp(GEN x, long prec)
1421 560 : { pari_APPLY_type(t_COL, gtomp(gel(x,i), prec)) }
1422 :
1423 : INLINE GEN
1424 14 : RgM_gtomp(GEN x, long prec)
1425 14 : { pari_APPLY_same(RgC_gtomp(gel(x,i), prec)) }
1426 :
1427 : INLINE GEN
1428 9122 : RgX_fpnorml2(GEN x, long prec)
1429 : {
1430 9122 : pari_sp av = avma;
1431 9122 : return gerepileupto(av, gnorml2(RgX_gtofp(x, prec)));
1432 : }
1433 : INLINE GEN
1434 177877 : RgC_fpnorml2(GEN x, long prec)
1435 : {
1436 177877 : pari_sp av = avma;
1437 177877 : return gerepileupto(av, gnorml2(RgC_gtofp(x, prec)));
1438 : }
1439 : INLINE GEN
1440 3804 : RgM_fpnorml2(GEN x, long prec)
1441 : {
1442 3804 : pari_sp av = avma;
1443 3804 : return gerepileupto(av, gnorml2(RgM_gtofp(x, prec)));
1444 : }
1445 :
1446 : /* y a t_REAL */
1447 : INLINE void
1448 216244 : affgr(GEN x, GEN y)
1449 : {
1450 : pari_sp av;
1451 216244 : switch(typ(x)) {
1452 5992 : case t_INT: affir(x,y); break;
1453 210252 : case t_REAL: affrr(x,y); break;
1454 0 : case t_FRAC: rdiviiz(gel(x,1),gel(x,2), y); break;
1455 0 : case t_QUAD: av = avma; affgr(quadtofp(x,realprec(y)), y); set_avma(av); break;
1456 0 : default: pari_err_TYPE2("=",x,y);
1457 : }
1458 216244 : }
1459 :
1460 : INLINE GEN
1461 187262 : affc_fixlg(GEN x, GEN res)
1462 : {
1463 187262 : if (typ(x) == t_COMPLEX)
1464 : {
1465 175700 : affrr_fixlg(gel(x,1), gel(res,1));
1466 175700 : affrr_fixlg(gel(x,2), gel(res,2));
1467 : }
1468 : else
1469 : {
1470 11562 : avma = (pari_sp)(res+3);
1471 11562 : res = cgetr(realprec(gel(res,1)));
1472 11562 : affrr_fixlg(x, res);
1473 : }
1474 187262 : return res;
1475 : }
1476 :
1477 : INLINE GEN
1478 0 : trunc_safe(GEN x) { long e; return gcvtoi(x,&e); }
1479 :
1480 : /*******************************************************************/
1481 : /* */
1482 : /* LENGTH CONVERSIONS */
1483 : /* */
1484 : /*******************************************************************/
1485 : INLINE long
1486 28204 : ndec2nlong(long x) { return 1 + (long)((x)*(LOG2_10/BITS_IN_LONG)); }
1487 : INLINE long
1488 27721 : ndec2prec(long x) { return 2 + ndec2nlong(x); }
1489 : INLINE long
1490 483 : ndec2nbits(long x) { return ndec2nlong(x) << TWOPOTBITS_IN_LONG; }
1491 : /* Fast implementation of ceil(x / (8*sizeof(long))); typecast to (ulong)
1492 : * to avoid overflow. Faster than 1 + ((x-1)>>TWOPOTBITS_IN_LONG)) :
1493 : * addl, shrl instead of subl, sarl, addl */
1494 : INLINE long
1495 1186318 : nbits2nlong(long x) {
1496 1186318 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1497 : }
1498 :
1499 : INLINE long
1500 288561867 : nbits2extraprec(long x) {
1501 288561867 : return (long)(((ulong)x+BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1502 : }
1503 :
1504 : /* Fast implementation of 2 + nbits2nlong(x) */
1505 : INLINE long
1506 106931040 : nbits2prec(long x) {
1507 106931040 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1508 : }
1509 : INLINE long
1510 7636469 : nbits2lg(long x) {
1511 7636469 : return (long)(((ulong)x+3*BITS_IN_LONG-1) >> TWOPOTBITS_IN_LONG);
1512 : }
1513 : /* ceil(x / sizeof(long)) */
1514 : INLINE long
1515 8603571 : nchar2nlong(long x) {
1516 8603571 : return (long)(((ulong)x+sizeof(long)-1) >> (TWOPOTBITS_IN_LONG-3L));
1517 : }
1518 : INLINE long
1519 1112162387 : prec2nbits(long x) { return (x-2) * BITS_IN_LONG; }
1520 : INLINE double
1521 563778 : bit_accuracy_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1522 : INLINE double
1523 235157 : prec2nbits_mul(long x, double y) { return (x-2) * (BITS_IN_LONG*y); }
1524 : INLINE long
1525 31700863 : bit_prec(GEN x) { return prec2nbits(realprec(x)); }
1526 : INLINE long
1527 1004221760 : bit_accuracy(long x) { return prec2nbits(x); }
1528 : INLINE long
1529 12365 : prec2ndec(long x) { return (long)prec2nbits_mul(x, LOG10_2); }
1530 : INLINE long
1531 186 : nbits2ndec(long x) { return (long)(x * LOG10_2); }
1532 : INLINE long
1533 1743 : precdbl(long x) {return (x - 1) << 1;}
1534 : INLINE long
1535 3315132771 : divsBIL(long n) { return n >> TWOPOTBITS_IN_LONG; }
1536 : INLINE long
1537 3274416900 : remsBIL(long n) { return n & (BITS_IN_LONG-1); }
1538 :
1539 : /*********************************************************************/
1540 : /** **/
1541 : /** OPERATIONS MODULO m **/
1542 : /** **/
1543 : /*********************************************************************/
1544 : /* Assume m > 0, more efficient if 0 <= a, b < m */
1545 :
1546 : INLINE GEN
1547 33685220 : Fp_red(GEN a, GEN m) { return modii(a, m); }
1548 : INLINE GEN
1549 72018555 : Fp_add(GEN a, GEN b, GEN m)
1550 : {
1551 72018555 : pari_sp av=avma;
1552 72018555 : GEN p = addii(a,b);
1553 70250828 : long s = signe(p);
1554 70250828 : if (!s) return p; /* = gen_0 */
1555 62643223 : if (s > 0) /* general case */
1556 : {
1557 62416768 : GEN t = subii(p, m);
1558 63435846 : s = signe(t);
1559 63435846 : if (!s) { set_avma(av); return gen_0; }
1560 57652290 : if (s < 0) { avma = (pari_sp)p; return p; }
1561 24296025 : if (cmpii(t, m) < 0) return gerepileuptoint(av, t); /* general case ! */
1562 1105855 : p = remii(t, m);
1563 : }
1564 : else
1565 226455 : p = modii(p, m);
1566 1332310 : return gerepileuptoint(av, p);
1567 : }
1568 : INLINE GEN
1569 57037138 : Fp_sub(GEN a, GEN b, GEN m)
1570 : {
1571 57037138 : pari_sp av=avma;
1572 57037138 : GEN p = subii(a,b);
1573 55513924 : long s = signe(p);
1574 55513924 : if (!s) return p; /* = gen_0 */
1575 49251587 : if (s > 0)
1576 : {
1577 23798793 : if (cmpii(p, m) < 0) return p; /* general case ! */
1578 1121229 : p = remii(p, m);
1579 : }
1580 : else
1581 : {
1582 25452794 : GEN t = addii(p, m);
1583 25386409 : if (!s) { set_avma(av); return gen_0; }
1584 25386409 : if (s > 0) return gerepileuptoint(av, t); /* general case ! */
1585 25386409 : p = modii(t, m);
1586 : }
1587 27242985 : return gerepileuptoint(av, p);
1588 : }
1589 : INLINE GEN
1590 11623312 : Fp_neg(GEN b, GEN m)
1591 : {
1592 11623312 : pari_sp av = avma;
1593 11623312 : long s = signe(b);
1594 : GEN p;
1595 11623312 : if (!s) return gen_0;
1596 8191022 : if (s > 0)
1597 : {
1598 7990897 : p = subii(m, b);
1599 7988616 : if (signe(p) >= 0) return p; /* general case ! */
1600 92070 : p = modii(p, m);
1601 : } else
1602 200125 : p = remii(negi(b), m);
1603 292195 : return gerepileuptoint(av, p);
1604 : }
1605 :
1606 : INLINE GEN
1607 23592 : Fp_halve(GEN a, GEN p)
1608 : {
1609 23592 : if (mpodd(a)) a = addii(a,p);
1610 23592 : return shifti(a,-1);
1611 : }
1612 :
1613 : /* assume 0 <= u < p and ps2 = p>>1 */
1614 : INLINE GEN
1615 16314129 : Fp_center(GEN u, GEN p, GEN ps2)
1616 16314129 : { return abscmpii(u,ps2)<=0? icopy(u): subii(u,p); }
1617 : /* same without copy */
1618 : INLINE GEN
1619 14912311 : Fp_center_i(GEN u, GEN p, GEN ps2)
1620 14912311 : { return abscmpii(u,ps2)<=0? u: subii(u,p); }
1621 :
1622 : /* x + y*z mod p */
1623 : INLINE GEN
1624 5040500 : Fp_addmul(GEN x, GEN y, GEN z, GEN p)
1625 : {
1626 : pari_sp av;
1627 5040500 : if (!signe(y) || !signe(z)) return Fp_red(x, p);
1628 4748866 : if (!signe(x)) return Fp_mul(z,y, p);
1629 4448053 : av = avma;
1630 4448053 : return gerepileuptoint(av, modii(addii(x, mulii(y,z)), p));
1631 : }
1632 :
1633 : INLINE GEN
1634 90736959 : Fp_mul(GEN a, GEN b, GEN m)
1635 : {
1636 90736959 : pari_sp av=avma;
1637 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1638 90736959 : (void)new_chunk(lg(a)+lg(b)+(lg(m)<<1));
1639 90720849 : p = mulii(a,b);
1640 90829187 : set_avma(av); return modii(p,m);
1641 : }
1642 : INLINE GEN
1643 34204920 : Fp_sqr(GEN a, GEN m)
1644 : {
1645 34204920 : pari_sp av=avma;
1646 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1647 34204920 : (void)new_chunk((lg(a)+lg(m))<<1);
1648 34110096 : p = sqri(a);
1649 30370345 : set_avma(av); return remii(p,m); /*Use remii: p >= 0 */
1650 : }
1651 : INLINE GEN
1652 66024743 : Fp_mulu(GEN a, ulong b, GEN m)
1653 : {
1654 66024743 : long l = lgefint(m);
1655 66024743 : if (l == 3)
1656 : {
1657 39899686 : ulong mm = m[2];
1658 39899686 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1659 : } else {
1660 26125057 : pari_sp av = avma;
1661 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1662 26125057 : (void)new_chunk(lg(a)+1+(l<<1));
1663 26044567 : p = muliu(a,b);
1664 24180846 : set_avma(av); return modii(p,m);
1665 : }
1666 : }
1667 : INLINE GEN
1668 0 : Fp_muls(GEN a, long b, GEN m)
1669 : {
1670 0 : long l = lgefint(m);
1671 0 : if (l == 3)
1672 : {
1673 0 : ulong mm = m[2];
1674 0 : if (b < 0)
1675 : {
1676 0 : ulong t = Fl_mul(umodiu(a, mm), -b, mm);
1677 0 : return t? utoipos(mm - t): gen_0;
1678 : }
1679 : else
1680 0 : return utoi( Fl_mul(umodiu(a, mm), b, mm) );
1681 : } else {
1682 0 : pari_sp av = avma;
1683 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1684 0 : (void)new_chunk(lg(a)+1+(l<<1));
1685 0 : p = mulis(a,b);
1686 0 : set_avma(av); return modii(p,m);
1687 : }
1688 : }
1689 :
1690 : INLINE GEN
1691 8714487 : Fp_inv(GEN a, GEN m)
1692 : {
1693 : GEN res;
1694 8714487 : if (! invmod(a,m,&res)) pari_err_INV("Fp_inv", mkintmod(res,m));
1695 8714301 : return res;
1696 : }
1697 : INLINE GEN
1698 313875 : Fp_invsafe(GEN a, GEN m)
1699 : {
1700 : GEN res;
1701 313875 : if (! invmod(a,m,&res)) return NULL;
1702 313875 : return res;
1703 : }
1704 : INLINE GEN
1705 2366890 : Fp_div(GEN a, GEN b, GEN m)
1706 : {
1707 2366890 : pari_sp av=avma;
1708 : GEN p; /*HACK: assume modii use <=lg(p)+(lg(m)<<1) space*/
1709 2366890 : (void)new_chunk(lg(a)+(lg(m)<<1));
1710 2366890 : p = mulii(a, Fp_inv(b,m));
1711 2366888 : set_avma(av); return modii(p,m);
1712 : }
1713 :
1714 : INLINE GEN
1715 842951 : Flx_mulu(GEN x, ulong a, ulong p) { return Flx_Fl_mul(x,a%p,p); }
1716 :
1717 : INLINE GEN
1718 0 : get_F2x_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1719 :
1720 : INLINE long
1721 448468 : get_F2x_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1722 :
1723 : INLINE long
1724 121548 : get_F2x_degree(GEN T) { return typ(T)==t_VEC? F2x_degree(gel(T,2)): F2x_degree(T); }
1725 :
1726 : INLINE GEN
1727 378 : get_F2xqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1728 :
1729 : INLINE long
1730 376495 : get_F2xqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1731 :
1732 : INLINE long
1733 201684 : get_F2xqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1734 :
1735 : INLINE GEN
1736 7447422 : get_Flx_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1737 :
1738 : INLINE long
1739 20031639 : get_Flx_var(GEN T) { return typ(T)==t_VEC? mael(T,2,1): T[1]; }
1740 :
1741 : INLINE long
1742 31474376 : get_Flx_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1743 :
1744 : INLINE GEN
1745 2258 : get_FlxqX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1746 :
1747 : INLINE long
1748 368931 : get_FlxqX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1749 :
1750 : INLINE long
1751 155787 : get_FlxqX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1752 :
1753 : INLINE GEN
1754 1608389 : get_FpX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1755 :
1756 : INLINE long
1757 2891032 : get_FpX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1758 :
1759 : INLINE long
1760 1881846 : get_FpX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1761 :
1762 : INLINE GEN
1763 142586 : get_FpXQX_mod(GEN T) { return typ(T)==t_VEC? gel(T,2): T; }
1764 :
1765 : INLINE long
1766 57357 : get_FpXQX_var(GEN T) { return typ(T)==t_VEC? varn(gel(T,2)): varn(T); }
1767 :
1768 : INLINE long
1769 2187 : get_FpXQX_degree(GEN T) { return typ(T)==t_VEC? degpol(gel(T,2)): degpol(T); }
1770 :
1771 : /*******************************************************************/
1772 : /* */
1773 : /* ADDMULII / SUBMULII */
1774 : /* */
1775 : /*******************************************************************/
1776 : /* x - y*z */
1777 : INLINE GEN
1778 13409827 : submulii(GEN x, GEN y, GEN z)
1779 : {
1780 13409827 : long lx = lgefint(x), ly, lz;
1781 : pari_sp av;
1782 : GEN t;
1783 13409827 : if (lx == 2) { t = mulii(z,y); togglesign(t); return t; }
1784 11599698 : ly = lgefint(y);
1785 11599698 : if (ly == 2) return icopy(x);
1786 10471470 : lz = lgefint(z);
1787 10471470 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1788 10471470 : t = mulii(z, y);
1789 10471470 : set_avma(av); return subii(x,t);
1790 : }
1791 : /* y*z - x */
1792 : INLINE GEN
1793 1188646 : mulsubii(GEN y, GEN z, GEN x)
1794 : {
1795 1188646 : long lx = lgefint(x), ly, lz;
1796 : pari_sp av;
1797 : GEN t;
1798 1188646 : if (lx == 2) return mulii(z,y);
1799 759394 : ly = lgefint(y);
1800 759394 : if (ly == 2) return negi(x);
1801 703302 : lz = lgefint(z);
1802 703302 : av = avma; (void)new_chunk(lx+ly+lz); /* HACK */
1803 703302 : t = mulii(z, y);
1804 703302 : set_avma(av); return subii(t,x);
1805 : }
1806 :
1807 : /* x - u*y */
1808 : INLINE GEN
1809 7595 : submuliu(GEN x, GEN y, ulong u)
1810 : {
1811 : pari_sp av;
1812 7595 : long ly = lgefint(y);
1813 7595 : if (ly == 2) return icopy(x);
1814 7595 : av = avma;
1815 7595 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1816 7595 : y = mului(u,y);
1817 7595 : set_avma(av); return subii(x, y);
1818 : }
1819 : /* x + u*y */
1820 : INLINE GEN
1821 7595 : addmuliu(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 addii(x, y);
1830 : }
1831 : /* x - u*y */
1832 : INLINE GEN
1833 120899870 : submuliu_inplace(GEN x, GEN y, ulong u)
1834 : {
1835 : pari_sp av;
1836 120899870 : long ly = lgefint(y);
1837 120899870 : if (ly == 2) return x;
1838 96726044 : av = avma;
1839 96726044 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1840 96726044 : y = mului(u,y);
1841 96726044 : set_avma(av); return subii(x, y);
1842 : }
1843 : /* x + u*y */
1844 : INLINE GEN
1845 119297417 : addmuliu_inplace(GEN x, GEN y, ulong u)
1846 : {
1847 : pari_sp av;
1848 119297417 : long ly = lgefint(y);
1849 119297417 : if (ly == 2) return x;
1850 96550364 : av = avma;
1851 96550364 : (void)new_chunk(3+ly+lgefint(x)); /* HACK */
1852 96550364 : y = mului(u,y);
1853 96550364 : set_avma(av); return addii(x, y);
1854 : }
1855 : /* ux + vy */
1856 : INLINE GEN
1857 20302902 : lincombii(GEN u, GEN v, GEN x, GEN y)
1858 : {
1859 20302902 : long lx = lgefint(x), ly;
1860 : GEN p1, p2;
1861 : pari_sp av;
1862 20302902 : if (lx == 2) return mulii(v,y);
1863 14352648 : ly = lgefint(y);
1864 14352648 : if (ly == 2) return mulii(u,x);
1865 13211507 : av = avma; (void)new_chunk(lx+ly+lgefint(u)+lgefint(v)); /* HACK */
1866 13211507 : p1 = mulii(u,x);
1867 13211507 : p2 = mulii(v,y);
1868 13211507 : set_avma(av); return addii(p1,p2);
1869 : }
1870 :
1871 : /*******************************************************************/
1872 : /* */
1873 : /* GEN SUBTYPES */
1874 : /* */
1875 : /*******************************************************************/
1876 :
1877 : INLINE int
1878 1167300512 : is_const_t(long t) { return (t < t_POLMOD); }
1879 : INLINE int
1880 5325 : is_extscalar_t(long t) { return (t <= t_POL); }
1881 : INLINE int
1882 1024885 : is_intreal_t(long t) { return (t <= t_REAL); }
1883 : INLINE int
1884 400041713 : is_matvec_t(long t) { return (t >= t_VEC && t <= t_MAT); }
1885 : INLINE int
1886 59172937 : is_noncalc_t(long tx) { return (tx) >= t_LIST; }
1887 : INLINE int
1888 1130946 : is_rational_t(long t) { return (t == t_INT || t == t_FRAC); }
1889 : INLINE int
1890 375953 : is_real_t(long t) { return (t == t_INT || t == t_REAL || t == t_FRAC); }
1891 : INLINE int
1892 2866420899 : is_recursive_t(long t) { return lontyp[t]; }
1893 : INLINE int
1894 179257371 : is_scalar_t(long t) { return (t < t_POL); }
1895 : INLINE int
1896 1190883 : is_vec_t(long t) { return (t == t_VEC || t == t_COL); }
1897 :
1898 : /*******************************************************************/
1899 : /* */
1900 : /* TRANSCENDENTAL */
1901 : /* */
1902 : /*******************************************************************/
1903 : INLINE GEN
1904 21757341 : sqrtr(GEN x) {
1905 21757341 : long s = signe(x);
1906 21757341 : if (s == 0) return real_0_bit(expo(x) >> 1);
1907 21723640 : if (s >= 0) return sqrtr_abs(x);
1908 29315 : retmkcomplex(gen_0, sqrtr_abs(x));
1909 : }
1910 : INLINE GEN
1911 0 : cbrtr_abs(GEN x) { return sqrtnr_abs(x, 3); }
1912 : INLINE GEN
1913 0 : cbrtr(GEN x) {
1914 0 : long s = signe(x);
1915 : GEN r;
1916 0 : if (s == 0) return real_0_bit(expo(x) / 3);
1917 0 : r = cbrtr_abs(x);
1918 0 : if (s < 0) togglesign(r);
1919 0 : return r;
1920 : }
1921 : INLINE GEN
1922 373769 : sqrtnr(GEN x, long n) {
1923 373769 : long s = signe(x);
1924 : GEN r;
1925 373769 : if (s == 0) return real_0_bit(expo(x) / n);
1926 373769 : r = sqrtnr_abs(x, n);
1927 373769 : if (s < 0) pari_err_IMPL("sqrtnr for x < 0");
1928 373769 : return r;
1929 : }
1930 : INLINE long
1931 212480 : logint(GEN B, GEN y) { return logintall(B,y,NULL); }
1932 : INLINE ulong
1933 1810842 : ulogint(ulong B, ulong y)
1934 : {
1935 : ulong r;
1936 : long e;
1937 1810842 : if (y == 2) return expu(B);
1938 1792999 : r = y;
1939 6011909 : for (e=1;; e++)
1940 : { /* here, r = y^e, r2 = y^(e-1) */
1941 10230819 : if (r >= B) return r == B? e: e-1;
1942 4218910 : r = umuluu_or_0(y, r);
1943 4218910 : if (!r) return e;
1944 : }
1945 : }
1946 :
1947 : /*******************************************************************/
1948 : /* */
1949 : /* MISCELLANEOUS */
1950 : /* */
1951 : /*******************************************************************/
1952 1024808 : INLINE int ismpzero(GEN x) { return is_intreal_t(typ(x)) && !signe(x); }
1953 556597565 : INLINE int isintzero(GEN x) { return typ(x) == t_INT && !signe(x); }
1954 7012260 : INLINE int isint1(GEN x) { return typ(x)==t_INT && equali1(x); }
1955 4613 : INLINE int isintm1(GEN x){ return typ(x)==t_INT && equalim1(x);}
1956 674545757 : INLINE int equali1(GEN n)
1957 674545757 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(1)) && n[2] == 1; }
1958 62132248 : INLINE int equalim1(GEN n)
1959 62132248 : { return (ulong) n[1] == (evallgefint(3UL) | evalsigne(-1)) && n[2] == 1; }
1960 : /* works only for POSITIVE integers */
1961 935016427 : INLINE int is_pm1(GEN n)
1962 935016427 : { return lgefint(n) == 3 && n[2] == 1; }
1963 220326745 : INLINE int is_bigint(GEN n)
1964 220326745 : { long l = lgefint(n); return l > 3 || (l == 3 && (n[2] & HIGHBIT)); }
1965 :
1966 2052630421 : INLINE int odd(long x) { return x & 1; }
1967 28590246 : INLINE int both_odd(long x, long y) { return x & y & 1; }
1968 :
1969 : INLINE int
1970 2635843477 : isonstack(GEN x)
1971 2635843477 : { return ((pari_sp)x >= pari_mainstack->bot
1972 2635843477 : && (pari_sp)x < pari_mainstack->top); }
1973 :
1974 : /* assume x != 0 and x t_REAL, return an approximation to log2(|x|) */
1975 : INLINE double
1976 21999132 : dbllog2r(GEN x)
1977 21999132 : { return log2((double)(ulong)x[2]) + (double)(expo(x) - (BITS_IN_LONG-1)); }
1978 :
1979 : INLINE GEN
1980 308639 : mul_content(GEN cx, GEN cy)
1981 : {
1982 308639 : if (!cx) return cy;
1983 108065 : if (!cy) return cx;
1984 79214 : return gmul(cx,cy);
1985 : }
1986 : INLINE GEN
1987 5901 : inv_content(GEN c) { return c? ginv(c): NULL; }
1988 : INLINE GEN
1989 1603238 : mul_denom(GEN dx, GEN dy)
1990 : {
1991 1603238 : if (!dx) return dy;
1992 1060336 : if (!dy) return dx;
1993 334376 : return mulii(dx,dy);
1994 : }
1995 :
1996 : /* POLYNOMIALS */
1997 : INLINE GEN
1998 17566814 : constant_coeff(GEN x) { return signe(x)? gel(x,2): gen_0; }
1999 : INLINE GEN
2000 81477027 : leading_coeff(GEN x) { return lg(x) == 2? gen_0: gel(x,lg(x)-1); }
2001 : INLINE ulong
2002 478560 : Flx_lead(GEN x) { return lg(x) == 2? 0: x[lg(x)-1]; }
2003 : INLINE ulong
2004 12348 : Flx_constant(GEN x) { return lg(x) == 2? 0: x[2]; }
2005 : INLINE long
2006 2800241026 : degpol(GEN x) { return lg(x)-3; }
2007 : INLINE long
2008 1364072787 : lgpol(GEN x) { return lg(x)-2; }
2009 : INLINE long
2010 115474195 : lgcols(GEN x) { return lg(gel(x,1)); }
2011 : INLINE long
2012 33454447 : nbrows(GEN x) { return lg(gel(x,1))-1; }
2013 : INLINE GEN
2014 0 : truecoef(GEN x, long n) { return polcoef(x,n,-1); }
2015 :
2016 : INLINE GEN
2017 555815 : ZXQ_mul(GEN y, GEN x, GEN T) { return ZX_rem(ZX_mul(y, x), T); }
2018 : INLINE GEN
2019 277905 : ZXQ_sqr(GEN x, GEN T) { return ZX_rem(ZX_sqr(x), T); }
2020 :
2021 : INLINE GEN
2022 57843056 : RgX_copy(GEN x)
2023 : {
2024 : long lx, i;
2025 57843056 : GEN y = cgetg_copy(x, &lx); y[1] = x[1];
2026 57843064 : for (i = 2; i<lx; i++) gel(y,i) = gcopy(gel(x,i));
2027 57843061 : return y;
2028 : }
2029 : /* have to use ulong to avoid silly warnings from gcc "assuming signed
2030 : * overflow does not occur" */
2031 : INLINE GEN
2032 2956710 : RgX_coeff(GEN x, long n)
2033 : {
2034 2956710 : ulong l = lg(x);
2035 2956710 : return (n < 0 || ((ulong)n+3) > l)? gen_0: gel(x,n+2);
2036 : }
2037 : INLINE GEN
2038 353293 : RgX_renormalize(GEN x) { return RgX_renormalize_lg(x, lg(x)); }
2039 : INLINE GEN
2040 6702010 : RgX_div(GEN x, GEN y) { return RgX_divrem(x,y,NULL); }
2041 : INLINE GEN
2042 1792 : RgXQX_div(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,NULL); }
2043 : INLINE GEN
2044 65155 : RgXQX_rem(GEN x, GEN y, GEN T) { return RgXQX_divrem(x,y,T,ONLY_REM); }
2045 : INLINE GEN
2046 884866 : FpX_div(GEN x, GEN y, GEN p) { return FpX_divrem(x,y,p, NULL); }
2047 : INLINE GEN
2048 4345041 : Flx_div(GEN x, GEN y, ulong p) { return Flx_divrem(x,y,p, NULL); }
2049 : INLINE GEN
2050 2582016 : F2x_div(GEN x, GEN y) { return F2x_divrem(x,y, NULL); }
2051 : INLINE GEN
2052 0 : FpV_FpC_mul(GEN x, GEN y, GEN p) { return FpV_dotproduct(x,y,p); }
2053 : INLINE GEN
2054 56926728 : pol0_Flx(long sv) { return mkvecsmall(sv); }
2055 : INLINE GEN
2056 22787177 : pol1_Flx(long sv) { return mkvecsmall2(sv, 1); }
2057 : INLINE GEN
2058 17651153 : polx_Flx(long sv) { return mkvecsmall3(sv, 0, 1); }
2059 : INLINE GEN
2060 0 : zero_zx(long sv) { return zero_Flx(sv); }
2061 : INLINE GEN
2062 0 : polx_zx(long sv) { return polx_Flx(sv); }
2063 : INLINE GEN
2064 0 : zx_shift(GEN x, long n) { return Flx_shift(x,n); }
2065 : INLINE GEN
2066 0 : zx_renormalize(GEN x, long l) { return Flx_renormalize(x,l); }
2067 : INLINE GEN
2068 1474 : zero_F2x(long sv) { return zero_Flx(sv); }
2069 : INLINE GEN
2070 11152734 : pol0_F2x(long sv) { return pol0_Flx(sv); }
2071 : INLINE GEN
2072 2869584 : pol1_F2x(long sv) { return pol1_Flx(sv); }
2073 : INLINE GEN
2074 683304 : polx_F2x(long sv) { return mkvecsmall2(sv, 2); }
2075 : INLINE int
2076 812381 : F2x_equal1(GEN x) { return Flx_equal1(x); }
2077 : INLINE int
2078 3095188 : F2x_equal(GEN V, GEN W) { return Flx_equal(V,W); }
2079 : INLINE GEN
2080 59175313 : F2x_copy(GEN x) { return leafcopy(x); }
2081 : INLINE GEN
2082 0 : F2v_copy(GEN x) { return leafcopy(x); }
2083 : INLINE GEN
2084 2273226 : Flv_copy(GEN x) { return leafcopy(x); }
2085 : INLINE GEN
2086 83236638 : Flx_copy(GEN x) { return leafcopy(x); }
2087 : INLINE GEN
2088 1863909 : vecsmall_copy(GEN x) { return leafcopy(x); }
2089 : INLINE int
2090 4854475 : Flx_equal1(GEN x) { return degpol(x)==0 && x[2] == 1; }
2091 : INLINE int
2092 18205 : ZX_equal1(GEN x) { return degpol(x)==0 && equali1(gel(x,2)); }
2093 : INLINE int
2094 5559415 : ZX_is_monic(GEN x) { return equali1(leading_coeff(x)); }
2095 :
2096 : INLINE GEN
2097 50526389 : ZX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2098 : INLINE GEN
2099 67211138 : FpX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2100 : INLINE GEN
2101 771228 : FpXX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2102 : INLINE GEN
2103 1237233 : FpXQX_renormalize(GEN x, long lx) { return ZXX_renormalize(x,lx); }
2104 : INLINE GEN
2105 111260841 : F2x_renormalize(GEN x, long lx) { return Flx_renormalize(x,lx); }
2106 : INLINE GEN
2107 32291 : F2v_to_F2x(GEN x, long sv) {
2108 32291 : GEN y = leafcopy(x);
2109 32291 : y[1] = sv; F2x_renormalize(y, lg(y)); return y;
2110 : }
2111 :
2112 : INLINE long
2113 0 : sturm(GEN x) { return sturmpart(x, NULL, NULL); }
2114 :
2115 : INLINE long
2116 7042 : gval(GEN x, long v) {
2117 7042 : pari_sp av = avma;
2118 7042 : long n = gvaluation(x, pol_x(v));
2119 7042 : set_avma(av); return n;
2120 : }
2121 :
2122 : INLINE void
2123 469118 : RgX_shift_inplace_init(long v)
2124 469118 : { if (v) (void)cgetg(v, t_VECSMALL); }
2125 : /* shift polynomial in place. assume v free cells have been left before x */
2126 : INLINE GEN
2127 469118 : RgX_shift_inplace(GEN x, long v)
2128 : {
2129 : long i, lx;
2130 : GEN y, z;
2131 469118 : if (!v) return x;
2132 253227 : lx = lg(x);
2133 253227 : if (lx == 2) return x;
2134 253227 : y = x + v;
2135 253227 : z = x + lx;
2136 : /* stackdummy from normalizepol: move it up */
2137 253227 : if (lg(z) != v) x[lx + v] = z[0];
2138 253227 : for (i = lx-1; i >= 2; i--) gel(y,i) = gel(x,i);
2139 253227 : for (i = v+1; i >= 2; i--) gel(x,i) = gen_0;
2140 : /* leave x[1] alone: it is correct */
2141 253227 : x[0] = evaltyp(t_POL) | evallg(lx+v); return x;
2142 : }
2143 :
2144 :
2145 : /* LINEAR ALGEBRA */
2146 : INLINE GEN
2147 131784 : zv_to_ZV(GEN x) { return vecsmall_to_vec(x); }
2148 : INLINE GEN
2149 5191030 : zc_to_ZC(GEN x) { return vecsmall_to_col(x); }
2150 : INLINE GEN
2151 438793 : ZV_to_zv(GEN x) { return vec_to_vecsmall(x); }
2152 : INLINE GEN
2153 0 : zx_to_zv(GEN x, long N) { return Flx_to_Flv(x,N); }
2154 : INLINE GEN
2155 0 : zv_to_zx(GEN x, long sv) { return Flv_to_Flx(x,sv); }
2156 : INLINE GEN
2157 0 : zm_to_zxV(GEN x, long sv) { return Flm_to_FlxV(x,sv); }
2158 : INLINE GEN
2159 0 : zero_zm(long x, long y) { return zero_Flm(x,y); }
2160 : INLINE GEN
2161 17127009 : zero_zv(long x) { return zero_Flv(x); }
2162 : INLINE GEN
2163 210 : zm_transpose(GEN x) { return Flm_transpose(x); }
2164 : INLINE GEN
2165 0 : zm_copy(GEN x) { return Flm_copy(x); }
2166 : INLINE GEN
2167 1903301 : zv_copy(GEN x) { return Flv_copy(x); }
2168 : INLINE GEN
2169 0 : zm_row(GEN x, long i) { return Flm_row(x,i); }
2170 :
2171 : INLINE GEN
2172 843568 : ZC_hnfrem(GEN x, GEN y) { return ZC_hnfremdiv(x,y,NULL); }
2173 : INLINE GEN
2174 35594 : ZM_hnfrem(GEN x, GEN y) { return ZM_hnfdivrem(x,y,NULL); }
2175 : INLINE GEN
2176 2380839 : ZM_lll(GEN x, double D, long f) { return ZM_lll_norms(x,D,f,NULL); }
2177 : INLINE void
2178 5649816 : RgM_dimensions(GEN x, long *m, long *n) { *n = lg(x)-1; *m = *n? nbrows(x): 0; }
2179 : INLINE GEN
2180 9920933 : RgM_shallowcopy(GEN x)
2181 : {
2182 : long l;
2183 9920933 : GEN y = cgetg_copy(x, &l);
2184 9920933 : while (--l > 0) gel(y,l) = leafcopy(gel(x,l));
2185 9920933 : return y;
2186 : }
2187 : INLINE GEN
2188 302 : F2m_copy(GEN x) { return RgM_shallowcopy(x); }
2189 :
2190 : INLINE GEN
2191 1312898 : Flm_copy(GEN x) { return RgM_shallowcopy(x); }
2192 :
2193 : /* divisibility: return 1 if y[i] | x[i] for all i, 0 otherwise. Assume
2194 : * x,y are ZV of the same length */
2195 : INLINE int
2196 23198 : ZV_dvd(GEN x, GEN y)
2197 : {
2198 23198 : long i, l = lg(x);
2199 36652 : for (i=1; i < l; i++)
2200 29519 : if ( ! dvdii( gel(x,i), gel(y,i) ) ) return 0;
2201 7133 : return 1;
2202 : }
2203 :
2204 : /* Fq */
2205 : INLINE GEN
2206 2798419 : Fq_red(GEN x, GEN T, GEN p)
2207 2798419 : { return typ(x)==t_INT? Fp_red(x,p): FpXQ_red(x,T,p); }
2208 : INLINE GEN
2209 43439 : Fq_to_FpXQ(GEN x, GEN T, GEN p /*unused*/)
2210 : {
2211 : (void) p;
2212 43439 : return typ(x)==t_INT ? scalarpol(x, get_FpX_var(T)): x;
2213 : }
2214 : INLINE GEN
2215 756 : Rg_to_Fq(GEN x, GEN T, GEN p) { return T? Rg_to_FpXQ(x,T,p): Rg_to_Fp(x,p); }
2216 :
2217 : INLINE GEN
2218 903 : gener_Fq_local(GEN T, GEN p, GEN L)
2219 : { return T? gener_FpXQ_local(T,p, L)
2220 903 : : pgener_Fp_local(p, L); }
2221 :
2222 : /* FpXQX */
2223 : INLINE GEN
2224 4347 : FpXQX_div(GEN x, GEN y, GEN T, GEN p) { return FpXQX_divrem(x, y, T, p, NULL); }
2225 : INLINE GEN
2226 34803 : FlxqX_div(GEN x, GEN y, GEN T, ulong p) { return FlxqX_divrem(x, y, T, p, NULL); }
2227 : INLINE GEN
2228 33278 : F2xqX_div(GEN x, GEN y, GEN T) { return F2xqX_divrem(x, y, T, NULL); }
2229 :
2230 : /* FqX */
2231 : INLINE GEN
2232 25431 : FqX_red(GEN z, GEN T, GEN p) { return T? FpXQX_red(z, T, p): FpX_red(z, p); }
2233 : INLINE GEN
2234 957187 : FqX_add(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2235 : INLINE GEN
2236 17404 : FqX_neg(GEN x,GEN T,GEN p) { return T? FpXX_neg(x,p): FpX_neg(x,p); }
2237 : INLINE GEN
2238 3234 : FqX_sub(GEN x,GEN y,GEN T,GEN p) { return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2239 : INLINE GEN
2240 655996 : FqX_Fp_mul(GEN P, GEN u, GEN T, GEN p)
2241 655996 : { return T? FpXX_Fp_mul(P, u, p): FpX_Fp_mul(P, u, p); }
2242 : INLINE GEN
2243 587707 : FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
2244 587707 : { return typ(U)==t_INT ? FqX_Fp_mul(P, U, T, p): FpXQX_FpXQ_mul(P, U, T, p); }
2245 : INLINE GEN
2246 95992 : FqX_mul(GEN x, GEN y, GEN T, GEN p)
2247 95992 : { return T? FpXQX_mul(x, y, T, p): FpX_mul(x, y, p); }
2248 : INLINE GEN
2249 489744 : FqX_mulu(GEN x, ulong y, GEN T, GEN p)
2250 489744 : { return T? FpXX_mulu(x, y, p): FpX_mulu(x, y, p); }
2251 : INLINE GEN
2252 6468 : FqX_sqr(GEN x, GEN T, GEN p)
2253 6468 : { return T? FpXQX_sqr(x, T, p): FpX_sqr(x, p); }
2254 : INLINE GEN
2255 1288 : FqX_powu(GEN x, ulong n, GEN T, GEN p)
2256 1288 : { return T? FpXQX_powu(x, n, T, p): FpX_powu(x, n, p); }
2257 : INLINE GEN
2258 0 : FqX_halve(GEN x, GEN T, GEN p)
2259 0 : { return T? FpXX_halve(x, p): FpX_halve(x, p); }
2260 : INLINE GEN
2261 5523 : FqX_div(GEN x, GEN y, GEN T, GEN p)
2262 5523 : { return T? FpXQX_divrem(x,y,T,p,NULL): FpX_divrem(x,y,p,NULL); }
2263 : INLINE GEN
2264 6095 : FqX_get_red(GEN S, GEN T, GEN p)
2265 6095 : { return T? FpXQX_get_red(S,T,p): FpX_get_red(S,p); }
2266 : INLINE GEN
2267 53108 : FqX_rem(GEN x, GEN y, GEN T, GEN p)
2268 53108 : { return T? FpXQX_rem(x,y,T,p): FpX_rem(x,y,p); }
2269 : INLINE GEN
2270 0 : FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
2271 0 : { return T? FpXQX_divrem(x,y,T,p,z): FpX_divrem(x,y,p,z); }
2272 : INLINE GEN
2273 5936 : FqX_div_by_X_x(GEN x, GEN y, GEN T, GEN p, GEN *z)
2274 5936 : { return T? FpXQX_div_by_X_x(x,y,T,p,z): FpX_div_by_X_x(x,y,p,z); }
2275 : INLINE GEN
2276 0 : FqX_halfgcd(GEN P,GEN Q,GEN T,GEN p)
2277 0 : {return T? FpXQX_halfgcd(P,Q,T,p): FpX_halfgcd(P,Q,p);}
2278 : INLINE GEN
2279 259098 : FqX_gcd(GEN P,GEN Q,GEN T,GEN p)
2280 259098 : {return T? FpXQX_gcd(P,Q,T,p): FpX_gcd(P,Q,p);}
2281 : INLINE GEN
2282 86994 : FqX_extgcd(GEN P,GEN Q,GEN T,GEN p, GEN *U, GEN *V)
2283 86994 : { return T? FpXQX_extgcd(P,Q,T,p,U,V): FpX_extgcd(P,Q,p,U,V); }
2284 : INLINE GEN
2285 3178 : FqX_normalize(GEN z, GEN T, GEN p)
2286 3178 : { return T? FpXQX_normalize(z, T, p): FpX_normalize(z, p); }
2287 : INLINE GEN
2288 272895 : FqX_deriv(GEN f, GEN T, GEN p) { return T? FpXX_deriv(f, p): FpX_deriv(f, p); }
2289 : INLINE GEN
2290 0 : FqX_integ(GEN f, GEN T, GEN p) { return T? FpXX_integ(f, p): FpX_integ(f, p); }
2291 : INLINE GEN
2292 74459 : FqX_factor(GEN f, GEN T, GEN p)
2293 74459 : { return T?FpXQX_factor(f, T, p): FpX_factor(f, p); }
2294 : INLINE GEN
2295 7 : FqX_factor_squarefree(GEN f, GEN T, GEN p)
2296 7 : { return T ? FpXQX_factor_squarefree(f, T, p): FpX_factor_squarefree(f, p); }
2297 : INLINE GEN
2298 7 : FqX_ddf(GEN f, GEN T, GEN p)
2299 7 : { return T ? FpXQX_ddf(f, T, p): FpX_ddf(f, p); }
2300 : INLINE GEN
2301 42 : FqX_degfact(GEN f, GEN T, GEN p)
2302 42 : { return T?FpXQX_degfact(f, T, p): FpX_degfact(f, p); }
2303 : INLINE GEN
2304 7126 : FqX_roots(GEN f, GEN T, GEN p)
2305 7126 : { return T?FpXQX_roots(f, T, p): FpX_roots(f, p); }
2306 : INLINE GEN
2307 203 : FqX_to_mod(GEN f, GEN T, GEN p)
2308 203 : { return T?FpXQX_to_mod(f, T, p): FpX_to_mod(f, p); }
2309 :
2310 : /*FqXQ*/
2311 : INLINE GEN
2312 0 : FqXQ_add(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2313 0 : { (void)S; return T? FpXX_add(x,y,p): FpX_add(x,y,p); }
2314 : INLINE GEN
2315 0 : FqXQ_sub(GEN x, GEN y, GEN S/*unused*/, GEN T, GEN p)
2316 0 : { (void)S; return T? FpXX_sub(x,y,p): FpX_sub(x,y,p); }
2317 : INLINE GEN
2318 0 : FqXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
2319 0 : { return T? FpXQXQ_div(x,y,S,T,p): FpXQ_div(x,y,S,p); }
2320 : INLINE GEN
2321 0 : FqXQ_inv(GEN x, GEN S, GEN T, GEN p)
2322 0 : { return T? FpXQXQ_inv(x,S,T,p): FpXQ_inv(x,S,p); }
2323 : INLINE GEN
2324 0 : FqXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
2325 0 : { return T? FpXQXQ_invsafe(x,S,T,p): FpXQ_inv(x,S,p); }
2326 : INLINE GEN
2327 22348 : FqXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
2328 22348 : { return T? FpXQXQ_mul(x,y,S,T,p): FpXQ_mul(x,y,S,p); }
2329 : INLINE GEN
2330 0 : FqXQ_sqr(GEN x, GEN S, GEN T, GEN p)
2331 0 : { return T? FpXQXQ_sqr(x,S,T,p): FpXQ_sqr(x,S,p); }
2332 : INLINE GEN
2333 0 : FqXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
2334 0 : { return T? FpXQXQ_pow(x,n,S,T,p): FpXQ_pow(x,n,S,p); }
2335 :
2336 : /*FqXn*/
2337 : INLINE GEN
2338 0 : FqXn_exp(GEN x, long n, GEN T, GEN p)
2339 0 : { return T? FpXQXn_exp(x,n,T,p): FpXn_exp(x,n,p); }
2340 : INLINE GEN
2341 0 : FqXn_inv(GEN x, long n, GEN T, GEN p)
2342 0 : { return T? FpXQXn_inv(x,n,T,p): FpXn_inv(x,n,p); }
2343 : INLINE GEN
2344 0 : FqXn_mul(GEN x, GEN y, long n, GEN T, GEN p)
2345 0 : { return T? FpXQXn_mul(x, y, n, T, p): FpXn_mul(x, y, n, p); }
2346 : INLINE GEN
2347 0 : FqXn_sqr(GEN x, long n, GEN T, GEN p)
2348 0 : { return T? FpXQXn_sqr(x,n,T,p): FpXn_sqr(x,n,p); }
2349 :
2350 : /*FpXQ*/
2351 : INLINE GEN
2352 0 : FpXQ_add(GEN x,GEN y,GEN T/*unused*/,GEN p)
2353 0 : { (void)T; return FpX_add(x,y,p); }
2354 : INLINE GEN
2355 0 : FpXQ_sub(GEN x,GEN y,GEN T/*unused*/,GEN p)
2356 0 : { (void)T; return FpX_sub(x,y,p); }
2357 :
2358 : /*Flxq*/
2359 : INLINE GEN
2360 0 : Flxq_add(GEN x,GEN y,GEN T/*unused*/,ulong p)
2361 0 : { (void)T; return Flx_add(x,y,p); }
2362 : INLINE GEN
2363 0 : Flxq_sub(GEN x,GEN y,GEN T/*unused*/,ulong p)
2364 0 : { (void)T; return Flx_sub(x,y,p); }
2365 :
2366 : /* F2x */
2367 :
2368 : INLINE ulong
2369 100496942 : F2x_coeff(GEN x,long v)
2370 : {
2371 100496942 : ulong u=(ulong)x[2+divsBIL(v)];
2372 100496824 : return (u>>remsBIL(v))&1UL;
2373 : }
2374 :
2375 : INLINE void
2376 4710205 : F2x_clear(GEN x,long v)
2377 : {
2378 4710205 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2379 4710204 : *u&=~(1UL<<remsBIL(v));
2380 4710203 : }
2381 :
2382 : INLINE void
2383 32748608 : F2x_set(GEN x,long v)
2384 : {
2385 32748608 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2386 32747374 : *u|=1UL<<remsBIL(v);
2387 32747045 : }
2388 :
2389 : INLINE void
2390 1501249 : F2x_flip(GEN x,long v)
2391 : {
2392 1501249 : ulong* u=(ulong*)&x[2+divsBIL(v)];
2393 1501250 : *u^=1UL<<remsBIL(v);
2394 1501251 : }
2395 :
2396 : /* F2v */
2397 :
2398 : INLINE ulong
2399 95878511 : F2v_coeff(GEN x,long v) { return F2x_coeff(x,v-1); }
2400 :
2401 : INLINE void
2402 4710206 : F2v_clear(GEN x,long v) { F2x_clear(x,v-1); }
2403 :
2404 : INLINE void
2405 8950457 : F2v_set(GEN x,long v) { F2x_set(x,v-1); }
2406 :
2407 : INLINE void
2408 1501248 : F2v_flip(GEN x,long v) { F2x_flip(x,v-1); }
2409 :
2410 : /* F2m */
2411 :
2412 : INLINE ulong
2413 11668772 : F2m_coeff(GEN x, long a, long b) { return F2v_coeff(gel(x,b), a); }
2414 :
2415 : INLINE void
2416 0 : F2m_clear(GEN x, long a, long b) { F2v_clear(gel(x,b), a); }
2417 :
2418 : INLINE void
2419 1362615 : F2m_set(GEN x, long a, long b) { F2v_set(gel(x,b), a); }
2420 :
2421 : INLINE void
2422 1501249 : F2m_flip(GEN x, long a, long b) { F2v_flip(gel(x,b), a); }
2423 :
2424 : /* ARITHMETIC */
2425 : INLINE GEN
2426 1071 : matpascal(long n) { return matqpascal(n, NULL); }
2427 : INLINE long
2428 2330804 : Z_issquare(GEN x) { return Z_issquareall(x, NULL); }
2429 : INLINE long
2430 14 : Z_ispower(GEN x, ulong k) { return Z_ispowerall(x, k, NULL); }
2431 : INLINE GEN
2432 5677221 : sqrti(GEN x) { return sqrtremi(x,NULL); }
2433 : INLINE GEN
2434 4217746 : gaddgs(GEN y, long s) { return gaddsg(s,y); }
2435 : INLINE int
2436 39724 : gcmpgs(GEN y, long s) { return -gcmpsg(s,y); }
2437 : INLINE int
2438 24570 : gequalgs(GEN y, long s) { return gequalsg(s,y); }
2439 : INLINE GEN
2440 0 : gmaxsg(long s, GEN y) { return gmaxgs(y,s); }
2441 : INLINE GEN
2442 0 : gminsg(long s, GEN y) { return gmings(y,s); }
2443 : INLINE GEN
2444 13210239 : gmulgs(GEN y, long s) { return gmulsg(s,y); }
2445 : INLINE GEN
2446 1245971 : gsubgs(GEN y, long s) { return gaddgs(y, -s); }
2447 : INLINE GEN
2448 678127 : gdivsg(long s, GEN y) { return gdiv(stoi(s), y); }
2449 :
2450 : /* x t_COMPLEX */
2451 : INLINE GEN
2452 11103624 : cxnorm(GEN x) { return gadd(gsqr(gel(x,1)), gsqr(gel(x,2))); }
2453 : /* q t_QUAD */
2454 : INLINE GEN
2455 623 : quadnorm(GEN q)
2456 : {
2457 623 : GEN X = gel(q,1), b = gel(X,3), c = gel(X,2);
2458 623 : GEN z, u = gel(q,3), v = gel(q,2);
2459 623 : if (typ(u) == t_INT && typ(v) == t_INT) /* generic case */
2460 : {
2461 308 : z = signe(b)? mulii(v, addii(u,v)): sqri(v);
2462 308 : return addii(z, mulii(c, sqri(u)));
2463 : }
2464 : else
2465 : {
2466 315 : z = signe(b)? gmul(v, gadd(u,v)): gsqr(v);
2467 315 : return gadd(z, gmul(c, gsqr(u)));
2468 : }
2469 : }
2470 : /* x a t_QUAD, return the attached discriminant */
2471 : INLINE GEN
2472 273 : quad_disc(GEN x)
2473 : {
2474 273 : GEN Q = gel(x,1), b = gel(Q,3), c = gel(Q,2), c4;
2475 273 : if (is_pm1(b))
2476 : {
2477 217 : pari_sp av = avma; (void)new_chunk(lgefint(c) + 1);
2478 217 : c4 = shifti(c,2); set_avma(av); return subsi(1, c4);
2479 : }
2480 56 : c4 = shifti(c,2); togglesign_safe(&c4); return c4;
2481 : }
2482 : INLINE GEN
2483 6480663 : qfb_disc3(GEN x, GEN y, GEN z) { return subii(sqri(y), shifti(mulii(x,z),2)); }
2484 : INLINE GEN
2485 6399785 : qfb_disc(GEN x) { return qfb_disc3(gel(x,1), gel(x,2), gel(x,3)); }
2486 :
2487 : INLINE GEN
2488 1251401 : sqrfrac(GEN x)
2489 : {
2490 1251401 : GEN z = cgetg(3,t_FRAC);
2491 1251401 : gel(z,1) = sqri(gel(x,1));
2492 1251401 : gel(z,2) = sqri(gel(x,2)); return z;
2493 : }
2494 :
2495 : INLINE void
2496 14712710 : normalize_frac(GEN z) {
2497 14712710 : if (signe(gel(z,2)) < 0) { togglesign(gel(z,1)); setabssign(gel(z,2)); }
2498 14712710 : }
2499 :
2500 : INLINE GEN
2501 251224 : powii(GEN x, GEN n)
2502 : {
2503 251224 : long ln = lgefint(n);
2504 251224 : if (ln == 3) {
2505 : GEN z;
2506 248606 : if (signe(n) > 0) return powiu(x, n[2]);
2507 5852 : z = cgetg(3, t_FRAC);
2508 5852 : gel(z,1) = gen_1;
2509 5852 : gel(z,2) = powiu(x, n[2]);
2510 5852 : return z;
2511 : }
2512 2618 : if (ln == 2) return gen_1; /* rare */
2513 : /* should never happen */
2514 0 : return powgi(x, n); /* overflow unless x = 0, 1, -1 */
2515 : }
2516 : INLINE GEN
2517 1246 : powIs(long n) {
2518 1246 : switch(n & 3)
2519 : {
2520 28 : case 1: return mkcomplex(gen_0,gen_1);
2521 378 : case 2: return gen_m1;
2522 518 : case 3: return mkcomplex(gen_0,gen_m1);
2523 : }
2524 322 : return gen_1;
2525 : }
2526 :
2527 : /*******************************************************************/
2528 : /* */
2529 : /* ASSIGNMENTS */
2530 : /* */
2531 : /*******************************************************************/
2532 0 : INLINE void mpexpz(GEN x, GEN z)
2533 0 : { pari_sp av = avma; gaffect(mpexp(x), z); set_avma(av); }
2534 0 : INLINE void mplogz(GEN x, GEN z)
2535 0 : { pari_sp av = avma; gaffect(mplog(x), z); set_avma(av); }
2536 0 : INLINE void mpcosz(GEN x, GEN z)
2537 0 : { pari_sp av = avma; gaffect(mpcos(x), z); set_avma(av); }
2538 0 : INLINE void mpsinz(GEN x, GEN z)
2539 0 : { pari_sp av = avma; gaffect(mpsin(x), z); set_avma(av); }
2540 0 : INLINE void gnegz(GEN x, GEN z)
2541 0 : { pari_sp av = avma; gaffect(gneg(x), z); set_avma(av); }
2542 0 : INLINE void gabsz(GEN x, long prec, GEN z)
2543 0 : { pari_sp av = avma; gaffect(gabs(x,prec), z); set_avma(av); }
2544 23318 : INLINE void gaddz(GEN x, GEN y, GEN z)
2545 23318 : { pari_sp av = avma; gaffect(gadd(x,y), z); set_avma(av); }
2546 0 : INLINE void gsubz(GEN x, GEN y, GEN z)
2547 0 : { pari_sp av = avma; gaffect(gsub(x,y), z); set_avma(av); }
2548 11673 : INLINE void gmulz(GEN x, GEN y, GEN z)
2549 11673 : { pari_sp av = avma; gaffect(gmul(x,y), z); set_avma(av); }
2550 0 : INLINE void gdivz(GEN x, GEN y, GEN z)
2551 0 : { pari_sp av = avma; gaffect(gdiv(x,y), z); set_avma(av); }
2552 0 : INLINE void gdiventz(GEN x, GEN y, GEN z)
2553 0 : { pari_sp av = avma; gaffect(gdivent(x,y), z); set_avma(av); }
2554 0 : INLINE void gmodz(GEN x, GEN y, GEN z)
2555 0 : { pari_sp av = avma; gaffect(gmod(x,y), z); set_avma(av); }
2556 0 : INLINE void gmul2nz(GEN x, long s, GEN z)
2557 0 : { pari_sp av = avma; gaffect(gmul2n(x,s), z); set_avma(av); }
2558 0 : INLINE void gshiftz(GEN x, long s, GEN z)
2559 0 : { pari_sp av = avma; gaffect(gshift(x,s), z); set_avma(av); }
2560 :
2561 : /*******************************************************************/
2562 : /* */
2563 : /* ELLIPTIC CURVES */
2564 : /* */
2565 : /*******************************************************************/
2566 3979744 : INLINE GEN ell_get_a1(GEN e) { return gel(e,1); }
2567 3095800 : INLINE GEN ell_get_a2(GEN e) { return gel(e,2); }
2568 3861695 : INLINE GEN ell_get_a3(GEN e) { return gel(e,3); }
2569 3888745 : INLINE GEN ell_get_a4(GEN e) { return gel(e,4); }
2570 4704924 : INLINE GEN ell_get_a6(GEN e) { return gel(e,5); }
2571 3318517 : INLINE GEN ell_get_b2(GEN e) { return gel(e,6); }
2572 1024949 : INLINE GEN ell_get_b4(GEN e) { return gel(e,7); }
2573 1630617 : INLINE GEN ell_get_b6(GEN e) { return gel(e,8); }
2574 1464001 : INLINE GEN ell_get_b8(GEN e) { return gel(e,9); }
2575 6167365 : INLINE GEN ell_get_c4(GEN e) { return gel(e,10); }
2576 7403844 : INLINE GEN ell_get_c6(GEN e) { return gel(e,11); }
2577 9654091 : INLINE GEN ell_get_disc(GEN e) { return gel(e,12); }
2578 1028909 : INLINE GEN ell_get_j(GEN e) { return gel(e,13); }
2579 11456574 : INLINE long ell_get_type(GEN e) { return mael(e,14,1); }
2580 1570434 : INLINE GEN ellff_get_field(GEN x) { return gmael(x, 15, 1); }
2581 683111 : INLINE GEN ellff_get_a4a6(GEN x) { return gmael(x, 15, 2); }
2582 1407 : INLINE GEN ellQp_get_zero(GEN x) { return gmael(x, 15, 1); }
2583 287 : INLINE long ellQp_get_prec(GEN E) { GEN z = ellQp_get_zero(E); return valp(z); }
2584 1085 : INLINE GEN ellQp_get_p(GEN E) { GEN z = ellQp_get_zero(E); return gel(z,2); }
2585 37156 : INLINE long ellR_get_prec(GEN x) { return nbits2prec(mael3(x, 15, 1, 1)); }
2586 12106 : INLINE long ellR_get_sign(GEN x) { return mael3(x, 15, 1, 2); }
2587 699475 : INLINE GEN ellnf_get_nf(GEN x) { return checknf_i(gmael(x,15,1)); }
2588 56 : INLINE GEN ellnf_get_bnf(GEN x) { return checkbnf_i(gmael(x,15,1)); }
2589 :
2590 4625062 : INLINE int checkell_i(GEN e) { return typ(e) == t_VEC && lg(e) == 17; }
2591 33935006 : INLINE int ell_is_inf(GEN z) { return lg(z) == 2; }
2592 809800 : INLINE GEN ellinf(void) { return mkvec(gen_0); }
2593 :
2594 : /*******************************************************************/
2595 : /* */
2596 : /* ALGEBRAIC NUMBER THEORY */
2597 : /* */
2598 : /*******************************************************************/
2599 8126890 : INLINE GEN modpr_get_pr(GEN x) { return gel(x,3); }
2600 609538 : INLINE GEN modpr_get_p(GEN x) { return pr_get_p(modpr_get_pr(x)); }
2601 2520394 : INLINE GEN modpr_get_T(GEN x) { return lg(x) == 4? NULL: gel(x,4); }
2602 :
2603 19370990 : INLINE GEN pr_get_p(GEN pr) { return gel(pr,1); }
2604 6273183 : INLINE GEN pr_get_gen(GEN pr){ return gel(pr,2); }
2605 : /* .[2] instead of itos works: e and f are small positive integers */
2606 2266326 : INLINE long pr_get_e(GEN pr) { return gel(pr,3)[2]; }
2607 8716129 : INLINE long pr_get_f(GEN pr) { return gel(pr,4)[2]; }
2608 6141792 : INLINE GEN pr_get_tau(GEN pr){ return gel(pr,5); }
2609 : INLINE int
2610 3051852 : pr_is_inert(GEN P) { return pr_get_f(P) == lg(pr_get_gen(P))-1; }
2611 : INLINE GEN
2612 217505 : pr_norm(GEN pr) { return powiu(pr_get_p(pr), pr_get_f(pr)); }
2613 : INLINE ulong
2614 39487 : upr_norm(GEN pr) { return upowuu(pr_get_p(pr)[2], pr_get_f(pr)); }
2615 :
2616 : /* assume nf a genuine nf */
2617 : INLINE long
2618 4528 : nf_get_varn(GEN nf) { return varn(gel(nf,1)); }
2619 : INLINE GEN
2620 30918661 : nf_get_pol(GEN nf) { return gel(nf,1); }
2621 : INLINE long
2622 24710932 : nf_get_degree(GEN nf) { return degpol( nf_get_pol(nf) ); }
2623 : INLINE long
2624 4092354 : nf_get_r1(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,1)); }
2625 : INLINE long
2626 1673 : nf_get_r2(GEN nf) { GEN x = gel(nf,2); return itou(gel(x,2)); }
2627 : INLINE GEN
2628 49826 : nf_get_disc(GEN nf) { return gel(nf,3); }
2629 : INLINE GEN
2630 765946 : nf_get_index(GEN nf) { return gel(nf,4); }
2631 : INLINE GEN
2632 2821420 : nf_get_M(GEN nf) { return gmael(nf,5,1); }
2633 : INLINE GEN
2634 73824 : nf_get_G(GEN nf) { return gmael(nf,5,2); }
2635 : INLINE GEN
2636 385499 : nf_get_roundG(GEN nf) { return gmael(nf,5,3); }
2637 : INLINE GEN
2638 24367 : nf_get_Tr(GEN nf) { return gmael(nf,5,4); }
2639 : INLINE GEN
2640 2324 : nf_get_diff(GEN nf) { return gmael(nf,5,5); }
2641 : INLINE GEN
2642 77 : nf_get_ramified_primes(GEN nf) { return gmael(nf,5,8); }
2643 : INLINE GEN
2644 291043 : nf_get_roots(GEN nf) { return gel(nf,6); }
2645 : INLINE GEN
2646 91 : nf_get_zk(GEN nf)
2647 : {
2648 91 : GEN y = gel(nf,7), D = gel(y, 1);
2649 91 : if (typ(D) == t_POL) D = gel(D, 2);
2650 91 : if (!equali1(D)) y = gdiv(y, D);
2651 91 : return y;
2652 : }
2653 : INLINE GEN
2654 247678 : nf_get_zkprimpart(GEN nf)
2655 : {
2656 247678 : GEN y = gel(nf,7);
2657 : /* test for old format of nf.zk: non normalized */
2658 247678 : if (!equali1(gel(nf,4)) && gequal1(gel(y,1))) y = Q_remove_denom(y,NULL);
2659 247678 : return y;
2660 : }
2661 : INLINE GEN
2662 248813 : nf_get_zkden(GEN nf)
2663 : {
2664 248813 : GEN y = gel(nf,7), D = gel(y,1);
2665 248813 : if (typ(D) == t_POL) D = gel(D,2);
2666 : /* test for old format of nf.zk: non normalized */
2667 248813 : if (!equali1(gel(nf,4)) && equali1(D)) D = Q_denom(y);
2668 248813 : return D;
2669 : }
2670 : INLINE GEN
2671 2336959 : nf_get_invzk(GEN nf) { return gel(nf,8); }
2672 : INLINE void
2673 19819 : nf_get_sign(GEN nf, long *r1, long *r2)
2674 : {
2675 19819 : GEN x = gel(nf,2);
2676 19819 : *r1 = itou(gel(x,1));
2677 19819 : *r2 = itou(gel(x,2));
2678 19819 : }
2679 :
2680 : INLINE GEN
2681 49651 : abgrp_get_no(GEN x) { return gel(x,1); }
2682 : INLINE GEN
2683 2094351 : abgrp_get_cyc(GEN x) { return gel(x,2); }
2684 : INLINE GEN
2685 396512 : abgrp_get_gen(GEN x) { return gel(x,3); }
2686 : INLINE GEN
2687 2062709 : bnf_get_nf(GEN bnf) { return gel(bnf,7); }
2688 : INLINE GEN
2689 806275 : bnf_get_clgp(GEN bnf) { return gmael(bnf,8,1); }
2690 : INLINE GEN
2691 4564 : bnf_get_no(GEN bnf) { return abgrp_get_no(bnf_get_clgp(bnf)); }
2692 : INLINE GEN
2693 434249 : bnf_get_cyc(GEN bnf) { return abgrp_get_cyc(bnf_get_clgp(bnf)); }
2694 : INLINE GEN
2695 367133 : bnf_get_gen(GEN bnf) { return abgrp_get_gen(bnf_get_clgp(bnf)); }
2696 : INLINE GEN
2697 846 : bnf_get_reg(GEN bnf) { return gmael(bnf,8,2); }
2698 : INLINE GEN
2699 481743 : bnf_get_logfu(GEN bnf) { return gel(bnf,3); }
2700 : INLINE GEN
2701 5868 : bnf_get_tuU(GEN bnf) { return gmael3(bnf,8,4,2); }
2702 : INLINE long
2703 24682 : bnf_get_tuN(GEN bnf) { return gmael3(bnf,8,4,1)[2]; }
2704 : INLINE GEN
2705 1806 : bnf_get_fu(GEN bnf) {
2706 1806 : GEN fu = bnf_get_fu_nocheck(bnf);
2707 1806 : if (typ(fu) == t_MAT) pari_err(e_MISC,"missing units in bnf");
2708 1806 : return fu;
2709 : }
2710 : INLINE GEN
2711 7170 : bnf_get_fu_nocheck(GEN bnf) { return gmael(bnf,8,5); }
2712 :
2713 : INLINE GEN
2714 746961 : bnr_get_bnf(GEN bnr) { return gel(bnr,1); }
2715 : INLINE GEN
2716 384712 : bnr_get_bid(GEN bnr) { return gel(bnr,2); }
2717 : INLINE GEN
2718 18130 : bnr_get_mod(GEN bnr) { return gmael(bnr,2,1); }
2719 : INLINE GEN
2720 27811 : bnr_get_nf(GEN bnr) { return gmael(bnr,1,7); }
2721 : INLINE GEN
2722 516571 : bnr_get_clgp(GEN bnr) { return gel(bnr,5); }
2723 : INLINE GEN
2724 45080 : bnr_get_no(GEN bnr) { return abgrp_get_no(bnr_get_clgp(bnr)); }
2725 : INLINE GEN
2726 459598 : bnr_get_cyc(GEN bnr) { return abgrp_get_cyc(bnr_get_clgp(bnr)); }
2727 : INLINE GEN
2728 70 : bnr_get_gen_nocheck(GEN bnr) { return abgrp_get_gen(bnr_get_clgp(bnr)); }
2729 : INLINE GEN
2730 11032 : bnr_get_gen(GEN bnr) {
2731 11032 : GEN G = bnr_get_clgp(bnr);
2732 11032 : if (lg(G) != 4)
2733 0 : pari_err(e_MISC,"missing bnr generators: please use bnrinit(,,1)");
2734 11032 : return gel(G,3);
2735 : }
2736 :
2737 : INLINE GEN
2738 301888 : bid_get_mod(GEN bid) { return gel(bid,1); }
2739 : INLINE GEN
2740 46361 : bid_get_ideal(GEN bid) { return gmael(bid,1,1); }
2741 : INLINE GEN
2742 518 : bid_get_arch(GEN bid) { return gmael(bid,1,2); }
2743 : INLINE GEN
2744 1059923 : bid_get_grp(GEN bid) { return gel(bid,2); }
2745 : INLINE GEN
2746 395527 : bid_get_fact(GEN bid) { return gmael(bid,3,1); }
2747 : INLINE GEN
2748 354031 : bid_get_fact2(GEN bid) { return gmael(bid,3,2); }
2749 : INLINE GEN
2750 354031 : bid_get_sprk(GEN bid) { return gmael(bid,4,1); }
2751 : INLINE GEN
2752 29939 : bid_get_sarch(GEN bid) { return gmael(bid,4,2); }
2753 : INLINE GEN
2754 374695 : bid_get_archp(GEN bid) { return gmael3(bid,4,2,2); }
2755 : INLINE GEN
2756 656129 : bid_get_U(GEN bid) { return gel(bid,5); }
2757 : INLINE GEN
2758 0 : bid_get_no(GEN bid) { return abgrp_get_no(bid_get_grp(bid)); }
2759 : INLINE GEN
2760 1031538 : bid_get_cyc(GEN bid) { return abgrp_get_cyc(bid_get_grp(bid)); }
2761 : INLINE GEN
2762 0 : bid_get_gen_nocheck(GEN bid) { return abgrp_get_gen(bid_get_grp(bid)); }
2763 : INLINE GEN
2764 27790 : bid_get_gen(GEN bid) {
2765 27790 : GEN G = bid_get_grp(bid);
2766 27790 : if (lg(G) != 4) pari_err(e_MISC,"missing bid generators. Use idealstar(,,2)");
2767 27790 : return abgrp_get_gen(G);
2768 : }
2769 :
2770 : INLINE GEN
2771 21293125 : znstar_get_N(GEN G) { return gmael(G,1,1); }
2772 : INLINE GEN
2773 2210873 : znstar_get_faN(GEN G) { return gel(G,3); }
2774 : INLINE GEN
2775 7 : znstar_get_no(GEN G) { return abgrp_get_no(gel(G,2)); }
2776 : INLINE GEN
2777 167545 : znstar_get_cyc(GEN G) { return abgrp_get_cyc(gel(G,2)); }
2778 : INLINE GEN
2779 7 : znstar_get_gen(GEN G) { return abgrp_get_gen(gel(G,2)); }
2780 : INLINE GEN
2781 2888417 : znstar_get_conreycyc(GEN G) { return gmael(G,4,5); }
2782 : INLINE GEN
2783 887572 : znstar_get_conreygen(GEN G) { return gmael(G,4,4); }
2784 : INLINE GEN
2785 28518 : znstar_get_Ui(GEN G) { return gmael(G,4,3); }
2786 : INLINE GEN
2787 118160 : znstar_get_U(GEN G) { return gel(G,5); }
2788 : INLINE GEN
2789 521549 : znstar_get_pe(GEN G) { return gmael(G,4,1); }
2790 : INLINE GEN
2791 19880 : gal_get_pol(GEN gal) { return gel(gal,1); }
2792 : INLINE GEN
2793 1309 : gal_get_p(GEN gal) { return gmael(gal,2,1); }
2794 : INLINE GEN
2795 84 : gal_get_e(GEN gal) { return gmael(gal,2,2); }
2796 : INLINE GEN
2797 15946 : gal_get_mod(GEN gal) { return gmael(gal,2,3); }
2798 : INLINE GEN
2799 16324 : gal_get_roots(GEN gal) { return gel(gal,3); }
2800 : INLINE GEN
2801 15904 : gal_get_invvdm(GEN gal) { return gel(gal,4); }
2802 : INLINE GEN
2803 15904 : gal_get_den(GEN gal) { return gel(gal,5); }
2804 : INLINE GEN
2805 66983 : gal_get_group(GEN gal) { return gel(gal,6); }
2806 : INLINE GEN
2807 1715 : gal_get_gen(GEN gal) { return gel(gal,7); }
2808 : INLINE GEN
2809 1365 : gal_get_orders(GEN gal) { return gel(gal,8); }
2810 :
2811 : /* assume rnf a genuine rnf */
2812 : INLINE long
2813 1233638 : rnf_get_degree(GEN rnf) { return degpol(rnf_get_pol(rnf)); }
2814 : INLINE long
2815 16394 : rnf_get_nfdegree(GEN rnf) { return degpol(nf_get_pol(rnf_get_nf(rnf))); }
2816 : INLINE long
2817 775698 : rnf_get_absdegree(GEN rnf) { return degpol(gmael(rnf,11,1)); }
2818 : INLINE GEN
2819 700 : rnf_get_idealdisc(GEN rnf) { return gmael(rnf,3,1); }
2820 : INLINE GEN
2821 742 : rnf_get_k(GEN rnf) { return gmael(rnf,11,3); }
2822 : INLINE GEN
2823 609 : rnf_get_alpha(GEN rnf) { return gmael(rnf, 11, 2); }
2824 : INLINE GEN
2825 384706 : rnf_get_nf(GEN rnf) { return gel(rnf,10); }
2826 : INLINE GEN
2827 3080 : rnf_get_nfzk(GEN rnf) { return gel(rnf,2); }
2828 : INLINE GEN
2829 205170 : rnf_get_polabs(GEN rnf) { return gmael(rnf,11,1); }
2830 : INLINE GEN
2831 1479849 : rnf_get_pol(GEN rnf) { return gel(rnf,1); }
2832 : INLINE GEN
2833 63 : rnf_get_disc(GEN rnf) { return gel(rnf,3); }
2834 : INLINE GEN
2835 105 : rnf_get_index(GEN rnf) { return gel(rnf,4); }
2836 : INLINE long
2837 0 : rnf_get_varn(GEN rnf) { return varn(gel(rnf,1)); }
2838 : INLINE GEN
2839 188580 : rnf_get_nfpol(GEN rnf) { return gmael(rnf,10,1); }
2840 : INLINE long
2841 3325 : rnf_get_nfvarn(GEN rnf) { return varn(gmael(rnf,10,1)); }
2842 : INLINE GEN
2843 3213 : rnf_get_zk(GEN rnf) { return gel(rnf,7); }
2844 : INLINE GEN
2845 96768 : rnf_get_map(GEN rnf) { return gel(rnf,11); }
2846 : INLINE GEN
2847 1197 : rnf_get_invzk(GEN rnf) { return gel(rnf,8); }
2848 :
2849 : /* I integral ZM (not HNF), G ZM, rounded Cholesky form of a weighted
2850 : * T2 matrix. Reduce I wrt G */
2851 : INLINE GEN
2852 14077 : idealpseudored(GEN I, GEN G)
2853 14077 : { return ZM_mul(I, ZM_lll(ZM_mul(G, I), 0.99, LLL_IM)); }
2854 :
2855 : /* I integral (not necessarily HNF), G ZM, rounded Cholesky form of a weighted
2856 : * T2 matrix. Return m in I with T2(m) small */
2857 : INLINE GEN
2858 127731 : idealpseudomin(GEN I, GEN G)
2859 : {
2860 127731 : GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
2861 127731 : return ZM_ZC_mul(I, gel(u,1));
2862 : }
2863 : /* I, G as in idealpseudomin. Return an irrational m in I with T2(m) small */
2864 : INLINE GEN
2865 297163 : idealpseudomin_nonscalar(GEN I, GEN G)
2866 : {
2867 297163 : GEN u = ZM_lll(ZM_mul(G, I), 0.99, LLL_IM);
2868 297163 : GEN m = ZM_ZC_mul(I, gel(u,1));
2869 297163 : if (ZV_isscalar(m) && lg(u) > 2) m = ZM_ZC_mul(I, gel(u,2));
2870 297163 : return m;
2871 : }
2872 :
2873 : INLINE GEN
2874 770 : idealred_elt(GEN nf, GEN I) {
2875 770 : pari_sp av = avma;
2876 770 : GEN u = idealpseudomin(I, nf_get_roundG(nf));
2877 770 : return gerepileupto(av, u);
2878 : }
2879 : INLINE GEN
2880 109444 : idealred(GEN nf, GEN I) { return idealred0(nf, I, NULL); }
2881 :
2882 : INLINE GEN
2883 2058 : idealchineseinit(GEN nf, GEN x)
2884 2058 : { return idealchinese(nf,x,NULL); }
2885 :
2886 : /*******************************************************************/
2887 : /* */
2888 : /* CLOSURES */
2889 : /* */
2890 : /*******************************************************************/
2891 227672307 : INLINE long closure_arity(GEN C) { return ((ulong)C[1])&ARITYBITS; }
2892 35442320 : INLINE long closure_is_variadic(GEN C) { return !!(((ulong)C[1])&VARARGBITS); }
2893 191921872 : INLINE const char *closure_codestr(GEN C) { return GSTR(gel(C,2))-1; }
2894 0 : INLINE GEN closure_get_code(GEN C) { return gel(C,2); }
2895 191896386 : INLINE GEN closure_get_oper(GEN C) { return gel(C,3); }
2896 191881799 : INLINE GEN closure_get_data(GEN C) { return gel(C,4); }
2897 9337 : INLINE GEN closure_get_dbg(GEN C) { return gel(C,5); }
2898 22412 : INLINE GEN closure_get_text(GEN C) { return gel(C,6); }
2899 1166082 : INLINE GEN closure_get_frame(GEN C) { return gel(C,7); }
2900 :
2901 : /*******************************************************************/
2902 : /* */
2903 : /* ERRORS */
2904 : /* */
2905 : /*******************************************************************/
2906 : INLINE long
2907 52065 : err_get_num(GEN e) { return e[1]; }
2908 : INLINE GEN
2909 77 : err_get_compo(GEN e, long i) { return gel(e, i+1); }
2910 :
2911 : INLINE void
2912 14 : pari_err_BUG(const char *f) { pari_err(e_BUG,f); }
2913 : INLINE void
2914 7 : pari_err_CONSTPOL(const char *f) { pari_err(e_CONSTPOL, f); }
2915 : INLINE void
2916 63 : pari_err_COPRIME(const char *f, GEN x, GEN y) { pari_err(e_COPRIME, f,x,y); }
2917 : INLINE void
2918 487 : pari_err_DIM(const char *f) { pari_err(e_DIM, f); }
2919 : INLINE void
2920 0 : pari_err_FILE(const char *f, const char *g) { pari_err(e_FILE, f,g); }
2921 : INLINE void
2922 0 : pari_err_FILEDESC(const char *f, long n) { pari_err(e_FILEDESC, f,n); }
2923 : INLINE void
2924 42 : pari_err_FLAG(const char *f) { pari_err(e_FLAG,f); }
2925 : INLINE void
2926 420 : pari_err_IMPL(const char *f) { pari_err(e_IMPL,f); }
2927 : INLINE void
2928 19716 : pari_err_INV(const char *f, GEN x) { pari_err(e_INV,f,x); }
2929 : INLINE void
2930 28 : pari_err_IRREDPOL(const char *f, GEN x) { pari_err(e_IRREDPOL, f,x); }
2931 : INLINE void
2932 1996 : 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); }
2933 : INLINE void
2934 203 : pari_err_COMPONENT(const char *f, const char *op, GEN l, GEN x) { pari_err(e_COMPONENT, f,op,l,x); }
2935 : INLINE void
2936 0 : pari_err_MAXPRIME(ulong c) { pari_err(e_MAXPRIME, c); }
2937 : INLINE void
2938 350 : pari_err_OP(const char *f, GEN x, GEN y) { pari_err(e_OP, f,x,y); }
2939 : INLINE void
2940 84 : pari_err_OVERFLOW(const char *f) { pari_err(e_OVERFLOW, f); }
2941 : INLINE void
2942 218 : pari_err_PREC(const char *f) { pari_err(e_PREC,f); }
2943 : INLINE void
2944 0 : pari_err_PACKAGE(const char *f) { pari_err(e_PACKAGE,f); }
2945 : INLINE void
2946 70 : pari_err_PRIME(const char *f, GEN x) { pari_err(e_PRIME, f,x); }
2947 : INLINE void
2948 749 : pari_err_MODULUS(const char *f, GEN x, GEN y) { pari_err(e_MODULUS, f,x,y); }
2949 : INLINE void
2950 49 : pari_err_ROOTS0(const char *f) { pari_err(e_ROOTS0, f); }
2951 : INLINE void
2952 77 : pari_err_SQRTN(const char *f, GEN x) { pari_err(e_SQRTN, f,x); }
2953 : INLINE void
2954 12468 : pari_err_TYPE(const char *f, GEN x) { pari_err(e_TYPE, f,x); }
2955 : INLINE void
2956 3073 : pari_err_TYPE2(const char *f, GEN x, GEN y) { pari_err(e_TYPE2, f,x,y); }
2957 : INLINE void
2958 203 : pari_err_VAR(const char *f, GEN x, GEN y) { pari_err(e_VAR, f,x,y); }
2959 : INLINE void
2960 175 : pari_err_PRIORITY(const char *f, GEN x, const char *op, long v)
2961 175 : { pari_err(e_PRIORITY, f,x,op,v); }
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