Line data Source code
1 : #line 2 "../src/kernel/none/level1.h"
2 : /* Copyright (C) 2000 The PARI group.
3 :
4 : This file is part of the PARI/GP package.
5 :
6 : PARI/GP is free software; you can redistribute it and/or modify it under the
7 : terms of the GNU General Public License as published by the Free Software
8 : Foundation; either version 2 of the License, or (at your option) any later
9 : version. It is distributed in the hope that it will be useful, but WITHOUT
10 : ANY WARRANTY WHATSOEVER.
11 :
12 : Check the License for details. You should have received a copy of it, along
13 : with the package; see the file 'COPYING'. If not, write to the Free Software
14 : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
15 :
16 : /* This file defines "level 1" kernel functions.
17 : * These functions can be inline; they are also defined externally in
18 : * mpinl.c, which includes this file and never needs to be changed */
19 :
20 : INLINE long
21 74222229856 : evallg(long x)
22 : {
23 74222229856 : if (x & ~LGBITS) pari_err_OVERFLOW("lg()");
24 74225527008 : return _evallg(x);
25 : }
26 : INLINE long
27 54655891 : evalvalp(long x)
28 : {
29 54655891 : long v = _evalvalp(x);
30 54655891 : if (v & ~VALPBITS) pari_err_OVERFLOW("valp()");
31 54655891 : return v;
32 : }
33 : INLINE long
34 10948100941 : evalexpo(long x)
35 : {
36 10948100941 : long v = _evalexpo(x);
37 10948100941 : if (v & ~EXPOBITS) pari_err_OVERFLOW("expo()");
38 10942600359 : return v;
39 : }
40 : INLINE long
41 21870171 : evalprecp(long x)
42 : {
43 21870171 : long v = _evalprecp(x);
44 21870171 : if (x & ~((1UL<<(BITS_IN_LONG-VALPnumBITS))-1)) pari_err_OVERFLOW("precp()");
45 21870174 : return v;
46 : }
47 :
48 : INLINE int
49 161875164 : varncmp(long x, long y)
50 : {
51 161875164 : if (varpriority[x] < varpriority[y]) return 1;
52 124736368 : if (varpriority[x] > varpriority[y]) return -1;
53 68435670 : return 0;
54 : }
55 : INLINE long
56 0 : varnmin(long x, long y)
57 0 : { return (varpriority[x] <= varpriority[y])? x: y; }
58 : INLINE long
59 203 : varnmax(long x, long y)
60 203 : { return (varpriority[x] >= varpriority[y])? x: y; }
61 :
62 : /* Inhibit some area gerepile-wise: declare it to be a non recursive
63 : * type, of length l. Thus gerepile won't inspect the zone, just copy it.
64 : * For the following situation:
65 : * z = cgetg(t,a); av = avma; garbage(); ltop = avma;
66 : * for (i=1; i<HUGE; i++) gel(z,i) = blah();
67 : * stackdummy(av,ltop);
68 : * loses (av-ltop) words but save a costly gerepile. */
69 : INLINE void
70 2817650241 : stackdummy(pari_sp av, pari_sp ltop) {
71 2817650241 : long l = ((GEN)av) - ((GEN)ltop);
72 2817650241 : if (l > 0) {
73 901207443 : GEN z = (GEN)ltop;
74 901207443 : z[0] = evaltyp(t_VECSMALL) | evallg(l);
75 : #ifdef DEBUG
76 : { long i; for (i = 1; i < l; i++) z[i] = 0; }
77 : #endif
78 : }
79 2817312369 : }
80 : INLINE void
81 71922006 : fixlg(GEN x, long ly) {
82 71922006 : long lx = lg(x), l = lx - ly;
83 71922006 : if (l > 0)
84 : { /* stackdummy(x+lx, x+ly) */
85 45405587 : GEN z = x + ly;
86 45405587 : z[0] = evaltyp(t_VECSMALL) | evallg(l);
87 45405648 : setlg(x, ly);
88 : #ifdef DEBUG
89 : { long i; for (i = 1; i < l; i++) z[i] = 0; }
90 : #endif
91 : }
92 71922140 : }
93 : /* update lg(z) before affrr(y, z) [ to cater for precision loss ]*/
94 : INLINE void
95 26524262 : affrr_fixlg(GEN y, GEN z) { fixlg(z, lg(y)); affrr(y, z); }
96 :
97 : /*******************************************************************/
98 : /* */
99 : /* ALLOCATE ON STACK */
100 : /* */
101 : /*******************************************************************/
102 : INLINE void
103 98417541698 : set_avma(ulong av) { avma = av; }
104 :
105 : INLINE double
106 296028476 : gc_double(pari_sp av, double d) { set_avma(av); return d; }
107 : INLINE long
108 137859507 : gc_long(pari_sp av, long s) { set_avma(av); return s; }
109 : INLINE ulong
110 20157842 : gc_ulong(pari_sp av, ulong s) { set_avma(av); return s; }
111 : INLINE int
112 33167251 : gc_bool(pari_sp av, int s) { set_avma(av); return s; }
113 : INLINE int
114 1177550 : gc_int(pari_sp av, int s) { set_avma(av); return s; }
115 : INLINE GEN
116 6050012 : gc_NULL(pari_sp av) { set_avma(av); return NULL; }
117 : INLINE GEN
118 9849174320 : gc_const(pari_sp av, GEN x) { set_avma(av); return x; }
119 :
120 : INLINE GEN
121 72192595909 : new_chunk(size_t x) /* x is a number of longs */
122 : {
123 72192595909 : GEN z = ((GEN) avma) - x;
124 : CHECK_CTRLC
125 72192595909 : if (x > (avma-pari_mainstack->bot) / sizeof(long))
126 7 : new_chunk_resize(x);
127 72192595902 : set_avma((pari_sp)z);
128 : #ifdef MEMSTEP
129 : if (DEBUGMEM>1 && pari_mainstack->memused != DISABLE_MEMUSED) {
130 : long d = (long)pari_mainstack->memused - (long)z;
131 : if (labs(d) > 4*MEMSTEP)
132 : {
133 : pari_mainstack->memused = (pari_sp)z;
134 : err_printf("...%4.0lf Mbytes used\n",
135 : (pari_mainstack->top-pari_mainstack->memused)/1048576.);
136 : }
137 : }
138 : #endif
139 72167302014 : return z;
140 : }
141 :
142 : INLINE char *
143 8032737 : stack_malloc(size_t N)
144 : {
145 8032737 : long n = nchar2nlong(N);
146 8032732 : return (char*)new_chunk(n);
147 : }
148 :
149 : INLINE char *
150 81678116 : stack_malloc_align(size_t N, long k)
151 : {
152 81678116 : ulong d = ((ulong)avma) % k, e = ((ulong)N) % k;
153 81678116 : if (d) (void)new_chunk(d/sizeof(long));
154 81678114 : if (e) N += k-e;
155 81678114 : return (char*) new_chunk(nchar2nlong(N));
156 : }
157 :
158 : INLINE char *
159 83564 : stack_calloc(size_t N)
160 : {
161 83564 : char *p = stack_malloc(N);
162 83562 : memset(p, 0, N); return p;
163 : }
164 :
165 : INLINE char *
166 489 : stack_calloc_align(size_t N, long k)
167 : {
168 489 : ulong d = ((ulong)avma) % k, e = ((ulong)N) % k;
169 489 : if (d) (void)new_chunk(d/sizeof(long));
170 489 : if (e) N += k-e;
171 489 : return stack_calloc(N);
172 : }
173 :
174 : /* cgetg(lg(x), typ(x)), set *lx. Implicit unsetisclone() */
175 : INLINE GEN
176 936089844 : cgetg_copy(GEN x, long *plx) {
177 : GEN y;
178 936089844 : *plx = lg(x); y = new_chunk((size_t)*plx);
179 936107855 : y[0] = x[0] & (TYPBITS|LGBITS); return y;
180 : }
181 : INLINE GEN
182 242119 : cgetg_block(long x, long y)
183 : {
184 242119 : GEN z = newblock((size_t)x);
185 242401 : z[0] = CLONEBIT | evaltyp(y) | evallg(x);
186 242280 : return z;
187 : }
188 : INLINE GEN
189 12360897253 : cgetg(long x, long y)
190 : {
191 12360897253 : GEN z = new_chunk((size_t)x);
192 12358253891 : z[0] = evaltyp(y) | evallg(x);
193 12355226882 : return z;
194 : }
195 : INLINE GEN
196 21835805348 : cgeti(long x)
197 : {
198 21835805348 : GEN z = new_chunk((size_t)x);
199 21791999342 : z[0] = evaltyp(t_INT) | evallg(x);
200 21775102536 : return z;
201 : }
202 : INLINE GEN
203 13536964262 : cgetipos(long x)
204 : {
205 13536964262 : GEN z = cgeti(x);
206 13514834645 : z[1] = evalsigne(1) | evallgefint(x);
207 13514834645 : return z;
208 : }
209 : INLINE GEN
210 304544735 : cgetineg(long x)
211 : {
212 304544735 : GEN z = cgeti(x);
213 304545200 : z[1] = evalsigne(-1) | evallgefint(x);
214 304545200 : return z;
215 : }
216 : INLINE GEN
217 33604 : cgetr_block(long x)
218 : {
219 33604 : GEN z = newblock((size_t)x);
220 33612 : z[0] = CLONEBIT | evaltyp(t_REAL) | evallg(x);
221 33610 : return z;
222 : }
223 : INLINE GEN
224 10884478026 : cgetr(long x)
225 : {
226 10884478026 : GEN z = new_chunk((size_t)x);
227 10868363400 : z[0] = evaltyp(t_REAL) | evallg(x);
228 10862545109 : return z;
229 : }
230 :
231 : /*******************************************************************/
232 : /* */
233 : /* COPY, NEGATION, ABSOLUTE VALUE */
234 : /* */
235 : /*******************************************************************/
236 : /* cannot do memcpy because sometimes x and y overlap */
237 : INLINE GEN
238 3483105787 : leafcopy(GEN x)
239 : {
240 3483105787 : register long lx = lg(x);
241 3483105787 : GEN y = new_chunk(lx); /* can't use cgetg_copy, in case x,y overlap */
242 18373675322 : while (--lx > 0) y[lx] = x[lx];
243 3482924797 : y[0] = x[0] & (TYPBITS|LGBITS); return y;
244 : }
245 : INLINE GEN
246 6581233799 : icopy(GEN x)
247 : {
248 6581233799 : long i = lgefint(x), lx = i;
249 6581233799 : GEN y = new_chunk(lx); /* can't use cgeti, in case x,y overlap */
250 27215866106 : while (--i > 0) y[i] = x[i];
251 6575802896 : y[0] = evaltyp(t_INT) | evallg(lx);
252 6578944326 : return y;
253 : }
254 : INLINE GEN
255 60913461 : icopyspec(GEN x, long nx)
256 : {
257 60913461 : long i = nx+2, lx = i;
258 60913461 : GEN y = new_chunk(lx); /* can't use cgeti, in case x,y overlap */
259 896489215 : x -= 2; while (--i >= 2) y[i] = x[i];
260 60912867 : y[1] = evalsigne(1) | evallgefint(lx);
261 60912867 : y[0] = evaltyp(t_INT) | evallg(lx);
262 60912650 : return y;
263 : }
264 594887111 : INLINE GEN rcopy(GEN x) { return leafcopy(x); }
265 294 : INLINE GEN mpcopy(GEN x) { return leafcopy(x); }
266 :
267 : INLINE GEN
268 629399698 : mpabs(GEN x) { GEN y = leafcopy(x); setabssign(y); return y; }
269 : INLINE GEN
270 2613808 : mpabs_shallow(GEN x) { return signe(x) < 0? mpabs(x): x; }
271 589125246 : INLINE GEN absi(GEN x) { return mpabs(x); }
272 54033859 : INLINE GEN absi_shallow(GEN x) { return signe(x) < 0? negi(x): x; }
273 232946 : INLINE GEN absr(GEN x) { return mpabs(x); }
274 :
275 : INLINE GEN
276 1444978975 : mpneg(GEN x) { GEN y = leafcopy(x); togglesign(y); return y; }
277 590388018 : INLINE GEN negi(GEN x) { return mpneg(x); }
278 1873973 : INLINE GEN negr(GEN x) { return mpneg(x); }
279 :
280 : /* negate in place */
281 : INLINE void
282 2208472007 : togglesign(GEN x) { if (x[1] & SIGNBITS) { x[1] ^= HIGHBIT; } }
283 : INLINE void
284 672884003 : setabssign(GEN x) { x[1] &= ~HIGHBIT; }
285 : /* negate in place, except universal constants */
286 : INLINE void
287 113146378 : togglesign_safe(GEN *px)
288 : {
289 113146378 : switch(*px - gen_1) /* gen_1, gen_2, gen_m1, gen_m2 */
290 : {
291 2381499 : case 0: *px = gen_m1; break;
292 4 : case 3: *px = gen_m2; break;
293 556922 : case 6: *px = gen_1; break;
294 0 : case 9: *px = gen_2; break;
295 110207953 : default: togglesign(*px);
296 : }
297 113149172 : }
298 : /* setsigne(y, signe(x)) */
299 : INLINE void
300 0 : affectsign(GEN x, GEN y)
301 : {
302 0 : y[1] = (x[1] & SIGNBITS) | (y[1] & ~SIGNBITS);
303 0 : }
304 : /* copies sign in place, except for universal constants */
305 : INLINE void
306 9914275 : affectsign_safe(GEN x, GEN *py)
307 : {
308 9914275 : if (((*py)[1] ^ x[1]) & HIGHBIT) togglesign_safe(py);
309 9914275 : }
310 : /*******************************************************************/
311 : /* */
312 : /* GEN -> LONG, LONG -> GEN */
313 : /* */
314 : /*******************************************************************/
315 : /* assume x != 0, return -x as a t_INT */
316 : INLINE GEN
317 301722947 : utoineg(ulong x) { GEN y = cgetineg(3); y[2] = x; return y; }
318 : /* assume x != 0, return utoi(x) */
319 : INLINE GEN
320 12016571630 : utoipos(ulong x) { GEN y = cgetipos(3); y[2] = x; return y; }
321 : INLINE GEN
322 10231785421 : utoi(ulong x) { return x? utoipos(x): gen_0; }
323 : INLINE GEN
324 453514486 : stoi(long x)
325 : {
326 453514486 : if (!x) return gen_0;
327 285530061 : return x > 0? utoipos((ulong)x): utoineg((ulong)-x);
328 : }
329 :
330 : /* x 2^BIL + y */
331 : INLINE GEN
332 7290546747 : uutoi(ulong x, ulong y)
333 : {
334 : GEN z;
335 7290546747 : if (!x) return utoi(y);
336 623874336 : z = cgetipos(4);
337 626778714 : *int_W_lg(z, 1, 4) = x;
338 626778714 : *int_W_lg(z, 0, 4) = y; return z;
339 : }
340 : /* - (x 2^BIL + y) */
341 : INLINE GEN
342 243986 : uutoineg(ulong x, ulong y)
343 : {
344 : GEN z;
345 243986 : if (!x) return y? utoineg(y): gen_0;
346 10365 : z = cgetineg(4);
347 10365 : *int_W_lg(z, 1, 4) = x;
348 10365 : *int_W_lg(z, 0, 4) = y; return z;
349 : }
350 :
351 : INLINE long
352 408552648 : itos(GEN x)
353 : {
354 408552648 : long s = signe(x);
355 : long u;
356 :
357 408552648 : if (!s) return 0;
358 394374979 : u = x[2];
359 394374979 : if (lgefint(x) > 3 || u < 0)
360 21 : pari_err_OVERFLOW("t_INT-->long assignment");
361 394373282 : return (s>0) ? u : -u;
362 : }
363 : /* as itos, but return 0 if too large. Cf is_bigint */
364 : INLINE long
365 46568581 : itos_or_0(GEN x) {
366 : long n;
367 46568581 : if (lgefint(x) != 3 || (n = x[2]) & HIGHBIT) return 0;
368 45445354 : return signe(x) > 0? n: -n;
369 : }
370 : INLINE ulong
371 125254782 : itou(GEN x)
372 : {
373 125254782 : switch(lgefint(x)) {
374 9615983 : case 2: return 0;
375 115638886 : case 3: return x[2];
376 0 : default:
377 0 : pari_err_OVERFLOW("t_INT-->ulong assignment");
378 : return 0; /* LCOV_EXCL_LINE */
379 : }
380 : }
381 :
382 : /* as itou, but return 0 if too large. Cf is_bigint */
383 : INLINE ulong
384 4375180 : itou_or_0(GEN x) {
385 4375180 : if (lgefint(x) != 3) return 0;
386 4364301 : return (ulong)x[2];
387 : }
388 :
389 : INLINE ulong
390 6619925 : umuluu_or_0(ulong x, ulong y)
391 : {
392 : ulong z;
393 : LOCAL_HIREMAINDER;
394 6619925 : z = mulll(x, y);
395 6619925 : return hiremainder? 0: z;
396 : }
397 : /* return x*y if <= n, else 0. Beware overflow */
398 : INLINE ulong
399 3170739 : umuluu_le(ulong x, ulong y, ulong n)
400 : {
401 : ulong z;
402 : LOCAL_HIREMAINDER;
403 3170739 : z = mulll(x, y);
404 3170739 : return (hiremainder || z > n)? 0: z;
405 : }
406 :
407 : INLINE GEN
408 165988305 : real_0_bit(long bitprec) { GEN x=cgetr(2); x[1]=evalexpo(bitprec); return x; }
409 : INLINE GEN
410 562269 : real_0(long prec) { return real_0_bit(-prec2nbits(prec)); }
411 : INLINE GEN
412 3183484 : real_1_bit(long bit) { return real_1(nbits2prec(bit)); }
413 : INLINE GEN
414 76134349 : real_1(long prec) {
415 76134349 : GEN x = cgetr(prec);
416 : long i;
417 76125819 : x[1] = evalsigne(1) | _evalexpo(0);
418 391280580 : x[2] = (long)HIGHBIT; for (i=3; i<prec; i++) x[i] = 0;
419 76125819 : return x;
420 : }
421 : INLINE GEN
422 182 : real_m1(long prec) {
423 182 : GEN x = cgetr(prec);
424 : long i;
425 182 : x[1] = evalsigne(-1) | _evalexpo(0);
426 1096 : x[2] = (long)HIGHBIT; for (i=3; i<prec; i++) x[i] = 0;
427 182 : return x;
428 : }
429 :
430 : /* 2.^n */
431 : INLINE GEN
432 696327 : real2n(long n, long prec) { GEN z = real_1(prec); setexpo(z, n); return z; }
433 : INLINE GEN
434 0 : real_m2n(long n, long prec) { GEN z = real_m1(prec); setexpo(z, n); return z; }
435 : INLINE GEN
436 193757773 : stor(long s, long prec) { GEN z = cgetr(prec); affsr(s,z); return z; }
437 : INLINE GEN
438 10126259 : utor(ulong s, long prec){ GEN z = cgetr(prec); affur(s,z); return z; }
439 : INLINE GEN
440 654453556 : itor(GEN x, long prec) { GEN z = cgetr(prec); affir(x,z); return z; }
441 : INLINE GEN
442 189750325 : rtor(GEN x, long prec) { GEN z = cgetr(prec); affrr(x,z); return z; }
443 :
444 12848482 : INLINE ulong int_bit(GEN x, long n)
445 : {
446 12848482 : long r, q = dvmdsBIL(n, &r);
447 12844778 : return q < lgefint(x)-2?((ulong)*int_W(x,q) >> r) & 1UL:0;
448 : }
449 :
450 : /*******************************************************************/
451 : /* */
452 : /* COMPARISON */
453 : /* */
454 : /*******************************************************************/
455 : INLINE int
456 1160304 : cmpss(long a, long b)
457 1160304 : { return a>b? 1: (a<b? -1: 0); }
458 :
459 : INLINE int
460 1386643492 : cmpuu(ulong a, ulong b)
461 1386643492 : { return a>b? 1: (a<b? -1: 0); }
462 :
463 : INLINE int
464 891109 : cmpir(GEN x, GEN y)
465 : {
466 : pari_sp av;
467 : GEN z;
468 :
469 891109 : if (!signe(x)) return -signe(y);
470 466846 : if (!signe(y))
471 : {
472 2213 : if (expo(y) >= expi(x)) return 0;
473 2185 : return signe(x);
474 : }
475 464633 : av=avma; z = itor(x, realprec(y)); set_avma(av);
476 464616 : return cmprr(z,y); /* cmprr does no memory adjustment */
477 : }
478 : INLINE int
479 437210 : cmpri(GEN x, GEN y) { return -cmpir(y,x); }
480 : INLINE int
481 100002 : cmpsr(long x, GEN y)
482 : {
483 : pari_sp av;
484 : GEN z;
485 :
486 100002 : if (!x) return -signe(y);
487 100002 : av=avma; z = stor(x, LOWDEFAULTPREC); set_avma(av);
488 100002 : return cmprr(z,y);
489 : }
490 : INLINE int
491 40131 : cmprs(GEN x, long y) { return -cmpsr(y,x); }
492 : /* compare x and y */
493 : INLINE int
494 4555424 : cmpui(ulong x, GEN y)
495 : {
496 : ulong p;
497 4555424 : if (!x) return -signe(y);
498 4555424 : if (signe(y) <= 0) return 1;
499 4555403 : if (lgefint(y) > 3) return -1;
500 2072994 : p = y[2]; if (p == x) return 0;
501 2034743 : return p < x ? 1 : -1;
502 : }
503 : INLINE int
504 4555423 : cmpiu(GEN x, ulong y) { return -cmpui(y,x); }
505 : /* compare x and |y| */
506 : INLINE int
507 39931196 : abscmpui(ulong x, GEN y)
508 : {
509 39931196 : long l = lgefint(y);
510 : ulong p;
511 :
512 39931196 : if (!x) return (l > 2)? -1: 0;
513 39931182 : if (l == 2) return 1;
514 39677160 : if (l > 3) return -1;
515 39656368 : p = y[2]; if (p == x) return 0;
516 38950674 : return p < x ? 1 : -1;
517 : }
518 : INLINE int
519 39085541 : abscmpiu(GEN x, ulong y) { return -abscmpui(y,x); }
520 : INLINE int
521 3538168 : cmpsi(long x, GEN y)
522 : {
523 : ulong p;
524 :
525 3538168 : if (!x) return -signe(y);
526 :
527 3537034 : if (x > 0)
528 : {
529 3536103 : if (signe(y)<=0) return 1;
530 3535774 : if (lgefint(y)>3) return -1;
531 3522022 : p = y[2]; if (p == (ulong)x) return 0;
532 3456657 : return p < (ulong)x ? 1 : -1;
533 : }
534 :
535 931 : if (signe(y)>=0) return -1;
536 147 : if (lgefint(y)>3) return 1;
537 147 : p = y[2]; if (p == (ulong)-x) return 0;
538 42 : return p < (ulong)(-x) ? -1 : 1;
539 : }
540 : INLINE int
541 3527277 : cmpis(GEN x, long y) { return -cmpsi(y,x); }
542 : INLINE int
543 1549164 : mpcmp(GEN x, GEN y)
544 : {
545 1549164 : if (typ(x)==t_INT)
546 60208 : return (typ(y)==t_INT) ? cmpii(x,y) : cmpir(x,y);
547 1488956 : return (typ(y)==t_INT) ? -cmpir(y,x) : cmprr(x,y);
548 : }
549 :
550 : /* x == y ? */
551 : INLINE int
552 1987560 : equalui(ulong x, GEN y)
553 : {
554 1987560 : if (!x) return !signe(y);
555 1987560 : if (signe(y) <= 0 || lgefint(y) != 3) return 0;
556 1977350 : return ((ulong)y[2] == (ulong)x);
557 : }
558 : /* x == y ? */
559 : INLINE int
560 580768 : equalsi(long x, GEN y)
561 : {
562 580768 : if (!x) return !signe(y);
563 580768 : if (x > 0)
564 : {
565 578668 : if (signe(y) <= 0 || lgefint(y) != 3) return 0;
566 528473 : return ((ulong)y[2] == (ulong)x);
567 : }
568 2100 : if (signe(y) >= 0 || lgefint(y) != 3) return 0;
569 1994 : return ((ulong)y[2] == (ulong)-x);
570 : }
571 : /* x == |y| ? */
572 : INLINE int
573 37228480 : absequalui(ulong x, GEN y)
574 : {
575 37228480 : if (!x) return !signe(y);
576 37228480 : return (lgefint(y) == 3 && (ulong)y[2] == x);
577 : }
578 : INLINE int
579 35707535 : absequaliu(GEN x, ulong y) { return absequalui(y,x); }
580 : INLINE int
581 580538 : equalis(GEN x, long y) { return equalsi(y,x); }
582 : INLINE int
583 1987560 : equaliu(GEN x, ulong y) { return equalui(y,x); }
584 :
585 : /* assume x != 0, is |x| == 2^n ? */
586 : INLINE int
587 717352 : absrnz_equal2n(GEN x) {
588 717352 : if ((ulong)x[2]==HIGHBIT)
589 : {
590 33016 : long i, lx = lg(x);
591 103208 : for (i = 3; i < lx; i++)
592 77376 : if (x[i]) return 0;
593 25832 : return 1;
594 : }
595 684336 : return 0;
596 : }
597 : /* assume x != 0, is |x| == 1 ? */
598 : INLINE int
599 2459854 : absrnz_equal1(GEN x) { return !expo(x) && absrnz_equal2n(x); }
600 :
601 : INLINE long
602 8273593498 : maxss(long x, long y) { return x>y?x:y; }
603 : INLINE long
604 1229051827 : minss(long x, long y) { return x<y?x:y; }
605 : INLINE long
606 8264667 : minuu(ulong x, ulong y) { return x<y?x:y; }
607 : INLINE long
608 9448608 : maxuu(ulong x, ulong y) { return x>y?x:y; }
609 : INLINE double
610 2693184 : maxdd(double x, double y) { return x>y?x:y; }
611 : INLINE double
612 2451017 : mindd(double x, double y) { return x<y?x:y; }
613 :
614 : /*******************************************************************/
615 : /* */
616 : /* ADD / SUB */
617 : /* */
618 : /*******************************************************************/
619 : INLINE GEN
620 25046 : subuu(ulong x, ulong y)
621 : {
622 : ulong z;
623 : LOCAL_OVERFLOW;
624 25046 : z = subll(x, y);
625 25046 : return overflow? utoineg(-z): utoi(z);
626 : }
627 : INLINE GEN
628 3260486389 : adduu(ulong x, ulong y) { ulong t = x+y; return uutoi((t < x), t); }
629 :
630 : INLINE GEN
631 25046 : addss(long x, long y)
632 : {
633 25046 : if (!x) return stoi(y);
634 25046 : if (!y) return stoi(x);
635 25046 : if (x > 0) return y > 0? adduu(x,y): subuu(x, -y);
636 :
637 25046 : if (y > 0) return subuu(y, -x);
638 : else { /* - adduu(-x, -y) */
639 0 : ulong t = (-x)+(-y); return uutoineg((t < (ulong)(-x)), t);
640 : }
641 : }
642 25046 : INLINE GEN subss(long x, long y) { return addss(-y,x); }
643 :
644 : INLINE GEN
645 6756845315 : subii(GEN x, GEN y)
646 : {
647 6756845315 : if (x==y) return gen_0; /* frequent with x = y = gen_0 */
648 4999786944 : return addii_sign(x, signe(x), y, -signe(y));
649 : }
650 : INLINE GEN
651 8605749535 : addii(GEN x, GEN y) { return addii_sign(x, signe(x), y, signe(y)); }
652 : INLINE GEN
653 2406187989 : addrr(GEN x, GEN y) { return addrr_sign(x, signe(x), y, signe(y)); }
654 : INLINE GEN
655 928197329 : subrr(GEN x, GEN y) { return addrr_sign(x, signe(x), y, -signe(y)); }
656 : INLINE GEN
657 338418191 : addir(GEN x, GEN y) { return addir_sign(x, signe(x), y, signe(y)); }
658 : INLINE GEN
659 2917436 : subir(GEN x, GEN y) { return addir_sign(x, signe(x), y, -signe(y)); }
660 : INLINE GEN
661 5843707 : subri(GEN x, GEN y) { return addir_sign(y, -signe(y), x, signe(x)); }
662 : INLINE GEN
663 116522370 : addsi(long x, GEN y) { return addsi_sign(x, y, signe(y)); }
664 : INLINE GEN
665 96856522 : addui(ulong x, GEN y) { return addui_sign(x, y, signe(y)); }
666 : INLINE GEN
667 6963279 : subsi(long x, GEN y) { return addsi_sign(x, y, -signe(y)); }
668 : INLINE GEN
669 62429991 : subui(ulong x, GEN y) { return addui_sign(x, y, -signe(y)); }
670 :
671 : /*******************************************************************/
672 : /* */
673 : /* MOD, REM, DIV */
674 : /* */
675 : /*******************************************************************/
676 125841420 : INLINE ulong mod2BIL(GEN x) { return *int_LSW(x); }
677 0 : INLINE long mod64(GEN x) { return mod2BIL(x) & 63; }
678 259 : INLINE long mod32(GEN x) { return mod2BIL(x) & 31; }
679 237152 : INLINE long mod16(GEN x) { return mod2BIL(x) & 15; }
680 52433185 : INLINE long mod8(GEN x) { return mod2BIL(x) & 7; }
681 7326438 : INLINE long mod4(GEN x) { return mod2BIL(x) & 3; }
682 50494264 : INLINE long mod2(GEN x) { return mod2BIL(x) & 1; }
683 : INLINE int
684 79522683 : mpodd(GEN x) { return signe(x) && mod2(x); }
685 : /* x mod 2^n, n < BITS_IN_LONG */
686 : INLINE ulong
687 22058715 : umodi2n(GEN x, long n)
688 : {
689 22058715 : long s = signe(x);
690 22058715 : const ulong _2n = 1UL << n;
691 : ulong m;
692 22058715 : if (!s) return 0;
693 22004881 : m = *int_LSW(x) & (_2n - 1);
694 22004881 : if (s < 0 && m) m = _2n - m;
695 22004881 : return m;
696 : }
697 0 : INLINE ulong Mod64(GEN x){ return umodi2n(x,6); }
698 167559 : INLINE ulong Mod32(GEN x){ return umodi2n(x,5); }
699 239722 : INLINE ulong Mod16(GEN x){ return umodi2n(x,4); }
700 1770832 : INLINE ulong Mod8(GEN x) { return umodi2n(x,3); }
701 18330282 : INLINE ulong Mod4(GEN x) { return umodi2n(x,2); }
702 1550073 : INLINE ulong Mod2(GEN x) { return umodi2n(x,1); }
703 :
704 : INLINE GEN
705 57766583 : truedivii(GEN a,GEN b) { return truedvmdii(a,b,NULL); }
706 : INLINE GEN
707 243909 : truedivis(GEN a, long b) { return truedvmdis(a,b,NULL); }
708 : INLINE GEN
709 6162526 : truedivsi(long a, GEN b) { return truedvmdsi(a,b,NULL); }
710 :
711 : INLINE GEN
712 12524791 : divii(GEN a, GEN b) { return dvmdii(a,b,NULL); }
713 : INLINE GEN
714 2027649952 : remii(GEN a, GEN b) { return dvmdii(a,b,ONLY_REM); }
715 :
716 : INLINE GEN
717 0 : divss(long x, long y) { return stoi(x / y); }
718 : INLINE GEN
719 0 : modss(long x, long y) { return utoi(smodss(x, y)); }
720 : INLINE GEN
721 0 : remss(long x, long y) { return stoi(x % y); }
722 : INLINE long
723 6422 : smodss(long x, long y)
724 : {
725 6422 : long r = x%y;
726 6422 : return (r >= 0)? r: labs(y) + r;
727 : }
728 : INLINE ulong
729 576549591 : umodsu(long x, ulong y)
730 : {
731 576549591 : return x>=0 ? x%y: Fl_neg((-x)%y, y);
732 : }
733 :
734 : INLINE long
735 0 : sdivss_rem(long x, long y, long *r)
736 : {
737 : long q;
738 : LOCAL_HIREMAINDER;
739 0 : if (!y) pari_err_INV("sdivss_rem",gen_0);
740 0 : hiremainder = 0; q = divll((ulong)labs(x),(ulong)labs(y));
741 0 : if (x < 0) { hiremainder = -((long)hiremainder); q = -q; }
742 0 : if (y < 0) q = -q;
743 0 : *r = hiremainder; return q;
744 : }
745 : INLINE GEN
746 0 : divss_rem(long x, long y, long *r) { return stoi(sdivss_rem(x,y,r)); }
747 : INLINE ulong
748 137544744 : udivuu_rem(ulong x, ulong y, ulong *r)
749 : {
750 137544744 : if (!y) pari_err_INV("udivuu_rem",gen_0);
751 137544744 : *r = x % y; return x / y;
752 : }
753 : INLINE ulong
754 670434 : ceildivuu(ulong a, ulong b)
755 : {
756 670434 : ulong c = a/b;
757 670434 : return (a%b)? c+1: c;
758 : }
759 :
760 : INLINE ulong
761 11400 : uabsdivui_rem(ulong x, GEN y, ulong *r)
762 : {
763 11400 : long q, s = signe(y);
764 : LOCAL_HIREMAINDER;
765 :
766 11400 : if (!s) pari_err_INV("uabsdivui_rem",gen_0);
767 11400 : if (!x || lgefint(y)>3) { *r = x; return 0; }
768 11092 : hiremainder=0; q = (long)divll(x, (ulong)y[2]);
769 11092 : if (s < 0) q = -q;
770 11092 : *r = hiremainder; return q;
771 : }
772 :
773 : /* assume d != 0 and |n| / d can be represented as an ulong.
774 : * Return |n|/d, set *r = |n| % d */
775 : INLINE ulong
776 10187366 : uabsdiviu_rem(GEN n, ulong d, ulong *r)
777 : {
778 10187366 : switch(lgefint(n))
779 : {
780 0 : case 2: *r = 0; return 0;
781 10187366 : case 3:
782 : {
783 10187366 : ulong nn = n[2];
784 10187366 : *r = nn % d; return nn / d;
785 : }
786 0 : default: /* 4 */
787 : {
788 : ulong n1, n0, q;
789 : LOCAL_HIREMAINDER;
790 0 : n0 = *int_W(n,0);
791 0 : n1 = *int_W(n,1);
792 0 : hiremainder = n1;
793 0 : q = divll(n0, d);
794 0 : *r = hiremainder; return q;
795 : }
796 : }
797 : }
798 :
799 : INLINE long
800 14961591 : sdivsi_rem(long x, GEN y, long *r)
801 : {
802 14961591 : long q, s = signe(y);
803 : LOCAL_HIREMAINDER;
804 :
805 14961591 : if (!s) pari_err_INV("sdivsi_rem",gen_0);
806 14961591 : if (!x || lgefint(y)>3 || ((long)y[2]) < 0) { *r = x; return 0; }
807 13021166 : hiremainder=0; q = (long)divll(labs(x), (ulong)y[2]);
808 13021166 : if (x < 0) { hiremainder = -((long)hiremainder); q = -q; }
809 13021166 : if (s < 0) q = -q;
810 13021166 : *r = hiremainder; return q;
811 : }
812 : INLINE GEN
813 0 : divsi_rem(long s, GEN y, long *r) { return stoi(sdivsi_rem(s,y,r)); }
814 :
815 : INLINE long
816 140 : sdivsi(long x, GEN y)
817 : {
818 140 : long q, s = signe(y);
819 :
820 140 : if (!s) pari_err_INV("sdivsi",gen_0);
821 140 : if (!x || lgefint(y)>3 || ((long)y[2]) < 0) return 0;
822 98 : q = labs(x) / y[2];
823 98 : if (x < 0) q = -q;
824 98 : if (s < 0) q = -q;
825 98 : return q;
826 : }
827 :
828 : INLINE GEN
829 0 : dvmdss(long x, long y, GEN *z)
830 : {
831 : long r;
832 0 : GEN q = divss_rem(x,y, &r);
833 0 : *z = stoi(r); return q;
834 : }
835 : INLINE long
836 4949802841 : dvmdsBIL(long n, long *r) { *r = remsBIL(n); return divsBIL(n); }
837 : INLINE ulong
838 161098197 : dvmduBIL(ulong n, ulong *r) { *r = remsBIL(n); return divsBIL(n); }
839 : INLINE GEN
840 0 : dvmdsi(long x, GEN y, GEN *z)
841 : {
842 : long r;
843 0 : GEN q = divsi_rem(x,y, &r);
844 0 : *z = stoi(r); return q;
845 : }
846 : INLINE GEN
847 0 : dvmdis(GEN x, long y, GEN *z)
848 : {
849 : long r;
850 0 : GEN q = divis_rem(x,y, &r);
851 0 : *z = stoi(r); return q;
852 : }
853 :
854 : INLINE long
855 19633892 : smodis(GEN x, long y)
856 : {
857 19633892 : pari_sp av = avma;
858 19633892 : long r; (void)divis_rem(x,y, &r);
859 19633892 : return gc_long(av, (r >= 0)? r: labs(y) + r);
860 : }
861 : INLINE GEN
862 19596902 : modis(GEN x, long y) { return stoi(smodis(x,y)); }
863 : INLINE GEN
864 8798820 : modsi(long x, GEN y) {
865 8798820 : long r; (void)sdivsi_rem(x, y, &r);
866 8798818 : return (r >= 0)? stoi(r): addsi_sign(r, y, 1);
867 : }
868 :
869 : INLINE ulong
870 814747 : umodui(ulong x, GEN y)
871 : {
872 814747 : if (!signe(y)) pari_err_INV("umodui",gen_0);
873 814747 : if (!x || lgefint(y) > 3) return x;
874 206589 : return x % (ulong)y[2];
875 : }
876 :
877 : INLINE ulong
878 210670 : ugcdiu(GEN x, ulong y) { return ugcd(umodiu(x,y), y); }
879 : INLINE ulong
880 4792 : ugcdui(ulong y, GEN x) { return ugcd(umodiu(x,y), y); }
881 :
882 : INLINE GEN
883 0 : remsi(long x, GEN y)
884 0 : { long r; (void)sdivsi_rem(x,y, &r); return stoi(r); }
885 : INLINE GEN
886 0 : remis(GEN x, long y)
887 : {
888 0 : pari_sp av = avma;
889 : long r;
890 0 : (void)divis_rem(x,y, &r); set_avma(av); return stoi(r);
891 : }
892 :
893 : INLINE GEN
894 0 : rdivis(GEN x, long y, long prec)
895 : {
896 0 : GEN z = cgetr(prec);
897 0 : pari_sp av = avma;
898 0 : affrr(divrs(itor(x,prec), y),z);
899 0 : set_avma(av); return z;
900 : }
901 : INLINE GEN
902 0 : rdivsi(long x, GEN y, long prec)
903 : {
904 0 : GEN z = cgetr(prec);
905 0 : pari_sp av = avma;
906 0 : affrr(divsr(x, itor(y,prec)), z);
907 0 : set_avma(av); return z;
908 : }
909 : INLINE GEN
910 839650 : rdivss(long x, long y, long prec)
911 : {
912 839650 : GEN z = cgetr(prec);
913 839650 : pari_sp av = avma;
914 839650 : affrr(divrs(stor(x, prec), y), z);
915 839650 : set_avma(av); return z;
916 : }
917 :
918 : INLINE void
919 7860120 : rdiviiz(GEN x, GEN y, GEN z)
920 : {
921 7860120 : long prec = realprec(z), lx = lgefint(x), ly = lgefint(y);
922 7860120 : if (lx == 2) { affur(0, z); return; }
923 7860120 : if (ly == 3)
924 : {
925 2084275 : affir(x, z); if (signe(y) < 0) togglesign(z);
926 2084207 : affrr(divru(z, y[2]), z);
927 : }
928 5775845 : else if (lx > prec + 1 || ly > prec + 1)
929 : {
930 2021187 : affir(x,z); affrr(divri(z, y), z);
931 : }
932 : else
933 : {
934 3754659 : long b = bit_accuracy(prec) + expi(y) - expi(x) + 1;
935 3754705 : GEN q = divii(b > 0? shifti(x, b): x, y);
936 3754805 : affir(q, z); if (b > 0) shiftr_inplace(z, -b);
937 : }
938 7860271 : set_avma((ulong)z);
939 : }
940 : INLINE GEN
941 7823168 : rdivii(GEN x, GEN y, long prec)
942 7823168 : { GEN z = cgetr(prec); rdiviiz(x, y, z); return z; }
943 : INLINE GEN
944 7478489 : fractor(GEN x, long prec)
945 7478489 : { return rdivii(gel(x,1), gel(x,2), prec); }
946 :
947 : INLINE int
948 13201324 : dvdii(GEN x, GEN y)
949 : {
950 13201324 : pari_sp av = avma;
951 : GEN r;
952 13201324 : if (!signe(x)) return 1;
953 11939520 : if (!signe(y)) return 0;
954 11939520 : r = remii(x,y);
955 11946513 : return gc_bool(av, r == gen_0);
956 : }
957 : INLINE int
958 154 : dvdsi(long x, GEN y)
959 : {
960 154 : if (x == 0) return 1;
961 49 : if (!signe(y)) return 0;
962 49 : if (lgefint(y) != 3) return 0;
963 49 : return x % y[2] == 0;
964 : }
965 : INLINE int
966 161 : dvdui(ulong x, GEN y)
967 : {
968 161 : if (x == 0) return 1;
969 161 : if (!signe(y)) return 0;
970 161 : if (lgefint(y) != 3) return 0;
971 161 : return x % y[2] == 0;
972 : }
973 : INLINE int
974 5663 : dvdis(GEN x, long y)
975 5663 : { return y? smodis(x, y) == 0: signe(x) == 0; }
976 : INLINE int
977 413814 : dvdiu(GEN x, ulong y)
978 413814 : { return y? umodiu(x, y) == 0: signe(x) == 0; }
979 :
980 : INLINE int
981 0 : dvdisz(GEN x, long y, GEN z)
982 : {
983 0 : const pari_sp av = avma;
984 : long r;
985 0 : GEN p1 = divis_rem(x,y, &r);
986 0 : set_avma(av); if (r) return 0;
987 0 : affii(p1,z); return 1;
988 : }
989 : INLINE int
990 0 : dvdiuz(GEN x, ulong y, GEN z)
991 : {
992 0 : const pari_sp av = avma;
993 : ulong r;
994 0 : GEN p1 = absdiviu_rem(x,y, &r);
995 0 : set_avma(av); if (r) return 0;
996 0 : affii(p1,z); return 1;
997 : }
998 : INLINE int
999 4742 : dvdiiz(GEN x, GEN y, GEN z)
1000 : {
1001 4742 : const pari_sp av=avma;
1002 4742 : GEN p2, p1 = dvmdii(x,y,&p2);
1003 4742 : if (signe(p2)) return gc_bool(av,0);
1004 4003 : affii(p1,z); return gc_bool(av,1);
1005 : }
1006 :
1007 : INLINE ulong
1008 77952765 : remlll_pre(ulong u2, ulong u1, ulong u0, ulong n, ulong ninv)
1009 : {
1010 77952765 : u1 = remll_pre(u2, u1, n, ninv);
1011 78975844 : return remll_pre(u1, u0, n, ninv);
1012 : }
1013 :
1014 : INLINE ulong
1015 1830506015 : Fl_sqr_pre(ulong a, ulong p, ulong pi)
1016 : {
1017 : register ulong x;
1018 : LOCAL_HIREMAINDER;
1019 1830506015 : x = mulll(a,a);
1020 1830506015 : return remll_pre(hiremainder, x, p, pi);
1021 : }
1022 :
1023 : INLINE ulong
1024 3055741138 : Fl_mul_pre(ulong a, ulong b, ulong p, ulong pi)
1025 : {
1026 : register ulong x;
1027 : LOCAL_HIREMAINDER;
1028 3055741138 : x = mulll(a,b);
1029 3055741138 : return remll_pre(hiremainder, x, p, pi);
1030 : }
1031 :
1032 : INLINE ulong
1033 6056853496 : Fl_addmul_pre(ulong y0, ulong x0, ulong x1, ulong p, ulong pi)
1034 : {
1035 : ulong l0, h0;
1036 : LOCAL_HIREMAINDER;
1037 6056853496 : hiremainder = y0;
1038 6056853496 : l0 = addmul(x0, x1); h0 = hiremainder;
1039 6056853496 : return remll_pre(h0, l0, p, pi);
1040 : }
1041 :
1042 : INLINE ulong
1043 52619395 : Fl_addmulmul_pre(ulong x0, ulong y0, ulong x1, ulong y1, ulong p, ulong pi)
1044 : {
1045 : ulong l0, l1, h0, h1;
1046 : LOCAL_OVERFLOW;
1047 : LOCAL_HIREMAINDER;
1048 52619395 : l0 = mulll(x0, y0); h0 = hiremainder;
1049 52619395 : l1 = mulll(x1, y1); h1 = hiremainder;
1050 52619395 : l0 = addll(l0, l1); h0 = addllx(h0, h1);
1051 52619395 : return overflow ? remlll_pre(1, h0, l0, p, pi): remll_pre(h0, l0, p, pi);
1052 : }
1053 :
1054 : INLINE ulong
1055 196161 : Fl_ellj_pre(ulong a4, ulong a6, ulong p, ulong pi)
1056 : {
1057 : /* a43 = 4 a4^3 */
1058 196161 : ulong a43 = Fl_double(Fl_double(
1059 : Fl_mul_pre(a4, Fl_sqr_pre(a4, p, pi), p, pi), p), p);
1060 : /* a62 = 27 a6^2 */
1061 196168 : ulong a62 = Fl_mul_pre(Fl_sqr_pre(a6, p, pi), 27 % p, p, pi);
1062 196168 : ulong z1 = Fl_mul_pre(a43, 1728 % p, p, pi);
1063 196166 : ulong z2 = Fl_add(a43, a62, p);
1064 196164 : return Fl_div(z1, z2, p);
1065 : }
1066 :
1067 : /*******************************************************************/
1068 : /* */
1069 : /* MP (INT OR REAL) */
1070 : /* */
1071 : /*******************************************************************/
1072 : INLINE GEN
1073 21 : mptrunc(GEN x) { return typ(x)==t_INT? icopy(x): truncr(x); }
1074 : INLINE GEN
1075 0 : mpfloor(GEN x) { return typ(x)==t_INT? icopy(x): floorr(x); }
1076 : INLINE GEN
1077 0 : mpceil(GEN x) { return typ(x)==t_INT? icopy(x): ceilr(x); }
1078 : INLINE GEN
1079 1343328 : mpround(GEN x) { return typ(x) == t_INT? icopy(x): roundr(x); }
1080 :
1081 : INLINE long
1082 638363 : mpexpo(GEN x) { return typ(x) == t_INT? expi(x): expo(x); }
1083 :
1084 : INLINE GEN
1085 114832192 : mpadd(GEN x, GEN y)
1086 : {
1087 114832192 : if (typ(x)==t_INT)
1088 20337074 : return (typ(y)==t_INT) ? addii(x,y) : addir(x,y);
1089 94495118 : return (typ(y)==t_INT) ? addir(y,x) : addrr(x,y);
1090 : }
1091 : INLINE GEN
1092 68457502 : mpsub(GEN x, GEN y)
1093 : {
1094 68457502 : if (typ(x)==t_INT)
1095 616722 : return (typ(y)==t_INT) ? subii(x,y) : subir(x,y);
1096 67840780 : return (typ(y)==t_INT) ? subri(x,y) : subrr(x,y);
1097 : }
1098 : INLINE GEN
1099 191286032 : mpmul(GEN x, GEN y)
1100 : {
1101 191286032 : if (typ(x)==t_INT)
1102 36379137 : return (typ(y)==t_INT) ? mulii(x,y) : mulir(x,y);
1103 154906895 : return (typ(y)==t_INT) ? mulir(y,x) : mulrr(x,y);
1104 : }
1105 : INLINE GEN
1106 23910168 : mpsqr(GEN x) { return (typ(x)==t_INT) ? sqri(x) : sqrr(x); }
1107 : INLINE GEN
1108 660527 : mpdiv(GEN x, GEN y)
1109 : {
1110 660527 : if (typ(x)==t_INT)
1111 254302 : return (typ(y)==t_INT) ? divii(x,y) : divir(x,y);
1112 406225 : return (typ(y)==t_INT) ? divri(x,y) : divrr(x,y);
1113 : }
1114 :
1115 : /*******************************************************************/
1116 : /* */
1117 : /* Z/nZ, n ULONG */
1118 : /* */
1119 : /*******************************************************************/
1120 : INLINE ulong
1121 392877094 : Fl_double(ulong a, ulong p)
1122 : {
1123 392877094 : ulong res = a << 1;
1124 392877094 : return (res >= p || res < a) ? res - p : res;
1125 : }
1126 : INLINE ulong
1127 73857385 : Fl_triple(ulong a, ulong p)
1128 : {
1129 73857385 : ulong res = a << 1;
1130 73857385 : if (res >= p || res < a) res -= p;
1131 73857385 : res += a;
1132 73857385 : return (res >= p || res < a)? res - p: res;
1133 : }
1134 : INLINE ulong
1135 15596015 : Fl_halve(ulong a, ulong p)
1136 : {
1137 : ulong ap, ap2;
1138 15596015 : if ((a&1UL)==0) return a>>1;
1139 7854632 : ap = a + p; ap2 = ap>>1;
1140 7854632 : return ap>=a ? ap2: (ap2|HIGHBIT);
1141 : }
1142 :
1143 : INLINE ulong
1144 3448636120 : Fl_add(ulong a, ulong b, ulong p)
1145 : {
1146 3448636120 : ulong res = a + b;
1147 3448636120 : return (res >= p || res < a) ? res - p : res;
1148 : }
1149 : INLINE ulong
1150 521011557 : Fl_neg(ulong x, ulong p) { return x ? p - x: 0; }
1151 :
1152 : INLINE ulong
1153 6374413459 : Fl_sub(ulong a, ulong b, ulong p)
1154 : {
1155 6374413459 : ulong res = a - b;
1156 6374413459 : return (res > a) ? res + p: res;
1157 : }
1158 :
1159 : /* centerlift(u mod p) */
1160 : INLINE long
1161 3486617 : Fl_center(ulong u, ulong p, ulong ps2) { return (long) (u > ps2)? u - p: u; }
1162 :
1163 : INLINE ulong
1164 1195781099 : Fl_mul(ulong a, ulong b, ulong p)
1165 : {
1166 : register ulong x;
1167 : LOCAL_HIREMAINDER;
1168 1195781099 : x = mulll(a,b);
1169 1195781099 : if (!hiremainder) return x % p;
1170 231722196 : (void)divll(x,p); return hiremainder;
1171 : }
1172 : INLINE ulong
1173 96525606 : Fl_sqr(ulong a, ulong p)
1174 : {
1175 : register ulong x;
1176 : LOCAL_HIREMAINDER;
1177 96525606 : x = mulll(a,a);
1178 96525606 : if (!hiremainder) return x % p;
1179 55115939 : (void)divll(x,p); return hiremainder;
1180 : }
1181 : /* don't assume that p is prime: can't special case a = 0 */
1182 : INLINE ulong
1183 23695269 : Fl_div(ulong a, ulong b, ulong p)
1184 23695269 : { return Fl_mul(a, Fl_inv(b, p), p); }
1185 :
1186 : /*******************************************************************/
1187 : /* */
1188 : /* DEFINED FROM EXISTING ONE EXPLOITING COMMUTATIVITY */
1189 : /* */
1190 : /*******************************************************************/
1191 : INLINE GEN
1192 1429639 : addri(GEN x, GEN y) { return addir(y,x); }
1193 : INLINE GEN
1194 103039866 : addis(GEN x, long s) { return addsi(s,x); }
1195 : INLINE GEN
1196 95862130 : addiu(GEN x, ulong s) { return addui(s,x); }
1197 : INLINE GEN
1198 6120355 : addrs(GEN x, long s) { return addsr(s,x); }
1199 :
1200 : INLINE GEN
1201 58741001 : subiu(GEN x, long y) { GEN z = subui(y, x); togglesign(z); return z; }
1202 : INLINE GEN
1203 2619 : subis(GEN x, long y) { return addsi(-y,x); }
1204 : INLINE GEN
1205 8829953 : subrs(GEN x, long y) { return addsr(-y,x); }
1206 :
1207 : INLINE GEN
1208 277412586 : mulis(GEN x, long s) { return mulsi(s,x); }
1209 : INLINE GEN
1210 166920378 : muliu(GEN x, ulong s) { return mului(s,x); }
1211 : INLINE GEN
1212 3187270 : mulru(GEN x, ulong s) { return mulur(s,x); }
1213 : INLINE GEN
1214 20189972 : mulri(GEN x, GEN s) { return mulir(s,x); }
1215 : INLINE GEN
1216 10271218 : mulrs(GEN x, long s) { return mulsr(s,x); }
1217 :
1218 : /*******************************************************************/
1219 : /* */
1220 : /* VALUATION, EXPONENT, SHIFTS */
1221 : /* */
1222 : /*******************************************************************/
1223 : INLINE long
1224 124333418 : vali(GEN x)
1225 : {
1226 : long i;
1227 : GEN xp;
1228 :
1229 124333418 : if (!signe(x)) return -1;
1230 124253521 : xp=int_LSW(x);
1231 129502002 : for (i=0; !*xp; i++) xp=int_nextW(xp);
1232 124253521 : return vals(*xp) + i * BITS_IN_LONG;
1233 : }
1234 :
1235 : /* assume x > 0 */
1236 : INLINE long
1237 474795317 : expu(ulong x) { return (BITS_IN_LONG-1) - (long)bfffo(x); }
1238 :
1239 : INLINE long
1240 1220343653 : expi(GEN x)
1241 : {
1242 1220343653 : const long lx=lgefint(x);
1243 1220343653 : return lx==2? -(long)HIGHEXPOBIT: bit_accuracy(lx)-(long)bfffo(*int_MSW(x))-1;
1244 : }
1245 :
1246 : INLINE GEN
1247 99931276 : shiftr(GEN x, long n)
1248 : {
1249 99931276 : const long e = evalexpo(expo(x)+n);
1250 99927445 : const GEN y = rcopy(x);
1251 :
1252 99916443 : if (e & ~EXPOBITS) pari_err_OVERFLOW("expo()");
1253 99916677 : y[1] = (y[1]&~EXPOBITS) | e; return y;
1254 : }
1255 : INLINE GEN
1256 132233636 : mpshift(GEN x,long s) { return (typ(x)==t_INT)?shifti(x,s):shiftr(x,s); }
1257 :
1258 : /* FIXME: adapt/use mpn_[lr]shift instead */
1259 : /* z2[imin..imax] := z1[imin..imax].f shifted left sh bits
1260 : * (feeding f from the right). Assume sh > 0 */
1261 : INLINE void
1262 5797943022 : shift_left(GEN z2, GEN z1, long imin, long imax, ulong f, ulong sh)
1263 : {
1264 5797943022 : GEN sb = z1 + imin, se = z1 + imax, te = z2 + imax;
1265 5797943022 : ulong l, m = BITS_IN_LONG - sh, k = f >> m;
1266 26363276639 : while (se > sb) {
1267 20565333617 : l = *se--;
1268 20565333617 : *te-- = (l << sh) | k;
1269 20565333617 : k = l >> m;
1270 : }
1271 5797943022 : *te = (((ulong)*se) << sh) | k;
1272 5797943022 : }
1273 : /* z2[imin..imax] := f.z1[imin..imax-1] shifted right sh bits
1274 : * (feeding f from the left). Assume sh > 0 */
1275 : INLINE void
1276 4716514213 : shift_right(GEN z2, GEN z1, long imin, long imax, ulong f, ulong sh)
1277 : {
1278 4716514213 : GEN sb = z1 + imin, se = z1 + imax, tb = z2 + imin;
1279 4716514213 : ulong k, l = *sb++, m = BITS_IN_LONG - sh;
1280 4716514213 : *tb++ = (l >> sh) | (f << m);
1281 25681778835 : while (sb < se) {
1282 20965264622 : k = l << m;
1283 20965264622 : l = *sb++;
1284 20965264622 : *tb++ = (l >> sh) | k;
1285 : }
1286 4716514213 : }
1287 :
1288 : /* Backward compatibility. Inefficient && unused */
1289 : extern ulong hiremainder;
1290 : INLINE ulong
1291 0 : shiftl(ulong x, ulong y)
1292 0 : { hiremainder = x>>(BITS_IN_LONG-y); return (x<<y); }
1293 :
1294 : INLINE ulong
1295 0 : shiftlr(ulong x, ulong y)
1296 0 : { hiremainder = x<<(BITS_IN_LONG-y); return (x>>y); }
1297 :
1298 : INLINE void
1299 187136688 : shiftr_inplace(GEN z, long d)
1300 : {
1301 187136688 : setexpo(z, expo(z)+d);
1302 187136798 : }
1303 :
1304 : /*******************************************************************/
1305 : /* */
1306 : /* ASSIGNMENT */
1307 : /* */
1308 : /*******************************************************************/
1309 : INLINE void
1310 178664447 : affii(GEN x, GEN y)
1311 : {
1312 178664447 : long lx = lgefint(x);
1313 178664447 : if (lg(y)<lx) pari_err_OVERFLOW("t_INT-->t_INT assignment");
1314 5865812490 : while (--lx) y[lx] = x[lx];
1315 178668323 : }
1316 : INLINE void
1317 3406869 : affsi(long s, GEN x)
1318 : {
1319 3406869 : if (!s) x[1] = evalsigne(0) | evallgefint(2);
1320 : else
1321 : {
1322 3252321 : if (s > 0) { x[1] = evalsigne( 1) | evallgefint(3); x[2] = s; }
1323 1304307 : else { x[1] = evalsigne(-1) | evallgefint(3); x[2] = -s; }
1324 : }
1325 3406869 : }
1326 : INLINE void
1327 7920609 : affui(ulong u, GEN x)
1328 : {
1329 7920609 : if (!u) x[1] = evalsigne(0) | evallgefint(2);
1330 7881466 : else { x[1] = evalsigne(1) | evallgefint(3); x[2] = u; }
1331 7920609 : }
1332 :
1333 : INLINE void
1334 193539153 : affsr(long x, GEN y)
1335 : {
1336 193539153 : long sh, i, ly = lg(y);
1337 :
1338 193539153 : if (!x)
1339 : {
1340 70966 : y[1] = evalexpo(-prec2nbits(ly));
1341 70966 : return;
1342 : }
1343 193468187 : if (x < 0) {
1344 3213 : x = -x; sh = bfffo(x);
1345 3213 : y[1] = evalsigne(-1) | _evalexpo((BITS_IN_LONG-1)-sh);
1346 : }
1347 : else
1348 : {
1349 193464974 : sh = bfffo(x);
1350 193464974 : y[1] = evalsigne(1) | _evalexpo((BITS_IN_LONG-1)-sh);
1351 : }
1352 1157100569 : y[2] = ((ulong)x)<<sh; for (i=3; i<ly; i++) y[i]=0;
1353 : }
1354 :
1355 : INLINE void
1356 10128307 : affur(ulong x, GEN y)
1357 : {
1358 10128307 : long sh, i, ly = lg(y);
1359 :
1360 10128307 : if (!x)
1361 : {
1362 1299417 : y[1] = evalexpo(-prec2nbits(ly));
1363 1299417 : return;
1364 : }
1365 8828890 : sh = bfffo(x);
1366 8828890 : y[1] = evalsigne(1) | _evalexpo((BITS_IN_LONG-1)-sh);
1367 29619387 : y[2] = x<<sh; for (i=3; i<ly; i++) y[i] = 0;
1368 : }
1369 :
1370 : INLINE void
1371 266662 : affiz(GEN x, GEN y) { if (typ(y)==t_INT) affii(x,y); else affir(x,y); }
1372 : INLINE void
1373 0 : affsz(long x, GEN y) { if (typ(y)==t_INT) affsi(x,y); else affsr(x,y); }
1374 : INLINE void
1375 679720 : mpaff(GEN x, GEN y) { if (typ(x)==t_INT) affiz(x, y); else affrr(x,y); }
1376 :
1377 : /*******************************************************************/
1378 : /* */
1379 : /* OPERATION + ASSIGNMENT */
1380 : /* */
1381 : /*******************************************************************/
1382 :
1383 0 : INLINE void addiiz(GEN x, GEN y, GEN z)
1384 0 : { pari_sp av = avma; affii(addii(x,y),z); set_avma(av); }
1385 0 : INLINE void addirz(GEN x, GEN y, GEN z)
1386 0 : { pari_sp av = avma; affrr(addir(x,y),z); set_avma(av); }
1387 0 : INLINE void addriz(GEN x, GEN y, GEN z)
1388 0 : { pari_sp av = avma; affrr(addri(x,y),z); set_avma(av); }
1389 1307080 : INLINE void addrrz(GEN x, GEN y, GEN z)
1390 1307080 : { pari_sp av = avma; affrr(addrr(x,y),z); set_avma(av); }
1391 0 : INLINE void addsiz(long s, GEN y, GEN z)
1392 0 : { pari_sp av = avma; affii(addsi(s,y),z); set_avma(av); }
1393 0 : INLINE void addsrz(long s, GEN y, GEN z)
1394 0 : { pari_sp av = avma; affrr(addsr(s,y),z); set_avma(av); }
1395 0 : INLINE void addssz(long s, long y, GEN z)
1396 0 : { pari_sp av = avma; affii(addss(s,y),z); set_avma(av); }
1397 :
1398 0 : INLINE void diviiz(GEN x, GEN y, GEN z)
1399 0 : { pari_sp av = avma; affii(divii(x,y),z); set_avma(av); }
1400 0 : INLINE void divirz(GEN x, GEN y, GEN z)
1401 0 : { pari_sp av = avma; mpaff(divir(x,y),z); set_avma(av); }
1402 0 : INLINE void divisz(GEN x, long y, GEN z)
1403 0 : { pari_sp av = avma; affii(divis(x,y),z); set_avma(av); }
1404 0 : INLINE void divriz(GEN x, GEN y, GEN z)
1405 0 : { pari_sp av = avma; affrr(divri(x,y),z); set_avma(av); }
1406 417 : INLINE void divrrz(GEN x, GEN y, GEN z)
1407 417 : { pari_sp av = avma; affrr(divrr(x,y),z); set_avma(av); }
1408 0 : INLINE void divrsz(GEN y, long s, GEN z)
1409 0 : { pari_sp av = avma; affrr(divrs(y,s),z); set_avma(av); }
1410 0 : INLINE void divsiz(long x, GEN y, GEN z)
1411 0 : { long junk; affsi(sdivsi_rem(x,y,&junk), z); }
1412 0 : INLINE void divsrz(long s, GEN y, GEN z)
1413 0 : { pari_sp av = avma; mpaff(divsr(s,y),z); set_avma(av); }
1414 0 : INLINE void divssz(long x, long y, GEN z)
1415 0 : { affsi(x/y, z); }
1416 :
1417 0 : INLINE void modisz(GEN y, long s, GEN z)
1418 0 : { affsi(smodis(y,s),z); }
1419 0 : INLINE void modsiz(long s, GEN y, GEN z)
1420 0 : { pari_sp av = avma; affii(modsi(s,y),z); set_avma(av); }
1421 0 : INLINE void modssz(long s, long y, GEN z)
1422 0 : { affsi(smodss(s,y),z); }
1423 :
1424 0 : INLINE void mpaddz(GEN x, GEN y, GEN z)
1425 0 : { pari_sp av = avma; mpaff(mpadd(x,y),z); set_avma(av); }
1426 0 : INLINE void mpsubz(GEN x, GEN y, GEN z)
1427 0 : { pari_sp av = avma; mpaff(mpsub(x,y),z); set_avma(av); }
1428 0 : INLINE void mpmulz(GEN x, GEN y, GEN z)
1429 0 : { pari_sp av = avma; mpaff(mpmul(x,y),z); set_avma(av); }
1430 :
1431 0 : INLINE void muliiz(GEN x, GEN y, GEN z)
1432 0 : { pari_sp av = avma; affii(mulii(x,y),z); set_avma(av); }
1433 0 : INLINE void mulirz(GEN x, GEN y, GEN z)
1434 0 : { pari_sp av = avma; mpaff(mulir(x,y),z); set_avma(av); }
1435 0 : INLINE void mulriz(GEN x, GEN y, GEN z)
1436 0 : { pari_sp av = avma; mpaff(mulri(x,y),z); set_avma(av); }
1437 260344 : INLINE void mulrrz(GEN x, GEN y, GEN z)
1438 260344 : { pari_sp av = avma; affrr(mulrr(x,y),z); set_avma(av); }
1439 0 : INLINE void mulsiz(long s, GEN y, GEN z)
1440 0 : { pari_sp av = avma; affii(mulsi(s,y),z); set_avma(av); }
1441 0 : INLINE void mulsrz(long s, GEN y, GEN z)
1442 0 : { pari_sp av = avma; mpaff(mulsr(s,y),z); set_avma(av); }
1443 0 : INLINE void mulssz(long s, long y, GEN z)
1444 0 : { pari_sp av = avma; affii(mulss(s,y),z); set_avma(av); }
1445 :
1446 0 : INLINE void remiiz(GEN x, GEN y, GEN z)
1447 0 : { pari_sp av = avma; affii(remii(x,y),z); set_avma(av); }
1448 0 : INLINE void remisz(GEN y, long s, GEN z)
1449 0 : { pari_sp av = avma; affii(remis(y,s),z); set_avma(av); }
1450 0 : INLINE void remsiz(long s, GEN y, GEN z)
1451 0 : { pari_sp av = avma; affii(remsi(s,y),z); set_avma(av); }
1452 0 : INLINE void remssz(long s, long y, GEN z)
1453 0 : { pari_sp av = avma; affii(remss(s,y),z); set_avma(av); }
1454 :
1455 0 : INLINE void subiiz(GEN x, GEN y, GEN z)
1456 0 : { pari_sp av = avma; affii(subii(x,y),z); set_avma(av); }
1457 0 : INLINE void subirz(GEN x, GEN y, GEN z)
1458 0 : { pari_sp av = avma; affrr(subir(x,y),z); set_avma(av); }
1459 0 : INLINE void subisz(GEN y, long s, GEN z)
1460 0 : { pari_sp av = avma; affii(addsi(-s,y),z); set_avma(av); }
1461 0 : INLINE void subriz(GEN x, GEN y, GEN z)
1462 0 : { pari_sp av = avma; affrr(subri(x,y),z); set_avma(av); }
1463 1296708 : INLINE void subrrz(GEN x, GEN y, GEN z)
1464 1296708 : { pari_sp av = avma; affrr(subrr(x,y),z); set_avma(av); }
1465 0 : INLINE void subrsz(GEN y, long s, GEN z)
1466 0 : { pari_sp av = avma; affrr(addsr(-s,y),z); set_avma(av); }
1467 0 : INLINE void subsiz(long s, GEN y, GEN z)
1468 0 : { pari_sp av = avma; affii(subsi(s,y),z); set_avma(av); }
1469 0 : INLINE void subsrz(long s, GEN y, GEN z)
1470 0 : { pari_sp av = avma; affrr(subsr(s,y),z); set_avma(av); }
1471 0 : INLINE void subssz(long x, long y, GEN z) { addssz(x,-y,z); }
1472 :
1473 : INLINE void
1474 0 : dvmdssz(long x, long y, GEN z, GEN t) {
1475 0 : pari_sp av = avma;
1476 : long r;
1477 0 : affii(divss_rem(x,y, &r), z); set_avma(av); affsi(r,t);
1478 0 : }
1479 : INLINE void
1480 0 : dvmdsiz(long x, GEN y, GEN z, GEN t) {
1481 0 : pari_sp av = avma;
1482 : long r;
1483 0 : affii(divsi_rem(x,y, &r), z); set_avma(av); affsi(r,t);
1484 0 : }
1485 : INLINE void
1486 0 : dvmdisz(GEN x, long y, GEN z, GEN t) {
1487 0 : pari_sp av = avma;
1488 : long r;
1489 0 : affii(divis_rem(x,y, &r),z); set_avma(av); affsi(r,t);
1490 0 : }
1491 : INLINE void
1492 0 : dvmdiiz(GEN x, GEN y, GEN z, GEN t) {
1493 0 : pari_sp av = avma;
1494 : GEN r;
1495 0 : affii(dvmdii(x,y,&r),z); affii(r,t); set_avma(av);
1496 0 : }
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