Annotation of OpenXM_contrib/pari-2.2/src/basemath/bibli2.c, Revision 1.1
1.1 ! noro 1: /* $Id: bibli2.c,v 1.23 2001/10/01 12:11:29 karim Exp $
! 2:
! 3: Copyright (C) 2000 The PARI group.
! 4:
! 5: This file is part of the PARI/GP package.
! 6:
! 7: PARI/GP is free software; you can redistribute it and/or modify it under the
! 8: terms of the GNU General Public License as published by the Free Software
! 9: Foundation. 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., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */
! 15:
! 16: /********************************************************************/
! 17: /** **/
! 18: /** BIBLIOTHEQUE MATHEMATIQUE **/
! 19: /** (deuxieme partie) **/
! 20: /** **/
! 21: /********************************************************************/
! 22: #include "pari.h"
! 23:
! 24: /********************************************************************/
! 25: /** **/
! 26: /** DEVELOPPEMENTS LIMITES **/
! 27: /** **/
! 28: /********************************************************************/
! 29:
! 30: GEN
! 31: tayl(GEN x, long v, long precdl)
! 32: {
! 33: long tetpil,i,vx = gvar9(x), av=avma;
! 34: GEN p1,y;
! 35:
! 36: if (v <= vx)
! 37: {
! 38: long p1[] = { evaltyp(t_SER)|m_evallg(2), 0 };
! 39: p1[1] = evalvalp(precdl) | evalvarn(v);
! 40: return gadd(p1,x);
! 41: }
! 42: p1=cgetg(v+2,t_VEC);
! 43: for (i=0; i<v; i++) p1[i+1]=lpolx[i];
! 44: p1[vx+1]=lpolx[v]; p1[v+1]=lpolx[vx];
! 45: y = tayl(changevar(x,p1), vx,precdl); tetpil=avma;
! 46: return gerepile(av,tetpil, changevar(y,p1));
! 47: }
! 48:
! 49: GEN
! 50: grando0(GEN x, long n, long do_clone)
! 51: {
! 52: long m, v, tx=typ(x);
! 53: GEN y;
! 54:
! 55: if (gcmp0(x)) err(talker,"zero argument in O()");
! 56: if (tx == t_INT)
! 57: {
! 58: if (!gcmp1(x)) /* bug 3 + O(1). We suppose x is a truc() */
! 59: {
! 60: y=cgetg(5,t_PADIC);
! 61: y[1] = evalvalp(n) | evalprecp(0);
! 62: y[2] = do_clone? lclone(x): licopy(x);
! 63: y[3] = un; y[4] = zero; return y;
! 64: }
! 65: v=0; m=0; /* 1 = x^0 */
! 66: }
! 67: else
! 68: {
! 69: if (tx != t_POL && ! is_rfrac_t(tx))
! 70: err(talker,"incorrect argument in O()");
! 71: v=gvar(x); m=n*gval(x,v);
! 72: }
! 73: return zeroser(v,m);
! 74: }
! 75:
! 76: /*******************************************************************/
! 77: /** **/
! 78: /** SPECIAL POLYNOMIALS **/
! 79: /** **/
! 80: /*******************************************************************/
! 81: #ifdef LONG_IS_64BIT
! 82: # define SQRTVERYBIGINT 3037000500 /* ceil(sqrt(VERYBIGINT)) */
! 83: #else
! 84: # define SQRTVERYBIGINT 46341
! 85: #endif
! 86:
! 87: /* Tchebichev polynomial: T0=1; T1=X; T(n)=2*X*T(n-1)-T(n-2)
! 88: * T(n) = (n/2) sum_{k=0}^{n/2} a_k x^(n-2k)
! 89: * where a_k = (-1)^k 2^(n-2k) (n-k-1)! / k!(n-2k)! is an integer
! 90: * and a_0 = 2^(n-1), a_k / a_{k-1} = - (n-2k+2)(n-2k+1) / 4k(n-k) */
! 91: GEN
! 92: tchebi(long n, long v) /* Assume 4*n < VERYBIGINT */
! 93: {
! 94: long av,k,l;
! 95: GEN q,a,r;
! 96:
! 97: if (v<0) v = 0;
! 98: if (n==0) return polun[v];
! 99: if (n==1) return polx[v];
! 100:
! 101: q = cgetg(n+3, t_POL); r = q + n+2;
! 102: a = shifti(gun, n-1);
! 103: *r-- = (long)a;
! 104: *r-- = zero;
! 105: if (n < SQRTVERYBIGINT)
! 106: for (k=1,l=n; l>1; k++,l-=2)
! 107: {
! 108: av = avma;
! 109: a = divis(mulis(a, l*(l-1)), 4*k*(n-k));
! 110: a = gerepileuptoint(av, negi(a));
! 111: *r-- = (long)a;
! 112: *r-- = zero;
! 113: }
! 114: else
! 115: for (k=1,l=n; l>1; k++,l-=2)
! 116: {
! 117: av = avma;
! 118: a = mulis(mulis(a, l), l-1);
! 119: a = divis(divis(a, 4*k), n-k);
! 120: a = gerepileuptoint(av, negi(a));
! 121: *r-- = (long)a;
! 122: *r-- = zero;
! 123: }
! 124: q[1] = evalsigne(1) | evalvarn(v) | evallgef(n+3);
! 125: return q;
! 126: }
! 127:
! 128: GEN addshiftw(GEN x, GEN y, long d);
! 129: /* Legendre polynomial */
! 130: /* L0=1; L1=X; (n+1)*L(n+1)=(2*n+1)*X*L(n)-n*L(n-1) */
! 131: GEN
! 132: legendre(long n, long v)
! 133: {
! 134: long av,tetpil,m,lim;
! 135: GEN p0,p1,p2;
! 136:
! 137: if (v<0) v = 0;
! 138: if (n==0) return polun[v];
! 139: if (n==1) return polx[v];
! 140:
! 141: p0=polun[v]; av=avma; lim=stack_lim(av,2);
! 142: p1=gmul2n(polx[v],1);
! 143: for (m=1; m<n; m++)
! 144: {
! 145: p2 = addshiftw(gmulsg(4*m+2,p1), gmulsg(-4*m,p0), 1);
! 146: setvarn(p2,v);
! 147: p0 = p1; tetpil=avma; p1 = gdivgs(p2,m+1);
! 148: if (low_stack(lim, stack_lim(av,2)))
! 149: {
! 150: GEN *gptr[2];
! 151: if(DEBUGMEM>1) err(warnmem,"legendre");
! 152: p0=gcopy(p0); gptr[0]=&p0; gptr[1]=&p1;
! 153: gerepilemanysp(av,tetpil,gptr,2);
! 154: }
! 155: }
! 156: tetpil=avma; return gerepile(av,tetpil,gmul2n(p1,-n));
! 157: }
! 158:
! 159: /* cyclotomic polynomial */
! 160: GEN
! 161: cyclo(long n, long v)
! 162: {
! 163: long av=avma,tetpil,d,q,m;
! 164: GEN yn,yd;
! 165:
! 166: if (n<=0) err(arither2);
! 167: if (v<0) v = 0;
! 168: yn = yd = polun[0];
! 169: for (d=1; d*d<=n; d++)
! 170: {
! 171: if (n%d) continue;
! 172: q=n/d;
! 173: m = mu(stoi(q));
! 174: if (m)
! 175: { /* y *= (x^d - 1) */
! 176: if (m>0) yn = addshiftw(yn, gneg(yn), d);
! 177: else yd = addshiftw(yd, gneg(yd), d);
! 178: }
! 179: if (q==d) break;
! 180: m = mu(stoi(d));
! 181: if (m)
! 182: { /* y *= (x^q - 1) */
! 183: if (m>0) yn = addshiftw(yn, gneg(yn), q);
! 184: else yd = addshiftw(yd, gneg(yd), q);
! 185: }
! 186: }
! 187: tetpil=avma; yn = gerepile(av,tetpil,gdeuc(yn,yd));
! 188: setvarn(yn,v); return yn;
! 189: }
! 190:
! 191: /* compute prod (L*x ± a[i]) */
! 192: GEN
! 193: roots_to_pol_intern(GEN L, GEN a, long v, int plus)
! 194: {
! 195: long i,k,lx = lg(a), code;
! 196: GEN p1,p2;
! 197: if (lx == 1) return polun[v];
! 198: p1 = cgetg(lx, t_VEC);
! 199: code = evalsigne(1)|evalvarn(v)|evallgef(5);
! 200: for (k=1,i=1; i<lx-1; i+=2)
! 201: {
! 202: p2 = cgetg(5,t_POL); p1[k++] = (long)p2;
! 203: p2[2] = lmul((GEN)a[i],(GEN)a[i+1]);
! 204: p2[3] = ladd((GEN)a[i],(GEN)a[i+1]);
! 205: if (plus == 0) p2[3] = lneg((GEN)p2[3]);
! 206: p2[4] = (long)L; p2[1] = code;
! 207: }
! 208: if (i < lx)
! 209: {
! 210: p2 = cgetg(4,t_POL); p1[k++] = (long)p2;
! 211: p2[1] = code = evalsigne(1)|evalvarn(v)|evallgef(4);
! 212: p2[2] = plus? a[i]: lneg((GEN)a[i]);
! 213: p2[3] = (long)L;
! 214: }
! 215: setlg(p1, k); return divide_conquer_prod(p1, gmul);
! 216: }
! 217:
! 218: GEN
! 219: roots_to_pol(GEN a, long v)
! 220: {
! 221: return roots_to_pol_intern(gun,a,v,0);
! 222: }
! 223:
! 224: /* prod_{i=1..r1} (x - a[i]) prod_{i=1..r2} (x - a[i])(x - conj(a[i]))*/
! 225: GEN
! 226: roots_to_pol_r1r2(GEN a, long r1, long v)
! 227: {
! 228: long i,k,lx = lg(a), code;
! 229: GEN p1;
! 230: if (lx == 1) return polun[v];
! 231: p1 = cgetg(lx, t_VEC);
! 232: code = evalsigne(1)|evalvarn(v)|evallgef(5);
! 233: for (k=1,i=1; i<r1; i+=2)
! 234: {
! 235: GEN p2 = cgetg(5,t_POL); p1[k++] = (long)p2;
! 236: p2[2] = lmul((GEN)a[i],(GEN)a[i+1]);
! 237: p2[3] = lneg(gadd((GEN)a[i],(GEN)a[i+1]));
! 238: p2[4] = un; p2[1] = code;
! 239: }
! 240: if (i < r1+1)
! 241: p1[k++] = ladd(polx[v], gneg((GEN)a[i]));
! 242: for (i=r1+1; i<lx; i++)
! 243: {
! 244: GEN p2 = cgetg(5,t_POL); p1[k++] = (long)p2;
! 245: p2[2] = lnorm((GEN)a[i]);
! 246: p2[3] = lneg(gtrace((GEN)a[i]));
! 247: p2[4] = un; p2[1] = code;
! 248: }
! 249: setlg(p1, k); return divide_conquer_prod(p1, gmul);
! 250: }
! 251:
! 252: /* finds an equation for the d-th degree subfield of Q(zeta_n).
! 253: * (Z/nZ)* must be cyclic.
! 254: */
! 255: GEN
! 256: subcyclo(GEN nn, GEN dd, int v)
! 257: {
! 258: long av=avma,tetpil,i,j,k,prec,q,d,p,pp,al,n,ex0,ex,aad,aa;
! 259: GEN a,z,pol,fa,powz,alpha;
! 260:
! 261: if (typ(dd)!=t_INT || signe(dd)<=0) err(typeer,"subcyclo");
! 262: if (is_bigint(dd)) err(talker,"degree too large in subcyclo");
! 263: if (typ(nn)!=t_INT || signe(nn)<=0) err(typeer,"subcyclo");
! 264: if (v<0) v = 0;
! 265: d=itos(dd); if (d==1) return polx[v];
! 266: if (is_bigint(nn)) err(impl,"subcyclo for huge cyclotomic fields");
! 267: n = nn[2]; if ((n & 3) == 2) n >>= 1;
! 268: if (n == 1) err(talker,"degree does not divide phi(n) in subcyclo");
! 269: fa = factor(stoi(n));
! 270: p = itos(gmael(fa,1,1));
! 271: al= itos(gmael(fa,2,1));
! 272: if (lg((GEN)fa[1]) > 2 || (p==2 && al>2))
! 273: err(impl,"subcyclo in non-cyclic case");
! 274: if (d < n)
! 275: {
! 276: k = 1 + svaluation(d,p,&i);
! 277: if (k<al) { al = k; nn = gpowgs(stoi(p),al); n = nn[2]; }
! 278: }
! 279: avma=av; q = (n/p)*(p-1); /* = phi(n) */
! 280: if (q == d) return cyclo(n,v);
! 281: if (q % d) err(talker,"degree does not divide phi(n) in subcyclo");
! 282: q /= d;
! 283: if (p==2)
! 284: {
! 285: pol = powgi(polx[v],gdeux); pol[2]=un; /* replace gzero */
! 286: return pol; /* = x^2 + 1 */
! 287: }
! 288: a=gener(stoi(n)); aa = mael(a,2,2);
! 289: a=gpowgs(a,d); aad = mael(a,2,2);
! 290: #if 1
! 291: prec = expi(binome(stoi(d*q-1),d)) + expi(stoi(n));
! 292: prec = 2 + (prec>>TWOPOTBITS_IN_LONG);
! 293: if (prec<DEFAULTPREC) prec = DEFAULTPREC;
! 294: if (DEBUGLEVEL) fprintferr("subcyclo prec = %ld\n",prec);
! 295: z = cgetg(3,t_COMPLEX); a=mppi(prec); setexpo(a,2); /* a = 2\pi */
! 296: gsincos(divrs(a,n),(GEN*)(z+2),(GEN*)(z+1),prec); /* z = e_n(1) */
! 297: powz = cgetg(n,t_VEC); powz[1] = (long)z;
! 298: k = (n+3)>>1;
! 299: for (i=2; i<k; i++) powz[i] = lmul(z,(GEN)powz[i-1]);
! 300: if ((q&1) == 0) /* totally real field, take real part */
! 301: {
! 302: for (i=1; i<k; i++) powz[i] = mael(powz,i,1);
! 303: for ( ; i<n; i++) powz[i] = powz[n-i];
! 304: }
! 305: else
! 306: for ( ; i<n; i++) powz[i] = lconj((GEN)powz[n-i]);
! 307:
! 308: alpha = cgetg(d+1,t_VEC) + 1; pol=gun;
! 309: for (ex0=1,k=0; k<d; k++, ex0=(ex0*aa)%n)
! 310: {
! 311: GEN p1 = gzero;
! 312: long av1 = avma; (void)new_chunk(2*prec + 3);
! 313: for (ex=ex0,i=0; i<q; i++)
! 314: {
! 315: for (pp=ex,j=0; j<al; j++)
! 316: {
! 317: p1 = gadd(p1,(GEN)powz[pp]);
! 318: pp = mulssmod(pp,p, n);
! 319: }
! 320: ex = mulssmod(ex,aad, n);
! 321: }
! 322: /* p1 = sum z^{p^k*h}, k = 0..al-1, h runs through the subgroup of order
! 323: * q = phi(n)/d of (Z/nZ)^* */
! 324: avma = av1; alpha[k] = lneg(p1);
! 325: }
! 326: pol = roots_to_pol_intern(gun,alpha-1,v, 1);
! 327: if (q&1) pol=greal(pol); /* already done otherwise */
! 328: tetpil=avma; return gerepile(av,tetpil,ground(pol));
! 329: #else
! 330: {
! 331: /* exact computation (much slower) */
! 332: GEN p1 = cgetg(n+2,t_POL)+2; for (i=0; i<n; i++) p1[i]=0;
! 333: for (ex=1,i=0; i<q; i++, ex=(ex*aad)%n)
! 334: for (pp=ex,j=0; j<al; j++, pp=(pp*p)%n) p1[pp]++;
! 335: for (i=0; i<n; i++) p1[i] = lstoi(p1[i]);
! 336: p1 = normalizepol_i(p1-2,n+2); setvarn(p1,v);
! 337: z = cyclo(n,v); a = caract2(z,gres(p1,z),v);
! 338: a = gdeuc(a, modulargcd(a,derivpol(a)));
! 339: return gerepileupto(av, a);
! 340: }
! 341: #endif
! 342: }
! 343:
! 344: /********************************************************************/
! 345: /** **/
! 346: /** HILBERT & PASCAL MATRICES **/
! 347: /** **/
! 348: /********************************************************************/
! 349: GEN
! 350: mathilbert(long n) /* Hilbert matrix of order n */
! 351: {
! 352: long i,j;
! 353: GEN a,p;
! 354:
! 355: if (n<0) n = 0;
! 356: p = cgetg(n+1,t_MAT);
! 357: for (j=1; j<=n; j++)
! 358: {
! 359: p[j]=lgetg(n+1,t_COL);
! 360: for (i=1+(j==1); i<=n; i++)
! 361: {
! 362: a=cgetg(3,t_FRAC); a[1]=un; a[2]=lstoi(i+j-1);
! 363: coeff(p,i,j)=(long)a;
! 364: }
! 365: }
! 366: if ( n ) mael(p,1,1)=un;
! 367: return p;
! 368: }
! 369:
! 370: /* q-Pascal triangle = (choose(i,j)_q) (ordinary binomial if q = NULL) */
! 371: GEN
! 372: matqpascal(long n, GEN q)
! 373: {
! 374: long i,j,I, av = avma;
! 375: GEN m, *qpow = NULL; /* gcc -Wall */
! 376:
! 377: if (n<0) n = -1;
! 378: n++; m = cgetg(n+1,t_MAT);
! 379: for (j=1; j<=n; j++) m[j] = lgetg(n+1,t_COL);
! 380: if (q)
! 381: {
! 382: I = (n+1)/2;
! 383: if (I > 1) { qpow = (GEN*)new_chunk(I+1); qpow[2]=q; }
! 384: for (j=3; j<=I; j++) qpow[j] = gmul(q, qpow[j-1]);
! 385: }
! 386: for (i=1; i<=n; i++)
! 387: {
! 388: I = (i+1)/2; coeff(m,i,1)=un;
! 389: if (q)
! 390: {
! 391: for (j=2; j<=I; j++)
! 392: coeff(m,i,j) = ladd(gmul(qpow[j],gcoeff(m,i-1,j)), gcoeff(m,i-1,j-1));
! 393: }
! 394: else
! 395: {
! 396: for (j=2; j<=I; j++)
! 397: coeff(m,i,j) = laddii(gcoeff(m,i-1,j), gcoeff(m,i-1,j-1));
! 398: }
! 399: for ( ; j<=i; j++) coeff(m,i,j) = coeff(m,i,i+1-j);
! 400: for ( ; j<=n; j++) coeff(m,i,j) = zero;
! 401: }
! 402: return gerepilecopy(av, m);
! 403: }
! 404:
! 405: /********************************************************************/
! 406: /** **/
! 407: /** LAPLACE TRANSFORM (OF A SERIES) **/
! 408: /** **/
! 409: /********************************************************************/
! 410:
! 411: GEN
! 412: laplace(GEN x)
! 413: {
! 414: ulong av = avma;
! 415: long i,l,ec;
! 416: GEN y,p1;
! 417:
! 418: if (typ(x)!=t_SER) err(talker,"not a series in laplace");
! 419: if (gcmp0(x)) return gcopy(x);
! 420:
! 421: ec = valp(x);
! 422: if (ec<0) err(talker,"negative valuation in laplace");
! 423: l=lg(x); y=cgetg(l,t_SER);
! 424: p1=mpfact(ec); y[1]=x[1];
! 425: for (i=2; i<l; i++)
! 426: {
! 427: y[i]=lmul(p1,(GEN)x[i]);
! 428: ec++; p1=mulsi(ec,p1);
! 429: }
! 430: return gerepilecopy(av,y);
! 431: }
! 432:
! 433: /********************************************************************/
! 434: /** **/
! 435: /** CONVOLUTION PRODUCT (OF TWO SERIES) **/
! 436: /** **/
! 437: /********************************************************************/
! 438:
! 439: GEN
! 440: convol(GEN x, GEN y)
! 441: {
! 442: long l,i,j,v, vx=varn(x), lx=lg(x), ly=lg(y), ex=valp(x), ey=valp(y);
! 443: GEN z;
! 444:
! 445: if (typ(x) != t_SER || typ(y) != t_SER)
! 446: err(talker,"not a series in convol");
! 447: if (gcmp0(x) || gcmp0(y))
! 448: err(talker,"zero series in convol");
! 449: if (varn(y) != vx)
! 450: err(talker,"different variables in convol");
! 451: v=ex; if (ey>v) v=ey;
! 452: l=ex+lx; i=ey+ly; if (i<l) l=i;
! 453: l -= v; if (l<3) err(talker,"non significant result in convol");
! 454: for (i=v+2; i < v+l; i++)
! 455: if (!gcmp0((GEN)x[i-ex]) && !gcmp0((GEN)y[i-ey])) { i++; break; }
! 456: if (i == l+v) return zeroser(vx, v+l-2);
! 457:
! 458: z = cgetg(l-i+3+v,t_SER);
! 459: z[1] = evalsigne(1) | evalvalp(i-3) | evalvarn(vx);
! 460: for (j=i-1; j<l+v; j++) z[j-i+3]=lmul((GEN)x[j-ex],(GEN)y[j-ey]);
! 461: return z;
! 462: }
! 463:
! 464: /******************************************************************/
! 465: /** **/
! 466: /** PRECISION CHANGES **/
! 467: /** **/
! 468: /******************************************************************/
! 469:
! 470: GEN
! 471: gprec(GEN x, long l)
! 472: {
! 473: long tx=typ(x),lx=lg(x),i,pr;
! 474: GEN y;
! 475:
! 476: if (l<=0) err(talker,"precision<=0 in gprec");
! 477: switch(tx)
! 478: {
! 479: case t_REAL:
! 480: pr = (long) (l*pariK1+3); y=cgetr(pr); affrr(x,y); break;
! 481:
! 482: case t_PADIC:
! 483: y=cgetg(lx,tx); copyifstack(x[2], y[2]);
! 484: if (!signe(x[4]))
! 485: {
! 486: y[1]=evalvalp(l+precp(x)) | evalprecp(0);
! 487: y[3]=un; y[4]=zero; return y;
! 488: }
! 489: y[1]=x[1]; setprecp(y,l);
! 490: y[3]=lpuigs((GEN)x[2],l);
! 491: y[4]=lmodii((GEN)x[4],(GEN)y[3]);
! 492: break;
! 493:
! 494: case t_SER:
! 495: if (gcmp0(x)) return zeroser(varn(x), l);
! 496: y=cgetg(l+2,t_SER); y[1]=x[1]; l++; i=l;
! 497: if (l>=lx)
! 498: for ( ; i>=lx; i--) y[i]=zero;
! 499: for ( ; i>=2; i--) y[i]=lcopy((GEN)x[i]);
! 500: break;
! 501:
! 502: case t_POL:
! 503: lx=lgef(x); y=cgetg(lx,tx); y[1]=x[1];
! 504: for (i=2; i<lx; i++) y[i]=lprec((GEN)x[i],l);
! 505: break;
! 506:
! 507: case t_COMPLEX: case t_POLMOD: case t_RFRAC: case t_RFRACN:
! 508: case t_VEC: case t_COL: case t_MAT:
! 509: y=cgetg(lx,tx);
! 510: for (i=1; i<lx; i++) y[i]=lprec((GEN)x[i],l);
! 511: break;
! 512: default: y=gcopy(x);
! 513: }
! 514: return y;
! 515: }
! 516:
! 517: /* internal: precision given in word length (including codewords) */
! 518: GEN
! 519: gprec_w(GEN x, long pr)
! 520: {
! 521: long tx=typ(x),lx,i;
! 522: GEN y;
! 523:
! 524: switch(tx)
! 525: {
! 526: case t_REAL:
! 527: y=cgetr(pr); affrr(x,y); break;
! 528:
! 529: case t_POL:
! 530: lx=lgef(x); y=cgetg(lx,tx); y[1]=x[1];
! 531: for (i=2; i<lx; i++) y[i]=(long)gprec_w((GEN)x[i],pr);
! 532: break;
! 533:
! 534: case t_COMPLEX: case t_POLMOD: case t_RFRAC: case t_RFRACN:
! 535: case t_VEC: case t_COL: case t_MAT:
! 536: lx=lg(x); y=cgetg(lx,tx);
! 537: for (i=1; i<lx; i++) y[i]=(long)gprec_w((GEN)x[i],pr);
! 538: break;
! 539: default: y=gprec(x,pr);
! 540: }
! 541: return y;
! 542: }
! 543:
! 544: /*******************************************************************/
! 545: /** **/
! 546: /** RECIPROCAL POLYNOMIAL **/
! 547: /** **/
! 548: /*******************************************************************/
! 549:
! 550: GEN
! 551: polrecip(GEN x)
! 552: {
! 553: long lx=lgef(x),i,j;
! 554: GEN y;
! 555:
! 556: if (typ(x) != t_POL) err(typeer,"polrecip");
! 557: y=cgetg(lx,t_POL); y[1]=x[1];
! 558: for (i=2,j=lx-1; i<lx; i++,j--) y[i]=lcopy((GEN)x[j]);
! 559: return normalizepol_i(y,lx);
! 560: }
! 561:
! 562: /* as above. Internal (don't copy or normalize) */
! 563: GEN
! 564: polrecip_i(GEN x)
! 565: {
! 566: long lx=lgef(x),i,j;
! 567: GEN y;
! 568:
! 569: y=cgetg(lx,t_POL); y[1]=x[1];
! 570: for (i=2,j=lx-1; i<lx; i++,j--) y[i]=x[j];
! 571: return y;
! 572: }
! 573:
! 574: /*******************************************************************/
! 575: /** **/
! 576: /** BINOMIAL COEFFICIENTS **/
! 577: /** **/
! 578: /*******************************************************************/
! 579:
! 580: GEN
! 581: binome(GEN n, long k)
! 582: {
! 583: long av,i;
! 584: GEN y;
! 585:
! 586: if (k <= 1)
! 587: {
! 588: if (is_noncalc_t(typ(n))) err(typeer,"binomial");
! 589: if (k < 0) return gzero;
! 590: if (k == 0) return gun;
! 591: return gcopy(n);
! 592: }
! 593: av = avma; y = n;
! 594: if (typ(n) == t_INT)
! 595: {
! 596: if (signe(n) > 0)
! 597: {
! 598: GEN z = subis(n,k);
! 599: if (cmpis(z,k) < 0) k = itos(z);
! 600: avma = av;
! 601: if (k <= 1)
! 602: {
! 603: if (k < 0) return gzero;
! 604: if (k == 0) return gun;
! 605: return gcopy(n);
! 606: }
! 607: }
! 608: for (i=2; i<=k; i++)
! 609: y = gdivgs(gmul(y,addis(n,i-1-k)), i);
! 610: }
! 611: else
! 612: {
! 613: for (i=2; i<=k; i++)
! 614: y = gdivgs(gmul(y,gaddgs(n,i-1-k)), i);
! 615: }
! 616: return gerepileupto(av, y);
! 617: }
! 618:
! 619: /********************************************************************/
! 620: /** **/
! 621: /** POLYNOMIAL INTERPOLATION **/
! 622: /** **/
! 623: /********************************************************************/
! 624: /* assume n > 1 */
! 625: GEN
! 626: polint_i(GEN xa, GEN ya, GEN x, long n, GEN *ptdy)
! 627: {
! 628: long av = avma,tetpil,i,m, ns=0, tx=typ(x);
! 629: GEN den,ho,hp,w,y,c,d,dy;
! 630:
! 631: if (!xa)
! 632: {
! 633: xa = cgetg(n+1, t_VEC);
! 634: for (i=1; i<=n; i++) xa[i] = lstoi(i);
! 635: xa++;
! 636: }
! 637: if (is_scalar_t(tx) && tx != t_INTMOD && tx != t_PADIC && tx != t_POLMOD)
! 638: {
! 639: GEN dif = NULL, dift;
! 640: for (i=0; i<n; i++)
! 641: {
! 642: dift = gabs(gsub(x,(GEN)xa[i]), MEDDEFAULTPREC);
! 643: if (!dif || gcmp(dift,dif)<0) { ns=i; dif=dift; }
! 644: }
! 645: }
! 646: c=new_chunk(n);
! 647: d=new_chunk(n); for (i=0; i<n; i++) c[i] = d[i] = ya[i];
! 648: y=(GEN)d[ns--];
! 649: dy = NULL; tetpil = 0; /* gcc -Wall */
! 650: for (m=1; m<n; m++)
! 651: {
! 652: for (i=0; i<n-m; i++)
! 653: {
! 654: ho = gsub((GEN)xa[i],x);
! 655: hp = gsub((GEN)xa[i+m],x); den = gsub(ho,hp);
! 656: if (gcmp0(den)) err(talker,"two abcissas are equal in polint");
! 657: w=gsub((GEN)c[i+1],(GEN)d[i]); den = gdiv(w,den);
! 658: c[i]=lmul(ho,den);
! 659: d[i]=lmul(hp,den);
! 660: }
! 661: dy = (2*(ns+1) < n-m)? (GEN)c[ns+1]: (GEN)d[ns--];
! 662: tetpil=avma; y=gadd(y,dy);
! 663: }
! 664: if (!ptdy) y = gerepile(av,tetpil,y);
! 665: else
! 666: {
! 667: GEN *gptr[2];
! 668: *ptdy=gcopy(dy); gptr[0]=&y; gptr[1]=ptdy;
! 669: gerepilemanysp(av,tetpil,gptr,2);
! 670: }
! 671: return y;
! 672: }
! 673:
! 674: GEN
! 675: polint(GEN xa, GEN ya, GEN x, GEN *ptdy)
! 676: {
! 677: long tx=typ(xa), ty, lx=lg(xa);
! 678:
! 679: if (ya) ty = typ(ya); else { ya = xa; ty = tx; xa = NULL; }
! 680:
! 681: if (! is_vec_t(tx) || ! is_vec_t(ty))
! 682: err(talker,"not vectors in polinterpolate");
! 683: if (lx != lg(ya))
! 684: err(talker,"different lengths in polinterpolate");
! 685: if (lx <= 2)
! 686: {
! 687: if (lx == 1) err(talker,"no data in polinterpolate");
! 688: ya=gcopy((GEN)ya[1]); if (ptdy) *ptdy = ya;
! 689: return ya;
! 690: }
! 691: if (!x) x = polx[0];
! 692: return polint_i(xa? xa+1: xa,ya+1,x,lx-1,ptdy);
! 693: }
! 694:
! 695: /***********************************************************************/
! 696: /* */
! 697: /* SET OPERATIONS */
! 698: /* */
! 699: /***********************************************************************/
! 700:
! 701: static GEN
! 702: gtostr(GEN x)
! 703: {
! 704: char *s=GENtostr(x);
! 705: x = strtoGENstr(s,0); free(s); return x;
! 706: }
! 707:
! 708: GEN
! 709: gtoset(GEN x)
! 710: {
! 711: ulong av;
! 712: long i,c,tx,lx;
! 713: GEN y;
! 714:
! 715: if (!x) return cgetg(1, t_VEC);
! 716: tx = typ(x); lx = lg(x);
! 717: if (!is_vec_t(tx))
! 718: {
! 719: if (tx != t_LIST)
! 720: { y=cgetg(2,t_VEC); y[1]=(long)gtostr(x); return y; }
! 721: lx = lgef(x)-1; x++;
! 722: }
! 723: if (lx==1) return cgetg(1,t_VEC);
! 724: av=avma; y=cgetg(lx,t_VEC);
! 725: for (i=1; i<lx; i++) y[i]=(long)gtostr((GEN)x[i]);
! 726: y = sort(y);
! 727: c=1;
! 728: for (i=2; i<lx; i++)
! 729: if (!gegal((GEN)y[i], (GEN)y[c])) y[++c] = y[i];
! 730: setlg(y,c+1); return gerepilecopy(av,y);
! 731: }
! 732:
! 733: long
! 734: setisset(GEN x)
! 735: {
! 736: long lx,i;
! 737:
! 738: if (typ(x)!=t_VEC) return 0;
! 739: lx=lg(x)-1; if (!lx) return 1;
! 740: for (i=1; i<lx; i++)
! 741: if (typ(x[i]) != t_STR || gcmp((GEN)x[i+1],(GEN)x[i])<=0) return 0;
! 742: return typ(x[i]) == t_STR;
! 743: }
! 744:
! 745: /* looks if y belongs to the set x and returns the index if yes, 0 if no */
! 746: long
! 747: setsearch(GEN x, GEN y, long flag)
! 748: {
! 749: long av = avma,lx,j,li,ri,fl, tx = typ(x);
! 750:
! 751: if (tx==t_VEC) lx = lg(x);
! 752: else
! 753: {
! 754: if (tx!=t_LIST) err(talker,"not a set in setsearch");
! 755: lx=lgef(x)-1; x++;
! 756: }
! 757: if (lx==1) return flag? 1: 0;
! 758:
! 759: if (typ(y) != t_STR) y = gtostr(y);
! 760: li=1; ri=lx-1;
! 761: do
! 762: {
! 763: j = (ri+li)>>1; fl = gcmp((GEN)x[j],y);
! 764: if (!fl) { avma=av; return flag? 0: j; }
! 765: if (fl<0) li=j+1; else ri=j-1;
! 766: } while (ri>=li);
! 767: avma=av; if (!flag) return 0;
! 768: return (fl<0)? j+1: j;
! 769: }
! 770:
! 771: GEN
! 772: setunion(GEN x, GEN y)
! 773: {
! 774: long av=avma,tetpil;
! 775: GEN z;
! 776:
! 777: if (typ(x) != t_VEC || typ(y) != t_VEC) err(talker,"not a set in setunion");
! 778: z=concatsp(x,y); tetpil=avma; return gerepile(av,tetpil,gtoset(z));
! 779: }
! 780:
! 781: GEN
! 782: setintersect(GEN x, GEN y)
! 783: {
! 784: long av=avma,i,lx,c;
! 785: GEN z;
! 786:
! 787: if (!setisset(x) || !setisset(y)) err(talker,"not a set in setintersect");
! 788: lx=lg(x); z=cgetg(lx,t_VEC); c=1;
! 789: for (i=1; i<lx; i++)
! 790: if (setsearch(y, (GEN)x[i], 0)) z[c++] = x[i];
! 791: setlg(z,c); return gerepilecopy(av,z);
! 792: }
! 793:
! 794: GEN
! 795: setminus(GEN x, GEN y)
! 796: {
! 797: long av=avma,i,lx,c;
! 798: GEN z;
! 799:
! 800: if (!setisset(x) || !setisset(y)) err(talker,"not a set in setminus");
! 801: lx=lg(x); z=cgetg(lx,t_VEC); c=1;
! 802: for (i=1; i<lx; i++)
! 803: if (setsearch(y, (GEN)x[i], 1)) z[c++] = x[i];
! 804: setlg(z,c); return gerepilecopy(av,z);
! 805: }
! 806:
! 807: /***********************************************************************/
! 808: /* */
! 809: /* OPERATIONS ON DIRICHLET SERIES */
! 810: /* */
! 811: /***********************************************************************/
! 812:
! 813: /* Addition, subtraction and scalar multiplication of Dirichlet series
! 814: are done on the corresponding vectors */
! 815:
! 816: static long
! 817: dirval(GEN x)
! 818: {
! 819: long i=1,lx=lg(x);
! 820: while (i<lx && gcmp0((GEN)x[i])) i++;
! 821: return i;
! 822: }
! 823:
! 824: GEN
! 825: dirmul(GEN x, GEN y)
! 826: {
! 827: ulong av = avma, lim = stack_lim(av,1);
! 828: long lx,ly,lz,dx,dy,i,j,k;
! 829: GEN z,p1;
! 830:
! 831: if (typ(x)!=t_VEC || typ(y)!=t_VEC) err(talker,"not a dirseries in dirmul");
! 832: dx=dirval(x); dy=dirval(y); lx=lg(x); ly=lg(y);
! 833: if (ly-dy<lx-dx) { z=y; y=x; x=z; lz=ly; ly=lx; lx=lz; lz=dy; dy=dx; dx=lz; }
! 834: lz=min(lx*dy,ly*dx);
! 835: z=cgetg(lz,t_VEC); for (i=1; i<lz; i++) z[i]=zero;
! 836: for (j=dx; j<lx; j++)
! 837: {
! 838: p1=(GEN)x[j];
! 839: if (!gcmp0(p1))
! 840: {
! 841: if (gcmp1(p1))
! 842: for (k=dy,i=j*dy; i<lz; i+=j,k++) z[i]=ladd((GEN)z[i],(GEN)y[k]);
! 843: else
! 844: {
! 845: if (gcmp_1(p1))
! 846: for (k=dy,i=j*dy; i<lz; i+=j,k++) z[i]=lsub((GEN)z[i],(GEN)y[k]);
! 847: else
! 848: for (k=dy,i=j*dy; i<lz; i+=j,k++) z[i]=ladd((GEN)z[i],gmul(p1,(GEN)y[k]));
! 849: }
! 850: }
! 851: if (low_stack(lim, stack_lim(av,1)))
! 852: {
! 853: if (DEBUGLEVEL) fprintferr("doubling stack in dirmul\n");
! 854: z = gerepilecopy(av,z);
! 855: }
! 856: }
! 857: return gerepilecopy(av,z);
! 858: }
! 859:
! 860: GEN
! 861: dirdiv(GEN x, GEN y)
! 862: {
! 863: ulong av = avma;
! 864: long lx,ly,lz,dx,dy,i,j;
! 865: GEN z,p1;
! 866:
! 867: if (typ(x)!=t_VEC || typ(y)!=t_VEC) err(talker,"not a dirseries in dirmul");
! 868: dx=dirval(x); dy=dirval(y); lx=lg(x); ly=lg(y);
! 869: if (dy!=1) err(talker,"not an invertible dirseries in dirdiv");
! 870: lz=min(lx,ly*dx); p1=(GEN)y[1];
! 871: if (!gcmp1(p1)) { y=gdiv(y,p1); x=gdiv(x,p1); }
! 872: else x=gcopy(x);
! 873: z=cgetg(lz,t_VEC); for (i=1; i<dx; i++) z[i]=zero;
! 874: for (j=dx; j<lz; j++)
! 875: {
! 876: p1=(GEN)x[j]; z[j]=(long)p1;
! 877: if (!gcmp0(p1))
! 878: {
! 879: if (gcmp1(p1))
! 880: for (i=j+j; i<lz; i+=j) x[i]=lsub((GEN)x[i],(GEN)y[i/j]);
! 881: else
! 882: {
! 883: if (gcmp_1(p1))
! 884: for (i=j+j; i<lz; i+=j) x[i]=ladd((GEN)x[i],(GEN)y[i/j]);
! 885: else
! 886: for (i=j+j; i<lz; i+=j) x[i]=lsub((GEN)x[i],gmul(p1,(GEN)y[i/j]));
! 887: }
! 888: }
! 889: }
! 890: return gerepilecopy(av,z);
! 891: }
! 892:
! 893: /*************************************************************************/
! 894: /** **/
! 895: /** RANDOM **/
! 896: /** **/
! 897: /*************************************************************************/
! 898: static long pari_randseed = 1;
! 899:
! 900: /* BSD rand gives this: seed = 1103515245*seed + 12345 */
! 901: long
! 902: mymyrand(void)
! 903: {
! 904: #if BITS_IN_RANDOM == 64
! 905: pari_randseed = (1000000000000654397*pari_randseed + 12347) & ~HIGHBIT;
! 906: #else
! 907: pari_randseed = (1000276549*pari_randseed + 12347) & 0x7fffffff;
! 908: #endif
! 909: return pari_randseed;
! 910: }
! 911:
! 912: GEN muluu(ulong x, ulong y);
! 913:
! 914: static ulong
! 915: gp_rand(void)
! 916: {
! 917: #define GLUE2(hi, lo) (((hi) << BITS_IN_HALFULONG) | (lo))
! 918: #if !defined(LONG_IS_64BIT) || BITS_IN_RANDOM == 64
! 919: return GLUE2((mymyrand()>>12)&LOWMASK,
! 920: (mymyrand()>>12)&LOWMASK);
! 921: #else
! 922: #define GLUE4(hi1,hi2, lo1,lo2) GLUE2(((hi1)<<16)|(hi2), ((lo1)<<16)|(lo2))
! 923: # define LOWMASK2 0xffffUL
! 924: return GLUE4((mymyrand()>>12)&LOWMASK2,
! 925: (mymyrand()>>12)&LOWMASK2,
! 926: (mymyrand()>>12)&LOWMASK2,
! 927: (mymyrand()>>12)&LOWMASK2);
! 928: #endif
! 929: }
! 930:
! 931: GEN
! 932: genrand(GEN N)
! 933: {
! 934: long lx,i,nz;
! 935: GEN x, p1;
! 936:
! 937: if (!N) return stoi(mymyrand());
! 938: if (typ(N)!=t_INT || signe(N)<=0) err(talker,"invalid bound in random");
! 939:
! 940: lx = lgefint(N); x = new_chunk(lx);
! 941: nz = lx-1; while (!N[nz]) nz--; /* nz = index of last non-zero word */
! 942: for (i=2; i<lx; i++)
! 943: {
! 944: ulong n = N[i], r;
! 945: if (n == 0) r = 0;
! 946: else
! 947: {
! 948: long av = avma;
! 949: if (i < nz) n++; /* allow for equality if we can go down later */
! 950: p1 = muluu(n, gp_rand()); /* < n * 2^32, so 0 <= first word < n */
! 951: r = (lgefint(p1)<=3)? 0: p1[2]; avma = av;
! 952: }
! 953: x[i] = r;
! 954: if (r < (ulong)N[i]) break;
! 955: }
! 956: for (i++; i<lx; i++) x[i] = gp_rand();
! 957: i=2; while (i<lx && !x[i]) i++;
! 958: i -= 2; x += i; lx -= i;
! 959: x[1] = evalsigne(lx>2) | evallgefint(lx);
! 960: x[0] = evaltyp(t_INT) | evallg(lx);
! 961: avma = (long)x; return x;
! 962: }
! 963:
! 964: long
! 965: setrand(long seed) { return (pari_randseed = seed); }
! 966:
! 967: long
! 968: getrand(void) { return pari_randseed; }
! 969:
! 970: long
! 971: getstack(void) { return top-avma; }
! 972:
! 973: long
! 974: gettime(void) { return timer(); }
! 975:
! 976: /***********************************************************************/
! 977: /** **/
! 978: /** PERMUTATIONS **/
! 979: /** **/
! 980: /***********************************************************************/
! 981:
! 982: GEN
! 983: numtoperm(long n, GEN x)
! 984: {
! 985: ulong av;
! 986: long i,a,r;
! 987: GEN v,w;
! 988:
! 989: if (n < 1) err(talker,"n too small (%ld) in numtoperm",n);
! 990: if (typ(x) != t_INT) err(arither1);
! 991: v = cgetg(n+1, t_VEC);
! 992: v[1]=1; av = avma;
! 993: if (signe(x) <= 0) x = modii(x, mpfact(n));
! 994: for (r=2; r<=n; r++)
! 995: {
! 996: x = dvmdis(x,r,&w); a = itos(w);
! 997: for (i=r; i>=a+2; i--) v[i] = v[i-1];
! 998: v[i]=r;
! 999: }
! 1000: avma = av;
! 1001: for (i=1; i<=n; i++) v[i] = lstoi(v[i]);
! 1002: return v;
! 1003: }
! 1004:
! 1005: GEN
! 1006: permtonum(GEN x)
! 1007: {
! 1008: long av=avma, lx=lg(x)-1, n=lx, last, ind, tx = typ(x);
! 1009: GEN ary,res;
! 1010:
! 1011: if (!is_vec_t(tx)) err(talker,"not a vector in permtonum");
! 1012: ary = cgetg(lx+1,t_VECSMALL);
! 1013: for (ind=1; ind<=lx; ind++)
! 1014: {
! 1015: res = (GEN)*++x;
! 1016: if (typ(res) != t_INT) err(typeer,"permtonum");
! 1017: ary[ind] = itos(res);
! 1018: }
! 1019: ary++; res = gzero;
! 1020: for (last=lx; last>0; last--)
! 1021: {
! 1022: lx--; ind = lx;
! 1023: while (ind>0 && ary[ind] != last) ind--;
! 1024: res = addis(mulis(res,last), ind);
! 1025: while (ind++<lx) ary[ind-1] = ary[ind];
! 1026: }
! 1027: if (!signe(res)) res = mpfact(n);
! 1028: return gerepileuptoint(av, res);
! 1029: }
! 1030:
! 1031: /********************************************************************/
! 1032: /** **/
! 1033: /** MODREVERSE **/
! 1034: /** **/
! 1035: /********************************************************************/
! 1036:
! 1037: GEN
! 1038: polymodrecip(GEN x)
! 1039: {
! 1040: long v,i,j,n,av,tetpil,lx;
! 1041: GEN p1,p2,p3,p,phi,y,col;
! 1042:
! 1043: if (typ(x)!=t_POLMOD) err(talker,"not a polymod in polymodrecip");
! 1044: p=(GEN)x[1]; phi=(GEN)x[2];
! 1045: v=varn(p); n=degpol(p); if (n<=0) return gcopy(x);
! 1046: if (n==1)
! 1047: {
! 1048: y=cgetg(3,t_POLMOD);
! 1049: if (typ(phi)==t_POL) phi = (GEN)phi[2];
! 1050: p1=cgetg(4,t_POL); p1[1]=p[1]; p1[2]=lneg(phi); p1[3]=un;
! 1051: y[1]=(long)p1;
! 1052: if (gcmp0((GEN)p[2])) p1 = zeropol(v);
! 1053: else
! 1054: {
! 1055: p1=cgetg(3,t_POL); av=avma;
! 1056: p1[1] = evalsigne(1) | evalvarn(n) | evallgef(3);
! 1057: p2=gdiv((GEN)p[2],(GEN)p[3]); tetpil=avma;
! 1058: p1[2] = lpile(av,tetpil,gneg(p2));
! 1059: }
! 1060: y[2]=(long)p1; return y;
! 1061: }
! 1062: if (gcmp0(phi) || typ(phi) != t_POL)
! 1063: err(talker,"reverse polymod does not exist");
! 1064: av=avma; y=cgetg(n+1,t_MAT);
! 1065: y[1]=(long)gscalcol_i(gun,n);
! 1066: p2=phi;
! 1067: for (j=2; j<=n; j++)
! 1068: {
! 1069: lx=lgef(p2); p1=cgetg(n+1,t_COL); y[j]=(long)p1;
! 1070: for (i=1; i<=lx-2; i++) p1[i]=p2[i+1];
! 1071: for ( ; i<=n; i++) p1[i]=zero;
! 1072: if (j<n) p2 = gmod(gmul(p2,phi), p);
! 1073: }
! 1074: col=cgetg(n+1,t_COL); col[1]=zero; col[2]=un;
! 1075: for (i=3; i<=n; i++) col[i]=zero;
! 1076: p1=gauss(y,col); p2=gtopolyrev(p1,v); p3=caract(x,v);
! 1077: tetpil=avma; return gerepile(av,tetpil,gmodulcp(p2,p3));
! 1078: }
! 1079:
! 1080: /********************************************************************/
! 1081: /** **/
! 1082: /** HEAPSORT **/
! 1083: /** **/
! 1084: /********************************************************************/
! 1085: static GEN vcmp_k;
! 1086: static int vcmp_lk;
! 1087: static int (*vcmp_cmp)(GEN,GEN);
! 1088:
! 1089: int
! 1090: pari_compare_int(int *a,int *b)
! 1091: {
! 1092: return *a - *b;
! 1093: }
! 1094:
! 1095: int
! 1096: pari_compare_long(long *a,long *b)
! 1097: {
! 1098: return *a - *b;
! 1099: }
! 1100:
! 1101: static int
! 1102: veccmp(GEN x, GEN y)
! 1103: {
! 1104: int i,s;
! 1105:
! 1106: for (i=1; i<vcmp_lk; i++)
! 1107: {
! 1108: s = vcmp_cmp((GEN) x[vcmp_k[i]], (GEN) y[vcmp_k[i]]);
! 1109: if (s) return s;
! 1110: }
! 1111: return 0;
! 1112: }
! 1113:
! 1114: static int
! 1115: longcmp(GEN x, GEN y)
! 1116: {
! 1117: return ((long)x > (long)y)? 1: ((x == y)? 0: -1);
! 1118: }
! 1119:
! 1120: /* Sort x = vector of elts, using cmp to compare them.
! 1121: * flag & cmp_IND: indirect sort: return permutation that would sort x
! 1122: * For private use:
! 1123: * flag & cmp_C : as cmp_IND, but return permutation as vector of C-longs
! 1124: */
! 1125: GEN
! 1126: gen_sort(GEN x, int flag, int (*cmp)(GEN,GEN))
! 1127: {
! 1128: long i,j,indxt,ir,l,tx=typ(x),lx=lg(x);
! 1129: GEN q,y,indx;
! 1130:
! 1131: if (!is_matvec_t(tx) && tx != t_VECSMALL) err(typeer,"gen_sort");
! 1132: if (flag & cmp_C) tx = t_VECSMALL;
! 1133: else if (flag & cmp_IND) tx = t_VEC;
! 1134: y = cgetg(lx, tx);
! 1135: if (lx==1) return y;
! 1136: if (lx==2)
! 1137: {
! 1138: if (flag & cmp_C)
! 1139: y[1] = 1;
! 1140: else if (flag & cmp_IND)
! 1141: y[1] = un;
! 1142: else
! 1143: y[1] = lcopy((GEN)x[1]);
! 1144: return y;
! 1145: }
! 1146: if (!cmp) cmp = &longcmp;
! 1147: indx = (GEN) gpmalloc(lx*sizeof(long));
! 1148: for (j=1; j<lx; j++) indx[j]=j;
! 1149:
! 1150: ir=lx-1; l=(ir>>1)+1;
! 1151: for(;;)
! 1152: {
! 1153: if (l>1)
! 1154: { l--; indxt = indx[l]; }
! 1155: else
! 1156: {
! 1157: indxt = indx[ir]; indx[ir]=indx[1]; ir--;
! 1158: if (ir == 1)
! 1159: {
! 1160: indx[1] = indxt;
! 1161: if (flag & cmp_C)
! 1162: for (i=1; i<lx; i++) y[i]=indx[i];
! 1163: else if (flag & cmp_IND)
! 1164: for (i=1; i<lx; i++) y[i]=lstoi(indx[i]);
! 1165: else
! 1166: for (i=1; i<lx; i++) y[i]=lcopy((GEN)x[indx[i]]);
! 1167: free(indx); return y;
! 1168: }
! 1169: }
! 1170: q = (GEN)x[indxt]; i=l;
! 1171: if (flag & cmp_REV)
! 1172: for (j=i<<1; j<=ir; j<<=1)
! 1173: {
! 1174: if (j<ir && cmp((GEN)x[indx[j]],(GEN)x[indx[j+1]]) > 0) j++;
! 1175: if (cmp(q,(GEN)x[indx[j]]) <= 0) break;
! 1176:
! 1177: indx[i]=indx[j]; i=j;
! 1178: }
! 1179: else
! 1180: for (j=i<<1; j<=ir; j<<=1)
! 1181: {
! 1182: if (j<ir && cmp((GEN)x[indx[j]],(GEN)x[indx[j+1]]) < 0) j++;
! 1183: if (cmp(q,(GEN)x[indx[j]]) >= 0) break;
! 1184:
! 1185: indx[i]=indx[j]; i=j;
! 1186: }
! 1187: indx[i]=indxt;
! 1188: }
! 1189: }
! 1190:
! 1191: #define sort_fun(flag) ((flag & cmp_LEX)? &lexcmp: &gcmp)
! 1192:
! 1193: GEN
! 1194: gen_vecsort(GEN x, GEN k, long flag)
! 1195: {
! 1196: long i,j,l,t, lx = lg(x), tmp[2];
! 1197:
! 1198: if (lx<=2) return gen_sort(x,flag,sort_fun(flag));
! 1199: t = typ(k); vcmp_cmp = sort_fun(flag);
! 1200: if (t==t_INT)
! 1201: {
! 1202: tmp[1] = (long)k; k = tmp;
! 1203: vcmp_lk = 2;
! 1204: }
! 1205: else
! 1206: {
! 1207: if (! is_vec_t(t)) err(talker,"incorrect lextype in vecsort");
! 1208: vcmp_lk = lg(k);
! 1209: }
! 1210: l = 0;
! 1211: vcmp_k = (GEN)gpmalloc(vcmp_lk * sizeof(long));
! 1212: for (i=1; i<vcmp_lk; i++)
! 1213: {
! 1214: j = itos((GEN)k[i]);
! 1215: if (j<=0) err(talker,"negative index in vecsort");
! 1216: vcmp_k[i]=j; if (j>l) l=j;
! 1217: }
! 1218: t = typ(x);
! 1219: if (! is_matvec_t(t)) err(typeer,"vecsort");
! 1220: for (j=1; j<lx; j++)
! 1221: {
! 1222: t = typ(x[j]);
! 1223: if (! is_vec_t(t)) err(typeer,"vecsort");
! 1224: if (lg((GEN)x[j]) <= l) err(talker,"index too large in vecsort");
! 1225: }
! 1226: x = gen_sort(x, flag, veccmp);
! 1227: free(vcmp_k); return x;
! 1228: }
! 1229:
! 1230: GEN
! 1231: vecsort0(GEN x, GEN k, long flag)
! 1232: {
! 1233: if (flag < 0 || flag >= cmp_C) err(flagerr,"vecsort");
! 1234: return k? gen_vecsort(x,k,flag): gen_sort(x,flag, sort_fun(flag));
! 1235: }
! 1236:
! 1237: GEN
! 1238: vecsort(GEN x, GEN k)
! 1239: {
! 1240: return gen_vecsort(x,k, 0);
! 1241: }
! 1242:
! 1243: GEN
! 1244: sindexsort(GEN x)
! 1245: {
! 1246: return gen_sort(x, cmp_IND | cmp_C, gcmp);
! 1247: }
! 1248:
! 1249: GEN
! 1250: sindexlexsort(GEN x)
! 1251: {
! 1252: return gen_sort(x, cmp_IND | cmp_C, lexcmp);
! 1253: }
! 1254:
! 1255: GEN
! 1256: indexsort(GEN x)
! 1257: {
! 1258: return gen_sort(x, cmp_IND, gcmp);
! 1259: }
! 1260:
! 1261: GEN
! 1262: indexlexsort(GEN x)
! 1263: {
! 1264: return gen_sort(x, cmp_IND, lexcmp);
! 1265: }
! 1266:
! 1267: GEN
! 1268: sort(GEN x)
! 1269: {
! 1270: return gen_sort(x, 0, gcmp);
! 1271: }
! 1272:
! 1273: GEN
! 1274: lexsort(GEN x)
! 1275: {
! 1276: return gen_sort(x, 0, lexcmp);
! 1277: }
! 1278:
! 1279: /* index of x in table T, 0 otherwise */
! 1280: long
! 1281: tablesearch(GEN T, GEN x, int (*cmp)(GEN,GEN))
! 1282: {
! 1283: long l=1,u=lg(T)-1,i,s;
! 1284:
! 1285: while (u>=l)
! 1286: {
! 1287: i = (l+u)>>1; s = cmp(x,(GEN)T[i]);
! 1288: if (!s) return i;
! 1289: if (s<0) u=i-1; else l=i+1;
! 1290: }
! 1291: return 0;
! 1292: }
! 1293:
! 1294: /* assume lg(x) = lg(y), x,y in Z^n */
! 1295: int
! 1296: cmp_vecint(GEN x, GEN y)
! 1297: {
! 1298: long fl,i, lx = lg(x);
! 1299: for (i=1; i<lx; i++)
! 1300: if (( fl = cmpii((GEN)x[i], (GEN)y[i]) )) return fl;
! 1301: return 0;
! 1302: }
! 1303:
! 1304: /* assume x and y come from the same primedec call (uniformizer unique) */
! 1305: int
! 1306: cmp_prime_over_p(GEN x, GEN y)
! 1307: {
! 1308: int k = mael(x,4,2) - mael(y,4,2); /* diff. between residue degree */
! 1309: return k? ((k > 0)? 1: -1)
! 1310: : cmp_vecint((GEN)x[2], (GEN)y[2]);
! 1311: }
! 1312:
! 1313: int
! 1314: cmp_prime_ideal(GEN x, GEN y)
! 1315: {
! 1316: int k = cmpii((GEN)x[1], (GEN)y[1]);
! 1317: return k? k: cmp_prime_over_p(x,y);
! 1318: }
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