src/float/transcendental/cl_LF_ratseries_pqab.cc

   1 // eval_rational_series().
   2
   3 // General includes.
   4 #include "cl_sysdep.h"
   5
   6 // Specification.
   7 #include "cl_LF_tran.h"
   8
   9
  10 // Implementation.
  11
  12 #include "cln/lfloat.h"
  13 #include "cln/integer.h"
  14 #include "cln/real.h"
  15 #include "cln/exception.h"
  16 #include "cl_LF.h"
  17
  18 namespace cln {
  19
  20 // Subroutine.
  21 // Evaluates S = sum(N1 <= n < N2, a(n)/b(n) * (p(N1)...p(n))/(q(N1)...q(n)))
  22 // and returns P = p(N1)...p(N2-1), Q = q(N1)...q(N2-1), B = B(N1)...B(N2-1)
  23 // and T = B*Q*S (all integers). On entry N1 < N2.
  24 // P will not be computed if a NULL pointer is passed.
  25
  26 static void eval_pqab_series_aux (uintC N1, uintC N2,
  27                                   const cl_pqab_series& args,
  28                                   cl_I* P, cl_I* Q, cl_I* B, cl_I* T)
  29 {
  30         switch (N2 - N1) {
  31         case 0:
  32                 throw runtime_exception(); break;
  33         case 1:
  34                 if (P) { *P = args.pv[N1]; }
  35                 *Q = args.qv[N1];
  36                 *B = args.bv[N1];
  37                 *T = args.av[N1] * args.pv[N1];
  38                 break;
  39         case 2: {
  40                 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
  41                 if (P) { *P = p01; }
  42                 *Q = args.qv[N1] * args.qv[N1+1];
  43                 *B = args.bv[N1] * args.bv[N1+1];
  44                 *T = args.bv[N1+1] * args.qv[N1+1] * args.av[N1] * args.pv[N1]
  45                    + args.bv[N1] * args.av[N1+1] * p01;
  46                 break;
  47                 }
  48         case 3: {
  49                 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
  50                 var cl_I p012 = p01 * args.pv[N1+2];
  51                 if (P) { *P = p012; }
  52                 var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
  53                 *Q = args.qv[N1] * q12;
  54                 var cl_I b12 = args.bv[N1+1] * args.bv[N1+2];
  55                 *B = args.bv[N1] * b12;
  56                 *T = b12 * q12 * args.av[N1] * args.pv[N1]
  57                    + args.bv[N1] * (args.bv[N1+2] * args.qv[N1+2] * args.av[N1+1] * p01
  58                                     + args.bv[N1+1] * args.av[N1+2] * p012);
  59                 break;
  60                 }
  61         case 4: {
  62                 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
  63                 var cl_I p012 = p01 * args.pv[N1+2];
  64                 var cl_I p0123 = p012 * args.pv[N1+3];
  65                 if (P) { *P = p0123; }
  66                 var cl_I q23 = args.qv[N1+2] * args.qv[N1+3];
  67                 var cl_I q123 = args.qv[N1+1] * q23;
  68                 *Q = args.qv[N1] * q123;
  69                 var cl_I b01 = args.bv[N1] * args.bv[N1+1];
  70                 var cl_I b23 = args.bv[N1+2] * args.bv[N1+3];
  71                 *B = b01 * b23;
  72                 *T = b23 * (args.bv[N1+1] * q123 * args.av[N1] * args.pv[N1]
  73                             + args.bv[N1] * q23 * args.av[N1+1] * p01)
  74                    + b01 * (args.bv[N1+3] * args.qv[N1+3] * args.av[N1+2] * p012
  75                             + args.bv[N1+2] * args.av[N1+3] * p0123);
  76                 break;
  77                 }
  78         default: {
  79                 var uintC Nm = (N1+N2)/2; // midpoint
  80                 // Compute left part.
  81                 var cl_I LP, LQ, LB, LT;
  82                 eval_pqab_series_aux(N1,Nm,args,&LP,&LQ,&LB,&LT);
  83                 // Compute right part.
  84                 var cl_I RP, RQ, RB, RT;
  85                 eval_pqab_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RB,&RT);
  86                 // Put together partial results.
  87                 if (P) { *P = LP*RP; }
  88                 *Q = LQ*RQ;
  89                 *B = LB*RB;
  90                 // S = LS + LP/LQ * RS, so T = RB*RQ*LT + LB*LP*RT.
  91                 *T = RB*RQ*LT + LB*LP*RT;
  92                 break;
  93                 }
  94         }
  95 }
  96
  97 static void eval_pqsab_series_aux (uintC N1, uintC N2,
  98                                    const cl_pqab_series& args,
  99                                    cl_I* P, cl_I* Q, uintC* QS, cl_I* B, cl_I* T)
 100 {
 101         switch (N2 - N1) {
 102         case 0:
 103                 throw runtime_exception(); break;
 104         case 1:
 105                 if (P) { *P = args.pv[N1]; }
 106                 *Q = args.qv[N1];
 107                 *QS = args.qsv[N1];
 108                 *B = args.bv[N1];
 109                 *T = args.av[N1] * args.pv[N1];
 110                 break;
 111         case 2: {
 112                 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
 113                 if (P) { *P = p01; }
 114                 *Q = args.qv[N1] * args.qv[N1+1];
 115                 *QS = args.qsv[N1] + args.qsv[N1+1];
 116                 *B = args.bv[N1] * args.bv[N1+1];
 117                 *T = ((args.bv[N1+1] * args.qv[N1+1] * args.av[N1] * args.pv[N1]) << args.qsv[N1+1])
 118                    + args.bv[N1] * args.av[N1+1] * p01;
 119                 break;
 120                 }
 121         case 3: {
 122                 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
 123                 var cl_I p012 = p01 * args.pv[N1+2];
 124                 if (P) { *P = p012; }
 125                 var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
 126                 *Q = args.qv[N1] * q12;
 127                 *QS = args.qsv[N1] + args.qsv[N1+1] + args.qsv[N1+2];
 128                 var cl_I b12 = args.bv[N1+1] * args.bv[N1+2];
 129                 *B = args.bv[N1] * b12;
 130                 *T = ((b12 * q12 * args.av[N1] * args.pv[N1]) << (args.qsv[N1+1] + args.qsv[N1+2]))
 131                    + args.bv[N1] * (((args.bv[N1+2] * args.qv[N1+2] * args.av[N1+1] * p01) << args.qsv[N1+2])
 132                                     + args.bv[N1+1] * args.av[N1+2] * p012);
 133                 break;
 134                 }
 135         case 4: {
 136                 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
 137                 var cl_I p012 = p01 * args.pv[N1+2];
 138                 var cl_I p0123 = p012 * args.pv[N1+3];
 139                 if (P) { *P = p0123; }
 140                 var cl_I q23 = args.qv[N1+2] * args.qv[N1+3];
 141                 var cl_I q123 = args.qv[N1+1] * q23;
 142                 *Q = args.qv[N1] * q123;
 143                 *QS = args.qsv[N1] + args.qsv[N1+1] + args.qsv[N1+2] + args.qsv[N1+3];
 144                 var cl_I b01 = args.bv[N1] * args.bv[N1+1];
 145                 var cl_I b23 = args.bv[N1+2] * args.bv[N1+3];
 146                 *B = b01 * b23;
 147                 *T = ((b23 * (((args.bv[N1+1] * q123 * args.av[N1] * args.pv[N1]) << args.qsv[N1+1])
 148                               + args.bv[N1] * q23 * args.av[N1+1] * p01)) << (args.qsv[N1+2] + args.qsv[N1+3]))
 149                    + b01 * (((args.bv[N1+3] * args.qv[N1+3] * args.av[N1+2] * p012) << args.qsv[N1+3])
 150                             + args.bv[N1+2] * args.av[N1+3] * p0123);
 151                 break;
 152                 }
 153         default: {
 154                 var uintC Nm = (N1+N2)/2; // midpoint
 155                 // Compute left part.
 156                 var cl_I LP, LQ, LB, LT;
 157                 var uintC LQS;
 158                 eval_pqsab_series_aux(N1,Nm,args,&LP,&LQ,&LQS,&LB,&LT);
 159                 // Compute right part.
 160                 var cl_I RP, RQ, RB, RT;
 161                 var uintC RQS;
 162                 eval_pqsab_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RQS,&RB,&RT);
 163                 // Put together partial results.
 164                 if (P) { *P = LP*RP; }
 165                 *Q = LQ*RQ;
 166                 *QS = LQS+RQS;
 167                 *B = LB*RB;
 168                 // S = LS + LP/LQ * RS, so T = RB*RQ*LT + LB*LP*RT.
 169                 *T = ((RB*RQ*LT) << RQS) + LB*LP*RT;
 170                 break;
 171                 }
 172         }
 173 }
 174
 175 const cl_LF eval_rational_series (uintC N, const cl_pqab_series& args, uintC len)
 176 {
 177         if (N==0)
 178                 return cl_I_to_LF(0,len);
 179         var cl_I Q, B, T;
 180         if (!args.qsv) {
 181                 eval_pqab_series_aux(0,N,args,NULL,&Q,&B,&T);
 182                 return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
 183         } else {
 184                 // Precomputation of the shift counts:
 185                 // Split qv[n] into qv[n]*2^qsv[n].
 186                 {
 187                         var cl_I* qp = args.qv;
 188                         var uintC* qsp = args.qsv;
 189                         for (var uintC n = 0; n < N; n++, qp++, qsp++) {
 190                                 // Pull out maximal power of 2 out of *qp = args.qv[n].
 191                                 var uintC qs = 0;
 192                                 if (!zerop(*qp)) {
 193                                         qs = ord2(*qp);
 194                                         if (qs > 0)
 195                                                 *qp = *qp >> qs;
 196                                 }
 197                                 *qsp = qs;
 198                         }
 199                 }
 200                 // Main computation.
 201                 var uintC QS;
 202                 eval_pqsab_series_aux(0,N,args,NULL,&Q,&QS,&B,&T);
 203                 return cl_I_to_LF(T,len) / scale_float(cl_I_to_LF(B*Q,len),QS);
 204         }
 205 }
 206
 207 static void eval_pqab_series_aux (uintC N1, uintC N2,
 208                                   cl_pqab_series_stream& args,
 209                                   cl_I* P, cl_I* Q, cl_I* B, cl_I* T)
 210 {
 211         switch (N2 - N1) {
 212         case 0:
 213                 throw runtime_exception(); break;
 214         case 1: {
 215                 var cl_pqab_series_term v0 = args.next(); // [N1]
 216                 if (P) { *P = v0.p; }
 217                 *Q = v0.q;
 218                 *B = v0.b;
 219                 *T = v0.a * v0.p;
 220                 break;
 221                 }
 222         case 2: {
 223                 var cl_pqab_series_term v0 = args.next(); // [N1]
 224                 var cl_pqab_series_term v1 = args.next(); // [N1+1]
 225                 var cl_I p01 = v0.p * v1.p;
 226                 if (P) { *P = p01; }
 227                 *Q = v0.q * v1.q;
 228                 *B = v0.b * v1.b;
 229                 *T = v1.b * v1.q * v0.a * v0.p
 230                    + v0.b * v1.a * p01;
 231                 break;
 232                 }
 233         case 3: {
 234                 var cl_pqab_series_term v0 = args.next(); // [N1]
 235                 var cl_pqab_series_term v1 = args.next(); // [N1+1]
 236                 var cl_pqab_series_term v2 = args.next(); // [N1+2]
 237                 var cl_I p01 = v0.p * v1.p;
 238                 var cl_I p012 = p01 * v2.p;
 239                 if (P) { *P = p012; }
 240                 var cl_I q12 = v1.q * v2.q;
 241                 *Q = v0.q * q12;
 242                 var cl_I b12 = v1.b * v2.b;
 243                 *B = v0.b * b12;
 244                 *T = b12 * q12 * v0.a * v0.p
 245                    + v0.b * (v2.b * v2.q * v1.a * p01
 246                              + v1.b * v2.a * p012);
 247                 break;
 248                 }
 249         case 4: {
 250                 var cl_pqab_series_term v0 = args.next(); // [N1]
 251                 var cl_pqab_series_term v1 = args.next(); // [N1+1]
 252                 var cl_pqab_series_term v2 = args.next(); // [N1+2]
 253                 var cl_pqab_series_term v3 = args.next(); // [N1+3]
 254                 var cl_I p01 = v0.p * v1.p;
 255                 var cl_I p012 = p01 * v2.p;
 256                 var cl_I p0123 = p012 * v3.p;
 257                 if (P) { *P = p0123; }
 258                 var cl_I q23 = v2.q * v3.q;
 259                 var cl_I q123 = v1.q * q23;
 260                 *Q = v0.q * q123;
 261                 var cl_I b01 = v0.b * v1.b;
 262                 var cl_I b23 = v2.b * v3.b;
 263                 *B = b01 * b23;
 264                 *T = b23 * (v1.b * q123 * v0.a * v0.p
 265                             + v0.b * q23 * v1.a * p01)
 266                    + b01 * (v3.b * v3.q * v2.a * p012
 267                             + v2.b * v3.a * p0123);
 268                 break;
 269                 }
 270         default: {
 271                 var uintC Nm = (N1+N2)/2; // midpoint
 272                 // Compute left part.
 273                 var cl_I LP, LQ, LB, LT;
 274                 eval_pqab_series_aux(N1,Nm,args,&LP,&LQ,&LB,&LT);
 275                 // Compute right part.
 276                 var cl_I RP, RQ, RB, RT;
 277                 eval_pqab_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RB,&RT);
 278                 // Put together partial results.
 279                 if (P) { *P = LP*RP; }
 280                 *Q = LQ*RQ;
 281                 *B = LB*RB;
 282                 // S = LS + LP/LQ * RS, so T = RB*RQ*LT + LB*LP*RT.
 283                 *T = RB*RQ*LT + LB*LP*RT;
 284                 break;
 285                 }
 286         }
 287 }
 288
 289 const cl_LF eval_rational_series (uintC N, cl_pqab_series_stream& args, uintC len)
 290 {
 291         if (N==0)
 292                 return cl_I_to_LF(0,len);
 293         var cl_I Q, B, T;
 294         eval_pqab_series_aux(0,N,args,NULL,&Q,&B,&T);
 295         return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
 296 }
 297
 298 static void eval_pqab_series_aux (uintC N1, uintC N2,
 299                                   cl_pqab_series_stream& args,
 300                                   cl_R* P, cl_R* Q, cl_R* B, cl_R* T,
 301                                   uintC trunclen)
 302 {
 303         switch (N2 - N1) {
 304         case 0:
 305                 throw runtime_exception(); break;
 306         case 1: {
 307                 var cl_pqab_series_term v0 = args.next(); // [N1]
 308                 if (P) { *P = v0.p; }
 309                 *Q = v0.q;
 310                 *B = v0.b;
 311                 *T = v0.a * v0.p;
 312                 break;
 313                 }
 314         case 2: {
 315                 var cl_pqab_series_term v0 = args.next(); // [N1]
 316                 var cl_pqab_series_term v1 = args.next(); // [N1+1]
 317                 var cl_I p01 = v0.p * v1.p;
 318                 if (P) { *P = p01; }
 319                 *Q = v0.q * v1.q;
 320                 *B = v0.b * v1.b;
 321                 *T = v1.b * v1.q * v0.a * v0.p
 322                    + v0.b * v1.a * p01;
 323                 break;
 324                 }
 325         case 3: {
 326                 var cl_pqab_series_term v0 = args.next(); // [N1]
 327                 var cl_pqab_series_term v1 = args.next(); // [N1+1]
 328                 var cl_pqab_series_term v2 = args.next(); // [N1+2]
 329                 var cl_I p01 = v0.p * v1.p;
 330                 var cl_I p012 = p01 * v2.p;
 331                 if (P) { *P = p012; }
 332                 var cl_I q12 = v1.q * v2.q;
 333                 *Q = v0.q * q12;
 334                 var cl_I b12 = v1.b * v2.b;
 335                 *B = v0.b * b12;
 336                 *T = b12 * q12 * v0.a * v0.p
 337                    + v0.b * (v2.b * v2.q * v1.a * p01
 338                              + v1.b * v2.a * p012);
 339                 break;
 340                 }
 341         case 4: {
 342                 var cl_pqab_series_term v0 = args.next(); // [N1]
 343                 var cl_pqab_series_term v1 = args.next(); // [N1+1]
 344                 var cl_pqab_series_term v2 = args.next(); // [N1+2]
 345                 var cl_pqab_series_term v3 = args.next(); // [N1+3]
 346                 var cl_I p01 = v0.p * v1.p;
 347                 var cl_I p012 = p01 * v2.p;
 348                 var cl_I p0123 = p012 * v3.p;
 349                 if (P) { *P = p0123; }
 350                 var cl_I q23 = v2.q * v3.q;
 351                 var cl_I q123 = v1.q * q23;
 352                 *Q = v0.q * q123;
 353                 var cl_I b01 = v0.b * v1.b;
 354                 var cl_I b23 = v2.b * v3.b;
 355                 *B = b01 * b23;
 356                 *T = b23 * (v1.b * q123 * v0.a * v0.p
 357                             + v0.b * q23 * v1.a * p01)
 358                    + b01 * (v3.b * v3.q * v2.a * p012
 359                             + v2.b * v3.a * p0123);
 360                 break;
 361                 }
 362         default: {
 363                 var uintC Nm = (N1+N2)/2; // midpoint
 364                 // Compute left part.
 365                 var cl_R LP, LQ, LB, LT;
 366                 eval_pqab_series_aux(N1,Nm,args,&LP,&LQ,&LB,&LT,trunclen);
 367                 // Compute right part.
 368                 var cl_R RP, RQ, RB, RT;
 369                 eval_pqab_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RB,&RT,trunclen);
 370                 // Put together partial results.
 371                 if (P) {
 372                         *P = LP*RP;
 373                         truncate_precision(*P,trunclen);
 374                 }
 375                 *Q = LQ*RQ;
 376                 truncate_precision(*Q,trunclen);
 377                 *B = LB*RB;
 378                 truncate_precision(*B,trunclen);
 379                 // S = LS + LP/LQ * RS, so T = RB*RQ*LT + LB*LP*RT.
 380                 *T = RB*RQ*LT + LB*LP*RT;
 381                 truncate_precision(*T,trunclen);
 382                 break;
 383                 }
 384         }
 385 }
 386
 387 const cl_LF eval_rational_series (uintC N, cl_pqab_series_stream& args, uintC len, uintC trunclen)
 388 {
 389         if (N==0)
 390                 return cl_I_to_LF(0,len);
 391         var cl_R Q, B, T;
 392         eval_pqab_series_aux(0,N,args,NULL,&Q,&B,&T,trunclen);
 393         return cl_R_to_LF(T,len) / cl_R_to_LF(B*Q,len);
 394 }
 395 // Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):
 396 // O(log(N)^2*M(N)).
 397
 398 }  // namespace cln