src/float/transcendental/cl_LF_ratseries_pqb.cc

   1 // eval_rational_series<bool>().
   2
   3 // General includes.
   4 #include "base/cl_sysdep.h"
   5
   6 // Specification.
   7 #include "float/transcendental/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 "float/lfloat/cl_LF.h"
  17 #include "base/cl_alloca.h"
  18
  19 namespace cln {
  20
  21 // Subroutine.
  22 // Evaluates S = sum(N1 <= n < N2, a(n)/b(n) * (p(N1)...p(n))/(q(N1)...q(n)))
  23 // and returns P = p(N1)...p(N2-1), Q = q(N1)...q(N2-1), B = B(N1)...B(N2-1)
  24 // and T = B*Q*S (all integers). On entry N1 < N2.
  25 // P will not be computed if a NULL pointer is passed.
  26
  27 static void eval_pqb_series_aux (uintC N1, uintC N2,
  28                                  const cl_pqb_series& args,
  29                                  cl_I* P, cl_I* Q, cl_I* B, cl_I* T)
  30 {
  31         switch (N2 - N1) {
  32         case 0:
  33                 throw runtime_exception(); break;
  34         case 1:
  35                 if (P) { *P = args.pv[N1]; }
  36                 *Q = args.qv[N1];
  37                 *B = args.bv[N1];
  38                 *T = args.pv[N1];
  39                 break;
  40         case 2: {
  41                 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
  42                 if (P) { *P = p01; }
  43                 *Q = args.qv[N1] * args.qv[N1+1];
  44                 *B = args.bv[N1] * args.bv[N1+1];
  45                 *T = args.bv[N1+1] * args.qv[N1+1] * args.pv[N1]
  46                    + args.bv[N1] * p01;
  47                 break;
  48                 }
  49         case 3: {
  50                 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
  51                 var cl_I p012 = p01 * args.pv[N1+2];
  52                 if (P) { *P = p012; }
  53                 var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
  54                 *Q = args.qv[N1] * q12;
  55                 var cl_I b12 = args.bv[N1+1] * args.bv[N1+2];
  56                 *B = args.bv[N1] * b12;
  57                 *T = b12 * q12 * args.pv[N1]
  58                    + args.bv[N1] * (args.bv[N1+2] * args.qv[N1+2] * p01
  59                                     + args.bv[N1+1] * p012);
  60                 break;
  61                 }
  62         case 4: {
  63                 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
  64                 var cl_I p012 = p01 * args.pv[N1+2];
  65                 var cl_I p0123 = p012 * args.pv[N1+3];
  66                 if (P) { *P = p0123; }
  67                 var cl_I q23 = args.qv[N1+2] * args.qv[N1+3];
  68                 var cl_I q123 = args.qv[N1+1] * q23;
  69                 *Q = args.qv[N1] * q123;
  70                 var cl_I b01 = args.bv[N1] * args.bv[N1+1];
  71                 var cl_I b23 = args.bv[N1+2] * args.bv[N1+3];
  72                 *B = b01 * b23;
  73                 *T = b23 * (args.bv[N1+1] * q123 * args.pv[N1]
  74                             + args.bv[N1] * q23 * p01)
  75                    + b01 * (args.bv[N1+3] * args.qv[N1+3] * p012
  76                             + args.bv[N1+2] * p0123);
  77                 break;
  78                 }
  79         default: {
  80                 var uintC Nm = (N1+N2)/2; // midpoint
  81                 // Compute left part.
  82                 var cl_I LP, LQ, LB, LT;
  83                 eval_pqb_series_aux(N1,Nm,args,&LP,&LQ,&LB,&LT);
  84                 // Compute right part.
  85                 var cl_I RP, RQ, RB, RT;
  86                 eval_pqb_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RB,&RT);
  87                 // Put together partial results.
  88                 if (P) { *P = LP*RP; }
  89                 *Q = LQ*RQ;
  90                 *B = LB*RB;
  91                 // S = LS + LP/LQ * RS, so T = RB*RQ*LT + LB*LP*RT.
  92                 *T = RB*RQ*LT + LB*LP*RT;
  93                 break;
  94                 }
  95         }
  96 }
  97
  98 template<>
  99 const cl_LF eval_rational_series<false> (uintC N, const cl_pqb_series& args, uintC len)
 100 {
 101         if (N==0)
 102                 return cl_I_to_LF(0,len);
 103         var cl_I Q, B, T;
 104         eval_pqb_series_aux(0,N,args,NULL,&Q,&B,&T);
 105         return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
 106 }
 107
 108 static void eval_pqsb_series_aux (uintC N1, uintC N2,
 109                                   const cl_pqb_series& args, const uintC* qsv,
 110                                   cl_I* P, cl_I* Q, uintC* QS, cl_I* B, cl_I* T)
 111 {
 112         switch (N2 - N1) {
 113         case 0:
 114                 throw runtime_exception(); break;
 115         case 1:
 116                 if (P) { *P = args.pv[N1]; }
 117                 *Q = args.qv[N1];
 118                 *QS = qsv[N1];
 119                 *B = args.bv[N1];
 120                 *T = args.pv[N1];
 121                 break;
 122         case 2: {
 123                 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
 124                 if (P) { *P = p01; }
 125                 *Q = args.qv[N1] * args.qv[N1+1];
 126                 *QS = qsv[N1] + qsv[N1+1];
 127                 *B = args.bv[N1] * args.bv[N1+1];
 128                 *T = ((args.bv[N1+1] * args.qv[N1+1] * args.pv[N1]) << qsv[N1+1])
 129                    + args.bv[N1] * p01;
 130                 break;
 131                 }
 132         case 3: {
 133                 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
 134                 var cl_I p012 = p01 * args.pv[N1+2];
 135                 if (P) { *P = p012; }
 136                 var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
 137                 *Q = args.qv[N1] * q12;
 138                 *QS = qsv[N1] + qsv[N1+1] + qsv[N1+2];
 139                 var cl_I b12 = args.bv[N1+1] * args.bv[N1+2];
 140                 *B = args.bv[N1] * b12;
 141                 *T = ((b12 * q12 * args.pv[N1]) << (qsv[N1+1] + qsv[N1+2]))
 142                    + args.bv[N1] * (((args.bv[N1+2] * args.qv[N1+2] * p01) << qsv[N1+2])
 143                                     + args.bv[N1+1] * p012);
 144                 break;
 145                 }
 146         case 4: {
 147                 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
 148                 var cl_I p012 = p01 * args.pv[N1+2];
 149                 var cl_I p0123 = p012 * args.pv[N1+3];
 150                 if (P) { *P = p0123; }
 151                 var cl_I q23 = args.qv[N1+2] * args.qv[N1+3];
 152                 var cl_I q123 = args.qv[N1+1] * q23;
 153                 *Q = args.qv[N1] * q123;
 154                 *QS = qsv[N1] + qsv[N1+1] + qsv[N1+2] + qsv[N1+3];
 155                 var cl_I b01 = args.bv[N1] * args.bv[N1+1];
 156                 var cl_I b23 = args.bv[N1+2] * args.bv[N1+3];
 157                 *B = b01 * b23;
 158                 *T = ((b23 * (((args.bv[N1+1] * q123 * args.pv[N1]) << qsv[N1+1])
 159                               + args.bv[N1] * q23 * p01)) << (qsv[N1+2] + qsv[N1+3]))
 160                    + b01 * (((args.bv[N1+3] * args.qv[N1+3] * p012) << qsv[N1+3])
 161                             + args.bv[N1+2] * p0123);
 162                 break;
 163                 }
 164         default: {
 165                 var uintC Nm = (N1+N2)/2; // midpoint
 166                 // Compute left part.
 167                 var cl_I LP, LQ, LB, LT;
 168                 var uintC LQS;
 169                 eval_pqsb_series_aux(N1,Nm,args,qsv,&LP,&LQ,&LQS,&LB,&LT);
 170                 // Compute right part.
 171                 var cl_I RP, RQ, RB, RT;
 172                 var uintC RQS;
 173                 eval_pqsb_series_aux(Nm,N2,args,qsv,(P?&RP:(cl_I*)0),&RQ,&RQS,&RB,&RT);
 174                 // Put together partial results.
 175                 if (P) { *P = LP*RP; }
 176                 *Q = LQ*RQ;
 177                 *QS = LQS+RQS;
 178                 *B = LB*RB;
 179                 // S = LS + LP/LQ * RS, so T = RB*RQ*LT + LB*LP*RT.
 180                 *T = ((RB*RQ*LT) << RQS) + LB*LP*RT;
 181                 break;
 182                 }
 183         }
 184 }
 185
 186 template<>
 187 const cl_LF eval_rational_series<true> (uintC N, const cl_pqb_series& args, uintC len)
 188 {
 189         if (N==0)
 190                 return cl_I_to_LF(0,len);
 191         var cl_I Q, B, T;
 192         // Precomputation of the shift counts:
 193         // Split qv[n] into qv[n]*2^qsv[n].
 194         CL_ALLOCA_STACK;
 195         var uintC* qsv = (uintC*) cl_alloca(N*sizeof(uintC));
 196         var cl_I* qp = args.qv;
 197         var uintC* qsp = qsv;
 198         for (var uintC n = 0; n < N; n++, qp++, qsp++) {
 199                 *qsp = pullout_shiftcount(*qp);
 200         }
 201         // Main computation.
 202         var uintC QS;
 203         eval_pqsb_series_aux(0,N,args,qsv,NULL,&Q,&QS,&B,&T);
 204         return cl_I_to_LF(T,len) / scale_float(cl_I_to_LF(B*Q,len),QS);
 205 }
 206
 207 static void eval_pqb_series_aux (uintC N1, uintC N2,
 208                                  cl_pqb_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_pqb_series_term v0 = args.next(); // [N1]
 216                 if (P) { *P = v0.p; }
 217                 *Q = v0.q;
 218                 *B = v0.b;
 219                 *T = v0.p;
 220                 break;
 221                 }
 222         case 2: {
 223                 var cl_pqb_series_term v0 = args.next(); // [N1]
 224                 var cl_pqb_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.p
 230                    + v0.b * p01;
 231                 break;
 232                 }
 233         case 3: {
 234                 var cl_pqb_series_term v0 = args.next(); // [N1]
 235                 var cl_pqb_series_term v1 = args.next(); // [N1+1]
 236                 var cl_pqb_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.p
 245                    + v0.b * (v2.b * v2.q * p01
 246                              + v1.b * p012);
 247                 break;
 248                 }
 249         case 4: {
 250                 var cl_pqb_series_term v0 = args.next(); // [N1]
 251                 var cl_pqb_series_term v1 = args.next(); // [N1+1]
 252                 var cl_pqb_series_term v2 = args.next(); // [N1+2]
 253                 var cl_pqb_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.p
 265                             + v0.b * q23 * p01)
 266                    + b01 * (v3.b * v3.q * p012
 267                             + v2.b * 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_pqb_series_aux(N1,Nm,args,&LP,&LQ,&LB,&LT);
 275                 // Compute right part.
 276                 var cl_I RP, RQ, RB, RT;
 277                 eval_pqb_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 template<>
 290 const cl_LF eval_rational_series<false> (uintC N, cl_pqb_series_stream& args, uintC len)
 291 {
 292         if (N==0)
 293                 return cl_I_to_LF(0,len);
 294         var cl_I Q, B, T;
 295         eval_pqb_series_aux(0,N,args,NULL,&Q,&B,&T);
 296         return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
 297 }
 298
 299 static void eval_pqb_series_aux (uintC N1, uintC N2,
 300                                  cl_pqb_series_stream& args,
 301                                  cl_R* P, cl_R* Q, cl_R* B, cl_R* T,
 302                                  uintC trunclen)
 303 {
 304         switch (N2 - N1) {
 305         case 0:
 306                 throw runtime_exception(); break;
 307         case 1: {
 308                 var cl_pqb_series_term v0 = args.next(); // [N1]
 309                 if (P) { *P = v0.p; }
 310                 *Q = v0.q;
 311                 *B = v0.b;
 312                 *T = v0.p;
 313                 break;
 314                 }
 315         case 2: {
 316                 var cl_pqb_series_term v0 = args.next(); // [N1]
 317                 var cl_pqb_series_term v1 = args.next(); // [N1+1]
 318                 var cl_I p01 = v0.p * v1.p;
 319                 if (P) { *P = p01; }
 320                 *Q = v0.q * v1.q;
 321                 *B = v0.b * v1.b;
 322                 *T = v1.b * v1.q * v0.p
 323                    + v0.b * p01;
 324                 break;
 325                 }
 326         case 3: {
 327                 var cl_pqb_series_term v0 = args.next(); // [N1]
 328                 var cl_pqb_series_term v1 = args.next(); // [N1+1]
 329                 var cl_pqb_series_term v2 = args.next(); // [N1+2]
 330                 var cl_I p01 = v0.p * v1.p;
 331                 var cl_I p012 = p01 * v2.p;
 332                 if (P) { *P = p012; }
 333                 var cl_I q12 = v1.q * v2.q;
 334                 *Q = v0.q * q12;
 335                 var cl_I b12 = v1.b * v2.b;
 336                 *B = v0.b * b12;
 337                 *T = b12 * q12 * v0.p
 338                    + v0.b * (v2.b * v2.q * p01
 339                              + v1.b * p012);
 340                 break;
 341                 }
 342         case 4: {
 343                 var cl_pqb_series_term v0 = args.next(); // [N1]
 344                 var cl_pqb_series_term v1 = args.next(); // [N1+1]
 345                 var cl_pqb_series_term v2 = args.next(); // [N1+2]
 346                 var cl_pqb_series_term v3 = args.next(); // [N1+3]
 347                 var cl_I p01 = v0.p * v1.p;
 348                 var cl_I p012 = p01 * v2.p;
 349                 var cl_I p0123 = p012 * v3.p;
 350                 if (P) { *P = p0123; }
 351                 var cl_I q23 = v2.q * v3.q;
 352                 var cl_I q123 = v1.q * q23;
 353                 *Q = v0.q * q123;
 354                 var cl_I b01 = v0.b * v1.b;
 355                 var cl_I b23 = v2.b * v3.b;
 356                 *B = b01 * b23;
 357                 *T = b23 * (v1.b * q123 * v0.p
 358                             + v0.b * q23 * p01)
 359                    + b01 * (v3.b * v3.q * p012
 360                             + v2.b * p0123);
 361                 break;
 362                 }
 363         default: {
 364                 var uintC Nm = (N1+N2)/2; // midpoint
 365                 // Compute left part.
 366                 var cl_R LP, LQ, LB, LT;
 367                 eval_pqb_series_aux(N1,Nm,args,&LP,&LQ,&LB,&LT,trunclen);
 368                 // Compute right part.
 369                 var cl_R RP, RQ, RB, RT;
 370                 eval_pqb_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RB,&RT,trunclen);
 371                 // Put together partial results.
 372                 if (P) {
 373                         *P = LP*RP;
 374                         truncate_precision(*P,trunclen);
 375                 }
 376                 *Q = LQ*RQ;
 377                 truncate_precision(*Q,trunclen);
 378                 *B = LB*RB;
 379                 truncate_precision(*B,trunclen);
 380                 // S = LS + LP/LQ * RS, so T = RB*RQ*LT + LB*LP*RT.
 381                 *T = RB*RQ*LT + LB*LP*RT;
 382                 truncate_precision(*T,trunclen);
 383                 break;
 384                 }
 385         }
 386 }
 387
 388 template<>
 389 const cl_LF eval_rational_series<false> (uintC N, cl_pqb_series_stream& args, uintC len, uintC trunclen)
 390 {
 391         if (N==0)
 392                 return cl_I_to_LF(0,len);
 393         var cl_R Q, B, T;
 394         eval_pqb_series_aux(0,N,args,NULL,&Q,&B,&T,trunclen);
 395         return cl_R_to_LF(T,len) / cl_R_to_LF(B*Q,len);
 396 }
 397
 398 // Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):
 399 // O(log(N)^2*M(N)).
 400
 401 }  // namespace cln