src/float/transcendental/cl_LF_ratseries_qb.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/exception.h"
  15 #include "float/lfloat/cl_LF.h"
  16
  17 namespace cln {
  18
  19 // Subroutine.
  20 // Evaluates S = sum(N1 <= n < N2, a(n)/b(n) * (p(N1)...p(n))/(q(N1)...q(n)))
  21 // and returns P = p(N1)...p(N2-1), Q = q(N1)...q(N2-1), B = B(N1)...B(N2-1)
  22 // and T = B*Q*S (all integers). On entry N1 < N2.
  23 // P will not be computed if a NULL pointer is passed.
  24
  25 static void eval_qb_series_aux (uintC N1, uintC N2,
  26                                 const cl_qb_series& args,
  27                                 cl_I* Q, cl_I* B, cl_I* T)
  28 {
  29         switch (N2 - N1) {
  30         case 0:
  31                 throw runtime_exception(); break;
  32         case 1:
  33                 *Q = args.qv[N1];
  34                 *B = args.bv[N1];
  35                 *T = 1;
  36                 break;
  37         case 2: {
  38                 *Q = args.qv[N1] * args.qv[N1+1];
  39                 *B = args.bv[N1] * args.bv[N1+1];
  40                 *T = args.bv[N1+1] * args.qv[N1+1]
  41                    + args.bv[N1];
  42                 break;
  43                 }
  44         case 3: {
  45                 var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
  46                 *Q = args.qv[N1] * q12;
  47                 var cl_I b12 = args.bv[N1+1] * args.bv[N1+2];
  48                 *B = args.bv[N1] * b12;
  49                 *T = b12 * q12
  50                    + args.bv[N1] * (args.bv[N1+2] * args.qv[N1+2]
  51                                     + args.bv[N1+1]);
  52                 break;
  53                 }
  54         case 4: {
  55                 var cl_I q23 = args.qv[N1+2] * args.qv[N1+3];
  56                 var cl_I q123 = args.qv[N1+1] * q23;
  57                 *Q = args.qv[N1] * q123;
  58                 var cl_I b01 = args.bv[N1] * args.bv[N1+1];
  59                 var cl_I b23 = args.bv[N1+2] * args.bv[N1+3];
  60                 *B = b01 * b23;
  61                 *T = b23 * (args.bv[N1+1] * q123
  62                             + args.bv[N1] * q23)
  63                    + b01 * (args.bv[N1+3] * args.qv[N1+3]
  64                             + args.bv[N1+2]);
  65                 break;
  66                 }
  67         default: {
  68                 var uintC Nm = (N1+N2)/2; // midpoint
  69                 // Compute left part.
  70                 var cl_I LQ, LB, LT;
  71                 eval_qb_series_aux(N1,Nm,args,&LQ,&LB,&LT);
  72                 // Compute right part.
  73                 var cl_I RQ, RB, RT;
  74                 eval_qb_series_aux(Nm,N2,args,&RQ,&RB,&RT);
  75                 // Put together partial results.
  76                 *Q = LQ*RQ;
  77                 *B = LB*RB;
  78                 // S = LS + 1/LQ * RS, so T = RB*RQ*LT + LB*RT.
  79                 *T = RB*RQ*LT + LB*RT;
  80                 break;
  81                 }
  82         }
  83 }
  84
  85 template<>
  86 const cl_LF eval_rational_series<false> (uintC N, const cl_qb_series& args, uintC len)
  87 {
  88         if (N==0)
  89                 return cl_I_to_LF(0,len);
  90         var cl_I Q, B, T;
  91         eval_qb_series_aux(0,N,args,&Q,&B,&T);
  92         return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
  93 }
  94
  95 static void eval_qb_series_aux (uintC N1, uintC N2,
  96                                 cl_qb_series_stream& args,
  97                                 cl_I* Q, cl_I* B, cl_I* T)
  98 {
  99         switch (N2 - N1) {
 100         case 0:
 101                 throw runtime_exception(); break;
 102         case 1: {
 103                 var cl_qb_series_term v0 = args.next(); // [N1]
 104                 *Q = v0.q;
 105                 *B = v0.b;
 106                 *T = 1;
 107                 break;
 108                 }
 109         case 2: {
 110                 var cl_qb_series_term v0 = args.next(); // [N1]
 111                 var cl_qb_series_term v1 = args.next(); // [N1+1]
 112                 *Q = v0.q * v1.q;
 113                 *B = v0.b * v1.b;
 114                 *T = v1.b * v1.q + v0.b;
 115                 break;
 116                 }
 117         case 3: {
 118                 var cl_qb_series_term v0 = args.next(); // [N1]
 119                 var cl_qb_series_term v1 = args.next(); // [N1+1]
 120                 var cl_qb_series_term v2 = args.next(); // [N1+2]
 121                 var cl_I q12 = v1.q * v2.q;
 122                 *Q = v0.q * q12;
 123                 var cl_I b12 = v1.b * v2.b;
 124                 *B = v0.b * b12;
 125                 *T = b12 * q12 + v0.b * (v2.b * v2.q + v1.b);
 126                 break;
 127                 }
 128         case 4: {
 129                 var cl_qb_series_term v0 = args.next(); // [N1]
 130                 var cl_qb_series_term v1 = args.next(); // [N1+1]
 131                 var cl_qb_series_term v2 = args.next(); // [N1+2]
 132                 var cl_qb_series_term v3 = args.next(); // [N1+3]
 133                 var cl_I q23 = v2.q * v3.q;
 134                 var cl_I q123 = v1.q * q23;
 135                 *Q = v0.q * q123;
 136                 var cl_I b01 = v0.b * v1.b;
 137                 var cl_I b23 = v2.b * v3.b;
 138                 *B = b01 * b23;
 139                 *T = b23 * (v1.b * q123 + v0.b * q23)
 140                    + b01 * (v3.b * v3.q + v2.b);
 141                 break;
 142                 }
 143         default: {
 144                 var uintC Nm = (N1+N2)/2; // midpoint
 145                 // Compute left part.
 146                 var cl_I LQ, LB, LT;
 147                 eval_qb_series_aux(N1,Nm,args,&LQ,&LB,&LT);
 148                 // Compute right part.
 149                 var cl_I RQ, RB, RT;
 150                 eval_qb_series_aux(Nm,N2,args,&RQ,&RB,&RT);
 151                 // Put together partial results.
 152                 *Q = LQ*RQ;
 153                 *B = LB*RB;
 154                 // S = LS + 1/LQ * RS, so T = RB*RQ*LT + LB*RT.
 155                 *T = RB*RQ*LT + LB*RT;
 156                 break;
 157                 }
 158         }
 159 }
 160
 161 template<>
 162 const cl_LF eval_rational_series<false> (uintC N, cl_qb_series_stream& args, uintC len)
 163 {
 164         if (N==0)
 165                 return cl_I_to_LF(0,len);
 166         var cl_I Q, B, T;
 167         eval_qb_series_aux(0,N,args,&Q,&B,&T);
 168         return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
 169 }
 170
 171 // Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):
 172 // O(log(N)^2*M(N)).
 173
 174 }  // namespace cln