src/float/transcendental/cl_LF_ratseries_q.cc

   1 // eval_rational_series<bool>().
   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/exception.h"
  15 #include "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_q_series_aux (uintC N1, uintC N2,
  26                                const cl_q_series& args,
  27                                cl_I* Q, 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                 *T = 1;
  35                 break;
  36         case 2: {
  37                 *Q = args.qv[N1] * args.qv[N1+1];
  38                 *T = args.qv[N1+1]
  39                    + 1;
  40                 break;
  41                 }
  42         case 3: {
  43                 var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
  44                 *Q = args.qv[N1] * q12;
  45                 *T = q12
  46                    + args.qv[N1+2]
  47                    + 1;
  48                 break;
  49                 }
  50         case 4: {
  51                 var cl_I q23 = args.qv[N1+2] * args.qv[N1+3];
  52                 var cl_I q123 = args.qv[N1+1] * q23;
  53                 *Q = args.qv[N1] * q123;
  54                 *T = q123
  55                    + q23
  56                    + args.qv[N1+3]
  57                    + 1;
  58                 break;
  59                 }
  60         default: {
  61                 var uintC Nm = (N1+N2)/2; // midpoint
  62                 // Compute left part.
  63                 var cl_I LQ, LT;
  64                 eval_q_series_aux(N1,Nm,args,&LQ,&LT);
  65                 // Compute right part.
  66                 var cl_I RQ, RT;
  67                 eval_q_series_aux(Nm,N2,args,&RQ,&RT);
  68                 // Put together partial results.
  69                 *Q = LQ*RQ;
  70                 // S = LS + 1/LQ * RS, so T = RQ*LT + RT.
  71                 *T = RQ*LT + RT;
  72                 break;
  73                 }
  74         }
  75 }
  76
  77 template<>
  78 const cl_LF eval_rational_series<false> (uintC N, const cl_q_series& args, uintC len)
  79 {
  80         if (N==0)
  81                 return cl_I_to_LF(0,len);
  82         var cl_I Q, T;
  83         eval_q_series_aux(0,N,args,&Q,&T);
  84         return cl_I_to_LF(T,len) / cl_I_to_LF(Q,len);
  85 }
  86
  87 static void eval_q_series_aux (uintC N1, uintC N2,
  88                                cl_q_series_stream& args,
  89                                cl_I* Q, cl_I* T)
  90 {
  91         switch (N2 - N1) {
  92         case 0:
  93                 throw runtime_exception(); break;
  94         case 1: {
  95                 var cl_q_series_term v0 = args.next(); // [N1]
  96                 *Q = v0.q;
  97                 *T = 1;
  98                 break;
  99                 }
 100         case 2: {
 101                 var cl_q_series_term v0 = args.next(); // [N1]
 102                 var cl_q_series_term v1 = args.next(); // [N1+1]
 103                 *Q = v0.q * v1.q;
 104                 *T = v1.q + 1;
 105                 break;
 106                 }
 107         case 3: {
 108                 var cl_q_series_term v0 = args.next(); // [N1]
 109                 var cl_q_series_term v1 = args.next(); // [N1+1]
 110                 var cl_q_series_term v2 = args.next(); // [N1+2]
 111                 var cl_I q12 = v1.q * v2.q;
 112                 *Q = v0.q * q12;
 113                 *T = q12 + v2.q + 1;
 114                 break;
 115                 }
 116         case 4: {
 117                 var cl_q_series_term v0 = args.next(); // [N1]
 118                 var cl_q_series_term v1 = args.next(); // [N1+1]
 119                 var cl_q_series_term v2 = args.next(); // [N1+2]
 120                 var cl_q_series_term v3 = args.next(); // [N1+3]
 121                 var cl_I q23 = v2.q * v3.q;
 122                 var cl_I q123 = v1.q * q23;
 123                 *Q = v0.q * q123;
 124                 *T = q123 + q23 + v3.q + 1;
 125                 break;
 126                 }
 127         default: {
 128                 var uintC Nm = (N1+N2)/2; // midpoint
 129                 // Compute left part.
 130                 var cl_I LQ, LT;
 131                 eval_q_series_aux(N1,Nm,args,&LQ,&LT);
 132                 // Compute right part.
 133                 var cl_I RQ, RT;
 134                 eval_q_series_aux(Nm,N2,args,&RQ,&RT);
 135                 // Put together partial results.
 136                 *Q = LQ*RQ;
 137                 // S = LS + 1/LQ * RS, so T = RQ*LT + RT.
 138                 *T = RQ*LT + RT;
 139                 break;
 140                 }
 141         }
 142 }
 143
 144 template<>
 145 const cl_LF eval_rational_series<false> (uintC N, cl_q_series_stream& args, uintC len)
 146 {
 147         if (N==0)
 148                 return cl_I_to_LF(0,len);
 149         var cl_I Q, T;
 150         eval_q_series_aux(0,N,args,&Q,&T);
 151         return cl_I_to_LF(T,len) / cl_I_to_LF(Q,len);
 152 }
 153 // Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):
 154 // O(log(N)^2*M(N)).
 155
 156 }  // namespace cln