1 // eval_rational_series().
7 #include "cl_LF_tran.h"
12 #include "cln/lfloat.h"
13 #include "cln/integer.h"
14 #include "cln/abort.h"
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.
25 static void eval_p_series_aux (uintL N1, uintL N2,
26 const cl_p_series& args,
33 if (P) { *P = args.pv[N1]; }
37 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
44 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
45 var cl_I p012 = p01 * args.pv[N1+2];
53 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
54 var cl_I p012 = p01 * args.pv[N1+2];
55 var cl_I p0123 = p012 * args.pv[N1+3];
56 if (P) { *P = p0123; }
64 var uintL Nm = (N1+N2)/2; // midpoint
67 eval_p_series_aux(N1,Nm,args,&LP,<);
68 // Compute right part.
70 eval_p_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RT);
71 // Put together partial results.
72 if (P) { *P = LP*RP; }
73 // S = LS + LP * RS, so T = LT + LP*RT.
80 const cl_LF eval_rational_series (uintL N, const cl_p_series& args, uintC len)
83 return cl_I_to_LF(0,len);
85 eval_p_series_aux(0,N,args,NULL,&T);
86 return cl_I_to_LF(T,len);
88 // Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):