1 // eval_rational_series().
7 #include "cl_LF_tran.h"
12 #include "cl_lfloat.h"
13 #include "cl_integer.h"
18 // Evaluates S = sum(N1 <= n < N2, a(n)/b(n) * (p(N1)...p(n))/(q(N1)...q(n)))
19 // and returns P = p(N1)...p(N2-1), Q = q(N1)...q(N2-1), B = B(N1)...B(N2-1)
20 // and T = B*Q*S (all integers). On entry N1 < N2.
21 // P will not be computed if a NULL pointer is passed.
23 static void eval_pa_series_aux (uintL N1, uintL N2,
24 const cl_pa_series& args,
31 if (P) { *P = args.pv[N1]; }
32 *T = args.av[N1] * args.pv[N1];
35 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
37 *T = args.av[N1] * args.pv[N1]
38 + args.av[N1+1] * p01;
42 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
43 var cl_I p012 = p01 * args.pv[N1+2];
45 *T = args.av[N1] * args.pv[N1]
47 + args.av[N1+2] * p012;
51 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
52 var cl_I p012 = p01 * args.pv[N1+2];
53 var cl_I p0123 = p012 * args.pv[N1+3];
54 if (P) { *P = p0123; }
55 *T = args.av[N1] * args.pv[N1]
57 + args.av[N1+2] * p012
58 + args.av[N1+3] * p0123;
62 var uintL Nm = (N1+N2)/2; // midpoint
65 eval_pa_series_aux(N1,Nm,args,&LP,<);
66 // Compute right part.
68 eval_pa_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RT);
69 // Put together partial results.
70 if (P) { *P = LP*RP; }
71 // S = LS + LP * RS, so T = LT + LP*RT.
78 const cl_LF eval_rational_series (uintL N, const cl_pa_series& args, uintC len)
81 return cl_I_to_LF(0,len);
83 eval_pa_series_aux(0,N,args,NULL,&T);
84 return cl_I_to_LF(T,len);
86 // Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):