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_qab_series_aux (uintL N1, uintL N2,
26 const cl_qab_series& args,
27 cl_I* Q, cl_I* B, cl_I* T)
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] * args.av[N1]
41 + args.bv[N1] * args.av[N1+1];
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 * args.av[N1]
50 + args.bv[N1] * (args.bv[N1+2] * args.qv[N1+2] * args.av[N1+1]
51 + args.bv[N1+1] * args.av[N1+2]);
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];
61 *T = b23 * (args.bv[N1+1] * q123 * args.av[N1]
62 + args.bv[N1] * q23 * args.av[N1+1])
63 + b01 * (args.bv[N1+3] * args.qv[N1+3] * args.av[N1+2]
64 + args.bv[N1+2] * args.av[N1+3]);
68 var uintL Nm = (N1+N2)/2; // midpoint
71 eval_qab_series_aux(N1,Nm,args,&LQ,&LB,<);
72 // Compute right part.
74 eval_qab_series_aux(Nm,N2,args,&RQ,&RB,&RT);
75 // Put together partial results.
78 // S = LS + 1/LQ * RS, so T = RB*RQ*LT + LB*RT.
79 *T = RB*RQ*LT + LB*RT;
85 const cl_LF eval_rational_series (uintL N, const cl_qab_series& args, uintC len)
88 return cl_I_to_LF(0,len);
90 eval_qab_series_aux(0,N,args,&Q,&B,&T);
91 return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
93 // Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):