1 // eval_rational_series<bool>().
4 #include "base/cl_sysdep.h"
7 #include "float/transcendental/cl_LF_tran.h"
12 #include "cln/lfloat.h"
13 #include "cln/integer.h"
14 #include "cln/exception.h"
15 #include "float/lfloat/cl_LF.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_q_series_aux (uintC N1, uintC N2,
26 const cl_q_series& args,
31 throw runtime_exception(); break;
37 *Q = args.qv[N1] * args.qv[N1+1];
43 var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
44 *Q = args.qv[N1] * q12;
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;
61 var uintC Nm = (N1+N2)/2; // midpoint
64 eval_q_series_aux(N1,Nm,args,&LQ,<);
65 // Compute right part.
67 eval_q_series_aux(Nm,N2,args,&RQ,&RT);
68 // Put together partial results.
70 // S = LS + 1/LQ * RS, so T = RQ*LT + RT.
78 const cl_LF eval_rational_series<false> (uintC N, const cl_q_series& args, uintC len)
81 return cl_I_to_LF(0,len);
83 eval_q_series_aux(0,N,args,&Q,&T);
84 return cl_I_to_LF(T,len) / cl_I_to_LF(Q,len);
87 static void eval_q_series_aux (uintC N1, uintC N2,
88 cl_q_series_stream& args,
93 throw runtime_exception(); break;
95 var cl_q_series_term v0 = args.next(); // [N1]
101 var cl_q_series_term v0 = args.next(); // [N1]
102 var cl_q_series_term v1 = args.next(); // [N1+1]
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;
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;
124 *T = q123 + q23 + v3.q + 1;
128 var uintC Nm = (N1+N2)/2; // midpoint
129 // Compute left part.
131 eval_q_series_aux(N1,Nm,args,&LQ,<);
132 // Compute right part.
134 eval_q_series_aux(Nm,N2,args,&RQ,&RT);
135 // Put together partial results.
137 // S = LS + 1/LQ * RS, so T = RQ*LT + RT.
145 const cl_LF eval_rational_series<false> (uintC N, cl_q_series_stream& args, uintC len)
148 return cl_I_to_LF(0,len);
150 eval_q_series_aux(0,N,args,&Q,&T);
151 return cl_I_to_LF(T,len) / cl_I_to_LF(Q,len);
153 // Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):