1 // eval_rational_series<bool>().
7 #include "cl_LF_tran.h"
12 #include "cln/lfloat.h"
13 #include "cln/integer.h"
14 #include "cln/exception.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_qb_series_aux (uintC N1, uintC N2,
26 const cl_qb_series& args,
27 cl_I* Q, cl_I* B, cl_I* T)
31 throw runtime_exception(); break;
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]
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;
50 + args.bv[N1] * (args.bv[N1+2] * args.qv[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
63 + b01 * (args.bv[N1+3] * args.qv[N1+3]
68 var uintC Nm = (N1+N2)/2; // midpoint
71 eval_qb_series_aux(N1,Nm,args,&LQ,&LB,<);
72 // Compute right part.
74 eval_qb_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;
86 const cl_LF eval_rational_series<false> (uintC N, const cl_qb_series& args, uintC len)
89 return cl_I_to_LF(0,len);
91 eval_qb_series_aux(0,N,args,&Q,&B,&T);
92 return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
95 static void eval_qb_series_aux (uintC N1, uintC N2,
96 cl_qb_series_stream& args,
97 cl_I* Q, cl_I* B, cl_I* T)
101 throw runtime_exception(); break;
103 var cl_qb_series_term v0 = args.next(); // [N1]
110 var cl_qb_series_term v0 = args.next(); // [N1]
111 var cl_qb_series_term v1 = args.next(); // [N1+1]
114 *T = v1.b * v1.q + v0.b;
118 var cl_qb_series_term v0 = args.next(); // [N1]
119 var cl_qb_series_term v1 = args.next(); // [N1+1]
120 var cl_qb_series_term v2 = args.next(); // [N1+2]
121 var cl_I q12 = v1.q * v2.q;
123 var cl_I b12 = v1.b * v2.b;
125 *T = b12 * q12 + v0.b * (v2.b * v2.q + v1.b);
129 var cl_qb_series_term v0 = args.next(); // [N1]
130 var cl_qb_series_term v1 = args.next(); // [N1+1]
131 var cl_qb_series_term v2 = args.next(); // [N1+2]
132 var cl_qb_series_term v3 = args.next(); // [N1+3]
133 var cl_I q23 = v2.q * v3.q;
134 var cl_I q123 = v1.q * q23;
136 var cl_I b01 = v0.b * v1.b;
137 var cl_I b23 = v2.b * v3.b;
139 *T = b23 * (v1.b * q123 + v0.b * q23)
140 + b01 * (v3.b * v3.q + v2.b);
144 var uintC Nm = (N1+N2)/2; // midpoint
145 // Compute left part.
147 eval_qb_series_aux(N1,Nm,args,&LQ,&LB,<);
148 // Compute right part.
150 eval_qb_series_aux(Nm,N2,args,&RQ,&RB,&RT);
151 // Put together partial results.
154 // S = LS + 1/LQ * RS, so T = RB*RQ*LT + LB*RT.
155 *T = RB*RQ*LT + LB*RT;
162 const cl_LF eval_rational_series<false> (uintC N, cl_qb_series_stream& args, uintC len)
165 return cl_I_to_LF(0,len);
167 eval_qb_series_aux(0,N,args,&Q,&B,&T);
168 return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
171 // Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):