1 // eval_rational_series().
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_pqab_series_aux (uintC N1, uintC N2,
26 const cl_pqab_series& args,
27 cl_I* P, cl_I* Q, cl_I* B, cl_I* T)
31 throw runtime_exception(); break;
33 if (P) { *P = args.pv[N1]; }
36 *T = args.av[N1] * args.pv[N1];
39 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
41 *Q = args.qv[N1] * args.qv[N1+1];
42 *B = args.bv[N1] * args.bv[N1+1];
43 *T = args.bv[N1+1] * args.qv[N1+1] * args.av[N1] * args.pv[N1]
44 + args.bv[N1] * args.av[N1+1] * p01;
48 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
49 var cl_I p012 = p01 * args.pv[N1+2];
51 var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
52 *Q = args.qv[N1] * q12;
53 var cl_I b12 = args.bv[N1+1] * args.bv[N1+2];
54 *B = args.bv[N1] * b12;
55 *T = b12 * q12 * args.av[N1] * args.pv[N1]
56 + args.bv[N1] * (args.bv[N1+2] * args.qv[N1+2] * args.av[N1+1] * p01
57 + args.bv[N1+1] * args.av[N1+2] * p012);
61 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
62 var cl_I p012 = p01 * args.pv[N1+2];
63 var cl_I p0123 = p012 * args.pv[N1+3];
64 if (P) { *P = p0123; }
65 var cl_I q23 = args.qv[N1+2] * args.qv[N1+3];
66 var cl_I q123 = args.qv[N1+1] * q23;
67 *Q = args.qv[N1] * q123;
68 var cl_I b01 = args.bv[N1] * args.bv[N1+1];
69 var cl_I b23 = args.bv[N1+2] * args.bv[N1+3];
71 *T = b23 * (args.bv[N1+1] * q123 * args.av[N1] * args.pv[N1]
72 + args.bv[N1] * q23 * args.av[N1+1] * p01)
73 + b01 * (args.bv[N1+3] * args.qv[N1+3] * args.av[N1+2] * p012
74 + args.bv[N1+2] * args.av[N1+3] * p0123);
78 var uintC Nm = (N1+N2)/2; // midpoint
80 var cl_I LP, LQ, LB, LT;
81 eval_pqab_series_aux(N1,Nm,args,&LP,&LQ,&LB,<);
82 // Compute right part.
83 var cl_I RP, RQ, RB, RT;
84 eval_pqab_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RB,&RT);
85 // Put together partial results.
86 if (P) { *P = LP*RP; }
89 // S = LS + LP/LQ * RS, so T = RB*RQ*LT + LB*LP*RT.
90 *T = RB*RQ*LT + LB*LP*RT;
96 static void eval_pqsab_series_aux (uintC N1, uintC N2,
97 const cl_pqab_series& args,
98 cl_I* P, cl_I* Q, uintC* QS, cl_I* B, cl_I* T)
102 throw runtime_exception(); break;
104 if (P) { *P = args.pv[N1]; }
108 *T = args.av[N1] * args.pv[N1];
111 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
113 *Q = args.qv[N1] * args.qv[N1+1];
114 *QS = args.qsv[N1] + args.qsv[N1+1];
115 *B = args.bv[N1] * args.bv[N1+1];
116 *T = ((args.bv[N1+1] * args.qv[N1+1] * args.av[N1] * args.pv[N1]) << args.qsv[N1+1])
117 + args.bv[N1] * args.av[N1+1] * p01;
121 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
122 var cl_I p012 = p01 * args.pv[N1+2];
123 if (P) { *P = p012; }
124 var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
125 *Q = args.qv[N1] * q12;
126 *QS = args.qsv[N1] + args.qsv[N1+1] + args.qsv[N1+2];
127 var cl_I b12 = args.bv[N1+1] * args.bv[N1+2];
128 *B = args.bv[N1] * b12;
129 *T = ((b12 * q12 * args.av[N1] * args.pv[N1]) << (args.qsv[N1+1] + args.qsv[N1+2]))
130 + args.bv[N1] * (((args.bv[N1+2] * args.qv[N1+2] * args.av[N1+1] * p01) << args.qsv[N1+2])
131 + args.bv[N1+1] * args.av[N1+2] * p012);
135 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
136 var cl_I p012 = p01 * args.pv[N1+2];
137 var cl_I p0123 = p012 * args.pv[N1+3];
138 if (P) { *P = p0123; }
139 var cl_I q23 = args.qv[N1+2] * args.qv[N1+3];
140 var cl_I q123 = args.qv[N1+1] * q23;
141 *Q = args.qv[N1] * q123;
142 *QS = args.qsv[N1] + args.qsv[N1+1] + args.qsv[N1+2] + args.qsv[N1+3];
143 var cl_I b01 = args.bv[N1] * args.bv[N1+1];
144 var cl_I b23 = args.bv[N1+2] * args.bv[N1+3];
146 *T = ((b23 * (((args.bv[N1+1] * q123 * args.av[N1] * args.pv[N1]) << args.qsv[N1+1])
147 + args.bv[N1] * q23 * args.av[N1+1] * p01)) << (args.qsv[N1+2] + args.qsv[N1+3]))
148 + b01 * (((args.bv[N1+3] * args.qv[N1+3] * args.av[N1+2] * p012) << args.qsv[N1+3])
149 + args.bv[N1+2] * args.av[N1+3] * p0123);
153 var uintC Nm = (N1+N2)/2; // midpoint
154 // Compute left part.
155 var cl_I LP, LQ, LB, LT;
157 eval_pqsab_series_aux(N1,Nm,args,&LP,&LQ,&LQS,&LB,<);
158 // Compute right part.
159 var cl_I RP, RQ, RB, RT;
161 eval_pqsab_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RQS,&RB,&RT);
162 // Put together partial results.
163 if (P) { *P = LP*RP; }
167 // S = LS + LP/LQ * RS, so T = RB*RQ*LT + LB*LP*RT.
168 *T = ((RB*RQ*LT) << RQS) + LB*LP*RT;
174 const cl_LF eval_rational_series (uintC N, const cl_pqab_series& args, uintC len)
177 return cl_I_to_LF(0,len);
180 eval_pqab_series_aux(0,N,args,NULL,&Q,&B,&T);
181 return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
183 // Precomputation of the shift counts:
184 // Split qv[n] into qv[n]*2^qsv[n].
186 var cl_I* qp = args.qv;
187 var uintC* qsp = args.qsv;
188 for (var uintC n = 0; n < N; n++, qp++, qsp++) {
189 // Pull out maximal power of 2 out of *qp = args.qv[n].
201 eval_pqsab_series_aux(0,N,args,NULL,&Q,&QS,&B,&T);
202 return cl_I_to_LF(T,len) / scale_float(cl_I_to_LF(B*Q,len),QS);
205 // Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):