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_pqb_series_aux (uintL N1, uintL N2,
24 const cl_pqb_series& args,
25 cl_I* P, cl_I* Q, cl_I* B, cl_I* T)
31 if (P) { *P = args.pv[N1]; }
37 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
39 *Q = args.qv[N1] * args.qv[N1+1];
40 *B = args.bv[N1] * args.bv[N1+1];
41 *T = args.bv[N1+1] * args.qv[N1+1] * args.pv[N1]
46 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
47 var cl_I p012 = p01 * args.pv[N1+2];
49 var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
50 *Q = args.qv[N1] * q12;
51 var cl_I b12 = args.bv[N1+1] * args.bv[N1+2];
52 *B = args.bv[N1] * b12;
53 *T = b12 * q12 * args.pv[N1]
54 + args.bv[N1] * (args.bv[N1+2] * args.qv[N1+2] * p01
55 + args.bv[N1+1] * p012);
59 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
60 var cl_I p012 = p01 * args.pv[N1+2];
61 var cl_I p0123 = p012 * args.pv[N1+3];
62 if (P) { *P = p0123; }
63 var cl_I q23 = args.qv[N1+2] * args.qv[N1+3];
64 var cl_I q123 = args.qv[N1+1] * q23;
65 *Q = args.qv[N1] * q123;
66 var cl_I b01 = args.bv[N1] * args.bv[N1+1];
67 var cl_I b23 = args.bv[N1+2] * args.bv[N1+3];
69 *T = b23 * (args.bv[N1+1] * q123 * args.pv[N1]
70 + args.bv[N1] * q23 * p01)
71 + b01 * (args.bv[N1+3] * args.qv[N1+3] * p012
72 + args.bv[N1+2] * p0123);
76 var uintL Nm = (N1+N2)/2; // midpoint
78 var cl_I LP, LQ, LB, LT;
79 eval_pqb_series_aux(N1,Nm,args,&LP,&LQ,&LB,<);
80 // Compute right part.
81 var cl_I RP, RQ, RB, RT;
82 eval_pqb_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RB,&RT);
83 // Put together partial results.
84 if (P) { *P = LP*RP; }
87 // S = LS + LP/LQ * RS, so T = RB*RQ*LT + LB*LP*RT.
88 *T = RB*RQ*LT + LB*LP*RT;
94 static void eval_pqsb_series_aux (uintL N1, uintL N2,
95 const cl_pqb_series& args,
96 cl_I* P, cl_I* Q, uintL* QS, cl_I* B, cl_I* T)
102 if (P) { *P = args.pv[N1]; }
109 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
111 *Q = args.qv[N1] * args.qv[N1+1];
112 *QS = args.qsv[N1] + args.qsv[N1+1];
113 *B = args.bv[N1] * args.bv[N1+1];
114 *T = ((args.bv[N1+1] * args.qv[N1+1] * args.pv[N1]) << args.qsv[N1+1])
119 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
120 var cl_I p012 = p01 * args.pv[N1+2];
121 if (P) { *P = p012; }
122 var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
123 *Q = args.qv[N1] * q12;
124 *QS = args.qsv[N1] + args.qsv[N1+1] + args.qsv[N1+2];
125 var cl_I b12 = args.bv[N1+1] * args.bv[N1+2];
126 *B = args.bv[N1] * b12;
127 *T = ((b12 * q12 * args.pv[N1]) << (args.qsv[N1+1] + args.qsv[N1+2]))
128 + args.bv[N1] * (((args.bv[N1+2] * args.qv[N1+2] * p01) << args.qsv[N1+2])
129 + args.bv[N1+1] * p012);
133 var cl_I p01 = args.pv[N1] * args.pv[N1+1];
134 var cl_I p012 = p01 * args.pv[N1+2];
135 var cl_I p0123 = p012 * args.pv[N1+3];
136 if (P) { *P = p0123; }
137 var cl_I q23 = args.qv[N1+2] * args.qv[N1+3];
138 var cl_I q123 = args.qv[N1+1] * q23;
139 *Q = args.qv[N1] * q123;
140 *QS = args.qsv[N1] + args.qsv[N1+1] + args.qsv[N1+2] + args.qsv[N1+3];
141 var cl_I b01 = args.bv[N1] * args.bv[N1+1];
142 var cl_I b23 = args.bv[N1+2] * args.bv[N1+3];
144 *T = ((b23 * (((args.bv[N1+1] * q123 * args.pv[N1]) << args.qsv[N1+1])
145 + args.bv[N1] * q23 * p01)) << (args.qsv[N1+2] + args.qsv[N1+3]))
146 + b01 * (((args.bv[N1+3] * args.qv[N1+3] * p012) << args.qsv[N1+3])
147 + args.bv[N1+2] * p0123);
151 var uintL Nm = (N1+N2)/2; // midpoint
152 // Compute left part.
153 var cl_I LP, LQ, LB, LT;
155 eval_pqsb_series_aux(N1,Nm,args,&LP,&LQ,&LQS,&LB,<);
156 // Compute right part.
157 var cl_I RP, RQ, RB, RT;
159 eval_pqsb_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RQS,&RB,&RT);
160 // Put together partial results.
161 if (P) { *P = LP*RP; }
165 // S = LS + LP/LQ * RS, so T = RB*RQ*LT + LB*LP*RT.
166 *T = ((RB*RQ*LT) << RQS) + LB*LP*RT;
172 const cl_LF eval_rational_series (uintL N, const cl_pqb_series& args, uintC len)
175 return cl_I_to_LF(0,len);
178 eval_pqb_series_aux(0,N,args,NULL,&Q,&B,&T);
179 return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
181 // Precomputation of the shift counts:
182 // Split qv[n] into qv[n]*2^qsv[n].
184 var cl_I* qp = args.qv;
185 var uintL* qsp = args.qsv;
186 for (var uintL n = 0; n < N; n++, qp++, qsp++) {
187 // Pull out maximal power of 2 out of *qp = args.qv[n].
199 eval_pqsb_series_aux(0,N,args,NULL,&Q,&QS,&B,&T);
200 return cl_I_to_LF(T,len) / scale_float(cl_I_to_LF(B*Q,len),QS);
203 // Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):