+
+static void eval_pq_series_aux (uintC N1, uintC N2,
+ cl_pq_series_stream& args,
+ cl_I* P, cl_I* Q, cl_I* T)
+{
+ switch (N2 - N1) {
+ case 0:
+ throw runtime_exception(); break;
+ case 1: {
+ var cl_pq_series_term v0 = args.next(); // [N1]
+ if (P) { *P = v0.p; }
+ *Q = v0.q;
+ *T = v0.p;
+ break;
+ }
+ case 2: {
+ var cl_pq_series_term v0 = args.next(); // [N1]
+ var cl_pq_series_term v1 = args.next(); // [N1+1]
+ var cl_I p01 = v0.p * v1.p;
+ if (P) { *P = p01; }
+ *Q = v0.q * v1.q;
+ *T = v1.q * v0.p
+ + p01;
+ break;
+ }
+ case 3: {
+ var cl_pq_series_term v0 = args.next(); // [N1]
+ var cl_pq_series_term v1 = args.next(); // [N1+1]
+ var cl_pq_series_term v2 = args.next(); // [N1+2]
+ var cl_I p01 = v0.p * v1.p;
+ var cl_I p012 = p01 * v2.p;
+ if (P) { *P = p012; }
+ var cl_I q12 = v1.q * v2.q;
+ *Q = v0.q * q12;
+ *T = q12 * v0.p
+ + v2.q * p01
+ + p012;
+ break;
+ }
+ case 4: {
+ var cl_pq_series_term v0 = args.next(); // [N1]
+ var cl_pq_series_term v1 = args.next(); // [N1+1]
+ var cl_pq_series_term v2 = args.next(); // [N1+2]
+ var cl_pq_series_term v3 = args.next(); // [N1+3]
+ var cl_I p01 = v0.p * v1.p;
+ var cl_I p012 = p01 * v2.p;
+ var cl_I p0123 = p012 * v3.p;
+ if (P) { *P = p0123; }
+ var cl_I q23 = v2.q * v3.q;
+ var cl_I q123 = v1.q * q23;
+ *Q = v0.q * q123;
+ *T = q123 * v0.p
+ + q23 * p01
+ + v3.q * p012
+ + p0123;
+ break;
+ }
+ default: {
+ var uintC Nm = (N1+N2)/2; // midpoint
+ // Compute left part.
+ var cl_I LP, LQ, LT;
+ eval_pq_series_aux(N1,Nm,args,&LP,&LQ,<);
+ // Compute right part.
+ var cl_I RP, RQ, RT;
+ eval_pq_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RT);
+ // Put together partial results.
+ if (P) { *P = LP*RP; }
+ *Q = LQ*RQ;
+ // S = LS + LP/LQ * RS, so T = RQ*LT + LP*RT.
+ *T = RQ*LT + LP*RT;
+ break;
+ }
+ }
+}
+
+const cl_LF eval_rational_series (uintC N, cl_pq_series_stream& args, uintC len)
+{
+ if (N==0)
+ return cl_I_to_LF(0,len);
+ var cl_I Q, T;
+ eval_pq_series_aux(0,N,args,NULL,&Q,&T);
+ return cl_I_to_LF(T,len) / cl_I_to_LF(Q,len);
+}
+
+static void eval_pq_series_aux (uintC N1, uintC N2,
+ cl_pq_series_stream& args,
+ cl_R* P, cl_R* Q, cl_R* T,
+ uintC trunclen)
+{
+ switch (N2 - N1) {
+ case 0:
+ throw runtime_exception(); break;
+ case 1: {
+ var cl_pq_series_term v0 = args.next(); // [N1]
+ if (P) { *P = v0.p; }
+ *Q = v0.q;
+ *T = v0.p;
+ break;
+ }
+ case 2: {
+ var cl_pq_series_term v0 = args.next(); // [N1]
+ var cl_pq_series_term v1 = args.next(); // [N1+1]
+ var cl_I p01 = v0.p * v1.p;
+ if (P) { *P = p01; }
+ *Q = v0.q * v1.q;
+ *T = v1.q * v0.p
+ + p01;
+ break;
+ }
+ case 3: {
+ var cl_pq_series_term v0 = args.next(); // [N1]
+ var cl_pq_series_term v1 = args.next(); // [N1+1]
+ var cl_pq_series_term v2 = args.next(); // [N1+2]
+ var cl_I p01 = v0.p * v1.p;
+ var cl_I p012 = p01 * v2.p;
+ if (P) { *P = p012; }
+ var cl_I q12 = v1.q * v2.q;
+ *Q = v0.q * q12;
+ *T = q12 * v0.p
+ + v2.q * p01
+ + p012;
+ break;
+ }
+ case 4: {
+ var cl_pq_series_term v0 = args.next(); // [N1]
+ var cl_pq_series_term v1 = args.next(); // [N1+1]
+ var cl_pq_series_term v2 = args.next(); // [N1+2]
+ var cl_pq_series_term v3 = args.next(); // [N1+3]
+ var cl_I p01 = v0.p * v1.p;
+ var cl_I p012 = p01 * v2.p;
+ var cl_I p0123 = p012 * v3.p;
+ if (P) { *P = p0123; }
+ var cl_I q23 = v2.q * v3.q;
+ var cl_I q123 = v1.q * q23;
+ *Q = v0.q * q123;
+ *T = q123 * v0.p
+ + q23 * p01
+ + v3.q * p012
+ + p0123;
+ break;
+ }
+ default: {
+ var uintC Nm = (N1+N2)/2; // midpoint
+ // Compute left part.
+ var cl_R LP, LQ, LT;
+ eval_pq_series_aux(N1,Nm,args,&LP,&LQ,<,trunclen);
+ // Compute right part.
+ var cl_R RP, RQ, RT;
+ eval_pq_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RT,trunclen);
+ // Put together partial results.
+ if (P) {
+ *P = LP*RP;
+ truncate_precision(*P,trunclen);
+ }
+ *Q = LQ*RQ;
+ truncate_precision(*Q,trunclen);
+ // S = LS + LP/LQ * RS, so T = RQ*LT + LP*RT.
+ *T = RQ*LT + LP*RT;
+ truncate_precision(*T,trunclen);
+ break;
+ }
+ }
+}
+
+const cl_LF eval_rational_series (uintC N, cl_pq_series_stream& args, uintC len, uintC trunclen)
+{
+ if (N==0)
+ return cl_I_to_LF(0,len);
+ var cl_R Q, T;
+ eval_pq_series_aux(0,N,args,NULL,&Q,&T,trunclen);
+ return cl_R_to_LF(T,len) / cl_R_to_LF(Q,len);
+}