+template<>
+const cl_LF eval_rational_series<true> (uintC N, const cl_pqa_series& args, uintC len)
+{
+ if (N==0)
+ return cl_I_to_LF(0,len);
+ var cl_I Q, T;
+ // Precomputation of the shift counts:
+ // Split qv[n] into qv[n]*2^qsv[n].
+ CL_ALLOCA_STACK;
+ var uintC* qsv = (uintC*) cl_alloca(N*sizeof(uintC));
+ var cl_I* qp = args.qv;
+ var uintC* qsp = qsv;
+ for (var uintC n = 0; n < N; n++, qp++, qsp++) {
+ *qsp = pullout_shiftcount(*qp);
+ }
+ // Main computation.
+ var uintC QS;
+ eval_pqsa_series_aux(0,N,args,qsv,NULL,&Q,&QS,&T);
+ return cl_I_to_LF(T,len) / scale_float(cl_I_to_LF(Q,len),QS);
+}
+
+static void eval_pqa_series_aux (uintC N1, uintC N2,
+ cl_pqa_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_pqa_series_term v0 = args.next(); // [N1]
+ if (P) { *P = v0.p; }
+ *Q = v0.q;
+ *T = v0.a * v0.p;
+ break;
+ }
+ case 2: {
+ var cl_pqa_series_term v0 = args.next(); // [N1]
+ var cl_pqa_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.a * v0.p
+ + v1.a * p01;
+ break;
+ }
+ case 3: {
+ var cl_pqa_series_term v0 = args.next(); // [N1]
+ var cl_pqa_series_term v1 = args.next(); // [N1+1]
+ var cl_pqa_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.a * v0.p
+ + v2.q * v1.a * p01
+ + v2.a * p012;
+ break;
+ }
+ case 4: {
+ var cl_pqa_series_term v0 = args.next(); // [N1]
+ var cl_pqa_series_term v1 = args.next(); // [N1+1]
+ var cl_pqa_series_term v2 = args.next(); // [N1+2]
+ var cl_pqa_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.a * v0.p
+ + q23 * v1.a * p01
+ + v3.q * v2.a * p012
+ + v3.a * p0123;
+ break;
+ }
+ default: {
+ var uintC Nm = (N1+N2)/2; // midpoint
+ // Compute left part.
+ var cl_I LP, LQ, LT;
+ eval_pqa_series_aux(N1,Nm,args,&LP,&LQ,<);
+ // Compute right part.
+ var cl_I RP, RQ, RT;
+ eval_pqa_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;
+ }
+ }
+}
+
+template<>
+const cl_LF eval_rational_series<false> (uintC N, cl_pqa_series_stream& args, uintC len)