* src/float/transcendental/cl_LF_tran.h (cl_pqd_series_stream): New.
* src/float/transcendental/cl_LF_ratsumseries_stream_pqd.cc: New file.
* src/float/transcendental/cl_LF_ratsumseries_stream_pqd_aux.cc: New file.
* src/float/transcendental/cl_LF_eulerconst.cc: Compute series coefficients
on demand, using a series stream object.
+2007-09-07 Richard B. Kreckel <kreckel@ginac.de>
+
+ More memory efficient Euler-Mascheroni constant:
+ * src/float/transcendental/cl_LF_tran.h (cl_pqd_series_stream): New.
+ * src/float/transcendental/cl_LF_ratsumseries_stream_pqd.cc: New file.
+ * src/float/transcendental/cl_LF_ratsumseries_stream_pqd_aux.cc: New
+ file.
+ * src/float/transcendental/cl_LF_eulerconst.cc: Compute series
+ coefficients on demand, using a series stream object.
+
2007-08-02 Richard B. Kreckel <kreckel@ginac.de>
* src/base/digitseq/cl_DS_div.cc (cl_recip_suitable): uintC arguments.
var uintC sx = (uintC)(0.25*0.693148*intDsize*actuallen)+1;
var uintC N = (uintC)(3.591121477*sx);
var cl_I x = square((cl_I)sx);
- CL_ALLOCA_STACK;
- var cl_pqd_series_term* args = (cl_pqd_series_term*) cl_alloca(N*sizeof(cl_pqd_series_term));
- var uintC n;
- for (n = 0; n < N; n++) {
- init1(cl_I, args[n].p) (x);
- init1(cl_I, args[n].q) (square((cl_I)(n+1)));
- init1(cl_I, args[n].d) (n+1);
- }
+ struct rational_series_stream : cl_pqd_series_stream {
+ uintC n;
+ cl_I x;
+ static cl_pqd_series_term computenext (cl_pqd_series_stream& thisss)
+ {
+ var rational_series_stream& thiss = (rational_series_stream&)thisss;
+ var uintC n = thiss.n;
+ var cl_pqd_series_term result;
+ result.p = thiss.x;
+ result.q = square((cl_I)(n+1));
+ result.d = n+1;
+ thiss.n = n+1;
+ return result;
+ }
+ rational_series_stream (const cl_I& _x)
+ : cl_pqd_series_stream (rational_series_stream::computenext),
+ n (0), x (_x) {}
+ } series(x);
var cl_pqd_series_result sums;
- eval_pqd_series_aux(N,args,sums);
+ eval_pqd_series_aux(N,series,sums);
// Instead of computing fsum = 1 + T/Q and gsum = V/(D*Q)
// and then dividing them, to compute gsum/fsum, we save two
// divisions by computing V/(D*(Q+T)).
cl_I_to_LF(sums.V,actuallen)
/ The(cl_LF)(sums.D * cl_I_to_LF(sums.Q+sums.T,actuallen))
- ln(cl_I_to_LF(sx,actuallen));
- for (n = 0; n < N; n++) {
- args[n].p.~cl_I();
- args[n].q.~cl_I();
- args[n].d.~cl_I();
- }
return shorten(result,len); // verkürzen und fertig
}
// Bit complexity (N = len): O(log(N)^2*M(N)).
--- /dev/null
+// eval_pqd_series().
+
+// General includes.
+#include "cl_sysdep.h"
+
+// Specification.
+#include "cl_LF_tran.h"
+
+
+// Implementation.
+
+#include "cln/lfloat.h"
+#include "cln/integer.h"
+#include "cl_LF.h"
+
+namespace cln {
+
+const cl_LF eval_pqd_series (uintC N, cl_pqd_series_stream& args, uintC len)
+{
+ if (N==0)
+ return cl_I_to_LF(0,len);
+ var cl_pqd_series_result sums;
+ eval_pqd_series_aux(N,args,sums);
+ // Instead of computing fsum = T/Q and gsum = V/(D*Q)
+ // and then dividing them, to compute gsum/fsum, we save two
+ // divisions by computing V/(D*T).
+ return
+ cl_I_to_LF(sums.V,len) / The(cl_LF)(sums.D * cl_I_to_LF(sums.T,len));
+}
+
+} // namespace cln
--- /dev/null
+// eval_pqd_series_aux().
+
+// General includes.
+#include "cl_sysdep.h"
+
+// Specification.
+#include "cl_LF_tran.h"
+
+
+// Implementation.
+
+#include "cln/integer.h"
+#include "cln/exception.h"
+
+namespace cln {
+
+void eval_pqd_series_aux (uintC N, cl_pqd_series_stream& args, cl_pqd_series_result& Z, bool rightmost)
+{
+ // N = N2-N1
+ switch (N) {
+ case 0:
+ throw runtime_exception(); break;
+ case 1: {
+ var cl_pqd_series_term v0 = args.next(); // [N1]
+ if (!rightmost) { Z.P = v0.p; }
+ Z.Q = v0.q;
+ Z.T = v0.p;
+ if (!rightmost) { Z.C = 1; }
+ Z.D = v0.d;
+ Z.V = v0.p;
+ break;
+ }
+ case 2: {
+ var cl_pqd_series_term v0 = args.next(); // [N1]
+ var cl_pqd_series_term v1 = args.next(); // [N1+1]
+ var cl_I p01 = v0.p * v1.p;
+ if (!rightmost) { Z.P = p01; }
+ Z.Q = v0.q * v1.q;
+ var cl_I p0q1 = v0.p * v1.q + p01;
+ Z.T = p0q1;
+ if (!rightmost) { Z.C = v1.d + v0.d; }
+ Z.D = v0.d * v1.d;
+ Z.V = v1.d * p0q1 + v0.d * p01;
+ break;
+ }
+ case 3: {
+ var cl_pqd_series_term v0 = args.next(); // [N1]
+ var cl_pqd_series_term v1 = args.next(); // [N1+1]
+ var cl_pqd_series_term v2 = args.next(); // [N1+2]
+ var cl_I p01 = v0.p * v1.p;
+ var cl_I p012 = p01 * v2.p;
+ if (!rightmost) { Z.P = p012; }
+ Z.Q = v0.q * v1.q * v2.q;
+ var cl_I p0q1 = v0.p * v1.q + p01;
+ Z.T = v2.q * p0q1 + p012;
+ var cl_I d01 = v0.d * v1.d;
+ if (!rightmost) { Z.C = (v1.d + v0.d) * v2.d + d01; }
+ Z.D = d01 * v2.d;
+ Z.V = v2.d * (v2.q * (v1.d * p0q1 + v0.d * p01) + (v1.d + v0.d) * p012) + d01 * p012;
+ break;
+ }
+ default: {
+ var uintC Nm = N/2; // midpoint
+ // Compute left part.
+ var cl_pqd_series_result L;
+ eval_pqd_series_aux(Nm,args,L,false);
+ // Compute right part.
+ var cl_pqd_series_result R;
+ eval_pqd_series_aux(N-Nm,args,R,rightmost);
+ // Put together partial results.
+ if (!rightmost) { Z.P = L.P * R.P; }
+ Z.Q = L.Q * R.Q;
+ // Z.S = L.S + L.P/L.Q*R.S;
+ var cl_I tmp = L.P * R.T;
+ Z.T = R.Q * L.T + tmp;
+ if (!rightmost) { Z.C = L.C * R.D + L.D * R.C; }
+ Z.D = L.D * R.D;
+ // Z.U = L.U + L.C/L.D * L.P/L.Q * R.S + L.P/L.Q * R.U;
+ // Z.V = R.D * R.Q * L.V + R.D * L.C * L.P * R.T + L.D * L.P * R.V;
+ Z.V = R.D * (R.Q * L.V + L.C * tmp) + L.D * L.P * R.V;
+ break;
+ }
+ }
+}
+
+} // namespace cln
cl_I D;
cl_I V;
};
+struct cl_pqd_series_stream {
+ cl_pqd_series_term (*nextfn)(cl_pqd_series_stream&);
+ cl_pqd_series_term next () { return nextfn(*this); }
+ // Constructor.
+ cl_pqd_series_stream( cl_pqd_series_term (*n)(cl_pqd_series_stream&)) : nextfn (n) {}
+};
extern void eval_pqd_series_aux (uintC N, cl_pqd_series_term* args, cl_pqd_series_result& Z, bool rightmost = true);
+extern void eval_pqd_series_aux (uintC N, cl_pqd_series_stream& args, cl_pqd_series_result& Z, bool rightmost = true);
// Ditto, but returns U/S.
extern const cl_LF eval_pqd_series (uintC N, cl_pqd_series_term* args, uintC len);
+extern const cl_LF eval_pqd_series (uintC N, cl_pqd_series_stream& args, uintC len);
} // namespace cln
git://www.ginac.de / cln.git / commitdiff