-// eval_rational_series().
+// eval_rational_series<bool>().
// General includes.
#include "cl_sysdep.h"
// Implementation.
-#include "cl_lfloat.h"
-#include "cl_integer.h"
-#include "cl_abort.h"
+#include "cln/lfloat.h"
+#include "cln/integer.h"
+#include "cln/real.h"
+#include "cln/exception.h"
#include "cl_LF.h"
+#include "cl_alloca.h"
+
+namespace cln {
// Subroutine.
// Evaluates S = sum(N1 <= n < N2, a(n)/b(n) * (p(N1)...p(n))/(q(N1)...q(n)))
// and T = B*Q*S (all integers). On entry N1 < N2.
// P will not be computed if a NULL pointer is passed.
-static void eval_pqa_series_aux (uintL N1, uintL N2,
+static void eval_pqa_series_aux (uintC N1, uintC N2,
const cl_pqa_series& args,
cl_I* P, cl_I* Q, cl_I* T)
{
switch (N2 - N1) {
case 0:
- cl_abort(); break;
+ throw runtime_exception(); break;
case 1:
if (P) { *P = args.pv[N1]; }
*Q = args.qv[N1];
break;
}
default: {
- var uintL Nm = (N1+N2)/2; // midpoint
+ 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,<);
}
}
-static void eval_pqsa_series_aux (uintL N1, uintL N2,
- const cl_pqa_series& args,
- cl_I* P, cl_I* Q, uintL* QS, cl_I* T)
+template<>
+const cl_LF eval_rational_series<false> (uintC N, const cl_pqa_series& args, uintC len)
+{
+ if (N==0)
+ return cl_I_to_LF(0,len);
+ var cl_I Q, T;
+ eval_pqa_series_aux(0,N,args,NULL,&Q,&T);
+ return cl_I_to_LF(T,len) / cl_I_to_LF(Q,len);
+}
+
+static void eval_pqsa_series_aux (uintC N1, uintC N2,
+ const cl_pqa_series& args, const uintC* qsv,
+ cl_I* P, cl_I* Q, uintC* QS, cl_I* T)
{
switch (N2 - N1) {
case 0:
- cl_abort(); break;
+ throw runtime_exception(); break;
case 1:
if (P) { *P = args.pv[N1]; }
*Q = args.qv[N1];
- *QS = args.qsv[N1];
+ *QS = qsv[N1];
*T = args.av[N1] * args.pv[N1];
break;
case 2: {
var cl_I p01 = args.pv[N1] * args.pv[N1+1];
if (P) { *P = p01; }
*Q = args.qv[N1] * args.qv[N1+1];
- *QS = args.qsv[N1] + args.qsv[N1+1];
- *T = ((args.qv[N1+1] * args.av[N1] * args.pv[N1]) << args.qsv[N1+1])
+ *QS = qsv[N1] + qsv[N1+1];
+ *T = ((args.qv[N1+1] * args.av[N1] * args.pv[N1]) << qsv[N1+1])
+ args.av[N1+1] * p01;
break;
}
if (P) { *P = p012; }
var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
*Q = args.qv[N1] * q12;
- *QS = args.qsv[N1] + args.qsv[N1+1] + args.qsv[N1+2];
- *T = ((q12 * args.av[N1] * args.pv[N1]) << (args.qsv[N1+1] + args.qsv[N1+2]))
- + ((args.qv[N1+2] * args.av[N1+1] * p01) << args.qsv[N1+2])
+ *QS = qsv[N1] + qsv[N1+1] + qsv[N1+2];
+ *T = ((q12 * args.av[N1] * args.pv[N1]) << (qsv[N1+1] + qsv[N1+2]))
+ + ((args.qv[N1+2] * args.av[N1+1] * p01) << qsv[N1+2])
+ args.av[N1+2] * p012;
break;
}
var cl_I q23 = args.qv[N1+2] * args.qv[N1+3];
var cl_I q123 = args.qv[N1+1] * q23;
*Q = args.qv[N1] * q123;
- *QS = args.qsv[N1] + args.qsv[N1+1] + args.qsv[N1+2] + args.qsv[N1+3];
- *T = ((((((q123 * args.av[N1] * args.pv[N1]) << args.qsv[N1+1])
- + q23 * args.av[N1+1] * p01) << args.qsv[N1+2])
- + args.qv[N1+3] * args.av[N1+2] * p012) << args.qsv[N1+3])
+ *QS = qsv[N1] + qsv[N1+1] + qsv[N1+2] + qsv[N1+3];
+ *T = ((((((q123 * args.av[N1] * args.pv[N1]) << qsv[N1+1])
+ + q23 * args.av[N1+1] * p01) << qsv[N1+2])
+ + args.qv[N1+3] * args.av[N1+2] * p012) << qsv[N1+3])
+ args.av[N1+3] * p0123;
break;
}
default: {
- var uintL Nm = (N1+N2)/2; // midpoint
+ var uintC Nm = (N1+N2)/2; // midpoint
// Compute left part.
var cl_I LP, LQ, LT;
- var uintL LQS;
- eval_pqsa_series_aux(N1,Nm,args,&LP,&LQ,&LQS,<);
+ var uintC LQS;
+ eval_pqsa_series_aux(N1,Nm,args,qsv,&LP,&LQ,&LQS,<);
// Compute right part.
var cl_I RP, RQ, RT;
- var uintL RQS;
- eval_pqsa_series_aux(Nm,N2,args,(P?&RP:(cl_I*)0),&RQ,&RQS,&RT);
+ var uintC RQS;
+ eval_pqsa_series_aux(Nm,N2,args,qsv,(P?&RP:(cl_I*)0),&RQ,&RQS,&RT);
// Put together partial results.
if (P) { *P = LP*RP; }
*Q = LQ*RQ;
}
}
-const cl_LF eval_rational_series (uintL N, const cl_pqa_series& args, uintC len)
+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)
{
if (N==0)
return cl_I_to_LF(0,len);
var cl_I Q, T;
- if (!args.qsv) {
- eval_pqa_series_aux(0,N,args,NULL,&Q,&T);
- return cl_I_to_LF(T,len) / cl_I_to_LF(Q,len);
- } else {
- // Precomputation of the shift counts:
- // Split qv[n] into qv[n]*2^qsv[n].
- {
- var cl_I* qp = args.qv;
- var uintL* qsp = args.qsv;
- for (var uintL n = 0; n < N; n++, qp++, qsp++) {
- // Pull out maximal power of 2 out of *qp = args.qv[n].
- var uintL qs = 0;
- if (!zerop(*qp)) {
- qs = ord2(*qp);
- if (qs > 0)
- *qp = *qp >> qs;
- }
- *qsp = qs;
- }
- }
- // Main computation.
- var uintL QS;
- eval_pqsa_series_aux(0,N,args,NULL,&Q,&QS,&T);
- return cl_I_to_LF(T,len) / scale_float(cl_I_to_LF(Q,len),QS);
+ eval_pqa_series_aux(0,N,args,NULL,&Q,&T);
+ return cl_I_to_LF(T,len) / cl_I_to_LF(Q,len);
+}
+
+static void eval_pqa_series_aux (uintC N1, uintC N2,
+ cl_pqa_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_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_R LP, LQ, LT;
+ eval_pqa_series_aux(N1,Nm,args,&LP,&LQ,<,trunclen);
+ // Compute right part.
+ var cl_R RP, RQ, RT;
+ eval_pqa_series_aux(Nm,N2,args,(P?&RP:(cl_R*)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;
+ }
}
}
+
+template<>
+const cl_LF eval_rational_series<false> (uintC N, cl_pqa_series_stream& args, uintC len, uintC trunclen)
+{
+ if (N==0)
+ return cl_I_to_LF(0,len);
+ var cl_R Q, T;
+ eval_pqa_series_aux(0,N,args,NULL,&Q,&T,trunclen);
+ return cl_R_to_LF(T,len) / cl_R_to_LF(Q,len);
+}
// Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):
// O(log(N)^2*M(N)).
+
+} // namespace cln
git://www.ginac.de / cln.git / blobdiff