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174 lines
4.3 KiB
174 lines
4.3 KiB
// eval_rational_series<bool>().
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// General includes.
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#include "cl_sysdep.h"
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// Specification.
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#include "cl_LF_tran.h"
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// Implementation.
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#include "cln/lfloat.h"
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#include "cln/integer.h"
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#include "cln/exception.h"
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#include "cl_LF.h"
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namespace cln {
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// Subroutine.
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// Evaluates S = sum(N1 <= n < N2, a(n)/b(n) * (p(N1)...p(n))/(q(N1)...q(n)))
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// and returns P = p(N1)...p(N2-1), Q = q(N1)...q(N2-1), B = B(N1)...B(N2-1)
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// and T = B*Q*S (all integers). On entry N1 < N2.
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// P will not be computed if a NULL pointer is passed.
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static void eval_qb_series_aux (uintC N1, uintC N2,
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const cl_qb_series& args,
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cl_I* Q, cl_I* B, cl_I* T)
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{
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switch (N2 - N1) {
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case 0:
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throw runtime_exception(); break;
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case 1:
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*Q = args.qv[N1];
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*B = args.bv[N1];
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*T = 1;
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break;
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case 2: {
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*Q = args.qv[N1] * args.qv[N1+1];
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*B = args.bv[N1] * args.bv[N1+1];
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*T = args.bv[N1+1] * args.qv[N1+1]
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+ args.bv[N1];
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break;
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}
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case 3: {
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var cl_I q12 = args.qv[N1+1] * args.qv[N1+2];
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*Q = args.qv[N1] * q12;
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var cl_I b12 = args.bv[N1+1] * args.bv[N1+2];
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*B = args.bv[N1] * b12;
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*T = b12 * q12
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+ args.bv[N1] * (args.bv[N1+2] * args.qv[N1+2]
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+ args.bv[N1+1]);
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break;
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}
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case 4: {
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var cl_I q23 = args.qv[N1+2] * args.qv[N1+3];
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var cl_I q123 = args.qv[N1+1] * q23;
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*Q = args.qv[N1] * q123;
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var cl_I b01 = args.bv[N1] * args.bv[N1+1];
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var cl_I b23 = args.bv[N1+2] * args.bv[N1+3];
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*B = b01 * b23;
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*T = b23 * (args.bv[N1+1] * q123
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+ args.bv[N1] * q23)
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+ b01 * (args.bv[N1+3] * args.qv[N1+3]
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+ args.bv[N1+2]);
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break;
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}
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default: {
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var uintC Nm = (N1+N2)/2; // midpoint
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// Compute left part.
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var cl_I LQ, LB, LT;
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eval_qb_series_aux(N1,Nm,args,&LQ,&LB,<);
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// Compute right part.
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var cl_I RQ, RB, RT;
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eval_qb_series_aux(Nm,N2,args,&RQ,&RB,&RT);
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// Put together partial results.
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*Q = LQ*RQ;
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*B = LB*RB;
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// S = LS + 1/LQ * RS, so T = RB*RQ*LT + LB*RT.
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*T = RB*RQ*LT + LB*RT;
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break;
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}
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}
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}
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template<>
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const cl_LF eval_rational_series<false> (uintC N, const cl_qb_series& args, uintC len)
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{
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if (N==0)
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return cl_I_to_LF(0,len);
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var cl_I Q, B, T;
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eval_qb_series_aux(0,N,args,&Q,&B,&T);
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return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
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}
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static void eval_qb_series_aux (uintC N1, uintC N2,
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cl_qb_series_stream& args,
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cl_I* Q, cl_I* B, cl_I* T)
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{
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switch (N2 - N1) {
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case 0:
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throw runtime_exception(); break;
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case 1: {
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var cl_qb_series_term v0 = args.next(); // [N1]
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*Q = v0.q;
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*B = v0.b;
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*T = 1;
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break;
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}
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case 2: {
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var cl_qb_series_term v0 = args.next(); // [N1]
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var cl_qb_series_term v1 = args.next(); // [N1+1]
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*Q = v0.q * v1.q;
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*B = v0.b * v1.b;
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*T = v1.b * v1.q + v0.b;
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break;
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}
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case 3: {
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var cl_qb_series_term v0 = args.next(); // [N1]
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var cl_qb_series_term v1 = args.next(); // [N1+1]
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var cl_qb_series_term v2 = args.next(); // [N1+2]
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var cl_I q12 = v1.q * v2.q;
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*Q = v0.q * q12;
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var cl_I b12 = v1.b * v2.b;
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*B = v0.b * b12;
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*T = b12 * q12 + v0.b * (v2.b * v2.q + v1.b);
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break;
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}
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case 4: {
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var cl_qb_series_term v0 = args.next(); // [N1]
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var cl_qb_series_term v1 = args.next(); // [N1+1]
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var cl_qb_series_term v2 = args.next(); // [N1+2]
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var cl_qb_series_term v3 = args.next(); // [N1+3]
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var cl_I q23 = v2.q * v3.q;
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var cl_I q123 = v1.q * q23;
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*Q = v0.q * q123;
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var cl_I b01 = v0.b * v1.b;
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var cl_I b23 = v2.b * v3.b;
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*B = b01 * b23;
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*T = b23 * (v1.b * q123 + v0.b * q23)
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+ b01 * (v3.b * v3.q + v2.b);
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break;
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}
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default: {
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var uintC Nm = (N1+N2)/2; // midpoint
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// Compute left part.
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var cl_I LQ, LB, LT;
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eval_qb_series_aux(N1,Nm,args,&LQ,&LB,<);
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// Compute right part.
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var cl_I RQ, RB, RT;
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eval_qb_series_aux(Nm,N2,args,&RQ,&RB,&RT);
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// Put together partial results.
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*Q = LQ*RQ;
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*B = LB*RB;
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// S = LS + 1/LQ * RS, so T = RB*RQ*LT + LB*RT.
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*T = RB*RQ*LT + LB*RT;
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break;
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}
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}
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}
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template<>
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const cl_LF eval_rational_series<false> (uintC N, cl_qb_series_stream& args, uintC len)
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{
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if (N==0)
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return cl_I_to_LF(0,len);
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var cl_I Q, B, T;
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eval_qb_series_aux(0,N,args,&Q,&B,&T);
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return cl_I_to_LF(T,len) / cl_I_to_LF(B*Q,len);
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}
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// Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):
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// O(log(N)^2*M(N)).
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} // namespace cln
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