*/
/*
- * GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
flag_accidental_zero = cln::zerop(t[k+1]);
t[k] = t[k] + t[k+1] * cln::expt(x[k], q+j-1-k) / cln::expt(cln::cl_I(q+j-1-k), s[k]);
}
+ q++;
+ t[j-1] = t[j-1] + cln::expt(x[j-1], q) / cln::expt(cln::cl_I(q),s[j-1]) * one;
+ for (int k=j-2; k>=0; k--) {
+ flag_accidental_zero = cln::zerop(t[k+1]);
+ t[k] = t[k] + t[k+1] * cln::expt(x[k], q+j-1-k) / cln::expt(cln::cl_I(q+j-1-k), s[k]);
+ }
} while ( (t[0] != t0buf) || flag_accidental_zero );
return t[0];
for (lst::const_iterator it = x.begin(); it != x.end(); ++it) {
if (!(*it).is_zero()) {
++depth;
- if (abs(*it) - y < -pow(10,-Digits+2)) {
+ if (abs(*it) - y < -pow(10,-Digits+1)) {
need_trafo = true;
- break;
}
if (abs((abs(*it) - y)/y) < 0.01) {
need_hoelder = true;
if (x.op(x.nops()-1).is_zero()) {
need_trafo = true;
}
- if (depth == 1 && !need_trafo) {
+ if (depth == 1 && x.nops() == 2 && !need_trafo) {
return -Li(x.nops(), y / x.op(x.nops()-1)).evalf();
}
+ // do acceleration transformation (hoelder convolution [BBB])
+ if (need_hoelder) {
+
+ ex result;
+ const int size = x.nops();
+ lst newx;
+ for (lst::const_iterator it = x.begin(); it != x.end(); ++it) {
+ newx.append(*it / y);
+ }
+
+ for (int r=0; r<=size; ++r) {
+ ex buffer = pow(-1, r);
+ ex p = 2;
+ bool adjustp;
+ do {
+ adjustp = false;
+ for (lst::const_iterator it = newx.begin(); it != newx.end(); ++it) {
+ if (*it == 1/p) {
+ p += (3-p)/2;
+ adjustp = true;
+ continue;
+ }
+ }
+ } while (adjustp);
+ ex q = p / (p-1);
+ lst qlstx;
+ lst qlsts;
+ for (int j=r; j>=1; --j) {
+ qlstx.append(1-newx.op(j-1));
+ if (newx.op(j-1).info(info_flags::real) && newx.op(j-1) > 1 && newx.op(j-1) <= 2) {
+ qlsts.append( s.op(j-1));
+ } else {
+ qlsts.append( -s.op(j-1));
+ }
+ }
+ if (qlstx.nops() > 0) {
+ buffer *= G_numeric(qlstx, qlsts, 1/q);
+ }
+ lst plstx;
+ lst plsts;
+ for (int j=r+1; j<=size; ++j) {
+ plstx.append(newx.op(j-1));
+ plsts.append(s.op(j-1));
+ }
+ if (plstx.nops() > 0) {
+ buffer *= G_numeric(plstx, plsts, 1/p);
+ }
+ result += buffer;
+ }
+ return result;
+ }
+
// convergence transformation
if (need_trafo) {
return result;
}
- // do acceleration transformation (hoelder convolution [BBB])
- if (need_hoelder) {
-
- ex result;
- const int size = x.nops();
- lst newx;
- for (lst::const_iterator it = x.begin(); it != x.end(); ++it) {
- newx.append(*it / y);
- }
-
- for (int r=0; r<=size; ++r) {
- ex buffer = pow(-1, r);
- ex p = 2;
- bool adjustp;
- do {
- adjustp = false;
- for (lst::const_iterator it = newx.begin(); it != newx.end(); ++it) {
- if (*it == 1/p) {
- p += (3-p)/2;
- adjustp = true;
- continue;
- }
- }
- } while (adjustp);
- ex q = p / (p-1);
- lst qlstx;
- lst qlsts;
- for (int j=r; j>=1; --j) {
- qlstx.append(1-newx.op(j-1));
- if (newx.op(j-1).info(info_flags::real) && newx.op(j-1) > 1 && newx.op(j-1) <= 2) {
- qlsts.append( s.op(j-1));
- } else {
- qlsts.append( -s.op(j-1));
- }
- }
- if (qlstx.nops() > 0) {
- buffer *= G_numeric(qlstx, qlsts, 1/q);
- }
- lst plstx;
- lst plsts;
- for (int j=r+1; j<=size; ++j) {
- plstx.append(newx.op(j-1));
- plsts.append(s.op(j-1));
- }
- if (plstx.nops() > 0) {
- buffer *= G_numeric(plstx, plsts, 1/p);
- }
- result += buffer;
- }
- return result;
- }
-
// do summation
lst newx;
lst m;
// check transformations for 0.95 <= |x| < 2.0
- // |(1-x)/(1+x)| < 0.9 -> circular area with center=9,53+0i and radius=9.47
+ // |(1-x)/(1+x)| < 0.9 -> circular area with center=9.53+0i and radius=9.47
if (cln::abs(x-9.53) <= 9.47) {
// x -> (1-x)/(1+x)
map_trafo_H_1mxt1px trafo;