S(0,p,x) now evaluates numerically

[ginac.git] / ginac / inifcns_nstdsums.cpp

diff --git a/ginac/inifcns_nstdsums.cpp b/ginac/inifcns_nstdsums.cpp
index 4b8122d23e33151d487405ea07d951c085e40770..ec9586ed9367160fcd3b5a97fb5a3dda4db84ebf 100644 (file)
--- a/ginac/inifcns_nstdsums.cpp
+++ b/ginac/inifcns_nstdsums.cpp
@@ -46,7 +46,7 @@
  */
 
 /*
- *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2004 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
@@ -189,7 +189,7 @@ cln::cl_N Li2_do_sum(const cln::cl_N& x)
 {
        cln::cl_N res = x;
        cln::cl_N resbuf;
-       cln::cl_N num = x;
+       cln::cl_N num = x * cln::cl_float(1, cln::float_format(Digits));
        cln::cl_I den = 1; // n^2 = 1
        unsigned i = 3;
        do {
@@ -208,7 +208,7 @@ cln::cl_N Li2_do_sum_Xn(const cln::cl_N& x)
 {
        std::vector<cln::cl_N>::const_iterator it = Xn[0].begin();
        cln::cl_N u = -cln::log(1-x);
-       cln::cl_N factor = u;
+       cln::cl_N factor = u * cln::cl_float(1, cln::float_format(Digits));
        cln::cl_N res = u - u*u/4;
        cln::cl_N resbuf;
        unsigned i = 1;
@@ -226,7 +226,7 @@ cln::cl_N Li2_do_sum_Xn(const cln::cl_N& x)
 // calculates Li(n,x), n>2 without Xn
 cln::cl_N Lin_do_sum(int n, const cln::cl_N& x)
 {
-       cln::cl_N factor = x;
+       cln::cl_N factor = x * cln::cl_float(1, cln::float_format(Digits));
        cln::cl_N res = x;
        cln::cl_N resbuf;
        int i=2;
@@ -245,7 +245,7 @@ cln::cl_N Lin_do_sum_Xn(int n, const cln::cl_N& x)
 {
        std::vector<cln::cl_N>::const_iterator it = Xn[n-2].begin();
        cln::cl_N u = -cln::log(1-x);
-       cln::cl_N factor = u;
+       cln::cl_N factor = u * cln::cl_float(1, cln::float_format(Digits));
        cln::cl_N res = u;
        cln::cl_N resbuf;
        unsigned i=2;
@@ -461,7 +461,7 @@ static ex Li_evalf(const ex& x1, const ex& x2)
                                return Li(x1, x2).hold();
                        }
                        conv *= x2.op(i);
-                       if (conv >= 1) {
+                       if (abs(conv) >= 1) {
                                return Li(x1, x2).hold();
                        }
                }
@@ -846,7 +846,9 @@ cln::cl_N S_do_sum(int n, int p, const cln::cl_N& x, const cln::float_format_t&
        }
 
        // should be done otherwise
-       cln::cl_N xf = x * cln::cl_float(1, prec);
+       cln::cl_F one = cln::cl_float(1, cln::float_format(Digits));
+       cln::cl_N xf = x * one;
+       //cln::cl_N xf = x * cln::cl_float(1, prec);
 
        cln::cl_N res;
        cln::cl_N resbuf;
@@ -937,9 +939,8 @@ numeric S_num(int n, int p, const numeric& x)
        else if (!x.imag().is_rational())
                prec = cln::float_format(cln::the<cln::cl_F>(cln::imagpart(value)));
 
-
        // [Kol] (5.3)
-       if (cln::realpart(value) < -0.5) {
+       if ((cln::realpart(value) < -0.5) || (n == 0)) {
 
                cln::cl_N result = cln::expt(cln::cl_I(-1),p) * cln::expt(cln::log(value),n)
                                   * cln::expt(cln::log(1-value),p) / cln::factorial(n) / cln::factorial(p);
@@ -1027,6 +1028,10 @@ static ex S_eval(const ex& n, const ex& p, const ex& x)
                        return S_num(ex_to<numeric>(n).to_int(), ex_to<numeric>(p).to_int(), ex_to<numeric>(x));
                }
        }
+       if (n.is_zero()) {
+               // [Kol] (5.3)
+               return pow(-log(1-x), p) / factorial(p);
+       }
        return S(n, p, x).hold();
 }
 
@@ -1086,6 +1091,10 @@ REGISTER_FUNCTION(S,
 // anonymous namespace for helper functions
 namespace {
 
+       
+// regulates the pole (used by 1/x-transformation)
+symbol H_polesign("IMSIGN");
+
 
 // convert parameters from H to Li representation
 // parameters are expected to be in expanded form, i.e. only 0, 1 and -1
@@ -1599,7 +1608,7 @@ struct map_trafo_H_1overx : public map_function
                                        }
                                        if (allthesame) {
                                                map_trafo_H_mult unify;
-                                               return unify((pow(H(lst(1),1/arg).hold() + H(lst(0),1/arg).hold() - I*Pi, parameter.nops())
+                                               return unify((pow(H(lst(1),1/arg).hold() + H(lst(0),1/arg).hold() + H_polesign, parameter.nops())
                                                       / factorial(parameter.nops())).expand());
                                        }
                                }
@@ -1926,6 +1935,11 @@ static ex H_evalf(const ex& x1, const ex& x2)
                        // x -> 1/x
                        map_trafo_H_1overx trafo;
                        res *= trafo(H(m, xtemp));
+                       if (cln::imagpart(x) <= 0) {
+                               res = res.subs(H_polesign == -I*Pi);
+                       } else {
+                               res = res.subs(H_polesign == I*Pi);
+                       }
                }
 
                // simplify result