lst convert_parameter_Li_to_H(const lst& m, const lst& x, ex& pf);
-// holding dummy-symbols for the G/Li transformations
-std::vector<ex> gsyms;
-
-
// type used by the transformation functions for G
typedef std::vector<int> Gparameter;
// G_eval1-function for G transformations
-ex G_eval1(int a, int scale)
+ex G_eval1(int a, int scale, const exvector& gsyms)
{
if (a != 0) {
const ex& scs = gsyms[std::abs(scale)];
// G_eval-function for G transformations
-ex G_eval(const Gparameter& a, int scale)
+ex G_eval(const Gparameter& a, int scale, const exvector& gsyms)
{
// check for properties of G
ex sc = gsyms[std::abs(scale)];
for (; it != a.end(); ++it) {
short_a.push_back(*it);
}
- ex result = G_eval1(a.front(), scale) * G_eval(short_a, scale);
+ ex result = G_eval1(a.front(), scale, gsyms) * G_eval(short_a, scale, gsyms);
it = short_a.begin();
for (int i=1; i<count_ones; ++i) {
++it;
for (; it2 != short_a.end(); ++it2) {
newa.push_back(*it2);
}
- result -= G_eval(newa, scale);
+ result -= G_eval(newa, scale, gsyms);
}
return result / count_ones;
}
// G({1,...,1};y) -> G({1};y)^k / k!
if (all_ones && a.size() > 1) {
- return pow(G_eval1(a.front(),scale), count_ones) / factorial(count_ones);
+ return pow(G_eval1(a.front(),scale, gsyms), count_ones) / factorial(count_ones);
}
// G({0,...,0};y) -> log(y)^k / k!
// handles trailing zeroes for an otherwise convergent integral
-ex trailing_zeros_G(const Gparameter& a, int scale)
+ex trailing_zeros_G(const Gparameter& a, int scale, const exvector& gsyms)
{
bool convergent;
int depth, trailing_zeros;
if ((trailing_zeros > 0) && (depth > 0)) {
ex result;
Gparameter new_a(a.begin(), a.end()-1);
- result += G_eval1(0, scale) * trailing_zeros_G(new_a, scale);
+ result += G_eval1(0, scale, gsyms) * trailing_zeros_G(new_a, scale, gsyms);
for (Gparameter::const_iterator it = a.begin(); it != last; ++it) {
Gparameter new_a(a.begin(), it);
new_a.push_back(0);
new_a.insert(new_a.end(), it, a.end()-1);
- result -= trailing_zeros_G(new_a, scale);
+ result -= trailing_zeros_G(new_a, scale, gsyms);
}
return result / trailing_zeros;
} else {
- return G_eval(a, scale);
+ return G_eval(a, scale, gsyms);
}
}
// G transformation [VSW] (57),(58)
-ex depth_one_trafo_G(const Gparameter& pending_integrals, const Gparameter& a, int scale)
+ex depth_one_trafo_G(const Gparameter& pending_integrals, const Gparameter& a, int scale, const exvector& gsyms)
{
// pendint = ( y1, b1, ..., br )
// a = ( 0, ..., 0, amin )
result -= I*Pi;
}
if (psize) {
- result *= trailing_zeros_G(convert_pending_integrals_G(pending_integrals), pending_integrals.front());
+ result *= trailing_zeros_G(convert_pending_integrals_G(pending_integrals),
+ pending_integrals.front(),
+ gsyms);
}
// G(y2_{-+}; sr)
- result += trailing_zeros_G(convert_pending_integrals_G(new_pending_integrals), new_pending_integrals.front());
+ result += trailing_zeros_G(convert_pending_integrals_G(new_pending_integrals),
+ new_pending_integrals.front(),
+ gsyms);
// G(0; sr)
new_pending_integrals.back() = 0;
- result -= trailing_zeros_G(convert_pending_integrals_G(new_pending_integrals), new_pending_integrals.front());
+ result -= trailing_zeros_G(convert_pending_integrals_G(new_pending_integrals),
+ new_pending_integrals.front(),
+ gsyms);
return result;
}
//term zeta_m
result -= zeta(a.size());
if (psize) {
- result *= trailing_zeros_G(convert_pending_integrals_G(pending_integrals), pending_integrals.front());
+ result *= trailing_zeros_G(convert_pending_integrals_G(pending_integrals),
+ pending_integrals.front(),
+ gsyms);
}
// term int_0^sr dt/t G_{m-1}( (1/y2)_{+-}; 1/t )
// = int_0^sr dt/t G_{m-1}( t_{+-}; y2 )
Gparameter new_a(a.begin()+1, a.end());
new_pending_integrals.push_back(0);
- result -= depth_one_trafo_G(new_pending_integrals, new_a, scale);
+ result -= depth_one_trafo_G(new_pending_integrals, new_a, scale, gsyms);
// term int_0^y2 dt/t G_{m-1}( (1/y2)_{+-}; 1/t )
// = int_0^y2 dt/t G_{m-1}( t_{+-}; y2 )
new_pending_integrals_2.push_back(scale);
new_pending_integrals_2.push_back(0);
if (psize) {
- result += trailing_zeros_G(convert_pending_integrals_G(pending_integrals), pending_integrals.front())
- * depth_one_trafo_G(new_pending_integrals_2, new_a, scale);
+ result += trailing_zeros_G(convert_pending_integrals_G(pending_integrals),
+ pending_integrals.front(),
+ gsyms)
+ * depth_one_trafo_G(new_pending_integrals_2, new_a, scale, gsyms);
} else {
- result += depth_one_trafo_G(new_pending_integrals_2, new_a, scale);
+ result += depth_one_trafo_G(new_pending_integrals_2, new_a, scale, gsyms);
}
return result;
// forward declaration
ex shuffle_G(const Gparameter & a0, const Gparameter & a1, const Gparameter & a2,
- const Gparameter& pendint, const Gparameter& a_old, int scale);
+ const Gparameter& pendint, const Gparameter& a_old, int scale,
+ const exvector& gsyms);
// G transformation [VSW]
-ex G_transform(const Gparameter& pendint, const Gparameter& a, int scale)
+ex G_transform(const Gparameter& pendint, const Gparameter& a, int scale,
+ const exvector& gsyms)
{
// main recursion routine
//
if (a.size() == 0) {
result = 1;
} else {
- result = G_eval(a, scale);
+ result = G_eval(a, scale, gsyms);
}
if (pendint.size() > 0) {
- result *= trailing_zeros_G(convert_pending_integrals_G(pendint), pendint.front());
+ result *= trailing_zeros_G(convert_pending_integrals_G(pendint),
+ pendint.front(),
+ gsyms);
}
return result;
}
if (trailing_zeros > 0) {
ex result;
Gparameter new_a(a.begin(), a.end()-1);
- result += G_eval1(0, scale) * G_transform(pendint, new_a, scale);
+ result += G_eval1(0, scale, gsyms) * G_transform(pendint, new_a, scale, gsyms);
for (Gparameter::const_iterator it = a.begin(); it != firstzero; ++it) {
Gparameter new_a(a.begin(), it);
new_a.push_back(0);
new_a.insert(new_a.end(), it, a.end()-1);
- result -= G_transform(pendint, new_a, scale);
+ result -= G_transform(pendint, new_a, scale, gsyms);
}
return result / trailing_zeros;
}
// convergence case
if (convergent) {
if (pendint.size() > 0) {
- return G_eval(convert_pending_integrals_G(pendint), pendint.front()) * G_eval(a, scale);
+ return G_eval(convert_pending_integrals_G(pendint),
+ pendint.front(), gsyms)*
+ G_eval(a, scale, gsyms);
} else {
- return G_eval(a, scale);
+ return G_eval(a, scale, gsyms);
}
}
// call basic transformation for depth equal one
if (depth == 1) {
- return depth_one_trafo_G(pendint, a, scale);
+ return depth_one_trafo_G(pendint, a, scale, gsyms);
}
// do recursion
Gparameter a1(a.begin(),min_it+1);
Gparameter a2(min_it+1,a.end());
- ex result = G_transform(pendint,a2,scale)*G_transform(empty,a1,scale);
+ ex result = G_transform(pendint, a2, scale, gsyms)*
+ G_transform(empty, a1, scale, gsyms);
- result -= shuffle_G(empty,a1,a2,pendint,a,scale);
+ result -= shuffle_G(empty, a1, a2, pendint, a, scale, gsyms);
return result;
}
Gparameter new_pendint = prepare_pending_integrals(pendint, a[min_it_pos]);
Gparameter new_a = a;
new_a[min_it_pos] = 0;
- ex result = G_transform(empty, new_a, scale);
+ ex result = G_transform(empty, new_a, scale, gsyms);
if (pendint.size() > 0) {
- result *= trailing_zeros_G(convert_pending_integrals_G(pendint), pendint.front());
+ result *= trailing_zeros_G(convert_pending_integrals_G(pendint),
+ pendint.front(), gsyms);
}
// other terms
if (changeit != new_a.begin()) {
// smallest in the middle
new_pendint.push_back(*changeit);
- result -= trailing_zeros_G(convert_pending_integrals_G(new_pendint), new_pendint.front())
- * G_transform(empty, new_a, scale);
+ result -= trailing_zeros_G(convert_pending_integrals_G(new_pendint),
+ new_pendint.front(), gsyms)*
+ G_transform(empty, new_a, scale, gsyms);
int buffer = *changeit;
*changeit = *min_it;
- result += G_transform(new_pendint, new_a, scale);
+ result += G_transform(new_pendint, new_a, scale, gsyms);
*changeit = buffer;
new_pendint.pop_back();
--changeit;
new_pendint.push_back(*changeit);
- result += trailing_zeros_G(convert_pending_integrals_G(new_pendint), new_pendint.front())
- * G_transform(empty, new_a, scale);
+ result += trailing_zeros_G(convert_pending_integrals_G(new_pendint),
+ new_pendint.front(), gsyms)*
+ G_transform(empty, new_a, scale, gsyms);
*changeit = *min_it;
- result -= G_transform(new_pendint, new_a, scale);
+ result -= G_transform(new_pendint, new_a, scale, gsyms);
} else {
// smallest at the front
new_pendint.push_back(scale);
- result += trailing_zeros_G(convert_pending_integrals_G(new_pendint), new_pendint.front())
- * G_transform(empty, new_a, scale);
+ result += trailing_zeros_G(convert_pending_integrals_G(new_pendint),
+ new_pendint.front(), gsyms)*
+ G_transform(empty, new_a, scale, gsyms);
new_pendint.back() = *changeit;
- result -= trailing_zeros_G(convert_pending_integrals_G(new_pendint), new_pendint.front())
- * G_transform(empty, new_a, scale);
+ result -= trailing_zeros_G(convert_pending_integrals_G(new_pendint),
+ new_pendint.front(), gsyms)*
+ G_transform(empty, new_a, scale, gsyms);
*changeit = *min_it;
- result += G_transform(new_pendint, new_a, scale);
+ result += G_transform(new_pendint, new_a, scale, gsyms);
}
return result;
}
// shuffles the two parameter list a1 and a2 and calls G_transform for every term except
// for the one that is equal to a_old
ex shuffle_G(const Gparameter & a0, const Gparameter & a1, const Gparameter & a2,
- const Gparameter& pendint, const Gparameter& a_old, int scale)
+ const Gparameter& pendint, const Gparameter& a_old, int scale,
+ const exvector& gsyms)
{
if (a1.size()==0 && a2.size()==0) {
// veto the one configuration we don't want
if ( a0 == a_old ) return 0;
- return G_transform(pendint,a0,scale);
+ return G_transform(pendint, a0, scale, gsyms);
}
if (a2.size()==0) {
Gparameter empty;
Gparameter aa0 = a0;
aa0.insert(aa0.end(),a1.begin(),a1.end());
- return shuffle_G(aa0,empty,empty,pendint,a_old,scale);
+ return shuffle_G(aa0, empty, empty, pendint, a_old, scale, gsyms);
}
if (a1.size()==0) {
Gparameter empty;
Gparameter aa0 = a0;
aa0.insert(aa0.end(),a2.begin(),a2.end());
- return shuffle_G(aa0,empty,empty,pendint,a_old,scale);
+ return shuffle_G(aa0, empty, empty, pendint, a_old, scale, gsyms);
}
Gparameter a1_removed(a1.begin()+1,a1.end());
a01.push_back( a1[0] );
a02.push_back( a2[0] );
- return shuffle_G(a01,a1_removed,a2,pendint,a_old,scale)
- + shuffle_G(a02,a1,a2_removed,pendint,a_old,scale);
+ return shuffle_G(a01, a1_removed, a2, pendint, a_old, scale, gsyms)
+ + shuffle_G(a02, a1, a2_removed, pendint, a_old, scale, gsyms);
}
// generate missing dummy-symbols
int i = 1;
- gsyms.clear();
+ // holding dummy-symbols for the G/Li transformations
+ exvector gsyms;
gsyms.push_back(symbol("GSYMS_ERROR"));
ex lastentry;
for (std::multimap<ex,int>::const_iterator it = sortmap.begin(); it != sortmap.end(); ++it) {
// do transformation
Gparameter pendint;
- ex result = G_transform(pendint, a, scale);
+ ex result = G_transform(pendint, a, scale, gsyms);
// replace dummy symbols with their values
result = result.eval().expand();
result = result.subs(subslst).evalf();
if (*it != _ex0) {
all_zero = false;
}
- s.append(+1);
+ if ( !ex_to<numeric>(*it).is_real() && ex_to<numeric>(*it).imag() < 0 ) {
+ s.append(-1);
+ }
+ else {
+ s.append(+1);
+ }
}
if (all_zero) {
return pow(log(y), x.nops()) / factorial(x.nops());
if (*it != _ex0) {
all_zero = false;
}
- s.append(+1);
+ if ( !ex_to<numeric>(*it).is_real() && ex_to<numeric>(*it).imag() < 0 ) {
+ s.append(-1);
+ }
+ else {
+ s.append(+1);
+ }
}
if (all_zero) {
return pow(log(y), x.nops()) / factorial(x.nops());
if (*itx != _ex0) {
all_zero = false;
}
- if (*its >= 0) {
- sn.append(+1);
- } else {
- sn.append(-1);
+ if ( ex_to<numeric>(*itx).is_real() ) {
+ if ( *its >= 0 ) {
+ sn.append(+1);
+ }
+ else {
+ sn.append(-1);
+ }
+ }
+ else {
+ if ( ex_to<numeric>(*itx).imag() > 0 ) {
+ sn.append(+1);
+ }
+ else {
+ sn.append(-1);
+ }
}
}
if (all_zero) {
if (*itx != _ex0) {
all_zero = false;
}
- if (*its >= 0) {
- sn.append(+1);
- } else {
- sn.append(-1);
+ if ( ex_to<numeric>(*itx).is_real() ) {
+ if ( *its >= 0 ) {
+ sn.append(+1);
+ }
+ else {
+ sn.append(-1);
+ }
+ }
+ else {
+ if ( ex_to<numeric>(*itx).imag() > 0 ) {
+ sn.append(+1);
+ }
+ else {
+ sn.append(-1);
+ }
}
}
if (all_zero) {
// parameters and data for [Cra] algorithm
const cln::cl_N lambda = cln::cl_N("319/320");
-int L1;
-int L2;
-std::vector<std::vector<cln::cl_N> > f_kj;
-std::vector<cln::cl_N> crB;
-std::vector<std::vector<cln::cl_N> > crG;
-std::vector<cln::cl_N> crX;
-
void halfcyclic_convolute(const std::vector<cln::cl_N>& a, const std::vector<cln::cl_N>& b, std::vector<cln::cl_N>& c)
{
// [Cra] section 4
-void initcX(const std::vector<int>& s)
+static void initcX(std::vector<cln::cl_N>& crX,
+ const std::vector<int>& s,
+ const int L2)
{
- const int k = s.size();
-
- crX.clear();
- crG.clear();
- crB.clear();
-
- for (int i=0; i<=L2; i++) {
- crB.push_back(bernoulli(i).to_cl_N() / cln::factorial(i));
- }
+ std::vector<cln::cl_N> crB(L2 + 1);
+ for (int i=0; i<=L2; i++)
+ crB[i] = bernoulli(i).to_cl_N() / cln::factorial(i);
int Sm = 0;
int Smp1 = 0;
- for (int m=0; m<k-1; m++) {
- std::vector<cln::cl_N> crGbuf;
- Sm = Sm + s[m];
+ std::vector<std::vector<cln::cl_N> > crG(s.size() - 1, std::vector<cln::cl_N>(L2 + 1));
+ for (int m=0; m < s.size() - 1; m++) {
+ Sm += s[m];
Smp1 = Sm + s[m+1];
- for (int i=0; i<=L2; i++) {
- crGbuf.push_back(cln::factorial(i + Sm - m - 2) / cln::factorial(i + Smp1 - m - 2));
- }
- crG.push_back(crGbuf);
+ for (int i = 0; i <= L2; i++)
+ crG[m][i] = cln::factorial(i + Sm - m - 2) / cln::factorial(i + Smp1 - m - 2);
}
crX = crB;
- for (int m=0; m<k-1; m++) {
- std::vector<cln::cl_N> Xbuf;
- for (int i=0; i<=L2; i++) {
- Xbuf.push_back(crX[i] * crG[m][i]);
- }
+ for (std::size_t m = 0; m < s.size() - 1; m++) {
+ std::vector<cln::cl_N> Xbuf(L2 + 1);
+ for (int i = 0; i <= L2; i++)
+ Xbuf[i] = crX[i] * crG[m][i];
+
halfcyclic_convolute(Xbuf, crB, crX);
}
}
// [Cra] section 4
-cln::cl_N crandall_Y_loop(const cln::cl_N& Sqk)
+static cln::cl_N crandall_Y_loop(const cln::cl_N& Sqk,
+ const std::vector<cln::cl_N>& crX)
{
cln::cl_F one = cln::cl_float(1, cln::float_format(Digits));
cln::cl_N factor = cln::expt(lambda, Sqk);
// [Cra] section 4
-void calc_f(int maxr)
+static void calc_f(std::vector<std::vector<cln::cl_N> >& f_kj,
+ const int maxr, const int L1)
{
- f_kj.clear();
- f_kj.resize(L1);
-
cln::cl_N t0, t1, t2, t3, t4;
int i, j, k;
std::vector<std::vector<cln::cl_N> >::iterator it = f_kj.begin();
// [Cra] (3.1)
-cln::cl_N crandall_Z(const std::vector<int>& s)
+static cln::cl_N crandall_Z(const std::vector<int>& s,
+ const std::vector<std::vector<cln::cl_N> >& f_kj)
{
const int j = s.size();
std::vector<int> r = s;
const int j = r.size();
+ std::size_t L1;
+
// decide on maximal size of f_kj for crandall_Z
if (Digits < 50) {
L1 = 150;
L1 = Digits * 3 + j*2;
}
+ std::size_t L2;
// decide on maximal size of crX for crandall_Y
if (Digits < 38) {
L2 = 63;
}
}
- calc_f(maxr);
+ std::vector<std::vector<cln::cl_N> > f_kj(L1);
+ calc_f(f_kj, maxr, L1);
const cln::cl_N r0factorial = cln::factorial(r[0]-1);
Srun -= skp1buf;
r.pop_back();
- initcX(r);
+ std::vector<cln::cl_N> crX;
+ initcX(crX, r, L2);
for (int q=0; q<skp1buf; q++) {
- cln::cl_N pp1 = crandall_Y_loop(Srun+q-k);
- cln::cl_N pp2 = crandall_Z(rz);
+ cln::cl_N pp1 = crandall_Y_loop(Srun+q-k, crX);
+ cln::cl_N pp2 = crandall_Z(rz, f_kj);
rz.front()--;
}
rz.insert(rz.begin(), r.back());
- initcX(rz);
+ std::vector<cln::cl_N> crX;
+ initcX(crX, rz, L2);
- res = (res + crandall_Y_loop(S-j)) / r0factorial + crandall_Z(rz);
+ res = (res + crandall_Y_loop(S-j, crX)) / r0factorial
+ + crandall_Z(rz, f_kj);
return res;
}
git://www.ginac.de / ginac.git / blobdiff