April 2008 - GiNaC-devel

[PATCH 1/8] inifcns_nstdsums.cpp: S_num takes cl_N as an argument instead of numeric.
by Alexei Sheplyakov 28 Jul '08

28 Jul '08

Implicit conversion from cl_N to numeric considered harmful. Using GiNaC::numeric for numerical computations incurs significant overhead, so one might want to do these computations using proper CLN types. Unfortunately, it's not easy due to automatic conversion from cln::cl_N to GiNaC::numeric. Here is a simple example: cl_N x, y; // initialize them return sin(x) + y*exp(y); The compiler complains about ambigously overloaded of functions, i.e. cl_N cln::sin(const cl_N&) versus numeric GiNaC::sin(const numeric&). Hence, I propose to disable *implicit* conversion from cl_N to numeric (this can be done by marking the numeric ctor as `explicit'). However, this change happens to be a bit nontrivial, because that evil conversion is used in GiNaC itself. So, I decided to rewrite those fragments of code. --- ginac/inifcns_nstdsums.cpp | 50 ++++++++++++++++++++++++++----------------- 1 files changed, 30 insertions(+), 20 deletions(-) diff --git a/ginac/inifcns_nstdsums.cpp b/ginac/inifcns_nstdsums.cpp index cd3511a..ea42a6e 100644 --- a/ginac/inifcns_nstdsums.cpp +++ b/ginac/inifcns_nstdsums.cpp @@ -320,7 +320,7 @@ cln::cl_N Lin_do_sum_Xn(int n, const cln::cl_N& x) // forward declaration needed by function Li_projection and C below -numeric S_num(int n, int p, const numeric& x); +const cln::cl_N S_num(int n, int p, const cln::cl_N& x); // helper function for classical polylog Li @@ -371,7 +371,7 @@ cln::cl_N Li_projection(int n, const cln::cl_N& x, const cln::float_format_t& pr } else { cln::cl_N result = -cln::expt(cln::log(x), n-1) * cln::log(1-x) / cln::factorial(n-1); for (int j=0; j<n-1; j++) { - result = result + (S_num(n-j-1, 1, 1).to_cl_N() - S_num(1, n-j-1, 1-x).to_cl_N()) + result = result + (S_num(n-j-1, 1, 1) - S_num(1, n-j-1, 1-x)) * cln::expt(cln::log(x), j) / cln::factorial(j); } return result; @@ -402,7 +402,7 @@ numeric Lin_numeric(int n, const numeric& x) cln::cl_N x_ = ex_to<numeric>(x).to_cl_N(); cln::cl_N result = -cln::expt(cln::log(x_), n-1) * cln::log(1-x_) / cln::factorial(n-1); for (int j=0; j<n-1; j++) { - result = result + (S_num(n-j-1, 1, 1).to_cl_N() - S_num(1, n-j-1, 1-x_).to_cl_N()) + result = result + (S_num(n-j-1, 1, 1) - S_num(1, n-j-1, 1-x_)) * cln::expt(cln::log(x_), j) / cln::factorial(j); } return result; @@ -1715,10 +1715,10 @@ cln::cl_N C(int n, int p) if (k == 0) { if (n & 1) { if (j & 1) { - result = result - 2 * cln::expt(cln::pi(),2*j) * S_num(n-2*j,p,1).to_cl_N() / cln::factorial(2*j); + result = result - 2 * cln::expt(cln::pi(),2*j) * S_num(n-2*j,p,1) / cln::factorial(2*j); } else { - result = result + 2 * cln::expt(cln::pi(),2*j) * S_num(n-2*j,p,1).to_cl_N() / cln::factorial(2*j); + result = result + 2 * cln::expt(cln::pi(),2*j) * S_num(n-2*j,p,1) / cln::factorial(2*j); } } } @@ -1726,23 +1726,23 @@ cln::cl_N C(int n, int p) if (k & 1) { if (j & 1) { result = result + cln::factorial(n+k-1) - * cln::expt(cln::pi(),2*j) * S_num(n+k-2*j,p-k,1).to_cl_N() + * cln::expt(cln::pi(),2*j) * S_num(n+k-2*j,p-k,1) / (cln::factorial(k) * cln::factorial(n-1) * cln::factorial(2*j)); } else { result = result - cln::factorial(n+k-1) - * cln::expt(cln::pi(),2*j) * S_num(n+k-2*j,p-k,1).to_cl_N() + * cln::expt(cln::pi(),2*j) * S_num(n+k-2*j,p-k,1) / (cln::factorial(k) * cln::factorial(n-1) * cln::factorial(2*j)); } } else { if (j & 1) { - result = result - cln::factorial(n+k-1) * cln::expt(cln::pi(),2*j) * S_num(n+k-2*j,p-k,1).to_cl_N() + result = result - cln::factorial(n+k-1) * cln::expt(cln::pi(),2*j) * S_num(n+k-2*j,p-k,1) / (cln::factorial(k) * cln::factorial(n-1) * cln::factorial(2*j)); } else { result = result + cln::factorial(n+k-1) - * cln::expt(cln::pi(),2*j) * S_num(n+k-2*j,p-k,1).to_cl_N() + * cln::expt(cln::pi(),2*j) * S_num(n+k-2*j,p-k,1) / (cln::factorial(k) * cln::factorial(n-1) * cln::factorial(2*j)); } } @@ -1855,7 +1855,7 @@ cln::cl_N S_projection(int n, int p, const cln::cl_N& x, const cln::float_format res2 = res2 + cln::expt(cln::cl_I(-1),r) * cln::expt(cln::log(1-x),r) * S_do_sum(p-r,n-s,1-x,prec) / cln::factorial(r); } - result = result + cln::expt(cln::log(x),s) * (S_num(n-s,p,1).to_cl_N() - res2) / cln::factorial(s); + result = result + cln::expt(cln::log(x),s) * (S_num(n-s,p,1) - res2) / cln::factorial(s); } return result; @@ -1866,7 +1866,7 @@ cln::cl_N S_projection(int n, int p, const cln::cl_N& x, const cln::float_format // helper function for S(n,p,x) -numeric S_num(int n, int p, const numeric& x) +const cln::cl_N S_num(int n, int p, const cln::cl_N& x) { if (x == 1) { if (n == 1) { @@ -1902,11 +1902,11 @@ numeric S_num(int n, int p, const numeric& x) // what is the desired float format? // first guess: default format cln::float_format_t prec = cln::default_float_format; - const cln::cl_N value = x.to_cl_N(); + const cln::cl_N value = x; // second guess: the argument's format - if (!x.real().is_rational()) + if (!instanceof(realpart(value), cln::cl_RA_ring)) prec = cln::float_format(cln::the<cln::cl_F>(cln::realpart(value))); - else if (!x.imag().is_rational()) + else if (!instanceof(imagpart(value), cln::cl_RA_ring)) prec = cln::float_format(cln::the<cln::cl_F>(cln::imagpart(value))); // [Kol] (5.3) @@ -1919,9 +1919,9 @@ numeric S_num(int n, int p, const numeric& x) cln::cl_N res2; for (int r=0; r<p; r++) { res2 = res2 + cln::expt(cln::cl_I(-1),r) * cln::expt(cln::log(1-value),r) - * S_num(p-r,n-s,1-value).to_cl_N() / cln::factorial(r); + * S_num(p-r,n-s,1-value) / cln::factorial(r); } - result = result + cln::expt(cln::log(value),s) * (S_num(n-s,p,1).to_cl_N() - res2) / cln::factorial(s); + result = result + cln::expt(cln::log(value),s) * (S_num(n-s,p,1) - res2) / cln::factorial(s); } return result; @@ -1936,7 +1936,7 @@ numeric S_num(int n, int p, const numeric& x) for (int r=0; r<=s; r++) { result = result + cln::expt(cln::cl_I(-1),s) * cln::expt(cln::log(-value),r) * cln::factorial(n+s-r-1) / cln::factorial(r) / cln::factorial(s-r) / cln::factorial(n-1) - * S_num(n+s-r,p-s,cln::recip(value)).to_cl_N(); + * S_num(n+s-r,p-s,cln::recip(value)); } } result = result * cln::expt(cln::cl_I(-1),n); @@ -1972,12 +1972,18 @@ numeric S_num(int n, int p, const numeric& x) static ex S_evalf(const ex& n, const ex& p, const ex& x) { if (n.info(info_flags::posint) && p.info(info_flags::posint)) { + const int n_ = ex_to<numeric>(n).to_int(); + const int p_ = ex_to<numeric>(p).to_int(); if (is_a<numeric>(x)) { - return S_num(ex_to<numeric>(n).to_int(), ex_to<numeric>(p).to_int(), ex_to<numeric>(x)); + const cln::cl_N x_ = ex_to<numeric>(x).to_cl_N(); + const cln::cl_N result = S_num(n_, p_, x_); + return numeric(result); } else { ex x_val = x.evalf(); if (is_a<numeric>(x_val)) { - return S_num(ex_to<numeric>(n).to_int(), ex_to<numeric>(p).to_int(), ex_to<numeric>(x_val)); + const cln::cl_N x_val_ = ex_to<numeric>(x_val).to_cl_N(); + const cln::cl_N result = S_num(n_, p_, x_val_); + return numeric(result); } } } @@ -2002,7 +2008,11 @@ static ex S_eval(const ex& n, const ex& p, const ex& x) return Li(n+1, x); } if (x.info(info_flags::numeric) && (!x.info(info_flags::crational))) { - return S_num(ex_to<numeric>(n).to_int(), ex_to<numeric>(p).to_int(), ex_to<numeric>(x)); + int n_ = ex_to<numeric>(n).to_int(); + int p_ = ex_to<numeric>(p).to_int(); + const cln::cl_N x_ = ex_to<numeric>(x).to_cl_N(); + const cln::cl_N result = S_num(n_, p_, x_); + return numeric(result); } } if (n.is_zero()) { -- 1.5.4.2 -- All science is either physics or stamp collecting.

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[PATCH] Function and ncmul
by Vladimir Kisil 26 Apr '08

26 Apr '08

Dear All, Consider the following program: #include <ginac/ginac.h> #include <fstream> using namespace std; using namespace GiNaC; int main(){ realsymbol a("a"); varidx mu(symbol("mu", "\\mu"), 1); ex e = clifford_unit(mu, diag_matrix(lst(-1))), e0=e.subs(mu==0); cout << e0*e0*exp(a*e0) << endl; // -> exp(e0*a) cout << exp(a*e0)*e0*e0 << endl; // -> exp(e0*a)*e0*e0 } The expression in the second output is not simplified for the following reason. When the method ncmul::eval() collects non-commuting terms, the function exp(e0*a) gets the type of its first noncommuting argument, i.e. e0 (this is defined by function::return_type()). So all three factors are of the same type. However, later on, when ncmul::eval() calls the method eval_ncmul() for the first term in the product, e.i. exp(e0*a), it falls back to basic::eval_ncmul() not clifford::eval_ncmul() as one may expect. I am providing below a small patch which makes the behaviour of class function more consistent in this respect. Best wishes, Vladimir -- Vladimir V. Kisil email: kisilv(a)maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/ Parent: 6850c16435de33396ccd505ff26b4d4574fa74cf (Fixed bug in mLi summation causing premature drop-out and made Nielsen polylog) Branch: master Follows: release_1-4-0 Precedes: Method function::eval_ncmul() is defined to match the behaviour of function::return_type() ------------------------------ ginac/function.pl ------------------------------ index e91278c..3b22143 100644 @@ -507,6 +507,7 @@ public: ex expand(unsigned options=0) const; ex eval(int level=0) const; ex evalf(int level=0) const; + ex eval_ncmul(const exvector & v) const; unsigned calchash() const; ex series(const relational & r, int order, unsigned options = 0) const; ex thiscontainer(const exvector & v) const; @@ -1053,6 +1054,16 @@ ${evalf_switch_statement} throw(std::logic_error("function::evalf(): invalid nparams")); } +/* +* This method is defined to be in line with behaviour of function::return_type() +*/ +ex function::eval_ncmul(const exvector & v) const +{ + // If this function is called then the list of arguments is non-empty + // and the first argument is non-commutative, see function::return_type() + return seq.begin()->eval_ncmul(v); +} + unsigned function::calchash() const { unsigned v = golden_ratio_hash(golden_ratio_hash((p_int)tinfo()) ^ serial);

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Function and ncmul
by Vladimir V. Kisil 26 Apr '08

26 Apr '08

Dear All, Consider the following program: #include <ginac/ginac.h> #include <fstream> using namespace std; using namespace GiNaC; int main(){ realsymbol a("a"); varidx mu(symbol("mu", "\\mu"), 1); ex e = clifford_unit(mu, diag_matrix(lst(-1))), e0=e.subs(mu==0), p1=e0*exp(a*e0), p2=exp(a*e0)*e0; cout << e0*p1 << endl; // -> exp(e0*a) cout << p2*e0 << endl; // -> exp(e0*a)*e0*e0 } The expression in the second output is not simplified for the following reason. When the method ncmul::eval() collects non-commuting the terms exp(e0*a) gets the type of its first noncommuting element, i.e. e0 (this is defined by function::return_type()). So all three factors are in the same type group. However when later ncmul::eval() calls the method eval_ncmul() for the first term in the product, e.i. exp(e0*a), it falls back to basic::eval_ncmul() not clifford::eval_ncmul() as one may expect. I provide below a small patch which makes the behaviour of class function more consistent in this respect. Best wishes, Vladimir -- Vladimir V. Kisil email: kisilv(a)maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/ Parent: 6850c16435de33396ccd505ff26b4d4574fa74cf (Fixed bug in mLi summation causing premature drop-out and made Nielsen polylog) Branch: master Follows: release_1-4-0 Precedes: Method function::eval_ncmul() is defined to match the behaviour of function::return_type() ------------------------------ ginac/function.pl ------------------------------ index e91278c..3b22143 100644 @@ -507,6 +507,7 @@ public: ex expand(unsigned options=0) const; ex eval(int level=0) const; ex evalf(int level=0) const; + ex eval_ncmul(const exvector & v) const; unsigned calchash() const; ex series(const relational & r, int order, unsigned options = 0) const; ex thiscontainer(const exvector & v) const; @@ -1053,6 +1054,16 @@ ${evalf_switch_statement} throw(std::logic_error("function::evalf(): invalid nparams")); } +/* +* This method is defined to be in line with behaviour of function::return_type() +*/ +ex function::eval_ncmul(const exvector & v) const +{ + // If this function is called then the list of arguments is non-empty + // and the first argument is non-commutative, see function::return_type() + return seq.begin()->eval_ncmul(v); +} + unsigned function::calchash() const { unsigned v = golden_ratio_hash(golden_ratio_hash((p_int)tinfo()) ^ serial);

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gcd
by Jens Vollinga 24 Apr '08

24 Apr '08

Hi, there must be some bug in gcd_heur(): "gcd(5/4+n, 25/8+n^2+15/4*n)" causes an infinite loop. Any ideas? Regards, Jens

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GiNaC release 1.4.3
by Jens Vollinga 04 Apr '08

04 Apr '08

Hello again everybody, in order to fulfill the increased demand for GiNaC releases we proudly present: GiNaC 1.4.3 The changes are: * Fixed bug in numerical evaluation of multiple polylogarithms and alternating multiple zeta values introduced in version 1.4.2. * Nielsen polylog now invalidates its lookup tables in case the precision (Digits) has been changed. * Added new checks for recent bugs in the numerical evaluation of Li and zeta. As always, this release can be downloaded from http://www.ginac.de/Download.html Best wishes, Jens

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[SCM] GiNaC -- a C++ library for symbolic computations tag, release_1-4-3, created. release_1-4-0-49-g314595d
by git＠ginac.de 04 Apr '08

04 Apr '08

This is an automated email from the git hooks/post-receive script. It was generated because a ref change was pushed to the repository containing the project "GiNaC -- a C++ library for symbolic computations". The tag, release_1-4-3 has been created at 314595d10b4a4471bd4637a9038b18dde4780513 (commit) - Log ----------------------------------------------------------------- commit 314595d10b4a4471bd4637a9038b18dde4780513 Author: Jens Vollinga <jensv(a)nikhef.nl> Date: Fri Apr 4 15:00:01 2008 +0200 Preparing for release 1.4.3. ----------------------------------------------------------------------- hooks/post-receive -- GiNaC -- a C++ library for symbolic computations

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[SCM] GiNaC -- a C++ library for symbolic computations branch, ginac_1-4, updated. release_1-4-0-49-g314595d
by git＠ginac.de 04 Apr '08

04 Apr '08

This is an automated email from the git hooks/post-receive script. It was generated because a ref change was pushed to the repository containing the project "GiNaC -- a C++ library for symbolic computations". The branch, ginac_1-4 has been updated via 314595d10b4a4471bd4637a9038b18dde4780513 (commit) from 37cce07bdc6d2508f026e66190f6a982dce2e2b0 (commit) Those revisions listed above that are new to this repository have not appeared on any other notification email; so we list those revisions in full, below. - Log ----------------------------------------------------------------- commit 314595d10b4a4471bd4637a9038b18dde4780513 Author: Jens Vollinga <jensv(a)nikhef.nl> Date: Fri Apr 4 15:00:01 2008 +0200 Preparing for release 1.4.3. ----------------------------------------------------------------------- Summary of changes: NEWS | 7 +++++++ configure.ac | 6 +++--- 2 files changed, 10 insertions(+), 3 deletions(-) hooks/post-receive -- GiNaC -- a C++ library for symbolic computations

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[SCM] GiNaC -- a C++ library for symbolic computations branch, master, updated. release_1-4-0-44-g6850c16
by git＠ginac.de 04 Apr '08

04 Apr '08

This is an automated email from the git hooks/post-receive script. It was generated because a ref change was pushed to the repository containing the project "GiNaC -- a C++ library for symbolic computations". The branch, master has been updated via 6850c16435de33396ccd505ff26b4d4574fa74cf (commit) via f152bcaada41397cdf12d21fc2c4172d77ab7cb2 (commit) via 1254f5ef941aa6ead793e843b637edc927f47c7d (commit) from fb45203612dcfd2e30f6e7a43273597bcd13f026 (commit) Those revisions listed above that are new to this repository have not appeared on any other notification email; so we list those revisions in full, below. - Log ----------------------------------------------------------------- commit 6850c16435de33396ccd505ff26b4d4574fa74cf Author: Jens Vollinga <jensv(a)nikhef.nl> Date: Fri Apr 4 14:48:19 2008 +0200 Fixed bug in mLi summation causing premature drop-out and made Nielsen polylog invalidate its lookup tables if precision has been changed. commit f152bcaada41397cdf12d21fc2c4172d77ab7cb2 Author: Jens Vollinga <jensv(a)nikhef.nl> Date: Fri Apr 4 14:47:07 2008 +0200 Added legacy tests for zeta and multiple polylog. commit 1254f5ef941aa6ead793e843b637edc927f47c7d Author: Jens Vollinga <vollinga(a)thep.physik.uni-mainz.de> Date: Wed Dec 13 20:04:23 2006 +0000 Check for fixed bug in multiple polylogs. ----------------------------------------------------------------------- Summary of changes: check/exam_inifcns_nstdsums.cpp | 76 +++++++++++++++++++++++++++++++++++++++ ginac/inifcns_nstdsums.cpp | 15 ++++++-- 2 files changed, 88 insertions(+), 3 deletions(-) hooks/post-receive -- GiNaC -- a C++ library for symbolic computations

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[SCM] GiNaC -- a C++ library for symbolic computations branch, ginac_1-4, updated. release_1-4-0-48-g37cce07
by git＠ginac.de 04 Apr '08

04 Apr '08

This is an automated email from the git hooks/post-receive script. It was generated because a ref change was pushed to the repository containing the project "GiNaC -- a C++ library for symbolic computations". The branch, ginac_1-4 has been updated via 37cce07bdc6d2508f026e66190f6a982dce2e2b0 (commit) via a4b348a2ec489af31dfabcfab96ad8a7e7658e3e (commit) via 501b1d3afa61c5737bffd3208bf7ae356be75080 (commit) from 1ae153fe5ac8ba7a9d65fc413b9dfe7a5f0bd7df (commit) Those revisions listed above that are new to this repository have not appeared on any other notification email; so we list those revisions in full, below. - Log ----------------------------------------------------------------- commit 37cce07bdc6d2508f026e66190f6a982dce2e2b0 Author: Jens Vollinga <jensv(a)nikhef.nl> Date: Fri Apr 4 14:48:19 2008 +0200 Fixed bug in mLi summation causing premature drop-out and made Nielsen polylog invalidate its lookup tables if precision has been changed. commit a4b348a2ec489af31dfabcfab96ad8a7e7658e3e Author: Jens Vollinga <jensv(a)nikhef.nl> Date: Fri Apr 4 14:47:07 2008 +0200 Added legacy tests for zeta and multiple polylog. commit 501b1d3afa61c5737bffd3208bf7ae356be75080 Author: Jens Vollinga <vollinga(a)thep.physik.uni-mainz.de> Date: Wed Dec 13 20:04:23 2006 +0000 Check for fixed bug in multiple polylogs. ----------------------------------------------------------------------- Summary of changes: check/exam_inifcns_nstdsums.cpp | 76 +++++++++++++++++++++++++++++++++++++++ ginac/inifcns_nstdsums.cpp | 15 ++++++-- 2 files changed, 88 insertions(+), 3 deletions(-) hooks/post-receive -- GiNaC -- a C++ library for symbolic computations

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[SCM] GiNaC -- a C++ library for symbolic computations branch, ginac_1-4, updated. release_1-4-0-43-g70eaf7b
by git＠ginac.de 04 Apr '08

04 Apr '08

This is an automated email from the git hooks/post-receive script. It was generated because a ref change was pushed to the repository containing the project "GiNaC -- a C++ library for symbolic computations". The branch, ginac_1-4 has been updated via 70eaf7b7ad5250df07323b5a2e35803f69b33b14 (commit) from 47c1eb8365109f015062719acc5f2709b4131206 (commit) Those revisions listed above that are new to this repository have not appeared on any other notification email; so we list those revisions in full, below. - Log ----------------------------------------------------------------- commit 70eaf7b7ad5250df07323b5a2e35803f69b33b14 Author: Jens Vollinga <jensv(a)nikhef.nl> Date: Thu Apr 3 11:56:57 2008 +0200 Fixed bugs found by Jianqiang Zhao. ----------------------------------------------------------------------- Summary of changes: ginac/inifcns_nstdsums.cpp | 8 +++++++- 1 files changed, 7 insertions(+), 1 deletions(-) hooks/post-receive -- GiNaC -- a C++ library for symbolic computations

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