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ginac-devel@ginac.de

May 2008

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[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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