This repository contains several short code which I am using and testing. They all computes the Laplace limit occurs in the field of basic orbital dynamics. At the meanwhile I am still evaluating the relative speed of them.
Legalese readers: No warranty, not fit for particular purpose...
Tested on Fourtuna, initial value with 2 d.p. Requested length 200 d.p. For laplace_mpfr, argument 800 is used to match the 200 d.p.
| Code | Runtime 1 | Runtime 2 | Runtime 3 |
|---|---|---|---|
| laplace.dc | 0m31.342s | 0m31.105s | 0m31.348s |
| laplace_mpfr | 0m0.043s | 0m0.036s | 0m0.033s |
Tested on Fourtuna, initial value with 5 d.p. Requested argument 10000, output should be 2500 d.p.
| Version | Runtime 1 | Runtime 2 | Runtime 3 |
|---|---|---|---|
| laplace_mpfr | 0m18.276s | 0m18.069s | 0m18.078s |
| laplace_mpfr2 | 0m6.531s | 0m6.555s | 0m6.520s |
| laplace_mpfr3 | 0m6.539s | 0m6.559s | 0m6.505s |
| laplace_mpfr4 | 0m0.028s | 0m0.022s | 0m0.021s |
| laplace_mpfr5 | 0m0.054s | 0m0.062s | 0m0.059s |
mpfr->mpfr2: Another equation is used which is faster mpfr2->mpfr3: Interrupt handling is added and now it could save and restore from continue.dat mpfr3->mpfr4: A end-order root finding method is used. Per iteration time is also shortened. mpfr5: Trying to use a 4-th order root finding method, but seems no improvement in total runtime. Will do parallelization.
Tested on Fourtuna, initial value with 5 d.p.
| Requested length | 2495 d.p. | 5000 d.p. |
|---|---|---|
| laplace_2ndConv.bc | 1m26.226s | 13m29.706s |
| laplace_4thConv.bc | 1m33.619s | 17m35.945s |