Problems with Log function in Boost C++ libraries -
i have code in order logarithm of number given generic base:
#include <boost/math/special_functions/powm1.hpp> #include <boost/math/special_functions/log1p.hpp> #include <boost/math/special_functions/sqrt1pm1.hpp> // ... // boost log returns boost::math::log1p(x) = log(e, x + 1) double res = (double)(boost::math::log1p(arg - 1)); // base conversion: log(new, y) = log(old, y) / log(old, new) // ==> log(base, arg) = log(e, arg) / log(e, base) res = (double)(res / ((double)boost::math::log1p(base - 1))); return res; as can see boot libs define neperian log , there tricky way log because lib gives not log(x) log(x+1). can see problem solved giving argument arg - 1 , should work.
well works, neperian log ok, mean, if run code:
#include <boost/math/special_functions/powm1.hpp> #include <boost/math/special_functions/log1p.hpp> #include <boost/math/special_functions/sqrt1pm1.hpp> // ... // boost log returns boost::math::log1p(x) = log(e, x + 1) double res = (double)(boost::math::log1p(arg - 1)); // base conversion: log(new, y) = log(old, y) / log(old, new) // ==> log(base, arg) = log(e, arg) / log(e, base) //res = (double)(res / ((double)boost::math::log1p(base - 1))); return res; everything ok, right when perform base change not good, wrong results... don't know, maybe it's math issue... know log(basea, x) = log(baseb, x)/log(baseb, basea)...
where do wrong??
well, may math issue concerning numerical stability , on... log in different base, what's best practice???????
i not sure happening may having rounding issue. issue 1 + delta delta small doubles not built hold delta precision 1 dominates enormously , delta considered insignificant.
the purpose of boost library allow pass in 1 , delta separately not lose precision of delta when take log, give number close 0.
an example delta = 0.00000000123456789
if add 1 subtract 1 again not see numbers double holds 15 places of precision number above +1 gives requires 17 whereas numbe have printed uses 9 places because leading zeros don't count.
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