second_order_root_finder (near) infinite loop

[TFiFiE]

halley_iterate and schroder_iterate can get stuck in a (virtually) infinite loop even when given a limited max_iter, because in the function:

math/include/boost/math/tools/roots.hpp

Line 483 in b22105f

T second_order_root_finder(F f, T guess, T min, T max, int digits, std::uintmax_t& max_iter) noexcept(policies::is_noexcept_error_policy<policies::policy<> >::value&& BOOST_MATH_IS_FLOAT(T) && noexcept(std::declval<F>()(std::declval<T>())))

the variable count might already be zero when either of the following functions is called:

math/include/boost/math/tools/roots.hpp

Line 612 in b22105f

delta = bracket_root_towards_min(f, guess, f0, min, max, count);

math/include/boost/math/tools/roots.hpp

Line 638 in b22105f

delta = bracket_root_towards_max(f, guess, f0, min, max, count);

where it will wrap around by any of:

math/include/boost/math/tools/roots.hpp

Line 383 in b22105f

while (--count && ((f_current < 0) == (f0 < 0)))

math/include/boost/math/tools/roots.hpp

Line 402 in b22105f

while (--count && ((f_current < 0) == (f0 < 0)))

math/include/boost/math/tools/roots.hpp

Line 439 in b22105f

while (--count && ((f_current < 0) == (f0 < 0)))

math/include/boost/math/tools/roots.hpp

Line 458 in b22105f

while (--count && ((f_current < 0) == (f0 < 0)))

becoming std::numeric_limits<boost::uintmax_t>::max() before reaching:

math/include/boost/math/tools/roots.hpp

Line 662 in b22105f

} while(count && (fabs(result * factor) < fabs(delta)));