log1p.hpp

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#ifndef __STAN__MATH__FUNCTIONS__LOG1P_HPP__
#define __STAN__MATH__FUNCTIONS__LOG1P_HPP__

#include <boost/math/tools/promotion.hpp>
#include <stdexcept>
#include <boost/throw_exception.hpp>

namespace stan {
  namespace math {

    template <typename T>
    inline typename boost::math::tools::promote_args<T>::type
    log1p(const T x) {
      using std::log;
      if (x < -1.0)
        BOOST_THROW_EXCEPTION(std::domain_error ("x can not be less than -1"));

      if (x > 1e-9 || x < -1e-9)
        return log(1.0 + x);     // direct, if distant from 1
      else if (x > 1e-16 || x < -1e-16)
        return x - 0.5 * x * x;  // 2nd order Taylor, if close to 1
      else
        return x;                // 1st order Taylor, if very close to 1
    }

  }
}

#endif