log_natural_()

template<typename F>

F fl::detail::log_natural_ ( F value )

inline

Definition at line 295 of file math.cpp.hpp.

                                            {
    if (value <= F(0)) return F(-1e30);  // -inf surrogate
    int e = 0;
    while (value >= F(2)) { value *= F(0.5); ++e; }
    while (value < F(1))  { value *= F(2);   --e; }
    // value ∈ [1, 2); evaluate log(value) via Taylor around 1: let u = value - 1.
    // log(1+u) = u - u²/2 + u³/3 - u⁴/4 + ...
    // Use enough terms for ~5-decimal accuracy on [0, 1].
    const F u  = value - F(1);
    const F u2 = u * u;
    const F u3 = u2 * u;
    const F u4 = u2 * u2;
    const F u5 = u4 * u;
    const F u6 = u4 * u2;
    const F u7 = u6 * u;
    F log_m = u - u2 * F(0.5) + u3 * F(1.0 / 3.0) - u4 * F(0.25)
              + u5 * F(0.2) - u6 * F(1.0 / 6.0) + u7 * F(1.0 / 7.0);
    const F kLn2 = F(0.69314718055994530942);
    return log_m + F(e) * kLn2;
}

References fl::FL_NO_EXCEPT, and fl::type_rank< T >::value.

Referenced by fl::log10_impl_double(), fl::log10_impl_float(), fl::log_impl_double(), fl::log_impl_float(), fl::pow_impl_double(), and fl::pow_impl_float().

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