多倍精度浮動小数点数型 mpf_class において対数関数 ln(x) を求める

gistfile1.cpp

void mpf_ln(mpf_class &r, const mpf_class &x){
    mp_bitcnt_t prec = x.get_prec();
    if(x > 0.5){
        mpf_class term = 1.0 - (1.0 / x), term_k = term, last = r;
        r = term_k;
        term_k *= term;
        r += term_k / 2.0;
        for(std::size_t i = 3; !mpf_eq(r.get_mpf_t(), last.get_mpf_t(), prec); ++i){
            last = r;
            term_k *= term;
            r += term_k / i;
        }
    }else if(x > 0.0){
        mpf_class term = x - 1.0, term_k = term, factor = 1.0, last = r;
        r = term;
        int sign = -1;
        term_k *= term;
        r += -term_k / 2.0;
        for(std::size_t i = 3; !mpf_eq(r.get_mpf_t(), last.get_mpf_t(), prec); ++i){
            last = r;
            term_k *= term;
            sign *= -1;
            r += term_k * sign / i;
        }
    }
}