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I need to very quickly calculate the Stirling approximation

I am writing a small library for statistical sampling, which should run as quickly as possible. In profiling, I found that about 40% of the time spent on this function is spent on calculating the Stirling approximation for the logarithm of the factorial. I am focusing optimization efforts on this snippet. Here is my code (which uses MPFR ):

const double AL[8] =
{ 0.0, 0.0, 0.6931471806, 1.791759469, 3.178053830, 4.787491743,
    6.579251212, 8.525161361 };
void HGD::mpfr_afc(mpfr_t &ret, const mpfr_t &val){

    if(mpfr_cmp_ui(val, 7) <= 0){
        mpfr_set_d(ret, AL[mpfr_get_ui(val, MPFR_RNDN)], MPFR_RNDN);
    }else{
        mpfr_set(ret, val, MPFR_RNDN);
        mpfr_add_d(ret, ret, 0.5, MPFR_RNDN);
        mpfr_log(LV, val, MPFR_RNDN);
        mpfr_mul(ret, LV, ret, MPFR_RNDN);
        mpfr_sub(ret, ret, val, MPFR_RNDN);
        mpfr_add_d(ret, ret, 0.399089934, MPFR_RNDN);
    }
}

I have several different ideas:

  • Comprehend more than the first 8 inputs to a function.
  • Optimize math (use a coarser approximation for less accuracy)
  • Using multiple threads for parallel computation on different inputs
  • Switch to your own arithmetic when numbers can be inserted into machine data types

?

+4
2

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+2

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float , , , . , , .

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+1

Source: https://habr.com/ru/post/1526464/

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