Found a 64bit double implementation library, but I cannot compile it

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lesto:
just a little problem (arduino IDE 1.0.1):

halfPI = PI / 2;

give some error with overloaded constructor. I've work around it because I'm not good with c++ :grin:

Try:

halfPI = bigPI / BigNumber (2);

You can probably cut down the precision of bigPI - that uses RAM and you are hardly going to need all those digits.

execution time (microseconds, precision of 5): 142256 vs 116(using float)

Yes, I didn't say it was fast. :slight_smile:

Arbitrary precision libraries tend to be slow by their nature.

Some of your stuff is inefficient:

 BigNumber negate = BigNumber(x < 0);
  if (x < 0){
     x*=-1;
  }

Why multiply when you can negate?

BigNumber acosine(BigNumber x) {
  boolean negate = false;
  
  if (x.isNegative ())
    {
    x -= x;
    negate = true;
    }

  BigNumber ret = -0.0187293;
  ret *= x;
  ret += 0.0742610;
  ret *= x;
  ret -= 0.2121144;
  ret *= x;
  ret += 1.5707288;
  BigNumber bigSqrt = x - BigNumber (1);
  ret *= bigSqrt.sqrt();
  ret -= 2 * ret;
  if (negate)
    return - bigPI - ret;
  else
    return bigPI + ret;
}

Try to keep multiplications down. Subtracting a number from 0 will be faster than multiplying by -1. Also I don't know why you were working on x as a float. Doesn't that throw away the extra precision? I haven't tested the changes, but they show what I had in mind.