Method arctan

__test__/theorem.js:1233–1249

(x)

  	const digits = 15
  	const Decimal = BigNumber.clone({ DECIMAL_PLACES: digits })
      function arctan(x) {
          var y = x;
          var yPrev = NaN;
          var x2 = x.times(x);
          var num = x;
          var sign = -1;
  
          for (var k = 3; !y.eq(yPrev); k += 2) {
              num = num.times(x2);
  
              yPrev = y;
              y = (sign > 0) ? y.plus(num.div(k)) : y.minus(num.div(k));
              sign = -sign;
          }
  
          return y;
      }
  
      // Machin: Pi / 4 = 4 * arctan(1 / 5) - arctan(1 / 239)
      // http://milan.milanovic.org/math/english/pi/machin.html