Module: BigMathR::Const::E

Defined in:
lib/bigdecimal/math_r/const/E_euler.rb,
ext/bigdecimal/math_r/math_r.c

Class Method Summary collapse

Class Method Details

.euler(prec) ⇒ BigDecimal

Implement by continued fraction.

Examples:

BigMathR::Const::E.euler(20)
#=> 0.271828182845904523536e1

Parameters:

  • prec (Integer) —

    Arbitrary precision

Returns:

  • (BigDecimal) —

    Constant e.

Raises:

  • (TypeError) —

    not an Integer

  • (RangeError) —

    Zero or negative precision



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# File 'lib/bigdecimal/math_r/const/E_euler.rb', line 16

def euler(prec)
  raise TypeError, "precision must be in Integer" unless prec.class == Integer
  raise RangeError, "Zero or negative precision" if prec <= 0
  n = BigDecimal.double_fig + prec

  zero = BigDecimal(0)
  one = BigDecimal(1)
  two = BigDecimal(2)

  c = one
  b = one
  p1 = one;  q1 = zero;  p2 = two;  q2 = one;
  i = one
  loop do
    prev = p2
    t = p1 * c + p2 * b;  p1 = p2;  p2 = t;
    t = q1 * c + q2 * b;  q1 = q2;  q2 = t;
    if q2.nonzero?
      p1 = p1.div(q2, n);  q1 = q1.div(q2, n);  p2 = p2.div(q2, n);  q2 = one;
    end
    i += one
    c = one
    b = (i + one) % 3 == 0 ? ((i.to_i.succ) / 3) * two : one
    break unless q2.nonzero? && prev != p2
  end
  p2.round(prec)
end

.euler_number(prec) ⇒ BigDecimal

Implement by series expansion: sum_(n=0)^infty 1/n!

Examples:

BigMathR::Const::E.napier(20)
#=> 0.27182818284590452354e1

Parameters:

  • prec (Integer) —

    Arbitrary precision

Returns:

  • (BigDecimal) —

    Natural logarithm of 2

Raises:

  • (TypeError) —

    not an Integer

  • (RangeError) —

    Zero or negative precision



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# File 'ext/bigdecimal/math_r/const.c', line 160

static VALUE
__impl_const_e_napier(VALUE unused_obj, VALUE prec)
{
	return E_napier(prec);
}

.napier(prec) ⇒ BigDecimal

Implement by series expansion: sum_(n=0)^infty 1/n!

Examples:

BigMathR::Const::E.napier(20)
#=> 0.27182818284590452354e1

Parameters:

  • prec (Integer) —

    Arbitrary precision

Returns:

  • (BigDecimal) —

    Natural logarithm of 2

Raises:

  • (TypeError) —

    not an Integer

  • (RangeError) —

    Zero or negative precision



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# File 'ext/bigdecimal/math_r/const.c', line 160

static VALUE
__impl_const_e_napier(VALUE unused_obj, VALUE prec)
{
	return E_napier(prec);
}