Module: BigMathR::Const::PI

Defined in:
lib/bigdecimal/math_r/const/PI_euler.rb,
lib/bigdecimal/math_r/const/PI_chudnovsky.rb,
lib/bigdecimal/math_r/const/PI_ramanujan1.rb,
lib/bigdecimal/math_r/const/PI_ramanujan2.rb,
ext/bigdecimal/math_r/math_r.c

Class Method Summary collapse

Class Method Details

.chudnovsky(prec) ⇒ BigDecimal

Implement by Chudnovsky’s formula

Examples:

BigMathR::Const::PI.chudnovsky(20)
#=> 0.31415926535897932385e1

Parameters:

  • prec (Integer) —

    Arbitrary precision

Returns:

  • (BigDecimal) —

    Constant PI

Raises:

  • (TypeError) —

    not an Integer

  • (RangeError) —

    Zero or negative precision



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# File 'lib/bigdecimal/math_r/const/PI_chudnovsky.rb', line 18

def chudnovsky(prec)
  raise TypeError, "precision must be an Integer" unless prec.class == Integer
  raise RangeError, "Zero or negative precision" if prec <= 0

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

  n = prec + BigDecimal.double_fig

  m1_640320_3 = BigDecimal(-1/262537412640768000r, n)
  p90856689_711822400 = BigDecimal(90856689/711822400r, n)
  p90856689_711822400 *= BigDecimal(10005).sqrt(n)

  _C = one
  _AB = BigDecimal(13591409/545140134r, n)
  _F = 1r

  d = one
  y = zero

  i = 0

  while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig

    d = BigDecimal(_F, m).mult(_AB * _C, m)
    y = y + d

    _AB += one
    _C *= m1_640320_3
    i = i.succ
    (6 * i - 5).step(6 * i) {|k| _F *= k}
    (3 * i - 2).step(3 * i) {|k| _F /= k}
    3.times { _F /= i }
  end
  
  y = y.mult(p90856689_711822400, n)
  one.div(y, prec)
end

.euler(prec) ⇒ BigDecimal

Implement by Euler’s formula.

Examples:

BigMathR::Const::PI.euler(20)
#=> 0.31415926535897932385e1

Parameters:

  • prec (Integer) —

    Arbitrary precision

Returns:

  • (BigDecimal) —

    Constant PI

Raises:

  • (TypeError) —

    not an Integer

  • (RangeError) —

    Zero or negative precision



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# File 'lib/bigdecimal/math_r/const/PI_euler.rb', line 18

def euler(prec)
  raise TypeError, "precision must be an Integer" unless prec.class == Integer
  raise RangeError, "Zero or negative precision" if prec <= 0
  n = BigDecimal.double_fig + prec
  one = BigDecimal(1)
  two = BigDecimal(2)
  s = BigDecimal(0)
  t = one
  t1 = BigDecimal(0)
  t2 = one
  n = prec + BigDecimal.double_fig
  while t.nonzero? && ((m = n - (s.exponent - t.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    s = s + t
    t1 = t1 + one;  t = t.mult(t1, m)
    t2 = t2 + two;  t = t.div(t2, m)
  end
  two.mult(s, prec)
end

.ramanujan1(prec) ⇒ BigDecimal

Implement by Ramanujan’s formula.

Examples:

BigMathR::Const::PI.ramanujan1(20)
#=> 0.31415926535897932385e1

Parameters:

  • prec (Integer) —

    Arbitrary precision

Returns:

  • (BigDecimal) —

    Constant PI

Raises:

  • (TypeError) —

    not an Integer

  • (RangeError) —

    Zero or negative precision



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# File 'lib/bigdecimal/math_r/const/PI_ramanujan1.rb', line 18

def ramanujan1(prec)
  raise TypeError, "precision must be an Integer" unless prec.class == Integer
  raise RangeError, "Zero or negative precision" if prec <= 0
  n = BigDecimal.double_fig + prec

  i = 0
  r = 1/9801r
  k = 1103

  d = BigDecimal(1)
  y = BigDecimal(0)

  while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    d = BigDecimal(r * k, m)
    y = y + d
    i = i.succ
    k += 26390
    r *= (2 * i - 1) * (4 * i - 3) * (4 * i - 1)
    r /= 96059601
    r /= 32
    3.times { r /= i }
  end
  BigDecimal(2).sqrt(n).div(y * BigDecimal(4), prec)
end

.ramanujan2(prec) ⇒ BigDecimal

Implement by Ramanujan’s formula.

Examples:

BigMathR::Const::PI.ramanujan2(20)
#=> 0.31415926535897932385e1

Parameters:

  • prec (Integer) —

    Arbitrary precision

Returns:

  • (BigDecimal) —

    Constant PI

Raises:

  • (TypeError) —

    not an Integer

  • (RangeError) —

    Zero or negative precision



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# File 'lib/bigdecimal/math_r/const/PI_ramanujan2.rb', line 18

def ramanujan2(prec)
  raise TypeError, "precision must be an Integer" unless prec.class == Integer
  raise RangeError, "Zero or negative precision" if prec <= 0
  n = BigDecimal.double_fig + prec

  i = 0
  r = 1/882r
  k = 1123

  d = BigDecimal(1)
  y = BigDecimal(0)

  while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    d = BigDecimal(r * k, m)
    y = y + d
    i = i.succ
    k += 21460
    r = -r
    r *= (2 * i - 1) * (4 * i - 3) * (4 * i - 1)
    r /= 777924
    r /= 32
    3.times { r /= i }
  end
  BigDecimal(4).div(y, prec)
end