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Edit File : math.rb \| Size : 5.92 KB
# #-- # Contents: # sqrt(x, prec) # sin (x, prec) # cos (x, prec) # atan(x, prec) Note: \|x\|<1, x=0.9999 may not converge. # exp (x, prec) # log (x, prec) # PI (prec) # E (prec) == exp(1.0,prec) # # where: # x ... BigDecimal number to be computed. # \|x\| must be small enough to get convergence. # prec ... Number of digits to be obtained. #++ # # Provides mathematical functions. # # Example: # # require "bigdecimal" # require "bigdecimal/math" # # include BigMath # # a = BigDecimal((PI(100)/2).to_s) # puts sin(a,100) # -> 0.10000000000000000000......E1 # module BigMath # Computes the square root of x to the specified number of digits of # precision. # # BigDecimal.new('2').sqrt(16).to_s # -> "0.14142135623730950488016887242096975E1" # def sqrt(x,prec) x.sqrt(prec) end # Computes the sine of x to the specified number of digits of precision. # # If x is infinite or NaN, returns NaN. def sin(x, prec) raise ArgumentError, "Zero or negative precision for sin" if prec <= 0 return BigDecimal("NaN") if x.infinite? \|\| x.nan? n = prec + BigDecimal.double_fig one = BigDecimal("1") two = BigDecimal("2") x1 = x x2 = x.mult(x,n) sign = 1 y = x d = y i = one z = one while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig sign = -sign x1 = x2.mult(x1,n) i += two z = (i-one) i d = sign * x1.div(z,m) y += d end y end # Computes the cosine of x to the specified number of digits of precision. # # If x is infinite or NaN, returns NaN. def cos(x, prec) raise ArgumentError, "Zero or negative precision for cos" if prec <= 0 return BigDecimal("NaN") if x.infinite? \|\| x.nan? n = prec + BigDecimal.double_fig one = BigDecimal("1") two = BigDecimal("2") x1 = one x2 = x.mult(x,n) sign = 1 y = one d = y i = BigDecimal("0") z = one while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig sign = -sign x1 = x2.mult(x1,n) i += two z = (i-one) i d = sign * x1.div(z,m) y += d end y end # Computes the arctangent of x to the specified number of digits of precision. # # If x is infinite or NaN, returns NaN. # Raises an argument error if x > 1. def atan(x, prec) raise ArgumentError, "Zero or negative precision for atan" if prec <= 0 return BigDecimal("NaN") if x.infinite? \|\| x.nan? raise ArgumentError, "x.abs must be less than 1.0" if x.abs>=1 n = prec + BigDecimal.double_fig y = x d = y t = x r = BigDecimal("3") x2 = x.mult(x,n) while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig t = -t.mult(x2,n) d = t.div(r,m) y += d r += 2 end y end # Computes the value of e (the base of natural logarithms) raised to the # power of x, to the specified number of digits of precision. # # If x is infinite or NaN, returns NaN. # # BigMath::exp(BigDecimal.new('1'), 10).to_s # -> "0.271828182845904523536028752390026306410273E1" def exp(x, prec) raise ArgumentError, "Zero or negative precision for exp" if prec <= 0 return BigDecimal("NaN") if x.infinite? \|\| x.nan? n = prec + BigDecimal.double_fig one = BigDecimal("1") x1 = one y = one d = y z = one i = 0 while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig x1 = x1.mult(x,n) i += 1 z = i d = x1.div(z,m) y += d end y end # Computes the natural logarithm of x to the specified number of digits # of precision. # # Returns x if x is infinite or NaN. # def log(x, prec) raise ArgumentError, "Zero or negative argument for log" if x <= 0 \|\| prec <= 0 return x if x.infinite? \|\| x.nan? one = BigDecimal("1") two = BigDecimal("2") n = prec + BigDecimal.double_fig x = (x - one).div(x + one,n) x2 = x.mult(x,n) y = x d = y i = one while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig x = x2.mult(x,n) i += two d = x.div(i,m) y += d end ytwo end # Computes the value of pi to the specified number of digits of precision. def PI(prec) raise ArgumentError, "Zero or negative argument for PI" if prec <= 0 n = prec + BigDecimal.double_fig zero = BigDecimal("0") one = BigDecimal("1") two = BigDecimal("2") m25 = BigDecimal("-0.04") m57121 = BigDecimal("-57121") pi = zero d = one k = one w = one t = BigDecimal("-80") while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig t = tm25 d = t.div(k,m) k = k+two pi = pi + d end d = one k = one w = one t = BigDecimal("956") while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig t = t.div(m57121,n) d = t.div(k,m) pi = pi + d k = k+two end pi end # Computes e (the base of natural logarithms) to the specified number of # digits of precision. def E(prec) raise ArgumentError, "Zero or negative precision for E" if prec <= 0 n = prec + BigDecimal.double_fig one = BigDecimal("1") y = one d = y z = one i = 0 while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0) m = BigDecimal.double_fig if m < BigDecimal.double_fig i += 1 z = i d = one.div(z,m) y += d end y end end Back

Edit File : math.rb | Size : 5.92 KB

#
#--
# Contents:
#   sqrt(x, prec)
#   sin (x, prec)
#   cos (x, prec)
#   atan(x, prec)  Note: |x|<1, x=0.9999 may not converge.
#   exp (x, prec)
#   log (x, prec)
#   PI  (prec)
#   E   (prec) == exp(1.0,prec)
#
# where:
#   x    ... BigDecimal number to be computed.
#            |x| must be small enough to get convergence.
#   prec ... Number of digits to be obtained.
#++
#
# Provides mathematical functions.
#
# Example:
#
#   require "bigdecimal"
#   require "bigdecimal/math"
#
#   include BigMath
#
#   a = BigDecimal((PI(100)/2).to_s)
#   puts sin(a,100) # -> 0.10000000000000000000......E1
#
module BigMath

# Computes the square root of x to the specified number of digits of 
  # precision.
  #
  # BigDecimal.new('2').sqrt(16).to_s 
  #  -> "0.14142135623730950488016887242096975E1"
  #
  def sqrt(x,prec)
    x.sqrt(prec)
  end

# Computes the sine of x to the specified number of digits of precision.
  #
  # If x is infinite or NaN, returns NaN.
  def sin(x, prec)
    raise ArgumentError, "Zero or negative precision for sin" if prec <= 0
    return BigDecimal("NaN") if x.infinite? || x.nan?
    n    = prec + BigDecimal.double_fig
    one  = BigDecimal("1")
    two  = BigDecimal("2")
    x1   = x
    x2   = x.mult(x,n)
    sign = 1
    y    = x
    d    = y
    i    = one
    z    = one
    while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
      m = BigDecimal.double_fig if m < BigDecimal.double_fig
      sign = -sign
      x1  = x2.mult(x1,n)
      i  += two
      z  *= (i-one) * i
      d   = sign * x1.div(z,m)
      y  += d
    end
    y
  end

# Computes the cosine of x to the specified number of digits of precision.
  #
  # If x is infinite or NaN, returns NaN.
  def cos(x, prec)
    raise ArgumentError, "Zero or negative precision for cos" if prec <= 0
    return BigDecimal("NaN") if x.infinite? || x.nan?
    n    = prec + BigDecimal.double_fig
    one  = BigDecimal("1")
    two  = BigDecimal("2")
    x1 = one
    x2 = x.mult(x,n)
    sign = 1
    y = one
    d = y
    i = BigDecimal("0")
    z = one
    while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
      m = BigDecimal.double_fig if m < BigDecimal.double_fig
      sign = -sign
      x1  = x2.mult(x1,n)
      i  += two
      z  *= (i-one) * i
      d   = sign * x1.div(z,m)
      y  += d
    end
    y
  end

# Computes the arctangent of x to the specified number of digits of precision.
  #
  # If x is infinite or NaN, returns NaN.
  # Raises an argument error if x > 1.
  def atan(x, prec)
    raise ArgumentError, "Zero or negative precision for atan" if prec <= 0
    return BigDecimal("NaN") if x.infinite? || x.nan?
    raise ArgumentError, "x.abs must be less than 1.0" if x.abs>=1
    n    = prec + BigDecimal.double_fig
    y = x
    d = y
    t = x
    r = BigDecimal("3")
    x2 = x.mult(x,n)
    while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
      m = BigDecimal.double_fig if m < BigDecimal.double_fig
      t = -t.mult(x2,n)
      d = t.div(r,m)
      y += d
      r += 2
    end
    y
  end

# Computes the value of e (the base of natural logarithms) raised to the 
  # power of x, to the specified number of digits of precision.
  #
  # If x is infinite or NaN, returns NaN.
  #
  # BigMath::exp(BigDecimal.new('1'), 10).to_s
  # -> "0.271828182845904523536028752390026306410273E1"
  def exp(x, prec)
    raise ArgumentError, "Zero or negative precision for exp" if prec <= 0
    return BigDecimal("NaN") if x.infinite? || x.nan?
    n    = prec + BigDecimal.double_fig
    one  = BigDecimal("1")
    x1 = one
    y  = one
    d  = y
    z  = one
    i  = 0
    while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
      m = BigDecimal.double_fig if m < BigDecimal.double_fig
      x1  = x1.mult(x,n)
      i += 1
      z *= i
      d  = x1.div(z,m)
      y += d
    end
    y
  end

# Computes the natural logarithm of x to the specified number of digits 
  # of precision.
  #
  # Returns x if x is infinite or NaN.
  #
  def log(x, prec)
    raise ArgumentError, "Zero or negative argument for log" if x <= 0 || prec <= 0
    return x if x.infinite? || x.nan?
    one = BigDecimal("1")
    two = BigDecimal("2")
    n  = prec + BigDecimal.double_fig
    x  = (x - one).div(x + one,n)
    x2 = x.mult(x,n)
    y  = x
    d  = y
    i = one
    while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
      m = BigDecimal.double_fig if m < BigDecimal.double_fig
      x  = x2.mult(x,n)
      i += two
      d  = x.div(i,m)
      y += d
    end
    y*two
  end

# Computes the value of pi to the specified number of digits of precision.
  def PI(prec)
    raise ArgumentError, "Zero or negative argument for PI" if prec <= 0
    n      = prec + BigDecimal.double_fig
    zero   = BigDecimal("0")
    one    = BigDecimal("1")
    two    = BigDecimal("2")

m25    = BigDecimal("-0.04")
    m57121 = BigDecimal("-57121")

pi     = zero

d = one
    k = one
    w = one
    t = BigDecimal("-80")
    while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0)
      m = BigDecimal.double_fig if m < BigDecimal.double_fig
      t   = t*m25
      d   = t.div(k,m)
      k   = k+two
      pi  = pi + d
    end

d = one
    k = one
    w = one
    t = BigDecimal("956")
    while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0)
      m = BigDecimal.double_fig if m < BigDecimal.double_fig
      t   = t.div(m57121,n)
      d   = t.div(k,m)
      pi  = pi + d
      k   = k+two
    end
    pi
  end

# Computes e (the base of natural logarithms) to the specified number of
  # digits of precision.
  def E(prec)
    raise ArgumentError, "Zero or negative precision for E" if prec <= 0
    n    = prec + BigDecimal.double_fig
    one  = BigDecimal("1")
    y  = one
    d  = y
    z  = one
    i  = 0
    while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
      m = BigDecimal.double_fig if m < BigDecimal.double_fig
      i += 1
      z *= i
      d  = one.div(z,m)
      y += d
    end
    y
  end
end

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