Module: BigMath

Defined in:
lib/bigdecimal/math.rb

Overview

-- 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

Instance Method Summary collapse

Instance Method Details

#atan(x, prec) ⇒ Object

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.

Raises:

  • (ArgumentError) 


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# File 'lib/bigdecimal/math.rb', line 103

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

#cos(x, prec) ⇒ Object

Computes the cosine of x to the specified number of digits of precision.

If x is infinite or NaN, returns NaN.

Raises:

  • (ArgumentError) 


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# File 'lib/bigdecimal/math.rb', line 74

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

#E(prec) ⇒ Object

Computes e (the base of natural logarithms) to the specified number of digits of precision.

Raises:

  • (ArgumentError) 


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# File 'lib/bigdecimal/math.rb', line 218

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

#exp(x, prec) ⇒ Object

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"

Raises:

  • (ArgumentError) 


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# File 'lib/bigdecimal/math.rb', line 130

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

#log(x, prec) ⇒ Object

Computes the natural logarithm of x to the specified number of digits of precision.

Returns x if x is infinite or NaN.

Raises:

  • (ArgumentError) 


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# File 'lib/bigdecimal/math.rb', line 156

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

#PI(prec) ⇒ Object

Computes the value of pi to the specified number of digits of precision.

Raises:

  • (ArgumentError) 


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# File 'lib/bigdecimal/math.rb', line 178

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

#sin(x, prec) ⇒ Object

Computes the sine of x to the specified number of digits of precision.

If x is infinite or NaN, returns NaN.

Raises:

  • (ArgumentError) 


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# File 'lib/bigdecimal/math.rb', line 46

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

#sqrt(x, prec) ⇒ Object

Computes the square root of x to the specified number of digits of precision.

BigDecimal.new('2').sqrt(16).to_s 

-> "0.14142135623730950488016887242096975E1"



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# File 'lib/bigdecimal/math.rb', line 39

def sqrt(x,prec)
  x.sqrt(prec)
end