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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
Computes e (the base of natural logarithms) to the specified number of digits of precision.
# File bigdecimal/lib/bigdecimal/math.rb, line 258 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
Computes the value of pi to the specified number of digits of precision.
# File bigdecimal/lib/bigdecimal/math.rb, line 218 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 the arctangent of x to the specified number of digits of precision.
If x is NaN, returns NaN.
# File bigdecimal/lib/bigdecimal/math.rb, line 121 def atan(x, prec) raise ArgumentError, "Zero or negative precision for atan" if prec <= 0 return BigDecimal("NaN") if x.nan? pi = PI(prec) x = -x if neg = x < 0 return pi.div(neg ? -2 : 2, prec) if x.infinite? return pi / (neg ? -4 : 4) if x.round(prec) == 1 x = BigDecimal("1").div(x, prec) if inv = x > 1 x = (-1 + sqrt(1 + x**2, prec))/x if dbl = x > 0.5 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 *= 2 if dbl y = pi / 2 - y if inv y = -y if neg y end
Computes the cosine of x to the specified number of digits of precision.
If x is infinite or NaN, returns NaN.
# File bigdecimal/lib/bigdecimal/math.rb, line 85 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") x = -x if x < 0 if x > (twopi = two * BigMath.PI(prec)) if x > 30 x %= twopi else x -= twopi while x > twopi end end 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 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”
# File bigdecimal/lib/bigdecimal/math.rb, line 156 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") x = -x if neg = x < 0 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 if neg one.div(y, prec) else y.round(prec - y.exponent) end end
Computes the natural logarithm of x to the specified number of digits of precision.
Returns x if x is infinite or NaN.
# File bigdecimal/lib/bigdecimal/math.rb, line 187 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 if (expo = x.exponent) < 0 || expo >= 3 x = x.mult(BigDecimal("1E#{-expo}"), n) else expo = nil end 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 if expo y += log(BigDecimal("10"),prec) * BigDecimal(expo.to_s) end y end
Computes the sine of x to the specified number of digits of precision.
If x is infinite or NaN, returns NaN.
# File bigdecimal/lib/bigdecimal/math.rb, line 49 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") x = -x if neg = x < 0 if x > (twopi = two * BigMath.PI(prec)) if x > 30 x %= twopi else x -= twopi while x > twopi end end 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 neg ? -y : y end
Computes the square root of x to the specified number of digits of precision.
BigDecimal.new('2').sqrt(16).to_s
-> "0.14142135623730950488016887242096975E1"
# File bigdecimal/lib/bigdecimal/math.rb, line 42 def sqrt(x,prec) x.sqrt(prec) end