Computes the natural logarithm of x to the specified number of digits of
precision.
Returns x if x is infinite or NaN.
# File ext/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