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# Added by John O. Woods, SciRuby project.
# Derived from GSL-1.9 source files in the specfunc/ dir.
module Distribution
module MathExtension
# Derived from GSL-1.9.
module Gammastar
C0 = 1.quo(12)
C1 = -1.quo(360)
C2 = 1.quo(1260)
C3 = -1.quo(1680)
C4 = 1.quo(1188)
C5 = -691.quo(360360)
C6 = 1.quo(156)
C7 = -3617.quo(122400)
class << self
def series x, with_error = false
# Use the Stirling series for the correction to Log(Gamma(x)),
# which is better behaved and easier to compute than the
# regular Stirling series for Gamma(x).
y = 1.quo(x*x)
ser = C0 + y*(C1 + y*(C2 + y*(C3 + y*(C4 + y*(C5 + y*(C6 + y*C7))))))
result = Math.exp(ser/x)
with_error ? [result, 2.0 * Float::EPSILON * result * [1, ser/x].max] : result
end
def evaluate x, with_error = false
raise(ArgumentError, "x must be positive") if x <= 0
if x < 0.5
STDERR.puts("Warning: Don't know error on lg_x, error for this function will be incorrect") if with_error
lg = Math.lgamma(x).first
lg_err = Float::EPSILON # Guess
lx = Math.log(x)
c = 0.5 * (LN2 + LNPI)
lnr_val = lg - (x-0.5)*lx + x - c
lnr_err = lg_err + 2.0*Float::EPSILON * ((x+0.5)*lx.abs + c)
with_error ? exp_err(lnr_val, lnr_err) : Math.exp(lnr_val)
elsif x < 2.0
t = 4.0/3.0*(x-0.5) - 1.0
ChebyshevSeries.evaluate(:gstar_a, t, with_error)
elsif x < 10.0
t = 0.25*(x-2.0) - 1.0
c = ChebyshevSeries.evaluate(:gstar_b, t, with_error)
c, c_err = c if with_error
result = c / (x*x) + 1.0 + 1.0/(12.0*x)
with_error ? [result, c_err / (x*x) + 2.0*Float::EPSILON*result.abs] : result
elsif x < 1.0/Math::ROOT4_FLOAT_EPSILON
series x, with_error
elsif x < 1.0 / Float::EPSILON # Stirling
xi = 1.0 / x
result = 1.0 + xi/12.0*(1.0 + xi/24.0*(1.0 - xi*(139.0/180.0 + 571.0/8640.0*xi)))
result_err = 2.0 * Float::EPSILON * result.abs
with_error ? [result,result_err] : result
else
with_error ? [1.0,1.0/x] : 1.0
end
end
end
end
end
end
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