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Fix lgamma precision when gamma(negative_x).abs nearly equals 1 #467

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Merged
mrkn merged 1 commit into from
Dec 12, 2025
+14 −5
Merged

Fix lgamma precision when gamma(negative_x).abs nearly equals 1 #467

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15 changes: 10 additions & 5 deletions lib/bigdecimal/math.rb
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Original file line number Diff line number Diff line change
Expand Up @@ -759,11 +759,16 @@ def lgamma(x, prec)
if x < 0.5
return [BigDecimal::INFINITY, 1] if x.frac.zero?

# Euler's reflection formula: gamma(z) * gamma(1-z) = pi/sin(pi*z)
pi = PI(prec2)
sin = _sinpix(x, pi, prec2)
log_gamma = BigMath.log(pi, prec2).sub(lgamma(1 - x, prec2).first + BigMath.log(sin.abs, prec2), prec)
[log_gamma, sin > 0 ? 1 : -1]
loop do
# Euler's reflection formula: gamma(z) * gamma(1-z) = pi/sin(pi*z)
pi = PI(prec2)
sin = _sinpix(x, pi, prec2)
log_gamma = BigMath.log(pi, prec2).sub(lgamma(1 - x, prec2).first + BigMath.log(sin.abs, prec2), prec)
return [log_gamma, sin > 0 ? 1 : -1] if prec2 + log_gamma.exponent > prec + BigDecimal.double_fig

# Retry with higher precision if loss of significance is too large
prec2 = prec2 * 3 / 2
end
elsif x.frac.zero? && x < 1000 * prec
log_gamma = BigMath.log(_gamma_positive_integer(x, prec2), prec)
[log_gamma, 1]
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4 changes: 4 additions & 0 deletions test/bigdecimal/test_bigmath.rb
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Expand Up @@ -580,5 +580,9 @@ def test_lgamma
assert_converge_in_precision {|n| lgamma(BigDecimal("987.65421"), n).first }
assert_converge_in_precision {|n| lgamma(BigDecimal("-1234.56789"), n).first }
assert_converge_in_precision {|n| lgamma(BigDecimal("1e+400"), n).first }

# gamma close 1 or -1 cases
assert_converge_in_precision {|n| lgamma(BigDecimal('-3.143580888349980058694358781820227899566'), n).first }
assert_converge_in_precision {|n| lgamma(BigDecimal('-4.991544640560047722345260122806465721667'), n).first }
end
end