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Remove calculating log(10) in BigMath.log for large/small x #484

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Merged
tompng merged 1 commit into from
Jan 28, 2026
+8 −5
Merged

Remove calculating log(10) in BigMath.log for large/small x #484

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13 changes: 8 additions & 5 deletions lib/bigdecimal.rb
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Original file line number Diff line number Diff line change
Expand Up @@ -303,10 +303,13 @@ def log(x, prec)

prec2 = prec + BigDecimal.double_fig

if x < 0.1 || x > 10
exponent = (3 * x).exponent - 1
x = x._decimal_shift(-exponent)
return log(10, prec2).mult(exponent, prec2).add(log(x, prec2), prec)
# Reduce x to near 1
if x > 1.01 || x < 0.99
# log(x) = log(x/exp(logx_approx)) + logx_approx
logx_approx = BigDecimal(BigDecimal::Internal.float_log(x), 0)
x = x.div(exp(logx_approx, prec2), prec2)
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@tompng tompng Jan 28, 2026

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Precision of exp should be larger than prec2 - logx_approx.exponent.abs theoretically and also experimentally. Just using prec2 is simple and enough.

else
logx_approx = BigDecimal(0)
end

# Solve exp(y) - x = 0 with Newton's method
Expand All @@ -317,7 +320,7 @@ def log(x, prec)
expy = exp(y, p + exp_additional_prec)
y = y.sub(expy.sub(x, p).div(expy, p), p)
end
y.mult(1, prec)
y.add(logx_approx, prec)
end

private_class_method def _exp_binary_splitting(x, prec) # :nodoc:
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