Remove calculating log(10) in BigMath.log for large/small x #484
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Remove slow calculation of log(10). Before: log(x) = log(10)*n + log(x/10**n) After: log(x) = log(x/exp(logx_approx)) + logx_approx
tompng
commented
Jan 28, 2026
| 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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Precision of exp should be larger than prec2 - logx_approx.exponent.abs theoretically and also experimentally. Just using prec2 is simple and enough.
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Remove slow calculation of
log(10).Before:
log(x) = log(10)*n + log(x/10**n)After:
log(x) = log(x/exp(logx_approx)) + logx_approxThis optimization is based on https://bugs.ruby-lang.org/issues/6857#note-4
When prec is 100, master branch got few times slower than v4.0.1. This pull request will make a bit better.