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Keep full precision when BigMath.exp receives a Rational - #572
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BigMath.exp converted a Rational argument with BigDecimal(x, prec), which only keeps prec significant digits of x. exp amplifies the relative error of x into an absolute error of the result, so for an argument with an integer part of k digits the result lost up to k digits of precision: BigMath.exp(10**19/3r, 50) # wrong after 31 digits BigMath.exp(10**19/3r, 1000) # reference Convert a Rational with prec + (number of integer digits) significant digits instead. Add a test that checks the result converges to the higher-precision value for large, small and negative Rationals. Refs ruby#444
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BigMath.expconverted a Rational argument withBigDecimal(x, prec), which keeps onlyprecsignificant digits ofx.expturns the relative error ofxinto an absolute error of the result, so an argument with ak-digit integer part lost up tokdigits of precision (first example in #444):A Rational is now converted with
prec + max(exponent, 0)significant digits, as suggested in the issue. TheTODOoncoerce_to_bigdecimalis kept becauselog,sinandcosstill need their own conversions.Adds
test_exp_rational, which fails without the change.Refs #444 (only the
BigMath.exppart)