Keep the base's precision when Pow or Exp takes an integer exponent - #104
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…patch] An integer exponent carried its own single significant digit into the result's precision, so 1.234.Pow(2) returned 2 and Exp(2) returned 7. An integer power is now treated as an exact count, like a counting number in a multiplication: - Pow computes integer powers up to 1024 by exact repeated squaring (a reciprocal for a negative power) and keeps the base's significant digits, so x.Pow(2) equals x * x. Larger integer powers keep the base's digits, capped at what the double they are computed in can hold. - Exp with an integer exponent keeps up to 15 significant digits, the precision of the double it is computed in. Fixes #103 Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NvZoJBSka1emZMaEXy4Cfj
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Fixes #103
What was wrong
PowandExpset their precision withLowestSignificantDigits(base, power). An integer exponent like2has 1 significant digit, so the result was rounded to 1 digit:1.234.Pow(2)21.523(equals1.234 * 1.234)1.234.Pow(3)21.879(equals1.234 * 1.234 * 1.234)(-2.5).Pow(3)-20-16(−15.625 to 2 digits)1.234.Pow(-2)0.70.6567Exp(2)77.38905609893065Change
Powwith an integer exponent up to 1024: the exponent is treated as an exact count, like a counting number in a multiplication.PreciseNumber. A negative power takes the reciprocal.x.Pow(2) == x * x. This path also keeps the sign of a negative base, as the triage suggested.Powwith a larger integer exponent: it still uses the log/exp path so that it can't build a huge intermediate. It keeps the base's digits, capped at 15 because the value is computed in adouble.Expwith an integer exponent: keeps 15 significant digits (Eis capped to thedoubleit is computed in).The commit carries
[patch], matching #102. Results only gain precision; nothing that returned a value now throws.Tests
New tests in
SignificantNumberTests:Pow_IntegerExponent_MatchesRepeatedMultiplicationchecksx.Pow(2) == x * xandx.Pow(3) == x * x * xforx = 1.234, including the exact values and the digit count.Pow_NegativeBaseAndOddExponent_KeepsBasePrecisionchecks(-2.5)^3→-16.Pow_NegativeIntegerExponent_MatchesReciprocalOfPowerchecks1.234^-2→0.6567.Exp_IntegerExponent_KeepsMoreThanOneSignificantDigitchecks thatExp(2)has more than 1 digit and matchesMath.Exp(2).Verification
main, all 4 new tests fail (2,-20,0.7and 1 digit).3^2,2^3and(-2)^3cases included.🤖 Generated with Claude Code
https://claude.ai/code/session_01NvZoJBSka1emZMaEXy4Cfj
Generated by Claude Code