Widen ln 2 by x's integer digits in Exp2 [patch] - #140
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Exp2 read ln 2 at a fixed significantDigits + guard digits. Multiplying by x scales that error by |x|, so a fractional power with about ten integer digits rounded its last digit wrong. Widen ln 2 by the integer digits of x, as Exp2M1 already does. Exp10 splits off its whole part first and does not have the problem. Fixes #123 Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_014jNTPLxThrQnZyafw1CZ1p
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This was referenced Sep 30, 2026
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Fixes #123
What changed
Exp2(x, d)read ln 2 at a fixedd + ExponentialGuardDigitsdigits. Multiplying byxscales the absolute error in ln 2 by |x|. Oncexhas about ten integer digits the guard digits are used up, and the last requested digit rounds the wrong way. ln 2 is now widened byIntegerDigitCount(x), which is whatExp2M1already does.Exp10was checked for the same pattern and does not have it: it splits off the whole power of ten before it multiplies by ln 10, so the series only ever sees a fraction in [0, 1).Tests
TestExp2RoundsTheLastDigitOfALargeFractionalPowercovers both rows from the issue. It compares significand and exponent directly, becauseToStringon these exponents runs out of memory:Exp2(7000000000.5, 3)→629e2107209967(was628e…)Exp2(-6000000000.5, 5)→73383e-1806179979(was73384e…)Each case is also checked against
Exp2(x, d + 40).ReduceSignificance(d). The test failed onmain(expected 629, actual 628) and passes with the fix. The full suite passes: 435 of 435.🤖 Generated with Claude Code
https://claude.ai/code/session_014jNTPLxThrQnZyafw1CZ1p
Generated by Claude Code