Stop ExpM1, LogP1 and the hyperbolics building million-digit sums for large arguments [patch]

[matt-edmondson]

Fixes #133

What was wrong

Add and Subtract are exact, so they align both operands to the smaller exponent. When one operand is millions of digits below the other, that builds a significand millions of digits wide, and the caller then rounds almost all of it away:

• ExpM1(-1e7) took about 10 s to return -1.
• ExpM1(-1e10) threw OverflowException, because Exp(-1e10) overflows its own exponent.
• LogP1, Sinh, Cosh, Asinh and Acosh took tens of seconds on arguments like 1e7 and 1e1000000.

Change

This is the general fix the triage comment suggested.

• New helpers. AddToPrecision and SubtractToPrecision (internal, in PreciseNumber.cs) check whether the smaller operand lies wholly below both the larger operand's last digit and the caller's rounding position (with 3 guard digits). If it does, the smaller operand is replaced by one unit of its sign at that position. The exact sum and this sticky sum fall strictly inside the same gap between neighbouring multiples of that digit. Every rounding boundary at the caller's precision is a multiple of it, including after the halving in Sinh/Cosh, so both sums round the same way.

• Where they're used.

  • ExpM1: the - 1.
  • LogP1: the 1 +.
  • Sinh/Cosh: the ± 1/e^x.
  • Asinh: 1 + x² and 1 + √….
  • Acosh: x ∓ 1.

  Near one these sums are still exact, because the helper only takes over when the gap exceeds the working width. The cancellation-sensitive small-argument paths described in CLAUDE.md are unchanged.

• Early return in ExpM1. It returns -1 once x < -3·(working + 1). Since ln 10 < 3, e^x there is below every kept digit. This covers Exp2M1 and Exp10M1 too, because they route through ExpM1.

• Docs. CLAUDE.md now describes the helpers and the new test file.

Tests

Added PreciseNumberLargeArgumentTests:

• ExpM1, Exp2M1 and Exp10M1 of -1e10 return -1.
• ExpM1(±…), Exp10M1(-1e7), LogP1(1e1000000), Sinh(±1e7), Cosh(-1e7), Asinh(±1e1000000) and Acosh(1e1000000) each finish within a 5 s budget. They run on the thread pool so the test fails fast instead of hanging. The test also checks they equal Exp(x), Log(x), e^x/2 and ln(2x) respectively.
• 50-digit results for ExpM1(-100), ExpM1(300), Exp10M1(100.5), LogP1(3.7e300), Sinh(300), Cosh(-300.5), Asinh(-2.5e300), Acosh(7.25e300) and Acosh(1e40) are pinned. These values were captured from the exact path before this change, and the bounded path reproduces every one.

How the tests were checked:

• With the library change reverted: 5 of the 6 new tests fail. One fails with the OverflowException; the other four overrun the 5 s budget. The digit-pinning test passes on both versions, which is what it exists to show.
• Full suite: 475/475 pass.

🤖 Generated with Claude Code

https://claude.ai/code/session_01TTeaDNAaTEviJbNWuEi5hP

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Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
95.0% Coverage on New Code
0.0% Duplication on New Code

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