[Rafael-SOWNet]

Fixes #2074. Follows #2072.

• The defect. A function's value was rounded onto zero below half the working digits, absolutely. The floor exists for the residual a function leaves at its own zeros: sin(pi) evaluates to about 1e-100. That residual is relative to the argument, though, and a function of an exact small argument cancels nothing. So sin(10^(-60)), tan, arcsin, arctan, erf, erfi, Si and Shi of it were all 0 at the default hundred digits.
• The change. The sine, cosine, tangent, logarithm, arcsine, arccosine and arctangent of a real argument, the error functions, and Si and Shi create their value at the argument's scale. Round a computed value onto zero only where its terms cancelled #2072 did the same for arithmetic, with the scale of what cancelled.
  • sin(pi), sin(100 pi), cos(pi/2), tan(pi) and arccos(1) are still 0.
  • The argument is passed as it is, and its modulus is taken only on the path that tests for a residual.
• Not changed. sinh(10^(-60)) is still 0. It is evaluated from e^(10^(-60)), which is 1 within half the digits, a cancellation the working precision cannot resolve.

AFunctionOfASmallArgumentTest checks nine values against mpmath, and five residuals that are still zero.

Results:

• Unit suite: passes (16,823).
• Corpus: the full Rubi corpus, run against the 2.6.0 run on the same harness (c614b2c8), is 48,305 of 48,305, with no row moved and no answer's allocation grown.
• Allocation: measured per evaluation against master. It is identical for sin(x) + cos(x) + tan(x) and ln(1 + x^2) * arctan(x), and 0.01% apart for erf(x) + Si(x).
• BREAKING-CHANGES: the entry gives the values on 2.6.0 and now.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura