[Rafael-SOWNet]

erfc(70) took 5.3 s, erfc(100) over 20 s, and erfc(1000) did not return. Each is below what the default precision represents and answers 0.

Number.Erfc worked out one working precision for both of its branches. It added Re(z^2)/ln 10 digits for the cancellation in 1 - erf(z), which only the series branch forms. Past the series' reach, erfc is its asymptotic series, which cancels nothing, yet it was carried with those digits too: 4343 at 100, and at 1000 the cap of 43430. That branch now works at the guard digits alone, as the method's documentation already said.

The same branch lost erfc's real part on the imaginary axis, where erfc(i y) is exactly 1 - i erfi(y). The asymptotic series leaves the 1 out, below its precision beside erfi(y), so erfc(20i) came back with a real part of 0. On the axis it is now 1 - erf(z), since erf already reads erf(i y) as i erfi(y). This turned up while comparing a double-precision erfc against the kernel for #1607.

Measured

	master	this
erfc(70)	5.3 s	9 ms
erfc(100)	> 20 s	3 ms
erfc(1000)	no return	3 ms
erfc(1000 + i)	no return	13 ms

• No value changes. I evaluated fourteen arguments in the asymptotic branch to 100 digits with downcasting off, from erfc(15.6) to erfc(100 + 99.5i), on both sides of the real line. All are identical to master's to the last digit.
• ErrorFunctionTest gains three rows in that branch, erfc(16), erfc(16 + 3i) and erfc(14 - 9i), which agree with mpmath at 200 digits to 40 digits. mpmath gives the same values at 400. It also gains erfc(20i), whose real part of 1 fails without the second commit ("expected 1, got 0E-199").
• It also gains a termination test, erfc(1000) and erfc(1000 + i) within 30 s. On master both fail. erfc(100) is not a row: it finishes in about 25 s, inside the budget, so it would not bind.
• The library builds for every target framework. The unit suite on b29be05 (net10.0): 13880 passed, 0 failed. ErrorFunctionTest on 0f19463: 44 of 44.

Closes #1606.

🤖 Generated with Claude Code