The fixed-point series run on System.Numerics.BigInteger, and a fixed-point value is read back as a decimal by scaling to a power of ten

[Rafael-SOWNet]

#1346 and #1347 put the logarithm, the exponential, the sine, the cosine and the arctangent into fixed point on PeterO's EInteger. Measured against mpmath on the same machine (#1338, the table), the transcendental rows were still 9–17× behind, and the reason is the integer type: one multiply of two hundred-digit integers is 1,271 ns in EInteger and 109 ns in System.Numerics.BigInteger (8,087 vs 1,364 at 500 digits, 75,850 vs 12,036 at 2,000), and the BCL's is at parity with CPython's int, which is what mpmath's digits live in.

The series run on BigInteger now, converted once on the way in and once on the way out as two's-complement bytes (EInteger.ToBytes(littleEndian: true) / EInteger.FromBytes), and the way out no longer multiplies by 5^bits and asks EDecimal to round a number of four times the digits: FromFixed scales the fixed-point integer to a power of ten six digits past the precision in BigInteger (the powers cached per context) and leaves only the rounding to EDecimal. That reading alone was 5 of the 25 µs at 100 digits and 65 of 228 at 500. The decimal layer above is untouched; no public API changes.

The hundred-digit values are the ones pinned before, to the last digit (NumericDigits, HighPrecisionFunctionsTest) — no BREAKING-CHANGES entry.

benchmark	before	after	allocation	time
EvalTrig	260,728	164,728	−36.8%	153 → 83 µs
EvalTrigPrecise (500 digits)	2,525,707	718,778	−71.5%	2.16 → 1.05 ms
EvalTranscendentalFresh	128,664	59,136	−54.0%	83 → 33 µs
SolveEasy	1,675,487	981,996	−41.4%	1.19 → 0.49 ms
SimplifyHard	189,604,392	182,277,112	−3.9%
every other entry			within 0.1%

Alone, one probe on both builds (best of seven batches, tiered compilation off, a fresh node per call since an entity caches its Evaled):

100 digits	before	after	mpmath
sin(x)	46.9 µs	15.2	5.6
ln(x)	52.4	18.0	4.5
e^x	32.3	10.0	4.3
arctan(x)	48.8	24.6	3.9

At 500 digits sin 1,273 → 228 µs, ln 3,921 → 777, e^x 2,774 → 548; at 2,000 digits sin 40.7 → 11.7 ms, ln 121 → 26. The remaining factor of 3–6 to mpmath is the term count (eighty artanh terms for a logarithm, twenty-five for a sine), which is the argument-reduction step next.

Baseline from this run; the performance log has the entry. Four suites green (11,345 / 134 / 18 / 41).

Part of #1338.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura