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Argument of a complex value carries the requested digits under N() - #440
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…r N(), as Arctan2 does, so N(Argument(e + iπ), 25) carries 25 digits; add regression tests against mpmath. Fix cortex-js#439
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…Argument; settle the remaining rows (#925) BigDecimal power-series kernels answer N(f, d) for AiryAi/Bi, Ei, li and integer-order Bessel I/J/K/Y once d exceeds a double's digits; a run with 10 more digits must agree, otherwise they decline to the native evaluation. A ce-patch carries Argument of a complex literal through bignum Arctan2 under N (upstream: cortex-js/compute-engine#440). Simplify folds rational expressions in GoldenRatio; fromWolfram reads Range with step 1. The remaining Wolfram triage rows are settled toward Wolfram or classified, none dropped; our-side bugs go to #911.
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… precision, integration gaps PR #436 (enumeratio, fix #434): the JavaScript target lowers HurwitzZeta, LerchPhi, PolyLog, EllipticK, the complete EllipticE, Hypergeometric2F1 and LambertW to the interpreter's complex kernel in `auto` and `complex` mode where the operand facts do not prove the value real; `strict` keeps the real kernel and its NaN; a complex operand takes the complex kernel in every mode. The verdict lives in one place (`complexContinuation`), read by both `isComplexValued` and the emitters. The GLSL and WGSL targets decline a provably complex value, now including a positive integer order on the cut `z > 1` (`PolyLog(2, 3)`, `LerchPhi(3, 2, 1)`). `Arcsec` and `Arccsc` of an operand of unknown magnitude type `complex | infinity | nan` instead of `number`, so the compiled lanes read the complex value. PR #440 (enumeratio, fix #439): `Argument` of a complex value passes the bignum parts to `Arctan2`, so `N(Argument(e + iπ), 25)` carries 25 digits. Also from #439: `Transpose` of an operand with no known shape is typed `unknown` (a union such as `matrix | vector` is transposed member by member), so `MatrixMultiply(q, Transpose(q))` with a free `q` stays unevaluated instead of an `incompatible-type` error. PR #441 (KingArth0r): definite integrals of more families evaluate in closed form — an absolute value or sign of a non-affine argument is split at its exact roots; integer-cell sums (Floor, Ceil, Fract with an affine weight) and `|sin(kx + m)|` over many periods no longer grow with the cell count; `∫₀¹ {1/x} dx = 1 − γ` and `∫₀¹ ⌊1/x⌋ dx = +∞`; primitives for Erf, Erfc, BesselJ(1, ·), BesselI(1, ·), Digamma, Trigamma and PolyGamma of an affine argument (and `d/dx LogGamma = Digamma`); the nested exponential `∫ e^{x + e^x} dx`; the Bose moments `∫₀^∞ xⁿ/(e^{ax} − 1) dx`. With the Rubi rules loaded, a provider antiderivative with no value at a bound falls back to the built-in one. Loading the rules compiles each distinct pattern once, and an invalid `stepBudget` is rejected before compilation. The PR's profiling script and JSON record are not included. Review fixes on top of the PRs: a user definition with its own `compile` handler keeps its own lane; compiled `HurwitzZeta(1, z)` for a non-real `z` is the pole; the period shortcut declines outside radian mode; exact coefficients in the cell sums stay exact; a polygamma integral between two consecutive poles evaluates; the infinite-bound inert decision reads the heads that contain the variable. ROADMAP: the antiderivative of Sin and Cos ignores the degree angular unit (found by the review; pre-existing). Fix #434 Fix #439 Co-authored-by: enumeratio <314378874+enumeratio@users.noreply.github.com> Co-authored-by: KingArthur <118565558+KingArth0r@users.noreply.github.com>
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Fix #439.
N(Argument(e + iπ), 25)was0.8575117863558462702910252, wrong from the 17th digit because the angle was the doubleatan2of the parts. We now pass the bignum parts toArctan2, so it is0.8575117863558462650068678(true0.857511786355846265006867751).Argument(2 + iπ)at 25 digits was1.003884821853887179762058and is1.003884821853887214148424.Argis the same operator.Exact operands,
Argument(∞·i)and the compiled JavaScript lane (doubles) are unchanged.