complex+saloon: implement complex transcendentals; wire %cplx into Saloon#59
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sigilante merged 5 commits intoJun 9, 2026
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…loon /lib/complex gains complex elementary functions (cexp, clog, csqrt, csin, ccos, ctan, cpow) in all four width doors (cs/cd/ch/cq). Kept self-contained -- like /lib/unum, /lib/fixed, /lib/twoc -- by giving each door its OWN real exp/sin/ cos/log/atan as naive Taylor/AGM series over the stdlib component float door, rather than depending on /lib/math (which would couple the kind-primitive to the special-functions lib and pull it into Lagoon's build). Saloon's Tier-B dispatch (+trans-scalar / +fun-scalar) gains a %cplx branch (complex bloqs 5/6/7/8 = ch/cs/cd/cq), so exp/sin/cos/tan/log/sqrt/pow now work on %cplx rays. Real-only / ordered functions (factorial, log-10, log-2, cbrt, pow-n) are undefined on complex and crash. Tests (validated vs numpy, all green on ~hex): - tests/lib/complex-fns: the full set at @cs, exp/log/sqrt at @cd, exp at @ch/@cq (cd matches complex128 to ~15 digits, cq to ~34). - tests/lib/saloon-cplx: ray-level %cplx dispatch through Saloon Tier B, plus factorial/cbrt crash-on-complex guards. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Edge-case testing surfaced a bug: the self-contained real +rlog lacked the x<=0 domain guard the unum +log has, so clog(0+0i) ran the atanh series on y=-1 and returned garbage (~-5.4) instead of the -inf singularity. Add a log(0) -> -inf guard to +rlog in all four doors (|z| is always >= 0, so 0 is the only singular input). Add /tests/lib/complex-edge: origin, real/imaginary axes, the csqrt/clog branch cut (-1, +-i), the csqrt sign branch (sqrt(-i) = 0.707 - 0.707i), the clog(0) singularity, off-axis (1+1i, 3+4i), and two large-argument cases locked as documented limitations (the naive series is ~0.2% off far from the origin). All validated against numpy complex64. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
complex-edge now covers the same edges across all four widths -- @cd/@ch/@cq get origin, the csqrt/clog branch cut (-1, -i), the clog(0)=-inf singularity, and the imaginary axis -- plus: - cpow edges: 2^0=1, 2^2=4, i^2=-1, (-1)^0.5=i, and the 0^2 corner (documented: yields NaN, since cpow routes through clog(0)=-inf -> exp(-inf), which the naive series can't represent -- locked as a known limitation, not correctness). - rounding: cexp(1+2i) under %n/%u/%d/%z gives four distinct bit patterns, confirming the rounding mode propagates bit-exactly through the complex ops. 39 cases total, all validated against numpy complex64/128. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Adds tests/lib/unum-edge (28 cases), the %unum analogue of complex-edge: - exact identities (exp0=1, cos0=1, sqt4=2, fact5=120, log1=0, acos1=0, ...) - sign (exp(-1)=1/e, atan(-1)=-pi/4) - NaR propagation (exp/sin/sqt/factorial of NaR -> NaR) - domain -> NaR (sqrt(-1)) - a posit8 cross-width spot (identity + NaR propagation) - large-argument breakdown / saturation, locked as DOCUMENTED limitations: exp(10)~21991 vs 22026; exp(50)/exp(100) saturate near maxpos; sin(10) blows up out of [-1,1] (no range reduction); log (atanh) holds up (log(100)~4.605). No bug found (the unum domain guards from the transcendental PR already hold); posits round-to-nearest-even so there is no rounding-mode axis to sweep. The large-arg cases are the #18 hazard made explicit, not asserted as correct. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
unum: posit transcendental edge-case sweep
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Stacked on #58 (unum transcendentals). Completes the
%cplxTier-B story so Saloon's transcendentals work on complex rays./lib/complex— complex elementary functionscexp,clog,csqrt,csin,ccos,ctan,cpowin all four width doors (cs/cd/ch/cq).Self-contained (no
/+ math): per the architecture discussion, each door carries its own realexp/sin/cos/log/atanas naive Taylor/AGM series over the stdlib component float door — consistent with/lib/unum//lib/fixed//lib/twoc, and avoids coupling the complex kind-primitive to the special-functions lib (or pullingmathinto Lagoon's build). Closed forms documented in the header;#18's Chebyshev rewrite would upgrade the real series in lockstep.Saloon —
%cplxdispatch+trans-scalar/+fun-scalargain a%cplxbranch (complex bloqs 5/6/7/8 = ch/cs/cd/cq).exp/sin/cos/tan/log/sqrt/powmap to the complex ops; real-only/ordered functions (factorial/log-10/log-2/cbrt/pow-n) are undefined on complex and crash.Tests (validated vs numpy, all green on
~hex)tests/lib/complex-fns— full set at@cs;exp/log/sqrtat@cd;expat@ch/@cq. (@cdmatches numpy complex128 to ~15 digits,@cqto ~34.)tests/lib/saloon-cplx— ray-level%cplxdispatch through Saloon Tier B (withsake %nfor deterministic rounding), plusfactorial/cbrtcrash-on-complex guards.Note: bare
+sa's default rnd isn't%n(the same "set rnd via+sake" expectation the eig tests follow); the%cplxtests usesake %nsince complex rounding is rnd-sensitive (unlike posits).🤖 Generated with Claude Code