Phase 1: /lib/complex + wire %cplx into Lagoon#46
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Implements the %cplx design (CPLX-DESIGN.md): complex-number arrays with a SoftBLAS-interleaved atom layout, element-wise ops, and complex linear algebra. /lib/complex (pure Hoon): cs (@cs, two @rs) and cd (@cd, two @rd) doors keyed on rounding mode. Packed atom = real low / imag high, matching SoftBLAS complexN_t. add/sub/mul, div (Smith's algorithm), neg, conj, abs (hypot, real-valued complex), equ/neq (bit equality). No total order (no gth/lth). Lagoon (sur + lib): %cplx in the kind union; bloq 6=cs 7=cd, prec needs no meta.tail. fun-scalar add/sub/mul/div + equ/neq (-> complex one/zero); gth/gte/lth/lte crash (complex unordered). New %conj op (identity on real kinds, so dotc reduces to dot there). trans-scalar %abs/%conj. New ray arms +conj and +dotc (Hermitian inner product, sum conj(a)*b). Bilinear dot, mmul, and cumsum use the generic round-each-step path (no exact complex accumulator). get-term -> @c aura terms; eye/ones constant 1+0i; scale raw-pack; change out of complex refuses (lossy). Tests (all green on ~hex): /tests/lib/complex (4: cs/cd arith, unary, compare), /tests/lib/lagoon-cplx (7: arith, unary, compare, ones, cumsum, dot vs dotc, mmul); %unum (14) and %int2 (5) regressions still pass. Oracle: tools/complex_check.py (NumPy complex64/128). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Extends +eig to complex Hermitian matrices via complex cyclic Jacobi. +eig now dispatches on kind: %cplx -> Hermitian path, else the symmetric path. The unitary rotation J that zeros a_pq has real diagonal c and complex off-diagonal b = s*(a_pq/|a_pq|) with J[q,p] = -conj(b); updates are A <- J^H*A*J, V <- V*J. Eigenvalues are real (%i754), eigenvectors unitary (%cplx) -- matching NumPy eigh. Works on @cs (bloq 6) and @cd (bloq 7); asserts exact Hermitian. Adds complex scalar helpers (cadd/csub/cmul/cdiv/cconj/cre/cpak/cabs-re over /lib/complex) and the Hermitian arms (hermitian, off-norm-h, frob-h, diag-real, rot-cols-h, rot-rows-h, sweep-herm, eig-herm). Durability: replaced the unbounded /lib/math Newton sqrt with an iteration-capped fsqt (50-step backstop, width-fixed feps). A sub-ULP rtol otherwise makes Newton oscillate between two adjacent floats forever, which OOM-crashed the ship while developing this. This also hardens the A1 path (regression-checked: all 18 symmetric tests still green). Tests (tests/lib/saloon-eigh, generated by tools/eigh_check.py vs numpy.linalg.eigvalsh) cover @cs 2x2/3x3/4x4 and @cd 3x3/4x4 Hermitian matrices; sort(computed eigenvalues) = sort(eigh). All 5 pass. Caveats documented in EIG-DESIGN.md: rtol width must match the component width (@rs for @cs, @rd for @cd); the exact Hermitian assert rejects +-0.0 mismatches in conjugate pairs. Note: this branch stacks on %cplx (PR #46) and eig A1 (PR #47); rebase once those land. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Implements Phase 1 of the
%cplxdesign (lagoon/CPLX-DESIGN.md, PR #45):complex-number arrays with a SoftBLAS-interleaved atom layout, element-wise
ops, and complex linear algebra. Unblocks Saloon eigenvalues/eigenvectors.
/lib/complex(pure Hoon)cs(@cs= two@rs) andcd(@cd= two@rd) doors keyed on roundingmode. Packed atom = real low / imag high, matching SoftBLAS
complexN_t(validated on ~hex:
(1+2i)·(3+4i) = -5+10i). Arms:add/sub/mul,div(Smith's algorithm),neg,conj,abs(hypot, returns real-valuedcomplex),
equ/neq(bit equality). No total order — nogth/lth.Lagoon (
sur+lib)%cplxin thekindunion;bloq6=cs7=cd(meta.tailunused).fun-scalar:add/sub/mul/div,equ/neq→ complexone/zero;gth/gte/lth/ltecrash (complex is unordered).%conjop (identity on real kinds, sodotc≡dotthere);trans-scalar%abs/%conj.conjanddotc(Hermitian inner productΣ conj(aᵢ)·bᵢ). Bilineardot,mmul,cumsumuse the genericround-each-step path (no exact complex accumulator).
get-term→@caura terms (%cs/%cd);eye/onesconstant1+0i;scaleraw-pack;changeout of complex refuses (lossy).Tests — all green on ~hex
/tests/lib/complex(4):cs/cdarith, unary, compare./tests/lib/lagoon-cplx(7): arith, unary (abs/conj), compare, ones,cumsum, dot (-18+68i) vs dotc (70-8i), complex mmul.
%unum(14) and%int2(5) still pass.tools/complex_check.py(NumPycomplex64/complex128).Not in scope (per design)
Jets (Phase 2: add
*dotu/cgemm/zgemmto our SoftBLAS); Salooneig(Phase 3);
@ch/@cqwidths;changeinto-complex.🤖 Generated with Claude Code