libmath: add jets for Chebyshev variants of libmath by sigilante · Pull Request #63 · urbit/numerics

sigilante · 2026-06-11T15:28:49Z

First slice of the transcendental jetting effort: wire the first jetted
math.hoon arm (@rd exp) and establish the structure + cross-repo mirror the
rest will follow.

The Hoon transcendentals themselves already merged; this PR adds only the
jet-anchoring structure and the vere-side mirror. (math.hoon's large diff
is almost entirely the ++ math re-indent — review with whitespace hidden; the
substantive change is ~18 lines.)

What changed

libmath/desk/lib/math.hoon — wrap the width doors in a %math engine
door under the shared %non chapter, mirroring /lib/lagoon's
%non/%lagoon jet structure. =< math keeps the /+ math + rd:math /
~(exp rd:math [%n rtol]) API unchanged. ~/ hints on the rd door and exp
arm.
libmath/vere/ (new) — hand-maintained mirror of the runtime jet code
(jets/i/math.c, the tree.c registration snippet, README). The jets live in
urbit/vere pkg/noun; a matching PR there will follow.
libmath/tools/rd_exp_check.c (new) — SoftFloat-f64 reference that proves
the jet is bit-exact to the Hoon (not merely faithful).

The gotcha (documented in the README)

A ~/-hinted engine core must be a door (^| =+ [rnd] ~/ %math |%), not a
bare |%: a sample-less ~/-core anchors its parent to the dashboard root,
so %math and everything under it miss the hot dashboard — the core registers
but no C jet ever attaches. Found by tracing _cj_hot_mean in the runtime
(math par=0 MISS → math par=non FOUND once it's a door).

Verified

exp:rd:math .~1 → 0x4005.bf0a.8b14.576a (bit-exact), 34 µs jetted vs
~970 µs interpreted; the rest of math.hoon (other fns/widths, the rounding-mode
door idiom) unchanged.

Follow-on

The remaining 14 fns × 4 widths follow this exact mold (one u3wi_ body + tree.c
entry + bit-exact harness each), plus the matching urbit/vere runtime PR.

🤖 Generated with Claude Code

@rd

Wrap math.hoon's width doors in a %math engine DOOR under the shared %non chapter (=< math preserves the /+ math + rd:math API), mirroring /lib/lagoon's %non/%lagoon jet structure, with ~/ hints on the rd door and exp arm. The engine MUST be a door (^| =+ [rnd] ~/ %math |%): a sample-less ~/-core anchors its parent to the dashboard root, so the jet never attaches (found by tracing _cj_hot_mean in the runtime). Mirror the vere-side C jet into libmath/vere/ (jets/i/math.c + tree-registration.snippet.c + README) for hand-maintained cross-repo sync -- the runtime jets live in urbit/vere (PR to follow). Add libmath/tools/rd_exp_check.c, the SoftFloat-f64 reference proving the jet is bit-exact to the Hoon. @rd exp verified jetted (34us vs ~970us interpreted), bit-exact 0x4005.bf0a.8b14.576a. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rd

Add @rd log as the second jetted transcendental, and refactor the vere master (libmath/vere/jets/i/math.c) so the SoftFloat algorithm cores (_rd_exp, _rd_log) are shared between the runtime jet and a standalone bit-exact harness (libmath/vere/test/, via -DMATH_JET_HARNESS) -- the C the test runs is byte-for-byte the C the jet runs, so they can't drift. log transcribes math.hoon ++rd ++log (2^e*m reduction + degree-9 atanh Horner); ~/ %log hint added. Verified bit-exact to the Hoon incl the subnormal and sqrt(2)-boundary branches, and jetted on-ship (log:rd:math .~2 = 0x3fe6.2e42.fefa.39ef). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rd

…-ship) Finish the @rd jet port begun with exp/log: add faithful softfloat cores + u3 wrappers for sin/cos/tan/atan/atan2/asin/acos/sqt/cbt/pow/pow-n/log-2/log-10, each transcribing its Hoon arm's exact reduction/coefficients/Horner order so jet output is bit-identical to the pure-Hoon reference, not merely faithful. - math.hoon: ~/ hints on all 15 @rd arms under the %math door anchor. - jets/i/math.c: 15 algorithm cores shared with the harness via -DMATH_JET_HARNESS, plus u3 ABI wrappers. Fix the 2-arg wrappers (atan2/pow/pow-n) to use brace-enclosed u3r_mean pairs {axis,&ptr} — the flat form failed -Werror=missing-braces and never compiled. - test/rd_check.c: add emit2() + atan2/pow/pow-n vectors. - test/verify_clean.sh: one-query-at-a-time on-ship diff, NO C-c. (SIGINT mid-event corrupts the loom; the old verify.sh's C-c spam was crashing the serf and masquerading as a jet bug.) Verified bit-exact on a fresh fakeship: 234/234 vectors, 0 DIFF (198 single-arg via verify_clean.sh, 36 two-arg via gen/m2.hoon in one event). sin x 200k under %bout = 431ms (~2.1us/call) confirms jetting. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

Mirror /lib/lagoon's layout: maintain both runtimes' vendored jet files under libmath/, in noun/jets/ form. The two math.c copies differ by exactly two lines -- the two-arg u3r_mean form (brace-pair {axis,&p} on 64-bit vere-ml64 vs flat varargs on 32-bit vere), because that macro's API diverged between the runtimes. Everything else (15 algorithm cores, 12 single-arg wrappers, helpers) is byte-identical: marshalling is chub-based and word-size-agnostic. - libmath/vere/ noun/jets/{i/math.c,135/tree.c,q.h,w.h} -- 32-bit - libmath/vere64/ noun/jets/{i/math.c,135/tree.c,q.h,w.h} -- 64-bit (+ test/) Both built and verified bit-exact: full -test suite (math-exp/log/sqrt/ainv/ atan/tan/trig/derived) passes ok=%.y on a jetted 32-bit AND 64-bit fakeship, plus the standalone harness's 234 single+two-arg vectors. Vendor 135 only (the stock test ships' hoon-version; apply to 136/137 only if a target needs them). Drop the now-redundant tree-registration.snippet.c (the full vendored tree.c plus the rewritten README supersede it). README documents the 2-line divergence, per-word-size apply steps, the door-anchor gotcha, -test verification, and the SIGINT-corrupts-the-loom warning. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rs

Add all 15 @rs (single-precision) transcendental jets, single-precision twins of the @rd cores (same reductions/coeffs, SoftFloat f32, chub marshalling so they stay word-size-agnostic). Registered under non/math/rs in 135/tree.c, q.h/w.h decls, and ~/ hints on the rs door arms. 74 harness vectors bit-exact; full -test %/tests/lib passes ok=%.y on both the 32- and 64-bit jetted runtimes. Also fix a latent rounding-mode bug (affected @rd atan2/pow/pow-n from #63, and the new @rs atan2/pow/pow-n/tan): the math doors carry r=?(%n %u %d %z) whose bunt is %z, and the composite arms used bare door ops (mul:^rd, (div y x)) that silently bound that %z bunt instead of honoring r. The transcendental KERNELS correctly hardcode ~(mul ^rd %n); only the composite assembly was wrong. - Hoon: thread r into the door helper arms (sun/san/toi/drg/grd/add/sub/mul/ div/fma -> ~(op ^rd r)) for the rd and rs doors, so pow/atan2/tan/pow-n honor the door's rounding mode. Kernels keep their explicit %n. - Jets: a file-static _math_rnd, set from the door's r (gate axis 60, mapping 'n'/'u'/'d'/'z' -> SoftFloat near_even/max/min/minMag), brackets the bare ops in the composite cores; kernel calls run at near_even. - test-pow-3-2h's expected was baked from the old %z behavior (its pd door is %n); corrected to the near-even value (exact arithmetic: 2.5*log3 -> ...43ce -> exp -> ...5643). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rh

Add all 15 @rh jets. Every @rh arm is narrow-sh(rs_fn(widen-hs(x))): widen f16->f32 (exact = f16_to_f32), compute in the @rs cores, narrow f32->f16 (= f32_to_f16). No new algorithm cores -- the @rs cores are reused. 16-bit chub marshalling keeps them word-size-agnostic. Per the refinement, @rh now inherits the door's rounding mode r instead of pinning %n (consistent with @rd/@rs): - Hoon: the arms thread r into the @rs delegation (~(exp rs [r ...])), so the @rs composites honor r; and narrow-sh, formerly a hardcoded round-half-to-even, now does directed rounding per r (overflow -> inf/max-finite, underflow -> 0/min-subnormal, with an exact-zero guard). - Jets: the wrapper sets _math_rnd from the door's r (axis 60); the cores run the rs kernels at near-even and narrow via f32_to_f16 at r. A harness spike (rd_check.c emit_narrow) confirmed the hand-rolled narrow-sh is bit-exact to SoftFloat f32_to_f16 across all four rounding modes and the edge cases (subnormals, the e>=143 overflow, the 0x7e00 NaN) -- it caught exactly one bug (directed rounding of exact zero), now fixed. Registered rh under non/math in 135/tree.c, q.h/w.h decls, ~/ hints on the @rh door. Full -test %/tests/lib (incl math-rh) passes ok=%.y on both the 32- and 64-bit jetted runtimes; jets fire (us) and honor r. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rd

Establish the @rq (quad, 128-bit) jet pipeline, proven bit-exact on exp: - Two-chub float128_t marshalling (read u3r_chub(0/1) into v[0..1]); stays word-size-agnostic, sidestepping the c3_w*[n=2|4] divergence of rq.c. - This SoftFloat build has only pointer-based f128M_*; thin by-value wrapper inlines (_rqm/_rqa/_rqs/_rqd/_rqq/_rqeq/...) keep the cores as readable as the @rd ones. - _rq_exp: Cody-Waite + degree-24 minimax (25 f128 coeffs, extracted from the Hoon programmatically), bias 16383. Bit-exact to (exp:rq:math ...) for 1/2/-1/0.1 (verified on-ship + harness emit exp-q). - Rounding dispatch: thread r into the @rq door helper arms (sun/san/toi/drg/ grd/add/sub/mul/div/fma -> ~(op ^rq r)) so the composite arms honor r, as in @rd/@rs. -test %/tests/lib still ok=%.y (no regression). Remaining: the other 14 @rq cores (log/trig/atan/ainv/sqt/cbt/derived) + the rq wrappers, registration, and ~/ hints -- mechanical, same pattern. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rs

Fix the @rq pow/pow-n/atan2 arms to use the bare door ops (mul/div/add/sub/toi/ san) instead of hardcoded ~(op ^rq %n), so they honor the door's r like the @rd/@rs composites do (tan already used a bare div). The transcendental kernels and log-2/log-10/lr keep their explicit %n, matching @rd/@rs. Verified: @rq div(1,3) gives ...5556 at %u vs ...5555 at %d/%n (honors r); full -test %/tests/lib still ok=%.y (the math-rq tests use %n doors, where bare ops == the old explicit %n, so no regression). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

…nd-nearest Explain why a correct/faithful transcendental fixes its internal arithmetic to round-nearest-even and takes no rounding-mode axis (the faithfulness bound is defined w.r.t. nearest; directed-rounding the true result is the Table-Maker's Dilemma), while the door's r governs only the composite arithmetic that assembles already-rounded kernel outputs. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rs

- @rq pow-n was missing the `?> &((gth n .0) (is-int n))` guard that @rd/@rs have, so e.g. pow-n(2,-2) returned garbage (8.0) via its @s counter loop. Give it the same guard + float-countdown structure as @rd/@rs; negatives/non-integers now crash loudly instead of returning nonsense. - @rh pow-n was delegating to @rs (widen->rs pow-n->narrow) -- a cross-door call. Make it native @rh repeated-multiply (it's exact integer multiplication, no polynomial, so no need for @rs). Threads the @rh door helpers for this. pow-n stays public (Saloon's %pow-n array op dispatches to pow-n:rX:math). Verified on-ship: pow-n(2,3)=8 (@rq and @rh), pow-n(2,-2) now rejects; -test ok=%.y. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rs

Begin the @rh-native rewrite (no cross-door @rs calls). exp and log now compute natively in f16 with derived half-precision minimax (cheb_check.py retargeted to f16, mpmath-designed, exhaustively verified <=1 ULP): - exp: Cody-Waite + deg-4 minimax. LOG2E=0x3dc5 LN2HI=0x3980 LN2LO=0x1dc8, c0..c4=0x3c00 0x3c00 0x3800 0x3160 0x295c. Two-branch scale2 (overflow split k>=16, subnormal split k<-14; f16 can't use 2^24 like @rs -- uses 2^11/2^10), overflow k>=17, underflow k<=-25. - log: 2^e*m reduction + deg-1 atanh [0x3555,0x3266]. SQRT2=0x3da8, subnormal pre-mul 2^10 (not 2^24). Both explicit %n throughout (kernels take no rounding axis) -- which fixes a real bug the old delegating arms had: narrow-sh honored the door's r, so the default %z bunt leaked into exp/log (e.g. exp(1) gave 0x416f toward-zero instead of the correct nearest 0x4170). -test %/tests/lib/math-rh ok=%.y. (Native @rh jets + remaining 11 arms still to come; binary still has the old delegating jets, so jetted exp:rh/log:rh lag the Hoon until rebuilt.) Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rs

Native f16 sin/cos via fdlibm ksin/kcos kernels (2 coeffs each: sc=[0xb155, 0x2044] cc=[0x2955,0x95b0]) + 3-part pi/2 reduction (INVPIO2=0x3918, P=0x3e00/ 0x2c80/0x0fed). All explicit %n. Replaces the @rs delegation. -test math-rh ok=%.y. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

…terals Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rh

Completes the native f16 @rh door -- no cross-door delegation remains (only widen-hs/narrow-sh conversions). tan is the sin/cos ratio; atan2/pow honor the door r via bare composite ops; cbt/log-2/log-10 reuse the native exp/log kernels; sqt is the stdlib f16 root; lr is the f16 log reduction. Updated test-tan-1 vector 0x3e3b->0x3e3a (native sin/cos ratio, 0.79 ULP, faithful). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

The 15 _rh_* cores now compute entirely in half-precision (SoftFloat f16 ops), mirroring the native Hoon arms op-for-op -- f16 minimax coeffs, lower poly degrees (sin/cos/atan/ainv shorter, ainv no denominator, acos no tiny branch). Verified bit-exact to all 20 math-rh.hoon vectors (test/rh_check.c) and faithful (<=1.01 ULP) across all 64k finite f16 inputs for exp/log/atan/asin/acos/sqt; sin/cos faithful for small |x|, lossy for large |x| exactly as the Hoon reduction intends (test/rh_sweep.c). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

Identical to vere64 except the 4 two-arg u3r_mean lines (flat varargs vs brace pairs), preserving the documented 32/64-bit invariant. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rh

The native f16 kernels read the global softfloat_roundingMode (via f16_mul/add etc.), but the @rh wrappers only set _math_rnd -- so a kernel called after a %z door op ran under round-toward-zero, corrupting sin/cos (exp/atan survived by luck). Mirror the @rd/@rs wrappers: _rh_jet/_rh_jet2 and the 15 u3qi_rh_* softpaths now set softfloat_roundingMode = near_even (kernels) and _math_rnd = door r (composites). Verified on a fresh fakeship (clean jet dashboard): sin 0x3abb, cos 0x3853, exp 0x4170, tan 0x3e3a(%n)/0x3e39(%z), -test ok=%.y. Hardened rh_check.c to pre-dirty the global mode so it catches this class. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

The full-Horner exp was ~1.10 ULP (not faithful) -- finely sampled vs MPFR it rounds the dominant ~1.0 result through the whole Horner chain. Replace with fdlibm's compensated form exp(r) = 1 - ((lo - r*c/(2-c)) - hi), c = r - t*P(t), keeping the leading 1+r out of the rounded sum. P is a deg-10 even minimax in t=r^2 (11 coeffs, fewer than the 25-term Taylor it replaces). Result: 0.87 ULP (faithful), validated against MPFR (tools/rq_check.c). cbt(-27) now lands on exactly -3 (was 1 ULP short); test vector updated. Derivation + the exact reduction constants live in tools/cheb_check.py exp-rq. All math-rq tests pass on a fresh fakeship. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

Fine-sampled audit completes the @rq kernel surface (rq_check.c covers exp/log/ sin/cos/sqrt vs MPFR; this covers atan/asin/acos via a 113-bit mpmath model, parsing the coeff lists straight out of math.hoon). Full @rq audit result -- every kernel faithful (<=1 ULP): exp 0.836 log 0.854 sin 0.752 cos 0.763 sqrt 0.500 atan 0.812 asin 0.975 acos 0.853 exp was the lone arm that needed fixing (the fdlibm reconstruction, prior commit); nothing else flagged. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rd

Brings the @rq exp jet core in line with the new Hoon arm (fdlibm rational form, deg-10 even minimax P). Verified via tools harness: exp(1) = the correctly- rounded e, exp(2)=e^2, exp(0)=1.0. (First core of the @rq jet port; the remaining 13 + wrappers + registration follow, modeled on the vere32 @rd jet -- f128/2-chub is the structural twin of f64/2-word on a 32-bit runtime.) Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rd

log/lr/log-2/log-10, sin/cos/trig kernels, tan (=div sin/cos), atan/atan2, asin/acos/ainv, sqt/cbt, pow/pow-n -- native f128, mirroring the @rd cores with the f128 minimax coeffs read from the Hoon (no cross-door calls; composites call the internal _rq_* C functions directly). Coeff arrays generated straight from math.hoon to avoid transcription error. Verified bit-exact to the math-rq.hoon vectors via test/rq_cores.c (13/13): log/log2/sin/cos/atan/asin/acos/sqt/cbt/pow/tan all match; tan confirmed against the live Hoon under the %n door. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rh

_rq_in/_rq_out (2-chub f128 I/O), _rq_jet/_rq_jet2 (1- and 2-arg, set softfloat_roundingMode=near-even + _math_rnd from axis 60), and u3qi/u3wi for all 15 @rq fns. Models the @rh wrappers (kernels near-even, composites honor door r) -- carries the softfloat_roundingMode-not-_math_rnd fix from the start. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rh

15 harms + the _135_non__math_rq_d core + the rq entry in _135_non__math_d, mirroring @rh; q.h/w.h declare the 15 u3qi_rq_*/u3wi_rq_*. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

Identical to vere64 except the 5 two-arg u3r_mean lines (flat varargs). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

@rh

Updates the stale '@rh/@rq not yet jetted' note; documents the @rq fdlibm exp reconstruction and the library-wide flat-Horner exp ULP caveat (deferred retrofit for @rd/@rs/@rh).

Adds the 16 ~/ hints for the @rq door (engine %rq + 15 arm hints), completing the hint set across all four math doors. Documents (vere64/README) that the math transcendental jets do NOT currently attach on-ship -- a structural issue, not kelvin. A lagoon control (mmul, the sibling userspace jet in the same `non` chapter) fires on the same hoon-version-136 ship; math does not. Cause: the `math` engine core makes the width doors grandchildren of the `non` chapter (chapter->engine->door->arm, 3-deep) vs the standard chapter->door->arm (lagoon's `la`, kernel two->by/two->in). The jet C code itself is correct (test/rq_cores.c harness 13/13); only on-ship attachment is blocked. Fix direction pending core-dev review. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

sigilante and others added 6 commits June 11, 2026 10:28

math: README — document @rs jets + composite rounding-mode handling

6cd1d93

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

sigilante changed the title ~~math: jet-anchor @rd exp + vere jet mirror~~ libmath: add jets for Chebyshev variants of libmath Jun 12, 2026

sigilante and others added 22 commits June 12, 2026 08:29

math: native f16 @rh atan + rh-atan sub-core; fix leading-zero hex li…

1b5fff0

…terals Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

math: native f16 @rh asin/acos + rh-ainv sub-core

bcd10e6

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

math: propagate native f16 @rh jets to 32-bit libmath/vere copy

837b6c7

Identical to vere64 except the 4 two-arg u3r_mean lines (flat varargs vs brace pairs), preserving the documented 32/64-bit invariant. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

math: register the @rq door jets (135/tree.c, q.h, w.h)

2b44227

15 harms + the _135_non__math_rq_d core + the rq entry in _135_non__math_d, mirroring @rh; q.h/w.h declare the 15 u3qi_rq_*/u3wi_rq_*. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

math: propagate @rq jets + registration to 32-bit libmath/vere

2e72306

Identical to vere64 except the 5 two-arg u3r_mean lines (flat varargs). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

docs: README -- all four doors (@rd/@rs/@rh/@rq) now jetted

7a0cb5f

Updates the stale '@rh/@rq not yet jetted' note; documents the @rq fdlibm exp reconstruction and the library-wide flat-Horner exp ULP caveat (deferred retrofit for @rd/@rs/@rh).

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libmath: add jets for Chebyshev variants of libmath#63

libmath: add jets for Chebyshev variants of libmath#63
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sigilante commented Jun 11, 2026

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sigilante commented Jun 11, 2026

What changed

The gotcha (documented in the README)

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