tannevaled · Oct 18, 2026 · Oct 17, 2026 · Oct 17, 2026 · Oct 18, 2026
diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml
@@ -61,6 +61,25 @@ jobs:
       - name: The stated conformance total matches the gate
         run: go run ./tools/conformancefigure
 
+      # The Ruby examples on this site state their own answers, and until now
+      # nothing ran them: a binding renamed or a return shape changed in the
+      # ruby repository left every example here claiming its old output, which
+      # reads as a promise and is the first thing a reader tries.
+      #
+      # rbgo is built from the ruby repository's main, so the examples are
+      # judged against the interpreter this site documents rather than against
+      # a release that may be behind it. A build that fails, or an interpreter
+      # that cannot be produced, exits 2 -- a REFUSAL, not a pass, for the same
+      # reason the baseline check above refuses.
+      - name: The Ruby examples print what the pages say they print
+        run: |
+          go run ./tools/docexample -selftest
+          # GOBIN names the destination: `go install` otherwise writes to
+          # $(go env GOPATH)/bin, and an install that lands somewhere else looks
+          # exactly like one that worked.
+          GOBIN=/tmp go install github.com/go-embedded-ruby/ruby/cmd/rbgo@main
+          go run ./tools/docexample -rbgo /tmp/rbgo -root docs
+
   deploy:
     # Only main publishes. A pull request stops after build above: it has no
     # business pushing to gh-pages, and `permissions: contents: write` is not

diff --git a/docs/index.md b/docs/index.md
@@ -174,10 +174,12 @@ Every feature below is **differential-tested against MRI Ruby 4.0.5**:
   reference object), `instance_variable_get`/`set`.
 - **Numeric & scientific stack:** `Complex`, `Rational`, the `Math` module, and a
   **cgo-free scientific stack** — `NDArray` (NumPy-style arrays), an `FFT` module
-  (numpy.fft-style transforms), `Image` (scikit-image-style processing) — plus
-  container/value types `Set`, `Bag` (multiset), `Time`, `Date` and
-  `BigDecimal`, each binding a pure-Go sibling library (go-ndarray / go-fft /
-  go-images / go-composites). See
+  (numpy.fft-style transforms), `Special` and `Stats` (scipy.special's 67 functions
+  and scipy.stats's 32 univariate distributions), `Integrate` and `Optimize`
+  (scipy.integrate's quadrature and scipy.optimize's root finders and minimisers),
+  `Image` (scikit-image-style processing) — plus container/value types `Set`, `Bag`
+  (multiset), `Time`, `Date` and `BigDecimal`, each binding a pure-Go sibling library
+  (go-ndarray / go-fft / go-numerics / go-statistics / go-images / go-composites). See
   [Scientific stack](scientific-stack.md).
 - **Native capability modules:** a set of `require`-able modules, each backed by a
   canonical pure-Go `go-ruby-*` library so the build stays **CGO=0**. They wrap
@@ -285,7 +287,8 @@ The full bound family (alphabetical, all native modules in `go.mod`):
 [`aasm`](https://github.com/go-ruby-aasm/aasm), [`abbrev`](https://github.com/go-ruby-abbrev/abbrev), [`acme`](https://github.com/go-ruby-acme/acme), [`actioncable`](https://github.com/go-ruby-actioncable/actioncable), [`actionmailer`](https://github.com/go-ruby-actionmailer/actionmailer), [`actionpack`](https://github.com/go-ruby-actionpack/actionpack), [`actionview`](https://github.com/go-ruby-actionview/actionview), [`activejob`](https://github.com/go-ruby-activejob/activejob), [`activemodel`](https://github.com/go-ruby-activemodel/activemodel), [`activerecord`](https://github.com/go-ruby-activerecord/activerecord), [`activestorage`](https://github.com/go-ruby-activestorage/activestorage), [`activesupport`](https://github.com/go-ruby-activesupport/activesupport), [`addressable`](https://github.com/go-ruby-addressable/addressable), [`age`](https://github.com/go-ruby-age/age), [`arrow`](https://github.com/go-ruby-arrow/arrow), [`async`](https://github.com/go-ruby-async/async), [`augeas`](https://github.com/go-ruby-augeas/augeas), [`base64`](https://github.com/go-ruby-base64/base64), [`bbolt`](https://github.com/go-ruby-bbolt/bbolt), [`bcrypt`](https://github.com/go-ruby-bcrypt/bcrypt), [`benchmark`](https://github.com/go-ruby-benchmark/benchmark), [`bigdecimal`](https://github.com/go-ruby-bigdecimal/bigdecimal), [`bleve`](https://github.com/go-ruby-bleve/bleve), [`builder`](https://github.com/go-ruby-builder/builder), [`bundler`](https://github.com/go-ruby-bundler/bundler), [`cancancan`](https://github.com/go-ruby-cancancan/cancancan), [`capistrano`](https://github.com/go-ruby-capistrano/capistrano), [`capybara`](https://github.com/go-ruby-capybara/capybara), [`cgi`](https://github.com/go-ruby-cgi/cgi), [`chronic`](https://github.com/go-ruby-chronic/chronic), [`cmath`](https://github.com/go-ruby-cmath/cmath), [`commonmark`](https://github.com/go-commonmark/commonmark), [`concurrent-ruby`](https://github.com/go-ruby-concurrent-ruby/concurrent-ruby), [`confd`](https://github.com/go-ruby-confd/confd), [`connection-pool`](https://github.com/go-ruby-connection-pool/connection-pool), [`csv`](https://github.com/go-ruby-csv/csv), [`date`](https://github.com/go-ruby-date/date), [`deep-merge`](https://github.com/go-ruby-deep-merge/deep-merge), [`devise`](https://github.com/go-ruby-devise/devise), [`did-you-mean`](https://github.com/go-ruby-did-you-mean/did-you-mean), [`digest`](https://github.com/go-ruby-digest/digest), [`dotenv`](https://github.com/go-ruby-dotenv/dotenv), [`dry-struct`](https://github.com/go-ruby-dry-struct/dry-struct), [`dry-types`](https://github.com/go-ruby-dry-types/dry-types), [`dry-validation`](https://github.com/go-ruby-dry-validation/dry-validation), [`erb`](https://github.com/go-ruby-erb/erb), [`erubi`](https://github.com/go-ruby-erubi/erubi), [`etcd`](https://github.com/go-ruby-etcd/etcd), [`excon`](https://github.com/go-ruby-excon/excon), [`facter`](https://github.com/go-ruby-facter/facter), [`factory-bot`](https://github.com/go-ruby-factory-bot/factory-bot), [`faker`](https://github.com/go-ruby-faker/faker), [`faraday`](https://github.com/go-ruby-faraday/faraday), [`fast-gettext`](https://github.com/go-ruby-fast-gettext/fast-gettext), [`find`](https://github.com/go-ruby-find/find), [`format`](https://github.com/go-ruby-format/format), [`friendly-id`](https://github.com/go-ruby-friendly-id/friendly-id), [`getoptlong`](https://github.com/go-ruby-getoptlong/getoptlong), [`grape`](https://github.com/go-ruby-grape/grape), [`graphql`](https://github.com/go-ruby-graphql/graphql), [`grpc`](https://github.com/go-ruby-grpc/grpc), [`haml`](https://github.com/go-ruby-haml/haml), [`hanami`](https://github.com/go-ruby-hanami/hanami), [`hcl2`](https://github.com/go-ruby-hcl2/hcl2), [`hiera`](https://github.com/go-ruby-hiera/hiera), [`hocon`](https://github.com/go-ruby-hocon/hocon), [`http`](https://github.com/go-ruby-http/http), [`httparty`](https://github.com/go-ruby-httparty/httparty), [`i18n`](https://github.com/go-ruby-i18n/i18n), [`images`](https://github.com/go-ruby-images/images), [`ipaddr`](https://github.com/go-ruby-ipaddr/ipaddr), [`irb`](https://github.com/go-ruby-irb/irb), [`jbuilder`](https://github.com/go-ruby-jbuilder/jbuilder), [`jekyll`](https://github.com/go-ruby-jekyll/jekyll), [`json`](https://github.com/go-ruby-json/json), [`jwt`](https://github.com/go-ruby-jwt/jwt), [`kafka`](https://github.com/go-ruby-kafka/kafka), [`kaminari`](https://github.com/go-ruby-kaminari/kaminari), [`kramdown`](https://github.com/go-kramdown/kramdown), [`liquid`](https://github.com/go-liquid/liquid), [`logger`](https://github.com/go-ruby-logger/logger), [`mail`](https://github.com/go-ruby-mail/mail), [`marshal`](https://github.com/go-ruby-marshal/marshal), [`matrix`](https://github.com/go-ruby-matrix/matrix), [`mime-types`](https://github.com/go-ruby-mime-types/mime-types), [`minitest`](https://github.com/go-ruby-minitest/minitest), [`money`](https://github.com/go-ruby-money/money), [`mongodb`](https://github.com/go-ruby-mongodb/mongodb), [`msgpack`](https://github.com/go-ruby-msgpack/msgpack), [`multi-json`](https://github.com/go-ruby-multi-json/multi-json), [`mustache`](https://github.com/go-mustache/mustache), [`mysql`](https://github.com/go-ruby-mysql/mysql), [`nats`](https://github.com/go-ruby-nats/nats), [`net-ftp`](https://github.com/go-ruby-net-ftp/net-ftp), [`net-http`](https://github.com/go-ruby-net-http/net-http), [`net-imap`](https://github.com/go-ruby-net-imap/net-imap), [`net-pop`](https://github.com/go-ruby-net-pop/net-pop), [`net-sftp`](https://github.com/go-ruby-net-sftp/net-sftp), [`net-smtp`](https://github.com/go-ruby-net-smtp/net-smtp), [`nokogiri`](https://github.com/go-nokogiri/nokogiri), [`oauth2`](https://github.com/go-ruby-oauth2/oauth2), [`observer`](https://github.com/go-ruby-observer/observer), [`oidc`](https://github.com/go-ruby-oidc/oidc), [`omniauth`](https://github.com/go-ruby-omniauth/omniauth), [`openbao`](https://github.com/go-ruby-openbao/openbao), [`openstack`](https://github.com/go-ruby-openstack/openstack), [`opentelemetry`](https://github.com/go-ruby-opentelemetry/opentelemetry), [`opentype`](https://github.com/go-ruby-opentype/opentype), [`optparse`](https://github.com/go-ruby-optparse/optparse), [`ostruct`](https://github.com/go-ruby-ostruct/ostruct), [`pagy`](https://github.com/go-ruby-pagy/pagy), [`paper-trail`](https://github.com/go-ruby-paper-trail/paper-trail), [`parquet`](https://github.com/go-ruby-parquet/parquet), [`parser`](https://github.com/go-ruby-parser/parser), [`pathname`](https://github.com/go-ruby-pathname/pathname), [`pg`](https://github.com/go-ruby-pg/pg), [`prawn`](https://github.com/go-ruby-prawn/prawn), [`prettyprint`](https://github.com/go-ruby-prettyprint/prettyprint), [`prime`](https://github.com/go-ruby-prime/prime), [`protobuf`](https://github.com/go-ruby-protobuf/protobuf), [`pstore`](https://github.com/go-ruby-pstore/pstore), [`public-suffix`](https://github.com/go-ruby-public-suffix/public-suffix), [`puma`](https://github.com/go-ruby-puma/puma), [`pundit`](https://github.com/go-ruby-pundit/pundit), [`puppet`](https://github.com/go-ruby-puppet/puppet), [`puppet-resource-api`](https://github.com/go-ruby-puppet-resource-api/puppet-resource-api), [`racc`](https://github.com/go-ruby-racc/racc), [`rack`](https://github.com/go-ruby-rack/rack), [`rails`](https://github.com/go-ruby-rails/rails), [`railties`](https://github.com/go-ruby-railties/railties), [`rake`](https://github.com/go-ruby-rake/rake), [`ransack`](https://github.com/go-ruby-ransack/ransack), [`rdoc`](https://github.com/go-ruby-rdoc/rdoc), [`redis`](https://github.com/go-ruby-redis/redis), [`regexp`](https://github.com/go-ruby-regexp/regexp), [`reline`](https://github.com/go-ruby-reline/reline), [`resolv`](https://github.com/go-ruby-resolv/resolv), [`resque`](https://github.com/go-ruby-resque/resque), [`rexml`](https://github.com/go-ruby-rexml/rexml), [`roda`](https://github.com/go-ruby-roda/roda), [`rolify`](https://github.com/go-ruby-rolify/rolify), [`rouge`](https://github.com/go-rouge/rouge), [`rqrcode`](https://github.com/go-ruby-rqrcode/rqrcode), [`rspec`](https://github.com/go-ruby-rspec/rspec), [`rss`](https://github.com/go-ruby-rss/rss), [`rubocop`](https://github.com/go-ruby-rubocop/rubocop), [`rubygems`](https://github.com/go-ruby-rubygems/rubygems), [`saml`](https://github.com/go-ruby-saml/saml), [`sass`](https://github.com/go-ruby-sass/sass), [`scanf`](https://github.com/go-ruby-scanf/scanf), [`securerandom`](https://github.com/go-ruby-securerandom/securerandom), [`semantic-puppet`](https://github.com/go-ruby-semantic-puppet/semantic-puppet), [`sequel`](https://github.com/go-ruby-sequel/sequel), [`shellwords`](https://github.com/go-ruby-shellwords/shellwords), [`shrine`](https://github.com/go-ruby-shrine/shrine), [`sidekiq`](https://github.com/go-ruby-sidekiq/sidekiq), [`simplecov`](https://github.com/go-ruby-simplecov/simplecov), [`sinatra`](https://github.com/go-ruby-sinatra/sinatra), [`slim`](https://github.com/go-ruby-slim/slim), [`sodium`](https://github.com/go-ruby-sodium/sodium), [`sqlite3`](https://github.com/go-ruby-sqlite3/sqlite3), [`strscan`](https://github.com/go-ruby-strscan/strscan), [`thor`](https://github.com/go-ruby-thor/thor), [`timecop`](https://github.com/go-ruby-timecop/timecop), [`toml`](https://github.com/go-ruby-toml/toml), [`tsort`](https://github.com/go-ruby-tsort/tsort), [`typhoeus`](https://github.com/go-ruby-typhoeus/typhoeus), [`tzinfo`](https://github.com/go-ruby-tzinfo/tzinfo), [`unicode-normalize`](https://github.com/go-ruby-unicode-normalize/unicode-normalize), [`uri`](https://github.com/go-ruby-uri/uri), [`vcr`](https://github.com/go-ruby-vcr/vcr), [`warden`](https://github.com/go-ruby-warden/warden), [`webauthn`](https://github.com/go-ruby-webauthn/webauthn), [`webmock`](https://github.com/go-ruby-webmock/webmock), [`webrick`](https://github.com/go-ruby-webrick/webrick), [`widgets`](https://github.com/go-ruby-widgets/widgets), [`xslt`](https://github.com/go-xslt/xslt), [`yaml`](https://github.com/go-ruby-yaml/yaml), [`zeitwerk`](https://github.com/go-ruby-zeitwerk/zeitwerk), [`zlib`](https://github.com/go-ruby-zlib/zlib), [`activeldap`](https://github.com/go-ruby-activeldap/activeldap), [`ldap`](https://github.com/go-ruby-ldap/ldap), [`fast-gettext-locale`](https://github.com/go-ruby-fast-gettext-locale/fast-gettext-locale) — each at `github.com/go-ruby-<name>/<name>`, except `commonmark`, `kramdown`, `liquid`, `mustache`, `nokogiri`, `rouge` and `xslt`, which are bound from `github.com/go-<name>/<name>`. (`set` is **not** bound: `Set` is implemented in-tree, over rbgo's own `object.Hash`.)
 
 The scientific / container stack ([go-ndarray](https://github.com/go-ndarray/ndarray),
-[go-fft](https://github.com/go-fft/fft), [go-images](https://github.com/go-images/images),
+[go-fft](https://github.com/go-fft/fft), [go-numerics](https://github.com/go-numerics),
+[go-statistics](https://github.com/go-statistics), [go-images](https://github.com/go-images/images),
 [go-composites](https://github.com/go-composites)) binds in the same way.
 
 ## How it differs from goruby

diff --git a/docs/scientific-stack.md b/docs/scientific-stack.md
@@ -49,6 +49,106 @@ bin-frequency helpers (`fftfreq`/`rfftfreq`), windows
 p FFT.fft([1, 2, 3, 4]).map { |c| c.real.round(3) }   # => [10.0, -2.0, -2.0, -2.0]
 ```
 
+## Special — scipy.special-style functions
+
+Binds [go-numerics/special](https://github.com/go-numerics/special) — no SciPy:
+**all 67** of its functions under 66 Ruby names, which are **scipy's own**. The
+names come from the correspondence that module measures itself against in ULPs
+(`bench/scipy_server.py` and `testdata/gen/fam_*.py`), so `Log1pExp` is
+`softplus` and `LogGamma` is `gammaln` rather than a transliteration of the Go
+name. Gamma (`gamma`/`gammaln`/`gammasgn`/`digamma`/`polygamma`/`factorial`),
+beta (`beta`/`betaln`/`binom`/`comb`/`perm`), error and normal
+(`erf`/`erfc`/`erfcx`/`erfinv`/`erfcinv`/`ndtr`/`ndtri`/`log_ndtr`), logistic
+(`expit`/`logit`/`softplus`/`xlogy`), reductions
+(`logsumexp`/`softmax`/`log_softmax`), `zeta` (Riemann, or Hurwitz with a second
+argument), the incomplete gamma and beta functions with their inverses, Bessel
+(`j0`…`k1e`, `jv`/`yv`/`iv`/`kv`, `jn_zeros`) and the complete elliptic
+integrals.
+
+Each is a **ufunc**, as scipy's is: a Float answers a Float, an `NDArray`
+answers an `NDArray` of the same shape, and a Float mixed with an array
+broadcasts.
+
+```ruby
+p Special.gamma(5.0)                                        # => 24.0
+p Special.erf(1.0)                                          # => 0.8427007929497149
+p Special.zeta(2.0)                                         # => 1.6449340668482264
+p Special.gamma(NDArray.from([1.0, 2.0, 3.0, 4.0], [2, 2])).to_a  # => [1.0, 1.0, 2.0, 6.0]
+```
+
+## Stats — scipy.stats-style distributions
+
+Binds [go-statistics/stats](https://github.com/go-statistics/stats) — no SciPy:
+the **32 univariate distributions**, again under scipy's names, which is why
+`StudentT` is `t`, `ChiSquared` is `chi2`, `DiscreteUniform` is `randint` and
+`Weibull` is `weibull_min`. Continuous
+`norm`/`cauchy`/`expon`/`gumbel_r`/`halfnorm`/`laplace`/`logistic`/`rayleigh`/
+`uniform`/`chi`/`chi2`/`gamma`/`invgamma`/`lognorm`/`lomax`/`pareto`/`t`/
+`triang`/`vonmises`/`weibull_min`/`beta`/`f`/`ncx2`/`reciprocal`; discrete
+`bernoulli`/`geom`/`poisson`/`zipf`/`binom`/`nbinom`/`randint`/`hypergeom`.
+
+Arguments follow scipy's order — the shape parameters, then `loc`, then `scale`
+— and every distribution answers the same method set, `Stats::Continuous` and
+`Stats::Discrete` differing only in the density: `pdf`/`logpdf` against
+`pmf`/`logpmf`, plus `cdf`/`logcdf`/`sf`/`logsf`/`ppf`/`isf`, the moments
+`mean`/`var`/`std`/`skew`/`kurtosis`/`median`/`entropy`/`moment`,
+`interval`/`support`, and `rvs(size…, seed:)`. The per-point methods are ufuncs
+too. A parameter outside its domain is refused at construction.
+
+```ruby
+p Stats.norm.pdf(0.0)            # => 0.3989422804014327
+p Stats.norm.ppf(0.975)          # => 1.9599639845400538
+p Stats.poisson(3.0).pmf(2)      # => 0.22404180765538775
+p Stats.binom(10, 0.5).mean      # => 5.0
+```
+
+## Integrate — scipy.integrate-style quadrature
+
+Binds [go-numerics/integrate](https://github.com/go-numerics/integrate) — no
+SciPy: adaptive `quad` (finite **or infinite** limits, `points:` for a known
+kink), the fixed rules `fixed_quad` and `romberg`, the sampled rules
+`trapezoid`/`simpson`/`romb`/`cumulative_trapezoid` (`x:` or `dx:`), the
+multiple integrals `dblquad` and `nquad`, and `gauss_legendre` for a rule's
+nodes and weights.
+
+The integrand is a **block**, which is how Ruby passes a callable — and which
+takes `&f` for a Proc or lambda without any further surface. `quad` answers
+scipy's `(value, abserr)` pair, so it destructures the same way.
+
+The two quadrature results in the example below are rounded, and the others on
+this page are not. Quadrature sums products, which Go fuses into an FMA on
+arm64 and not on amd64, so the last bit of `quad`'s answer differs between
+architectures: `0.3333333333333333` on one and `0.33333333333333337` on the
+other. The special functions do not drift that way — their kernels are kept
+FMA-free on purpose — which is why only these two carry a `round`.
+
+```ruby
+v, err = Integrate.quad(0.0, 1.0) { |x| x * x }
+p v.round(12)                                             # => 0.333333333333
+p Integrate.quad(0.0, Float::INFINITY) { |x| Math.exp(-x) }[0].round(12)  # => 1.0
+p Integrate.trapezoid([0.0, 1.0, 4.0], dx: 1.0)           # => 3.0
+```
+
+## Optimize — scipy.optimize-style root finding and minimisation
+
+Binds [go-numerics/optimize](https://github.com/go-numerics/optimize) — no
+SciPy: the bracketing root finders `brentq`/`brenth`/`bisect`/`ridder` and
+`newton` (secant, Newton–Raphson with `fprime:`, Halley with `fprime2:`),
+`minimize_scalar` and `fminbound`, `minimize` over several variables
+(`BFGS`/`CG`/`Nelder-Mead`/`Powell`/`L-BFGS-B`, with `bounds:`), plus
+`curve_fit`, `approx_fprime` and `bracket`.
+
+Return shapes are scipy's: one number is a Float, a tuple an Array (`curve_fit`
+is `(popt, pcov)`), and an `OptimizeResult` or `RootResults` a Hash with symbol
+keys — which `full_output: true` asks a root finder for.
+
+```ruby
+p Optimize.brentq(0.0, 2.0) { |x| x * x - 2 }             # => 1.4142135623731364
+p Optimize.minimize_scalar { |x| (x - 3.0) ** 2 }[:x]     # => 3.0
+r = Optimize.minimize([0.0, 0.0]) { |v| (v[0] - 1.0) ** 2 + (v[1] - 2.0) ** 2 }
+p r[:x].map { |z| z.round(6) }                            # => [1.0, 2.0]
+```
+
 ## Image — scikit-image-style processing
 
 Binds [go-images](https://github.com/go-images/images): `Image.new`/`load`/`save`