@johnhenry/math-plus-special

The one canonical double-precision erf / erfc / GELU for Math Plus. Zero dependencies, pure TypeScript.

import { erf, erfc, gelu, geluDerivative } from "@johnhenry/math-plus-special";

erf(0.5);                    // 0.5204998778130465
erfc(10);                    // 2.0884875837625446e-45 (no 1 - erf cancellation)
gelu(-30);                   // exact x·Φ(x), keeps relative accuracy in the left tail
gelu(1.2, "tanh");           // PyTorch's approximate="tanh"

Why this is its own package

AGENTS.md's canonical-implementation rule: one construct, one implementation. This module began in @johnhenry/math-plus-tensor-core (#122), which still re-exports every name here and applies them in Tensor.erf() / erfc() / gelu(). But @johnhenry/math-plus-frame-arrow deliberately has no static dependency on the tensor track (tensor-core is only its optional, lazily imported peer), so its fn.erf() carried a second, lower-accuracy copy. Both now depend on this zero-dependency leaf instead.

Consumers: tensor-core (re-export + Tensor methods), tensor-compile's IR evaluator, tensor-webgpu's WGSL lowering (ERF_F32_PARAMS), tensor-autograd's GELU backward (via Tensor.erfc()), frame-arrow's fn.erf.

Exports

| Name | What | |---|---| | erf(x), erfc(x) | ~1e-15 / ~3.5e-15 relative (erfc wherever the result is a normal f64) | | gelu(x, approximate = "none"), geluErf, geluTanh | Exact x·Φ(x) or the tanh approximation, PyTorch's names | | geluDerivative(x, approximate) | Derivative of whichever forward was computed | | checkGeluApproximate(v), type GeluApproximate | Option validation for JS callers | | erfSeries, erfcContinuedFraction, ERF_SERIES_CUTOFF, ERF_F32_PARAMS | The algorithm's pieces, exported so the f32 WGSL lowering can be verified against the f64 original |

Algorithm and accuracy notes are in src/index.ts. Tests: oracle-free properties (test/special.test.ts) and a SciPy differential oracle (test/special-oracle.test.ts, scripts/special_oracle.py; same $MATH_PLUS_SCIPY_ORACLE_PYTHON / $MATH_PLUS_ORACLE_PYTHON / python3 resolution and skip-don't-fail rule as the rest of the repo).

Not included

Complex arguments, erfinv / erfcinv, scaled erfcx. @johnhenry/math's own SpecialFunctions.erf (a separate repo) is not replaced by this package.