Hisab

Hisab (Arabic: حساب — calculation) — higher mathematics library for AGNOS

Higher math for the AGNOS ecosystem. Provides typed mathematical operations — linear algebra, geometry, calculus, numerical methods, automatic differentiation, symbolic algebra, and more — built on glam.

Used by impetus (physics), kiran (engine), joshua (simulation), aethersafha (compositor), svara (vocal synthesis), and prani (creature vocal synthesis).

For expression evaluation and unit conversion, see abaco.

Features

Feature	Default	Description
`transforms`	yes	2D/3D affine transforms, projections, slerp/lerp, reverse-Z, glam re-exports, HSV/HSL/Oklab color, premultiplied alpha, Porter-Duff compositing, HDR tone mapping (Reinhard, ACES), depth linearization, dual quaternions, CSS decompose, spherical harmonics
`geo`	yes	Primitives (Ray, Plane, AABB, Sphere, OBB, Capsule, Triangle), intersections, closest-point queries, barycentric coordinates, BVH, k-d tree, quadtree, octree, spatial hash, 2D+3D GJK/EPA, MPR/XenoCollide, SAP broadphase, CCD/TOI, sequential impulse with friction, SDFs + CSG, convex decomposition, Delaunay triangulation, Voronoi diagrams, tangent space
`calc`	yes	Differentiation, integration (trapezoidal, Simpson, Gauss-Legendre, adaptive, Monte Carlo), Bezier 2D/3D, Catmull-Rom, B-splines, NURBS, Hermite TCB, monotone cubic (Fritsch-Carlson), easing, spring dynamics, gradient/Jacobian/Hessian, Perlin/fBm noise
`num`	yes	Root finding (Newton-Raphson, bisection), LU/Cholesky/QR/SVD, FFT/DST/DCT/2D-FFT, optimization (GD, CG, BFGS, LM), ODE (RK4, DOPRI45, backward Euler, BDF-2/3/4/5), SDE (Euler-Maruyama, Milstein), symplectic integrators (Euler, Verlet, leapfrog, Yoshida 4th-order), sparse CSR (spmv, spmvt, Cholesky, LU), GMRES, PGS+SOR, BiCGSTAB, eigendecomposition, inertia tensors, Lyapunov exponents, Halton/Sobol sequences, compensated summation (Kahan, Neumaier), PCG32 RNG
`autodiff`	no	Forward-mode (dual numbers) and reverse-mode (tape-based) automatic differentiation
`interval`	no	Interval arithmetic for verified numerics
`symbolic`	no	Symbolic expression tree with evaluation, differentiation, simplification, substitution
`tensor`	no	N-dimensional dense tensor with reshape, matmul, transpose
`parallel`	no	Rayon-powered parallel batch operations (transform, intersection, matvec)
`ai`	no	Daimon/hoosh AI client (network deps)
`logging`	no	Structured logging via `HISAB_LOG` env var
`full`	—	Enables all features

Quick Start

[dependencies]
hisab = "1.2"

use hisab::{Vec3, Quat, Transform3D, Ray, Sphere};
use hisab::geo::ray_sphere;
use hisab::calc::integral_simpson;
use hisab::num::newton_raphson;

// 3D transform with composition
let a = Transform3D::new(Vec3::new(1.0, 2.0, 3.0), Quat::IDENTITY, Vec3::ONE);
let b = Transform3D::new(Vec3::ZERO, Quat::from_rotation_y(0.5), Vec3::splat(2.0));
let combined = a.compose(&b);
let world_pos = combined.apply_to_point(Vec3::ZERO);

// Ray-sphere intersection
let ray = Ray::new(Vec3::ZERO, Vec3::Z).unwrap();
let sphere = Sphere::new(Vec3::new(0.0, 0.0, 5.0), 1.0).unwrap();
let hit = ray_sphere(&ray, &sphere); // Some(4.0)

// Numerical integration
let area = integral_simpson(|x| x * x, 0.0, 1.0, 100).unwrap(); // ~0.3333

// Root finding
let sqrt2 = newton_raphson(|x| x * x - 2.0, |x| 2.0 * x, 1.0, 1e-10, 100).unwrap();

Architecture

See docs/architecture/overview.md for the full module map, data flow, and design principles.

Building

cargo build
cargo test --all-features   # 786 tests
make bench                  # criterion benchmarks with history tracking

License