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DSArith.jl

DSArith.jl is a Julia implementation of Discrete Stochastic Arithmetic (DSA) with CESTAC-style significance estimation.

It helps you evaluate whether floating-point results are numerically trustworthy, not only whether code runs.

Software overview

DSArith executes each floating-point expression over multiple synchronized stochastic lanes (DSFloat{T,N}), then estimates result quality from lane dispersion.

Core ideas:

  • random directed rounding at each lane and operation,
  • confidence-based significant digit estimation,
  • computational zero detection (@.0),
  • numerical instability diagnostics (cancellation, branching, division, multiplication).

Implemented functionality

  • DS floating-point type: DSFloat with lane-level samples.
  • Execution context: DSAContext / DSAConfig for lane count, seeds, and diagnostics.
  • Elementary function family: roots, trigonometric/inverse trigonometric, hyperbolic/inverse hyperbolic, exponential, and logarithmic functions on DSFloat.
  • Statistical quality metrics: mean_value, std_value, significant_digits, accuracy.
  • Numerical status checks: iscomputedzero, stochastic_string, report.
  • Stochastic relations: s_eq, s_gt, s_ge, s_lt, s_le.
  • Diagnostics: event counters and instability detection helpers.
  • Data uncertainty helpers: uncertain input construction and perturbation utilities.

Installation

import Pkg
Pkg.add(url="https://github.com/chenxinye/DSArith.jl")  # source install
# Pkg.add("DSArith")  # use this if DSArith is available in your registry setup

Quick start

using DSArith

x = ds(10864.0)
y = ds(18817.0)
r = 9x^4 - y^4 + 2y^2

println(stochastic_string(r))
println(report(r))

Documentation map

  • Theory: formulas and interpretation of significance.
  • Examples: representative instability and robustness cases.
  • API Reference: full exported interface index.
  • References: key literature behind CESTAC/CADNA and Rump benchmark.