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---

Probabilistic Rounding with Instruction Set Management

This library provides a vectorized implementation of two probabilistic rounding modes:

1. Up-Down Rounding Mode: Add +/- 1 ulp with equal probabilities (1/2). Do not preserve exact operations.
2. Stochastic Rounding: As described in Fasi and Mikaitis: Algorithms for Stochastically Rounded Elementary Arithmetic Operations, extended here to support the FMA operator.

The library leverages the Highway library, a high-performance C++ library for portable vector instructions across platforms. It uses dynamic dispatch to efficiently execute functions across different architectures.

Features

The library is available in three interfaces:

• Array Interface: Supports probabilistic rounding (PR) on contiguous arrays, providing a simple and flexible interface.
• Dynamic Interface: Provides an interface for single vector instructions with dynamic dispatch to automatically select the best implementation for the target architecture.
• Static Interface: Provides an interface for single vector instructions with static dispatch, delivering optimal performance by bypassing architecture selection. This mode is not portable across architectures.

This combination of features makes the library versatile for scientific computing, numerical analysis, and high-performance applications requiring probabilistic rounding.

Binary releases

Linux x86-64 and aarch64 binaries are attached to each GitHub release. Choose the highest architecture level supported by every machine that will run the static-dispatch library:

Architecture component	Minimum CPU features
x86-64	Baseline x86-64
x86-64-v2	SSE3, SSSE3, SSE4.1, SSE4.2, and POPCNT
x86-64-v3	AVX, AVX2, BMI1/2, F16C, FMA, and related features
x86-64-v4	AVX-512 foundation and the standard v4 extensions
aarch64	Armv8-A with NEON (experimental, see Arm support)

For example, set the desired release and install the baseline package under /usr/local:

VERSION=X.Y.Z
LLVM_MAJOR=20
curl -LO "https://github.com/verificarlo/prism/releases/download/v${VERSION}/prism-${VERSION}-linux-x86-64-llvm${LLVM_MAJOR}.tar.gz"
sudo tar -C /usr/local --strip-components=1 -xzf "prism-${VERSION}-linux-x86-64-llvm${LLVM_MAJOR}.tar.gz"
sudo ldconfig

On Arm, use the linux-aarch64 archive instead.

Each release also includes SHA256SUMS. Archives are built on Ubuntu 22.04 (x86-64 and arm64 runners) for LLVM 20, the latest version tested in CI; the llvmN suffix in the archive name records it. They contain shared and static libraries, public headers, and generated LLVM IR files. To consume the IR files with an earlier LLVM version (17 to 19), build from source with that version. Package documentation and build metadata are installed under share/doc/prism; BUILD-INFO.txt lists the Highway targets each library was built for. The dynamic-dispatch library selects a supported vector target at runtime; the static-dispatch library requires the CPU level named by the archive.

Requirements

• clang, clang++
• parallel (install)
• bazelisk (install)

Build and install from source

The default build requests -march=native and falls back to -mtune=native when the compiler does not support it. Pass --with-arch to build the static-dispatch library for a specific CPU level.

./autogen.sh
./configure
# ./configure --with-arch=x86-64-v3
make
make install

Tests

bazel test tests:all

Current status

The library is tested on x86-64. Arm (aarch64) support is experimental; see below.

Arm support (experimental)

• NEON targets are built by default and tested in CI on Neoverse N2 runners with LLVM 18 and 20. The aarch64 release archives contain NEON code only; their dynamic library selects the best NEON target (up to NEON_BF16) at runtime.
• SVE targets are opt-in with ./configure --enable-experimental-sve and need clang >= 22: Highway generates no SVE code with older clang, and clang 21 only supports SVE2_128.
• -march=native falls back to a generic Armv8 CPU when clang does not know the host CPU; pass --with-arch (e.g. armv9-a+sve2) in that case.
• make target-info prints the Highway targets the static and dynamic libraries were built for, and the target the dynamic library selects on this machine.

On a Cortex-X925 (128-bit SVE2 vectors), SVE is not faster than NEON with GCC or clang 22: the array interface is about 13% slower for stochastic rounding and 50-67% slower for up-down rounding. NEON is therefore the default.

Testing wider SVE vectors

CI also runs the functional tests with 256- and 512-bit SVE vectors under QEMU user mode (the statistical accuracy tests are too slow to emulate). To do the same locally after configuring with --enable-experimental-sve:

# sve-default-vector-length is in bytes: 32 for 256-bit, 64 for 512-bit vectors.
bazel test "--run_under=qemu-aarch64-static -cpu max,sve-default-vector-length=64" //tests/array:all

Publications

If you use PRISM, please cite the relevant papers (see also CITATION.cff):

• I. González-Pepe, H. Akhaddar, T. Glatard, Y. Chatelain. Fuzzy PyTorch: Rapid Numerical Variability Evaluation for Deep Learning Models. Transactions on Machine Learning Research, 2026. arXiv:2605.25991
• Y. Chatelain, P. de Oliveira Castro. Stochastic Rounding in Low-Precision Transformer Inference: A Variable-Precision Emulation Study of a Small GPT-2. 2026. arXiv:2610.01889