Torch Floating Point

A PyTorch library for custom floating point quantization with autograd support. This library provides efficient implementations of custom floating point formats with automatic differentiation capabilities.

Features

• Custom Floating Point Formats: Support for arbitrary floating point configurations (sign bits, exponent bits, mantissa bits, bias)
• Autograd Support: Full PyTorch autograd integration for training with quantized weights
• CUDA Support: GPU acceleration for both forward and backward passes
• Straight-Through Estimator: Gradient-friendly quantization for training

Installation

Install the PyTorch build you will run first (CPU or CUDA). This package compiles an extension against that torch.

From PyPI (Recommended)

pip install torch-floating-point --no-build-isolation

A C++ compiler is required. For CUDA kernels, also install a CUDA toolkit that matches torch.version.cuda (pip's torch wheel does not include nvcc). Set FORCE_CPU=1 to skip CUDA, or FORCE_CUDA=1 to require it.

From Source

git clone https://github.com/SamirMoustafa/torch-floating-point.git
cd torch-floating-point
pip install --no-build-isolation -e .

Quick Start

import torch
from floating_point import FloatingPoint, Round

# Define a custom 8-bit floating point format (1 sign, 4 exponent, 3 mantissa bits)
fp8 = FloatingPoint(sign_bits=1, exponent_bits=4, mantissa_bits=3, bias=7, bits=8)

# Create a rounding function
rounder = Round(fp8)

# Create a tensor with gradients
x = torch.randn(10, requires_grad=True)

# Quantize the tensor
quantized = rounder(x)

# Use in training (gradients flow through)
loss = quantized.sum()
loss.backward()

print(f"Original: {x}")
print(f"Quantized: {quantized}")
print(f"Gradients: {x.grad}")

Training with Custom Floating Point Weights

import torch
import torch.nn as nn
from floating_point import FloatingPoint, Round


class FloatPointLinear(nn.Module):
    def __init__(self, in_features, out_features, fp_config):
        super().__init__()
        self.weight = nn.Parameter(torch.randn(out_features, in_features))
        self.bias = nn.Parameter(torch.randn(out_features))
        self.rounder = Round(fp_config)

    def forward(self, x):
        quantized_weight = self.rounder(self.weight)
        return torch.nn.functional.linear(x, quantized_weight, self.bias)


# Define custom floating point format
fp8 = FloatingPoint(sign_bits=1, exponent_bits=4, mantissa_bits=3, bias=7, bits=8)

# Create model with quantized weights
model = FloatPointLinear(10, 5, fp8)
optimizer = torch.optim.Adam(model.parameters(), lr=0.01)
criterion = nn.MSELoss()

# Create simple data
x = torch.randn(32, 10)
y = torch.randn(32, 5)

# Training loop
for epoch in range(5):
    optimizer.zero_grad()

    # Forward pass
    output = model(x)
    loss = criterion(output, y)

    # Backward pass
    loss.backward()
    optimizer.step()

    print(f"Epoch {epoch + 1}: Loss = {loss.item():.6f}")

Common layouts (OFP8 / MX)

E4M3 and E5M2 are OCP OFP8 encodings (Micikevicius et al., 2022). E2M1 and UE8M0 come from OCP MX (Rouhani et al., 2023). CUDA __nv_* comments below are aliases; decode goldens match cuda_fp4.h / cuda_fp8.h. AMD MI300 FP8 is HIP FNUZ, not OCP. For block-scaled y = (e - z) * s * s_global, use BlockRound. Constructors for FP6, E1M2, UE4M3, FNUZ, INT, and BFP mag are in the docs (not package exports).

from floating_point import FloatingPoint

# E2M1  (__nv_fp4_e2m1; reserved_exponent=False)
fp4_e2m1 = FloatingPoint(sign_bits=1, exponent_bits=2, mantissa_bits=1, bias=1, bits=4, reserved_exponent=False)

# E4M3-FN (__nv_fp8_e4m3): max finite ±448; codes 127/255 are NaN
fp8_e4m3fn = FloatingPoint(
    sign_bits=1,
    exponent_bits=4,
    mantissa_bits=3,
    bias=7,
    bits=8,
    max_mantissa_at_max_exponent=6,
    reserved_exponent=False,
)

# E5M2 (__nv_fp8_e5m2)
fp8_e5m2 = FloatingPoint(sign_bits=1, exponent_bits=5, mantissa_bits=2, bias=15, bits=8, reserved_exponent=True)

# UE8M0 (__nv_fp8_e8m0): codes 0..254 → 2^(E-127); 255 → NaN
fp8_e8m0 = FloatingPoint(sign_bits=0, exponent_bits=8, mantissa_bits=0, bias=127, bits=8, reserved_exponent=True)

Block-scaled Round (NVFP4 / MX)

Shared per-block scale: y = (e - z) * s * s_global with e = Round_elem(x / (s * s_global) + z). Absmax mode detaches s (STE on x only); pass scales= for learnable QAT scales with gradients. s_global= is the optional second-level tensor scale (NVFP4).

OCP MX (MXFP8 / MXFP4) uses UE8M0 scales and block_size=32. NVFP4 is NVIDIA-only: E2M1 + E4M3 (UE4M3) scales, block_size=16, plus FP32 s_global (NVIDIA, 2025). NVIDIA block UE8M0 uses ue8m0_ceil; the OCP sample is ocp_floor; AWS Trainium3 is ocp_floor_x2. Element-wise Round(fp8_e8m0) remains nearest. Recipe tables with source URLs: the docs.

from floating_point import BlockFormat, BlockRound

nvfp4 = BlockFormat(fp4_e2m1, fp8_e4m3fn, 16, 6.0, "nearest")
mxfp8 = BlockFormat(fp8_e4m3fn, fp8_e8m0, 32, 448.0, "ue8m0_ceil")
mxfp8_ocp = BlockFormat(fp8_e4m3fn, fp8_e8m0, 32, 448.0, "ocp_floor")

y = BlockRound(nvfp4)(x)  # absmax scales, STE on x only
y = BlockRound(nvfp4)(x, scales=learnable_s)  # grad into scales
y = BlockRound(nvfp4)(x, s_global=tensor_scale)
y = BlockRound(mxfp8)(x)
y = BlockRound(nvfp4, rounder=MyRound)(x)

Contributing

See CONTRIBUTING.md for setup, tests, and pull-request expectations. Short version:

1. Fork the repository
2. Create a feature branch (git checkout -b feature/amazing-feature)
3. Install development dependencies (make env)
4. Make your changes
5. Run tests (make test)
6. Run linting (make lint)
7. Commit your changes (git commit -m 'Add amazing feature')
8. Push to the branch (git push origin feature/amazing-feature)
9. Open a Pull Request

License

This project is licensed under the MIT License - see the LICENSE file for details.

Citation

If you use this library in your research, please cite:

@software{moustafa2026torchfloatingpoint,
  title={Torch Floating Point: a PyTorch library for custom floating-point formats with automatic differentiation},
  author={Samir Moustafa},
  year={2026},
  version={0.0.22},
  url={https://github.com/SamirMoustafa/torch-floating-point}
}

Support

• Issues: GitHub Issues
• Discussions: GitHub Discussions
• Email: samir.moustafa.97@gmail.com