EFT Dot Fortran

A Fortran implementation of Error-Free Transformation (EFT) based dot products for high-precision computation.

Features

• Support for both single precision (real32) and double precision (real64)
• Optional FMA (Fused Multiply-Add) support via compile flag

Files

• src/eftdot.f90: Main EFT dot product module
• tests/test.f90: Test program for accuracy benchmarking
• tests/gen_dot_data.py: Generates ill-conditioned test vectors using accupy (accupy: https://github.com/sigma-py/accupy)
• tests/plot_res.py: Plots accuracy comparison results

Usage

Build Library

# Compile library and module
$ make

# Enable FMA optimization (uncomment in Makefile)
# FFLAGS += -D_FMA -mfma

Run Tests

# Run full accuracy benchmark (generates data, runs tests, plots results)
$ make tests

# Clean build artifacts
$ make clean

Non-installation Usage

Codes in eftdot.f90 can be directly copied and used anywhere.

Example: Using dot2

use eftdot
integer, parameter :: n = 3
real(sp) :: x(n), y(n), result

x = [1.0_sp, 2.0_sp, 3.0_sp]
y = [4.0_sp, 5.0_sp, 6.0_sp]

! Compensated dot product
call dot2(x, y, n, result)

Example: Using dotk for higher accuracy

use eftdot
integer, parameter :: n = 100
real(sp) :: x(n), y(n), result

! k=3 provides approximately double precision accuracy for SP inputs
call dotk(x, y, n, 3, result)

API Reference

dot2(x, y, n, res)

Compensated dot product using TwoProduct and TwoSum error-free transformations.

• x, y: Input vectors (single or double precision)
• n: Vector length
• res: Result with improved accuracy

dotk(x, y, n, k, res)

K-fold compensated dot product for higher accuracy.

• x, y: Input vectors
• n: Vector length
• k: Number of compensation passes (k=2 is equivalent to dot2)
• res: High-accuracy result

Reference

Ogita, T., Rump, S. M., & Oishi, S. I. (2005). Accurate sum and dot product. SIAM Journal on Scientific Computing, 26(6), 1955-1988.