arithmetic_geometric_mean_fortran

A Fortran library for computing the arithmetic-geometric mean (AGM) of two non-negative floating-point numbers.

Features

• Support for real32, real64, and real128 precision
• Elemental functions (works with scalars and arrays)
• Two computation interfaces:
  • Lightweight functions: Fast computation returning only the final AGM value
  • Type-bound methods: Full computation with iteration history storage for convergence analysis
• Single-file library for easy integration

Requirements

Fortran compiler with support for:

• iso_fortran_env intrinsic module
  • real32, real64 types (required)
  • real128 type (optional, compiler-dependent)
• ieee_arithmetic intrinsic module
  • ieee_quiet_nan
  • ieee_unordered
  • ieee_value

Installation

Option 1: Using fpm

To use this library within your fpm project, add the following to your package fpm.toml file:

[dependencies]
arithmetic_geometric_mean_fortran = { git = "https://github.com/DSCF-1224/arithmetic_geometric_mean_fortran.git" }

Option 2: Manual Integration

Since this library consists of a single source file, so that you can

1. Download arithmetic_geometric_mean_fortran.f90
2. Include it in your compilation

API Reference

Functions

interface	description
arithmetic_geometric_mean	Computes AGM with automatic input validation
arithmetic_geometric_mean_kernel	Computes AGM without automatic input validation

Types

• arithmetic_geometric_mean_real32_type
• arithmetic_geometric_mean_real64_type
• arithmetic_geometric_mean_real128_type

Each type provides:

procedure	type	description
compute	subroutine	Type-bound subroutine that performs AGM computation and stores iteration history
max	interface	Extracts the final AGM value / AGM value at a specific iteration
min	interface	Extracts the final AGM value / AGM value at a specific iteration
n_iter	function	Returns the number of iterations performed
gap	interface	Extracts the final gap (a-g) / gap at a specific iteration

Examples

program	description
demo_basic_usage	Demonstrates both function and type-bound interfaces
demo_n_iter	Shows how to access iteration history

Run examples using fpm:

fpm run --example demo_basic_usage
fpm run --example demo_n_iter
fpm run --example  # Run all examples

The --profile subcommand is also available.

Testing

Run tests using fpm:

fpm test --profile debug

fpm test --profile release

Documentation