.. SPDX-FileCopyrightText: 1992-2026 NWO-I/SRON Space Research Organisation Netherlands
..
.. SPDX-License-Identifier: CC-BY-4.0

Mathematical Constants (cspex)
===============================

**Module**: ``utils_cspex``

Overview
--------

Provides fundamental mathematical constants and precision definitions used throughout SPEX.

Key Features
------------

- Double precision arithmetic (15-digit accuracy)
- Common mathematical constants (π, √2, etc.)
- Useful numeric constants (zero, one, two, etc.)
- Consistent precision across all SPEX modules

API Reference
-------------

Constants
~~~~~~~~~

**Mathematical Constants**

.. list-table::
   :widths: 20 30 50
   :header-rows: 1

   * - Constant
     - Value
     - Description
   * - ``pi``
     - 3.14159265358979323846
     - Mathematical constant π
   * - ``twopi``
     - 6.28318530717958647692
     - 2 × π
   * - ``fourpi``
     - 12.56637061435917295385
     - 4 × π
   * - ``sqrtpi``
     - 1.7724538509055159
     - √π

**Common Values**

.. list-table::
   :widths: 20 30 50
   :header-rows: 1

   * - Constant
     - Value
     - Description
   * - ``zero``
     - 0.0
     - Double precision zero
   * - ``half``
     - 0.5
     - Double precision 0.5
   * - ``one``
     - 1.0
     - Double precision one
   * - ``two``
     - 2.0
     - Double precision two

Usage Examples
--------------

**Basic Usage**

.. code-block:: fortran

   use utils_cspex, only: dp, pi, twopi, zero, one
   
   real(dp) :: radius, circumference
   radius = 5.0_dp
   circumference = twopi * radius

**Precision Calculations**

.. code-block:: fortran

   use utils_cspex, only: dp, sqrtpi
   
   real(dp) :: result
   result = sqrtpi * some_value

**Type Definitions**

.. code-block:: fortran

   use utils_cspex, only: dp
   
   real(dp) :: high_precision_value
   integer :: precision_bits
   
   precision_bits = selected_real_kind(15, 307)  ! Same as dp

Notes
-----

- All constants are defined with ``dp`` (double precision) type
- Constants use ``_dp`` suffix for literal values
- Module has no dependencies - safe to use anywhere
- Designed for maximum numerical stability

See Also
--------

- :doc:`../data/energy` - Energy unit conversions
- :doc:`../core/system` - System information