Contents of objects
==================

We detail the content of the objects in the sd_listr8 data structure, those in the sd_listis data structure are identical in every way with the only difference between the objects". BINT ",". LPAS "and". VALE "that contain integers instead of real ones. The structure may seem complicated for storing a list of reals. The object". VALE "would suffice. It actually contains the list. The structure is designed to take advantage of the fact that the numbers in the list can be evenly spaced: list "in constant step" by pieces. In this case, some algorithms use this concept of constant step. The description of the list is in fact doubled:


*'. VALE ': contains the list of values,


*'. BINT ','. LPAS 'and'. NBPA ': contain information equivalent to this list.

Suppose we want to store the list of 8 reals:


.. csv-table::

    "1"," :math:`\mathit{a0}\mathrm{=}\mathit{a0}`"
    "2"," :math:`\mathit{a1}\mathrm{=}\mathit{a0}+1\mathrm{\ast }\mathit{dt1}`"
    "3"," :math:`\mathit{a2}\mathrm{=}\mathit{a0}+2\mathrm{\ast }\mathit{dt1}`"
    "4"," :math:`\mathit{a3}\mathrm{=}\mathit{a2}+1\mathrm{\ast }\mathit{dt2}`"
    "5"," :math:`\mathit{a4}\mathrm{=}\mathit{a2}+2\mathrm{\ast }\mathit{dt2}`"
    "6"," :math:`\mathit{a5}\mathrm{=}\mathit{a2}+3\mathrm{\ast }\mathit{dt2}`"
    "7"," :math:`\mathit{a6}\mathrm{=}\mathit{a5}+1\mathrm{\ast }\mathit{dt3}`"
    "8"," :math:`\mathit{a7}\mathrm{=}\mathit{a5}+2\mathrm{\ast }\mathit{dt3}`"


The content of the objects". VALE "and". BINT "will be:

'. VALE ': S V R8 dim=8

.. code-block:: text


    v (1) = a0

    v (2) = a1

    ...

    v (8) = a7

This object contains the values in the list.

.. code-block:: text

'. BINT ': S V R8 dim=4

.. code-block:: text


    v (1) = a0

    v (2) = a2

    v (3) = a5

    v (4) = a7

This object contains the ends of areas where the step is constant.

The objects." LPAS "and". NBPA "will contain:

'. LPAS ': S V R8 dim = 3 (This object contains the values of the "steps")

.. csv-table::

    ":math:`v(1)\mathrm{=}\mathit{d1}` ", "value of the 1st step"
    ":math:`v(2)\mathrm{=}\mathit{d2}` ", "2nd step value"
    ":math:`v(3)\mathrm{=}\mathit{d3}` ", "3rd step value"


'. NBPA ': S V I dim = 3 (This object contains the number of "steps" for each interval)

.. csv-table::

    ":math:`v(1)\mathrm{=}2` ", "number of intervals of length :math:`\mathit{d1}`"
    ":math:`v(2)\mathrm{=}3` ", "number of intervals of length :math:`\mathit{d2}`"
    ":math:`v(3)\mathrm{=}2` ", "number of intervals of length :math:`\mathit{d3}`"


In the (general) case where the list has several items:


* long (LPAS) = long (NBPA)


* long (BINT) = long (NBPA) + 1

note

*For real lists, it may happen that the value of the "constant step" (object ".* LPAS *") is not an exact divisor of the length of the "zones" (object ".* BINT *") (object ".* *"). As a result, the last "step" in an area may be slightly different from the other steps in the zone. This difference cannot be greater than* :math:`{10}^{-3}` *(in relative value) .*

Special case of the list with only 1 element:

In case the list has only one item:

.. code-block:: text
 long (VALE) = long (BINT) = long (LPAS) = long () = long (NBPA) = 1 VALE (1) = BINT (1)