View source for Floating point conversion, rounding, and precision rules

===Conversion===
<p>Values can be stored in floating point fields using any of the file update statements (for example, STORE RECORD) or can be stored in a %variable. When the value to be stored is supplied as a string, <var class="product">Model&nbsp;204</var> attempts to convert the string to floating point.      </p>
<p>Significant digits past the fifteenth digit are ignored and are treated as zeros regardless of the precision of the value's receptacle. This applies to numbers assigned to fields or %variables or used in arithmetic expressions.    </p>
===Mapping and precision adjustment===
<p>For 8-byte and 16-byte floating point numbers, <var class="product">Model&nbsp;204</var> maintains 15 significant decimal digits of precision. For 4-byte floating point numbers, <var class="product">Model&nbsp;204</var> maintains six significant digits of precision.</p>
<p>Floating point format is an approximate numeric representation that cannot always directly represent decimal values. To provide exact equality in comparisons, <var class="product">Model&nbsp;204</var> maps floating point numbers to the floating point number closest in value to a 6- or 15-digit decimal number. This mapping process is, in effect, a decimal rounding process. This mapping occurs in the following cases:</p>
<ol>
<li>Decimal rounding occurs after addition and subtraction arithmetic operations involving floating point numbers.</li>
<li>If the field is defined as KEY, the value to be indexed is rounded.</li>
<li>If the field is defined as ORDERED NUMERIC, the value to be indexed is rounded.</li>
<li>If the field is used in a direct Table B search in a FIND statement, both the value to be searched for and each field accessed in Table B are rounded.</li>
<li>If the field is to be used as a key in a SORT statement, the value is rounded before being concatenated to the key.          </li>
</ol>
====Assigning floating point numbers to floating point numbers of different lengths====
<p>[[#Assigning floating point numbers to floating point numbers of different lengths|Assigning floating point numbers to floating point numbers of different lengths]] indicates how precision is adjusted with floating point numbers of different lengths.</p>

<table>
<caption>Floating point precision adjustment</caption>
<tr class="head">
<th>Assignment, comparison, <br>or conversion</th>
<th valign="middle">Precision adjustment</th>
</tr>

<tr>
<td>FLOAT 8 to FLOAT 4</td>
<td>Hexadecimal rounding (that is, if second half of an 8-byte floating point number has its high order bit on, a bit is added to the first half of the 8-byte number).</td>
</tr>
<tr>
<td nowrap>FLOAT 16 to FLOAT 8</td>
<td>Truncated.</td>
</tr>
<tr>
<td>FLOAT 4 to FLOAT 8</td>
<td>Decimal rounding (that is, value is converted to the 8-byte floating point number closest in value to the 6-digit decimal representation of the FLOAT 4 value).</td>
</tr>
<tr>
<td>FLOAT 8 to FLOAT 16</td>
<td>Padded with zeros.</td>
</tr>
</table>
[[Category:SOUL]]