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| <h1 title="Package" class="title">Package org.apache.commons.math3.dfp</h1> |
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| <div class="block">Decimal floating point library for Java</div> |
| </div> |
| <p>See: <a href="#package_description">Description</a></p> |
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| <th class="colFirst" scope="col">Interface</th> |
| <th class="colLast" scope="col">Description</th> |
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| <td class="colFirst"><a href="../../../../../org/apache/commons/math3/dfp/UnivariateDfpFunction.html" title="interface in org.apache.commons.math3.dfp">UnivariateDfpFunction</a></td> |
| <td class="colLast"> |
| <div class="block">An interface representing a univariate <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp"><code>Dfp</code></a> function.</div> |
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| <td class="colFirst"><a href="../../../../../org/apache/commons/math3/dfp/BracketingNthOrderBrentSolverDFP.html" title="class in org.apache.commons.math3.dfp">BracketingNthOrderBrentSolverDFP</a></td> |
| <td class="colLast"> |
| <div class="block">This class implements a modification of the <a |
| href="http://mathworld.wolfram.com/BrentsMethod.html"> Brent algorithm</a>.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp">Dfp</a></td> |
| <td class="colLast"> |
| <div class="block">Decimal floating point library for Java</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><a href="../../../../../org/apache/commons/math3/dfp/DfpDec.html" title="class in org.apache.commons.math3.dfp">DfpDec</a></td> |
| <td class="colLast"> |
| <div class="block">Subclass of <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp"><code>Dfp</code></a> which hides the radix-10000 artifacts of the superclass.</div> |
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| <td class="colFirst"><a href="../../../../../org/apache/commons/math3/dfp/DfpField.html" title="class in org.apache.commons.math3.dfp">DfpField</a></td> |
| <td class="colLast"> |
| <div class="block">Field for Decimal floating point instances.</div> |
| </td> |
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| <td class="colFirst"><a href="../../../../../org/apache/commons/math3/dfp/DfpMath.html" title="class in org.apache.commons.math3.dfp">DfpMath</a></td> |
| <td class="colLast"> |
| <div class="block">Mathematical routines for use with <a href="../../../../../org/apache/commons/math3/dfp/Dfp.html" title="class in org.apache.commons.math3.dfp"><code>Dfp</code></a>.</div> |
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| <th class="colFirst" scope="col">Enum</th> |
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| <td class="colFirst"><a href="../../../../../org/apache/commons/math3/dfp/DfpField.RoundingMode.html" title="enum in org.apache.commons.math3.dfp">DfpField.RoundingMode</a></td> |
| <td class="colLast"> |
| <div class="block">Enumerate for rounding modes.</div> |
| </td> |
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| <h2 title="Package org.apache.commons.math3.dfp Description">Package org.apache.commons.math3.dfp Description</h2> |
| <div class="block">Decimal floating point library for Java |
| |
| <p>Another floating point class. This one is built using radix 10000 |
| which is 10<sup>4</sup>, so its almost decimal.</p> |
| |
| <p>The design goals here are: |
| <ol> |
| <li>Decimal math, or close to it</li> |
| <li>Settable precision (but no mix between numbers using different settings)</li> |
| <li>Portability. Code should be keep as portable as possible.</li> |
| <li>Performance</li> |
| <li>Accuracy - Results should always be +/- 1 ULP for basic |
| algebraic operation</li> |
| <li>Comply with IEEE 854-1987 as much as possible. |
| (See IEEE 854-1987 notes below)</li> |
| </ol></p> |
| |
| <p>Trade offs: |
| <ol> |
| <li>Memory foot print. I'm using more memory than necessary to |
| represent numbers to get better performance.</li> |
| <li>Digits are bigger, so rounding is a greater loss. So, if you |
| really need 12 decimal digits, better use 4 base 10000 digits |
| there can be one partially filled.</li> |
| </ol></p> |
| |
| <p>Numbers are represented in the following form: |
| <pre> |
| n = sign × mant × (radix)<sup>exp</sup>;</p> |
| </pre> |
| where sign is ±1, mantissa represents a fractional number between |
| zero and one. mant[0] is the least significant digit. |
| exp is in the range of -32767 to 32768</p> |
| |
| <p>IEEE 854-1987 Notes and differences</p> |
| |
| <p>IEEE 854 requires the radix to be either 2 or 10. The radix here is |
| 10000, so that requirement is not met, but it is possible that a |
| subclassed can be made to make it behave as a radix 10 |
| number. It is my opinion that if it looks and behaves as a radix |
| 10 number then it is one and that requirement would be met.</p> |
| |
| <p>The radix of 10000 was chosen because it should be faster to operate |
| on 4 decimal digits at once instead of one at a time. Radix 10 behavior |
| can be realized by add an additional rounding step to ensure that |
| the number of decimal digits represented is constant.</p> |
| |
| <p>The IEEE standard specifically leaves out internal data encoding, |
| so it is reasonable to conclude that such a subclass of this radix |
| 10000 system is merely an encoding of a radix 10 system.</p> |
| |
| <p>IEEE 854 also specifies the existence of "sub-normal" numbers. This |
| class does not contain any such entities. The most significant radix |
| 10000 digit is always non-zero. Instead, we support "gradual underflow" |
| by raising the underflow flag for numbers less with exponent less than |
| expMin, but don't flush to zero until the exponent reaches MIN_EXP-digits. |
| Thus the smallest number we can represent would be: |
| 1E(-(MIN_EXP-digits-1)∗4), eg, for digits=5, MIN_EXP=-32767, that would |
| be 1e-131092.</p> |
| |
| <p>IEEE 854 defines that the implied radix point lies just to the right |
| of the most significant digit and to the left of the remaining digits. |
| This implementation puts the implied radix point to the left of all |
| digits including the most significant one. The most significant digit |
| here is the one just to the right of the radix point. This is a fine |
| detail and is really only a matter of definition. Any side effects of |
| this can be rendered invisible by a subclass.</p></div> |
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