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diff --git a/src/main/java/org/apache/commons/math/dfp/package.html b/src/main/java/org/apache/commons/math/dfp/package.html new file mode 100644 index 0000000..f63dd6e --- /dev/null +++ b/src/main/java/org/apache/commons/math/dfp/package.html @@ -0,0 +1,88 @@ +<html> +<!-- + Licensed to the Apache Software Foundation (ASF) under one or more + contributor license agreements. See the NOTICE file distributed with + this work for additional information regarding copyright ownership. + The ASF licenses this file to You under the Apache License, Version 2.0 + (the "License"); you may not use this file except in compliance with + the License. You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. + --> + <!-- $Revision: 992696 $ $Date: 2010-09-05 00:57:31 +0200 (dim. 05 sept. 2010) $ --> + <body> +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> + </body> +</html> |