| /* |
| * 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. |
| */ |
| /** |
| * |
| * 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>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>Numbers are represented in the following form: |
| * <div style="white-space: pre"><code> |
| * n = sign × mant × (radix)<sup>exp</sup>; |
| * </code></div> |
| * 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>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> |
| * |
| */ |
| package org.apache.commons.math4.legacy.core.dfp; |
