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/*
* 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
*
* Another floating point class. This one is built using radix 10000
* which is 104, so its almost decimal.
*
* The design goals here are:
*
* - Decimal math, or close to it
* - Settable precision (but no mix between numbers using different settings)
* - Portability. Code should be keep as portable as possible.
* - Performance
* - Accuracy - Results should always be +/- 1 ULP for basic
* algebraic operation
* - Comply with IEEE 854-1987 as much as possible.
* (See IEEE 854-1987 notes below)
*
*
* Trade offs:
*
* - Memory foot print. I'm using more memory than necessary to
* represent numbers to get better performance.
* - 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.
*
*
* Numbers are represented in the following form:
*
* n = sign × mant × (radix)exp;
*
* 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
*
* IEEE 854-1987 Notes and differences
*
* 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.
*
* 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.
*
* 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.
*
* 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.
*
* 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.
*
*/
package org.apache.commons.math3.dfp;