diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/complex/package-info.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/complex/package-info.java index 62d047c1f..5b87c3a11 100644 --- a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/complex/package-info.java +++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/complex/package-info.java @@ -14,10 +14,9 @@ * See the License for the specific language governing permissions and * limitations under the License. */ + /** - * - * Complex number type and implementations of complex transcendental - * functions. - * + * Complex number type implementations have been moved to + * Another floating point class. This one is built using radix 10000 - * which is 104, so its almost decimal.

- * - *

The design goals here are: - *

    - *
  1. Decimal math, or close to it
    2. - *
  2. Settable precision (but no mix between numbers using different settings)
    3. - *
  3. Portability. Code should be keep as portable as possible.
    4. - *
  4. Performance
    5. - *
  5. Accuracy - Results should always be +/- 1 ULP for basic - * algebraic operation
    6. - *
  6. Comply with IEEE 854-1987 as much as possible. - * (See IEEE 854-1987 notes below)
    7. - *
- * - *

Trade offs: - *

    - *
  1. Memory foot print. I'm using more memory than necessary to - * represent numbers to get better performance.
    2. - *
  2. 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.
    3. - *
- * - *

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.math4.legacy.dfp;