Java example source code file (Dfp.java)
The Dfp.java Java example source code/*
* 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.
*/
package org.apache.commons.math3.dfp;
import java.util.Arrays;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.util.FastMath;
/**
* Decimal floating point library for Java
*
* <p>Another floating point class. This one is built using radix 10000
* which is 10<sup>4, so its almost decimal.
*
* <p>The design goals here are:
* <ol>
* <li>Decimal math, or close to it
* <li>Settable precision (but no mix between numbers using different settings)
* <li>Portability. Code should be kept as portable as possible.
* <li>Performance
* <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:
* <pre>
* n = sign × mant × (radix)<sup>exp;
* </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>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 adding 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>
* @see DfpField
* @since 2.2
*/
public class Dfp implements RealFieldElement<Dfp> {
/** The radix, or base of this system. Set to 10000 */
public static final int RADIX = 10000;
/** The minimum exponent before underflow is signaled. Flush to zero
* occurs at minExp-DIGITS */
public static final int MIN_EXP = -32767;
/** The maximum exponent before overflow is signaled and results flushed
* to infinity */
public static final int MAX_EXP = 32768;
/** The amount under/overflows are scaled by before going to trap handler */
public static final int ERR_SCALE = 32760;
/** Indicator value for normal finite numbers. */
public static final byte FINITE = 0;
/** Indicator value for Infinity. */
public static final byte INFINITE = 1;
/** Indicator value for signaling NaN. */
public static final byte SNAN = 2;
/** Indicator value for quiet NaN. */
public static final byte QNAN = 3;
/** String for NaN representation. */
private static final String NAN_STRING = "NaN";
/** String for positive infinity representation. */
private static final String POS_INFINITY_STRING = "Infinity";
/** String for negative infinity representation. */
private static final String NEG_INFINITY_STRING = "-Infinity";
/** Name for traps triggered by addition. */
private static final String ADD_TRAP = "add";
/** Name for traps triggered by multiplication. */
private static final String MULTIPLY_TRAP = "multiply";
/** Name for traps triggered by division. */
private static final String DIVIDE_TRAP = "divide";
/** Name for traps triggered by square root. */
private static final String SQRT_TRAP = "sqrt";
/** Name for traps triggered by alignment. */
private static final String ALIGN_TRAP = "align";
/** Name for traps triggered by truncation. */
private static final String TRUNC_TRAP = "trunc";
/** Name for traps triggered by nextAfter. */
private static final String NEXT_AFTER_TRAP = "nextAfter";
/** Name for traps triggered by lessThan. */
private static final String LESS_THAN_TRAP = "lessThan";
/** Name for traps triggered by greaterThan. */
private static final String GREATER_THAN_TRAP = "greaterThan";
/** Name for traps triggered by newInstance. */
private static final String NEW_INSTANCE_TRAP = "newInstance";
/** Mantissa. */
protected int[] mant;
/** Sign bit: 1 for positive, -1 for negative. */
protected byte sign;
/** Exponent. */
protected int exp;
/** Indicator for non-finite / non-number values. */
protected byte nans;
/** Factory building similar Dfp's. */
private final DfpField field;
/** Makes an instance with a value of zero.
* @param field field to which this instance belongs
*/
protected Dfp(final DfpField field) {
mant = new int[field.getRadixDigits()];
sign = 1;
exp = 0;
nans = FINITE;
this.field = field;
}
/** Create an instance from a byte value.
* @param field field to which this instance belongs
* @param x value to convert to an instance
*/
protected Dfp(final DfpField field, byte x) {
this(field, (long) x);
}
/** Create an instance from an int value.
* @param field field to which this instance belongs
* @param x value to convert to an instance
*/
protected Dfp(final DfpField field, int x) {
this(field, (long) x);
}
/** Create an instance from a long value.
* @param field field to which this instance belongs
* @param x value to convert to an instance
*/
protected Dfp(final DfpField field, long x) {
// initialize as if 0
mant = new int[field.getRadixDigits()];
nans = FINITE;
this.field = field;
boolean isLongMin = false;
if (x == Long.MIN_VALUE) {
// special case for Long.MIN_VALUE (-9223372036854775808)
// we must shift it before taking its absolute value
isLongMin = true;
++x;
}
// set the sign
if (x < 0) {
sign = -1;
x = -x;
} else {
sign = 1;
}
exp = 0;
while (x != 0) {
System.arraycopy(mant, mant.length - exp, mant, mant.length - 1 - exp, exp);
mant[mant.length - 1] = (int) (x % RADIX);
x /= RADIX;
exp++;
}
if (isLongMin) {
// remove the shift added for Long.MIN_VALUE
// we know in this case that fixing the last digit is sufficient
for (int i = 0; i < mant.length - 1; i++) {
if (mant[i] != 0) {
mant[i]++;
break;
}
}
}
}
/** Create an instance from a double value.
* @param field field to which this instance belongs
* @param x value to convert to an instance
*/
protected Dfp(final DfpField field, double x) {
// initialize as if 0
mant = new int[field.getRadixDigits()];
sign = 1;
exp = 0;
nans = FINITE;
this.field = field;
long bits = Double.doubleToLongBits(x);
long mantissa = bits & 0x000fffffffffffffL;
int exponent = (int) ((bits & 0x7ff0000000000000L) >> 52) - 1023;
if (exponent == -1023) {
// Zero or sub-normal
if (x == 0) {
// make sure 0 has the right sign
if ((bits & 0x8000000000000000L) != 0) {
sign = -1;
}
return;
}
exponent++;
// Normalize the subnormal number
while ( (mantissa & 0x0010000000000000L) == 0) {
exponent--;
mantissa <<= 1;
}
mantissa &= 0x000fffffffffffffL;
}
if (exponent == 1024) {
// infinity or NAN
if (x != x) {
sign = (byte) 1;
nans = QNAN;
} else if (x < 0) {
sign = (byte) -1;
nans = INFINITE;
} else {
sign = (byte) 1;
nans = INFINITE;
}
return;
}
Dfp xdfp = new Dfp(field, mantissa);
xdfp = xdfp.divide(new Dfp(field, 4503599627370496l)).add(field.getOne()); // Divide by 2^52, then add one
xdfp = xdfp.multiply(DfpMath.pow(field.getTwo(), exponent));
if ((bits & 0x8000000000000000L) != 0) {
xdfp = xdfp.negate();
}
System.arraycopy(xdfp.mant, 0, mant, 0, mant.length);
sign = xdfp.sign;
exp = xdfp.exp;
nans = xdfp.nans;
}
/** Copy constructor.
* @param d instance to copy
*/
public Dfp(final Dfp d) {
mant = d.mant.clone();
sign = d.sign;
exp = d.exp;
nans = d.nans;
field = d.field;
}
/** Create an instance from a String representation.
* @param field field to which this instance belongs
* @param s string representation of the instance
*/
protected Dfp(final DfpField field, final String s) {
// initialize as if 0
mant = new int[field.getRadixDigits()];
sign = 1;
exp = 0;
nans = FINITE;
this.field = field;
boolean decimalFound = false;
final int rsize = 4; // size of radix in decimal digits
final int offset = 4; // Starting offset into Striped
final char[] striped = new char[getRadixDigits() * rsize + offset * 2];
// Check some special cases
if (s.equals(POS_INFINITY_STRING)) {
sign = (byte) 1;
nans = INFINITE;
return;
}
if (s.equals(NEG_INFINITY_STRING)) {
sign = (byte) -1;
nans = INFINITE;
return;
}
if (s.equals(NAN_STRING)) {
sign = (byte) 1;
nans = QNAN;
return;
}
// Check for scientific notation
int p = s.indexOf("e");
if (p == -1) { // try upper case?
p = s.indexOf("E");
}
final String fpdecimal;
int sciexp = 0;
if (p != -1) {
// scientific notation
fpdecimal = s.substring(0, p);
String fpexp = s.substring(p+1);
boolean negative = false;
for (int i=0; i<fpexp.length(); i++)
{
if (fpexp.charAt(i) == '-')
{
negative = true;
continue;
}
if (fpexp.charAt(i) >= '0' && fpexp.charAt(i) <= '9') {
sciexp = sciexp * 10 + fpexp.charAt(i) - '0';
}
}
if (negative) {
sciexp = -sciexp;
}
} else {
// normal case
fpdecimal = s;
}
// If there is a minus sign in the number then it is negative
if (fpdecimal.indexOf("-") != -1) {
sign = -1;
}
// First off, find all of the leading zeros, trailing zeros, and significant digits
p = 0;
// Move p to first significant digit
int decimalPos = 0;
for (;;) {
if (fpdecimal.charAt(p) >= '1' && fpdecimal.charAt(p) <= '9') {
break;
}
if (decimalFound && fpdecimal.charAt(p) == '0') {
decimalPos--;
}
if (fpdecimal.charAt(p) == '.') {
decimalFound = true;
}
p++;
if (p == fpdecimal.length()) {
break;
}
}
// Copy the string onto Stripped
int q = offset;
striped[0] = '0';
striped[1] = '0';
striped[2] = '0';
striped[3] = '0';
int significantDigits=0;
for(;;) {
if (p == (fpdecimal.length())) {
break;
}
// Don't want to run pass the end of the array
if (q == mant.length*rsize+offset+1) {
break;
}
if (fpdecimal.charAt(p) == '.') {
decimalFound = true;
decimalPos = significantDigits;
p++;
continue;
}
if (fpdecimal.charAt(p) < '0' || fpdecimal.charAt(p) > '9') {
p++;
continue;
}
striped[q] = fpdecimal.charAt(p);
q++;
p++;
significantDigits++;
}
// If the decimal point has been found then get rid of trailing zeros.
if (decimalFound && q != offset) {
for (;;) {
q--;
if (q == offset) {
break;
}
if (striped[q] == '0') {
significantDigits--;
} else {
break;
}
}
}
// special case of numbers like "0.00000"
if (decimalFound && significantDigits == 0) {
decimalPos = 0;
}
// Implicit decimal point at end of number if not present
if (!decimalFound) {
decimalPos = q-offset;
}
// Find the number of significant trailing zeros
q = offset; // set q to point to first sig digit
p = significantDigits-1+offset;
while (p > q) {
if (striped[p] != '0') {
break;
}
p--;
}
// Make sure the decimal is on a mod 10000 boundary
int i = ((rsize * 100) - decimalPos - sciexp % rsize) % rsize;
q -= i;
decimalPos += i;
// Make the mantissa length right by adding zeros at the end if necessary
while ((p - q) < (mant.length * rsize)) {
for (i = 0; i < rsize; i++) {
striped[++p] = '0';
}
}
// Ok, now we know how many trailing zeros there are,
// and where the least significant digit is
for (i = mant.length - 1; i >= 0; i--) {
mant[i] = (striped[q] - '0') * 1000 +
(striped[q+1] - '0') * 100 +
(striped[q+2] - '0') * 10 +
(striped[q+3] - '0');
q += 4;
}
exp = (decimalPos+sciexp) / rsize;
if (q < striped.length) {
// Is there possible another digit?
round((striped[q] - '0')*1000);
}
}
/** Creates an instance with a non-finite value.
* @param field field to which this instance belongs
* @param sign sign of the Dfp to create
* @param nans code of the value, must be one of {@link #INFINITE},
* {@link #SNAN}, {@link #QNAN}
*/
protected Dfp(final DfpField field, final byte sign, final byte nans) {
this.field = field;
this.mant = new int[field.getRadixDigits()];
this.sign = sign;
this.exp = 0;
this.nans = nans;
}
/** Create an instance with a value of 0.
* Use this internally in preference to constructors to facilitate subclasses
* @return a new instance with a value of 0
*/
public Dfp newInstance() {
return new Dfp(getField());
}
/** Create an instance from a byte value.
* @param x value to convert to an instance
* @return a new instance with value x
*/
public Dfp newInstance(final byte x) {
return new Dfp(getField(), x);
}
/** Create an instance from an int value.
* @param x value to convert to an instance
* @return a new instance with value x
*/
public Dfp newInstance(final int x) {
return new Dfp(getField(), x);
}
/** Create an instance from a long value.
* @param x value to convert to an instance
* @return a new instance with value x
*/
public Dfp newInstance(final long x) {
return new Dfp(getField(), x);
}
/** Create an instance from a double value.
* @param x value to convert to an instance
* @return a new instance with value x
*/
public Dfp newInstance(final double x) {
return new Dfp(getField(), x);
}
/** Create an instance by copying an existing one.
* Use this internally in preference to constructors to facilitate subclasses.
* @param d instance to copy
* @return a new instance with the same value as d
*/
public Dfp newInstance(final Dfp d) {
// make sure we don't mix number with different precision
if (field.getRadixDigits() != d.field.getRadixDigits()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
final Dfp result = newInstance(getZero());
result.nans = QNAN;
return dotrap(DfpField.FLAG_INVALID, NEW_INSTANCE_TRAP, d, result);
}
return new Dfp(d);
}
/** Create an instance from a String representation.
* Use this internally in preference to constructors to facilitate subclasses.
* @param s string representation of the instance
* @return a new instance parsed from specified string
*/
public Dfp newInstance(final String s) {
return new Dfp(field, s);
}
/** Creates an instance with a non-finite value.
* @param sig sign of the Dfp to create
* @param code code of the value, must be one of {@link #INFINITE},
* {@link #SNAN}, {@link #QNAN}
* @return a new instance with a non-finite value
*/
public Dfp newInstance(final byte sig, final byte code) {
return field.newDfp(sig, code);
}
/** Get the {@link org.apache.commons.math3.Field Field} (really a {@link DfpField}) to which the instance belongs.
* <p>
* The field is linked to the number of digits and acts as a factory
* for {@link Dfp} instances.
* </p>
* @return {@link org.apache.commons.math3.Field Field} (really a {@link DfpField}) to which the instance belongs
*/
public DfpField getField() {
return field;
}
/** Get the number of radix digits of the instance.
* @return number of radix digits
*/
public int getRadixDigits() {
return field.getRadixDigits();
}
/** Get the constant 0.
* @return a Dfp with value zero
*/
public Dfp getZero() {
return field.getZero();
}
/** Get the constant 1.
* @return a Dfp with value one
*/
public Dfp getOne() {
return field.getOne();
}
/** Get the constant 2.
* @return a Dfp with value two
*/
public Dfp getTwo() {
return field.getTwo();
}
/** Shift the mantissa left, and adjust the exponent to compensate.
*/
protected void shiftLeft() {
for (int i = mant.length - 1; i > 0; i--) {
mant[i] = mant[i-1];
}
mant[0] = 0;
exp--;
}
/* Note that shiftRight() does not call round() as that round() itself
uses shiftRight() */
/** Shift the mantissa right, and adjust the exponent to compensate.
*/
protected void shiftRight() {
for (int i = 0; i < mant.length - 1; i++) {
mant[i] = mant[i+1];
}
mant[mant.length - 1] = 0;
exp++;
}
/** Make our exp equal to the supplied one, this may cause rounding.
* Also causes de-normalized numbers. These numbers are generally
* dangerous because most routines assume normalized numbers.
* Align doesn't round, so it will return the last digit destroyed
* by shifting right.
* @param e desired exponent
* @return last digit destroyed by shifting right
*/
protected int align(int e) {
int lostdigit = 0;
boolean inexact = false;
int diff = exp - e;
int adiff = diff;
if (adiff < 0) {
adiff = -adiff;
}
if (diff == 0) {
return 0;
}
if (adiff > (mant.length + 1)) {
// Special case
Arrays.fill(mant, 0);
exp = e;
field.setIEEEFlagsBits(DfpField.FLAG_INEXACT);
dotrap(DfpField.FLAG_INEXACT, ALIGN_TRAP, this, this);
return 0;
}
for (int i = 0; i < adiff; i++) {
if (diff < 0) {
/* Keep track of loss -- only signal inexact after losing 2 digits.
* the first lost digit is returned to add() and may be incorporated
* into the result.
*/
if (lostdigit != 0) {
inexact = true;
}
lostdigit = mant[0];
shiftRight();
} else {
shiftLeft();
}
}
if (inexact) {
field.setIEEEFlagsBits(DfpField.FLAG_INEXACT);
dotrap(DfpField.FLAG_INEXACT, ALIGN_TRAP, this, this);
}
return lostdigit;
}
/** Check if instance is less than x.
* @param x number to check instance against
* @return true if instance is less than x and neither are NaN, false otherwise
*/
public boolean lessThan(final Dfp x) {
// make sure we don't mix number with different precision
if (field.getRadixDigits() != x.field.getRadixDigits()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
final Dfp result = newInstance(getZero());
result.nans = QNAN;
dotrap(DfpField.FLAG_INVALID, LESS_THAN_TRAP, x, result);
return false;
}
/* if a nan is involved, signal invalid and return false */
if (isNaN() || x.isNaN()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
dotrap(DfpField.FLAG_INVALID, LESS_THAN_TRAP, x, newInstance(getZero()));
return false;
}
return compare(this, x) < 0;
}
/** Check if instance is greater than x.
* @param x number to check instance against
* @return true if instance is greater than x and neither are NaN, false otherwise
*/
public boolean greaterThan(final Dfp x) {
// make sure we don't mix number with different precision
if (field.getRadixDigits() != x.field.getRadixDigits()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
final Dfp result = newInstance(getZero());
result.nans = QNAN;
dotrap(DfpField.FLAG_INVALID, GREATER_THAN_TRAP, x, result);
return false;
}
/* if a nan is involved, signal invalid and return false */
if (isNaN() || x.isNaN()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
dotrap(DfpField.FLAG_INVALID, GREATER_THAN_TRAP, x, newInstance(getZero()));
return false;
}
return compare(this, x) > 0;
}
/** Check if instance is less than or equal to 0.
* @return true if instance is not NaN and less than or equal to 0, false otherwise
*/
public boolean negativeOrNull() {
if (isNaN()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
dotrap(DfpField.FLAG_INVALID, LESS_THAN_TRAP, this, newInstance(getZero()));
return false;
}
return (sign < 0) || ((mant[mant.length - 1] == 0) && !isInfinite());
}
/** Check if instance is strictly less than 0.
* @return true if instance is not NaN and less than or equal to 0, false otherwise
*/
public boolean strictlyNegative() {
if (isNaN()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
dotrap(DfpField.FLAG_INVALID, LESS_THAN_TRAP, this, newInstance(getZero()));
return false;
}
return (sign < 0) && ((mant[mant.length - 1] != 0) || isInfinite());
}
/** Check if instance is greater than or equal to 0.
* @return true if instance is not NaN and greater than or equal to 0, false otherwise
*/
public boolean positiveOrNull() {
if (isNaN()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
dotrap(DfpField.FLAG_INVALID, LESS_THAN_TRAP, this, newInstance(getZero()));
return false;
}
return (sign > 0) || ((mant[mant.length - 1] == 0) && !isInfinite());
}
/** Check if instance is strictly greater than 0.
* @return true if instance is not NaN and greater than or equal to 0, false otherwise
*/
public boolean strictlyPositive() {
if (isNaN()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
dotrap(DfpField.FLAG_INVALID, LESS_THAN_TRAP, this, newInstance(getZero()));
return false;
}
return (sign > 0) && ((mant[mant.length - 1] != 0) || isInfinite());
}
/** Get the absolute value of instance.
* @return absolute value of instance
* @since 3.2
*/
public Dfp abs() {
Dfp result = newInstance(this);
result.sign = 1;
return result;
}
/** Check if instance is infinite.
* @return true if instance is infinite
*/
public boolean isInfinite() {
return nans == INFINITE;
}
/** Check if instance is not a number.
* @return true if instance is not a number
*/
public boolean isNaN() {
return (nans == QNAN) || (nans == SNAN);
}
/** Check if instance is equal to zero.
* @return true if instance is equal to zero
*/
public boolean isZero() {
if (isNaN()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
dotrap(DfpField.FLAG_INVALID, LESS_THAN_TRAP, this, newInstance(getZero()));
return false;
}
return (mant[mant.length - 1] == 0) && !isInfinite();
}
/** Check if instance is equal to x.
* @param other object to check instance against
* @return true if instance is equal to x and neither are NaN, false otherwise
*/
@Override
public boolean equals(final Object other) {
if (other instanceof Dfp) {
final Dfp x = (Dfp) other;
if (isNaN() || x.isNaN() || field.getRadixDigits() != x.field.getRadixDigits()) {
return false;
}
return compare(this, x) == 0;
}
return false;
}
/**
* Gets a hashCode for the instance.
* @return a hash code value for this object
*/
@Override
public int hashCode() {
return 17 + (isZero() ? 0 : (sign << 8)) + (nans << 16) + exp + Arrays.hashCode(mant);
}
/** Check if instance is not equal to x.
* @param x number to check instance against
* @return true if instance is not equal to x and neither are NaN, false otherwise
*/
public boolean unequal(final Dfp x) {
if (isNaN() || x.isNaN() || field.getRadixDigits() != x.field.getRadixDigits()) {
return false;
}
return greaterThan(x) || lessThan(x);
}
/** Compare two instances.
* @param a first instance in comparison
* @param b second instance in comparison
* @return -1 if a<b, 1 if a>b and 0 if a==b
* Note this method does not properly handle NaNs or numbers with different precision.
*/
private static int compare(final Dfp a, final Dfp b) {
// Ignore the sign of zero
if (a.mant[a.mant.length - 1] == 0 && b.mant[b.mant.length - 1] == 0 &&
a.nans == FINITE && b.nans == FINITE) {
return 0;
}
if (a.sign != b.sign) {
if (a.sign == -1) {
return -1;
} else {
return 1;
}
}
// deal with the infinities
if (a.nans == INFINITE && b.nans == FINITE) {
return a.sign;
}
if (a.nans == FINITE && b.nans == INFINITE) {
return -b.sign;
}
if (a.nans == INFINITE && b.nans == INFINITE) {
return 0;
}
// Handle special case when a or b is zero, by ignoring the exponents
if (b.mant[b.mant.length-1] != 0 && a.mant[b.mant.length-1] != 0) {
if (a.exp < b.exp) {
return -a.sign;
}
if (a.exp > b.exp) {
return a.sign;
}
}
// compare the mantissas
for (int i = a.mant.length - 1; i >= 0; i--) {
if (a.mant[i] > b.mant[i]) {
return a.sign;
}
if (a.mant[i] < b.mant[i]) {
return -a.sign;
}
}
return 0;
}
/** Round to nearest integer using the round-half-even method.
* That is round to nearest integer unless both are equidistant.
* In which case round to the even one.
* @return rounded value
* @since 3.2
*/
public Dfp rint() {
return trunc(DfpField.RoundingMode.ROUND_HALF_EVEN);
}
/** Round to an integer using the round floor mode.
* That is, round toward -Infinity
* @return rounded value
* @since 3.2
*/
public Dfp floor() {
return trunc(DfpField.RoundingMode.ROUND_FLOOR);
}
/** Round to an integer using the round ceil mode.
* That is, round toward +Infinity
* @return rounded value
* @since 3.2
*/
public Dfp ceil() {
return trunc(DfpField.RoundingMode.ROUND_CEIL);
}
/** Returns the IEEE remainder.
* @param d divisor
* @return this less n × d, where n is the integer closest to this/d
* @since 3.2
*/
public Dfp remainder(final Dfp d) {
final Dfp result = this.subtract(this.divide(d).rint().multiply(d));
// IEEE 854-1987 says that if the result is zero, then it carries the sign of this
if (result.mant[mant.length-1] == 0) {
result.sign = sign;
}
return result;
}
/** Does the integer conversions with the specified rounding.
* @param rmode rounding mode to use
* @return truncated value
*/
protected Dfp trunc(final DfpField.RoundingMode rmode) {
boolean changed = false;
if (isNaN()) {
return newInstance(this);
}
if (nans == INFINITE) {
return newInstance(this);
}
if (mant[mant.length-1] == 0) {
// a is zero
return newInstance(this);
}
/* If the exponent is less than zero then we can certainly
* return zero */
if (exp < 0) {
field.setIEEEFlagsBits(DfpField.FLAG_INEXACT);
Dfp result = newInstance(getZero());
result = dotrap(DfpField.FLAG_INEXACT, TRUNC_TRAP, this, result);
return result;
}
/* If the exponent is greater than or equal to digits, then it
* must already be an integer since there is no precision left
* for any fractional part */
if (exp >= mant.length) {
return newInstance(this);
}
/* General case: create another dfp, result, that contains the
* a with the fractional part lopped off. */
Dfp result = newInstance(this);
for (int i = 0; i < mant.length-result.exp; i++) {
changed |= result.mant[i] != 0;
result.mant[i] = 0;
}
if (changed) {
switch (rmode) {
case ROUND_FLOOR:
if (result.sign == -1) {
// then we must increment the mantissa by one
result = result.add(newInstance(-1));
}
break;
case ROUND_CEIL:
if (result.sign == 1) {
// then we must increment the mantissa by one
result = result.add(getOne());
}
break;
case ROUND_HALF_EVEN:
default:
final Dfp half = newInstance("0.5");
Dfp a = subtract(result); // difference between this and result
a.sign = 1; // force positive (take abs)
if (a.greaterThan(half)) {
a = newInstance(getOne());
a.sign = sign;
result = result.add(a);
}
/** If exactly equal to 1/2 and odd then increment */
if (a.equals(half) && result.exp > 0 && (result.mant[mant.length-result.exp]&1) != 0) {
a = newInstance(getOne());
a.sign = sign;
result = result.add(a);
}
break;
}
field.setIEEEFlagsBits(DfpField.FLAG_INEXACT); // signal inexact
result = dotrap(DfpField.FLAG_INEXACT, TRUNC_TRAP, this, result);
return result;
}
return result;
}
/** Convert this to an integer.
* If greater than 2147483647, it returns 2147483647. If less than -2147483648 it returns -2147483648.
* @return converted number
*/
public int intValue() {
Dfp rounded;
int result = 0;
rounded = rint();
if (rounded.greaterThan(newInstance(2147483647))) {
return 2147483647;
}
if (rounded.lessThan(newInstance(-2147483648))) {
return -2147483648;
}
for (int i = mant.length - 1; i >= mant.length - rounded.exp; i--) {
result = result * RADIX + rounded.mant[i];
}
if (rounded.sign == -1) {
result = -result;
}
return result;
}
/** Get the exponent of the greatest power of 10000 that is
* less than or equal to the absolute value of this. I.E. if
* this is 10<sup>6 then log10K would return 1.
* @return integer base 10000 logarithm
*/
public int log10K() {
return exp - 1;
}
/** Get the specified power of 10000.
* @param e desired power
* @return 10000<sup>e
*/
public Dfp power10K(final int e) {
Dfp d = newInstance(getOne());
d.exp = e + 1;
return d;
}
/** Get the exponent of the greatest power of 10 that is less than or equal to abs(this).
* @return integer base 10 logarithm
* @since 3.2
*/
public int intLog10() {
if (mant[mant.length-1] > 1000) {
return exp * 4 - 1;
}
if (mant[mant.length-1] > 100) {
return exp * 4 - 2;
}
if (mant[mant.length-1] > 10) {
return exp * 4 - 3;
}
return exp * 4 - 4;
}
/** Return the specified power of 10.
* @param e desired power
* @return 10<sup>e
*/
public Dfp power10(final int e) {
Dfp d = newInstance(getOne());
if (e >= 0) {
d.exp = e / 4 + 1;
} else {
d.exp = (e + 1) / 4;
}
switch ((e % 4 + 4) % 4) {
case 0:
break;
case 1:
d = d.multiply(10);
break;
case 2:
d = d.multiply(100);
break;
default:
d = d.multiply(1000);
}
return d;
}
/** Negate the mantissa of this by computing the complement.
* Leaves the sign bit unchanged, used internally by add.
* Denormalized numbers are handled properly here.
* @param extra ???
* @return ???
*/
protected int complement(int extra) {
extra = RADIX-extra;
for (int i = 0; i < mant.length; i++) {
mant[i] = RADIX-mant[i]-1;
}
int rh = extra / RADIX;
extra -= rh * RADIX;
for (int i = 0; i < mant.length; i++) {
final int r = mant[i] + rh;
rh = r / RADIX;
mant[i] = r - rh * RADIX;
}
return extra;
}
/** Add x to this.
* @param x number to add
* @return sum of this and x
*/
public Dfp add(final Dfp x) {
// make sure we don't mix number with different precision
if (field.getRadixDigits() != x.field.getRadixDigits()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
final Dfp result = newInstance(getZero());
result.nans = QNAN;
return dotrap(DfpField.FLAG_INVALID, ADD_TRAP, x, result);
}
/* handle special cases */
if (nans != FINITE || x.nans != FINITE) {
if (isNaN()) {
return this;
}
if (x.isNaN()) {
return x;
}
if (nans == INFINITE && x.nans == FINITE) {
return this;
}
if (x.nans == INFINITE && nans == FINITE) {
return x;
}
if (x.nans == INFINITE && nans == INFINITE && sign == x.sign) {
return x;
}
if (x.nans == INFINITE && nans == INFINITE && sign != x.sign) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
Dfp result = newInstance(getZero());
result.nans = QNAN;
result = dotrap(DfpField.FLAG_INVALID, ADD_TRAP, x, result);
return result;
}
}
/* copy this and the arg */
Dfp a = newInstance(this);
Dfp b = newInstance(x);
/* initialize the result object */
Dfp result = newInstance(getZero());
/* Make all numbers positive, but remember their sign */
final byte asign = a.sign;
final byte bsign = b.sign;
a.sign = 1;
b.sign = 1;
/* The result will be signed like the arg with greatest magnitude */
byte rsign = bsign;
if (compare(a, b) > 0) {
rsign = asign;
}
/* Handle special case when a or b is zero, by setting the exponent
of the zero number equal to the other one. This avoids an alignment
which would cause catastropic loss of precision */
if (b.mant[mant.length-1] == 0) {
b.exp = a.exp;
}
if (a.mant[mant.length-1] == 0) {
a.exp = b.exp;
}
/* align number with the smaller exponent */
int aextradigit = 0;
int bextradigit = 0;
if (a.exp < b.exp) {
aextradigit = a.align(b.exp);
} else {
bextradigit = b.align(a.exp);
}
/* complement the smaller of the two if the signs are different */
if (asign != bsign) {
if (asign == rsign) {
bextradigit = b.complement(bextradigit);
} else {
aextradigit = a.complement(aextradigit);
}
}
/* add the mantissas */
int rh = 0; /* acts as a carry */
for (int i = 0; i < mant.length; i++) {
final int r = a.mant[i]+b.mant[i]+rh;
rh = r / RADIX;
result.mant[i] = r - rh * RADIX;
}
result.exp = a.exp;
result.sign = rsign;
/* handle overflow -- note, when asign!=bsign an overflow is
* normal and should be ignored. */
if (rh != 0 && (asign == bsign)) {
final int lostdigit = result.mant[0];
result.shiftRight();
result.mant[mant.length-1] = rh;
final int excp = result.round(lostdigit);
if (excp != 0) {
result = dotrap(excp, ADD_TRAP, x, result);
}
}
/* normalize the result */
for (int i = 0; i < mant.length; i++) {
if (result.mant[mant.length-1] != 0) {
break;
}
result.shiftLeft();
if (i == 0) {
result.mant[0] = aextradigit+bextradigit;
aextradigit = 0;
bextradigit = 0;
}
}
/* result is zero if after normalization the most sig. digit is zero */
if (result.mant[mant.length-1] == 0) {
result.exp = 0;
if (asign != bsign) {
// Unless adding 2 negative zeros, sign is positive
result.sign = 1; // Per IEEE 854-1987 Section 6.3
}
}
/* Call round to test for over/under flows */
final int excp = result.round(aextradigit + bextradigit);
if (excp != 0) {
result = dotrap(excp, ADD_TRAP, x, result);
}
return result;
}
/** Returns a number that is this number with the sign bit reversed.
* @return the opposite of this
*/
public Dfp negate() {
Dfp result = newInstance(this);
result.sign = (byte) - result.sign;
return result;
}
/** Subtract x from this.
* @param x number to subtract
* @return difference of this and a
*/
public Dfp subtract(final Dfp x) {
return add(x.negate());
}
/** Round this given the next digit n using the current rounding mode.
* @param n ???
* @return the IEEE flag if an exception occurred
*/
protected int round(int n) {
boolean inc = false;
switch (field.getRoundingMode()) {
case ROUND_DOWN:
inc = false;
break;
case ROUND_UP:
inc = n != 0; // round up if n!=0
break;
case ROUND_HALF_UP:
inc = n >= 5000; // round half up
break;
case ROUND_HALF_DOWN:
inc = n > 5000; // round half down
break;
case ROUND_HALF_EVEN:
inc = n > 5000 || (n == 5000 && (mant[0] & 1) == 1); // round half-even
break;
case ROUND_HALF_ODD:
inc = n > 5000 || (n == 5000 && (mant[0] & 1) == 0); // round half-odd
break;
case ROUND_CEIL:
inc = sign == 1 && n != 0; // round ceil
break;
case ROUND_FLOOR:
default:
inc = sign == -1 && n != 0; // round floor
break;
}
if (inc) {
// increment if necessary
int rh = 1;
for (int i = 0; i < mant.length; i++) {
final int r = mant[i] + rh;
rh = r / RADIX;
mant[i] = r - rh * RADIX;
}
if (rh != 0) {
shiftRight();
mant[mant.length-1] = rh;
}
}
// check for exceptional cases and raise signals if necessary
if (exp < MIN_EXP) {
// Gradual Underflow
field.setIEEEFlagsBits(DfpField.FLAG_UNDERFLOW);
return DfpField.FLAG_UNDERFLOW;
}
if (exp > MAX_EXP) {
// Overflow
field.setIEEEFlagsBits(DfpField.FLAG_OVERFLOW);
return DfpField.FLAG_OVERFLOW;
}
if (n != 0) {
// Inexact
field.setIEEEFlagsBits(DfpField.FLAG_INEXACT);
return DfpField.FLAG_INEXACT;
}
return 0;
}
/** Multiply this by x.
* @param x multiplicand
* @return product of this and x
*/
public Dfp multiply(final Dfp x) {
// make sure we don't mix number with different precision
if (field.getRadixDigits() != x.field.getRadixDigits()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
final Dfp result = newInstance(getZero());
result.nans = QNAN;
return dotrap(DfpField.FLAG_INVALID, MULTIPLY_TRAP, x, result);
}
Dfp result = newInstance(getZero());
/* handle special cases */
if (nans != FINITE || x.nans != FINITE) {
if (isNaN()) {
return this;
}
if (x.isNaN()) {
return x;
}
if (nans == INFINITE && x.nans == FINITE && x.mant[mant.length-1] != 0) {
result = newInstance(this);
result.sign = (byte) (sign * x.sign);
return result;
}
if (x.nans == INFINITE && nans == FINITE && mant[mant.length-1] != 0) {
result = newInstance(x);
result.sign = (byte) (sign * x.sign);
return result;
}
if (x.nans == INFINITE && nans == INFINITE) {
result = newInstance(this);
result.sign = (byte) (sign * x.sign);
return result;
}
if ( (x.nans == INFINITE && nans == FINITE && mant[mant.length-1] == 0) ||
(nans == INFINITE && x.nans == FINITE && x.mant[mant.length-1] == 0) ) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
result = newInstance(getZero());
result.nans = QNAN;
result = dotrap(DfpField.FLAG_INVALID, MULTIPLY_TRAP, x, result);
return result;
}
}
int[] product = new int[mant.length*2]; // Big enough to hold even the largest result
for (int i = 0; i < mant.length; i++) {
int rh = 0; // acts as a carry
for (int j=0; j<mant.length; j++) {
int r = mant[i] * x.mant[j]; // multiply the 2 digits
r += product[i+j] + rh; // add to the product digit with carry in
rh = r / RADIX;
product[i+j] = r - rh * RADIX;
}
product[i+mant.length] = rh;
}
// Find the most sig digit
int md = mant.length * 2 - 1; // default, in case result is zero
for (int i = mant.length * 2 - 1; i >= 0; i--) {
if (product[i] != 0) {
md = i;
break;
}
}
// Copy the digits into the result
for (int i = 0; i < mant.length; i++) {
result.mant[mant.length - i - 1] = product[md - i];
}
// Fixup the exponent.
result.exp = exp + x.exp + md - 2 * mant.length + 1;
result.sign = (byte)((sign == x.sign)?1:-1);
if (result.mant[mant.length-1] == 0) {
// if result is zero, set exp to zero
result.exp = 0;
}
final int excp;
if (md > (mant.length-1)) {
excp = result.round(product[md-mant.length]);
} else {
excp = result.round(0); // has no effect except to check status
}
if (excp != 0) {
result = dotrap(excp, MULTIPLY_TRAP, x, result);
}
return result;
}
/** Multiply this by a single digit x.
* @param x multiplicand
* @return product of this and x
*/
public Dfp multiply(final int x) {
if (x >= 0 && x < RADIX) {
return multiplyFast(x);
} else {
return multiply(newInstance(x));
}
}
/** Multiply this by a single digit 0<=x<radix.
* There are speed advantages in this special case.
* @param x multiplicand
* @return product of this and x
*/
private Dfp multiplyFast(final int x) {
Dfp result = newInstance(this);
/* handle special cases */
if (nans != FINITE) {
if (isNaN()) {
return this;
}
if (nans == INFINITE && x != 0) {
result = newInstance(this);
return result;
}
if (nans == INFINITE && x == 0) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
result = newInstance(getZero());
result.nans = QNAN;
result = dotrap(DfpField.FLAG_INVALID, MULTIPLY_TRAP, newInstance(getZero()), result);
return result;
}
}
/* range check x */
if (x < 0 || x >= RADIX) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
result = newInstance(getZero());
result.nans = QNAN;
result = dotrap(DfpField.FLAG_INVALID, MULTIPLY_TRAP, result, result);
return result;
}
int rh = 0;
for (int i = 0; i < mant.length; i++) {
final int r = mant[i] * x + rh;
rh = r / RADIX;
result.mant[i] = r - rh * RADIX;
}
int lostdigit = 0;
if (rh != 0) {
lostdigit = result.mant[0];
result.shiftRight();
result.mant[mant.length-1] = rh;
}
if (result.mant[mant.length-1] == 0) { // if result is zero, set exp to zero
result.exp = 0;
}
final int excp = result.round(lostdigit);
if (excp != 0) {
result = dotrap(excp, MULTIPLY_TRAP, result, result);
}
return result;
}
/** Divide this by divisor.
* @param divisor divisor
* @return quotient of this by divisor
*/
public Dfp divide(Dfp divisor) {
int dividend[]; // current status of the dividend
int quotient[]; // quotient
int remainder[];// remainder
int qd; // current quotient digit we're working with
int nsqd; // number of significant quotient digits we have
int trial=0; // trial quotient digit
int minadj; // minimum adjustment
boolean trialgood; // Flag to indicate a good trail digit
int md=0; // most sig digit in result
int excp; // exceptions
// make sure we don't mix number with different precision
if (field.getRadixDigits() != divisor.field.getRadixDigits()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
final Dfp result = newInstance(getZero());
result.nans = QNAN;
return dotrap(DfpField.FLAG_INVALID, DIVIDE_TRAP, divisor, result);
}
Dfp result = newInstance(getZero());
/* handle special cases */
if (nans != FINITE || divisor.nans != FINITE) {
if (isNaN()) {
return this;
}
if (divisor.isNaN()) {
return divisor;
}
if (nans == INFINITE && divisor.nans == FINITE) {
result = newInstance(this);
result.sign = (byte) (sign * divisor.sign);
return result;
}
if (divisor.nans == INFINITE && nans == FINITE) {
result = newInstance(getZero());
result.sign = (byte) (sign * divisor.sign);
return result;
}
if (divisor.nans == INFINITE && nans == INFINITE) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
result = newInstance(getZero());
result.nans = QNAN;
result = dotrap(DfpField.FLAG_INVALID, DIVIDE_TRAP, divisor, result);
return result;
}
}
/* Test for divide by zero */
if (divisor.mant[mant.length-1] == 0) {
field.setIEEEFlagsBits(DfpField.FLAG_DIV_ZERO);
result = newInstance(getZero());
result.sign = (byte) (sign * divisor.sign);
result.nans = INFINITE;
result = dotrap(DfpField.FLAG_DIV_ZERO, DIVIDE_TRAP, divisor, result);
return result;
}
dividend = new int[mant.length+1]; // one extra digit needed
quotient = new int[mant.length+2]; // two extra digits needed 1 for overflow, 1 for rounding
remainder = new int[mant.length+1]; // one extra digit needed
/* Initialize our most significant digits to zero */
dividend[mant.length] = 0;
quotient[mant.length] = 0;
quotient[mant.length+1] = 0;
remainder[mant.length] = 0;
/* copy our mantissa into the dividend, initialize the
quotient while we are at it */
for (int i = 0; i < mant.length; i++) {
dividend[i] = mant[i];
quotient[i] = 0;
remainder[i] = 0;
}
/* outer loop. Once per quotient digit */
nsqd = 0;
for (qd = mant.length+1; qd >= 0; qd--) {
/* Determine outer limits of our quotient digit */
// r = most sig 2 digits of dividend
final int divMsb = dividend[mant.length]*RADIX+dividend[mant.length-1];
int min = divMsb / (divisor.mant[mant.length-1]+1);
int max = (divMsb + 1) / divisor.mant[mant.length-1];
trialgood = false;
while (!trialgood) {
// try the mean
trial = (min+max)/2;
/* Multiply by divisor and store as remainder */
int rh = 0;
for (int i = 0; i < mant.length + 1; i++) {
int dm = (i<mant.length)?divisor.mant[i]:0;
final int r = (dm * trial) + rh;
rh = r / RADIX;
remainder[i] = r - rh * RADIX;
}
/* subtract the remainder from the dividend */
rh = 1; // carry in to aid the subtraction
for (int i = 0; i < mant.length + 1; i++) {
final int r = ((RADIX-1) - remainder[i]) + dividend[i] + rh;
rh = r / RADIX;
remainder[i] = r - rh * RADIX;
}
/* Lets analyze what we have here */
if (rh == 0) {
// trial is too big -- negative remainder
max = trial-1;
continue;
}
/* find out how far off the remainder is telling us we are */
minadj = (remainder[mant.length] * RADIX)+remainder[mant.length-1];
minadj /= divisor.mant[mant.length-1] + 1;
if (minadj >= 2) {
min = trial+minadj; // update the minimum
continue;
}
/* May have a good one here, check more thoroughly. Basically
its a good one if it is less than the divisor */
trialgood = false; // assume false
for (int i = mant.length - 1; i >= 0; i--) {
if (divisor.mant[i] > remainder[i]) {
trialgood = true;
}
if (divisor.mant[i] < remainder[i]) {
break;
}
}
if (remainder[mant.length] != 0) {
trialgood = false;
}
if (trialgood == false) {
min = trial+1;
}
}
/* Great we have a digit! */
quotient[qd] = trial;
if (trial != 0 || nsqd != 0) {
nsqd++;
}
if (field.getRoundingMode() == DfpField.RoundingMode.ROUND_DOWN && nsqd == mant.length) {
// We have enough for this mode
break;
}
if (nsqd > mant.length) {
// We have enough digits
break;
}
/* move the remainder into the dividend while left shifting */
dividend[0] = 0;
for (int i = 0; i < mant.length; i++) {
dividend[i + 1] = remainder[i];
}
}
/* Find the most sig digit */
md = mant.length; // default
for (int i = mant.length + 1; i >= 0; i--) {
if (quotient[i] != 0) {
md = i;
break;
}
}
/* Copy the digits into the result */
for (int i=0; i<mant.length; i++) {
result.mant[mant.length-i-1] = quotient[md-i];
}
/* Fixup the exponent. */
result.exp = exp - divisor.exp + md - mant.length;
result.sign = (byte) ((sign == divisor.sign) ? 1 : -1);
if (result.mant[mant.length-1] == 0) { // if result is zero, set exp to zero
result.exp = 0;
}
if (md > (mant.length-1)) {
excp = result.round(quotient[md-mant.length]);
} else {
excp = result.round(0);
}
if (excp != 0) {
result = dotrap(excp, DIVIDE_TRAP, divisor, result);
}
return result;
}
/** Divide by a single digit less than radix.
* Special case, so there are speed advantages. 0 <= divisor < radix
* @param divisor divisor
* @return quotient of this by divisor
*/
public Dfp divide(int divisor) {
// Handle special cases
if (nans != FINITE) {
if (isNaN()) {
return this;
}
if (nans == INFINITE) {
return newInstance(this);
}
}
// Test for divide by zero
if (divisor == 0) {
field.setIEEEFlagsBits(DfpField.FLAG_DIV_ZERO);
Dfp result = newInstance(getZero());
result.sign = sign;
result.nans = INFINITE;
result = dotrap(DfpField.FLAG_DIV_ZERO, DIVIDE_TRAP, getZero(), result);
return result;
}
// range check divisor
if (divisor < 0 || divisor >= RADIX) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
Dfp result = newInstance(getZero());
result.nans = QNAN;
result = dotrap(DfpField.FLAG_INVALID, DIVIDE_TRAP, result, result);
return result;
}
Dfp result = newInstance(this);
int rl = 0;
for (int i = mant.length-1; i >= 0; i--) {
final int r = rl*RADIX + result.mant[i];
final int rh = r / divisor;
rl = r - rh * divisor;
result.mant[i] = rh;
}
if (result.mant[mant.length-1] == 0) {
// normalize
result.shiftLeft();
final int r = rl * RADIX; // compute the next digit and put it in
final int rh = r / divisor;
rl = r - rh * divisor;
result.mant[0] = rh;
}
final int excp = result.round(rl * RADIX / divisor); // do the rounding
if (excp != 0) {
result = dotrap(excp, DIVIDE_TRAP, result, result);
}
return result;
}
/** {@inheritDoc} */
public Dfp reciprocal() {
return field.getOne().divide(this);
}
/** Compute the square root.
* @return square root of the instance
* @since 3.2
*/
public Dfp sqrt() {
// check for unusual cases
if (nans == FINITE && mant[mant.length-1] == 0) {
// if zero
return newInstance(this);
}
if (nans != FINITE) {
if (nans == INFINITE && sign == 1) {
// if positive infinity
return newInstance(this);
}
if (nans == QNAN) {
return newInstance(this);
}
if (nans == SNAN) {
Dfp result;
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
result = newInstance(this);
result = dotrap(DfpField.FLAG_INVALID, SQRT_TRAP, null, result);
return result;
}
}
if (sign == -1) {
// if negative
Dfp result;
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
result = newInstance(this);
result.nans = QNAN;
result = dotrap(DfpField.FLAG_INVALID, SQRT_TRAP, null, result);
return result;
}
Dfp x = newInstance(this);
/* Lets make a reasonable guess as to the size of the square root */
if (x.exp < -1 || x.exp > 1) {
x.exp = this.exp / 2;
}
/* Coarsely estimate the mantissa */
switch (x.mant[mant.length-1] / 2000) {
case 0:
x.mant[mant.length-1] = x.mant[mant.length-1]/2+1;
break;
case 2:
x.mant[mant.length-1] = 1500;
break;
case 3:
x.mant[mant.length-1] = 2200;
break;
default:
x.mant[mant.length-1] = 3000;
}
Dfp dx = newInstance(x);
/* Now that we have the first pass estimate, compute the rest
by the formula dx = (y - x*x) / (2x); */
Dfp px = getZero();
Dfp ppx = getZero();
while (x.unequal(px)) {
dx = newInstance(x);
dx.sign = -1;
dx = dx.add(this.divide(x));
dx = dx.divide(2);
ppx = px;
px = x;
x = x.add(dx);
if (x.equals(ppx)) {
// alternating between two values
break;
}
// if dx is zero, break. Note testing the most sig digit
// is a sufficient test since dx is normalized
if (dx.mant[mant.length-1] == 0) {
break;
}
}
return x;
}
/** Get a string representation of the instance.
* @return string representation of the instance
*/
@Override
public String toString() {
if (nans != FINITE) {
// if non-finite exceptional cases
if (nans == INFINITE) {
return (sign < 0) ? NEG_INFINITY_STRING : POS_INFINITY_STRING;
} else {
return NAN_STRING;
}
}
if (exp > mant.length || exp < -1) {
return dfp2sci();
}
return dfp2string();
}
/** Convert an instance to a string using scientific notation.
* @return string representation of the instance in scientific notation
*/
protected String dfp2sci() {
char rawdigits[] = new char[mant.length * 4];
char outputbuffer[] = new char[mant.length * 4 + 20];
int p;
int q;
int e;
int ae;
int shf;
// Get all the digits
p = 0;
for (int i = mant.length - 1; i >= 0; i--) {
rawdigits[p++] = (char) ((mant[i] / 1000) + '0');
rawdigits[p++] = (char) (((mant[i] / 100) %10) + '0');
rawdigits[p++] = (char) (((mant[i] / 10) % 10) + '0');
rawdigits[p++] = (char) (((mant[i]) % 10) + '0');
}
// Find the first non-zero one
for (p = 0; p < rawdigits.length; p++) {
if (rawdigits[p] != '0') {
break;
}
}
shf = p;
// Now do the conversion
q = 0;
if (sign == -1) {
outputbuffer[q++] = '-';
}
if (p != rawdigits.length) {
// there are non zero digits...
outputbuffer[q++] = rawdigits[p++];
outputbuffer[q++] = '.';
while (p<rawdigits.length) {
outputbuffer[q++] = rawdigits[p++];
}
} else {
outputbuffer[q++] = '0';
outputbuffer[q++] = '.';
outputbuffer[q++] = '0';
outputbuffer[q++] = 'e';
outputbuffer[q++] = '0';
return new String(outputbuffer, 0, 5);
}
outputbuffer[q++] = 'e';
// Find the msd of the exponent
e = exp * 4 - shf - 1;
ae = e;
if (e < 0) {
ae = -e;
}
// Find the largest p such that p < e
for (p = 1000000000; p > ae; p /= 10) {
// nothing to do
}
if (e < 0) {
outputbuffer[q++] = '-';
}
while (p > 0) {
outputbuffer[q++] = (char)(ae / p + '0');
ae %= p;
p /= 10;
}
return new String(outputbuffer, 0, q);
}
/** Convert an instance to a string using normal notation.
* @return string representation of the instance in normal notation
*/
protected String dfp2string() {
char buffer[] = new char[mant.length*4 + 20];
int p = 1;
int q;
int e = exp;
boolean pointInserted = false;
buffer[0] = ' ';
if (e <= 0) {
buffer[p++] = '0';
buffer[p++] = '.';
pointInserted = true;
}
while (e < 0) {
buffer[p++] = '0';
buffer[p++] = '0';
buffer[p++] = '0';
buffer[p++] = '0';
e++;
}
for (int i = mant.length - 1; i >= 0; i--) {
buffer[p++] = (char) ((mant[i] / 1000) + '0');
buffer[p++] = (char) (((mant[i] / 100) % 10) + '0');
buffer[p++] = (char) (((mant[i] / 10) % 10) + '0');
buffer[p++] = (char) (((mant[i]) % 10) + '0');
if (--e == 0) {
buffer[p++] = '.';
pointInserted = true;
}
}
while (e > 0) {
buffer[p++] = '0';
buffer[p++] = '0';
buffer[p++] = '0';
buffer[p++] = '0';
e--;
}
if (!pointInserted) {
// Ensure we have a radix point!
buffer[p++] = '.';
}
// Suppress leading zeros
q = 1;
while (buffer[q] == '0') {
q++;
}
if (buffer[q] == '.') {
q--;
}
// Suppress trailing zeros
while (buffer[p-1] == '0') {
p--;
}
// Insert sign
if (sign < 0) {
buffer[--q] = '-';
}
return new String(buffer, q, p - q);
}
/** Raises a trap. This does not set the corresponding flag however.
* @param type the trap type
* @param what - name of routine trap occurred in
* @param oper - input operator to function
* @param result - the result computed prior to the trap
* @return The suggested return value from the trap handler
*/
public Dfp dotrap(int type, String what, Dfp oper, Dfp result) {
Dfp def = result;
switch (type) {
case DfpField.FLAG_INVALID:
def = newInstance(getZero());
def.sign = result.sign;
def.nans = QNAN;
break;
case DfpField.FLAG_DIV_ZERO:
if (nans == FINITE && mant[mant.length-1] != 0) {
// normal case, we are finite, non-zero
def = newInstance(getZero());
def.sign = (byte)(sign*oper.sign);
def.nans = INFINITE;
}
if (nans == FINITE && mant[mant.length-1] == 0) {
// 0/0
def = newInstance(getZero());
def.nans = QNAN;
}
if (nans == INFINITE || nans == QNAN) {
def = newInstance(getZero());
def.nans = QNAN;
}
if (nans == INFINITE || nans == SNAN) {
def = newInstance(getZero());
def.nans = QNAN;
}
break;
case DfpField.FLAG_UNDERFLOW:
if ( (result.exp+mant.length) < MIN_EXP) {
def = newInstance(getZero());
def.sign = result.sign;
} else {
def = newInstance(result); // gradual underflow
}
result.exp += ERR_SCALE;
break;
case DfpField.FLAG_OVERFLOW:
result.exp -= ERR_SCALE;
def = newInstance(getZero());
def.sign = result.sign;
def.nans = INFINITE;
break;
default: def = result; break;
}
return trap(type, what, oper, def, result);
}
/** Trap handler. Subclasses may override this to provide trap
* functionality per IEEE 854-1987.
*
* @param type The exception type - e.g. FLAG_OVERFLOW
* @param what The name of the routine we were in e.g. divide()
* @param oper An operand to this function if any
* @param def The default return value if trap not enabled
* @param result The result that is specified to be delivered per
* IEEE 854, if any
* @return the value that should be return by the operation triggering the trap
*/
protected Dfp trap(int type, String what, Dfp oper, Dfp def, Dfp result) {
return def;
}
/** Returns the type - one of FINITE, INFINITE, SNAN, QNAN.
* @return type of the number
*/
public int classify() {
return nans;
}
/** Creates an instance that is the same as x except that it has the sign of y.
* abs(x) = dfp.copysign(x, dfp.one)
* @param x number to get the value from
* @param y number to get the sign from
* @return a number with the value of x and the sign of y
*/
public static Dfp copysign(final Dfp x, final Dfp y) {
Dfp result = x.newInstance(x);
result.sign = y.sign;
return result;
}
/** Returns the next number greater than this one in the direction of x.
* If this==x then simply returns this.
* @param x direction where to look at
* @return closest number next to instance in the direction of x
*/
public Dfp nextAfter(final Dfp x) {
// make sure we don't mix number with different precision
if (field.getRadixDigits() != x.field.getRadixDigits()) {
field.setIEEEFlagsBits(DfpField.FLAG_INVALID);
final Dfp result = newInstance(getZero());
result.nans = QNAN;
return dotrap(DfpField.FLAG_INVALID, NEXT_AFTER_TRAP, x, result);
}
// if this is greater than x
boolean up = false;
if (this.lessThan(x)) {
up = true;
}
if (compare(this, x) == 0) {
return newInstance(x);
}
if (lessThan(getZero())) {
up = !up;
}
final Dfp inc;
Dfp result;
if (up) {
inc = newInstance(getOne());
inc.exp = this.exp-mant.length+1;
inc.sign = this.sign;
if (this.equals(getZero())) {
inc.exp = MIN_EXP-mant.length;
}
result = add(inc);
} else {
inc = newInstance(getOne());
inc.exp = this.exp;
inc.sign = this.sign;
if (this.equals(inc)) {
inc.exp = this.exp-mant.length;
} else {
inc.exp = this.exp-mant.length+1;
}
if (this.equals(getZero())) {
inc.exp = MIN_EXP-mant.length;
}
result = this.subtract(inc);
}
if (result.classify() == INFINITE && this.classify() != INFINITE) {
field.setIEEEFlagsBits(DfpField.FLAG_INEXACT);
result = dotrap(DfpField.FLAG_INEXACT, NEXT_AFTER_TRAP, x, result);
}
if (result.equals(getZero()) && this.equals(getZero()) == false) {
field.setIEEEFlagsBits(DfpField.FLAG_INEXACT);
result = dotrap(DfpField.FLAG_INEXACT, NEXT_AFTER_TRAP, x, result);
}
return result;
}
/** Convert the instance into a double.
* @return a double approximating the instance
* @see #toSplitDouble()
*/
public double toDouble() {
if (isInfinite()) {
if (lessThan(getZero())) {
return Double.NEGATIVE_INFINITY;
} else {
return Double.POSITIVE_INFINITY;
}
}
if (isNaN()) {
return Double.NaN;
}
Dfp y = this;
boolean negate = false;
int cmp0 = compare(this, getZero());
if (cmp0 == 0) {
return sign < 0 ? -0.0 : +0.0;
} else if (cmp0 < 0) {
y = negate();
negate = true;
}
/* Find the exponent, first estimate by integer log10, then adjust.
Should be faster than doing a natural logarithm. */
int exponent = (int)(y.intLog10() * 3.32);
if (exponent < 0) {
exponent--;
}
Dfp tempDfp = DfpMath.pow(getTwo(), exponent);
while (tempDfp.lessThan(y) || tempDfp.equals(y)) {
tempDfp = tempDfp.multiply(2);
exponent++;
}
exponent--;
/* We have the exponent, now work on the mantissa */
y = y.divide(DfpMath.pow(getTwo(), exponent));
if (exponent > -1023) {
y = y.subtract(getOne());
}
if (exponent < -1074) {
return 0;
}
if (exponent > 1023) {
return negate ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY;
}
y = y.multiply(newInstance(4503599627370496l)).rint();
String str = y.toString();
str = str.substring(0, str.length()-1);
long mantissa = Long.parseLong(str);
if (mantissa == 4503599627370496L) {
// Handle special case where we round up to next power of two
mantissa = 0;
exponent++;
}
/* Its going to be subnormal, so make adjustments */
if (exponent <= -1023) {
exponent--;
}
while (exponent < -1023) {
exponent++;
mantissa >>>= 1;
}
long bits = mantissa | ((exponent + 1023L) << 52);
double x = Double.longBitsToDouble(bits);
if (negate) {
x = -x;
}
return x;
}
/** Convert the instance into a split double.
* @return an array of two doubles which sum represent the instance
* @see #toDouble()
*/
public double[] toSplitDouble() {
double split[] = new double[2];
long mask = 0xffffffffc0000000L;
split[0] = Double.longBitsToDouble(Double.doubleToLongBits(toDouble()) & mask);
split[1] = subtract(newInstance(split[0])).toDouble();
return split;
}
/** {@inheritDoc}
* @since 3.2
*/
public double getReal() {
return toDouble();
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp add(final double a) {
return add(newInstance(a));
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp subtract(final double a) {
return subtract(newInstance(a));
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp multiply(final double a) {
return multiply(newInstance(a));
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp divide(final double a) {
return divide(newInstance(a));
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp remainder(final double a) {
return remainder(newInstance(a));
}
/** {@inheritDoc}
* @since 3.2
*/
public long round() {
return FastMath.round(toDouble());
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp signum() {
if (isNaN() || isZero()) {
return this;
} else {
return newInstance(sign > 0 ? +1 : -1);
}
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp copySign(final Dfp s) {
if ((sign >= 0 && s.sign >= 0) || (sign < 0 && s.sign < 0)) { // Sign is currently OK
return this;
}
return negate(); // flip sign
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp copySign(final double s) {
long sb = Double.doubleToLongBits(s);
if ((sign >= 0 && sb >= 0) || (sign < 0 && sb < 0)) { // Sign is currently OK
return this;
}
return negate(); // flip sign
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp scalb(final int n) {
return multiply(DfpMath.pow(getTwo(), n));
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp hypot(final Dfp y) {
return multiply(this).add(y.multiply(y)).sqrt();
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp cbrt() {
return rootN(3);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp rootN(final int n) {
return (sign >= 0) ?
DfpMath.pow(this, getOne().divide(n)) :
DfpMath.pow(negate(), getOne().divide(n)).negate();
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp pow(final double p) {
return DfpMath.pow(this, newInstance(p));
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp pow(final int n) {
return DfpMath.pow(this, n);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp pow(final Dfp e) {
return DfpMath.pow(this, e);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp exp() {
return DfpMath.exp(this);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp expm1() {
return DfpMath.exp(this).subtract(getOne());
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp log() {
return DfpMath.log(this);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp log1p() {
return DfpMath.log(this.add(getOne()));
}
// TODO: deactivate this implementation (and return type) in 4.0
/** Get the exponent of the greatest power of 10 that is less than or equal to abs(this).
* @return integer base 10 logarithm
* @deprecated as of 3.2, replaced by {@link #intLog10()}, in 4.0 the return type
* will be changed to Dfp
*/
@Deprecated
public int log10() {
return intLog10();
}
// TODO: activate this implementation (and return type) in 4.0
// /** {@inheritDoc}
// * @since 3.2
// */
// public Dfp log10() {
// return DfpMath.log(this).divide(DfpMath.log(newInstance(10)));
// }
/** {@inheritDoc}
* @since 3.2
*/
public Dfp cos() {
return DfpMath.cos(this);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp sin() {
return DfpMath.sin(this);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp tan() {
return DfpMath.tan(this);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp acos() {
return DfpMath.acos(this);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp asin() {
return DfpMath.asin(this);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp atan() {
return DfpMath.atan(this);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp atan2(final Dfp x)
throws DimensionMismatchException {
// compute r = sqrt(x^2+y^2)
final Dfp r = x.multiply(x).add(multiply(this)).sqrt();
if (x.sign >= 0) {
// compute atan2(y, x) = 2 atan(y / (r + x))
return getTwo().multiply(divide(r.add(x)).atan());
} else {
// compute atan2(y, x) = +/- pi - 2 atan(y / (r - x))
final Dfp tmp = getTwo().multiply(divide(r.subtract(x)).atan());
final Dfp pmPi = newInstance((tmp.sign <= 0) ? -FastMath.PI : FastMath.PI);
return pmPi.subtract(tmp);
}
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp cosh() {
return DfpMath.exp(this).add(DfpMath.exp(negate())).divide(2);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp sinh() {
return DfpMath.exp(this).subtract(DfpMath.exp(negate())).divide(2);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp tanh() {
final Dfp ePlus = DfpMath.exp(this);
final Dfp eMinus = DfpMath.exp(negate());
return ePlus.subtract(eMinus).divide(ePlus.add(eMinus));
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp acosh() {
return multiply(this).subtract(getOne()).sqrt().add(this).log();
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp asinh() {
return multiply(this).add(getOne()).sqrt().add(this).log();
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp atanh() {
return getOne().add(this).divide(getOne().subtract(this)).log().divide(2);
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp linearCombination(final Dfp[] a, final Dfp[] b)
throws DimensionMismatchException {
if (a.length != b.length) {
throw new DimensionMismatchException(a.length, b.length);
}
Dfp r = getZero();
for (int i = 0; i < a.length; ++i) {
r = r.add(a[i].multiply(b[i]));
}
return r;
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp linearCombination(final double[] a, final Dfp[] b)
throws DimensionMismatchException {
if (a.length != b.length) {
throw new DimensionMismatchException(a.length, b.length);
}
Dfp r = getZero();
for (int i = 0; i < a.length; ++i) {
r = r.add(b[i].multiply(a[i]));
}
return r;
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp linearCombination(final Dfp a1, final Dfp b1, final Dfp a2, final Dfp b2) {
return a1.multiply(b1).add(a2.multiply(b2));
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp linearCombination(final double a1, final Dfp b1, final double a2, final Dfp b2) {
return b1.multiply(a1).add(b2.multiply(a2));
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp linearCombination(final Dfp a1, final Dfp b1,
final Dfp a2, final Dfp b2,
final Dfp a3, final Dfp b3) {
return a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3));
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp linearCombination(final double a1, final Dfp b1,
final double a2, final Dfp b2,
final double a3, final Dfp b3) {
return b1.multiply(a1).add(b2.multiply(a2)).add(b3.multiply(a3));
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp linearCombination(final Dfp a1, final Dfp b1, final Dfp a2, final Dfp b2,
final Dfp a3, final Dfp b3, final Dfp a4, final Dfp b4) {
return a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3)).add(a4.multiply(b4));
}
/** {@inheritDoc}
* @since 3.2
*/
public Dfp linearCombination(final double a1, final Dfp b1, final double a2, final Dfp b2,
final double a3, final Dfp b3, final double a4, final Dfp b4) {
return b1.multiply(a1).add(b2.multiply(a2)).add(b3.multiply(a3)).add(b4.multiply(a4));
}
}
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