com.Ostermiller.util.SignificantFigures Maven / Gradle / Ivy
/*
* Copyright (C) 2002-2007 Stephen Ostermiller
* http://ostermiller.org/contact.pl?regarding=Java+Utilities
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* See COPYING.TXT for details.
*/
package com.Ostermiller.util;
/**
* A number with an associated number of significant figures.
* This class handles parsing numbers, determining the number
* of significant figures, adjusting the number of significant
* figures (including scientific rounding), and displaying the number.
* More information about this class is available from ostermiller.org.
*
* When parsing a number to determine the number of significant figures,
* these rules are used:
*
* - Non-zero digits are always significant.
* - All zeros between other significant digits are significant.
* - All zeros left of the decimal point between a significant digit and the decimal point are significant.
* - All trailing zeros to the right of the decimal point are significant.
* - If the number is contains no digits other than zero, every zero is significant.
*
*
* When rounding a number the following rules are used:
*
* - If the greatest insignificant digit is less than five, round down.
* - If the greatest insignificant digit is greater than five, round up.
* - If the greatest insignificant digit is five and followed by some non-zero digit, round up.
* - If the greatest insignificant digit is five and followed only by zeros, and the least significant
* digit is odd, round up.
* - If the greatest insignificant digit is five and followed only by zeros, and the least significant
* digit is even, round down.
*
*
*
* Example of using this class to multiply numbers and display the result
* with the proper number of significant figures:
*
String[] arguments = {"1.0", "2.0", ...}
* SignificantFigures number;
* int sigFigs = Integer.MAX_VALUE;
* double result = 1D;
* for (int i=0; i<arguments.length; i++){
* number = new SignificantFigures(arguments[i]);
* sigFigs = Math.min(sigFigs, number.getNumberSignificantFigures());
* result *= number.doubleValue();
* }
* number = new SignificantFigures(result);
* number.setNumberSignificantFigures(sigFigs);
* System.out.println(number);
*
* Example of using this class to add numbers and display the result
* with the proper number of significant figures:
*
String[] arguments = {"1.0", "2.0", ...}
* SignificantFigures number;
* int leastSD = Integer.MIN_VALUE;
* int mostSD = Integer.MIN_VALUE;
* double result = 0D;
* for (int i=0; i<arguments.length; i++){
* number = new SignificantFigures(arguments[i]);
* leastSD = Math.max(leastSD, number.getLSD());
* mostSD = Math.max(mostSD, number.getMSD());
* result += number.doubleValue();
* }
* number = new SignificantFigures(result);
* number.setLMSD(leastSD, mostSD);
* System.out.println(number);
*
* @author Stephen Ostermiller http://ostermiller.org/contact.pl?regarding=Java+Utilities
* @since ostermillerutils 1.00.00
*/
public class SignificantFigures extends Number {
/**
*
*/
private static final long serialVersionUID = -1130798283937219608L;
/**
* In the case the a number
* could not be parsed, the original is stored
* for toString purposes.
*
* @since ostermillerutils 1.00.00
*/
private String original;
/**
* Buffer of the significant digits.
*
* @since ostermillerutils 1.00.00
*/
private StringBuffer digits;
/**
* The exponent of the digits if a
* decimal place were inserted after
* the first digit.
*
* @since ostermillerutils 1.00.00
*/
private int mantissa = -1;
/**
* positive if true, negative if false.
*
* @since ostermillerutils 1.00.00
*/
private boolean sign = true;
/**
* True if this number has no non-zero digits.
*
* @since ostermillerutils 1.00.00
*/
private boolean isZero = false;
/**
* Create a SignificantFigures object from a String representation of a number.
*
* @param number String representation of the number.
* @throws NumberFormatException if the String is not a valid number.
*
* @since ostermillerutils 1.00.00
*/
public SignificantFigures(String number) throws NumberFormatException {
original = number;
parse(original);
}
/**
* Create a SignificantFigures object from a byte.
*
* @param number an 8 bit integer.
*
* @since ostermillerutils 1.00.00
*/
public SignificantFigures(byte number){
original = Byte.toString(number);
try {
parse(original);
} catch (NumberFormatException nfe){
digits = null;
}
}
/**
* Create a SignificantFigures object from a short.
*
* @param number a 16 bit integer.
*
* @since ostermillerutils 1.00.00
*/
public SignificantFigures(short number){
original = Short.toString(number);
try {
parse(original);
} catch (NumberFormatException nfe){
digits = null;
}
}
/**
* Create a SignificantFigures object from an integer.
*
* @param number a 32 bit integer.
*
* @since ostermillerutils 1.00.00
*/
public SignificantFigures(int number){
original = String.valueOf(number);
try {
parse(original);
} catch (NumberFormatException nfe){
digits = null;
}
}
/**
* Create a SignificantFigures object from a long.
*
* @param number a 64 bit integer.
*
* @since ostermillerutils 1.00.00
*/
public SignificantFigures(long number){
original = Long.toString(number);
try {
parse(original);
} catch (NumberFormatException nfe){
digits = null;
}
}
/**
* Create a SignificantFigures object from a float.
*
* @param number a 32 bit floating point.
*
* @since ostermillerutils 1.00.00
*/
public SignificantFigures(float number){
original = Float.toString(number);
try {
parse(original);
} catch (NumberFormatException nfe){
digits = null;
}
}
/**
* Create a SignificantFigures object from a double.
*
* @param number a 64 bit floating point.
*
* @since ostermillerutils 1.00.00
*/
public SignificantFigures(double number){
original = Double.toString(number);
try {
parse(original);
} catch (NumberFormatException nfe){
digits = null;
}
}
/**
* Create a SignificantFigures object from a java number such as
* a BigDecimal, BigInteger, Byte, Double, Float, Integer, Long, or
* Short.
*
* @param number a number.
*
* @since ostermillerutils 1.00.00
*/
public SignificantFigures(Number number){
original = number.toString();
try {
parse(original);
} catch (NumberFormatException nfe){
digits = null;
}
}
/**
* Get the number of significant digits.
*
* If this number is not a number or infinity zero
* will be returned.
*
* @return the number of significant digits in this number.
*
* @since ostermillerutils 1.00.00
*/
public int getNumberSignificantFigures() {
if (digits == null) return 0;
return digits.length();
}
/**
* Adjust the number of significant figures such that the least
* significant digit is at the given place. This method may add
* significant zeros to the end of this number, or remove significant
* digits from this number.
*
* It is possible to remove all significant digits from this number which
* will cause the string representation of this number to become "NaN". This
* could become a problem if you are adding numbers and the result is close
* to zero. All of the significant digits may get removed, even though the
* result could be zero with some number of significant digits. Its is safes
* to use the setLMSD() method which will make a zero with the appropriate
* number of significant figures in such instances.
*
* This method has no effect if this number is not a number or infinity.
*
* @param place the desired place of the least significant digit.
* @return this number.
*
* @since ostermillerutils 1.00.00
*/
public SignificantFigures setLSD(int place){
setLMSD(place, Integer.MIN_VALUE);
return this;
}
/**
* Adjust the number of significant figures such that the least
* significant digit is at the given place. This method may add
* significant zeros to the end of this number, or remove significant
* digits from this number.
*
* If all significant digits are removed from this number by truncating to
* the least significant place, a zero will be created with significant figures
* from the least to most significant places.
*
* This method has no effect if this number is not a number or infinity.
*
* @param leastPlace the desired place of the least significant digit or Integer.MIN_VALUE to ignore.
* @param mostPlace the desired place of the most significant digit or Integer.MIN_VALUE to ignore.
* @return this number
*
* @since ostermillerutils 1.00.00
*/
public SignificantFigures setLMSD(int leastPlace, int mostPlace){
if (digits != null && leastPlace != Integer.MIN_VALUE){
int significantFigures = digits.length();
int current = mantissa - significantFigures + 1;
int newLength = significantFigures - leastPlace + current;
if (newLength <= 0){
if (mostPlace == Integer.MIN_VALUE){
original = "NaN";
digits = null;
} else {
newLength = mostPlace - leastPlace + 1;
digits.setLength(newLength);
mantissa = leastPlace;
for (int i=0; i
* If this number is not a number or infinity Integer.MIN_VALUE
* will be returned.
*
* @return the decimal place of the least significant digit.
*
* @since ostermillerutils 1.00.00
*/
public int getLSD(){
if (digits == null) return Integer.MIN_VALUE;
return mantissa - digits.length() + 1;
}
/**
* Get the decimal place of the most significant digit.
*
* If this number is not a number or infinity Integer.MIN_VALUE
* will be returned.
*
* @return the decimal place of the least significant digit.
*
* @since ostermillerutils 1.00.00
*/
public int getMSD(){
if (digits == null) return Integer.MIN_VALUE;
return mantissa + 1;
}
/**
* Formats this number.
* If the number is less than 10^-3 or greater than or equal to 10^7,
* or the number might have an ambiguous number of significant figures,
* scientific notation will be used.
*
* A string such as "NaN" or "Infinity" may be returned by this method.
*
* @return representation of this number.
*
* @since ostermillerutils 1.00.00
*/
@Override public String toString() {
if (digits == null) return original;
StringBuffer digits = new StringBuffer(this.digits.toString());
int length = digits.length();
if (mantissa <= -4 || mantissa >= 7 ||
(mantissa >= length &&
digits.charAt(digits.length()-1) == '0') ||
(isZero && mantissa != 0)) {
// use scientific notation.
if (length > 1){
digits.insert(1, '.');
}
if (mantissa != 0){
digits.append("E" + mantissa);
}
} else if (mantissa <= -1){
digits.insert(0, "0.");
for (int i=mantissa; i<-1; i++){
digits.insert(2, '0');
}
} else if (mantissa+1 == length){
if (length > 1 && digits.charAt(digits.length()-1) == '0'){
digits.append('.');
}
} else if (mantissa < length){
digits.insert(mantissa+1, '.');
} else {
for (int i=length; i<=mantissa; i++){
digits.append('0');
}
}
if (!sign) {
digits.insert(0, '-');
}
return digits.toString();
}
/**
* Formats this number in scientific notation.
*
* A string such as "NaN" or "Infinity" may be returned by this method.
*
* @return representation of this number in scientific notation.
*
* @since ostermillerutils 1.00.00
*/
public String toScientificNotation() {
if (digits == null) return original;
StringBuffer digits = new StringBuffer(this.digits.toString());
int length = digits.length();
if (length > 1){
digits.insert(1, '.');
}
if (mantissa != 0){
digits.append("E" + mantissa);
}
if (!sign) {
digits.insert(0, '-');
}
return digits.toString();
}
/**
* Parsing state:
* Initial state before anything read.
*
* @since ostermillerutils 1.00.00
*/
private final static int INITIAL = 0;
/**
* Parsing state:
* State in which a possible sign and
* possible leading zeros have been read.
*
* @since ostermillerutils 1.00.00
*/
private final static int LEADZEROS = 1;
/**
* Parsing state:
* State in which a possible sign and
* at least one non-zero digit
* has been read followed by some number of
* zeros. The decimal place has no
* been encountered yet.
*
* @since ostermillerutils 1.00.00
*/
private final static int MIDZEROS = 2;
/**
* Parsing state:
* State in which a possible sign and
* at least one non-zero digit
* has been read. The decimal place has no
* been encountered yet.
*
* @since ostermillerutils 1.00.00
*/
private final static int DIGITS = 3;
/**
* Parsing state:
* State in which only a possible sign,
* leading zeros, and a decimal point
* have been encountered.
*
* @since ostermillerutils 1.00.00
*/
private final static int LEADZEROSDOT = 4;
/**
* Parsing state:
* State in which a possible sign,
* at least one nonzero digit and a
* decimal point have been encountered.
*
* @since ostermillerutils 1.00.00
*/
private final static int DIGITSDOT = 5;
/**
* Parsing state:
* State in which the exponent symbol
* 'E' has been encountered.
*
* @since ostermillerutils 1.00.00
*/
private final static int MANTISSA = 6;
/**
* Parsing state:
* State in which the exponent symbol
* 'E' has been encountered followed
* by a possible sign or some number
* of digits.
*
* @since ostermillerutils 1.00.00
*/
private final static int MANTISSADIGIT = 7;
/**
* Parse a number from the given string.
* A valid number has an optional sign, some digits
* with an optional decimal point, and an optional
* scientific notation part consisting of an 'E' followed
* by an optional sign, followed by some digits.
*
* @param number String representation of a number.
* @throws NumberFormatException if the string is not a valid number.
*
* @since ostermillerutils 1.00.00
*/
private void parse(String number) throws NumberFormatException {
int length = number.length();
digits = new StringBuffer(length);
int state = INITIAL;
int mantissaStart = -1;
boolean foundMantissaDigit = false;
// sometimes we don't know if a zero will be
// significant or not when it is encountered.
// keep track of the number of them so that
// the all can be made significant if we find
// out that they are.
int zeroCount = 0;
int leadZeroCount = 0;
for (int i=0; i 0){
// if nothing but zeros all zeros are significant.
for (int j=0; j
* This method has no effect if this number is not a number or infinity.
*
* @param significantFigures desired number of significant figures.
* @return This number.
*
* @since ostermillerutils 1.00.00
*/
public SignificantFigures setNumberSignificantFigures(int significantFigures){
if (significantFigures <= 0) throw new IllegalArgumentException("Desired number of significant figures must be positive.");
if (digits != null) {
int length = digits.length();
if (length < significantFigures){
// number is not long enough, pad it with zeros.
for (int i=length; i significantFigures){
// number is too long chop some of it off with rounding.
boolean addOne; // we need to round up if true.
char firstInSig = digits.charAt(significantFigures);
if (firstInSig < '5'){
// first non-significant digit less than five, round down.
addOne = false;
} else if (firstInSig == '5'){
// first non-significant digit equal to five
addOne = false;
for (int i=significantFigures+1; !addOne && i=0; i--){
char digit = digits.charAt(i);
if (digit < '9'){
digits.setCharAt(i, (char)(digit+1));
addOne = false;
} else {
digits.setCharAt(i, '0');
}
}
if (addOne){
// if the number was all nines
digits.insert(0, '1');
mantissa++;
}
// chop it to the correct number of figures.
digits.setLength(significantFigures);
}
}
return this;
}
/**
* Returns the value of this number as a byte.
*
* @return the numeric value represented by this object after conversion to type byte.
* @throws NumberFormatException if this number cannot be converted to a byte.
*
* @since ostermillerutils 1.00.00
*/
@Override public byte byteValue() throws NumberFormatException {
return Byte.parseByte(original);
}
/**
* Returns the value of this number as a double.
*
* @return the numeric value represented by this object after conversion to type double.
* @throws NumberFormatException if this number cannot be converted to a double.
*
* @since ostermillerutils 1.00.00
*/
@Override public double doubleValue() throws NumberFormatException {
return Double.parseDouble(original);
}
/**
* Returns the value of this number as a float.
*
* @return the numeric value represented by this object after conversion to type float.
* @throws NumberFormatException if this number cannot be converted to a float.
*
* @since ostermillerutils 1.00.00
*/
@Override public float floatValue() throws NumberFormatException {
return Float.parseFloat(original);
}
/**
* Returns the value of this number as a int.
*
* @return the numeric value represented by this object after conversion to type int.
* @throws NumberFormatException if this number cannot be converted to a int.
*
* @since ostermillerutils 1.00.00
*/
@Override public int intValue() throws NumberFormatException {
return Integer.parseInt(original);
}
/**
* Returns the value of this number as a long.
*
* @return the numeric value represented by this object after conversion to type long.
* @throws NumberFormatException if this number cannot be converted to a long.
*
* @since ostermillerutils 1.00.00
*/
@Override public long longValue() throws NumberFormatException {
return Long.parseLong(original);
}
/**
* Returns the value of this number as a short.
*
* @return the numeric value represented by this object after conversion to type short.
* @throws NumberFormatException if this number cannot be converted to a short.
*
* @since ostermillerutils 1.00.00
*/
@Override public short shortValue() throws NumberFormatException {
return Short.parseShort(original);
}
/**
* Convenience method to display a number with the correct
* significant digits.
*
* @param number the number to display
* @param significantFigures the number of significant figures to display.
* @return the number formatted with the correct significant figures
*
* @since ostermillerutils 1.02.07
*/
public static String format(byte number, int significantFigures){
SignificantFigures sf = new SignificantFigures(number);
sf.setNumberSignificantFigures(significantFigures);
return sf.toString();
}
/**
* Convenience method to display a number with the correct
* significant digits.
*
* @param number the number to display
* @param significantFigures the number of significant figures to display.
* @return the number formatted with the correct significant figures
*
* @since ostermillerutils 1.02.07
*/
public static String format(double number, int significantFigures){
SignificantFigures sf = new SignificantFigures(number);
sf.setNumberSignificantFigures(significantFigures);
return sf.toString();
}
/**
* Convenience method to display a number with the correct
* significant digits.
*
* @param number the number to display
* @param significantFigures the number of significant figures to display.
* @return the number formatted with the correct significant figures
*
* @since ostermillerutils 1.02.07
*/
public static String format(float number, int significantFigures){
SignificantFigures sf = new SignificantFigures(number);
sf.setNumberSignificantFigures(significantFigures);
return sf.toString();
}
/**
* Convenience method to display a number with the correct
* significant digits.
*
* @param number the number to display
* @param significantFigures the number of significant figures to display.
* @return the number formatted with the correct significant figures
*
* @since ostermillerutils 1.02.07
*/
public static String format(int number, int significantFigures){
SignificantFigures sf = new SignificantFigures(number);
sf.setNumberSignificantFigures(significantFigures);
return sf.toString();
}
/**
* Convenience method to display a number with the correct
* significant digits.
*
* @param number the number to display
* @param significantFigures the number of significant figures to display.
* @return the number formatted with the correct significant figures
*
* @since ostermillerutils 1.02.07
*/
public static String format(long number, int significantFigures){
SignificantFigures sf = new SignificantFigures(number);
sf.setNumberSignificantFigures(significantFigures);
return sf.toString();
}
/**
* Convenience method to display a number with the correct
* significant digits.
*
* @param number the number to display
* @param significantFigures the number of significant figures to display.
* @return the number formatted with the correct significant figures
*
* @since ostermillerutils 1.02.07
*/
public static String format(Number number, int significantFigures){
SignificantFigures sf = new SignificantFigures(number);
sf.setNumberSignificantFigures(significantFigures);
return sf.toString();
}
/**
* Convenience method to display a number with the correct
* significant digits.
*
* @param number the number to display
* @param significantFigures the number of significant figures to display.
* @return the number formatted with the correct significant figures
*
* @since ostermillerutils 1.02.07
*/
public static String format(short number, int significantFigures){
SignificantFigures sf = new SignificantFigures(number);
sf.setNumberSignificantFigures(significantFigures);
return sf.toString();
}
/**
* Convenience method to display a number with the correct
* significant digits.
*
* @param number the number to display
* @param significantFigures the number of significant figures to display.
* @return the number formatted with the correct significant figures
* @throws NumberFormatException if the String is not a valid number.
*
* @since ostermillerutils 1.02.07
*/
public static String format(String number, int significantFigures) throws NumberFormatException {
SignificantFigures sf = new SignificantFigures(number);
sf.setNumberSignificantFigures(significantFigures);
return sf.toString();
}
}