package org.exist.util;
import java.math.BigInteger;
/**
* This is a utility class that handles formatting of numbers as strings.
* <p>
* The algorithm for converting a floating point number to a string is taken from Guy L. Steele and
* Jon L. White, <i>How to Print Floating-Point Numbers Accurately</i>, ACM SIGPLAN 1990. It is algorithm
* (FPP)<sup>2</sup> from that paper. There are three separate implementations of the algorithm:
* <ul>
* <li>One using long arithmetic and generating non-exponential output representations
* <li>One using BigInteger arithmetic and generating non-exponential output representation
* <li>One using BigInteger arithmetic and generating exponential output representations
* </ul>
* <p>
* The choice of method depends on the value of the number being formatted.
* <p>
* The module contains some residual code (mainly the routine for formatting integers) from the class
* AppenderHelper by Jack Shirazi in the O'Reilly book <i>Java Performance Tuning</i>. The floating point routines
* in that module were found to be unsuitable, since they used floating point arithmetic which introduces
* rounding errors.
* <p>
* There are several reasons for doing this conversion within Saxon, rather than leaving it all to Java.
* Firstly, there are differences in the required output format, notably the absence of ".0" when formatting
* whole numbers, and the different rules for the range of numbers where exponential notation is used.
* Secondly, there are bugs in some Java implementations, for example JDK outputs 0.001 as 0.0010, and
* IKVM/GNU gets things very wrong sometimes. Finally, this implementation is faster for "everyday" numbers,
* though it is slower for more extreme numbers. It would probably be reasonable to hand over formatting
* to the Java platform (at least when running the Sun JDK) for exponents outside the range -7 to +7.
*/
public class FloatingPointConverter {
public static FloatingPointConverter THE_INSTANCE = new FloatingPointConverter();
private FloatingPointConverter(){}
/**
* char array holding the characters for the string "-Infinity".
*/
private static final char[] NEGATIVE_INFINITY = {'-', 'I', 'N', 'F'};
/**
* char array holding the characters for the string "Infinity".
*/
private static final char[] POSITIVE_INFINITY = {'I', 'N', 'F'};
/**
* char array holding the characters for the string "NaN".
*/
private static final char[] NaN = {'N', 'a', 'N'};
private static final char[] charForDigit = {
'0', '1', '2', '3', '4', '5', '6', '7', '8', '9'
};
private static final long doubleSignMask = 0x8000000000000000L;
private static final long doubleExpMask = 0x7ff0000000000000L;
private static final int doubleExpShift = 52;
private static final int doubleExpBias = 1023;
private static final long doubleFractMask = 0xfffffffffffffL;
private static final int floatSignMask = 0x80000000;
private static final int floatExpMask = 0x7f800000;
private static final int floatExpShift = 23;
private static final int floatExpBias = 127;
private static final int floatFractMask = 0x7fffff;
private static final BigInteger TEN = BigInteger.valueOf(10);
private static final BigInteger NINE = BigInteger.valueOf(9);
/**
* Format an integer, appending the string representation of the integer to a string buffer
* @param s the string buffer
* @param i the integer to be formatted
* @return the supplied string buffer, containing the appended integer
*/
public static FastStringBuffer appendInt(FastStringBuffer s, int i) {
if (i < 0) {
if (i == Integer.MIN_VALUE) {
//cannot make this positive due to integer overflow
s.append("-2147483648");
return s;
}
s.append('-');
i = -i;
}
int c;
if (i < 10) {
//one digit
s.append(charForDigit[i]);
return s;
} else if (i < 100) {
//two digits
s.append(charForDigit[i / 10]);
s.append(charForDigit[i % 10]);
return s;
} else if (i < 1000) {
//three digits
s.append(charForDigit[i / 100]);
s.append(charForDigit[(c = i % 100) / 10]);
s.append(charForDigit[c % 10]);
return s;
} else if (i < 10000) {
//four digits
s.append(charForDigit[i / 1000]);
s.append(charForDigit[(c = i % 1000) / 100]);
s.append(charForDigit[(c %= 100) / 10]);
s.append(charForDigit[c % 10]);
return s;
} else if (i < 100000) {
//five digits
s.append(charForDigit[i / 10000]);
s.append(charForDigit[(c = i % 10000) / 1000]);
s.append(charForDigit[(c %= 1000) / 100]);
s.append(charForDigit[(c %= 100) / 10]);
s.append(charForDigit[c % 10]);
return s;
} else if (i < 1000000) {
//six digits
s.append(charForDigit[i / 100000]);
s.append(charForDigit[(c = i % 100000) / 10000]);
s.append(charForDigit[(c %= 10000) / 1000]);
s.append(charForDigit[(c %= 1000) / 100]);
s.append(charForDigit[(c %= 100) / 10]);
s.append(charForDigit[c % 10]);
return s;
} else if (i < 10000000) {
//seven digits
s.append(charForDigit[i / 1000000]);
s.append(charForDigit[(c = i % 1000000) / 100000]);
s.append(charForDigit[(c %= 100000) / 10000]);
s.append(charForDigit[(c %= 10000) / 1000]);
s.append(charForDigit[(c %= 1000) / 100]);
s.append(charForDigit[(c %= 100) / 10]);
s.append(charForDigit[c % 10]);
return s;
} else if (i < 100000000) {
//eight digits
s.append(charForDigit[i / 10000000]);
s.append(charForDigit[(c = i % 10000000) / 1000000]);
s.append(charForDigit[(c %= 1000000) / 100000]);
s.append(charForDigit[(c %= 100000) / 10000]);
s.append(charForDigit[(c %= 10000) / 1000]);
s.append(charForDigit[(c %= 1000) / 100]);
s.append(charForDigit[(c %= 100) / 10]);
s.append(charForDigit[c % 10]);
return s;
} else if (i < 1000000000) {
//nine digits
s.append(charForDigit[i / 100000000]);
s.append(charForDigit[(c = i % 100000000) / 10000000]);
s.append(charForDigit[(c %= 10000000) / 1000000]);
s.append(charForDigit[(c %= 1000000) / 100000]);
s.append(charForDigit[(c %= 100000) / 10000]);
s.append(charForDigit[(c %= 10000) / 1000]);
s.append(charForDigit[(c %= 1000) / 100]);
s.append(charForDigit[(c %= 100) / 10]);
s.append(charForDigit[c % 10]);
return s;
} else {
//ten digits
s.append(charForDigit[i / 1000000000]);
s.append(charForDigit[(c = i % 1000000000) / 100000000]);
s.append(charForDigit[(c %= 100000000) / 10000000]);
s.append(charForDigit[(c %= 10000000) / 1000000]);
s.append(charForDigit[(c %= 1000000) / 100000]);
s.append(charForDigit[(c %= 100000) / 10000]);
s.append(charForDigit[(c %= 10000) / 1000]);
s.append(charForDigit[(c %= 1000) / 100]);
s.append(charForDigit[(c %= 100) / 10]);
s.append(charForDigit[c % 10]);
return s;
}
}
/**
* Implementation of the (FPP)2 algorithm from Steele and White, for doubles in the range
* 0.01 to 1000000, and floats in the range 0.000001 to 1000000.
* In this range (a) XPath requires that the output should not be in exponential
* notation, and (b) the arithmetic can be handled using longs rather than BigIntegers
* @param sb the string buffer to which the formatted result is to be appended
* @param e the exponent of the floating point number
* @param f the fraction part of the floating point number, such that the "real" value of the
* number is f * 2^(e-p), with p>=0 and 0 lt f lt 2^p
* @param p the precision
*/
private static void fppfpp(FastStringBuffer sb, int e, long f, int p) {
long R = f << Math.max(e-p, 0);
long S = 1L << Math.max(0, -(e-p));
long Mminus = 1L << Math.max(e-p, 0);
long Mplus = Mminus;
boolean initial = true;
// simpleFixup
if (f == 1L << (p-1)) {
Mplus = Mplus << 1;
R = R << 1;
S = S << 1;
}
int k = 0;
while (R < (S+9)/10) { // (S+9)/10 == ceiling(S/10)
k--;
R = R*10;
Mminus = Mminus * 10;
Mplus = Mplus * 10;
}
while (2*R + Mplus >= 2*S) {
S = S*10;
k++;
}
for (int z=k; z<0; z++) {
if (initial) {
sb.append("0.");
}
initial = false;
sb.append('0');
}
// end simpleFixup
//int H = k-1;
boolean low;
boolean high;
int U;
while (true) {
k--;
U = (int)(R*10 / S);
R = R*10 % S;
Mminus = Mminus * 10;
Mplus = Mplus * 10;
low = 2*R < Mminus;
high = 2*R > 2*S - Mplus;
if (low || high) break;
if (k == -1) {
if (initial) {
sb.append('0');
}
sb.append('.');
}
sb.append(charForDigit[U]);
initial = false;
}
if (high && (!low || 2*R > S)) {
U++;
}
if (k == -1) {
if (initial) {
sb.append('0');
}
sb.append('.');
}
sb.append(charForDigit[U]);
for (int z=0; z<k; z++) {
sb.append('0');
}
}
/**
* Implementation of the (FPP)2 algorithm from Steele and White, for doubles in the range
* 0.000001 to 0.01. In this range XPath requires that the output should not be in exponential
* notation, but the scale factors are large enough to exceed the capacity of long arithmetic.
* @param sb the string buffer to which the formatted result is to be appended
* @param e the exponent of the floating point number
* @param f the fraction part of the floating point number, such that the "real" value of the
* number is f * 2^(e-p), with p>=0 and 0 lt f lt 2^p
* @param p the precision
*/
private static void fppfppBig(FastStringBuffer sb, int e, long f, int p) {
//long R = f << Math.max(e-p, 0);
BigInteger R = BigInteger.valueOf(f).shiftLeft(Math.max(e-p, 0));
//long S = 1L << Math.max(0, -(e-p));
BigInteger S = BigInteger.ONE.shiftLeft(Math.max(0, -(e-p)));
//long Mminus = 1 << Math.max(e-p, 0);
BigInteger Mminus = BigInteger.ONE.shiftLeft(Math.max(e-p, 0));
//long Mplus = Mminus;
BigInteger Mplus = Mminus;
boolean initial = true;
// simpleFixup
if (f == 1L << (p-1)) {
Mplus = Mplus.shiftLeft(1);
R = R.shiftLeft(1);
S = S.shiftLeft(1);
}
int k = 0;
while (R.compareTo(S.add(NINE).divide(TEN)) < 0) { // (S+9)/10 == ceiling(S/10)
k--;
R = R.multiply(TEN);
Mminus = Mminus.multiply(TEN);
Mplus = Mplus.multiply(TEN);
}
while (R.shiftLeft(1).add(Mplus).compareTo(S.shiftLeft(1)) >= 0) {
S = S.multiply(TEN);
k++;
}
for (int z=k; z<0; z++) {
if (initial) {
sb.append("0.");
}
initial = false;
sb.append('0');
}
// end simpleFixup
//int H = k-1;
boolean low;
boolean high;
int U;
while (true) {
k--;
BigInteger R10 = R.multiply(TEN);
U = R10.divide(S).intValue();
R = R10.mod(S);
Mminus = Mminus.multiply(TEN);
Mplus = Mplus.multiply(TEN);
BigInteger R2 = R.shiftLeft(1);
low = R2.compareTo(Mminus) < 0;
high = R2.compareTo(S.shiftLeft(1).subtract(Mplus)) > 0;
if (low || high) break;
if (k == -1) {
if (initial) {
sb.append('0');
}
sb.append('.');
}
sb.append(charForDigit[U]);
initial = false;
}
if (high && (!low || R.shiftLeft(1).compareTo(S) > 0)) {
U++;
}
if (k == -1) {
if (initial) {
sb.append('0');
}
sb.append('.');
}
sb.append(charForDigit[U]);
for (int z=0; z<k; z++) {
sb.append('0');
}
}
/**
* Implementation of the (FPP)2 algorithm from Steele and White, for numbers outside the range
* 0.000001 to 1000000. In this range XPath requires that the output should be in exponential
* notation
* @param sb the string buffer to which the formatted result is to be appended
* @param e the exponent of the floating point number
* @param f the fraction part of the floating point number, such that the "real" value of the
* number is f * 2^(e-p), with p>=0 and 0 lt f lt 2^p
* @param p the precision
*/
private static void fppfppExponential(FastStringBuffer sb, int e, long f, int p) {
//long R = f << Math.max(e-p, 0);
BigInteger R = BigInteger.valueOf(f).shiftLeft(Math.max(e-p, 0));
//long S = 1L << Math.max(0, -(e-p));
BigInteger S = BigInteger.ONE.shiftLeft(Math.max(0, -(e-p)));
//long Mminus = 1 << Math.max(e-p, 0);
BigInteger Mminus = BigInteger.ONE.shiftLeft(Math.max(e-p, 0));
//long Mplus = Mminus;
BigInteger Mplus = Mminus;
boolean initial = true;
boolean doneDot = false;
// simpleFixup
if (f == 1L << (p-1)) {
Mplus = Mplus.shiftLeft(1);
R = R.shiftLeft(1);
S = S.shiftLeft(1);
}
int k = 0;
while (R.compareTo(S.add(NINE).divide(TEN)) < 0) { // (S+9)/10 == ceiling(S/10)
k--;
R = R.multiply(TEN);
Mminus = Mminus.multiply(TEN);
Mplus = Mplus.multiply(TEN);
}
while (R.shiftLeft(1).add(Mplus).compareTo(S.shiftLeft(1)) >= 0) {
S = S.multiply(TEN);
k++;
}
// end simpleFixup
int H = k-1;
boolean low;
boolean high;
int U;
while (true) {
k--;
BigInteger R10 = R.multiply(TEN);
U = R10.divide(S).intValue();
R = R10.mod(S);
Mminus = Mminus.multiply(TEN);
Mplus = Mplus.multiply(TEN);
BigInteger R2 = R.shiftLeft(1);
low = R2.compareTo(Mminus) < 0;
high = R2.compareTo(S.shiftLeft(1).subtract(Mplus)) > 0;
if (low || high) break;
sb.append(charForDigit[U]);
if (initial) {
sb.append('.');
doneDot = true;
}
initial = false;
}
if (high && (!low || R.shiftLeft(1).compareTo(S) > 0)) {
U++;
}
sb.append(charForDigit[U]);
if (!doneDot) {
sb.append(".0");
}
sb.append('E');
appendInt(sb, H);
}
/**
* Append a string representation of a double value to a string buffer
* @param s the string buffer to which the result will be appended
* @param value the double to be formatted
* @return the original string buffer, now containing the string representation of the supplied double
*/
public static FastStringBuffer appendDouble(FastStringBuffer s, double value) {
double d = value;
if (d == Double.NEGATIVE_INFINITY) {
s.append(NEGATIVE_INFINITY);
} else if (d == Double.POSITIVE_INFINITY) {
s.append(POSITIVE_INFINITY);
} else if (d != d) {
s.append(NaN);
} else if (d == 0.0) {
if ((Double.doubleToLongBits(d) & doubleSignMask) != 0) {
s.append('-');
}
s.append('0');
} else if (d == Double.MAX_VALUE) {
s.append("1.7976931348623157E308");
} else if (d == -Double.MAX_VALUE) {
s.append("-1.7976931348623157E308");
} else if (d == Double.MIN_VALUE) {
s.append("4.9E-324");
} else if (d == -Double.MIN_VALUE) {
s.append("-4.9E-324");
} else {
if (d < 0) {
s.append('-');
d = -d;
}
boolean exponential = (d >= 1000000 || d < 0.000001);
long bits = Double.doubleToLongBits(d);
long fraction = (1L<<52) | (bits & doubleFractMask);
long rawExp = (bits & doubleExpMask) >> doubleExpShift;
int exp = (int)rawExp - doubleExpBias;
if (rawExp == 0) {
// don't know how to handle this currently: hand it over to Java to deal with
s.append(Double.toString(value));
return s;
}
if (exponential) {
fppfppExponential(s, exp, fraction, 52);
} else {
if (d <= 0.01) {
fppfppBig(s, exp, fraction, 52);
} else {
fppfpp(s, exp, fraction, 52);
}
}
// test code
// try {
// if (Double.parseDouble(s.toString()) != value) {
// System.err.println("*** Round-trip failed: input " + value +
// '(' + Double.doubleToLongBits(value) + ')' +
// " != output " + s.toString() +
// '(' + Double.doubleToLongBits(Double.parseDouble(s.toString())) + ')' );
// }
// } catch (NumberFormatException e) {
// System.err.println("*** Bad float " + s.toString() + " for input " + value);
// }
}
return s;
}
/**
* Append a string representation of a float value to a string buffer
* @param s the string buffer to which the result will be appended
* @param value the float to be formatted
* @return the original string buffer, now containing the string representation of the supplied float
*/
public static FastStringBuffer appendFloat(FastStringBuffer s, float value) {
float f = value;
if (f == Float.NEGATIVE_INFINITY) {
s.append(NEGATIVE_INFINITY);
} else if (f == Float.POSITIVE_INFINITY) {
s.append(POSITIVE_INFINITY);
} else if (f != f) {
s.append(NaN);
} else if (f == 0.0) {
if ((Float.floatToIntBits(f) & floatSignMask) != 0) {
s.append('-');
}
s.append('0');
} else if (f == Float.MAX_VALUE) {
s.append("3.4028235E38");
} else if (f == -Float.MAX_VALUE) {
s.append("-3.4028235E38");
} else if (f == Float.MIN_VALUE) {
s.append("1.4E-45");
} else if (f == -Float.MIN_VALUE) {
s.append("-1.4E-45");
} else {
if (f < 0) {
s.append('-');
f = -f;
}
boolean exponential = (f >= 1000000 || f < 0.000001F);
int bits = Float.floatToIntBits(f);
int fraction = (1<<23) | (bits & floatFractMask);
int rawExp = ((bits & floatExpMask) >> floatExpShift);
int exp = rawExp - floatExpBias;
int precision = 23;
if (rawExp == 0) {
// don't know how to handle this currently: hand it over to Java to deal with
s.append(Float.toString(value));
return s;
}
if (exponential) {
fppfppExponential(s, exp, fraction, precision);
} else {
fppfpp(s, exp, fraction, precision);
}
// test code
// try {
// if (Float.parseFloat(s.toString()) != value) {
// System.err.println("*** Round-trip failed: input " + value +
// '(' + Float.floatToIntBits(value) + ')' +
// " != output " + s.toString() +
// '(' + Float.floatToIntBits(Float.parseFloat(s.toString())) + ')' );
// }
// } catch (NumberFormatException e) {
// System.err.println("*** Bad float " + s.toString() + " for input " + value);
// }
}
return s;
}
// public static void main(String[] args) {
// if (args.length > 0 && args[0].equals("F")) {
// if (args.length == 2) {
// StringTokenizer tok = new StringTokenizer(args[1], ",");
// while (tok.hasMoreElements()) {
// String input = tok.nextToken();
// float f = Float.parseFloat(input);
// FastStringBuffer sb = new FastStringBuffer(20);
// appendFloat(sb, f);
// System.err.println("input: " + input + " output: " + sb.toString() + " java: " + f);
// }
// } else {
// Random gen = new Random();
// for (int i=1; i<1000; i++) {
// int p=gen.nextInt(999*i*i);
// int q=gen.nextInt(999*i*i);
// String input = (p + "." + q);
// float f = Float.parseFloat(input);
// FastStringBuffer sb = new FastStringBuffer(20);
// appendFloat(sb, f);
// System.err.println("input: " + input + " output: " + sb.toString() + " java: " + f);
// }
// }
// } else {
// if (args.length == 2) {
// StringTokenizer tok = new StringTokenizer(args[1], ",");
// while (tok.hasMoreElements()) {
// String input = tok.nextToken();
// double f = Double.parseDouble(input);
// FastStringBuffer sb = new FastStringBuffer(20);
// appendDouble(sb, f);
// System.err.println("input: " + input + " output: " + sb.toString() + " java: " + f);
// }
// } else {
// long start = System.currentTimeMillis();
// Random gen = new Random();
// for (int i=1; i<100000; i++) {
// //int p=gen.nextInt(999*i*i);
// int q=gen.nextInt(999*i);
// //String input = (p + "." + q);
// String input = "0.000" + q;
// double f = Double.parseDouble(input);
// FastStringBuffer sb = new FastStringBuffer(20);
// appendDouble(sb, f);
// //System.err.println("input: " + input + " output: " + sb.toString() + " java: " + f);
// }
// System.err.println("** elapsed time " + (System.currentTimeMillis() - start));
// }
// }
// }
}
//
// The contents of this file are subject to the Mozilla Public License Version 1.0 (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.mozilla.org/MPL/
//
// Software distributed under the License is distributed on an "AS IS" basis,
// WITHOUT WARRANTY OF ANY KIND, either express or implied.
// See the License for the specific language governing rights and limitations under the License.
//
// The Original Code is: all this file.
//
// The Initial Developer of the Original Code is Michael H. Kay, based on a published algorithm by
// Guy L. Steele and Jon L. White.
//
// Contributor(s): the appendInt routine, and some of the constant declarations (and some of the ideas) are
// from the class AppenderHelper by Jack Shirazi in the O'Reilly book Java Performance Tuning..
//