8043740: Doubles with large exponents overflow to Infinity incorrectly
Summary: Modify test of exponent overflow to account for subsequent decrement.
Reviewed-by: darcy
Contributed-by: Sandipan Razzaque <me@sandipan.net>
/*
* Copyright (c) 1996, 2013, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code 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
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
package sun.misc;
import java.util.Arrays;
import java.util.regex.*;
/**
* A class for converting between ASCII and decimal representations of a single
* or double precision floating point number. Most conversions are provided via
* static convenience methods, although a <code>BinaryToASCIIConverter</code>
* instance may be obtained and reused.
*/
public class FloatingDecimal{
//
// Constants of the implementation;
// most are IEEE-754 related.
// (There are more really boring constants at the end.)
//
static final int EXP_SHIFT = DoubleConsts.SIGNIFICAND_WIDTH - 1;
static final long FRACT_HOB = ( 1L<<EXP_SHIFT ); // assumed High-Order bit
static final long EXP_ONE = ((long)DoubleConsts.EXP_BIAS)<<EXP_SHIFT; // exponent of 1.0
static final int MAX_SMALL_BIN_EXP = 62;
static final int MIN_SMALL_BIN_EXP = -( 63 / 3 );
static final int MAX_DECIMAL_DIGITS = 15;
static final int MAX_DECIMAL_EXPONENT = 308;
static final int MIN_DECIMAL_EXPONENT = -324;
static final int BIG_DECIMAL_EXPONENT = 324; // i.e. abs(MIN_DECIMAL_EXPONENT)
static final int MAX_NDIGITS = 1100;
static final int SINGLE_EXP_SHIFT = FloatConsts.SIGNIFICAND_WIDTH - 1;
static final int SINGLE_FRACT_HOB = 1<<SINGLE_EXP_SHIFT;
static final int SINGLE_MAX_DECIMAL_DIGITS = 7;
static final int SINGLE_MAX_DECIMAL_EXPONENT = 38;
static final int SINGLE_MIN_DECIMAL_EXPONENT = -45;
static final int SINGLE_MAX_NDIGITS = 200;
static final int INT_DECIMAL_DIGITS = 9;
/**
* Converts a double precision floating point value to a <code>String</code>.
*
* @param d The double precision value.
* @return The value converted to a <code>String</code>.
*/
public static String toJavaFormatString(double d) {
return getBinaryToASCIIConverter(d).toJavaFormatString();
}
/**
* Converts a single precision floating point value to a <code>String</code>.
*
* @param f The single precision value.
* @return The value converted to a <code>String</code>.
*/
public static String toJavaFormatString(float f) {
return getBinaryToASCIIConverter(f).toJavaFormatString();
}
/**
* Appends a double precision floating point value to an <code>Appendable</code>.
* @param d The double precision value.
* @param buf The <code>Appendable</code> with the value appended.
*/
public static void appendTo(double d, Appendable buf) {
getBinaryToASCIIConverter(d).appendTo(buf);
}
/**
* Appends a single precision floating point value to an <code>Appendable</code>.
* @param f The single precision value.
* @param buf The <code>Appendable</code> with the value appended.
*/
public static void appendTo(float f, Appendable buf) {
getBinaryToASCIIConverter(f).appendTo(buf);
}
/**
* Converts a <code>String</code> to a double precision floating point value.
*
* @param s The <code>String</code> to convert.
* @return The double precision value.
* @throws NumberFormatException If the <code>String</code> does not
* represent a properly formatted double precision value.
*/
public static double parseDouble(String s) throws NumberFormatException {
return readJavaFormatString(s).doubleValue();
}
/**
* Converts a <code>String</code> to a single precision floating point value.
*
* @param s The <code>String</code> to convert.
* @return The single precision value.
* @throws NumberFormatException If the <code>String</code> does not
* represent a properly formatted single precision value.
*/
public static float parseFloat(String s) throws NumberFormatException {
return readJavaFormatString(s).floatValue();
}
/**
* A converter which can process single or double precision floating point
* values into an ASCII <code>String</code> representation.
*/
public interface BinaryToASCIIConverter {
/**
* Converts a floating point value into an ASCII <code>String</code>.
* @return The value converted to a <code>String</code>.
*/
public String toJavaFormatString();
/**
* Appends a floating point value to an <code>Appendable</code>.
* @param buf The <code>Appendable</code> to receive the value.
*/
public void appendTo(Appendable buf);
/**
* Retrieves the decimal exponent most closely corresponding to this value.
* @return The decimal exponent.
*/
public int getDecimalExponent();
/**
* Retrieves the value as an array of digits.
* @param digits The digit array.
* @return The number of valid digits copied into the array.
*/
public int getDigits(char[] digits);
/**
* Indicates the sign of the value.
* @return <code>value < 0.0</code>.
*/
public boolean isNegative();
/**
* Indicates whether the value is either infinite or not a number.
*
* @return <code>true</code> if and only if the value is <code>NaN</code>
* or infinite.
*/
public boolean isExceptional();
/**
* Indicates whether the value was rounded up during the binary to ASCII
* conversion.
*
* @return <code>true</code> if and only if the value was rounded up.
*/
public boolean digitsRoundedUp();
/**
* Indicates whether the binary to ASCII conversion was exact.
*
* @return <code>true</code> if any only if the conversion was exact.
*/
public boolean decimalDigitsExact();
}
/**
* A <code>BinaryToASCIIConverter</code> which represents <code>NaN</code>
* and infinite values.
*/
private static class ExceptionalBinaryToASCIIBuffer implements BinaryToASCIIConverter {
final private String image;
private boolean isNegative;
public ExceptionalBinaryToASCIIBuffer(String image, boolean isNegative) {
this.image = image;
this.isNegative = isNegative;
}
@Override
public String toJavaFormatString() {
return image;
}
@Override
public void appendTo(Appendable buf) {
if (buf instanceof StringBuilder) {
((StringBuilder) buf).append(image);
} else if (buf instanceof StringBuffer) {
((StringBuffer) buf).append(image);
} else {
assert false;
}
}
@Override
public int getDecimalExponent() {
throw new IllegalArgumentException("Exceptional value does not have an exponent");
}
@Override
public int getDigits(char[] digits) {
throw new IllegalArgumentException("Exceptional value does not have digits");
}
@Override
public boolean isNegative() {
return isNegative;
}
@Override
public boolean isExceptional() {
return true;
}
@Override
public boolean digitsRoundedUp() {
throw new IllegalArgumentException("Exceptional value is not rounded");
}
@Override
public boolean decimalDigitsExact() {
throw new IllegalArgumentException("Exceptional value is not exact");
}
}
private static final String INFINITY_REP = "Infinity";
private static final int INFINITY_LENGTH = INFINITY_REP.length();
private static final String NAN_REP = "NaN";
private static final int NAN_LENGTH = NAN_REP.length();
private static final BinaryToASCIIConverter B2AC_POSITIVE_INFINITY = new ExceptionalBinaryToASCIIBuffer(INFINITY_REP, false);
private static final BinaryToASCIIConverter B2AC_NEGATIVE_INFINITY = new ExceptionalBinaryToASCIIBuffer("-" + INFINITY_REP, true);
private static final BinaryToASCIIConverter B2AC_NOT_A_NUMBER = new ExceptionalBinaryToASCIIBuffer(NAN_REP, false);
private static final BinaryToASCIIConverter B2AC_POSITIVE_ZERO = new BinaryToASCIIBuffer(false, new char[]{'0'});
private static final BinaryToASCIIConverter B2AC_NEGATIVE_ZERO = new BinaryToASCIIBuffer(true, new char[]{'0'});
/**
* A buffered implementation of <code>BinaryToASCIIConverter</code>.
*/
static class BinaryToASCIIBuffer implements BinaryToASCIIConverter {
private boolean isNegative;
private int decExponent;
private int firstDigitIndex;
private int nDigits;
private final char[] digits;
private final char[] buffer = new char[26];
//
// The fields below provide additional information about the result of
// the binary to decimal digits conversion done in dtoa() and roundup()
// methods. They are changed if needed by those two methods.
//
// True if the dtoa() binary to decimal conversion was exact.
private boolean exactDecimalConversion = false;
// True if the result of the binary to decimal conversion was rounded-up
// at the end of the conversion process, i.e. roundUp() method was called.
private boolean decimalDigitsRoundedUp = false;
/**
* Default constructor; used for non-zero values,
* <code>BinaryToASCIIBuffer</code> may be thread-local and reused
*/
BinaryToASCIIBuffer(){
this.digits = new char[20];
}
/**
* Creates a specialized value (positive and negative zeros).
*/
BinaryToASCIIBuffer(boolean isNegative, char[] digits){
this.isNegative = isNegative;
this.decExponent = 0;
this.digits = digits;
this.firstDigitIndex = 0;
this.nDigits = digits.length;
}
@Override
public String toJavaFormatString() {
int len = getChars(buffer);
return new String(buffer, 0, len);
}
@Override
public void appendTo(Appendable buf) {
int len = getChars(buffer);
if (buf instanceof StringBuilder) {
((StringBuilder) buf).append(buffer, 0, len);
} else if (buf instanceof StringBuffer) {
((StringBuffer) buf).append(buffer, 0, len);
} else {
assert false;
}
}
@Override
public int getDecimalExponent() {
return decExponent;
}
@Override
public int getDigits(char[] digits) {
System.arraycopy(this.digits,firstDigitIndex,digits,0,this.nDigits);
return this.nDigits;
}
@Override
public boolean isNegative() {
return isNegative;
}
@Override
public boolean isExceptional() {
return false;
}
@Override
public boolean digitsRoundedUp() {
return decimalDigitsRoundedUp;
}
@Override
public boolean decimalDigitsExact() {
return exactDecimalConversion;
}
private void setSign(boolean isNegative) {
this.isNegative = isNegative;
}
/**
* This is the easy subcase --
* all the significant bits, after scaling, are held in lvalue.
* negSign and decExponent tell us what processing and scaling
* has already been done. Exceptional cases have already been
* stripped out.
* In particular:
* lvalue is a finite number (not Inf, nor NaN)
* lvalue > 0L (not zero, nor negative).
*
* The only reason that we develop the digits here, rather than
* calling on Long.toString() is that we can do it a little faster,
* and besides want to treat trailing 0s specially. If Long.toString
* changes, we should re-evaluate this strategy!
*/
private void developLongDigits( int decExponent, long lvalue, int insignificantDigits ){
if ( insignificantDigits != 0 ){
// Discard non-significant low-order bits, while rounding,
// up to insignificant value.
long pow10 = FDBigInteger.LONG_5_POW[insignificantDigits] << insignificantDigits; // 10^i == 5^i * 2^i;
long residue = lvalue % pow10;
lvalue /= pow10;
decExponent += insignificantDigits;
if ( residue >= (pow10>>1) ){
// round up based on the low-order bits we're discarding
lvalue++;
}
}
int digitno = digits.length -1;
int c;
if ( lvalue <= Integer.MAX_VALUE ){
assert lvalue > 0L : lvalue; // lvalue <= 0
// even easier subcase!
// can do int arithmetic rather than long!
int ivalue = (int)lvalue;
c = ivalue%10;
ivalue /= 10;
while ( c == 0 ){
decExponent++;
c = ivalue%10;
ivalue /= 10;
}
while ( ivalue != 0){
digits[digitno--] = (char)(c+'0');
decExponent++;
c = ivalue%10;
ivalue /= 10;
}
digits[digitno] = (char)(c+'0');
} else {
// same algorithm as above (same bugs, too )
// but using long arithmetic.
c = (int)(lvalue%10L);
lvalue /= 10L;
while ( c == 0 ){
decExponent++;
c = (int)(lvalue%10L);
lvalue /= 10L;
}
while ( lvalue != 0L ){
digits[digitno--] = (char)(c+'0');
decExponent++;
c = (int)(lvalue%10L);
lvalue /= 10;
}
digits[digitno] = (char)(c+'0');
}
this.decExponent = decExponent+1;
this.firstDigitIndex = digitno;
this.nDigits = this.digits.length - digitno;
}
private void dtoa( int binExp, long fractBits, int nSignificantBits, boolean isCompatibleFormat)
{
assert fractBits > 0 ; // fractBits here can't be zero or negative
assert (fractBits & FRACT_HOB)!=0 ; // Hi-order bit should be set
// Examine number. Determine if it is an easy case,
// which we can do pretty trivially using float/long conversion,
// or whether we must do real work.
final int tailZeros = Long.numberOfTrailingZeros(fractBits);
// number of significant bits of fractBits;
final int nFractBits = EXP_SHIFT+1-tailZeros;
// reset flags to default values as dtoa() does not always set these
// flags and a prior call to dtoa() might have set them to incorrect
// values with respect to the current state.
decimalDigitsRoundedUp = false;
exactDecimalConversion = false;
// number of significant bits to the right of the point.
int nTinyBits = Math.max( 0, nFractBits - binExp - 1 );
if ( binExp <= MAX_SMALL_BIN_EXP && binExp >= MIN_SMALL_BIN_EXP ){
// Look more closely at the number to decide if,
// with scaling by 10^nTinyBits, the result will fit in
// a long.
if ( (nTinyBits < FDBigInteger.LONG_5_POW.length) && ((nFractBits + N_5_BITS[nTinyBits]) < 64 ) ){
//
// We can do this:
// take the fraction bits, which are normalized.
// (a) nTinyBits == 0: Shift left or right appropriately
// to align the binary point at the extreme right, i.e.
// where a long int point is expected to be. The integer
// result is easily converted to a string.
// (b) nTinyBits > 0: Shift right by EXP_SHIFT-nFractBits,
// which effectively converts to long and scales by
// 2^nTinyBits. Then multiply by 5^nTinyBits to
// complete the scaling. We know this won't overflow
// because we just counted the number of bits necessary
// in the result. The integer you get from this can
// then be converted to a string pretty easily.
//
if ( nTinyBits == 0 ) {
int insignificant;
if ( binExp > nSignificantBits ){
insignificant = insignificantDigitsForPow2(binExp-nSignificantBits-1);
} else {
insignificant = 0;
}
if ( binExp >= EXP_SHIFT ){
fractBits <<= (binExp-EXP_SHIFT);
} else {
fractBits >>>= (EXP_SHIFT-binExp) ;
}
developLongDigits( 0, fractBits, insignificant );
return;
}
//
// The following causes excess digits to be printed
// out in the single-float case. Our manipulation of
// halfULP here is apparently not correct. If we
// better understand how this works, perhaps we can
// use this special case again. But for the time being,
// we do not.
// else {
// fractBits >>>= EXP_SHIFT+1-nFractBits;
// fractBits//= long5pow[ nTinyBits ];
// halfULP = long5pow[ nTinyBits ] >> (1+nSignificantBits-nFractBits);
// developLongDigits( -nTinyBits, fractBits, insignificantDigits(halfULP) );
// return;
// }
//
}
}
//
// This is the hard case. We are going to compute large positive
// integers B and S and integer decExp, s.t.
// d = ( B / S )// 10^decExp
// 1 <= B / S < 10
// Obvious choices are:
// decExp = floor( log10(d) )
// B = d// 2^nTinyBits// 10^max( 0, -decExp )
// S = 10^max( 0, decExp)// 2^nTinyBits
// (noting that nTinyBits has already been forced to non-negative)
// I am also going to compute a large positive integer
// M = (1/2^nSignificantBits)// 2^nTinyBits// 10^max( 0, -decExp )
// i.e. M is (1/2) of the ULP of d, scaled like B.
// When we iterate through dividing B/S and picking off the
// quotient bits, we will know when to stop when the remainder
// is <= M.
//
// We keep track of powers of 2 and powers of 5.
//
int decExp = estimateDecExp(fractBits,binExp);
int B2, B5; // powers of 2 and powers of 5, respectively, in B
int S2, S5; // powers of 2 and powers of 5, respectively, in S
int M2, M5; // powers of 2 and powers of 5, respectively, in M
B5 = Math.max( 0, -decExp );
B2 = B5 + nTinyBits + binExp;
S5 = Math.max( 0, decExp );
S2 = S5 + nTinyBits;
M5 = B5;
M2 = B2 - nSignificantBits;
//
// the long integer fractBits contains the (nFractBits) interesting
// bits from the mantissa of d ( hidden 1 added if necessary) followed
// by (EXP_SHIFT+1-nFractBits) zeros. In the interest of compactness,
// I will shift out those zeros before turning fractBits into a
// FDBigInteger. The resulting whole number will be
// d * 2^(nFractBits-1-binExp).
//
fractBits >>>= tailZeros;
B2 -= nFractBits-1;
int common2factor = Math.min( B2, S2 );
B2 -= common2factor;
S2 -= common2factor;
M2 -= common2factor;
//
// HACK!! For exact powers of two, the next smallest number
// is only half as far away as we think (because the meaning of
// ULP changes at power-of-two bounds) for this reason, we
// hack M2. Hope this works.
//
if ( nFractBits == 1 ) {
M2 -= 1;
}
if ( M2 < 0 ){
// oops.
// since we cannot scale M down far enough,
// we must scale the other values up.
B2 -= M2;
S2 -= M2;
M2 = 0;
}
//
// Construct, Scale, iterate.
// Some day, we'll write a stopping test that takes
// account of the asymmetry of the spacing of floating-point
// numbers below perfect powers of 2
// 26 Sept 96 is not that day.
// So we use a symmetric test.
//
int ndigit = 0;
boolean low, high;
long lowDigitDifference;
int q;
//
// Detect the special cases where all the numbers we are about
// to compute will fit in int or long integers.
// In these cases, we will avoid doing FDBigInteger arithmetic.
// We use the same algorithms, except that we "normalize"
// our FDBigIntegers before iterating. This is to make division easier,
// as it makes our fist guess (quotient of high-order words)
// more accurate!
//
// Some day, we'll write a stopping test that takes
// account of the asymmetry of the spacing of floating-point
// numbers below perfect powers of 2
// 26 Sept 96 is not that day.
// So we use a symmetric test.
//
// binary digits needed to represent B, approx.
int Bbits = nFractBits + B2 + (( B5 < N_5_BITS.length )? N_5_BITS[B5] : ( B5*3 ));
// binary digits needed to represent 10*S, approx.
int tenSbits = S2+1 + (( (S5+1) < N_5_BITS.length )? N_5_BITS[(S5+1)] : ( (S5+1)*3 ));
if ( Bbits < 64 && tenSbits < 64){
if ( Bbits < 32 && tenSbits < 32){
// wa-hoo! They're all ints!
int b = ((int)fractBits * FDBigInteger.SMALL_5_POW[B5] ) << B2;
int s = FDBigInteger.SMALL_5_POW[S5] << S2;
int m = FDBigInteger.SMALL_5_POW[M5] << M2;
int tens = s * 10;
//
// Unroll the first iteration. If our decExp estimate
// was too high, our first quotient will be zero. In this
// case, we discard it and decrement decExp.
//
ndigit = 0;
q = b / s;
b = 10 * ( b % s );
m *= 10;
low = (b < m );
high = (b+m > tens );
assert q < 10 : q; // excessively large digit
if ( (q == 0) && ! high ){
// oops. Usually ignore leading zero.
decExp--;
} else {
digits[ndigit++] = (char)('0' + q);
}
//
// HACK! Java spec sez that we always have at least
// one digit after the . in either F- or E-form output.
// Thus we will need more than one digit if we're using
// E-form
//
if ( !isCompatibleFormat ||decExp < -3 || decExp >= 8 ){
high = low = false;
}
while( ! low && ! high ){
q = b / s;
b = 10 * ( b % s );
m *= 10;
assert q < 10 : q; // excessively large digit
if ( m > 0L ){
low = (b < m );
high = (b+m > tens );
} else {
// hack -- m might overflow!
// in this case, it is certainly > b,
// which won't
// and b+m > tens, too, since that has overflowed
// either!
low = true;
high = true;
}
digits[ndigit++] = (char)('0' + q);
}
lowDigitDifference = (b<<1) - tens;
exactDecimalConversion = (b == 0);
} else {
// still good! they're all longs!
long b = (fractBits * FDBigInteger.LONG_5_POW[B5] ) << B2;
long s = FDBigInteger.LONG_5_POW[S5] << S2;
long m = FDBigInteger.LONG_5_POW[M5] << M2;
long tens = s * 10L;
//
// Unroll the first iteration. If our decExp estimate
// was too high, our first quotient will be zero. In this
// case, we discard it and decrement decExp.
//
ndigit = 0;
q = (int) ( b / s );
b = 10L * ( b % s );
m *= 10L;
low = (b < m );
high = (b+m > tens );
assert q < 10 : q; // excessively large digit
if ( (q == 0) && ! high ){
// oops. Usually ignore leading zero.
decExp--;
} else {
digits[ndigit++] = (char)('0' + q);
}
//
// HACK! Java spec sez that we always have at least
// one digit after the . in either F- or E-form output.
// Thus we will need more than one digit if we're using
// E-form
//
if ( !isCompatibleFormat || decExp < -3 || decExp >= 8 ){
high = low = false;
}
while( ! low && ! high ){
q = (int) ( b / s );
b = 10 * ( b % s );
m *= 10;
assert q < 10 : q; // excessively large digit
if ( m > 0L ){
low = (b < m );
high = (b+m > tens );
} else {
// hack -- m might overflow!
// in this case, it is certainly > b,
// which won't
// and b+m > tens, too, since that has overflowed
// either!
low = true;
high = true;
}
digits[ndigit++] = (char)('0' + q);
}
lowDigitDifference = (b<<1) - tens;
exactDecimalConversion = (b == 0);
}
} else {
//
// We really must do FDBigInteger arithmetic.
// Fist, construct our FDBigInteger initial values.
//
FDBigInteger Sval = FDBigInteger.valueOfPow52(S5, S2);
int shiftBias = Sval.getNormalizationBias();
Sval = Sval.leftShift(shiftBias); // normalize so that division works better
FDBigInteger Bval = FDBigInteger.valueOfMulPow52(fractBits, B5, B2 + shiftBias);
FDBigInteger Mval = FDBigInteger.valueOfPow52(M5 + 1, M2 + shiftBias + 1);
FDBigInteger tenSval = FDBigInteger.valueOfPow52(S5 + 1, S2 + shiftBias + 1); //Sval.mult( 10 );
//
// Unroll the first iteration. If our decExp estimate
// was too high, our first quotient will be zero. In this
// case, we discard it and decrement decExp.
//
ndigit = 0;
q = Bval.quoRemIteration( Sval );
low = (Bval.cmp( Mval ) < 0);
high = tenSval.addAndCmp(Bval,Mval)<=0;
assert q < 10 : q; // excessively large digit
if ( (q == 0) && ! high ){
// oops. Usually ignore leading zero.
decExp--;
} else {
digits[ndigit++] = (char)('0' + q);
}
//
// HACK! Java spec sez that we always have at least
// one digit after the . in either F- or E-form output.
// Thus we will need more than one digit if we're using
// E-form
//
if (!isCompatibleFormat || decExp < -3 || decExp >= 8 ){
high = low = false;
}
while( ! low && ! high ){
q = Bval.quoRemIteration( Sval );
assert q < 10 : q; // excessively large digit
Mval = Mval.multBy10(); //Mval = Mval.mult( 10 );
low = (Bval.cmp( Mval ) < 0);
high = tenSval.addAndCmp(Bval,Mval)<=0;
digits[ndigit++] = (char)('0' + q);
}
if ( high && low ){
Bval = Bval.leftShift(1);
lowDigitDifference = Bval.cmp(tenSval);
} else {
lowDigitDifference = 0L; // this here only for flow analysis!
}
exactDecimalConversion = (Bval.cmp( FDBigInteger.ZERO ) == 0);
}
this.decExponent = decExp+1;
this.firstDigitIndex = 0;
this.nDigits = ndigit;
//
// Last digit gets rounded based on stopping condition.
//
if ( high ){
if ( low ){
if ( lowDigitDifference == 0L ){
// it's a tie!
// choose based on which digits we like.
if ( (digits[firstDigitIndex+nDigits-1]&1) != 0 ) {
roundup();
}
} else if ( lowDigitDifference > 0 ){
roundup();
}
} else {
roundup();
}
}
}
// add one to the least significant digit.
// in the unlikely event there is a carry out, deal with it.
// assert that this will only happen where there
// is only one digit, e.g. (float)1e-44 seems to do it.
//
private void roundup() {
int i = (firstDigitIndex + nDigits - 1);
int q = digits[i];
if (q == '9') {
while (q == '9' && i > firstDigitIndex) {
digits[i] = '0';
q = digits[--i];
}
if (q == '9') {
// carryout! High-order 1, rest 0s, larger exp.
decExponent += 1;
digits[firstDigitIndex] = '1';
return;
}
// else fall through.
}
digits[i] = (char) (q + 1);
decimalDigitsRoundedUp = true;
}
/**
* Estimate decimal exponent. (If it is small-ish,
* we could double-check.)
*
* First, scale the mantissa bits such that 1 <= d2 < 2.
* We are then going to estimate
* log10(d2) ~=~ (d2-1.5)/1.5 + log(1.5)
* and so we can estimate
* log10(d) ~=~ log10(d2) + binExp * log10(2)
* take the floor and call it decExp.
*/
static int estimateDecExp(long fractBits, int binExp) {
double d2 = Double.longBitsToDouble( EXP_ONE | ( fractBits & DoubleConsts.SIGNIF_BIT_MASK ) );
double d = (d2-1.5D)*0.289529654D + 0.176091259 + (double)binExp * 0.301029995663981;
long dBits = Double.doubleToRawLongBits(d); //can't be NaN here so use raw
int exponent = (int)((dBits & DoubleConsts.EXP_BIT_MASK) >> EXP_SHIFT) - DoubleConsts.EXP_BIAS;
boolean isNegative = (dBits & DoubleConsts.SIGN_BIT_MASK) != 0; // discover sign
if(exponent>=0 && exponent<52) { // hot path
long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent;
int r = (int)(( (dBits&DoubleConsts.SIGNIF_BIT_MASK) | FRACT_HOB )>>(EXP_SHIFT-exponent));
return isNegative ? (((mask & dBits) == 0L ) ? -r : -r-1 ) : r;
} else if (exponent < 0) {
return (((dBits&~DoubleConsts.SIGN_BIT_MASK) == 0) ? 0 :
( (isNegative) ? -1 : 0) );
} else { //if (exponent >= 52)
return (int)d;
}
}
private static int insignificantDigits(int insignificant) {
int i;
for ( i = 0; insignificant >= 10L; i++ ) {
insignificant /= 10L;
}
return i;
}
/**
* Calculates
* <pre>
* insignificantDigitsForPow2(v) == insignificantDigits(1L<<v)
* </pre>
*/
private static int insignificantDigitsForPow2(int p2) {
if(p2>1 && p2 < insignificantDigitsNumber.length) {
return insignificantDigitsNumber[p2];
}
return 0;
}
/**
* If insignificant==(1L << ixd)
* i = insignificantDigitsNumber[idx] is the same as:
* int i;
* for ( i = 0; insignificant >= 10L; i++ )
* insignificant /= 10L;
*/
private static int[] insignificantDigitsNumber = {
0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3,
4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7,
8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11,
12, 12, 12, 12, 13, 13, 13, 14, 14, 14,
15, 15, 15, 15, 16, 16, 16, 17, 17, 17,
18, 18, 18, 19
};
// approximately ceil( log2( long5pow[i] ) )
private static final int[] N_5_BITS = {
0,
3,
5,
7,
10,
12,
14,
17,
19,
21,
24,
26,
28,
31,
33,
35,
38,
40,
42,
45,
47,
49,
52,
54,
56,
59,
61,
};
private int getChars(char[] result) {
assert nDigits <= 19 : nDigits; // generous bound on size of nDigits
int i = 0;
if (isNegative) {
result[0] = '-';
i = 1;
}
if (decExponent > 0 && decExponent < 8) {
// print digits.digits.
int charLength = Math.min(nDigits, decExponent);
System.arraycopy(digits, firstDigitIndex, result, i, charLength);
i += charLength;
if (charLength < decExponent) {
charLength = decExponent - charLength;
Arrays.fill(result,i,i+charLength,'0');
i += charLength;
result[i++] = '.';
result[i++] = '0';
} else {
result[i++] = '.';
if (charLength < nDigits) {
int t = nDigits - charLength;
System.arraycopy(digits, firstDigitIndex+charLength, result, i, t);
i += t;
} else {
result[i++] = '0';
}
}
} else if (decExponent <= 0 && decExponent > -3) {
result[i++] = '0';
result[i++] = '.';
if (decExponent != 0) {
Arrays.fill(result, i, i-decExponent, '0');
i -= decExponent;
}
System.arraycopy(digits, firstDigitIndex, result, i, nDigits);
i += nDigits;
} else {
result[i++] = digits[firstDigitIndex];
result[i++] = '.';
if (nDigits > 1) {
System.arraycopy(digits, firstDigitIndex+1, result, i, nDigits - 1);
i += nDigits - 1;
} else {
result[i++] = '0';
}
result[i++] = 'E';
int e;
if (decExponent <= 0) {
result[i++] = '-';
e = -decExponent + 1;
} else {
e = decExponent - 1;
}
// decExponent has 1, 2, or 3, digits
if (e <= 9) {
result[i++] = (char) (e + '0');
} else if (e <= 99) {
result[i++] = (char) (e / 10 + '0');
result[i++] = (char) (e % 10 + '0');
} else {
result[i++] = (char) (e / 100 + '0');
e %= 100;
result[i++] = (char) (e / 10 + '0');
result[i++] = (char) (e % 10 + '0');
}
}
return i;
}
}
private static final ThreadLocal<BinaryToASCIIBuffer> threadLocalBinaryToASCIIBuffer =
new ThreadLocal<BinaryToASCIIBuffer>() {
@Override
protected BinaryToASCIIBuffer initialValue() {
return new BinaryToASCIIBuffer();
}
};
private static BinaryToASCIIBuffer getBinaryToASCIIBuffer() {
return threadLocalBinaryToASCIIBuffer.get();
}
/**
* A converter which can process an ASCII <code>String</code> representation
* of a single or double precision floating point value into a
* <code>float</code> or a <code>double</code>.
*/
interface ASCIIToBinaryConverter {
double doubleValue();
float floatValue();
}
/**
* A <code>ASCIIToBinaryConverter</code> container for a <code>double</code>.
*/
static class PreparedASCIIToBinaryBuffer implements ASCIIToBinaryConverter {
final private double doubleVal;
final private float floatVal;
public PreparedASCIIToBinaryBuffer(double doubleVal, float floatVal) {
this.doubleVal = doubleVal;
this.floatVal = floatVal;
}
@Override
public double doubleValue() {
return doubleVal;
}
@Override
public float floatValue() {
return floatVal;
}
}
static final ASCIIToBinaryConverter A2BC_POSITIVE_INFINITY = new PreparedASCIIToBinaryBuffer(Double.POSITIVE_INFINITY, Float.POSITIVE_INFINITY);
static final ASCIIToBinaryConverter A2BC_NEGATIVE_INFINITY = new PreparedASCIIToBinaryBuffer(Double.NEGATIVE_INFINITY, Float.NEGATIVE_INFINITY);
static final ASCIIToBinaryConverter A2BC_NOT_A_NUMBER = new PreparedASCIIToBinaryBuffer(Double.NaN, Float.NaN);
static final ASCIIToBinaryConverter A2BC_POSITIVE_ZERO = new PreparedASCIIToBinaryBuffer(0.0d, 0.0f);
static final ASCIIToBinaryConverter A2BC_NEGATIVE_ZERO = new PreparedASCIIToBinaryBuffer(-0.0d, -0.0f);
/**
* A buffered implementation of <code>ASCIIToBinaryConverter</code>.
*/
static class ASCIIToBinaryBuffer implements ASCIIToBinaryConverter {
boolean isNegative;
int decExponent;
char digits[];
int nDigits;
ASCIIToBinaryBuffer( boolean negSign, int decExponent, char[] digits, int n)
{
this.isNegative = negSign;
this.decExponent = decExponent;
this.digits = digits;
this.nDigits = n;
}
/**
* Takes a FloatingDecimal, which we presumably just scanned in,
* and finds out what its value is, as a double.
*
* AS A SIDE EFFECT, SET roundDir TO INDICATE PREFERRED
* ROUNDING DIRECTION in case the result is really destined
* for a single-precision float.
*/
@Override
public double doubleValue() {
int kDigits = Math.min(nDigits, MAX_DECIMAL_DIGITS + 1);
//
// convert the lead kDigits to a long integer.
//
// (special performance hack: start to do it using int)
int iValue = (int) digits[0] - (int) '0';
int iDigits = Math.min(kDigits, INT_DECIMAL_DIGITS);
for (int i = 1; i < iDigits; i++) {
iValue = iValue * 10 + (int) digits[i] - (int) '0';
}
long lValue = (long) iValue;
for (int i = iDigits; i < kDigits; i++) {
lValue = lValue * 10L + (long) ((int) digits[i] - (int) '0');
}
double dValue = (double) lValue;
int exp = decExponent - kDigits;
//
// lValue now contains a long integer with the value of
// the first kDigits digits of the number.
// dValue contains the (double) of the same.
//
if (nDigits <= MAX_DECIMAL_DIGITS) {
//
// possibly an easy case.
// We know that the digits can be represented
// exactly. And if the exponent isn't too outrageous,
// the whole thing can be done with one operation,
// thus one rounding error.
// Note that all our constructors trim all leading and
// trailing zeros, so simple values (including zero)
// will always end up here
//
if (exp == 0 || dValue == 0.0) {
return (isNegative) ? -dValue : dValue; // small floating integer
}
else if (exp >= 0) {
if (exp <= MAX_SMALL_TEN) {
//
// Can get the answer with one operation,
// thus one roundoff.
//
double rValue = dValue * SMALL_10_POW[exp];
return (isNegative) ? -rValue : rValue;
}
int slop = MAX_DECIMAL_DIGITS - kDigits;
if (exp <= MAX_SMALL_TEN + slop) {
//
// We can multiply dValue by 10^(slop)
// and it is still "small" and exact.
// Then we can multiply by 10^(exp-slop)
// with one rounding.
//
dValue *= SMALL_10_POW[slop];
double rValue = dValue * SMALL_10_POW[exp - slop];
return (isNegative) ? -rValue : rValue;
}
//
// Else we have a hard case with a positive exp.
//
} else {
if (exp >= -MAX_SMALL_TEN) {
//
// Can get the answer in one division.
//
double rValue = dValue / SMALL_10_POW[-exp];
return (isNegative) ? -rValue : rValue;
}
//
// Else we have a hard case with a negative exp.
//
}
}
//
// Harder cases:
// The sum of digits plus exponent is greater than
// what we think we can do with one error.
//
// Start by approximating the right answer by,
// naively, scaling by powers of 10.
//
if (exp > 0) {
if (decExponent > MAX_DECIMAL_EXPONENT + 1) {
//
// Lets face it. This is going to be
// Infinity. Cut to the chase.
//
return (isNegative) ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY;
}
if ((exp & 15) != 0) {
dValue *= SMALL_10_POW[exp & 15];
}
if ((exp >>= 4) != 0) {
int j;
for (j = 0; exp > 1; j++, exp >>= 1) {
if ((exp & 1) != 0) {
dValue *= BIG_10_POW[j];
}
}
//
// The reason for the weird exp > 1 condition
// in the above loop was so that the last multiply
// would get unrolled. We handle it here.
// It could overflow.
//
double t = dValue * BIG_10_POW[j];
if (Double.isInfinite(t)) {
//
// It did overflow.
// Look more closely at the result.
// If the exponent is just one too large,
// then use the maximum finite as our estimate
// value. Else call the result infinity
// and punt it.
// ( I presume this could happen because
// rounding forces the result here to be
// an ULP or two larger than
// Double.MAX_VALUE ).
//
t = dValue / 2.0;
t *= BIG_10_POW[j];
if (Double.isInfinite(t)) {
return (isNegative) ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY;
}
t = Double.MAX_VALUE;
}
dValue = t;
}
} else if (exp < 0) {
exp = -exp;
if (decExponent < MIN_DECIMAL_EXPONENT - 1) {
//
// Lets face it. This is going to be
// zero. Cut to the chase.
//
return (isNegative) ? -0.0 : 0.0;
}
if ((exp & 15) != 0) {
dValue /= SMALL_10_POW[exp & 15];
}
if ((exp >>= 4) != 0) {
int j;
for (j = 0; exp > 1; j++, exp >>= 1) {
if ((exp & 1) != 0) {
dValue *= TINY_10_POW[j];
}
}
//
// The reason for the weird exp > 1 condition
// in the above loop was so that the last multiply
// would get unrolled. We handle it here.
// It could underflow.
//
double t = dValue * TINY_10_POW[j];
if (t == 0.0) {
//
// It did underflow.
// Look more closely at the result.
// If the exponent is just one too small,
// then use the minimum finite as our estimate
// value. Else call the result 0.0
// and punt it.
// ( I presume this could happen because
// rounding forces the result here to be
// an ULP or two less than
// Double.MIN_VALUE ).
//
t = dValue * 2.0;
t *= TINY_10_POW[j];
if (t == 0.0) {
return (isNegative) ? -0.0 : 0.0;
}
t = Double.MIN_VALUE;
}
dValue = t;
}
}
//
// dValue is now approximately the result.
// The hard part is adjusting it, by comparison
// with FDBigInteger arithmetic.
// Formulate the EXACT big-number result as
// bigD0 * 10^exp
//
if (nDigits > MAX_NDIGITS) {
nDigits = MAX_NDIGITS + 1;
digits[MAX_NDIGITS] = '1';
}
FDBigInteger bigD0 = new FDBigInteger(lValue, digits, kDigits, nDigits);
exp = decExponent - nDigits;
long ieeeBits = Double.doubleToRawLongBits(dValue); // IEEE-754 bits of double candidate
final int B5 = Math.max(0, -exp); // powers of 5 in bigB, value is not modified inside correctionLoop
final int D5 = Math.max(0, exp); // powers of 5 in bigD, value is not modified inside correctionLoop
bigD0 = bigD0.multByPow52(D5, 0);
bigD0.makeImmutable(); // prevent bigD0 modification inside correctionLoop
FDBigInteger bigD = null;
int prevD2 = 0;
correctionLoop:
while (true) {
// here ieeeBits can't be NaN, Infinity or zero
int binexp = (int) (ieeeBits >>> EXP_SHIFT);
long bigBbits = ieeeBits & DoubleConsts.SIGNIF_BIT_MASK;
if (binexp > 0) {
bigBbits |= FRACT_HOB;
} else { // Normalize denormalized numbers.
assert bigBbits != 0L : bigBbits; // doubleToBigInt(0.0)
int leadingZeros = Long.numberOfLeadingZeros(bigBbits);
int shift = leadingZeros - (63 - EXP_SHIFT);
bigBbits <<= shift;
binexp = 1 - shift;
}
binexp -= DoubleConsts.EXP_BIAS;
int lowOrderZeros = Long.numberOfTrailingZeros(bigBbits);
bigBbits >>>= lowOrderZeros;
final int bigIntExp = binexp - EXP_SHIFT + lowOrderZeros;
final int bigIntNBits = EXP_SHIFT + 1 - lowOrderZeros;
//
// Scale bigD, bigB appropriately for
// big-integer operations.
// Naively, we multiply by powers of ten
// and powers of two. What we actually do
// is keep track of the powers of 5 and
// powers of 2 we would use, then factor out
// common divisors before doing the work.
//
int B2 = B5; // powers of 2 in bigB
int D2 = D5; // powers of 2 in bigD
int Ulp2; // powers of 2 in halfUlp.
if (bigIntExp >= 0) {
B2 += bigIntExp;
} else {
D2 -= bigIntExp;
}
Ulp2 = B2;
// shift bigB and bigD left by a number s. t.
// halfUlp is still an integer.
int hulpbias;
if (binexp <= -DoubleConsts.EXP_BIAS) {
// This is going to be a denormalized number
// (if not actually zero).
// half an ULP is at 2^-(DoubleConsts.EXP_BIAS+EXP_SHIFT+1)
hulpbias = binexp + lowOrderZeros + DoubleConsts.EXP_BIAS;
} else {
hulpbias = 1 + lowOrderZeros;
}
B2 += hulpbias;
D2 += hulpbias;
// if there are common factors of 2, we might just as well
// factor them out, as they add nothing useful.
int common2 = Math.min(B2, Math.min(D2, Ulp2));
B2 -= common2;
D2 -= common2;
Ulp2 -= common2;
// do multiplications by powers of 5 and 2
FDBigInteger bigB = FDBigInteger.valueOfMulPow52(bigBbits, B5, B2);
if (bigD == null || prevD2 != D2) {
bigD = bigD0.leftShift(D2);
prevD2 = D2;
}
//
// to recap:
// bigB is the scaled-big-int version of our floating-point
// candidate.
// bigD is the scaled-big-int version of the exact value
// as we understand it.
// halfUlp is 1/2 an ulp of bigB, except for special cases
// of exact powers of 2
//
// the plan is to compare bigB with bigD, and if the difference
// is less than halfUlp, then we're satisfied. Otherwise,
// use the ratio of difference to halfUlp to calculate a fudge
// factor to add to the floating value, then go 'round again.
//
FDBigInteger diff;
int cmpResult;
boolean overvalue;
if ((cmpResult = bigB.cmp(bigD)) > 0) {
overvalue = true; // our candidate is too big.
diff = bigB.leftInplaceSub(bigD); // bigB is not user further - reuse
if ((bigIntNBits == 1) && (bigIntExp > -DoubleConsts.EXP_BIAS + 1)) {
// candidate is a normalized exact power of 2 and
// is too big (larger than Double.MIN_NORMAL). We will be subtracting.
// For our purposes, ulp is the ulp of the
// next smaller range.
Ulp2 -= 1;
if (Ulp2 < 0) {
// rats. Cannot de-scale ulp this far.
// must scale diff in other direction.
Ulp2 = 0;
diff = diff.leftShift(1);
}
}
} else if (cmpResult < 0) {
overvalue = false; // our candidate is too small.
diff = bigD.rightInplaceSub(bigB); // bigB is not user further - reuse
} else {
// the candidate is exactly right!
// this happens with surprising frequency
break correctionLoop;
}
cmpResult = diff.cmpPow52(B5, Ulp2);
if ((cmpResult) < 0) {
// difference is small.
// this is close enough
break correctionLoop;
} else if (cmpResult == 0) {
// difference is exactly half an ULP
// round to some other value maybe, then finish
if ((ieeeBits & 1) != 0) { // half ties to even
ieeeBits += overvalue ? -1 : 1; // nextDown or nextUp
}
break correctionLoop;
} else {
// difference is non-trivial.
// could scale addend by ratio of difference to
// halfUlp here, if we bothered to compute that difference.
// Most of the time ( I hope ) it is about 1 anyway.
ieeeBits += overvalue ? -1 : 1; // nextDown or nextUp
if (ieeeBits == 0 || ieeeBits == DoubleConsts.EXP_BIT_MASK) { // 0.0 or Double.POSITIVE_INFINITY
break correctionLoop; // oops. Fell off end of range.
}
continue; // try again.
}
}
if (isNegative) {
ieeeBits |= DoubleConsts.SIGN_BIT_MASK;
}
return Double.longBitsToDouble(ieeeBits);
}
/**
* Takes a FloatingDecimal, which we presumably just scanned in,
* and finds out what its value is, as a float.
* This is distinct from doubleValue() to avoid the extremely
* unlikely case of a double rounding error, wherein the conversion
* to double has one rounding error, and the conversion of that double
* to a float has another rounding error, IN THE WRONG DIRECTION,
* ( because of the preference to a zero low-order bit ).
*/
@Override
public float floatValue() {
int kDigits = Math.min(nDigits, SINGLE_MAX_DECIMAL_DIGITS + 1);
//
// convert the lead kDigits to an integer.
//
int iValue = (int) digits[0] - (int) '0';
for (int i = 1; i < kDigits; i++) {
iValue = iValue * 10 + (int) digits[i] - (int) '0';
}
float fValue = (float) iValue;
int exp = decExponent - kDigits;
//
// iValue now contains an integer with the value of
// the first kDigits digits of the number.
// fValue contains the (float) of the same.
//
if (nDigits <= SINGLE_MAX_DECIMAL_DIGITS) {
//
// possibly an easy case.
// We know that the digits can be represented
// exactly. And if the exponent isn't too outrageous,
// the whole thing can be done with one operation,
// thus one rounding error.
// Note that all our constructors trim all leading and
// trailing zeros, so simple values (including zero)
// will always end up here.
//
if (exp == 0 || fValue == 0.0f) {
return (isNegative) ? -fValue : fValue; // small floating integer
} else if (exp >= 0) {
if (exp <= SINGLE_MAX_SMALL_TEN) {
//
// Can get the answer with one operation,
// thus one roundoff.
//
fValue *= SINGLE_SMALL_10_POW[exp];
return (isNegative) ? -fValue : fValue;
}
int slop = SINGLE_MAX_DECIMAL_DIGITS - kDigits;
if (exp <= SINGLE_MAX_SMALL_TEN + slop) {
//
// We can multiply fValue by 10^(slop)
// and it is still "small" and exact.
// Then we can multiply by 10^(exp-slop)
// with one rounding.
//
fValue *= SINGLE_SMALL_10_POW[slop];
fValue *= SINGLE_SMALL_10_POW[exp - slop];
return (isNegative) ? -fValue : fValue;
}
//
// Else we have a hard case with a positive exp.
//
} else {
if (exp >= -SINGLE_MAX_SMALL_TEN) {
//
// Can get the answer in one division.
//
fValue /= SINGLE_SMALL_10_POW[-exp];
return (isNegative) ? -fValue : fValue;
}
//
// Else we have a hard case with a negative exp.
//
}
} else if ((decExponent >= nDigits) && (nDigits + decExponent <= MAX_DECIMAL_DIGITS)) {
//
// In double-precision, this is an exact floating integer.
// So we can compute to double, then shorten to float
// with one round, and get the right answer.
//
// First, finish accumulating digits.
// Then convert that integer to a double, multiply
// by the appropriate power of ten, and convert to float.
//
long lValue = (long) iValue;
for (int i = kDigits; i < nDigits; i++) {
lValue = lValue * 10L + (long) ((int) digits[i] - (int) '0');
}
double dValue = (double) lValue;
exp = decExponent - nDigits;
dValue *= SMALL_10_POW[exp];
fValue = (float) dValue;
return (isNegative) ? -fValue : fValue;
}
//
// Harder cases:
// The sum of digits plus exponent is greater than
// what we think we can do with one error.
//
// Start by approximating the right answer by,
// naively, scaling by powers of 10.
// Scaling uses doubles to avoid overflow/underflow.
//
double dValue = fValue;
if (exp > 0) {
if (decExponent > SINGLE_MAX_DECIMAL_EXPONENT + 1) {
//
// Lets face it. This is going to be
// Infinity. Cut to the chase.
//
return (isNegative) ? Float.NEGATIVE_INFINITY : Float.POSITIVE_INFINITY;
}
if ((exp & 15) != 0) {
dValue *= SMALL_10_POW[exp & 15];
}
if ((exp >>= 4) != 0) {
int j;
for (j = 0; exp > 0; j++, exp >>= 1) {
if ((exp & 1) != 0) {
dValue *= BIG_10_POW[j];
}
}
}
} else if (exp < 0) {
exp = -exp;
if (decExponent < SINGLE_MIN_DECIMAL_EXPONENT - 1) {
//
// Lets face it. This is going to be
// zero. Cut to the chase.
//
return (isNegative) ? -0.0f : 0.0f;
}
if ((exp & 15) != 0) {
dValue /= SMALL_10_POW[exp & 15];
}
if ((exp >>= 4) != 0) {
int j;
for (j = 0; exp > 0; j++, exp >>= 1) {
if ((exp & 1) != 0) {
dValue *= TINY_10_POW[j];
}
}
}
}
fValue = Math.max(Float.MIN_VALUE, Math.min(Float.MAX_VALUE, (float) dValue));
//
// fValue is now approximately the result.
// The hard part is adjusting it, by comparison
// with FDBigInteger arithmetic.
// Formulate the EXACT big-number result as
// bigD0 * 10^exp
//
if (nDigits > SINGLE_MAX_NDIGITS) {
nDigits = SINGLE_MAX_NDIGITS + 1;
digits[SINGLE_MAX_NDIGITS] = '1';
}
FDBigInteger bigD0 = new FDBigInteger(iValue, digits, kDigits, nDigits);
exp = decExponent - nDigits;
int ieeeBits = Float.floatToRawIntBits(fValue); // IEEE-754 bits of float candidate
final int B5 = Math.max(0, -exp); // powers of 5 in bigB, value is not modified inside correctionLoop
final int D5 = Math.max(0, exp); // powers of 5 in bigD, value is not modified inside correctionLoop
bigD0 = bigD0.multByPow52(D5, 0);
bigD0.makeImmutable(); // prevent bigD0 modification inside correctionLoop
FDBigInteger bigD = null;
int prevD2 = 0;
correctionLoop:
while (true) {
// here ieeeBits can't be NaN, Infinity or zero
int binexp = ieeeBits >>> SINGLE_EXP_SHIFT;
int bigBbits = ieeeBits & FloatConsts.SIGNIF_BIT_MASK;
if (binexp > 0) {
bigBbits |= SINGLE_FRACT_HOB;
} else { // Normalize denormalized numbers.
assert bigBbits != 0 : bigBbits; // floatToBigInt(0.0)
int leadingZeros = Integer.numberOfLeadingZeros(bigBbits);
int shift = leadingZeros - (31 - SINGLE_EXP_SHIFT);
bigBbits <<= shift;
binexp = 1 - shift;
}
binexp -= FloatConsts.EXP_BIAS;
int lowOrderZeros = Integer.numberOfTrailingZeros(bigBbits);
bigBbits >>>= lowOrderZeros;
final int bigIntExp = binexp - SINGLE_EXP_SHIFT + lowOrderZeros;
final int bigIntNBits = SINGLE_EXP_SHIFT + 1 - lowOrderZeros;
//
// Scale bigD, bigB appropriately for
// big-integer operations.
// Naively, we multiply by powers of ten
// and powers of two. What we actually do
// is keep track of the powers of 5 and
// powers of 2 we would use, then factor out
// common divisors before doing the work.
//
int B2 = B5; // powers of 2 in bigB
int D2 = D5; // powers of 2 in bigD
int Ulp2; // powers of 2 in halfUlp.
if (bigIntExp >= 0) {
B2 += bigIntExp;
} else {
D2 -= bigIntExp;
}
Ulp2 = B2;
// shift bigB and bigD left by a number s. t.
// halfUlp is still an integer.
int hulpbias;
if (binexp <= -FloatConsts.EXP_BIAS) {
// This is going to be a denormalized number
// (if not actually zero).
// half an ULP is at 2^-(FloatConsts.EXP_BIAS+SINGLE_EXP_SHIFT+1)
hulpbias = binexp + lowOrderZeros + FloatConsts.EXP_BIAS;
} else {
hulpbias = 1 + lowOrderZeros;
}
B2 += hulpbias;
D2 += hulpbias;
// if there are common factors of 2, we might just as well
// factor them out, as they add nothing useful.
int common2 = Math.min(B2, Math.min(D2, Ulp2));
B2 -= common2;
D2 -= common2;
Ulp2 -= common2;
// do multiplications by powers of 5 and 2
FDBigInteger bigB = FDBigInteger.valueOfMulPow52(bigBbits, B5, B2);
if (bigD == null || prevD2 != D2) {
bigD = bigD0.leftShift(D2);
prevD2 = D2;
}
//
// to recap:
// bigB is the scaled-big-int version of our floating-point
// candidate.
// bigD is the scaled-big-int version of the exact value
// as we understand it.
// halfUlp is 1/2 an ulp of bigB, except for special cases
// of exact powers of 2
//
// the plan is to compare bigB with bigD, and if the difference
// is less than halfUlp, then we're satisfied. Otherwise,
// use the ratio of difference to halfUlp to calculate a fudge
// factor to add to the floating value, then go 'round again.
//
FDBigInteger diff;
int cmpResult;
boolean overvalue;
if ((cmpResult = bigB.cmp(bigD)) > 0) {
overvalue = true; // our candidate is too big.
diff = bigB.leftInplaceSub(bigD); // bigB is not user further - reuse
if ((bigIntNBits == 1) && (bigIntExp > -FloatConsts.EXP_BIAS + 1)) {
// candidate is a normalized exact power of 2 and
// is too big (larger than Float.MIN_NORMAL). We will be subtracting.
// For our purposes, ulp is the ulp of the
// next smaller range.
Ulp2 -= 1;
if (Ulp2 < 0) {
// rats. Cannot de-scale ulp this far.
// must scale diff in other direction.
Ulp2 = 0;
diff = diff.leftShift(1);
}
}
} else if (cmpResult < 0) {
overvalue = false; // our candidate is too small.
diff = bigD.rightInplaceSub(bigB); // bigB is not user further - reuse
} else {
// the candidate is exactly right!
// this happens with surprising frequency
break correctionLoop;
}
cmpResult = diff.cmpPow52(B5, Ulp2);
if ((cmpResult) < 0) {
// difference is small.
// this is close enough
break correctionLoop;
} else if (cmpResult == 0) {
// difference is exactly half an ULP
// round to some other value maybe, then finish
if ((ieeeBits & 1) != 0) { // half ties to even
ieeeBits += overvalue ? -1 : 1; // nextDown or nextUp
}
break correctionLoop;
} else {
// difference is non-trivial.
// could scale addend by ratio of difference to
// halfUlp here, if we bothered to compute that difference.
// Most of the time ( I hope ) it is about 1 anyway.
ieeeBits += overvalue ? -1 : 1; // nextDown or nextUp
if (ieeeBits == 0 || ieeeBits == FloatConsts.EXP_BIT_MASK) { // 0.0 or Float.POSITIVE_INFINITY
break correctionLoop; // oops. Fell off end of range.
}
continue; // try again.
}
}
if (isNegative) {
ieeeBits |= FloatConsts.SIGN_BIT_MASK;
}
return Float.intBitsToFloat(ieeeBits);
}
/**
* All the positive powers of 10 that can be
* represented exactly in double/float.
*/
private static final double[] SMALL_10_POW = {
1.0e0,
1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5,
1.0e6, 1.0e7, 1.0e8, 1.0e9, 1.0e10,
1.0e11, 1.0e12, 1.0e13, 1.0e14, 1.0e15,
1.0e16, 1.0e17, 1.0e18, 1.0e19, 1.0e20,
1.0e21, 1.0e22
};
private static final float[] SINGLE_SMALL_10_POW = {
1.0e0f,
1.0e1f, 1.0e2f, 1.0e3f, 1.0e4f, 1.0e5f,
1.0e6f, 1.0e7f, 1.0e8f, 1.0e9f, 1.0e10f
};
private static final double[] BIG_10_POW = {
1e16, 1e32, 1e64, 1e128, 1e256 };
private static final double[] TINY_10_POW = {
1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
private static final int MAX_SMALL_TEN = SMALL_10_POW.length-1;
private static final int SINGLE_MAX_SMALL_TEN = SINGLE_SMALL_10_POW.length-1;
}
/**
* Returns a <code>BinaryToASCIIConverter</code> for a <code>double</code>.
* The returned object is a <code>ThreadLocal</code> variable of this class.
*
* @param d The double precision value to convert.
* @return The converter.
*/
public static BinaryToASCIIConverter getBinaryToASCIIConverter(double d) {
return getBinaryToASCIIConverter(d, true);
}
/**
* Returns a <code>BinaryToASCIIConverter</code> for a <code>double</code>.
* The returned object is a <code>ThreadLocal</code> variable of this class.
*
* @param d The double precision value to convert.
* @param isCompatibleFormat
* @return The converter.
*/
static BinaryToASCIIConverter getBinaryToASCIIConverter(double d, boolean isCompatibleFormat) {
long dBits = Double.doubleToRawLongBits(d);
boolean isNegative = (dBits&DoubleConsts.SIGN_BIT_MASK) != 0; // discover sign
long fractBits = dBits & DoubleConsts.SIGNIF_BIT_MASK;
int binExp = (int)( (dBits&DoubleConsts.EXP_BIT_MASK) >> EXP_SHIFT );
// Discover obvious special cases of NaN and Infinity.
if ( binExp == (int)(DoubleConsts.EXP_BIT_MASK>>EXP_SHIFT) ) {
if ( fractBits == 0L ){
return isNegative ? B2AC_NEGATIVE_INFINITY : B2AC_POSITIVE_INFINITY;
} else {
return B2AC_NOT_A_NUMBER;
}
}
// Finish unpacking
// Normalize denormalized numbers.
// Insert assumed high-order bit for normalized numbers.
// Subtract exponent bias.
int nSignificantBits;
if ( binExp == 0 ){
if ( fractBits == 0L ){
// not a denorm, just a 0!
return isNegative ? B2AC_NEGATIVE_ZERO : B2AC_POSITIVE_ZERO;
}
int leadingZeros = Long.numberOfLeadingZeros(fractBits);
int shift = leadingZeros-(63-EXP_SHIFT);
fractBits <<= shift;
binExp = 1 - shift;
nSignificantBits = 64-leadingZeros; // recall binExp is - shift count.
} else {
fractBits |= FRACT_HOB;
nSignificantBits = EXP_SHIFT+1;
}
binExp -= DoubleConsts.EXP_BIAS;
BinaryToASCIIBuffer buf = getBinaryToASCIIBuffer();
buf.setSign(isNegative);
// call the routine that actually does all the hard work.
buf.dtoa(binExp, fractBits, nSignificantBits, isCompatibleFormat);
return buf;
}
private static BinaryToASCIIConverter getBinaryToASCIIConverter(float f) {
int fBits = Float.floatToRawIntBits( f );
boolean isNegative = (fBits&FloatConsts.SIGN_BIT_MASK) != 0;
int fractBits = fBits&FloatConsts.SIGNIF_BIT_MASK;
int binExp = (fBits&FloatConsts.EXP_BIT_MASK) >> SINGLE_EXP_SHIFT;
// Discover obvious special cases of NaN and Infinity.
if ( binExp == (FloatConsts.EXP_BIT_MASK>>SINGLE_EXP_SHIFT) ) {
if ( fractBits == 0L ){
return isNegative ? B2AC_NEGATIVE_INFINITY : B2AC_POSITIVE_INFINITY;
} else {
return B2AC_NOT_A_NUMBER;
}
}
// Finish unpacking
// Normalize denormalized numbers.
// Insert assumed high-order bit for normalized numbers.
// Subtract exponent bias.
int nSignificantBits;
if ( binExp == 0 ){
if ( fractBits == 0 ){
// not a denorm, just a 0!
return isNegative ? B2AC_NEGATIVE_ZERO : B2AC_POSITIVE_ZERO;
}
int leadingZeros = Integer.numberOfLeadingZeros(fractBits);
int shift = leadingZeros-(31-SINGLE_EXP_SHIFT);
fractBits <<= shift;
binExp = 1 - shift;
nSignificantBits = 32 - leadingZeros; // recall binExp is - shift count.
} else {
fractBits |= SINGLE_FRACT_HOB;
nSignificantBits = SINGLE_EXP_SHIFT+1;
}
binExp -= FloatConsts.EXP_BIAS;
BinaryToASCIIBuffer buf = getBinaryToASCIIBuffer();
buf.setSign(isNegative);
// call the routine that actually does all the hard work.
buf.dtoa(binExp, ((long)fractBits)<<(EXP_SHIFT-SINGLE_EXP_SHIFT), nSignificantBits, true);
return buf;
}
@SuppressWarnings("fallthrough")
static ASCIIToBinaryConverter readJavaFormatString( String in ) throws NumberFormatException {
boolean isNegative = false;
boolean signSeen = false;
int decExp;
char c;
parseNumber:
try{
in = in.trim(); // don't fool around with white space.
// throws NullPointerException if null
int len = in.length();
if ( len == 0 ) {
throw new NumberFormatException("empty String");
}
int i = 0;
switch (in.charAt(i)){
case '-':
isNegative = true;
//FALLTHROUGH
case '+':
i++;
signSeen = true;
}
c = in.charAt(i);
if(c == 'N') { // Check for NaN
if((len-i)==NAN_LENGTH && in.indexOf(NAN_REP,i)==i) {
return A2BC_NOT_A_NUMBER;
}
// something went wrong, throw exception
break parseNumber;
} else if(c == 'I') { // Check for Infinity strings
if((len-i)==INFINITY_LENGTH && in.indexOf(INFINITY_REP,i)==i) {
return isNegative? A2BC_NEGATIVE_INFINITY : A2BC_POSITIVE_INFINITY;
}
// something went wrong, throw exception
break parseNumber;
} else if (c == '0') { // check for hexadecimal floating-point number
if (len > i+1 ) {
char ch = in.charAt(i+1);
if (ch == 'x' || ch == 'X' ) { // possible hex string
return parseHexString(in);
}
}
} // look for and process decimal floating-point string
char[] digits = new char[ len ];
int nDigits= 0;
boolean decSeen = false;
int decPt = 0;
int nLeadZero = 0;
int nTrailZero= 0;
skipLeadingZerosLoop:
while (i < len) {
c = in.charAt(i);
if (c == '0') {
nLeadZero++;
} else if (c == '.') {
if (decSeen) {
// already saw one ., this is the 2nd.
throw new NumberFormatException("multiple points");
}
decPt = i;
if (signSeen) {
decPt -= 1;
}
decSeen = true;
} else {
break skipLeadingZerosLoop;
}
i++;
}
digitLoop:
while (i < len) {
c = in.charAt(i);
if (c >= '1' && c <= '9') {
digits[nDigits++] = c;
nTrailZero = 0;
} else if (c == '0') {
digits[nDigits++] = c;
nTrailZero++;
} else if (c == '.') {
if (decSeen) {
// already saw one ., this is the 2nd.
throw new NumberFormatException("multiple points");
}
decPt = i;
if (signSeen) {
decPt -= 1;
}
decSeen = true;
} else {
break digitLoop;
}
i++;
}
nDigits -=nTrailZero;
//
// At this point, we've scanned all the digits and decimal
// point we're going to see. Trim off leading and trailing
// zeros, which will just confuse us later, and adjust
// our initial decimal exponent accordingly.
// To review:
// we have seen i total characters.
// nLeadZero of them were zeros before any other digits.
// nTrailZero of them were zeros after any other digits.
// if ( decSeen ), then a . was seen after decPt characters
// ( including leading zeros which have been discarded )
// nDigits characters were neither lead nor trailing
// zeros, nor point
//
//
// special hack: if we saw no non-zero digits, then the
// answer is zero!
// Unfortunately, we feel honor-bound to keep parsing!
//
boolean isZero = (nDigits == 0);
if ( isZero && nLeadZero == 0 ){
// we saw NO DIGITS AT ALL,
// not even a crummy 0!
// this is not allowed.
break parseNumber; // go throw exception
}
//
// Our initial exponent is decPt, adjusted by the number of
// discarded zeros. Or, if there was no decPt,
// then its just nDigits adjusted by discarded trailing zeros.
//
if ( decSeen ){
decExp = decPt - nLeadZero;
} else {
decExp = nDigits + nTrailZero;
}
//
// Look for 'e' or 'E' and an optionally signed integer.
//
if ( (i < len) && (((c = in.charAt(i) )=='e') || (c == 'E') ) ){
int expSign = 1;
int expVal = 0;
int reallyBig = Integer.MAX_VALUE / 10;
boolean expOverflow = false;
switch( in.charAt(++i) ){
case '-':
expSign = -1;
//FALLTHROUGH
case '+':
i++;
}
int expAt = i;
expLoop:
while ( i < len ){
if ( expVal >= reallyBig ){
// the next character will cause integer
// overflow.
expOverflow = true;
}
c = in.charAt(i++);
if(c>='0' && c<='9') {
expVal = expVal*10 + ( (int)c - (int)'0' );
} else {
i--; // back up.
break expLoop; // stop parsing exponent.
}
}
int expLimit = BIG_DECIMAL_EXPONENT + nDigits + nTrailZero;
if (expOverflow || (expVal > expLimit)) {
// There is still a chance that the exponent will be safe to
// use: if it would eventually decrease due to a negative
// decExp, and that number is below the limit. We check for
// that here.
if (!expOverflow && (expSign == 1 && decExp < 0)
&& (expVal + decExp) < expLimit) {
// Cannot overflow: adding a positive and negative number.
decExp += expVal;
} else {
//
// The intent here is to end up with
// infinity or zero, as appropriate.
// The reason for yielding such a small decExponent,
// rather than something intuitive such as
// expSign*Integer.MAX_VALUE, is that this value
// is subject to further manipulation in
// doubleValue() and floatValue(), and I don't want
// it to be able to cause overflow there!
// (The only way we can get into trouble here is for
// really outrageous nDigits+nTrailZero, such as 2
// billion.)
//
decExp = expSign * expLimit;
}
} else {
// this should not overflow, since we tested
// for expVal > (MAX+N), where N >= abs(decExp)
decExp = decExp + expSign*expVal;
}
// if we saw something not a digit ( or end of string )
// after the [Ee][+-], without seeing any digits at all
// this is certainly an error. If we saw some digits,
// but then some trailing garbage, that might be ok.
// so we just fall through in that case.
// HUMBUG
if ( i == expAt ) {
break parseNumber; // certainly bad
}
}
//
// We parsed everything we could.
// If there are leftovers, then this is not good input!
//
if ( i < len &&
((i != len - 1) ||
(in.charAt(i) != 'f' &&
in.charAt(i) != 'F' &&
in.charAt(i) != 'd' &&
in.charAt(i) != 'D'))) {
break parseNumber; // go throw exception
}
if(isZero) {
return isNegative ? A2BC_NEGATIVE_ZERO : A2BC_POSITIVE_ZERO;
}
return new ASCIIToBinaryBuffer(isNegative, decExp, digits, nDigits);
} catch ( StringIndexOutOfBoundsException e ){ }
throw new NumberFormatException("For input string: \"" + in + "\"");
}
private static class HexFloatPattern {
/**
* Grammar is compatible with hexadecimal floating-point constants
* described in section 6.4.4.2 of the C99 specification.
*/
private static final Pattern VALUE = Pattern.compile(
//1 234 56 7 8 9
"([-+])?0[xX](((\\p{XDigit}+)\\.?)|((\\p{XDigit}*)\\.(\\p{XDigit}+)))[pP]([-+])?(\\p{Digit}+)[fFdD]?"
);
}
/**
* Converts string s to a suitable floating decimal; uses the
* double constructor and sets the roundDir variable appropriately
* in case the value is later converted to a float.
*
* @param s The <code>String</code> to parse.
*/
static ASCIIToBinaryConverter parseHexString(String s) {
// Verify string is a member of the hexadecimal floating-point
// string language.
Matcher m = HexFloatPattern.VALUE.matcher(s);
boolean validInput = m.matches();
if (!validInput) {
// Input does not match pattern
throw new NumberFormatException("For input string: \"" + s + "\"");
} else { // validInput
//
// We must isolate the sign, significand, and exponent
// fields. The sign value is straightforward. Since
// floating-point numbers are stored with a normalized
// representation, the significand and exponent are
// interrelated.
//
// After extracting the sign, we normalized the
// significand as a hexadecimal value, calculating an
// exponent adjust for any shifts made during
// normalization. If the significand is zero, the
// exponent doesn't need to be examined since the output
// will be zero.
//
// Next the exponent in the input string is extracted.
// Afterwards, the significand is normalized as a *binary*
// value and the input value's normalized exponent can be
// computed. The significand bits are copied into a
// double significand; if the string has more logical bits
// than can fit in a double, the extra bits affect the
// round and sticky bits which are used to round the final
// value.
//
// Extract significand sign
String group1 = m.group(1);
boolean isNegative = ((group1 != null) && group1.equals("-"));
// Extract Significand magnitude
//
// Based on the form of the significand, calculate how the
// binary exponent needs to be adjusted to create a
// normalized//hexadecimal* floating-point number; that
// is, a number where there is one nonzero hex digit to
// the left of the (hexa)decimal point. Since we are
// adjusting a binary, not hexadecimal exponent, the
// exponent is adjusted by a multiple of 4.
//
// There are a number of significand scenarios to consider;
// letters are used in indicate nonzero digits:
//
// 1. 000xxxx => x.xxx normalized
// increase exponent by (number of x's - 1)*4
//
// 2. 000xxx.yyyy => x.xxyyyy normalized
// increase exponent by (number of x's - 1)*4
//
// 3. .000yyy => y.yy normalized
// decrease exponent by (number of zeros + 1)*4
//
// 4. 000.00000yyy => y.yy normalized
// decrease exponent by (number of zeros to right of point + 1)*4
//
// If the significand is exactly zero, return a properly
// signed zero.
//
String significandString = null;
int signifLength = 0;
int exponentAdjust = 0;
{
int leftDigits = 0; // number of meaningful digits to
// left of "decimal" point
// (leading zeros stripped)
int rightDigits = 0; // number of digits to right of
// "decimal" point; leading zeros
// must always be accounted for
//
// The significand is made up of either
//
// 1. group 4 entirely (integer portion only)
//
// OR
//
// 2. the fractional portion from group 7 plus any
// (optional) integer portions from group 6.
//
String group4;
if ((group4 = m.group(4)) != null) { // Integer-only significand
// Leading zeros never matter on the integer portion
significandString = stripLeadingZeros(group4);
leftDigits = significandString.length();
} else {
// Group 6 is the optional integer; leading zeros
// never matter on the integer portion
String group6 = stripLeadingZeros(m.group(6));
leftDigits = group6.length();
// fraction
String group7 = m.group(7);
rightDigits = group7.length();
// Turn "integer.fraction" into "integer"+"fraction"
significandString =
((group6 == null) ? "" : group6) + // is the null
// check necessary?
group7;
}
significandString = stripLeadingZeros(significandString);
signifLength = significandString.length();
//
// Adjust exponent as described above
//
if (leftDigits >= 1) { // Cases 1 and 2
exponentAdjust = 4 * (leftDigits - 1);
} else { // Cases 3 and 4
exponentAdjust = -4 * (rightDigits - signifLength + 1);
}
// If the significand is zero, the exponent doesn't
// matter; return a properly signed zero.
if (signifLength == 0) { // Only zeros in input
return isNegative ? A2BC_NEGATIVE_ZERO : A2BC_POSITIVE_ZERO;
}
}
// Extract Exponent
//
// Use an int to read in the exponent value; this should
// provide more than sufficient range for non-contrived
// inputs. If reading the exponent in as an int does
// overflow, examine the sign of the exponent and
// significand to determine what to do.
//
String group8 = m.group(8);
boolean positiveExponent = (group8 == null) || group8.equals("+");
long unsignedRawExponent;
try {
unsignedRawExponent = Integer.parseInt(m.group(9));
}
catch (NumberFormatException e) {
// At this point, we know the exponent is
// syntactically well-formed as a sequence of
// digits. Therefore, if an NumberFormatException
// is thrown, it must be due to overflowing int's
// range. Also, at this point, we have already
// checked for a zero significand. Thus the signs
// of the exponent and significand determine the
// final result:
//
// significand
// + -
// exponent + +infinity -infinity
// - +0.0 -0.0
return isNegative ?
(positiveExponent ? A2BC_NEGATIVE_INFINITY : A2BC_NEGATIVE_ZERO)
: (positiveExponent ? A2BC_POSITIVE_INFINITY : A2BC_POSITIVE_ZERO);
}
long rawExponent =
(positiveExponent ? 1L : -1L) * // exponent sign
unsignedRawExponent; // exponent magnitude
// Calculate partially adjusted exponent
long exponent = rawExponent + exponentAdjust;
// Starting copying non-zero bits into proper position in
// a long; copy explicit bit too; this will be masked
// later for normal values.
boolean round = false;
boolean sticky = false;
int nextShift = 0;
long significand = 0L;
// First iteration is different, since we only copy
// from the leading significand bit; one more exponent
// adjust will be needed...
// IMPORTANT: make leadingDigit a long to avoid
// surprising shift semantics!
long leadingDigit = getHexDigit(significandString, 0);
//
// Left shift the leading digit (53 - (bit position of
// leading 1 in digit)); this sets the top bit of the
// significand to 1. The nextShift value is adjusted
// to take into account the number of bit positions of
// the leadingDigit actually used. Finally, the
// exponent is adjusted to normalize the significand
// as a binary value, not just a hex value.
//
if (leadingDigit == 1) {
significand |= leadingDigit << 52;
nextShift = 52 - 4;
// exponent += 0
} else if (leadingDigit <= 3) { // [2, 3]
significand |= leadingDigit << 51;
nextShift = 52 - 5;
exponent += 1;
} else if (leadingDigit <= 7) { // [4, 7]
significand |= leadingDigit << 50;
nextShift = 52 - 6;
exponent += 2;
} else if (leadingDigit <= 15) { // [8, f]
significand |= leadingDigit << 49;
nextShift = 52 - 7;
exponent += 3;
} else {
throw new AssertionError("Result from digit conversion too large!");
}
// The preceding if-else could be replaced by a single
// code block based on the high-order bit set in
// leadingDigit. Given leadingOnePosition,
// significand |= leadingDigit << (SIGNIFICAND_WIDTH - leadingOnePosition);
// nextShift = 52 - (3 + leadingOnePosition);
// exponent += (leadingOnePosition-1);
//
// Now the exponent variable is equal to the normalized
// binary exponent. Code below will make representation
// adjustments if the exponent is incremented after
// rounding (includes overflows to infinity) or if the
// result is subnormal.
//
// Copy digit into significand until the significand can't
// hold another full hex digit or there are no more input
// hex digits.
int i = 0;
for (i = 1;
i < signifLength && nextShift >= 0;
i++) {
long currentDigit = getHexDigit(significandString, i);
significand |= (currentDigit << nextShift);
nextShift -= 4;
}
// After the above loop, the bulk of the string is copied.
// Now, we must copy any partial hex digits into the
// significand AND compute the round bit and start computing
// sticky bit.
if (i < signifLength) { // at least one hex input digit exists
long currentDigit = getHexDigit(significandString, i);
// from nextShift, figure out how many bits need
// to be copied, if any
switch (nextShift) { // must be negative
case -1:
// three bits need to be copied in; can
// set round bit
significand |= ((currentDigit & 0xEL) >> 1);
round = (currentDigit & 0x1L) != 0L;
break;
case -2:
// two bits need to be copied in; can
// set round and start sticky
significand |= ((currentDigit & 0xCL) >> 2);
round = (currentDigit & 0x2L) != 0L;
sticky = (currentDigit & 0x1L) != 0;
break;
case -3:
// one bit needs to be copied in
significand |= ((currentDigit & 0x8L) >> 3);
// Now set round and start sticky, if possible
round = (currentDigit & 0x4L) != 0L;
sticky = (currentDigit & 0x3L) != 0;
break;
case -4:
// all bits copied into significand; set
// round and start sticky
round = ((currentDigit & 0x8L) != 0); // is top bit set?
// nonzeros in three low order bits?
sticky = (currentDigit & 0x7L) != 0;
break;
default:
throw new AssertionError("Unexpected shift distance remainder.");
// break;
}
// Round is set; sticky might be set.
// For the sticky bit, it suffices to check the
// current digit and test for any nonzero digits in
// the remaining unprocessed input.
i++;
while (i < signifLength && !sticky) {
currentDigit = getHexDigit(significandString, i);
sticky = sticky || (currentDigit != 0);
i++;
}
}
// else all of string was seen, round and sticky are
// correct as false.
// Float calculations
int floatBits = isNegative ? FloatConsts.SIGN_BIT_MASK : 0;
if (exponent >= FloatConsts.MIN_EXPONENT) {
if (exponent > FloatConsts.MAX_EXPONENT) {
// Float.POSITIVE_INFINITY
floatBits |= FloatConsts.EXP_BIT_MASK;
} else {
int threshShift = DoubleConsts.SIGNIFICAND_WIDTH - FloatConsts.SIGNIFICAND_WIDTH - 1;
boolean floatSticky = (significand & ((1L << threshShift) - 1)) != 0 || round || sticky;
int iValue = (int) (significand >>> threshShift);
if ((iValue & 3) != 1 || floatSticky) {
iValue++;
}
floatBits |= (((((int) exponent) + (FloatConsts.EXP_BIAS - 1))) << SINGLE_EXP_SHIFT) + (iValue >> 1);
}
} else {
if (exponent < FloatConsts.MIN_SUB_EXPONENT - 1) {
// 0
} else {
// exponent == -127 ==> threshShift = 53 - 2 + (-149) - (-127) = 53 - 24
int threshShift = (int) ((DoubleConsts.SIGNIFICAND_WIDTH - 2 + FloatConsts.MIN_SUB_EXPONENT) - exponent);
assert threshShift >= DoubleConsts.SIGNIFICAND_WIDTH - FloatConsts.SIGNIFICAND_WIDTH;
assert threshShift < DoubleConsts.SIGNIFICAND_WIDTH;
boolean floatSticky = (significand & ((1L << threshShift) - 1)) != 0 || round || sticky;
int iValue = (int) (significand >>> threshShift);
if ((iValue & 3) != 1 || floatSticky) {
iValue++;
}
floatBits |= iValue >> 1;
}
}
float fValue = Float.intBitsToFloat(floatBits);
// Check for overflow and update exponent accordingly.
if (exponent > DoubleConsts.MAX_EXPONENT) { // Infinite result
// overflow to properly signed infinity
return isNegative ? A2BC_NEGATIVE_INFINITY : A2BC_POSITIVE_INFINITY;
} else { // Finite return value
if (exponent <= DoubleConsts.MAX_EXPONENT && // (Usually) normal result
exponent >= DoubleConsts.MIN_EXPONENT) {
// The result returned in this block cannot be a
// zero or subnormal; however after the
// significand is adjusted from rounding, we could
// still overflow in infinity.
// AND exponent bits into significand; if the
// significand is incremented and overflows from
// rounding, this combination will update the
// exponent correctly, even in the case of
// Double.MAX_VALUE overflowing to infinity.
significand = ((( exponent +
(long) DoubleConsts.EXP_BIAS) <<
(DoubleConsts.SIGNIFICAND_WIDTH - 1))
& DoubleConsts.EXP_BIT_MASK) |
(DoubleConsts.SIGNIF_BIT_MASK & significand);
} else { // Subnormal or zero
// (exponent < DoubleConsts.MIN_EXPONENT)
if (exponent < (DoubleConsts.MIN_SUB_EXPONENT - 1)) {
// No way to round back to nonzero value
// regardless of significand if the exponent is
// less than -1075.
return isNegative ? A2BC_NEGATIVE_ZERO : A2BC_POSITIVE_ZERO;
} else { // -1075 <= exponent <= MIN_EXPONENT -1 = -1023
//
// Find bit position to round to; recompute
// round and sticky bits, and shift
// significand right appropriately.
//
sticky = sticky || round;
round = false;
// Number of bits of significand to preserve is
// exponent - abs_min_exp +1
// check:
// -1075 +1074 + 1 = 0
// -1023 +1074 + 1 = 52
int bitsDiscarded = 53 -
((int) exponent - DoubleConsts.MIN_SUB_EXPONENT + 1);
assert bitsDiscarded >= 1 && bitsDiscarded <= 53;
// What to do here:
// First, isolate the new round bit
round = (significand & (1L << (bitsDiscarded - 1))) != 0L;
if (bitsDiscarded > 1) {
// create mask to update sticky bits; low
// order bitsDiscarded bits should be 1
long mask = ~((~0L) << (bitsDiscarded - 1));
sticky = sticky || ((significand & mask) != 0L);
}
// Now, discard the bits
significand = significand >> bitsDiscarded;
significand = ((((long) (DoubleConsts.MIN_EXPONENT - 1) + // subnorm exp.
(long) DoubleConsts.EXP_BIAS) <<
(DoubleConsts.SIGNIFICAND_WIDTH - 1))
& DoubleConsts.EXP_BIT_MASK) |
(DoubleConsts.SIGNIF_BIT_MASK & significand);
}
}
// The significand variable now contains the currently
// appropriate exponent bits too.
//
// Determine if significand should be incremented;
// making this determination depends on the least
// significant bit and the round and sticky bits.
//
// Round to nearest even rounding table, adapted from
// table 4.7 in "Computer Arithmetic" by IsraelKoren.
// The digit to the left of the "decimal" point is the
// least significant bit, the digits to the right of
// the point are the round and sticky bits
//
// Number Round(x)
// x0.00 x0.
// x0.01 x0.
// x0.10 x0.
// x0.11 x1. = x0. +1
// x1.00 x1.
// x1.01 x1.
// x1.10 x1. + 1
// x1.11 x1. + 1
//
boolean leastZero = ((significand & 1L) == 0L);
if ((leastZero && round && sticky) ||
((!leastZero) && round)) {
significand++;
}
double value = isNegative ?
Double.longBitsToDouble(significand | DoubleConsts.SIGN_BIT_MASK) :
Double.longBitsToDouble(significand );
return new PreparedASCIIToBinaryBuffer(value, fValue);
}
}
}
/**
* Returns <code>s</code> with any leading zeros removed.
*/
static String stripLeadingZeros(String s) {
// return s.replaceFirst("^0+", "");
if(!s.isEmpty() && s.charAt(0)=='0') {
for(int i=1; i<s.length(); i++) {
if(s.charAt(i)!='0') {
return s.substring(i);
}
}
return "";
}
return s;
}
/**
* Extracts a hexadecimal digit from position <code>position</code>
* of string <code>s</code>.
*/
static int getHexDigit(String s, int position) {
int value = Character.digit(s.charAt(position), 16);
if (value <= -1 || value >= 16) {
throw new AssertionError("Unexpected failure of digit conversion of " +
s.charAt(position));
}
return value;
}
}