--- a/jdk/src/java.base/share/classes/sun/misc/FloatingDecimal.java Thu Dec 24 10:33:21 2015 -0800
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,2552 +0,0 @@
-/*
- * 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}.
- */
- 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 {
- private final 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 {
- private final double doubleVal;
- private final 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;
- }
-}