src/share/classes/sun/misc/FormattedFloatingDecimal.java
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@@ -1,7 +1,7 @@
/*
- * Copyright (c) 2003, 2011, Oracle and/or its affiliates. All rights reserved.
+ * Copyright (c) 2003, 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
@@ -23,1744 +23,327 @@
* questions.
*/
package sun.misc;
-import sun.misc.DoubleConsts;
-import sun.misc.FloatConsts;
-import java.util.regex.*;
+import java.util.Arrays;
public class FormattedFloatingDecimal{
- boolean isExceptional;
- boolean isNegative;
- int decExponent; // value set at construction, then immutable
- int decExponentRounded;
- char digits[];
- int nDigits;
- int bigIntExp;
- int bigIntNBits;
- boolean mustSetRoundDir = false;
- boolean fromHex = false;
- int roundDir = 0; // set by doubleValue
- int precision; // number of digits to the right of decimal
public enum Form { SCIENTIFIC, COMPATIBLE, DECIMAL_FLOAT, GENERAL };
- private Form form;
- private FormattedFloatingDecimal( boolean negSign, int decExponent, char []digits, int n, boolean e, int precision, Form form )
- {
- isNegative = negSign;
- isExceptional = e;
- this.decExponent = decExponent;
- this.digits = digits;
- this.nDigits = n;
- this.precision = precision;
- this.form = form;
+ public static FormattedFloatingDecimal valueOf(double d, int precision, Form form){
+ FloatingDecimal.BinaryToASCIIConverter fdConverter =
+ FloatingDecimal.getBinaryToASCIIConverter(d, form == Form.COMPATIBLE);
+ return new FormattedFloatingDecimal(precision,form, fdConverter);
}
- /*
- * Constants of the implementation
- * Most are IEEE-754 related.
- * (There are more really boring constants at the end.)
- */
- static final long signMask = 0x8000000000000000L;
- static final long expMask = 0x7ff0000000000000L;
- static final long fractMask= ~(signMask|expMask);
- static final int expShift = 52;
- static final int expBias = 1023;
- static final long fractHOB = ( 1L<<expShift ); // assumed High-Order bit
- static final long expOne = ((long)expBias)<<expShift; // exponent of 1.0
- static final int maxSmallBinExp = 62;
- static final int minSmallBinExp = -( 63 / 3 );
- static final int maxDecimalDigits = 15;
- static final int maxDecimalExponent = 308;
- static final int minDecimalExponent = -324;
- static final int bigDecimalExponent = 324; // i.e. abs(minDecimalExponent)
-
- static final long highbyte = 0xff00000000000000L;
- static final long highbit = 0x8000000000000000L;
- static final long lowbytes = ~highbyte;
-
- static final int singleSignMask = 0x80000000;
- static final int singleExpMask = 0x7f800000;
- static final int singleFractMask = ~(singleSignMask|singleExpMask);
- static final int singleExpShift = 23;
- static final int singleFractHOB = 1<<singleExpShift;
- static final int singleExpBias = 127;
- static final int singleMaxDecimalDigits = 7;
- static final int singleMaxDecimalExponent = 38;
- static final int singleMinDecimalExponent = -45;
-
- static final int intDecimalDigits = 9;
-
-
- /*
- * count number of bits from high-order 1 bit to low-order 1 bit,
- * inclusive.
- */
- private static int
- countBits( long v ){
- //
- // the strategy is to shift until we get a non-zero sign bit
- // then shift until we have no bits left, counting the difference.
- // we do byte shifting as a hack. Hope it helps.
- //
- if ( v == 0L ) return 0;
-
- while ( ( v & highbyte ) == 0L ){
- v <<= 8;
- }
- while ( v > 0L ) { // i.e. while ((v&highbit) == 0L )
- v <<= 1;
- }
-
- int n = 0;
- while (( v & lowbytes ) != 0L ){
- v <<= 8;
- n += 8;
- }
- while ( v != 0L ){
- v <<= 1;
- n += 1;
- }
- return n;
- }
-
- /*
- * Keep big powers of 5 handy for future reference.
- */
- private static FDBigInt b5p[];
-
- private static synchronized FDBigInt
- big5pow( int p ){
- assert p >= 0 : p; // negative power of 5
- if ( b5p == null ){
- b5p = new FDBigInt[ p+1 ];
- }else if (b5p.length <= p ){
- FDBigInt t[] = new FDBigInt[ p+1 ];
- System.arraycopy( b5p, 0, t, 0, b5p.length );
- b5p = t;
- }
- if ( b5p[p] != null )
- return b5p[p];
- else if ( p < small5pow.length )
- return b5p[p] = new FDBigInt( small5pow[p] );
- else if ( p < long5pow.length )
- return b5p[p] = new FDBigInt( long5pow[p] );
- else {
- // construct the value.
- // recursively.
- int q, r;
- // in order to compute 5^p,
- // compute its square root, 5^(p/2) and square.
- // or, let q = p / 2, r = p -q, then
- // 5^p = 5^(q+r) = 5^q * 5^r
- q = p >> 1;
- r = p - q;
- FDBigInt bigq = b5p[q];
- if ( bigq == null )
- bigq = big5pow ( q );
- if ( r < small5pow.length ){
- return (b5p[p] = bigq.mult( small5pow[r] ) );
- }else{
- FDBigInt bigr = b5p[ r ];
- if ( bigr == null )
- bigr = big5pow( r );
- return (b5p[p] = bigq.mult( bigr ) );
- }
- }
+ private int decExponentRounded;
+ private char[] mantissa;
+ private char[] exponent;
+
+ private static final ThreadLocal<Object> threadLocalCharBuffer =
+ new ThreadLocal<Object>() {
+ @Override
+ protected Object initialValue() {
+ return new char[20];
}
+ };
- //
- // a common operation
- //
- private static FDBigInt
- multPow52( FDBigInt v, int p5, int p2 ){
- if ( p5 != 0 ){
- if ( p5 < small5pow.length ){
- v = v.mult( small5pow[p5] );
- } else {
- v = v.mult( big5pow( p5 ) );
- }
- }
- if ( p2 != 0 ){
- v.lshiftMe( p2 );
- }
- return v;
+ private static char[] getBuffer(){
+ return (char[]) threadLocalCharBuffer.get();
}
- //
- // another common operation
- //
- private static FDBigInt
- constructPow52( int p5, int p2 ){
- FDBigInt v = new FDBigInt( big5pow( p5 ) );
- if ( p2 != 0 ){
- v.lshiftMe( p2 );
- }
- return v;
+ private FormattedFloatingDecimal(int precision, Form form, FloatingDecimal.BinaryToASCIIConverter fdConverter) {
+ if (fdConverter.isExceptional()) {
+ this.mantissa = fdConverter.toJavaFormatString().toCharArray();
+ this.exponent = null;
+ return;
}
-
- /*
- * Make a floating double into a FDBigInt.
- * This could also be structured as a FDBigInt
- * constructor, but we'd have to build a lot of knowledge
- * about floating-point representation into it, and we don't want to.
- *
- * AS A SIDE EFFECT, THIS METHOD WILL SET THE INSTANCE VARIABLES
- * bigIntExp and bigIntNBits
- *
- */
- private FDBigInt
- doubleToBigInt( double dval ){
- long lbits = Double.doubleToLongBits( dval ) & ~signMask;
- int binexp = (int)(lbits >>> expShift);
- lbits &= fractMask;
- if ( binexp > 0 ){
- lbits |= fractHOB;
+ char[] digits = getBuffer();
+ int nDigits = fdConverter.getDigits(digits);
+ int decExp = fdConverter.getDecimalExponent();
+ int exp;
+ boolean isNegative = fdConverter.isNegative();
+ switch (form) {
+ case COMPATIBLE:
+ exp = decExp;
+ this.decExponentRounded = exp;
+ fillCompatible(precision, digits, nDigits, exp, isNegative);
+ break;
+ case DECIMAL_FLOAT:
+ exp = applyPrecision(decExp, digits, nDigits, decExp + precision);
+ fillDecimal(precision, digits, nDigits, exp, isNegative);
+ this.decExponentRounded = exp;
+ break;
+ case SCIENTIFIC:
+ exp = applyPrecision(decExp, digits, nDigits, precision + 1);
+ fillScientific(precision, digits, nDigits, exp, isNegative);
+ this.decExponentRounded = exp;
+ break;
+ case GENERAL:
+ exp = applyPrecision(decExp, digits, nDigits, precision);
+ // adjust precision to be the number of digits to right of decimal
+ // the real exponent to be output is actually exp - 1, not exp
+ if (exp - 1 < -4 || exp - 1 >= precision) {
+ // form = Form.SCIENTIFIC;
+ precision--;
+ fillScientific(precision, digits, nDigits, exp, isNegative);
} else {
- assert lbits != 0L : lbits; // doubleToBigInt(0.0)
- binexp +=1;
- while ( (lbits & fractHOB ) == 0L){
- lbits <<= 1;
- binexp -= 1;
+ // form = Form.DECIMAL_FLOAT;
+ precision = precision - exp;
+ fillDecimal(precision, digits, nDigits, exp, isNegative);
}
+ this.decExponentRounded = exp;
+ break;
+ default:
+ assert false;
}
- binexp -= expBias;
- int nbits = countBits( lbits );
- /*
- * We now know where the high-order 1 bit is,
- * and we know how many there are.
- */
- int lowOrderZeros = expShift+1-nbits;
- lbits >>>= lowOrderZeros;
-
- bigIntExp = binexp+1-nbits;
- bigIntNBits = nbits;
- return new FDBigInt( lbits );
}
- /*
- * Compute a number that is the ULP of the given value,
- * for purposes of addition/subtraction. Generally easy.
- * More difficult if subtracting and the argument
- * is a normalized a power of 2, as the ULP changes at these points.
- */
- private static double ulp( double dval, boolean subtracting ){
- long lbits = Double.doubleToLongBits( dval ) & ~signMask;
- int binexp = (int)(lbits >>> expShift);
- double ulpval;
- if ( subtracting && ( binexp >= expShift ) && ((lbits&fractMask) == 0L) ){
- // for subtraction from normalized, powers of 2,
- // use next-smaller exponent
- binexp -= 1;
- }
- if ( binexp > expShift ){
- ulpval = Double.longBitsToDouble( ((long)(binexp-expShift))<<expShift );
- } else if ( binexp == 0 ){
- ulpval = Double.MIN_VALUE;
- } else {
- ulpval = Double.longBitsToDouble( 1L<<(binexp-1) );
+ // returns the exponent after rounding has been done by applyPrecision
+ public int getExponentRounded() {
+ return decExponentRounded - 1;
}
- if ( subtracting ) ulpval = - ulpval;
- return ulpval;
+ public char[] getMantissa(){
+ return mantissa;
}
- /*
- * Round a double to a float.
- * In addition to the fraction bits of the double,
- * look at the class instance variable roundDir,
- * which should help us avoid double-rounding error.
- * roundDir was set in hardValueOf if the estimate was
- * close enough, but not exact. It tells us which direction
- * of rounding is preferred.
- */
- float
- stickyRound( double dval ){
- long lbits = Double.doubleToLongBits( dval );
- long binexp = lbits & expMask;
- if ( binexp == 0L || binexp == expMask ){
- // what we have here is special.
- // don't worry, the right thing will happen.
- return (float) dval;
+ public char[] getExponent(){
+ return exponent;
}
- lbits += (long)roundDir; // hack-o-matic.
- return (float)Double.longBitsToDouble( lbits );
- }
-
- /*
- * 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!
+ /**
+ * Returns new decExp in case of overflow.
*/
- private void
- developLongDigits( int decExponent, long lvalue, long insignificant ){
- char digits[];
- int ndigits;
- int digitno;
- int c;
- //
- // Discard non-significant low-order bits, while rounding,
- // up to insignificant value.
- int i;
- for ( i = 0; insignificant >= 10L; i++ )
- insignificant /= 10L;
- if ( i != 0 ){
- long pow10 = long5pow[i] << i; // 10^i == 5^i * 2^i;
- long residue = lvalue % pow10;
- lvalue /= pow10;
- decExponent += i;
- if ( residue >= (pow10>>1) ){
- // round up based on the low-order bits we're discarding
- lvalue++;
- }
- }
- 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;
- ndigits = 10;
- digits = perThreadBuffer.get();
- digitno = ndigits-1;
- 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.
- ndigits = 20;
- digits = perThreadBuffer.get();
- digitno = ndigits-1;
- 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');
- }
- char result [];
- ndigits -= digitno;
- result = new char[ ndigits ];
- System.arraycopy( digits, digitno, result, 0, ndigits );
- this.digits = result;
- this.decExponent = decExponent+1;
- this.nDigits = ndigits;
- }
-
- //
- // 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;
- int q = digits[ i = (nDigits-1)];
- if ( q == '9' ){
- while ( q == '9' && i > 0 ){
- digits[i] = '0';
- q = digits[--i];
- }
- if ( q == '9' ){
- // carryout! High-order 1, rest 0s, larger exp.
- decExponent += 1;
- digits[0] = '1';
- return;
- }
- // else fall through.
- }
- digits[i] = (char)(q+1);
- }
-
- // Given the desired number of digits predict the result's exponent.
- private int checkExponent(int length) {
- if (length >= nDigits || length < 0)
- return decExponent;
-
- for (int i = 0; i < length; i++)
- if (digits[i] != '9')
- // a '9' anywhere in digits will absorb the round
- return decExponent;
- return decExponent + (digits[length] >= '5' ? 1 : 0);
- }
-
- // Unlike roundup(), this method does not modify digits. It also
- // rounds at a particular precision.
- private char [] applyPrecision(int length) {
- char [] result = new char[nDigits];
- for (int i = 0; i < result.length; i++) result[i] = '0';
-
- if (length >= nDigits || length < 0) {
+ private static int applyPrecision(int decExp, char[] digits, int nDigits, int prec) {
+ if (prec >= nDigits || prec < 0) {
// no rounding necessary
- System.arraycopy(digits, 0, result, 0, nDigits);
- return result;
+ return decExp;
}
- if (length == 0) {
+ if (prec == 0) {
// only one digit (0 or 1) is returned because the precision
// excludes all significant digits
if (digits[0] >= '5') {
- result[0] = '1';
+ digits[0] = '1';
+ Arrays.fill(digits, 1, nDigits, '0');
+ return decExp + 1;
+ } else {
+ Arrays.fill(digits, 0, nDigits, '0');
+ return decExp;
}
- return result;
}
-
- int i = length;
- int q = digits[i];
- if (q >= '5' && i > 0) {
+ int q = digits[prec];
+ if (q >= '5') {
+ int i = prec;
q = digits[--i];
if ( q == '9' ) {
while ( q == '9' && i > 0 ){
q = digits[--i];
}
if ( q == '9' ){
// carryout! High-order 1, rest 0s, larger exp.
- result[0] = '1';
- return result;
- }
- }
- result[i] = (char)(q + 1);
- }
- while (--i >= 0) {
- result[i] = digits[i];
- }
- return result;
- }
-
- /*
- * FIRST IMPORTANT CONSTRUCTOR: DOUBLE
- */
- public FormattedFloatingDecimal( double d )
- {
- this(d, Integer.MAX_VALUE, Form.COMPATIBLE);
- }
-
- public FormattedFloatingDecimal( double d, int precision, Form form )
- {
- long dBits = Double.doubleToLongBits( d );
- long fractBits;
- int binExp;
- int nSignificantBits;
-
- this.precision = precision;
- this.form = form;
-
- // discover and delete sign
- if ( (dBits&signMask) != 0 ){
- isNegative = true;
- dBits ^= signMask;
- } else {
- isNegative = false;
- }
- // Begin to unpack
- // Discover obvious special cases of NaN and Infinity.
- binExp = (int)( (dBits&expMask) >> expShift );
- fractBits = dBits&fractMask;
- if ( binExp == (int)(expMask>>expShift) ) {
- isExceptional = true;
- if ( fractBits == 0L ){
- digits = infinity;
- } else {
- digits = notANumber;
- isNegative = false; // NaN has no sign!
- }
- nDigits = digits.length;
- return;
- }
- isExceptional = false;
- // Finish unpacking
- // Normalize denormalized numbers.
- // Insert assumed high-order bit for normalized numbers.
- // Subtract exponent bias.
- if ( binExp == 0 ){
- if ( fractBits == 0L ){
- // not a denorm, just a 0!
- decExponent = 0;
- digits = zero;
- nDigits = 1;
- return;
+ digits[0] = '1';
+ Arrays.fill(digits, 1, nDigits, '0');
+ return decExp+1;
}
- while ( (fractBits&fractHOB) == 0L ){
- fractBits <<= 1;
- binExp -= 1;
}
- nSignificantBits = expShift + binExp +1; // recall binExp is - shift count.
- binExp += 1;
+ digits[i] = (char)(q + 1);
+ Arrays.fill(digits, i+1, nDigits, '0');
} else {
- fractBits |= fractHOB;
- nSignificantBits = expShift+1;
+ Arrays.fill(digits, prec, nDigits, '0');
}
- binExp -= expBias;
- // call the routine that actually does all the hard work.
- dtoa( binExp, fractBits, nSignificantBits );
+ return decExp;
}
- /*
- * SECOND IMPORTANT CONSTRUCTOR: SINGLE
+ /**
+ * Fills mantissa and exponent char arrays for compatible format.
*/
- public FormattedFloatingDecimal( float f )
- {
- this(f, Integer.MAX_VALUE, Form.COMPATIBLE);
- }
- public FormattedFloatingDecimal( float f, int precision, Form form )
- {
- int fBits = Float.floatToIntBits( f );
- int fractBits;
- int binExp;
- int nSignificantBits;
-
- this.precision = precision;
- this.form = form;
-
- // discover and delete sign
- if ( (fBits&singleSignMask) != 0 ){
- isNegative = true;
- fBits ^= singleSignMask;
- } else {
- isNegative = false;
+ private void fillCompatible(int precision, char[] digits, int nDigits, int exp, boolean isNegative) {
+ int startIndex = isNegative ? 1 : 0;
+ if (exp > 0 && exp < 8) {
+ // print digits.digits.
+ if (nDigits < exp) {
+ int extraZeros = exp - nDigits;
+ mantissa = create(isNegative, nDigits + extraZeros + 2);
+ System.arraycopy(digits, 0, mantissa, startIndex, nDigits);
+ Arrays.fill(mantissa, startIndex + nDigits, startIndex + nDigits + extraZeros, '0');
+ mantissa[startIndex + nDigits + extraZeros] = '.';
+ mantissa[startIndex + nDigits + extraZeros+1] = '0';
+ } else if (exp < nDigits) {
+ int t = Math.min(nDigits - exp, precision);
+ mantissa = create(isNegative, exp + 1 + t);
+ System.arraycopy(digits, 0, mantissa, startIndex, exp);
+ mantissa[startIndex + exp ] = '.';
+ System.arraycopy(digits, exp, mantissa, startIndex+exp+1, t);
+ } else { // exp == digits.length
+ mantissa = create(isNegative, nDigits + 2);
+ System.arraycopy(digits, 0, mantissa, startIndex, nDigits);
+ mantissa[startIndex + nDigits ] = '.';
+ mantissa[startIndex + nDigits +1] = '0';
+ }
+ } else if (exp <= 0 && exp > -3) {
+ int zeros = Math.max(0, Math.min(-exp, precision));
+ int t = Math.max(0, Math.min(nDigits, precision + exp));
+ // write '0' s before the significant digits
+ if (zeros > 0) {
+ mantissa = create(isNegative, zeros + 2 + t);
+ mantissa[startIndex] = '0';
+ mantissa[startIndex+1] = '.';
+ Arrays.fill(mantissa, startIndex + 2, startIndex + 2 + zeros, '0');
+ if (t > 0) {
+ // copy only when significant digits are within the precision
+ System.arraycopy(digits, 0, mantissa, startIndex + 2 + zeros, t);
}
- // Begin to unpack
- // Discover obvious special cases of NaN and Infinity.
- binExp = (fBits&singleExpMask) >> singleExpShift;
- fractBits = fBits&singleFractMask;
- if ( binExp == (singleExpMask>>singleExpShift) ) {
- isExceptional = true;
- if ( fractBits == 0L ){
- digits = infinity;
+ } else if (t > 0) {
+ mantissa = create(isNegative, zeros + 2 + t);
+ mantissa[startIndex] = '0';
+ mantissa[startIndex + 1] = '.';
+ // copy only when significant digits are within the precision
+ System.arraycopy(digits, 0, mantissa, startIndex + 2, t);
} else {
- digits = notANumber;
- isNegative = false; // NaN has no sign!
- }
- nDigits = digits.length;
- return;
- }
- isExceptional = false;
- // Finish unpacking
- // Normalize denormalized numbers.
- // Insert assumed high-order bit for normalized numbers.
- // Subtract exponent bias.
- if ( binExp == 0 ){
- if ( fractBits == 0 ){
- // not a denorm, just a 0!
- decExponent = 0;
- digits = zero;
- nDigits = 1;
- return;
- }
- while ( (fractBits&singleFractHOB) == 0 ){
- fractBits <<= 1;
- binExp -= 1;
+ this.mantissa = create(isNegative, 1);
+ this.mantissa[startIndex] = '0';
}
- nSignificantBits = singleExpShift + binExp +1; // recall binExp is - shift count.
- binExp += 1;
} else {
- fractBits |= singleFractHOB;
- nSignificantBits = singleExpShift+1;
- }
- binExp -= singleExpBias;
- // call the routine that actually does all the hard work.
- dtoa( binExp, ((long)fractBits)<<(expShift-singleExpShift), nSignificantBits );
- }
-
- private void
- dtoa( int binExp, long fractBits, int nSignificantBits )
- {
- int nFractBits; // number of significant bits of fractBits;
- int nTinyBits; // number of these to the right of the point.
- int decExp;
-
- // 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.
- nFractBits = countBits( fractBits );
- nTinyBits = Math.max( 0, nFractBits - binExp - 1 );
- if ( binExp <= maxSmallBinExp && binExp >= minSmallBinExp ){
- // Look more closely at the number to decide if,
- // with scaling by 10^nTinyBits, the result will fit in
- // a long.
- if ( (nTinyBits < long5pow.length) && ((nFractBits + n5bits[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 expShift-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.
- */
- long halfULP;
- if ( nTinyBits == 0 ) {
- if ( binExp > nSignificantBits ){
- halfULP = 1L << ( binExp-nSignificantBits-1);
+ if (nDigits > 1) {
+ mantissa = create(isNegative, nDigits + 1);
+ mantissa[startIndex] = digits[0];
+ mantissa[startIndex + 1] = '.';
+ System.arraycopy(digits, 1, mantissa, startIndex + 2, nDigits - 1);
+ } else {
+ mantissa = create(isNegative, 3);
+ mantissa[startIndex] = digits[0];
+ mantissa[startIndex + 1] = '.';
+ mantissa[startIndex + 2] = '0';
+ }
+ int e, expStartIntex;
+ boolean isNegExp = (exp <= 0);
+ if (isNegExp) {
+ e = -exp + 1;
+ expStartIntex = 1;
} else {
- halfULP = 0L;
+ e = exp - 1;
+ expStartIntex = 0;
}
- if ( binExp >= expShift ){
- fractBits <<= (binExp-expShift);
+ // decExponent has 1, 2, or 3, digits
+ if (e <= 9) {
+ exponent = create(isNegExp,1);
+ exponent[expStartIntex] = (char) (e + '0');
+ } else if (e <= 99) {
+ exponent = create(isNegExp,2);
+ exponent[expStartIntex] = (char) (e / 10 + '0');
+ exponent[expStartIntex+1] = (char) (e % 10 + '0');
} else {
- fractBits >>>= (expShift-binExp) ;
- }
- developLongDigits( 0, fractBits, halfULP );
- 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 >>>= expShift+1-nFractBits;
- * fractBits *= long5pow[ nTinyBits ];
- * halfULP = long5pow[ nTinyBits ] >> (1+nSignificantBits-nFractBits);
- * developLongDigits( -nTinyBits, fractBits, halfULP );
- * return;
- * }
- */
+ exponent = create(isNegExp,3);
+ exponent[expStartIntex] = (char) (e / 100 + '0');
+ e %= 100;
+ exponent[expStartIntex+1] = (char) (e / 10 + '0');
+ exponent[expStartIntex+2] = (char) (e % 10 + '0');
}
}
- /*
- * 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.
- */
-
- /*
- * 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.
- * FIXME -- use more precise constants here. It costs no more.
- */
- double d2 = Double.longBitsToDouble(
- expOne | ( fractBits &~ fractHOB ) );
- decExp = (int)Math.floor(
- (d2-1.5D)*0.289529654D + 0.176091259 + (double)binExp * 0.301029995663981 );
- 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
- int Bbits; // binary digits needed to represent B, approx.
- int tenSbits; // binary digits needed to represent 10*S, approx.
- FDBigInt Sval, Bval, Mval;
-
- 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 (expShift+1-nFractBits) zeros. In the interest of compactness,
- * I will shift out those zeros before turning fractBits into a
- * FDBigInt. The resulting whole number will be
- * d * 2^(nFractBits-1-binExp).
- */
- fractBits >>>= (expShift+1-nFractBits);
- 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 assymetry 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.
- */
- char digits[] = this.digits = new char[18];
- 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 FDBigInt arithmetic.
- * We use the same algorithms, except that we "normalize"
- * our FDBigInts 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 assymetry 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.
- */
- Bbits = nFractBits + B2 + (( B5 < n5bits.length )? n5bits[B5] : ( B5*3 ));
- tenSbits = S2+1 + (( (S5+1) < n5bits.length )? n5bits[(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 * small5pow[B5] ) << B2;
- int s = small5pow[S5] << S2;
- int m = small5pow[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 (! (form == Form.COMPATIBLE && -3 < decExp && 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;
- } else {
- // still good! they're all longs!
- long b = (fractBits * long5pow[B5] ) << B2;
- long s = long5pow[S5] << S2;
- long m = long5pow[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 (! (form == Form.COMPATIBLE && -3 < decExp && 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 );
+ private static char[] create(boolean isNegative, int size) {
+ if(isNegative) {
+ char[] r = new char[size +1];
+ r[0] = '-';
+ return r;
} 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;
+ return new char[size];
}
- digits[ndigit++] = (char)('0' + q);
}
- lowDigitDifference = (b<<1) - tens;
- }
- } else {
- FDBigInt tenSval;
- int shiftBias;
/*
- * We really must do FDBigInt arithmetic.
- * Fist, construct our FDBigInt initial values.
+ * Fills mantissa char arrays for DECIMAL_FLOAT format.
+ * Exponent should be equal to null.
*/
- Bval = multPow52( new FDBigInt( fractBits ), B5, B2 );
- Sval = constructPow52( S5, S2 );
- Mval = constructPow52( M5, M2 );
-
-
- // normalize so that division works better
- Bval.lshiftMe( shiftBias = Sval.normalizeMe() );
- Mval.lshiftMe( shiftBias );
- tenSval = 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 );
- Mval = Mval.mult( 10 );
- low = (Bval.cmp( Mval ) < 0);
- high = (Bval.add( Mval ).cmp( tenSval ) > 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 (! (form == Form.COMPATIBLE && -3 < decExp && decExp < 8)) {
- high = low = false;
- }
- while( ! low && ! high ){
- q = Bval.quoRemIteration( Sval );
- Mval = Mval.mult( 10 );
- assert q < 10 : q; // excessively large digit
- low = (Bval.cmp( Mval ) < 0);
- high = (Bval.add( Mval ).cmp( tenSval ) > 0 );
- digits[ndigit++] = (char)('0' + q);
- }
- if ( high && low ){
- Bval.lshiftMe(1);
- lowDigitDifference = Bval.cmp(tenSval);
- } else
- lowDigitDifference = 0L; // this here only for flow analysis!
- }
- this.decExponent = decExp+1;
- this.digits = digits;
- 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[nDigits-1]&1) != 0 ) roundup();
- } else if ( lowDigitDifference > 0 ){
- roundup();
- }
- } else {
- roundup();
- }
- }
- }
-
- public String
- toString(){
- // most brain-dead version
- StringBuffer result = new StringBuffer( nDigits+8 );
- if ( isNegative ){ result.append( '-' ); }
- if ( isExceptional ){
- result.append( digits, 0, nDigits );
- } else {
- result.append( "0.");
- result.append( digits, 0, nDigits );
- result.append('e');
- result.append( decExponent );
- }
- return new String(result);
- }
-
- // returns the exponent before rounding
- public int getExponent() {
- return decExponent - 1;
- }
-
- // returns the exponent after rounding has been done by applyPrecision
- public int getExponentRounded() {
- return decExponentRounded - 1;
- }
-
- public int getChars(char[] result) {
- assert nDigits <= 19 : nDigits; // generous bound on size of nDigits
- int i = 0;
- if (isNegative) { result[0] = '-'; i = 1; }
- if (isExceptional) {
- System.arraycopy(digits, 0, result, i, nDigits);
- i += nDigits;
- } else {
- char digits [] = this.digits;
- int exp = decExponent;
- switch (form) {
- case COMPATIBLE:
- break;
- case DECIMAL_FLOAT:
- exp = checkExponent(decExponent + precision);
- digits = applyPrecision(decExponent + precision);
- break;
- case SCIENTIFIC:
- exp = checkExponent(precision + 1);
- digits = applyPrecision(precision + 1);
- break;
- case GENERAL:
- exp = checkExponent(precision);
- digits = applyPrecision(precision);
- // adjust precision to be the number of digits to right of decimal
- // the real exponent to be output is actually exp - 1, not exp
- if (exp - 1 < -4 || exp - 1 >= precision) {
- form = Form.SCIENTIFIC;
- precision--;
- } else {
- form = Form.DECIMAL_FLOAT;
- precision = precision - exp;
- }
- break;
- default:
- assert false;
- }
- decExponentRounded = exp;
-
- if (exp > 0
- && ((form == Form.COMPATIBLE && (exp < 8))
- || (form == Form.DECIMAL_FLOAT)))
- {
+ private void fillDecimal(int precision, char[] digits, int nDigits, int exp, boolean isNegative) {
+ int startIndex = isNegative ? 1 : 0;
+ if (exp > 0) {
// print digits.digits.
- int charLength = Math.min(nDigits, exp);
- System.arraycopy(digits, 0, result, i, charLength);
- i += charLength;
- if (charLength < exp) {
- charLength = exp-charLength;
- for (int nz = 0; nz < charLength; nz++)
- result[i++] = '0';
+ if (nDigits < exp) {
+ mantissa = create(isNegative,exp);
+ System.arraycopy(digits, 0, mantissa, startIndex, nDigits);
+ Arrays.fill(mantissa, startIndex + nDigits, startIndex + exp, '0');
// Do not append ".0" for formatted floats since the user
// may request that it be omitted. It is added as necessary
// by the Formatter.
- if (form == Form.COMPATIBLE) {
- result[i++] = '.';
- result[i++] = '0';
- }
} else {
+ int t = Math.min(nDigits - exp, precision);
+ mantissa = create(isNegative, exp + (t > 0 ? (t + 1) : 0));
+ System.arraycopy(digits, 0, mantissa, startIndex, exp);
// Do not append ".0" for formatted floats since the user
// may request that it be omitted. It is added as necessary
// by the Formatter.
- if (form == Form.COMPATIBLE) {
- result[i++] = '.';
- if (charLength < nDigits) {
- int t = Math.min(nDigits - charLength, precision);
- System.arraycopy(digits, charLength, result, i, t);
- i += t;
- } else {
- result[i++] = '0';
- }
- } else {
- int t = Math.min(nDigits - charLength, precision);
if (t > 0) {
- result[i++] = '.';
- System.arraycopy(digits, charLength, result, i, t);
- i += t;
+ mantissa[startIndex + exp] = '.';
+ System.arraycopy(digits, exp, mantissa, startIndex + exp + 1, t);
}
}
- }
- } else if (exp <= 0
- && ((form == Form.COMPATIBLE && exp > -3)
- || (form == Form.DECIMAL_FLOAT)))
- {
- // print 0.0* digits
- result[i++] = '0';
- if (exp != 0) {
+ } else if (exp <= 0) {
+ int zeros = Math.max(0, Math.min(-exp, precision));
+ int t = Math.max(0, Math.min(nDigits, precision + exp));
// write '0' s before the significant digits
- int t = Math.min(-exp, precision);
- if (t > 0) {
- result[i++] = '.';
- for (int nz = 0; nz < t; nz++)
- result[i++] = '0';
- }
- }
- int t = Math.min(digits.length, precision + exp);
+ if (zeros > 0) {
+ mantissa = create(isNegative, zeros + 2 + t);
+ mantissa[startIndex] = '0';
+ mantissa[startIndex+1] = '.';
+ Arrays.fill(mantissa, startIndex + 2, startIndex + 2 + zeros, '0');
if (t > 0) {
- if (i == 1)
- result[i++] = '.';
// copy only when significant digits are within the precision
- System.arraycopy(digits, 0, result, i, t);
- i += t;
+ System.arraycopy(digits, 0, mantissa, startIndex + 2 + zeros, t);
}
+ } else if (t > 0) {
+ mantissa = create(isNegative, zeros + 2 + t);
+ mantissa[startIndex] = '0';
+ mantissa[startIndex + 1] = '.';
+ // copy only when significant digits are within the precision
+ System.arraycopy(digits, 0, mantissa, startIndex + 2, t);
} else {
- result[i++] = digits[0];
- if (form == Form.COMPATIBLE) {
- result[i++] = '.';
- if (nDigits > 1) {
- System.arraycopy(digits, 1, result, i, nDigits-1);
- i += nDigits-1;
- } else {
- result[i++] = '0';
+ this.mantissa = create(isNegative, 1);
+ this.mantissa[startIndex] = '0';
}
- result[i++] = 'E';
- } else {
- if (nDigits > 1) {
- int t = Math.min(nDigits -1, precision);
- if (t > 0) {
- result[i++] = '.';
- System.arraycopy(digits, 1, result, i, t);
- i += t;
}
}
- result[i++] = 'e';
+
+ /**
+ * Fills mantissa and exponent char arrays for SCIENTIFIC format.
+ */
+ private void fillScientific(int precision, char[] digits, int nDigits, int exp, boolean isNegative) {
+ int startIndex = isNegative ? 1 : 0;
+ int t = Math.max(0, Math.min(nDigits - 1, precision));
+ if (t > 0) {
+ mantissa = create(isNegative, t + 2);
+ mantissa[startIndex] = digits[0];
+ mantissa[startIndex + 1] = '.';
+ System.arraycopy(digits, 1, mantissa, startIndex + 2, t);
+ } else {
+ mantissa = create(isNegative, 1);
+ mantissa[startIndex] = digits[0];
}
+ char expSign;
int e;
if (exp <= 0) {
- result[i++] = '-';
- e = -exp+1;
+ expSign = '-';
+ e = -exp + 1;
} else {
- if (form != Form.COMPATIBLE)
- result[i++] = '+';
- e = exp-1;
+ expSign = '+' ;
+ e = exp - 1;
}
// decExponent has 1, 2, or 3, digits
if (e <= 9) {
- if (form != Form.COMPATIBLE)
- result[i++] = '0';
- result[i++] = (char)(e+'0');
+ exponent = new char[] { expSign,
+ '0', (char) (e + '0') };
} else if (e <= 99) {
- result[i++] = (char)(e/10 +'0');
- result[i++] = (char)(e%10 + '0');
+ exponent = new char[] { expSign,
+ (char) (e / 10 + '0'), (char) (e % 10 + '0') };
} else {
- result[i++] = (char)(e/100+'0');
+ char hiExpChar = (char) (e / 100 + '0');
e %= 100;
- result[i++] = (char)(e/10+'0');
- result[i++] = (char)(e%10 + '0');
- }
- }
- }
- return i;
- }
-
- // Per-thread buffer for string/stringbuffer conversion
- private static ThreadLocal<char[]> perThreadBuffer = new ThreadLocal<char[]>() {
- protected synchronized char[] initialValue() {
- return new char[26];
- }
- };
-
- /*
- * Take a FormattedFloatingDecimal, which we presumably just scanned in,
- * and find 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.
- */
-
- public strictfp double doubleValue(){
- int kDigits = Math.min( nDigits, maxDecimalDigits+1 );
- long lValue;
- double dValue;
- double rValue, tValue;
-
- // First, check for NaN and Infinity values
- if(digits == infinity || digits == notANumber) {
- if(digits == notANumber)
- return Double.NaN;
- else
- return (isNegative?Double.NEGATIVE_INFINITY:Double.POSITIVE_INFINITY);
- }
- else {
- if (mustSetRoundDir) {
- roundDir = 0;
- }
- /*
- * 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, intDecimalDigits );
- for ( int i=1; i < iDigits; i++ ){
- iValue = iValue*10 + (int)digits[i]-(int)'0';
- }
- lValue = (long)iValue;
- for ( int i=iDigits; i < kDigits; i++ ){
- lValue = lValue*10L + (long)((int)digits[i]-(int)'0');
- }
- 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 <= maxDecimalDigits ){
- /*
- * 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 <= maxSmallTen ){
- /*
- * Can get the answer with one operation,
- * thus one roundoff.
- */
- rValue = dValue * small10pow[exp];
- if ( mustSetRoundDir ){
- tValue = rValue / small10pow[exp];
- roundDir = ( tValue == dValue ) ? 0
- :( tValue < dValue ) ? 1
- : -1;
- }
- return (isNegative)? -rValue : rValue;
- }
- int slop = maxDecimalDigits - kDigits;
- if ( exp <= maxSmallTen+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 *= small10pow[slop];
- rValue = dValue * small10pow[exp-slop];
-
- if ( mustSetRoundDir ){
- tValue = rValue / small10pow[exp-slop];
- roundDir = ( tValue == dValue ) ? 0
- :( tValue < dValue ) ? 1
- : -1;
+ exponent = new char[] { expSign,
+ hiExpChar, (char) (e / 10 + '0'), (char) (e % 10 + '0') };
}
- return (isNegative)? -rValue : rValue;
}
- /*
- * Else we have a hard case with a positive exp.
- */
- } else {
- if ( exp >= -maxSmallTen ){
- /*
- * Can get the answer in one division.
- */
- rValue = dValue / small10pow[-exp];
- tValue = rValue * small10pow[-exp];
- if ( mustSetRoundDir ){
- roundDir = ( tValue == dValue ) ? 0
- :( tValue < dValue ) ? 1
- : -1;
- }
- 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 > maxDecimalExponent+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 *= small10pow[exp&15];
- }
- if ( (exp>>=4) != 0 ){
- int j;
- for( j = 0; exp > 1; j++, exp>>=1 ){
- if ( (exp&1)!=0)
- dValue *= big10pow[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 * big10pow[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 *= big10pow[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 < minDecimalExponent-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 /= small10pow[exp&15];
- }
- if ( (exp>>=4) != 0 ){
- int j;
- for( j = 0; exp > 1; j++, exp>>=1 ){
- if ( (exp&1)!=0)
- dValue *= tiny10pow[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 * tiny10pow[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 *= tiny10pow[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 FDBigInt arithmetic.
- * Formulate the EXACT big-number result as
- * bigD0 * 10^exp
- */
- FDBigInt bigD0 = new FDBigInt( lValue, digits, kDigits, nDigits );
- exp = decExponent - nDigits;
-
- correctionLoop:
- while(true){
- /* AS A SIDE EFFECT, THIS METHOD WILL SET THE INSTANCE VARIABLES
- * bigIntExp and bigIntNBits
- */
- FDBigInt bigB = doubleToBigInt( dValue );
-
- /*
- * Scale bigD, bigB appropriately for
- * big-integer operations.
- * Naively, we multipy 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, 5 in bigB
- int D2, D5; // powers of 2, 5 in bigD
- int Ulp2; // powers of 2 in halfUlp.
- if ( exp >= 0 ){
- B2 = B5 = 0;
- D2 = D5 = exp;
- } else {
- B2 = B5 = -exp;
- D2 = D5 = 0;
- }
- 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 ( bigIntExp+bigIntNBits <= -expBias+1 ){
- // This is going to be a denormalized number
- // (if not actually zero).
- // half an ULP is at 2^-(expBias+expShift+1)
- hulpbias = bigIntExp+ expBias + expShift;
- } else {
- hulpbias = expShift + 2 - bigIntNBits;
- }
- 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
- bigB = multPow52( bigB, B5, B2 );
- FDBigInt bigD = multPow52( new FDBigInt( bigD0 ), D5, 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.
- //
- FDBigInt diff;
- int cmpResult;
- boolean overvalue;
- if ( (cmpResult = bigB.cmp( bigD ) ) > 0 ){
- overvalue = true; // our candidate is too big.
- diff = bigB.sub( bigD );
- if ( (bigIntNBits == 1) && (bigIntExp > -expBias) ){
- // candidate is a normalized exact power of 2 and
- // is too big. 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.lshiftMe( 1 );
- }
- }
- } else if ( cmpResult < 0 ){
- overvalue = false; // our candidate is too small.
- diff = bigD.sub( bigB );
- } else {
- // the candidate is exactly right!
- // this happens with surprising fequency
- break correctionLoop;
- }
- FDBigInt halfUlp = constructPow52( B5, Ulp2 );
- if ( (cmpResult = diff.cmp( halfUlp ) ) < 0 ){
- // difference is small.
- // this is close enough
- if (mustSetRoundDir) {
- roundDir = overvalue ? -1 : 1;
- }
- break correctionLoop;
- } else if ( cmpResult == 0 ){
- // difference is exactly half an ULP
- // round to some other value maybe, then finish
- dValue += 0.5*ulp( dValue, overvalue );
- // should check for bigIntNBits == 1 here??
- if (mustSetRoundDir) {
- roundDir = overvalue ? -1 : 1;
- }
- 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.
- dValue += ulp( dValue, overvalue );
- if ( dValue == 0.0 || dValue == Double.POSITIVE_INFINITY )
- break correctionLoop; // oops. Fell off end of range.
- continue; // try again.
- }
-
- }
- return (isNegative)? -dValue : dValue;
- }
- }
-
- /*
- * Take a FormattedFloatingDecimal, which we presumably just scanned in,
- * and find 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 converstion
- * 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 ).
- */
-
- public strictfp float floatValue(){
- int kDigits = Math.min( nDigits, singleMaxDecimalDigits+1 );
- int iValue;
- float fValue;
-
- // First, check for NaN and Infinity values
- if(digits == infinity || digits == notANumber) {
- if(digits == notANumber)
- return Float.NaN;
- else
- return (isNegative?Float.NEGATIVE_INFINITY:Float.POSITIVE_INFINITY);
- }
- else {
- /*
- * convert the lead kDigits to an integer.
- */
- iValue = (int)digits[0]-(int)'0';
- for ( int i=1; i < kDigits; i++ ){
- iValue = iValue*10 + (int)digits[i]-(int)'0';
- }
- 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 <= singleMaxDecimalDigits ){
- /*
- * 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 <= singleMaxSmallTen ){
- /*
- * Can get the answer with one operation,
- * thus one roundoff.
- */
- fValue *= singleSmall10pow[exp];
- return (isNegative)? -fValue : fValue;
- }
- int slop = singleMaxDecimalDigits - kDigits;
- if ( exp <= singleMaxSmallTen+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.
- */
- fValue *= singleSmall10pow[slop];
- fValue *= singleSmall10pow[exp-slop];
- return (isNegative)? -fValue : fValue;
- }
- /*
- * Else we have a hard case with a positive exp.
- */
- } else {
- if ( exp >= -singleMaxSmallTen ){
- /*
- * Can get the answer in one division.
- */
- fValue /= singleSmall10pow[-exp];
- return (isNegative)? -fValue : fValue;
- }
- /*
- * Else we have a hard case with a negative exp.
- */
- }
- } else if ( (decExponent >= nDigits) && (nDigits+decExponent <= maxDecimalDigits) ){
- /*
- * 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 *= small10pow[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 weeding out obviously out-of-range
- * results, then convert to double and go to
- * common hard-case code.
- */
- if ( decExponent > singleMaxDecimalExponent+1 ){
- /*
- * Lets face it. This is going to be
- * Infinity. Cut to the chase.
- */
- return (isNegative)? Float.NEGATIVE_INFINITY : Float.POSITIVE_INFINITY;
- } else if ( decExponent < singleMinDecimalExponent-1 ){
- /*
- * Lets face it. This is going to be
- * zero. Cut to the chase.
- */
- return (isNegative)? -0.0f : 0.0f;
- }
-
- /*
- * Here, we do 'way too much work, but throwing away
- * our partial results, and going and doing the whole
- * thing as double, then throwing away half the bits that computes
- * when we convert back to float.
- *
- * The alternative is to reproduce the whole multiple-precision
- * algorythm for float precision, or to try to parameterize it
- * for common usage. The former will take about 400 lines of code,
- * and the latter I tried without success. Thus the semi-hack
- * answer here.
- */
- mustSetRoundDir = !fromHex;
- double dValue = doubleValue();
- return stickyRound( dValue );
- }
- }
-
-
- /*
- * All the positive powers of 10 that can be
- * represented exactly in double/float.
- */
- private static final double small10pow[] = {
- 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 singleSmall10pow[] = {
- 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 big10pow[] = {
- 1e16, 1e32, 1e64, 1e128, 1e256 };
- private static final double tiny10pow[] = {
- 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
-
- private static final int maxSmallTen = small10pow.length-1;
- private static final int singleMaxSmallTen = singleSmall10pow.length-1;
-
- private static final int small5pow[] = {
- 1,
- 5,
- 5*5,
- 5*5*5,
- 5*5*5*5,
- 5*5*5*5*5,
- 5*5*5*5*5*5,
- 5*5*5*5*5*5*5,
- 5*5*5*5*5*5*5*5,
- 5*5*5*5*5*5*5*5*5,
- 5*5*5*5*5*5*5*5*5*5,
- 5*5*5*5*5*5*5*5*5*5*5,
- 5*5*5*5*5*5*5*5*5*5*5*5,
- 5*5*5*5*5*5*5*5*5*5*5*5*5
- };
-
-
- private static final long long5pow[] = {
- 1L,
- 5L,
- 5L*5,
- 5L*5*5,
- 5L*5*5*5,
- 5L*5*5*5*5,
- 5L*5*5*5*5*5,
- 5L*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5,
- 5L*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5*5,
- };
-
- // approximately ceil( log2( long5pow[i] ) )
- private static final int n5bits[] = {
- 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 static final char infinity[] = { 'I', 'n', 'f', 'i', 'n', 'i', 't', 'y' };
- private static final char notANumber[] = { 'N', 'a', 'N' };
- private static final char zero[] = { '0', '0', '0', '0', '0', '0', '0', '0' };
}