| /* |
| * Copyright (c) 1996, 2004, 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 sun.misc.FpUtils; |
| import sun.misc.DoubleConsts; |
| import sun.misc.FloatConsts; |
| import java.util.regex.*; |
| |
| public class FloatingDecimal{ |
| boolean isExceptional; |
| boolean isNegative; |
| int decExponent; |
| char digits[]; |
| int nDigits; |
| int bigIntExp; |
| int bigIntNBits; |
| boolean mustSetRoundDir = false; |
| boolean fromHex = false; |
| int roundDir = 0; // set by doubleValue |
| |
| private FloatingDecimal( boolean negSign, int decExponent, char []digits, int n, boolean e ) |
| { |
| isNegative = negSign; |
| isExceptional = e; |
| this.decExponent = decExponent; |
| this.digits = digits; |
| this.nDigits = n; |
| } |
| |
| /* |
| * 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 ) ); |
| } |
| } |
| } |
| |
| // |
| // 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; |
| } |
| |
| // |
| // 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; |
| } |
| |
| /* |
| * 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; |
| } else { |
| assert lbits != 0L : lbits; // doubleToBigInt(0.0) |
| binexp +=1; |
| while ( (lbits & fractHOB ) == 0L){ |
| lbits <<= 1; |
| binexp -= 1; |
| } |
| } |
| 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) ); |
| } |
| if ( subtracting ) ulpval = - ulpval; |
| |
| return ulpval; |
| } |
| |
| /* |
| * 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; |
| } |
| 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! |
| */ |
| 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 = (char[])(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 = (char[])(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); |
| } |
| |
| /* |
| * FIRST IMPORTANT CONSTRUCTOR: DOUBLE |
| */ |
| public FloatingDecimal( double d ) |
| { |
| long dBits = Double.doubleToLongBits( d ); |
| long fractBits; |
| int binExp; |
| int nSignificantBits; |
| |
| // 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; |
| } |
| while ( (fractBits&fractHOB) == 0L ){ |
| fractBits <<= 1; |
| binExp -= 1; |
| } |
| nSignificantBits = expShift + binExp +1; // recall binExp is - shift count. |
| binExp += 1; |
| } else { |
| fractBits |= fractHOB; |
| nSignificantBits = expShift+1; |
| } |
| binExp -= expBias; |
| // call the routine that actually does all the hard work. |
| dtoa( binExp, fractBits, nSignificantBits ); |
| } |
| |
| /* |
| * SECOND IMPORTANT CONSTRUCTOR: SINGLE |
| */ |
| public FloatingDecimal( float f ) |
| { |
| int fBits = Float.floatToIntBits( f ); |
| int fractBits; |
| int binExp; |
| int nSignificantBits; |
| |
| // discover and delete sign |
| if ( (fBits&singleSignMask) != 0 ){ |
| isNegative = true; |
| fBits ^= singleSignMask; |
| } else { |
| isNegative = false; |
| } |
| // Begin to unpack |
| // Discover obvious special cases of NaN and Infinity. |
| binExp = (int)( (fBits&singleExpMask) >> singleExpShift ); |
| fractBits = fBits&singleFractMask; |
| if ( binExp == (int)(singleExpMask>>singleExpShift) ) { |
| 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 == 0 ){ |
| // not a denorm, just a 0! |
| decExponent = 0; |
| digits = zero; |
| nDigits = 1; |
| return; |
| } |
| while ( (fractBits&singleFractHOB) == 0 ){ |
| fractBits <<= 1; |
| binExp -= 1; |
| } |
| 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); |
| } else { |
| halfULP = 0L; |
| } |
| if ( binExp >= expShift ){ |
| fractBits <<= (binExp-expShift); |
| } 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; |
| * } |
| */ |
| } |
| } |
| /* |
| * 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 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. |
| */ |
| 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 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. |
| */ |
| 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 ( 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; |
| } 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 ( 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; |
| } |
| } else { |
| FDBigInt tenSval; |
| int shiftBias; |
| |
| /* |
| * We really must do FDBigInt arithmetic. |
| * Fist, construct our FDBigInt initial values. |
| */ |
| 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 ( decExp < -3 || 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); |
| } |
| |
| public String toJavaFormatString() { |
| char result[] = (char[])(perThreadBuffer.get()); |
| int i = getChars(result); |
| return new String(result, 0, i); |
| } |
| |
| 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 (isExceptional) { |
| System.arraycopy(digits, 0, result, i, nDigits); |
| i += nDigits; |
| } else { |
| if (decExponent > 0 && decExponent < 8) { |
| // print digits.digits. |
| int charLength = Math.min(nDigits, decExponent); |
| System.arraycopy(digits, 0, result, i, charLength); |
| i += charLength; |
| if (charLength < decExponent) { |
| charLength = decExponent-charLength; |
| System.arraycopy(zero, 0, result, i, charLength); |
| i += charLength; |
| result[i++] = '.'; |
| result[i++] = '0'; |
| } else { |
| result[i++] = '.'; |
| if (charLength < nDigits) { |
| int t = nDigits - charLength; |
| System.arraycopy(digits, charLength, result, i, t); |
| i += t; |
| } else { |
| result[i++] = '0'; |
| } |
| } |
| } else if (decExponent <=0 && decExponent > -3) { |
| result[i++] = '0'; |
| result[i++] = '.'; |
| if (decExponent != 0) { |
| System.arraycopy(zero, 0, result, i, -decExponent); |
| i -= decExponent; |
| } |
| System.arraycopy(digits, 0, result, i, nDigits); |
| i += nDigits; |
| } else { |
| result[i++] = digits[0]; |
| result[i++] = '.'; |
| if (nDigits > 1) { |
| System.arraycopy(digits, 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; |
| } |
| |
| // Per-thread buffer for string/stringbuffer conversion |
| private static ThreadLocal perThreadBuffer = new ThreadLocal() { |
| protected synchronized Object initialValue() { |
| return new char[26]; |
| } |
| }; |
| |
| public void appendTo(Appendable buf) { |
| char result[] = (char[])(perThreadBuffer.get()); |
| int i = getChars(result); |
| if (buf instanceof StringBuilder) |
| ((StringBuilder) buf).append(result, 0, i); |
| else if (buf instanceof StringBuffer) |
| ((StringBuffer) buf).append(result, 0, i); |
| else |
| assert false; |
| } |
| |
| public static FloatingDecimal |
| 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 l = in.length(); |
| if ( l == 0 ) throw new NumberFormatException("empty String"); |
| int i = 0; |
| switch ( c = in.charAt( i ) ){ |
| case '-': |
| isNegative = true; |
| //FALLTHROUGH |
| case '+': |
| i++; |
| signSeen = true; |
| } |
| |
| // Check for NaN and Infinity strings |
| c = in.charAt(i); |
| if(c == 'N' || c == 'I') { // possible NaN or infinity |
| boolean potentialNaN = false; |
| char targetChars[] = null; // char array of "NaN" or "Infinity" |
| |
| if(c == 'N') { |
| targetChars = notANumber; |
| potentialNaN = true; |
| } else { |
| targetChars = infinity; |
| } |
| |
| // compare Input string to "NaN" or "Infinity" |
| int j = 0; |
| while(i < l && j < targetChars.length) { |
| if(in.charAt(i) == targetChars[j]) { |
| i++; j++; |
| } |
| else // something is amiss, throw exception |
| break parseNumber; |
| } |
| |
| // For the candidate string to be a NaN or infinity, |
| // all characters in input string and target char[] |
| // must be matched ==> j must equal targetChars.length |
| // and i must equal l |
| if( (j == targetChars.length) && (i == l) ) { // return NaN or infinity |
| return (potentialNaN ? new FloatingDecimal(Double.NaN) // NaN has no sign |
| : new FloatingDecimal(isNegative? |
| Double.NEGATIVE_INFINITY: |
| Double.POSITIVE_INFINITY)) ; |
| } |
| else { // something went wrong, throw exception |
| break parseNumber; |
| } |
| |
| } else if (c == '0') { // check for hexadecimal floating-point number |
| if (l > 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[ l ]; |
| int nDigits= 0; |
| boolean decSeen = false; |
| int decPt = 0; |
| int nLeadZero = 0; |
| int nTrailZero= 0; |
| digitLoop: |
| while ( i < l ){ |
| switch ( c = in.charAt( i ) ){ |
| case '0': |
| if ( nDigits > 0 ){ |
| nTrailZero += 1; |
| } else { |
| nLeadZero += 1; |
| } |
| break; // out of switch. |
| case '1': |
| case '2': |
| case '3': |
| case '4': |
| case '5': |
| case '6': |
| case '7': |
| case '8': |
| case '9': |
| while ( nTrailZero > 0 ){ |
| digits[nDigits++] = '0'; |
| nTrailZero -= 1; |
| } |
| digits[nDigits++] = c; |
| break; // out of switch. |
| case '.': |
| if ( decSeen ){ |
| // already saw one ., this is the 2nd. |
| throw new NumberFormatException("multiple points"); |
| } |
| decPt = i; |
| if ( signSeen ){ |
| decPt -= 1; |
| } |
| decSeen = true; |
| break; // out of switch. |
| default: |
| break digitLoop; |
| } |
| i++; |
| } |
| /* |
| * 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! |
| */ |
| if ( nDigits == 0 ){ |
| digits = zero; |
| nDigits = 1; |
| if ( 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 < l) && (((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 < l ){ |
| if ( expVal >= reallyBig ){ |
| // the next character will cause integer |
| // overflow. |
| expOverflow = true; |
| } |
| switch ( c = in.charAt(i++) ){ |
| case '0': |
| case '1': |
| case '2': |
| case '3': |
| case '4': |
| case '5': |
| case '6': |
| case '7': |
| case '8': |
| case '9': |
| expVal = expVal*10 + ( (int)c - (int)'0' ); |
| continue; |
| default: |
| i--; // back up. |
| break expLoop; // stop parsing exponent. |
| } |
| } |
| int expLimit = bigDecimalExponent+nDigits+nTrailZero; |
| if ( expOverflow || ( expVal > expLimit ) ){ |
| // |
| // 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 < l && |
| ((i != l - 1) || |
| (in.charAt(i) != 'f' && |
| in.charAt(i) != 'F' && |
| in.charAt(i) != 'd' && |
| in.charAt(i) != 'D'))) { |
| break parseNumber; // go throw exception |
| } |
| |
| return new FloatingDecimal( isNegative, decExp, digits, nDigits, false ); |
| } catch ( StringIndexOutOfBoundsException e ){ } |
| throw new NumberFormatException("For input string: \"" + in + "\""); |
| } |
| |
| /* |
| * Take a FloatingDecimal, 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 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; |
| } |
| 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 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, 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 frequency |
| 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 FloatingDecimal, 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 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 ). |
| */ |
| |
| public 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 |
| * algorithm 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' }; |
| |
| |
| /* |
| * Grammar is compatible with hexadecimal floating-point constants |
| * described in section 6.4.4.2 of the C99 specification. |
| */ |
| private static Pattern hexFloatPattern = null; |
| private static synchronized Pattern getHexFloatPattern() { |
| if (hexFloatPattern == null) { |
| hexFloatPattern = Pattern.compile( |
| //1 234 56 7 8 9 |
| "([-+])?0[xX](((\\p{XDigit}+)\\.?)|((\\p{XDigit}*)\\.(\\p{XDigit}+)))[pP]([-+])?(\\p{Digit}+)[fFdD]?" |
| ); |
| } |
| return hexFloatPattern; |
| } |
| |
| /* |
| * Convert string s to a suitable floating decimal; uses the |
| * double constructor and set the roundDir variable appropriately |
| * in case the value is later converted to a float. |
| */ |
| static FloatingDecimal parseHexString(String s) { |
| // Verify string is a member of the hexadecimal floating-point |
| // string language. |
| Matcher m = getHexFloatPattern().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); |
| double sign = (( group1 == null ) || group1.equals("+"))? 1.0 : -1.0; |
| |
| |
| // 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 new FloatingDecimal(sign * 0.0); |
| } |
| } |
| |
| // 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 new FloatingDecimal(sign * (positiveExponent ? |
| Double.POSITIVE_INFINITY : 0.0)); |
| } |
| |
| 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 bitsCopied=0; |
| 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. |
| |
| |
| // Check for overflow and update exponent accordingly. |
| |
| if (exponent > DoubleConsts.MAX_EXPONENT) { // Infinite result |
| // overflow to properly signed infinity |
| return new FloatingDecimal(sign * Double.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 = (( ((long)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 new FloatingDecimal(sign * 0.0); |
| } 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 incremented = false; |
| boolean leastZero = ((significand & 1L) == 0L); |
| if( ( leastZero && round && sticky ) || |
| ((!leastZero) && round )) { |
| incremented = true; |
| significand++; |
| } |
| |
| FloatingDecimal fd = new FloatingDecimal(FpUtils.rawCopySign( |
| Double.longBitsToDouble(significand), |
| sign)); |
| |
| /* |
| * Set roundingDir variable field of fd properly so |
| * that the input string can be properly rounded to a |
| * float value. There are two cases to consider: |
| * |
| * 1. rounding to double discards sticky bit |
| * information that would change the result of a float |
| * rounding (near halfway case between two floats) |
| * |
| * 2. rounding to double rounds up when rounding up |
| * would not occur when rounding to float. |
| * |
| * For former case only needs to be considered when |
| * the bits rounded away when casting to float are all |
| * zero; otherwise, float round bit is properly set |
| * and sticky will already be true. |
| * |
| * The lower exponent bound for the code below is the |
| * minimum (normalized) subnormal exponent - 1 since a |
| * value with that exponent can round up to the |
| * minimum subnormal value and the sticky bit |
| * information must be preserved (i.e. case 1). |
| */ |
| if ((exponent >= FloatConsts.MIN_SUB_EXPONENT-1) && |
| (exponent <= FloatConsts.MAX_EXPONENT ) ){ |
| // Outside above exponent range, the float value |
| // will be zero or infinity. |
| |
| /* |
| * If the low-order 28 bits of a rounded double |
| * significand are 0, the double could be a |
| * half-way case for a rounding to float. If the |
| * double value is a half-way case, the double |
| * significand may have to be modified to round |
| * the the right float value (see the stickyRound |
| * method). If the rounding to double has lost |
| * what would be float sticky bit information, the |
| * double significand must be incremented. If the |
| * double value's significand was itself |
| * incremented, the float value may end up too |
| * large so the increment should be undone. |
| */ |
| if ((significand & 0xfffffffL) == 0x0L) { |
| // For negative values, the sign of the |
| // roundDir is the same as for positive values |
| // since adding 1 increasing the significand's |
| // magnitude and subtracting 1 decreases the |
| // significand's magnitude. If neither round |
| // nor sticky is true, the double value is |
| // exact and no adjustment is required for a |
| // proper float rounding. |
| if( round || sticky) { |
| if (leastZero) { // prerounding lsb is 0 |
| // If round and sticky were both true, |
| // and the least significant |
| // significand bit were 0, the rounded |
| // significand would not have its |
| // low-order bits be zero. Therefore, |
| // we only need to adjust the |
| // significand if round XOR sticky is |
| // true. |
| if (round ^ sticky) { |
| fd.roundDir = 1; |
| } |
| } |
| else { // prerounding lsb is 1 |
| // If the prerounding lsb is 1 and the |
| // resulting significand has its |
| // low-order bits zero, the significand |
| // was incremented. Here, we undo the |
| // increment, which will ensure the |
| // right guard and sticky bits for the |
| // float rounding. |
| if (round) |
| fd.roundDir = -1; |
| } |
| } |
| } |
| } |
| |
| fd.fromHex = true; |
| return fd; |
| } |
| } |
| } |
| |
| /** |
| * Return <code>s</code> with any leading zeros removed. |
| */ |
| static String stripLeadingZeros(String s) { |
| return s.replaceFirst("^0+", ""); |
| } |
| |
| /** |
| * Extract 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; |
| } |
| |
| |
| } |
| |
| /* |
| * A really, really simple bigint package |
| * tailored to the needs of floating base conversion. |
| */ |
| class FDBigInt { |
| int nWords; // number of words used |
| int data[]; // value: data[0] is least significant |
| |
| |
| public FDBigInt( int v ){ |
| nWords = 1; |
| data = new int[1]; |
| data[0] = v; |
| } |
| |
| public FDBigInt( long v ){ |
| data = new int[2]; |
| data[0] = (int)v; |
| data[1] = (int)(v>>>32); |
| nWords = (data[1]==0) ? 1 : 2; |
| } |
| |
| public FDBigInt( FDBigInt other ){ |
| data = new int[nWords = other.nWords]; |
| System.arraycopy( other.data, 0, data, 0, nWords ); |
| } |
| |
| private FDBigInt( int [] d, int n ){ |
| data = d; |
| nWords = n; |
| } |
| |
| public FDBigInt( long seed, char digit[], int nd0, int nd ){ |
| int n= (nd+8)/9; // estimate size needed. |
| if ( n < 2 ) n = 2; |
| data = new int[n]; // allocate enough space |
| data[0] = (int)seed; // starting value |
| data[1] = (int)(seed>>>32); |
| nWords = (data[1]==0) ? 1 : 2; |
| int i = nd0; |
| int limit = nd-5; // slurp digits 5 at a time. |
| int v; |
| while ( i < limit ){ |
| int ilim = i+5; |
| v = (int)digit[i++]-(int)'0'; |
| while( i <ilim ){ |
| v = 10*v + (int)digit[i++]-(int)'0'; |
| } |
| multaddMe( 100000, v); // ... where 100000 is 10^5. |
| } |
| int factor = 1; |
| v = 0; |
| while ( i < nd ){ |
| v = 10*v + (int)digit[i++]-(int)'0'; |
| factor *= 10; |
| } |
| if ( factor != 1 ){ |
| multaddMe( factor, v ); |
| } |
| } |
| |
| /* |
| * Left shift by c bits. |
| * Shifts this in place. |
| */ |
| public void |
| lshiftMe( int c )throws IllegalArgumentException { |
| if ( c <= 0 ){ |
| if ( c == 0 ) |
| return; // silly. |
| else |
| throw new IllegalArgumentException("negative shift count"); |
| } |
| int wordcount = c>>5; |
| int bitcount = c & 0x1f; |
| int anticount = 32-bitcount; |
| int t[] = data; |
| int s[] = data; |
| if ( nWords+wordcount+1 > t.length ){ |
| // reallocate. |
| t = new int[ nWords+wordcount+1 ]; |
| } |
| int target = nWords+wordcount; |
| int src = nWords-1; |
| if ( bitcount == 0 ){ |
| // special hack, since an anticount of 32 won't go! |
| System.arraycopy( s, 0, t, wordcount, nWords ); |
| target = wordcount-1; |
| } else { |
| t[target--] = s[src]>>>anticount; |
| while ( src >= 1 ){ |
| t[target--] = (s[src]<<bitcount) | (s[--src]>>>anticount); |
| } |
| t[target--] = s[src]<<bitcount; |
| } |
| while( target >= 0 ){ |
| t[target--] = 0; |
| } |
| data = t; |
| nWords += wordcount + 1; |
| // may have constructed high-order word of 0. |
| // if so, trim it |
| while ( nWords > 1 && data[nWords-1] == 0 ) |
| nWords--; |
| } |
| |
| /* |
| * normalize this number by shifting until |
| * the MSB of the number is at 0x08000000. |
| * This is in preparation for quoRemIteration, below. |
| * The idea is that, to make division easier, we want the |
| * divisor to be "normalized" -- usually this means shifting |
| * the MSB into the high words sign bit. But because we know that |
| * the quotient will be 0 < q < 10, we would like to arrange that |
| * the dividend not span up into another word of precision. |
| * (This needs to be explained more clearly!) |
| */ |
| public int |
| normalizeMe() throws IllegalArgumentException { |
| int src; |
| int wordcount = 0; |
| int bitcount = 0; |
| int v = 0; |
| for ( src= nWords-1 ; src >= 0 && (v=data[src]) == 0 ; src--){ |
| wordcount += 1; |
| } |
| if ( src < 0 ){ |
| // oops. Value is zero. Cannot normalize it! |
| throw new IllegalArgumentException("zero value"); |
| } |
| /* |
| * In most cases, we assume that wordcount is zero. This only |
| * makes sense, as we try not to maintain any high-order |
| * words full of zeros. In fact, if there are zeros, we will |
| * simply SHORTEN our number at this point. Watch closely... |
| */ |
| nWords -= wordcount; |
| /* |
| * Compute how far left we have to shift v s.t. its highest- |
| * order bit is in the right place. Then call lshiftMe to |
| * do the work. |
| */ |
| if ( (v & 0xf0000000) != 0 ){ |
| // will have to shift up into the next word. |
| // too bad. |
| for( bitcount = 32 ; (v & 0xf0000000) != 0 ; bitcount-- ) |
| v >>>= 1; |
| } else { |
| while ( v <= 0x000fffff ){ |
| // hack: byte-at-a-time shifting |
| v <<= 8; |
| bitcount += 8; |
| } |
| while ( v <= 0x07ffffff ){ |
| v <<= 1; |
| bitcount += 1; |
| } |
| } |
| if ( bitcount != 0 ) |
| lshiftMe( bitcount ); |
| return bitcount; |
| } |
| |
| /* |
| * Multiply a FDBigInt by an int. |
| * Result is a new FDBigInt. |
| */ |
| public FDBigInt |
| mult( int iv ) { |
| long v = iv; |
| int r[]; |
| long p; |
| |
| // guess adequate size of r. |
| r = new int[ ( v * ((long)data[nWords-1]&0xffffffffL) > 0xfffffffL ) ? nWords+1 : nWords ]; |
| p = 0L; |
| for( int i=0; i < nWords; i++ ) { |
| p += v * ((long)data[i]&0xffffffffL); |
| r[i] = (int)p; |
| p >>>= 32; |
| } |
| if ( p == 0L){ |
| return new FDBigInt( r, nWords ); |
| } else { |
| r[nWords] = (int)p; |
| return new FDBigInt( r, nWords+1 ); |
| } |
| } |
| |
| /* |
| * Multiply a FDBigInt by an int and add another int. |
| * Result is computed in place. |
| * Hope it fits! |
| */ |
| public void |
| multaddMe( int iv, int addend ) { |
| long v = iv; |
| long p; |
| |
| // unroll 0th iteration, doing addition. |
| p = v * ((long)data[0]&0xffffffffL) + ((long)addend&0xffffffffL); |
| data[0] = (int)p; |
| p >>>= 32; |
| for( int i=1; i < nWords; i++ ) { |
| p += v * ((long)data[i]&0xffffffffL); |
| data[i] = (int)p; |
| p >>>= 32; |
| } |
| if ( p != 0L){ |
| data[nWords] = (int)p; // will fail noisily if illegal! |
| nWords++; |
| } |
| } |
| |
| /* |
| * Multiply a FDBigInt by another FDBigInt. |
| * Result is a new FDBigInt. |
| */ |
| public FDBigInt |
| mult( FDBigInt other ){ |
| // crudely guess adequate size for r |
| int r[] = new int[ nWords + other.nWords ]; |
| int i; |
| // I think I am promised zeros... |
| |
| for( i = 0; i < this.nWords; i++ ){ |
| long v = (long)this.data[i] & 0xffffffffL; // UNSIGNED CONVERSION |
| long p = 0L; |
| int j; |
| for( j = 0; j < other.nWords; j++ ){ |
| p += ((long)r[i+j]&0xffffffffL) + v*((long)other.data[j]&0xffffffffL); // UNSIGNED CONVERSIONS ALL 'ROUND. |
| r[i+j] = (int)p; |
| p >>>= 32; |
| } |
| r[i+j] = (int)p; |
| } |
| // compute how much of r we actually needed for all that. |
| for ( i = r.length-1; i> 0; i--) |
| if ( r[i] != 0 ) |
| break; |
| return new FDBigInt( r, i+1 ); |
| } |
| |
| /* |
| * Add one FDBigInt to another. Return a FDBigInt |
| */ |
| public FDBigInt |
| add( FDBigInt other ){ |
| int i; |
| int a[], b[]; |
| int n, m; |
| long c = 0L; |
| // arrange such that a.nWords >= b.nWords; |
| // n = a.nWords, m = b.nWords |
| if ( this.nWords >= other.nWords ){ |
| a = this.data; |
| n = this.nWords; |
| b = other.data; |
| m = other.nWords; |
| } else { |
| a = other.data; |
| n = other.nWords; |
| b = this.data; |
| m = this.nWords; |
| } |
| int r[] = new int[ n ]; |
| for ( i = 0; i < n; i++ ){ |
| c += (long)a[i] & 0xffffffffL; |
| if ( i < m ){ |
| c += (long)b[i] & 0xffffffffL; |
| } |
| r[i] = (int) c; |
| c >>= 32; // signed shift. |
| } |
| if ( c != 0L ){ |
| // oops -- carry out -- need longer result. |
| int s[] = new int[ r.length+1 ]; |
| System.arraycopy( r, 0, s, 0, r.length ); |
| s[i++] = (int)c; |
| return new FDBigInt( s, i ); |
| } |
| return new FDBigInt( r, i ); |
| } |
| |
| /* |
| * Subtract one FDBigInt from another. Return a FDBigInt |
| * Assert that the result is positive. |
| */ |
| public FDBigInt |
| sub( FDBigInt other ){ |
| int r[] = new int[ this.nWords ]; |
| int i; |
| int n = this.nWords; |
| int m = other.nWords; |
| int nzeros = 0; |
| long c = 0L; |
| for ( i = 0; i < n; i++ ){ |
| c += (long)this.data[i] & 0xffffffffL; |
| if ( i < m ){ |
| c -= (long)other.data[i] & 0xffffffffL; |
| } |
| if ( ( r[i] = (int) c ) == 0 ) |
| nzeros++; |
| else |
| nzeros = 0; |
| c >>= 32; // signed shift |
| } |
| assert c == 0L : c; // borrow out of subtract |
| assert dataInRangeIsZero(i, m, other); // negative result of subtract |
| return new FDBigInt( r, n-nzeros ); |
| } |
| |
| private static boolean dataInRangeIsZero(int i, int m, FDBigInt other) { |
| while ( i < m ) |
| if (other.data[i++] != 0) |
| return false; |
| return true; |
| } |
| |
| /* |
| * Compare FDBigInt with another FDBigInt. Return an integer |
| * >0: this > other |
| * 0: this == other |
| * <0: this < other |
| */ |
| public int |
| cmp( FDBigInt other ){ |
| int i; |
| if ( this.nWords > other.nWords ){ |
| // if any of my high-order words is non-zero, |
| // then the answer is evident |
| int j = other.nWords-1; |
| for ( i = this.nWords-1; i > j ; i-- ) |
| if ( this.data[i] != 0 ) return 1; |
| }else if ( this.nWords < other.nWords ){ |
| // if any of other's high-order words is non-zero, |
| // then the answer is evident |
| int j = this.nWords-1; |
| for ( i = other.nWords-1; i > j ; i-- ) |
| if ( other.data[i] != 0 ) return -1; |
| } else{ |
| i = this.nWords-1; |
| } |
| for ( ; i > 0 ; i-- ) |
| if ( this.data[i] != other.data[i] ) |
| break; |
| // careful! want unsigned compare! |
| // use brute force here. |
| int a = this.data[i]; |
| int b = other.data[i]; |
| if ( a < 0 ){ |
| // a is really big, unsigned |
| if ( b < 0 ){ |
| return a-b; // both big, negative |
| } else { |
| return 1; // b not big, answer is obvious; |
| } |
| } else { |
| // a is not really big |
| if ( b < 0 ) { |
| // but b is really big |
| return -1; |
| } else { |
| return a - b; |
| } |
| } |
| } |
| |
| /* |
| * Compute |
| * q = (int)( this / S ) |
| * this = 10 * ( this mod S ) |
| * Return q. |
| * This is the iteration step of digit development for output. |
| * We assume that S has been normalized, as above, and that |
| * "this" has been lshift'ed accordingly. |
| * Also assume, of course, that the result, q, can be expressed |
| * as an integer, 0 <= q < 10. |
| */ |
| public int |
| quoRemIteration( FDBigInt S )throws IllegalArgumentException { |
| // ensure that this and S have the same number of |
| // digits. If S is properly normalized and q < 10 then |
| // this must be so. |
| if ( nWords != S.nWords ){ |
| throw new IllegalArgumentException("disparate values"); |
| } |
| // estimate q the obvious way. We will usually be |
| // right. If not, then we're only off by a little and |
| // will re-add. |
| int n = nWords-1; |
| long q = ((long)data[n]&0xffffffffL) / (long)S.data[n]; |
| long diff = 0L; |
| for ( int i = 0; i <= n ; i++ ){ |
| diff += ((long)data[i]&0xffffffffL) - q*((long)S.data[i]&0xffffffffL); |
| data[i] = (int)diff; |
| diff >>= 32; // N.B. SIGNED shift. |
| } |
| if ( diff != 0L ) { |
| // damn, damn, damn. q is too big. |
| // add S back in until this turns +. This should |
| // not be very many times! |
| long sum = 0L; |
| while ( sum == 0L ){ |
| sum = 0L; |
| for ( int i = 0; i <= n; i++ ){ |
| sum += ((long)data[i]&0xffffffffL) + ((long)S.data[i]&0xffffffffL); |
| data[i] = (int) sum; |
| sum >>= 32; // Signed or unsigned, answer is 0 or 1 |
| } |
| /* |
| * Originally the following line read |
| * "if ( sum !=0 && sum != -1 )" |
| * but that would be wrong, because of the |
| * treatment of the two values as entirely unsigned, |
| * it would be impossible for a carry-out to be interpreted |
| * as -1 -- it would have to be a single-bit carry-out, or |
| * +1. |
| */ |
| assert sum == 0 || sum == 1 : sum; // carry out of division correction |
| q -= 1; |
| } |
| } |
| // finally, we can multiply this by 10. |
| // it cannot overflow, right, as the high-order word has |
| // at least 4 high-order zeros! |
| long p = 0L; |
| for ( int i = 0; i <= n; i++ ){ |
| p += 10*((long)data[i]&0xffffffffL); |
| data[i] = (int)p; |
| p >>= 32; // SIGNED shift. |
| } |
| assert p == 0L : p; // Carry out of *10 |
| return (int)q; |
| } |
| |
| public long |
| longValue(){ |
| // if this can be represented as a long, return the value |
| assert this.nWords > 0 : this.nWords; // longValue confused |
| |
| if (this.nWords == 1) |
| return ((long)data[0]&0xffffffffL); |
| |
| assert dataInRangeIsZero(2, this.nWords, this); // value too big |
| assert data[1] >= 0; // value too big |
| return ((long)(data[1]) << 32) | ((long)data[0]&0xffffffffL); |
| } |
| |
| public String |
| toString() { |
| StringBuffer r = new StringBuffer(30); |
| r.append('['); |
| int i = Math.min( nWords-1, data.length-1) ; |
| if ( nWords > data.length ){ |
| r.append( "("+data.length+"<"+nWords+"!)" ); |
| } |
| for( ; i> 0 ; i-- ){ |
| r.append( Integer.toHexString( data[i] ) ); |
| r.append(' '); |
| } |
| r.append( Integer.toHexString( data[0] ) ); |
| r.append(']'); |
| return new String( r ); |
| } |
| } |