| /* |
| * Copyright (c) 1996, 2016, 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 jdk.internal.math; |
| |
| import java.util.Arrays; |
| import java.util.regex.*; |
| |
| /** |
| * A class for converting between ASCII and decimal representations of a single |
| * or double precision floating point number. Most conversions are provided via |
| * static convenience methods, although a <code>BinaryToASCIIConverter</code> |
| * instance may be obtained and reused. |
| */ |
| public class FloatingDecimal{ |
| // |
| // Constants of the implementation; |
| // most are IEEE-754 related. |
| // (There are more really boring constants at the end.) |
| // |
| static final int EXP_SHIFT = DoubleConsts.SIGNIFICAND_WIDTH - 1; |
| static final long FRACT_HOB = ( 1L<<EXP_SHIFT ); // assumed High-Order bit |
| static final long EXP_ONE = ((long)DoubleConsts.EXP_BIAS)<<EXP_SHIFT; // exponent of 1.0 |
| static final int MAX_SMALL_BIN_EXP = 62; |
| static final int MIN_SMALL_BIN_EXP = -( 63 / 3 ); |
| static final int MAX_DECIMAL_DIGITS = 15; |
| static final int MAX_DECIMAL_EXPONENT = 308; |
| static final int MIN_DECIMAL_EXPONENT = -324; |
| static final int BIG_DECIMAL_EXPONENT = 324; // i.e. abs(MIN_DECIMAL_EXPONENT) |
| static final int MAX_NDIGITS = 1100; |
| |
| static final int SINGLE_EXP_SHIFT = FloatConsts.SIGNIFICAND_WIDTH - 1; |
| static final int SINGLE_FRACT_HOB = 1<<SINGLE_EXP_SHIFT; |
| static final int SINGLE_MAX_DECIMAL_DIGITS = 7; |
| static final int SINGLE_MAX_DECIMAL_EXPONENT = 38; |
| static final int SINGLE_MIN_DECIMAL_EXPONENT = -45; |
| static final int SINGLE_MAX_NDIGITS = 200; |
| |
| static final int INT_DECIMAL_DIGITS = 9; |
| |
| /** |
| * Converts a double precision floating point value to a <code>String</code>. |
| * |
| * @param d The double precision value. |
| * @return The value converted to a <code>String</code>. |
| */ |
| public static String toJavaFormatString(double d) { |
| return getBinaryToASCIIConverter(d).toJavaFormatString(); |
| } |
| |
| /** |
| * Converts a single precision floating point value to a <code>String</code>. |
| * |
| * @param f The single precision value. |
| * @return The value converted to a <code>String</code>. |
| */ |
| public static String toJavaFormatString(float f) { |
| return getBinaryToASCIIConverter(f).toJavaFormatString(); |
| } |
| |
| /** |
| * Appends a double precision floating point value to an <code>Appendable</code>. |
| * @param d The double precision value. |
| * @param buf The <code>Appendable</code> with the value appended. |
| */ |
| public static void appendTo(double d, Appendable buf) { |
| getBinaryToASCIIConverter(d).appendTo(buf); |
| } |
| |
| /** |
| * Appends a single precision floating point value to an <code>Appendable</code>. |
| * @param f The single precision value. |
| * @param buf The <code>Appendable</code> with the value appended. |
| */ |
| public static void appendTo(float f, Appendable buf) { |
| getBinaryToASCIIConverter(f).appendTo(buf); |
| } |
| |
| /** |
| * Converts a <code>String</code> to a double precision floating point value. |
| * |
| * @param s The <code>String</code> to convert. |
| * @return The double precision value. |
| * @throws NumberFormatException If the <code>String</code> does not |
| * represent a properly formatted double precision value. |
| */ |
| public static double parseDouble(String s) throws NumberFormatException { |
| return readJavaFormatString(s).doubleValue(); |
| } |
| |
| /** |
| * Converts a <code>String</code> to a single precision floating point value. |
| * |
| * @param s The <code>String</code> to convert. |
| * @return The single precision value. |
| * @throws NumberFormatException If the <code>String</code> does not |
| * represent a properly formatted single precision value. |
| */ |
| public static float parseFloat(String s) throws NumberFormatException { |
| return readJavaFormatString(s).floatValue(); |
| } |
| |
| /** |
| * A converter which can process single or double precision floating point |
| * values into an ASCII <code>String</code> representation. |
| */ |
| public interface BinaryToASCIIConverter { |
| /** |
| * Converts a floating point value into an ASCII <code>String</code>. |
| * @return The value converted to a <code>String</code>. |
| */ |
| public String toJavaFormatString(); |
| |
| /** |
| * Appends a floating point value to an <code>Appendable</code>. |
| * @param buf The <code>Appendable</code> to receive the value. |
| */ |
| public void appendTo(Appendable buf); |
| |
| /** |
| * Retrieves the decimal exponent most closely corresponding to this value. |
| * @return The decimal exponent. |
| */ |
| public int getDecimalExponent(); |
| |
| /** |
| * Retrieves the value as an array of digits. |
| * @param digits The digit array. |
| * @return The number of valid digits copied into the array. |
| */ |
| public int getDigits(char[] digits); |
| |
| /** |
| * Indicates the sign of the value. |
| * @return {@code value < 0.0}. |
| */ |
| public boolean isNegative(); |
| |
| /** |
| * Indicates whether the value is either infinite or not a number. |
| * |
| * @return <code>true</code> if and only if the value is <code>NaN</code> |
| * or infinite. |
| */ |
| public boolean isExceptional(); |
| |
| /** |
| * Indicates whether the value was rounded up during the binary to ASCII |
| * conversion. |
| * |
| * @return <code>true</code> if and only if the value was rounded up. |
| */ |
| public boolean digitsRoundedUp(); |
| |
| /** |
| * Indicates whether the binary to ASCII conversion was exact. |
| * |
| * @return <code>true</code> if any only if the conversion was exact. |
| */ |
| public boolean decimalDigitsExact(); |
| } |
| |
| /** |
| * A <code>BinaryToASCIIConverter</code> which represents <code>NaN</code> |
| * and infinite values. |
| */ |
| private static class ExceptionalBinaryToASCIIBuffer implements BinaryToASCIIConverter { |
| private final String image; |
| private boolean isNegative; |
| |
| public ExceptionalBinaryToASCIIBuffer(String image, boolean isNegative) { |
| this.image = image; |
| this.isNegative = isNegative; |
| } |
| |
| @Override |
| public String toJavaFormatString() { |
| return image; |
| } |
| |
| @Override |
| public void appendTo(Appendable buf) { |
| if (buf instanceof StringBuilder) { |
| ((StringBuilder) buf).append(image); |
| } else if (buf instanceof StringBuffer) { |
| ((StringBuffer) buf).append(image); |
| } else { |
| assert false; |
| } |
| } |
| |
| @Override |
| public int getDecimalExponent() { |
| throw new IllegalArgumentException("Exceptional value does not have an exponent"); |
| } |
| |
| @Override |
| public int getDigits(char[] digits) { |
| throw new IllegalArgumentException("Exceptional value does not have digits"); |
| } |
| |
| @Override |
| public boolean isNegative() { |
| return isNegative; |
| } |
| |
| @Override |
| public boolean isExceptional() { |
| return true; |
| } |
| |
| @Override |
| public boolean digitsRoundedUp() { |
| throw new IllegalArgumentException("Exceptional value is not rounded"); |
| } |
| |
| @Override |
| public boolean decimalDigitsExact() { |
| throw new IllegalArgumentException("Exceptional value is not exact"); |
| } |
| } |
| |
| private static final String INFINITY_REP = "Infinity"; |
| private static final int INFINITY_LENGTH = INFINITY_REP.length(); |
| private static final String NAN_REP = "NaN"; |
| private static final int NAN_LENGTH = NAN_REP.length(); |
| |
| private static final BinaryToASCIIConverter B2AC_POSITIVE_INFINITY = new ExceptionalBinaryToASCIIBuffer(INFINITY_REP, false); |
| private static final BinaryToASCIIConverter B2AC_NEGATIVE_INFINITY = new ExceptionalBinaryToASCIIBuffer("-" + INFINITY_REP, true); |
| private static final BinaryToASCIIConverter B2AC_NOT_A_NUMBER = new ExceptionalBinaryToASCIIBuffer(NAN_REP, false); |
| private static final BinaryToASCIIConverter B2AC_POSITIVE_ZERO = new BinaryToASCIIBuffer(false, new char[]{'0'}); |
| private static final BinaryToASCIIConverter B2AC_NEGATIVE_ZERO = new BinaryToASCIIBuffer(true, new char[]{'0'}); |
| |
| /** |
| * A buffered implementation of <code>BinaryToASCIIConverter</code>. |
| */ |
| static class BinaryToASCIIBuffer implements BinaryToASCIIConverter { |
| private boolean isNegative; |
| private int decExponent; |
| private int firstDigitIndex; |
| private int nDigits; |
| private final char[] digits; |
| private final char[] buffer = new char[26]; |
| |
| // |
| // The fields below provide additional information about the result of |
| // the binary to decimal digits conversion done in dtoa() and roundup() |
| // methods. They are changed if needed by those two methods. |
| // |
| |
| // True if the dtoa() binary to decimal conversion was exact. |
| private boolean exactDecimalConversion = false; |
| |
| // True if the result of the binary to decimal conversion was rounded-up |
| // at the end of the conversion process, i.e. roundUp() method was called. |
| private boolean decimalDigitsRoundedUp = false; |
| |
| /** |
| * Default constructor; used for non-zero values, |
| * <code>BinaryToASCIIBuffer</code> may be thread-local and reused |
| */ |
| BinaryToASCIIBuffer(){ |
| this.digits = new char[20]; |
| } |
| |
| /** |
| * Creates a specialized value (positive and negative zeros). |
| */ |
| BinaryToASCIIBuffer(boolean isNegative, char[] digits){ |
| this.isNegative = isNegative; |
| this.decExponent = 0; |
| this.digits = digits; |
| this.firstDigitIndex = 0; |
| this.nDigits = digits.length; |
| } |
| |
| @Override |
| public String toJavaFormatString() { |
| int len = getChars(buffer); |
| return new String(buffer, 0, len); |
| } |
| |
| @Override |
| public void appendTo(Appendable buf) { |
| int len = getChars(buffer); |
| if (buf instanceof StringBuilder) { |
| ((StringBuilder) buf).append(buffer, 0, len); |
| } else if (buf instanceof StringBuffer) { |
| ((StringBuffer) buf).append(buffer, 0, len); |
| } else { |
| assert false; |
| } |
| } |
| |
| @Override |
| public int getDecimalExponent() { |
| return decExponent; |
| } |
| |
| @Override |
| public int getDigits(char[] digits) { |
| System.arraycopy(this.digits,firstDigitIndex,digits,0,this.nDigits); |
| return this.nDigits; |
| } |
| |
| @Override |
| public boolean isNegative() { |
| return isNegative; |
| } |
| |
| @Override |
| public boolean isExceptional() { |
| return false; |
| } |
| |
| @Override |
| public boolean digitsRoundedUp() { |
| return decimalDigitsRoundedUp; |
| } |
| |
| @Override |
| public boolean decimalDigitsExact() { |
| return exactDecimalConversion; |
| } |
| |
| private void setSign(boolean isNegative) { |
| this.isNegative = isNegative; |
| } |
| |
| /** |
| * This is the easy subcase -- |
| * all the significant bits, after scaling, are held in lvalue. |
| * negSign and decExponent tell us what processing and scaling |
| * has already been done. Exceptional cases have already been |
| * stripped out. |
| * In particular: |
| * lvalue is a finite number (not Inf, nor NaN) |
| * lvalue > 0L (not zero, nor negative). |
| * |
| * The only reason that we develop the digits here, rather than |
| * calling on Long.toString() is that we can do it a little faster, |
| * and besides want to treat trailing 0s specially. If Long.toString |
| * changes, we should re-evaluate this strategy! |
| */ |
| private void developLongDigits( int decExponent, long lvalue, int insignificantDigits ){ |
| if ( insignificantDigits != 0 ){ |
| // Discard non-significant low-order bits, while rounding, |
| // up to insignificant value. |
| long pow10 = FDBigInteger.LONG_5_POW[insignificantDigits] << insignificantDigits; // 10^i == 5^i * 2^i; |
| long residue = lvalue % pow10; |
| lvalue /= pow10; |
| decExponent += insignificantDigits; |
| if ( residue >= (pow10>>1) ){ |
| // round up based on the low-order bits we're discarding |
| lvalue++; |
| } |
| } |
| int digitno = digits.length -1; |
| int c; |
| if ( lvalue <= Integer.MAX_VALUE ){ |
| assert lvalue > 0L : lvalue; // lvalue <= 0 |
| // even easier subcase! |
| // can do int arithmetic rather than long! |
| int ivalue = (int)lvalue; |
| c = ivalue%10; |
| ivalue /= 10; |
| while ( c == 0 ){ |
| decExponent++; |
| c = ivalue%10; |
| ivalue /= 10; |
| } |
| while ( ivalue != 0){ |
| digits[digitno--] = (char)(c+'0'); |
| decExponent++; |
| c = ivalue%10; |
| ivalue /= 10; |
| } |
| digits[digitno] = (char)(c+'0'); |
| } else { |
| // same algorithm as above (same bugs, too ) |
| // but using long arithmetic. |
| c = (int)(lvalue%10L); |
| lvalue /= 10L; |
| while ( c == 0 ){ |
| decExponent++; |
| c = (int)(lvalue%10L); |
| lvalue /= 10L; |
| } |
| while ( lvalue != 0L ){ |
| digits[digitno--] = (char)(c+'0'); |
| decExponent++; |
| c = (int)(lvalue%10L); |
| lvalue /= 10; |
| } |
| digits[digitno] = (char)(c+'0'); |
| } |
| this.decExponent = decExponent+1; |
| this.firstDigitIndex = digitno; |
| this.nDigits = this.digits.length - digitno; |
| } |
| |
| private void dtoa( int binExp, long fractBits, int nSignificantBits, boolean isCompatibleFormat) |
| { |
| assert fractBits > 0 ; // fractBits here can't be zero or negative |
| assert (fractBits & FRACT_HOB)!=0 ; // Hi-order bit should be set |
| // Examine number. Determine if it is an easy case, |
| // which we can do pretty trivially using float/long conversion, |
| // or whether we must do real work. |
| final int tailZeros = Long.numberOfTrailingZeros(fractBits); |
| |
| // number of significant bits of fractBits; |
| final int nFractBits = EXP_SHIFT+1-tailZeros; |
| |
| // reset flags to default values as dtoa() does not always set these |
| // flags and a prior call to dtoa() might have set them to incorrect |
| // values with respect to the current state. |
| decimalDigitsRoundedUp = false; |
| exactDecimalConversion = false; |
| |
| // number of significant bits to the right of the point. |
| int nTinyBits = Math.max( 0, nFractBits - binExp - 1 ); |
| if ( binExp <= MAX_SMALL_BIN_EXP && binExp >= MIN_SMALL_BIN_EXP ){ |
| // Look more closely at the number to decide if, |
| // with scaling by 10^nTinyBits, the result will fit in |
| // a long. |
| if ( (nTinyBits < FDBigInteger.LONG_5_POW.length) && ((nFractBits + N_5_BITS[nTinyBits]) < 64 ) ){ |
| // |
| // We can do this: |
| // take the fraction bits, which are normalized. |
| // (a) nTinyBits == 0: Shift left or right appropriately |
| // to align the binary point at the extreme right, i.e. |
| // where a long int point is expected to be. The integer |
| // result is easily converted to a string. |
| // (b) nTinyBits > 0: Shift right by EXP_SHIFT-nFractBits, |
| // which effectively converts to long and scales by |
| // 2^nTinyBits. Then multiply by 5^nTinyBits to |
| // complete the scaling. We know this won't overflow |
| // because we just counted the number of bits necessary |
| // in the result. The integer you get from this can |
| // then be converted to a string pretty easily. |
| // |
| if ( nTinyBits == 0 ) { |
| int insignificant; |
| if ( binExp > nSignificantBits ){ |
| insignificant = insignificantDigitsForPow2(binExp-nSignificantBits-1); |
| } else { |
| insignificant = 0; |
| } |
| if ( binExp >= EXP_SHIFT ){ |
| fractBits <<= (binExp-EXP_SHIFT); |
| } else { |
| fractBits >>>= (EXP_SHIFT-binExp) ; |
| } |
| developLongDigits( 0, fractBits, insignificant ); |
| return; |
| } |
| // |
| // The following causes excess digits to be printed |
| // out in the single-float case. Our manipulation of |
| // halfULP here is apparently not correct. If we |
| // better understand how this works, perhaps we can |
| // use this special case again. But for the time being, |
| // we do not. |
| // else { |
| // fractBits >>>= EXP_SHIFT+1-nFractBits; |
| // fractBits//= long5pow[ nTinyBits ]; |
| // halfULP = long5pow[ nTinyBits ] >> (1+nSignificantBits-nFractBits); |
| // developLongDigits( -nTinyBits, fractBits, insignificantDigits(halfULP) ); |
| // return; |
| // } |
| // |
| } |
| } |
| // |
| // This is the hard case. We are going to compute large positive |
| // integers B and S and integer decExp, s.t. |
| // d = ( B / S )// 10^decExp |
| // 1 <= B / S < 10 |
| // Obvious choices are: |
| // decExp = floor( log10(d) ) |
| // B = d// 2^nTinyBits// 10^max( 0, -decExp ) |
| // S = 10^max( 0, decExp)// 2^nTinyBits |
| // (noting that nTinyBits has already been forced to non-negative) |
| // I am also going to compute a large positive integer |
| // M = (1/2^nSignificantBits)// 2^nTinyBits// 10^max( 0, -decExp ) |
| // i.e. M is (1/2) of the ULP of d, scaled like B. |
| // When we iterate through dividing B/S and picking off the |
| // quotient bits, we will know when to stop when the remainder |
| // is <= M. |
| // |
| // We keep track of powers of 2 and powers of 5. |
| // |
| int decExp = estimateDecExp(fractBits,binExp); |
| int B2, B5; // powers of 2 and powers of 5, respectively, in B |
| int S2, S5; // powers of 2 and powers of 5, respectively, in S |
| int M2, M5; // powers of 2 and powers of 5, respectively, in M |
| |
| B5 = Math.max( 0, -decExp ); |
| B2 = B5 + nTinyBits + binExp; |
| |
| S5 = Math.max( 0, decExp ); |
| S2 = S5 + nTinyBits; |
| |
| M5 = B5; |
| M2 = B2 - nSignificantBits; |
| |
| // |
| // the long integer fractBits contains the (nFractBits) interesting |
| // bits from the mantissa of d ( hidden 1 added if necessary) followed |
| // by (EXP_SHIFT+1-nFractBits) zeros. In the interest of compactness, |
| // I will shift out those zeros before turning fractBits into a |
| // FDBigInteger. The resulting whole number will be |
| // d * 2^(nFractBits-1-binExp). |
| // |
| fractBits >>>= tailZeros; |
| B2 -= nFractBits-1; |
| int common2factor = Math.min( B2, S2 ); |
| B2 -= common2factor; |
| S2 -= common2factor; |
| M2 -= common2factor; |
| |
| // |
| // HACK!! For exact powers of two, the next smallest number |
| // is only half as far away as we think (because the meaning of |
| // ULP changes at power-of-two bounds) for this reason, we |
| // hack M2. Hope this works. |
| // |
| if ( nFractBits == 1 ) { |
| M2 -= 1; |
| } |
| |
| if ( M2 < 0 ){ |
| // oops. |
| // since we cannot scale M down far enough, |
| // we must scale the other values up. |
| B2 -= M2; |
| S2 -= M2; |
| M2 = 0; |
| } |
| // |
| // Construct, Scale, iterate. |
| // Some day, we'll write a stopping test that takes |
| // account of the asymmetry of the spacing of floating-point |
| // numbers below perfect powers of 2 |
| // 26 Sept 96 is not that day. |
| // So we use a symmetric test. |
| // |
| int ndigit = 0; |
| boolean low, high; |
| long lowDigitDifference; |
| int q; |
| |
| // |
| // Detect the special cases where all the numbers we are about |
| // to compute will fit in int or long integers. |
| // In these cases, we will avoid doing FDBigInteger arithmetic. |
| // We use the same algorithms, except that we "normalize" |
| // our FDBigIntegers before iterating. This is to make division easier, |
| // as it makes our fist guess (quotient of high-order words) |
| // more accurate! |
| // |
| // Some day, we'll write a stopping test that takes |
| // account of the asymmetry of the spacing of floating-point |
| // numbers below perfect powers of 2 |
| // 26 Sept 96 is not that day. |
| // So we use a symmetric test. |
| // |
| // binary digits needed to represent B, approx. |
| int Bbits = nFractBits + B2 + (( B5 < N_5_BITS.length )? N_5_BITS[B5] : ( B5*3 )); |
| |
| // binary digits needed to represent 10*S, approx. |
| int tenSbits = S2+1 + (( (S5+1) < N_5_BITS.length )? N_5_BITS[(S5+1)] : ( (S5+1)*3 )); |
| if ( Bbits < 64 && tenSbits < 64){ |
| if ( Bbits < 32 && tenSbits < 32){ |
| // wa-hoo! They're all ints! |
| int b = ((int)fractBits * FDBigInteger.SMALL_5_POW[B5] ) << B2; |
| int s = FDBigInteger.SMALL_5_POW[S5] << S2; |
| int m = FDBigInteger.SMALL_5_POW[M5] << M2; |
| int tens = s * 10; |
| // |
| // Unroll the first iteration. If our decExp estimate |
| // was too high, our first quotient will be zero. In this |
| // case, we discard it and decrement decExp. |
| // |
| ndigit = 0; |
| q = b / s; |
| b = 10 * ( b % s ); |
| m *= 10; |
| low = (b < m ); |
| high = (b+m > tens ); |
| assert q < 10 : q; // excessively large digit |
| if ( (q == 0) && ! high ){ |
| // oops. Usually ignore leading zero. |
| decExp--; |
| } else { |
| digits[ndigit++] = (char)('0' + q); |
| } |
| // |
| // HACK! Java spec sez that we always have at least |
| // one digit after the . in either F- or E-form output. |
| // Thus we will need more than one digit if we're using |
| // E-form |
| // |
| if ( !isCompatibleFormat ||decExp < -3 || decExp >= 8 ){ |
| high = low = false; |
| } |
| while( ! low && ! high ){ |
| q = b / s; |
| b = 10 * ( b % s ); |
| m *= 10; |
| assert q < 10 : q; // excessively large digit |
| if ( m > 0L ){ |
| low = (b < m ); |
| high = (b+m > tens ); |
| } else { |
| // hack -- m might overflow! |
| // in this case, it is certainly > b, |
| // which won't |
| // and b+m > tens, too, since that has overflowed |
| // either! |
| low = true; |
| high = true; |
| } |
| digits[ndigit++] = (char)('0' + q); |
| } |
| lowDigitDifference = (b<<1) - tens; |
| exactDecimalConversion = (b == 0); |
| } else { |
| // still good! they're all longs! |
| long b = (fractBits * FDBigInteger.LONG_5_POW[B5] ) << B2; |
| long s = FDBigInteger.LONG_5_POW[S5] << S2; |
| long m = FDBigInteger.LONG_5_POW[M5] << M2; |
| long tens = s * 10L; |
| // |
| // Unroll the first iteration. If our decExp estimate |
| // was too high, our first quotient will be zero. In this |
| // case, we discard it and decrement decExp. |
| // |
| ndigit = 0; |
| q = (int) ( b / s ); |
| b = 10L * ( b % s ); |
| m *= 10L; |
| low = (b < m ); |
| high = (b+m > tens ); |
| assert q < 10 : q; // excessively large digit |
| if ( (q == 0) && ! high ){ |
| // oops. Usually ignore leading zero. |
| decExp--; |
| } else { |
| digits[ndigit++] = (char)('0' + q); |
| } |
| // |
| // HACK! Java spec sez that we always have at least |
| // one digit after the . in either F- or E-form output. |
| // Thus we will need more than one digit if we're using |
| // E-form |
| // |
| if ( !isCompatibleFormat || decExp < -3 || decExp >= 8 ){ |
| high = low = false; |
| } |
| while( ! low && ! high ){ |
| q = (int) ( b / s ); |
| b = 10 * ( b % s ); |
| m *= 10; |
| assert q < 10 : q; // excessively large digit |
| if ( m > 0L ){ |
| low = (b < m ); |
| high = (b+m > tens ); |
| } else { |
| // hack -- m might overflow! |
| // in this case, it is certainly > b, |
| // which won't |
| // and b+m > tens, too, since that has overflowed |
| // either! |
| low = true; |
| high = true; |
| } |
| digits[ndigit++] = (char)('0' + q); |
| } |
| lowDigitDifference = (b<<1) - tens; |
| exactDecimalConversion = (b == 0); |
| } |
| } else { |
| // |
| // We really must do FDBigInteger arithmetic. |
| // Fist, construct our FDBigInteger initial values. |
| // |
| FDBigInteger Sval = FDBigInteger.valueOfPow52(S5, S2); |
| int shiftBias = Sval.getNormalizationBias(); |
| Sval = Sval.leftShift(shiftBias); // normalize so that division works better |
| |
| FDBigInteger Bval = FDBigInteger.valueOfMulPow52(fractBits, B5, B2 + shiftBias); |
| FDBigInteger Mval = FDBigInteger.valueOfPow52(M5 + 1, M2 + shiftBias + 1); |
| |
| FDBigInteger tenSval = FDBigInteger.valueOfPow52(S5 + 1, S2 + shiftBias + 1); //Sval.mult( 10 ); |
| // |
| // Unroll the first iteration. If our decExp estimate |
| // was too high, our first quotient will be zero. In this |
| // case, we discard it and decrement decExp. |
| // |
| ndigit = 0; |
| q = Bval.quoRemIteration( Sval ); |
| low = (Bval.cmp( Mval ) < 0); |
| high = tenSval.addAndCmp(Bval,Mval)<=0; |
| |
| assert q < 10 : q; // excessively large digit |
| if ( (q == 0) && ! high ){ |
| // oops. Usually ignore leading zero. |
| decExp--; |
| } else { |
| digits[ndigit++] = (char)('0' + q); |
| } |
| // |
| // HACK! Java spec sez that we always have at least |
| // one digit after the . in either F- or E-form output. |
| // Thus we will need more than one digit if we're using |
| // E-form |
| // |
| if (!isCompatibleFormat || decExp < -3 || decExp >= 8 ){ |
| high = low = false; |
| } |
| while( ! low && ! high ){ |
| q = Bval.quoRemIteration( Sval ); |
| assert q < 10 : q; // excessively large digit |
| Mval = Mval.multBy10(); //Mval = Mval.mult( 10 ); |
| low = (Bval.cmp( Mval ) < 0); |
| high = tenSval.addAndCmp(Bval,Mval)<=0; |
| digits[ndigit++] = (char)('0' + q); |
| } |
| if ( high && low ){ |
| Bval = Bval.leftShift(1); |
| lowDigitDifference = Bval.cmp(tenSval); |
| } else { |
| lowDigitDifference = 0L; // this here only for flow analysis! |
| } |
| exactDecimalConversion = (Bval.cmp( FDBigInteger.ZERO ) == 0); |
| } |
| this.decExponent = decExp+1; |
| this.firstDigitIndex = 0; |
| this.nDigits = ndigit; |
| // |
| // Last digit gets rounded based on stopping condition. |
| // |
| if ( high ){ |
| if ( low ){ |
| if ( lowDigitDifference == 0L ){ |
| // it's a tie! |
| // choose based on which digits we like. |
| if ( (digits[firstDigitIndex+nDigits-1]&1) != 0 ) { |
| roundup(); |
| } |
| } else if ( lowDigitDifference > 0 ){ |
| roundup(); |
| } |
| } else { |
| roundup(); |
| } |
| } |
| } |
| |
| // add one to the least significant digit. |
| // in the unlikely event there is a carry out, deal with it. |
| // assert that this will only happen where there |
| // is only one digit, e.g. (float)1e-44 seems to do it. |
| // |
| private void roundup() { |
| int i = (firstDigitIndex + nDigits - 1); |
| int q = digits[i]; |
| if (q == '9') { |
| while (q == '9' && i > firstDigitIndex) { |
| digits[i] = '0'; |
| q = digits[--i]; |
| } |
| if (q == '9') { |
| // carryout! High-order 1, rest 0s, larger exp. |
| decExponent += 1; |
| digits[firstDigitIndex] = '1'; |
| return; |
| } |
| // else fall through. |
| } |
| digits[i] = (char) (q + 1); |
| decimalDigitsRoundedUp = true; |
| } |
| |
| /** |
| * Estimate decimal exponent. (If it is small-ish, |
| * we could double-check.) |
| * |
| * First, scale the mantissa bits such that 1 <= d2 < 2. |
| * We are then going to estimate |
| * log10(d2) ~=~ (d2-1.5)/1.5 + log(1.5) |
| * and so we can estimate |
| * log10(d) ~=~ log10(d2) + binExp * log10(2) |
| * take the floor and call it decExp. |
| */ |
| static int estimateDecExp(long fractBits, int binExp) { |
| double d2 = Double.longBitsToDouble( EXP_ONE | ( fractBits & DoubleConsts.SIGNIF_BIT_MASK ) ); |
| double d = (d2-1.5D)*0.289529654D + 0.176091259 + (double)binExp * 0.301029995663981; |
| long dBits = Double.doubleToRawLongBits(d); //can't be NaN here so use raw |
| int exponent = (int)((dBits & DoubleConsts.EXP_BIT_MASK) >> EXP_SHIFT) - DoubleConsts.EXP_BIAS; |
| boolean isNegative = (dBits & DoubleConsts.SIGN_BIT_MASK) != 0; // discover sign |
| if(exponent>=0 && exponent<52) { // hot path |
| long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent; |
| int r = (int)(( (dBits&DoubleConsts.SIGNIF_BIT_MASK) | FRACT_HOB )>>(EXP_SHIFT-exponent)); |
| return isNegative ? (((mask & dBits) == 0L ) ? -r : -r-1 ) : r; |
| } else if (exponent < 0) { |
| return (((dBits&~DoubleConsts.SIGN_BIT_MASK) == 0) ? 0 : |
| ( (isNegative) ? -1 : 0) ); |
| } else { //if (exponent >= 52) |
| return (int)d; |
| } |
| } |
| |
| private static int insignificantDigits(int insignificant) { |
| int i; |
| for ( i = 0; insignificant >= 10L; i++ ) { |
| insignificant /= 10L; |
| } |
| return i; |
| } |
| |
| /** |
| * Calculates |
| * <pre> |
| * insignificantDigitsForPow2(v) == insignificantDigits(1L<<v) |
| * </pre> |
| */ |
| private static int insignificantDigitsForPow2(int p2) { |
| if(p2>1 && p2 < insignificantDigitsNumber.length) { |
| return insignificantDigitsNumber[p2]; |
| } |
| return 0; |
| } |
| |
| /** |
| * If insignificant==(1L << ixd) |
| * i = insignificantDigitsNumber[idx] is the same as: |
| * int i; |
| * for ( i = 0; insignificant >= 10L; i++ ) |
| * insignificant /= 10L; |
| */ |
| private static int[] insignificantDigitsNumber = { |
| 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, |
| 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, |
| 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, |
| 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, |
| 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, |
| 18, 18, 18, 19 |
| }; |
| |
| // approximately ceil( log2( long5pow[i] ) ) |
| private static final int[] N_5_BITS = { |
| 0, |
| 3, |
| 5, |
| 7, |
| 10, |
| 12, |
| 14, |
| 17, |
| 19, |
| 21, |
| 24, |
| 26, |
| 28, |
| 31, |
| 33, |
| 35, |
| 38, |
| 40, |
| 42, |
| 45, |
| 47, |
| 49, |
| 52, |
| 54, |
| 56, |
| 59, |
| 61, |
| }; |
| |
| private int getChars(char[] result) { |
| assert nDigits <= 19 : nDigits; // generous bound on size of nDigits |
| int i = 0; |
| if (isNegative) { |
| result[0] = '-'; |
| i = 1; |
| } |
| if (decExponent > 0 && decExponent < 8) { |
| // print digits.digits. |
| int charLength = Math.min(nDigits, decExponent); |
| System.arraycopy(digits, firstDigitIndex, result, i, charLength); |
| i += charLength; |
| if (charLength < decExponent) { |
| charLength = decExponent - charLength; |
| Arrays.fill(result,i,i+charLength,'0'); |
| i += charLength; |
| result[i++] = '.'; |
| result[i++] = '0'; |
| } else { |
| result[i++] = '.'; |
| if (charLength < nDigits) { |
| int t = nDigits - charLength; |
| System.arraycopy(digits, firstDigitIndex+charLength, result, i, t); |
| i += t; |
| } else { |
| result[i++] = '0'; |
| } |
| } |
| } else if (decExponent <= 0 && decExponent > -3) { |
| result[i++] = '0'; |
| result[i++] = '.'; |
| if (decExponent != 0) { |
| Arrays.fill(result, i, i-decExponent, '0'); |
| i -= decExponent; |
| } |
| System.arraycopy(digits, firstDigitIndex, result, i, nDigits); |
| i += nDigits; |
| } else { |
| result[i++] = digits[firstDigitIndex]; |
| result[i++] = '.'; |
| if (nDigits > 1) { |
| System.arraycopy(digits, firstDigitIndex+1, result, i, nDigits - 1); |
| i += nDigits - 1; |
| } else { |
| result[i++] = '0'; |
| } |
| result[i++] = 'E'; |
| int e; |
| if (decExponent <= 0) { |
| result[i++] = '-'; |
| e = -decExponent + 1; |
| } else { |
| e = decExponent - 1; |
| } |
| // decExponent has 1, 2, or 3, digits |
| if (e <= 9) { |
| result[i++] = (char) (e + '0'); |
| } else if (e <= 99) { |
| result[i++] = (char) (e / 10 + '0'); |
| result[i++] = (char) (e % 10 + '0'); |
| } else { |
| result[i++] = (char) (e / 100 + '0'); |
| e %= 100; |
| result[i++] = (char) (e / 10 + '0'); |
| result[i++] = (char) (e % 10 + '0'); |
| } |
| } |
| return i; |
| } |
| |
| } |
| |
| private static final ThreadLocal<BinaryToASCIIBuffer> threadLocalBinaryToASCIIBuffer = |
| new ThreadLocal<BinaryToASCIIBuffer>() { |
| @Override |
| protected BinaryToASCIIBuffer initialValue() { |
| return new BinaryToASCIIBuffer(); |
| } |
| }; |
| |
| private static BinaryToASCIIBuffer getBinaryToASCIIBuffer() { |
| return threadLocalBinaryToASCIIBuffer.get(); |
| } |
| |
| /** |
| * A converter which can process an ASCII <code>String</code> representation |
| * of a single or double precision floating point value into a |
| * <code>float</code> or a <code>double</code>. |
| */ |
| interface ASCIIToBinaryConverter { |
| |
| double doubleValue(); |
| |
| float floatValue(); |
| |
| } |
| |
| /** |
| * A <code>ASCIIToBinaryConverter</code> container for a <code>double</code>. |
| */ |
| static class PreparedASCIIToBinaryBuffer implements ASCIIToBinaryConverter { |
| private final double doubleVal; |
| private final float floatVal; |
| |
| public PreparedASCIIToBinaryBuffer(double doubleVal, float floatVal) { |
| this.doubleVal = doubleVal; |
| this.floatVal = floatVal; |
| } |
| |
| @Override |
| public double doubleValue() { |
| return doubleVal; |
| } |
| |
| @Override |
| public float floatValue() { |
| return floatVal; |
| } |
| } |
| |
| static final ASCIIToBinaryConverter A2BC_POSITIVE_INFINITY = new PreparedASCIIToBinaryBuffer(Double.POSITIVE_INFINITY, Float.POSITIVE_INFINITY); |
| static final ASCIIToBinaryConverter A2BC_NEGATIVE_INFINITY = new PreparedASCIIToBinaryBuffer(Double.NEGATIVE_INFINITY, Float.NEGATIVE_INFINITY); |
| static final ASCIIToBinaryConverter A2BC_NOT_A_NUMBER = new PreparedASCIIToBinaryBuffer(Double.NaN, Float.NaN); |
| static final ASCIIToBinaryConverter A2BC_POSITIVE_ZERO = new PreparedASCIIToBinaryBuffer(0.0d, 0.0f); |
| static final ASCIIToBinaryConverter A2BC_NEGATIVE_ZERO = new PreparedASCIIToBinaryBuffer(-0.0d, -0.0f); |
| |
| /** |
| * A buffered implementation of <code>ASCIIToBinaryConverter</code>. |
| */ |
| static class ASCIIToBinaryBuffer implements ASCIIToBinaryConverter { |
| boolean isNegative; |
| int decExponent; |
| char digits[]; |
| int nDigits; |
| |
| ASCIIToBinaryBuffer( boolean negSign, int decExponent, char[] digits, int n) |
| { |
| this.isNegative = negSign; |
| this.decExponent = decExponent; |
| this.digits = digits; |
| this.nDigits = n; |
| } |
| |
| /** |
| * Takes a FloatingDecimal, which we presumably just scanned in, |
| * and finds out what its value is, as a double. |
| * |
| * AS A SIDE EFFECT, SET roundDir TO INDICATE PREFERRED |
| * ROUNDING DIRECTION in case the result is really destined |
| * for a single-precision float. |
| */ |
| @Override |
| public double doubleValue() { |
| int kDigits = Math.min(nDigits, MAX_DECIMAL_DIGITS + 1); |
| // |
| // convert the lead kDigits to a long integer. |
| // |
| // (special performance hack: start to do it using int) |
| int iValue = (int) digits[0] - (int) '0'; |
| int iDigits = Math.min(kDigits, INT_DECIMAL_DIGITS); |
| for (int i = 1; i < iDigits; i++) { |
| iValue = iValue * 10 + (int) digits[i] - (int) '0'; |
| } |
| long lValue = (long) iValue; |
| for (int i = iDigits; i < kDigits; i++) { |
| lValue = lValue * 10L + (long) ((int) digits[i] - (int) '0'); |
| } |
| double dValue = (double) lValue; |
| int exp = decExponent - kDigits; |
| // |
| // lValue now contains a long integer with the value of |
| // the first kDigits digits of the number. |
| // dValue contains the (double) of the same. |
| // |
| |
| if (nDigits <= MAX_DECIMAL_DIGITS) { |
| // |
| // possibly an easy case. |
| // We know that the digits can be represented |
| // exactly. And if the exponent isn't too outrageous, |
| // the whole thing can be done with one operation, |
| // thus one rounding error. |
| // Note that all our constructors trim all leading and |
| // trailing zeros, so simple values (including zero) |
| // will always end up here |
| // |
| if (exp == 0 || dValue == 0.0) { |
| return (isNegative) ? -dValue : dValue; // small floating integer |
| } |
| else if (exp >= 0) { |
| if (exp <= MAX_SMALL_TEN) { |
| // |
| // Can get the answer with one operation, |
| // thus one roundoff. |
| // |
| double rValue = dValue * SMALL_10_POW[exp]; |
| return (isNegative) ? -rValue : rValue; |
| } |
| int slop = MAX_DECIMAL_DIGITS - kDigits; |
| if (exp <= MAX_SMALL_TEN + slop) { |
| // |
| // We can multiply dValue by 10^(slop) |
| // and it is still "small" and exact. |
| // Then we can multiply by 10^(exp-slop) |
| // with one rounding. |
| // |
| dValue *= SMALL_10_POW[slop]; |
| double rValue = dValue * SMALL_10_POW[exp - slop]; |
| return (isNegative) ? -rValue : rValue; |
| } |
| // |
| // Else we have a hard case with a positive exp. |
| // |
| } else { |
| if (exp >= -MAX_SMALL_TEN) { |
| // |
| // Can get the answer in one division. |
| // |
| double rValue = dValue / SMALL_10_POW[-exp]; |
| return (isNegative) ? -rValue : rValue; |
| } |
| // |
| // Else we have a hard case with a negative exp. |
| // |
| } |
| } |
| |
| // |
| // Harder cases: |
| // The sum of digits plus exponent is greater than |
| // what we think we can do with one error. |
| // |
| // Start by approximating the right answer by, |
| // naively, scaling by powers of 10. |
| // |
| if (exp > 0) { |
| if (decExponent > MAX_DECIMAL_EXPONENT + 1) { |
| // |
| // Lets face it. This is going to be |
| // Infinity. Cut to the chase. |
| // |
| return (isNegative) ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY; |
| } |
| if ((exp & 15) != 0) { |
| dValue *= SMALL_10_POW[exp & 15]; |
| } |
| if ((exp >>= 4) != 0) { |
| int j; |
| for (j = 0; exp > 1; j++, exp >>= 1) { |
| if ((exp & 1) != 0) { |
| dValue *= BIG_10_POW[j]; |
| } |
| } |
| // |
| // The reason for the weird exp > 1 condition |
| // in the above loop was so that the last multiply |
| // would get unrolled. We handle it here. |
| // It could overflow. |
| // |
| double t = dValue * BIG_10_POW[j]; |
| if (Double.isInfinite(t)) { |
| // |
| // It did overflow. |
| // Look more closely at the result. |
| // If the exponent is just one too large, |
| // then use the maximum finite as our estimate |
| // value. Else call the result infinity |
| // and punt it. |
| // ( I presume this could happen because |
| // rounding forces the result here to be |
| // an ULP or two larger than |
| // Double.MAX_VALUE ). |
| // |
| t = dValue / 2.0; |
| t *= BIG_10_POW[j]; |
| if (Double.isInfinite(t)) { |
| return (isNegative) ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY; |
| } |
| t = Double.MAX_VALUE; |
| } |
| dValue = t; |
| } |
| } else if (exp < 0) { |
| exp = -exp; |
| if (decExponent < MIN_DECIMAL_EXPONENT - 1) { |
| // |
| // Lets face it. This is going to be |
| // zero. Cut to the chase. |
| // |
| return (isNegative) ? -0.0 : 0.0; |
| } |
| if ((exp & 15) != 0) { |
| dValue /= SMALL_10_POW[exp & 15]; |
| } |
| if ((exp >>= 4) != 0) { |
| int j; |
| for (j = 0; exp > 1; j++, exp >>= 1) { |
| if ((exp & 1) != 0) { |
| dValue *= TINY_10_POW[j]; |
| } |
| } |
| // |
| // The reason for the weird exp > 1 condition |
| // in the above loop was so that the last multiply |
| // would get unrolled. We handle it here. |
| // It could underflow. |
| // |
| double t = dValue * TINY_10_POW[j]; |
| if (t == 0.0) { |
| // |
| // It did underflow. |
| // Look more closely at the result. |
| // If the exponent is just one too small, |
| // then use the minimum finite as our estimate |
| // value. Else call the result 0.0 |
| // and punt it. |
| // ( I presume this could happen because |
| // rounding forces the result here to be |
| // an ULP or two less than |
| // Double.MIN_VALUE ). |
| // |
| t = dValue * 2.0; |
| t *= TINY_10_POW[j]; |
| if (t == 0.0) { |
| return (isNegative) ? -0.0 : 0.0; |
| } |
| t = Double.MIN_VALUE; |
| } |
| dValue = t; |
| } |
| } |
| |
| // |
| // dValue is now approximately the result. |
| // The hard part is adjusting it, by comparison |
| // with FDBigInteger arithmetic. |
| // Formulate the EXACT big-number result as |
| // bigD0 * 10^exp |
| // |
| if (nDigits > MAX_NDIGITS) { |
| nDigits = MAX_NDIGITS + 1; |
| digits[MAX_NDIGITS] = '1'; |
| } |
| FDBigInteger bigD0 = new FDBigInteger(lValue, digits, kDigits, nDigits); |
| exp = decExponent - nDigits; |
| |
| long ieeeBits = Double.doubleToRawLongBits(dValue); // IEEE-754 bits of double candidate |
| final int B5 = Math.max(0, -exp); // powers of 5 in bigB, value is not modified inside correctionLoop |
| final int D5 = Math.max(0, exp); // powers of 5 in bigD, value is not modified inside correctionLoop |
| bigD0 = bigD0.multByPow52(D5, 0); |
| bigD0.makeImmutable(); // prevent bigD0 modification inside correctionLoop |
| FDBigInteger bigD = null; |
| int prevD2 = 0; |
| |
| correctionLoop: |
| while (true) { |
| // here ieeeBits can't be NaN, Infinity or zero |
| int binexp = (int) (ieeeBits >>> EXP_SHIFT); |
| long bigBbits = ieeeBits & DoubleConsts.SIGNIF_BIT_MASK; |
| if (binexp > 0) { |
| bigBbits |= FRACT_HOB; |
| } else { // Normalize denormalized numbers. |
| assert bigBbits != 0L : bigBbits; // doubleToBigInt(0.0) |
| int leadingZeros = Long.numberOfLeadingZeros(bigBbits); |
| int shift = leadingZeros - (63 - EXP_SHIFT); |
| bigBbits <<= shift; |
| binexp = 1 - shift; |
| } |
| binexp -= DoubleConsts.EXP_BIAS; |
| int lowOrderZeros = Long.numberOfTrailingZeros(bigBbits); |
| bigBbits >>>= lowOrderZeros; |
| final int bigIntExp = binexp - EXP_SHIFT + lowOrderZeros; |
| final int bigIntNBits = EXP_SHIFT + 1 - lowOrderZeros; |
| |
| // |
| // Scale bigD, bigB appropriately for |
| // big-integer operations. |
| // Naively, we multiply by powers of ten |
| // and powers of two. What we actually do |
| // is keep track of the powers of 5 and |
| // powers of 2 we would use, then factor out |
| // common divisors before doing the work. |
| // |
| int B2 = B5; // powers of 2 in bigB |
| int D2 = D5; // powers of 2 in bigD |
| int Ulp2; // powers of 2 in halfUlp. |
| if (bigIntExp >= 0) { |
| B2 += bigIntExp; |
| } else { |
| D2 -= bigIntExp; |
| } |
| Ulp2 = B2; |
| // shift bigB and bigD left by a number s. t. |
| // halfUlp is still an integer. |
| int hulpbias; |
| if (binexp <= -DoubleConsts.EXP_BIAS) { |
| // This is going to be a denormalized number |
| // (if not actually zero). |
| // half an ULP is at 2^-(DoubleConsts.EXP_BIAS+EXP_SHIFT+1) |
| hulpbias = binexp + lowOrderZeros + DoubleConsts.EXP_BIAS; |
| } else { |
| hulpbias = 1 + lowOrderZeros; |
| } |
| B2 += hulpbias; |
| D2 += hulpbias; |
| // if there are common factors of 2, we might just as well |
| // factor them out, as they add nothing useful. |
| int common2 = Math.min(B2, Math.min(D2, Ulp2)); |
| B2 -= common2; |
| D2 -= common2; |
| Ulp2 -= common2; |
| // do multiplications by powers of 5 and 2 |
| FDBigInteger bigB = FDBigInteger.valueOfMulPow52(bigBbits, B5, B2); |
| if (bigD == null || prevD2 != D2) { |
| bigD = bigD0.leftShift(D2); |
| prevD2 = D2; |
| } |
| // |
| // to recap: |
| // bigB is the scaled-big-int version of our floating-point |
| // candidate. |
| // bigD is the scaled-big-int version of the exact value |
| // as we understand it. |
| // halfUlp is 1/2 an ulp of bigB, except for special cases |
| // of exact powers of 2 |
| // |
| // the plan is to compare bigB with bigD, and if the difference |
| // is less than halfUlp, then we're satisfied. Otherwise, |
| // use the ratio of difference to halfUlp to calculate a fudge |
| // factor to add to the floating value, then go 'round again. |
| // |
| FDBigInteger diff; |
| int cmpResult; |
| boolean overvalue; |
| if ((cmpResult = bigB.cmp(bigD)) > 0) { |
| overvalue = true; // our candidate is too big. |
| diff = bigB.leftInplaceSub(bigD); // bigB is not user further - reuse |
| if ((bigIntNBits == 1) && (bigIntExp > -DoubleConsts.EXP_BIAS + 1)) { |
| // candidate is a normalized exact power of 2 and |
| // is too big (larger than Double.MIN_NORMAL). We will be subtracting. |
| // For our purposes, ulp is the ulp of the |
| // next smaller range. |
| Ulp2 -= 1; |
| if (Ulp2 < 0) { |
| // rats. Cannot de-scale ulp this far. |
| // must scale diff in other direction. |
| Ulp2 = 0; |
| diff = diff.leftShift(1); |
| } |
| } |
| } else if (cmpResult < 0) { |
| overvalue = false; // our candidate is too small. |
| diff = bigD.rightInplaceSub(bigB); // bigB is not user further - reuse |
| } else { |
| // the candidate is exactly right! |
| // this happens with surprising frequency |
| break correctionLoop; |
| } |
| cmpResult = diff.cmpPow52(B5, Ulp2); |
| if ((cmpResult) < 0) { |
| // difference is small. |
| // this is close enough |
| break correctionLoop; |
| } else if (cmpResult == 0) { |
| // difference is exactly half an ULP |
| // round to some other value maybe, then finish |
| if ((ieeeBits & 1) != 0) { // half ties to even |
| ieeeBits += overvalue ? -1 : 1; // nextDown or nextUp |
| } |
| break correctionLoop; |
| } else { |
| // difference is non-trivial. |
| // could scale addend by ratio of difference to |
| // halfUlp here, if we bothered to compute that difference. |
| // Most of the time ( I hope ) it is about 1 anyway. |
| ieeeBits += overvalue ? -1 : 1; // nextDown or nextUp |
| if (ieeeBits == 0 || ieeeBits == DoubleConsts.EXP_BIT_MASK) { // 0.0 or Double.POSITIVE_INFINITY |
| break correctionLoop; // oops. Fell off end of range. |
| } |
| continue; // try again. |
| } |
| |
| } |
| if (isNegative) { |
| ieeeBits |= DoubleConsts.SIGN_BIT_MASK; |
| } |
| return Double.longBitsToDouble(ieeeBits); |
| } |
| |
| /** |
| * Takes a FloatingDecimal, which we presumably just scanned in, |
| * and finds out what its value is, as a float. |
| * This is distinct from doubleValue() to avoid the extremely |
| * unlikely case of a double rounding error, wherein the conversion |
| * to double has one rounding error, and the conversion of that double |
| * to a float has another rounding error, IN THE WRONG DIRECTION, |
| * ( because of the preference to a zero low-order bit ). |
| */ |
| @Override |
| public float floatValue() { |
| int kDigits = Math.min(nDigits, SINGLE_MAX_DECIMAL_DIGITS + 1); |
| // |
| // convert the lead kDigits to an integer. |
| // |
| int iValue = (int) digits[0] - (int) '0'; |
| for (int i = 1; i < kDigits; i++) { |
| iValue = iValue * 10 + (int) digits[i] - (int) '0'; |
| } |
| float fValue = (float) iValue; |
| int exp = decExponent - kDigits; |
| // |
| // iValue now contains an integer with the value of |
| // the first kDigits digits of the number. |
| // fValue contains the (float) of the same. |
| // |
| |
| if (nDigits <= SINGLE_MAX_DECIMAL_DIGITS) { |
| // |
| // possibly an easy case. |
| // We know that the digits can be represented |
| // exactly. And if the exponent isn't too outrageous, |
| // the whole thing can be done with one operation, |
| // thus one rounding error. |
| // Note that all our constructors trim all leading and |
| // trailing zeros, so simple values (including zero) |
| // will always end up here. |
| // |
| if (exp == 0 || fValue == 0.0f) { |
| return (isNegative) ? -fValue : fValue; // small floating integer |
| } else if (exp >= 0) { |
| if (exp <= SINGLE_MAX_SMALL_TEN) { |
| // |
| // Can get the answer with one operation, |
| // thus one roundoff. |
| // |
| fValue *= SINGLE_SMALL_10_POW[exp]; |
| return (isNegative) ? -fValue : fValue; |
| } |
| int slop = SINGLE_MAX_DECIMAL_DIGITS - kDigits; |
| if (exp <= SINGLE_MAX_SMALL_TEN + slop) { |
| // |
| // We can multiply fValue by 10^(slop) |
| // and it is still "small" and exact. |
| // Then we can multiply by 10^(exp-slop) |
| // with one rounding. |
| // |
| fValue *= SINGLE_SMALL_10_POW[slop]; |
| fValue *= SINGLE_SMALL_10_POW[exp - slop]; |
| return (isNegative) ? -fValue : fValue; |
| } |
| // |
| // Else we have a hard case with a positive exp. |
| // |
| } else { |
| if (exp >= -SINGLE_MAX_SMALL_TEN) { |
| // |
| // Can get the answer in one division. |
| // |
| fValue /= SINGLE_SMALL_10_POW[-exp]; |
| return (isNegative) ? -fValue : fValue; |
| } |
| // |
| // Else we have a hard case with a negative exp. |
| // |
| } |
| } else if ((decExponent >= nDigits) && (nDigits + decExponent <= MAX_DECIMAL_DIGITS)) { |
| // |
| // In double-precision, this is an exact floating integer. |
| // So we can compute to double, then shorten to float |
| // with one round, and get the right answer. |
| // |
| // First, finish accumulating digits. |
| // Then convert that integer to a double, multiply |
| // by the appropriate power of ten, and convert to float. |
| // |
| long lValue = (long) iValue; |
| for (int i = kDigits; i < nDigits; i++) { |
| lValue = lValue * 10L + (long) ((int) digits[i] - (int) '0'); |
| } |
| double dValue = (double) lValue; |
| exp = decExponent - nDigits; |
| dValue *= SMALL_10_POW[exp]; |
| fValue = (float) dValue; |
| return (isNegative) ? -fValue : fValue; |
| |
| } |
| // |
| // Harder cases: |
| // The sum of digits plus exponent is greater than |
| // what we think we can do with one error. |
| // |
| // Start by approximating the right answer by, |
| // naively, scaling by powers of 10. |
| // Scaling uses doubles to avoid overflow/underflow. |
| // |
| double dValue = fValue; |
| if (exp > 0) { |
| if (decExponent > SINGLE_MAX_DECIMAL_EXPONENT + 1) { |
| // |
| // Lets face it. This is going to be |
| // Infinity. Cut to the chase. |
| // |
| return (isNegative) ? Float.NEGATIVE_INFINITY : Float.POSITIVE_INFINITY; |
| } |
| if ((exp & 15) != 0) { |
| dValue *= SMALL_10_POW[exp & 15]; |
| } |
| if ((exp >>= 4) != 0) { |
| int j; |
| for (j = 0; exp > 0; j++, exp >>= 1) { |
| if ((exp & 1) != 0) { |
| dValue *= BIG_10_POW[j]; |
| } |
| } |
| } |
| } else if (exp < 0) { |
| exp = -exp; |
| if (decExponent < SINGLE_MIN_DECIMAL_EXPONENT - 1) { |
| // |
| // Lets face it. This is going to be |
| // zero. Cut to the chase. |
| // |
| return (isNegative) ? -0.0f : 0.0f; |
| } |
| if ((exp & 15) != 0) { |
| dValue /= SMALL_10_POW[exp & 15]; |
| } |
| if ((exp >>= 4) != 0) { |
| int j; |
| for (j = 0; exp > 0; j++, exp >>= 1) { |
| if ((exp & 1) != 0) { |
| dValue *= TINY_10_POW[j]; |
| } |
| } |
| } |
| } |
| fValue = Math.max(Float.MIN_VALUE, Math.min(Float.MAX_VALUE, (float) dValue)); |
| |
| // |
| // fValue is now approximately the result. |
| // The hard part is adjusting it, by comparison |
| // with FDBigInteger arithmetic. |
| // Formulate the EXACT big-number result as |
| // bigD0 * 10^exp |
| // |
| if (nDigits > SINGLE_MAX_NDIGITS) { |
| nDigits = SINGLE_MAX_NDIGITS + 1; |
| digits[SINGLE_MAX_NDIGITS] = '1'; |
| } |
| FDBigInteger bigD0 = new FDBigInteger(iValue, digits, kDigits, nDigits); |
| exp = decExponent - nDigits; |
| |
| int ieeeBits = Float.floatToRawIntBits(fValue); // IEEE-754 bits of float candidate |
| final int B5 = Math.max(0, -exp); // powers of 5 in bigB, value is not modified inside correctionLoop |
| final int D5 = Math.max(0, exp); // powers of 5 in bigD, value is not modified inside correctionLoop |
| bigD0 = bigD0.multByPow52(D5, 0); |
| bigD0.makeImmutable(); // prevent bigD0 modification inside correctionLoop |
| FDBigInteger bigD = null; |
| int prevD2 = 0; |
| |
| correctionLoop: |
| while (true) { |
| // here ieeeBits can't be NaN, Infinity or zero |
| int binexp = ieeeBits >>> SINGLE_EXP_SHIFT; |
| int bigBbits = ieeeBits & FloatConsts.SIGNIF_BIT_MASK; |
| if (binexp > 0) { |
| bigBbits |= SINGLE_FRACT_HOB; |
| } else { // Normalize denormalized numbers. |
| assert bigBbits != 0 : bigBbits; // floatToBigInt(0.0) |
| int leadingZeros = Integer.numberOfLeadingZeros(bigBbits); |
| int shift = leadingZeros - (31 - SINGLE_EXP_SHIFT); |
| bigBbits <<= shift; |
| binexp = 1 - shift; |
| } |
| binexp -= FloatConsts.EXP_BIAS; |
| int lowOrderZeros = Integer.numberOfTrailingZeros(bigBbits); |
| bigBbits >>>= lowOrderZeros; |
| final int bigIntExp = binexp - SINGLE_EXP_SHIFT + lowOrderZeros; |
| final int bigIntNBits = SINGLE_EXP_SHIFT + 1 - lowOrderZeros; |
| |
| // |
| // Scale bigD, bigB appropriately for |
| // big-integer operations. |
| // Naively, we multiply by powers of ten |
| // and powers of two. What we actually do |
| // is keep track of the powers of 5 and |
| // powers of 2 we would use, then factor out |
| // common divisors before doing the work. |
| // |
| int B2 = B5; // powers of 2 in bigB |
| int D2 = D5; // powers of 2 in bigD |
| int Ulp2; // powers of 2 in halfUlp. |
| if (bigIntExp >= 0) { |
| B2 += bigIntExp; |
| } else { |
| D2 -= bigIntExp; |
| } |
| Ulp2 = B2; |
| // shift bigB and bigD left by a number s. t. |
| // halfUlp is still an integer. |
| int hulpbias; |
| if (binexp <= -FloatConsts.EXP_BIAS) { |
| // This is going to be a denormalized number |
| // (if not actually zero). |
| // half an ULP is at 2^-(FloatConsts.EXP_BIAS+SINGLE_EXP_SHIFT+1) |
| hulpbias = binexp + lowOrderZeros + FloatConsts.EXP_BIAS; |
| } else { |
| hulpbias = 1 + lowOrderZeros; |
| } |
| B2 += hulpbias; |
| D2 += hulpbias; |
| // if there are common factors of 2, we might just as well |
| // factor them out, as they add nothing useful. |
| int common2 = Math.min(B2, Math.min(D2, Ulp2)); |
| B2 -= common2; |
| D2 -= common2; |
| Ulp2 -= common2; |
| // do multiplications by powers of 5 and 2 |
| FDBigInteger bigB = FDBigInteger.valueOfMulPow52(bigBbits, B5, B2); |
| if (bigD == null || prevD2 != D2) { |
| bigD = bigD0.leftShift(D2); |
| prevD2 = D2; |
| } |
| // |
| // to recap: |
| // bigB is the scaled-big-int version of our floating-point |
| // candidate. |
| // bigD is the scaled-big-int version of the exact value |
| // as we understand it. |
| // halfUlp is 1/2 an ulp of bigB, except for special cases |
| // of exact powers of 2 |
| // |
| // the plan is to compare bigB with bigD, and if the difference |
| // is less than halfUlp, then we're satisfied. Otherwise, |
| // use the ratio of difference to halfUlp to calculate a fudge |
| // factor to add to the floating value, then go 'round again. |
| // |
| FDBigInteger diff; |
| int cmpResult; |
| boolean overvalue; |
| if ((cmpResult = bigB.cmp(bigD)) > 0) { |
| overvalue = true; // our candidate is too big. |
| diff = bigB.leftInplaceSub(bigD); // bigB is not user further - reuse |
| if ((bigIntNBits == 1) && (bigIntExp > -FloatConsts.EXP_BIAS + 1)) { |
| // candidate is a normalized exact power of 2 and |
| // is too big (larger than Float.MIN_NORMAL). We will be subtracting. |
| // For our purposes, ulp is the ulp of the |
| // next smaller range. |
| Ulp2 -= 1; |
| if (Ulp2 < 0) { |
| // rats. Cannot de-scale ulp this far. |
| // must scale diff in other direction. |
| Ulp2 = 0; |
| diff = diff.leftShift(1); |
| } |
| } |
| } else if (cmpResult < 0) { |
| overvalue = false; // our candidate is too small. |
| diff = bigD.rightInplaceSub(bigB); // bigB is not user further - reuse |
| } else { |
| // the candidate is exactly right! |
| // this happens with surprising frequency |
| break correctionLoop; |
| } |
| cmpResult = diff.cmpPow52(B5, Ulp2); |
| if ((cmpResult) < 0) { |
| // difference is small. |
| // this is close enough |
| break correctionLoop; |
| } else if (cmpResult == 0) { |
| // difference is exactly half an ULP |
| // round to some other value maybe, then finish |
| if ((ieeeBits & 1) != 0) { // half ties to even |
| ieeeBits += overvalue ? -1 : 1; // nextDown or nextUp |
| } |
| break correctionLoop; |
| } else { |
| // difference is non-trivial. |
| // could scale addend by ratio of difference to |
| // halfUlp here, if we bothered to compute that difference. |
| // Most of the time ( I hope ) it is about 1 anyway. |
| ieeeBits += overvalue ? -1 : 1; // nextDown or nextUp |
| if (ieeeBits == 0 || ieeeBits == FloatConsts.EXP_BIT_MASK) { // 0.0 or Float.POSITIVE_INFINITY |
| break correctionLoop; // oops. Fell off end of range. |
| } |
| continue; // try again. |
| } |
| |
| } |
| if (isNegative) { |
| ieeeBits |= FloatConsts.SIGN_BIT_MASK; |
| } |
| return Float.intBitsToFloat(ieeeBits); |
| } |
| |
| |
| /** |
| * All the positive powers of 10 that can be |
| * represented exactly in double/float. |
| */ |
| private static final double[] SMALL_10_POW = { |
| 1.0e0, |
| 1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5, |
| 1.0e6, 1.0e7, 1.0e8, 1.0e9, 1.0e10, |
| 1.0e11, 1.0e12, 1.0e13, 1.0e14, 1.0e15, |
| 1.0e16, 1.0e17, 1.0e18, 1.0e19, 1.0e20, |
| 1.0e21, 1.0e22 |
| }; |
| |
| private static final float[] SINGLE_SMALL_10_POW = { |
| 1.0e0f, |
| 1.0e1f, 1.0e2f, 1.0e3f, 1.0e4f, 1.0e5f, |
| 1.0e6f, 1.0e7f, 1.0e8f, 1.0e9f, 1.0e10f |
| }; |
| |
| private static final double[] BIG_10_POW = { |
| 1e16, 1e32, 1e64, 1e128, 1e256 }; |
| private static final double[] TINY_10_POW = { |
| 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 }; |
| |
| private static final int MAX_SMALL_TEN = SMALL_10_POW.length-1; |
| private static final int SINGLE_MAX_SMALL_TEN = SINGLE_SMALL_10_POW.length-1; |
| |
| } |
| |
| /** |
| * Returns a <code>BinaryToASCIIConverter</code> for a <code>double</code>. |
| * The returned object is a <code>ThreadLocal</code> variable of this class. |
| * |
| * @param d The double precision value to convert. |
| * @return The converter. |
| */ |
| public static BinaryToASCIIConverter getBinaryToASCIIConverter(double d) { |
| return getBinaryToASCIIConverter(d, true); |
| } |
| |
| /** |
| * Returns a <code>BinaryToASCIIConverter</code> for a <code>double</code>. |
| * The returned object is a <code>ThreadLocal</code> variable of this class. |
| * |
| * @param d The double precision value to convert. |
| * @param isCompatibleFormat |
| * @return The converter. |
| */ |
| static BinaryToASCIIConverter getBinaryToASCIIConverter(double d, boolean isCompatibleFormat) { |
| long dBits = Double.doubleToRawLongBits(d); |
| boolean isNegative = (dBits&DoubleConsts.SIGN_BIT_MASK) != 0; // discover sign |
| long fractBits = dBits & DoubleConsts.SIGNIF_BIT_MASK; |
| int binExp = (int)( (dBits&DoubleConsts.EXP_BIT_MASK) >> EXP_SHIFT ); |
| // Discover obvious special cases of NaN and Infinity. |
| if ( binExp == (int)(DoubleConsts.EXP_BIT_MASK>>EXP_SHIFT) ) { |
| if ( fractBits == 0L ){ |
| return isNegative ? B2AC_NEGATIVE_INFINITY : B2AC_POSITIVE_INFINITY; |
| } else { |
| return B2AC_NOT_A_NUMBER; |
| } |
| } |
| // Finish unpacking |
| // Normalize denormalized numbers. |
| // Insert assumed high-order bit for normalized numbers. |
| // Subtract exponent bias. |
| int nSignificantBits; |
| if ( binExp == 0 ){ |
| if ( fractBits == 0L ){ |
| // not a denorm, just a 0! |
| return isNegative ? B2AC_NEGATIVE_ZERO : B2AC_POSITIVE_ZERO; |
| } |
| int leadingZeros = Long.numberOfLeadingZeros(fractBits); |
| int shift = leadingZeros-(63-EXP_SHIFT); |
| fractBits <<= shift; |
| binExp = 1 - shift; |
| nSignificantBits = 64-leadingZeros; // recall binExp is - shift count. |
| } else { |
| fractBits |= FRACT_HOB; |
| nSignificantBits = EXP_SHIFT+1; |
| } |
| binExp -= DoubleConsts.EXP_BIAS; |
| BinaryToASCIIBuffer buf = getBinaryToASCIIBuffer(); |
| buf.setSign(isNegative); |
| // call the routine that actually does all the hard work. |
| buf.dtoa(binExp, fractBits, nSignificantBits, isCompatibleFormat); |
| return buf; |
| } |
| |
| private static BinaryToASCIIConverter getBinaryToASCIIConverter(float f) { |
| int fBits = Float.floatToRawIntBits( f ); |
| boolean isNegative = (fBits&FloatConsts.SIGN_BIT_MASK) != 0; |
| int fractBits = fBits&FloatConsts.SIGNIF_BIT_MASK; |
| int binExp = (fBits&FloatConsts.EXP_BIT_MASK) >> SINGLE_EXP_SHIFT; |
| // Discover obvious special cases of NaN and Infinity. |
| if ( binExp == (FloatConsts.EXP_BIT_MASK>>SINGLE_EXP_SHIFT) ) { |
| if ( fractBits == 0L ){ |
| return isNegative ? B2AC_NEGATIVE_INFINITY : B2AC_POSITIVE_INFINITY; |
| } else { |
| return B2AC_NOT_A_NUMBER; |
| } |
| } |
| // Finish unpacking |
| // Normalize denormalized numbers. |
| // Insert assumed high-order bit for normalized numbers. |
| // Subtract exponent bias. |
| int nSignificantBits; |
| if ( binExp == 0 ){ |
| if ( fractBits == 0 ){ |
| // not a denorm, just a 0! |
| return isNegative ? B2AC_NEGATIVE_ZERO : B2AC_POSITIVE_ZERO; |
| } |
| int leadingZeros = Integer.numberOfLeadingZeros(fractBits); |
| int shift = leadingZeros-(31-SINGLE_EXP_SHIFT); |
| fractBits <<= shift; |
| binExp = 1 - shift; |
| nSignificantBits = 32 - leadingZeros; // recall binExp is - shift count. |
| } else { |
| fractBits |= SINGLE_FRACT_HOB; |
| nSignificantBits = SINGLE_EXP_SHIFT+1; |
| } |
| binExp -= FloatConsts.EXP_BIAS; |
| BinaryToASCIIBuffer buf = getBinaryToASCIIBuffer(); |
| buf.setSign(isNegative); |
| // call the routine that actually does all the hard work. |
| buf.dtoa(binExp, ((long)fractBits)<<(EXP_SHIFT-SINGLE_EXP_SHIFT), nSignificantBits, true); |
| return buf; |
| } |
| |
| @SuppressWarnings("fallthrough") |
| static ASCIIToBinaryConverter readJavaFormatString( String in ) throws NumberFormatException { |
| boolean isNegative = false; |
| boolean signSeen = false; |
| int decExp; |
| char c; |
| |
| parseNumber: |
| try{ |
| in = in.trim(); // don't fool around with white space. |
| // throws NullPointerException if null |
| int len = in.length(); |
| if ( len == 0 ) { |
| throw new NumberFormatException("empty String"); |
| } |
| int i = 0; |
| switch (in.charAt(i)){ |
| case '-': |
| isNegative = true; |
| //FALLTHROUGH |
| case '+': |
| i++; |
| signSeen = true; |
| } |
| c = in.charAt(i); |
| if(c == 'N') { // Check for NaN |
| if((len-i)==NAN_LENGTH && in.indexOf(NAN_REP,i)==i) { |
| return A2BC_NOT_A_NUMBER; |
| } |
| // something went wrong, throw exception |
| break parseNumber; |
| } else if(c == 'I') { // Check for Infinity strings |
| if((len-i)==INFINITY_LENGTH && in.indexOf(INFINITY_REP,i)==i) { |
| return isNegative? A2BC_NEGATIVE_INFINITY : A2BC_POSITIVE_INFINITY; |
| } |
| // something went wrong, throw exception |
| break parseNumber; |
| } else if (c == '0') { // check for hexadecimal floating-point number |
| if (len > i+1 ) { |
| char ch = in.charAt(i+1); |
| if (ch == 'x' || ch == 'X' ) { // possible hex string |
| return parseHexString(in); |
| } |
| } |
| } // look for and process decimal floating-point string |
| |
| char[] digits = new char[ len ]; |
| int nDigits= 0; |
| boolean decSeen = false; |
| int decPt = 0; |
| int nLeadZero = 0; |
| int nTrailZero= 0; |
| |
| skipLeadingZerosLoop: |
| while (i < len) { |
| c = in.charAt(i); |
| if (c == '0') { |
| nLeadZero++; |
| } else if (c == '.') { |
| if (decSeen) { |
| // already saw one ., this is the 2nd. |
| throw new NumberFormatException("multiple points"); |
| } |
| decPt = i; |
| if (signSeen) { |
| decPt -= 1; |
| } |
| decSeen = true; |
| } else { |
| break skipLeadingZerosLoop; |
| } |
| i++; |
| } |
| digitLoop: |
| while (i < len) { |
| c = in.charAt(i); |
| if (c >= '1' && c <= '9') { |
| digits[nDigits++] = c; |
| nTrailZero = 0; |
| } else if (c == '0') { |
| digits[nDigits++] = c; |
| nTrailZero++; |
| } else if (c == '.') { |
| if (decSeen) { |
| // already saw one ., this is the 2nd. |
| throw new NumberFormatException("multiple points"); |
| } |
| decPt = i; |
| if (signSeen) { |
| decPt -= 1; |
| } |
| decSeen = true; |
| } else { |
| break digitLoop; |
| } |
| i++; |
| } |
| nDigits -=nTrailZero; |
| // |
| // At this point, we've scanned all the digits and decimal |
| // point we're going to see. Trim off leading and trailing |
| // zeros, which will just confuse us later, and adjust |
| // our initial decimal exponent accordingly. |
| // To review: |
| // we have seen i total characters. |
| // nLeadZero of them were zeros before any other digits. |
| // nTrailZero of them were zeros after any other digits. |
| // if ( decSeen ), then a . was seen after decPt characters |
| // ( including leading zeros which have been discarded ) |
| // nDigits characters were neither lead nor trailing |
| // zeros, nor point |
| // |
| // |
| // special hack: if we saw no non-zero digits, then the |
| // answer is zero! |
| // Unfortunately, we feel honor-bound to keep parsing! |
| // |
| boolean isZero = (nDigits == 0); |
| if ( isZero && nLeadZero == 0 ){ |
| // we saw NO DIGITS AT ALL, |
| // not even a crummy 0! |
| // this is not allowed. |
| break parseNumber; // go throw exception |
| } |
| // |
| // Our initial exponent is decPt, adjusted by the number of |
| // discarded zeros. Or, if there was no decPt, |
| // then its just nDigits adjusted by discarded trailing zeros. |
| // |
| if ( decSeen ){ |
| decExp = decPt - nLeadZero; |
| } else { |
| decExp = nDigits + nTrailZero; |
| } |
| |
| // |
| // Look for 'e' or 'E' and an optionally signed integer. |
| // |
| if ( (i < len) && (((c = in.charAt(i) )=='e') || (c == 'E') ) ){ |
| int expSign = 1; |
| int expVal = 0; |
| int reallyBig = Integer.MAX_VALUE / 10; |
| boolean expOverflow = false; |
| switch( in.charAt(++i) ){ |
| case '-': |
| expSign = -1; |
| //FALLTHROUGH |
| case '+': |
| i++; |
| } |
| int expAt = i; |
| expLoop: |
| while ( i < len ){ |
| if ( expVal >= reallyBig ){ |
| // the next character will cause integer |
| // overflow. |
| expOverflow = true; |
| } |
| c = in.charAt(i++); |
| if(c>='0' && c<='9') { |
| expVal = expVal*10 + ( (int)c - (int)'0' ); |
| } else { |
| i--; // back up. |
| break expLoop; // stop parsing exponent. |
| } |
| } |
| int expLimit = BIG_DECIMAL_EXPONENT + nDigits + nTrailZero; |
| if (expOverflow || (expVal > expLimit)) { |
| // There is still a chance that the exponent will be safe to |
| // use: if it would eventually decrease due to a negative |
| // decExp, and that number is below the limit. We check for |
| // that here. |
| if (!expOverflow && (expSign == 1 && decExp < 0) |
| && (expVal + decExp) < expLimit) { |
| // Cannot overflow: adding a positive and negative number. |
| decExp += expVal; |
| } else { |
| // |
| // The intent here is to end up with |
| // infinity or zero, as appropriate. |
| // The reason for yielding such a small decExponent, |
| // rather than something intuitive such as |
| // expSign*Integer.MAX_VALUE, is that this value |
| // is subject to further manipulation in |
| // doubleValue() and floatValue(), and I don't want |
| // it to be able to cause overflow there! |
| // (The only way we can get into trouble here is for |
| // really outrageous nDigits+nTrailZero, such as 2 |
| // billion.) |
| // |
| decExp = expSign * expLimit; |
| } |
| } else { |
| // this should not overflow, since we tested |
| // for expVal > (MAX+N), where N >= abs(decExp) |
| decExp = decExp + expSign*expVal; |
| } |
| |
| // if we saw something not a digit ( or end of string ) |
| // after the [Ee][+-], without seeing any digits at all |
| // this is certainly an error. If we saw some digits, |
| // but then some trailing garbage, that might be ok. |
| // so we just fall through in that case. |
| // HUMBUG |
| if ( i == expAt ) { |
| break parseNumber; // certainly bad |
| } |
| } |
| // |
| // We parsed everything we could. |
| // If there are leftovers, then this is not good input! |
| // |
| if ( i < len && |
| ((i != len - 1) || |
| (in.charAt(i) != 'f' && |
| in.charAt(i) != 'F' && |
| in.charAt(i) != 'd' && |
| in.charAt(i) != 'D'))) { |
| break parseNumber; // go throw exception |
| } |
| if(isZero) { |
| return isNegative ? A2BC_NEGATIVE_ZERO : A2BC_POSITIVE_ZERO; |
| } |
| return new ASCIIToBinaryBuffer(isNegative, decExp, digits, nDigits); |
| } catch ( StringIndexOutOfBoundsException e ){ } |
| throw new NumberFormatException("For input string: \"" + in + "\""); |
| } |
| |
| private static class HexFloatPattern { |
| /** |
| * Grammar is compatible with hexadecimal floating-point constants |
| * described in section 6.4.4.2 of the C99 specification. |
| */ |
| private static final Pattern VALUE = Pattern.compile( |
| //1 234 56 7 8 9 |
| "([-+])?0[xX](((\\p{XDigit}+)\\.?)|((\\p{XDigit}*)\\.(\\p{XDigit}+)))[pP]([-+])?(\\p{Digit}+)[fFdD]?" |
| ); |
| } |
| |
| /** |
| * Converts string s to a suitable floating decimal; uses the |
| * double constructor and sets the roundDir variable appropriately |
| * in case the value is later converted to a float. |
| * |
| * @param s The <code>String</code> to parse. |
| */ |
| static ASCIIToBinaryConverter parseHexString(String s) { |
| // Verify string is a member of the hexadecimal floating-point |
| // string language. |
| Matcher m = HexFloatPattern.VALUE.matcher(s); |
| boolean validInput = m.matches(); |
| if (!validInput) { |
| // Input does not match pattern |
| throw new NumberFormatException("For input string: \"" + s + "\""); |
| } else { // validInput |
| // |
| // We must isolate the sign, significand, and exponent |
| // fields. The sign value is straightforward. Since |
| // floating-point numbers are stored with a normalized |
| // representation, the significand and exponent are |
| // interrelated. |
| // |
| // After extracting the sign, we normalized the |
| // significand as a hexadecimal value, calculating an |
| // exponent adjust for any shifts made during |
| // normalization. If the significand is zero, the |
| // exponent doesn't need to be examined since the output |
| // will be zero. |
| // |
| // Next the exponent in the input string is extracted. |
| // Afterwards, the significand is normalized as a *binary* |
| // value and the input value's normalized exponent can be |
| // computed. The significand bits are copied into a |
| // double significand; if the string has more logical bits |
| // than can fit in a double, the extra bits affect the |
| // round and sticky bits which are used to round the final |
| // value. |
| // |
| // Extract significand sign |
| String group1 = m.group(1); |
| boolean isNegative = ((group1 != null) && group1.equals("-")); |
| |
| // Extract Significand magnitude |
| // |
| // Based on the form of the significand, calculate how the |
| // binary exponent needs to be adjusted to create a |
| // normalized//hexadecimal* floating-point number; that |
| // is, a number where there is one nonzero hex digit to |
| // the left of the (hexa)decimal point. Since we are |
| // adjusting a binary, not hexadecimal exponent, the |
| // exponent is adjusted by a multiple of 4. |
| // |
| // There are a number of significand scenarios to consider; |
| // letters are used in indicate nonzero digits: |
| // |
| // 1. 000xxxx => x.xxx normalized |
| // increase exponent by (number of x's - 1)*4 |
| // |
| // 2. 000xxx.yyyy => x.xxyyyy normalized |
| // increase exponent by (number of x's - 1)*4 |
| // |
| // 3. .000yyy => y.yy normalized |
| // decrease exponent by (number of zeros + 1)*4 |
| // |
| // 4. 000.00000yyy => y.yy normalized |
| // decrease exponent by (number of zeros to right of point + 1)*4 |
| // |
| // If the significand is exactly zero, return a properly |
| // signed zero. |
| // |
| |
| String significandString = null; |
| int signifLength = 0; |
| int exponentAdjust = 0; |
| { |
| int leftDigits = 0; // number of meaningful digits to |
| // left of "decimal" point |
| // (leading zeros stripped) |
| int rightDigits = 0; // number of digits to right of |
| // "decimal" point; leading zeros |
| // must always be accounted for |
| // |
| // The significand is made up of either |
| // |
| // 1. group 4 entirely (integer portion only) |
| // |
| // OR |
| // |
| // 2. the fractional portion from group 7 plus any |
| // (optional) integer portions from group 6. |
| // |
| String group4; |
| if ((group4 = m.group(4)) != null) { // Integer-only significand |
| // Leading zeros never matter on the integer portion |
| significandString = stripLeadingZeros(group4); |
| leftDigits = significandString.length(); |
| } else { |
| // Group 6 is the optional integer; leading zeros |
| // never matter on the integer portion |
| String group6 = stripLeadingZeros(m.group(6)); |
| leftDigits = group6.length(); |
| |
| // fraction |
| String group7 = m.group(7); |
| rightDigits = group7.length(); |
| |
| // Turn "integer.fraction" into "integer"+"fraction" |
| significandString = |
| ((group6 == null) ? "" : group6) + // is the null |
| // check necessary? |
| group7; |
| } |
| |
| significandString = stripLeadingZeros(significandString); |
| signifLength = significandString.length(); |
| |
| // |
| // Adjust exponent as described above |
| // |
| if (leftDigits >= 1) { // Cases 1 and 2 |
| exponentAdjust = 4 * (leftDigits - 1); |
| } else { // Cases 3 and 4 |
| exponentAdjust = -4 * (rightDigits - signifLength + 1); |
| } |
| |
| // If the significand is zero, the exponent doesn't |
| // matter; return a properly signed zero. |
| |
| if (signifLength == 0) { // Only zeros in input |
| return isNegative ? A2BC_NEGATIVE_ZERO : A2BC_POSITIVE_ZERO; |
| } |
| } |
| |
| // Extract Exponent |
| // |
| // Use an int to read in the exponent value; this should |
| // provide more than sufficient range for non-contrived |
| // inputs. If reading the exponent in as an int does |
| // overflow, examine the sign of the exponent and |
| // significand to determine what to do. |
| // |
| String group8 = m.group(8); |
| boolean positiveExponent = (group8 == null) || group8.equals("+"); |
| long unsignedRawExponent; |
| try { |
| unsignedRawExponent = Integer.parseInt(m.group(9)); |
| } |
| catch (NumberFormatException e) { |
| // At this point, we know the exponent is |
| // syntactically well-formed as a sequence of |
| // digits. Therefore, if an NumberFormatException |
| // is thrown, it must be due to overflowing int's |
| // range. Also, at this point, we have already |
| // checked for a zero significand. Thus the signs |
| // of the exponent and significand determine the |
| // final result: |
| // |
| // significand |
| // + - |
| // exponent + +infinity -infinity |
| // - +0.0 -0.0 |
| return isNegative ? |
| (positiveExponent ? A2BC_NEGATIVE_INFINITY : A2BC_NEGATIVE_ZERO) |
| : (positiveExponent ? A2BC_POSITIVE_INFINITY : A2BC_POSITIVE_ZERO); |
| |
| } |
| |
| long rawExponent = |
| (positiveExponent ? 1L : -1L) * // exponent sign |
| unsignedRawExponent; // exponent magnitude |
| |
| // Calculate partially adjusted exponent |
| long exponent = rawExponent + exponentAdjust; |
| |
| // Starting copying non-zero bits into proper position in |
| // a long; copy explicit bit too; this will be masked |
| // later for normal values. |
| |
| boolean round = false; |
| boolean sticky = false; |
| int nextShift = 0; |
| long significand = 0L; |
| // First iteration is different, since we only copy |
| // from the leading significand bit; one more exponent |
| // adjust will be needed... |
| |
| // IMPORTANT: make leadingDigit a long to avoid |
| // surprising shift semantics! |
| long leadingDigit = getHexDigit(significandString, 0); |
| |
| // |
| // Left shift the leading digit (53 - (bit position of |
| // leading 1 in digit)); this sets the top bit of the |
| // significand to 1. The nextShift value is adjusted |
| // to take into account the number of bit positions of |
| // the leadingDigit actually used. Finally, the |
| // exponent is adjusted to normalize the significand |
| // as a binary value, not just a hex value. |
| // |
| if (leadingDigit == 1) { |
| significand |= leadingDigit << 52; |
| nextShift = 52 - 4; |
| // exponent += 0 |
| } else if (leadingDigit <= 3) { // [2, 3] |
| significand |= leadingDigit << 51; |
| nextShift = 52 - 5; |
| exponent += 1; |
| } else if (leadingDigit <= 7) { // [4, 7] |
| significand |= leadingDigit << 50; |
| nextShift = 52 - 6; |
| exponent += 2; |
| } else if (leadingDigit <= 15) { // [8, f] |
| significand |= leadingDigit << 49; |
| nextShift = 52 - 7; |
| exponent += 3; |
| } else { |
| throw new AssertionError("Result from digit conversion too large!"); |
| } |
| // The preceding if-else could be replaced by a single |
| // code block based on the high-order bit set in |
| // leadingDigit. Given leadingOnePosition, |
| |
| // significand |= leadingDigit << (SIGNIFICAND_WIDTH - leadingOnePosition); |
| // nextShift = 52 - (3 + leadingOnePosition); |
| // exponent += (leadingOnePosition-1); |
| |
| // |
| // Now the exponent variable is equal to the normalized |
| // binary exponent. Code below will make representation |
| // adjustments if the exponent is incremented after |
| // rounding (includes overflows to infinity) or if the |
| // result is subnormal. |
| // |
| |
| // Copy digit into significand until the significand can't |
| // hold another full hex digit or there are no more input |
| // hex digits. |
| int i = 0; |
| for (i = 1; |
| i < signifLength && nextShift >= 0; |
| i++) { |
| long currentDigit = getHexDigit(significandString, i); |
| significand |= (currentDigit << nextShift); |
| nextShift -= 4; |
| } |
| |
| // After the above loop, the bulk of the string is copied. |
| // Now, we must copy any partial hex digits into the |
| // significand AND compute the round bit and start computing |
| // sticky bit. |
| |
| if (i < signifLength) { // at least one hex input digit exists |
| long currentDigit = getHexDigit(significandString, i); |
| |
| // from nextShift, figure out how many bits need |
| // to be copied, if any |
| switch (nextShift) { // must be negative |
| case -1: |
| // three bits need to be copied in; can |
| // set round bit |
| significand |= ((currentDigit & 0xEL) >> 1); |
| round = (currentDigit & 0x1L) != 0L; |
| break; |
| |
| case -2: |
| // two bits need to be copied in; can |
| // set round and start sticky |
| significand |= ((currentDigit & 0xCL) >> 2); |
| round = (currentDigit & 0x2L) != 0L; |
| sticky = (currentDigit & 0x1L) != 0; |
| break; |
| |
| case -3: |
| // one bit needs to be copied in |
| significand |= ((currentDigit & 0x8L) >> 3); |
| // Now set round and start sticky, if possible |
| round = (currentDigit & 0x4L) != 0L; |
| sticky = (currentDigit & 0x3L) != 0; |
| break; |
| |
| case -4: |
| // all bits copied into significand; set |
| // round and start sticky |
| round = ((currentDigit & 0x8L) != 0); // is top bit set? |
| // nonzeros in three low order bits? |
| sticky = (currentDigit & 0x7L) != 0; |
| break; |
| |
| default: |
| throw new AssertionError("Unexpected shift distance remainder."); |
| // break; |
| } |
| |
| // Round is set; sticky might be set. |
| |
| // For the sticky bit, it suffices to check the |
| // current digit and test for any nonzero digits in |
| // the remaining unprocessed input. |
| i++; |
| while (i < signifLength && !sticky) { |
| currentDigit = getHexDigit(significandString, i); |
| sticky = sticky || (currentDigit != 0); |
| i++; |
| } |
| |
| } |
| // else all of string was seen, round and sticky are |
| // correct as false. |
| |
| // Float calculations |
| int floatBits = isNegative ? FloatConsts.SIGN_BIT_MASK : 0; |
| if (exponent >= Float.MIN_EXPONENT) { |
| if (exponent > Float.MAX_EXPONENT) { |
| // Float.POSITIVE_INFINITY |
| floatBits |= FloatConsts.EXP_BIT_MASK; |
| } else { |
| int threshShift = DoubleConsts.SIGNIFICAND_WIDTH - FloatConsts.SIGNIFICAND_WIDTH - 1; |
| boolean floatSticky = (significand & ((1L << threshShift) - 1)) != 0 || round || sticky; |
| int iValue = (int) (significand >>> threshShift); |
| if ((iValue & 3) != 1 || floatSticky) { |
| iValue++; |
| } |
| floatBits |= (((((int) exponent) + (FloatConsts.EXP_BIAS - 1))) << SINGLE_EXP_SHIFT) + (iValue >> 1); |
| } |
| } else { |
| if (exponent < FloatConsts.MIN_SUB_EXPONENT - 1) { |
| // 0 |
| } else { |
| // exponent == -127 ==> threshShift = 53 - 2 + (-149) - (-127) = 53 - 24 |
| int threshShift = (int) ((DoubleConsts.SIGNIFICAND_WIDTH - 2 + FloatConsts.MIN_SUB_EXPONENT) - exponent); |
| assert threshShift >= DoubleConsts.SIGNIFICAND_WIDTH - FloatConsts.SIGNIFICAND_WIDTH; |
| assert threshShift < DoubleConsts.SIGNIFICAND_WIDTH; |
| boolean floatSticky = (significand & ((1L << threshShift) - 1)) != 0 || round || sticky; |
| int iValue = (int) (significand >>> threshShift); |
| if ((iValue & 3) != 1 || floatSticky) { |
| iValue++; |
| } |
| floatBits |= iValue >> 1; |
| } |
| } |
| float fValue = Float.intBitsToFloat(floatBits); |
| |
| // Check for overflow and update exponent accordingly. |
| if (exponent > Double.MAX_EXPONENT) { // Infinite result |
| // overflow to properly signed infinity |
| return isNegative ? A2BC_NEGATIVE_INFINITY : A2BC_POSITIVE_INFINITY; |
| } else { // Finite return value |
| if (exponent <= Double.MAX_EXPONENT && // (Usually) normal result |
| exponent >= Double.MIN_EXPONENT) { |
| |
| // The result returned in this block cannot be a |
| // zero or subnormal; however after the |
| // significand is adjusted from rounding, we could |
| // still overflow in infinity. |
| |
| // AND exponent bits into significand; if the |
| // significand is incremented and overflows from |
| // rounding, this combination will update the |
| // exponent correctly, even in the case of |
| // Double.MAX_VALUE overflowing to infinity. |
| |
| significand = ((( exponent + |
| (long) DoubleConsts.EXP_BIAS) << |
| (DoubleConsts.SIGNIFICAND_WIDTH - 1)) |
| & DoubleConsts.EXP_BIT_MASK) | |
| (DoubleConsts.SIGNIF_BIT_MASK & significand); |
| |
| } else { // Subnormal or zero |
| // (exponent < Double.MIN_EXPONENT) |
| |
| if (exponent < (DoubleConsts.MIN_SUB_EXPONENT - 1)) { |
| // No way to round back to nonzero value |
| // regardless of significand if the exponent is |
| // less than -1075. |
| return isNegative ? A2BC_NEGATIVE_ZERO : A2BC_POSITIVE_ZERO; |
| } else { // -1075 <= exponent <= MIN_EXPONENT -1 = -1023 |
| // |
| // Find bit position to round to; recompute |
| // round and sticky bits, and shift |
| // significand right appropriately. |
| // |
| |
| sticky = sticky || round; |
| round = false; |
| |
| // Number of bits of significand to preserve is |
| // exponent - abs_min_exp +1 |
| // check: |
| // -1075 +1074 + 1 = 0 |
| // -1023 +1074 + 1 = 52 |
| |
| int bitsDiscarded = 53 - |
| ((int) exponent - DoubleConsts.MIN_SUB_EXPONENT + 1); |
| assert bitsDiscarded >= 1 && bitsDiscarded <= 53; |
| |
| // What to do here: |
| // First, isolate the new round bit |
| round = (significand & (1L << (bitsDiscarded - 1))) != 0L; |
| if (bitsDiscarded > 1) { |
| // create mask to update sticky bits; low |
| // order bitsDiscarded bits should be 1 |
| long mask = ~((~0L) << (bitsDiscarded - 1)); |
| sticky = sticky || ((significand & mask) != 0L); |
| } |
| |
| // Now, discard the bits |
| significand = significand >> bitsDiscarded; |
| |
| significand = ((((long) (Double.MIN_EXPONENT - 1) + // subnorm exp. |
| (long) DoubleConsts.EXP_BIAS) << |
| (DoubleConsts.SIGNIFICAND_WIDTH - 1)) |
| & DoubleConsts.EXP_BIT_MASK) | |
| (DoubleConsts.SIGNIF_BIT_MASK & significand); |
| } |
| } |
| |
| // The significand variable now contains the currently |
| // appropriate exponent bits too. |
| |
| // |
| // Determine if significand should be incremented; |
| // making this determination depends on the least |
| // significant bit and the round and sticky bits. |
| // |
| // Round to nearest even rounding table, adapted from |
| // table 4.7 in "Computer Arithmetic" by IsraelKoren. |
| // The digit to the left of the "decimal" point is the |
| // least significant bit, the digits to the right of |
| // the point are the round and sticky bits |
| // |
| // Number Round(x) |
| // x0.00 x0. |
| // x0.01 x0. |
| // x0.10 x0. |
| // x0.11 x1. = x0. +1 |
| // x1.00 x1. |
| // x1.01 x1. |
| // x1.10 x1. + 1 |
| // x1.11 x1. + 1 |
| // |
| boolean leastZero = ((significand & 1L) == 0L); |
| if ((leastZero && round && sticky) || |
| ((!leastZero) && round)) { |
| significand++; |
| } |
| |
| double value = isNegative ? |
| Double.longBitsToDouble(significand | DoubleConsts.SIGN_BIT_MASK) : |
| Double.longBitsToDouble(significand ); |
| |
| return new PreparedASCIIToBinaryBuffer(value, fValue); |
| } |
| } |
| } |
| |
| /** |
| * Returns <code>s</code> with any leading zeros removed. |
| */ |
| static String stripLeadingZeros(String s) { |
| // return s.replaceFirst("^0+", ""); |
| if(!s.isEmpty() && s.charAt(0)=='0') { |
| for(int i=1; i<s.length(); i++) { |
| if(s.charAt(i)!='0') { |
| return s.substring(i); |
| } |
| } |
| return ""; |
| } |
| return s; |
| } |
| |
| /** |
| * Extracts a hexadecimal digit from position <code>position</code> |
| * of string <code>s</code>. |
| */ |
| static int getHexDigit(String s, int position) { |
| int value = Character.digit(s.charAt(position), 16); |
| if (value <= -1 || value >= 16) { |
| throw new AssertionError("Unexpected failure of digit conversion of " + |
| s.charAt(position)); |
| } |
| return value; |
| } |
| } |