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third-party-mirror/openjdk/jdk25u/HEAD/./src/java.base/share/classes/jdk/internal/math/FloatingDecimal.java
blob: 6f59338d4c8fd320eb76fed0a3024ae8b478ded8 [file]
/*
* Copyright (c) 1996, 2024, 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 jdk.internal.vm.annotation.Stable;
import java.util.Arrays;
/**
* 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 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, BINARY_64_IX).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, BINARY_32_IX).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>.
*/
String toJavaFormatString();
/**
* Appends a floating point value to an <code>Appendable</code>.
* @param buf The <code>Appendable</code> to receive the value.
*/
void appendTo(Appendable buf);
/**
* Retrieves the decimal exponent most closely corresponding to this value.
* @return The decimal exponent.
*/
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.
*/
int getDigits(char[] digits);
/**
* Indicates the sign of the value.
* @return {@code value < 0.0}.
*/
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.
*/
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.
*/
boolean digitsRoundedUp();
/**
* Indicates whether the binary to ASCII conversion was exact.
*
* @return <code>true</code> if any only if the conversion was exact.
*/
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 final 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 String NAN_REP = "NaN";
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(long 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 final 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;
byte[] digits;
int nDigits;
ASCIIToBinaryBuffer( boolean negSign, int decExponent, byte[] 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.clamp((float) dValue, Float.MIN_VALUE, Float.MAX_VALUE);
//
// 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;
}
/**
* The input must match the {@link Double#valueOf(String) rules described here},
* about leading and trailing whitespaces, and the grammar.
*
* @param in the non-null input
* @param ix one of the {@code BINARY_<S>_IX} constants, where {@code <S>}
* is one of 16, 32, 64
* @return an appropriate binary converter
* @throws NullPointerException if the input is null
* @throws NumberFormatException if the input is malformed
*/
static ASCIIToBinaryConverter readJavaFormatString(String in, int ix) {
/*
* The scanning proper does not allocate any object,
* nor does it perform any costly computation.
* This means that all scanning errors are detected without consuming
* any heap, before actually throwing.
*
* Once scanning is complete, the method determines the length
* of a prefix of the significand that is sufficient for correct
* rounding according to roundTiesToEven.
* The actual value of the prefix length might not be optimal,
* but is always a safe choice.
*
* For hexadecimal input, the prefix is processed by this method directly,
* without allocating objects before creating the returned instance.
*
* For decimal input, the prefix is copied to the returned instance,
* along with the other information needed for the conversion.
* For comparison, the prefix length is at most
* 23 for BINARY_16_IX (Float16, once integrated in java.base)
* 114 for BINARY_32_IX (float)
* 769 for BINARY_64_IX (double)
*/
int len = in.length(); // fail fast on null
/* Skip leading whitespaces. */
int i = skipWhitespaces(in, 0); // main running index
if (i == len) {
throw new NumberFormatException("empty String");
}
/* Scan opt significand sign. */
int ch; // running char
int ssign = ' '; // ' ' iff sign is implicit
if ((ch = in.charAt(i)) == '-' || ch == '+') { // i < len
ssign = ch;
++i;
}
/*
* In some places the idiom
* (ch | 0b10_0000) == lowercase-letter
* is used as a shortcut for
* ch == lowercase-letter || ch == that-same-letter-as-uppercase
*
* Determine whether we are facing a symbolic value or hex notation.
*/
boolean isDec = true; // decimal input until proven to the contrary
if (i < len) {
ch = in.charAt(i);
if (ch == 'I') {
scanSymbolic(in, i, "Infinity");
return ssign != '-' ? A2BC_POSITIVE_INFINITY : A2BC_NEGATIVE_INFINITY;
}
if (ch == 'N') {
scanSymbolic(in, i, "NaN");
return A2BC_NOT_A_NUMBER; // ignore sign
}
if (ch == '0' && i < len - 1 && (in.charAt(i + 1) | 0b10_0000) == 'x') {
isDec = false;
i += 2;
}
}
int pt = 0; // index after point, 0 iff absent
int start = i; // index of start of the significand, excluding opt sign
/* Skip opt leading zeros, including an opt point. */
while (i < len && ((ch = in.charAt(i)) == '0' || ch == '.')) {
++i;
if (ch == '.') {
pt = checkMultiplePoints(pt, i);
}
}
int lz = i; // index after leading group of zeros or point
/*
* Scan all remaining chars of the significand, including an opt point.
* Also locate the index after the end of the trailing group of non-zeros
* inside this range of the input.
*/
int tnz = 0; // index after trailing group of non-zeros, 0 iff absent
while (i < len && (isDigit(ch = in.charAt(i), isDec) || ch == '.')) {
i++;
if (ch == '.') {
pt = checkMultiplePoints(pt, i);
} else if (ch != '0') {
tnz = i;
}
}
check(in, i - start > (pt != 0 ? 1 : 0)); // must have at least one digit
int stop = i; // index after the significand
/* Scan exponent part, optional for dec, mandatory for hex. */
long ep = 0; // exponent, implicitly 0
boolean hasExp = false;
if (i < len && ((ch = in.charAt(i) | 0b10_0000) == 'e' && isDec
|| ch == 'p' && !isDec)) {
++i;
/* Scan opt exponent sign. */
int esign = ' '; // esign == ' ' iff the sign is implicit
if (i < len && ((ch = in.charAt(i)) == '-' || ch == '+')) {
esign = ch;
++i;
}
/* Scan the exponent digits. Accumulate in ep, clamping at 10^10. */
while (i < len && isDigit(ch = in.charAt(i), true)) { // ep is decimal
++i;
ep = appendDecDigit(ep, ch);
}
check(in, i - stop >= 3 // at least 3 chars after significand
|| i - stop == 2 && esign == ' '); // 2 chars, one is digit
if (esign == '-') {
ep = -ep;
}
hasExp = true;
}
/*
* |ep| < 10^10, or |ep| = 10^10 when considered "large".
* A "large" ep either generates a zero or an infinity.
*/
check(in, isDec | hasExp);
/* Skip opt [FfDd]? suffix. */
if (i < len && (((ch = in.charAt(i) | 0b10_0000)) == 'f' || ch == 'd')) {
++i;
}
/* Skip optional trailing whitespaces, then must be at the end of input. */
check(in, skipWhitespaces(in, i) == len);
/* By now, the input is syntactically correct. */
if (tnz == 0) { // all zero digits, so ignore ep and point
return ssign != '-' ? A2BC_POSITIVE_ZERO : A2BC_NEGATIVE_ZERO;
}
/*
* Virtually adjust the point position to be just after
* the last non-zero digit by adjusting the exponent accordingly
* (without modifying the physical pt, as it is used later on).
*
* Determine the count of digits, excluding leading and trailing zeros.
*
* These are the possible situations:
* |lz |tnz |stop
* 00000000123456000000234567000000000
*
* |pt |lz |tnz |stop
* .00000000123456000000234567000000000
*
* |pt |lz |tnz |stop
* 00.000000123456000000234567000000000
*
* |pt=lz |tnz |stop
* 00000000.123456000000234567000000000
*
* |lz |pt |tnz |stop
* 000000001234.56000000234567000000000
*
* |lz |pt |tnz |stop
* 0000000012345600.0000234567000000000
*
* |lz |pt |tnz |stop
* 00000000123456000000.234567000000000
*
* |lz |pt |tnz |stop
* 0000000012345600000023.4567000000000
*
* |lz |pt=tnz |stop
* 00000000123456000000234567.000000000
*
* |lz |tnz |pt |stop
* 0000000012345600000023456700000.0000
*
* |lz |tnz |pt=stop
* 00000000123456000000234567000000000.
*
* In decimal, moving the point by one position means correcting ep by 1.
* In hexadecimal, it means correcting ep by 4.
*/
long emult = isDec ? 1L : 4L;
int n = tnz - lz; // number of significant digits, 1st approximation
if (pt == 0) {
ep += emult * (stop - tnz);
} else {
ep += emult * (pt - tnz);
if (pt > tnz) { // '.' was counted as a position, adjust ep
ep -= emult;
} else if (lz < pt) { // lz < pt <= tnz
n -= 1;
}
}
/*
* n = number of significant digits (that is, not counting leading nor
* trailing zeros)
* |ep| < 10^11
*
* The magnitude x of the input meets
* x = f 10^ep (decimal)
* x = f 2^ep (hexadecimal)
* Integer f = <f_1 ... f_n> consists of the n decimal or hexadecimal
* digits found in part [lz, tnz) of the input, and f_1 != 0, f_n != 0.
*/
if (!isDec) { // hexadecimal conversion is performed entirely here
/*
* Rounding the leftmost P bits +1 rounding bit +1 sticky bit
* has the same outcome as rounding all bits.
* In terms of hex digits, we need room for HEX_COUNT of them.
*/
int j = 0;
i = lz;
long c = 0;
int le = Math.min(n, HEX_COUNT[ix]);
while (j < le) {
if ((ch = in.charAt(i++)) != '.') {
++j;
c = c << 4 | digitFor(ch);
}
}
if (n > le) {
c |= 0b1; // force a sticky bit
ep += 4L * (n - le);
}
int bl = Long.SIZE - Long.numberOfLeadingZeros(c); // bit length
/*
* Let x = c 2^ep, so 2^(ep+bl-1) <= x < 2^(ep+bl)
* When ep + bl < Q_MIN then x certainly rounds to zero.
* When ep + bl - 1 > E_MAX then x surely rounds to infinity.
*/
if (ep < Q_MIN[ix] - bl) {
return buildZero(ix, ssign);
}
if (ep > E_MAX[ix] - bl + 1) {
return buildInfinity(ix, ssign);
}
int q = (int) ep; // narrowing conversion is safe
int shr; // (sh)ift to (r)ight iff shr > 0
if (q > E_MIN[ix] - bl) {
shr = bl - P[ix];
q += shr;
} else {
shr = Q_MIN[ix] - q;
q = Q_MIN[ix];
}
if (shr > 0) {
long thr = 1L << shr;
long tail = (c & thr - 1) << 1;
c >>>= shr;
if (tail > thr || tail == thr && (c & 0b1) != 0) {
c += 1;
if (c >= 1L << P[ix]) { // but in fact it can't be >
c >>>= 1;
q += 1;
}
}
} else {
c <<= -shr;
}
/* For now throw on BINARY_16_IX, until Float16 is integrated in java.base. */
return switch (ix) {
case BINARY_32_IX ->
new PreparedASCIIToBinaryBuffer(Double.NaN, buildFloat(ssign, q, c));
case BINARY_64_IX ->
new PreparedASCIIToBinaryBuffer(buildDouble(ssign, q, c), Float.NaN);
default -> throw new AssertionError("unexpected");
};
}
/*
* For decimal inputs, we copy an appropriate prefix of the input and
* rely on another method to do the (sometimes intensive) math conversion.
*
* Define e' = n + ep, which leads to
* x = <0 . f_1 ... f_n> 10^e', 10^(e'-1) <= x < 10^e'
* If e' <= EP_MIN then x rounds to zero.
* Similarly, if e' >= EP_MAX then x rounds to infinity.
* (See the comments on the fields for their semantics.)
* We return immediately in these cases.
* Otherwise, e' fits in an int named e.
*/
int e = Math.clamp(ep + n, EP_MIN[ix], EP_MAX[ix]);
if (e == EP_MIN[ix]) { // e' <= E_MIN
return ssign != '-' ? A2BC_POSITIVE_ZERO : A2BC_NEGATIVE_ZERO;
}
if (e == EP_MAX[ix]) { // e' >= E_MAX
return ssign != '-' ? A2BC_POSITIVE_INFINITY : A2BC_NEGATIVE_INFINITY;
}
/*
* For further considerations, x also needs to be seen as
* x = beta 2^q
* with real beta and integer q meeting
* 2^(P-1) <= beta < 2^P and q >= Q_MIN
* 0 < beta < 2^(P-1) and q = Q_MIN
* The (unique) solution is
* q = max(floor(log2(x)) - (P-1), Q_MIN), beta = x 2^(-q)
* It's usually costly to determine q as here.
* However, estimates to q are cheaper and quick to compute.
*
* Indeed, it's a matter of some simple maths to show that, by defining
* ql = max(floor((e-1) log2(10)) - (P-1), Q_MIN)
* qh = max(floor(e log2(10)) - (P-1), Q_MIN)
* then the following hold
* ql <= q <= qh, and qh - ql <= 4
* Since by now e is relatively small, we can leverage flog2pow10().
*
* When q >= Q_MIN, consider the interval [ 2^(P-1+q), 2^(P+q) ).
* It contains all floating-point values of the form
* c 2^q, c integer, 2^(P-1) <= c < 2^P (normal values)
* When q = Q_MIN also consider the interval [0, 2^(P-1+q) )
* which contains all floating-point values of the form
* c 2^q, c integer, 0 <= c < 2^(P-1) (subnormal values and zero)
* For these c values, all numbers of the form
* (c + 1/2) 2^q
* also belong to the intervals.
* These are the boundaries of the rounding intervals and are key for
* correct rounding.
*
* First assume ql > 0, so q > 0.
* All rounding boundaries (c + 1/2) 2^q are integers.
* Hence, to correctly round x, it's enough to retain its integer part,
* +1 non-zero sticky digit iff the fractional part is non-zero.
* (Well, the sticky digit is only needed when the integer part
* coincides with a boundary, but that's hard to detect at this stage.
* Adding the sticky digit is always safe.)
* If n > e we pass the digits <f_1 ... f_e 3> (3 is as good as any other
* non-zero sticky digit) and the exponent e to the conversion routine.
* If n <= e we pass all the digits <f_1 ... f_n> (no sticky digit,
* as the fractional part is empty) and the exponent e to the converter.
*
* Now assume qh <= 0, so q <= 0.
* The boundaries (c + 1/2) 2^q = (2c + 1) 2^(q-1) have a fractional part
* of 1 - q digits: some (or zero) leading zeros, the rightmost is 5.
* A correct rounding needs to retain the integer part of x (if any),
* 1 - q digits of the fractional part, +1 non-zero sticky digit iff
* the rest of the fractional part beyond the 1 - q digits is non-zero.
* (Again, the sticky digit is only needed when the digit in f at the
* same position as the last 5 of the rounding boundary is 5 as well.
* But let's keep it simple for now.)
* However, q is unknown, so use the conservative ql instead.
* More precisely, if n > e + 1 - ql we pass the leftmost e + 1 - ql
* digits of f, sticky 3, and e.
* Otherwise, n <= e + 1 - ql.
* We pass all n digits of f, no sticky digit, and e to the converter.
*
* Otherwise, ql <= 0 < qh, so -4 < q <= 4.
* Again, since q is not known exactly, we proceed as in the previous
* case, with ql as a safe replacement for q.
*/
int ql = Math.max(MathUtils.flog2pow10(e - 1) - (P[ix] - 1), Q_MIN[ix]);
int np = e + Math.max(2 - ql, 1);
byte[] digits = new byte[Math.min(n, np)];
if (n >= np) {
copyDigits(in, digits, np - 1, lz);
digits[np - 1] = '3'; // append any non-zero sticky digit
} else {
copyDigits(in, digits, n, lz);
}
return new ASCIIToBinaryBuffer(ssign == '-', e, digits, digits.length);
}
private static PreparedASCIIToBinaryBuffer buildZero(int ix, int ssign) {
/* For now throw on BINARY_16_IX, until Float16 is integrated in java.base. */
return switch (ix) {
case BINARY_32_IX ->
new PreparedASCIIToBinaryBuffer(
Double.NaN,
ssign != '-' ? 0.0f : -0.0f);
case BINARY_64_IX ->
new PreparedASCIIToBinaryBuffer(
ssign != '-' ? 0.0d : -0.0d,
Float.NaN);
default -> throw new AssertionError("unexpected");
};
}
private static PreparedASCIIToBinaryBuffer buildInfinity(int ix, int ssign) {
/* For now throw on BINARY_16_IX, until Float16 is integrated in java.base. */
return switch (ix) {
case BINARY_32_IX ->
new PreparedASCIIToBinaryBuffer(
Double.NaN,
ssign != '-' ? Float.POSITIVE_INFINITY : Float.NEGATIVE_INFINITY);
case BINARY_64_IX ->
new PreparedASCIIToBinaryBuffer(
ssign != '-' ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY,
Float.NaN);
default -> throw new AssertionError("unexpected");
};
}
private static double buildDouble(int ssign, int q, long c) {
long be = c < 1L << P[BINARY_64_IX] - 1
? 0
: q + ((DoubleConsts.EXP_BIAS - 1) + P[BINARY_64_IX]);
long bits = (ssign != '-' ? 0L : 1L << Double.SIZE - 1)
| be << P[BINARY_64_IX] - 1
| c & DoubleConsts.SIGNIF_BIT_MASK;
return Double.longBitsToDouble(bits);
}
private static float buildFloat(int ssign, int q, long c) {
int be = c < 1L << P[BINARY_32_IX] - 1
? 0
: q + ((FloatConsts.EXP_BIAS - 1) + P[BINARY_32_IX]);
int bits = (ssign != '-' ? 0 : 1 << Float.SIZE - 1)
| be << P[BINARY_32_IX] - 1
| (int) c & FloatConsts.SIGNIF_BIT_MASK;
return Float.intBitsToFloat(bits);
}
private static void copyDigits(String in, byte[] digits, int len, int i) {
int ch;
int j = 0;
while (j < len) {
if ((ch = in.charAt(i++)) != '.') {
digits[j++] = (byte) ch;
}
}
}
/* Arithmetically "appends the dec digit" ch to v >= 0, clamping at 10^10. */
private static long appendDecDigit(long v, int ch) {
return v < 10_000_000_000L / 10 ? 10 * v + (ch - '0') : 10_000_000_000L;
}
/* Whether ch is a digit char '0-9', 'A-F', or 'a-f', depending on isDec. */
private static boolean isDigit(int ch, boolean isDec) {
int lch; // lowercase ch
return '0' <= ch && ch <= '9' ||
!isDec && 'a' <= (lch = ch | 0b10_0000) && lch <= 'f';
}
/* Returns the numeric value of ch, assuming it is a hexdigit. */
private static int digitFor(int ch) {
return ch <= '9' ? ch - '0' : (ch | 0b10_0000) - ('a' - 10);
}
/*
* Starting at i, skips all chars in ['\0', ' '].
* Returns the index after the whitespaces.
*/
private static int skipWhitespaces(String in, int i) {
int len = in.length();
for (; i < len && in.charAt(i) <= ' '; ++i); // empty body
return i;
}
/*
* Attempts to scan sub and optional trailing whitespaces, starting at index i.
* The optional whitespaces must be at the end of in.
*/
private static void scanSymbolic(String in, int i, String sub) {
int high = i + sub.length(); // might overflow, checked in next line
check(in, i <= high && high <= in.length()
&& in.indexOf(sub, i, high) == i
&& skipWhitespaces(in, high) == in.length());
}
/*
* Returns i if this is the first time the scanner detects a point.
* Throws otherwise.
*/
private static int checkMultiplePoints(int pt, int i) {
if (pt != 0) {
throw new NumberFormatException("multiple points");
}
return i;
}
private static final int MAX_OUT = 1_000;
private static final String OMITTED = " ... ";
private static final int L_HALF = (MAX_OUT - OMITTED.length()) / 2;
private static final int R_HALF = MAX_OUT - (L_HALF + OMITTED.length());
private static void check(String in, boolean expected) {
if (!expected) {
int len = in.length();
if (len > MAX_OUT) { // discard middle chars to achieve a length of MAX_OUT
in = in.substring(0, L_HALF) + OMITTED + in.substring(len - R_HALF);
}
throw new NumberFormatException("For input string: \"" + in + "\"");
}
}
/*
* According to IEEE 754-2019, a finite positive binary floating-point
* of precision P is (uniquely) expressed as
* c 2^q
* where integers c and q meet
* Q_MIN <= q <= Q_MAX
* either 2^(P-1) <= c < 2^P (normal)
* or 0 < c < 2^(P-1) & q = Q_MIN (subnormal)
* c = <d_0 d_1 ... d_(P-1)>, d_i in [0, 2)
*
* Equivalently, the fp value can be (uniquely) expressed as
* m 2^ep
* where integer ep and real f meet
* ep = q + P - 1
* m = c 2^(1-P)
* Hence,
* E_MIN = Q_MIN + P - 1, E_MAX = Q_MAX + P - 1,
* 1 <= m < 2 (normal)
* m < 1 (subnormal)
* m = <d_0 . d_1 ... d_(P-1)>
* with a (binary) point between d_0 and d_1
*/
/*
* These constants are used to indicate the IEEE binary floating-point format
* as an index (ix) to some methods and static arrays in this class.
*/
private static final int BINARY_16_IX = 0;
private static final int BINARY_32_IX = 1;
private static final int BINARY_64_IX = 2;
// private static final int BINARY_128_IX = 3;
// private static final int BINARY_256_IX = 4;
/* The precision of the format. */
@Stable
private static final int[] P = {
11, 24, 53, // 113, 237,
};
/*
* EP_MIN = max{e : 10^e <= MIN_VALUE/2}.
* Note that MIN_VALUE/2 is the 0 threshold.
* Less or equal values round to 0 when using roundTiesToEven.
* Equivalently, EP_MIN = floor(log10(2^(Q_MIN-1))).
*/
@Stable
private static final int[] EP_MIN = {
-8, -46, -324, // -4_966, -78_985,
};
/*
* EP_MAX = min{e : MAX_VALUE + ulp(MAX_VALUE)/2 <= 10^(e-1)}.
* Note that MAX_VALUE + ulp(MAX_VALUE)/2 is the infinity threshold.
* Greater or equal values round to infinity when using roundTiesToEven.
* Equivalently, EP_MAX = ceil(log10((2^P - 1/2) 2^Q_MAX)) + 1.
*/
@Stable
private static final int[] EP_MAX = {
6, 40, 310, // 4_934, 78_915,
};
/* Exponent width. */
@Stable
private static final int[] W = {
(1 << 4 + BINARY_16_IX) - P[BINARY_16_IX],
(1 << 4 + BINARY_32_IX) - P[BINARY_32_IX],
(1 << 4 + BINARY_64_IX) - P[BINARY_64_IX],
// (1 << 4 + BINARY_128_IX) - P[BINARY_128_IX],
// (1 << 4 + BINARY_256_IX) - P[BINARY_256_IX],
};
/* Maximum exponent in the m 2^e representation. */
@Stable
private static final int[] E_MAX = {
(1 << W[BINARY_16_IX] - 1) - 1,
(1 << W[BINARY_32_IX] - 1) - 1,
(1 << W[BINARY_64_IX] - 1) - 1,
// (1 << W[BINARY_128_IX] - 1) - 1,
// (1 << W[BINARY_256_IX] - 1) - 1,
};
/* Minimum exponent in the m 2^e representation. */
@Stable
private static final int[] E_MIN = {
1 - E_MAX[BINARY_16_IX],
1 - E_MAX[BINARY_32_IX],
1 - E_MAX[BINARY_64_IX],
// 1 - E_MAX[BINARY_128_IX],
// 1 - E_MAX[BINARY_256_IX],
};
/* Minimum exponent in the c 2^q representation. */
@Stable
private static final int[] Q_MIN = {
E_MIN[BINARY_16_IX] - (P[BINARY_16_IX] - 1),
E_MIN[BINARY_32_IX] - (P[BINARY_32_IX] - 1),
E_MIN[BINARY_64_IX] - (P[BINARY_64_IX] - 1),
// E_MIN[BINARY_128_IX] - (P[BINARY_128_IX] - 1),
// E_MIN[BINARY_256_IX] - (P[BINARY_256_IX] - 1),
};
/*
* The most significant P +1 rounding bit +1 sticky bit = P + 2 bits in a
* hexadecimal string need up to HEX_COUNT = floor(P/4) + 2 hex digits.
*/
@Stable
private static final int[] HEX_COUNT = {
P[BINARY_16_IX] / 4 + 2,
P[BINARY_32_IX] / 4 + 2,
P[BINARY_64_IX] / 4 + 2,
// P[BINARY_128_IX] / 4 + 2,
// P[BINARY_256_IX] / 4 + 2,
};
}