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/*
* Copyright (c) 2021, 2022, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* The Universal Permissive License (UPL), Version 1.0
*
* Subject to the condition set forth below, permission is hereby granted to any
* person obtaining a copy of this software, associated documentation and/or
* data (collectively the "Software"), free of charge and under any and all
* copyright rights in the Software, and any and all patent rights owned or
* freely licensable by each licensor hereunder covering either (i) the
* unmodified Software as contributed to or provided by such licensor, or (ii)
* the Larger Works (as defined below), to deal in both
*
* (a) the Software, and
*
* (b) any piece of software and/or hardware listed in the lrgrwrks.txt file if
* one is included with the Software each a "Larger Work" to which the Software
* is contributed by such licensors),
*
* without restriction, including without limitation the rights to copy, create
* derivative works of, display, perform, and distribute the Software and make,
* use, sell, offer for sale, import, export, have made, and have sold the
* Software and the Larger Work(s), and to sublicense the foregoing rights on
* either these or other terms.
*
* This license is subject to the following condition:
*
* The above copyright notice and either this complete permission notice or at a
* minimum a reference to the UPL must be included in all copies or substantial
* portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
package org.pkl.thirdparty.truffle.api.strings;
import static org.pkl.thirdparty.truffle.api.strings.NumberConversion.numberFormatException;
import static org.pkl.thirdparty.truffle.api.strings.TStringOps.readValue;
import java.nio.charset.StandardCharsets;
import org.pkl.thirdparty.truffle.api.CompilerDirectives.CompilationFinal;
import org.pkl.thirdparty.truffle.api.CompilerDirectives.TruffleBoundary;
import org.pkl.thirdparty.truffle.api.nodes.Node;
import org.pkl.thirdparty.truffle.api.profiles.InlinedBranchProfile;
import org.pkl.thirdparty.truffle.api.strings.TruffleString.NumberFormatException.Reason;
/*
* MIT License
*
* Copyright (c) 2021 Werner Randelshofer, Switzerland.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of this software and
* associated documentation files (the "Software"), to deal in the Software without restriction,
* including without limitation the rights to use, copy, modify, merge, publish, distribute,
* sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all copies or
* substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT
* NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
* DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
/**
* This is a C++ to Java port of Daniel Lemire's fast_double_parser.
*
*
* The code has been changed, so that it parses the same syntax as
* {@link Double#parseDouble(String)}.
*
* References:
*
* - Daniel Lemire, fast_double_parser, 4x faster than strtod. Apache License 2.0 or Boost
* Software License.
* - github.com
*
* - Daniel Lemire, fast_float number parsing library: 4x faster than strtod. Apache License 2.0.
*
* - github.com
*
* - Daniel Lemire, Number Parsing at a Gigabyte per Second, Software: Practice and Experience 51
* (8), 2021. arXiv.2101.11408v3 [cs.DS] 24 Feb 2021
* - arxiv.org
*
*
* @see https://github.com/
* wrandelshofer/FastDoubleParser
* @see https://github.com/lemire/
* fast_double_parser
*/
final class FastDoubleParser {
private static final long MINIMAL_NINETEEN_DIGIT_INTEGER = 1000_00000_00000_00000L;
private static final int MINIMAL_EIGHT_DIGIT_INTEGER = 10_000_000;
/**
* Special value in {@link #CHAR_TO_HEX_MAP} for the decimal point character.
*/
private static final byte DECIMAL_POINT_CLASS = -4;
/**
* Special value in {@link #CHAR_TO_HEX_MAP} for characters that are neither a hex digit nor a
* decimal point character..
*/
private static final byte OTHER_CLASS = -1;
/**
* A table of 128 entries or of entries up to including character 'p' would suffice.
*
* However for some reason, performance is best, if this table has exactly 256 entries.
*/
@CompilationFinal(dimensions = 1) private static final byte[] CHAR_TO_HEX_MAP = new byte[256];
static {
for (char ch = 0; ch < CHAR_TO_HEX_MAP.length; ch++) {
CHAR_TO_HEX_MAP[ch] = OTHER_CLASS;
}
for (char ch = '0'; ch <= '9'; ch++) {
CHAR_TO_HEX_MAP[ch] = (byte) (ch - '0');
}
for (char ch = 'A'; ch <= 'F'; ch++) {
CHAR_TO_HEX_MAP[ch] = (byte) (ch - 'A' + 10);
}
for (char ch = 'a'; ch <= 'f'; ch++) {
CHAR_TO_HEX_MAP[ch] = (byte) (ch - 'a' + 10);
}
for (char ch = '.'; ch <= '.'; ch++) {
CHAR_TO_HEX_MAP[ch] = DECIMAL_POINT_CLASS;
}
}
private static boolean isDigit(int c) {
return '0' <= c && c <= '9';
}
/**
* Returns a Double object holding the double value represented by the argument string
* {@code str}.
*
* This method can be used as a drop in for method {@link Double#valueOf(String)}. (Assuming
* that the API of this method has not changed since Java SE 16).
*
* Leading and trailing whitespace characters in {@code str} are ignored. Whitespace is removed
* as if by the {@link String#trim()} method; that is, characters in the range [U+0000,U+0020].
*
* The rest of {@code str} should constitute a FloatValue as described by the lexical syntax
* rules shown below:
*
* - FloatValue:
*
- [Sign] {@code NaN}
*
- [Sign] {@code Infinity}
*
- [Sign] DecimalFloatingPointLiteral
*
- [Sign] HexFloatingPointLiteral
*
- SignedInteger
*
*
*
* - HexFloatingPointLiteral:
*
- HexSignificand BinaryExponent
*
*
*
* - HexSignificand:
*
- HexNumeral
*
- HexNumeral {@code .}
*
- {@code 0x} [HexDigits] {@code .} HexDigits
*
- {@code 0X} [HexDigits] {@code .} HexDigits
*
*
*
* - HexSignificand:
*
- HexNumeral
*
- HexNumeral {@code .}
*
- {@code 0x} [HexDigits] {@code .} HexDigits
*
- {@code 0X} [HexDigits] {@code .} HexDigits
*
*
*
* - BinaryExponent:
*
- BinaryExponentIndicator SignedInteger
*
*
*
* - BinaryExponentIndicator:
*
- {@code p}
*
- {@code P}
*
*
*
* - DecimalFloatingPointLiteral:
*
- Digits {@code .} [Digits] [ExponentPart]
*
- {@code .} Digits [ExponentPart]
*
- Digits ExponentPart
*
*
*
* - ExponentPart:
*
- ExponentIndicator SignedInteger
*
*
*
* - ExponentIndicator:
*
- (one of)
*
- e E
*
*
*
* - SignedInteger:
*
- [Sign] Digits
*
*
*
* - Sign:
*
- (one of)
*
- + -
*
*
*
* - Digits:
*
- Digit {Digit}
*
*
*
* - HexNumeral:
*
- {@code 0} {@code x} HexDigits
*
- {@code 0} {@code X} HexDigits
*
*
*
* - HexDigits:
*
- HexDigit {HexDigit}
*
*
*
* - HexDigit:
*
- (one of)
*
- {@code 0 1 2 3 4 5 6 7 8 9 a b c d e f A B C D E F}
*
*
*
*
* @param arrayA the string to be parsed, a byte array with characters in ISO-8859-1, ASCII or
* UTF-8 encoding
* @param off The index of the first byte to parse
* @param len The number of bytes to parse
* @return the parsed double value
* @throws NumberFormatException if the string can not be parsed
*/
static double parseDouble(Node location, AbstractTruffleString a, Object arrayA, int strideA, int off, int len, InlinedBranchProfile errorProfile) throws TruffleString.NumberFormatException {
final int endIndex = len + off;
// Skip leading whitespace
// -------------------
int index = skipWhitespace(a, arrayA, strideA, off, endIndex);
if (index == endIndex) {
errorProfile.enter(location);
throw numberFormatException(a, Reason.EMPTY);
}
int ch = readValue(a, arrayA, strideA, index);
// Parse optional sign
// -------------------
final boolean isNegative = ch == '-';
if (isNegative || ch == '+') {
ch = ++index < endIndex ? readValue(a, arrayA, strideA, index) : 0;
if (ch == 0) {
errorProfile.enter(location);
throw numberFormatException(a, off, len, Reason.LONE_SIGN);
}
}
// Parse NaN or Infinity
// ---------------------
if (ch == 'N') {
return parseNaN(location, a, arrayA, strideA, index, endIndex, off, errorProfile);
} else if (ch == 'I') {
return parseInfinity(location, a, arrayA, strideA, index, endIndex, isNegative, off, errorProfile);
}
// Parse optional leading zero
// ---------------------------
final boolean hasLeadingZero = ch == '0';
if (hasLeadingZero) {
ch = ++index < endIndex ? readValue(a, arrayA, strideA, index) : 0;
if (ch == 'x' || ch == 'X') {
return parseRestOfHexFloatingPointLiteral(location, a, arrayA, strideA, index + 1, off, endIndex, isNegative, errorProfile);
}
}
return parseRestOfDecimalFloatLiteral(location, a, arrayA, strideA, index, off, endIndex, isNegative, hasLeadingZero, errorProfile);
}
/**
* Tries to parse eight digits from a byte array provided in a long.
*
* @param value an array of 8 bytes in a long
* @return the parsed digits or -1 on failure
*/
private static int tryToParseEightDigits(long value) {
long val = value - 0x3030303030303030L;
long l = ((value + 0x4646464646464646L) | val) & 0x8080808080808080L;
if (l != 0L) {
return -1;
}
long mask = 0x000000FF000000FFL;
long mul1 = 0x000F424000000064L; // 100 + (1000000ULL << 32)
long mul2 = 0x0000271000000001L; // 1 + (10000ULL << 32)
val = (val * 10) + (val >>> 8); // val = (val * 2561) >> 8;
val = (((val & mask) * mul1) + (((val >>> 16) & mask) * mul2)) >>> 32;
return (int) (val);
}
private static double parseInfinity(Node location, AbstractTruffleString a, Object arrayA, int strideA, int curIndex, int endIndex, boolean negative, int off, InlinedBranchProfile errorProfile)
throws TruffleString.NumberFormatException {
int index = curIndex;
if (index + 7 < endIndex && regionMatches(location, a, arrayA, strideA, index, TStringConstants.getInfinity(a.encoding()))) {
index = skipWhitespace(a, arrayA, strideA, index + 8, endIndex);
if (index < endIndex) {
errorProfile.enter(location);
throw numberFormatException(a, off, endIndex - off, Reason.INVALID_CODEPOINT);
}
return negative ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY;
} else {
errorProfile.enter(location);
throw numberFormatException(a, off, endIndex - off, Reason.INVALID_CODEPOINT);
}
}
private static double parseNaN(Node location, AbstractTruffleString a, Object arrayA, int strideA, int curIndex, int endIndex, int off, InlinedBranchProfile errorProfile)
throws TruffleString.NumberFormatException {
int index = curIndex;
if (index + 2 < endIndex && regionMatches(location, a, arrayA, strideA, index, TStringConstants.getNaN(a.encoding()))) {
index = skipWhitespace(a, arrayA, strideA, index + 3, endIndex);
if (index < endIndex) {
errorProfile.enter(location);
throw numberFormatException(a, off, endIndex - off, Reason.INVALID_CODEPOINT);
}
return Double.NaN;
} else {
errorProfile.enter(location);
throw numberFormatException(a, off, endIndex - off, Reason.INVALID_CODEPOINT);
}
}
private static boolean regionMatches(Node location, AbstractTruffleString a, Object arrayA, int strideA, int index, TruffleString b) {
return TStringOps.regionEqualsWithOrMaskWithStride(location, a, arrayA, strideA, index, b, b.data(), b.stride(), 0, null, b.length());
}
/**
* Parses the following rules (more rules are defined in {@link #parseDouble}).
*
* - RestOfDecimalFloatingPointLiteral:
*
- [Digits] {@code .} [Digits] [ExponentPart]
*
- {@code .} Digits [ExponentPart]
*
- [Digits] ExponentPart
*
*
*
*
* @param location
* @param a the input string
* @param curIndex index to the first character of RestOfHexFloatingPointLiteral
* @param endIndex the end index of the string
* @param isNegative if the resulting number is negative
* @param hasLeadingZero if the digit '0' has been consumed
* @return a double representation
*/
private static double parseRestOfDecimalFloatLiteral(Node location, AbstractTruffleString a, Object arrayA, int strideA, int curIndex, int startIndex, int endIndex,
boolean isNegative, boolean hasLeadingZero, InlinedBranchProfile errorProfile) throws TruffleString.NumberFormatException {
int index = curIndex;
// Parse digits
// ------------
// Note: a multiplication by a constant is cheaper than an
// arbitrary integer multiplication.
int len = endIndex - startIndex;
long digits = 0; // digits is treated as an unsigned long
int exponent = 0;
final int indexOfFirstDigit = index;
int virtualIndexOfPoint = -1;
final int digitCount;
int ch = 0;
for (; index < endIndex; index++) {
ch = readValue(a, arrayA, strideA, index);
if (isDigit(ch)) {
// This might overflow, we deal with it later.
digits = 10 * digits + ch - '0';
} else if (ch == '.') {
if (virtualIndexOfPoint != -1) {
errorProfile.enter(location);
throw numberFormatException(a, startIndex, len, Reason.MULTIPLE_DECIMAL_POINTS);
}
virtualIndexOfPoint = index;
if (strideA == 0) {
while (index < endIndex - 9) {
long val = TStringOps.readS3(arrayA, a.offset() + index + 1, (a.length() - (index + 1)) >> 3);
int parsed = tryToParseEightDigits(val);
if (parsed >= 0) {
// This might overflow, we deal with it later.
digits = digits * 100_000_000L + parsed;
index += 8;
} else {
break;
}
}
}
} else {
break;
}
}
final int indexAfterDigits = index;
if (virtualIndexOfPoint == -1) {
digitCount = indexAfterDigits - indexOfFirstDigit;
virtualIndexOfPoint = indexAfterDigits;
} else {
digitCount = indexAfterDigits - indexOfFirstDigit - 1;
exponent = virtualIndexOfPoint - index + 1;
}
// Parse exponent number
// ---------------------
long expNumber = 0;
final boolean hasExponent = (ch == 'e') || (ch == 'E');
if (hasExponent) {
ch = ++index < endIndex ? readValue(a, arrayA, strideA, index) : 0;
boolean negExp = ch == '-';
if (negExp || ch == '+') {
ch = ++index < endIndex ? readValue(a, arrayA, strideA, index) : 0;
}
if (!isDigit(ch)) {
errorProfile.enter(location);
throw numberFormatException(a, startIndex, len, Reason.INVALID_CODEPOINT);
}
do {
// Guard against overflow of exp_number
if (expNumber < MINIMAL_EIGHT_DIGIT_INTEGER) {
expNumber = 10 * expNumber + ch - '0';
}
ch = ++index < endIndex ? readValue(a, arrayA, strideA, index) : 0;
} while (isDigit(ch));
if (negExp) {
expNumber = -expNumber;
}
exponent += (int) expNumber;
}
// Skip trailing whitespace
// ------------------------
index = skipWhitespace(a, arrayA, strideA, index, endIndex);
if (index < endIndex || !hasLeadingZero && digitCount == 0) {
errorProfile.enter(location);
throw numberFormatException(a, startIndex, len, Reason.EMPTY);
}
// Re-parse digits in case of a potential overflow
// -----------------------------------------------
final boolean isDigitsTruncated;
int skipCountInTruncatedDigits = 0; // counts +1 if we skipped over the decimal point
if (digitCount > 19) {
digits = 0;
for (index = indexOfFirstDigit; index < indexAfterDigits; index++) {
ch = readValue(a, arrayA, strideA, index);
if (ch == '.') {
skipCountInTruncatedDigits++;
} else {
if (Long.compareUnsigned(digits, MINIMAL_NINETEEN_DIGIT_INTEGER) < 0) {
digits = 10 * digits + ch - '0';
} else {
break;
}
}
}
isDigitsTruncated = index < indexAfterDigits;
} else {
isDigitsTruncated = false;
}
double result = FastDoubleMath.decFloatLiteralToDouble(index, isNegative, digits, exponent, virtualIndexOfPoint, expNumber, isDigitsTruncated, skipCountInTruncatedDigits);
return Double.isNaN(result) ? parseViaJavaString(location, a, arrayA, strideA, startIndex, len) : result;
}
/**
* Parses the following rules (more rules are defined in {@link #parseDouble}).
*
* - RestOfDecimalFloatingPointLiteral:
*
- [Digits] {@code .} [Digits] [ExponentPart]
*
- {@code .} Digits [ExponentPart]
*
- [Digits] ExponentPart
*
*/
private static double parseViaJavaString(Node location, AbstractTruffleString a, Object arrayA, int strideA, int startIndex, int len) {
final byte[] arrayStr;
final int offsetStr;
if (arrayA instanceof byte[] && strideA == 0) {
arrayStr = (byte[]) arrayA;
offsetStr = a.offset() + startIndex;
} else {
arrayStr = new byte[len];
TStringOps.arraycopyWithStride(location, arrayA, a.offset(), strideA, startIndex, arrayStr, 0, 0, 0, len);
offsetStr = 0;
}
return callJavaStringParseDouble(len, arrayStr, offsetStr);
}
@TruffleBoundary
private static double callJavaStringParseDouble(int len, byte[] arrayStr, int offsetStr) {
return Double.parseDouble(new String(arrayStr, offsetStr, len, StandardCharsets.ISO_8859_1));
}
/**
* Parses the following rules (more rules are defined in {@link #parseDouble}).
*
* - RestOfHexFloatingPointLiteral:
*
- RestOfHexSignificand BinaryExponent
*
*
*
* - RestOfHexSignificand:
*
- HexDigits
*
- HexDigits {@code .}
*
- [HexDigits] {@code .} HexDigits
*
*
*
*
* @param a the input string
* @param curIndex index to the first character of RestOfHexFloatingPointLiteral
* @param startIndex the start index of the string
* @param endIndex the end index of the string
* @param isNegative if the resulting number is negative
* @return a double representation
*/
private static double parseRestOfHexFloatingPointLiteral(Node location, AbstractTruffleString a, Object arrayA, int strideA, int curIndex, int startIndex, int endIndex, boolean isNegative,
InlinedBranchProfile errorProfile) throws TruffleString.NumberFormatException {
int index = curIndex;
int len = endIndex - startIndex;
if (index >= endIndex) {
errorProfile.enter(location);
throw numberFormatException(a, startIndex, len, Reason.MALFORMED_HEX_ESCAPE);
}
// Parse digits
// ------------
long digits = 0; // digits is treated as an unsigned long
int exponent = 0;
final int indexOfFirstDigit = index;
int virtualIndexOfPoint = -1;
final int digitCount;
int ch = 0;
for (; index < endIndex; index++) {
ch = readValue(a, arrayA, strideA, index);
// Table look up is faster than a sequence of if-else-branches.
int hexValue = ch > 0x7f ? OTHER_CLASS : CHAR_TO_HEX_MAP[ch];
if (hexValue >= 0) {
digits = (digits << 4) | hexValue; // This might overflow, we deal with it
// later.
} else if (hexValue == DECIMAL_POINT_CLASS) {
if (virtualIndexOfPoint != -1) {
errorProfile.enter(location);
throw numberFormatException(a, startIndex, len, Reason.MULTIPLE_DECIMAL_POINTS);
}
virtualIndexOfPoint = index;
} else {
break;
}
}
final int indexAfterDigits = index;
if (virtualIndexOfPoint == -1) {
digitCount = indexAfterDigits - indexOfFirstDigit;
virtualIndexOfPoint = indexAfterDigits;
} else {
digitCount = indexAfterDigits - indexOfFirstDigit - 1;
exponent = Math.min(virtualIndexOfPoint - index + 1, MINIMAL_EIGHT_DIGIT_INTEGER) * 4;
}
// Parse exponent number
// ---------------------
long expNumber = 0;
final boolean hasExponent = (ch == 'p') || (ch == 'P');
if (hasExponent) {
ch = ++index < endIndex ? readValue(a, arrayA, strideA, index) : 0;
boolean negExp = ch == '-';
if (negExp || ch == '+') {
ch = ++index < endIndex ? readValue(a, arrayA, strideA, index) : 0;
}
if (!isDigit(ch)) {
errorProfile.enter(location);
throw numberFormatException(a, startIndex, len, Reason.INVALID_CODEPOINT);
}
do {
// Guard against overflow of exp_number
if (expNumber < MINIMAL_EIGHT_DIGIT_INTEGER) {
expNumber = 10 * expNumber + ch - '0';
}
ch = ++index < endIndex ? readValue(a, arrayA, strideA, index) : 0;
} while (isDigit(ch));
if (negExp) {
expNumber = -expNumber;
}
exponent += (int) expNumber;
}
// Skip trailing whitespace
// ------------------------
index = skipWhitespace(a, arrayA, strideA, index, endIndex);
if (index < endIndex || digitCount == 0 && readValue(a, arrayA, strideA, virtualIndexOfPoint) != '.' || !hasExponent) {
errorProfile.enter(location);
throw numberFormatException(a, startIndex, len, Reason.EMPTY);
}
// Re-parse digits in case of a potential overflow
// -----------------------------------------------
final boolean isDigitsTruncated;
int skipCountInTruncatedDigits = 0; // counts +1 if we skipped over the decimal point
if (digitCount > 16) {
digits = 0;
for (index = indexOfFirstDigit; index < indexAfterDigits; index++) {
ch = readValue(a, arrayA, strideA, index);
// Table look up is faster than a sequence of if-else-branches.
int hexValue = ch > 0x7f ? OTHER_CLASS : CHAR_TO_HEX_MAP[ch];
if (hexValue >= 0) {
if (Long.compareUnsigned(digits, MINIMAL_NINETEEN_DIGIT_INTEGER) < 0) {
digits = (digits << 4) | hexValue;
} else {
break;
}
} else {
skipCountInTruncatedDigits++;
}
}
isDigitsTruncated = (index < indexAfterDigits);
} else {
isDigitsTruncated = false;
}
double d = FastDoubleMath.hexFloatLiteralToDouble(index, isNegative, digits, exponent, virtualIndexOfPoint, expNumber, isDigitsTruncated, skipCountInTruncatedDigits);
return Double.isNaN(d) ? parseViaJavaString(location, a, arrayA, strideA, startIndex, len) : d;
}
private static int skipWhitespace(AbstractTruffleString a, Object arrayA, int strideA, int startIndex, int endIndex) {
int index = startIndex;
for (; index < endIndex; index++) {
if (readValue(a, arrayA, strideA, index) > 0x20) {
break;
}
}
return index;
}
/**
* This class provides the mathematical functions needed by {@link FastDoubleParser}.
*
* This is a C++ to Java port of Daniel Lemire's fast_double_parser.
*
* The code contains enhancements from Daniel Lemire's fast_float_parser, so that it can parse
* double Strings with very long sequences of numbers
*
* References:
*
* - Daniel Lemire, fast_double_parser, 4x faster than strtod. Apache License 2.0 or Boost
* Software License.
* - github.com
*
* - Daniel Lemire, fast_float number parsing library: 4x faster than strtod. Apache License
* 2.0.
* - github.com
*
* - Daniel Lemire, Number Parsing at a Gigabyte per Second, Software: Practice and Experience
* 51 (8), 2021. arXiv.2101.11408v3 [cs.DS] 24 Feb 2021
* - arxiv.org
*
*
*/
private static final class FastDoubleMath {
/**
* The smallest non-zero float (binary64) is 2^-1074. We take as input numbers of the form w
* x 10^q where w < 2^64. We have that {@literal w * 10^-343 < 2^(64-344) 5^-343 < 2^-1076}.
*
* However, we have that
* {@literal (2^64-1) * 10^-342 = (2^64-1) * 2^-342 * 5^-342 > 2^-1074}. Thus it is possible
* for a number of the form w * 10^-342 where w is a 64-bit value to be a non-zero
* floating-point number.
*
* ********
*
* If we are solely interested in the *normal* numbers then the smallest value is 2^-1022.
* We can generate a value larger than 2^-1022 with expressions of the form w * 10^-326.
* Thus we need to pick FASTFLOAT_SMALLEST_POWER >= -326.
*
* ********
*
* Any number of form w * 10^309 where w>= 1 is going to be infinite in binary64 so we never
* need to worry about powers of 5 greater than 308.
*/
private static final int FASTFLOAT_DEC_SMALLEST_POWER = -325;
private static final int FASTFLOAT_DEC_LARGEST_POWER = 308;
private static final int FASTFLOAT_HEX_SMALLEST_POWER = Double.MIN_EXPONENT;
private static final int FASTFLOAT_HEX_LARGEST_POWER = Double.MAX_EXPONENT;
/**
* Precomputed powers of ten from 10^0 to 10^22. These can be represented exactly using the
* double type.
*/
@CompilationFinal(dimensions = 1) private static final double[] powerOfTen = {
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,
1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22};
/**
* When mapping numbers from decimal to binary, we go from w * 10^q to m * 2^p but we have
* 10^q = 5^q * 2^q, so effectively we are trying to match w * 2^q * 5^q to m * 2^p. Thus
* the powers of two are not a concern since they can be represented exactly using the
* binary notation, only the powers of five affect the binary significand.
*
*
* The mantissas of powers of ten from -308 to 308, extended out to sixty four bits. The
* array contains the powers of ten approximated as a 64-bit mantissa. It goes from
* 10^FASTFLOAT_SMALLEST_POWER to 10^FASTFLOAT_LARGEST_POWER (inclusively). The mantissa is
* truncated, and never rounded up. Uses about 5KB.
*/
@CompilationFinal(dimensions = 1) private static final long[] MANTISSA_64 = {
0xa5ced43b7e3e9188L, 0xcf42894a5dce35eaL,
0x818995ce7aa0e1b2L, 0xa1ebfb4219491a1fL,
0xca66fa129f9b60a6L, 0xfd00b897478238d0L,
0x9e20735e8cb16382L, 0xc5a890362fddbc62L,
0xf712b443bbd52b7bL, 0x9a6bb0aa55653b2dL,
0xc1069cd4eabe89f8L, 0xf148440a256e2c76L,
0x96cd2a865764dbcaL, 0xbc807527ed3e12bcL,
0xeba09271e88d976bL, 0x93445b8731587ea3L,
0xb8157268fdae9e4cL, 0xe61acf033d1a45dfL,
0x8fd0c16206306babL, 0xb3c4f1ba87bc8696L,
0xe0b62e2929aba83cL, 0x8c71dcd9ba0b4925L,
0xaf8e5410288e1b6fL, 0xdb71e91432b1a24aL,
0x892731ac9faf056eL, 0xab70fe17c79ac6caL,
0xd64d3d9db981787dL, 0x85f0468293f0eb4eL,
0xa76c582338ed2621L, 0xd1476e2c07286faaL,
0x82cca4db847945caL, 0xa37fce126597973cL,
0xcc5fc196fefd7d0cL, 0xff77b1fcbebcdc4fL,
0x9faacf3df73609b1L, 0xc795830d75038c1dL,
0xf97ae3d0d2446f25L, 0x9becce62836ac577L,
0xc2e801fb244576d5L, 0xf3a20279ed56d48aL,
0x9845418c345644d6L, 0xbe5691ef416bd60cL,
0xedec366b11c6cb8fL, 0x94b3a202eb1c3f39L,
0xb9e08a83a5e34f07L, 0xe858ad248f5c22c9L,
0x91376c36d99995beL, 0xb58547448ffffb2dL,
0xe2e69915b3fff9f9L, 0x8dd01fad907ffc3bL,
0xb1442798f49ffb4aL, 0xdd95317f31c7fa1dL,
0x8a7d3eef7f1cfc52L, 0xad1c8eab5ee43b66L,
0xd863b256369d4a40L, 0x873e4f75e2224e68L,
0xa90de3535aaae202L, 0xd3515c2831559a83L,
0x8412d9991ed58091L, 0xa5178fff668ae0b6L,
0xce5d73ff402d98e3L, 0x80fa687f881c7f8eL,
0xa139029f6a239f72L, 0xc987434744ac874eL,
0xfbe9141915d7a922L, 0x9d71ac8fada6c9b5L,
0xc4ce17b399107c22L, 0xf6019da07f549b2bL,
0x99c102844f94e0fbL, 0xc0314325637a1939L,
0xf03d93eebc589f88L, 0x96267c7535b763b5L,
0xbbb01b9283253ca2L, 0xea9c227723ee8bcbL,
0x92a1958a7675175fL, 0xb749faed14125d36L,
0xe51c79a85916f484L, 0x8f31cc0937ae58d2L,
0xb2fe3f0b8599ef07L, 0xdfbdcece67006ac9L,
0x8bd6a141006042bdL, 0xaecc49914078536dL,
0xda7f5bf590966848L, 0x888f99797a5e012dL,
0xaab37fd7d8f58178L, 0xd5605fcdcf32e1d6L,
0x855c3be0a17fcd26L, 0xa6b34ad8c9dfc06fL,
0xd0601d8efc57b08bL, 0x823c12795db6ce57L,
0xa2cb1717b52481edL, 0xcb7ddcdda26da268L,
0xfe5d54150b090b02L, 0x9efa548d26e5a6e1L,
0xc6b8e9b0709f109aL, 0xf867241c8cc6d4c0L,
0x9b407691d7fc44f8L, 0xc21094364dfb5636L,
0xf294b943e17a2bc4L, 0x979cf3ca6cec5b5aL,
0xbd8430bd08277231L, 0xece53cec4a314ebdL,
0x940f4613ae5ed136L, 0xb913179899f68584L,
0xe757dd7ec07426e5L, 0x9096ea6f3848984fL,
0xb4bca50b065abe63L, 0xe1ebce4dc7f16dfbL,
0x8d3360f09cf6e4bdL, 0xb080392cc4349decL,
0xdca04777f541c567L, 0x89e42caaf9491b60L,
0xac5d37d5b79b6239L, 0xd77485cb25823ac7L,
0x86a8d39ef77164bcL, 0xa8530886b54dbdebL,
0xd267caa862a12d66L, 0x8380dea93da4bc60L,
0xa46116538d0deb78L, 0xcd795be870516656L,
0x806bd9714632dff6L, 0xa086cfcd97bf97f3L,
0xc8a883c0fdaf7df0L, 0xfad2a4b13d1b5d6cL,
0x9cc3a6eec6311a63L, 0xc3f490aa77bd60fcL,
0xf4f1b4d515acb93bL, 0x991711052d8bf3c5L,
0xbf5cd54678eef0b6L, 0xef340a98172aace4L,
0x9580869f0e7aac0eL, 0xbae0a846d2195712L,
0xe998d258869facd7L, 0x91ff83775423cc06L,
0xb67f6455292cbf08L, 0xe41f3d6a7377eecaL,
0x8e938662882af53eL, 0xb23867fb2a35b28dL,
0xdec681f9f4c31f31L, 0x8b3c113c38f9f37eL,
0xae0b158b4738705eL, 0xd98ddaee19068c76L,
0x87f8a8d4cfa417c9L, 0xa9f6d30a038d1dbcL,
0xd47487cc8470652bL, 0x84c8d4dfd2c63f3bL,
0xa5fb0a17c777cf09L, 0xcf79cc9db955c2ccL,
0x81ac1fe293d599bfL, 0xa21727db38cb002fL,
0xca9cf1d206fdc03bL, 0xfd442e4688bd304aL,
0x9e4a9cec15763e2eL, 0xc5dd44271ad3cdbaL,
0xf7549530e188c128L, 0x9a94dd3e8cf578b9L,
0xc13a148e3032d6e7L, 0xf18899b1bc3f8ca1L,
0x96f5600f15a7b7e5L, 0xbcb2b812db11a5deL,
0xebdf661791d60f56L, 0x936b9fcebb25c995L,
0xb84687c269ef3bfbL, 0xe65829b3046b0afaL,
0x8ff71a0fe2c2e6dcL, 0xb3f4e093db73a093L,
0xe0f218b8d25088b8L, 0x8c974f7383725573L,
0xafbd2350644eeacfL, 0xdbac6c247d62a583L,
0x894bc396ce5da772L, 0xab9eb47c81f5114fL,
0xd686619ba27255a2L, 0x8613fd0145877585L,
0xa798fc4196e952e7L, 0xd17f3b51fca3a7a0L,
0x82ef85133de648c4L, 0xa3ab66580d5fdaf5L,
0xcc963fee10b7d1b3L, 0xffbbcfe994e5c61fL,
0x9fd561f1fd0f9bd3L, 0xc7caba6e7c5382c8L,
0xf9bd690a1b68637bL, 0x9c1661a651213e2dL,
0xc31bfa0fe5698db8L, 0xf3e2f893dec3f126L,
0x986ddb5c6b3a76b7L, 0xbe89523386091465L,
0xee2ba6c0678b597fL, 0x94db483840b717efL,
0xba121a4650e4ddebL, 0xe896a0d7e51e1566L,
0x915e2486ef32cd60L, 0xb5b5ada8aaff80b8L,
0xe3231912d5bf60e6L, 0x8df5efabc5979c8fL,
0xb1736b96b6fd83b3L, 0xddd0467c64bce4a0L,
0x8aa22c0dbef60ee4L, 0xad4ab7112eb3929dL,
0xd89d64d57a607744L, 0x87625f056c7c4a8bL,
0xa93af6c6c79b5d2dL, 0xd389b47879823479L,
0x843610cb4bf160cbL, 0xa54394fe1eedb8feL,
0xce947a3da6a9273eL, 0x811ccc668829b887L,
0xa163ff802a3426a8L, 0xc9bcff6034c13052L,
0xfc2c3f3841f17c67L, 0x9d9ba7832936edc0L,
0xc5029163f384a931L, 0xf64335bcf065d37dL,
0x99ea0196163fa42eL, 0xc06481fb9bcf8d39L,
0xf07da27a82c37088L, 0x964e858c91ba2655L,
0xbbe226efb628afeaL, 0xeadab0aba3b2dbe5L,
0x92c8ae6b464fc96fL, 0xb77ada0617e3bbcbL,
0xe55990879ddcaabdL, 0x8f57fa54c2a9eab6L,
0xb32df8e9f3546564L, 0xdff9772470297ebdL,
0x8bfbea76c619ef36L, 0xaefae51477a06b03L,
0xdab99e59958885c4L, 0x88b402f7fd75539bL,
0xaae103b5fcd2a881L, 0xd59944a37c0752a2L,
0x857fcae62d8493a5L, 0xa6dfbd9fb8e5b88eL,
0xd097ad07a71f26b2L, 0x825ecc24c873782fL,
0xa2f67f2dfa90563bL, 0xcbb41ef979346bcaL,
0xfea126b7d78186bcL, 0x9f24b832e6b0f436L,
0xc6ede63fa05d3143L, 0xf8a95fcf88747d94L,
0x9b69dbe1b548ce7cL, 0xc24452da229b021bL,
0xf2d56790ab41c2a2L, 0x97c560ba6b0919a5L,
0xbdb6b8e905cb600fL, 0xed246723473e3813L,
0x9436c0760c86e30bL, 0xb94470938fa89bceL,
0xe7958cb87392c2c2L, 0x90bd77f3483bb9b9L,
0xb4ecd5f01a4aa828L, 0xe2280b6c20dd5232L,
0x8d590723948a535fL, 0xb0af48ec79ace837L,
0xdcdb1b2798182244L, 0x8a08f0f8bf0f156bL,
0xac8b2d36eed2dac5L, 0xd7adf884aa879177L,
0x86ccbb52ea94baeaL, 0xa87fea27a539e9a5L,
0xd29fe4b18e88640eL, 0x83a3eeeef9153e89L,
0xa48ceaaab75a8e2bL, 0xcdb02555653131b6L,
0x808e17555f3ebf11L, 0xa0b19d2ab70e6ed6L,
0xc8de047564d20a8bL, 0xfb158592be068d2eL,
0x9ced737bb6c4183dL, 0xc428d05aa4751e4cL,
0xf53304714d9265dfL, 0x993fe2c6d07b7fabL,
0xbf8fdb78849a5f96L, 0xef73d256a5c0f77cL,
0x95a8637627989aadL, 0xbb127c53b17ec159L,
0xe9d71b689dde71afL, 0x9226712162ab070dL,
0xb6b00d69bb55c8d1L, 0xe45c10c42a2b3b05L,
0x8eb98a7a9a5b04e3L, 0xb267ed1940f1c61cL,
0xdf01e85f912e37a3L, 0x8b61313bbabce2c6L,
0xae397d8aa96c1b77L, 0xd9c7dced53c72255L,
0x881cea14545c7575L, 0xaa242499697392d2L,
0xd4ad2dbfc3d07787L, 0x84ec3c97da624ab4L,
0xa6274bbdd0fadd61L, 0xcfb11ead453994baL,
0x81ceb32c4b43fcf4L, 0xa2425ff75e14fc31L,
0xcad2f7f5359a3b3eL, 0xfd87b5f28300ca0dL,
0x9e74d1b791e07e48L, 0xc612062576589ddaL,
0xf79687aed3eec551L, 0x9abe14cd44753b52L,
0xc16d9a0095928a27L, 0xf1c90080baf72cb1L,
0x971da05074da7beeL, 0xbce5086492111aeaL,
0xec1e4a7db69561a5L, 0x9392ee8e921d5d07L,
0xb877aa3236a4b449L, 0xe69594bec44de15bL,
0x901d7cf73ab0acd9L, 0xb424dc35095cd80fL,
0xe12e13424bb40e13L, 0x8cbccc096f5088cbL,
0xafebff0bcb24aafeL, 0xdbe6fecebdedd5beL,
0x89705f4136b4a597L, 0xabcc77118461cefcL,
0xd6bf94d5e57a42bcL, 0x8637bd05af6c69b5L,
0xa7c5ac471b478423L, 0xd1b71758e219652bL,
0x83126e978d4fdf3bL, 0xa3d70a3d70a3d70aL,
0xccccccccccccccccL, 0x8000000000000000L,
0xa000000000000000L, 0xc800000000000000L,
0xfa00000000000000L, 0x9c40000000000000L,
0xc350000000000000L, 0xf424000000000000L,
0x9896800000000000L, 0xbebc200000000000L,
0xee6b280000000000L, 0x9502f90000000000L,
0xba43b74000000000L, 0xe8d4a51000000000L,
0x9184e72a00000000L, 0xb5e620f480000000L,
0xe35fa931a0000000L, 0x8e1bc9bf04000000L,
0xb1a2bc2ec5000000L, 0xde0b6b3a76400000L,
0x8ac7230489e80000L, 0xad78ebc5ac620000L,
0xd8d726b7177a8000L, 0x878678326eac9000L,
0xa968163f0a57b400L, 0xd3c21bcecceda100L,
0x84595161401484a0L, 0xa56fa5b99019a5c8L,
0xcecb8f27f4200f3aL, 0x813f3978f8940984L,
0xa18f07d736b90be5L, 0xc9f2c9cd04674edeL,
0xfc6f7c4045812296L, 0x9dc5ada82b70b59dL,
0xc5371912364ce305L, 0xf684df56c3e01bc6L,
0x9a130b963a6c115cL, 0xc097ce7bc90715b3L,
0xf0bdc21abb48db20L, 0x96769950b50d88f4L,
0xbc143fa4e250eb31L, 0xeb194f8e1ae525fdL,
0x92efd1b8d0cf37beL, 0xb7abc627050305adL,
0xe596b7b0c643c719L, 0x8f7e32ce7bea5c6fL,
0xb35dbf821ae4f38bL, 0xe0352f62a19e306eL,
0x8c213d9da502de45L, 0xaf298d050e4395d6L,
0xdaf3f04651d47b4cL, 0x88d8762bf324cd0fL,
0xab0e93b6efee0053L, 0xd5d238a4abe98068L,
0x85a36366eb71f041L, 0xa70c3c40a64e6c51L,
0xd0cf4b50cfe20765L, 0x82818f1281ed449fL,
0xa321f2d7226895c7L, 0xcbea6f8ceb02bb39L,
0xfee50b7025c36a08L, 0x9f4f2726179a2245L,
0xc722f0ef9d80aad6L, 0xf8ebad2b84e0d58bL,
0x9b934c3b330c8577L, 0xc2781f49ffcfa6d5L,
0xf316271c7fc3908aL, 0x97edd871cfda3a56L,
0xbde94e8e43d0c8ecL, 0xed63a231d4c4fb27L,
0x945e455f24fb1cf8L, 0xb975d6b6ee39e436L,
0xe7d34c64a9c85d44L, 0x90e40fbeea1d3a4aL,
0xb51d13aea4a488ddL, 0xe264589a4dcdab14L,
0x8d7eb76070a08aecL, 0xb0de65388cc8ada8L,
0xdd15fe86affad912L, 0x8a2dbf142dfcc7abL,
0xacb92ed9397bf996L, 0xd7e77a8f87daf7fbL,
0x86f0ac99b4e8dafdL, 0xa8acd7c0222311bcL,
0xd2d80db02aabd62bL, 0x83c7088e1aab65dbL,
0xa4b8cab1a1563f52L, 0xcde6fd5e09abcf26L,
0x80b05e5ac60b6178L, 0xa0dc75f1778e39d6L,
0xc913936dd571c84cL, 0xfb5878494ace3a5fL,
0x9d174b2dcec0e47bL, 0xc45d1df942711d9aL,
0xf5746577930d6500L, 0x9968bf6abbe85f20L,
0xbfc2ef456ae276e8L, 0xefb3ab16c59b14a2L,
0x95d04aee3b80ece5L, 0xbb445da9ca61281fL,
0xea1575143cf97226L, 0x924d692ca61be758L,
0xb6e0c377cfa2e12eL, 0xe498f455c38b997aL,
0x8edf98b59a373fecL, 0xb2977ee300c50fe7L,
0xdf3d5e9bc0f653e1L, 0x8b865b215899f46cL,
0xae67f1e9aec07187L, 0xda01ee641a708de9L,
0x884134fe908658b2L, 0xaa51823e34a7eedeL,
0xd4e5e2cdc1d1ea96L, 0x850fadc09923329eL,
0xa6539930bf6bff45L, 0xcfe87f7cef46ff16L,
0x81f14fae158c5f6eL, 0xa26da3999aef7749L,
0xcb090c8001ab551cL, 0xfdcb4fa002162a63L,
0x9e9f11c4014dda7eL, 0xc646d63501a1511dL,
0xf7d88bc24209a565L, 0x9ae757596946075fL,
0xc1a12d2fc3978937L, 0xf209787bb47d6b84L,
0x9745eb4d50ce6332L, 0xbd176620a501fbffL,
0xec5d3fa8ce427affL, 0x93ba47c980e98cdfL,
0xb8a8d9bbe123f017L, 0xe6d3102ad96cec1dL,
0x9043ea1ac7e41392L, 0xb454e4a179dd1877L,
0xe16a1dc9d8545e94L, 0x8ce2529e2734bb1dL,
0xb01ae745b101e9e4L, 0xdc21a1171d42645dL,
0x899504ae72497ebaL, 0xabfa45da0edbde69L,
0xd6f8d7509292d603L, 0x865b86925b9bc5c2L,
0xa7f26836f282b732L, 0xd1ef0244af2364ffL,
0x8335616aed761f1fL, 0xa402b9c5a8d3a6e7L,
0xcd036837130890a1L, 0x802221226be55a64L,
0xa02aa96b06deb0fdL, 0xc83553c5c8965d3dL,
0xfa42a8b73abbf48cL, 0x9c69a97284b578d7L,
0xc38413cf25e2d70dL, 0xf46518c2ef5b8cd1L,
0x98bf2f79d5993802L, 0xbeeefb584aff8603L,
0xeeaaba2e5dbf6784L, 0x952ab45cfa97a0b2L,
0xba756174393d88dfL, 0xe912b9d1478ceb17L,
0x91abb422ccb812eeL, 0xb616a12b7fe617aaL,
0xe39c49765fdf9d94L, 0x8e41ade9fbebc27dL,
0xb1d219647ae6b31cL, 0xde469fbd99a05fe3L,
0x8aec23d680043beeL, 0xada72ccc20054ae9L,
0xd910f7ff28069da4L, 0x87aa9aff79042286L,
0xa99541bf57452b28L, 0xd3fa922f2d1675f2L,
0x847c9b5d7c2e09b7L, 0xa59bc234db398c25L,
0xcf02b2c21207ef2eL, 0x8161afb94b44f57dL,
0xa1ba1ba79e1632dcL, 0xca28a291859bbf93L,
0xfcb2cb35e702af78L, 0x9defbf01b061adabL,
0xc56baec21c7a1916L, 0xf6c69a72a3989f5bL,
0x9a3c2087a63f6399L, 0xc0cb28a98fcf3c7fL,
0xf0fdf2d3f3c30b9fL, 0x969eb7c47859e743L,
0xbc4665b596706114L, 0xeb57ff22fc0c7959L,
0x9316ff75dd87cbd8L, 0xb7dcbf5354e9beceL,
0xe5d3ef282a242e81L, 0x8fa475791a569d10L,
0xb38d92d760ec4455L, 0xe070f78d3927556aL,
0x8c469ab843b89562L, 0xaf58416654a6babbL,
0xdb2e51bfe9d0696aL, 0x88fcf317f22241e2L,
0xab3c2fddeeaad25aL, 0xd60b3bd56a5586f1L,
0x85c7056562757456L, 0xa738c6bebb12d16cL,
0xd106f86e69d785c7L, 0x82a45b450226b39cL,
0xa34d721642b06084L, 0xcc20ce9bd35c78a5L,
0xff290242c83396ceL, 0x9f79a169bd203e41L,
0xc75809c42c684dd1L, 0xf92e0c3537826145L,
0x9bbcc7a142b17ccbL, 0xc2abf989935ddbfeL,
0xf356f7ebf83552feL, 0x98165af37b2153deL,
0xbe1bf1b059e9a8d6L, 0xeda2ee1c7064130cL,
0x9485d4d1c63e8be7L, 0xb9a74a0637ce2ee1L,
0xe8111c87c5c1ba99L, 0x910ab1d4db9914a0L,
0xb54d5e4a127f59c8L, 0xe2a0b5dc971f303aL,
0x8da471a9de737e24L, 0xb10d8e1456105dadL,
0xdd50f1996b947518L, 0x8a5296ffe33cc92fL,
0xace73cbfdc0bfb7bL, 0xd8210befd30efa5aL,
0x8714a775e3e95c78L, 0xa8d9d1535ce3b396L,
0xd31045a8341ca07cL, 0x83ea2b892091e44dL,
0xa4e4b66b68b65d60L, 0xce1de40642e3f4b9L,
0x80d2ae83e9ce78f3L, 0xa1075a24e4421730L,
0xc94930ae1d529cfcL, 0xfb9b7cd9a4a7443cL,
0x9d412e0806e88aa5L, 0xc491798a08a2ad4eL,
0xf5b5d7ec8acb58a2L, 0x9991a6f3d6bf1765L,
0xbff610b0cc6edd3fL, 0xeff394dcff8a948eL,
0x95f83d0a1fb69cd9L, 0xbb764c4ca7a4440fL,
0xea53df5fd18d5513L, 0x92746b9be2f8552cL,
0xb7118682dbb66a77L, 0xe4d5e82392a40515L,
0x8f05b1163ba6832dL, 0xb2c71d5bca9023f8L,
0xdf78e4b2bd342cf6L, 0x8bab8eefb6409c1aL,
0xae9672aba3d0c320L, 0xda3c0f568cc4f3e8L,
0x8865899617fb1871L, 0xaa7eebfb9df9de8dL,
0xd51ea6fa85785631L, 0x8533285c936b35deL,
0xa67ff273b8460356L, 0xd01fef10a657842cL,
0x8213f56a67f6b29bL, 0xa298f2c501f45f42L,
0xcb3f2f7642717713L, 0xfe0efb53d30dd4d7L,
0x9ec95d1463e8a506L, 0xc67bb4597ce2ce48L,
0xf81aa16fdc1b81daL, 0x9b10a4e5e9913128L,
0xc1d4ce1f63f57d72L, 0xf24a01a73cf2dccfL,
0x976e41088617ca01L, 0xbd49d14aa79dbc82L,
0xec9c459d51852ba2L, 0x93e1ab8252f33b45L,
0xb8da1662e7b00a17L, 0xe7109bfba19c0c9dL,
0x906a617d450187e2L, 0xb484f9dc9641e9daL,
0xe1a63853bbd26451L, 0x8d07e33455637eb2L,
0xb049dc016abc5e5fL, 0xdc5c5301c56b75f7L,
0x89b9b3e11b6329baL, 0xac2820d9623bf429L,
0xd732290fbacaf133L, 0x867f59a9d4bed6c0L,
0xa81f301449ee8c70L, 0xd226fc195c6a2f8cL,
0x83585d8fd9c25db7L, 0xa42e74f3d032f525L,
0xcd3a1230c43fb26fL, 0x80444b5e7aa7cf85L,
0xa0555e361951c366L, 0xc86ab5c39fa63440L,
0xfa856334878fc150L, 0x9c935e00d4b9d8d2L,
0xc3b8358109e84f07L, 0xf4a642e14c6262c8L,
0x98e7e9cccfbd7dbdL, 0xbf21e44003acdd2cL,
0xeeea5d5004981478L, 0x95527a5202df0ccbL,
0xbaa718e68396cffdL, 0xe950df20247c83fdL,
0x91d28b7416cdd27eL, 0xb6472e511c81471dL,
0xe3d8f9e563a198e5L, 0x8e679c2f5e44ff8fL};
/**
* A complement to mantissa_64 complete to a 128-bit mantissa. Uses about 5KB but is rarely
* accessed.
*/
@CompilationFinal(dimensions = 1) private static final long[] MANTISSA_128 = {
0x419ea3bd35385e2dL, 0x52064cac828675b9L,
0x7343efebd1940993L, 0x1014ebe6c5f90bf8L,
0xd41a26e077774ef6L, 0x8920b098955522b4L,
0x55b46e5f5d5535b0L, 0xeb2189f734aa831dL,
0xa5e9ec7501d523e4L, 0x47b233c92125366eL,
0x999ec0bb696e840aL, 0xc00670ea43ca250dL,
0x380406926a5e5728L, 0xc605083704f5ecf2L,
0xf7864a44c633682eL, 0x7ab3ee6afbe0211dL,
0x5960ea05bad82964L, 0x6fb92487298e33bdL,
0xa5d3b6d479f8e056L, 0x8f48a4899877186cL,
0x331acdabfe94de87L, 0x9ff0c08b7f1d0b14L,
0x7ecf0ae5ee44dd9L, 0xc9e82cd9f69d6150L,
0xbe311c083a225cd2L, 0x6dbd630a48aaf406L,
0x92cbbccdad5b108L, 0x25bbf56008c58ea5L,
0xaf2af2b80af6f24eL, 0x1af5af660db4aee1L,
0x50d98d9fc890ed4dL, 0xe50ff107bab528a0L,
0x1e53ed49a96272c8L, 0x25e8e89c13bb0f7aL,
0x77b191618c54e9acL, 0xd59df5b9ef6a2417L,
0x4b0573286b44ad1dL, 0x4ee367f9430aec32L,
0x229c41f793cda73fL, 0x6b43527578c1110fL,
0x830a13896b78aaa9L, 0x23cc986bc656d553L,
0x2cbfbe86b7ec8aa8L, 0x7bf7d71432f3d6a9L,
0xdaf5ccd93fb0cc53L, 0xd1b3400f8f9cff68L,
0x23100809b9c21fa1L, 0xabd40a0c2832a78aL,
0x16c90c8f323f516cL, 0xae3da7d97f6792e3L,
0x99cd11cfdf41779cL, 0x40405643d711d583L,
0x482835ea666b2572L, 0xda3243650005eecfL,
0x90bed43e40076a82L, 0x5a7744a6e804a291L,
0x711515d0a205cb36L, 0xd5a5b44ca873e03L,
0xe858790afe9486c2L, 0x626e974dbe39a872L,
0xfb0a3d212dc8128fL, 0x7ce66634bc9d0b99L,
0x1c1fffc1ebc44e80L, 0xa327ffb266b56220L,
0x4bf1ff9f0062baa8L, 0x6f773fc3603db4a9L,
0xcb550fb4384d21d3L, 0x7e2a53a146606a48L,
0x2eda7444cbfc426dL, 0xfa911155fefb5308L,
0x793555ab7eba27caL, 0x4bc1558b2f3458deL,
0x9eb1aaedfb016f16L, 0x465e15a979c1cadcL,
0xbfacd89ec191ec9L, 0xcef980ec671f667bL,
0x82b7e12780e7401aL, 0xd1b2ecb8b0908810L,
0x861fa7e6dcb4aa15L, 0x67a791e093e1d49aL,
0xe0c8bb2c5c6d24e0L, 0x58fae9f773886e18L,
0xaf39a475506a899eL, 0x6d8406c952429603L,
0xc8e5087ba6d33b83L, 0xfb1e4a9a90880a64L,
0x5cf2eea09a55067fL, 0xf42faa48c0ea481eL,
0xf13b94daf124da26L, 0x76c53d08d6b70858L,
0x54768c4b0c64ca6eL, 0xa9942f5dcf7dfd09L,
0xd3f93b35435d7c4cL, 0xc47bc5014a1a6dafL,
0x359ab6419ca1091bL, 0xc30163d203c94b62L,
0x79e0de63425dcf1dL, 0x985915fc12f542e4L,
0x3e6f5b7b17b2939dL, 0xa705992ceecf9c42L,
0x50c6ff782a838353L, 0xa4f8bf5635246428L,
0x871b7795e136be99L, 0x28e2557b59846e3fL,
0x331aeada2fe589cfL, 0x3ff0d2c85def7621L,
0xfed077a756b53a9L, 0xd3e8495912c62894L,
0x64712dd7abbbd95cL, 0xbd8d794d96aacfb3L,
0xecf0d7a0fc5583a0L, 0xf41686c49db57244L,
0x311c2875c522ced5L, 0x7d633293366b828bL,
0xae5dff9c02033197L, 0xd9f57f830283fdfcL,
0xd072df63c324fd7bL, 0x4247cb9e59f71e6dL,
0x52d9be85f074e608L, 0x67902e276c921f8bL,
0xba1cd8a3db53b6L, 0x80e8a40eccd228a4L,
0x6122cd128006b2cdL, 0x796b805720085f81L,
0xcbe3303674053bb0L, 0xbedbfc4411068a9cL,
0xee92fb5515482d44L, 0x751bdd152d4d1c4aL,
0xd262d45a78a0635dL, 0x86fb897116c87c34L,
0xd45d35e6ae3d4da0L, 0x8974836059cca109L,
0x2bd1a438703fc94bL, 0x7b6306a34627ddcfL,
0x1a3bc84c17b1d542L, 0x20caba5f1d9e4a93L,
0x547eb47b7282ee9cL, 0xe99e619a4f23aa43L,
0x6405fa00e2ec94d4L, 0xde83bc408dd3dd04L,
0x9624ab50b148d445L, 0x3badd624dd9b0957L,
0xe54ca5d70a80e5d6L, 0x5e9fcf4ccd211f4cL,
0x7647c3200069671fL, 0x29ecd9f40041e073L,
0xf468107100525890L, 0x7182148d4066eeb4L,
0xc6f14cd848405530L, 0xb8ada00e5a506a7cL,
0xa6d90811f0e4851cL, 0x908f4a166d1da663L,
0x9a598e4e043287feL, 0x40eff1e1853f29fdL,
0xd12bee59e68ef47cL, 0x82bb74f8301958ceL,
0xe36a52363c1faf01L, 0xdc44e6c3cb279ac1L,
0x29ab103a5ef8c0b9L, 0x7415d448f6b6f0e7L,
0x111b495b3464ad21L, 0xcab10dd900beec34L,
0x3d5d514f40eea742L, 0xcb4a5a3112a5112L,
0x47f0e785eaba72abL, 0x59ed216765690f56L,
0x306869c13ec3532cL, 0x1e414218c73a13fbL,
0xe5d1929ef90898faL, 0xdf45f746b74abf39L,
0x6b8bba8c328eb783L, 0x66ea92f3f326564L,
0xc80a537b0efefebdL, 0xbd06742ce95f5f36L,
0x2c48113823b73704L, 0xf75a15862ca504c5L,
0x9a984d73dbe722fbL, 0xc13e60d0d2e0ebbaL,
0x318df905079926a8L, 0xfdf17746497f7052L,
0xfeb6ea8bedefa633L, 0xfe64a52ee96b8fc0L,
0x3dfdce7aa3c673b0L, 0x6bea10ca65c084eL,
0x486e494fcff30a62L, 0x5a89dba3c3efccfaL,
0xf89629465a75e01cL, 0xf6bbb397f1135823L,
0x746aa07ded582e2cL, 0xa8c2a44eb4571cdcL,
0x92f34d62616ce413L, 0x77b020baf9c81d17L,
0xace1474dc1d122eL, 0xd819992132456baL,
0x10e1fff697ed6c69L, 0xca8d3ffa1ef463c1L,
0xbd308ff8a6b17cb2L, 0xac7cb3f6d05ddbdeL,
0x6bcdf07a423aa96bL, 0x86c16c98d2c953c6L,
0xe871c7bf077ba8b7L, 0x11471cd764ad4972L,
0xd598e40d3dd89bcfL, 0x4aff1d108d4ec2c3L,
0xcedf722a585139baL, 0xc2974eb4ee658828L,
0x733d226229feea32L, 0x806357d5a3f525fL,
0xca07c2dcb0cf26f7L, 0xfc89b393dd02f0b5L,
0xbbac2078d443ace2L, 0xd54b944b84aa4c0dL,
0xa9e795e65d4df11L, 0x4d4617b5ff4a16d5L,
0x504bced1bf8e4e45L, 0xe45ec2862f71e1d6L,
0x5d767327bb4e5a4cL, 0x3a6a07f8d510f86fL,
0x890489f70a55368bL, 0x2b45ac74ccea842eL,
0x3b0b8bc90012929dL, 0x9ce6ebb40173744L,
0xcc420a6a101d0515L, 0x9fa946824a12232dL,
0x47939822dc96abf9L, 0x59787e2b93bc56f7L,
0x57eb4edb3c55b65aL, 0xede622920b6b23f1L,
0xe95fab368e45ecedL, 0x11dbcb0218ebb414L,
0xd652bdc29f26a119L, 0x4be76d3346f0495fL,
0x6f70a4400c562ddbL, 0xcb4ccd500f6bb952L,
0x7e2000a41346a7a7L, 0x8ed400668c0c28c8L,
0x728900802f0f32faL, 0x4f2b40a03ad2ffb9L,
0xe2f610c84987bfa8L, 0xdd9ca7d2df4d7c9L,
0x91503d1c79720dbbL, 0x75a44c6397ce912aL,
0xc986afbe3ee11abaL, 0xfbe85badce996168L,
0xfae27299423fb9c3L, 0xdccd879fc967d41aL,
0x5400e987bbc1c920L, 0x290123e9aab23b68L,
0xf9a0b6720aaf6521L, 0xf808e40e8d5b3e69L,
0xb60b1d1230b20e04L, 0xb1c6f22b5e6f48c2L,
0x1e38aeb6360b1af3L, 0x25c6da63c38de1b0L,
0x579c487e5a38ad0eL, 0x2d835a9df0c6d851L,
0xf8e431456cf88e65L, 0x1b8e9ecb641b58ffL,
0xe272467e3d222f3fL, 0x5b0ed81dcc6abb0fL,
0x98e947129fc2b4e9L, 0x3f2398d747b36224L,
0x8eec7f0d19a03aadL, 0x1953cf68300424acL,
0x5fa8c3423c052dd7L, 0x3792f412cb06794dL,
0xe2bbd88bbee40bd0L, 0x5b6aceaeae9d0ec4L,
0xf245825a5a445275L, 0xeed6e2f0f0d56712L,
0x55464dd69685606bL, 0xaa97e14c3c26b886L,
0xd53dd99f4b3066a8L, 0xe546a8038efe4029L,
0xde98520472bdd033L, 0x963e66858f6d4440L,
0xdde7001379a44aa8L, 0x5560c018580d5d52L,
0xaab8f01e6e10b4a6L, 0xcab3961304ca70e8L,
0x3d607b97c5fd0d22L, 0x8cb89a7db77c506aL,
0x77f3608e92adb242L, 0x55f038b237591ed3L,
0x6b6c46dec52f6688L, 0x2323ac4b3b3da015L,
0xabec975e0a0d081aL, 0x96e7bd358c904a21L,
0x7e50d64177da2e54L, 0xdde50bd1d5d0b9e9L,
0x955e4ec64b44e864L, 0xbd5af13bef0b113eL,
0xecb1ad8aeacdd58eL, 0x67de18eda5814af2L,
0x80eacf948770ced7L, 0xa1258379a94d028dL,
0x96ee45813a04330L, 0x8bca9d6e188853fcL,
0x775ea264cf55347dL, 0x95364afe032a819dL,
0x3a83ddbd83f52204L, 0xc4926a9672793542L,
0x75b7053c0f178293L, 0x5324c68b12dd6338L,
0xd3f6fc16ebca5e03L, 0x88f4bb1ca6bcf584L,
0x2b31e9e3d06c32e5L, 0x3aff322e62439fcfL,
0x9befeb9fad487c2L, 0x4c2ebe687989a9b3L,
0xf9d37014bf60a10L, 0x538484c19ef38c94L,
0x2865a5f206b06fb9L, 0xf93f87b7442e45d3L,
0xf78f69a51539d748L, 0xb573440e5a884d1bL,
0x31680a88f8953030L, 0xfdc20d2b36ba7c3dL,
0x3d32907604691b4cL, 0xa63f9a49c2c1b10fL,
0xfcf80dc33721d53L, 0xd3c36113404ea4a8L,
0x645a1cac083126e9L, 0x3d70a3d70a3d70a3L,
0xccccccccccccccccL, 0x0L,
0x0L, 0x0L,
0x0L, 0x0L,
0x0L, 0x0L,
0x0L, 0x0L,
0x0L, 0x0L,
0x0L, 0x0L,
0x0L, 0x0L,
0x0L, 0x0L,
0x0L, 0x0L,
0x0L, 0x0L,
0x0L, 0x0L,
0x0L, 0x0L,
0x0L, 0x0L,
0x0L, 0x4000000000000000L,
0x5000000000000000L, 0xa400000000000000L,
0x4d00000000000000L, 0xf020000000000000L,
0x6c28000000000000L, 0xc732000000000000L,
0x3c7f400000000000L, 0x4b9f100000000000L,
0x1e86d40000000000L, 0x1314448000000000L,
0x17d955a000000000L, 0x5dcfab0800000000L,
0x5aa1cae500000000L, 0xf14a3d9e40000000L,
0x6d9ccd05d0000000L, 0xe4820023a2000000L,
0xdda2802c8a800000L, 0xd50b2037ad200000L,
0x4526f422cc340000L, 0x9670b12b7f410000L,
0x3c0cdd765f114000L, 0xa5880a69fb6ac800L,
0x8eea0d047a457a00L, 0x72a4904598d6d880L,
0x47a6da2b7f864750L, 0x999090b65f67d924L,
0xfff4b4e3f741cf6dL, 0xbff8f10e7a8921a4L,
0xaff72d52192b6a0dL, 0x9bf4f8a69f764490L,
0x2f236d04753d5b4L, 0x1d762422c946590L,
0x424d3ad2b7b97ef5L, 0xd2e0898765a7deb2L,
0x63cc55f49f88eb2fL, 0x3cbf6b71c76b25fbL,
0x8bef464e3945ef7aL, 0x97758bf0e3cbb5acL,
0x3d52eeed1cbea317L, 0x4ca7aaa863ee4bddL,
0x8fe8caa93e74ef6aL, 0xb3e2fd538e122b44L,
0x60dbbca87196b616L, 0xbc8955e946fe31cdL,
0x6babab6398bdbe41L, 0xc696963c7eed2dd1L,
0xfc1e1de5cf543ca2L, 0x3b25a55f43294bcbL,
0x49ef0eb713f39ebeL, 0x6e3569326c784337L,
0x49c2c37f07965404L, 0xdc33745ec97be906L,
0x69a028bb3ded71a3L, 0xc40832ea0d68ce0cL,
0xf50a3fa490c30190L, 0x792667c6da79e0faL,
0x577001b891185938L, 0xed4c0226b55e6f86L,
0x544f8158315b05b4L, 0x696361ae3db1c721L,
0x3bc3a19cd1e38e9L, 0x4ab48a04065c723L,
0x62eb0d64283f9c76L, 0x3ba5d0bd324f8394L,
0xca8f44ec7ee36479L, 0x7e998b13cf4e1ecbL,
0x9e3fedd8c321a67eL, 0xc5cfe94ef3ea101eL,
0xbba1f1d158724a12L, 0x2a8a6e45ae8edc97L,
0xf52d09d71a3293bdL, 0x593c2626705f9c56L,
0x6f8b2fb00c77836cL, 0xb6dfb9c0f956447L,
0x4724bd4189bd5eacL, 0x58edec91ec2cb657L,
0x2f2967b66737e3edL, 0xbd79e0d20082ee74L,
0xecd8590680a3aa11L, 0xe80e6f4820cc9495L,
0x3109058d147fdcddL, 0xbd4b46f0599fd415L,
0x6c9e18ac7007c91aL, 0x3e2cf6bc604ddb0L,
0x84db8346b786151cL, 0xe612641865679a63L,
0x4fcb7e8f3f60c07eL, 0xe3be5e330f38f09dL,
0x5cadf5bfd3072cc5L, 0x73d9732fc7c8f7f6L,
0x2867e7fddcdd9afaL, 0xb281e1fd541501b8L,
0x1f225a7ca91a4226L, 0x3375788de9b06958L,
0x52d6b1641c83aeL, 0xc0678c5dbd23a49aL,
0xf840b7ba963646e0L, 0xb650e5a93bc3d898L,
0xa3e51f138ab4cebeL, 0xc66f336c36b10137L,
0xb80b0047445d4184L, 0xa60dc059157491e5L,
0x87c89837ad68db2fL, 0x29babe4598c311fbL,
0xf4296dd6fef3d67aL, 0x1899e4a65f58660cL,
0x5ec05dcff72e7f8fL, 0x76707543f4fa1f73L,
0x6a06494a791c53a8L, 0x487db9d17636892L,
0x45a9d2845d3c42b6L, 0xb8a2392ba45a9b2L,
0x8e6cac7768d7141eL, 0x3207d795430cd926L,
0x7f44e6bd49e807b8L, 0x5f16206c9c6209a6L,
0x36dba887c37a8c0fL, 0xc2494954da2c9789L,
0xf2db9baa10b7bd6cL, 0x6f92829494e5acc7L,
0xcb772339ba1f17f9L, 0xff2a760414536efbL,
0xfef5138519684abaL, 0x7eb258665fc25d69L,
0xef2f773ffbd97a61L, 0xaafb550ffacfd8faL,
0x95ba2a53f983cf38L, 0xdd945a747bf26183L,
0x94f971119aeef9e4L, 0x7a37cd5601aab85dL,
0xac62e055c10ab33aL, 0x577b986b314d6009L,
0xed5a7e85fda0b80bL, 0x14588f13be847307L,
0x596eb2d8ae258fc8L, 0x6fca5f8ed9aef3bbL,
0x25de7bb9480d5854L, 0xaf561aa79a10ae6aL,
0x1b2ba1518094da04L, 0x90fb44d2f05d0842L,
0x353a1607ac744a53L, 0x42889b8997915ce8L,
0x69956135febada11L, 0x43fab9837e699095L,
0x94f967e45e03f4bbL, 0x1d1be0eebac278f5L,
0x6462d92a69731732L, 0x7d7b8f7503cfdcfeL,
0x5cda735244c3d43eL, 0x3a0888136afa64a7L,
0x88aaa1845b8fdd0L, 0x8aad549e57273d45L,
0x36ac54e2f678864bL, 0x84576a1bb416a7ddL,
0x656d44a2a11c51d5L, 0x9f644ae5a4b1b325L,
0x873d5d9f0dde1feeL, 0xa90cb506d155a7eaL,
0x9a7f12442d588f2L, 0xc11ed6d538aeb2fL,
0x8f1668c8a86da5faL, 0xf96e017d694487bcL,
0x37c981dcc395a9acL, 0x85bbe253f47b1417L,
0x93956d7478ccec8eL, 0x387ac8d1970027b2L,
0x6997b05fcc0319eL, 0x441fece3bdf81f03L,
0xd527e81cad7626c3L, 0x8a71e223d8d3b074L,
0xf6872d5667844e49L, 0xb428f8ac016561dbL,
0xe13336d701beba52L, 0xecc0024661173473L,
0x27f002d7f95d0190L, 0x31ec038df7b441f4L,
0x7e67047175a15271L, 0xf0062c6e984d386L,
0x52c07b78a3e60868L, 0xa7709a56ccdf8a82L,
0x88a66076400bb691L, 0x6acff893d00ea435L,
0x583f6b8c4124d43L, 0xc3727a337a8b704aL,
0x744f18c0592e4c5cL, 0x1162def06f79df73L,
0x8addcb5645ac2ba8L, 0x6d953e2bd7173692L,
0xc8fa8db6ccdd0437L, 0x1d9c9892400a22a2L,
0x2503beb6d00cab4bL, 0x2e44ae64840fd61dL,
0x5ceaecfed289e5d2L, 0x7425a83e872c5f47L,
0xd12f124e28f77719L, 0x82bd6b70d99aaa6fL,
0x636cc64d1001550bL, 0x3c47f7e05401aa4eL,
0x65acfaec34810a71L, 0x7f1839a741a14d0dL,
0x1ede48111209a050L, 0x934aed0aab460432L,
0xf81da84d5617853fL, 0x36251260ab9d668eL,
0xc1d72b7c6b426019L, 0xb24cf65b8612f81fL,
0xdee033f26797b627L, 0x169840ef017da3b1L,
0x8e1f289560ee864eL, 0xf1a6f2bab92a27e2L,
0xae10af696774b1dbL, 0xacca6da1e0a8ef29L,
0x17fd090a58d32af3L, 0xddfc4b4cef07f5b0L,
0x4abdaf101564f98eL, 0x9d6d1ad41abe37f1L,
0x84c86189216dc5edL, 0x32fd3cf5b4e49bb4L,
0x3fbc8c33221dc2a1L, 0xfabaf3feaa5334aL,
0x29cb4d87f2a7400eL, 0x743e20e9ef511012L,
0x914da9246b255416L, 0x1ad089b6c2f7548eL,
0xa184ac2473b529b1L, 0xc9e5d72d90a2741eL,
0x7e2fa67c7a658892L, 0xddbb901b98feeab7L,
0x552a74227f3ea565L, 0xd53a88958f87275fL,
0x8a892abaf368f137L, 0x2d2b7569b0432d85L,
0x9c3b29620e29fc73L, 0x8349f3ba91b47b8fL,
0x241c70a936219a73L, 0xed238cd383aa0110L,
0xf4363804324a40aaL, 0xb143c6053edcd0d5L,
0xdd94b7868e94050aL, 0xca7cf2b4191c8326L,
0xfd1c2f611f63a3f0L, 0xbc633b39673c8cecL,
0xd5be0503e085d813L, 0x4b2d8644d8a74e18L,
0xddf8e7d60ed1219eL, 0xcabb90e5c942b503L,
0x3d6a751f3b936243L, 0xcc512670a783ad4L,
0x27fb2b80668b24c5L, 0xb1f9f660802dedf6L,
0x5e7873f8a0396973L, 0xdb0b487b6423e1e8L,
0x91ce1a9a3d2cda62L, 0x7641a140cc7810fbL,
0xa9e904c87fcb0a9dL, 0x546345fa9fbdcd44L,
0xa97c177947ad4095L, 0x49ed8eabcccc485dL,
0x5c68f256bfff5a74L, 0x73832eec6fff3111L,
0xc831fd53c5ff7eabL, 0xba3e7ca8b77f5e55L,
0x28ce1bd2e55f35ebL, 0x7980d163cf5b81b3L,
0xd7e105bcc332621fL, 0x8dd9472bf3fefaa7L,
0xb14f98f6f0feb951L, 0x6ed1bf9a569f33d3L,
0xa862f80ec4700c8L, 0xcd27bb612758c0faL,
0x8038d51cb897789cL, 0xe0470a63e6bd56c3L,
0x1858ccfce06cac74L, 0xf37801e0c43ebc8L,
0xd30560258f54e6baL, 0x47c6b82ef32a2069L,
0x4cdc331d57fa5441L, 0xe0133fe4adf8e952L,
0x58180fddd97723a6L, 0x570f09eaa7ea7648L};
/**
* Prevents instantiation.
*/
private FastDoubleMath() {
}
static double decFloatLiteralToDouble(int index, boolean isNegative, long digits, int exponent, int virtualIndexOfPoint, long expNumber, boolean isDigitsTruncated,
int skipCountInTruncatedDigits) {
if (digits == 0) {
return isNegative ? -0.0 : 0.0;
}
final double outDouble;
if (isDigitsTruncated) {
final long exponentOfTruncatedDigits = virtualIndexOfPoint - index + skipCountInTruncatedDigits + expNumber;
// We have too many digits. We may have to round up.
// To know whether rounding up is needed, we may have to examine up to 768 digits.
// There are cases, in which rounding has no effect.
if (FASTFLOAT_DEC_SMALLEST_POWER <= exponentOfTruncatedDigits && exponentOfTruncatedDigits <= FASTFLOAT_DEC_LARGEST_POWER) {
double withoutRounding = tryDecToDoubleWithFastAlgorithm(isNegative, digits, (int) exponentOfTruncatedDigits);
double roundedUp = tryDecToDoubleWithFastAlgorithm(isNegative, digits + 1, (int) exponentOfTruncatedDigits);
if (!Double.isNaN(withoutRounding) && doubleEquals(roundedUp, withoutRounding)) {
return withoutRounding;
}
}
// We have to take a slow path.
// return Double.parseDouble(str.toString());
outDouble = Double.NaN;
} else if (FASTFLOAT_DEC_SMALLEST_POWER <= exponent && exponent <= FASTFLOAT_DEC_LARGEST_POWER) {
outDouble = tryDecToDoubleWithFastAlgorithm(isNegative, digits, exponent);
} else {
outDouble = Double.NaN;
}
return outDouble;
}
/**
* Computes {@code uint128 product = (uint64)x * (uint64)y}.
*
* References:
*
* - Getting the high part of 64 bit integer multiplication
* -
* stackoverflow
*
*
* @param x uint64 factor x
* @param y uint64 factor y
* @return uint128 product of x and y
*/
private static Value128 fullMultiplication(long x, long y) {
long x0 = x & 0xffffffffL;
long x1 = x >>> 32;
long y0 = y & 0xffffffffL;
long y1 = y >>> 32;
long p11 = x1 * y1;
long p01 = x0 * y1;
long p10 = x1 * y0;
long p00 = x0 * y0;
// 64-bit product + two 32-bit values
long middle = p10 + (p00 >>> 32) + (p01 & 0xffffffffL);
return new Value128(
// 64-bit product + two 32-bit values
p11 + (middle >>> 32) + (p01 >>> 32),
// Add LOW PART and lower half of MIDDLE PART
(middle << 32) | (p00 & 0xffffffffL));
}
private static double hexFloatLiteralToDouble(int index, boolean isNegative, long digits, long exponent, int virtualIndexOfPoint, long expNumber, boolean isDigitsTruncated,
int skipCountInTruncatedDigits) {
if (digits == 0) {
return isNegative ? -0.0 : 0.0;
}
final double outDouble;
if (isDigitsTruncated) {
final long truncatedExponent = (virtualIndexOfPoint - index + skipCountInTruncatedDigits) * 4L + expNumber;
// We have too many digits. We may have to round up.
// To know whether rounding up is needed, we may have to examine up to 768 digits.
// There are cases, in which rounding has no effect.
if (FASTFLOAT_HEX_SMALLEST_POWER <= truncatedExponent && truncatedExponent <= FASTFLOAT_HEX_LARGEST_POWER) {
double withoutRounding = tryHexToDoubleWithFastAlgorithm(isNegative, digits, (int) truncatedExponent);
double roundedUp = tryHexToDoubleWithFastAlgorithm(isNegative, digits + 1, (int) truncatedExponent);
if (!Double.isNaN(withoutRounding) && doubleEquals(withoutRounding, roundedUp)) {
return withoutRounding;
}
}
// We have to take a slow path.
outDouble = Double.NaN;
} else if (FASTFLOAT_HEX_SMALLEST_POWER <= exponent && exponent <= FASTFLOAT_HEX_LARGEST_POWER) {
outDouble = tryHexToDoubleWithFastAlgorithm(isNegative, digits, (int) exponent);
} else {
outDouble = Double.NaN;
}
return outDouble;
}
/**
* Attempts to compute {@literal digits * 10^(power)} exactly; and if "negative" is true,
* negate the result.
*
* This function will only work in some cases, when it does not work it returns null. This
* should work *most of the time* (like 99% of the time). We assume that power is in the
* [FASTFLOAT_SMALLEST_POWER, FASTFLOAT_LARGEST_POWER] interval: the caller is responsible
* for this check.
*
* @param isNegative whether the number is negative
* @param curDigits uint64 the digits of the number
* @param power int32 the exponent of the number
* @return the computed double on success, {@link Double#NaN} on failure
*/
private static double tryDecToDoubleWithFastAlgorithm(boolean isNegative, long curDigits, int power) {
long digits = curDigits;
if (digits == 0 || power < -380 - 19) {
return isNegative ? -0.0 : 0.0;
}
if (power > 380) {
return isNegative ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY;
}
// we start with a fast path
// It was described in
// Clinger WD. How to read floating point numbers accurately.
// ACM SIGPLAN Notices. 1990
if (-22 <= power && power <= 22 && Long.compareUnsigned(digits, 0x1fffffffffffffL) <= 0) {
// convert the integer into a double. This is lossless since
// 0 <= i <= 2^53 - 1.
double d = digits;
//
// The general idea is as follows.
// If 0 <= s < 2^53 and if 10^0 <= p <= 10^22 then
// 1) Both s and p can be represented exactly as 64-bit floating-point
// values (binary64).
// 2) Because s and p can be represented exactly as floating-point values,
// then s * p and s / p will produce correctly rounded values.
//
if (power < 0) {
d = d / powerOfTen[-power];
} else {
d = d * powerOfTen[power];
}
return (isNegative) ? -d : d;
}
// The fast path has now failed, so we are falling back on the slower path.
// We are going to need to do some 64-bit arithmetic to get a more precise product.
// We use a table lookup approach.
// It is safe because
// power >= FASTFLOAT_SMALLEST_POWER
// and power <= FASTFLOAT_LARGEST_POWER
// We recover the mantissa of the power, it has a leading 1. It is always
// rounded down.
long factorMantissa = MANTISSA_64[power - FASTFLOAT_DEC_SMALLEST_POWER];
// The exponent is 1024 + 63 + power
// + floor(log(5**power)/log(2)).
// The 1024 comes from the ieee64 standard.
// The 63 comes from the fact that we use a 64-bit word.
//
// Computing floor(log(5**power)/log(2)) could be
// slow. Instead we use a fast function.
//
// For power in (-400,350), we have that
// (((152170 + 65536) * power ) >> 16);
// is equal to
// floor(log(5**power)/log(2)) + power when power >= 0
// and it is equal to
// ceil(log(5**-power)/log(2)) + power when power < 0
//
//
// The 65536 is (1<<16) and corresponds to
// (65536 * power) >> 16 ---> power
//
// ((152170 * power ) >> 16) is equal to
// floor(log(5**power)/log(2))
//
// Note that this is not magic: 152170/(1<<16) is
// approximately equal to log(5)/log(2).
// The 1<<16 value is a power of two; we could use a
// larger power of 2 if we wanted to.
//
long exponent = (((152170 + 65536) * power) >> 16) + 1024 + 63;
// We want the most significant bit of digits to be 1. Shift if needed.
int lz = Long.numberOfLeadingZeros(digits);
digits <<= lz;
// We want the most significant 64 bits of the product. We know
// this will be non-zero because the most significant bit of i is
// 1.
Value128 product = fullMultiplication(digits, factorMantissa);
long lower = product.low;
long upper = product.high;
// We know that upper has at most one leading zero because
// both i and factor_mantissa have a leading one. This means
// that the result is at least as large as ((1<<63)*(1<<63))/(1<<64).
// As long as the first 9 bits of "upper" are not "1", then we
// know that we have an exact computed value for the leading
// 55 bits because any imprecision would play out as a +1, in
// the worst case.
// Having 55 bits is necessary because
// we need 53 bits for the mantissa but we have to have one rounding bit and
// we can waste a bit if the most significant bit of the product is zero.
// We expect this next branch to be rarely taken (say 1% of the time).
// When (upper & 0x1FF) == 0x1FF, it can be common for
// lower + i < lower to be true (proba. much higher than 1%).
if ((upper & 0x1FF) == 0x1FF && Long.compareUnsigned(lower + digits, lower) < 0) {
long factorMantissaLow = MANTISSA_128[power - FASTFLOAT_DEC_SMALLEST_POWER];
// next, we compute the 64-bit x 128-bit multiplication, getting a 192-bit
// result (three 64-bit values)
product = fullMultiplication(digits, factorMantissaLow);
long productLow = product.low;
long productMiddle2 = product.high;
long productMiddle1 = lower;
long productHigh = upper;
long productMiddle = productMiddle1 + productMiddle2;
if (Long.compareUnsigned(productMiddle, productMiddle1) < 0) {
productHigh++; // overflow carry
}
// we want to check whether mantissa *i + i would affect our result
// This does happen, e.g. with 7.3177701707893310e+15
if (((productMiddle + 1 == 0) && ((productHigh & 0x1ff) == 0x1ff) &&
(productLow + Long.compareUnsigned(digits, productLow) < 0))) {
// let us be prudent and bail out.
return Double.NaN;
}
upper = productHigh;
// lower = product_middle;
}
// The final mantissa should be 53 bits with a leading 1.
// We shift it so that it occupies 54 bits with a leading 1.
long upperbit = upper >>> 63;
long mantissa = upper >>> (upperbit + 9);
lz += (int) (1 ^ upperbit);
// Here we have mantissa < (1<<54).
// We have to round to even. The "to even" part
// is only a problem when we are right in between two floats
// which we guard against.
// If we have lots of trailing zeros, we may fall right between two
// floating-point values.
if (((upper & 0x1ff) == 0x1ff) || ((upper & 0x1ff) == 0) && (mantissa & 3) == 1) {
// if mantissa & 1 == 1 we might need to round up.
//
// Scenarios:
// 1. We are not in the middle. Then we should round up.
//
// 2. We are right in the middle. Whether we round up depends
// on the last significant bit: if it is "one" then we round
// up (round to even) otherwise, we do not.
//
// So if the last significant bit is 1, we can safely round up.
// Hence we only need to bail out if (mantissa & 3) == 1.
// Otherwise we may need more accuracy or analysis to determine whether
// we are exactly between two floating-point numbers.
// It can be triggered with 1e23.
// Note: because the factor_mantissa and factor_mantissa_low are
// almost always rounded down (except for small positive powers),
// almost always should round up.
return Double.NaN;
}
mantissa += 1;
mantissa >>>= 1;
// Here we have mantissa < (1<<53), unless there was an overflow
if (mantissa >= (1L << 53)) {
// This will happen when parsing values such as 7.2057594037927933e+16
mantissa = (1L << 52);
lz--; // undo previous addition
}
mantissa &= ~(1L << 52);
long realExponent = exponent - lz;
// we have to check that real_exponent is in range, otherwise we bail out
if ((realExponent < 1) || (realExponent > 2046)) {
return Double.NaN;
}
long bits = mantissa | realExponent << 52 | (isNegative ? 1L << 63 : 0L);
return Double.longBitsToDouble(bits);
}
/**
* Attempts to compute {@literal digits * 2^(power)} exactly; and if "negative" is true,
* negate the result.
*
* This function will only work in some cases, when it does not work it returns null.
*
* @param isNegative whether the number is negative
* @param digits uint64 the digits of the number
* @param power int32 the exponent of the number
* @return the computed double on success, null on failure
*/
private static double tryHexToDoubleWithFastAlgorithm(boolean isNegative, long digits, int power) {
if (digits == 0 || power < Double.MIN_EXPONENT - 54) {
return isNegative ? -0.0 : 0.0;
}
if (power > Double.MAX_EXPONENT) {
return isNegative ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY;
}
// we start with a fast path
// We try to mimic the fast described by Clinger WD for decimal
// float number literals. How to read floating point numbers accurately.
// ACM SIGPLAN Notices. 1990
if (Long.compareUnsigned(digits, 0x1fffffffffffffL) <= 0) {
// convert the integer into a double. This is lossless since
// 0 <= i <= 2^53 - 1.
double d = digits;
//
// The general idea is as follows.
// If 0 <= s < 2^53 then
// 1) Both s and p can be represented exactly as 64-bit floating-point
// values (binary64).
// 2) Because s and p can be represented exactly as floating-point values,
// then s * p will produce correctly rounded values.
//
d = d * Math.scalb(1d, power);
if (isNegative) {
d = -d;
}
return d;
}
// The fast path has failed
return Double.NaN;
}
private static boolean doubleEquals(double withoutRounding, double roundedUp) {
return Double.doubleToLongBits(roundedUp) == Double.doubleToLongBits(withoutRounding);
}
private static final class Value128 {
final long high;
final long low;
private Value128(long high, long low) {
this.high = high;
this.low = low;
}
}
}
}