RyuDouble.java
/* Copyright 2018 Ulf Adams
* Licensed to the Hipparchus project under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The Hipparchus project licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* https://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/*
* This is not the original file distributed by Ulf Adams in project
* https://github.com/ulfjack/ryu
* It has been modified by the Hipparchus project.
*/
package org.hipparchus.util;
import java.math.BigInteger;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
/**
* An implementation of Ryū for double.
* <p>
* Ryū generates the shortest decimal representation of a floating point number
* that maintains round-trip safety. That is, a correct parser can recover the
* exact original number. Ryū is very fast (about 10 time faster than {@code
* Double.toString()}).
* </p>
* @see <a href="https://dl.acm.org/citation.cfm?doid=3296979.3192369">Ryū: fast float-to-string conversion</a>
*/
public final class RyuDouble {
/** Default low switch level to scientific notation. */
public static final int DEFAULT_LOW_EXP = -3;
/** Default high switch level to scientific notation. */
public static final int DEFAULT_HIGH_EXP = 7;
/** Number of bits in a double mantissa. */
private static final int DOUBLE_MANTISSA_BITS = 52;
/** Bit mask for retrieving mantissa. */
private static final long DOUBLE_MANTISSA_MASK = (1L << DOUBLE_MANTISSA_BITS) - 1;
/** Number of bits in a double exponant. */
private static final int DOUBLE_EXPONENT_BITS = 11;
/** Bit mask for retrieving exponent. */
private static final int DOUBLE_EXPONENT_MASK = (1 << DOUBLE_EXPONENT_BITS) - 1;
/** Bias of the exponent. */
private static final int DOUBLE_EXPONENT_BIAS = (1 << (DOUBLE_EXPONENT_BITS - 1)) - 1;
/** Size of the factors table for positive exponents. */
private static final int POS_TABLE_SIZE = 326;
/** Size of the factors table for negative exponents. */
private static final int NEG_TABLE_SIZE = 291;
/** Bit count for complete entries in the positive exponent tables. */
private static final int POW5_BITCOUNT = 121; // max 3*31 = 124
/** Bit count for split entries in the positive exponent tables. */
private static final int POW5_QUARTER_BITCOUNT = 31;
/** Split table for positive exponents. */
private static final int[][] POW5_SPLIT = new int[POS_TABLE_SIZE][4];
/** Bit count for complete entries in the negative exponent tables. */
private static final int POW5_INV_BITCOUNT = 122; // max 3*31 = 124
/** Bit count for split entries in the negative exponent tables. */
private static final int POW5_INV_QUARTER_BITCOUNT = 31;
/** Split table for negative exponents. */
private static final int[][] POW5_INV_SPLIT = new int[NEG_TABLE_SIZE][4];
/** Create the tables. */
static {
final BigInteger mask = BigInteger.valueOf(1).shiftLeft(POW5_QUARTER_BITCOUNT).subtract(BigInteger.ONE);
final BigInteger invMask = BigInteger.valueOf(1).shiftLeft(POW5_INV_QUARTER_BITCOUNT).subtract(BigInteger.ONE);
for (int i = 0; i < FastMath.max(POS_TABLE_SIZE, NEG_TABLE_SIZE); i++) {
final BigInteger pow = BigInteger.valueOf(5).pow(i);
final int pow5len = pow.bitLength();
if (i < POW5_SPLIT.length) {
for (int j = 0; j < 4; j++) {
POW5_SPLIT[i][j] = pow.
shiftRight(pow5len - POW5_BITCOUNT + (3 - j) * POW5_QUARTER_BITCOUNT).
and(mask).
intValueExact();
}
}
if (i < POW5_INV_SPLIT.length) {
// We want floor(log_2 5^q) here, which is pow5len - 1.
final int j = pow5len - 1 + POW5_INV_BITCOUNT;
final BigInteger inv = BigInteger.ONE.shiftLeft(j).divide(pow).add(BigInteger.ONE);
for (int k = 0; k < 4; k++) {
if (k == 0) {
POW5_INV_SPLIT[i][k] = inv.shiftRight((3 - k) * POW5_INV_QUARTER_BITCOUNT).intValueExact();
} else {
POW5_INV_SPLIT[i][k] = inv.shiftRight((3 - k) * POW5_INV_QUARTER_BITCOUNT).and(invMask).intValueExact();
}
}
}
}
}
/** Private constructor for a utility class.
*/
private RyuDouble() {
// nothing to do
}
/** Convert a double to shortest string representation, preserving full accuracy.
* <p>
* This implementation uses the same specifications as {@code Double.toString()},
* i.e. it uses scientific notation if for numbers smaller than 10⁻³ or larger
* than 10⁺⁷, and decimal notion in between. That is it call {@link #doubleToString(double,
* int, int) doubleToString(value, -3, 7)}.
* </p>
* @param value double number to convert
* @return shortest string representation
* @see #doubleToString(double, int, int)
* @see #DEFAULT_LOW_EXP
* @see #DEFAULT_HIGH_EXP
*/
public static String doubleToString(double value) {
return doubleToString(value, DEFAULT_LOW_EXP, DEFAULT_HIGH_EXP);
}
/** Convert a double to shortest string representation, preserving full accuracy.
* <p>
* Number inside of the interval [10<sup>lowExp</sup>, 10<sup>highExp</sup>]
* are represented using decimal notation, numbers outside of this
* range are represented using scientific notation.
* </p>
* @param value double number to convert
* @param lowExp lowest decimal exponent for which decimal notation can be used
* @param highExp highest decimal exponent for which decimal notation can be used
* @return shortest string representation
* @see #doubleToString(double)
* @see #DEFAULT_LOW_EXP
* @see #DEFAULT_HIGH_EXP
*/
public static String doubleToString(double value, int lowExp, int highExp) {
// Step 1: Decode the floating point number, and unify normalized and subnormal cases.
// First, handle all the trivial cases.
if (Double.isNaN(value)) {
return "NaN";
}
if (value == Double.POSITIVE_INFINITY) {
return "Infinity";
}
if (value == Double.NEGATIVE_INFINITY) {
return "-Infinity";
}
long bits = Double.doubleToLongBits(value);
if (bits == 0) {
return "0.0";
}
if (bits == 0x8000000000000000L) {
return "-0.0";
}
// Otherwise extract the mantissa and exponent bits and run the full algorithm.
final int ieeeExponent = (int) ((bits >>> DOUBLE_MANTISSA_BITS) & DOUBLE_EXPONENT_MASK);
final long ieeeMantissa = bits & DOUBLE_MANTISSA_MASK;
int e2;
final long m2;
if (ieeeExponent == 0) {
// Denormal number - no implicit leading 1, and the exponent is 1, not 0.
e2 = 1 - DOUBLE_EXPONENT_BIAS - DOUBLE_MANTISSA_BITS;
m2 = ieeeMantissa;
} else {
// Add implicit leading 1.
e2 = ieeeExponent - DOUBLE_EXPONENT_BIAS - DOUBLE_MANTISSA_BITS;
m2 = ieeeMantissa | (1L << DOUBLE_MANTISSA_BITS);
}
final boolean sign = bits < 0;
// Step 2: Determine the interval of legal decimal representations.
final boolean even = (m2 & 1) == 0;
final long mv = 4 * m2;
final long mp = 4 * m2 + 2;
final int mmShift = ((m2 != (1L << DOUBLE_MANTISSA_BITS)) || (ieeeExponent <= 1)) ? 1 : 0;
final long mm = 4 * m2 - 1 - mmShift;
e2 -= 2;
// Step 3: Convert to a decimal power base using 128-bit arithmetic.
// -1077 = 1 - 1023 - 53 - 2 <= e_2 - 2 <= 2046 - 1023 - 53 - 2 = 968
long dv;
long dp;
long dm;
final int e10;
boolean dmIsTrailingZeros = false;
boolean dvIsTrailingZeros = false;
if (e2 >= 0) {
final int q = FastMath.max(0, ((e2 * 78913) >>> 18) - 1);
// k = constant + floor(log_2(5^q))
final int k = POW5_INV_BITCOUNT + pow5bits(q) - 1;
final int i = -e2 + q + k;
dv = mulPow5InvDivPow2(mv, q, i);
dp = mulPow5InvDivPow2(mp, q, i);
dm = mulPow5InvDivPow2(mm, q, i);
e10 = q;
if (q <= 21) {
if (mv % 5 == 0) {
dvIsTrailingZeros = multipleOfPowerOf5(mv, q);
} else if (even) {
dmIsTrailingZeros = multipleOfPowerOf5(mm, q);
} else if (multipleOfPowerOf5(mp, q)) {
dp--;
}
}
} else {
final int q = FastMath.max(0, ((-e2 * 732923) >>> 20) - 1);
final int i = -e2 - q;
final int k = pow5bits(i) - POW5_BITCOUNT;
final int j = q - k;
dv = mulPow5divPow2(mv, i, j);
dp = mulPow5divPow2(mp, i, j);
dm = mulPow5divPow2(mm, i, j);
e10 = q + e2;
if (q <= 1) {
dvIsTrailingZeros = true;
if (even) {
dmIsTrailingZeros = mmShift == 1;
} else {
dp--;
}
} else if (q < 63) {
dvIsTrailingZeros = (mv & ((1L << (q - 1)) - 1)) == 0;
}
}
// Step 4: Find the shortest decimal representation in the interval of legal representations.
//
// We do some extra work here in order to follow Float/Double.toString semantics. In particular,
// that requires printing in scientific format if and only if the exponent is between lowExp and highExp,
// and it requires printing at least two decimal digits.
//
// Above, we moved the decimal dot all the way to the right, so now we need to count digits to
// figure out the correct exponent for scientific notation.
final int vplength = decimalLength(dp);
int exp = e10 + vplength - 1;
// use scientific notation if and only if outside this range.
final boolean scientificNotation = !((exp >= lowExp) && (exp < highExp));
int removed = 0;
int lastRemovedDigit = 0;
long output;
if (dmIsTrailingZeros || dvIsTrailingZeros) {
while (dp / 10 > dm / 10) {
if ((dp < 100) && scientificNotation) {
// Double.toString semantics requires printing at least two digits.
break;
}
dmIsTrailingZeros &= dm % 10 == 0;
dvIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (int) (dv % 10);
dp /= 10;
dv /= 10;
dm /= 10;
removed++;
}
if (dmIsTrailingZeros && even) {
while (dm % 10 == 0) {
if ((dp < 100) && scientificNotation) {
// Double.toString semantics requires printing at least two digits.
break;
}
dvIsTrailingZeros &= lastRemovedDigit == 0;
lastRemovedDigit = (int) (dv % 10);
dp /= 10;
dv /= 10;
dm /= 10;
removed++;
}
}
if (dvIsTrailingZeros && (lastRemovedDigit == 5) && (dv % 2 == 0)) {
// Round even if the exact numbers is .....50..0.
lastRemovedDigit = 4;
}
output = dv +
((dv == dm && !(dmIsTrailingZeros && even)) || (lastRemovedDigit >= 5) ? 1 : 0);
} else {
while (dp / 10 > dm / 10) {
if ((dp < 100) && scientificNotation) {
// Double.toString semantics requires printing at least two digits.
break;
}
lastRemovedDigit = (int) (dv % 10);
dp /= 10;
dv /= 10;
dm /= 10;
removed++;
}
output = dv + ((dv == dm || (lastRemovedDigit >= 5)) ? 1 : 0);
}
int olength = vplength - removed;
// Step 5: Print the decimal representation.
// We follow Double.toString semantics here,
// but adjusting the boundaries at which we switch to scientific notation
char[] result = new char[14 - lowExp + highExp];
int index = 0;
if (sign) {
result[index++] = '-';
}
// Values in the interval [10^lowExp, 10^highExp) are special.
if (scientificNotation) {
// Print in the format x.xxxxxE-yy.
for (int i = 0; i < olength - 1; i++) {
int c = (int) (output % 10);
output /= 10;
result[index + olength - i] = (char) ('0' + c);
}
result[index] = (char) ('0' + output % 10);
result[index + 1] = '.';
index += olength + 1;
if (olength == 1) {
result[index++] = '0';
}
// Print 'E', the exponent sign, and the exponent, which has at most three digits.
result[index++] = 'E';
if (exp < 0) {
result[index++] = '-';
exp = -exp;
}
if (exp >= 100) {
result[index++] = (char) ('0' + exp / 100);
exp %= 100;
result[index++] = (char) ('0' + exp / 10);
} else if (exp >= 10) {
result[index++] = (char) ('0' + exp / 10);
}
result[index++] = (char) ('0' + exp % 10);
return String.valueOf(result, 0, index);
} else {
// Otherwise follow the Java spec for values in the interval [10^lowExp, 10^highExp).
if (exp < 0) {
// Decimal dot is before any of the digits.
result[index++] = '0';
result[index++] = '.';
for (int i = -1; i > exp; i--) {
result[index++] = '0';
}
int current = index;
for (int i = 0; i < olength; i++) {
result[current + olength - i - 1] = (char) ('0' + output % 10);
output /= 10;
index++;
}
} else if (exp + 1 >= olength) {
// Decimal dot is after any of the digits.
for (int i = 0; i < olength; i++) {
result[index + olength - i - 1] = (char) ('0' + output % 10);
output /= 10;
}
index += olength;
for (int i = olength; i < exp + 1; i++) {
result[index++] = '0';
}
result[index++] = '.';
result[index++] = '0';
} else {
// Decimal dot is somewhere between the digits.
int current = index + 1;
for (int i = 0; i < olength; i++) {
if (olength - i - 1 == exp) {
result[current + olength - i - 1] = '.';
current--;
}
result[current + olength - i - 1] = (char) ('0' + output % 10);
output /= 10;
}
index += olength + 1;
}
return String.valueOf(result, 0, index);
}
}
/** Get the number of bits of 5<sup>e</sup>.
* @param e exponent
* @return number of bits of 5<sup>e</sup>
*/
private static int pow5bits(int e) {
return ((e * 1217359) >>> 19) + 1;
}
/** Compute decimal length of an integer.
* @param v integer to check
* @return decimal length of {@code v}
*/
private static int decimalLength(long v) {
if (v >= 1000000000000000000L) {
return 19;
}
if (v >= 100000000000000000L) {
return 18;
}
if (v >= 10000000000000000L) {
return 17;
}
if (v >= 1000000000000000L) {
return 16;
}
if (v >= 100000000000000L) {
return 15;
}
if (v >= 10000000000000L) {
return 14;
}
if (v >= 1000000000000L) {
return 13;
}
if (v >= 100000000000L) {
return 12;
}
if (v >= 10000000000L) {
return 11;
}
if (v >= 1000000000L) {
return 10;
}
if (v >= 100000000L) {
return 9;
}
if (v >= 10000000L) {
return 8;
}
if (v >= 1000000L) {
return 7;
}
if (v >= 100000L) {
return 6;
}
if (v >= 10000L) {
return 5;
}
if (v >= 1000L) {
return 4;
}
if (v >= 100L) {
return 3;
}
if (v >= 10L) {
return 2;
}
return 1;
}
private static boolean multipleOfPowerOf5(long value, int q) {
return pow5Factor(value) >= q;
}
/** Compute largest power of 5 that divides the value.
* @param value value to check
* @return largest power of 5 that divides the value
*/
private static int pow5Factor(long value) {
// We want to find the largest power of 5 that divides value.
if ((value % 5) != 0) {
return 0;
}
if ((value % 25) != 0) {
return 1;
}
if ((value % 125) != 0) {
return 2;
}
if ((value % 625) != 0) {
return 3;
}
int count = 4;
value /= 625;
while (value > 0) {
if (value % 5 != 0) {
return count;
}
value /= 5;
count++;
}
throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_SMALL, value, 0);
}
/**
* Compute the high digits of m * 5^p / 10^q = m * 5^(p - q) / 2^q = m * 5^i / 2^j, with q chosen
* such that m * 5^i / 2^j has sufficiently many decimal digits to represent the original floating
* point number.
* @param m mantissa
* @param i power of 5
* @param j power of 2
* @return high digits of m * 5^i / 2^j
*/
private static long mulPow5divPow2(final long m, final int i, final int j) {
// m has at most 55 bits.
long mHigh = m >>> 31;
long mLow = m & 0x7fffffff;
long bits13 = mHigh * POW5_SPLIT[i][0]; // 124
long bits03 = mLow * POW5_SPLIT[i][0]; // 93
long bits12 = mHigh * POW5_SPLIT[i][1]; // 93
long bits02 = mLow * POW5_SPLIT[i][1]; // 62
long bits11 = mHigh * POW5_SPLIT[i][2]; // 62
long bits01 = mLow * POW5_SPLIT[i][2]; // 31
long bits10 = mHigh * POW5_SPLIT[i][3]; // 31
long bits00 = mLow * POW5_SPLIT[i][3]; // 0
int actualShift = j - 3 * 31 - 21;
if (actualShift < 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_SMALL,
j, 3 * 31 + 21);
}
return ((((((((bits00 >>> 31) + bits01 + bits10) >>> 31) +
bits02 + bits11) >>> 31) +
bits03 + bits12) >>> 21) +
(bits13 << 10)) >>> actualShift;
}
/**
* Compute the high digits of m / 5^i / 2^j such that the result is accurate to at least 9
* decimal digits. i and j are already chosen appropriately.
* @param m mantissa
* @param i power of 5
* @param j power of 2
* @return high digits of m / 5^i / 2^j
*/
private static long mulPow5InvDivPow2(final long m, final int i, final int j) {
// m has at most 55 bits.
final long mHigh = m >>> 31;
final long mLow = m & 0x7fffffff;
final long bits13 = mHigh * POW5_INV_SPLIT[i][0];
final long bits03 = mLow * POW5_INV_SPLIT[i][0];
final long bits12 = mHigh * POW5_INV_SPLIT[i][1];
final long bits02 = mLow * POW5_INV_SPLIT[i][1];
final long bits11 = mHigh * POW5_INV_SPLIT[i][2];
final long bits01 = mLow * POW5_INV_SPLIT[i][2];
final long bits10 = mHigh * POW5_INV_SPLIT[i][3];
final long bits00 = mLow * POW5_INV_SPLIT[i][3];
final int actualShift = j - 3 * 31 - 21;
if (actualShift < 0) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_SMALL,
j, 3 * 31 + 21);
}
return ((((((((bits00 >>> 31) + bits01 + bits10) >>> 31) +
bits02 + bits11) >>> 31) +
bits03 + bits12) >>> 21) +
(bits13 << 10)) >>> actualShift;
}
}