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1610 lines (1546 loc) · 65.9 KB
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/*
* Copyright (c) 1994, 2025, Oracle and/or its affiliates. All rights reserved.
* Copyright (c) 2025, Alibaba Group Holding Limited. 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 java.lang;
import java.lang.invoke.MethodHandles;
import java.lang.constant.Constable;
import java.lang.constant.ConstantDesc;
import java.util.Optional;
import jdk.internal.math.FloatingDecimal;
import jdk.internal.math.DoubleConsts;
import jdk.internal.math.DoubleToDecimal;
import jdk.internal.util.DecimalDigits;
import jdk.internal.vm.annotation.IntrinsicCandidate;
/**
* The {@code Double} class is the {@linkplain
* java.lang##wrapperClass wrapper class} for values of the primitive
* type {@code double}. An object of type {@code Double} contains a
* single field whose type is {@code double}.
*
* <p>In addition, this class provides several methods for converting a
* {@code double} to a {@code String} and a
* {@code String} to a {@code double}, as well as other
* constants and methods useful when dealing with a
* {@code double}.
*
* <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a>
* class; programmers should treat instances that are
* {@linkplain #equals(Object) equal} as interchangeable and should not
* use instances for synchronization, or unpredictable behavior may
* occur. For example, in a future release, synchronization may fail.
*
* <h2><a id=equivalenceRelation>Floating-point Equality, Equivalence,
* and Comparison</a></h2>
*
* IEEE 754 floating-point values include finite nonzero values,
* signed zeros ({@code +0.0} and {@code -0.0}), signed infinities
* ({@linkplain Double#POSITIVE_INFINITY positive infinity} and
* {@linkplain Double#NEGATIVE_INFINITY negative infinity}), and
* {@linkplain Double#NaN NaN} (not-a-number).
*
* <p>An <em>equivalence relation</em> on a set of values is a boolean
* relation on pairs of values that is reflexive, symmetric, and
* transitive. For more discussion of equivalence relations and object
* equality, see the {@link Object#equals Object.equals}
* specification. An equivalence relation partitions the values it
* operates over into sets called <i>equivalence classes</i>. All the
* members of the equivalence class are equal to each other under the
* relation. An equivalence class may contain only a single member. At
* least for some purposes, all the members of an equivalence class
* are substitutable for each other. In particular, in a numeric
* expression equivalent values can be <em>substituted</em> for one
* another without changing the result of the expression, meaning
* changing the equivalence class of the result of the expression.
*
* <p>Notably, the built-in {@code ==} operation on floating-point
* values is <em>not</em> an equivalence relation. Despite not
* defining an equivalence relation, the semantics of the IEEE 754
* {@code ==} operator were deliberately designed to meet other needs
* of numerical computation. There are two exceptions where the
* properties of an equivalence relation are not satisfied by {@code
* ==} on floating-point values:
*
* <ul>
*
* <li>If {@code v1} and {@code v2} are both NaN, then {@code v1
* == v2} has the value {@code false}. Therefore, for two NaN
* arguments the <em>reflexive</em> property of an equivalence
* relation is <em>not</em> satisfied by the {@code ==} operator.
*
* <li>If {@code v1} represents {@code +0.0} while {@code v2}
* represents {@code -0.0}, or vice versa, then {@code v1 == v2} has
* the value {@code true} even though {@code +0.0} and {@code -0.0}
* are distinguishable under various floating-point operations. For
* example, {@code 1.0/+0.0} evaluates to positive infinity while
* {@code 1.0/-0.0} evaluates to <em>negative</em> infinity and
* positive infinity and negative infinity are neither equal to each
* other nor equivalent to each other. Thus, while a signed zero input
* most commonly determines the sign of a zero result, because of
* dividing by zero, {@code +0.0} and {@code -0.0} may not be
* substituted for each other in general. The sign of a zero input
* also has a non-substitutable effect on the result of some math
* library methods.
*
* </ul>
*
* <p>For ordered comparisons using the built-in comparison operators
* ({@code <}, {@code <=}, etc.), NaN values have another anomalous
* situation: a NaN is neither less than, nor greater than, nor equal
* to any value, including itself. This means the <i>trichotomy of
* comparison</i> does <em>not</em> hold.
*
* <p>To provide the appropriate semantics for {@code equals} and
* {@code compareTo} methods, those methods cannot simply be wrappers
* around {@code ==} or ordered comparison operations. Instead, {@link
* Double#equals equals} uses {@linkplain ##repEquivalence representation
* equivalence}, defining NaN arguments to be equal to each other,
* restoring reflexivity, and defining {@code +0.0} to <em>not</em> be
* equal to {@code -0.0}. For comparisons, {@link Double#compareTo
* compareTo} defines a total order where {@code -0.0} is less than
* {@code +0.0} and where a NaN is equal to itself and considered
* greater than positive infinity.
*
* <p>The operational semantics of {@code equals} and {@code
* compareTo} are expressed in terms of {@linkplain #doubleToLongBits
* bit-wise converting} the floating-point values to integral values.
*
* <p>The <em>natural ordering</em> implemented by {@link #compareTo
* compareTo} is {@linkplain Comparable consistent with equals}. That
* is, two objects are reported as equal by {@code equals} if and only
* if {@code compareTo} on those objects returns zero.
*
* <p>The adjusted behaviors defined for {@code equals} and {@code
* compareTo} allow instances of wrapper classes to work properly with
* conventional data structures. For example, defining NaN
* values to be {@code equals} to one another allows NaN to be used as
* an element of a {@link java.util.HashSet HashSet} or as the key of
* a {@link java.util.HashMap HashMap}. Similarly, defining {@code
* compareTo} as a total ordering, including {@code +0.0}, {@code
* -0.0}, and NaN, allows instances of wrapper classes to be used as
* elements of a {@link java.util.SortedSet SortedSet} or as keys of a
* {@link java.util.SortedMap SortedMap}.
*
* <p>Comparing numerical equality to various useful equivalence
* relations that can be defined over floating-point values:
*
* <dl>
* <dt><a id=fpNumericalEq></a><dfn>{@index "numerical equality"}</dfn> ({@code ==}
* operator): (<em>Not</em> an equivalence relation)</dt>
* <dd>Two floating-point values represent the same extended real
* number. The extended real numbers are the real numbers augmented
* with positive infinity and negative infinity. Under numerical
* equality, {@code +0.0} and {@code -0.0} are equal since they both
* map to the same real value, 0. A NaN does not map to any real
* number and is not equal to any value, including itself.
* </dd>
*
* <dt><dfn>{@index "bit-wise equivalence"}</dfn>:</dt>
* <dd>The bits of the two floating-point values are the same. This
* equivalence relation for {@code double} values {@code a} and {@code
* b} is implemented by the expression
* <br>{@code Double.doubleTo}<code><b>Raw</b></code>{@code LongBits(a) == Double.doubleTo}<code><b>Raw</b></code>{@code LongBits(b)}<br>
* Under this relation, {@code +0.0} and {@code -0.0} are
* distinguished from each other and every bit pattern encoding a NaN
* is distinguished from every other bit pattern encoding a NaN.
* </dd>
*
* <dt><dfn><a id=repEquivalence></a>{@index "representation equivalence"}</dfn>:</dt>
* <dd>The two floating-point values represent the same IEEE 754
* <i>datum</i>. In particular, for {@linkplain #isFinite(double)
* finite} values, the sign, {@linkplain Math#getExponent(double)
* exponent}, and significand components of the floating-point values
* are the same. Under this relation:
* <ul>
* <li> {@code +0.0} and {@code -0.0} are distinguished from each other.
* <li> every bit pattern encoding a NaN is considered equivalent to each other
* <li> positive infinity is equivalent to positive infinity; negative
* infinity is equivalent to negative infinity.
* </ul>
* Expressions implementing this equivalence relation include:
* <ul>
* <li>{@code Double.doubleToLongBits(a) == Double.doubleToLongBits(b)}
* <li>{@code Double.valueOf(a).equals(Double.valueOf(b))}
* <li>{@code Double.compare(a, b) == 0}
* </ul>
* Note that representation equivalence is often an appropriate notion
* of equivalence to test the behavior of {@linkplain StrictMath math
* libraries}.
* </dd>
* </dl>
*
* For two binary floating-point values {@code a} and {@code b}, if
* neither of {@code a} and {@code b} is zero or NaN, then the three
* relations numerical equality, bit-wise equivalence, and
* representation equivalence of {@code a} and {@code b} have the same
* {@code true}/{@code false} value. In other words, for binary
* floating-point values, the three relations only differ if at least
* one argument is zero or NaN.
*
* <h2><a id=decimalToBinaryConversion>Decimal ↔ Binary Conversion Issues</a></h2>
*
* Many surprising results of binary floating-point arithmetic trace
* back to aspects of decimal to binary conversion and binary to
* decimal conversion. While integer values can be exactly represented
* in any base, which fractional values can be exactly represented in
* a base is a function of the base. For example, in base 10, 1/3 is a
* repeating fraction (0.33333....); but in base 3, 1/3 is exactly
* 0.1<sub>(3)</sub>, that is 1 × 3<sup>-1</sup>.
* Similarly, in base 10, 1/10 is exactly representable as 0.1
* (1 × 10<sup>-1</sup>), but in base 2, it is a
* repeating fraction (0.0001100110011...<sub>(2)</sub>).
*
* <p>Values of the {@code float} type have {@value Float#PRECISION}
* bits of precision and values of the {@code double} type have
* {@value Double#PRECISION} bits of precision. Therefore, since 0.1
* is a repeating fraction in base 2 with a four-bit repeat, {@code
* 0.1f} != {@code 0.1d}. In more detail, including hexadecimal
* floating-point literals:
*
* <ul>
* <li>The exact numerical value of {@code 0.1f} ({@code 0x1.99999a0000000p-4f}) is
* 0.100000001490116119384765625.
* <li>The exact numerical value of {@code 0.1d} ({@code 0x1.999999999999ap-4d}) is
* 0.1000000000000000055511151231257827021181583404541015625.
* </ul>
*
* These are the closest {@code float} and {@code double} values,
* respectively, to the numerical value of 0.1. These results are
* consistent with a {@code float} value having the equivalent of 6 to
* 9 digits of decimal precision and a {@code double} value having the
* equivalent of 15 to 17 digits of decimal precision. (The
* equivalent precision varies according to the different relative
* densities of binary and decimal values at different points along the
* real number line.)
*
* <p>This representation hazard of decimal fractions is one reason to
* use caution when storing monetary values as {@code float} or {@code
* double}. Alternatives include:
* <ul>
* <li>using {@link java.math.BigDecimal BigDecimal} to store decimal
* fractional values exactly
*
* <li>scaling up so the monetary value is an integer — for
* example, multiplying by 100 if the value is denominated in cents or
* multiplying by 1000 if the value is denominated in mills —
* and then storing that scaled value in an integer type
*
*</ul>
*
* <p>For each finite floating-point value and a given floating-point
* type, there is a contiguous region of the real number line which
* maps to that value. Under the default round to nearest rounding
* policy (JLS {@jls 15.4}), this contiguous region for a value is
* typically one {@linkplain Math#ulp ulp} (unit in the last place)
* wide and centered around the exactly representable value. (At
* exponent boundaries, the region is asymmetrical and larger on the
* side with the larger exponent.) For example, for {@code 0.1f}, the
* region can be computed as follows:
*
* <br>// Numeric values listed are exact values
* <br>oneTenthApproxAsFloat = 0.100000001490116119384765625;
* <br>ulpOfoneTenthApproxAsFloat = Math.ulp(0.1f) = 7.450580596923828125E-9;
* <br>// Numeric range that is converted to the float closest to 0.1, _excludes_ endpoints
* <br>(oneTenthApproxAsFloat - ½ulpOfoneTenthApproxAsFloat, oneTenthApproxAsFloat + ½ulpOfoneTenthApproxAsFloat) =
* <br>(0.0999999977648258209228515625, 0.1000000052154064178466796875)
*
* <p>In particular, a correctly rounded decimal to binary conversion
* of any string representing a number in this range, say by {@link
* Float#parseFloat(String)}, will be converted to the same value:
*
* {@snippet lang="java" :
* Float.parseFloat("0.0999999977648258209228515625000001"); // rounds up to oneTenthApproxAsFloat
* Float.parseFloat("0.099999998"); // rounds up to oneTenthApproxAsFloat
* Float.parseFloat("0.1"); // rounds up to oneTenthApproxAsFloat
* Float.parseFloat("0.100000001490116119384765625"); // exact conversion
* Float.parseFloat("0.100000005215406417846679687"); // rounds down to oneTenthApproxAsFloat
* Float.parseFloat("0.100000005215406417846679687499999"); // rounds down to oneTenthApproxAsFloat
* }
*
* <p>Similarly, an analogous range can be constructed for the {@code
* double} type based on the exact value of {@code double}
* approximation to {@code 0.1d} and the numerical value of {@code
* Math.ulp(0.1d)} and likewise for other particular numerical values
* in the {@code float} and {@code double} types.
*
* <p>As seen in the above conversions, compared to the exact
* numerical value the operation would have without rounding, the same
* floating-point value as a result can be:
* <ul>
* <li>greater than the exact result
* <li>equal to the exact result
* <li>less than the exact result
* </ul>
*
* A floating-point value doesn't "know" whether it was the result of
* rounding up, or rounding down, or an exact operation; it contains
* no history of how it was computed. Consequently, the sum of
* {@snippet lang="java" :
* 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f;
* // Numerical value of computed sum: 1.00000011920928955078125,
* // the next floating-point value larger than 1.0f, equal to Math.nextUp(1.0f).
* }
* or
* {@snippet lang="java" :
* 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d;
* // Numerical value of computed sum: 0.99999999999999988897769753748434595763683319091796875,
* // the next floating-point value smaller than 1.0d, equal to Math.nextDown(1.0d).
* }
*
* should <em>not</em> be expected to be exactly equal to 1.0, but
* only to be close to 1.0. Consequently, the following code is an
* infinite loop:
*
* {@snippet lang="java" :
* double d = 0.0;
* while (d != 1.0) { // Surprising infinite loop
* d += 0.1; // Sum never _exactly_ equals 1.0
* }
* }
*
* Instead, use an integer loop count for counted loops:
*
* {@snippet lang="java" :
* double d = 0.0;
* for (int i = 0; i < 10; i++) {
* d += 0.1;
* } // Value of d is equal to Math.nextDown(1.0).
* }
*
* or test against a floating-point limit using ordered comparisons
* ({@code <}, {@code <=}, {@code >}, {@code >=}):
*
* {@snippet lang="java" :
* double d = 0.0;
* while (d <= 1.0) {
* d += 0.1;
* } // Value of d approximately 1.0999999999999999
* }
*
* While floating-point arithmetic may have surprising results, IEEE
* 754 floating-point arithmetic follows a principled design and its
* behavior is predictable on the Java platform.
*
* @jls 4.2.3 Floating-Point Types and Values
* @jls 4.2.4 Floating-Point Operations
* @jls 15.21.1 Numerical Equality Operators == and !=
* @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
*
* @spec https://standards.ieee.org/ieee/754/6210/
* IEEE Standard for Floating-Point Arithmetic
*
* @since 1.0
*/
@jdk.internal.ValueBased
public final class Double extends Number
implements Comparable<Double>, Constable, ConstantDesc {
/**
* A constant holding the positive infinity of type
* {@code double}. It is equal to the value returned by
* {@code Double.longBitsToDouble(0x7ff0000000000000L)}.
*/
public static final double POSITIVE_INFINITY = 1.0 / 0.0;
/**
* A constant holding the negative infinity of type
* {@code double}. It is equal to the value returned by
* {@code Double.longBitsToDouble(0xfff0000000000000L)}.
*/
public static final double NEGATIVE_INFINITY = -1.0 / 0.0;
/**
* A constant holding a Not-a-Number (NaN) value of type {@code double}.
* It is {@linkplain Double##equivalenceRelation equivalent} to the
* value returned by {@code Double.longBitsToDouble(0x7ff8000000000000L)}.
*/
public static final double NaN = 0.0d / 0.0;
/**
* A constant holding the largest positive finite value of type
* {@code double},
* (2-2<sup>-52</sup>)·2<sup>1023</sup>. It is equal to
* the hexadecimal floating-point literal
* {@code 0x1.fffffffffffffP+1023} and also equal to
* {@code Double.longBitsToDouble(0x7fefffffffffffffL)}.
*/
public static final double MAX_VALUE = 0x1.fffffffffffffP+1023; // 1.7976931348623157e+308
/**
* A constant holding the smallest positive normal value of type
* {@code double}, 2<sup>-1022</sup>. It is equal to the
* hexadecimal floating-point literal {@code 0x1.0p-1022} and also
* equal to {@code Double.longBitsToDouble(0x0010000000000000L)}.
*
* @since 1.6
*/
public static final double MIN_NORMAL = 0x1.0p-1022; // 2.2250738585072014E-308
/**
* A constant holding the smallest positive nonzero value of type
* {@code double}, 2<sup>-1074</sup>. It is equal to the
* hexadecimal floating-point literal
* {@code 0x0.0000000000001P-1022} and also equal to
* {@code Double.longBitsToDouble(0x1L)}.
*/
public static final double MIN_VALUE = 0x0.0000000000001P-1022; // 4.9e-324
/**
* The number of bits used to represent a {@code double} value,
* {@value}.
*
* @since 1.5
*/
public static final int SIZE = 64;
/**
* The number of bits in the significand of a {@code double}
* value, {@value}. This is the parameter N in section {@jls
* 4.2.3} of <cite>The Java Language Specification</cite>.
*
* @since 19
*/
public static final int PRECISION = 53;
/**
* Maximum exponent a finite {@code double} variable may have,
* {@value}. It is equal to the value returned by {@code
* Math.getExponent(Double.MAX_VALUE)}.
*
* @since 1.6
*/
public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 1023
/**
* Minimum exponent a normalized {@code double} variable may have,
* {@value}. It is equal to the value returned by {@code
* Math.getExponent(Double.MIN_NORMAL)}.
*
* @since 1.6
*/
public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -1022
/**
* The number of bytes used to represent a {@code double} value,
* {@value}.
*
* @since 1.8
*/
public static final int BYTES = SIZE / Byte.SIZE;
/**
* The {@code Class} instance representing the primitive type
* {@code double}.
*
* @since 1.1
*/
public static final Class<Double> TYPE = Class.getPrimitiveClass("double");
/**
* Returns a string representation of the {@code double}
* argument. All characters mentioned below are ASCII characters.
* <ul>
* <li>If the argument is NaN, the result is the string
* "{@code NaN}".
* <li>Otherwise, the result is a string that represents the sign and
* magnitude (absolute value) of the argument. If the sign is negative,
* the first character of the result is '{@code -}'
* ({@code '\u005Cu002D'}); if the sign is positive, no sign character
* appears in the result. As for the magnitude <i>m</i>:
* <ul>
* <li>If <i>m</i> is infinity, it is represented by the characters
* {@code "Infinity"}; thus, positive infinity produces the result
* {@code "Infinity"} and negative infinity produces the result
* {@code "-Infinity"}.
*
* <li>If <i>m</i> is zero, it is represented by the characters
* {@code "0.0"}; thus, negative zero produces the result
* {@code "-0.0"} and positive zero produces the result
* {@code "0.0"}.
*
* <li> Otherwise <i>m</i> is positive and finite.
* It is converted to a string in two stages:
* <ul>
* <li> <em>Selection of a decimal</em>:
* A well-defined decimal <i>d</i><sub><i>m</i></sub>
* is selected to represent <i>m</i>.
* This decimal is (almost always) the <em>shortest</em> one that
* rounds to <i>m</i> according to the round to nearest
* rounding policy of IEEE 754 floating-point arithmetic.
* <li> <em>Formatting as a string</em>:
* The decimal <i>d</i><sub><i>m</i></sub> is formatted as a string,
* either in plain or in computerized scientific notation,
* depending on its value.
* </ul>
* </ul>
* </ul>
*
* <p>A <em>decimal</em> is a number of the form
* <i>s</i>×10<sup><i>i</i></sup>
* for some (unique) integers <i>s</i> > 0 and <i>i</i> such that
* <i>s</i> is not a multiple of 10.
* These integers are the <em>significand</em> and
* the <em>exponent</em>, respectively, of the decimal.
* The <em>length</em> of the decimal is the (unique)
* positive integer <i>n</i> meeting
* 10<sup><i>n</i>-1</sup> ≤ <i>s</i> < 10<sup><i>n</i></sup>.
*
* <p>The decimal <i>d</i><sub><i>m</i></sub> for a finite positive <i>m</i>
* is defined as follows:
* <ul>
* <li>Let <i>R</i> be the set of all decimals that round to <i>m</i>
* according to the usual <em>round to nearest</em> rounding policy of
* IEEE 754 floating-point arithmetic.
* <li>Let <i>p</i> be the minimal length over all decimals in <i>R</i>.
* <li>When <i>p</i> ≥ 2, let <i>T</i> be the set of all decimals
* in <i>R</i> with length <i>p</i>.
* Otherwise, let <i>T</i> be the set of all decimals
* in <i>R</i> with length 1 or 2.
* <li>Define <i>d</i><sub><i>m</i></sub> as the decimal in <i>T</i>
* that is closest to <i>m</i>.
* Or if there are two such decimals in <i>T</i>,
* select the one with the even significand.
* </ul>
*
* <p>The (uniquely) selected decimal <i>d</i><sub><i>m</i></sub>
* is then formatted.
* Let <i>s</i>, <i>i</i> and <i>n</i> be the significand, exponent and
* length of <i>d</i><sub><i>m</i></sub>, respectively.
* Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let
* <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>
* be the usual decimal expansion of <i>s</i>.
* Note that <i>s</i><sub>1</sub> ≠ 0
* and <i>s</i><sub><i>n</i></sub> ≠ 0.
* Below, the decimal point {@code '.'} is {@code '\u005Cu002E'}
* and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}.
* <ul>
* <li>Case -3 ≤ <i>e</i> < 0:
* <i>d</i><sub><i>m</i></sub> is formatted as
* <code>0.0</code>…<code>0</code><!--
* --><i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>,
* where there are exactly -(<i>n</i> + <i>i</i>) zeroes between
* the decimal point and <i>s</i><sub>1</sub>.
* For example, 123 × 10<sup>-4</sup> is formatted as
* {@code 0.0123}.
* <li>Case 0 ≤ <i>e</i> < 7:
* <ul>
* <li>Subcase <i>i</i> ≥ 0:
* <i>d</i><sub><i>m</i></sub> is formatted as
* <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub><!--
* --><code>0</code>…<code>0.0</code>,
* where there are exactly <i>i</i> zeroes
* between <i>s</i><sub><i>n</i></sub> and the decimal point.
* For example, 123 × 10<sup>2</sup> is formatted as
* {@code 12300.0}.
* <li>Subcase <i>i</i> < 0:
* <i>d</i><sub><i>m</i></sub> is formatted as
* <i>s</i><sub>1</sub>…<!--
* --><i>s</i><sub><i>n</i>+<i>i</i></sub><code>.</code><!--
* --><i>s</i><sub><i>n</i>+<i>i</i>+1</sub>…<!--
* --><i>s</i><sub><i>n</i></sub>,
* where there are exactly -<i>i</i> digits to the right of
* the decimal point.
* For example, 123 × 10<sup>-1</sup> is formatted as
* {@code 12.3}.
* </ul>
* <li>Case <i>e</i> < -3 or <i>e</i> ≥ 7:
* computerized scientific notation is used to format
* <i>d</i><sub><i>m</i></sub>.
* Here <i>e</i> is formatted as by {@link Integer#toString(int)}.
* <ul>
* <li>Subcase <i>n</i> = 1:
* <i>d</i><sub><i>m</i></sub> is formatted as
* <i>s</i><sub>1</sub><code>.0E</code><i>e</i>.
* For example, 1 × 10<sup>23</sup> is formatted as
* {@code 1.0E23}.
* <li>Subcase <i>n</i> > 1:
* <i>d</i><sub><i>m</i></sub> is formatted as
* <i>s</i><sub>1</sub><code>.</code><i>s</i><sub>2</sub><!--
* -->…<i>s</i><sub><i>n</i></sub><code>E</code><i>e</i>.
* For example, 123 × 10<sup>-21</sup> is formatted as
* {@code 1.23E-19}.
* </ul>
* </ul>
*
* <p>To create localized string representations of a floating-point
* value, use subclasses of {@link java.text.NumberFormat}.
*
* @apiNote
* This method corresponds to the general functionality of the
* convertToDecimalCharacter operation defined in IEEE 754;
* however, that operation is defined in terms of specifying the
* number of significand digits used in the conversion.
* Code to do such a conversion in the Java platform includes
* converting the {@code double} to a {@link java.math.BigDecimal
* BigDecimal} exactly and then rounding the {@code BigDecimal} to
* the desired number of digits; sample code:
* {@snippet lang=java :
* double d = 0.1;
* int digits = 25;
* BigDecimal bd = new BigDecimal(d);
* String result = bd.round(new MathContext(digits, RoundingMode.HALF_UP));
* // 0.1000000000000000055511151
* }
*
* @param d the {@code double} to be converted.
* @return a string representation of the argument.
*/
public static String toString(double d) {
return DoubleToDecimal.toString(d);
}
/**
* Returns a hexadecimal string representation of the
* {@code double} argument. All characters mentioned below
* are ASCII characters.
*
* <ul>
* <li>If the argument is NaN, the result is the string
* "{@code NaN}".
* <li>Otherwise, the result is a string that represents the sign
* and magnitude of the argument. If the sign is negative, the
* first character of the result is '{@code -}'
* ({@code '\u005Cu002D'}); if the sign is positive, no sign
* character appears in the result. As for the magnitude <i>m</i>:
*
* <ul>
* <li>If <i>m</i> is infinity, it is represented by the string
* {@code "Infinity"}; thus, positive infinity produces the
* result {@code "Infinity"} and negative infinity produces
* the result {@code "-Infinity"}.
*
* <li>If <i>m</i> is zero, it is represented by the string
* {@code "0x0.0p0"}; thus, negative zero produces the result
* {@code "-0x0.0p0"} and positive zero produces the result
* {@code "0x0.0p0"}.
*
* <li>If <i>m</i> is a {@code double} value with a
* normalized representation, substrings are used to represent the
* significand and exponent fields. The significand is
* represented by the characters {@code "0x1."}
* followed by a lowercase hexadecimal representation of the rest
* of the significand as a fraction. Trailing zeros in the
* hexadecimal representation are removed unless all the digits
* are zero, in which case a single zero is used. Next, the
* exponent is represented by {@code "p"} followed
* by a decimal string of the unbiased exponent as if produced by
* a call to {@link Integer#toString(int) Integer.toString} on the
* exponent value.
*
* <li>If <i>m</i> is a {@code double} value with a subnormal
* representation, the significand is represented by the
* characters {@code "0x0."} followed by a
* hexadecimal representation of the rest of the significand as a
* fraction. Trailing zeros in the hexadecimal representation are
* removed. Next, the exponent is represented by
* {@code "p-1022"}. Note that there must be at
* least one nonzero digit in a subnormal significand.
*
* </ul>
*
* </ul>
*
* <table class="striped">
* <caption>Examples</caption>
* <thead>
* <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th>
* </thead>
* <tbody style="text-align:right">
* <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td>
* <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td>
* <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td>
* <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td>
* <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td>
* <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td>
* <tr><th scope="row">{@code Double.MAX_VALUE}</th>
* <td>{@code 0x1.fffffffffffffp1023}</td>
* <tr><th scope="row">{@code Minimum Normal Value}</th>
* <td>{@code 0x1.0p-1022}</td>
* <tr><th scope="row">{@code Maximum Subnormal Value}</th>
* <td>{@code 0x0.fffffffffffffp-1022}</td>
* <tr><th scope="row">{@code Double.MIN_VALUE}</th>
* <td>{@code 0x0.0000000000001p-1022}</td>
* </tbody>
* </table>
*
* @apiNote
* This method corresponds to the convertToHexCharacter operation
* defined in IEEE 754.
*
* @param d the {@code double} to be converted.
* @return a hex string representation of the argument.
* @since 1.5
*/
public static String toHexString(double d) {
/*
* Modeled after the "a" conversion specifier in C99, section
* 7.19.6.1; however, the output of this method is more
* tightly specified.
*/
if (!isFinite(d)) {
// For infinity and NaN, use the decimal output.
return Double.toString(d);
}
long doubleToLongBits = Double.doubleToLongBits(d);
boolean negative = doubleToLongBits < 0;
if (d == 0.0) {
return negative ? "-0x0.0p0" : "0x0.0p0";
}
d = Math.abs(d);
// Check if the value is subnormal (less than the smallest normal value)
boolean subnormal = d < Double.MIN_NORMAL;
// Isolate significand bits and OR in a high-order bit
// so that the string representation has a known length.
// This ensures we always have 13 hex digits to work with (52 bits / 4 bits per hex digit)
long signifBits = doubleToLongBits & DoubleConsts.SIGNIF_BIT_MASK;
// Calculate the number of trailing zeros in the significand (in groups of 4 bits)
// This is used to remove trailing zeros from the hex representation
// We limit to 12 because we want to keep at least 1 hex digit (13 total - 12 = 1)
// assert 0 <= trailingZeros && trailingZeros <= 12
int trailingZeros = Long.numberOfTrailingZeros(signifBits | 1L << 4 * 12) >> 2;
// Determine the exponent value based on whether the number is subnormal or normal
// Subnormal numbers use the minimum exponent, normal numbers use the actual exponent
int exp = subnormal ? Double.MIN_EXPONENT : Math.getExponent(d);
// Calculate the total length of the resulting string:
// Sign (optional) + prefix "0x" + implicit bit + "." + hex digits + "p" + exponent
int charlen = (negative ? 1 : 0) // sign character
+ 4 // "0x1." or "0x0."
+ 13 - trailingZeros // hex digits (13 max, minus trailing zeros)
+ 1 // "p"
+ DecimalDigits.stringSize(exp) // exponent
;
// Create a byte array to hold the result characters
byte[] chars = new byte[charlen];
int index = 0;
// Add the sign character if the number is negative
if (negative) { // value is negative
chars[index++] = '-';
}
// Add the prefix and the implicit bit ('1' for normal, '0' for subnormal)
// Subnormal values have a 0 implicit bit; normal values have a 1 implicit bit.
chars[index ] = '0'; // Hex prefix
chars[index + 1] = 'x'; // Hex prefix
chars[index + 2] = (byte) (subnormal ? '0' : '1'); // Implicit bit
chars[index + 3] = '.'; // Decimal point
index += 4;
// Convert significand to hex digits manually to avoid creating temporary strings
// Extract the 13 hex digits (52 bits) from signifBits
// We need to extract bits 48-51, 44-47, ..., 0-3 (13 groups of 4 bits)
for (int sh = 4 * 12, end = 4 * trailingZeros; sh >= end; sh -= 4) {
// Extract 4 bits at a time from left to right
// Shift right by sh positions and mask with 0xF
// Integer.digits maps values 0-15 to '0'-'f' characters
chars[index++] = Integer.digits[((int)(signifBits >> sh)) & 0xF];
}
// Add the exponent indicator
chars[index] = 'p';
// Append the exponent value to the character array
// This method writes the decimal representation of exp directly into the byte array
DecimalDigits.uncheckedGetCharsLatin1(exp, charlen, chars);
return String.newStringWithLatin1Bytes(chars);
}
/**
* Returns a {@code Double} object holding the
* {@code double} value represented by the argument string
* {@code s}.
*
* <p>If {@code s} is {@code null}, then a
* {@code NullPointerException} is thrown.
*
* <p>Leading and trailing whitespace characters in {@code s}
* are ignored. Whitespace is removed as if by the {@link
* String#trim} method; that is, both ASCII space and control
* characters are removed. The rest of {@code s} should
* constitute a <i>FloatValue</i> as described by the lexical
* syntax rules:
*
* <blockquote>
* <dl>
* <dt><i>FloatValue:</i>
* <dd><i>Sign<sub>opt</sub></i> {@code NaN}
* <dd><i>Sign<sub>opt</sub></i> {@code Infinity}
* <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i>
* <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i>
* <dd><i>SignedInteger</i>
* </dl>
*
* <dl>
* <dt><i>HexFloatingPointLiteral</i>:
* <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i>
* </dl>
*
* <dl>
* <dt><i>HexSignificand:</i>
* <dd><i>HexNumeral</i>
* <dd><i>HexNumeral</i> {@code .}
* <dd>{@code 0x} <i>HexDigits<sub>opt</sub>
* </i>{@code .}<i> HexDigits</i>
* <dd>{@code 0X}<i> HexDigits<sub>opt</sub>
* </i>{@code .} <i>HexDigits</i>
* </dl>
*
* <dl>
* <dt><i>BinaryExponent:</i>
* <dd><i>BinaryExponentIndicator SignedInteger</i>
* </dl>
*
* <dl>
* <dt><i>BinaryExponentIndicator:</i>
* <dd>{@code p}
* <dd>{@code P}
* </dl>
*
* </blockquote>
*
* where <i>Sign</i>, <i>FloatingPointLiteral</i>,
* <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and
* <i>FloatTypeSuffix</i> are as defined in the lexical structure
* sections of
* <cite>The Java Language Specification</cite>,
* except that underscores are not accepted between digits.
* If {@code s} does not have the form of
* a <i>FloatValue</i>, then a {@code NumberFormatException}
* is thrown. Otherwise, {@code s} is regarded as
* representing an exact decimal value in the usual
* "computerized scientific notation" or as an exact
* hexadecimal value; this exact numerical value is then
* conceptually converted to an "infinitely precise"
* binary value that is then rounded to type {@code double}
* by the usual round-to-nearest rule of IEEE 754 floating-point
* arithmetic, which includes preserving the sign of a zero
* value.
*
* Note that the round-to-nearest rule also implies overflow and
* underflow behaviour; if the exact value of {@code s} is large
* enough in magnitude (greater than or equal to ({@link
* #MAX_VALUE} + {@link Math#ulp(double) ulp(MAX_VALUE)}/2),
* rounding to {@code double} will result in an infinity and if the
* exact value of {@code s} is small enough in magnitude (less
* than or equal to {@link #MIN_VALUE}/2), rounding to float will
* result in a zero.
*
* Finally, after rounding a {@code Double} object representing
* this {@code double} value is returned.
*
* <p>Note that trailing format specifiers, specifiers that
* determine the type of a floating-point literal
* ({@code 1.0f} is a {@code float} value;
* {@code 1.0d} is a {@code double} value), do
* <em>not</em> influence the results of this method. In other
* words, the numerical value of the input string is converted
* directly to the target floating-point type. The two-step
* sequence of conversions, string to {@code float} followed
* by {@code float} to {@code double}, is <em>not</em>
* equivalent to converting a string directly to
* {@code double}. For example, the {@code float}
* literal {@code 0.1f} is equal to the {@code double}
* value {@code 0.10000000149011612}; the {@code float}
* literal {@code 0.1f} represents a different numerical
* value than the {@code double} literal
* {@code 0.1}. (The numerical value 0.1 cannot be exactly
* represented in a binary floating-point number.)
*
* <p>To avoid calling this method on an invalid string and having
* a {@code NumberFormatException} be thrown, the regular
* expression below can be used to screen the input string:
*
* {@snippet lang="java" :
* final String Digits = "(\\p{Digit}+)";
* final String HexDigits = "(\\p{XDigit}+)";
* // an exponent is 'e' or 'E' followed by an optionally
* // signed decimal integer.
* final String Exp = "[eE][+-]?"+Digits;
* final String fpRegex =
* ("[\\x00-\\x20]*"+ // Optional leading "whitespace"
* "[+-]?(" + // Optional sign character
* "NaN|" + // "NaN" string
* "Infinity|" + // "Infinity" string
*
* // A decimal floating-point string representing a finite positive
* // number without a leading sign has at most five basic pieces:
* // Digits . Digits ExponentPart FloatTypeSuffix
* //
* // Since this method allows integer-only strings as input
* // in addition to strings of floating-point literals, the
* // two sub-patterns below are simplifications of the grammar
* // productions from section 3.10.2 of
* // The Java Language Specification.
*
* // Digits ._opt Digits_opt ExponentPart_opt FloatTypeSuffix_opt
* "((("+Digits+"(\\.)?("+Digits+"?)("+Exp+")?)|"+
*
* // . Digits ExponentPart_opt FloatTypeSuffix_opt
* "(\\.("+Digits+")("+Exp+")?)|"+
*
* // Hexadecimal strings
* "((" +
* // 0[xX] HexDigits ._opt BinaryExponent FloatTypeSuffix_opt
* "(0[xX]" + HexDigits + "(\\.)?)|" +
*
* // 0[xX] HexDigits_opt . HexDigits BinaryExponent FloatTypeSuffix_opt
* "(0[xX]" + HexDigits + "?(\\.)" + HexDigits + ")" +
*
* ")[pP][+-]?" + Digits + "))" +
* "[fFdD]?))" +
* "[\\x00-\\x20]*");// Optional trailing "whitespace"
* // @link region substring="Pattern.matches" target ="java.util.regex.Pattern#matches"
* if (Pattern.matches(fpRegex, myString))
* Double.valueOf(myString); // Will not throw NumberFormatException
* // @end
* else {
* // Perform suitable alternative action
* }
* }
*
* @apiNote To interpret localized string representations of a
* floating-point value, or string representations that have
* non-ASCII digits, use {@link java.text.NumberFormat}. For
* example,
* {@snippet lang="java" :
* NumberFormat.getInstance(l).parse(s).doubleValue();
* }
* where {@code l} is the desired locale, or
* {@link java.util.Locale#ROOT} if locale insensitive.
*
* @apiNote
* This method corresponds to the convertFromDecimalCharacter and
* convertFromHexCharacter operations defined in IEEE 754.
*
* @param s the string to be parsed.
* @return a {@code Double} object holding the value
* represented by the {@code String} argument.
* @throws NumberFormatException if the string does not contain a
* parsable number.
* @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
*/
public static Double valueOf(String s) throws NumberFormatException {
return new Double(parseDouble(s));
}
/**
* Returns a {@code Double} instance representing the specified
* {@code double} value.
* If a new {@code Double} instance is not required, this method
* should generally be used in preference to the constructor
* {@link #Double(double)}, as this method is likely to yield
* significantly better space and time performance by caching
* frequently requested values.
*
* @param d a double value.
* @return a {@code Double} instance representing {@code d}.
* @since 1.5
*/
@IntrinsicCandidate
public static Double valueOf(double d) {
return new Double(d);
}
/**
* Returns a new {@code double} initialized to the value
* represented by the specified {@code String}, as performed
* by the {@code valueOf} method of class
* {@code Double}.
*
* @param s the string to be parsed.
* @return the {@code double} value represented by the string
* argument.
* @throws NullPointerException if the string is null
* @throws NumberFormatException if the string does not contain
* a parsable {@code double}.
* @see java.lang.Double#valueOf(String)
* @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
* @since 1.2
*/
public static double parseDouble(String s) throws NumberFormatException {
return FloatingDecimal.parseDouble(s);
}
/**
* Returns {@code true} if the specified number is a
* Not-a-Number (NaN) value, {@code false} otherwise.
*
* @apiNote