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/*
* Copyright (C) 2014 The Android Open Source Project
* Copyright (c) 1994, 2013, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* questions.
*/
package java.lang;
import dalvik.annotation.optimization.CriticalNative;
import java.util.Random;
import sun.misc.FloatConsts;
import sun.misc.DoubleConsts;
/**
* The class {@code Math} contains methods for performing basic
* numeric operations such as the elementary exponential, logarithm,
* square root, and trigonometric functions.
*
* Unlike some of the numeric methods of class
* {@code StrictMath}, all implementations of the equivalent
* functions of class {@code Math} are not defined to return the
* bit-for-bit same results. This relaxation permits
* better-performing implementations where strict reproducibility is
* not required.
*
*
By default many of the {@code Math} methods simply call
* the equivalent method in {@code StrictMath} for their
* implementation. Code generators are encouraged to use
* platform-specific native libraries or microprocessor instructions,
* where available, to provide higher-performance implementations of
* {@code Math} methods. Such higher-performance
* implementations still must conform to the specification for
* {@code Math}.
*
*
The quality of implementation specifications concern two
* properties, accuracy of the returned result and monotonicity of the
* method. Accuracy of the floating-point {@code Math} methods is
* measured in terms of ulps, units in the last place. For a
* given floating-point format, an {@linkplain #ulp(double) ulp} of a
* specific real number value is the distance between the two
* floating-point values bracketing that numerical value. When
* discussing the accuracy of a method as a whole rather than at a
* specific argument, the number of ulps cited is for the worst-case
* error at any argument. If a method always has an error less than
* 0.5 ulps, the method always returns the floating-point number
* nearest the exact result; such a method is correctly
* rounded. A correctly rounded method is generally the best a
* floating-point approximation can be; however, it is impractical for
* many floating-point methods to be correctly rounded. Instead, for
* the {@code Math} class, a larger error bound of 1 or 2 ulps is
* allowed for certain methods. Informally, with a 1 ulp error bound,
* when the exact result is a representable number, the exact result
* should be returned as the computed result; otherwise, either of the
* two floating-point values which bracket the exact result may be
* returned. For exact results large in magnitude, one of the
* endpoints of the bracket may be infinite. Besides accuracy at
* individual arguments, maintaining proper relations between the
* method at different arguments is also important. Therefore, most
* methods with more than 0.5 ulp errors are required to be
* semi-monotonic: whenever the mathematical function is
* non-decreasing, so is the floating-point approximation, likewise,
* whenever the mathematical function is non-increasing, so is the
* floating-point approximation. Not all approximations that have 1
* ulp accuracy will automatically meet the monotonicity requirements.
*
*
* The platform uses signed two's complement integer arithmetic with
* int and long primitive types. The developer should choose
* the primitive type to ensure that arithmetic operations consistently
* produce correct results, which in some cases means the operations
* will not overflow the range of values of the computation.
* The best practice is to choose the primitive type and algorithm to avoid
* overflow. In cases where the size is {@code int} or {@code long} and
* overflow errors need to be detected, the methods {@code addExact},
* {@code subtractExact}, {@code multiplyExact}, and {@code toIntExact}
* throw an {@code ArithmeticException} when the results overflow.
* For other arithmetic operations such as divide, absolute value,
* increment, decrement, and negation overflow occurs only with
* a specific minimum or maximum value and should be checked against
* the minimum or maximum as appropriate.
*
* @author unascribed
* @author Joseph D. Darcy
* @since JDK1.0
*/
public final class Math {
// Android-changed: Numerous methods in this class are re-implemented in native for performance.
// Those methods are also annotated @CriticalNative.
/**
* Don't let anyone instantiate this class.
*/
private Math() {}
/**
* The {@code double} value that is closer than any other to
* e, the base of the natural logarithms.
*/
public static final double E = 2.7182818284590452354;
/**
* The {@code double} value that is closer than any other to
* pi, the ratio of the circumference of a circle to its
* diameter.
*/
public static final double PI = 3.14159265358979323846;
/**
* Returns the trigonometric sine of an angle. Special cases:
*
- If the argument is NaN or an infinity, then the
* result is NaN.
*
- If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
* The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param a an angle, in radians.
* @return the sine of the argument.
*/
@CriticalNative
public static native double sin(double a);
/**
* Returns the trigonometric cosine of an angle. Special cases:
*
- If the argument is NaN or an infinity, then the
* result is NaN.
*
* The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param a an angle, in radians.
* @return the cosine of the argument.
*/
@CriticalNative
public static native double cos(double a);
/**
* Returns the trigonometric tangent of an angle. Special cases:
*
- If the argument is NaN or an infinity, then the result
* is NaN.
*
- If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
* The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param a an angle, in radians.
* @return the tangent of the argument.
*/
@CriticalNative
public static native double tan(double a);
/**
* Returns the arc sine of a value; the returned angle is in the
* range -pi/2 through pi/2. Special cases:
*
- If the argument is NaN or its absolute value is greater
* than 1, then the result is NaN.
*
- If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
* The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param a the value whose arc sine is to be returned.
* @return the arc sine of the argument.
*/
@CriticalNative
public static native double asin(double a);
/**
* Returns the arc cosine of a value; the returned angle is in the
* range 0.0 through pi. Special case:
*
- If the argument is NaN or its absolute value is greater
* than 1, then the result is NaN.
*
* The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param a the value whose arc cosine is to be returned.
* @return the arc cosine of the argument.
*/
@CriticalNative
public static native double acos(double a);
/**
* Returns the arc tangent of a value; the returned angle is in the
* range -pi/2 through pi/2. Special cases:
*
- If the argument is NaN, then the result is NaN.
*
- If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
* The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param a the value whose arc tangent is to be returned.
* @return the arc tangent of the argument.
*/
@CriticalNative
public static native double atan(double a);
/**
* Converts an angle measured in degrees to an approximately
* equivalent angle measured in radians. The conversion from
* degrees to radians is generally inexact.
*
* @param angdeg an angle, in degrees
* @return the measurement of the angle {@code angdeg}
* in radians.
* @since 1.2
*/
public static double toRadians(double angdeg) {
return angdeg / 180.0 * PI;
}
/**
* Converts an angle measured in radians to an approximately
* equivalent angle measured in degrees. The conversion from
* radians to degrees is generally inexact; users should
* not expect {@code cos(toRadians(90.0))} to exactly
* equal {@code 0.0}.
*
* @param angrad an angle, in radians
* @return the measurement of the angle {@code angrad}
* in degrees.
* @since 1.2
*/
public static double toDegrees(double angrad) {
return angrad * 180.0 / PI;
}
/**
* Returns Euler's number e raised to the power of a
* {@code double} value. Special cases:
*
- If the argument is NaN, the result is NaN.
*
- If the argument is positive infinity, then the result is
* positive infinity.
*
- If the argument is negative infinity, then the result is
* positive zero.
*
* The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param a the exponent to raise e to.
* @return the value e{@code a},
* where e is the base of the natural logarithms.
*/
@CriticalNative
public static native double exp(double a);
/**
* Returns the natural logarithm (base e) of a {@code double}
* value. Special cases:
*
- If the argument is NaN or less than zero, then the result
* is NaN.
*
- If the argument is positive infinity, then the result is
* positive infinity.
*
- If the argument is positive zero or negative zero, then the
* result is negative infinity.
*
* The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param a a value
* @return the value ln {@code a}, the natural logarithm of
* {@code a}.
*/
@CriticalNative
public static native double log(double a);
/**
* Returns the base 10 logarithm of a {@code double} value.
* Special cases:
*
*
- If the argument is NaN or less than zero, then the result
* is NaN.
*
- If the argument is positive infinity, then the result is
* positive infinity.
*
- If the argument is positive zero or negative zero, then the
* result is negative infinity.
*
- If the argument is equal to 10n for
* integer n, then the result is n.
*
*
* The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param a a value
* @return the base 10 logarithm of {@code a}.
* @since 1.5
*/
@CriticalNative
public static native double log10(double a);
/**
* Returns the correctly rounded positive square root of a
* {@code double} value.
* Special cases:
*
- If the argument is NaN or less than zero, then the result
* is NaN.
*
- If the argument is positive infinity, then the result is positive
* infinity.
*
- If the argument is positive zero or negative zero, then the
* result is the same as the argument.
* Otherwise, the result is the {@code double} value closest to
* the true mathematical square root of the argument value.
*
* @param a a value.
* @return the positive square root of {@code a}.
* If the argument is NaN or less than zero, the result is NaN.
*/
@CriticalNative
public static native double sqrt(double a);
/**
* Returns the cube root of a {@code double} value. For
* positive finite {@code x}, {@code cbrt(-x) ==
* -cbrt(x)}; that is, the cube root of a negative value is
* the negative of the cube root of that value's magnitude.
*
* Special cases:
*
*
*
* - If the argument is NaN, then the result is NaN.
*
*
- If the argument is infinite, then the result is an infinity
* with the same sign as the argument.
*
*
- If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
*
*
* The computed result must be within 1 ulp of the exact result.
*
* @param a a value.
* @return the cube root of {@code a}.
* @since 1.5
*/
@CriticalNative
public static native double cbrt(double a);
/**
* Computes the remainder operation on two arguments as prescribed
* by the IEEE 754 standard.
* The remainder value is mathematically equal to
* f1 - f2 × n,
* where n is the mathematical integer closest to the exact
* mathematical value of the quotient {@code f1/f2}, and if two
* mathematical integers are equally close to {@code f1/f2},
* then n is the integer that is even. If the remainder is
* zero, its sign is the same as the sign of the first argument.
* Special cases:
*
- If either argument is NaN, or the first argument is infinite,
* or the second argument is positive zero or negative zero, then the
* result is NaN.
*
- If the first argument is finite and the second argument is
* infinite, then the result is the same as the first argument.
*
* @param f1 the dividend.
* @param f2 the divisor.
* @return the remainder when {@code f1} is divided by
* {@code f2}.
*/
@CriticalNative
public static native double IEEEremainder(double f1, double f2);
/**
* Returns the smallest (closest to negative infinity)
* {@code double} value that is greater than or equal to the
* argument and is equal to a mathematical integer. Special cases:
* - If the argument value is already equal to a
* mathematical integer, then the result is the same as the
* argument.
- If the argument is NaN or an infinity or
* positive zero or negative zero, then the result is the same as
* the argument.
- If the argument value is less than zero but
* greater than -1.0, then the result is negative zero.
Note
* that the value of {@code Math.ceil(x)} is exactly the
* value of {@code -Math.floor(-x)}.
*
*
* @param a a value.
* @return the smallest (closest to negative infinity)
* floating-point value that is greater than or equal to
* the argument and is equal to a mathematical integer.
*/
@CriticalNative
public static native double ceil(double a);
/**
* Returns the largest (closest to positive infinity)
* {@code double} value that is less than or equal to the
* argument and is equal to a mathematical integer. Special cases:
* - If the argument value is already equal to a
* mathematical integer, then the result is the same as the
* argument.
- If the argument is NaN or an infinity or
* positive zero or negative zero, then the result is the same as
* the argument.
*
* @param a a value.
* @return the largest (closest to positive infinity)
* floating-point value that less than or equal to the argument
* and is equal to a mathematical integer.
*/
@CriticalNative
public static native double floor(double a);
/**
* Returns the {@code double} value that is closest in value
* to the argument and is equal to a mathematical integer. If two
* {@code double} values that are mathematical integers are
* equally close, the result is the integer value that is
* even. Special cases:
* - If the argument value is already equal to a mathematical
* integer, then the result is the same as the argument.
*
- If the argument is NaN or an infinity or positive zero or negative
* zero, then the result is the same as the argument.
*
* @param a a {@code double} value.
* @return the closest floating-point value to {@code a} that is
* equal to a mathematical integer.
*/
@CriticalNative
public static native double rint(double a);
/**
* Returns the angle theta from the conversion of rectangular
* coordinates ({@code x}, {@code y}) to polar
* coordinates (r, theta).
* This method computes the phase theta by computing an arc tangent
* of {@code y/x} in the range of -pi to pi. Special
* cases:
* - If either argument is NaN, then the result is NaN.
*
- If the first argument is positive zero and the second argument
* is positive, or the first argument is positive and finite and the
* second argument is positive infinity, then the result is positive
* zero.
*
- If the first argument is negative zero and the second argument
* is positive, or the first argument is negative and finite and the
* second argument is positive infinity, then the result is negative zero.
*
- If the first argument is positive zero and the second argument
* is negative, or the first argument is positive and finite and the
* second argument is negative infinity, then the result is the
* {@code double} value closest to pi.
*
- If the first argument is negative zero and the second argument
* is negative, or the first argument is negative and finite and the
* second argument is negative infinity, then the result is the
* {@code double} value closest to -pi.
*
- If the first argument is positive and the second argument is
* positive zero or negative zero, or the first argument is positive
* infinity and the second argument is finite, then the result is the
* {@code double} value closest to pi/2.
*
- If the first argument is negative and the second argument is
* positive zero or negative zero, or the first argument is negative
* infinity and the second argument is finite, then the result is the
* {@code double} value closest to -pi/2.
*
- If both arguments are positive infinity, then the result is the
* {@code double} value closest to pi/4.
*
- If the first argument is positive infinity and the second argument
* is negative infinity, then the result is the {@code double}
* value closest to 3*pi/4.
*
- If the first argument is negative infinity and the second argument
* is positive infinity, then the result is the {@code double} value
* closest to -pi/4.
*
- If both arguments are negative infinity, then the result is the
* {@code double} value closest to -3*pi/4.
*
* The computed result must be within 2 ulps of the exact result.
* Results must be semi-monotonic.
*
* @param y the ordinate coordinate
* @param x the abscissa coordinate
* @return the theta component of the point
* (r, theta)
* in polar coordinates that corresponds to the point
* (x, y) in Cartesian coordinates.
*/
@CriticalNative
public static native double atan2(double y, double x);
/**
* Returns the value of the first argument raised to the power of the
* second argument. Special cases:
*
*
- If the second argument is positive or negative zero, then the
* result is 1.0.
*
- If the second argument is 1.0, then the result is the same as the
* first argument.
*
- If the second argument is NaN, then the result is NaN.
*
- If the first argument is NaN and the second argument is nonzero,
* then the result is NaN.
*
*
- If
*
* - the absolute value of the first argument is greater than 1
* and the second argument is positive infinity, or
*
- the absolute value of the first argument is less than 1 and
* the second argument is negative infinity,
*
* then the result is positive infinity.
*
* - If
*
* - the absolute value of the first argument is greater than 1 and
* the second argument is negative infinity, or
*
- the absolute value of the
* first argument is less than 1 and the second argument is positive
* infinity,
*
* then the result is positive zero.
*
* - If the absolute value of the first argument equals 1 and the
* second argument is infinite, then the result is NaN.
*
*
- If
*
* - the first argument is positive zero and the second argument
* is greater than zero, or
*
- the first argument is positive infinity and the second
* argument is less than zero,
*
* then the result is positive zero.
*
* - If
*
* - the first argument is positive zero and the second argument
* is less than zero, or
*
- the first argument is positive infinity and the second
* argument is greater than zero,
*
* then the result is positive infinity.
*
* - If
*
* - the first argument is negative zero and the second argument
* is greater than zero but not a finite odd integer, or
*
- the first argument is negative infinity and the second
* argument is less than zero but not a finite odd integer,
*
* then the result is positive zero.
*
* - If
*
* - the first argument is negative zero and the second argument
* is a positive finite odd integer, or
*
- the first argument is negative infinity and the second
* argument is a negative finite odd integer,
*
* then the result is negative zero.
*
* - If
*
* - the first argument is negative zero and the second argument
* is less than zero but not a finite odd integer, or
*
- the first argument is negative infinity and the second
* argument is greater than zero but not a finite odd integer,
*
* then the result is positive infinity.
*
* - If
*
* - the first argument is negative zero and the second argument
* is a negative finite odd integer, or
*
- the first argument is negative infinity and the second
* argument is a positive finite odd integer,
*
* then the result is negative infinity.
*
* - If the first argument is finite and less than zero
*
* - if the second argument is a finite even integer, the
* result is equal to the result of raising the absolute value of
* the first argument to the power of the second argument
*
*
- if the second argument is a finite odd integer, the result
* is equal to the negative of the result of raising the absolute
* value of the first argument to the power of the second
* argument
*
*
- if the second argument is finite and not an integer, then
* the result is NaN.
*
*
* - If both arguments are integers, then the result is exactly equal
* to the mathematical result of raising the first argument to the power
* of the second argument if that result can in fact be represented
* exactly as a {@code double} value.
*
* (In the foregoing descriptions, a floating-point value is
* considered to be an integer if and only if it is finite and a
* fixed point of the method {@link #ceil ceil} or,
* equivalently, a fixed point of the method {@link #floor
* floor}. A value is a fixed point of a one-argument
* method if and only if the result of applying the method to the
* value is equal to the value.)
*
*
The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param a the base.
* @param b the exponent.
* @return the value {@code a}{@code b}.
*/
@CriticalNative
public static native double pow(double a, double b);
/**
* Returns the closest {@code int} to the argument, with ties
* rounding to positive infinity.
*
*
* Special cases:
*
- If the argument is NaN, the result is 0.
*
- If the argument is negative infinity or any value less than or
* equal to the value of {@code Integer.MIN_VALUE}, the result is
* equal to the value of {@code Integer.MIN_VALUE}.
*
- If the argument is positive infinity or any value greater than or
* equal to the value of {@code Integer.MAX_VALUE}, the result is
* equal to the value of {@code Integer.MAX_VALUE}.
*
* @param a a floating-point value to be rounded to an integer.
* @return the value of the argument rounded to the nearest
* {@code int} value.
* @see java.lang.Integer#MAX_VALUE
* @see java.lang.Integer#MIN_VALUE
*/
public static int round(float a) {
int intBits = Float.floatToRawIntBits(a);
int biasedExp = (intBits & FloatConsts.EXP_BIT_MASK)
>> (FloatConsts.SIGNIFICAND_WIDTH - 1);
int shift = (FloatConsts.SIGNIFICAND_WIDTH - 2
+ FloatConsts.EXP_BIAS) - biasedExp;
if ((shift & -32) == 0) { // shift >= 0 && shift < 32
// a is a finite number such that pow(2,-32) <= ulp(a) < 1
int r = ((intBits & FloatConsts.SIGNIF_BIT_MASK)
| (FloatConsts.SIGNIF_BIT_MASK + 1));
if (intBits < 0) {
r = -r;
}
// In the comments below each Java expression evaluates to the value
// the corresponding mathematical expression:
// (r) evaluates to a / ulp(a)
// (r >> shift) evaluates to floor(a * 2)
// ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
// (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
return ((r >> shift) + 1) >> 1;
} else {
// a is either
// - a finite number with abs(a) < exp(2,FloatConsts.SIGNIFICAND_WIDTH-32) < 1/2
// - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
// - an infinity or NaN
return (int) a;
}
}
/**
* Returns the closest {@code long} to the argument, with ties
* rounding to positive infinity.
*
* Special cases:
*
- If the argument is NaN, the result is 0.
*
- If the argument is negative infinity or any value less than or
* equal to the value of {@code Long.MIN_VALUE}, the result is
* equal to the value of {@code Long.MIN_VALUE}.
*
- If the argument is positive infinity or any value greater than or
* equal to the value of {@code Long.MAX_VALUE}, the result is
* equal to the value of {@code Long.MAX_VALUE}.
*
* @param a a floating-point value to be rounded to a
* {@code long}.
* @return the value of the argument rounded to the nearest
* {@code long} value.
* @see java.lang.Long#MAX_VALUE
* @see java.lang.Long#MIN_VALUE
*/
public static long round(double a) {
long longBits = Double.doubleToRawLongBits(a);
long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK)
>> (DoubleConsts.SIGNIFICAND_WIDTH - 1);
long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2
+ DoubleConsts.EXP_BIAS) - biasedExp;
if ((shift & -64) == 0) { // shift >= 0 && shift < 64
// a is a finite number such that pow(2,-64) <= ulp(a) < 1
long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK)
| (DoubleConsts.SIGNIF_BIT_MASK + 1));
if (longBits < 0) {
r = -r;
}
// In the comments below each Java expression evaluates to the value
// the corresponding mathematical expression:
// (r) evaluates to a / ulp(a)
// (r >> shift) evaluates to floor(a * 2)
// ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
// (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
return ((r >> shift) + 1) >> 1;
} else {
// a is either
// - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2
// - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
// - an infinity or NaN
return (long) a;
}
}
private static final class RandomNumberGeneratorHolder {
static final Random randomNumberGenerator = new Random();
}
/**
* Returns a {@code double} value with a positive sign, greater
* than or equal to {@code 0.0} and less than {@code 1.0}.
* Returned values are chosen pseudorandomly with (approximately)
* uniform distribution from that range.
*
* When this method is first called, it creates a single new
* pseudorandom-number generator, exactly as if by the expression
*
*
{@code new java.util.Random()}
*
* This new pseudorandom-number generator is used thereafter for
* all calls to this method and is used nowhere else.
*
* This method is properly synchronized to allow correct use by
* more than one thread. However, if many threads need to generate
* pseudorandom numbers at a great rate, it may reduce contention
* for each thread to have its own pseudorandom-number generator.
*
* @return a pseudorandom {@code double} greater than or equal
* to {@code 0.0} and less than {@code 1.0}.
* @see Random#nextDouble()
*/
public static double random() {
return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
}
// Android-added: setRandomSeedInternal(long), called after zygote forks.
// This allows different processes to have different random seeds.
/**
* Set the seed for the pseudo random generator used by {@link #random()}
* and {@link #randomIntInternal()}.
*
* @hide for internal use only.
*/
public static void setRandomSeedInternal(long seed) {
RandomNumberGeneratorHolder.randomNumberGenerator.setSeed(seed);
}
// Android-added: randomIntInternal() method: like random() but for int.
/**
* @hide for internal use only.
*/
public static int randomIntInternal() {
return RandomNumberGeneratorHolder.randomNumberGenerator.nextInt();
}
// Android-added: randomLongInternal() method: like random() but for long.
/**
* @hide for internal use only.
*/
public static long randomLongInternal() {
return RandomNumberGeneratorHolder.randomNumberGenerator.nextLong();
}
/**
* Returns the sum of its arguments,
* throwing an exception if the result overflows an {@code int}.
*
* @param x the first value
* @param y the second value
* @return the result
* @throws ArithmeticException if the result overflows an int
* @since 1.8
*/
public static int addExact(int x, int y) {
int r = x + y;
// HD 2-12 Overflow iff both arguments have the opposite sign of the result
if (((x ^ r) & (y ^ r)) < 0) {
throw new ArithmeticException("integer overflow");
}
return r;
}
/**
* Returns the sum of its arguments,
* throwing an exception if the result overflows a {@code long}.
*
* @param x the first value
* @param y the second value
* @return the result
* @throws ArithmeticException if the result overflows a long
* @since 1.8
*/
public static long addExact(long x, long y) {
long r = x + y;
// HD 2-12 Overflow iff both arguments have the opposite sign of the result
if (((x ^ r) & (y ^ r)) < 0) {
throw new ArithmeticException("long overflow");
}
return r;
}
/**
* Returns the difference of the arguments,
* throwing an exception if the result overflows an {@code int}.
*
* @param x the first value
* @param y the second value to subtract from the first
* @return the result
* @throws ArithmeticException if the result overflows an int
* @since 1.8
*/
public static int subtractExact(int x, int y) {
int r = x - y;
// HD 2-12 Overflow iff the arguments have different signs and
// the sign of the result is different than the sign of x
if (((x ^ y) & (x ^ r)) < 0) {
throw new ArithmeticException("integer overflow");
}
return r;
}
/**
* Returns the difference of the arguments,
* throwing an exception if the result overflows a {@code long}.
*
* @param x the first value
* @param y the second value to subtract from the first
* @return the result
* @throws ArithmeticException if the result overflows a long
* @since 1.8
*/
public static long subtractExact(long x, long y) {
long r = x - y;
// HD 2-12 Overflow iff the arguments have different signs and
// the sign of the result is different than the sign of x
if (((x ^ y) & (x ^ r)) < 0) {
throw new ArithmeticException("long overflow");
}
return r;
}
/**
* Returns the product of the arguments,
* throwing an exception if the result overflows an {@code int}.
*
* @param x the first value
* @param y the second value
* @return the result
* @throws ArithmeticException if the result overflows an int
* @since 1.8
*/
public static int multiplyExact(int x, int y) {
long r = (long)x * (long)y;
if ((int)r != r) {
throw new ArithmeticException("integer overflow");
}
return (int)r;
}
/**
* Returns the product of the arguments,
* throwing an exception if the result overflows a {@code long}.
*
* @param x the first value
* @param y the second value
* @return the result
* @throws ArithmeticException if the result overflows a long
* @since 1.8
*/
public static long multiplyExact(long x, long y) {
long r = x * y;
long ax = Math.abs(x);
long ay = Math.abs(y);
if (((ax | ay) >>> 31 != 0)) {
// Some bits greater than 2^31 that might cause overflow
// Check the result using the divide operator
// and check for the special case of Long.MIN_VALUE * -1
if (((y != 0) && (r / y != x)) ||
(x == Long.MIN_VALUE && y == -1)) {
throw new ArithmeticException("long overflow");
}
}
return r;
}
/**
* Returns the argument incremented by one, throwing an exception if the
* result overflows an {@code int}.
*
* @param a the value to increment
* @return the result
* @throws ArithmeticException if the result overflows an int
* @since 1.8
*/
public static int incrementExact(int a) {
if (a == Integer.MAX_VALUE) {
throw new ArithmeticException("integer overflow");
}
return a + 1;
}
/**
* Returns the argument incremented by one, throwing an exception if the
* result overflows a {@code long}.
*
* @param a the value to increment
* @return the result
* @throws ArithmeticException if the result overflows a long
* @since 1.8
*/
public static long incrementExact(long a) {
if (a == Long.MAX_VALUE) {
throw new ArithmeticException("long overflow");
}
return a + 1L;
}
/**
* Returns the argument decremented by one, throwing an exception if the
* result overflows an {@code int}.
*
* @param a the value to decrement
* @return the result
* @throws ArithmeticException if the result overflows an int
* @since 1.8
*/
public static int decrementExact(int a) {
if (a == Integer.MIN_VALUE) {
throw new ArithmeticException("integer overflow");
}
return a - 1;
}
/**
* Returns the argument decremented by one, throwing an exception if the
* result overflows a {@code long}.
*
* @param a the value to decrement
* @return the result
* @throws ArithmeticException if the result overflows a long
* @since 1.8
*/
public static long decrementExact(long a) {
if (a == Long.MIN_VALUE) {
throw new ArithmeticException("long overflow");
}
return a - 1L;
}
/**
* Returns the negation of the argument, throwing an exception if the
* result overflows an {@code int}.
*
* @param a the value to negate
* @return the result
* @throws ArithmeticException if the result overflows an int
* @since 1.8
*/
public static int negateExact(int a) {
if (a == Integer.MIN_VALUE) {
throw new ArithmeticException("integer overflow");
}
return -a;
}
/**
* Returns the negation of the argument, throwing an exception if the
* result overflows a {@code long}.
*
* @param a the value to negate
* @return the result
* @throws ArithmeticException if the result overflows a long
* @since 1.8
*/
public static long negateExact(long a) {
if (a == Long.MIN_VALUE) {
throw new ArithmeticException("long overflow");
}
return -a;
}
/**
* Returns the value of the {@code long} argument;
* throwing an exception if the value overflows an {@code int}.
*
* @param value the long value
* @return the argument as an int
* @throws ArithmeticException if the {@code argument} overflows an int
* @since 1.8
*/
public static int toIntExact(long value) {
if ((int)value != value) {
throw new ArithmeticException("integer overflow");
}
return (int)value;
}
/**
* Returns the largest (closest to positive infinity)
* {@code int} value that is less than or equal to the algebraic quotient.
* There is one special case, if the dividend is the
* {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
* then integer overflow occurs and
* the result is equal to the {@code Integer.MIN_VALUE}.
*
* Normal integer division operates under the round to zero rounding mode
* (truncation). This operation instead acts under the round toward
* negative infinity (floor) rounding mode.
* The floor rounding mode gives different results than truncation
* when the exact result is negative.
*
* - If the signs of the arguments are the same, the results of
* {@code floorDiv} and the {@code /} operator are the same.
* For example, {@code floorDiv(4, 3) == 1} and {@code (4 / 3) == 1}.
* - If the signs of the arguments are different, the quotient is negative and
* {@code floorDiv} returns the integer less than or equal to the quotient
* and the {@code /} operator returns the integer closest to zero.
* For example, {@code floorDiv(-4, 3) == -2},
* whereas {@code (-4 / 3) == -1}.
*
*
*
*
* @param x the dividend
* @param y the divisor
* @return the largest (closest to positive infinity)
* {@code int} value that is less than or equal to the algebraic quotient.
* @throws ArithmeticException if the divisor {@code y} is zero
* @see #floorMod(int, int)
* @see #floor(double)
* @since 1.8
*/
public static int floorDiv(int x, int y) {
int r = x / y;
// if the signs are different and modulo not zero, round down
if ((x ^ y) < 0 && (r * y != x)) {
r--;
}
return r;
}
/**
* Returns the largest (closest to positive infinity)
* {@code long} value that is less than or equal to the algebraic quotient.
* There is one special case, if the dividend is the
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
* then integer overflow occurs and
* the result is equal to the {@code Long.MIN_VALUE}.
*
* Normal integer division operates under the round to zero rounding mode
* (truncation). This operation instead acts under the round toward
* negative infinity (floor) rounding mode.
* The floor rounding mode gives different results than truncation
* when the exact result is negative.
*
* For examples, see {@link #floorDiv(int, int)}.
*
* @param x the dividend
* @param y the divisor
* @return the largest (closest to positive infinity)
* {@code long} value that is less than or equal to the algebraic quotient.
* @throws ArithmeticException if the divisor {@code y} is zero
* @see #floorMod(long, long)
* @see #floor(double)
* @since 1.8
*/
public static long floorDiv(long x, long y) {
long r = x / y;
// if the signs are different and modulo not zero, round down
if ((x ^ y) < 0 && (r * y != x)) {
r--;
}
return r;
}
/**
* Returns the floor modulus of the {@code int} arguments.
*
* The floor modulus is {@code x - (floorDiv(x, y) * y)},
* has the same sign as the divisor {@code y}, and
* is in the range of {@code -abs(y) < r < +abs(y)}.
*
*
* The relationship between {@code floorDiv} and {@code floorMod} is such that:
*
* - {@code floorDiv(x, y) * y + floorMod(x, y) == x}
*
*
* The difference in values between {@code floorMod} and
* the {@code %} operator is due to the difference between
* {@code floorDiv} that returns the integer less than or equal to the quotient
* and the {@code /} operator that returns the integer closest to zero.
*
* Examples:
*
* - If the signs of the arguments are the same, the results
* of {@code floorMod} and the {@code %} operator are the same.
*
* - {@code floorMod(4, 3) == 1}; and {@code (4 % 3) == 1}
*
* - If the signs of the arguments are different, the results differ from the {@code %} operator.
*
* - {@code floorMod(+4, -3) == -2}; and {@code (+4 % -3) == +1}
* - {@code floorMod(-4, +3) == +2}; and {@code (-4 % +3) == -1}
* - {@code floorMod(-4, -3) == -1}; and {@code (-4 % -3) == -1 }
*
*
*
*
* If the signs of arguments are unknown and a positive modulus
* is needed it can be computed as {@code (floorMod(x, y) + abs(y)) % abs(y)}.
*
* @param x the dividend
* @param y the divisor
* @return the floor modulus {@code x - (floorDiv(x, y) * y)}
* @throws ArithmeticException if the divisor {@code y} is zero
* @see #floorDiv(int, int)
* @since 1.8
*/
public static int floorMod(int x, int y) {
int r = x - floorDiv(x, y) * y;
return r;
}
/**
* Returns the floor modulus of the {@code long} arguments.
*
* The floor modulus is {@code x - (floorDiv(x, y) * y)},
* has the same sign as the divisor {@code y}, and
* is in the range of {@code -abs(y) < r < +abs(y)}.
*
*
* The relationship between {@code floorDiv} and {@code floorMod} is such that:
*
* - {@code floorDiv(x, y) * y + floorMod(x, y) == x}
*
*
* For examples, see {@link #floorMod(int, int)}.
*
* @param x the dividend
* @param y the divisor
* @return the floor modulus {@code x - (floorDiv(x, y) * y)}
* @throws ArithmeticException if the divisor {@code y} is zero
* @see #floorDiv(long, long)
* @since 1.8
*/
public static long floorMod(long x, long y) {
return x - floorDiv(x, y) * y;
}
/**
* Returns the absolute value of an {@code int} value.
* If the argument is not negative, the argument is returned.
* If the argument is negative, the negation of the argument is returned.
*
*
Note that if the argument is equal to the value of
* {@link Integer#MIN_VALUE}, the most negative representable
* {@code int} value, the result is that same value, which is
* negative.
*
* @param a the argument whose absolute value is to be determined
* @return the absolute value of the argument.
*/
public static int abs(int a) {
return (a < 0) ? -a : a;
}
/**
* Returns the absolute value of a {@code long} value.
* If the argument is not negative, the argument is returned.
* If the argument is negative, the negation of the argument is returned.
*
*
Note that if the argument is equal to the value of
* {@link Long#MIN_VALUE}, the most negative representable
* {@code long} value, the result is that same value, which
* is negative.
*
* @param a the argument whose absolute value is to be determined
* @return the absolute value of the argument.
*/
public static long abs(long a) {
return (a < 0) ? -a : a;
}
/**
* Returns the absolute value of a {@code float} value.
* If the argument is not negative, the argument is returned.
* If the argument is negative, the negation of the argument is returned.
* Special cases:
*
- If the argument is positive zero or negative zero, the
* result is positive zero.
*
- If the argument is infinite, the result is positive infinity.
*
- If the argument is NaN, the result is NaN.
* In other words, the result is the same as the value of the expression:
* {@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
*
* @param a the argument whose absolute value is to be determined
* @return the absolute value of the argument.
*/
public static float abs(float a) {
// Android-changed: Implementation modified to exactly match ART intrinsics behavior.
// Note, as a "quality of implementation", rather than pure "spec compliance",
// we require that Math.abs() clears the sign bit (but changes nothing else)
// for all numbers, including NaN (signaling NaN may become quiet though).
// http://b/30758343
return Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a));
}
/**
* Returns the absolute value of a {@code double} value.
* If the argument is not negative, the argument is returned.
* If the argument is negative, the negation of the argument is returned.
* Special cases:
*
- If the argument is positive zero or negative zero, the result
* is positive zero.
*
- If the argument is infinite, the result is positive infinity.
*
- If the argument is NaN, the result is NaN.
* In other words, the result is the same as the value of the expression:
* {@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
*
* @param a the argument whose absolute value is to be determined
* @return the absolute value of the argument.
*/
public static double abs(double a) {
// Android-changed: Implementation modified to exactly match ART intrinsics behavior.
// Note, as a "quality of implementation", rather than pure "spec compliance",
// we require that Math.abs() clears the sign bit (but changes nothing else)
// for all numbers, including NaN (signaling NaN may become quiet though).
// http://b/30758343
return Double.longBitsToDouble(0x7fffffffffffffffL & Double.doubleToRawLongBits(a));
}
/**
* Returns the greater of two {@code int} values. That is, the
* result is the argument closer to the value of
* {@link Integer#MAX_VALUE}. If the arguments have the same value,
* the result is that same value.
*
* @param a an argument.
* @param b another argument.
* @return the larger of {@code a} and {@code b}.
*/
public static int max(int a, int b) {
return (a >= b) ? a : b;
}
/**
* Returns the greater of two {@code long} values. That is, the
* result is the argument closer to the value of
* {@link Long#MAX_VALUE}. If the arguments have the same value,
* the result is that same value.
*
* @param a an argument.
* @param b another argument.
* @return the larger of {@code a} and {@code b}.
*/
public static long max(long a, long b) {
return (a >= b) ? a : b;
}
// Use raw bit-wise conversions on guaranteed non-NaN arguments.
private static long negativeZeroFloatBits = Float.floatToRawIntBits(-0.0f);
private static long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d);
/**
* Returns the greater of two {@code float} values. That is,
* the result is the argument closer to positive infinity. If the
* arguments have the same value, the result is that same
* value. If either value is NaN, then the result is NaN. Unlike
* the numerical comparison operators, this method considers
* negative zero to be strictly smaller than positive zero. If one
* argument is positive zero and the other negative zero, the
* result is positive zero.
*
* @param a an argument.
* @param b another argument.
* @return the larger of {@code a} and {@code b}.
*/
public static float max(float a, float b) {
if (a != a)
return a; // a is NaN
if ((a == 0.0f) &&
(b == 0.0f) &&
(Float.floatToRawIntBits(a) == negativeZeroFloatBits)) {
// Raw conversion ok since NaN can't map to -0.0.
return b;
}
return (a >= b) ? a : b;
}
/**
* Returns the greater of two {@code double} values. That
* is, the result is the argument closer to positive infinity. If
* the arguments have the same value, the result is that same
* value. If either value is NaN, then the result is NaN. Unlike
* the numerical comparison operators, this method considers
* negative zero to be strictly smaller than positive zero. If one
* argument is positive zero and the other negative zero, the
* result is positive zero.
*
* @param a an argument.
* @param b another argument.
* @return the larger of {@code a} and {@code b}.
*/
public static double max(double a, double b) {
if (a != a)
return a; // a is NaN
if ((a == 0.0d) &&
(b == 0.0d) &&
(Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) {
// Raw conversion ok since NaN can't map to -0.0.
return b;
}
return (a >= b) ? a : b;
}
/**
* Returns the smaller of two {@code int} values. That is,
* the result the argument closer to the value of
* {@link Integer#MIN_VALUE}. If the arguments have the same
* value, the result is that same value.
*
* @param a an argument.
* @param b another argument.
* @return the smaller of {@code a} and {@code b}.
*/
public static int min(int a, int b) {
return (a <= b) ? a : b;
}
/**
* Returns the smaller of two {@code long} values. That is,
* the result is the argument closer to the value of
* {@link Long#MIN_VALUE}. If the arguments have the same
* value, the result is that same value.
*
* @param a an argument.
* @param b another argument.
* @return the smaller of {@code a} and {@code b}.
*/
public static long min(long a, long b) {
return (a <= b) ? a : b;
}
/**
* Returns the smaller of two {@code float} values. That is,
* the result is the value closer to negative infinity. If the
* arguments have the same value, the result is that same
* value. If either value is NaN, then the result is NaN. Unlike
* the numerical comparison operators, this method considers
* negative zero to be strictly smaller than positive zero. If
* one argument is positive zero and the other is negative zero,
* the result is negative zero.
*
* @param a an argument.
* @param b another argument.
* @return the smaller of {@code a} and {@code b}.
*/
public static float min(float a, float b) {
if (a != a)
return a; // a is NaN
if ((a == 0.0f) &&
(b == 0.0f) &&
(Float.floatToRawIntBits(b) == negativeZeroFloatBits)) {
// Raw conversion ok since NaN can't map to -0.0.
return b;
}
return (a <= b) ? a : b;
}
/**
* Returns the smaller of two {@code double} values. That
* is, the result is the value closer to negative infinity. If the
* arguments have the same value, the result is that same
* value. If either value is NaN, then the result is NaN. Unlike
* the numerical comparison operators, this method considers
* negative zero to be strictly smaller than positive zero. If one
* argument is positive zero and the other is negative zero, the
* result is negative zero.
*
* @param a an argument.
* @param b another argument.
* @return the smaller of {@code a} and {@code b}.
*/
public static double min(double a, double b) {
if (a != a)
return a; // a is NaN
if ((a == 0.0d) &&
(b == 0.0d) &&
(Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) {
// Raw conversion ok since NaN can't map to -0.0.
return b;
}
return (a <= b) ? a : b;
}
/**
* Returns the size of an ulp of the argument. An ulp, unit in
* the last place, of a {@code double} value is the positive
* distance between this floating-point value and the {@code
* double} value next larger in magnitude. Note that for non-NaN
* x, ulp(-x) == ulp(x).
*
*
Special Cases:
*
* - If the argument is NaN, then the result is NaN.
*
- If the argument is positive or negative infinity, then the
* result is positive infinity.
*
- If the argument is positive or negative zero, then the result is
* {@code Double.MIN_VALUE}.
*
- If the argument is ±{@code Double.MAX_VALUE}, then
* the result is equal to 2971.
*
*
* @param d the floating-point value whose ulp is to be returned
* @return the size of an ulp of the argument
* @author Joseph D. Darcy
* @since 1.5
*/
public static double ulp(double d) {
int exp = getExponent(d);
switch(exp) {
case DoubleConsts.MAX_EXPONENT+1: // NaN or infinity
return Math.abs(d);
case DoubleConsts.MIN_EXPONENT-1: // zero or subnormal
return Double.MIN_VALUE;
default:
assert exp <= DoubleConsts.MAX_EXPONENT && exp >= DoubleConsts.MIN_EXPONENT;
// ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
exp = exp - (DoubleConsts.SIGNIFICAND_WIDTH-1);
if (exp >= DoubleConsts.MIN_EXPONENT) {
return powerOfTwoD(exp);
}
else {
// return a subnormal result; left shift integer
// representation of Double.MIN_VALUE appropriate
// number of positions
return Double.longBitsToDouble(1L <<
(exp - (DoubleConsts.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1)) ));
}
}
}
/**
* Returns the size of an ulp of the argument. An ulp, unit in
* the last place, of a {@code float} value is the positive
* distance between this floating-point value and the {@code
* float} value next larger in magnitude. Note that for non-NaN
* x, ulp(-x) == ulp(x).
*
* Special Cases:
*
* - If the argument is NaN, then the result is NaN.
*
- If the argument is positive or negative infinity, then the
* result is positive infinity.
*
- If the argument is positive or negative zero, then the result is
* {@code Float.MIN_VALUE}.
*
- If the argument is ±{@code Float.MAX_VALUE}, then
* the result is equal to 2104.
*
*
* @param f the floating-point value whose ulp is to be returned
* @return the size of an ulp of the argument
* @author Joseph D. Darcy
* @since 1.5
*/
public static float ulp(float f) {
int exp = getExponent(f);
switch(exp) {
case FloatConsts.MAX_EXPONENT+1: // NaN or infinity
return Math.abs(f);
case FloatConsts.MIN_EXPONENT-1: // zero or subnormal
return FloatConsts.MIN_VALUE;
default:
assert exp <= FloatConsts.MAX_EXPONENT && exp >= FloatConsts.MIN_EXPONENT;
// ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
exp = exp - (FloatConsts.SIGNIFICAND_WIDTH-1);
if (exp >= FloatConsts.MIN_EXPONENT) {
return powerOfTwoF(exp);
}
else {
// return a subnormal result; left shift integer
// representation of FloatConsts.MIN_VALUE appropriate
// number of positions
return Float.intBitsToFloat(1 <<
(exp - (FloatConsts.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1)) ));
}
}
}
/**
* Returns the signum function of the argument; zero if the argument
* is zero, 1.0 if the argument is greater than zero, -1.0 if the
* argument is less than zero.
*
* Special Cases:
*
* - If the argument is NaN, then the result is NaN.
*
- If the argument is positive zero or negative zero, then the
* result is the same as the argument.
*
*
* @param d the floating-point value whose signum is to be returned
* @return the signum function of the argument
* @author Joseph D. Darcy
* @since 1.5
*/
public static double signum(double d) {
return (d == 0.0 || Double.isNaN(d))?d:copySign(1.0, d);
}
/**
* Returns the signum function of the argument; zero if the argument
* is zero, 1.0f if the argument is greater than zero, -1.0f if the
* argument is less than zero.
*
* Special Cases:
*
* - If the argument is NaN, then the result is NaN.
*
- If the argument is positive zero or negative zero, then the
* result is the same as the argument.
*
*
* @param f the floating-point value whose signum is to be returned
* @return the signum function of the argument
* @author Joseph D. Darcy
* @since 1.5
*/
public static float signum(float f) {
return (f == 0.0f || Float.isNaN(f))?f:copySign(1.0f, f);
}
/**
* Returns the hyperbolic sine of a {@code double} value.
* The hyperbolic sine of x is defined to be
* (ex - e-x)/2
* where e is {@linkplain Math#E Euler's number}.
*
* Special cases:
*
*
* - If the argument is NaN, then the result is NaN.
*
*
- If the argument is infinite, then the result is an infinity
* with the same sign as the argument.
*
*
- If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
*
*
* The computed result must be within 2.5 ulps of the exact result.
*
* @param x The number whose hyperbolic sine is to be returned.
* @return The hyperbolic sine of {@code x}.
* @since 1.5
*/
@CriticalNative
public static native double sinh(double x);
/**
* Returns the hyperbolic cosine of a {@code double} value.
* The hyperbolic cosine of x is defined to be
* (ex + e-x)/2
* where e is {@linkplain Math#E Euler's number}.
*
*
Special cases:
*
*
* - If the argument is NaN, then the result is NaN.
*
*
- If the argument is infinite, then the result is positive
* infinity.
*
*
- If the argument is zero, then the result is {@code 1.0}.
*
*
*
* The computed result must be within 2.5 ulps of the exact result.
*
* @param x The number whose hyperbolic cosine is to be returned.
* @return The hyperbolic cosine of {@code x}.
* @since 1.5
*/
@CriticalNative
public static native double cosh(double x);
/**
* Returns the hyperbolic tangent of a {@code double} value.
* The hyperbolic tangent of x is defined to be
* (ex - e-x)/(ex + e-x),
* in other words, {@linkplain Math#sinh
* sinh(x)}/{@linkplain Math#cosh cosh(x)}. Note
* that the absolute value of the exact tanh is always less than
* 1.
*
*
Special cases:
*
*
* - If the argument is NaN, then the result is NaN.
*
*
- If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
*
- If the argument is positive infinity, then the result is
* {@code +1.0}.
*
*
- If the argument is negative infinity, then the result is
* {@code -1.0}.
*
*
*
* The computed result must be within 2.5 ulps of the exact result.
* The result of {@code tanh} for any finite input must have
* an absolute value less than or equal to 1. Note that once the
* exact result of tanh is within 1/2 of an ulp of the limit value
* of ±1, correctly signed ±{@code 1.0} should
* be returned.
*
* @param x The number whose hyperbolic tangent is to be returned.
* @return The hyperbolic tangent of {@code x}.
* @since 1.5
*/
@CriticalNative
public static native double tanh(double x);
/**
* Returns sqrt(x2 +y2)
* without intermediate overflow or underflow.
*
*
Special cases:
*
*
* - If either argument is infinite, then the result
* is positive infinity.
*
*
- If either argument is NaN and neither argument is infinite,
* then the result is NaN.
*
*
*
* The computed result must be within 1 ulp of the exact
* result. If one parameter is held constant, the results must be
* semi-monotonic in the other parameter.
*
* @param x a value
* @param y a value
* @return sqrt(x2 +y2)
* without intermediate overflow or underflow
* @since 1.5
*/
@CriticalNative
public static native double hypot(double x, double y);
/**
* Returns ex -1. Note that for values of
* x near 0, the exact sum of
* {@code expm1(x)} + 1 is much closer to the true
* result of ex than {@code exp(x)}.
*
*
Special cases:
*
* - If the argument is NaN, the result is NaN.
*
*
- If the argument is positive infinity, then the result is
* positive infinity.
*
*
- If the argument is negative infinity, then the result is
* -1.0.
*
*
- If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
*
*
* The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic. The result of
* {@code expm1} for any finite input must be greater than or
* equal to {@code -1.0}. Note that once the exact result of
* e{@code x} - 1 is within 1/2
* ulp of the limit value -1, {@code -1.0} should be
* returned.
*
* @param x the exponent to raise e to in the computation of
* e{@code x} -1.
* @return the value e{@code x} - 1.
* @since 1.5
*/
@CriticalNative
public static native double expm1(double x);
/**
* Returns the natural logarithm of the sum of the argument and 1.
* Note that for small values {@code x}, the result of
* {@code log1p(x)} is much closer to the true result of ln(1
* + {@code x}) than the floating-point evaluation of
* {@code log(1.0+x)}.
*
*
Special cases:
*
*
*
* - If the argument is NaN or less than -1, then the result is
* NaN.
*
*
- If the argument is positive infinity, then the result is
* positive infinity.
*
*
- If the argument is negative one, then the result is
* negative infinity.
*
*
- If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
*
*
* The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param x a value
* @return the value ln({@code x} + 1), the natural
* log of {@code x} + 1
* @since 1.5
*/
@CriticalNative
public static native double log1p(double x);
/**
* Returns the first floating-point argument with the sign of the
* second floating-point argument. Note that unlike the {@link
* StrictMath#copySign(double, double) StrictMath.copySign}
* method, this method does not require NaN {@code sign}
* arguments to be treated as positive values; implementations are
* permitted to treat some NaN arguments as positive and other NaN
* arguments as negative to allow greater performance.
*
* @param magnitude the parameter providing the magnitude of the result
* @param sign the parameter providing the sign of the result
* @return a value with the magnitude of {@code magnitude}
* and the sign of {@code sign}.
* @since 1.6
*/
public static double copySign(double magnitude, double sign) {
return Double.longBitsToDouble((Double.doubleToRawLongBits(sign) &
(DoubleConsts.SIGN_BIT_MASK)) |
(Double.doubleToRawLongBits(magnitude) &
(DoubleConsts.EXP_BIT_MASK |
DoubleConsts.SIGNIF_BIT_MASK)));
}
/**
* Returns the first floating-point argument with the sign of the
* second floating-point argument. Note that unlike the {@link
* StrictMath#copySign(float, float) StrictMath.copySign}
* method, this method does not require NaN {@code sign}
* arguments to be treated as positive values; implementations are
* permitted to treat some NaN arguments as positive and other NaN
* arguments as negative to allow greater performance.
*
* @param magnitude the parameter providing the magnitude of the result
* @param sign the parameter providing the sign of the result
* @return a value with the magnitude of {@code magnitude}
* and the sign of {@code sign}.
* @since 1.6
*/
public static float copySign(float magnitude, float sign) {
return Float.intBitsToFloat((Float.floatToRawIntBits(sign) &
(FloatConsts.SIGN_BIT_MASK)) |
(Float.floatToRawIntBits(magnitude) &
(FloatConsts.EXP_BIT_MASK |
FloatConsts.SIGNIF_BIT_MASK)));
}
/**
* Returns the unbiased exponent used in the representation of a
* {@code float}. Special cases:
*
*
* - If the argument is NaN or infinite, then the result is
* {@link Float#MAX_EXPONENT} + 1.
*
- If the argument is zero or subnormal, then the result is
* {@link Float#MIN_EXPONENT} -1.
*
* @param f a {@code float} value
* @return the unbiased exponent of the argument
* @since 1.6
*/
public static int getExponent(float f) {
/*
* Bitwise convert f to integer, mask out exponent bits, shift
* to the right and then subtract out float's bias adjust to
* get true exponent value
*/
return ((Float.floatToRawIntBits(f) & FloatConsts.EXP_BIT_MASK) >>
(FloatConsts.SIGNIFICAND_WIDTH - 1)) - FloatConsts.EXP_BIAS;
}
/**
* Returns the unbiased exponent used in the representation of a
* {@code double}. Special cases:
*
*
* - If the argument is NaN or infinite, then the result is
* {@link Double#MAX_EXPONENT} + 1.
*
- If the argument is zero or subnormal, then the result is
* {@link Double#MIN_EXPONENT} -1.
*
* @param d a {@code double} value
* @return the unbiased exponent of the argument
* @since 1.6
*/
public static int getExponent(double d) {
/*
* Bitwise convert d to long, mask out exponent bits, shift
* to the right and then subtract out double's bias adjust to
* get true exponent value.
*/
return (int)(((Double.doubleToRawLongBits(d) & DoubleConsts.EXP_BIT_MASK) >>
(DoubleConsts.SIGNIFICAND_WIDTH - 1)) - DoubleConsts.EXP_BIAS);
}
/**
* Returns the floating-point number adjacent to the first
* argument in the direction of the second argument. If both
* arguments compare as equal the second argument is returned.
*
*
* Special cases:
*
* - If either argument is a NaN, then NaN is returned.
*
*
- If both arguments are signed zeros, {@code direction}
* is returned unchanged (as implied by the requirement of
* returning the second argument if the arguments compare as
* equal).
*
*
- If {@code start} is
* ±{@link Double#MIN_VALUE} and {@code direction}
* has a value such that the result should have a smaller
* magnitude, then a zero with the same sign as {@code start}
* is returned.
*
*
- If {@code start} is infinite and
* {@code direction} has a value such that the result should
* have a smaller magnitude, {@link Double#MAX_VALUE} with the
* same sign as {@code start} is returned.
*
*
- If {@code start} is equal to ±
* {@link Double#MAX_VALUE} and {@code direction} has a
* value such that the result should have a larger magnitude, an
* infinity with same sign as {@code start} is returned.
*
*
* @param start starting floating-point value
* @param direction value indicating which of
* {@code start}'s neighbors or {@code start} should
* be returned
* @return The floating-point number adjacent to {@code start} in the
* direction of {@code direction}.
* @since 1.6
*/
public static double nextAfter(double start, double direction) {
/*
* The cases:
*
* nextAfter(+infinity, 0) == MAX_VALUE
* nextAfter(+infinity, +infinity) == +infinity
* nextAfter(-infinity, 0) == -MAX_VALUE
* nextAfter(-infinity, -infinity) == -infinity
*
* are naturally handled without any additional testing
*/
// First check for NaN values
if (Double.isNaN(start) || Double.isNaN(direction)) {
// return a NaN derived from the input NaN(s)
return start + direction;
} else if (start == direction) {
return direction;
} else { // start > direction or start < direction
// Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
// then bitwise convert start to integer.
long transducer = Double.doubleToRawLongBits(start + 0.0d);
/*
* IEEE 754 floating-point numbers are lexicographically
* ordered if treated as signed- magnitude integers .
* Since Java's integers are two's complement,
* incrementing" the two's complement representation of a
* logically negative floating-point value *decrements*
* the signed-magnitude representation. Therefore, when
* the integer representation of a floating-point values
* is less than zero, the adjustment to the representation
* is in the opposite direction than would be expected at
* first .
*/
if (direction > start) { // Calculate next greater value
transducer = transducer + (transducer >= 0L ? 1L:-1L);
} else { // Calculate next lesser value
assert direction < start;
if (transducer > 0L)
--transducer;
else
if (transducer < 0L )
++transducer;
/*
* transducer==0, the result is -MIN_VALUE
*
* The transition from zero (implicitly
* positive) to the smallest negative
* signed magnitude value must be done
* explicitly.
*/
else
transducer = DoubleConsts.SIGN_BIT_MASK | 1L;
}
return Double.longBitsToDouble(transducer);
}
}
/**
* Returns the floating-point number adjacent to the first
* argument in the direction of the second argument. If both
* arguments compare as equal a value equivalent to the second argument
* is returned.
*
*
* Special cases:
*
* - If either argument is a NaN, then NaN is returned.
*
*
- If both arguments are signed zeros, a value equivalent
* to {@code direction} is returned.
*
*
- If {@code start} is
* ±{@link Float#MIN_VALUE} and {@code direction}
* has a value such that the result should have a smaller
* magnitude, then a zero with the same sign as {@code start}
* is returned.
*
*
- If {@code start} is infinite and
* {@code direction} has a value such that the result should
* have a smaller magnitude, {@link Float#MAX_VALUE} with the
* same sign as {@code start} is returned.
*
*
- If {@code start} is equal to ±
* {@link Float#MAX_VALUE} and {@code direction} has a
* value such that the result should have a larger magnitude, an
* infinity with same sign as {@code start} is returned.
*
*
* @param start starting floating-point value
* @param direction value indicating which of
* {@code start}'s neighbors or {@code start} should
* be returned
* @return The floating-point number adjacent to {@code start} in the
* direction of {@code direction}.
* @since 1.6
*/
public static float nextAfter(float start, double direction) {
/*
* The cases:
*
* nextAfter(+infinity, 0) == MAX_VALUE
* nextAfter(+infinity, +infinity) == +infinity
* nextAfter(-infinity, 0) == -MAX_VALUE
* nextAfter(-infinity, -infinity) == -infinity
*
* are naturally handled without any additional testing
*/
// First check for NaN values
if (Float.isNaN(start) || Double.isNaN(direction)) {
// return a NaN derived from the input NaN(s)
return start + (float)direction;
} else if (start == direction) {
return (float)direction;
} else { // start > direction or start < direction
// Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
// then bitwise convert start to integer.
int transducer = Float.floatToRawIntBits(start + 0.0f);
/*
* IEEE 754 floating-point numbers are lexicographically
* ordered if treated as signed- magnitude integers .
* Since Java's integers are two's complement,
* incrementing" the two's complement representation of a
* logically negative floating-point value *decrements*
* the signed-magnitude representation. Therefore, when
* the integer representation of a floating-point values
* is less than zero, the adjustment to the representation
* is in the opposite direction than would be expected at
* first.
*/
if (direction > start) {// Calculate next greater value
transducer = transducer + (transducer >= 0 ? 1:-1);
} else { // Calculate next lesser value
assert direction < start;
if (transducer > 0)
--transducer;
else
if (transducer < 0 )
++transducer;
/*
* transducer==0, the result is -MIN_VALUE
*
* The transition from zero (implicitly
* positive) to the smallest negative
* signed magnitude value must be done
* explicitly.
*/
else
transducer = FloatConsts.SIGN_BIT_MASK | 1;
}
return Float.intBitsToFloat(transducer);
}
}
/**
* Returns the floating-point value adjacent to {@code d} in
* the direction of positive infinity. This method is
* semantically equivalent to {@code nextAfter(d,
* Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
* implementation may run faster than its equivalent
* {@code nextAfter} call.
*
* Special Cases:
*
* - If the argument is NaN, the result is NaN.
*
*
- If the argument is positive infinity, the result is
* positive infinity.
*
*
- If the argument is zero, the result is
* {@link Double#MIN_VALUE}
*
*
*
* @param d starting floating-point value
* @return The adjacent floating-point value closer to positive
* infinity.
* @since 1.6
*/
public static double nextUp(double d) {
if( Double.isNaN(d) || d == Double.POSITIVE_INFINITY)
return d;
else {
d += 0.0d;
return Double.longBitsToDouble(Double.doubleToRawLongBits(d) +
((d >= 0.0d)?+1L:-1L));
}
}
/**
* Returns the floating-point value adjacent to {@code f} in
* the direction of positive infinity. This method is
* semantically equivalent to {@code nextAfter(f,
* Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
* implementation may run faster than its equivalent
* {@code nextAfter} call.
*
* Special Cases:
*
* - If the argument is NaN, the result is NaN.
*
*
- If the argument is positive infinity, the result is
* positive infinity.
*
*
- If the argument is zero, the result is
* {@link Float#MIN_VALUE}
*
*
*
* @param f starting floating-point value
* @return The adjacent floating-point value closer to positive
* infinity.
* @since 1.6
*/
public static float nextUp(float f) {
if( Float.isNaN(f) || f == FloatConsts.POSITIVE_INFINITY)
return f;
else {
f += 0.0f;
return Float.intBitsToFloat(Float.floatToRawIntBits(f) +
((f >= 0.0f)?+1:-1));
}
}
/**
* Returns the floating-point value adjacent to {@code d} in
* the direction of negative infinity. This method is
* semantically equivalent to {@code nextAfter(d,
* Double.NEGATIVE_INFINITY)}; however, a
* {@code nextDown} implementation may run faster than its
* equivalent {@code nextAfter} call.
*
* Special Cases:
*
* - If the argument is NaN, the result is NaN.
*
*
- If the argument is negative infinity, the result is
* negative infinity.
*
*
- If the argument is zero, the result is
* {@code -Double.MIN_VALUE}
*
*
*
* @param d starting floating-point value
* @return The adjacent floating-point value closer to negative
* infinity.
* @since 1.8
*/
public static double nextDown(double d) {
if (Double.isNaN(d) || d == Double.NEGATIVE_INFINITY)
return d;
else {
if (d == 0.0)
return -Double.MIN_VALUE;
else
return Double.longBitsToDouble(Double.doubleToRawLongBits(d) +
((d > 0.0d)?-1L:+1L));
}
}
/**
* Returns the floating-point value adjacent to {@code f} in
* the direction of negative infinity. This method is
* semantically equivalent to {@code nextAfter(f,
* Float.NEGATIVE_INFINITY)}; however, a
* {@code nextDown} implementation may run faster than its
* equivalent {@code nextAfter} call.
*
* Special Cases:
*
* - If the argument is NaN, the result is NaN.
*
*
- If the argument is negative infinity, the result is
* negative infinity.
*
*
- If the argument is zero, the result is
* {@code -Float.MIN_VALUE}
*
*
*
* @param f starting floating-point value
* @return The adjacent floating-point value closer to negative
* infinity.
* @since 1.8
*/
public static float nextDown(float f) {
if (Float.isNaN(f) || f == Float.NEGATIVE_INFINITY)
return f;
else {
if (f == 0.0f)
return -Float.MIN_VALUE;
else
return Float.intBitsToFloat(Float.floatToRawIntBits(f) +
((f > 0.0f)?-1:+1));
}
}
/**
* Returns {@code d} ×
* 2{@code scaleFactor} rounded as if performed
* by a single correctly rounded floating-point multiply to a
* member of the double value set. See the Java
* Language Specification for a discussion of floating-point
* value sets. If the exponent of the result is between {@link
* Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
* answer is calculated exactly. If the exponent of the result
* would be larger than {@code Double.MAX_EXPONENT}, an
* infinity is returned. Note that if the result is subnormal,
* precision may be lost; that is, when {@code scalb(x, n)}
* is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
* x. When the result is non-NaN, the result has the same
* sign as {@code d}.
*
* Special cases:
*
* - If the first argument is NaN, NaN is returned.
*
- If the first argument is infinite, then an infinity of the
* same sign is returned.
*
- If the first argument is zero, then a zero of the same
* sign is returned.
*
*
* @param d number to be scaled by a power of two.
* @param scaleFactor power of 2 used to scale {@code d}
* @return {@code d} × 2{@code scaleFactor}
* @since 1.6
*/
public static double scalb(double d, int scaleFactor) {
/*
* This method does not need to be declared strictfp to
* compute the same correct result on all platforms. When
* scaling up, it does not matter what order the
* multiply-store operations are done; the result will be
* finite or overflow regardless of the operation ordering.
* However, to get the correct result when scaling down, a
* particular ordering must be used.
*
* When scaling down, the multiply-store operations are
* sequenced so that it is not possible for two consecutive
* multiply-stores to return subnormal results. If one
* multiply-store result is subnormal, the next multiply will
* round it away to zero. This is done by first multiplying
* by 2 ^ (scaleFactor % n) and then multiplying several
* times by by 2^n as needed where n is the exponent of number
* that is a covenient power of two. In this way, at most one
* real rounding error occurs. If the double value set is
* being used exclusively, the rounding will occur on a
* multiply. If the double-extended-exponent value set is
* being used, the products will (perhaps) be exact but the
* stores to d are guaranteed to round to the double value
* set.
*
* It is _not_ a valid implementation to first multiply d by
* 2^MIN_EXPONENT and then by 2 ^ (scaleFactor %
* MIN_EXPONENT) since even in a strictfp program double
* rounding on underflow could occur; e.g. if the scaleFactor
* argument was (MIN_EXPONENT - n) and the exponent of d was a
* little less than -(MIN_EXPONENT - n), meaning the final
* result would be subnormal.
*
* Since exact reproducibility of this method can be achieved
* without any undue performance burden, there is no
* compelling reason to allow double rounding on underflow in
* scalb.
*/
// magnitude of a power of two so large that scaling a finite
// nonzero value by it would be guaranteed to over or
// underflow; due to rounding, scaling down takes takes an
// additional power of two which is reflected here
final int MAX_SCALE = DoubleConsts.MAX_EXPONENT + -DoubleConsts.MIN_EXPONENT +
DoubleConsts.SIGNIFICAND_WIDTH + 1;
int exp_adjust = 0;
int scale_increment = 0;
double exp_delta = Double.NaN;
// Make sure scaling factor is in a reasonable range
if(scaleFactor < 0) {
scaleFactor = Math.max(scaleFactor, -MAX_SCALE);
scale_increment = -512;
exp_delta = twoToTheDoubleScaleDown;
}
else {
scaleFactor = Math.min(scaleFactor, MAX_SCALE);
scale_increment = 512;
exp_delta = twoToTheDoubleScaleUp;
}
// Calculate (scaleFactor % +/-512), 512 = 2^9, using
// technique from "Hacker's Delight" section 10-2.
int t = (scaleFactor >> 9-1) >>> 32 - 9;
exp_adjust = ((scaleFactor + t) & (512 -1)) - t;
d *= powerOfTwoD(exp_adjust);
scaleFactor -= exp_adjust;
while(scaleFactor != 0) {
d *= exp_delta;
scaleFactor -= scale_increment;
}
return d;
}
/**
* Returns {@code f} ×
* 2{@code scaleFactor} rounded as if performed
* by a single correctly rounded floating-point multiply to a
* member of the float value set. See the Java
* Language Specification for a discussion of floating-point
* value sets. If the exponent of the result is between {@link
* Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
* answer is calculated exactly. If the exponent of the result
* would be larger than {@code Float.MAX_EXPONENT}, an
* infinity is returned. Note that if the result is subnormal,
* precision may be lost; that is, when {@code scalb(x, n)}
* is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
* x. When the result is non-NaN, the result has the same
* sign as {@code f}.
*
* Special cases:
*
* - If the first argument is NaN, NaN is returned.
*
- If the first argument is infinite, then an infinity of the
* same sign is returned.
*
- If the first argument is zero, then a zero of the same
* sign is returned.
*
*
* @param f number to be scaled by a power of two.
* @param scaleFactor power of 2 used to scale {@code f}
* @return {@code f} × 2{@code scaleFactor}
* @since 1.6
*/
public static float scalb(float f, int scaleFactor) {
// magnitude of a power of two so large that scaling a finite
// nonzero value by it would be guaranteed to over or
// underflow; due to rounding, scaling down takes takes an
// additional power of two which is reflected here
final int MAX_SCALE = FloatConsts.MAX_EXPONENT + -FloatConsts.MIN_EXPONENT +
FloatConsts.SIGNIFICAND_WIDTH + 1;
// Make sure scaling factor is in a reasonable range
scaleFactor = Math.max(Math.min(scaleFactor, MAX_SCALE), -MAX_SCALE);
/*
* Since + MAX_SCALE for float fits well within the double
* exponent range and + float -> double conversion is exact
* the multiplication below will be exact. Therefore, the
* rounding that occurs when the double product is cast to
* float will be the correctly rounded float result. Since
* all operations other than the final multiply will be exact,
* it is not necessary to declare this method strictfp.
*/
return (float)((double)f*powerOfTwoD(scaleFactor));
}
// Constants used in scalb
static double twoToTheDoubleScaleUp = powerOfTwoD(512);
static double twoToTheDoubleScaleDown = powerOfTwoD(-512);
/**
* Returns a floating-point power of two in the normal range.
*/
static double powerOfTwoD(int n) {
assert(n >= DoubleConsts.MIN_EXPONENT && n <= DoubleConsts.MAX_EXPONENT);
return Double.longBitsToDouble((((long)n + (long)DoubleConsts.EXP_BIAS) <<
(DoubleConsts.SIGNIFICAND_WIDTH-1))
& DoubleConsts.EXP_BIT_MASK);
}
/**
* Returns a floating-point power of two in the normal range.
*/
static float powerOfTwoF(int n) {
assert(n >= FloatConsts.MIN_EXPONENT && n <= FloatConsts.MAX_EXPONENT);
return Float.intBitsToFloat(((n + FloatConsts.EXP_BIAS) <<
(FloatConsts.SIGNIFICAND_WIDTH-1))
& FloatConsts.EXP_BIT_MASK);
}
}