Contents
- Description
- Field Summary
- Method Summary
- Field Details
- Method Details
- sin(double)
- cos(double)
- tan(double)
- asin(double)
- acos(double)
- atan(double)
- toRadians(double)
- toDegrees(double)
- exp(double)
- log(double)
- log10(double)
- sqrt(double)
- cbrt(double)
- IEEEremainder(double, double)
- ceil(double)
- floor(double)
- rint(double)
- atan2(double, double)
- pow(double, double)
- round(float)
- round(double)
- random()
- addExact(int, int)
- addExact(long, long)
- subtractExact(int, int)
- subtractExact(long, long)
- multiplyExact(int, int)
- multiplyExact(long, int)
- multiplyExact(long, long)
- divideExact(int, int)
- divideExact(long, long)
- floorDivExact(int, int)
- floorDivExact(long, long)
- ceilDivExact(int, int)
- ceilDivExact(long, long)
- incrementExact(int)
- incrementExact(long)
- decrementExact(int)
- decrementExact(long)
- negateExact(int)
- negateExact(long)
- toIntExact(long)
- multiplyFull(int, int)
- multiplyHigh(long, long)
- unsignedMultiplyHigh(long, long)
- floorDiv(int, int)
- floorDiv(long, int)
- floorDiv(long, long)
- floorMod(int, int)
- floorMod(long, int)
- floorMod(long, long)
- ceilDiv(int, int)
- ceilDiv(long, int)
- ceilDiv(long, long)
- ceilMod(int, int)
- ceilMod(long, int)
- ceilMod(long, long)
- abs(int)
- absExact(int)
- abs(long)
- absExact(long)
- abs(float)
- abs(double)
- max(int, int)
- max(long, long)
- max(float, float)
- max(double, double)
- min(int, int)
- min(long, long)
- min(float, float)
- min(double, double)
- clamp(long, int, int)
- clamp(long, long, long)
- clamp(double, double, double)
- clamp(float, float, float)
- fma(double, double, double)
- fma(float, float, float)
- ulp(double)
- ulp(float)
- signum(double)
- signum(float)
- sinh(double)
- cosh(double)
- tanh(double)
- hypot(double, double)
- expm1(double)
- log1p(double)
- copySign(double, double)
- copySign(float, float)
- getExponent(float)
- getExponent(double)
- nextAfter(double, double)
- nextAfter(float, double)
- nextUp(double)
- nextUp(float)
- nextDown(double)
- nextDown(float)
- scalb(double, int)
- scalb(float, int)
- unsignedMultiplyExact(int, int)
- unsignedMultiplyExact(long, int)
- unsignedMultiplyExact(long, long)
- powExact(int, int)
- unsignedPowExact(int, int)
- powExact(long, int)
- unsignedPowExact(long, int)
Class Math
java.lang.Object
java.lang.Math
The class Math contains methods for performing basic
numeric operations such as the elementary exponential, logarithm,
square root, and trigonometric functions.
Since:
1.0
External Specifications
Unlike some of the numeric methods of class StrictMath, all implementations of the equivalent functions of class 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 Math methods simply call the equivalent method in 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 Math methods. Such higher-performance implementations still must conform to the specification for Math.
The quality of implementation specifications concern two properties, accuracy of the returned result and monotonicity of the method. Accuracy of the floating-point Math methods is measured in terms of ulps, units in the last place. For a given floating-point format, an 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 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 int or long and overflow errors need to be detected, the methods whose names end with Exact throw an ArithmeticException when the results overflow.
IEEE 754 Recommended Operations
The 2019 revision of the IEEE 754 floating-point standard includes a section of recommended operations and the semantics of those operations if they are included in a programming environment. The recommended operations present in this class include sin, cos, tan, asin, acos, atan, exp, expm1, log, log10, log1p, sinh, cosh, tanh, hypot, and pow. (The sqrt operation is a required part of IEEE 754 from a different section of the standard.) The special case behavior of the recommended operations generally follows the guidance of the IEEE 754 standard. However, the pow method defines different behavior for some arguments, as noted in its specification. The IEEE 754 standard defines its operations to be correctly rounded, which is a more stringent quality of implementation condition than required for most of the methods in question that are also included in this class.-
Field Summary
FieldsModifier and TypeFieldDescriptionstatic final doubleThe double value that is closer than any other to e, the base of the natural logarithms.static final doubleThe double value that is closer than any other to pi (π), the ratio of the circumference of a circle to its diameter.static final doubleThe double value that is closer than any other to tau (τ), the ratio of the circumference of a circle to its radius. -
Method Summary
All MethodsStatic MethodsConcrete MethodsModifier and TypeMethodDescriptionstatic doubleabs(double a)Returns the absolute value of a double value.static floatabs(float a)Returns the absolute value of a float value.static intabs(int a)Returns the absolute value of an int value.static longabs(long a)Returns the absolute value of a long value.static intabsExact(int a)Returns the mathematical absolute value of an int value if it is exactly representable as an int, throwing ArithmeticException if the result overflows the positive int range.static longabsExact(long a)Returns the mathematical absolute value of an long value if it is exactly representable as an long, throwing ArithmeticException if the result overflows the positive long range.static doubleacos(double a)Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi.static intaddExact(int x, int y)Returns the sum of its arguments, throwing an exception if the result overflows an int.static longaddExact(long x, long y)Returns the sum of its arguments, throwing an exception if the result overflows a long.static doubleasin(double a)Returns the arc sine of a value; the returned angle is in the range −pi/2 through pi/2.static doubleatan(double a)Returns the arc tangent of a value; the returned angle is in the range −pi/2 through pi/2.static doubleatan2(double y, double x)Returns the angle theta from the conversion of rectangular coordinates (x, y) to polar coordinates (r, theta).static doublecbrt(double a)Returns the cube root of a double value.static doubleceil(double a)Returns the smallest (closest to negative infinity) double value that is greater than or equal to the argument and is equal to a mathematical integer.static intceilDiv(int x, int y)Returns the smallest (closest to negative infinity) int value that is greater than or equal to the algebraic quotient.static longceilDiv(long x, int y)Returns the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient.static longceilDiv(long x, long y)Returns the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient.static intceilDivExact(int x, int y)Returns the smallest (closest to negative infinity) int value that is greater than or equal to the algebraic quotient.static longceilDivExact(long x, long y)Returns the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient.static intceilMod(int x, int y)Returns the ceiling modulus of the int arguments.static intceilMod(long x, int y)Returns the ceiling modulus of the long and int arguments.static longceilMod(long x, long y)Returns the ceiling modulus of the long arguments.static doubleclamp(double value, double min, double max)Clamps the value to fit between min and max.static floatclamp(float value, float min, float max)Clamps the value to fit between min and max.static intclamp(long value, int min, int max)Clamps the value to fit between min and max.static longclamp(long value, long min, long max)Clamps the value to fit between min and max.static doublecopySign(double magnitude, double sign)Returns the first floating-point argument with the sign of the second floating-point argument.static floatcopySign(float magnitude, float sign)Returns the first floating-point argument with the sign of the second floating-point argument.static doublecos(double a)Returns the trigonometric cosine of an angle.static doublecosh(double x)Returns the hyperbolic cosine of a double value.static intdecrementExact(int a)Returns the argument decremented by one, throwing an exception if the result overflows an int.static longdecrementExact(long a)Returns the argument decremented by one, throwing an exception if the result overflows a long.static intdivideExact(int x, int y)Returns the quotient of the arguments, throwing an exception if the result overflows an int.static longdivideExact(long x, long y)Returns the quotient of the arguments, throwing an exception if the result overflows a long.static doubleexp(double a)Returns Euler's number e raised to the power of a double value.static doubleexpm1(double x)Returns ex −1.static doublefloor(double a)Returns the largest (closest to positive infinity) double value that is less than or equal to the argument and is equal to a mathematical integer.static intfloorDiv(int x, int y)Returns the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient.static longfloorDiv(long x, int y)Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient.static longfloorDiv(long x, long y)Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient.static intfloorDivExact(int x, int y)Returns the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient.static longfloorDivExact(long x, long y)Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient.static intfloorMod(int x, int y)Returns the floor modulus of the int arguments.static intfloorMod(long x, int y)Returns the floor modulus of the long and int arguments.static longfloorMod(long x, long y)Returns the floor modulus of the long arguments.static doublefma(double a, double b, double c)Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest double.static floatfma(float a, float b, float c)Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest float.static intgetExponent(double d)Returns the unbiased exponent used in the representation of a double.static intgetExponent(float f)Returns the unbiased exponent used in the representation of a float.static doublehypot(double x, double y)Returns sqrt(x2 +y2) without intermediate overflow or underflow.static doubleIEEEremainder(double f1, double f2)Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard.static intincrementExact(int a)Returns the argument incremented by one, throwing an exception if the result overflows an int.static longincrementExact(long a)Returns the argument incremented by one, throwing an exception if the result overflows a long.static doublelog(double a)Returns the natural logarithm (base e) of a double value.static doublelog10(double a)Returns the base 10 logarithm of a double value.static doublelog1p(double x)Returns the natural logarithm of the sum of the argument and 1.static doublemax(double a, double b)Returns the greater of two double values.static floatmax(float a, float b)Returns the greater of two float values.static intmax(int a, int b)Returns the greater of two int values.static longmax(long a, long b)Returns the greater of two long values.static doublemin(double a, double b)Returns the smaller of two double values.static floatmin(float a, float b)Returns the smaller of two float values.static intmin(int a, int b)Returns the smaller of two int values.static longmin(long a, long b)Returns the smaller of two long values.static intmultiplyExact(int x, int y)Returns the product of the arguments, throwing an exception if the result overflows an int.static longmultiplyExact(long x, int y)Returns the product of the arguments, throwing an exception if the result overflows a long.static longmultiplyExact(long x, long y)Returns the product of the arguments, throwing an exception if the result overflows a long.static longmultiplyFull(int x, int y)Returns the exact mathematical product of the arguments.static longmultiplyHigh(long x, long y)Returns as a long the most significant 64 bits of the 128-bit product of two 64-bit factors.static intnegateExact(int a)Returns the negation of the argument, throwing an exception if the result overflows an int.static longnegateExact(long a)Returns the negation of the argument, throwing an exception if the result overflows a long.static doublenextAfter(double start, double direction)Returns the floating-point number adjacent to the first argument in the direction of the second argument.static floatnextAfter(float start, double direction)Returns the floating-point number adjacent to the first argument in the direction of the second argument.static doublenextDown(double d)Returns the floating-point value adjacent to d in the direction of negative infinity.static floatnextDown(float f)Returns the floating-point value adjacent to f in the direction of negative infinity.static doublenextUp(double d)Returns the floating-point value adjacent to d in the direction of positive infinity.static floatnextUp(float f)Returns the floating-point value adjacent to f in the direction of positive infinity.static doublepow(double a, double b)Returns the value of the first argument raised to the power of the second argument.static intpowExact(int x, int n)Returns x raised to the power of n, throwing an exception if the result overflows an int.static longpowExact(long x, int n)Returns x raised to the power of n, throwing an exception if the result overflows a long.static doublerandom()Returns a double value with a positive sign, greater than or equal to 0.0 and less than 1.0.static doublerint(double a)Returns the double value that is closest in value to the argument and is equal to a mathematical integer.static longround(double a)Returns the closest long to the argument, with ties rounding to positive infinity.static intround(float a)Returns the closest int to the argument, with ties rounding to positive infinity.static doublescalb(double d, int scaleFactor)Returns d × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply.static floatscalb(float f, int scaleFactor)Returns f × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply.static doublesignum(double d)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.static floatsignum(float f)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.static doublesin(double a)Returns the trigonometric sine of an angle.static doublesinh(double x)Returns the hyperbolic sine of a double value.static doublesqrt(double a)Returns the correctly rounded positive square root of a double value.static intsubtractExact(int x, int y)Returns the difference of the arguments, throwing an exception if the result overflows an int.static longsubtractExact(long x, long y)Returns the difference of the arguments, throwing an exception if the result overflows a long.static doubletan(double a)Returns the trigonometric tangent of an angle.static doubletanh(double x)Returns the hyperbolic tangent of a double value.static doubletoDegrees(double angrad)Converts an angle measured in radians to an approximately equivalent angle measured in degrees.static inttoIntExact(long value)Returns the value of the long argument, throwing an exception if the value overflows an int.static doubletoRadians(double angdeg)Converts an angle measured in degrees to an approximately equivalent angle measured in radians.static doubleulp(double d)Returns the size of an ulp of the argument.static floatulp(float f)Returns the size of an ulp of the argument.static intunsignedMultiplyExact(int x, int y)Returns the product of the unsigned arguments, throwing an exception if the result overflows an unsigned int.static longunsignedMultiplyExact(long x, int y)Returns the product of the unsigned arguments, throwing an exception if the result overflows an unsigned long.static longunsignedMultiplyExact(long x, long y)Returns the product of the unsigned arguments, throwing an exception if the result overflows an unsigned long.static longunsignedMultiplyHigh(long x, long y)Returns as a long the most significant 64 bits of the unsigned 128-bit product of two unsigned 64-bit factors.static intunsignedPowExact(int x, int n)Returns unsigned x raised to the power of n, throwing an exception if the result overflows an unsigned int.static longunsignedPowExact(long x, int n)Returns unsigned x raised to the power of n, throwing an exception if the result overflows an unsigned long.Methods declared in class Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, waitModifier and TypeMethodDescriptionprotected Objectclone()Creates and returns a copy of this object.booleanIndicates whether some other object is "equal to" this one.protected voidfinalize()Deprecated, for removal: This API element is subject to removal in a future version.Finalization is deprecated and subject to removal in a future release.final Class<?>getClass()Returns the runtime class of this Object.inthashCode()Returns a hash code value for this object.final voidnotify()Wakes up a single thread that is waiting on this object's monitor.final voidWakes up all threads that are waiting on this object's monitor.toString()Returns a string representation of the object.final voidwait()Causes the current thread to wait until it is awakened, typically by being notified or interrupted.final voidwait(long timeoutMillis)Causes the current thread to wait until it is awakened, typically by being notified or interrupted, or until a certain amount of real time has elapsed.final voidwait(long timeoutMillis, int nanos)Causes the current thread to wait until it is awakened, typically by being notified or interrupted, or until a certain amount of real time has elapsed.
-
Field Details
-
E
public static final double EThe double value that is closer than any other to e, the base of the natural logarithms.See Also: -
PI
public static final double PIThe double value that is closer than any other to pi (π), the ratio of the circumference of a circle to its diameter.See Also: -
TAU
public static final double TAUThe double value that is closer than any other to tau (τ), the ratio of the circumference of a circle to its radius.API Note: The value of pi is one half that of tau; in other words, tau is double pi . Since: 19 See Also:
-
-
Method Details
-
sin
public static double sin(double a)Returns the trigonometric sine of an angle. Special cases:Parameters: a - an angle, in radians. Returns: the sine of the argument.- 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.
-
cos
public static double cos(double a)Returns the trigonometric cosine of an angle. Special cases:Parameters: a - an angle, in radians. Returns: the cosine of the argument.- If the argument is NaN or an infinity, then the result is NaN.
- If the argument is zero, then the result is 1.0.
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
-
tan
public static double tan(double a)Returns the trigonometric tangent of an angle. Special cases:Parameters: a - an angle, in radians. Returns: the tangent of the argument.- 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 1.25 ulps of the exact result. Results must be semi-monotonic.
-
asin
public static double asin(double a)Returns the arc sine of a value; the returned angle is in the range −pi/2 through pi/2. Special cases:Parameters: a - the value whose arc sine is to be returned. Returns: the arc sine of the argument.- 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.
-
acos
public static double acos(double a)Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi. Special case:Parameters: a - the value whose arc cosine is to be returned. Returns: the arc cosine of the argument.- If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
- If the argument is 1.0, the result is positive zero.
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
-
atan
public static double atan(double a)Returns the arc tangent of a value; the returned angle is in the range −pi/2 through pi/2. Special cases:Parameters: a - the value whose arc tangent is to be returned. Returns: the arc tangent of the argument.- 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 infinite, then the result is the closest value to pi/2 with the same sign as the input.
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
-
toRadians
public static double toRadians(double angdeg)Converts an angle measured in degrees to an approximately equivalent angle measured in radians. The conversion from degrees to radians is generally inexact.Parameters: angdeg - an angle, in degrees Returns: the measurement of the angle angdeg in radians. Since: 1.2 -
toDegrees
public static double toDegrees(double angrad)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 cos(toRadians(90.0)) to exactly equal 0.0.Parameters: angrad - an angle, in radians Returns: the measurement of the angle angrad in degrees. Since: 1.2 -
exp
public static double exp(double a)Returns Euler's number e raised to the power of a double value. Special cases:Parameters: a - the exponent to raise e to. Returns: the value ea, where e is the base of the natural logarithms.- 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.
- If the argument is zero, then the result is 1.0.
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
-
log
public static double log(double a)Returns the natural logarithm (base e) of a double value. Special cases:Parameters: a - a value Returns: the value ln a, the natural logarithm of a.- 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 1.0, then the result is positive zero.
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
-
log10
public static double log10(double a)Returns the base 10 logarithm of a double value. Special cases:Parameters: a - a value Returns: the base 10 logarithm of a. Since: 1.5- 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. In particular, if the argument is 1.0 (100), then the result is positive zero.
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
-
sqrt
public static double sqrt(double a)Returns the correctly rounded positive square root of a double value. Special cases:API Note: This method corresponds to the squareRoot operation defined in IEEE 754. Parameters: a - a value. Returns: the positive square root of a. If the argument is NaN or less than zero, the result is NaN.- 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.
-
cbrt
public static double cbrt(double a)Returns the cube root of a double value. For positive finite x, 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:Parameters: a - a value. Returns: the cube root of a. Since: 1.5- 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.
-
IEEEremainder
public static double IEEEremainder(double f1, double f2)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 f1/f2, and if two mathematical integers are equally close to 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:Parameters: f1 - the dividend. f2 - the divisor. Returns: the remainder when f1 is divided by f2.- 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.
-
ceil
public static double ceil(double a)Returns the smallest (closest to negative infinity) double value that is greater than or equal to the argument and is equal to a mathematical integer. Special cases:API Note: This method corresponds to the roundToIntegralTowardPositive operation defined in IEEE 754. Parameters: a - a value. Returns: 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.- 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.
-
floor
public static double floor(double a)Returns the largest (closest to positive infinity) double value that is less than or equal to the argument and is equal to a mathematical integer. Special cases:API Note: This method corresponds to the roundToIntegralTowardNegative operation defined in IEEE 754. Parameters: a - a value. Returns: the largest (closest to positive infinity) floating-point value that less than or equal to the argument and is equal to a mathematical integer.- 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.
-
rint
public static double rint(double a)Returns the double value that is closest in value to the argument and is equal to a mathematical integer. If two double values that are mathematical integers are equally close, the result is the integer value that is even. Special cases:API Note: This method corresponds to the roundToIntegralTiesToEven operation defined in IEEE 754. Parameters: a - a double value. Returns: the closest floating-point value to a that is equal to a mathematical integer.- 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.
-
atan2
public static double atan2(double y, double x)Returns the angle theta from the conversion of rectangular coordinates (x, y) to polar coordinates (r, theta). This method computes the phase theta by computing an arc tangent of y/x in the range of −pi to pi. Special cases:API Note: For y with a positive sign and finite nonzero x, the exact mathematical value of atan2 is equal to:- 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 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 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 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 double value closest to -pi/2.
- If both arguments are positive infinity, then the result is the 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 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 double value closest to -pi/4.
- If both arguments are negative infinity, then the result is the double value closest to -3*pi/4.
The computed result must be within 2 ulps of the exact result. Results must be semi-monotonic.
- If x > 0, atan(abs(y/x))
- If x < 0, π - atan(abs(y/x))
-
pow
public static double pow(double a, double b)Returns the value of the first argument raised to the power of the second argument. Special cases:API Note: The special cases definitions of this method differ from the special case definitions of the IEEE 754 recommended pow operation for ±1.0 raised to an infinite power. This method treats such cases as indeterminate and specifies a NaN is returned. The IEEE 754 specification treats the infinite power as a large integer (large-magnitude floating-point numbers are numerically integers, specifically even integers) and therefore specifies 1.0 be returned. Parameters: a - the base. b - the exponent. Returns: the value ab.- 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,
- 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,
- 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,
- 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,
- 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,
- 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,
- 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,
- 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,
- 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 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 ceil or, equivalently, a fixed point of the method 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.
-
round
public static int round(float a)Returns the closest int to the argument, with ties rounding to positive infinity.Parameters: a - a floating-point value to be rounded to an integer. Returns: the value of the argument rounded to the nearest int value. See Also: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 Integer.MIN_VALUE, the result is equal to the value of Integer.MIN_VALUE.
- If the argument is positive infinity or any value greater than or equal to the value of Integer.MAX_VALUE, the result is equal to the value of Integer.MAX_VALUE.
-
round
public static long round(double a)Returns the closest long to the argument, with ties rounding to positive infinity.Parameters: a - a floating-point value to be rounded to a long. Returns: the value of the argument rounded to the nearest long value. See Also: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 Long.MIN_VALUE, the result is equal to the value of Long.MIN_VALUE.
- If the argument is positive infinity or any value greater than or equal to the value of Long.MAX_VALUE, the result is equal to the value of Long.MAX_VALUE.
-
random
public static double random()Returns a double value with a positive sign, greater than or equal to 0.0 and less than 1.0. Returned values are chosen pseudorandomly with (approximately) uniform distribution from that range.API Note: As the largest double value less than 1.0 is Math.nextDown(1.0), a value x in the closed range [x1,x2] where x1<=x2 may be defined by the statements double f = Math.random()/Math.nextDown(1.0); double x = x1*(1.0 - f) + x2*f; Returns: a pseudorandom double greater than or equal to 0.0 and less than 1.0. See Also:When this method is first called, it creates a single new pseudorandom-number generator, exactly as if by the expression 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.
-
addExact
public static int addExact(int x, int y)Returns the sum of its arguments, throwing an exception if the result overflows an int.Parameters: x - the first value y - the second value Returns: the result Throws: ArithmeticException - if the result overflows an int Since: 1.8 -
addExact
public static long addExact(long x, long y)Returns the sum of its arguments, throwing an exception if the result overflows a long.Parameters: x - the first value y - the second value Returns: the result Throws: ArithmeticException - if the result overflows a long Since: 1.8 -
subtractExact
public static int subtractExact(int x, int y)Returns the difference of the arguments, throwing an exception if the result overflows an int.Parameters: x - the first value y - the second value to subtract from the first Returns: the result Throws: ArithmeticException - if the result overflows an int Since: 1.8 -
subtractExact
public static long subtractExact(long x, long y)Returns the difference of the arguments, throwing an exception if the result overflows a long.Parameters: x - the first value y - the second value to subtract from the first Returns: the result Throws: ArithmeticException - if the result overflows a long Since: 1.8 -
multiplyExact
public static int multiplyExact(int x, int y)Returns the product of the arguments, throwing an exception if the result overflows an int.Parameters: x - the first value y - the second value Returns: the result Throws: ArithmeticException - if the result overflows an int Since: 1.8 -
multiplyExact
public static long multiplyExact(long x, int y)Returns the product of the arguments, throwing an exception if the result overflows a long.Parameters: x - the first value y - the second value Returns: the result Throws: ArithmeticException - if the result overflows a long Since: 9 -
multiplyExact
public static long multiplyExact(long x, long y)Returns the product of the arguments, throwing an exception if the result overflows a long.Parameters: x - the first value y - the second value Returns: the result Throws: ArithmeticException - if the result overflows a long Since: 1.8 -
divideExact
public static int divideExact(int x, int y)Returns the quotient of the arguments, throwing an exception if the result overflows an int. Such overflow occurs in this method if x is Integer.MIN_VALUE and y is -1. In contrast, if Integer.MIN_VALUE / -1 were evaluated directly, the result would be Integer.MIN_VALUE and no exception would be thrown.Parameters: x - the dividend y - the divisor Returns: the quotient x / y Throws: ArithmeticException - if y is zero or the quotient overflows an int See Java Language Specification: 15.17.2 Division Operator /If y is zero, an ArithmeticException is thrown (JLS 15.17.2).
The built-in remainder operator "%" is a suitable counterpart both for this method and for the built-in division operator "/".
Since: 18 -
divideExact
public static long divideExact(long x, long y)Returns the quotient of the arguments, throwing an exception if the result overflows a long. Such overflow occurs in this method if x is Long.MIN_VALUE and y is -1. In contrast, if Long.MIN_VALUE / -1 were evaluated directly, the result would be Long.MIN_VALUE and no exception would be thrown.Parameters: x - the dividend y - the divisor Returns: the quotient x / y Throws: ArithmeticException - if y is zero or the quotient overflows a long See Java Language Specification: 15.17.2 Division Operator /If y is zero, an ArithmeticException is thrown (JLS 15.17.2).
The built-in remainder operator "%" is a suitable counterpart both for this method and for the built-in division operator "/".
Since: 18 -
floorDivExact
public static int floorDivExact(int x, int y)Returns the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient. This method is identical to floorDiv(int,int) except that it throws an ArithmeticException when the dividend is Integer.MIN_VALUE and the divisor is -1 instead of ignoring the integer overflow and returning Integer.MIN_VALUE.Parameters: x - the dividend y - the divisor Returns: the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient. Throws: ArithmeticException - if the divisor y is zero, or the dividend x is Integer.MIN_VALUE and the divisor y is -1. Since: 18 See Also:The floor modulus method floorMod(int,int) is a suitable counterpart both for this method and for the floorDiv(int,int) method.
For examples, see floorDiv(int, int).
-
floorDivExact
public static long floorDivExact(long x, long y)Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. This method is identical to floorDiv(long,long) except that it throws an ArithmeticException when the dividend is Long.MIN_VALUE and the divisor is -1 instead of ignoring the integer overflow and returning Long.MIN_VALUE.Parameters: x - the dividend y - the divisor Returns: the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. Throws: ArithmeticException - if the divisor y is zero, or the dividend x is Long.MIN_VALUE and the divisor y is -1. Since: 18 See Also:The floor modulus method floorMod(long,long) is a suitable counterpart both for this method and for the floorDiv(long,long) method.
For examples, see floorDiv(int, int).
-
ceilDivExact
public static int ceilDivExact(int x, int y)Returns the smallest (closest to negative infinity) int value that is greater than or equal to the algebraic quotient. This method is identical to ceilDiv(int,int) except that it throws an ArithmeticException when the dividend is Integer.MIN_VALUE and the divisor is -1 instead of ignoring the integer overflow and returning Integer.MIN_VALUE.Parameters: x - the dividend y - the divisor Returns: the smallest (closest to negative infinity) int value that is greater than or equal to the algebraic quotient. Throws: ArithmeticException - if the divisor y is zero, or the dividend x is Integer.MIN_VALUE and the divisor y is -1. Since: 18 See Also:The ceil modulus method ceilMod(int,int) is a suitable counterpart both for this method and for the ceilDiv(int,int) method.
For examples, see ceilDiv(int, int).
-
ceilDivExact
public static long ceilDivExact(long x, long y)Returns the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient. This method is identical to ceilDiv(long,long) except that it throws an ArithmeticException when the dividend is Long.MIN_VALUE and the divisor is -1 instead of ignoring the integer overflow and returning Long.MIN_VALUE.Parameters: x - the dividend y - the divisor Returns: the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient. Throws: ArithmeticException - if the divisor y is zero, or the dividend x is Long.MIN_VALUE and the divisor y is -1. Since: 18 See Also:The ceil modulus method ceilMod(long,long) is a suitable counterpart both for this method and for the ceilDiv(long,long) method.
For examples, see ceilDiv(int, int).
-
incrementExact
public static int incrementExact(int a)Returns the argument incremented by one, throwing an exception if the result overflows an int. The overflow only occurs for the maximum value.Parameters: a - the value to increment Returns: the result Throws: ArithmeticException - if the result overflows an int Since: 1.8 -
incrementExact
public static long incrementExact(long a)Returns the argument incremented by one, throwing an exception if the result overflows a long. The overflow only occurs for the maximum value.Parameters: a - the value to increment Returns: the result Throws: ArithmeticException - if the result overflows a long Since: 1.8 -
decrementExact
public static int decrementExact(int a)Returns the argument decremented by one, throwing an exception if the result overflows an int. The overflow only occurs for the minimum value.Parameters: a - the value to decrement Returns: the result Throws: ArithmeticException - if the result overflows an int Since: 1.8 -
decrementExact
public static long decrementExact(long a)Returns the argument decremented by one, throwing an exception if the result overflows a long. The overflow only occurs for the minimum value.Parameters: a - the value to decrement Returns: the result Throws: ArithmeticException - if the result overflows a long Since: 1.8 -
negateExact
public static int negateExact(int a)Returns the negation of the argument, throwing an exception if the result overflows an int. The overflow only occurs for the minimum value.Parameters: a - the value to negate Returns: the result Throws: ArithmeticException - if the result overflows an int Since: 1.8 -
negateExact
public static long negateExact(long a)Returns the negation of the argument, throwing an exception if the result overflows a long. The overflow only occurs for the minimum value.Parameters: a - the value to negate Returns: the result Throws: ArithmeticException - if the result overflows a long Since: 1.8 -
toIntExact
public static int toIntExact(long value)Returns the value of the long argument, throwing an exception if the value overflows an int.Parameters: value - the long value Returns: the argument as an int Throws: ArithmeticException - if the argument overflows an int Since: 1.8 -
multiplyFull
public static long multiplyFull(int x, int y)Returns the exact mathematical product of the arguments.Parameters: x - the first value y - the second value Returns: the result Since: 9 -
multiplyHigh
public static long multiplyHigh(long x, long y)Returns as a long the most significant 64 bits of the 128-bit product of two 64-bit factors.Parameters: x - the first value y - the second value Returns: the result Since: 9 See Also: -
unsignedMultiplyHigh
public static long unsignedMultiplyHigh(long x, long y)Returns as a long the most significant 64 bits of the unsigned 128-bit product of two unsigned 64-bit factors.Parameters: x - the first value y - the second value Returns: the result Since: 18 See Also: -
floorDiv
public static int floorDiv(int x, int y)Returns the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient. There is one special case: if the dividend is Integer.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Integer.MIN_VALUE.Parameters: x - the dividend y - the divisor Returns: the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient. Throws: ArithmeticException - if the divisor y is zero Since: 1.8 See Also: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 from truncation when the exact quotient is not an integer and is negative.
- If the signs of the arguments are the same, the results of
floorDiv and the / operator are the same.
For example, floorDiv(4, 3) == 1 and (4 / 3) == 1. - If the signs of the arguments are different, floorDiv
returns the largest integer less than or equal to the quotient
while the / operator returns the smallest integer greater
than or equal to the quotient.
They differ if and only if the quotient is not an integer.
For example, floorDiv(-4, 3) == -2, whereas (-4 / 3) == -1.
- If the signs of the arguments are the same, the results of
floorDiv and the / operator are the same.
-
floorDiv
public static long floorDiv(long x, int y)Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. There is one special case: if the dividend is Long.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Long.MIN_VALUE.Parameters: x - the dividend y - the divisor Returns: the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. Throws: ArithmeticException - if the divisor y is zero Since: 9 See Also: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 from truncation when the exact result is not an integer and is negative.
For examples, see floorDiv(int, int).
-
floorDiv
public static long floorDiv(long x, long y)Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. There is one special case: if the dividend is Long.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Long.MIN_VALUE.Parameters: x - the dividend y - the divisor Returns: the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. Throws: ArithmeticException - if the divisor y is zero Since: 1.8 See Also: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 from truncation when the exact result is not an integer and is negative.
For examples, see floorDiv(int, int).
-
floorMod
public static int floorMod(int x, int y)Returns the floor modulus of the int arguments.Parameters: x - the dividend y - the divisor Returns: the floor modulus x - (floorDiv(x, y) * y) Throws: ArithmeticException - if the divisor y is zero Since: 1.8 See Also:The floor modulus is r = x - (floorDiv(x, y) * y), has the same sign as the divisor y or is zero, and is in the range of -abs(y) < r < +abs(y).
The relationship between floorDiv and floorMod is such that:
- floorDiv(x, y) * y + floorMod(x, y) == x
The difference in values between floorMod and the % operator is due to the difference between floorDiv and the / operator, as detailed in floorDiv(int, int).
Examples:
- Regardless of the signs of the arguments, floorMod(x, y) is zero exactly when x % y is zero as well.
- If neither floorMod(x, y) nor x % y is zero,
they differ exactly when the signs of the arguments differ.
- floorMod(+4, +3) == +1; and (+4 % +3) == +1
- floorMod(-4, -3) == -1; and (-4 % -3) == -1
- floorMod(+4, -3) == -2; and (+4 % -3) == +1
- floorMod(-4, +3) == +2; and (-4 % +3) == -1
-
floorMod
public static int floorMod(long x, int y)Returns the floor modulus of the long and int arguments.Parameters: x - the dividend y - the divisor Returns: the floor modulus x - (floorDiv(x, y) * y) Throws: ArithmeticException - if the divisor y is zero Since: 9 See Also:The floor modulus is r = x - (floorDiv(x, y) * y), has the same sign as the divisor y or is zero, and is in the range of -abs(y) < r < +abs(y).
The relationship between floorDiv and floorMod is such that:
- floorDiv(x, y) * y + floorMod(x, y) == x
For examples, see floorMod(int, int).
-
floorMod
public static long floorMod(long x, long y)Returns the floor modulus of the long arguments.Parameters: x - the dividend y - the divisor Returns: the floor modulus x - (floorDiv(x, y) * y) Throws: ArithmeticException - if the divisor y is zero Since: 1.8 See Also:The floor modulus is r = x - (floorDiv(x, y) * y), has the same sign as the divisor y or is zero, and is in the range of -abs(y) < r < +abs(y).
The relationship between floorDiv and floorMod is such that:
- floorDiv(x, y) * y + floorMod(x, y) == x
For examples, see floorMod(int, int).
-
ceilDiv
public static int ceilDiv(int x, int y)Returns the smallest (closest to negative infinity) int value that is greater than or equal to the algebraic quotient. There is one special case: if the dividend is Integer.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Integer.MIN_VALUE.Parameters: x - the dividend y - the divisor Returns: the smallest (closest to negative infinity) int value that is greater than or equal to the algebraic quotient. Throws: ArithmeticException - if the divisor y is zero Since: 18 See Also:Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward positive infinity (ceiling) rounding mode. The ceiling rounding mode gives different results from truncation when the exact quotient is not an integer and is positive.
- If the signs of the arguments are different, the results of
ceilDiv and the / operator are the same.
For example, ceilDiv(-4, 3) == -1 and (-4 / 3) == -1. - If the signs of the arguments are the same, ceilDiv
returns the smallest integer greater than or equal to the quotient
while the / operator returns the largest integer less
than or equal to the quotient.
They differ if and only if the quotient is not an integer.
For example, ceilDiv(4, 3) == 2, whereas (4 / 3) == 1.
- If the signs of the arguments are different, the results of
ceilDiv and the / operator are the same.
-
ceilDiv
public static long ceilDiv(long x, int y)Returns the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient. There is one special case: if the dividend is Long.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Long.MIN_VALUE.Parameters: x - the dividend y - the divisor Returns: the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient. Throws: ArithmeticException - if the divisor y is zero Since: 18 See Also:Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward positive infinity (ceiling) rounding mode. The ceiling rounding mode gives different results from truncation when the exact result is not an integer and is positive.
For examples, see ceilDiv(int, int).
-
ceilDiv
public static long ceilDiv(long x, long y)Returns the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient. There is one special case: if the dividend is Long.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Long.MIN_VALUE.Parameters: x - the dividend y - the divisor Returns: the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient. Throws: ArithmeticException - if the divisor y is zero Since: 18 See Also:Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward positive infinity (ceiling) rounding mode. The ceiling rounding mode gives different results from truncation when the exact result is not an integer and is positive.
For examples, see ceilDiv(int, int).
-
ceilMod
public static int ceilMod(int x, int y)Returns the ceiling modulus of the int arguments.Parameters: x - the dividend y - the divisor Returns: the ceiling modulus x - (ceilDiv(x, y) * y) Throws: ArithmeticException - if the divisor y is zero Since: 18 See Also:The ceiling modulus is r = x - (ceilDiv(x, y) * y), has the opposite sign as the divisor y or is zero, and is in the range of -abs(y) < r < +abs(y).
The relationship between ceilDiv and ceilMod is such that:
- ceilDiv(x, y) * y + ceilMod(x, y) == x
The difference in values between ceilMod and the % operator is due to the difference between ceilDiv and the / operator, as detailed in ceilDiv(int, int).
Examples:
- Regardless of the signs of the arguments, ceilMod(x, y) is zero exactly when x % y is zero as well.
- If neither ceilMod(x, y) nor x % y is zero,
they differ exactly when the signs of the arguments are the same.
- ceilMod(+4, +3) == -2; and (+4 % +3) == +1
- ceilMod(-4, -3) == +2; and (-4 % -3) == -1
- ceilMod(+4, -3) == +1; and (+4 % -3) == +1
- ceilMod(-4, +3) == -1; and (-4 % +3) == -1
-
ceilMod
public static int ceilMod(long x, int y)Returns the ceiling modulus of the long and int arguments.Parameters: x - the dividend y - the divisor Returns: the ceiling modulus x - (ceilDiv(x, y) * y) Throws: ArithmeticException - if the divisor y is zero Since: 18 See Also:The ceiling modulus is r = x - (ceilDiv(x, y) * y), has the opposite sign as the divisor y or is zero, and is in the range of -abs(y) < r < +abs(y).
The relationship between ceilDiv and ceilMod is such that:
- ceilDiv(x, y) * y + ceilMod(x, y) == x
For examples, see ceilMod(int, int).
-
ceilMod
public static long ceilMod(long x, long y)Returns the ceiling modulus of the long arguments.Parameters: x - the dividend y - the divisor Returns: the ceiling modulus x - (ceilDiv(x, y) * y) Throws: ArithmeticException - if the divisor y is zero Since: 18 See Also:The ceiling modulus is r = x - (ceilDiv(x, y) * y), has the opposite sign as the divisor y or is zero, and is in the range of -abs(y) < r < +abs(y).
The relationship between ceilDiv and ceilMod is such that:
- ceilDiv(x, y) * y + ceilMod(x, y) == x
For examples, see ceilMod(int, int).
-
abs
public static int abs(int a)Returns the absolute value of an int value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.Parameters: a - the argument whose absolute value is to be determined Returns: the absolute value of the argument. See Also:Note that if the argument is equal to the value of Integer.MIN_VALUE, the most negative representable int value, the result is that same value, which is negative. In contrast, the absExact(int) method throws an ArithmeticException for this value.
-
absExact
public static int absExact(int a)Returns the mathematical absolute value of an int value if it is exactly representable as an int, throwing ArithmeticException if the result overflows the positive int range.Parameters: a - the argument whose absolute value is to be determined Returns: the absolute value of the argument, unless overflow occurs Throws: ArithmeticException - if the argument is Integer.MIN_VALUE Since: 15 See Also:Since the range of two's complement integers is asymmetric with one additional negative value (JLS 4.2.1), the mathematical absolute value of Integer.MIN_VALUE overflows the positive int range, so an exception is thrown for that argument.
-
abs
public static long abs(long a)Returns the absolute value of a long value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.Parameters: a - the argument whose absolute value is to be determined Returns: the absolute value of the argument. See Also:Note that if the argument is equal to the value of Long.MIN_VALUE, the most negative representable long value, the result is that same value, which is negative. In contrast, the absExact(long) method throws an ArithmeticException for this value.
-
absExact
public static long absExact(long a)Returns the mathematical absolute value of an long value if it is exactly representable as an long, throwing ArithmeticException if the result overflows the positive long range.Parameters: a - the argument whose absolute value is to be determined Returns: the absolute value of the argument, unless overflow occurs Throws: ArithmeticException - if the argument is Long.MIN_VALUE Since: 15 See Also:Since the range of two's complement integers is asymmetric with one additional negative value (JLS 4.2.1), the mathematical absolute value of Long.MIN_VALUE overflows the positive long range, so an exception is thrown for that argument.
-
abs
public static float abs(float a)Returns the absolute value of a 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:API Note: As implied by the above, one valid implementation of this method is given by the expression below which computes a float with the same exponent and significand as the argument but with a guaranteed zero sign bit indicating a positive value:- 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.
Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a)) Parameters: a - the argument whose absolute value is to be determined Returns: the absolute value of the argument. -
abs
public static double abs(double a)Returns the absolute value of a 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:API Note: As implied by the above, one valid implementation of this method is given by the expression below which computes a double with the same exponent and significand as the argument but with a guaranteed zero sign bit indicating a positive value:- 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.
Double.longBitsToDouble((Double.doubleToRawLongBits(a)<<1)>>>1) Parameters: a - the argument whose absolute value is to be determined Returns: the absolute value of the argument. -
max
public static int max(int a, int b)Returns the greater of two int values. That is, the result is the argument closer to the value of Integer.MAX_VALUE. If the arguments have the same value, the result is that same value.Parameters: a - an argument. b - another argument. Returns: the larger of a and b. -
max
public static long max(long a, long b)Returns the greater of two long values. That is, the result is the argument closer to the value of Long.MAX_VALUE. If the arguments have the same value, the result is that same value.Parameters: a - an argument. b - another argument. Returns: the larger of a and b. -
max
public static float max(float a, float b)Returns the greater of two 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.API Note: This method corresponds to the maximum operation defined in IEEE 754. Parameters: a - an argument. b - another argument. Returns: the larger of a and b. -
max
public static double max(double a, double b)Returns the greater of two 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.API Note: This method corresponds to the maximum operation defined in IEEE 754. Parameters: a - an argument. b - another argument. Returns: the larger of a and b. -
min
public static int min(int a, int b)Returns the smaller of two int values. That is, the result the argument closer to the value of Integer.MIN_VALUE. If the arguments have the same value, the result is that same value.Parameters: a - an argument. b - another argument. Returns: the smaller of a and b. -
min
public static long min(long a, long b)Returns the smaller of two long values. That is, the result is the argument closer to the value of Long.MIN_VALUE. If the arguments have the same value, the result is that same value.Parameters: a - an argument. b - another argument. Returns: the smaller of a and b. -
min
public static float min(float a, float b)Returns the smaller of two 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.API Note: This method corresponds to the minimum operation defined in IEEE 754. Parameters: a - an argument. b - another argument. Returns: the smaller of a and b. -
min
public static double min(double a, double b)Returns the smaller of two 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.API Note: This method corresponds to the minimum operation defined in IEEE 754. Parameters: a - an argument. b - another argument. Returns: the smaller of a and b. -
clamp
public static int clamp(long value, int min, int max)Clamps the value to fit between min and max. If the value is less than min, then min is returned. If the value is greater than max, then max is returned. Otherwise, the original value is returned.Parameters: value - value to clamp min - minimal allowed value max - maximal allowed value Returns: a clamped value that fits into min..max interval Throws: IllegalArgumentException - if min > max Since: 21While the original value of type long may not fit into the int type, the bounds have the int type, so the result always fits the int type. This allows to use method to safely cast long value to int with saturation.
-
clamp
public static long clamp(long value, long min, long max)Clamps the value to fit between min and max. If the value is less than min, then min is returned. If the value is greater than max, then max is returned. Otherwise, the original value is returned.Parameters: value - value to clamp min - minimal allowed value max - maximal allowed value Returns: a clamped value that fits into min..max interval Throws: IllegalArgumentException - if min > max Since: 21 -
clamp
public static double clamp(double value, double min, double max)Clamps the value to fit between min and max. If the value is less than min, then min is returned. If the value is greater than max, then max is returned. Otherwise, the original value is returned. If value is NaN, the result is also NaN.Parameters: value - value to clamp min - minimal allowed value max - maximal allowed value Returns: a clamped value that fits into min..max interval Throws: IllegalArgumentException - if either of min and max arguments is NaN, or min > max, or min is +0.0, and max is -0.0. Since: 21Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. E.g., clamp(-0.0, 0.0, 1.0) returns 0.0.
-
clamp
public static float clamp(float value, float min, float max)Clamps the value to fit between min and max. If the value is less than min, then min is returned. If the value is greater than max, then max is returned. Otherwise, the original value is returned. If value is NaN, the result is also NaN.Parameters: value - value to clamp min - minimal allowed value max - maximal allowed value Returns: a clamped value that fits into min..max interval Throws: IllegalArgumentException - if either of min and max arguments is NaN, or min > max, or min is +0.0f, and max is -0.0f. Since: 21Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. E.g., clamp(-0.0f, 0.0f, 1.0f) returns 0.0f.
-
fma
public static double fma(double a, double b, double c)Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest double. The rounding is done using the round to nearest even rounding mode. In contrast, if a * b + c is evaluated as a regular floating-point expression, two rounding errors are involved, the first for the multiply operation, the second for the addition operation.API Note: This method corresponds to the fusedMultiplyAdd operation defined in IEEE 754. Parameters: a - a value b - a value c - a value Returns: (a × b + c) computed, as if with unlimited range and precision, and rounded once to the nearest double value Since: 9Special cases:
- If any argument is NaN, the result is NaN.
- If one of the first two arguments is infinite and the other is zero, the result is NaN.
- If the exact product of the first two arguments is infinite (in other words, at least one of the arguments is infinite and the other is neither zero nor NaN) and the third argument is an infinity of the opposite sign, the result is NaN.
Note that fma(a, 1.0, c) returns the same result as (a + c). However, fma(a, b, +0.0) does not always return the same result as (a * b) since fma(-0.0, +0.0, +0.0) is +0.0 while (-0.0 * +0.0) is -0.0; fma(a, b, -0.0) is equivalent to (a * b) however.
-
fma
public static float fma(float a, float b, float c)Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest float. The rounding is done using the round to nearest even rounding mode. In contrast, if a * b + c is evaluated as a regular floating-point expression, two rounding errors are involved, the first for the multiply operation, the second for the addition operation.API Note: This method corresponds to the fusedMultiplyAdd operation defined in IEEE 754. Parameters: a - a value b - a value c - a value Returns: (a × b + c) computed, as if with unlimited range and precision, and rounded once to the nearest float value Since: 9Special cases:
- If any argument is NaN, the result is NaN.
- If one of the first two arguments is infinite and the other is zero, the result is NaN.
- If the exact product of the first two arguments is infinite (in other words, at least one of the arguments is infinite and the other is neither zero nor NaN) and the third argument is an infinity of the opposite sign, the result is NaN.
Note that fma(a, 1.0f, c) returns the same result as (a + c). However, fma(a, b, +0.0f) does not always return the same result as (a * b) since fma(-0.0f, +0.0f, +0.0f) is +0.0f while (-0.0f * +0.0f) is -0.0f; fma(a, b, -0.0f) is equivalent to (a * b) however.
-
ulp
public static double ulp(double d)Returns the size of an ulp of the argument. An ulp, unit in the last place, of a double value is the positive distance between this floating-point value and the double value next larger in magnitude. Note that for non-NaN x, ulp(-x) == ulp(x).Parameters: d - the floating-point value whose ulp is to be returned Returns: the size of an ulp of the argument Since: 1.5Special 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 Double.MIN_VALUE.
- If the argument is ±Double.MAX_VALUE, then the result is equal to 2971.
-
ulp
public static float ulp(float f)Returns the size of an ulp of the argument. An ulp, unit in the last place, of a float value is the positive distance between this floating-point value and the float value next larger in magnitude. Note that for non-NaN x, ulp(-x) == ulp(x).Parameters: f - the floating-point value whose ulp is to be returned Returns: the size of an ulp of the argument Since: 1.5Special 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 Float.MIN_VALUE.
- If the argument is ±Float.MAX_VALUE, then the result is equal to 2104.
-
signum
public static double signum(double d)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.Parameters: d - the floating-point value whose signum is to be returned Returns: the signum function of the argument Since: 1.5Special 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.
-
signum
public static float signum(float f)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.Parameters: f - the floating-point value whose signum is to be returned Returns: the signum function of the argument Since: 1.5Special 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.
-
sinh
public static double sinh(double x)Returns the hyperbolic sine of a double value. The hyperbolic sine of x is defined to be (ex − e−x)/2 where e is Euler's number.Parameters: x - The number whose hyperbolic sine is to be returned. Returns: The hyperbolic sine of x. Since: 1.5Special 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.
-
cosh
public static double cosh(double x)Returns the hyperbolic cosine of a double value. The hyperbolic cosine of x is defined to be (ex + e−x)/2 where e is Euler's number.Parameters: x - The number whose hyperbolic cosine is to be returned. Returns: The hyperbolic cosine of x. Since: 1.5Special 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 1.0.
The computed result must be within 2.5 ulps of the exact result.
-
tanh
public static double tanh(double x)Returns the hyperbolic tangent of a double value. The hyperbolic tangent of x is defined to be (ex − e−x)/(ex + e−x), in other words, sinh(x)/cosh(x). Note that the absolute value of the exact tanh is always less than 1.Parameters: x - The number whose hyperbolic tangent is to be returned. Returns: The hyperbolic tangent of x. Since: 1.5Special 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 +1.0.
- If the argument is negative infinity, then the result is -1.0.
The computed result must be within 2.5 ulps of the exact result. The result of 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 ±1.0 should be returned.
-
hypot
public static double hypot(double x, double y)Returns sqrt(x2 +y2) without intermediate overflow or underflow.Parameters: x - a value y - a value Returns: sqrt(x2 +y2) without intermediate overflow or underflow Since: 1.5Special 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.
- If both arguments are zero, the result is positive zero.
The computed result must be within 1.5 ulps of the exact result. If one parameter is held constant, the results must be semi-monotonic in the other parameter.
-
expm1
public static double expm1(double x)Returns ex −1. Note that for values of x near 0, the exact sum of expm1(x) + 1 is much closer to the true result of ex than exp(x).Parameters: x - the exponent to raise e to in the computation of ex −1. Returns: the value ex - 1. Since: 1.5Special 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 expm1 for any finite input must be greater than or equal to -1.0. Note that once the exact result of ex - 1 is within 1/2 ulp of the limit value -1, -1.0 should be returned.
-
log1p
public static double log1p(double x)Returns the natural logarithm of the sum of the argument and 1. Note that for small values x, the result of log1p(x) is much closer to the true result of ln(1 + x) than the floating-point evaluation of log(1.0+x).Parameters: x - a value Returns: the value ln(x + 1), the natural log of x + 1 Since: 1.5Special 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.
-
copySign
public static double copySign(double magnitude, double sign)Returns the first floating-point argument with the sign of the second floating-point argument. Note that unlike the StrictMath.copySign method, this method does not require NaN 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.API Note: This method corresponds to the copySign operation defined in IEEE 754. Parameters: magnitude - the parameter providing the magnitude of the result sign - the parameter providing the sign of the result Returns: a value with the magnitude of magnitude and the sign of sign. Since: 1.6 -
copySign
public static float copySign(float magnitude, float sign)Returns the first floating-point argument with the sign of the second floating-point argument. Note that unlike the StrictMath.copySign method, this method does not require NaN 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.API Note: This method corresponds to the copySign operation defined in IEEE 754. Parameters: magnitude - the parameter providing the magnitude of the result sign - the parameter providing the sign of the result Returns: a value with the magnitude of magnitude and the sign of sign. Since: 1.6 -
getExponent
public static int getExponent(float f)Returns the unbiased exponent used in the representation of a float. Special cases:API Note: This method is analogous to the logB operation defined in IEEE 754, but returns a different value on subnormal arguments. Parameters: f - a float value Returns: the unbiased exponent of the argument Since: 1.6- If the argument is NaN or infinite, then the result is Float.MAX_EXPONENT + 1.
- If the argument is zero or subnormal, then the result is Float.MIN_EXPONENT - 1.
-
getExponent
public static int getExponent(double d)Returns the unbiased exponent used in the representation of a double. Special cases:API Note: This method is analogous to the logB operation defined in IEEE 754, but returns a different value on subnormal arguments. Parameters: d - a double value Returns: the unbiased exponent of the argument Since: 1.6- If the argument is NaN or infinite, then the result is Double.MAX_EXPONENT + 1.
- If the argument is zero or subnormal, then the result is Double.MIN_EXPONENT - 1.
-
nextAfter
public static double nextAfter(double start, double direction)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.Parameters: start - starting floating-point value direction - value indicating which of start's neighbors or start should be returned Returns: The floating-point number adjacent to start in the direction of direction. Since: 1.6Special cases:
- If either argument is a NaN, then NaN is returned.
- If both arguments are signed zeros, direction is returned unchanged (as implied by the requirement of returning the second argument if the arguments compare as equal).
- If start is ±Double.MIN_VALUE and direction has a value such that the result should have a smaller magnitude, then a zero with the same sign as start is returned.
- If start is infinite and direction has a value such that the result should have a smaller magnitude, Double.MAX_VALUE with the same sign as start is returned.
- If start is equal to ± Double.MAX_VALUE and direction has a value such that the result should have a larger magnitude, an infinity with same sign as start is returned.
-
nextAfter
public static float nextAfter(float start, double direction)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.Parameters: start - starting floating-point value direction - value indicating which of start's neighbors or start should be returned Returns: The floating-point number adjacent to start in the direction of direction. Since: 1.6Special cases:
- If either argument is a NaN, then NaN is returned.
- If both arguments are signed zeros, a value equivalent to direction is returned.
- If start is ±Float.MIN_VALUE and direction has a value such that the result should have a smaller magnitude, then a zero with the same sign as start is returned.
- If start is infinite and direction has a value such that the result should have a smaller magnitude, Float.MAX_VALUE with the same sign as start is returned.
- If start is equal to ± Float.MAX_VALUE and direction has a value such that the result should have a larger magnitude, an infinity with same sign as start is returned.
-
nextUp
public static double nextUp(double d)Returns the floating-point value adjacent to d in the direction of positive infinity. This method is semantically equivalent to nextAfter(d, Double.POSITIVE_INFINITY); however, a nextUp implementation may run faster than its equivalent nextAfter call.API Note: This method corresponds to the nextUp operation defined in IEEE 754. Parameters: d - starting floating-point value Returns: The adjacent floating-point value closer to positive infinity. Since: 1.6Special 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 Double.MIN_VALUE
-
nextUp
public static float nextUp(float f)Returns the floating-point value adjacent to f in the direction of positive infinity. This method is semantically equivalent to nextAfter(f, Float.POSITIVE_INFINITY); however, a nextUp implementation may run faster than its equivalent nextAfter call.API Note: This method corresponds to the nextUp operation defined in IEEE 754. Parameters: f - starting floating-point value Returns: The adjacent floating-point value closer to positive infinity. Since: 1.6Special 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 Float.MIN_VALUE
-
nextDown
public static double nextDown(double d)Returns the floating-point value adjacent to d in the direction of negative infinity. This method is semantically equivalent to nextAfter(d, Double.NEGATIVE_INFINITY); however, a nextDown implementation may run faster than its equivalent nextAfter call.API Note: This method corresponds to the nextDown operation defined in IEEE 754. Parameters: d - starting floating-point value Returns: The adjacent floating-point value closer to negative infinity. Since: 1.8Special 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 -Double.MIN_VALUE
-
nextDown
public static float nextDown(float f)Returns the floating-point value adjacent to f in the direction of negative infinity. This method is semantically equivalent to nextAfter(f, Float.NEGATIVE_INFINITY); however, a nextDown implementation may run faster than its equivalent nextAfter call.API Note: This method corresponds to the nextDown operation defined in IEEE 754. Parameters: f - starting floating-point value Returns: The adjacent floating-point value closer to negative infinity. Since: 1.8Special 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 -Float.MIN_VALUE
-
scalb
public static double scalb(double d, int scaleFactor)Returns d × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply. If the exponent of the result is between Double.MIN_EXPONENT and Double.MAX_EXPONENT, the answer is calculated exactly. If the exponent of the result would be larger than Double.MAX_EXPONENT, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when scalb(x, n) is subnormal, scalb(scalb(x, n), -n) may not equal x. When the result is non-NaN, the result has the same sign as d.API Note: This method corresponds to the scaleB operation defined in IEEE 754. Parameters: d - number to be scaled by a power of two. scaleFactor - power of 2 used to scale d Returns: d × 2scaleFactor Since: 1.6Special 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.
-
scalb
public static float scalb(float f, int scaleFactor)Returns f × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply. If the exponent of the result is between Float.MIN_EXPONENT and Float.MAX_EXPONENT, the answer is calculated exactly. If the exponent of the result would be larger than Float.MAX_EXPONENT, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when scalb(x, n) is subnormal, scalb(scalb(x, n), -n) may not equal x. When the result is non-NaN, the result has the same sign as f.API Note: This method corresponds to the scaleB operation defined in IEEE 754. Parameters: f - number to be scaled by a power of two. scaleFactor - power of 2 used to scale f Returns: f × 2scaleFactor Since: 1.6Special 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.
-
unsignedMultiplyExact
public static int unsignedMultiplyExact(int x, int y)Returns the product of the unsigned arguments, throwing an exception if the result overflows an unsigned int.Parameters: x - the first unsigned value y - the second unsigned value Returns: the result Throws: ArithmeticException - if the result overflows an unsigned int Since: 25 -
unsignedMultiplyExact
public static long unsignedMultiplyExact(long x, int y)Returns the product of the unsigned arguments, throwing an exception if the result overflows an unsigned long.Parameters: x - the first unsigned value y - the second unsigned value Returns: the result Throws: ArithmeticException - if the result overflows an unsigned long Since: 25 -
unsignedMultiplyExact
public static long unsignedMultiplyExact(long x, long y)Returns the product of the unsigned arguments, throwing an exception if the result overflows an unsigned long.Parameters: x - the first unsigned value y - the second unsigned value Returns: the result Throws: ArithmeticException - if the result overflows an unsigned long Since: 25 -
powExact
public static int powExact(int x, int n)Returns x raised to the power of n, throwing an exception if the result overflows an int. When n is 0, the returned value is 1.Parameters: x - the base. n - the exponent. Returns: x raised to the power of n. Throws: ArithmeticException - when n is negative, or when the result overflows an int. Since: 25 -
unsignedPowExact
public static int unsignedPowExact(int x, int n)Returns unsigned x raised to the power of n, throwing an exception if the result overflows an unsigned int. When n is 0, the returned value is 1.Parameters: x - the unsigned base. n - the exponent. Returns: x raised to the power of n. Throws: ArithmeticException - when n is negative, or when the result overflows an unsigned int. Since: 25 -
powExact
public static long powExact(long x, int n)Returns x raised to the power of n, throwing an exception if the result overflows a long. When n is 0, the returned value is 1.Parameters: x - the base. n - the exponent. Returns: x raised to the power of n. Throws: ArithmeticException - when n is negative, or when the result overflows a long. Since: 25 -
unsignedPowExact
public static long unsignedPowExact(long x, int n)Returns unsigned x raised to the power of n, throwing an exception if the result overflows an unsigned long. When n is 0, the returned value is 1.Parameters: x - the unsigned base. n - the exponent. Returns: x raised to the power of n. Throws: ArithmeticException - when n is negative, or when the result overflows an unsigned long. Since: 25
-
Report a bug or suggest an enhancement
For further API reference and developer documentation see the Java SE Documentation, which contains more detailed, developer-targeted descriptions with conceptual overviews, definitions of terms, workarounds, and working code examples. Other versions.
Java is a trademark or registered trademark of Oracle and/or its affiliates in the US and other countries.
Copyright © 1993, 2026, Oracle and/or its affiliates, 500 Oracle Parkway, Redwood Shores, CA 94065 USA.
All rights reserved. Use is subject to license terms and the documentation redistribution policy.