Field Summary

Method Summary

Field Details

• E

  public static final double E

  Thedouble value that is closer than any other toe, the base of the natural logarithms.

  See Also:

  • Constant Field Values

• PI

  public static final double PI

  Thedouble value that is closer than any other topi (π), the ratio of the circumference of a circle to its diameter.

  See Also:

  • Constant Field Values

• TAU

  public static final double TAU

  Thedouble value that is closer than any other totau (τ), the ratio of the circumference of a circle to its radius.

  API Note:

  The value ofpi is one half that oftau; in other words,tau is doublepi .

  Since:

  19

  See Also:

  • Constant Field Values

Method Details

• sin

  public static double sin(double a)

  Returns the trigonometric sine of an angle. Special cases:

  • If the argument is NaN or an infinity, then the result is NaN.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

  The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

  Parameters:

  a - an angle, in radians.

  Returns:

  the sine of the argument.

• cos

  public static double cos(double a)

  Returns the trigonometric cosine of an angle. Special cases:

  • If the argument is NaN or an infinity, then the result is NaN.
  • If the argument is zero, then the result is1.0.

  The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

  Parameters:

  a - an angle, in radians.

  Returns:

  the cosine of the argument.

• tan

  public static double tan(double a)

  Returns the trigonometric tangent of an angle. Special cases:

  • If the argument is NaN or an infinity, then the result is NaN.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

  The computed result must be within 1.25 ulps of the exact result. Results must be semi-monotonic.

  Parameters:

  a - an angle, in radians.

  Returns:

  the tangent of the argument.

• asin

  public static double asin(double a)

  Returns the arc sine of a value; the returned angle is in the range −pi/2 throughpi/2. Special cases:

  • If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

  The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

  Parameters:

  a - the value whose arc sine is to be returned.

  Returns:

  the arc sine of the argument.

• acos

  public static double acos(double a)

  Returns the arc cosine of a value; the returned angle is in the range 0.0 throughpi. Special case:

  • If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
  • If the argument is1.0, the result is positive zero.

  The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

  Parameters:

  a - the value whose arc cosine is to be returned.

  Returns:

  the arc cosine of the argument.

• atan

  public static double atan(double a)

  Returns the arc tangent of a value; the returned angle is in the range −pi/2 throughpi/2. Special cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is zero, then the result is a zero with the same sign as the argument.
  • If the argument isinfinite, then the result is the closest value topi/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.

  Parameters:

  a - the value whose arc tangent is to be returned.

  Returns:

  the arc tangent of the argument.

• 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 angleangdeg 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 shouldnot expectcos(toRadians(90.0)) to exactly equal0.0.

  Parameters:

  angrad - an angle, in radians

  Returns:

  the measurement of the angleangrad in degrees.

  Since:

  1.2

• exp

  public static double exp(double a)

  Returns Euler's numbere raised to the power of adouble value. Special cases:

  • If the argument is NaN, the result is NaN.
  • If the argument is positive infinity, then the result is positive infinity.
  • If the argument is negative infinity, then the result is positive zero.
  • If the argument is zero, then the result is1.0.

  The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

  Parameters:

  a - the exponent to raisee to.

  Returns:

  the valuee^a, wheree is the base of the natural logarithms.

• log

  public static double log(double a)

  Returns the natural logarithm (basee) of adouble value. Special cases:

  • If the argument is NaN or less than zero, then the result is NaN.
  • If the argument is positive infinity, then the result is positive infinity.
  • If the argument is positive zero or negative zero, then the result is negative infinity.
  • If the argument is1.0, then the result is positive zero.

  The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

  Parameters:

  a - a value

  Returns:

  the value ln a, the natural logarithm ofa.

• log10

  public static double log10(double a)

  Returns the base 10 logarithm of adouble value. Special cases:

  • If the argument is NaN or less than zero, then the result is NaN.
  • If the argument is positive infinity, then the result is positive infinity.
  • If the argument is positive zero or negative zero, then the result is negative infinity.
  • If the argument is equal to 10ⁿ for integern, then the result isn. In particular, if the argument is1.0 (10⁰), then the result is positive zero.

  The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

  Parameters:

  a - a value

  Returns:

  the base 10 logarithm ofa.

  Since:

  1.5

• sqrt

  public static double sqrt(double a)

  Returns the correctly rounded positive square root of adouble value. Special cases:

  • If the argument is NaN or less than zero, then the result is NaN.
  • If the argument is positive infinity, then the result is positive infinity.
  • If the argument is positive zero or negative zero, then the result is the same as the argument.

  Otherwise, the result is thedouble value closest to the true mathematical square root of the argument value.

  API Note:

  This method corresponds to the squareRoot operation defined in IEEE 754.

  Parameters:

  a - a value.

  Returns:

  the positive square root ofa. If the argument is NaN or less than zero, the result is NaN.

• cbrt

  public static double cbrt(double a)

  Returns the cube root of adouble value. For positive finitex,cbrt(-x) == -cbrt(x); that is, the cube root of a negative value is the negative of the cube root of that value's magnitude. Special cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is infinite, then the result is an infinity with the same sign as the argument.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

  The computed result must be within 1 ulp of the exact result.

  Parameters:

  a - a value.

  Returns:

  the cube root ofa.

  Since:

  1.5

• 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 tof1 - f2 × n, wheren is the mathematical integer closest to the exact mathematical value of the quotientf1/f2, and if two mathematical integers are equally close tof1/f2, thenn is the integer that is even. If the remainder is zero, its sign is the same as the sign of the first argument. Special cases:

  • If either argument is NaN, or the first argument is infinite, or the second argument is positive zero or negative zero, then the result is NaN.
  • If the first argument is finite and the second argument is infinite, then the result is the same as the first argument.

  Parameters:

  f1 - the dividend.

  f2 - the divisor.

  Returns:

  the remainder whenf1 is divided byf2.

• 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:

  • If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
  • If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
  • If the argument value is less than zero but greater than -1.0, then the result is negative zero.

  Note that the value ofMath.ceil(x) is exactly the value of-Math.floor(-x).

  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.

• 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:

  • 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.

  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.

• rint

  public static double rint(double a)

  Returns thedouble value that is closest in value to the argument and is equal to a mathematical integer. If twodouble values that are mathematical integers are equally close, the result is the integer value that is even. Special cases:

  • If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
  • If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.

  API Note:

  This method corresponds to the roundToIntegralTiesToEven operation defined in IEEE 754.

  Parameters:

  a - adouble value.

  Returns:

  the closest floating-point value toa that is equal to a mathematical integer.

• atan2

  public static double atan2(double y, double x)

  Returns the angletheta from the conversion of rectangular coordinates (x, y) to polar coordinates (r, theta). This method computes the phasetheta by computing an arc tangent ofy/x in the range of −pi topi. Special cases:

  • If either argument is NaN, then the result is NaN.
  • If the first argument is positive zero and the second argument is positive, or the first argument is positive and finite and the second argument is positive infinity, then the result is positive zero.
  • If the first argument is negative zero and the second argument is positive, or the first argument is negative and finite and the second argument is positive infinity, then the result is negative zero.
  • If the first argument is positive zero and the second argument is negative, or the first argument is positive and finite and the second argument is negative infinity, then the result is thedouble value closest topi.
  • 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 thedouble 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 thedouble value closest topi/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 thedouble value closest to -pi/2.
  • If both arguments are positive infinity, then the result is thedouble value closest topi/4.
  • If the first argument is positive infinity and the second argument is negative infinity, then the result is thedouble value closest to 3*pi/4.
  • If the first argument is negative infinity and the second argument is positive infinity, then the result is thedouble value closest to -pi/4.
  • If both arguments are negative infinity, then the result is thedouble value closest to -3*pi/4.

  The computed result must be within 2 ulps of the exact result. Results must be semi-monotonic.

  API Note:

  Fory with a positive sign and finite nonzerox, the exact mathematical value ofatan2 is equal to:

  • Ifx > 0, atan(abs(y/x))
  • Ifx < 0, π - atan(abs(y/x))

  Parameters:

  y - the ordinate coordinate

  x - the abscissa coordinate

  Returns:

  thetheta component of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates.

• 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:

  • If the second argument is positive or negative zero, then the result is 1.0.
  • If the second argument is 1.0, then the result is the same as the first argument.
  • If the second argument is NaN, then the result is NaN.
  • If the first argument is NaN and the second argument is nonzero, then the result is NaN.
  • If
    • the absolute value of the first argument is greater than 1 and the second argument is positive infinity, or
    • the absolute value of the first argument is less than 1 and the second argument is negative infinity,
    then the result is positive infinity.
  • If
    • the absolute value of the first argument is greater than 1 and the second argument is negative infinity, or
    • the absolute value of the first argument is less than 1 and the second argument is positive infinity,
    then the result is positive zero.
  • If the absolute value of the first argument equals 1 and the second argument is infinite, then the result is NaN.
  • If
    • the first argument is positive zero and the second argument is greater than zero, or
    • the first argument is positive infinity and the second argument is less than zero,
    then the result is positive zero.
  • If
    • the first argument is positive zero and the second argument is less than zero, or
    • the first argument is positive infinity and the second argument is greater than zero,
    then the result is positive infinity.
  • If
    • the first argument is negative zero and the second argument is greater than zero but not a finite odd integer, or
    • the first argument is negative infinity and the second argument is less than zero but not a finite odd integer,
    then the result is positive zero.
  • If
    • the first argument is negative zero and the second argument is a positive finite odd integer, or
    • the first argument is negative infinity and the second argument is a negative finite odd integer,
    then the result is negative zero.
  • If
    • the first argument is negative zero and the second argument is less than zero but not a finite odd integer, or
    • the first argument is negative infinity and the second argument is greater than zero but not a finite odd integer,
    then the result is positive infinity.
  • If
    • the first argument is negative zero and the second argument is a negative finite odd integer, or
    • the first argument is negative infinity and the second argument is a positive finite odd integer,
    then the result is negative infinity.
  • If the first argument is finite and less than zero
    • if the second argument is a finite even integer, the result is equal to the result of raising the absolute value of the first argument to the power of the second argument
    • if the second argument is a finite odd integer, the result is equal to the negative of the result of raising the absolute value of the first argument to the power of the second argument
    • if the second argument is finite and not an integer, then the result is NaN.
  • If both arguments are integers, then the result is exactly equal to the mathematical result of raising the first argument to the power of the second argument if that result can in fact be represented exactly as adouble 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 methodceil or, equivalently, a fixed point of the methodfloor. 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.

  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 specifies1.0 be returned.

  Parameters:

  a - the base.

  b - the exponent.

  Returns:

  the valueab.

• round

  public static int round(float a)

  Returns the closestint to the argument, with ties rounding to positive infinity.

  Special cases:

  • If the argument is NaN, the result is 0.
  • If the argument is negative infinity or any value less than or equal to the value ofInteger.MIN_VALUE, the result is equal to the value ofInteger.MIN_VALUE.
  • If the argument is positive infinity or any value greater than or equal to the value ofInteger.MAX_VALUE, the result is equal to the value ofInteger.MAX_VALUE.

  Parameters:

  a - a floating-point value to be rounded to an integer.

  Returns:

  the value of the argument rounded to the nearestint value.

  See Also:

  • Integer.MAX_VALUE
  • Integer.MIN_VALUE

• round

  public static long round(double a)

  Returns the closestlong to the argument, with ties rounding to positive infinity.

  Special cases:

  • If the argument is NaN, the result is 0.
  • If the argument is negative infinity or any value less than or equal to the value ofLong.MIN_VALUE, the result is equal to the value ofLong.MIN_VALUE.
  • If the argument is positive infinity or any value greater than or equal to the value ofLong.MAX_VALUE, the result is equal to the value ofLong.MAX_VALUE.

  Parameters:

  a - a floating-point value to be rounded to along.

  Returns:

  the value of the argument rounded to the nearestlong value.

  See Also:

  • Long.MAX_VALUE
  • Long.MIN_VALUE

• random

  public static double random()

  Returns adouble value with a positive sign, greater than or equal to0.0 and less than1.0. Returned values are chosen pseudorandomly with (approximately) uniform distribution from that range.

  When this method is first called, it creates a single new pseudorandom-number generator, exactly as if by the expression

  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.

  API Note:

  As the largestdouble value less than1.0 isMath.nextDown(1.0), a valuex in the closed range[x1,x2] wherex1<=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 pseudorandomdouble greater than or equal to0.0 and less than1.0.

  See Also:

  • nextDown(double)
  • Random.nextDouble()

• addExact

  public static int addExact(int x, int y)

  Returns the sum of its arguments, throwing an exception if the result overflows anint.

  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 along.

  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 anint.

  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 along.

  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 anint.

  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 along.

  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 along.

  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 anint. Such overflow occurs in this method ifx isInteger.MIN_VALUE andy is-1. In contrast, ifInteger.MIN_VALUE / -1 were evaluated directly, the result would beInteger.MIN_VALUE and no exception would be thrown.

  Ify is zero, anArithmeticException is thrown (JLS15.17.2).

  The built-in remainder operator "%" is a suitable counterpart both for this method and for the built-in division operator "/".

  Parameters:

  x - the dividend

  y - the divisor

  Returns:

  the quotientx / y

  Throws:

  ArithmeticException - ify is zero or the quotient overflows an int

  SeeJava Language Specification:

  15.17.2 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 along. Such overflow occurs in this method ifx isLong.MIN_VALUE andy is-1. In contrast, ifLong.MIN_VALUE / -1 were evaluated directly, the result would beLong.MIN_VALUE and no exception would be thrown.

  Ify is zero, anArithmeticException is thrown (JLS15.17.2).

  The built-in remainder operator "%" is a suitable counterpart both for this method and for the built-in division operator "/".

  Parameters:

  x - the dividend

  y - the divisor

  Returns:

  the quotientx / y

  Throws:

  ArithmeticException - ify is zero or the quotient overflows a long

  SeeJava Language Specification:

  15.17.2 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 tofloorDiv(int,int) except that it throws anArithmeticException when the dividend isInteger.MIN_VALUE and the divisor is-1 instead of ignoring the integer overflow and returningInteger.MIN_VALUE.

  The floor modulus methodfloorMod(int,int) is a suitable counterpart both for this method and for thefloorDiv(int,int) method.

  For examples, seefloorDiv(int, int).

  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 divisory is zero, or the dividendx isInteger.MIN_VALUE and the divisory is-1.

  Since:

  18

  See Also:

  • 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 tofloorDiv(long,long) except that it throws anArithmeticException when the dividend isLong.MIN_VALUE and the divisor is-1 instead of ignoring the integer overflow and returningLong.MIN_VALUE.

  The floor modulus methodfloorMod(long,long) is a suitable counterpart both for this method and for thefloorDiv(long,long) method.

  For examples, seefloorDiv(int, int).

  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 divisory is zero, or the dividendx isLong.MIN_VALUE and the divisory is-1.

  Since:

  18

  See Also:

  • floorDiv(long,long)

• 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 toceilDiv(int,int) except that it throws anArithmeticException when the dividend isInteger.MIN_VALUE and the divisor is-1 instead of ignoring the integer overflow and returningInteger.MIN_VALUE.

  The ceil modulus methodceilMod(int,int) is a suitable counterpart both for this method and for theceilDiv(int,int) method.

  For examples, seeceilDiv(int, int).

  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 divisory is zero, or the dividendx isInteger.MIN_VALUE and the divisory is-1.

  Since:

  18

  See Also:

  • 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 toceilDiv(long,long) except that it throws anArithmeticException when the dividend isLong.MIN_VALUE and the divisor is-1 instead of ignoring the integer overflow and returningLong.MIN_VALUE.

  The ceil modulus methodceilMod(long,long) is a suitable counterpart both for this method and for theceilDiv(long,long) method.

  For examples, seeceilDiv(int, int).

  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 divisory is zero, or the dividendx isLong.MIN_VALUE and the divisory is-1.

  Since:

  18

  See Also:

  • ceilDiv(long,long)

• incrementExact

  public static int incrementExact(int a)

  Returns the argument incremented by one, throwing an exception if the result overflows anint. The overflow only occurs forthe 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 along. The overflow only occurs forthe 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 anint. The overflow only occurs forthe 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 along. The overflow only occurs forthe 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 anint. The overflow only occurs forthe 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 along. The overflow only occurs forthe 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 thelong argument, throwing an exception if the value overflows anint.

  Parameters:

  value - the long value

  Returns:

  the argument as an int

  Throws:

  ArithmeticException - if theargument 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 along 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(long, long)

• unsignedMultiplyHigh

  public static long unsignedMultiplyHigh(long x, long y)

  Returns as along 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:

  • multiplyHigh(long, long)

• 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 isInteger.MIN_VALUE and the divisor is-1, then integer overflow occurs and the result is equal toInteger.MIN_VALUE.

  Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results from truncation when the exact quotient is not an integer and is negative.

  • If the signs of the arguments are the same, the results offloorDiv 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.

  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 divisory is zero

  Since:

  1.8

  See Also:

  • floorMod(int, int)
  • floor(double)

• 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 isLong.MIN_VALUE and the divisor is-1, then integer overflow occurs and the result is equal toLong.MIN_VALUE.

  Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results from truncation when the exact result is not an integer and is negative.

  For examples, seefloorDiv(int, int).

  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 divisory is zero

  Since:

  9

  See Also:

  • floorMod(long, int)
  • floor(double)

• 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 isLong.MIN_VALUE and the divisor is-1, then integer overflow occurs and the result is equal toLong.MIN_VALUE.

  Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results from truncation when the exact result is not an integer and is negative.

  For examples, seefloorDiv(int, int).

  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 divisory is zero

  Since:

  1.8

  See Also:

  • floorMod(long, long)
  • floor(double)

• floorMod

  public static int floorMod(int x, int y)

  Returns the floor modulus of theint arguments.

  The floor modulus isr = x - (floorDiv(x, y) * y), has the same sign as the divisory or is zero, and is in the range of-abs(y) < r < +abs(y).

  The relationship betweenfloorDiv andfloorMod is such that:

  • floorDiv(x, y) * y + floorMod(x, y) == x

  The difference in values betweenfloorMod and the% operator is due to the difference betweenfloorDiv and the/ operator, as detailed infloorDiv(int, int).

  Examples:

  • Regardless of the signs of the arguments,floorMod(x, y) is zero exactly whenx % y is zero as well.
  • If neitherfloorMod(x, y) norx % 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

  Parameters:

  x - the dividend

  y - the divisor

  Returns:

  the floor modulusx - (floorDiv(x, y) * y)

  Throws:

  ArithmeticException - if the divisory is zero

  Since:

  1.8

  See Also:

  • floorDiv(int, int)

• floorMod

  public static int floorMod(long x, int y)

  Returns the floor modulus of thelong andint arguments.

  The floor modulus isr = x - (floorDiv(x, y) * y), has the same sign as the divisory or is zero, and is in the range of-abs(y) < r < +abs(y).

  The relationship betweenfloorDiv andfloorMod is such that:

  • floorDiv(x, y) * y + floorMod(x, y) == x

  For examples, seefloorMod(int, int).

  Parameters:

  x - the dividend

  y - the divisor

  Returns:

  the floor modulusx - (floorDiv(x, y) * y)

  Throws:

  ArithmeticException - if the divisory is zero

  Since:

  9

  See Also:

  • floorDiv(long, int)

• floorMod

  public static long floorMod(long x, long y)

  Returns the floor modulus of thelong arguments.

  The floor modulus isr = x - (floorDiv(x, y) * y), has the same sign as the divisory or is zero, and is in the range of-abs(y) < r < +abs(y).

  The relationship betweenfloorDiv andfloorMod is such that:

  • floorDiv(x, y) * y + floorMod(x, y) == x

  For examples, seefloorMod(int, int).

  Parameters:

  x - the dividend

  y - the divisor

  Returns:

  the floor modulusx - (floorDiv(x, y) * y)

  Throws:

  ArithmeticException - if the divisory is zero

  Since:

  1.8

  See Also:

  • floorDiv(long, long)

• 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 isInteger.MIN_VALUE and the divisor is-1, then integer overflow occurs and the result is equal toInteger.MIN_VALUE.

  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 ofceilDiv 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.

  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 divisory is zero

  Since:

  18

  See Also:

  • ceilMod(int, int)
  • ceil(double)

• 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 isLong.MIN_VALUE and the divisor is-1, then integer overflow occurs and the result is equal toLong.MIN_VALUE.

  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, seeceilDiv(int, int).

  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 divisory is zero

  Since:

  18

  See Also:

  • ceilMod(int, int)
  • ceil(double)

• 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 isLong.MIN_VALUE and the divisor is-1, then integer overflow occurs and the result is equal toLong.MIN_VALUE.

  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, seeceilDiv(int, int).

  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 divisory is zero

  Since:

  18

  See Also:

  • ceilMod(int, int)
  • ceil(double)

• ceilMod

  public static int ceilMod(int x, int y)

  Returns the ceiling modulus of theint arguments.

  The ceiling modulus isr = x - (ceilDiv(x, y) * y), has the opposite sign as the divisory or is zero, and is in the range of-abs(y) < r < +abs(y).

  The relationship betweenceilDiv andceilMod is such that:

  • ceilDiv(x, y) * y + ceilMod(x, y) == x

  The difference in values betweenceilMod and the% operator is due to the difference betweenceilDiv and the/ operator, as detailed inceilDiv(int, int).

  Examples:

  • Regardless of the signs of the arguments,ceilMod(x, y) is zero exactly whenx % y is zero as well.
  • If neitherceilMod(x, y) norx % 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

  Parameters:

  x - the dividend

  y - the divisor

  Returns:

  the ceiling modulusx - (ceilDiv(x, y) * y)

  Throws:

  ArithmeticException - if the divisory is zero

  Since:

  18

  See Also:

  • ceilDiv(int, int)

• ceilMod

  public static int ceilMod(long x, int y)

  Returns the ceiling modulus of thelong andint arguments.

  The ceiling modulus isr = x - (ceilDiv(x, y) * y), has the opposite sign as the divisory or is zero, and is in the range of-abs(y) < r < +abs(y).

  The relationship betweenceilDiv andceilMod is such that:

  • ceilDiv(x, y) * y + ceilMod(x, y) == x

  For examples, seeceilMod(int, int).

  Parameters:

  x - the dividend

  y - the divisor

  Returns:

  the ceiling modulusx - (ceilDiv(x, y) * y)

  Throws:

  ArithmeticException - if the divisory is zero

  Since:

  18

  See Also:

  • ceilDiv(long, int)

• ceilMod

  public static long ceilMod(long x, long y)

  Returns the ceiling modulus of thelong arguments.

  The ceiling modulus isr = x - (ceilDiv(x, y) * y), has the opposite sign as the divisory or is zero, and is in the range of-abs(y) < r < +abs(y).

  The relationship betweenceilDiv andceilMod is such that:

  • ceilDiv(x, y) * y + ceilMod(x, y) == x

  For examples, seeceilMod(int, int).

  Parameters:

  x - the dividend

  y - the divisor

  Returns:

  the ceiling modulusx - (ceilDiv(x, y) * y)

  Throws:

  ArithmeticException - if the divisory is zero

  Since:

  18

  See Also:

  • ceilDiv(long, long)

• abs

  public static int abs(int a)

  Returns the absolute value of anint value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.

  Note that if the argument is equal to the value ofInteger.MIN_VALUE, the most negative representableint value, the result is that same value, which is negative. In contrast, theabsExact(int) method throws anArithmeticException for this value.

  Parameters:

  a - the argument whose absolute value is to be determined

  Returns:

  the absolute value of the argument.

  See Also:

  • absExact(int)

• absExact

  public static int absExact(int a)

  Returns the mathematical absolute value of anint value if it is exactly representable as anint, throwingArithmeticException if the result overflows the positiveint range.

  Since the range of two's complement integers is asymmetric with one additional negative value (JLS4.2.1), the mathematical absolute value ofInteger.MIN_VALUE overflows the positiveint range, so an exception is thrown for that argument.

  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 isInteger.MIN_VALUE

  Since:

  15

  See Also:

  • abs(int)

• abs

  public static long abs(long a)

  Returns the absolute value of along value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.

  Note that if the argument is equal to the value ofLong.MIN_VALUE, the most negative representablelong value, the result is that same value, which is negative. In contrast, theabsExact(long) method throws anArithmeticException for this value.

  Parameters:

  a - the argument whose absolute value is to be determined

  Returns:

  the absolute value of the argument.

  See Also:

  • absExact(long)

• absExact

  public static long absExact(long a)

  Returns the mathematical absolute value of anlong value if it is exactly representable as anlong, throwingArithmeticException if the result overflows the positivelong range.

  Since the range of two's complement integers is asymmetric with one additional negative value (JLS4.2.1), the mathematical absolute value ofLong.MIN_VALUE overflows the positivelong range, so an exception is thrown for that argument.

  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 isLong.MIN_VALUE

  Since:

  15

  See Also:

  • abs(long)

• abs

  public static float abs(float a)

  Returns the absolute value of afloat value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:

  • If the argument is positive zero or negative zero, the result is positive zero.
  • If the argument is infinite, the result is positive infinity.
  • If the argument is NaN, the result is NaN.

  API Note:

  As implied by the above, one valid implementation of this method is given by the expression below which computes afloat with the same exponent and significand as the argument but with a guaranteed zero sign bit indicating a positive value:
  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 adouble value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:

  • If the argument is positive zero or negative zero, the result is positive zero.
  • If the argument is infinite, the result is positive infinity.
  • If the argument is NaN, the result is NaN.

  API Note:

  As implied by the above, one valid implementation of this method is given by the expression below which computes adouble with the same exponent and significand as the argument but with a guaranteed zero sign bit indicating a positive value:
  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 twoint values. That is, the result is the argument closer to the value ofInteger.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 ofa andb.

• max

  public static long max(long a, long b)

  Returns the greater of twolong values. That is, the result is the argument closer to the value ofLong.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 ofa andb.

• max

  public static float max(float a, float b)

  Returns the greater of twofloat 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 ofa andb.

• max

  public static double max(double a, double b)

  Returns the greater of twodouble 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 ofa andb.

• min

  public static int min(int a, int b)

  Returns the smaller of twoint values. That is, the result the argument closer to the value ofInteger.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 ofa andb.

• min

  public static long min(long a, long b)

  Returns the smaller of twolong values. That is, the result is the argument closer to the value ofLong.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 ofa andb.

• min

  public static float min(float a, float b)

  Returns the smaller of twofloat 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 ofa andb.

• min

  public static double min(double a, double b)

  Returns the smaller of twodouble 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 ofa andb.

• 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 thanmin, thenmin is returned. If the value is greater thanmax, thenmax is returned. Otherwise, the original value is returned.

  While 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.

  Parameters:

  value - value to clamp

  min - minimal allowed value

  max - maximal allowed value

  Returns:

  a clamped value that fits intomin..max interval

  Throws:

  IllegalArgumentException - ifmin > max

  Since:

  21

• 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 thanmin, thenmin is returned. If the value is greater thanmax, thenmax 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 intomin..max interval

  Throws:

  IllegalArgumentException - ifmin > 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 thanmin, thenmin is returned. If the value is greater thanmax, thenmax is returned. Otherwise, the original value is returned. If value is NaN, the result is also NaN.

  Unlike 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.

  Parameters:

  value - value to clamp

  min - minimal allowed value

  max - maximal allowed value

  Returns:

  a clamped value that fits intomin..max interval

  Throws:

  IllegalArgumentException - if either ofmin andmax arguments is NaN, ormin > max, ormin is +0.0, andmax is -0.0.

  Since:

  21

• 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 thanmin, thenmin is returned. If the value is greater thanmax, thenmax is returned. Otherwise, the original value is returned. If value is NaN, the result is also NaN.

  Unlike 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.

  Parameters:

  value - value to clamp

  min - minimal allowed value

  max - maximal allowed value

  Returns:

  a clamped value that fits intomin..max interval

  Throws:

  IllegalArgumentException - if either ofmin andmax arguments is NaN, ormin > max, ormin is +0.0f, andmax is -0.0f.

  Since:

  21

• 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 nearestdouble. The rounding is done using theround to nearest even rounding mode. In contrast, ifa * 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.

  Special 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 thatfma(a, 1.0, c) returns the same result as (a + c). However,fma(a, b, +0.0) doesnot always return the same result as (a * b) sincefma(-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.

  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 nearestdouble value

  Since:

  9

• 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 nearestfloat. The rounding is done using theround to nearest even rounding mode. In contrast, ifa * 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.

  Special 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 thatfma(a, 1.0f, c) returns the same result as (a + c). However,fma(a, b, +0.0f) doesnot always return the same result as (a * b) sincefma(-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.

  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 nearestfloat value

  Since:

  9

• ulp

  public static double ulp(double d)

  Returns the size of an ulp of the argument. An ulp, unit in the last place, of adouble value is the positive distance between this floating-point value and the double value next larger in magnitude. Note that for non-NaNx,ulp(-x) == ulp(x).

  Special Cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is positive or negative infinity, then the result is positive infinity.
  • If the argument is positive or negative zero, then the result isDouble.MIN_VALUE.
  • If the argument is ±Double.MAX_VALUE, then the result is equal to 2⁹⁷¹.

  Parameters:

  d - the floating-point value whose ulp is to be returned

  Returns:

  the size of an ulp of the argument

  Since:

  1.5

• ulp

  public static float ulp(float f)

  Returns the size of an ulp of the argument. An ulp, unit in the last place, of afloat value is the positive distance between this floating-point value and the float value next larger in magnitude. Note that for non-NaNx,ulp(-x) == ulp(x).

  Special Cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is positive or negative infinity, then the result is positive infinity.
  • If the argument is positive or negative zero, then the result isFloat.MIN_VALUE.
  • If the argument is ±Float.MAX_VALUE, then the result is equal to 2¹⁰⁴.

  Parameters:

  f - the floating-point value whose ulp is to be returned

  Returns:

  the size of an ulp of the argument

  Since:

  1.5

• 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.

  Special Cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is positive zero or negative zero, then the result is the same as the argument.

  Parameters:

  d - the floating-point value whose signum is to be returned

  Returns:

  the signum function of the argument

  Since:

  1.5

• 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.

  Special Cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is positive zero or negative zero, then the result is the same as the argument.

  Parameters:

  f - the floating-point value whose signum is to be returned

  Returns:

  the signum function of the argument

  Since:

  1.5

• sinh

  public static double sinh(double x)

  Returns the hyperbolic sine of adouble value. The hyperbolic sine ofx is defined to be (e^x − e^−x)/2 wheree isEuler's number.

  Special cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is infinite, then the result is an infinity with the same sign as the argument.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

  The computed result must be within 2.5 ulps of the exact result.

  Parameters:

  x - The number whose hyperbolic sine is to be returned.

  Returns:

  The hyperbolic sine ofx.

  Since:

  1.5

• cosh

  public static double cosh(double x)

  Returns the hyperbolic cosine of adouble value. The hyperbolic cosine ofx is defined to be (e^x + e^−x)/2 wheree isEuler's number.

  Special cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is infinite, then the result is positive infinity.
  • If the argument is zero, then the result is1.0.

  The computed result must be within 2.5 ulps of the exact result.

  Parameters:

  x - The number whose hyperbolic cosine is to be returned.

  Returns:

  The hyperbolic cosine ofx.

  Since:

  1.5

• tanh

  public static double tanh(double x)

  Returns the hyperbolic tangent of adouble value. The hyperbolic tangent ofx is defined to be (e^x − e^−x)/(e^x + e^−x), in other words,sinh(x)/cosh(x). Note that the absolute value of the exact tanh is always less than 1.

  Special cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is zero, then the result is a zero with the same sign as the argument.
  • If the argument is positive infinity, then the result is+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 oftanh 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.

  Parameters:

  x - The number whose hyperbolic tangent is to be returned.

  Returns:

  The hyperbolic tangent ofx.

  Since:

  1.5

• hypot

  public static double hypot(double x, double y)

  Returns sqrt(x² +y²) without intermediate overflow or underflow.

  Special cases:

  • If either argument is infinite, then the result is positive infinity.
  • If either argument is NaN and neither argument is infinite, then the result is NaN.
  • 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.

  Parameters:

  x - a value

  y - a value

  Returns:

  sqrt(x² +y²) without intermediate overflow or underflow

  Since:

  1.5

• expm1

  public static double expm1(double x)

  Returnse^x −1. Note that for values ofx near 0, the exact sum ofexpm1(x) + 1 is much closer to the true result ofe^x thanexp(x).

  Special cases:

  • If the argument is NaN, the result is NaN.
  • If the argument is positive infinity, then the result is positive infinity.
  • If the argument is negative infinity, then the result is -1.0.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

  The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic. The result ofexpm1 for any finite input must be greater than or equal to-1.0. Note that once the exact result ofe^x - 1 is within 1/2 ulp of the limit value -1,-1.0 should be returned.

  Parameters:

  x - the exponent to raisee to in the computation ofe^x −1.

  Returns:

  the valuee^x - 1.

  Since:

  1.5

• log1p

  public static double log1p(double x)

  Returns the natural logarithm of the sum of the argument and 1. Note that for small valuesx, the result oflog1p(x) is much closer to the true result of ln(1 +x) than the floating-point evaluation oflog(1.0+x).

  Special cases:

  • If the argument is NaN or less than -1, then the result is NaN.
  • If the argument is positive infinity, then the result is positive infinity.
  • If the argument is negative one, then the result is negative infinity.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

  The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

  Parameters:

  x - a value

  Returns:

  the value ln(x + 1), the natural log ofx + 1

  Since:

  1.5

• 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 theStrictMath.copySign method, this method does not require NaNsign 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 ofmagnitude and the sign ofsign.

  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 theStrictMath.copySign method, this method does not require NaNsign 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 ofmagnitude and the sign ofsign.

  Since:

  1.6

• getExponent

  public static int getExponent(float f)

  Returns the unbiased exponent used in the representation of afloat. Special cases:

  • If the argument is NaN or infinite, then the result isFloat.MAX_EXPONENT + 1.
  • If the argument is zero or subnormal, then the result isFloat.MIN_EXPONENT - 1.

  API Note:

  This method is analogous to the logB operation defined in IEEE 754, but returns a different value on subnormal arguments.

  Parameters:

  f - afloat value

  Returns:

  the unbiased exponent of the argument

  Since:

  1.6

• getExponent

  public static int getExponent(double d)

  Returns the unbiased exponent used in the representation of adouble. Special cases:

  • If the argument is NaN or infinite, then the result isDouble.MAX_EXPONENT + 1.
  • If the argument is zero or subnormal, then the result isDouble.MIN_EXPONENT - 1.

  API Note:

  This method is analogous to the logB operation defined in IEEE 754, but returns a different value on subnormal arguments.

  Parameters:

  d - adouble value

  Returns:

  the unbiased exponent of the argument

  Since:

  1.6

• 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.

  Special 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).
  • Ifstart is ±Double.MIN_VALUE anddirection has a value such that the result should have a smaller magnitude, then a zero with the same sign asstart is returned.
  • Ifstart is infinite anddirection has a value such that the result should have a smaller magnitude,Double.MAX_VALUE with the same sign asstart is returned.
  • Ifstart is equal to ±Double.MAX_VALUE anddirection has a value such that the result should have a larger magnitude, an infinity with same sign asstart is returned.

  Parameters:

  start - starting floating-point value

  direction - value indicating which ofstart's neighbors orstart should be returned

  Returns:

  The floating-point number adjacent tostart in the direction ofdirection.

  Since:

  1.6

• 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.

  Special cases:

  • If either argument is a NaN, then NaN is returned.
  • If both arguments are signed zeros, a value equivalent todirection is returned.
  • Ifstart is ±Float.MIN_VALUE anddirection has a value such that the result should have a smaller magnitude, then a zero with the same sign asstart is returned.
  • Ifstart is infinite anddirection has a value such that the result should have a smaller magnitude,Float.MAX_VALUE with the same sign asstart is returned.
  • Ifstart is equal to ±Float.MAX_VALUE anddirection has a value such that the result should have a larger magnitude, an infinity with same sign asstart is returned.

  Parameters:

  start - starting floating-point value

  direction - value indicating which ofstart's neighbors orstart should be returned

  Returns:

  The floating-point number adjacent tostart in the direction ofdirection.

  Since:

  1.6

• nextUp

  public static double nextUp(double d)

  Returns the floating-point value adjacent tod in the direction of positive infinity. This method is semantically equivalent tonextAfter(d, Double.POSITIVE_INFINITY); however, anextUp implementation may run faster than its equivalentnextAfter call.

  Special Cases:

  • If the argument is NaN, the result is NaN.
  • If the argument is positive infinity, the result is positive infinity.
  • If the argument is zero, the result isDouble.MIN_VALUE

  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:

  1.6

• nextUp

  public static float nextUp(float f)

  Returns the floating-point value adjacent tof in the direction of positive infinity. This method is semantically equivalent tonextAfter(f, Float.POSITIVE_INFINITY); however, anextUp implementation may run faster than its equivalentnextAfter call.

  Special Cases:

  • If the argument is NaN, the result is NaN.
  • If the argument is positive infinity, the result is positive infinity.
  • If the argument is zero, the result isFloat.MIN_VALUE

  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:

  1.6

• nextDown

  public static double nextDown(double d)

  Returns the floating-point value adjacent tod in the direction of negative infinity. This method is semantically equivalent tonextAfter(d, Double.NEGATIVE_INFINITY); however, anextDown implementation may run faster than its equivalentnextAfter call.

  Special Cases:

  • If the argument is NaN, the result is NaN.
  • If the argument is negative infinity, the result is negative infinity.
  • If the argument is zero, the result is-Double.MIN_VALUE

  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:

  1.8

• nextDown

  public static float nextDown(float f)

  Returns the floating-point value adjacent tof in the direction of negative infinity. This method is semantically equivalent tonextAfter(f, Float.NEGATIVE_INFINITY); however, anextDown implementation may run faster than its equivalentnextAfter call.

  Special Cases:

  • If the argument is NaN, the result is NaN.
  • If the argument is negative infinity, the result is negative infinity.
  • If the argument is zero, the result is-Float.MIN_VALUE

  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:

  1.8

• scalb

  public static double scalb(double d, int scaleFactor)

  Returnsd × 2^scaleFactor rounded as if performed by a single correctly rounded floating-point multiply. If the exponent of the result is betweenDouble.MIN_EXPONENT andDouble.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, whenscalb(x, n) is subnormal,scalb(scalb(x, n), -n) may not equalx. When the result is non-NaN, the result has the same sign asd.

  Special cases:

  • If the first argument is NaN, NaN is returned.
  • If the first argument is infinite, then an infinity of the same sign is returned.
  • If the first argument is zero, then a zero of the same sign is returned.

  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 scaled

  Returns:

  d × 2^scaleFactor

  Since:

  1.6

• scalb

  public static float scalb(float f, int scaleFactor)

  Returnsf × 2^scaleFactor rounded as if performed by a single correctly rounded floating-point multiply. If the exponent of the result is betweenFloat.MIN_EXPONENT andFloat.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, whenscalb(x, n) is subnormal,scalb(scalb(x, n), -n) may not equalx. When the result is non-NaN, the result has the same sign asf.

  Special cases:

  • If the first argument is NaN, NaN is returned.
  • If the first argument is infinite, then an infinity of the same sign is returned.
  • If the first argument is zero, then a zero of the same sign is returned.

  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 scalef

  Returns:

  f × 2^scaleFactor

  Since:

  1.6