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 toits 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 circleto its radius.

  API Note:

  The value ofpi is one half that oftau; in otherwords,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 theresult is NaN.
  • If the argument is zero, then the result is a zero with thesame 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 resultis NaN.
  • If the argument is zero, then the result is a zero with thesame 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 therange −pi/2 throughpi/2. Special cases:

  • If the argument is NaN or its absolute value is greaterthan 1, then the result is NaN.
  • If the argument is zero, then the result is a zero with thesame 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 therange 0.0 throughpi. Special case:

  • If the argument is NaN or its absolute value is greaterthan 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 therange −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 thesame sign as the argument.
  • If the argument isinfinite,then the result is the closest value topi/2 with thesame 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 approximatelyequivalent angle measured in radians. The conversion fromdegrees 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 approximatelyequivalent angle measured in degrees. The conversion fromradians to degrees is generally inexact; users shouldnot expectcos(toRadians(90.0)) to exactlyequal0.0.

  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 ispositive infinity.
  • If the argument is negative infinity, then the result ispositive 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 adoublevalue. Special cases:

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

  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 resultis NaN.
  • If the argument is positive infinity, then the result ispositive infinity.
  • If the argument is positive zero or negative zero, then theresult is negative infinity.
  • If the argument is equal to 10ⁿ forintegern, then the result isn. In particular,if the argument is1.0 (10⁰), then theresult 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 resultis NaN.
  • If the argument is positive infinity, then the result is positiveinfinity.
  • If the argument is positive zero or negative zero, then theresult is the same as the argument.

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

  API Note:

  This method corresponds to the squareRoot operation defined inIEEE 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. Forpositive finitex,cbrt(-x) ==-cbrt(x); that is, the cube root of a negative value isthe 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 infinitywith the same sign as the argument.
  • If the argument is zero, then the result is a zero with thesame 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 prescribedby the IEEE 754 standard.The remainder value is mathematically equal tof1 - f2 × n,wheren is the mathematical integer closest to the exactmathematical value of the quotientf1/f2, and if twomathematical integers are equally close tof1/f2,thenn is the integer that is even. If the remainder iszero, 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 theresult is NaN.
  • If the first argument is finite and the second argument isinfinite, 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 theargument and is equal to a mathematical integer. Special cases:

  • If the argument value is already equal to amathematical integer, then the result is the same as theargument.
  • If the argument is NaN or an infinity orpositive zero or negative zero, then the result is the same asthe argument.
  • If the argument value is less than zero butgreater than -1.0, then the result is negative zero.

  Notethat the value ofMath.ceil(x) is exactly thevalue of-Math.floor(-x).

  API Note:

  This method corresponds to the roundToIntegralTowardPositiveoperation 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 theargument and is equal to a mathematical integer. Special cases:

  • If the argument value is already equal to amathematical integer, then the result is the same as theargument.
  • If the argument is NaN or an infinity orpositive zero or negative zero, then the result is the same asthe argument.

  API Note:

  This method corresponds to the roundToIntegralTowardNegativeoperation 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 valueto the argument and is equal to a mathematical integer. If twodouble values that are mathematical integers areequally close, the result is the integer value that iseven. Special cases:

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

  API Note:

  This method corresponds to the roundToIntegralTiesToEvenoperation 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 rectangularcoordinates (x, y) to polarcoordinates (r, theta).This method computes the phasetheta by computing an arc tangentofy/x in the range of −pi topi. Specialcases:

  • If either argument is NaN, then the result is NaN.
  • If the first argument is positive zero and the second argumentis positive, or the first argument is positive and finite and thesecond argument is positive infinity, then the result is positivezero.
  • If the first argument is negative zero and the second argumentis positive, or the first argument is negative and finite and thesecond argument is positive infinity, then the result is negative zero.
  • If the first argument is positive zero and the second argumentis negative, or the first argument is positive and finite and thesecond argument is negative infinity, then the result is thedouble value closest topi.
  • If the first argument is negative zero and the second argumentis negative, or the first argument is negative and finite and thesecond argument is negative infinity, then the result is thedouble value closest to -pi.
  • If the first argument is positive and the second argument ispositive zero or negative zero, or the first argument is positiveinfinity 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 ispositive zero or negative zero, or the first argument is negativeinfinity 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 argumentis negative infinity, then the result is thedoublevalue closest to 3*pi/4.
  • If the first argument is negative infinity and the second argumentis positive infinity, then the result is thedouble valueclosest 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 isequal 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 thesecond argument. Special cases:

  • If the second argument is positive or negative zero, then theresult is 1.0.
  • If the second argument is 1.0, then the result is the same as thefirst 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 1and the second argument is positive infinity, or
    • the absolute value of the first argument is less than 1 andthe second argument is negative infinity,
    then the result is positive infinity.
  • If
    • the absolute value of the first argument is greater than 1 andthe second argument is negative infinity, or
    • the absolute value of thefirst argument is less than 1 and the second argument is positiveinfinity,
    then the result is positive zero.
  • If the absolute value of the first argument equals 1 and thesecond argument is infinite, then the result is NaN.
  • If
    • the first argument is positive zero and the second argumentis greater than zero, or
    • the first argument is positive infinity and the secondargument is less than zero,
    then the result is positive zero.
  • If
    • the first argument is positive zero and the second argumentis less than zero, or
    • the first argument is positive infinity and the secondargument is greater than zero,
    then the result is positive infinity.
  • If
    • the first argument is negative zero and the second argumentis greater than zero but not a finite odd integer, or
    • the first argument is negative infinity and the secondargument 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 argumentis a positive finite odd integer, or
    • the first argument is negative infinity and the secondargument is a negative finite odd integer,
    then the result is negative zero.
  • If
    • the first argument is negative zero and the second argumentis less than zero but not a finite odd integer, or
    • the first argument is negative infinity and the secondargument 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 argumentis a negative finite odd integer, or
    • the first argument is negative infinity and the secondargument 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, theresult is equal to the result of raising the absolute value ofthe first argument to the power of the second argument
    • if the second argument is a finite odd integer, the resultis equal to the negative of the result of raising the absolutevalue of the first argument to the power of the secondargument
    • if the second argument is finite and not an integer, thenthe result is NaN.
  • If both arguments are integers, then the result is exactly equalto the mathematical result of raising the first argument to the powerof the second argument if that result can in fact be representedexactly as adouble value.

  (In the foregoing descriptions, a floating-point value isconsidered to be an integer if and only if it is finite and afixed point of the methodceil or,equivalently, a fixed point of the methodfloor. A value is a fixed point of a one-argumentmethod if and only if the result of applying the method to thevalue 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 thespecial case definitions of the IEEE 754 recommendedpow operation for ±1.0 raised to an infinitepower. This method treats such cases as indeterminate andspecifies a NaN is returned. The IEEE 754 specification treatsthe infinite power as a large integer (large-magnitudefloating-point numbers are numerically integers, specificallyeven 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 tiesrounding 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 orequal to the value ofInteger.MIN_VALUE, the result isequal to the value ofInteger.MIN_VALUE.
  • If the argument is positive infinity or any value greater than orequal to the value ofInteger.MAX_VALUE, the result isequal 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 tiesrounding 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 orequal to the value ofLong.MIN_VALUE, the result isequal to the value ofLong.MIN_VALUE.
  • If the argument is positive infinity or any value greater than orequal to the value ofLong.MAX_VALUE, the result isequal 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, greaterthan 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 newpseudorandom-number generator, exactly as if by the expression

  new java.util.Random()

  This new pseudorandom-number generator is used thereafter forall calls to this method and is used nowhere else.

  This method is properly synchronized to allow correct use bymore than one thread. However, if many threads need to generatepseudorandom numbers at a great rate, it may reduce contentionfor each thread to have its own pseudorandom-number generator.

  API Note:

  As the largestdouble value less than1.0isMath.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 equalto0.0 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 resultoverflows 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 theresult 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 bethrown.

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

  The built-in remainder operator "%" is a suitable counterpartboth 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 quotientoverflows 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 theresult 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 bethrown.

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

  The built-in remainder operator "%" is a suitable counterpartboth 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 quotientoverflows 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 itthrows 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 suitablecounterpart 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 thedividendx isInteger.MIN_VALUE and the divisoryis-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 itthrows 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 suitablecounterpart 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 thedividendx isLong.MIN_VALUE and the divisoryis-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 itthrows 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 suitablecounterpart 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 thedividendx isInteger.MIN_VALUE and the divisoryis-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 itthrows 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 suitablecounterpart 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 thedividendx isLong.MIN_VALUE and the divisoryis-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 theresult 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 theresult 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 theresult 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 theresult 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 theresult 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 theresult 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-bitproduct 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 unsigned128-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 andthe 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 towardnegative infinity (floor) rounding mode.The floor rounding mode gives different results from truncationwhen 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 andthe 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 towardnegative infinity (floor) rounding mode.The floor rounding mode gives different results from truncationwhen 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 andthe 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 towardnegative infinity (floor) rounding mode.The floor rounding mode gives different results from truncationwhen 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, andis 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% operatoris 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, andis 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, andis 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 andthe 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 towardpositive infinity (ceiling) rounding mode.The ceiling rounding mode gives different results from truncationwhen 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 andthe 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 towardpositive infinity (ceiling) rounding mode.The ceiling rounding mode gives different results from truncationwhen 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 andthe 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 towardpositive infinity (ceiling) rounding mode.The ceiling rounding mode gives different results from truncationwhen 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, andis 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% operatoris 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, andis 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, andis 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 representableintvalue, the result is that same value, which is negative. Incontrast, 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 valueif it is exactly representable as anint, throwingArithmeticException if the result overflows thepositiveint range.

  Since the range of two's complement integers is asymmetricwith one additional negative value (JLS4.2.1), themathematical absolute value ofInteger.MIN_VALUEoverflows the positiveint range, so an exception isthrown 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 representablelongvalue, the result is that same value, which is negative. Incontrast, 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 valueif it is exactly representable as anlong, throwingArithmeticException if the result overflows thepositivelong range.

  Since the range of two's complement integers is asymmetricwith one additional negative value (JLS4.2.1), themathematical absolute value ofLong.MIN_VALUE overflowsthe positivelong range, so an exception is thrown forthat 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, theresult 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 ofthis method is given by the expression below which computes afloat with the same exponent and significand as theargument but with a guaranteed zero sign bit indicating apositive 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 resultis 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 ofthis method is given by the expression below which computes adouble with the same exponent and significand as theargument but with a guaranteed zero sign bit indicating apositive 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, theresult 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, theresult 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 thearguments have the same value, the result is that samevalue. If either value is NaN, then the result is NaN. Unlikethe numerical comparison operators, this method considersnegative zero to be strictly smaller than positive zero. If oneargument is positive zero and the other negative zero, theresult is positive zero.

  API Note:

  This method corresponds to the maximum operation defined inIEEE 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. Thatis, the result is the argument closer to positive infinity. Ifthe arguments have the same value, the result is that samevalue. If either value is NaN, then the result is NaN. Unlikethe numerical comparison operators, this method considersnegative zero to be strictly smaller than positive zero. If oneargument is positive zero and the other negative zero, theresult is positive zero.

  API Note:

  This method corresponds to the maximum operation defined inIEEE 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 samevalue, 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 samevalue, 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 thearguments have the same value, the result is that samevalue. If either value is NaN, then the result is NaN. Unlikethe numerical comparison operators, this method considersnegative zero to be strictly smaller than positive zero. Ifone 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 inIEEE 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. Thatis, the result is the value closer to negative infinity. If thearguments have the same value, the result is that samevalue. If either value is NaN, then the result is NaN. Unlikethe numerical comparison operators, this method considersnegative zero to be strictly smaller than positive zero. If oneargument is positive zero and the other is negative zero, theresult is negative zero.

  API Note:

  This method corresponds to the minimum operation defined inIEEE 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 lessthanmin, thenmin is returned. If the value is greaterthanmax, thenmax is returned. Otherwise, the originalvalue 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 withsaturation.

  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 lessthanmin, thenmin is returned. If the value is greaterthanmax, thenmax is returned. Otherwise, the originalvalue 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 lessthanmin, thenmin is returned. If the value is greaterthanmax, thenmax is returned. Otherwise, the originalvalue is returned. If value is NaN, the result is also NaN.

  Unlike the numerical comparison operators, this method considersnegative 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 andmaxarguments 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 lessthanmin, thenmin is returned. If the value is greaterthanmax, thenmax is returned. Otherwise, the originalvalue is returned. If value is NaN, the result is also NaN.

  Unlike the numerical comparison operators, this method considersnegative 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 andmaxarguments 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 summedwith the third argument and then rounded once to the nearestdouble.The rounding is done using theround to nearest evenrounding mode.In contrast, ifa * b + c is evaluated as a regularfloating-point expression, two rounding errors are involved,the first for the multiply operation, the second for theaddition operation.

  Special cases:

  • If any argument is NaN, the result is NaN.
  • If one of the first two arguments is infinite and theother 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 andthe other is neither zero nor NaN) and the third argument is aninfinity of the opposite sign, the result is NaN.

  Note thatfma(a, 1.0, c) returns the sameresult as (a + c). However,fma(a, b, +0.0) doesnot always return thesame 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) isequivalent to (a * b) however.

  API Note:

  This method corresponds to the fusedMultiplyAddoperation 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 roundedonce 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 summedwith the third argument and then rounded once to the nearestfloat.The rounding is done using theround to nearest evenrounding mode.In contrast, ifa * b + c is evaluated as a regularfloating-point expression, two rounding errors are involved,the first for the multiply operation, the second for theaddition operation.

  Special cases:

  • If any argument is NaN, the result is NaN.
  • If one of the first two arguments is infinite and theother 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 andthe other is neither zero nor NaN) and the third argument is aninfinity of the opposite sign, the result is NaN.

  Note thatfma(a, 1.0f, c) returns the sameresult as (a + c). However,fma(a, b, +0.0f) doesnot always return thesame 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) isequivalent to (a * b) however.

  API Note:

  This method corresponds to the fusedMultiplyAddoperation 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 roundedonce 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 inthe last place, of adouble value is the positivedistance between this floating-point value and thedouble 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 theresult is positive infinity.
  • If the argument is positive or negative zero, then the result isDouble.MIN_VALUE.
  • If the argument is ±Double.MAX_VALUE, thenthe 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 inthe last place, of afloat value is the positivedistance between this floating-point value and thefloat 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 theresult is positive infinity.
  • If the argument is positive or negative zero, then the result isFloat.MIN_VALUE.
  • If the argument is ±Float.MAX_VALUE, thenthe 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 argumentis zero, 1.0 if the argument is greater than zero, -1.0 if theargument 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 argumentis zero, 1.0f if the argument is greater than zero, -1.0f if theargument 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)/2wheree 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 infinitywith the same sign as the argument.
  • If the argument is zero, then the result is a zero with thesame 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)/2wheree isEuler's number.

  Special cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is infinite, then the result is positiveinfinity.
  • 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). Notethat the absolute value of the exact tanh is always less than1.

  Special cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is zero, then the result is a zero with thesame 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 havean absolute value less than or equal to 1. Note that once theexact result of tanh is within 1/2 of an ulp of the limit valueof ±1, correctly signed ±1.0 shouldbe 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 resultis 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 exactresult. If one parameter is held constant, the results must besemi-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 trueresult ofe^x thanexp(x).

  Special cases:

  • If the argument is NaN, the result is NaN.
  • If the argument is positive infinity, then the result ispositive 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 thesame 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 orequal to-1.0. Note that once the exact result ofe^x - 1 is within 1/2ulp of the limit value -1,-1.0 should bereturned.

  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 isNaN.
  • If the argument is positive infinity, then the result ispositive infinity.
  • If the argument is negative one, then the result isnegative infinity.
  • If the argument is zero, then the result is a zero with thesame 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 naturallog ofx + 1

  Since:

  1.5

• copySign

  public static double copySign(double magnitude, double sign)

  Returns the first floating-point argument with the sign of thesecond floating-point argument. Note that unlike theStrictMath.copySignmethod, this method does not require NaNsignarguments to be treated as positive values; implementations arepermitted to treat some NaN arguments as positive and other NaNarguments as negative to allow greater performance.

  API Note:

  This method corresponds to the copySign operation defined inIEEE 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 ofmagnitudeand 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 thesecond floating-point argument. Note that unlike theStrictMath.copySignmethod, this method does not require NaNsignarguments to be treated as positive values; implementations arepermitted to treat some NaN arguments as positive and other NaNarguments as negative to allow greater performance.

  API Note:

  This method corresponds to the copySign operation defined inIEEE 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 ofmagnitudeand 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 IEEE754, 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 IEEE754, 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 firstargument in the direction of the second argument. If botharguments 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,directionis returned unchanged (as implied by the requirement ofreturning the second argument if the arguments compare asequal).
  • Ifstart is±Double.MIN_VALUE anddirectionhas a value such that the result should have a smallermagnitude, then a zero with the same sign asstartis returned.
  • Ifstart is infinite anddirection has a value such that the result shouldhave a smaller magnitude,Double.MAX_VALUE with thesame sign asstart is returned.
  • Ifstart is equal to ±Double.MAX_VALUE anddirection has avalue such that the result should have a larger magnitude, aninfinity with same sign asstart is returned.

  Parameters:

  start - starting floating-point value

  direction - value indicating which ofstart's neighbors orstart shouldbe returned

  Returns:

  The floating-point number adjacent tostart in thedirection ofdirection.

  Since:

  1.6

• nextAfter

  public static float nextAfter(float start, double direction)

  Returns the floating-point number adjacent to the firstargument in the direction of the second argument. If botharguments compare as equal a value equivalent to the second argumentis returned.

  Special cases:

  • If either argument is a NaN, then NaN is returned.
  • If both arguments are signed zeros, a value equivalenttodirection is returned.
  • Ifstart is±Float.MIN_VALUE anddirectionhas a value such that the result should have a smallermagnitude, then a zero with the same sign asstartis returned.
  • Ifstart is infinite anddirection has a value such that the result shouldhave a smaller magnitude,Float.MAX_VALUE with thesame sign asstart is returned.
  • Ifstart is equal to ±Float.MAX_VALUE anddirection has avalue such that the result should have a larger magnitude, aninfinity with same sign asstart is returned.

  Parameters:

  start - starting floating-point value

  direction - value indicating which ofstart's neighbors orstart shouldbe returned

  Returns:

  The floating-point number adjacent tostart in thedirection ofdirection.

  Since:

  1.6

• nextUp

  public static double nextUp(double d)

  Returns the floating-point value adjacent tod inthe direction of positive infinity. This method issemantically equivalent tonextAfter(d,Double.POSITIVE_INFINITY); however, anextUpimplementation 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 ispositive infinity.
  • If the argument is zero, the result isDouble.MIN_VALUE

  API Note:

  This method corresponds to the nextUpoperation defined in IEEE 754.

  Parameters:

  d - starting floating-point value

  Returns:

  The adjacent floating-point value closer to positiveinfinity.

  Since:

  1.6

• nextUp

  public static float nextUp(float f)

  Returns the floating-point value adjacent tof inthe direction of positive infinity. This method issemantically equivalent tonextAfter(f,Float.POSITIVE_INFINITY); however, anextUpimplementation 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 ispositive infinity.
  • If the argument is zero, the result isFloat.MIN_VALUE

  API Note:

  This method corresponds to the nextUpoperation defined in IEEE 754.

  Parameters:

  f - starting floating-point value

  Returns:

  The adjacent floating-point value closer to positiveinfinity.

  Since:

  1.6

• nextDown

  public static double nextDown(double d)

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

  Special Cases:

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

  API Note:

  This method corresponds to the nextDownoperation defined in IEEE 754.

  Parameters:

  d - starting floating-point value

  Returns:

  The adjacent floating-point value closer to negativeinfinity.

  Since:

  1.8

• nextDown

  public static float nextDown(float f)

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

  Special Cases:

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

  API Note:

  This method corresponds to the nextDownoperation defined in IEEE 754.

  Parameters:

  f - starting floating-point value

  Returns:

  The adjacent floating-point value closer to negativeinfinity.

  Since:

  1.8

• scalb

  public static double scalb(double d, int scaleFactor)

  Returnsd × 2^scaleFactorrounded as if performed by a single correctly roundedfloating-point multiply. If the exponent of the result isbetweenDouble.MIN_EXPONENT andDouble.MAX_EXPONENT, the answer is calculated exactly. If theexponent of the result would be larger thanDouble.MAX_EXPONENT, an infinity is returned. Note that ifthe 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, theresult 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 thesame sign is returned.
  • If the first argument is zero, then a zero of the samesign is returned.

  API Note:

  This method corresponds to the scaleB operationdefined 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^scaleFactorrounded as if performed by a single correctly roundedfloating-point multiply. If the exponent of the result isbetweenFloat.MIN_EXPONENT andFloat.MAX_EXPONENT, the answer is calculated exactly. If theexponent of the result would be larger thanFloat.MAX_EXPONENT, an infinity is returned. Note that if theresult 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, theresult 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 thesame sign is returned.
  • If the first argument is zero, then a zero of the samesign is returned.

  API Note:

  This method corresponds to the scaleB operationdefined 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

• unsignedMultiplyExact

  public static int unsignedMultiplyExact(int x, int y)

  Returns the product of the unsigned arguments,throwing an exception if the result overflows an unsignedint.

  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 unsignedlong.

  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 unsignedlong.

  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)

  Returnsx raised to the power ofn,throwing an exception if the result overflows anint.Whenn is 0, the returned value is 1.

  Parameters:

  x - the base.

  n - the exponent.

  Returns:

  x raised to the power ofn.

  Throws:

  ArithmeticException - whenn is negative, or when the result overflows an int.

  Since:

  25

• unsignedPowExact

  public static int unsignedPowExact(int x, int n)

  Returns unsignedx raised to the power ofn,throwing an exception if the result overflows an unsignedint.Whenn is 0, the returned value is 1.

  Parameters:

  x - the unsigned base.

  n - the exponent.

  Returns:

  x raised to the power ofn.

  Throws:

  ArithmeticException - whenn is negative, or when the result overflows an unsigned int.

  Since:

  25

• powExact

  public static long powExact(long x, int n)

  Returnsx raised to the power ofn,throwing an exception if the result overflows along.Whenn is 0, the returned value is 1.

  Parameters:

  x - the base.

  n - the exponent.

  Returns:

  x raised to the power ofn.

  Throws:

  ArithmeticException - whenn is negative, or when the result overflows a long.

  Since:

  25

• unsignedPowExact

  public static long unsignedPowExact(long x, int n)

  Returns unsignedx raised to the power ofn,throwing an exception if the result overflows an unsignedlong.Whenn is 0, the returned value is 1.

  Parameters:

  x - the unsigned base.

  n - the exponent.

  Returns:

  x raised to the power ofn.

  Throws:

  ArithmeticException - whenn is negative, or when the result overflows an unsigned long.

  Since:

  25