Package org.apache.commons.math3.util

Class FastMath

java.lang.Object
org.apache.commons.math3.util.FastMath
public class FastMath extends Object
Faster, more accurate, portable alternative to Math and StrictMath for large scale computation.

FastMath is a drop-in replacement for both Math and StrictMath. This means that for any method in Math (say Math.sin(x) or Math.cbrt(y)), user can directly change the class and use the methods as is (using FastMath.sin(x) or FastMath.cbrt(y) in the previous example).

FastMath speed is achieved by relying heavily on optimizing compilers to native code present in many JVMs today and use of large tables. The larger tables are lazily initialised on first use, so that the setup time does not penalise methods that don't need them.

Note that FastMath is extensively used inside Apache Commons Math, so by calling some algorithms, the overhead when the the tables need to be intialised will occur regardless of the end-user calling FastMath methods directly or not. Performance figures for a specific JVM and hardware can be evaluated by running the FastMathTestPerformance tests in the test directory of the source distribution.

FastMath accuracy should be mostly independent of the JVM as it relies only on IEEE-754 basic operations and on embedded tables. Almost all operations are accurate to about 0.5 ulp throughout the domain range. This statement, of course is only a rough global observed behavior, it is not a guarantee for every double numbers input (see William Kahan's Table Maker's Dilemma).

FastMath additionally implements the following methods not found in Math/StrictMath:

The following methods are found in Math/StrictMath since 1.6 only, they are provided by FastMath even in 1.5 Java virtual machines

Since:
2.2

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    static final double
    E
    Napier's constant e, base of the natural logarithm.
    static final double
    PI
    Archimede's constant PI, ratio of circle circumference to diameter.

  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    abs(double x)
    Absolute value.
    static float
    abs(float x)
    Absolute value.
    static int
    abs(int x)
    Absolute value.
    static long
    abs(long x)
    Absolute value.
    static double
    acos(double x)
    Compute the arc cosine of a number.
    static double
    acosh(double a)
    Compute the inverse hyperbolic cosine of a number.
    static int
    addExact(int a, int b)
    Add two numbers, detecting overflows.
    static long
    addExact(long a, long b)
    Add two numbers, detecting overflows.
    static double
    asin(double x)
    Compute the arc sine of a number.
    static double
    asinh(double a)
    Compute the inverse hyperbolic sine of a number.
    static double
    atan(double x)
    Arctangent function
    static double
    atan2(double y, double x)
    Two arguments arctangent function
    static double
    atanh(double a)
    Compute the inverse hyperbolic tangent of a number.
    static double
    cbrt(double x)
    Compute the cubic root of a number.
    static double
    ceil(double x)
    Get the smallest whole number larger than x.
    static double
    copySign(double magnitude, double sign)
    Returns the first argument with the sign of the second argument.
    static float
    copySign(float magnitude, float sign)
    Returns the first argument with the sign of the second argument.
    static double
    cos(double x)
    Cosine function.
    static double
    cosh(double x)
    Compute the hyperbolic cosine of a number.
    static int
    decrementExact(int n)
    Decrement a number, detecting overflows.
    static long
    decrementExact(long n)
    Decrement a number, detecting overflows.
    static double
    exp(double x)
    Exponential function.
    static double
    expm1(double x)
    Compute exp(x) - 1
    static double
    floor(double x)
    Get the largest whole number smaller than x.
    static int
    floorDiv(int a, int b)
    Finds q such that a = q b + r with 0 invalid input: '<'= r invalid input: '<' b if b > 0 and b invalid input: '<' r invalid input: '<'= 0 if b invalid input: '<' 0.
    static long
    floorDiv(long a, long b)
    Finds q such that a = q b + r with 0 invalid input: '<'= r invalid input: '<' b if b > 0 and b invalid input: '<' r invalid input: '<'= 0 if b invalid input: '<' 0.
    static int
    floorMod(int a, int b)
    Finds r such that a = q b + r with 0 invalid input: '<'= r invalid input: '<' b if b > 0 and b invalid input: '<' r invalid input: '<'= 0 if b invalid input: '<' 0.
    static long
    floorMod(long a, long b)
    Finds r such that a = q b + r with 0 invalid input: '<'= r invalid input: '<' b if b > 0 and b invalid input: '<' r invalid input: '<'= 0 if b invalid input: '<' 0.
    static int
    getExponent(double d)
    Return the exponent of a double number, removing the bias.
    static int
    getExponent(float f)
    Return the exponent of a float number, removing the bias.
    static double
    hypot(double x, double y)
    Returns the hypotenuse of a triangle with sides x and y - sqrt(x2 +y2)
    avoiding intermediate overflow or underflow.
    static double
    IEEEremainder(double dividend, double divisor)
    Computes the remainder as prescribed by the IEEE 754 standard.
    static int
    incrementExact(int n)
    Increment a number, detecting overflows.
    static long
    incrementExact(long n)
    Increment a number, detecting overflows.
    static double
    log(double x)
    Natural logarithm.
    static double
    log(double base, double x)
    Computes the logarithm in a given base.
    static double
    log10(double x)
    Compute the base 10 logarithm.
    static double
    log1p(double x)
    Computes log(1 + x).
    static void
    main(String[] a)
    Print out contents of arrays, and check the length.
    static double
    max(double a, double b)
    Compute the maximum of two values
    static float
    max(float a, float b)
    Compute the maximum of two values
    static int
    max(int a, int b)
    Compute the maximum of two values
    static long
    max(long a, long b)
    Compute the maximum of two values
    static double
    min(double a, double b)
    Compute the minimum of two values
    static float
    min(float a, float b)
    Compute the minimum of two values
    static int
    min(int a, int b)
    Compute the minimum of two values
    static long
    min(long a, long b)
    Compute the minimum of two values
    static int
    multiplyExact(int a, int b)
    Multiply two numbers, detecting overflows.
    static long
    multiplyExact(long a, long b)
    Multiply two numbers, detecting overflows.
    static double
    nextAfter(double d, double direction)
    Get the next machine representable number after a number, moving in the direction of another number.
    static float
    nextAfter(float f, double direction)
    Get the next machine representable number after a number, moving in the direction of another number.
    static double
    nextDown(double a)
    Compute next number towards negative infinity.
    static float
    nextDown(float a)
    Compute next number towards negative infinity.
    static double
    nextUp(double a)
    Compute next number towards positive infinity.
    static float
    nextUp(float a)
    Compute next number towards positive infinity.
    static double
    pow(double x, double y)
    Power function.
    static double
    pow(double d, int e)
    Raise a double to an int power.
    static double
    pow(double d, long e)
    Raise a double to a long power.
    static double
    random()
    Returns a pseudo-random number between 0.0 and 1.0.
    static double
    rint(double x)
    Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.
    static long
    round(double x)
    Get the closest long to x.
    static int
    round(float x)
    Get the closest int to x.
    static double
    scalb(double d, int n)
    Multiply a double number by a power of 2.
    static float
    scalb(float f, int n)
    Multiply a float number by a power of 2.
    static double
    signum(double a)
    Compute the signum of a number.
    static float
    signum(float a)
    Compute the signum of a number.
    static double
    sin(double x)
    Sine function.
    static double
    sinh(double x)
    Compute the hyperbolic sine of a number.
    static double
    sqrt(double a)
    Compute the square root of a number.
    static int
    subtractExact(int a, int b)
    Subtract two numbers, detecting overflows.
    static long
    subtractExact(long a, long b)
    Subtract two numbers, detecting overflows.
    static double
    tan(double x)
    Tangent function.
    static double
    tanh(double x)
    Compute the hyperbolic tangent of a number.
    static double
    toDegrees(double x)
    Convert radians to degrees, with error of less than 0.5 ULP
    static int
    toIntExact(long n)
    Convert a long to interger, detecting overflows
    static double
    toRadians(double x)
    Convert degrees to radians, with error of less than 0.5 ULP
    static double
    ulp(double x)
    Compute least significant bit (Unit in Last Position) for a number.
    static float
    ulp(float x)
    Compute least significant bit (Unit in Last Position) for a number.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • PI

      public static final double PI
      Archimede's constant PI, ratio of circle circumference to diameter.
      See Also:

    • E

      public static final double E
      Napier's constant e, base of the natural logarithm.
      See Also:

  • Method Details

    • sqrt

      public static double sqrt(double a)
      Compute the square root of a number.

      Note: this implementation currently delegates to Math.sqrt(double)

      Parameters:
      a - number on which evaluation is done
      Returns:
      square root of a

    • cosh

      public static double cosh(double x)
      Compute the hyperbolic cosine of a number.
      Parameters:
      x - number on which evaluation is done
      Returns:
      hyperbolic cosine of x

    • sinh

      public static double sinh(double x)
      Compute the hyperbolic sine of a number.
      Parameters:
      x - number on which evaluation is done
      Returns:
      hyperbolic sine of x

    • tanh

      public static double tanh(double x)
      Compute the hyperbolic tangent of a number.
      Parameters:
      x - number on which evaluation is done
      Returns:
      hyperbolic tangent of x

    • acosh

      public static double acosh(double a)
      Compute the inverse hyperbolic cosine of a number.
      Parameters:
      a - number on which evaluation is done
      Returns:
      inverse hyperbolic cosine of a

    • asinh

      public static double asinh(double a)
      Compute the inverse hyperbolic sine of a number.
      Parameters:
      a - number on which evaluation is done
      Returns:
      inverse hyperbolic sine of a

    • atanh

      public static double atanh(double a)
      Compute the inverse hyperbolic tangent of a number.
      Parameters:
      a - number on which evaluation is done
      Returns:
      inverse hyperbolic tangent of a

    • signum

      public static double signum(double a)
      Compute the signum of a number. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise
      Parameters:
      a - number on which evaluation is done
      Returns:
      -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a

    • signum

      public static float signum(float a)
      Compute the signum of a number. The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise
      Parameters:
      a - number on which evaluation is done
      Returns:
      -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a

    • nextUp

      public static double nextUp(double a)
      Compute next number towards positive infinity.
      Parameters:
      a - number to which neighbor should be computed
      Returns:
      neighbor of a towards positive infinity

    • nextUp

      public static float nextUp(float a)
      Compute next number towards positive infinity.
      Parameters:
      a - number to which neighbor should be computed
      Returns:
      neighbor of a towards positive infinity

    • nextDown

      public static double nextDown(double a)
      Compute next number towards negative infinity.
      Parameters:
      a - number to which neighbor should be computed
      Returns:
      neighbor of a towards negative infinity
      Since:
      3.4

    • nextDown

      public static float nextDown(float a)
      Compute next number towards negative infinity.
      Parameters:
      a - number to which neighbor should be computed
      Returns:
      neighbor of a towards negative infinity
      Since:
      3.4

    • random

      public static double random()
      Returns a pseudo-random number between 0.0 and 1.0.

      Note: this implementation currently delegates to Math.random()

      Returns:
      a random number between 0.0 and 1.0

    • exp

      public static double exp(double x)
      Exponential function. Computes exp(x), function result is nearly rounded. It will be correctly rounded to the theoretical value for 99.9% of input values, otherwise it will have a 1 ULP error. Method: Lookup intVal = exp(int(x)) Lookup fracVal = exp(int(x-int(x) / 1024.0) * 1024.0 ); Compute z as the exponential of the remaining bits by a polynomial minus one exp(x) = intVal * fracVal * (1 + z) Accuracy: Calculation is done with 63 bits of precision, so result should be correctly rounded for 99.9% of input values, with less than 1 ULP error otherwise.
      Parameters:
      x - a double
      Returns:
      double ex

    • expm1

      public static double expm1(double x)
      Compute exp(x) - 1
      Parameters:
      x - number to compute shifted exponential
      Returns:
      exp(x) - 1

    • log

      public static double log(double x)
      Natural logarithm.
      Parameters:
      x - a double
      Returns:
      log(x)

    • log1p

      public static double log1p(double x)
      Computes log(1 + x).
      Parameters:
      x - Number.
      Returns:
      log(1 + x).

    • log10

      public static double log10(double x)
      Compute the base 10 logarithm.
      Parameters:
      x - a number
      Returns:
      log10(x)

    • log

      public static double log(double base, double x)
      Computes the logarithm in a given base. Returns NaN if either argument is negative. If base is 0 and x is positive, 0 is returned. If base is positive and x is 0, Double.NEGATIVE_INFINITY is returned. If both arguments are 0, the result is NaN.
      Parameters:
      base - Base of the logarithm, must be greater than 0.
      x - Argument, must be greater than 0.
      Returns:
      the value of the logarithm, i.e. the number y such that basey = x.
      Since:
      1.2 (previously in MathUtils, moved as of version 3.0)

    • pow

      public static double pow(double x, double y)
      Power function. Compute x^y.
      Parameters:
      x - a double
      y - a double
      Returns:
      double

    • pow

      public static double pow(double d, int e)
      Raise a double to an int power.
      Parameters:
      d - Number to raise.
      e - Exponent.
      Returns:
      de
      Since:
      3.1

    • pow

      public static double pow(double d, long e)
      Raise a double to a long power.
      Parameters:
      d - Number to raise.
      e - Exponent.
      Returns:
      de
      Since:
      3.6

    • sin

      public static double sin(double x)
      Sine function.
      Parameters:
      x - Argument.
      Returns:
      sin(x)

    • cos

      public static double cos(double x)
      Cosine function.
      Parameters:
      x - Argument.
      Returns:
      cos(x)

    • tan

      public static double tan(double x)
      Tangent function.
      Parameters:
      x - Argument.
      Returns:
      tan(x)

    • atan

      public static double atan(double x)
      Arctangent function
      Parameters:
      x - a number
      Returns:
      atan(x)

    • atan2

      public static double atan2(double y, double x)
      Two arguments arctangent function
      Parameters:
      y - ordinate
      x - abscissa
      Returns:
      phase angle of point (x,y) between -PI and PI

    • asin

      public static double asin(double x)
      Compute the arc sine of a number.
      Parameters:
      x - number on which evaluation is done
      Returns:
      arc sine of x

    • acos

      public static double acos(double x)
      Compute the arc cosine of a number.
      Parameters:
      x - number on which evaluation is done
      Returns:
      arc cosine of x

    • cbrt

      public static double cbrt(double x)
      Compute the cubic root of a number.
      Parameters:
      x - number on which evaluation is done
      Returns:
      cubic root of x

    • toRadians

      public static double toRadians(double x)
      Convert degrees to radians, with error of less than 0.5 ULP
      Parameters:
      x - angle in degrees
      Returns:
      x converted into radians

    • toDegrees

      public static double toDegrees(double x)
      Convert radians to degrees, with error of less than 0.5 ULP
      Parameters:
      x - angle in radians
      Returns:
      x converted into degrees

    • abs

      public static int abs(int x)
      Absolute value.
      Parameters:
      x - number from which absolute value is requested
      Returns:
      abs(x)

    • abs

      public static long abs(long x)
      Absolute value.
      Parameters:
      x - number from which absolute value is requested
      Returns:
      abs(x)

    • abs

      public static float abs(float x)
      Absolute value.
      Parameters:
      x - number from which absolute value is requested
      Returns:
      abs(x)

    • abs

      public static double abs(double x)
      Absolute value.
      Parameters:
      x - number from which absolute value is requested
      Returns:
      abs(x)

    • ulp

      public static double ulp(double x)
      Compute least significant bit (Unit in Last Position) for a number.
      Parameters:
      x - number from which ulp is requested
      Returns:
      ulp(x)

    • ulp

      public static float ulp(float x)
      Compute least significant bit (Unit in Last Position) for a number.
      Parameters:
      x - number from which ulp is requested
      Returns:
      ulp(x)

    • scalb

      public static double scalb(double d, int n)
      Multiply a double number by a power of 2.
      Parameters:
      d - number to multiply
      n - power of 2
      Returns:
      d × 2n

    • scalb

      public static float scalb(float f, int n)
      Multiply a float number by a power of 2.
      Parameters:
      f - number to multiply
      n - power of 2
      Returns:
      f × 2n

    • nextAfter

      public static double nextAfter(double d, double direction)
      Get the next machine representable number after a number, moving in the direction of another number.

      The ordering is as follows (increasing):

      • -INFINITY
      • -MAX_VALUE
      • -MIN_VALUE
      • -0.0
      • +0.0
      • +MIN_VALUE
      • +MAX_VALUE
      • +INFINITY

      • If arguments compare equal, then the second argument is returned.

        If direction is greater than d, the smallest machine representable number strictly greater than d is returned; if less, then the largest representable number strictly less than d is returned.

        If d is infinite and direction does not bring it back to finite numbers, it is returned unchanged.

      Parameters:
      d - base number
      direction - (the only important thing is whether direction is greater or smaller than d)
      Returns:
      the next machine representable number in the specified direction

    • nextAfter

      public static float nextAfter(float f, double direction)
      Get the next machine representable number after a number, moving in the direction of another number.

      The ordering is as follows (increasing):

      • -INFINITY
      • -MAX_VALUE
      • -MIN_VALUE
      • -0.0
      • +0.0
      • +MIN_VALUE
      • +MAX_VALUE
      • +INFINITY

      • If arguments compare equal, then the second argument is returned.

        If direction is greater than f, the smallest machine representable number strictly greater than f is returned; if less, then the largest representable number strictly less than f is returned.

        If f is infinite and direction does not bring it back to finite numbers, it is returned unchanged.

      Parameters:
      f - base number
      direction - (the only important thing is whether direction is greater or smaller than f)
      Returns:
      the next machine representable number in the specified direction

    • floor

      public static double floor(double x)
      Get the largest whole number smaller than x.
      Parameters:
      x - number from which floor is requested
      Returns:
      a double number f such that f is an integer f invalid input: '<'= x invalid input: '<' f + 1.0

    • ceil

      public static double ceil(double x)
      Get the smallest whole number larger than x.
      Parameters:
      x - number from which ceil is requested
      Returns:
      a double number c such that c is an integer c - 1.0 invalid input: '<' x invalid input: '<'= c

    • rint

      public static double rint(double x)
      Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.
      Parameters:
      x - number from which nearest whole number is requested
      Returns:
      a double number r such that r is an integer r - 0.5 invalid input: '<'= x invalid input: '<'= r + 0.5

    • round

      public static long round(double x)
      Get the closest long to x.
      Parameters:
      x - number from which closest long is requested
      Returns:
      closest long to x

    • round

      public static int round(float x)
      Get the closest int to x.
      Parameters:
      x - number from which closest int is requested
      Returns:
      closest int to x

    • min

      public static int min(int a, int b)
      Compute the minimum of two values
      Parameters:
      a - first value
      b - second value
      Returns:
      a if a is lesser or equal to b, b otherwise

    • min

      public static long min(long a, long b)
      Compute the minimum of two values
      Parameters:
      a - first value
      b - second value
      Returns:
      a if a is lesser or equal to b, b otherwise

    • min

      public static float min(float a, float b)
      Compute the minimum of two values
      Parameters:
      a - first value
      b - second value
      Returns:
      a if a is lesser or equal to b, b otherwise

    • min

      public static double min(double a, double b)
      Compute the minimum of two values
      Parameters:
      a - first value
      b - second value
      Returns:
      a if a is lesser or equal to b, b otherwise

    • max

      public static int max(int a, int b)
      Compute the maximum of two values
      Parameters:
      a - first value
      b - second value
      Returns:
      b if a is lesser or equal to b, a otherwise

    • max

      public static long max(long a, long b)
      Compute the maximum of two values
      Parameters:
      a - first value
      b - second value
      Returns:
      b if a is lesser or equal to b, a otherwise

    • max

      public static float max(float a, float b)
      Compute the maximum of two values
      Parameters:
      a - first value
      b - second value
      Returns:
      b if a is lesser or equal to b, a otherwise

    • max

      public static double max(double a, double b)
      Compute the maximum of two values
      Parameters:
      a - first value
      b - second value
      Returns:
      b if a is lesser or equal to b, a otherwise

    • hypot

      public static double hypot(double x, double y)
      Returns the hypotenuse of a triangle with sides x and y - sqrt(x2 +y2)
      avoiding intermediate overflow or underflow.
      • If either argument is infinite, then the result is positive infinity.
      • else, if either argument is NaN then the result is NaN.
      Parameters:
      x - a value
      y - a value
      Returns:
      sqrt(x2 +y2)

    • IEEEremainder

      public static double IEEEremainder(double dividend, double divisor)
      Computes the remainder as prescribed by the IEEE 754 standard. The remainder value is mathematically equal to x - y*n where n is the mathematical integer closest to the exact mathematical value of the quotient x/y. If two mathematical integers are equally close to x/y then n is the integer that is even.

      • If either operand is NaN, the result is NaN.
      • If the result is not NaN, the sign of the result equals the sign of the dividend.
      • If the dividend is an infinity, or the divisor is a zero, or both, the result is NaN.
      • If the dividend is finite and the divisor is an infinity, the result equals the dividend.
      • If the dividend is a zero and the divisor is finite, the result equals the dividend.

      Note: this implementation currently delegates to StrictMath.IEEEremainder(double, double)

      Parameters:
      dividend - the number to be divided
      divisor - the number by which to divide
      Returns:
      the remainder, rounded

    • toIntExact

      public static int toIntExact(long n) throws MathArithmeticException
      Convert a long to interger, detecting overflows
      Parameters:
      n - number to convert to int
      Returns:
      integer with same valie as n if no overflows occur
      Throws:
      MathArithmeticException - if n cannot fit into an int
      Since:
      3.4

    • incrementExact

      public static int incrementExact(int n) throws MathArithmeticException
      Increment a number, detecting overflows.
      Parameters:
      n - number to increment
      Returns:
      n+1 if no overflows occur
      Throws:
      MathArithmeticException - if an overflow occurs
      Since:
      3.4

    • incrementExact

      public static long incrementExact(long n) throws MathArithmeticException
      Increment a number, detecting overflows.
      Parameters:
      n - number to increment
      Returns:
      n+1 if no overflows occur
      Throws:
      MathArithmeticException - if an overflow occurs
      Since:
      3.4

    • decrementExact

      public static int decrementExact(int n) throws MathArithmeticException
      Decrement a number, detecting overflows.
      Parameters:
      n - number to decrement
      Returns:
      n-1 if no overflows occur
      Throws:
      MathArithmeticException - if an overflow occurs
      Since:
      3.4

    • decrementExact

      public static long decrementExact(long n) throws MathArithmeticException
      Decrement a number, detecting overflows.
      Parameters:
      n - number to decrement
      Returns:
      n-1 if no overflows occur
      Throws:
      MathArithmeticException - if an overflow occurs
      Since:
      3.4

    • addExact

      public static int addExact(int a, int b) throws MathArithmeticException
      Add two numbers, detecting overflows.
      Parameters:
      a - first number to add
      b - second number to add
      Returns:
      a+b if no overflows occur
      Throws:
      MathArithmeticException - if an overflow occurs
      Since:
      3.4

    • addExact

      public static long addExact(long a, long b) throws MathArithmeticException
      Add two numbers, detecting overflows.
      Parameters:
      a - first number to add
      b - second number to add
      Returns:
      a+b if no overflows occur
      Throws:
      MathArithmeticException - if an overflow occurs
      Since:
      3.4

    • subtractExact

      public static int subtractExact(int a, int b)
      Subtract two numbers, detecting overflows.
      Parameters:
      a - first number
      b - second number to subtract from a
      Returns:
      a-b if no overflows occur
      Throws:
      MathArithmeticException - if an overflow occurs
      Since:
      3.4

    • subtractExact

      public static long subtractExact(long a, long b)
      Subtract two numbers, detecting overflows.
      Parameters:
      a - first number
      b - second number to subtract from a
      Returns:
      a-b if no overflows occur
      Throws:
      MathArithmeticException - if an overflow occurs
      Since:
      3.4

    • multiplyExact

      public static int multiplyExact(int a, int b)
      Multiply two numbers, detecting overflows.
      Parameters:
      a - first number to multiply
      b - second number to multiply
      Returns:
      a*b if no overflows occur
      Throws:
      MathArithmeticException - if an overflow occurs
      Since:
      3.4

    • multiplyExact

      public static long multiplyExact(long a, long b)
      Multiply two numbers, detecting overflows.
      Parameters:
      a - first number to multiply
      b - second number to multiply
      Returns:
      a*b if no overflows occur
      Throws:
      MathArithmeticException - if an overflow occurs
      Since:
      3.4

    • floorDiv

      public static int floorDiv(int a, int b) throws MathArithmeticException
      Finds q such that a = q b + r with 0 invalid input: '<'= r invalid input: '<' b if b > 0 and b invalid input: '<' r invalid input: '<'= 0 if b invalid input: '<' 0.

      This methods returns the same value as integer division when a and b are same signs, but returns a different value when they are opposite (i.e. q is negative).

      Parameters:
      a - dividend
      b - divisor
      Returns:
      q such that a = q b + r with 0 invalid input: '<'= r invalid input: '<' b if b > 0 and b invalid input: '<' r invalid input: '<'= 0 if b invalid input: '<' 0
      Throws:
      MathArithmeticException - if b == 0
      Since:
      3.4
      See Also:

    • floorDiv

      public static long floorDiv(long a, long b) throws MathArithmeticException
      Finds q such that a = q b + r with 0 invalid input: '<'= r invalid input: '<' b if b > 0 and b invalid input: '<' r invalid input: '<'= 0 if b invalid input: '<' 0.

      This methods returns the same value as integer division when a and b are same signs, but returns a different value when they are opposite (i.e. q is negative).

      Parameters:
      a - dividend
      b - divisor
      Returns:
      q such that a = q b + r with 0 invalid input: '<'= r invalid input: '<' b if b > 0 and b invalid input: '<' r invalid input: '<'= 0 if b invalid input: '<' 0
      Throws:
      MathArithmeticException - if b == 0
      Since:
      3.4
      See Also:

    • floorMod

      public static int floorMod(int a, int b) throws MathArithmeticException
      Finds r such that a = q b + r with 0 invalid input: '<'= r invalid input: '<' b if b > 0 and b invalid input: '<' r invalid input: '<'= 0 if b invalid input: '<' 0.

      This methods returns the same value as integer modulo when a and b are same signs, but returns a different value when they are opposite (i.e. q is negative).

      Parameters:
      a - dividend
      b - divisor
      Returns:
      r such that a = q b + r with 0 invalid input: '<'= r invalid input: '<' b if b > 0 and b invalid input: '<' r invalid input: '<'= 0 if b invalid input: '<' 0
      Throws:
      MathArithmeticException - if b == 0
      Since:
      3.4
      See Also:

    • floorMod

      public static long floorMod(long a, long b)
      Finds r such that a = q b + r with 0 invalid input: '<'= r invalid input: '<' b if b > 0 and b invalid input: '<' r invalid input: '<'= 0 if b invalid input: '<' 0.

      This methods returns the same value as integer modulo when a and b are same signs, but returns a different value when they are opposite (i.e. q is negative).

      Parameters:
      a - dividend
      b - divisor
      Returns:
      r such that a = q b + r with 0 invalid input: '<'= r invalid input: '<' b if b > 0 and b invalid input: '<' r invalid input: '<'= 0 if b invalid input: '<' 0
      Throws:
      MathArithmeticException - if b == 0
      Since:
      3.4
      See Also:

    • copySign

      public static double copySign(double magnitude, double sign)
      Returns the first argument with the sign of the second argument. A NaN sign argument is treated as positive.
      Parameters:
      magnitude - the value to return
      sign - the sign for the returned value
      Returns:
      the magnitude with the same sign as the sign argument

    • copySign

      public static float copySign(float magnitude, float sign)
      Returns the first argument with the sign of the second argument. A NaN sign argument is treated as positive.
      Parameters:
      magnitude - the value to return
      sign - the sign for the returned value
      Returns:
      the magnitude with the same sign as the sign argument

    • getExponent

      public static int getExponent(double d)
      Return the exponent of a double number, removing the bias.

      For double numbers of the form 2x, the unbiased exponent is exactly x.

      Parameters:
      d - number from which exponent is requested
      Returns:
      exponent for d in IEEE754 representation, without bias

    • getExponent

      public static int getExponent(float f)
      Return the exponent of a float number, removing the bias.

      For float numbers of the form 2x, the unbiased exponent is exactly x.

      Parameters:
      f - number from which exponent is requested
      Returns:
      exponent for d in IEEE754 representation, without bias

    • main

      public static void main(String[] a)
      Print out contents of arrays, and check the length.

      used to generate the preset arrays originally.

      Parameters:
      a - unused