Class StrictMath

java.lang.Object
- java.lang.StrictMath

public final class StrictMath
extends Object

The class StrictMath contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.

To help ensure portability of Java programs, the definitions of some of the numeric functions in this package require that they produce the same results as certain published algorithms. These algorithms are available from the well-known network library netlib as the package "Freely Distributable Math Library," fdlibm. These algorithms, which are written in the C programming language, are then to be understood as executed with all floating-point operations following the rules of Java floating-point arithmetic.

The Java math library is defined with respect to fdlibm version 5.3. Where fdlibm provides more than one definition for a function (such as acos), use the "IEEE 754 core function" version (residing in a file whose name begins with the letter e). The methods which require fdlibm semantics are sin, cos, tan, asin, acos, atan, exp, log, log10, cbrt, atan2, pow, sinh, cosh, tanh, hypot, expm1, and log1p.

The platform uses signed two's complement integer arithmetic with int and long primitive types. The developer should choose the primitive type to ensure that arithmetic operations consistently produce correct results, which in some cases means the operations will not overflow the range of values of the computation. The best practice is to choose the primitive type and algorithm to avoid overflow. In cases where the size is int or long and overflow errors need to be detected, the methods addExact, subtractExact, multiplyExact, and toIntExact throw an ArithmeticException when the results overflow. For other arithmetic operations such as divide, absolute value, increment by one, decrement by one, and negation overflow occurs only with a specific minimum or maximum value and should be checked against the minimum or maximum as appropriate.

Since:: 1.3

Field Summary

Fields
Modifier and Type	Field	Description
`static double`	`E`	The `double` value that is closer than any other to e, the base of the natural logarithms.
`static double`	`PI`	The `double` value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter.

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method	Description
`static double`	`abs(double a)`	Returns the absolute value of a `double` value.
`static float`	`abs(float a)`	Returns the absolute value of a `float` value.
`static int`	`abs(int a)`	Returns the absolute value of an `int` value.
`static long`	`abs(long a)`	Returns the absolute value of a `long` value.
`static double`	`acos(double a)`	Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi.
`static int`	`addExact(int x, int y)`	Returns the sum of its arguments, throwing an exception if the result overflows an `int`.
`static long`	`addExact(long x, long y)`	Returns the sum of its arguments, throwing an exception if the result overflows a `long`.
`static double`	`asin(double a)`	Returns the arc sine of a value; the returned angle is in the range -pi/2 through pi/2.
`static double`	`atan(double a)`	Returns the arc tangent of a value; the returned angle is in the range -pi/2 through pi/2.
`static double`	`atan2(double y, double x)`	Returns the angle theta from the conversion of rectangular coordinates (`x`, `y`) to polar coordinates (r, theta).
`static double`	`cbrt(double a)`	Returns the cube root of a `double` value.
`static double`	`ceil(double a)`	Returns the smallest (closest to negative infinity) `double` value that is greater than or equal to the argument and is equal to a mathematical integer.
`static double`	`copySign(double magnitude, double sign)`	Returns the first floating-point argument with the sign of the second floating-point argument.
`static float`	`copySign(float magnitude, float sign)`	Returns the first floating-point argument with the sign of the second floating-point argument.
`static double`	`cos(double a)`	Returns the trigonometric cosine of an angle.
`static double`	`cosh(double x)`	Returns the hyperbolic cosine of a `double` value.
`static double`	`exp(double a)`	Returns Euler's number e raised to the power of a `double` value.
`static double`	`expm1(double x)`	Returns e^x -1.
`static double`	`floor(double a)`	Returns the largest (closest to positive infinity) `double` value that is less than or equal to the argument and is equal to a mathematical integer.
`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.
`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.
`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.
`static int`	`floorMod(int x, int y)`	Returns the floor modulus of the `int` arguments.
`static int`	`floorMod(long x, int y)`	Returns the floor modulus of the `long` and `int` arguments.
`static long`	`floorMod(long x, long y)`	Returns the floor modulus of the `long` arguments.
`static double`	`fma(double a, double b, double c)`	Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest `double`.
`static float`	`fma(float a, float b, float c)`	Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest `float`.
`static int`	`getExponent(double d)`	Returns the unbiased exponent used in the representation of a `double`.
`static int`	`getExponent(float f)`	Returns the unbiased exponent used in the representation of a `float`.
`static double`	`hypot(double x, double y)`	Returns sqrt(x² +y²) without intermediate overflow or underflow.
`static double`	`IEEEremainder(double f1, double f2)`	Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard.
`static double`	`log(double a)`	Returns the natural logarithm (base e) of a `double` value.
`static double`	`log10(double a)`	Returns the base 10 logarithm of a `double` value.
`static double`	`log1p(double x)`	Returns the natural logarithm of the sum of the argument and 1.
`static double`	`max(double a, double b)`	Returns the greater of two `double` values.
`static float`	`max(float a, float b)`	Returns the greater of two `float` values.
`static int`	`max(int a, int b)`	Returns the greater of two `int` values.
`static long`	`max(long a, long b)`	Returns the greater of two `long` values.
`static double`	`min(double a, double b)`	Returns the smaller of two `double` values.
`static float`	`min(float a, float b)`	Returns the smaller of two `float` values.
`static int`	`min(int a, int b)`	Returns the smaller of two `int` values.
`static long`	`min(long a, long b)`	Returns the smaller of two `long` values.
`static int`	`multiplyExact(int x, int y)`	Returns the product of the arguments, throwing an exception if the result overflows an `int`.
`static long`	`multiplyExact(long x, int y)`	Returns the product of the arguments, throwing an exception if the result overflows a `long`.
`static long`	`multiplyExact(long x, long y)`	Returns the product of the arguments, throwing an exception if the result overflows a `long`.
`static long`	`multiplyFull(int x, int y)`	Returns the exact mathematical product of the arguments.
`static long`	`multiplyHigh(long x, long y)`	Returns as a `long` the most significant 64 bits of the 128-bit product of two 64-bit factors.
`static double`	`nextAfter(double start, double direction)`	Returns the floating-point number adjacent to the first argument in the direction of the second argument.
`static float`	`nextAfter(float start, double direction)`	Returns the floating-point number adjacent to the first argument in the direction of the second argument.
`static double`	`nextDown(double d)`	Returns the floating-point value adjacent to `d` in the direction of negative infinity.
`static float`	`nextDown(float f)`	Returns the floating-point value adjacent to `f` in the direction of negative infinity.
`static double`	`nextUp(double d)`	Returns the floating-point value adjacent to `d` in the direction of positive infinity.
`static float`	`nextUp(float f)`	Returns the floating-point value adjacent to `f` in the direction of positive infinity.
`static double`	`pow(double a, double b)`	Returns the value of the first argument raised to the power of the second argument.
`static double`	`random()`	Returns a `double` value with a positive sign, greater than or equal to `0.0` and less than `1.0`.
`static double`	`rint(double a)`	Returns the `double` value that is closest in value to the argument and is equal to a mathematical integer.
`static long`	`round(double a)`	Returns the closest `long` to the argument, with ties rounding to positive infinity.
`static int`	`round(float a)`	Returns the closest `int` to the argument, with ties rounding to positive infinity.
`static double`	`scalb(double d, int scaleFactor)`	Returns `d` × 2^scaleFactor rounded as if performed by a single correctly rounded floating-point multiply to a member of the double value set.
`static float`	`scalb(float f, int scaleFactor)`	Returns `f` × 2^scaleFactor rounded as if performed by a single correctly rounded floating-point multiply to a member of the float value set.
`static double`	`signum(double d)`	Returns the signum function of the argument; zero if the argument is zero, 1.0 if the argument is greater than zero, -1.0 if the argument is less than zero.
`static float`	`signum(float f)`	Returns the signum function of the argument; zero if the argument is zero, 1.0f if the argument is greater than zero, -1.0f if the argument is less than zero.
`static double`	`sin(double a)`	Returns the trigonometric sine of an angle.
`static double`	`sinh(double x)`	Returns the hyperbolic sine of a `double` value.
`static double`	`sqrt(double a)`	Returns the correctly rounded positive square root of a `double` value.
`static int`	`subtractExact(int x, int y)`	Returns the difference of the arguments, throwing an exception if the result overflows an `int`.
`static long`	`subtractExact(long x, long y)`	Returns the difference of the arguments, throwing an exception if the result overflows a `long`.
`static double`	`tan(double a)`	Returns the trigonometric tangent of an angle.
`static double`	`tanh(double x)`	Returns the hyperbolic tangent of a `double` value.
`static double`	`toDegrees(double angrad)`	Converts an angle measured in radians to an approximately equivalent angle measured in degrees.
`static int`	`toIntExact(long value)`	Returns the value of the `long` argument; throwing an exception if the value overflows an `int`.
`static double`	`toRadians(double angdeg)`	Converts an angle measured in degrees to an approximately equivalent angle measured in radians.
`static double`	`ulp(double d)`	Returns the size of an ulp of the argument.
`static float`	`ulp(float f)`	Returns the size of an ulp of the argument.

Methods declared in class java.lang.Object

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

Field Detail

E

public static final double E

The double value that is closer than any other to e, the base of the natural logarithms.

See Also:: Constant Field Values

PI

public static final double PI

The double value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter.

See Also:: Constant Field Values

Method Detail

sin

public static double sin(double a)

Returns the trigonometric sine of an angle. Special cases:

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

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.

Parameters:: a - an angle, in radians.
Returns:: the cosine of the argument.

tan

public static double tan(double a)

Returns the trigonometric tangent of an angle. Special cases:

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

Parameters:: a - an angle, in radians.
Returns:: the tangent of the argument.

asin

public static double asin(double a)

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

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

Parameters:: a - the value whose arc sine is to be returned.
Returns:: the arc sine of the argument.

acos

public static double acos(double a)

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

If the argument is NaN or its absolute value is greater than 1, then the result is NaN.

Parameters:: a - the value whose arc cosine is to be returned.
Returns:: the arc cosine of the argument.

atan

public static double atan(double a)

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

If the argument is NaN, then the result is NaN.
If the argument is zero, then the result is a zero with the same sign as the argument.

Parameters:: a - the value whose arc tangent is to be returned.
Returns:: the arc tangent of the argument.

toRadians

public static double toRadians(double angdeg)

Converts an angle measured in degrees to an approximately equivalent angle measured in radians. The conversion from degrees to radians is generally inexact.

Parameters:: angdeg - an angle, in degrees
Returns:: the measurement of the angle angdeg in radians.

toDegrees

public static double toDegrees(double angrad)

Converts an angle measured in radians to an approximately equivalent angle measured in degrees. The conversion from radians to degrees is generally inexact; users should not expect cos(toRadians(90.0)) to exactly equal 0.0.

Parameters:: angrad - an angle, in radians
Returns:: the measurement of the angle angrad in degrees.

exp

public static double exp(double a)

Returns Euler's number e raised to the power of a double value. Special cases:

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

Parameters:: a - the exponent to raise e to.
Returns:: the value e^a, where e is the base of the natural logarithms.

log

public static double log(double a)

Returns the natural logarithm (base e) of a double value. Special cases:

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

Parameters:: a - a value
Returns:: the value ln a, the natural logarithm of a.

log10

public static double log10(double a)

Returns the base 10 logarithm of a double value. Special cases:

If the argument is NaN or less than zero, then the result is NaN.
If the argument is positive infinity, then the result is positive infinity.
If the argument is positive zero or negative zero, then the result is negative infinity.
If the argument is equal to 10ⁿ for integer n, then the result is n.

Parameters:: a - a value
Returns:: the base 10 logarithm of a.
Since:: 1.5

sqrt

public static double sqrt(double a)

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

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

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

Parameters:: a - a value.
Returns:: the positive square root of a.

cbrt

public static double cbrt(double a)

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

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

Parameters:: a - a value.
Returns:: the cube root of a.
Since:: 1.5

IEEEremainder

public static double IEEEremainder(double f1,
                                   double f2)

Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. The remainder value is mathematically equal to f1 - f2 × n, where n is the mathematical integer closest to the exact mathematical value of the quotient f1/f2, and if two mathematical integers are equally close to f1/f2, then n is the integer that is even. If the remainder is zero, its sign is the same as the sign of the first argument. Special cases:

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

Parameters:: f1 - the dividend.; f2 - the divisor.
Returns:: the remainder when f1 is divided by f2.

ceil

public static double ceil(double a)

Returns the smallest (closest to negative infinity) double value that is greater than or equal to the argument and is equal to a mathematical integer. Special cases:

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

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

Parameters:: a - a value.
Returns:: the smallest (closest to negative infinity) floating-point value that is greater than or equal to the argument and is equal to a mathematical integer.

floor

public static double floor(double a)

Returns the largest (closest to positive infinity) double value that is less than or equal to the argument and is equal to a mathematical integer. Special cases:

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

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

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

Parameters:: a - a value.
Returns:: the closest floating-point value to a that is equal to a mathematical integer.

atan2

public static double atan2(double y,
                           double x)

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

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

Parameters:: y - the ordinate coordinate; x - the abscissa coordinate
Returns:: the theta component of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates.

pow

public static double pow(double a,
                         double b)

Returns the value of the first argument raised to the power of the second argument. Special cases:

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

(In the foregoing descriptions, a floating-point value is considered to be an integer if and only if it is finite and a fixed point of the method ceil or, equivalently, a fixed point of the method floor. A value is a fixed point of a one-argument method if and only if the result of applying the method to the value is equal to the value.)

Parameters:: a - base.; b - the exponent.
Returns:: the value a^b.

round

public static int round(float a)

Returns the closest int to the argument, with ties rounding to positive infinity.

Special cases:

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

Parameters:: a - a floating-point value to be rounded to an integer.
Returns:: the value of the argument rounded to the nearest int value.
See Also:: Integer.MAX_VALUE, Integer.MIN_VALUE

round

public static long round(double a)

Returns the closest long to the argument, with ties rounding to positive infinity.

Special cases:

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

Parameters:: a - a floating-point value to be rounded to a long.
Returns:: the value of the argument rounded to the nearest long value.
See Also:: Long.MAX_VALUE, Long.MIN_VALUE

random

public static double random()

Returns a double value with a positive sign, greater than or equal to 0.0 and less than 1.0. Returned values are chosen pseudorandomly with (approximately) uniform distribution from that range.

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

new java.util.Random()

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

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

Returns:: a pseudorandom double greater than or equal to 0.0 and less than 1.0.
See Also:: Random.nextDouble()

addExact

public static int addExact(int x,
                           int y)

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

Parameters:: x - the first value; y - the second value
Returns:: the result
Throws:: ArithmeticException - if the result overflows an int
Since:: 1.8
See Also:: Math.addExact(int,int)

addExact

public static long addExact(long x,
                            long y)

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

Parameters:: x - the first value; y - the second value
Returns:: the result
Throws:: ArithmeticException - if the result overflows a long
Since:: 1.8
See Also:: Math.addExact(long,long)

subtractExact

public static int subtractExact(int x,
                                int y)

Returns the difference of the arguments, throwing an exception if the result overflows an int.

Parameters:: x - the first value; y - the second value to subtract from the first
Returns:: the result
Throws:: ArithmeticException - if the result overflows an int
Since:: 1.8
See Also:: Math.subtractExact(int,int)

subtractExact

public static long subtractExact(long x,
                                 long y)

Returns the difference of the arguments, throwing an exception if the result overflows a long.

Parameters:: x - the first value; y - the second value to subtract from the first
Returns:: the result
Throws:: ArithmeticException - if the result overflows a long
Since:: 1.8
See Also:: Math.subtractExact(long,long)

multiplyExact

public static int multiplyExact(int x,
                                int y)

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

Parameters:: x - the first value; y - the second value
Returns:: the result
Throws:: ArithmeticException - if the result overflows an int
Since:: 1.8
See Also:: Math.multiplyExact(int,int)

multiplyExact

public static long multiplyExact(long x,
                                 int y)

Returns the product of the arguments, throwing an exception if the result overflows a long.

Parameters:: x - the first value; y - the second value
Returns:: the result
Throws:: ArithmeticException - if the result overflows a long
Since:: 9
See Also:: Math.multiplyExact(long,int)

multiplyExact

public static long multiplyExact(long x,
                                 long y)

Returns the product of the arguments, throwing an exception if the result overflows a long.

Parameters:: x - the first value; y - the second value
Returns:: the result
Throws:: ArithmeticException - if the result overflows a long
Since:: 1.8
See Also:: Math.multiplyExact(long,long)

toIntExact

public static int toIntExact(long value)

Returns the value of the long argument; throwing an exception if the value overflows an int.

Parameters:: value - the long value
Returns:: the argument as an int
Throws:: ArithmeticException - if the argument overflows an int
Since:: 1.8
See Also:: Math.toIntExact(long)

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
See Also:: Math.multiplyFull(int,int)

multiplyHigh

public static long multiplyHigh(long x,
                                long y)

Returns as a long the most significant 64 bits of the 128-bit product of two 64-bit factors.

Parameters:: x - the first value; y - the second value
Returns:: the result
Since:: 9
See Also:: Math.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 is the Integer.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to the Integer.MIN_VALUE.

See Math.floorDiv for examples and a comparison to the integer division / operator.

Parameters:: x - the dividend; y - the divisor
Returns:: the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient.
Throws:: ArithmeticException - if the divisor y is zero
Since:: 1.8
See Also:: Math.floorDiv(int, int), Math.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 is the Long.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Long.MIN_VALUE.

See Math.floorDiv for examples and a comparison to the integer division / operator.

Parameters:: x - the dividend; y - the divisor
Returns:: the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient.
Throws:: ArithmeticException - if the divisor y is zero
Since:: 9
See Also:: Math.floorDiv(long, int), Math.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 is the Long.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to the Long.MIN_VALUE.

See Math.floorDiv for examples and a comparison to the integer division / operator.

Parameters:: x - the dividend; y - the divisor
Returns:: the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient.
Throws:: ArithmeticException - if the divisor y is zero
Since:: 1.8
See Also:: Math.floorDiv(long, long), Math.floor(double)

floorMod

public static int floorMod(int x,
                           int y)

Returns the floor modulus of the int arguments.

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

The relationship between floorDiv and floorMod is such that:

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

See Math.floorMod for examples and a comparison to the % operator.

Parameters:: x - the dividend; y - the divisor
Returns:: the floor modulus x - (floorDiv(x, y) * y)
Throws:: ArithmeticException - if the divisor y is zero
Since:: 1.8
See Also:: Math.floorMod(int, int), floorDiv(int, int)

floorMod

public static int floorMod(long x,
                           int y)

Returns the floor modulus of the long and int arguments.

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

The relationship between floorDiv and floorMod is such that:

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

See Math.floorMod for examples and a comparison to the % operator.

Parameters:: x - the dividend; y - the divisor
Returns:: the floor modulus x - (floorDiv(x, y) * y)
Throws:: ArithmeticException - if the divisor y is zero
Since:: 9
See Also:: Math.floorMod(long, int), floorDiv(long, int)

floorMod

public static long floorMod(long x,
                            long y)

Returns the floor modulus of the long arguments.

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

The relationship between floorDiv and floorMod is such that:

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

See Math.floorMod for examples and a comparison to the % operator.

Parameters:: x - the dividend; y - the divisor
Returns:: the floor modulus x - (floorDiv(x, y) * y)
Throws:: ArithmeticException - if the divisor y is zero
Since:: 1.8
See Also:: Math.floorMod(long, long), floorDiv(long, long)

abs

public static int abs(int a)

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

Note that if the argument is equal to the value of Integer.MIN_VALUE, the most negative representable int value, the result is that same value, which is negative.

Parameters:: a - the argument whose absolute value is to be determined.
Returns:: the absolute value of the argument.

abs

public static long abs(long a)

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

Note that if the argument is equal to the value of Long.MIN_VALUE, the most negative representable long value, the result is that same value, which is negative.

Parameters:: a - the argument whose absolute value is to be determined.
Returns:: the absolute value of the argument.

abs

public static float abs(float a)

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

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

API Note:: As implied by the above, one valid implementation of this method is given by the expression below which computes a float with the same exponent and significand as the argument but with a guaranteed zero sign bit indicating a positive value:
Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a))
Parameters:: a - the argument whose absolute value is to be determined
Returns:: the absolute value of the argument.

abs

public static double abs(double a)

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

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

API Note:: As implied by the above, one valid implementation of this method is given by the expression below which computes a double with the same exponent and significand as the argument but with a guaranteed zero sign bit indicating a positive value:
Double.longBitsToDouble((Double.doubleToRawLongBits(a)<<1)>>>1)
Parameters:: a - the argument whose absolute value is to be determined
Returns:: the absolute value of the argument.

max

public static int max(int a,
                      int b)

Returns the greater of two int values. That is, the result is the argument closer to the value of Integer.MAX_VALUE. If the arguments have the same value, the result is that same value.

Parameters:: a - an argument.; b - another argument.
Returns:: the larger of a and b.

max

public static long max(long a,
                       long b)

Returns the greater of two long values. That is, the result is the argument closer to the value of Long.MAX_VALUE. If the arguments have the same value, the result is that same value.

Parameters:: a - an argument.; b - another argument.
Returns:: the larger of a and b.

max

public static float max(float a,
                        float b)

Returns the greater of two float values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero.

Parameters:: a - an argument.; b - another argument.
Returns:: the larger of a and b.

max

public static double max(double a,
                         double b)

Returns the greater of two double values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero.

Parameters:: a - an argument.; b - another argument.
Returns:: the larger of a and b.

min

public static int min(int a,
                      int b)

Returns the smaller of two int values. That is, the result the argument closer to the value of Integer.MIN_VALUE. If the arguments have the same value, the result is that same value.

Parameters:: a - an argument.; b - another argument.
Returns:: the smaller of a and b.

min

public static long min(long a,
                       long b)

Returns the smaller of two long values. That is, the result is the argument closer to the value of Long.MIN_VALUE. If the arguments have the same value, the result is that same value.

Parameters:: a - an argument.; b - another argument.
Returns:: the smaller of a and b.

min

public static float min(float a,
                        float b)

Returns the smaller of two float values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero.

Parameters:: a - an argument.; b - another argument.
Returns:: the smaller of a and b.

min

public static double min(double a,
                         double b)

Returns the smaller of two double values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero.

Parameters:: a - an argument.; b - another argument.
Returns:: the smaller of a and b.

fma

public static double fma(double a,
                         double b,
                         double c)

Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest double. The rounding is done using the round to nearest even rounding mode. In contrast, if a * b + c is evaluated as a regular floating-point expression, two rounding errors are involved, the first for the multiply operation, the second for the addition operation.

Special cases:

If any argument is NaN, the result is NaN.
If one of the first two arguments is infinite and the other is zero, the result is NaN.
If the exact product of the first two arguments is infinite (in other words, at least one of the arguments is infinite and the other is neither zero nor NaN) and the third argument is an infinity of the opposite sign, the result is NaN.

Note that fusedMac(a, 1.0, c) returns the same result as (a + c). However, fusedMac(a, b, +0.0) does not always return the same result as (a * b) since fusedMac(-0.0, +0.0, +0.0) is +0.0 while (-0.0 * +0.0) is -0.0; fusedMac(a, b, -0.0) is equivalent to (a * b) however.

API Note:: This method corresponds to the fusedMultiplyAdd operation defined in IEEE 754-2008.
Parameters:: a - a value; b - a value; c - a value
Returns:: (a × b + c) computed, as if with unlimited range and precision, and rounded once to the nearest double value
Since:: 9

fma

public static float fma(float a,
                        float b,
                        float c)

Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest float. The rounding is done using the round to nearest even rounding mode. In contrast, if a * b + c is evaluated as a regular floating-point expression, two rounding errors are involved, the first for the multiply operation, the second for the addition operation.

Special cases:

If any argument is NaN, the result is NaN.
If one of the first two arguments is infinite and the other is zero, the result is NaN.
If the exact product of the first two arguments is infinite (in other words, at least one of the arguments is infinite and the other is neither zero nor NaN) and the third argument is an infinity of the opposite sign, the result is NaN.

Note that fma(a, 1.0f, c) returns the same result as (a + c). However, fma(a, b, +0.0f) does not always return the same result as (a * b) since fma(-0.0f, +0.0f, +0.0f) is +0.0f while (-0.0f * +0.0f) is -0.0f; fma(a, b, -0.0f) is equivalent to (a * b) however.

API Note:: This method corresponds to the fusedMultiplyAdd operation defined in IEEE 754-2008.
Parameters:: a - a value; b - a value; c - a value
Returns:: (a × b + c) computed, as if with unlimited range and precision, and rounded once to the nearest float value
Since:: 9

ulp

public static double ulp(double d)

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

Special Cases:

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

Parameters:: d - the floating-point value whose ulp is to be returned
Returns:: the size of an ulp of the argument
Since:: 1.5

ulp

public static float ulp(float f)

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

Special Cases:

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

Parameters:: f - the floating-point value whose ulp is to be returned
Returns:: the size of an ulp of the argument
Since:: 1.5

signum

public static double signum(double d)

Returns the signum function of the argument; zero if the argument is zero, 1.0 if the argument is greater than zero, -1.0 if the argument is less than zero.

Special Cases:

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

Parameters:: d - the floating-point value whose signum is to be returned
Returns:: the signum function of the argument
Since:: 1.5

signum

public static float signum(float f)

Returns the signum function of the argument; zero if the argument is zero, 1.0f if the argument is greater than zero, -1.0f if the argument is less than zero.

Special Cases:

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

Parameters:: f - the floating-point value whose signum is to be returned
Returns:: the signum function of the argument
Since:: 1.5

sinh

public static double sinh(double x)

Returns the hyperbolic sine of a double value. The hyperbolic sine of x is defined to be (e^x - e^-x)/2 where e is Euler's number.

Special cases:

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

Parameters:: x - The number whose hyperbolic sine is to be returned.
Returns:: The hyperbolic sine of x.
Since:: 1.5

cosh

public static double cosh(double x)

Returns the hyperbolic cosine of a double value. The hyperbolic cosine of x is defined to be (e^x + e^-x)/2 where e is Euler's number.

Special cases:

If the argument is NaN, then the result is NaN.
If the argument is infinite, then the result is positive infinity.
If the argument is zero, then the result is 1.0.

Parameters:: x - The number whose hyperbolic cosine is to be returned.
Returns:: The hyperbolic cosine of x.
Since:: 1.5

tanh

public static double tanh(double x)

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

Special cases:

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

Parameters:: x - The number whose hyperbolic tangent is to be returned.
Returns:: The hyperbolic tangent of x.
Since:: 1.5

hypot

public static double hypot(double x,
                           double y)

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

Special cases:

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

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)

Returns e^x -1. Note that for values of x near 0, the exact sum of expm1(x) + 1 is much closer to the true result of e^x than exp(x).

Special cases:

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

Parameters:: x - the exponent to raise e to in the computation of e^x -1.
Returns:: the value e^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 values x, the result of log1p(x) is much closer to the true result of ln(1 + x) than the floating-point evaluation of log(1.0+x).

Special cases:

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

Parameters:: x - a value
Returns:: the value ln(x + 1), the natural log of x + 1
Since:: 1.5

copySign

public static double copySign(double magnitude,
                              double sign)

Returns the first floating-point argument with the sign of the second floating-point argument. For this method, a NaN sign argument is always treated as if it were positive.

Parameters:: magnitude - the parameter providing the magnitude of the result; sign - the parameter providing the sign of the result
Returns:: a value with the magnitude of magnitude and the sign of sign.
Since:: 1.6

copySign

public static float copySign(float magnitude,
                             float sign)

Returns the first floating-point argument with the sign of the second floating-point argument. For this method, a NaN sign argument is always treated as if it were positive.

Parameters:: magnitude - the parameter providing the magnitude of the result; sign - the parameter providing the sign of the result
Returns:: a value with the magnitude of magnitude and the sign of sign.
Since:: 1.6

getExponent

public static int getExponent(float f)

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

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

Parameters:: f - a float 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 a double. Special cases:

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

Parameters:: d - a double value
Returns:: the unbiased exponent of the argument
Since:: 1.6

nextAfter

public static double nextAfter(double start,
                               double direction)

Returns the floating-point number adjacent to the first argument in the direction of the second argument. If both arguments compare as equal the second argument is returned.

Special cases:

If either argument is a NaN, then NaN is returned.
If both arguments are signed zeros, direction is returned unchanged (as implied by the requirement of returning the second argument if the arguments compare as equal).
If start is ±Double.MIN_VALUE and direction has a value such that the result should have a smaller magnitude, then a zero with the same sign as start is returned.
If start is infinite and direction has a value such that the result should have a smaller magnitude, Double.MAX_VALUE with the same sign as start is returned.
If start is equal to ± Double.MAX_VALUE and direction has a value such that the result should have a larger magnitude, an infinity with same sign as start is returned.

Parameters:: start - starting floating-point value; direction - value indicating which of start's neighbors or start should be returned
Returns:: The floating-point number adjacent to start in the direction of direction.
Since:: 1.6

nextAfter

public static float nextAfter(float start,
                              double direction)

Returns the floating-point number adjacent to the first argument in the direction of the second argument. If both arguments compare as equal a value equivalent to the second argument is returned.

Special cases:

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

Parameters:: start - starting floating-point value; direction - value indicating which of start's neighbors or start should be returned
Returns:: The floating-point number adjacent to start in the direction of direction.
Since:: 1.6

nextUp

public static double nextUp(double d)

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

Special Cases:

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

Parameters:: d - starting floating-point value
Returns:: The adjacent floating-point value closer to positive infinity.
Since:: 1.6

nextUp

public static float nextUp(float f)

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

Special Cases:

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

Parameters:: f - starting floating-point value
Returns:: The adjacent floating-point value closer to positive infinity.
Since:: 1.6

nextDown

public static double nextDown(double d)

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

Special Cases:

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

Parameters:: d - starting floating-point value
Returns:: The adjacent floating-point value closer to negative infinity.
Since:: 1.8

nextDown

public static float nextDown(float f)

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

Special Cases:

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

Parameters:: f - starting floating-point value
Returns:: The adjacent floating-point value closer to negative infinity.
Since:: 1.8

scalb

public static double scalb(double d,
                           int scaleFactor)

Returns d × 2^scaleFactor rounded as if performed by a single correctly rounded floating-point multiply to a member of the double value set. See the Java Language Specification for a discussion of floating-point value sets. If the exponent of the result is between Double.MIN_EXPONENT and Double.MAX_EXPONENT, the answer is calculated exactly. If the exponent of the result would be larger than Double.MAX_EXPONENT, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when scalb(x, n) is subnormal, scalb(scalb(x, n), -n) may not equal x. When the result is non-NaN, the result has the same sign as d.

Special cases:

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

Parameters:: d - number to be scaled by a power of two.; scaleFactor - power of 2 used to scale d
Returns:: d × 2^scaleFactor
Since:: 1.6

scalb

public static float scalb(float f,
                          int scaleFactor)

Returns f × 2^scaleFactor rounded as if performed by a single correctly rounded floating-point multiply to a member of the float value set. See the Java Language Specification for a discussion of floating-point value sets. If the exponent of the result is between Float.MIN_EXPONENT and Float.MAX_EXPONENT, the answer is calculated exactly. If the exponent of the result would be larger than Float.MAX_EXPONENT, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when scalb(x, n) is subnormal, scalb(scalb(x, n), -n) may not equal x. When the result is non-NaN, the result has the same sign as f.

Special cases:

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

Parameters:: f - number to be scaled by a power of two.; scaleFactor - power of 2 used to scale f
Returns:: f × 2^scaleFactor
Since:: 1.6