public final class StrictMath extends Object
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 wellknown 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 floatingpoint
operations following the rules of Java floatingpoint 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

Method Summary
Modifier and Type Method Description static double
abs(double a)
Returns the absolute value of adouble
value.static float
abs(float a)
Returns the absolute value of afloat
value.static int
abs(int a)
Returns the absolute value of anint
value.static long
abs(long a)
Returns the absolute value of along
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 anint
.static long
addExact(long x, long y)
Returns the sum of its arguments, throwing an exception if the result overflows along
.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 adouble
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 floatingpoint argument with the sign of the second floatingpoint argument.static float
copySign(float magnitude, float sign)
Returns the first floatingpoint argument with the sign of the second floatingpoint argument.static double
cos(double a)
Returns the trigonometric cosine of an angle.static double
cosh(double x)
Returns the hyperbolic cosine of adouble
value.static double
exp(double a)
Returns Euler's number e raised to the power of adouble
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 theint
arguments.static int
floorMod(long x, int y)
Returns the floor modulus of thelong
andint
arguments.static long
floorMod(long x, long y)
Returns the floor modulus of thelong
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 nearestdouble
.static float
fma(float a, float b, float c)
Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearestfloat
.static int
getExponent(double d)
Returns the unbiased exponent used in the representation of adouble
.static int
getExponent(float f)
Returns the unbiased exponent used in the representation of afloat
.static double
hypot(double x, double y)
Returns sqrt(x^{2} +y^{2}) 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 adouble
value.static double
log10(double a)
Returns the base 10 logarithm of adouble
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 twodouble
values.static float
max(float a, float b)
Returns the greater of twofloat
values.static int
max(int a, int b)
Returns the greater of twoint
values.static long
max(long a, long b)
Returns the greater of twolong
values.static double
min(double a, double b)
Returns the smaller of twodouble
values.static float
min(float a, float b)
Returns the smaller of twofloat
values.static int
min(int a, int b)
Returns the smaller of twoint
values.static long
min(long a, long b)
Returns the smaller of twolong
values.static int
multiplyExact(int x, int y)
Returns the product of the arguments, throwing an exception if the result overflows anint
.static long
multiplyExact(long x, int y)
Returns the product of the arguments, throwing an exception if the result overflows along
.static long
multiplyExact(long x, long y)
Returns the product of the arguments, throwing an exception if the result overflows along
.static long
multiplyFull(int x, int y)
Returns the exact mathematical product of the arguments.static long
multiplyHigh(long x, long y)
Returns as along
the most significant 64 bits of the 128bit product of two 64bit factors.static double
nextAfter(double start, double direction)
Returns the floatingpoint number adjacent to the first argument in the direction of the second argument.static float
nextAfter(float start, double direction)
Returns the floatingpoint number adjacent to the first argument in the direction of the second argument.static double
nextDown(double d)
Returns the floatingpoint value adjacent tod
in the direction of negative infinity.static float
nextDown(float f)
Returns the floatingpoint value adjacent tof
in the direction of negative infinity.static double
nextUp(double d)
Returns the floatingpoint value adjacent tod
in the direction of positive infinity.static float
nextUp(float f)
Returns the floatingpoint value adjacent tof
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 adouble
value with a positive sign, greater than or equal to0.0
and less than1.0
.static double
rint(double a)
Returns thedouble
value that is closest in value to the argument and is equal to a mathematical integer.static long
round(double a)
Returns the closestlong
to the argument, with ties rounding to positive infinity.static int
round(float a)
Returns the closestint
to the argument, with ties rounding to positive infinity.static double
scalb(double d, int scaleFactor)
Returnsd
× 2^{scaleFactor} rounded as if performed by a single correctly rounded floatingpoint multiply to a member of the double value set.static float
scalb(float f, int scaleFactor)
Returnsf
× 2^{scaleFactor} rounded as if performed by a single correctly rounded floatingpoint 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 adouble
value.static double
sqrt(double a)
Returns the correctly rounded positive square root of adouble
value.static int
subtractExact(int x, int y)
Returns the difference of the arguments, throwing an exception if the result overflows anint
.static long
subtractExact(long x, long y)
Returns the difference of the arguments, throwing an exception if the result overflows along
.static double
tan(double a)
Returns the trigonometric tangent of an angle.static double
tanh(double x)
Returns the hyperbolic tangent of adouble
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 thelong
argument; throwing an exception if the value overflows anint
.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.

Field Details

E
public static final double EThedouble
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 PIThedouble
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 Details

sin
public static double sin(double a)Returns the trigonometric sine of an angle. Special cases: If the argument is NaN or an infinity, then the result is NaN.
 If the argument is zero, then the result is a zero with the same sign as the argument.
 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 expectcos(toRadians(90.0))
to exactly equal0.0
. 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 adouble
value. Special cases: If the argument is NaN, the result is NaN.
 If the argument is positive infinity, then the result is positive infinity.
 If the argument is negative infinity, then the result is positive zero.
 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 adouble
value. Special cases: If the argument is NaN or less than zero, then the result is NaN.
 If the argument is positive infinity, then the result is positive infinity.
 If the argument is positive zero or negative zero, then the result is negative infinity.
 Parameters:
a
 a value Returns:
 the value ln
a
, the natural logarithm ofa
.

log10
public static double log10(double a)Returns the base 10 logarithm of adouble
value. Special cases: If the argument is NaN or less than zero, then the result is NaN.
 If the argument is positive infinity, then the result is positive infinity.
 If the argument is positive zero or negative zero, then the result is negative infinity.
 If the argument is equal to 10^{n} 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 adouble
value. Special cases: If the argument is NaN or less than zero, then the result is NaN.
 If the argument is positive infinity, then the result is positive infinity.
 If the argument is positive zero or negative zero, then the result is the same as the argument.
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 adouble
value. For positive finitex
,cbrt(x) == cbrt(x)
; that is, the cube root of a negative value is the negative of the cube root of that value's magnitude. Special cases: If the argument is NaN, then the result is NaN.
 If the argument is infinite, then the result is an infinity with the same sign as the argument.
 If the argument is zero, then the result is a zero with the same sign as the argument.
 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 tof1  f2
× n, where n is the mathematical integer closest to the exact mathematical value of the quotientf1/f2
, and if two mathematical integers are equally close tof1/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 byf2
.

ceil
public static double ceil(double a)Returns the smallest (closest to negative infinity)double
value that is greater than or equal to the argument and is equal to a mathematical integer. Special cases: If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
 If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
 If the argument value is less than zero but greater than 1.0, then the result is negative zero.
StrictMath.ceil(x)
is exactly the value ofStrictMath.floor(x)
. Parameters:
a
 a value. Returns:
 the smallest (closest to negative infinity) floatingpoint 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) floatingpoint value that less than or equal to the argument and is equal to a mathematical integer.

rint
public static double rint(double a)Returns thedouble
value that is closest in value to the argument and is equal to a mathematical integer. If twodouble
values that are mathematical integers are equally close 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 floatingpoint 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 ofy/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 coordinatex
 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,
 If
 the absolute value of the first argument is greater than 1 and the second argument is negative infinity, or
 the absolute value of the first argument is less than 1 and the second argument is positive infinity,
 If the absolute value of the first argument equals 1 and the second argument is infinite, then the result is NaN.
 If
 the first argument is positive zero and the second argument is greater than zero, or
 the first argument is positive infinity and the second argument is less than zero,
 If
 the first argument is positive zero and the second argument is less than zero, or
 the first argument is positive infinity and the second argument is greater than zero,
 If
 the first argument is negative zero and the second argument is greater than zero but not a finite odd integer, or
 the first argument is negative infinity and the second argument is less than zero but not a finite odd integer,
 If
 the first argument is negative zero and the second argument is a positive finite odd integer, or
 the first argument is negative infinity and the second argument is a negative finite odd integer,
 If
 the first argument is negative zero and the second argument is less than zero but not a finite odd integer, or
 the first argument is negative infinity and the second argument is greater than zero but not a finite odd integer,
 If
 the first argument is negative zero and the second argument is a negative finite odd integer, or
 the first argument is negative infinity and the second argument is a positive finite odd integer,
 If the first argument is finite and less than zero
 if the second argument is a finite even integer, the result is equal to the result of raising the absolute value of the first argument to the power of the second argument
 if the second argument is a finite odd integer, the result is equal to the negative of the result of raising the absolute value of the first argument to the power of the second argument
 if the second argument is finite and not an integer, then the result is NaN.
 If both arguments are integers, then the result is exactly equal
to the mathematical result of raising the first argument to the power
of the second argument if that result can in fact be represented
exactly as a
double
value.
(In the foregoing descriptions, a floatingpoint 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 methodfloor
. A value is a fixed point of a oneargument 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 closestint
to the argument, with ties rounding to positive infinity.Special cases:
 If the argument is NaN, the result is 0.
 If the argument is negative infinity or any value less than or
equal to the value of
Integer.MIN_VALUE
, the result is equal to the value ofInteger.MIN_VALUE
.  If the argument is positive infinity or any value greater than or
equal to the value of
Integer.MAX_VALUE
, the result is equal to the value ofInteger.MAX_VALUE
.
 Parameters:
a
 a floatingpoint 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 closestlong
to the argument, with ties rounding to positive infinity.Special cases:
 If the argument is NaN, the result is 0.
 If the argument is negative infinity or any value less than or
equal to the value of
Long.MIN_VALUE
, the result is equal to the value ofLong.MIN_VALUE
.  If the argument is positive infinity or any value greater than or
equal to the value of
Long.MAX_VALUE
, the result is equal to the value ofLong.MAX_VALUE
.
 Parameters:
a
 a floatingpoint value to be rounded to along
. 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 adouble
value with a positive sign, greater than or equal to0.0
and less than1.0
. Returned values are chosen pseudorandomly with (approximately) uniform distribution from that range.When this method is first called, it creates a single new pseudorandomnumber generator, exactly as if by the expression
This new pseudorandomnumber generator is used thereafter for all calls to this method and is used nowhere else.new java.util.Random()
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 pseudorandomnumber generator.
 Returns:
 a pseudorandom
double
greater than or equal to0.0
and less than1.0
.  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 anint
. Parameters:
x
 the first valuey
 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 along
. Parameters:
x
 the first valuey
 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 anint
. Parameters:
x
 the first valuey
 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 along
. Parameters:
x
 the first valuey
 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 anint
. Parameters:
x
 the first valuey
 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 along
. Parameters:
x
 the first valuey
 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 along
. Parameters:
x
 the first valuey
 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 thelong
argument; throwing an exception if the value overflows anint
. Parameters:
value
 the long value Returns:
 the argument as an int
 Throws:
ArithmeticException
 if theargument
overflows an int Since:
 1.8
 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 valuey
 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 along
the most significant 64 bits of the 128bit product of two 64bit factors. Parameters:
x
 the first valuey
 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 is1
, then integer overflow occurs and the result is equal to theInteger.MIN_VALUE
.See
Math.floorDiv
for examples and a comparison to the integer division/
operator. Parameters:
x
 the dividendy
 the divisor Returns:
 the largest (closest to positive infinity)
int
value that is less than or equal to the algebraic quotient.  Throws:
ArithmeticException
 if the divisory
is zero Since:
 1.8
 See Also:
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 is1
, then integer overflow occurs and the result is equal toLong.MIN_VALUE
.See
Math.floorDiv
for examples and a comparison to the integer division/
operator. Parameters:
x
 the dividendy
 the divisor Returns:
 the largest (closest to positive infinity)
int
value that is less than or equal to the algebraic quotient.  Throws:
ArithmeticException
 if the divisory
is zero Since:
 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 is1
, then integer overflow occurs and the result is equal to theLong.MIN_VALUE
.See
Math.floorDiv
for examples and a comparison to the integer division/
operator. Parameters:
x
 the dividendy
 the divisor Returns:
 the largest (closest to positive infinity)
long
value that is less than or equal to the algebraic quotient.  Throws:
ArithmeticException
 if the divisory
is zero Since:
 1.8
 See Also:
Math.floorDiv(long, long)
,Math.floor(double)

floorMod
public static int floorMod(int x, int y)Returns the floor modulus of theint
arguments.The floor modulus is
x  (floorDiv(x, y) * y)
, has the same sign as the divisory
, and is in the range ofabs(y) < r < +abs(y)
.The relationship between
floorDiv
andfloorMod
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 dividendy
 the divisor Returns:
 the floor modulus
x  (floorDiv(x, y) * y)
 Throws:
ArithmeticException
 if the divisory
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 thelong
andint
arguments.The floor modulus is
x  (floorDiv(x, y) * y)
, has the same sign as the divisory
, and is in the range ofabs(y) < r < +abs(y)
.The relationship between
floorDiv
andfloorMod
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 dividendy
 the divisor Returns:
 the floor modulus
x  (floorDiv(x, y) * y)
 Throws:
ArithmeticException
 if the divisory
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 thelong
arguments.The floor modulus is
x  (floorDiv(x, y) * y)
, has the same sign as the divisory
, and is in the range ofabs(y) < r < +abs(y)
.The relationship between
floorDiv
andfloorMod
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 dividendy
 the divisor Returns:
 the floor modulus
x  (floorDiv(x, y) * y)
 Throws:
ArithmeticException
 if the divisory
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 anint
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.Note that if the argument is equal to the value of
Integer.MIN_VALUE
, the most negative representableint
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 along
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.Note that if the argument is equal to the value of
Long.MIN_VALUE
, the most negative representablelong
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 afloat
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases: If the argument is positive zero or negative zero, the result is positive zero.
 If the argument is infinite, the result is positive infinity.
 If the argument is NaN, the result is NaN.
 API Note:
 As implied by the above, one valid implementation of
this method is given by the expression below which computes 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 adouble
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases: If the argument is positive zero or negative zero, the result is positive zero.
 If the argument is infinite, the result is positive infinity.
 If the argument is NaN, the result is NaN.
 API Note:
 As implied by the above, one valid implementation of
this method is given by the expression below which computes 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 twoint
values. That is, the result is the argument closer to the value ofInteger.MAX_VALUE
. If the arguments have the same value, the result is that same value. Parameters:
a
 an argument.b
 another argument. Returns:
 the larger of
a
andb
.

max
public static long max(long a, long b)Returns the greater of twolong
values. That is, the result is the argument closer to the value ofLong.MAX_VALUE
. If the arguments have the same value, the result is that same value. Parameters:
a
 an argument.b
 another argument. Returns:
 the larger of
a
andb
.

max
public static float max(float a, float b)Returns the greater of twofloat
values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero. Parameters:
a
 an argument.b
 another argument. Returns:
 the larger of
a
andb
.

max
public static double max(double a, double b)Returns the greater of twodouble
values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero. Parameters:
a
 an argument.b
 another argument. Returns:
 the larger of
a
andb
.

min
public static int min(int a, int b)Returns the smaller of twoint
values. That is, the result the argument closer to the value ofInteger.MIN_VALUE
. If the arguments have the same value, the result is that same value. Parameters:
a
 an argument.b
 another argument. Returns:
 the smaller of
a
andb
.

min
public static long min(long a, long b)Returns the smaller of twolong
values. That is, the result is the argument closer to the value ofLong.MIN_VALUE
. If the arguments have the same value, the result is that same value. Parameters:
a
 an argument.b
 another argument. Returns:
 the smaller of
a
andb
.

min
public static float min(float a, float b)Returns the smaller of twofloat
values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero. Parameters:
a
 an argument.b
 another argument. Returns:
 the smaller of
a
andb.

min
public static double min(double a, double b)Returns the smaller of twodouble
values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero. Parameters:
a
 an argument.b
 another argument. Returns:
 the smaller of
a
andb
.

fma
public static double fma(double a, double b, double c)Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearestdouble
. The rounding is done using the round to nearest even rounding mode. In contrast, ifa * b + c
is evaluated as a regular floatingpoint 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
) sincefusedMac(0.0, +0.0, +0.0)
is+0.0
while (0.0 * +0.0
) is0.0
;fusedMac(a, b, 0.0)
is equivalent to (a * b
) however. API Note:
 This method corresponds to the fusedMultiplyAdd operation defined in IEEE 7542008.
 Parameters:
a
 a valueb
 a valuec
 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 nearestfloat
. The rounding is done using the round to nearest even rounding mode. In contrast, ifa * b + c
is evaluated as a regular floatingpoint 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
) sincefma(0.0f, +0.0f, +0.0f)
is+0.0f
while (0.0f * +0.0f
) is0.0f
;fma(a, b, 0.0f)
is equivalent to (a * b
) however. API Note:
 This method corresponds to the fusedMultiplyAdd operation defined in IEEE 7542008.
 Parameters:
a
 a valueb
 a valuec
 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 adouble
value is the positive distance between this floatingpoint value and thedouble
value next larger in magnitude. Note that for nonNaN 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 2^{971}.
 Parameters:
d
 the floatingpoint value whose ulp is to be returned Returns:
 the size of an ulp of the argument
 Since:
 1.5

ulp
public static float ulp(float f)Returns the size of an ulp of the argument. An ulp, unit in the last place, of afloat
value is the positive distance between this floatingpoint value and thefloat
value next larger in magnitude. Note that for nonNaN 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 2^{104}.
 Parameters:
f
 the floatingpoint 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 floatingpoint 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 floatingpoint value whose signum is to be returned Returns:
 the signum function of the argument
 Since:
 1.5

sinh
public static double sinh(double x)Returns the hyperbolic sine of adouble
value. The hyperbolic sine 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 adouble
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 adouble
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(x^{2} +y^{2}) 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 valuey
 a value Returns:
 sqrt(x^{2} +y^{2}) 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 ofexpm1(x)
+ 1 is much closer to the true result of e^{x} thanexp(x)
.Special cases:
 If the argument is NaN, the result is NaN.
 If the argument is positive infinity, then the result is positive infinity.
 If the argument is negative infinity, then the result is 1.0.
 If the argument is zero, then the result is a zero with the same sign as the argument.
 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 valuesx
, the result oflog1p(x)
is much closer to the true result of ln(1 +x
) than the floatingpoint evaluation oflog(1.0+x)
.Special cases:
 If the argument is NaN or less than 1, then the result is NaN.
 If the argument is positive infinity, then the result is positive infinity.
 If the argument is negative one, then the result is negative infinity.
 If the argument is zero, then the result is a zero with the same sign as the argument.
 Parameters:
x
 a value Returns:
 the value ln(
x
+ 1), the natural log ofx
+ 1  Since:
 1.5

copySign
public static double copySign(double magnitude, double sign)Returns the first floatingpoint argument with the sign of the second floatingpoint argument. For this method, a NaNsign
argument is always treated as if it were positive. Parameters:
magnitude
 the parameter providing the magnitude of the resultsign
 the parameter providing the sign of the result Returns:
 a value with the magnitude of
magnitude
and the sign ofsign
.  Since:
 1.6

copySign
public static float copySign(float magnitude, float sign)Returns the first floatingpoint argument with the sign of the second floatingpoint argument. For this method, a NaNsign
argument is always treated as if it were positive. Parameters:
magnitude
 the parameter providing the magnitude of the resultsign
 the parameter providing the sign of the result Returns:
 a value with the magnitude of
magnitude
and the sign ofsign
.  Since:
 1.6

getExponent
public static int getExponent(float f)Returns the unbiased exponent used in the representation of afloat
. Special cases: If the argument is NaN or infinite, then the result is
Float.MAX_EXPONENT
+ 1.  If the argument is zero or subnormal, then the result is
Float.MIN_EXPONENT
1.
 Parameters:
f
 afloat
value Returns:
 the unbiased exponent of the argument
 Since:
 1.6
 If the argument is NaN or infinite, then the result is

getExponent
public static int getExponent(double d)Returns the unbiased exponent used in the representation of adouble
. Special cases: If the argument is NaN or infinite, then the result is
Double.MAX_EXPONENT
+ 1.  If the argument is zero or subnormal, then the result is
Double.MIN_EXPONENT
1.
 Parameters:
d
 adouble
value Returns:
 the unbiased exponent of the argument
 Since:
 1.6
 If the argument is NaN or infinite, then the result is

nextAfter
public static double nextAfter(double start, double direction)Returns the floatingpoint 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
anddirection
has a value such that the result should have a smaller magnitude, then a zero with the same sign asstart
is returned.  If
start
is infinite anddirection
has a value such that the result should have a smaller magnitude,Double.MAX_VALUE
with the same sign asstart
is returned.  If
start
is equal to ±Double.MAX_VALUE
anddirection
has a value such that the result should have a larger magnitude, an infinity with same sign asstart
is returned.
 Parameters:
start
 starting floatingpoint valuedirection
 value indicating which ofstart
's neighbors orstart
should be returned Returns:
 The floatingpoint number adjacent to
start
in the direction ofdirection
.  Since:
 1.6

nextAfter
public static float nextAfter(float start, double direction)Returns the floatingpoint 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
anddirection
has a value such that the result should have a smaller magnitude, then a zero with the same sign asstart
is returned.  If
start
is infinite anddirection
has a value such that the result should have a smaller magnitude,Float.MAX_VALUE
with the same sign asstart
is returned.  If
start
is equal to ±Float.MAX_VALUE
anddirection
has a value such that the result should have a larger magnitude, an infinity with same sign asstart
is returned.
 Parameters:
start
 starting floatingpoint valuedirection
 value indicating which ofstart
's neighbors orstart
should be returned Returns:
 The floatingpoint number adjacent to
start
in the direction ofdirection
.  Since:
 1.6

nextUp
public static double nextUp(double d)Returns the floatingpoint value adjacent tod
in the direction of positive infinity. This method is semantically equivalent tonextAfter(d, Double.POSITIVE_INFINITY)
; however, anextUp
implementation may run faster than its equivalentnextAfter
call.Special Cases:
 If the argument is NaN, the result is NaN.
 If the argument is positive infinity, the result is positive infinity.
 If the argument is zero, the result is
Double.MIN_VALUE
 Parameters:
d
 starting floatingpoint value Returns:
 The adjacent floatingpoint value closer to positive infinity.
 Since:
 1.6

nextUp
public static float nextUp(float f)Returns the floatingpoint value adjacent tof
in the direction of positive infinity. This method is semantically equivalent tonextAfter(f, Float.POSITIVE_INFINITY)
; however, anextUp
implementation may run faster than its equivalentnextAfter
call.Special Cases:
 If the argument is NaN, the result is NaN.
 If the argument is positive infinity, the result is positive infinity.
 If the argument is zero, the result is
Float.MIN_VALUE
 Parameters:
f
 starting floatingpoint value Returns:
 The adjacent floatingpoint value closer to positive infinity.
 Since:
 1.6

nextDown
public static double nextDown(double d)Returns the floatingpoint value adjacent tod
in the direction of negative infinity. This method is semantically equivalent tonextAfter(d, Double.NEGATIVE_INFINITY)
; however, anextDown
implementation may run faster than its equivalentnextAfter
call.Special Cases:
 If the argument is NaN, the result is NaN.
 If the argument is negative infinity, the result is negative infinity.
 If the argument is zero, the result is
Double.MIN_VALUE
 Parameters:
d
 starting floatingpoint value Returns:
 The adjacent floatingpoint value closer to negative infinity.
 Since:
 1.8

nextDown
public static float nextDown(float f)Returns the floatingpoint value adjacent tof
in the direction of negative infinity. This method is semantically equivalent tonextAfter(f, Float.NEGATIVE_INFINITY)
; however, anextDown
implementation may run faster than its equivalentnextAfter
call.Special Cases:
 If the argument is NaN, the result is NaN.
 If the argument is negative infinity, the result is negative infinity.
 If the argument is zero, the result is
Float.MIN_VALUE
 Parameters:
f
 starting floatingpoint value Returns:
 The adjacent floatingpoint value closer to negative infinity.
 Since:
 1.8

scalb
public static double scalb(double d, int scaleFactor)Returnsd
× 2^{scaleFactor} rounded as if performed by a single correctly rounded floatingpoint multiply to a member of the double value set. See the Java Language Specification for a discussion of floatingpoint value sets. If the exponent of the result is betweenDouble.MIN_EXPONENT
andDouble.MAX_EXPONENT
, the answer is calculated exactly. If the exponent of the result would be larger thanDouble.MAX_EXPONENT
, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, whenscalb(x, n)
is subnormal,scalb(scalb(x, n), n)
may not equal x. When the result is nonNaN, the result has the same sign asd
.Special cases:
 If the first argument is NaN, NaN is returned.
 If the first argument is infinite, then an infinity of the same sign is returned.
 If the first argument is zero, then a zero of the same sign is returned.
 Parameters:
d
 number to be scaled by a power of two.scaleFactor
 power of 2 used to scaled
 Returns:
d
× 2^{scaleFactor} Since:
 1.6

scalb
public static float scalb(float f, int scaleFactor)Returnsf
× 2^{scaleFactor} rounded as if performed by a single correctly rounded floatingpoint multiply to a member of the float value set. See the Java Language Specification for a discussion of floatingpoint value sets. If the exponent of the result is betweenFloat.MIN_EXPONENT
andFloat.MAX_EXPONENT
, the answer is calculated exactly. If the exponent of the result would be larger thanFloat.MAX_EXPONENT
, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, whenscalb(x, n)
is subnormal,scalb(scalb(x, n), n)
may not equal x. When the result is nonNaN, the result has the same sign asf
.Special cases:
 If the first argument is NaN, NaN is returned.
 If the first argument is infinite, then an infinity of the same sign is returned.
 If the first argument is zero, then a zero of the same sign is returned.
 Parameters:
f
 number to be scaled by a power of two.scaleFactor
 power of 2 used to scalef
 Returns:
f
× 2^{scaleFactor} Since:
 1.6
