Math
public
final
class
Math
extends Object
java.lang.Object  
↳  java.lang.Math 
The class Math
contains methods for performing basic
numeric operations such as the elementary exponential, logarithm,
square root, and trigonometric functions.
Unlike some of the numeric methods of class
StrictMath
, all implementations of the equivalent
functions of class Math
are not defined to return the
bitforbit same results. This relaxation permits
betterperforming implementations where strict reproducibility is
not required.
By default many of the Math
methods simply call
the equivalent method in StrictMath
for their
implementation. Code generators are encouraged to use
platformspecific native libraries or microprocessor instructions,
where available, to provide higherperformance implementations of
Math
methods. Such higherperformance
implementations still must conform to the specification for
Math
.
The quality of implementation specifications concern two
properties, accuracy of the returned result and monotonicity of the
method. Accuracy of the floatingpoint Math
methods is
measured in terms of ulps, units in the last place. For a
given floatingpoint format, an ulp of a
specific real number value is the distance between the two
floatingpoint values bracketing that numerical value. When
discussing the accuracy of a method as a whole rather than at a
specific argument, the number of ulps cited is for the worstcase
error at any argument. If a method always has an error less than
0.5 ulps, the method always returns the floatingpoint number
nearest the exact result; such a method is correctly
rounded. A correctly rounded method is generally the best a
floatingpoint approximation can be; however, it is impractical for
many floatingpoint methods to be correctly rounded. Instead, for
the Math
class, a larger error bound of 1 or 2 ulps is
allowed for certain methods. Informally, with a 1 ulp error bound,
when the exact result is a representable number, the exact result
should be returned as the computed result; otherwise, either of the
two floatingpoint values which bracket the exact result may be
returned. For exact results large in magnitude, one of the
endpoints of the bracket may be infinite. Besides accuracy at
individual arguments, maintaining proper relations between the
method at different arguments is also important. Therefore, most
methods with more than 0.5 ulp errors are required to be
semimonotonic: whenever the mathematical function is
nondecreasing, so is the floatingpoint approximation, likewise,
whenever the mathematical function is nonincreasing, so is the
floatingpoint approximation. Not all approximations that have 1
ulp accuracy will automatically meet the monotonicity requirements.
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, decrement, and negation overflow occurs only with
a specific minimum or maximum value and should be checked against
the minimum or maximum as appropriate.
Summary
Constants  

double 
E
The 
double 
PI
The 
Public methods  

static
double

IEEEremainder(double f1, double f2)
Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. 
static
long

abs(long a)
Returns the absolute value of a 
static
int

abs(int a)
Returns the absolute value of an 
static
float

abs(float a)
Returns the absolute value of a 
static
double

abs(double a)
Returns the absolute value of a 
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 
static
long

addExact(long x, long y)
Returns the sum of its arguments,
throwing an exception if the result overflows a 
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 ( 
static
double

cbrt(double a)
Returns the cube root of a 
static
double

ceil(double a)
Returns the smallest (closest to negative infinity)

static
float

copySign(float magnitude, float sign)
Returns the first floatingpoint argument with the sign of the second floatingpoint argument. 
static
double

copySign(double magnitude, double 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 a 
static
long

decrementExact(long a)
Returns the argument decremented by one, throwing an exception if the
result overflows a 
static
int

decrementExact(int a)
Returns the argument decremented by one, throwing an exception if the
result overflows an 
static
double

exp(double a)
Returns Euler's number e raised to the power of a

static
double

expm1(double x)
Returns e^{x} 1. 
static
double

floor(double a)
Returns the largest (closest to positive infinity)

static
int

floorDiv(int x, int y)
Returns the largest (closest to positive infinity)

static
long

floorDiv(long x, long y)
Returns the largest (closest to positive infinity)

static
long

floorMod(long x, long y)
Returns the floor modulus of the 
static
int

floorMod(int x, int y)
Returns the floor modulus of the 
static
int

getExponent(double d)
Returns the unbiased exponent used in the representation of a

static
int

getExponent(float f)
Returns the unbiased exponent used in the representation of a

static
double

hypot(double x, double y)
Returns sqrt(x^{2} +y^{2}) without intermediate overflow or underflow. 
static
int

incrementExact(int a)
Returns the argument incremented by one, throwing an exception if the
result overflows an 
static
long

incrementExact(long a)
Returns the argument incremented by one, throwing an exception if the
result overflows a 
static
double

log(double a)
Returns the natural logarithm (base e) of a 
static
double

log10(double a)
Returns the base 10 logarithm of a 
static
double

log1p(double x)
Returns the natural logarithm of the sum of the argument and 1. 
static
int

max(int a, int b)
Returns the greater of two 
static
long

max(long a, long b)
Returns the greater of two 
static
float

max(float a, float b)
Returns the greater of two 
static
double

max(double a, double b)
Returns the greater of two 
static
float

min(float a, float b)
Returns the smaller of two 
static
double

min(double a, double b)
Returns the smaller of two 
static
int

min(int a, int b)
Returns the smaller of two 
static
long

min(long a, long b)
Returns the smaller of two 
static
int

multiplyExact(int x, int y)
Returns the product of the arguments,
throwing an exception if the result overflows an 
static
long

multiplyExact(long x, long y)
Returns the product of the arguments,
throwing an exception if the result overflows a 
static
int

negateExact(int a)
Returns the negation of the argument, throwing an exception if the
result overflows an 
static
long

negateExact(long a)
Returns the negation of the argument, throwing an exception if the
result overflows a 
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 to 
static
float

nextDown(float f)
Returns the floatingpoint value adjacent to 
static
float

nextUp(float f)
Returns the floatingpoint value adjacent to 
static
double

nextUp(double d)
Returns the floatingpoint value adjacent to 
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 
static
double

rint(double a)
Returns the 
static
long

round(double a)
Returns the closest 
static
int

round(float a)
Returns the closest 
static
float

scalb(float f, int scaleFactor)
Returns 
static
double

scalb(double d, int scaleFactor)
Returns 
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 
static
double

sqrt(double a)
Returns the correctly rounded positive square root of a

static
long

subtractExact(long x, long y)
Returns the difference of the arguments,
throwing an exception if the result overflows a 
static
int

subtractExact(int x, int y)
Returns the difference of the arguments,
throwing an exception if the result overflows an 
static
double

tan(double a)
Returns the trigonometric tangent of an angle. 
static
double

tanh(double x)
Returns the hyperbolic tangent of a 
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 
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. 
Inherited methods  

Constants
E
public static final double E
The double
value that is closer than any other to
e, the base of the natural logarithms.
Constant Value: 2.718281828459045
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.
Constant Value: 3.141592653589793
Public methods
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 
double : the dividend. 
f2 
double : the divisor. 
Returns  

double 
the remainder when f1 is divided by
f2 .

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 
long : the argument whose absolute value is to be determined 
Returns  

long 
the absolute value of the argument. 
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 
int : the argument whose absolute value is to be determined 
Returns  

int 
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.
Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))
Parameters  

a 
float : the argument whose absolute value is to be determined 
Returns  

float 
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.
Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)
Parameters  

a 
double : the argument whose absolute value is to be determined 
Returns  

double 
the absolute value 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.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
Parameters  

a 
double : the value whose arc cosine is to be returned. 
Returns  

double 
the arc cosine of the argument. 
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 
int : the first value 
y 
int : the second value 
Returns  

int 
the result 
Throws  

ArithmeticException 
if the result overflows an 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 
long : the first value 
y 
long : the second value 
Returns  

long 
the result 
Throws  

ArithmeticException 
if the result overflows a long 
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.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
Parameters  

a 
double : the value whose arc sine is to be returned. 
Returns  

double 
the arc sine 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.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
Parameters  

a 
double : the value whose arc tangent is to be returned. 
Returns  

double 
the arc tangent of the argument. 
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.
The computed result must be within 2 ulps of the exact result. Results must be semimonotonic.
Parameters  

y 
double : the ordinate coordinate 
x 
double : the abscissa coordinate 
Returns  

double 
the theta component of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates. 
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.
The computed result must be within 1 ulp of the exact result.
Parameters  

a 
double : a value. 
Returns  

double 
the cube root of a . 
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.
Math.ceil(x)
is exactly the
value of Math.floor(x)
.
Parameters  

a 
double : a value. 
Returns  

double 
the smallest (closest to negative infinity) floatingpoint value that is greater than or equal to the argument and is equal to a mathematical integer. 
copySign
public static float copySign (float magnitude, float sign)
Returns the first floatingpoint argument with the sign of the
second floatingpoint argument. Note that unlike the StrictMath.copySign
method, this method does not require NaN sign
arguments to be treated as positive values; implementations are
permitted to treat some NaN arguments as positive and other NaN
arguments as negative to allow greater performance.
Parameters  

magnitude 
float : the parameter providing the magnitude of the result 
sign 
float : the parameter providing the sign of the result 
Returns  

float 
a value with the magnitude of magnitude
and the sign of sign . 
copySign
public static double copySign (double magnitude, double sign)
Returns the first floatingpoint argument with the sign of the
second floatingpoint argument. Note that unlike the StrictMath.copySign
method, this method does not require NaN sign
arguments to be treated as positive values; implementations are
permitted to treat some NaN arguments as positive and other NaN
arguments as negative to allow greater performance.
Parameters  

magnitude 
double : the parameter providing the magnitude of the result 
sign 
double : the parameter providing the sign of the result 
Returns  

double 
a value with the magnitude of magnitude
and the sign of sign . 
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.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
Parameters  

a 
double : an angle, in radians. 
Returns  

double 
the cosine of the argument. 
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
.
The computed result must be within 2.5 ulps of the exact result.
Parameters  

x 
double : The number whose hyperbolic cosine is to be returned. 
Returns  

double 
The hyperbolic cosine of x . 
decrementExact
public static long decrementExact (long a)
Returns the argument decremented by one, throwing an exception if the
result overflows a long
.
Parameters  

a 
long : the value to decrement 
Returns  

long 
the result 
Throws  

ArithmeticException 
if the result overflows a long 
decrementExact
public static int decrementExact (int a)
Returns the argument decremented by one, throwing an exception if the
result overflows an int
.
Parameters  

a 
int : the value to decrement 
Returns  

int 
the result 
Throws  

ArithmeticException 
if the result overflows an int 
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.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
Parameters  

a 
double : the exponent to raise e to. 
Returns  

double 
the value e^{a}, where e is the base of the natural logarithms. 
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.
The computed result must be within 1 ulp of the exact result.
Results must be semimonotonic. The result of
expm1
for any finite input must be greater than or
equal to 1.0
. Note that once the exact result of
e^{x}  1 is within 1/2
ulp of the limit value 1, 1.0
should be
returned.
Parameters  

x 
double : the exponent to raise e to in the computation of
e^{x} 1. 
Returns  

double 
the value e^{x}  1. 
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 
double : a value. 
Returns  

double 
the largest (closest to positive infinity) floatingpoint value that less than or equal to the argument and is equal to a mathematical integer. 
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
.
Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results than truncation when the exact result is negative.
 If the signs of the arguments are the same, the results of
floorDiv
and the/
operator are the same.
For example,floorDiv(4, 3) == 1
and(4 / 3) == 1
.  If the signs of the arguments are different, the quotient is negative and
floorDiv
returns the integer less than or equal to the quotient and the/
operator returns the integer closest to zero.
For example,floorDiv(4, 3) == 2
, whereas(4 / 3) == 1
.
Parameters  

x 
int : the dividend 
y 
int : the divisor 
Returns  

int 
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 
See also:
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
.
Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results than truncation when the exact result is negative.
For examples, see floorDiv(int, int)
.
Parameters  

x 
long : the dividend 
y 
long : the divisor 
Returns  

long 
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 
See also:
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
For examples, see floorMod(int, int)
.
Parameters  

x 
long : the dividend 
y 
long : the divisor 
Returns  

long 
the floor modulus x  (floorDiv(x, y) * y) 
Throws  

ArithmeticException 
if the divisor y is zero 
See also:
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
The difference in values between floorMod
and
the %
operator is due to the difference between
floorDiv
that returns the integer less than or equal to the quotient
and the /
operator that returns the integer closest to zero.
Examples:
 If the signs of the arguments are the same, the results
of
floorMod
and the%
operator are the same.
floorMod(4, 3) == 1
; and(4 % 3) == 1
 If the signs of the arguments are different, the results differ from the
%
operator.
floorMod(+4, 3) == 2
; and(+4 % 3) == +1
floorMod(4, +3) == +2
; and(4 % +3) == 1
floorMod(4, 3) == 1
; and(4 % 3) == 1
If the signs of arguments are unknown and a positive modulus
is needed it can be computed as (floorMod(x, y) + abs(y)) % abs(y)
.
Parameters  

x 
int : the dividend 
y 
int : the divisor 
Returns  

int 
the floor modulus x  (floorDiv(x, y) * y) 
Throws  

ArithmeticException 
if the divisor y is zero 
See also:
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 
double : a double value 
Returns  

int 
the unbiased exponent of the argument 
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 
float : a float value 
Returns  

int 
the unbiased exponent of the argument 
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.
The computed result must be within 1 ulp of the exact result. If one parameter is held constant, the results must be semimonotonic in the other parameter.
Parameters  

x 
double : a value 
y 
double : a value 
Returns  

double 
sqrt(x^{2} +y^{2}) without intermediate overflow or underflow 
incrementExact
public static int incrementExact (int a)
Returns the argument incremented by one, throwing an exception if the
result overflows an int
.
Parameters  

a 
int : the value to increment 
Returns  

int 
the result 
Throws  

ArithmeticException 
if the result overflows an int 
incrementExact
public static long incrementExact (long a)
Returns the argument incremented by one, throwing an exception if the
result overflows a long
.
Parameters  

a 
long : the value to increment 
Returns  

long 
the result 
Throws  

ArithmeticException 
if the result overflows a long 
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.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
Parameters  

a 
double : a value 
Returns  

double 
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 10^{n} for integer n, then the result is n.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
Parameters  

a 
double : a value 
Returns  

double 
the base 10 logarithm of a . 
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 floatingpoint 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.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
Parameters  

x 
double : a value 
Returns  

double 
the value ln(x + 1), the natural
log of x + 1 
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 
int : an argument. 
b 
int : another argument. 
Returns  

int 
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 
long : an argument. 
b 
long : another argument. 
Returns  

long 
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 
float : an argument. 
b 
float : another argument. 
Returns  

float 
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 
double : an argument. 
b 
double : another argument. 
Returns  

double 
the larger 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 
float : an argument. 
b 
float : another argument. 
Returns  

float 
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 
double : an argument. 
b 
double : another argument. 
Returns  

double 
the smaller 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 
int : an argument. 
b 
int : another argument. 
Returns  

int 
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 
long : an argument. 
b 
long : another argument. 
Returns  

long 
the smaller of a and b .

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 
int : the first value 
y 
int : the second value 
Returns  

int 
the result 
Throws  

ArithmeticException 
if the result overflows an 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 
long : the first value 
y 
long : the second value 
Returns  

long 
the result 
Throws  

ArithmeticException 
if the result overflows a long 
negateExact
public static int negateExact (int a)
Returns the negation of the argument, throwing an exception if the
result overflows an int
.
Parameters  

a 
int : the value to negate 
Returns  

int 
the result 
Throws  

ArithmeticException 
if the result overflows an int 
negateExact
public static long negateExact (long a)
Returns the negation of the argument, throwing an exception if the
result overflows a long
.
Parameters  

a 
long : the value to negate 
Returns  

long 
the result 
Throws  

ArithmeticException 
if the result overflows a long 
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 
double : starting floatingpoint value 
direction 
double : value indicating which of
start 's neighbors or start should
be returned 
Returns  

double 
The floatingpoint number adjacent to start in the
direction of direction . 
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 
float : starting floatingpoint value 
direction 
double : value indicating which of
start 's neighbors or start should
be returned 
Returns  

float 
The floatingpoint number adjacent to start in the
direction of direction . 
nextDown
public static double nextDown (double d)
Returns the floatingpoint 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 
double : starting floatingpoint value 
Returns  

double 
The adjacent floatingpoint value closer to negative infinity. 
nextDown
public static float nextDown (float f)
Returns the floatingpoint 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 
float : starting floatingpoint value 
Returns  

float 
The adjacent floatingpoint value closer to negative infinity. 
nextUp
public static float nextUp (float f)
Returns the floatingpoint 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 
float : starting floatingpoint value 
Returns  

float 
The adjacent floatingpoint value closer to positive infinity. 
nextUp
public static double nextUp (double d)
Returns the floatingpoint 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 
double : starting floatingpoint value 
Returns  

double 
The adjacent floatingpoint value closer to positive infinity. 
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 method floor
. 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.)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
Parameters  

a 
double : the base. 
b 
double : the exponent. 
Returns  

double 
the value a ^{b}.

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 pseudorandomnumber generator, exactly as if by the expression
new java.util.Random()
This new pseudorandomnumber 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 pseudorandomnumber generator.
Returns  

double 
a pseudorandom double greater than or equal
to 0.0 and less than 1.0 . 
See also:
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, 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 
double : a double value. 
Returns  

double 
the closest floatingpoint value to a that is
equal to a mathematical integer.

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 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 
double : a floatingpoint value to be rounded to a
long . 
Returns  

long 
the value of the argument rounded to the nearest
long value. 
See also:
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 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 
float : a floatingpoint value to be rounded to an integer. 
Returns  

int 
the value of the argument rounded to the nearest
int value. 
See also:
scalb
public static float scalb (float f, int scaleFactor)
Returns f
×
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 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 nonNaN, 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 
float : number to be scaled by a power of two. 
scaleFactor 
int : power of 2 used to scale f 
Returns  

float 
f × 2^{scaleFactor} 
scalb
public static double scalb (double d, int scaleFactor)
Returns d
×
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 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 nonNaN, 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 
double : number to be scaled by a power of two. 
scaleFactor 
int : power of 2 used to scale d 
Returns  

double 
d × 2^{scaleFactor} 
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 
double : the floatingpoint value whose signum is to be returned 
Returns  

double 
the signum function of the argument 
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 
float : the floatingpoint value whose signum is to be returned 
Returns  

float 
the signum function of the argument 
sin
public static double sin (double a)
Returns the trigonometric sine of an angle. Special cases:
 If the argument is NaN or an infinity, then the result is NaN.
 If the argument is zero, then the result is a zero with the same sign as the argument.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
Parameters  

a 
double : an angle, in radians. 
Returns  

double 
the sine of the argument. 
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.
The computed result must be within 2.5 ulps of the exact result.
Parameters  

x 
double : The number whose hyperbolic sine is to be returned. 
Returns  

double 
The hyperbolic sine of x . 
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.
double
value closest to
the true mathematical square root of the argument value.
Parameters  

a 
double : a value. 
Returns  

double 
the positive square root of a .
If the argument is NaN or less than zero, the result is NaN.

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 
long : the first value 
y 
long : the second value to subtract from the first 
Returns  

long 
the result 
Throws  

ArithmeticException 
if the result overflows a 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 
int : the first value 
y 
int : the second value to subtract from the first 
Returns  

int 
the result 
Throws  

ArithmeticException 
if the result overflows an int 
tan
public static double tan (double a)
Returns the trigonometric tangent of an angle. Special cases:
 If the argument is NaN or an infinity, then the result is NaN.
 If the argument is zero, then the result is a zero with the same sign as the argument.
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
Parameters  

a 
double : an angle, in radians. 
Returns  

double 
the tangent of the argument. 
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
.
The computed result must be within 2.5 ulps of the exact result.
The result of tanh
for any finite input must have
an absolute value less than or equal to 1. Note that once the
exact result of tanh is within 1/2 of an ulp of the limit value
of ±1, correctly signed ±1.0
should
be returned.
Parameters  

x 
double : The number whose hyperbolic tangent is to be returned. 
Returns  

double 
The hyperbolic tangent of x . 
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 
double : an angle, in radians 
Returns  

double 
the measurement of the angle angrad
in degrees. 
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 
long : the long value 
Returns  

int 
the argument as an int 
Throws  

ArithmeticException 
if the argument overflows an int 
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 
double : an angle, in degrees 
Returns  

double 
the measurement of the angle angdeg
in radians. 
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 floatingpoint value and the double
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 
double : the floatingpoint value whose ulp is to be returned 
Returns  

double 
the size of an ulp of the argument 
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 floatingpoint value and the float
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 
float : the floatingpoint value whose ulp is to be returned 
Returns  

float 
the size of an ulp of the argument 
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