public final class Math extends Object
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 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.
Modifier and Type  Field  Description 

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

static double 
abs(double a) 
Returns the absolute value of a
double value. 
static float 
abs(float a) 
Returns the absolute value of a
float value. 
static int 
abs(int a) 
Returns the absolute value of an
int value. 
static long 
abs(long a) 
Returns the absolute value of a
long value. 
static double 
acos(double a) 
Returns the arc cosine of a value; the returned angle is in the
range 0.0 through pi.

static int 
addExact(int x,
int y) 
Returns the sum of its arguments,
throwing an exception if the result overflows an
int . 
static long 
addExact(long x,
long y) 
Returns the sum of its arguments,
throwing an exception if the result overflows a
long . 
static double 
asin(double a) 
Returns the arc sine of a value; the returned angle is in the
range pi/2 through pi/2.

static double 
atan(double a) 
Returns the arc tangent of a value; the returned angle is in the
range pi/2 through pi/2.

static double 
atan2(double y,
double x) 
Returns the angle theta from the conversion of rectangular
coordinates (
x , y ) to polar
coordinates (r, theta). 
static double 
cbrt(double a) 
Returns the cube root of a
double value. 
static double 
ceil(double a) 
Returns the smallest (closest to negative infinity)
double value that is greater than or equal to the
argument and is equal to a mathematical integer. 
static double 
copySign(double magnitude,
double sign) 
Returns the first 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 a
double value. 
static int 
decrementExact(int a) 
Returns the argument decremented by one, throwing an exception if the
result overflows an
int . 
static long 
decrementExact(long a) 
Returns the argument decremented by one, throwing an exception if the
result overflows a
long . 
static double 
exp(double a) 
Returns Euler's number e raised to the power of a
double value. 
static double 
expm1(double x) 
Returns e^{x} 1.

static double 
floor(double a) 
Returns the largest (closest to positive infinity)
double value that is less than or equal to the
argument and is equal to a mathematical integer. 
static int 
floorDiv(int x,
int y) 
Returns the largest (closest to positive infinity)
int value that is less than or equal to the algebraic quotient. 
static long 
floorDiv(long x,
int y) 
Returns the largest (closest to positive infinity)
long value that is less than or equal to the algebraic quotient. 
static long 
floorDiv(long x,
long y) 
Returns the largest (closest to positive infinity)
long value that is less than or equal to the algebraic quotient. 
static int 
floorMod(int x,
int y) 
Returns the floor modulus of the
int arguments. 
static int 
floorMod(long x,
int y) 
Returns the floor modulus of the
long and int arguments. 
static long 
floorMod(long x,
long y) 
Returns the floor modulus of the
long arguments. 
static double 
fma(double a,
double b,
double c) 
Returns the fused multiply add of the three arguments; that is,
returns the exact product of the first two arguments summed
with the third argument and then rounded once to the nearest
double . 
static float 
fma(float a,
float b,
float c) 
Returns the fused multiply add of the three arguments; that is,
returns the exact product of the first two arguments summed
with the third argument and then rounded once to the nearest
float . 
static int 
getExponent(double d) 
Returns the unbiased exponent used in the representation of a
double . 
static int 
getExponent(float f) 
Returns the unbiased exponent used in the representation of a
float . 
static double 
hypot(double x,
double y) 
Returns sqrt(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 int 
incrementExact(int a) 
Returns the argument incremented by one, throwing an exception if the
result overflows an
int . 
static long 
incrementExact(long a) 
Returns the argument incremented by one, throwing an exception if the
result overflows a
long . 
static double 
log(double a) 
Returns the natural logarithm (base e) of a
double
value. 
static double 
log10(double a) 
Returns the base 10 logarithm of a
double value. 
static double 
log1p(double x) 
Returns the natural logarithm of the sum of the argument and 1.

static double 
max(double a,
double b) 
Returns the greater of two
double values. 
static float 
max(float a,
float b) 
Returns the greater of two
float values. 
static int 
max(int a,
int b) 
Returns the greater of two
int values. 
static long 
max(long a,
long b) 
Returns the greater of two
long values. 
static double 
min(double a,
double b) 
Returns the smaller of two
double values. 
static float 
min(float a,
float b) 
Returns the smaller of two
float values. 
static int 
min(int a,
int b) 
Returns the smaller of two
int values. 
static long 
min(long a,
long b) 
Returns the smaller of two
long values. 
static int 
multiplyExact(int x,
int y) 
Returns the product of the arguments,
throwing an exception if the result overflows an
int . 
static long 
multiplyExact(long x,
int y) 
Returns the product of the arguments, throwing an exception if the result
overflows a
long . 
static long 
multiplyExact(long x,
long y) 
Returns the product of the arguments,
throwing an exception if the result overflows a
long . 
static long 
multiplyFull(int x,
int y) 
Returns the exact mathematical product of the arguments.

static long 
multiplyHigh(long x,
long y) 
Returns as a
long the most significant 64 bits of the 128bit
product of two 64bit factors. 
static int 
negateExact(int a) 
Returns the negation of the argument, throwing an exception if the
result overflows an
int . 
static long 
negateExact(long a) 
Returns the negation of the argument, throwing an exception if the
result overflows a
long . 
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
d in
the direction of negative infinity. 
static float 
nextDown(float f) 
Returns the floatingpoint value adjacent to
f in
the direction of negative infinity. 
static double 
nextUp(double d) 
Returns the floatingpoint value adjacent to
d in
the direction of positive infinity. 
static float 
nextUp(float f) 
Returns the floatingpoint value adjacent to
f in
the direction of positive infinity. 
static double 
pow(double a,
double b) 
Returns the value of the first argument raised to the power of the
second argument.

static double 
random() 
Returns a
double value with a positive sign, greater
than or equal to 0.0 and less than 1.0 . 
static double 
rint(double a) 
Returns the
double value that is closest in value
to the argument and is equal to a mathematical integer. 
static long 
round(double a) 
Returns the closest
long to the argument, with ties
rounding to positive infinity. 
static int 
round(float a) 
Returns the closest
int to the argument, with ties
rounding to positive infinity. 
static double 
scalb(double d,
int scaleFactor) 
Returns
d ×
2^{scaleFactor} rounded as if performed
by a single correctly rounded floatingpoint multiply to a
member of the double value set. 
static float 
scalb(float f,
int scaleFactor) 
Returns
f ×
2^{scaleFactor} rounded as if performed
by a single correctly rounded 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 a
double value. 
static double 
sqrt(double a) 
Returns the correctly rounded positive square root of a
double value. 
static int 
subtractExact(int x,
int y) 
Returns the difference of the arguments,
throwing an exception if the result overflows an
int . 
static long 
subtractExact(long x,
long y) 
Returns the difference of the arguments,
throwing an exception if the result overflows a
long . 
static double 
tan(double a) 
Returns the trigonometric tangent of an angle.

static double 
tanh(double x) 
Returns the hyperbolic tangent of a
double value. 
static double 
toDegrees(double angrad) 
Converts an angle measured in radians to an approximately
equivalent angle measured in degrees.

static int 
toIntExact(long value) 
Returns the value of the
long argument;
throwing an exception if the value overflows an int . 
static double 
toRadians(double angdeg) 
Converts an angle measured in degrees to an approximately
equivalent angle measured in radians.

static double 
ulp(double d) 
Returns the size of an ulp of the argument.

static float 
ulp(float f) 
Returns the size of an ulp of the argument.

public static final double E
double
value that is closer than any other to
e, the base of the natural logarithms.public static final double PI
double
value that is closer than any other to
pi, the ratio of the circumference of a circle to its
diameter.public static double sin(double a)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 an angle, in radians.public static double cos(double a)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 an angle, in radians.public static double tan(double a)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 an angle, in radians.public static double asin(double a)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 the value whose arc sine is to be returned.public static double acos(double a)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 the value whose arc cosine is to be returned.public static double atan(double a)
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 the value whose arc tangent is to be returned.public static double toRadians(double angdeg)
angdeg
 an angle, in degreesangdeg
in radians.public static double toDegrees(double angrad)
cos(toRadians(90.0))
to exactly
equal 0.0
.angrad
 an angle, in radiansangrad
in degrees.public static double exp(double a)
double
value. Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 the exponent to raise e to.public static double log(double a)
double
value. Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 a valuea
, the natural logarithm of
a
.public static double log10(double a)
double
value.
Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a
 a valuea
.public static double sqrt(double a)
double
value.
Special cases:
double
value closest to
the true mathematical square root of the argument value.a
 a value.a
.
If the argument is NaN or less than zero, the result is NaN.public static double cbrt(double 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:
The computed result must be within 1 ulp of the exact result.
a
 a value.a
.public static double IEEEremainder(double f1, double f2)
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:
f1
 the dividend.f2
 the divisor.f1
is divided by
f2
.public static double ceil(double a)
double
value that is greater than or equal to the
argument and is equal to a mathematical integer. Special cases:
Math.ceil(x)
is exactly the
value of Math.floor(x)
.a
 a value.public static double floor(double a)
double
value that is less than or equal to the
argument and is equal to a mathematical integer. Special cases:
a
 a value.public static double rint(double a)
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:
a
 a double
value.a
that is
equal to a mathematical integer.public static double atan2(double y, double x)
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:
double
value closest to pi.
double
value closest to pi.
double
value closest to pi/2.
double
value closest to pi/2.
double
value closest to pi/4.
double
value closest to 3*pi/4.
double
value
closest to pi/4.
double
value closest to 3*pi/4.The computed result must be within 2 ulps of the exact result. Results must be semimonotonic.
y
 the ordinate coordinatex
 the abscissa coordinatepublic static double pow(double a, double b)
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.
a
 the base.b
 the exponent.a
^{b}.public static int round(float a)
int
to the argument, with ties
rounding to positive infinity.
Special cases:
Integer.MIN_VALUE
, the result is
equal to the value of Integer.MIN_VALUE
.
Integer.MAX_VALUE
, the result is
equal to the value of Integer.MAX_VALUE
.a
 a floatingpoint value to be rounded to an integer.int
value.Integer.MAX_VALUE
,
Integer.MIN_VALUE
public static long round(double a)
long
to the argument, with ties
rounding to positive infinity.
Special cases:
Long.MIN_VALUE
, the result is
equal to the value of Long.MIN_VALUE
.
Long.MAX_VALUE
, the result is
equal to the value of Long.MAX_VALUE
.a
 a floatingpoint value to be rounded to a
long
.long
value.Long.MAX_VALUE
,
Long.MIN_VALUE
public static double random()
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.
double
greater than or equal
to 0.0
and less than 1.0
.nextDown(double)
,
Random.nextDouble()
double
value less than 1.0
is Math.nextDown(1.0)
, a value x
in the closed range
[x1,x2]
where x1<=x2
may be defined by the statements
double f = Math.random()/Math.nextDown(1.0); double x = x1*(1.0  f) + x2*f;
public static int addExact(int x, int y)
int
.x
 the first valuey
 the second valueArithmeticException
 if the result overflows an intpublic static long addExact(long x, long y)
long
.x
 the first valuey
 the second valueArithmeticException
 if the result overflows a longpublic static int subtractExact(int x, int y)
int
.x
 the first valuey
 the second value to subtract from the firstArithmeticException
 if the result overflows an intpublic static long subtractExact(long x, long y)
long
.x
 the first valuey
 the second value to subtract from the firstArithmeticException
 if the result overflows a longpublic static int multiplyExact(int x, int y)
int
.x
 the first valuey
 the second valueArithmeticException
 if the result overflows an intpublic static long multiplyExact(long x, int y)
long
.x
 the first valuey
 the second valueArithmeticException
 if the result overflows a longpublic static long multiplyExact(long x, long y)
long
.x
 the first valuey
 the second valueArithmeticException
 if the result overflows a longpublic static int incrementExact(int a)
int
.a
 the value to incrementArithmeticException
 if the result overflows an intpublic static long incrementExact(long a)
long
.a
 the value to incrementArithmeticException
 if the result overflows a longpublic static int decrementExact(int a)
int
.a
 the value to decrementArithmeticException
 if the result overflows an intpublic static long decrementExact(long a)
long
.a
 the value to decrementArithmeticException
 if the result overflows a longpublic static int negateExact(int a)
int
.a
 the value to negateArithmeticException
 if the result overflows an intpublic static long negateExact(long a)
long
.a
 the value to negateArithmeticException
 if the result overflows a longpublic static int toIntExact(long value)
long
argument;
throwing an exception if the value overflows an int
.value
 the long valueArithmeticException
 if the argument
overflows an intpublic static long multiplyFull(int x, int y)
x
 the first valuey
 the second valuepublic static long multiplyHigh(long x, long y)
long
the most significant 64 bits of the 128bit
product of two 64bit factors.x
 the first valuey
 the second valuepublic static int floorDiv(int x, int y)
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 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 from truncation when the exact result is negative.
floorDiv
and the /
operator are the same. floorDiv(4, 3) == 1
and (4 / 3) == 1
.floorDiv
returns the integer less than or equal to the quotient
and the /
operator returns the integer closest to zero.floorDiv(4, 3) == 2
,
whereas (4 / 3) == 1
.
x
 the dividendy
 the divisorint
value that is less than or equal to the algebraic quotient.ArithmeticException
 if the divisor y
is zerofloorMod(int, int)
,
floor(double)
public static long floorDiv(long x, int y)
long
value that is less than or equal to the algebraic quotient.
There is one special case, if the dividend is the
Long.MIN_VALUE and the divisor is 1
,
then integer overflow occurs and
the result is equal to Long.MIN_VALUE
.
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 from truncation when the exact result is negative.
For examples, see floorDiv(int, int)
.
x
 the dividendy
 the divisorint
value that is less than or equal to the algebraic quotient.ArithmeticException
 if the divisor y
is zerofloorMod(long, int)
,
floor(double)
public static long floorDiv(long x, long y)
long
value that is less than or equal to the algebraic quotient.
There is one special case, if the dividend is the
Long.MIN_VALUE and the divisor is 1
,
then integer overflow occurs and
the result is equal to Long.MIN_VALUE
.
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 from truncation when the exact result is negative.
For examples, see floorDiv(int, int)
.
x
 the dividendy
 the divisorlong
value that is less than or equal to the algebraic quotient.ArithmeticException
 if the divisor y
is zerofloorMod(long, long)
,
floor(double)
public static int floorMod(int x, int y)
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:
floorMod
and the %
operator are the same. floorMod(4, 3) == 1
; and (4 % 3) == 1
%
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)
.
x
 the dividendy
 the divisorx  (floorDiv(x, y) * y)
ArithmeticException
 if the divisor y
is zerofloorDiv(int, int)
public static int floorMod(long x, int y)
long
and int
arguments.
The floor modulus is x  (floorDiv(x, y) * y)
,
has the same sign as the divisor y
, and
is in the range of abs(y) < r < +abs(y)
.
The relationship between floorDiv
and floorMod
is such that:
floorDiv(x, y) * y + floorMod(x, y) == x
For examples, see floorMod(int, int)
.
x
 the dividendy
 the divisorx  (floorDiv(x, y) * y)
ArithmeticException
 if the divisor y
is zerofloorDiv(long, int)
public static long floorMod(long x, long y)
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)
.
x
 the dividendy
 the divisorx  (floorDiv(x, y) * y)
ArithmeticException
 if the divisor y
is zerofloorDiv(long, long)
public static int abs(int a)
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.
a
 the argument whose absolute value is to be determinedpublic static long abs(long 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.
a
 the argument whose absolute value is to be determinedpublic static float abs(float 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:
a
 the argument whose absolute value is to be determinedfloat
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))
public static double abs(double 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:
a
 the argument whose absolute value is to be determineddouble
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)
public static int max(int a, int b)
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.a
 an argument.b
 another argument.a
and b
.public static long max(long a, long b)
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.a
 an argument.b
 another argument.a
and b
.public static float max(float a, float b)
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.a
 an argument.b
 another argument.a
and b
.public static double max(double a, double b)
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.a
 an argument.b
 another argument.a
and b
.public static int min(int a, int b)
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.a
 an argument.b
 another argument.a
and b
.public static long min(long a, long b)
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.a
 an argument.b
 another argument.a
and b
.public static float min(float a, float b)
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.a
 an argument.b
 another argument.a
and b
.public static double min(double a, double b)
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.a
 an argument.b
 another argument.a
and b
.public static double fma(double a, double b, double c)
double
.
The rounding is done using the round to nearest even
rounding mode.
In contrast, if a * 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:
Note that fma(a, 1.0, c)
returns the same
result as (a + c
). However,
fma(a, b, +0.0)
does not always return the
same result as (a * b
) since
fma(0.0, +0.0, +0.0)
is +0.0
while
(0.0 * +0.0
) is 0.0
; fma(a, b, 0.0)
is
equivalent to (a * b
) however.
a
 a valueb
 a valuec
 a valuedouble
valuepublic static float fma(float a, float b, float c)
float
.
The rounding is done using the round to nearest even
rounding mode.
In contrast, if a * 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:
Note that fma(a, 1.0f, c)
returns the same
result as (a + c
). However,
fma(a, b, +0.0f)
does not always return the
same result as (a * b
) since
fma(0.0f, +0.0f, +0.0f)
is +0.0f
while
(0.0f * +0.0f
) is 0.0f
; fma(a, b, 0.0f)
is
equivalent to (a * b
) however.
a
 a valueb
 a valuec
 a valuefloat
valuepublic static double ulp(double d)
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:
Double.MIN_VALUE
.
Double.MAX_VALUE
, then
the result is equal to 2^{971}.
d
 the floatingpoint value whose ulp is to be returnedpublic static float ulp(float f)
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:
Float.MIN_VALUE
.
Float.MAX_VALUE
, then
the result is equal to 2^{104}.
f
 the floatingpoint value whose ulp is to be returnedpublic static double signum(double d)
Special Cases:
d
 the floatingpoint value whose signum is to be returnedpublic static float signum(float f)
Special Cases:
f
 the floatingpoint value whose signum is to be returnedpublic static double sinh(double x)
double
value.
The hyperbolic sine of x is defined to be
(e^{x}  e^{x})/2
where e is Euler's number.
Special cases:
The computed result must be within 2.5 ulps of the exact result.
x
 The number whose hyperbolic sine is to be returned.x
.public static double cosh(double x)
double
value.
The hyperbolic cosine of x is defined to be
(e^{x} + e^{x})/2
where e is Euler's number.
Special cases:
1.0
.
The computed result must be within 2.5 ulps of the exact result.
x
 The number whose hyperbolic cosine is to be returned.x
.public static double tanh(double x)
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:
+1.0
.
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.
x
 The number whose hyperbolic tangent is to be returned.x
.public static double hypot(double x, double y)
Special cases:
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.
x
 a valuey
 a valuepublic static double expm1(double x)
expm1(x)
+ 1 is much closer to the true
result of e^{x} than exp(x)
.
Special cases:
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.
x
 the exponent to raise e to in the computation of
e^{x} 1.public static double log1p(double x)
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:
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
x
 a valuex
+ 1), the natural
log of x
+ 1public static double copySign(double magnitude, double sign)
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.magnitude
 the parameter providing the magnitude of the resultsign
 the parameter providing the sign of the resultmagnitude
and the sign of sign
.public static float copySign(float magnitude, float sign)
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.magnitude
 the parameter providing the magnitude of the resultsign
 the parameter providing the sign of the resultmagnitude
and the sign of sign
.public static int getExponent(float f)
float
. Special cases:
Float.MAX_EXPONENT
+ 1.
Float.MIN_EXPONENT
1.
f
 a float
valuepublic static int getExponent(double d)
double
. Special cases:
Double.MAX_EXPONENT
+ 1.
Double.MIN_EXPONENT
1.
d
 a double
valuepublic static double nextAfter(double start, double direction)
Special cases:
direction
is returned unchanged (as implied by the requirement of
returning the second argument if the arguments compare as
equal).
start
is
±Double.MIN_VALUE
and direction
has a value such that the result should have a smaller
magnitude, then a zero with the same sign as start
is returned.
start
is infinite and
direction
has a value such that the result should
have a smaller magnitude, Double.MAX_VALUE
with the
same sign as start
is returned.
start
is equal to ±
Double.MAX_VALUE
and direction
has a
value such that the result should have a larger magnitude, an
infinity with same sign as start
is returned.
start
 starting floatingpoint valuedirection
 value indicating which of
start
's neighbors or start
should
be returnedstart
in the
direction of direction
.public static float nextAfter(float start, double direction)
Special cases:
direction
is returned.
start
is
±Float.MIN_VALUE
and direction
has a value such that the result should have a smaller
magnitude, then a zero with the same sign as start
is returned.
start
is infinite and
direction
has a value such that the result should
have a smaller magnitude, Float.MAX_VALUE
with the
same sign as start
is returned.
start
is equal to ±
Float.MAX_VALUE
and direction
has a
value such that the result should have a larger magnitude, an
infinity with same sign as start
is returned.
start
 starting floatingpoint valuedirection
 value indicating which of
start
's neighbors or start
should
be returnedstart
in the
direction of direction
.public static double nextUp(double d)
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:
Double.MIN_VALUE
d
 starting floatingpoint valuepublic static float nextUp(float f)
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:
Float.MIN_VALUE
f
 starting floatingpoint valuepublic static double nextDown(double d)
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:
Double.MIN_VALUE
d
 starting floatingpoint valuepublic static float nextDown(float f)
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:
Float.MIN_VALUE
f
 starting floatingpoint valuepublic static double scalb(double d, int scaleFactor)
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:
d
 number to be scaled by a power of two.scaleFactor
 power of 2 used to scale d
d
× 2^{scaleFactor}public static float scalb(float f, int scaleFactor)
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:
f
 number to be scaled by a power of two.scaleFactor
 power of 2 used to scale f
f
× 2^{scaleFactor}