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.
Constants  

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

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

Computes the remainder operation on two arguments as prescribed
by the IEEE 754 standard.
 
Returns the absolute value of a
double value.  
Returns the absolute value of a
long value.  
Returns the absolute value of a
float value.  
Returns the absolute value of an
int value.  
Returns the arc cosine of a value; the returned angle is in the
range 0.0 through pi.
 
Returns the arc sine of a value; the returned angle is in the
range pi/2 through pi/2.
 
Returns the arc tangent of a value; the returned angle is in the
range pi/2 through pi/2.
 
Returns the angle theta from the conversion of rectangular
coordinates (
x , y ) to polar
coordinates (r, theta).  
Returns the cube root of a
double value.  
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.  
Returns the first floatingpoint argument with the sign of the
second floatingpoint argument.
 
Returns the first floatingpoint argument with the sign of the
second floatingpoint argument.
 
Returns the trigonometric cosine of an angle.
 
Returns the hyperbolic cosine of a
double value.  
Returns Euler's number e raised to the power of a
double value.  
Returns e^{x} 1.
 
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.  
Returns the unbiased exponent used in the representation of a
float .  
Returns the unbiased exponent used in the representation of a
double .  
Returns sqrt(x^{2} +y^{2})
without intermediate overflow or underflow.
 
Returns the natural logarithm (base e) of a
double
value.  
Returns the base 10 logarithm of a
double value.  
Returns the natural logarithm of the sum of the argument and 1.
 
Returns the greater of two
long values.  
Returns the greater of two
int values.  
Returns the greater of two
double values.  
Returns the greater of two
float values.  
Returns the smaller of two
int values.  
Returns the smaller of two
long values.  
Returns the smaller of two
double values.  
Returns the smaller of two
float values.  
Returns the floatingpoint number adjacent to the first
argument in the direction of the second argument.
 
Returns the floatingpoint number adjacent to the first
argument in the direction of the second argument.
 
Returns the floatingpoint value adjacent to
d in
the direction of positive infinity.  
Returns the floatingpoint value adjacent to
f in
the direction of positive infinity.  
Returns the value of the first argument raised to the power of the
second argument.
 
Returns a
double value with a positive sign, greater
than or equal to 0.0 and less than 1.0 .  
Returns the
double value that is closest in value
to the argument and is equal to a mathematical integer.  
Returns the closest
long to the argument.  
Returns the closest
int to the argument.  
Return
d ×
2^{scaleFactor} rounded as if performed
by a single correctly rounded floatingpoint multiply to a
member of the double value set.  
Return
f ×
2^{scaleFactor} rounded as if performed
by a single correctly rounded floatingpoint multiply to a
member of the float value set.  
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.
 
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.
 
Returns the trigonometric sine of an angle.
 
Returns the hyperbolic sine of a
double value.  
Returns the correctly rounded positive square root of a
double value.  
Returns the trigonometric tangent of an angle.
 
Returns the hyperbolic tangent of a
double value.  
Converts an angle measured in radians to an approximately
equivalent angle measured in degrees.
 
Converts an angle measured in degrees to an approximately
equivalent angle measured in radians.
 
Returns the size of an ulp of the argument.
 
Returns the size of an ulp of the argument.

[Expand]
Inherited Methods  

From class
java.lang.Object

The double
value that is closer than any other to
e, the base of the natural logarithms.
The double
value that is closer than any other to
pi, the ratio of the circumference of a circle to its
diameter.
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:
f1  the dividend. 

f2  the divisor. 
f1
is divided by
f2
.
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:
Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)
a  the argument whose absolute value is to be determined 

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
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 determined 

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:
Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))
a  the argument whose absolute value is to be determined 

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
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 determined 

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

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

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

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:
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 coordinate 

x  the abscissa coordinate 
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:
The computed result must be within 1 ulp of the exact result.
a  a value. 

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:
Math.ceil(x)
is exactly the
value of Math.floor(x)
.a  a value. 

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.
magnitude  the parameter providing the magnitude of the result 

sign  the parameter providing the sign of the result 
magnitude
and the sign of 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.
magnitude  the parameter providing the magnitude of the result 

sign  the parameter providing the sign of the result 
magnitude
and the sign of sign
.Returns the trigonometric cosine of an angle. Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a  an angle, in radians. 

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:
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
.Returns Euler's number e raised to the power of 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. 

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:
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. 

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:
a  a value. 

Returns the unbiased exponent used in the representation of a
float
. Special cases:
MAX_EXPONENT
+ 1.
MIN_EXPONENT
1.
f  a float value 

Returns the unbiased exponent used in the representation of a
double
. Special cases:
MAX_EXPONENT
+ 1.
MIN_EXPONENT
1.
d  a double value 

Returns sqrt(x^{2} +y^{2}) without intermediate overflow or underflow.
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 value 

y  a value 
Returns the natural logarithm (base e) of a double
value. Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a  a value 

a
, the natural logarithm of
a
.
Returns the base 10 logarithm of a double
value.
Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a  a value 

a
.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:
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
x  a value 

x
+ 1), the natural
log of x
+ 1Returns the greater of two long
values. That is, the
result is the argument closer to the value of
MAX_VALUE
. If the arguments have the same value,
the result is that same value.
a  an argument. 

b  another argument. 
a
and b
.
Returns the greater of two int
values. That is, the
result is the argument closer to the value of
MAX_VALUE
. If the arguments have the same value,
the result is that same value.
a  an argument. 

b  another argument. 
a
and 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.
a  an argument. 

b  another argument. 
a
and 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.
a  an argument. 

b  another argument. 
a
and b
.
Returns the smaller of two int
values. That is,
the result the argument closer to the value of
MIN_VALUE
. If the arguments have the same
value, the result is that same value.
a  an argument. 

b  another argument. 
a
and b
.
Returns the smaller of two long
values. That is,
the result is the argument closer to the value of
MIN_VALUE
. If the arguments have the same
value, the result is that same value.
a  an argument. 

b  another argument. 
a
and 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.
a  an argument. 

b  another argument. 
a
and 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.
a  an argument. 

b  another argument. 
a
and b
.
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:
direction
is returned.
start
is
±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, MAX_VALUE
with the
same sign as start
is returned.
start
is equal to ±
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 value 

direction  value indicating which of
start 's neighbors or start should
be returned 
start
in the
direction of 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:
direction
is returned unchanged (as implied by the requirement of
returning the second argument if the arguments compare as
equal).
start
is
±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, MAX_VALUE
with the
same sign as start
is returned.
start
is equal to ±
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 value 

direction  value indicating which of
start 's neighbors or start should
be returned 
start
in the
direction of direction
.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:
MIN_VALUE
d  starting floatingpoint value 

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:
MIN_VALUE
f  starting floatingpoint value 

Returns the value of the first argument raised to the power of the second argument. Special cases:
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}.
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.
double
greater than or equal
to 0.0
and less than 1.0
.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:
a  a double value. 

a
that is
equal to a mathematical integer.
Returns the closest long
to the argument. The result
is rounded to an integer by adding 1/2, taking the floor of the
result, and casting the result to type long
. In other
words, the result is equal to the value of the expression:
(long)Math.floor(a + 0.5d)
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.Returns the closest int
to the argument. The
result is rounded to an integer by adding 1/2, taking the
floor of the result, and casting the result to type int
.
In other words, the result is equal to the value of the expression:
(int)Math.floor(a + 0.5f)
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.Return 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 MIN_EXPONENT
and 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}Return 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 MIN_EXPONENT
and 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}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:
d  the floatingpoint value whose signum is to be returned 

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:
f  the floatingpoint value whose signum is to be returned 

Returns the trigonometric sine of an angle. Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a  an angle, in radians. 

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:
The computed result must be within 2.5 ulps of the exact result.
x  The number whose hyperbolic sine is to be returned. 

x
.Returns the correctly rounded positive square root of 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.
Returns the trigonometric tangent of an angle. Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semimonotonic.
a  an angle, in radians. 

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:
+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
.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
.
angrad  an angle, in radians 

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

angdeg
in radians.Returns the size of an ulp of the argument. An ulp 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:
Float.MIN_VALUE
.
Float.MAX_VALUE
, then
the result is equal to 2^{104}.
f  the floatingpoint value whose ulp is to be returned 

Returns the size of an ulp of the argument. An ulp 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:
Double.MIN_VALUE
.
Double.MAX_VALUE
, then
the result is equal to 2^{971}.
d  the floatingpoint value whose ulp is to be returned 
