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 bit-for-bit same results. This relaxation
permits better-performing 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 platform-specific native
libraries or microprocessor instructions, where available, to provide
higher-performance implementations of Math
methods. Such
higher-performance 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 floating-point Math
methods is
measured in terms of ulps, units in the last place. For a given
floating-point format, an ulp of a specific real number value is the
difference between the two floating-point values closest to 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
worst-case error at any argument. If a method always has an error less
than 0.5 ulps, the method always returns the floating-point number
nearest the exact result; such a method is correctly rounded. A
correctly rounded method is generally the best a floating-point
approximation can be; however, it is impractical for many
floating-point 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; otherwise,
either of the two floating-point numbers closest to the exact result
may be returned. Besides accuracy at individual arguments, maintaining
proper relations between the method at different arguments is also
important. Therefore, methods with more than 0.5 ulp errors are
required to be semi-monotonic: whenever the mathematical
function is non-decreasing, so is the floating-point approximation,
likewise, whenever the mathematical function is non-increasing, so is
the floating-point approximation. Not all approximations that have 1
ulp accuracy will automatically meet the monotonicity requirements.
Field Summary | |
static double |
E
The double
value that is closer than any other to e, the base of the
natural logarithms. |
static double |
PI
The double
value that is closer than any other to pi, the ratio of the
circumference of a circle to its diameter. |
Method Summary | |
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 an angle, in the range of 0.0 through pi. |
static double |
asin(double a)
Returns the arc sine of an angle, in the range of -pi/2 through pi/2. |
static double |
atan(double a)
Returns the arc tangent of an angle, in the range of -pi/2 through pi/2. |
static double |
atan2(double y,
double x) Converts rectangular coordinates ( x , y ) to polar
(r, theta). |
static double |
ceil(double a)
Returns the smallest (closest to negative infinity) double value that
is not less than the argument and is equal to a mathematical integer. |
static double |
cos(double a)
Returns the trigonometric cosine of an angle. |
static double |
exp(double a)
Returns Euler's number e raised to the power of a double
value. |
static double |
floor(double a)
Returns the largest (closest to positive infinity) double value that
is not greater than the argument and is equal to a mathematical integer. |
static double |
IEEEremainder(double f1,
double f2) Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. |
static double |
log(double a)
Returns the natural logarithm (base e) of a double value. |
static double |
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 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. |
static int |
round(float a)
Returns the closest int to the argument. |
static double |
sin(double a)
Returns the trigonometric sine of an angle. |
static double |
sqrt(double a)
Returns the correctly rounded positive square root of a double value. |
static double |
tan(double a)
Returns the trigonometric tangent of an angle. |
static double |
toDegrees(double angrad)
Converts an angle measured in radians to an approximately equivalent angle measured in degrees. |
static double |
toRadians(double angdeg)
Converts an angle measured in degrees to an approximately equivalent angle measured in radians. |
Methods inherited from class java.lang.Object |
clone,
equals,
finalize,
getClass,
hashCode,
notify,
notifyAll,
toString,
wait,
wait,
wait |
Field Detail |
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.
Method Detail |
public static double sin(double a)
A result must be within 1 ulp of the correctly rounded result. Results must be semi-monotonic.
a
- an angle, in radians. public static double cos(double a)
A result must be within 1 ulp of the correctly rounded result. Results must be semi-monotonic.
a
- an angle, in radians. public static double tan(double a)
A result must be within 1 ulp of the correctly rounded result. Results must be semi-monotonic.
a
- an angle, in radians. public static double asin(double a)
A result must be within 1 ulp of the correctly rounded result. Results must be semi-monotonic.
a
- the value whose arc sine is to be returned. public static double acos(double a)
A result must be within 1 ulp of the correctly rounded result. Results must be semi-monotonic.
a
- the value whose arc cosine is to be
returned. public static double atan(double a)
A result must be within 1 ulp of the correctly rounded result. Results must be semi-monotonic.
a
- the value whose arc tangent is to be
returned. public static double toRadians(double angdeg)
angdeg
- an angle, in degrees angdeg
in radians.public static double toDegrees(double angrad)
cos(toRadians(90.0))
to exactly equal 0.0
.
angrad
- an angle, in radians angrad
in degrees.public static double exp(double a)
double
value. Special cases:
A result must be within 1 ulp of the correctly rounded result. Results must be semi-monotonic.
a
- the exponent to raise e to. public static double log(double a)
double
value. Special cases:
A result must be within 1 ulp of the correctly rounded result. Results must be semi-monotonic.
a
- a number greater than 0.0
. a
, the natural logarithm of a
.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 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 not less than 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 not greater than 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 (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.A result must be within 2 ulps of the correctly rounded result. Results must be semi-monotonic.
y
- the ordinate coordinatex
- the abscissa coordinate public static double pow(double a,
double b)
double
value.(In the foregoing descriptions, a floating-point value is
considered to be an integer if and only if it is finite and a fixed
point of the method ceil
or, equivalently, a fixed point of the method floor
.
A
value is a fixed point of a one-argument method if and only if the
result of applying the method to the value is equal to the value.)
A result must be within 1 ulp of the correctly rounded result. Results must be semi-monotonic.
a
- the base.b
- the exponent. a^{b}
.public static int round(float a)
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 floating-point 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. 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 floating-point 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 pseudorandom-number generator, exactly as if by the expression
This new pseudorandom-number generator is used thereafter for all calls to this method and is used nowhere else.new java.util.Random
This method is properly synchronized to allow correct use by more than one thread. However, if many threads need to generate pseudorandom numbers at a great rate, it may reduce contention for each thread to have its own pseudorandom-number generator.
double
greater than or equal to 0.0
and less than 1.0
.Random.nextDouble()
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
determined Integer.MIN_VALUE
public 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
determined Long.MIN_VALUE
public 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:
Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))
a
- the argument whose absolute value is to be
determined 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:
Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)
a
- the argument whose absolute value is to be
determined 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
.Long.MAX_VALUE
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
.Long.MAX_VALUE
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 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 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
.Long.MIN_VALUE
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
.Long.MIN_VALUE
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 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 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
.