The class StrictMath
contains methods for performing basic
numeric operations such as the elementary exponential, logarithm,
square root, and trigonometric functions.
To help ensure portability of Java programs, the definitions of
some of the numeric functions in this package require that they
produce the same results as certain published algorithms. These
algorithms are available from the well-known network library
netlib
as the package "Freely Distributable Math
Library," fdlibm
. These
algorithms, which are written in the C programming language, are
then to be understood as executed with all floating-point
operations following the rules of Java floating-point arithmetic.
The Java math library is defined with respect to
fdlibm
version 5.3. Where fdlibm
provides
more than one definition for a function (such as
acos
), use the "IEEE 754 core function" version
(residing in a file whose name begins with the letter
e
). The methods which require fdlibm
semantics are sin
, cos
, tan
,
asin
, acos
, atan
,
exp
, log
, log10
,
cbrt
, atan2
, pow
,
sinh
, cosh
, tanh
,
hypot
, expm1
, and log1p
.
The platform uses signed two's complement integer arithmetic with
int and long primitive types. The developer should choose
the primitive type to ensure that arithmetic operations consistently
produce correct results, which in some cases means the operations
will not overflow the range of values of the computation.
The best practice is to choose the primitive type and algorithm to avoid
overflow. In cases where the size is int
or long
and
overflow errors need to be detected, the methods addExact
,
subtractExact
, multiplyExact
, and toIntExact
throw an ArithmeticException
when the results overflow.
For other arithmetic operations such as divide, absolute value,
increment, decrement, and negation overflow occurs only with
a specific minimum or maximum value and should be checked against
the minimum or maximum as appropriate.
Constant Summary
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 Method Summary
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
long value. |
static int |
abs(int a)
Returns the absolute value of an
int value. |
static float |
abs(float a)
Returns the absolute value of a
float value. |
static double |
abs(double a)
Returns the absolute value of a
double 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 float |
copySign(float magnitude, float sign)
Returns the first floating-point argument with the sign of the
second floating-point argument.
|
static double |
copySign(double magnitude, double sign)
Returns the first floating-point argument with the sign of the
second floating-point 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 double |
exp(double a)
Returns Euler's number e raised to the power of a
double value. |
static double |
expm1(double x)
Returns ex -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, long y)
Returns the largest (closest to positive infinity)
long value that is less than or equal to the algebraic quotient. |
static long |
floorMod(long x, long y)
Returns the floor modulus of the
long arguments. |
static int |
floorMod(int x, int y)
Returns the floor modulus of the
int arguments. |
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(x2 +y2)
without intermediate overflow or underflow.
|
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 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 float |
max(float a, float b)
Returns the greater of two
float values. |
static double |
max(double a, double b)
Returns the greater of two
double values. |
static float |
min(float a, float b)
Returns the smaller of two
float values. |
static double |
min(double a, double b)
Returns the smaller of two
double 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, long y)
Returns the product of the arguments,
throwing an exception if the result overflows a
long . |
static double |
nextAfter(double start, double direction)
Returns the floating-point number adjacent to the first
argument in the direction of the second argument.
|
static float |
nextAfter(float start, double direction)
Returns the floating-point number adjacent to the first
argument in the direction of the second argument.
|
static double |
nextDown(double d)
Returns the floating-point value adjacent to
d in
the direction of negative infinity. |
static float |
nextDown(float f)
Returns the floating-point value adjacent to
f in
the direction of negative infinity. |
static float |
nextUp(float f)
Returns the floating-point value adjacent to
f in
the direction of positive infinity. |
static double |
nextUp(double d)
Returns the floating-point value adjacent to
d 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 float |
scalb(float f, int scaleFactor)
Returns
f ×
2scaleFactor rounded as if performed
by a single correctly rounded floating-point multiply to a
member of the float value set. |
static double |
scalb(double d, int scaleFactor)
Returns
d ×
2scaleFactor rounded as if performed
by a single correctly rounded floating-point multiply to a
member of the double 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 long |
subtractExact(long x, long y)
Returns the difference of the arguments,
throwing an exception if the result overflows a
long . |
static int |
subtractExact(int x, int y)
Returns the difference of the arguments,
throwing an exception if the result overflows an
int . |
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.
|
Inherited Method Summary
Constants
public static final double E
The double
value that is closer than any other to
e, the base of the natural logarithms.
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.
Public Methods
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 | the dividend. |
---|---|
f2 | the divisor. |
Returns
- the remainder when
f1
is divided byf2
.
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 | the argument whose absolute value is to be determined. |
---|
Returns
- the absolute value of the argument.
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 | the argument whose absolute value is to be determined. |
---|
Returns
- the absolute value of the argument.
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 | the argument whose absolute value is to be determined |
---|
Returns
- the absolute value of the argument.
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 | the argument whose absolute value is to be determined |
---|
Returns
- the absolute value of the argument.
public static double acos (double a)
Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi. Special case:
- If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
Parameters
a | the value whose arc cosine is to be returned. |
---|
Returns
- the arc cosine of the argument.
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 | the first value |
---|---|
y | the second value |
Returns
- the result
Throws
ArithmeticException | if the result overflows an int |
---|
See Also
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 | the first value |
---|---|
y | the second value |
Returns
- the result
Throws
ArithmeticException | if the result overflows a long |
---|
See Also
public static double asin (double a)
Returns the arc sine of a value; the returned angle is in the range -pi/2 through pi/2. Special cases:
- If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
- If the argument is zero, then the result is a zero with the same sign as the argument.
Parameters
a | the value whose arc sine is to be returned. |
---|
Returns
- the arc sine of the argument.
public static double atan (double a)
Returns the arc tangent of a value; the returned angle is in the range -pi/2 through pi/2. Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is zero, then the result is a zero with the same sign as the argument.
Parameters
a | the value whose arc tangent is to be returned. |
---|
Returns
- the arc tangent of the argument.
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.
Parameters
y | the ordinate coordinate |
---|---|
x | the abscissa coordinate |
Returns
- the theta component of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates.
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.
Parameters
a | a value. |
---|
Returns
- the cube root of
a
.
public static double ceil (double a)
Returns the smallest (closest to negative infinity)
double
value that is greater than or equal to the
argument and is equal to a mathematical integer. Special cases:
- If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
- If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
- If the argument value is less than zero but greater than -1.0, then the result is negative zero.
StrictMath.ceil(x)
is exactly the
value of -StrictMath.floor(-x)
.Parameters
a | a value. |
---|
Returns
- the smallest (closest to negative infinity) floating-point value that is greater than or equal to the argument and is equal to a mathematical integer.
public static float copySign (float magnitude, float sign)
Returns the first floating-point argument with the sign of the
second floating-point argument. For this method, a NaN
sign
argument is always treated as if it were
positive.
Parameters
magnitude | the parameter providing the magnitude of the result |
---|---|
sign | the parameter providing the sign of the result |
Returns
- a value with the magnitude of
magnitude
and the sign ofsign
.
public static double copySign (double magnitude, double sign)
Returns the first floating-point argument with the sign of the
second floating-point argument. For this method, a NaN
sign
argument is always treated as if it were
positive.
Parameters
magnitude | the parameter providing the magnitude of the result |
---|---|
sign | the parameter providing the sign of the result |
Returns
- a value with the magnitude of
magnitude
and the sign ofsign
.
public static double cos (double a)
Returns the trigonometric cosine of an angle. Special cases:
- If the argument is NaN or an infinity, then the result is NaN.
Parameters
a | an angle, in radians. |
---|
Returns
- the cosine of the argument.
public static double cosh (double x)
Returns the hyperbolic cosine of a double
value.
The hyperbolic cosine of x is defined to be
(ex + e-x)/2
where e is {@linkplain Math#E Euler's number}.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is positive infinity.
- If the argument is zero, then the result is
1.0
.
Parameters
x | The number whose hyperbolic cosine is to be returned. |
---|
Returns
- The hyperbolic cosine of
x
.
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.
Parameters
a | the exponent to raise e to. |
---|
Returns
- the value e
a
, where e is the base of the natural logarithms.
public static double expm1 (double x)
Returns ex -1. Note that for values of
x near 0, the exact sum of
expm1(x)
+ 1 is much closer to the true
result of ex 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.
Parameters
x | the exponent to raise e to in the computation of
ex -1. |
---|
Returns
- the value e
x
- 1.
public static double floor (double a)
Returns the largest (closest to positive infinity)
double
value that is less than or equal to the
argument and is equal to a mathematical integer. Special cases:
- If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
- If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
Parameters
a | a value. |
---|
Returns
- the largest (closest to positive infinity) floating-point value that less than or equal to the argument and is equal to a mathematical integer.
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
{@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is -1
,
then integer overflow occurs and
the result is equal to the Integer.MIN_VALUE
.
See Math.floorDiv
for examples and
a comparison to the integer division /
operator.
Parameters
x | the dividend |
---|---|
y | the divisor |
Returns
- the largest (closest to positive infinity)
int
value that is less than or equal to the algebraic quotient.
Throws
ArithmeticException | if the divisor y is zero |
---|
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
{@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is -1
,
then integer overflow occurs and
the result is equal to the Long.MIN_VALUE
.
See Math.floorDiv
for examples and
a comparison to the integer division /
operator.
Parameters
x | the dividend |
---|---|
y | the divisor |
Returns
- the largest (closest to positive infinity)
long
value that is less than or equal to the algebraic quotient.
Throws
ArithmeticException | if the divisor y is zero |
---|
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
See Math.floorMod
for examples and
a comparison to the %
operator.
Parameters
x | the dividend |
---|---|
y | the divisor |
Returns
- the floor modulus
x - (floorDiv(x, y) * y)
Throws
ArithmeticException | if the divisor y is zero |
---|
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
See Math.floorMod
for examples and
a comparison to the %
operator.
Parameters
x | the dividend |
---|---|
y | the divisor |
Returns
- the floor modulus
x - (floorDiv(x, y) * y)
Throws
ArithmeticException | if the divisor y is zero |
---|
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 | a double value |
---|
Returns
- the unbiased exponent of the argument
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 | a float value |
---|
Returns
- the unbiased exponent of the argument
public static double hypot (double x, double y)
Returns sqrt(x2 +y2) without intermediate overflow or underflow.
Special cases:
- If either argument is infinite, then the result is positive infinity.
- If either argument is NaN and neither argument is infinite, then the result is NaN.
Parameters
x | a value |
---|---|
y | a value |
Returns
- sqrt(x2 +y2) without intermediate overflow or underflow
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.
Parameters
a | a value |
---|
Returns
- the value ln
a
, the natural logarithm ofa
.
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 10n for integer n, then the result is n.
Parameters
a | a value |
---|
Returns
- the base 10 logarithm of
a
.
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 floating-point 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.
Parameters
x | a value |
---|
Returns
- the value ln(
x
+ 1), the natural log ofx
+ 1
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 | an argument. |
---|---|
b | another argument. |
Returns
- the larger of
a
andb
.
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 | an argument. |
---|---|
b | another argument. |
Returns
- the larger of
a
andb
.
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 | an argument. |
---|---|
b | another argument. |
Returns
- the larger of
a
andb
.
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 | an argument. |
---|---|
b | another argument. |
Returns
- the larger of
a
andb
.
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 | an argument. |
---|---|
b | another argument. |
Returns
- the smaller of
a
andb.
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 | an argument. |
---|---|
b | another argument. |
Returns
- the smaller of
a
andb
.
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 | an argument. |
---|---|
b | another argument. |
Returns
- the smaller of
a
andb
.
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 | an argument. |
---|---|
b | another argument. |
Returns
- the smaller of
a
andb
.
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 | the first value |
---|---|
y | the second value |
Returns
- the result
Throws
ArithmeticException | if the result overflows an int |
---|
See Also
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 | the first value |
---|---|
y | the second value |
Returns
- the result
Throws
ArithmeticException | if the result overflows a long |
---|
See Also
public static double nextAfter (double start, double direction)
Returns the floating-point number adjacent to the first argument in the direction of the second argument. If both arguments compare as equal the second argument is returned.
Special cases:
- If either argument is a NaN, then NaN is returned.
- If both arguments are signed zeros,
direction
is returned unchanged (as implied by the requirement of returning the second argument if the arguments compare as equal). - If
start
is ±Double.MIN_VALUE
anddirection
has a value such that the result should have a smaller magnitude, then a zero with the same sign asstart
is returned. - If
start
is infinite anddirection
has a value such that the result should have a smaller magnitude,Double.MAX_VALUE
with the same sign asstart
is returned. - If
start
is equal to ±Double.MAX_VALUE
anddirection
has a value such that the result should have a larger magnitude, an infinity with same sign asstart
is returned.
Parameters
start | starting floating-point value |
---|---|
direction | value indicating which of
start 's neighbors or start should
be returned |
Returns
- The floating-point number adjacent to
start
in the direction ofdirection
.
public static float nextAfter (float start, double direction)
Returns the floating-point number adjacent to the first argument in the direction of the second argument. If both arguments compare as equal a value equivalent to the second argument is returned.
Special cases:
- If either argument is a NaN, then NaN is returned.
- If both arguments are signed zeros, a value equivalent
to
direction
is returned. - If
start
is ±Float.MIN_VALUE
anddirection
has a value such that the result should have a smaller magnitude, then a zero with the same sign asstart
is returned. - If
start
is infinite anddirection
has a value such that the result should have a smaller magnitude,Float.MAX_VALUE
with the same sign asstart
is returned. - If
start
is equal to ±Float.MAX_VALUE
anddirection
has a value such that the result should have a larger magnitude, an infinity with same sign asstart
is returned.
Parameters
start | starting floating-point value |
---|---|
direction | value indicating which of
start 's neighbors or start should
be returned |
Returns
- The floating-point number adjacent to
start
in the direction ofdirection
.
public static double nextDown (double d)
Returns the floating-point 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 | starting floating-point value |
---|
Returns
- The adjacent floating-point value closer to negative infinity.
public static float nextDown (float f)
Returns the floating-point 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 | starting floating-point value |
---|
Returns
- The adjacent floating-point value closer to negative infinity.
public static float nextUp (float f)
Returns the floating-point 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 | starting floating-point value |
---|
Returns
- The adjacent floating-point value closer to positive infinity.
public static double nextUp (double d)
Returns the floating-point 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 | starting floating-point value |
---|
Returns
- The adjacent floating-point value closer to positive infinity.
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 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.)
Parameters
a | base. |
---|---|
b | the exponent. |
Returns
- the value
a
b
.
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 pseudorandom-number generator, exactly as if by the expression
new java.util.Random()
This new pseudorandom-number 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 pseudorandom-number generator.
Returns
- a pseudorandom
double
greater than or equal to0.0
and less than1.0
.
See Also
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 to the value of the argument, the result is the
integer value that is even. Special cases:
- If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
- If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
Parameters
a | a value. |
---|
Returns
- the closest floating-point value to
a
that is equal to a mathematical integer.
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 | a floating-point value to be rounded to a
long . |
---|
Returns
- the value of the argument rounded to the nearest
long
value.
See Also
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 | a floating-point value to be rounded to an integer. |
---|
Returns
- the value of the argument rounded to the nearest
int
value.
See Also
public static float scalb (float f, int scaleFactor)
Returns f
×
2scaleFactor
rounded as if performed
by a single correctly rounded floating-point multiply to a
member of the float value set. See the Java
Language Specification for a discussion of floating-point
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 non-NaN, 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 | number to be scaled by a power of two. |
---|---|
scaleFactor | power of 2 used to scale f |
Returns
f
× 2scaleFactor
public static double scalb (double d, int scaleFactor)
Returns d
×
2scaleFactor
rounded as if performed
by a single correctly rounded floating-point multiply to a
member of the double value set. See the Java
Language Specification for a discussion of floating-point
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 non-NaN, 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 | number to be scaled by a power of two. |
---|---|
scaleFactor | power of 2 used to scale d |
Returns
d
× 2scaleFactor
public static double signum (double d)
Returns the signum function of the argument; zero if the argument is zero, 1.0 if the argument is greater than zero, -1.0 if the argument is less than zero.
Special Cases:
- If the argument is NaN, then the result is NaN.
- If the argument is positive zero or negative zero, then the result is the same as the argument.
Parameters
d | the floating-point value whose signum is to be returned |
---|
Returns
- the signum function of the argument
public static float signum (float f)
Returns the signum function of the argument; zero if the argument is zero, 1.0f if the argument is greater than zero, -1.0f if the argument is less than zero.
Special Cases:
- If the argument is NaN, then the result is NaN.
- If the argument is positive zero or negative zero, then the result is the same as the argument.
Parameters
f | the floating-point value whose signum is to be returned |
---|
Returns
- the signum function of the argument
public static double sin (double a)
Returns the trigonometric sine of an angle. Special cases:
- If the argument is NaN or an infinity, then the result is NaN.
- If the argument is zero, then the result is a zero with the same sign as the argument.
Parameters
a | an angle, in radians. |
---|
Returns
- the sine of the argument.
public static double sinh (double x)
Returns the hyperbolic sine of a double
value.
The hyperbolic sine of x is defined to be
(ex - e-x)/2
where e is {@linkplain Math#E Euler's number}.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is an infinity with the same sign as the argument.
- If the argument is zero, then the result is a zero with the same sign as the argument.
Parameters
x | The number whose hyperbolic sine is to be returned. |
---|
Returns
- The hyperbolic sine of
x
.
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 | a value. |
---|
Returns
- the positive square root of
a
.
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 | the first value |
---|---|
y | the second value to subtract from the first |
Returns
- the result
Throws
ArithmeticException | if the result overflows a long |
---|
See Also
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 | the first value |
---|---|
y | the second value to subtract from the first |
Returns
- the result
Throws
ArithmeticException | if the result overflows an int |
---|
See Also
public static double tan (double a)
Returns the trigonometric tangent of an angle. Special cases:
- If the argument is NaN or an infinity, then the result is NaN.
- If the argument is zero, then the result is a zero with the same sign as the argument.
Parameters
a | an angle, in radians. |
---|
Returns
- the tangent of the argument.
public static double tanh (double x)
Returns the hyperbolic tangent of a double
value.
The hyperbolic tangent of x is defined to be
(ex - e-x)/(ex + e-x),
in other words, {@linkplain Math#sinh
sinh(x)}/{@linkplain Math#cosh cosh(x)}. Note
that the absolute value of the exact tanh is always less than
1.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is zero, then the result is a zero with the same sign as the argument.
- If the argument is positive infinity, then the result is
+1.0
. - If the argument is negative infinity, then the result is
-1.0
.
Parameters
x | The number whose hyperbolic tangent is to be returned. |
---|
Returns
- The hyperbolic tangent of
x
.
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 | an angle, in radians |
---|
Returns
- the measurement of the angle
angrad
in degrees.
public static int toIntExact (long value)
Returns the value of the long
argument;
throwing an exception if the value overflows an int
.
Parameters
value | the long value |
---|
Returns
- the argument as an int
Throws
ArithmeticException | if the argument overflows an int |
---|
See Also
public static double toRadians (double angdeg)
Converts an angle measured in degrees to an approximately equivalent angle measured in radians. The conversion from degrees to radians is generally inexact.
Parameters
angdeg | an angle, in degrees |
---|
Returns
- the measurement of the angle
angdeg
in radians.
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 floating-point value and the double
value next larger in magnitude. Note that for non-NaN
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 2971.
Parameters
d | the floating-point value whose ulp is to be returned |
---|
Returns
- the size of an ulp of the argument
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 floating-point value and the float
value next larger in magnitude. Note that for non-NaN
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 2104.
Parameters
f | the floating-point value whose ulp is to be returned |
---|
Returns
- the size of an ulp of the argument