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FlexDoc/Javadoc 2.0 Demo Java Doc |
Class Math
java.lang.Math
public final class 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 distance between the two
floating-point 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 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 as the computed result; otherwise, either of the
two floating-point 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
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.
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, toIntExact,
incrementExact, decrementExact and negateExact
throw an ArithmeticException when the results overflow.
For the arithmetic operations divide and absolute value, overflow
occurs only with a specific minimum or maximum value and
should be checked against the minimum or maximum as appropriate.
The 2019 revision of the IEEE 754 floating-point standard includes
a section of recommended operations and the semantics of those
operations if they are included in a programming environment. The
recommended operations present in this class include
sin,
cos,
tan,
asin,
acos,
atan,
exp,
expm1,
log,
log10,
log1p,
sinh,
cosh,
tanh,
hypot, and
pow. (The
sqrt
operation is a required part of IEEE 754 from a different section
of the standard.) The special case behavior of the recommended
operations generally follows the guidance of the IEEE 754
standard. However, the
pow method defines different
behavior for some arguments, as noted in its specification. The IEEE 754 standard defines its operations to be
correctly rounded, which is a more stringent quality of
implementation condition than required for most of the methods in
question that are also included in this class.
Since:
1.0
Author:
Joseph D. Darcy
Field Summary |
static final double |
The double value that is closer than any other to
e, the base of the natural logarithms.
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static final double |
The double value that is closer than any other to
pi, the ratio of the circumference of a circle to its
diameter.
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Method Summary |
static double |
Returns the absolute value of a double value.
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static float |
Returns the absolute value of a float value.
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static int |
Returns the absolute value of an int value.
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static long |
Returns the absolute value of a long value.
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static int |
Returns the mathematical absolute value of an int value
if it is exactly representable as an int, throwing
ArithmeticException if the result overflows the
positive int range.
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static long |
Returns the mathematical absolute value of an long value
if it is exactly representable as an long, throwing
ArithmeticException if the result overflows the
positive long range.
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static double |
Returns the arc cosine of a value; the returned angle is in the
range 0.0 through pi.
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static int |
Returns the sum of its arguments,
throwing an exception if the result overflows an int.
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static long |
Returns the sum of its arguments,
throwing an exception if the result overflows a long.
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static double |
Returns the arc sine of a value; the returned angle is in the
range -pi/2 through pi/2.
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static double |
Returns the arc tangent of a value; the returned angle is in the
range -pi/2 through pi/2.
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static double |
atan2(double y, double x)
Returns the angle theta from the conversion of rectangular
coordinates (x, y) to polar
coordinates (r, theta).
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static double |
Returns the cube root of a double value.
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static double |
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.
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static double |
Returns the first floating-point argument with the sign of the
second floating-point argument.
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static float |
Returns the first floating-point argument with the sign of the
second floating-point argument.
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static double |
Returns the trigonometric cosine of an angle.
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static double |
Returns the hyperbolic cosine of a double value.
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static int |
Returns the argument decremented by one, throwing an exception if the
result overflows an int.
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static long |
Returns the argument decremented by one, throwing an exception if the
result overflows a long.
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static double |
Returns Euler's number e raised to the power of a
double value.
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static double |
Returns ex -1.
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static double |
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.
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static int |
Returns the largest (closest to positive infinity)
int value that is less than or equal to the algebraic quotient.
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static long |
Returns the largest (closest to positive infinity)
long value that is less than or equal to the algebraic quotient.
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static long |
Returns the largest (closest to positive infinity)
long value that is less than or equal to the algebraic quotient.
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static int |
Returns the floor modulus of the int arguments.
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static int |
Returns the floor modulus of the long and int arguments.
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static long |
Returns the floor modulus of the long arguments.
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static double |
fma(double a, double b, double c)
Returns the fused multiply add of the three arguments; that is,
returns the exact product of the first two arguments summed
with the third argument and then rounded once to the nearest
double.
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static float |
fma(float a, float b, float c)
Returns the fused multiply add of the three arguments; that is,
returns the exact product of the first two arguments summed
with the third argument and then rounded once to the nearest
float.
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static int |
Returns the unbiased exponent used in the representation of a
double.
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static int |
Returns the unbiased exponent used in the representation of a
float.
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static double |
hypot(double x, double y)
Returns sqrt(x2 +y2)
without intermediate overflow or underflow.
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static double |
Computes the remainder operation on two arguments as prescribed
by the IEEE 754 standard.
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static int |
Returns the argument incremented by one, throwing an exception if the
result overflows an int.
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static long |
Returns the argument incremented by one, throwing an exception if the
result overflows a long.
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static double |
Returns the natural logarithm (base e) of a double
value.
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static double |
Returns the base 10 logarithm of a double value.
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static double |
Returns the natural logarithm of the sum of the argument and 1.
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static double |
Returns the greater of two double values.
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static float |
Returns the greater of two float values.
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static int |
Returns the greater of two int values.
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static long |
Returns the greater of two long values.
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static double |
Returns the smaller of two double values.
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static float |
Returns the smaller of two float values.
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static int |
Returns the smaller of two int values.
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static long |
Returns the smaller of two long values.
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static int |
Returns the product of the arguments,
throwing an exception if the result overflows an int.
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static long |
Returns the product of the arguments, throwing an exception if the result
overflows a long.
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static long |
Returns the product of the arguments,
throwing an exception if the result overflows a long.
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static long |
Returns the exact mathematical product of the arguments.
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static long |
Returns as a long the most significant 64 bits of the 128-bit
product of two 64-bit factors.
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static int |
Returns the negation of the argument, throwing an exception if the
result overflows an int.
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static long |
Returns the negation of the argument, throwing an exception if the
result overflows a long.
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static double |
Returns the floating-point number adjacent to the first
argument in the direction of the second argument.
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static float |
Returns the floating-point number adjacent to the first
argument in the direction of the second argument.
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static double |
Returns the floating-point value adjacent to d in
the direction of negative infinity.
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static float |
Returns the floating-point value adjacent to f in
the direction of negative infinity.
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static double |
Returns the floating-point value adjacent to d in
the direction of positive infinity.
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static float |
Returns the floating-point value adjacent to f in
the direction of positive infinity.
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static double |
Returns the value of the first argument raised to the power of the
second argument.
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static double |
Returns a double value with a positive sign, greater
than or equal to 0.0 and less than 1.0.
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static double |
Returns the double value that is closest in value
to the argument and is equal to a mathematical integer.
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static long |
Returns the closest long to the argument, with ties
rounding to positive infinity.
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static int |
Returns the closest int to the argument, with ties
rounding to positive infinity.
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static double |
scalb(double d, int scaleFactor)
Returns d × 2scaleFactor
rounded as if performed by a single correctly rounded
floating-point multiply.
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static float |
scalb(float f, int scaleFactor)
Returns f × 2scaleFactor
rounded as if performed by a single correctly rounded
floating-point multiply.
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static double |
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.
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static float |
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.
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static double |
Returns the trigonometric sine of an angle.
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static double |
Returns the hyperbolic sine of a double value.
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static double |
Returns the correctly rounded positive square root of a
double value.
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static int |
Returns the difference of the arguments,
throwing an exception if the result overflows an int.
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static long |
Returns the difference of the arguments,
throwing an exception if the result overflows a long.
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static double |
Returns the trigonometric tangent of an angle.
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static double |
Returns the hyperbolic tangent of a double value.
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static double |
Converts an angle measured in radians to an approximately
equivalent angle measured in degrees.
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static int |
Returns the value of the long argument,
throwing an exception if the value overflows an int.
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static double |
Converts an angle measured in degrees to an approximately
equivalent angle measured in radians.
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static double |
Returns the size of an ulp of the argument.
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static float |
Returns the size of an ulp of the argument.
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Methods inherited from class java.lang. Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
public static final double E
The
double value that is closer than any other to
e, the base of the natural logarithms.
See Also:
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.
See Also:
public static double sin |
(double a) |
Returns the trigonometric sine of an angle. Special cases:
- If the argument is NaN or an infinity, then the
result is NaN.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - an angle, in radians.
Returns:
the sine of the argument.
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.
- If the argument is zero, then the result is 1.0.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - an angle, in radians.
Returns:
the cosine of the argument.
public static double tan |
(double a) |
Returns the trigonometric tangent of an angle. Special cases:
- If the argument is NaN or an infinity, then the result
is NaN.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - an angle, in radians.
Returns:
the tangent of the argument.
public static double asin |
(double a) |
Returns the arc sine of a value; the returned angle is in the
range -
pi/2 through
pi/2. Special cases:
- If the argument is NaN or its absolute value is greater
than 1, then the result is NaN.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - the value whose arc sine is to be returned.
Returns:
the arc sine 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.
- If the argument is 1.0, the result is positive zero.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - the value whose arc cosine is to be returned.
Returns:
the arc cosine 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.
- If the argument is infinite,
then the result is the closest value to pi/2 with the
same sign as the input.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - the value whose arc tangent is to be returned.
Returns:
the arc tangent of the argument.
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.
Since:
1.2
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.
Since:
1.2
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.
- If the argument is zero, then the result is 1.0.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - the exponent to raise e to.
Returns:
the value ea,
where e is the base of the natural logarithms.
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.
- If the argument is 1.0, then the result is positive
zero.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - a value
Returns:
the value ln a, the natural logarithm of
a.
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. In particular,
if the argument is 1.0 (100), then the
result is positive zero.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - a value
Returns:
the base 10 logarithm of a.
Since:
1.5
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.
Otherwise, the result is the
double value closest to
the true mathematical square root of the argument value.
Parameters:
a - a value.
Returns:
the positive square root of a.
If the argument is NaN or less than zero, the result is NaN.
public static double cbrt |
(double a) |
Returns the cube root of a
double value. For
positive finite
x,
cbrt(-x) ==
-cbrt(x); that is, the cube root of a negative value is
the negative of the cube root of that value's magnitude.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is an infinity
with the same sign as the argument.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 1 ulp of the exact result.
Parameters:
a - a value.
Returns:
the cube root of a.
Since:
1.5
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 by
f2.
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.
Note
that the value of
Math.ceil(x) is exactly the
value of
-Math.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 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 double rint |
(double a) |
Returns the
double value that is closest in value
to the argument and is equal to a mathematical integer. If two
double values that are mathematical integers are
equally close, the result is the integer value that is
even. Special cases:
- If the argument value is already equal to a mathematical
integer, then the result is the same as the argument.
- If the argument is NaN or an infinity or positive zero or negative
zero, then the result is the same as the argument.
Parameters:
a - a double value.
Returns:
the closest floating-point value to a that is
equal to a mathematical integer.
public static double atan2 |
(double y, double x) |
Returns the angle
theta from the conversion of rectangular
coordinates (
x,
y) to polar
coordinates (r,
theta).
This method computes the phase
theta by computing an arc tangent
of
y/x in the range of -
pi to
pi. Special
cases:
- If either argument is NaN, then the result is NaN.
- If the first argument is positive zero and the second argument
is positive, or the first argument is positive and finite and the
second argument is positive infinity, then the result is positive
zero.
- If the first argument is negative zero and the second argument
is positive, or the first argument is negative and finite and the
second argument is positive infinity, then the result is negative zero.
- If the first argument is positive zero and the second argument
is negative, or the first argument is positive and finite and the
second argument is negative infinity, then the result is the
double value closest to pi.
- If the first argument is negative zero and the second argument
is negative, or the first argument is negative and finite and the
second argument is negative infinity, then the result is the
double value closest to -pi.
- If the first argument is positive and the second argument is
positive zero or negative zero, or the first argument is positive
infinity and the second argument is finite, then the result is the
double value closest to pi/2.
- If the first argument is negative and the second argument is
positive zero or negative zero, or the first argument is negative
infinity and the second argument is finite, then the result is the
double value closest to -pi/2.
- If both arguments are positive infinity, then the result is the
double value closest to pi/4.
- If the first argument is positive infinity and the second argument
is negative infinity, then the result is the double
value closest to 3*pi/4.
- If the first argument is negative infinity and the second argument
is positive infinity, then the result is the double value
closest to -pi/4.
- If both arguments are negative infinity, then the result is the
double value closest to -3*pi/4.
The computed result must be within 2 ulps of the exact result.
Results must be semi-monotonic.
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 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,
then the result is positive 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,
then the result is positive zero.
- 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,
then the result is positive 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,
then the result is positive infinity.
- 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,
then the result is positive zero.
- 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,
then the result is negative zero.
- 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,
then the result is positive infinity.
- 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,
then the result is negative infinity.
- 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.)
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - the base.
b - the exponent.
Returns:
the value ab.
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 of Integer.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 of Integer.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 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 of Long.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 of Long.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 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
to 0.0 and less than 1.0.
See Also:
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:
Since:
1.8
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:
Since:
1.8
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:
Since:
1.8
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:
Since:
1.8
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:
Since:
1.8
public static long multiplyExact |
(long x, int 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:
Since:
9
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:
Since:
1.8
public static int incrementExact |
(int a) |
Returns the argument incremented by one, throwing an exception if the
result overflows an
int.
The overflow only occurs for
the maximum value.
Parameters:
a - the value to increment
Returns:
the result
Throws:
Since:
1.8
public static long incrementExact |
(long a) |
Returns the argument incremented by one, throwing an exception if the
result overflows a
long.
The overflow only occurs for
the maximum value.
Parameters:
a - the value to increment
Returns:
the result
Throws:
Since:
1.8
public static int decrementExact |
(int a) |
Returns the argument decremented by one, throwing an exception if the
result overflows an
int.
The overflow only occurs for
the minimum value.
Parameters:
a - the value to decrement
Returns:
the result
Throws:
Since:
1.8
public static long decrementExact |
(long a) |
Returns the argument decremented by one, throwing an exception if the
result overflows a
long.
The overflow only occurs for
the minimum value.
Parameters:
a - the value to decrement
Returns:
the result
Throws:
Since:
1.8
public static int negateExact |
(int a) |
Returns the negation of the argument, throwing an exception if the
result overflows an
int.
The overflow only occurs for
the minimum value.
Parameters:
a - the value to negate
Returns:
the result
Throws:
Since:
1.8
public static long negateExact |
(long a) |
Returns the negation of the argument, throwing an exception if the
result overflows a
long.
The overflow only occurs for
the minimum value.
Parameters:
a - the value to negate
Returns:
the result
Throws:
Since:
1.8
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:
Since:
1.8
public static long multiplyFull |
(int x, int y) |
Returns the exact mathematical product of the arguments.
Parameters:
x - the first value
y - the second value
Returns:
the result
Since:
9
public static long multiplyHigh |
(long x, long y) |
Returns as a
long the most significant 64 bits of the 128-bit
product of two 64-bit factors.
Parameters:
x - the first value
y - the second value
Returns:
the result
Since:
9
public static int floorDiv |
(int x, int y) |
Returns the largest (closest to positive infinity)
int value that is less than or equal to the algebraic quotient.
There is one special case, if the dividend is the
Integer.MIN_VALUE and the divisor is
-1,
then integer overflow occurs and
the result is equal to
Integer.MIN_VALUE.
Normal integer division operates under the round to zero rounding mode
(truncation). This operation instead acts under the round toward
negative infinity (floor) rounding mode.
The floor rounding mode gives different results from truncation
when the exact result is negative.
- If the signs of the arguments are the same, the results of
floorDiv and the / operator are the same.
For example, floorDiv(4, 3) == 1 and (4 / 3) == 1.
- If the signs of the arguments are different, the quotient is negative and
floorDiv returns the integer less than or equal to the quotient
and the / operator returns the integer closest to zero.
For example, floorDiv(-4, 3) == -2,
whereas (-4 / 3) == -1.
Parameters:
x - 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:
Since:
1.8
See Also:
public static long floorDiv |
(long x, int y) |
Returns the largest (closest to positive infinity)
long value that is less than or equal to the algebraic quotient.
There is one special case, if the dividend is the
Long.MIN_VALUE and the divisor is
-1,
then integer overflow occurs and
the result is equal to
Long.MIN_VALUE.
Normal integer division operates under the round to zero rounding mode
(truncation). This operation instead acts under the round toward
negative infinity (floor) rounding mode.
The floor rounding mode gives different results from truncation
when the exact result is negative.
For examples, see floorDiv(int, int).
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:
Since:
9
See Also:
public static long floorDiv |
(long x, long y) |
Returns the largest (closest to positive infinity)
long value that is less than or equal to the algebraic quotient.
There is one special case, if the dividend is the
Long.MIN_VALUE and the divisor is
-1,
then integer overflow occurs and
the result is equal to
Long.MIN_VALUE.
Normal integer division operates under the round to zero rounding mode
(truncation). This operation instead acts under the round toward
negative infinity (floor) rounding mode.
The floor rounding mode gives different results from truncation
when the exact result is negative.
For examples, see floorDiv(int, int).
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:
Since:
1.8
See Also:
public static int floorMod |
(int x, int y) |
Returns the floor modulus of the
int arguments.
The floor modulus is x - (floorDiv(x, y) * y),
has the same sign as the divisor y, and
is in the range of -abs(y) < r < +abs(y).
The relationship between floorDiv and floorMod is such that:
- floorDiv(x, y) * y + floorMod(x, y) == x
The difference in values between floorMod and
the % operator is due to the difference between
floorDiv that returns the integer less than or equal to the quotient
and the / operator that returns the integer closest to zero.
Examples:
- If the signs of the arguments are the same, the results
of floorMod and the % operator are the same.
- floorMod(+4, +3) == +1; and (+4 % +3) == +1
- floorMod(-4, -3) == -1; and (-4 % -3) == -1
- If the signs of the arguments are different, the results
differ from the % operator.
- floorMod(+4, -3) == -2; and (+4 % -3) == +1
- floorMod(-4, +3) == +2; and (-4 % +3) == -1
If the signs of arguments are unknown and a positive modulus
is needed it can be computed as (floorMod(x, y) + abs(y)) % abs(y).
Parameters:
x - the dividend
y - the divisor
Returns:
the floor modulus x - (floorDiv(x, y) * y)
Throws:
Since:
1.8
See Also:
public static int floorMod |
(long x, int y) |
Returns the floor modulus of the
long and
int arguments.
The floor modulus is x - (floorDiv(x, y) * y),
has the same sign as the divisor y, and
is in the range of -abs(y) < r < +abs(y).
The relationship between floorDiv and floorMod is such that:
- floorDiv(x, y) * y + floorMod(x, y) == x
For examples, see floorMod(int, int).
Parameters:
x - the dividend
y - the divisor
Returns:
the floor modulus x - (floorDiv(x, y) * y)
Throws:
Since:
9
See Also:
public static long floorMod |
(long x, long y) |
Returns the floor modulus of the
long arguments.
The floor modulus is x - (floorDiv(x, y) * y),
has the same sign as the divisor y, and
is in the range of -abs(y) < r < +abs(y).
The relationship between floorDiv and floorMod is such that:
- floorDiv(x, y) * y + floorMod(x, y) == x
For examples, see floorMod(int, int).
Parameters:
x - the dividend
y - the divisor
Returns:
the floor modulus x - (floorDiv(x, y) * y)
Throws:
Since:
1.8
See Also:
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. In
contrast, the absExact(int) method throws an
ArithmeticException for this value.
Parameters:
a - the argument whose absolute value is to be determined
Returns:
the absolute value of the argument.
See Also:
public static int absExact |
(int a) |
Returns the mathematical absolute value of an
int value
if it is exactly representable as an
int, throwing
ArithmeticException if the result overflows the
positive
int range.
Since the range of two's complement integers is asymmetric
with one additional negative value (JLS {@jls 4.2.1}), the
mathematical absolute value of Integer.MIN_VALUE
overflows the positive int range, so an exception is
thrown for that argument.
Parameters:
a - the argument whose absolute value is to be determined
Returns:
the absolute value of the argument, unless overflow occurs
Throws:
Since:
15
See Also:
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. In
contrast, the absExact(long) method throws an
ArithmeticException for this value.
Parameters:
a - the argument whose absolute value is to be determined
Returns:
the absolute value of the argument.
See Also:
public static long absExact |
(long a) |
Returns the mathematical absolute value of an
long value
if it is exactly representable as an
long, throwing
ArithmeticException if the result overflows the
positive
long range.
Since the range of two's complement integers is asymmetric
with one additional negative value (JLS {@jls 4.2.1}), the
mathematical absolute value of Long.MIN_VALUE overflows
the positive long range, so an exception is thrown for
that argument.
Parameters:
a - the argument whose absolute value is to be determined
Returns:
the absolute value of the argument, unless overflow occurs
Throws:
Since:
15
See Also:
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.
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.
Parameters:
a - the argument whose absolute value is to be determined
Returns:
the absolute value of the argument.
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 and b.
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 and b.
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 and b.
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 and b.
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 and b.
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 and b.
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 and b.
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 and b.
public static double fma |
(double a, double b, double c) |
Returns the fused multiply add of the three arguments; that is,
returns the exact product of the first two arguments summed
with the third argument and then rounded once to the nearest
double.
The rounding is done using the
round to nearest even
rounding mode.
In contrast, if
a * b + c is evaluated as a regular
floating-point expression, two rounding errors are involved,
the first for the multiply operation, the second for the
addition operation.
Special cases:
- If any argument is NaN, the result is NaN.
- If one of the first two arguments is infinite and the
other is zero, the result is NaN.
- If the exact product of the first two arguments is infinite
(in other words, at least one of the arguments is infinite and
the other is neither zero nor NaN) and the third argument is an
infinity of the opposite sign, the result is NaN.
Note that fma(a, 1.0, c) returns the same
result as (a + c). However,
fma(a, b, +0.0) does not always return the
same result as (a * b) since
fma(-0.0, +0.0, +0.0) is +0.0 while
(-0.0 * +0.0) is -0.0; fma(a, b, -0.0) is
equivalent to (a * b) however.
Parameters:
a - a value
b - a value
c - a value
Returns:
(a × b + c)
computed, as if with unlimited range and precision, and rounded
once to the nearest double value
Since:
9
public static float fma |
(float a, float b, float c) |
Returns the fused multiply add of the three arguments; that is,
returns the exact product of the first two arguments summed
with the third argument and then rounded once to the nearest
float.
The rounding is done using the
round to nearest even
rounding mode.
In contrast, if
a * b + c is evaluated as a regular
floating-point expression, two rounding errors are involved,
the first for the multiply operation, the second for the
addition operation.
Special cases:
- If any argument is NaN, the result is NaN.
- If one of the first two arguments is infinite and the
other is zero, the result is NaN.
- If the exact product of the first two arguments is infinite
(in other words, at least one of the arguments is infinite and
the other is neither zero nor NaN) and the third argument is an
infinity of the opposite sign, the result is NaN.
Note that fma(a, 1.0f, c) returns the same
result as (a + c). However,
fma(a, b, +0.0f) does not always return the
same result as (a * b) since
fma(-0.0f, +0.0f, +0.0f) is +0.0f while
(-0.0f * +0.0f) is -0.0f; fma(a, b, -0.0f) is
equivalent to (a * b) however.
Parameters:
a - a value
b - a value
c - a value
Returns:
(a × b + c)
computed, as if with unlimited range and precision, and rounded
once to the nearest float value
Since:
9
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
Since:
1.5
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
Since:
1.5
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
Since:
1.5
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
Since:
1.5
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
Euler's number.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is an infinity
with the same sign as the argument.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 2.5 ulps of the exact result.
Parameters:
x - The number whose hyperbolic sine is to be returned.
Returns:
The hyperbolic sine of x.
Since:
1.5
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
Euler's number.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is positive
infinity.
- If the argument is zero, then the result is 1.0.
The computed result must be within 2.5 ulps of the exact result.
Parameters:
x - The number whose hyperbolic cosine is to be returned.
Returns:
The hyperbolic cosine of x.
Since:
1.5
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,
sinh(x)/
cosh(x). Note
that the absolute value of the exact tanh is always less than
1.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
- If the argument is positive infinity, then the result is
+1.0.
- If the argument is negative infinity, then the result is
-1.0.
The computed result must be within 2.5 ulps of the exact result.
The result of tanh for any finite input must have
an absolute value less than or equal to 1. Note that once the
exact result of tanh is within 1/2 of an ulp of the limit value
of ±1, correctly signed ±1.0 should
be returned.
Parameters:
x - The number whose hyperbolic tangent is to be returned.
Returns:
The hyperbolic tangent of x.
Since:
1.5
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.
- If both arguments are zero, the result is positive zero.
The computed result must be within 1 ulp of the exact
result. If one parameter is held constant, the results must be
semi-monotonic in the other parameter.
Parameters:
Returns:
sqrt(x2 +y2)
without intermediate overflow or underflow
Since:
1.5
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.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic. The result of
expm1 for any finite input must be greater than or
equal to -1.0. Note that once the exact result of
ex - 1 is within 1/2
ulp of the limit value -1, -1.0 should be
returned.
Parameters:
x - the exponent to raise e to in the computation of
ex -1.
Returns:
the value ex - 1.
Since:
1.5
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.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
x - a value
Returns:
the value ln(x + 1), the natural
log of x + 1
Since:
1.5
public static double copySign |
(double magnitude, double sign) |
Returns the first floating-point argument with the sign of the
second floating-point argument. Note that unlike the
StrictMath.copySign
method, this method does not require NaN
sign
arguments to be treated as positive values; implementations are
permitted to treat some NaN arguments as positive and other NaN
arguments as negative to allow greater performance.
Parameters:
magnitude - 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 of sign.
Since:
1.6
public static float copySign |
(float magnitude, float sign) |
Returns the first floating-point argument with the sign of the
second floating-point argument. Note that unlike the
StrictMath.copySign
method, this method does not require NaN
sign
arguments to be treated as positive values; implementations are
permitted to treat some NaN arguments as positive and other NaN
arguments as negative to allow greater performance.
Parameters:
magnitude - 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 of sign.
Since:
1.6
public static int getExponent |
(float f) |
Returns the unbiased exponent used in the representation of a
float. Special cases:
Parameters:
f - a float value
Returns:
the unbiased exponent of the argument
Since:
1.6
public static int getExponent |
(double d) |
Returns the unbiased exponent used in the representation of a
double. Special cases:
Parameters:
d - a double value
Returns:
the unbiased exponent of the argument
Since:
1.6
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 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.
- If start is infinite and
direction has a value such that the result should
have a smaller magnitude, Double.MAX_VALUE with the
same sign as start is returned.
- If start is equal to ±
Double.MAX_VALUE and direction has a
value such that the result should have a larger magnitude, an
infinity with same sign as start is returned.
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 of direction.
Since:
1.6
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 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.
- If start is infinite and
direction has a value such that the result should
have a smaller magnitude, Float.MAX_VALUE with the
same sign as start is returned.
- If start is equal to ±
Float.MAX_VALUE and direction has a
value such that the result should have a larger magnitude, an
infinity with same sign as start is returned.
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 of direction.
Since:
1.6
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.
Since:
1.6
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.
Since:
1.6
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.
Since:
1.8
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.
Since:
1.8
public static double scalb |
(double d, int scaleFactor) |
Returns
d × 2
scaleFactor
rounded as if performed by a single correctly rounded
floating-point multiply. 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
Since:
1.6
public static float scalb |
(float f, int scaleFactor) |
Returns
f × 2
scaleFactor
rounded as if performed by a single correctly rounded
floating-point multiply. 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
Since:
1.6
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