public final class Math extends Object
Math
contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.
Unlike some of the numeric methods of class StrictMath
, all implementations of the equivalent functions of class Math
are not defined to return the 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
, 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.
Modifier and Type | Field and Description |
---|---|
static double |
E
The
double value that is closer than any other to
e, the base of the natural logarithms.
|
static double |
PI
The
double value that is closer than any other to
pi, the ratio of the circumference of a circle to its diameter.
|
Modifier and Type | Method and Description |
---|---|
static double |
abs(double a)
Returns the absolute value of a
double value.
|
static float |
abs(float a)
Returns the absolute value of a
float value.
|
static int |
abs(int a)
Returns the absolute value of an
int value.
|
static long |
abs(long a)
Returns the absolute value of a
long value.
|
static double |
acos(double a)
Returns the arc cosine of a value; the returned angle is in the range 0.0 through
pi.
|
static int |
addExact(int x, int y)
Returns the sum of its arguments, throwing an exception if the result overflows an
int .
|
static long |
addExact(long x, long y)
Returns the sum of its arguments, throwing an exception if the result overflows a
long .
|
static double |
asin(double a)
Returns the arc sine of a value; the returned angle is in the range -
pi/2 through
pi/2.
|
static double |
atan(double a)
Returns the arc tangent of a value; the returned angle is in the range -
pi/2 through
pi/2.
|
static double |
atan2(double y, double x)
Returns the angle
theta from the conversion of rectangular coordinates (
x ,
y ) to polar coordinates (r,
theta).
|
static double |
cbrt(double a)
Returns the cube root of a
double value.
|
static double |
ceil(double a)
Returns the smallest (closest to negative infinity)
double value that is greater than or equal to the argument and is equal to a mathematical integer.
|
static double |
copySign(double magnitude, double sign)
Returns the first floating-point argument with the sign of the second floating-point argument.
|
static float |
copySign(float magnitude, float 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 int |
decrementExact(int a)
Returns the argument decremented by one, throwing an exception if the result overflows an
int .
|
static long |
decrementExact(long a)
Returns the argument decremented by one, throwing an exception if the result overflows a
long .
|
static double |
exp(double a)
Returns Euler's number
e raised to the power of a
double value.
|
static double |
expm1(double x)
Returns
e
x -1.
|
static double |
floor(double a)
Returns the largest (closest to positive infinity)
double value that is less than or equal to the argument and is equal to a mathematical integer.
|
static int |
floorDiv(int x, int y)
Returns the largest (closest to positive infinity)
int value that is less than or equal to the algebraic quotient.
|
static long |
floorDiv(long x, long y)
Returns the largest (closest to positive infinity)
long value that is less than or equal to the algebraic quotient.
|
static int |
floorMod(int x, int y)
Returns the floor modulus of the
int arguments.
|
static long |
floorMod(long x, long y)
Returns the floor modulus of the
long 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(
x
2 +
y
2) without intermediate overflow or underflow.
|
static double |
IEEEremainder(double f1, double f2)
Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard.
|
static int |
incrementExact(int a)
Returns the argument incremented by one, throwing an exception if the result overflows an
int .
|
static long |
incrementExact(long a)
Returns the argument incremented by one, throwing an exception if the result overflows a
long .
|
static double |
log(double a)
Returns the natural logarithm (base
e) of a
double value.
|
static double |
log10(double a)
Returns the base 10 logarithm of a
double value.
|
static double |
log1p(double x)
Returns the natural logarithm of the sum of the argument and 1.
|
static double |
max(double a, double b)
Returns the greater of two
double values.
|
static float |
max(float a, float b)
Returns the greater of two
float values.
|
static int |
max(int a, int b)
Returns the greater of two
int values.
|
static long |
max(long a, long b)
Returns the greater of two
long values.
|
static double |
min(double a, double b)
Returns the smaller of two
double values.
|
static float |
min(float a, float b)
Returns the smaller of two
float values.
|
static int |
min(int a, int b)
Returns the smaller of two
int values.
|
static long |
min(long a, long b)
Returns the smaller of two
long values.
|
static int |
multiplyExact(int x, int y)
Returns the product of the arguments, throwing an exception if the result overflows an
int .
|
static long |
multiplyExact(long x, long y)
Returns the product of the arguments, throwing an exception if the result overflows a
long .
|
static int |
negateExact(int a)
Returns the negation of the argument, throwing an exception if the result overflows an
int .
|
static long |
negateExact(long a)
Returns the negation of the argument, throwing an exception if the result overflows a
long .
|
static double |
nextAfter(double start, double direction)
Returns the 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 double |
nextUp(double d)
Returns the floating-point value adjacent to
d in the direction of positive infinity.
|
static float |
nextUp(float f)
Returns the floating-point value adjacent to
f in the direction of positive infinity.
|
static double |
pow(double a, double b)
Returns the value of the first argument raised to the power of the second argument.
|
static double |
random()
Returns a
double value with a positive sign, greater than or equal to
0.0 and less than
1.0 .
|
static double |
rint(double a)
Returns the
double value that is closest in value to the argument and is equal to a mathematical integer.
|
static long |
round(double a)
Returns the closest
long to the argument, with ties rounding to positive infinity.
|
static int |
round(float a)
Returns the closest
int to the argument, with ties rounding to positive infinity.
|
static double |
scalb(double d, int scaleFactor)
Returns
d × 2
scaleFactor rounded as if performed by a single correctly rounded floating-point multiply to a member of the double value set.
|
static float |
scalb(float f, int scaleFactor)
Returns
f × 2
scaleFactor rounded as if performed by a single correctly rounded floating-point multiply to a member of the float value set.
|
static double |
signum(double d)
Returns the signum function of the argument; zero if the argument is zero, 1.0 if the argument is greater than zero, -1.0 if the argument is less than zero.
|
static float |
signum(float f)
Returns the signum function of the argument; zero if the argument is zero, 1.0f if the argument is greater than zero, -1.0f if the argument is less than zero.
|
static double |
sin(double a)
Returns the trigonometric sine of an angle.
|
static double |
sinh(double x)
Returns the hyperbolic sine of a
double value.
|
static double |
sqrt(double a)
Returns the correctly rounded positive square root of a
double value.
|
static int |
subtractExact(int x, int y)
Returns the difference of the arguments, throwing an exception if the result overflows an
int .
|
static long |
subtractExact(long x, long y)
Returns the difference of the arguments, throwing an exception if the result overflows a
long .
|
static double |
tan(double a)
Returns the trigonometric tangent of an angle.
|
static double |
tanh(double x)
Returns the hyperbolic tangent of a
double value.
|
static double |
toDegrees(double angrad)
Converts an angle measured in radians to an approximately equivalent angle measured in degrees.
|
static int |
toIntExact(long value)
Returns the value of the
long argument; throwing an exception if the value overflows an
int .
|
static double |
toRadians(double angdeg)
Converts an angle measured in degrees to an approximately equivalent angle measured in radians.
|
static double |
ulp(double d)
Returns the size of an ulp of the argument.
|
static float |
ulp(float f)
Returns the size of an ulp of the argument.
|
public static final double E
double
value that is closer than any other to
e, the base of the natural logarithms.
public static final double PI
double
value that is closer than any other to
pi, the ratio of the circumference of a circle to its diameter.
public static double sin(double a)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a
- an angle, in radians.
public static double cos(double a)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a
- an angle, in radians.
public static double tan(double a)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a
- an angle, in radians.
public static double asin(double a)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a
- the value whose arc sine is to be returned.
public static double acos(double a)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a
- the value whose arc cosine is to be returned.
public static double atan(double a)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a
- the value whose arc tangent is to be returned.
public static double toRadians(double angdeg)
angdeg
- an angle, in degrees
angdeg
in radians.
public static double toDegrees(double angrad)
cos(toRadians(90.0))
to exactly equal
0.0
.
angrad
- an angle, in radians
angrad
in degrees.
public static double exp(double a)
double
value. Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a
- the exponent to raise
e to.
a
, where
e is the base of the natural logarithms.
public static double log(double a)
double
value. Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a
- a value
a
, the natural logarithm of
a
.
public static double log10(double a)
double
value. Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a
- a value
a
.
public static double sqrt(double a)
double
value. Special cases:
double
value closest to the true mathematical square root of the argument value.
a
- a value.
a
. If the argument is NaN or less than zero, the result is NaN.
public static double cbrt(double a)
double
value. For positive finite
x
,
cbrt(-x) == -cbrt(x)
; that is, the cube root of a negative value is the negative of the cube root of that value's magnitude. Special cases:
The computed result must be within 1 ulp of the exact result.
a
- a value.
a
.
public static double IEEEremainder(double f1, double f2)
f1 - f2
×
n, where
n is the mathematical integer closest to the exact mathematical value of the quotient
f1/f2
, and if two mathematical integers are equally close to
f1/f2
, then
n is the integer that is even. If the remainder is zero, its sign is the same as the sign of the first argument. Special cases:
f1
- the dividend.
f2
- the divisor.
f1
is divided by
f2
.
public static double ceil(double a)
double
value that is greater than or equal to the argument and is equal to a mathematical integer. Special cases:
Math.ceil(x)
is exactly the value of
-Math.floor(-x)
.
a
- a value.
public static double floor(double a)
double
value that is less than or equal to the argument and is equal to a mathematical integer. Special cases:
a
- a value.
public static double rint(double a)
double
value that is closest in value to the argument and is equal to a mathematical integer. If two
double
values that are mathematical integers are equally close, the result is the integer value that is even. Special cases:
a
- a
double
value.
a
that is equal to a mathematical integer.
public static double atan2(double y, double x)
x
,
y
) to polar coordinates (r,
theta). This method computes the phase
theta by computing an arc tangent of
y/x
in the range of -
pi to
pi. Special cases:
double
value closest to pi. double
value closest to -pi. double
value closest to pi/2. double
value closest to -pi/2. double
value closest to pi/4. double
value closest to 3*pi/4. double
value closest to -pi/4. double
value closest to -3*pi/4.The computed result must be within 2 ulps of the exact result. Results must be semi-monotonic.
y
- the ordinate coordinate
x
- the abscissa coordinate
public static double pow(double a, double b)
double
value.(In the foregoing descriptions, a floating-point value is considered to be an integer if and only if it is finite and a fixed point of the method ceil
or, equivalently, a fixed point of the method floor
. A value is a fixed point of a one-argument method if and only if the result of applying the method to the value is equal to the value.)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a
- the base.
b
- the exponent.
a
b
.
public static int round(float a)
int
to the argument, with ties rounding to positive infinity.
Special cases:
Integer.MIN_VALUE
, the result is equal to the value of Integer.MIN_VALUE
. Integer.MAX_VALUE
, the result is equal to the value of Integer.MAX_VALUE
.a
- a floating-point value to be rounded to an integer.
int
value.
Integer.MAX_VALUE
,
Integer.MIN_VALUE
public static long round(double a)
long
to the argument, with ties rounding to positive infinity.
Special cases:
Long.MIN_VALUE
, the result is equal to the value of Long.MIN_VALUE
. Long.MAX_VALUE
, the result is equal to the value of Long.MAX_VALUE
.a
- a floating-point value to be rounded to a
long
.
long
value.
Long.MAX_VALUE
,
Long.MIN_VALUE
public static double random()
double
value with a positive sign, greater than or equal to
0.0
and less than
1.0
. Returned values are chosen pseudorandomly with (approximately) uniform distribution from that range.
When this method is first called, it creates a single new pseudorandom-number generator, exactly as if by the expression
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.
double
greater than or equal to
0.0
and less than
1.0
.
Random.nextDouble()
public static int addExact(int x, int y)
int
.
x
- the first value
y
- the second value
ArithmeticException
- if the result overflows an int
public static long addExact(long x, long y)
long
.
x
- the first value
y
- the second value
ArithmeticException
- if the result overflows a long
public static int subtractExact(int x, int y)
int
.
x
- the first value
y
- the second value to subtract from the first
ArithmeticException
- if the result overflows an int
public static long subtractExact(long x, long y)
long
.
x
- the first value
y
- the second value to subtract from the first
ArithmeticException
- if the result overflows a long
public static int multiplyExact(int x, int y)
int
.
x
- the first value
y
- the second value
ArithmeticException
- if the result overflows an int
public static long multiplyExact(long x, long y)
long
.
x
- the first value
y
- the second value
ArithmeticException
- if the result overflows a long
public static int incrementExact(int a)
int
.
a
- the value to increment
ArithmeticException
- if the result overflows an int
public static long incrementExact(long a)
long
.
a
- the value to increment
ArithmeticException
- if the result overflows a long
public static int decrementExact(int a)
int
.
a
- the value to decrement
ArithmeticException
- if the result overflows an int
public static long decrementExact(long a)
long
.
a
- the value to decrement
ArithmeticException
- if the result overflows a long
public static int negateExact(int a)
int
.
a
- the value to negate
ArithmeticException
- if the result overflows an int
public static long negateExact(long a)
long
.
a
- the value to negate
ArithmeticException
- if the result overflows a long
public static int toIntExact(long value)
long
argument; throwing an exception if the value overflows an
int
.
value
- the long value
ArithmeticException
- if the
argument
overflows an int
public static int floorDiv(int x, int y)
int
value that is less than or equal to the algebraic quotient. There is one special case, if the dividend is the
Integer.MIN_VALUE and the divisor is
-1
, then integer overflow occurs and the result is equal to the
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 than truncation when the exact result is negative.
floorDiv
and the /
operator are the same. floorDiv(4, 3) == 1
and (4 / 3) == 1
.floorDiv
returns the integer less than or equal to the quotient and the /
operator returns the integer closest to zero.floorDiv(-4, 3) == -2
, whereas (-4 / 3) == -1
. x
- the dividend
y
- the divisor
int
value that is less than or equal to the algebraic quotient.
ArithmeticException
- if the divisor
y
is zero
floorMod(int, int)
,
floor(double)
public static long floorDiv(long x, long y)
long
value that is less than or equal to the algebraic quotient. There is one special case, if the dividend is the
Long.MIN_VALUE and the divisor is
-1
, then integer overflow occurs and the result is equal to the
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 than truncation when the exact result is negative.
For examples, see floorDiv(int, int)
.
x
- the dividend
y
- the divisor
long
value that is less than or equal to the algebraic quotient.
ArithmeticException
- if the divisor
y
is zero
floorMod(long, long)
,
floor(double)
public static int floorMod(int x, int y)
int
arguments.
The floor modulus is x - (floorDiv(x, y) * y)
, has the same sign as the divisor y
, and is in the range of -abs(y) < r < +abs(y)
.
The relationship between floorDiv
and floorMod
is such that:
floorDiv(x, y) * y + floorMod(x, y) == x
The difference in values between floorMod
and the %
operator is due to the difference between floorDiv
that returns the integer less than or equal to the quotient and the /
operator that returns the integer closest to zero.
Examples:
floorMod
and the %
operator are the same. floorMod(4, 3) == 1
; and (4 % 3) == 1
%
operator.floorMod(+4, -3) == -2
; and (+4 % -3) == +1
floorMod(-4, +3) == +2
; and (-4 % +3) == -1
floorMod(-4, -3) == -1
; and (-4 % -3) == -1
If the signs of arguments are unknown and a positive modulus is needed it can be computed as (floorMod(x, y) + abs(y)) % abs(y)
.
x
- the dividend
y
- the divisor
x - (floorDiv(x, y) * y)
ArithmeticException
- if the divisor
y
is zero
floorDiv(int, int)
public static long floorMod(long x, long y)
long
arguments.
The floor modulus is x - (floorDiv(x, y) * y)
, has the same sign as the divisor y
, and is in the range of -abs(y) < r < +abs(y)
.
The relationship between floorDiv
and floorMod
is such that:
floorDiv(x, y) * y + floorMod(x, y) == x
For examples, see floorMod(int, int)
.
x
- the dividend
y
- the divisor
x - (floorDiv(x, y) * y)
ArithmeticException
- if the divisor
y
is zero
floorDiv(long, long)
public static int abs(int a)
int
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.
Note that if the argument is equal to the value of Integer
, the most negative representable int
value, the result is that same value, which is negative.
a
- the argument whose absolute value is to be determined
public static long abs(long a)
long
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.
Note that if the argument is equal to the value of Long
, the most negative representable long
value, the result is that same value, which is negative.
a
- the argument whose absolute value is to be determined
public static float abs(float a)
float
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:
Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))
a
- the argument whose absolute value is to be determined
public static double abs(double a)
double
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:
Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)
a
- the argument whose absolute value is to be determined
public static int max(int a, int b)
int
values. That is, the result is the argument closer to the value of
Integer.MAX_VALUE
. If the arguments have the same value, the result is that same value.
a
- an argument.
b
- another argument.
a
and
b
.
public static long max(long a, long b)
long
values. That is, the result is the argument closer to the value of
Long.MAX_VALUE
. If the arguments have the same value, the result is that same value.
a
- an argument.
b
- another argument.
a
and
b
.
public static float max(float a, float b)
float
values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero.
a
- an argument.
b
- another argument.
a
and
b
.
public static double max(double a, double b)
double
values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero.
a
- an argument.
b
- another argument.
a
and
b
.
public static int min(int a, int b)
int
values. That is, the result the argument closer to the value of
Integer.MIN_VALUE
. If the arguments have the same value, the result is that same value.
a
- an argument.
b
- another argument.
a
and
b
.
public static long min(long a, long b)
long
values. That is, the result is the argument closer to the value of
Long.MIN_VALUE
. If the arguments have the same value, the result is that same value.
a
- an argument.
b
- another argument.
a
and
b
.
public static float min(float a, float b)
float
values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero.
a
- an argument.
b
- another argument.
a
and
b
.
public static double min(double a, double b)
double
values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero.
a
- an argument.
b
- another argument.
a
and
b
.
public static double ulp(double d)
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:
Double.MIN_VALUE
. Double.MAX_VALUE
, then the result is equal to 2971. d
- the floating-point value whose ulp is to be returned
public static float ulp(float f)
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:
Float.MIN_VALUE
. Float.MAX_VALUE
, then the result is equal to 2104. f
- the floating-point value whose ulp is to be returned
public static double signum(double d)
Special Cases:
d
- the floating-point value whose signum is to be returned
public static float signum(float f)
Special Cases:
f
- the floating-point value whose signum is to be returned
public static double sinh(double x)
double
value. The hyperbolic sine of
x is defined to be (
ex - e-x)/2 where
e is
Euler's number.
Special cases:
The computed result must be within 2.5 ulps of the exact result.
x
- The number whose hyperbolic sine is to be returned.
x
.
public static double cosh(double x)
double
value. The hyperbolic cosine of
x is defined to be (
ex + e-x)/2 where
e is
Euler's number.
Special cases:
1.0
. The computed result must be within 2.5 ulps of the exact result.
x
- The number whose hyperbolic cosine is to be returned.
x
.
public static double tanh(double x)
double
value. The hyperbolic tangent of
x is defined to be (
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:
+1.0
. -1.0
. The computed result must be within 2.5 ulps of the exact result. The result of tanh
for any finite input must have an absolute value less than or equal to 1. Note that once the exact result of tanh is within 1/2 of an ulp of the limit value of ±1, correctly signed ±1.0
should be returned.
x
- The number whose hyperbolic tangent is to be returned.
x
.
public static double hypot(double x, double y)
Special cases:
The computed result must be within 1 ulp of the exact result. If one parameter is held constant, the results must be semi-monotonic in the other parameter.
x
- a value
y
- a value
public static double expm1(double x)
expm1(x)
+ 1 is much closer to the true result of
e
x than
exp(x)
.
Special cases:
The computed result must be within 1 ulp of the exact result. Results must be 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.
x
- the exponent to raise
e to in the computation of
e
x
-1.
x
- 1.
public static double log1p(double x)
x
, the result of
log1p(x)
is much closer to the true result of ln(1 +
x
) than the floating-point evaluation of
log(1.0+x)
.
Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
x
- a value
x
+ 1), the natural log of
x
+ 1
public static double copySign(double magnitude, double sign)
StrictMath.copySign
method, this method does not require NaN
sign
arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.
magnitude
- the parameter providing the magnitude of the result
sign
- the parameter providing the sign of the result
magnitude
and the sign of
sign
.
public static float copySign(float magnitude, float sign)
StrictMath.copySign
method, this method does not require NaN
sign
arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.
magnitude
- the parameter providing the magnitude of the result
sign
- the parameter providing the sign of the result
magnitude
and the sign of
sign
.
public static int getExponent(float f)
float
. Special cases:
Float.MAX_EXPONENT
+ 1. Float.MIN_EXPONENT
-1. f
- a
float
value
public static int getExponent(double d)
double
. Special cases:
Double.MAX_EXPONENT
+ 1. Double.MIN_EXPONENT
-1. d
- a
double
value
public static double nextAfter(double start, double direction)
Special cases:
direction
is returned unchanged (as implied by the requirement of returning the second argument if the arguments compare as equal). start
is ±Double.MIN_VALUE
and direction
has a value such that the result should have a smaller magnitude, then a zero with the same sign as start
is returned. start
is infinite and direction
has a value such that the result should have a smaller magnitude, Double.MAX_VALUE
with the same sign as start
is returned. start
is equal to ± Double.MAX_VALUE
and direction
has a value such that the result should have a larger magnitude, an infinity with same sign as start
is returned. start
- starting floating-point value
direction
- value indicating which of
start
's neighbors or
start
should be returned
start
in the direction of
direction
.
public static float nextAfter(float start, double direction)
Special cases:
direction
is returned. start
is ±Float.MIN_VALUE
and direction
has a value such that the result should have a smaller magnitude, then a zero with the same sign as start
is returned. start
is infinite and direction
has a value such that the result should have a smaller magnitude, Float.MAX_VALUE
with the same sign as start
is returned. start
is equal to ± Float.MAX_VALUE
and direction
has a value such that the result should have a larger magnitude, an infinity with same sign as start
is returned. start
- starting floating-point value
direction
- value indicating which of
start
's neighbors or
start
should be returned
start
in the direction of
direction
.
public static double nextUp(double d)
d
in the direction of positive infinity. This method is semantically equivalent to
nextAfter(d, Double.POSITIVE_INFINITY)
; however, a
nextUp
implementation may run faster than its equivalent
nextAfter
call.
Special Cases:
Double.MIN_VALUE
d
- starting floating-point value
public static float nextUp(float f)
f
in the direction of positive infinity. This method is semantically equivalent to
nextAfter(f, Float.POSITIVE_INFINITY)
; however, a
nextUp
implementation may run faster than its equivalent
nextAfter
call.
Special Cases:
Float.MIN_VALUE
f
- starting floating-point value
public static double nextDown(double d)
d
in the direction of negative infinity. This method is semantically equivalent to
nextAfter(d, Double.NEGATIVE_INFINITY)
; however, a
nextDown
implementation may run faster than its equivalent
nextAfter
call.
Special Cases:
-Double.MIN_VALUE
d
- starting floating-point value
public static float nextDown(float f)
f
in the direction of negative infinity. This method is semantically equivalent to
nextAfter(f, Float.NEGATIVE_INFINITY)
; however, a
nextDown
implementation may run faster than its equivalent
nextAfter
call.
Special Cases:
-Float.MIN_VALUE
f
- starting floating-point value
public static double scalb(double d, int scaleFactor)
d
× 2
scaleFactor
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:
d
- number to be scaled by a power of two.
scaleFactor
- power of 2 used to scale
d
d
× 2
scaleFactor
public static float scalb(float f, int scaleFactor)
f
× 2
scaleFactor
rounded as if performed by a single correctly rounded 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:
f
- number to be scaled by a power of two.
scaleFactor
- power of 2 used to scale
f
f
× 2
scaleFactor