public final class StrictMath extends Object
StrictMath
contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions. To help ensure portability of Java programs, the definitions of some of the numeric functions in this package require that they produce the same results as certain published algorithms. These algorithms are available from the well-known network library netlib
as the package "Freely Distributable Math Library," fdlibm
. These algorithms, which are written in the C programming language, are then to be understood to be transliterated into Java and executed with all floating-point and integer operations following the rules of Java arithmetic. The following transformations are used in the transliteration:
double
in C is expressed using Java platform methods that perform bit-wise conversions from double
to
long
and long
to double
. int
values in C are mapped to signed
int
values in Java with updates to operations to replicate unsigned semantics where the results on the same textual operation would differ. For example, >>
shifts on unsigned C values are replaced with >>>
shifts on signed Java values. Sized comparisons on unsigned C values (<
, <=
, >
, >=
) are replaced with semantically equivalent calls to compareUnsigned
. The Java math library is defined with respect to fdlibm
version 5.3. Where fdlibm
provides more than one definition for a function (such as acos
), use the "IEEE 754 core function" version (residing in a file whose name begins with the letter e
). The methods which require fdlibm
semantics are sin
, cos
, tan
, asin
, acos
, atan
, exp
, log
, log10
, cbrt
, atan2
, pow
, sinh
, cosh
, tanh
, hypot
, expm1
, and log1p
.
The platform uses signed two's complement integer arithmetic with int and long primitive types. The developer should choose the primitive type to ensure that arithmetic operations consistently produce correct results, which in some cases means the operations will not overflow the range of values of the computation. The best practice is to choose the primitive type and algorithm to avoid overflow. In cases where the size is int
or long
and overflow errors need to be detected, the methods whose names end with Exact
throw an ArithmeticException
when the results overflow.
Math
class discusses how the shared quality of implementation criteria for selected Math
and StrictMath
methods relate to the IEEE 754 recommended operations.Modifier and Type | Field | Description |
---|---|---|
static final double |
E |
The double value that is closer than any other to e, the base of the natural logarithms. |
static final double |
PI |
The double value that is closer than any other to pi (π), the ratio of the circumference of a circle to its diameter. |
static final double |
TAU |
The double value that is closer than any other to tau (τ), the ratio of the circumference of a circle to its radius. |
Modifier and Type | Method | Description |
---|---|---|
static double |
abs |
Returns the absolute value of a double value. |
static float |
abs |
Returns the absolute value of a float value. |
static int |
abs |
Returns the absolute value of an int value. |
static long |
abs |
Returns the absolute value of a long value. |
static int |
absExact |
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. |
static long |
absExact |
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. |
static double |
acos |
Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi. |
static int |
addExact |
Returns the sum of its arguments, throwing an exception if the result overflows an int . |
static long |
addExact |
Returns the sum of its arguments, throwing an exception if the result overflows a long . |
static double |
asin |
Returns the arc sine of a value; the returned angle is in the range -pi/2 through pi/2. |
static double |
atan |
Returns the arc tangent of a value; the returned angle is in the range -pi/2 through pi/2. |
static double |
atan2 |
Returns the angle theta from the conversion of rectangular coordinates ( x , y ) to polar coordinates (r, theta). |
static double |
cbrt |
Returns the cube root of a double value. |
static double |
ceil |
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 int |
ceilDiv |
Returns the smallest (closest to negative infinity) int value that is greater than or equal to the algebraic quotient. |
static long |
ceilDiv |
Returns the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient. |
static long |
ceilDiv |
Returns the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient. |
static int |
ceilDivExact |
Returns the smallest (closest to negative infinity) int value that is greater than or equal to the algebraic quotient. |
static long |
ceilDivExact |
Returns the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient. |
static int |
ceilMod |
Returns the ceiling modulus of the int arguments. |
static int |
ceilMod |
Returns the ceiling modulus of the long and int arguments. |
static long |
ceilMod |
Returns the ceiling modulus of the long arguments. |
static double |
clamp |
Clamps the value to fit between min and max. |
static float |
clamp |
Clamps the value to fit between min and max. |
static int |
clamp |
Clamps the value to fit between min and max. |
static long |
clamp |
Clamps the value to fit between min and max. |
static double |
copySign |
Returns the first floating-point argument with the sign of the second floating-point argument. |
static float |
copySign |
Returns the first floating-point argument with the sign of the second floating-point argument. |
static double |
cos |
Returns the trigonometric cosine of an angle. |
static double |
cosh |
Returns the hyperbolic cosine of a double value. |
static int |
decrementExact |
Returns the argument decremented by one, throwing an exception if the result overflows an int . |
static long |
decrementExact |
Returns the argument decremented by one, throwing an exception if the result overflows a long . |
static int |
divideExact |
Returns the quotient of the arguments, throwing an exception if the result overflows an int . |
static long |
divideExact |
Returns the quotient of the arguments, throwing an exception if the result overflows a long . |
static double |
exp |
Returns Euler's number e raised to the power of a double value. |
static double |
expm1 |
Returns ex -1. |
static double |
floor |
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 |
Returns the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient. |
static long |
floorDiv |
Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. |
static long |
floorDiv |
Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. |
static int |
floorDivExact |
Returns the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient. |
static long |
floorDivExact |
Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. |
static int |
floorMod |
Returns the floor modulus of the int arguments. |
static int |
floorMod |
Returns the floor modulus of the long and int arguments. |
static long |
floorMod |
Returns the floor modulus of the long arguments. |
static double |
fma |
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 . |
static float |
fma |
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 . |
static int |
getExponent |
Returns the unbiased exponent used in the representation of a double . |
static int |
getExponent |
Returns the unbiased exponent used in the representation of a float . |
static double |
hypot |
Returns sqrt(x2 +y2) without intermediate overflow or underflow. |
static double |
IEEEremainder |
Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. |
static int |
incrementExact |
Returns the argument incremented by one, throwing an exception if the result overflows an int . |
static long |
incrementExact |
Returns the argument incremented by one, throwing an exception if the result overflows a long . |
static double |
log |
Returns the natural logarithm (base e) of a double value. |
static double |
log10 |
Returns the base 10 logarithm of a double value. |
static double |
log1p |
Returns the natural logarithm of the sum of the argument and 1. |
static double |
max |
Returns the greater of two double values. |
static float |
max |
Returns the greater of two float values. |
static int |
max |
Returns the greater of two int values. |
static long |
max |
Returns the greater of two long values. |
static double |
min |
Returns the smaller of two double values. |
static float |
min |
Returns the smaller of two float values. |
static int |
min |
Returns the smaller of two int values. |
static long |
min |
Returns the smaller of two long values. |
static int |
multiplyExact |
Returns the product of the arguments, throwing an exception if the result overflows an int . |
static long |
multiplyExact |
Returns the product of the arguments, throwing an exception if the result overflows a long . |
static long |
multiplyExact |
Returns the product of the arguments, throwing an exception if the result overflows a long . |
static long |
multiplyFull |
Returns the exact mathematical product of the arguments. |
static long |
multiplyHigh |
Returns as a long the most significant 64 bits of the 128-bit product of two 64-bit factors. |
static int |
negateExact |
Returns the negation of the argument, throwing an exception if the result overflows an int . |
static long |
negateExact |
Returns the negation of the argument, throwing an exception if the result overflows a long . |
static double |
nextAfter |
Returns the floating-point number adjacent to the first argument in the direction of the second argument. |
static float |
nextAfter |
Returns the floating-point number adjacent to the first argument in the direction of the second argument. |
static double |
nextDown |
Returns the floating-point value adjacent to d in the direction of negative infinity. |
static float |
nextDown |
Returns the floating-point value adjacent to f in the direction of negative infinity. |
static double |
nextUp |
Returns the floating-point value adjacent to d in the direction of positive infinity. |
static float |
nextUp |
Returns the floating-point value adjacent to f in the direction of positive infinity. |
static double |
pow |
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 |
Returns the double value that is closest in value to the argument and is equal to a mathematical integer. |
static long |
round |
Returns the closest long to the argument, with ties rounding to positive infinity. |
static int |
round |
Returns the closest int to the argument, with ties rounding to positive infinity. |
static double |
scalb |
Returns d × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply. |
static float |
scalb |
Returns f × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply. |
static double |
signum |
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 |
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 |
Returns the trigonometric sine of an angle. |
static double |
sinh |
Returns the hyperbolic sine of a double value. |
static double |
sqrt |
Returns the correctly rounded positive square root of a double value. |
static int |
subtractExact |
Returns the difference of the arguments, throwing an exception if the result overflows an int . |
static long |
subtractExact |
Returns the difference of the arguments, throwing an exception if the result overflows a long . |
static double |
tan |
Returns the trigonometric tangent of an angle. |
static double |
tanh |
Returns the hyperbolic tangent of a double value. |
static double |
toDegrees |
Converts an angle measured in radians to an approximately equivalent angle measured in degrees. |
static int |
toIntExact |
Returns the value of the long argument, throwing an exception if the value overflows an int . |
static double |
toRadians |
Converts an angle measured in degrees to an approximately equivalent angle measured in radians. |
static double |
ulp |
Returns the size of an ulp of the argument. |
static float |
ulp |
Returns the size of an ulp of the argument. |
static long |
unsignedMultiplyHigh |
Returns as a long the most significant 64 bits of the unsigned 128-bit product of two unsigned 64-bit factors. |
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 (π), the ratio of the circumference of a circle to its diameter.public static final double TAU
double
value that is closer than any other to tau (τ), the ratio of the circumference of a circle to its radius.public static double sin(double a)
a
- an angle, in radians.public static double cos(double a)
1.0
. a
- an angle, in radians.public static double tan(double a)
a
- an angle, in radians.public static double asin(double a)
a
- the value whose arc sine is to be returned.public static double acos(double a)
1.0
, the result is positive zero. a
- the value whose arc cosine is to be returned.public static double atan(double a)
a
- the value whose arc tangent is to be returned.public static double toRadians(double angdeg)
angdeg
- an angle, in degreesangdeg
in radians.public static double toDegrees(double angrad)
cos(toRadians(90.0))
to exactly equal 0.0
.angrad
- an angle, in radiansangrad
in degrees.public static double exp(double a)
double
value. Special cases: 1.0
. 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: 1.0
, then the result is positive zero. a
- a valuea
, the natural logarithm of a
.public static double log10(double a)
double
value. Special cases: 1.0
(100), then the result is positive zero. a
- a valuea
.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
.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: 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: StrictMath.ceil(x)
is exactly the value of -StrictMath.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 to the value of the argument, the result is the integer value that is even. Special cases: a
- a 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.atan2
is equal to: y
- the ordinate coordinatex
- the abscissa coordinatepublic 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.)
pow
operation for ±1.0
raised to an infinite power. This method treats such cases as indeterminate and specifies a NaN is returned. The IEEE 754 specification treats the infinite power as a large integer (large-magnitude floating-point numbers are numerically integers, specifically even integers) and therefore specifies 1.0
be returned.a
- 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.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.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
.public static int addExact(int x, int y)
int
.x
- the first valuey
- the second valueArithmeticException
- if the result overflows an intpublic static long addExact(long x, long y)
long
.x
- the first valuey
- the second valueArithmeticException
- if the result overflows a longpublic static int subtractExact(int x, int y)
int
.x
- the first valuey
- the second value to subtract from the firstArithmeticException
- if the result overflows an intpublic static long subtractExact(long x, long y)
long
.x
- the first valuey
- the second value to subtract from the firstArithmeticException
- if the result overflows a longpublic static int multiplyExact(int x, int y)
int
.x
- the first valuey
- the second valueArithmeticException
- if the result overflows an intpublic static long multiplyExact(long x, int y)
long
.x
- the first valuey
- the second valueArithmeticException
- if the result overflows a longpublic static long multiplyExact(long x, long y)
long
.x
- the first valuey
- the second valueArithmeticException
- if the result overflows a longpublic static int divideExact(int x, int y)
int
. Such overflow occurs in this method if x
is Integer.MIN_VALUE
and y
is -1
. In contrast, if Integer.MIN_VALUE / -1
were evaluated directly, the result would be Integer.MIN_VALUE
and no exception would be thrown. If y
is zero, an ArithmeticException
is thrown (JLS 15.17.2).
The built-in remainder operator "%
" is a suitable counterpart both for this method and for the built-in division operator "/
".
x
- the dividendy
- the divisorx / y
ArithmeticException
- if y
is zero or the quotient overflows an intpublic static long divideExact(long x, long y)
long
. Such overflow occurs in this method if x
is Long.MIN_VALUE
and y
is -1
. In contrast, if Long.MIN_VALUE / -1
were evaluated directly, the result would be Long.MIN_VALUE
and no exception would be thrown. If y
is zero, an ArithmeticException
is thrown (JLS 15.17.2).
The built-in remainder operator "%
" is a suitable counterpart both for this method and for the built-in division operator "/
".
x
- the dividendy
- the divisorx / y
ArithmeticException
- if y
is zero or the quotient overflows a longpublic static int floorDivExact(int x, int y)
int
value that is less than or equal to the algebraic quotient. This method is identical to floorDiv(int,int)
except that it throws an ArithmeticException
when the dividend is Integer.MIN_VALUE and the divisor is -1
instead of ignoring the integer overflow and returning Integer.MIN_VALUE
. The floor modulus method floorMod(int,int)
is a suitable counterpart both for this method and for the floorDiv(int,int)
method.
See Math.floorDiv
for examples and a comparison to the integer division /
operator.
x
- the dividendy
- the divisorint
value that is less than or equal to the algebraic quotient.ArithmeticException
- if the divisor y
is zero, or the dividend x
is Integer.MIN_VALUE
and the divisor y
is -1
.public static long floorDivExact(long x, long y)
long
value that is less than or equal to the algebraic quotient. This method is identical to floorDiv(long,long)
except that it throws an ArithmeticException
when the dividend is Long.MIN_VALUE and the divisor is -1
instead of ignoring the integer overflow and returning Long.MIN_VALUE
. The floor modulus method floorMod(long,long)
is a suitable counterpart both for this method and for the floorDiv(long,long)
method.
For examples, see Math.floorDiv
.
x
- the dividendy
- the divisorlong
value that is less than or equal to the algebraic quotient.ArithmeticException
- if the divisor y
is zero, or the dividend x
is Long.MIN_VALUE
and the divisor y
is -1
.public static int ceilDivExact(int x, int y)
int
value that is greater than or equal to the algebraic quotient. This method is identical to ceilDiv(int,int)
except that it throws an ArithmeticException
when the dividend is Integer.MIN_VALUE and the divisor is -1
instead of ignoring the integer overflow and returning Integer.MIN_VALUE
. The ceil modulus method ceilMod(int,int)
is a suitable counterpart both for this method and for the ceilDiv(int,int)
method.
See Math.ceilDiv
for examples and a comparison to the integer division /
operator.
x
- the dividendy
- the divisorint
value that is greater than or equal to the algebraic quotient.ArithmeticException
- if the divisor y
is zero, or the dividend x
is Integer.MIN_VALUE
and the divisor y
is -1
.public static long ceilDivExact(long x, long y)
long
value that is greater than or equal to the algebraic quotient. This method is identical to ceilDiv(long,long)
except that it throws an ArithmeticException
when the dividend is Long.MIN_VALUE and the divisor is -1
instead of ignoring the integer overflow and returning Long.MIN_VALUE
. The ceil modulus method ceilMod(long,long)
is a suitable counterpart both for this method and for the ceilDiv(long,long)
method.
For examples, see Math.ceilDiv
.
x
- the dividendy
- the divisorlong
value that is greater than or equal to the algebraic quotient.ArithmeticException
- if the divisor y
is zero, or the dividend x
is Long.MIN_VALUE
and the divisor y
is -1
.public static int incrementExact(int a)
int
. The overflow only occurs for the maximum value.a
- the value to incrementArithmeticException
- if the result overflows an intpublic static long incrementExact(long a)
long
. The overflow only occurs for the maximum value.a
- the value to incrementArithmeticException
- if the result overflows a longpublic static int decrementExact(int a)
int
. The overflow only occurs for the minimum value.a
- the value to decrementArithmeticException
- if the result overflows an intpublic static long decrementExact(long a)
long
. The overflow only occurs for the minimum value.a
- the value to decrementArithmeticException
- if the result overflows a longpublic static int negateExact(int a)
int
. The overflow only occurs for the minimum value.a
- the value to negateArithmeticException
- if the result overflows an intpublic static long negateExact(long a)
long
. The overflow only occurs for the minimum value.a
- the value to negateArithmeticException
- if the result overflows a longpublic static int toIntExact(long value)
long
argument, throwing an exception if the value overflows an int
.value
- the long valueArithmeticException
- if the argument
overflows an intpublic static long multiplyFull(int x, int y)
x
- the first valuey
- the second valuepublic static long multiplyHigh(long x, long y)
long
the most significant 64 bits of the 128-bit product of two 64-bit factors.x
- the first valuey
- the second valuepublic static long unsignedMultiplyHigh(long x, long y)
long
the most significant 64 bits of the unsigned 128-bit product of two unsigned 64-bit factors.x
- the first valuey
- the second valuepublic 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 Integer.MIN_VALUE and the divisor is -1
, then integer overflow occurs and the result is equal to Integer.MIN_VALUE
. See Math.floorDiv
for examples and a comparison to the integer division /
operator.
x
- the dividendy
- the divisorint
value that is less than or equal to the algebraic quotient.ArithmeticException
- if the divisor y
is zeropublic static long floorDiv(long x, int y)
long
value that is less than or equal to the algebraic quotient. There is one special case: if the dividend is Long.MIN_VALUE and the divisor is -1
, then integer overflow occurs and the result is equal to Long.MIN_VALUE
. See Math.floorDiv
for examples and a comparison to the integer division /
operator.
x
- the dividendy
- the divisorlong
value that is less than or equal to the algebraic quotient.ArithmeticException
- if the divisor y
is zeropublic 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 Long.MIN_VALUE and the divisor is -1
, then integer overflow occurs and the result is equal to Long.MIN_VALUE
. See Math.floorDiv
for examples and a comparison to the integer division /
operator.
x
- the dividendy
- the divisorlong
value that is less than or equal to the algebraic quotient.ArithmeticException
- if the divisor y
is zeropublic static int floorMod(int x, int y)
int
arguments. The floor modulus is r = x - (floorDiv(x, y) * y)
, has the same sign as the divisor y
or is zero, and is in the range of -abs(y) < r < +abs(y)
.
The relationship between floorDiv
and floorMod
is such that:
floorDiv(x, y) * y + floorMod(x, y) == x
See Math.floorMod
for examples and a comparison to the %
operator.
x
- the dividendy
- the divisorx - (floorDiv(x, y) * y)
ArithmeticException
- if the divisor y
is zeropublic static int floorMod(long x, int y)
long
and int
arguments. The floor modulus is r = x - (floorDiv(x, y) * y)
, has the same sign as the divisor y
or is zero, and is in the range of -abs(y) < r < +abs(y)
.
The relationship between floorDiv
and floorMod
is such that:
floorDiv(x, y) * y + floorMod(x, y) == x
See Math.floorMod
for examples and a comparison to the %
operator.
x
- the dividendy
- the divisorx - (floorDiv(x, y) * y)
ArithmeticException
- if the divisor y
is zeropublic static long floorMod(long x, long y)
long
arguments. The floor modulus is r = x - (floorDiv(x, y) * y)
, has the same sign as the divisor y
or is zero, and is in the range of -abs(y) < r < +abs(y)
.
The relationship between floorDiv
and floorMod
is such that:
floorDiv(x, y) * y + floorMod(x, y) == x
See Math.floorMod
for examples and a comparison to the %
operator.
x
- the dividendy
- the divisorx - (floorDiv(x, y) * y)
ArithmeticException
- if the divisor y
is zeropublic static int ceilDiv(int x, int y)
int
value that is greater than or equal to the algebraic quotient. There is one special case: if the dividend is Integer.MIN_VALUE and the divisor is -1
, then integer overflow occurs and the result is equal to Integer.MIN_VALUE
. See Math.ceilDiv
for examples and a comparison to the integer division /
operator.
x
- the dividendy
- the divisorint
value that is greater than or equal to the algebraic quotient.ArithmeticException
- if the divisor y
is zeropublic static long ceilDiv(long x, int y)
long
value that is greater than or equal to the algebraic quotient. There is one special case: if the dividend is Long.MIN_VALUE and the divisor is -1
, then integer overflow occurs and the result is equal to Long.MIN_VALUE
. See Math.ceilDiv
for examples and a comparison to the integer division /
operator.
x
- the dividendy
- the divisorlong
value that is greater than or equal to the algebraic quotient.ArithmeticException
- if the divisor y
is zeropublic static long ceilDiv(long x, long y)
long
value that is greater than or equal to the algebraic quotient. There is one special case: if the dividend is Long.MIN_VALUE and the divisor is -1
, then integer overflow occurs and the result is equal to Long.MIN_VALUE
. See Math.ceilDiv
for examples and a comparison to the integer division /
operator.
x
- the dividendy
- the divisorlong
value that is greater than or equal to the algebraic quotient.ArithmeticException
- if the divisor y
is zeropublic static int ceilMod(int x, int y)
int
arguments. The ceiling modulus is r = x - (ceilDiv(x, y) * y)
, has the opposite sign as the divisor y
or is zero, and is in the range of -abs(y) < r < +abs(y)
.
The relationship between ceilDiv
and ceilMod
is such that:
ceilDiv(x, y) * y + ceilMod(x, y) == x
See Math.ceilMod
for examples and a comparison to the %
operator.
x
- the dividendy
- the divisorx - (ceilDiv(x, y) * y)
ArithmeticException
- if the divisor y
is zeropublic static int ceilMod(long x, int y)
long
and int
arguments. The ceiling modulus is r = x - (ceilDiv(x, y) * y)
, has the opposite sign as the divisor y
or is zero, and is in the range of -abs(y) < r < +abs(y)
.
The relationship between ceilDiv
and ceilMod
is such that:
ceilDiv(x, y) * y + ceilMod(x, y) == x
See Math.ceilMod
for examples and a comparison to the %
operator.
x
- the dividendy
- the divisorx - (ceilDiv(x, y) * y)
ArithmeticException
- if the divisor y
is zeropublic static long ceilMod(long x, long y)
long
arguments. The ceiling modulus is r = x - (ceilDiv(x, y) * y)
, has the opposite sign as the divisor y
or is zero, and is in the range of -abs(y) < r < +abs(y)
.
The relationship between ceilDiv
and ceilMod
is such that:
ceilDiv(x, y) * y + ceilMod(x, y) == x
See Math.ceilMod
for examples and a comparison to the %
operator.
x
- the dividendy
- the divisorx - (ceilDiv(x, y) * y)
ArithmeticException
- if the divisor y
is zeropublic static int abs(int a)
int
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Note that if the argument is equal to the value of Integer.MIN_VALUE
, the most negative representable int
value, the result is that same value, which is negative. In contrast, the absExact(int)
method throws an ArithmeticException
for this value.
a
- the argument whose absolute value is to be determined.public static int absExact(int a)
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 4.2.1), the mathematical absolute value of Integer.MIN_VALUE
overflows the positive int
range, so an exception is thrown for that argument.
a
- the argument whose absolute value is to be determinedArithmeticException
- if the argument is Integer.MIN_VALUE
public static long abs(long a)
long
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Note that if the argument is equal to the value of Long.MIN_VALUE
, the most negative representable long
value, the result is that same value, which is negative. In contrast, the absExact(long)
method throws an ArithmeticException
for this value.
a
- the argument whose absolute value is to be determined.public static long absExact(long a)
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 4.2.1), the mathematical absolute value of Long.MIN_VALUE
overflows the positive long
range, so an exception is thrown for that argument.
a
- the argument whose absolute value is to be determinedArithmeticException
- if the argument is Long.MIN_VALUE
public static float abs(float a)
float
value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases: float
with the same exponent and significand as the argument but with a guaranteed zero sign bit indicating a positive value: Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a))
a
- the argument whose absolute value is to be determinedpublic 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
with the same exponent and significand as the argument but with a guaranteed zero sign bit indicating a positive value: Double.longBitsToDouble((Double.doubleToRawLongBits(a)<<1)>>>1)
a
- the argument whose absolute value is to be determinedpublic 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 int clamp(long value, int min, int max)
min
, then min
is returned. If the value is greater than max
, then max
is returned. Otherwise, the original value is returned. While the original value of type long may not fit into the int type, the bounds have the int type, so the result always fits the int type. This allows to use method to safely cast long value to int with saturation.
value
- value to clampmin
- minimal allowed valuemax
- maximal allowed valuemin..max
intervalIllegalArgumentException
- if min > max
public static long clamp(long value, long min, long max)
min
, then min
is returned. If the value is greater than max
, then max
is returned. Otherwise, the original value is returned.value
- value to clampmin
- minimal allowed valuemax
- maximal allowed valuemin..max
intervalIllegalArgumentException
- if min > max
public static double clamp(double value, double min, double max)
min
, then min
is returned. If the value is greater than max
, then max
is returned. Otherwise, the original value is returned. If value is NaN, the result is also NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. E.g., clamp(-0.0, 0.0, 1.0)
returns 0.0.
value
- value to clampmin
- minimal allowed valuemax
- maximal allowed valuemin..max
intervalIllegalArgumentException
- if either of min
and max
arguments is NaN, or min > max
, or min
is +0.0, and max
is -0.0.public static float clamp(float value, float min, float max)
min
, then min
is returned. If the value is greater than max
, then max
is returned. Otherwise, the original value is returned. If value is NaN, the result is also NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. E.g., clamp(-0.0f, 0.0f, 1.0f)
returns 0.0f.
value
- value to clampmin
- minimal allowed valuemax
- maximal allowed valuemin..max
intervalIllegalArgumentException
- if either of min
and max
arguments is NaN, or min > max
, or min
is +0.0f, and max
is -0.0f.public static double fma(double a, double b, double c)
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:
Note that fusedMac(a, 1.0, c)
returns the same result as (a + c
). However, fusedMac(a, b, +0.0)
does not always return the same result as (a * b
) since fusedMac(-0.0, +0.0, +0.0)
is +0.0
while (-0.0 * +0.0
) is -0.0
; fusedMac(a, b, -0.0)
is equivalent to (a * b
) however.
a
- a valueb
- a valuec
- a valuedouble
valuepublic static float fma(float a, float b, float c)
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:
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.
a
- a valueb
- a valuec
- a valuefloat
valuepublic 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 returnedpublic 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 returnedpublic static double signum(double d)
Special Cases:
d
- the floating-point value whose signum is to be returnedpublic static float signum(float f)
Special Cases:
f
- the floating-point value whose signum is to be returnedpublic 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:
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
. 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
. x
- The number whose hyperbolic tangent is to be returned.x
.public static double hypot(double x, double y)
Special cases:
x
- a valuey
- a valuepublic static double expm1(double x)
expm1(x)
+ 1 is much closer to the true result of ex than exp(x)
. Special cases:
x
- the exponent to raise e to in the computation of ex
-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:
x
- a valuex
+ 1), the natural log of x
+ 1public static double copySign(double magnitude, double sign)
sign
argument is always treated as if it were positive.magnitude
- the parameter providing the magnitude of the resultsign
- the parameter providing the sign of the resultmagnitude
and the sign of sign
.public static float copySign(float magnitude, float sign)
sign
argument is always treated as if it were positive.magnitude
- the parameter providing the magnitude of the resultsign
- the parameter providing the sign of the resultmagnitude
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
valuepublic static int getExponent(double d)
double
. Special cases: Double.MAX_EXPONENT
+ 1. Double.MIN_EXPONENT
-1. d
- a double
valuepublic 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 valuedirection
- value indicating which of start
's neighbors or start
should be returnedstart
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 valuedirection
- value indicating which of start
's neighbors or start
should be returnedstart
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 valuepublic 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 valuepublic 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 valuepublic 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 valuepublic static double scalb(double d, int scaleFactor)
d
× 2scaleFactor
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:
d
- number to be scaled by a power of two.scaleFactor
- power of 2 used to scale d
d
× 2scaleFactor
public static float scalb(float f, int scaleFactor)
f
× 2scaleFactor
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:
f
- number to be scaled by a power of two.scaleFactor
- power of 2 used to scale f
f
× 2scaleFactor
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Various third party code in OpenJDK is licensed under different licenses (see Debian package).
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https://docs.oracle.com/en/java/javase/21/docs/api/java.base/java/lang/StrictMath.html