public final class StrictMath extends Object
The class StrictMath
contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.
To help ensure portability of Java programs, the definitions of some of the numeric functions in this package require that they produce the same results as certain published algorithms. These algorithms are available from the well-known network library netlib
as the package "Freely Distributable Math Library," fdlibm
. These algorithms, which are written in the C programming language, are then to be understood as executed with all floating-point operations following the rules of Java floating-point arithmetic.
The Java math library is defined with respect to fdlibm
version 5.3. Where fdlibm
provides more than one definition for a function (such as acos
), use the "IEEE 754 core function" version (residing in a file whose name begins with the letter e
). The methods which require fdlibm
semantics are sin
, cos
, tan
, asin
, acos
, atan
, exp
, log
, log10
, cbrt
, atan2
, pow
, sinh
, cosh
, tanh
, hypot
, expm1
, and log1p
.
The platform uses signed two's complement integer arithmetic with int and long primitive types. The developer should choose the primitive type to ensure that arithmetic operations consistently produce correct results, which in some cases means the operations will not overflow the range of values of the computation. The best practice is to choose the primitive type and algorithm to avoid overflow. In cases where the size is int
or long
and overflow errors need to be detected, the methods addExact
, subtractExact
, multiplyExact
, and toIntExact
throw an ArithmeticException
when the results overflow. For other arithmetic operations such as divide, absolute value, increment, decrement, and negation overflow occurs only with a specific minimum or maximum value and should be checked against the minimum or maximum as appropriate.
public static final double E
The double
value that is closer than any other to e, the base of the natural logarithms.
public static final double PI
The double
value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter.
public static double sin(double a)
Returns the trigonometric sine of an angle. Special cases:
a
- an angle, in radians.public static double cos(double a)
Returns the trigonometric cosine of an angle. Special cases:
a
- an angle, in radians.public static double tan(double a)
Returns the trigonometric tangent of an angle. Special cases:
a
- an angle, in radians.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:
a
- the value whose arc sine is to be returned.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:
a
- the value whose arc cosine is to be returned.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:
a
- the value whose arc tangent is to be returned.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.
angdeg
- an angle, in degreesangdeg
in radians.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
.
angrad
- an angle, in radiansangrad
in degrees.public static double exp(double a)
Returns Euler's number e raised to the power of a double
value. Special cases:
a
- the exponent to raise e to.a
, 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:
a
- a valuea
, the natural logarithm of a
.public static double log10(double a)
Returns the base 10 logarithm of a double
value. Special cases:
a
- a valuea
.public static double sqrt(double a)
Returns the correctly rounded positive square root of 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)
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:
a
- a value.a
.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:
f1
- the dividend.f2
- the divisor.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:
StrictMath.ceil(x)
is exactly the value of -StrictMath.floor(-x)
. a
- a value.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:
a
- a value.public static double rint(double a)
Returns the double
value that is closest in value to the argument and is equal to a mathematical integer. If two double
values that are mathematical integers are equally close to the value of the argument, the result is the integer value that is even. Special cases:
a
- a value.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:
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.y
- the ordinate coordinatex
- the abscissa coordinatepublic static double pow(double a, double b)
Returns the value of the first argument raised to the power of the second argument. Special cases:
double
value.(In the foregoing descriptions, a floating-point value is considered to be an integer if and only if it is finite and a fixed point of the method ceil
or, equivalently, a fixed point of the method floor
. A value is a fixed point of a one-argument method if and only if the result of applying the method to the value is equal to the value.)
a
- base.b
- the exponent.a
b
.public static int round(float a)
Returns the closest 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)
Returns the closest 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()
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.
double
greater than or equal to 0.0
and less than 1.0
.Random.nextDouble()
public static int addExact(int x, int y)
Returns the sum of its arguments, throwing an exception if the result overflows an int
.
x
- the first valuey
- the second valueArithmeticException
- if the result overflows an intMath.addExact(int,int)
public static long addExact(long x, long y)
Returns the sum of its arguments, throwing an exception if the result overflows a long
.
x
- the first valuey
- the second valueArithmeticException
- if the result overflows a longMath.addExact(long,long)
public static int subtractExact(int x, int y)
Returns the difference of the arguments, throwing an exception if the result overflows an int
.
x
- the first valuey
- the second value to subtract from the firstArithmeticException
- if the result overflows an intMath.subtractExact(int,int)
public static long subtractExact(long x, long y)
Returns the difference of the arguments, throwing an exception if the result overflows a long
.
x
- the first valuey
- the second value to subtract from the firstArithmeticException
- if the result overflows a longMath.subtractExact(long,long)
public static int multiplyExact(int x, int y)
Returns the product of the arguments, throwing an exception if the result overflows an int
.
x
- the first valuey
- the second valueArithmeticException
- if the result overflows an intMath.multiplyExact(int,int)
public static long multiplyExact(long x, long y)
Returns the product of the arguments, throwing an exception if the result overflows a long
.
x
- the first valuey
- the second valueArithmeticException
- if the result overflows a longMath.multiplyExact(long,long)
public static int toIntExact(long value)
Returns the value of the long
argument; throwing an exception if the value overflows an int
.
value
- the long valueArithmeticException
- if the argument
overflows an intMath.toIntExact(long)
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 the 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 zeroMath.floorDiv(int, int)
, Math.floor(double)
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 the 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 zeroMath.floorDiv(long, long)
, Math.floor(double)
public static int floorMod(int x, int y)
Returns the floor modulus of the int
arguments.
The floor modulus is x - (floorDiv(x, y) * y)
, has the same sign as the divisor y
, and is in the range of -abs(y) < r < +abs(y)
.
The relationship between floorDiv
and floorMod
is such that:
floorDiv(x, y) * y + floorMod(x, y) == x
See Math.floorMod
for examples and a comparison to the %
operator.
x
- the dividendy
- the divisorx - (floorDiv(x, y) * y)
ArithmeticException
- if the divisor y
is zeroMath.floorMod(int, int)
, floorDiv(int, int)
public static long floorMod(long x, long y)
Returns the floor modulus of the long
arguments.
The floor modulus is x - (floorDiv(x, y) * y)
, has the same sign as the divisor y
, and is in the range of -abs(y) < r < +abs(y)
.
The relationship between floorDiv
and floorMod
is such that:
floorDiv(x, y) * y + floorMod(x, y) == x
See Math.floorMod
for examples and a comparison to the %
operator.
x
- the dividendy
- the divisorx - (floorDiv(x, y) * y)
ArithmeticException
- if the divisor y
is zeroMath.floorMod(long, long)
, floorDiv(long, long)
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.
a
- the argument whose absolute value is to be determined.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.
a
- the argument whose absolute value is to be determined.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:
Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))
a
- the argument whose absolute value is to be determinedpublic 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:
Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)
a
- the argument whose absolute value is to be determinedpublic 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.
a
- an argument.b
- another argument.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.
a
- an argument.b
- another argument.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.
a
- an argument.b
- another argument.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.
a
- an argument.b
- another argument.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.
a
- an argument.b
- another argument.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.
a
- an argument.b
- another argument.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.
a
- an argument.b
- another argument.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.
a
- an argument.b
- another argument.a
and b
.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:
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)
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:
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)
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:
d
- the floating-point value whose signum is to be returnedpublic 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:
f
- the floating-point value whose signum is to be returnedpublic 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:
x
- The number whose hyperbolic sine is to be returned.x
.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:
1.0
. x
- The number whose hyperbolic cosine is to be returned.x
.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:
+1.0
. -1.0
. x
- The number whose hyperbolic tangent is to be returned.x
.public static double hypot(double x, double y)
Returns sqrt(x2 +y2) without intermediate overflow or underflow.
Special cases:
x
- a valuey
- a valuepublic 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:
x
- the exponent to raise e to in the computation of ex
-1.x
- 1.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:
x
- a valuex
+ 1), the natural log of x
+ 1public static double copySign(double magnitude, double sign)
Returns the first floating-point argument with the sign of the second floating-point argument. For this method, a NaN sign
argument is always treated as if it were positive.
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)
Returns the first floating-point argument with the sign of the second floating-point argument. For this method, a NaN sign
argument is always treated as if it were positive.
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)
Returns the unbiased exponent used in the representation of a float
. Special cases:
Float.MAX_EXPONENT
+ 1. Float.MIN_EXPONENT
-1. f
- a float
valuepublic static int getExponent(double d)
Returns the unbiased exponent used in the representation of a double
. Special cases:
Double.MAX_EXPONENT
+ 1. Double.MIN_EXPONENT
-1. d
- a double
valuepublic 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:
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)
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:
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)
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:
Double.MIN_VALUE
d
- starting floating-point valuepublic 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:
Float.MIN_VALUE
f
- starting floating-point valuepublic 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:
-Double.MIN_VALUE
d
- starting floating-point valuepublic 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:
-Float.MIN_VALUE
f
- starting floating-point valuepublic static double scalb(double d, int scaleFactor)
Returns d
× 2scaleFactor
rounded as if performed by a single correctly rounded floating-point multiply to a member of the double value set. See the Java Language Specification for a discussion of floating-point value sets. If the exponent of the result is between Double.MIN_EXPONENT
and Double.MAX_EXPONENT
, the answer is calculated exactly. If the exponent of the result would be larger than Double.MAX_EXPONENT
, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when scalb(x, n)
is subnormal, scalb(scalb(x, n), -n)
may not equal x. When the result is non-NaN, the result has the same sign as d
.
Special cases:
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)
Returns f
× 2scaleFactor
rounded as if performed by a single correctly rounded floating-point multiply to a member of the float value set. See the Java Language Specification for a discussion of floating-point value sets. If the exponent of the result is between Float.MIN_EXPONENT
and Float.MAX_EXPONENT
, the answer is calculated exactly. If the exponent of the result would be larger than Float.MAX_EXPONENT
, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when scalb(x, n)
is subnormal, scalb(scalb(x, n), -n)
may not equal x. When the result is non-NaN, the result has the same sign as f
.
Special cases:
f
- number to be scaled by a power of two.scaleFactor
- power of 2 used to scale f
f
× 2scaleFactor
© 1993–2017, Oracle and/or its affiliates. All rights reserved.
Documentation extracted from Debian's OpenJDK Development Kit package.
Licensed under the GNU General Public License, version 2, with the Classpath Exception.
Various third party code in OpenJDK is licensed under different licenses (see Debian package).
Java and OpenJDK are trademarks or registered trademarks of Oracle and/or its affiliates.