Class: java.lang.StrictMath
- public final class StrictMath
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.
Methods
-
IEEEremaindertop
public static native 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 tof1 - f2× n, where n is the mathematical integer closest to the exact mathematical value of the quotientf1/f2, and if two mathematical integers are equally close tof1/f2, then n is the integer that is even. If the remainder is zero, its sign is the same as the sign of the first argument. Special cases:- If either argument is NaN, or the first argument is infinite, or the second argument is positive zero or negative zero, then the result is NaN.
- If the first argument is finite and the second argument is infinite, then the result is the same as the first argument.
-
abstop
public static double abs(double a)Returns the absolute value of adoublevalue. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:- If the argument is positive zero or negative zero, the result is positive zero.
- If the argument is infinite, the result is positive infinity.
- If the argument is NaN, the result is NaN.
Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1) -
abstop
public static float abs(float a)Returns the absolute value of afloatvalue. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:- If the argument is positive zero or negative zero, the result is positive zero.
- If the argument is infinite, the result is positive infinity.
- If the argument is NaN, the result is NaN.
Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))
-
abstop
public static int abs(int a)Returns the absolute value of anintvalue.. 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 representableintvalue, the result is that same value, which is negative. -
abstop
public static long abs(long a)Returns the absolute value of alongvalue. 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 representablelongvalue, the result is that same value, which is negative. -
acostop
public static native double acos(double a)Returns the arc cosine of an angle, in the range of 0.0 through pi. Special case:- If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
-
asintop
public static native double asin(double a)Returns the arc sine of an angle, in the range of -pi/2 through pi/2. Special cases:- If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
- If the argument is zero, then the result is a zero with the same sign as the argument.
-
atantop
public static native double atan(double a)Returns the arc tangent of an angle, in the range of -pi/2 through pi/2. Special cases:- If the argument is NaN, then the result is NaN.
- If the argument is zero, then the result is a zero with the same sign as the argument.
-
atan2top
public static native double atan2(double y, double x)Converts rectangular coordinates (x,y) to polar (r, theta). This method computes the phase theta by computing an arc tangent ofy/xin the range of -pi to pi. Special cases:- If either argument is NaN, then the result is NaN.
- If the first argument is positive zero and the second argument is positive, or the first argument is positive and finite and the second argument is positive infinity, then the result is positive zero.
- If the first argument is negative zero and the second argument is positive, or the first argument is negative and finite and the second argument is positive infinity, then the result is negative zero.
- If the first argument is positive zero and the second argument
is negative, or the first argument is positive and finite and the
second argument is negative infinity, then the result is the
doublevalue closest to pi. - If the first argument is negative zero and the second argument
is negative, or the first argument is negative and finite and the
second argument is negative infinity, then the result is the
doublevalue closest to -pi. - If the first argument is positive and the second argument is
positive zero or negative zero, or the first argument is positive
infinity and the second argument is finite, then the result is the
doublevalue closest to pi/2. - If the first argument is negative and the second argument is
positive zero or negative zero, or the first argument is negative
infinity and the second argument is finite, then the result is the
doublevalue closest to -pi/2. - If both arguments are positive infinity, then the result is the
doublevalue closest to pi/4. - If the first argument is positive infinity and the second argument
is negative infinity, then the result is the
doublevalue closest to 3*pi/4. - If the first argument is negative infinity and the second argument
is positive infinity, then the result is the
doublevalue closest to -pi/4. - If both arguments are negative infinity, then the result is the
doublevalue closest to -3*pi/4.
-
cbrttop
public static native double cbrt(double a)Returns the cube root of adoublevalue. For positive finitex,cbrt(-x) == -cbrt(x); that is, the cube root of a negative value is the negative of the cube root of that value's magnitude. Special cases:- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is an infinity with the same sign as the argument.
- If the argument is zero, then the result is a zero with the same sign as the argument.
-
ceiltop
public static native double ceil(double a)Returns the smallest (closest to negative infinity)doublevalue that is greater than or equal to the argument and is equal to a mathematical integer. Special cases:- If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
- If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
- If the argument value is less than zero but greater than -1.0, then the result is negative zero.
StrictMath.ceil(x)is exactly the value of-StrictMath.floor(-x). -
costop
public static native double cos(double a)Returns the trigonometric cosine of an angle. Special cases:- If the argument is NaN or an infinity, then the result is NaN.
-
coshtop
public static native double cosh(double x)Returns the hyperbolic cosine of adoublevalue. The hyperbolic cosine of x is defined to be (ex + e-x)/2 where e is Euler's number.Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is positive infinity.
- If the argument is zero, then the result is
1.0.
-
exptop
public static native double exp(double a)Returns Euler's number e raised to the power of adoublevalue. Special cases:- If the argument is NaN, the result is NaN.
- If the argument is positive infinity, then the result is positive infinity.
- If the argument is negative infinity, then the result is positive zero.
-
expm1top
public static native double expm1(double x)Returns ex -1. Note that for values of x near 0, the exact sum ofexpm1(x)+ 1 is much closer to the true result of ex thanexp(x).Special cases:
- If the argument is NaN, the result is NaN.
- If the argument is positive infinity, then the result is positive infinity.
- If the argument is negative infinity, then the result is -1.0.
- If the argument is zero, then the result is a zero with the same sign as the argument.
-
floortop
public static native double floor(double a)Returns the largest (closest to positive infinity)doublevalue that is less than or equal to the argument and is equal to a mathematical integer. Special cases:- If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
- If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
-
hypottop
public static native double hypot(double x, double y)Returns sqrt(x2 +y2) without intermediate overflow or underflow.Special cases:
- If either argument is infinite, then the result is positive infinity.
- If either argument is NaN and neither argument is infinite, then the result is NaN.
-
logtop
public static native double log(double a)Returns the natural logarithm (base e) of adoublevalue. Special cases:- If the argument is NaN or less than zero, then the result is NaN.
- If the argument is positive infinity, then the result is positive infinity.
- If the argument is positive zero or negative zero, then the result is negative infinity.
-
log10top
public static native double log10(double a)Returns the base 10 logarithm of adoublevalue. Special cases:- If the argument is NaN or less than zero, then the result is NaN.
- If the argument is positive infinity, then the result is positive infinity.
- If the argument is positive zero or negative zero, then the result is negative infinity.
- If the argument is equal to 10n for integer n, then the result is n.
-
log1ptop
public static native double log1p(double x)Returns the natural logarithm of the sum of the argument and 1. Note that for small valuesx, the result oflog1p(x)is much closer to the true result of ln(1 +x) than the floating-point evaluation oflog(1.0+x).Special cases:
- If the argument is NaN or less than -1, then the result is NaN.
- If the argument is positive infinity, then the result is positive infinity.
- If the argument is negative one, then the result is negative infinity.
- If the argument is zero, then the result is a zero with the same sign as the argument.
-
maxtop
public static double max(double a, double b)Returns the greater of twodoublevalues. 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. -
maxtop
public static float max(float a, float b)Returns the greater of twofloatvalues. 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. -
maxtop
public static int max(int a, int b)Returns the greater of twointvalues. That is, the result is the argument closer to the value ofInteger.MAX_VALUE. If the arguments have the same value, the result is that same value. -
maxtop
public static long max(long a, long b)Returns the greater of twolongvalues. That is, the result is the argument closer to the value ofLong.MAX_VALUE. If the arguments have the same value, the result is that same value. -
mintop
public static double min(double a, double b)Returns the smaller of twodoublevalues. 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. -
mintop
public static float min(float a, float b)Returns the smaller of twofloatvalues. 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. -
mintop
public static int min(int a, int b)Returns the smaller of twointvalues. That is, the result the argument closer to the value ofInteger.MIN_VALUE. If the arguments have the same value, the result is that same value. -
mintop
public static long min(long a, long b)Returns the smaller of twolongvalues. That is, the result is the argument closer to the value ofLong.MIN_VALUE. If the arguments have the same value, the result is that same value. -
powtop
public static native double pow(double a, double b)Returns the value of the first argument raised to the power of the second argument. Special cases:- If the second argument is positive or negative zero, then the result is 1.0.
- If the second argument is 1.0, then the result is the same as the first argument.
- If the second argument is NaN, then the result is NaN.
- If the first argument is NaN and the second argument is nonzero, then the result is NaN.
- If
- the absolute value of the first argument is greater than 1 and the second argument is positive infinity, or
- the absolute value of the first argument is less than 1 and the second argument is negative infinity,
- If
- the absolute value of the first argument is greater than 1 and the second argument is negative infinity, or
- the absolute value of the first argument is less than 1 and the second argument is positive infinity,
- If the absolute value of the first argument equals 1 and the second argument is infinite, then the result is NaN.
- If
- the first argument is positive zero and the second argument is greater than zero, or
- the first argument is positive infinity and the second argument is less than zero,
- If
- the first argument is positive zero and the second argument is less than zero, or
- the first argument is positive infinity and the second argument is greater than zero,
- If
- the first argument is negative zero and the second argument is greater than zero but not a finite odd integer, or
- the first argument is negative infinity and the second argument is less than zero but not a finite odd integer,
- If
- the first argument is negative zero and the second argument is a positive finite odd integer, or
- the first argument is negative infinity and the second argument is a negative finite odd integer,
- If
- the first argument is negative zero and the second argument is less than zero but not a finite odd integer, or
- the first argument is negative infinity and the second argument is greater than zero but not a finite odd integer,
- If
- the first argument is negative zero and the second argument is a negative finite odd integer, or
- the first argument is negative infinity and the second argument is a positive finite odd integer,
- If the first argument is finite and less than zero
- if the second argument is a finite even integer, the result is equal to the result of raising the absolute value of the first argument to the power of the second argument
- if the second argument is a finite odd integer, the result is equal to the negative of the result of raising the absolute value of the first argument to the power of the second argument
- if the second argument is finite and not an integer, then the result is NaN.
- If both arguments are integers, then the result is exactly equal
to the mathematical result of raising the first argument to the power
of the second argument if that result can in fact be represented
exactly as a
doublevalue.
(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.)
-
randomtop
public static double random()Returns adoublevalue with a positive sign, greater than or equal to0.0and less than1.0. 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
This new pseudorandom-number generator is used thereafter for all calls to this method and is used nowhere else.new java.util.Random
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.
-
rinttop
public static double rint(double a)Returns thedoublevalue that is closest in value to the argument and is equal to a mathematical integer. If twodoublevalues that are mathematical integers are equally close to the value of the argument, the result is the integer value that is even. Special cases:- If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
- If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
-
roundtop
public static long round(double a)Returns the closestlongto the argument. The result is rounded to an integer by adding 1/2, taking the floor of the result, and casting the result to typelong. In other words, the result is equal to the value of the expression:(long)Math.floor(a + 0.5d)
Special cases:
- If the argument is NaN, the result is 0.
- If the argument is negative infinity or any value less than or
equal to the value of
Long.MIN_VALUE, the result is equal to the value ofLong.MIN_VALUE. - If the argument is positive infinity or any value greater than or
equal to the value of
Long.MAX_VALUE, the result is equal to the value ofLong.MAX_VALUE.
-
roundtop
public static int round(float a)Returns the closestintto the argument. The result is rounded to an integer by adding 1/2, taking the floor of the result, and casting the result to typeint. In other words, the result is equal to the value of the expression:(int)Math.floor(a + 0.5f)
Special cases:
- If the argument is NaN, the result is 0.
- If the argument is negative infinity or any value less than or
equal to the value of
Integer.MIN_VALUE, the result is equal to the value ofInteger.MIN_VALUE. - If the argument is positive infinity or any value greater than or
equal to the value of
Integer.MAX_VALUE, the result is equal to the value ofInteger.MAX_VALUE.
-
signumtop
public static double signum(double d)Returns the signum function of the argument; zero if the argument is zero, 1.0 if the argument is greater than zero, -1.0 if the argument is less than zero.Special Cases:
- If the argument is NaN, then the result is NaN.
- If the argument is positive zero or negative zero, then the result is the same as the argument.
-
signumtop
public static float signum(float f)Returns the signum function of the argument; zero if the argument is zero, 1.0f if the argument is greater than zero, -1.0f if the argument is less than zero.Special Cases:
- If the argument is NaN, then the result is NaN.
- If the argument is positive zero or negative zero, then the result is the same as the argument.
-
sintop
public static native double sin(double a)Returns the trigonometric sine of an angle. Special cases:- If the argument is NaN or an infinity, then the result is NaN.
- If the argument is zero, then the result is a zero with the same sign as the argument.
-
sinhtop
public static native double sinh(double x)Returns the hyperbolic sine of adoublevalue. The hyperbolic sine of x is defined to be (ex - e-x)/2 where e is Euler's number.Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is an infinity with the same sign as the argument.
- If the argument is zero, then the result is a zero with the same sign as the argument.
-
sqrttop
public static native double sqrt(double a)Returns the correctly rounded positive square root of adoublevalue. Special cases:- If the argument is NaN or less than zero, then the result is NaN.
- If the argument is positive infinity, then the result is positive infinity.
- If the argument is positive zero or negative zero, then the result is the same as the argument.
doublevalue closest to the true mathematical square root of the argument value. -
tantop
public static native double tan(double a)Returns the trigonometric tangent of an angle. Special cases:- If the argument is NaN or an infinity, then the result is NaN.
- If the argument is zero, then the result is a zero with the same sign as the argument.
-
tanhtop
public static native double tanh(double x)Returns the hyperbolic tangent of adoublevalue. The hyperbolic tangent of x is defined to be (ex - e-x)/(ex + e-x), in other words, sinh(x)/cosh(x). Note that the absolute value of the exact tanh is always less than 1.Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is zero, then the result is a zero with the same sign as the argument.
- If the argument is positive infinity, then the result is
+1.0. - If the argument is negative infinity, then the result is
-1.0.
-
toDegreestop
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 expectcos(toRadians(90.0))to exactly equal0.0. -
toRadianstop
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. -
ulptop
public static double ulp(double d)Returns the size of an ulp of the argument. An ulp of adoublevalue is the positive distance between this floating-point value and thedoublevalue next larger in magnitude. Note that for non-NaN x,ulp(-x) == ulp(x).Special Cases:
- If the argument is NaN, then the result is NaN.
- If the argument is positive or negative infinity, then the result is positive infinity.
- If the argument is positive or negative zero, then the result is
Double.MIN_VALUE. - If the argument is ±
Double.MAX_VALUE, then the result is equal to 2971.
-
ulptop
public static float ulp(float f)Returns the size of an ulp of the argument. An ulp of afloatvalue is the positive distance between this floating-point value and thefloatvalue next larger in magnitude. Note that for non-NaN x,ulp(-x) == ulp(x).Special Cases:
- If the argument is NaN, then the result is NaN.
- If the argument is positive or negative infinity, then the result is positive infinity.
- If the argument is positive or negative zero, then the result is
Float.MIN_VALUE. - If the argument is ±
Float.MAX_VALUE, then the result is equal to 2104.
Fields
-
E
public static final double E = 2.718281828459045Thedoublevalue that is closer than any other to e, the base of the natural logarithms. -
PI
public static final double PI = 3.141592653589793Thedoublevalue that is closer than any other to pi, the ratio of the circumference of a circle to its diameter.
