public final classMathextendsObject
Math contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.Unlike some of the numeric methods of classStrictMath, all implementations of the equivalent functions of classMath are not defined to return the bit-for-bit same results. This relaxation permits better-performing implementations where strict reproducibility is not required.
By default many of theMath methods simply call the equivalent method inStrictMath for their implementation. Code generators are encouraged to use platform-specific native libraries or microprocessor instructions, where available, to provide higher-performance implementations ofMath methods. Such higher-performance implementations still must conform to the specification forMath.
The quality of implementation specifications concern two properties, accuracy of the returned result and monotonicity of the method. Accuracy of the floating-pointMath methods is measured in terms ofulps, units in the last place. For a given floating-point format, anulp of a specific real number value is the distance between the two floating-point values bracketing that numerical value. When discussing the accuracy of a method as a whole rather than at a specific argument, the number of ulps cited is for the worst-case error at any argument. If a method always has an error less than 0.5 ulps, the method always returns the floating-point number nearest the exact result; such a method iscorrectly rounded. A correctly rounded method is generally the best a floating-point approximation can be; however, it is impractical for many floating-point methods to be correctly rounded. Instead, for theMath class, a larger error bound of 1 or 2 ulps is allowed for certain methods. Informally, with a 1 ulp error bound, when the exact result is a representable number, the exact result should be returned as the computed result; otherwise, either of the two floating-point values which bracket the exact result may be returned. For exact results large in magnitude, one of the endpoints of the bracket may be infinite. Besides accuracy at individual arguments, maintaining proper relations between the method at different arguments is also important. Therefore, most methods with more than 0.5 ulp errors are required to besemi-monotonic: whenever the mathematical function is non-decreasing, so is the floating-point approximation, likewise, whenever the mathematical function is non-increasing, so is the floating-point approximation. Not all approximations that have 1 ulp accuracy will automatically meet the monotonicity requirements.
The platform uses signed two's complement integer arithmetic with int and long primitive types. The developer should choose the primitive type to ensure that arithmetic operations consistently produce correct results, which in some cases means the operations will not overflow the range of values of the computation. The best practice is to choose the primitive type and algorithm to avoid overflow. In cases where the size isint orlong and overflow errors need to be detected, the methodsaddExact,subtractExact,multiplyExact, andtoIntExact throw anArithmeticException when the results overflow. For other arithmetic operations such as divide, absolute value, increment, decrement, and negation overflow occurs only with a specific minimum or maximum value and should be checked against the minimum or maximum as appropriate.
| Modifier and Type | Field | Description |
|---|---|---|
static double | E | The double value that is closer than any other toe, the base of the natural logarithms. |
static double | PI | The double value that is closer than any other topi, the ratio of the circumference of a circle to its diameter. |
| Modifier and Type | Method | Description |
|---|---|---|
static double | abs(double a) | Returns the absolute value of a double value. |
static float | abs(float a) | Returns the absolute value of a float value. |
static int | abs(int a) | Returns the absolute value of an int value. |
static long | abs(long a) | Returns the absolute value of a long value. |
static double | acos(double a) | Returns the arc cosine of a value; the returned angle is in the range 0.0 throughpi. |
static int | addExact(int x, int y) | Returns the sum of its arguments, throwing an exception if the result overflows an int. |
static long | addExact(long x, long y) | Returns the sum of its arguments, throwing an exception if the result overflows a long. |
static double | asin(double a) | Returns the arc sine of a value; the returned angle is in the range -pi/2 throughpi/2. |
static double | atan(double a) | Returns the arc tangent of a value; the returned angle is in the range -pi/2 throughpi/2. |
static double | atan2(double y, double x) | Returns the angletheta from the conversion of rectangular coordinates ( x, y) to polar coordinates (r, theta). |
static double | cbrt(double a) | Returns the cube root of a double value. |
static double | ceil(double a) | Returns the smallest (closest to negative infinity) double value that is greater than or equal to the argument and is equal to a mathematical integer. |
static double | copySign(double magnitude, double sign) | Returns the first floating-point argument with the sign of the second floating-point argument. |
static float | copySign(float magnitude, float sign) | Returns the first floating-point argument with the sign of the second floating-point argument. |
static double | cos(double a) | Returns the trigonometric cosine of an angle. |
static double | cosh(double x) | Returns the hyperbolic cosine of a double value. |
static int | decrementExact(int a) | Returns the argument decremented by one, throwing an exception if the result overflows an int. |
static long | decrementExact(long a) | Returns the argument decremented by one, throwing an exception if the result overflows a long. |
static double | exp(double a) | Returns Euler's numbere raised to the power of a double value. |
static double | expm1(double x) | Returnsex -1. |
static double | floor(double a) | Returns the largest (closest to positive infinity) double value that is less than or equal to the argument and is equal to a mathematical integer. |
static int | floorDiv(int x, int y) | Returns the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient. |
static long | floorDiv(long x, long y) | Returns the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. |
static int | floorMod(int x, int y) | Returns the floor modulus of the int arguments. |
static long | floorMod(long x, long y) | Returns the floor modulus of the long arguments. |
static int | getExponent(double d) | Returns the unbiased exponent used in the representation of a double. |
static int | getExponent(float f) | Returns the unbiased exponent used in the representation of a float. |
static double | hypot(double x, double y) | Returns sqrt(x2 +y2) without intermediate overflow or underflow. |
static double | IEEEremainder(double f1, double f2) | Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. |
static int | incrementExact(int a) | Returns the argument incremented by one, throwing an exception if the result overflows an int. |
static long | incrementExact(long a) | Returns the argument incremented by one, throwing an exception if the result overflows a long. |
static double | log(double a) | Returns the natural logarithm (basee) of a double value. |
static double | log10(double a) | Returns the base 10 logarithm of a double value. |
static double | log1p(double x) | Returns the natural logarithm of the sum of the argument and 1. |
static double | max(double a, double b) | Returns the greater of two double values. |
static float | max(float a, float b) | Returns the greater of two float values. |
static int | max(int a, int b) | Returns the greater of two int values. |
static long | max(long a, long b) | Returns the greater of two long values. |
static double | min(double a, double b) | Returns the smaller of two double values. |
static float | min(float a, float b) | Returns the smaller of two float values. |
static int | min(int a, int b) | Returns the smaller of two int values. |
static long | min(long a, long b) | Returns the smaller of two long values. |
static int | multiplyExact(int x, int y) | Returns the product of the arguments, throwing an exception if the result overflows an int. |
static long | multiplyExact(long x, long y) | Returns the product of the arguments, throwing an exception if the result overflows a long. |
static int | negateExact(int a) | Returns the negation of the argument, throwing an exception if the result overflows an int. |
static long | negateExact(long a) | Returns the negation of the argument, throwing an exception if the result overflows a long. |
static double | nextAfter(double start, double direction) | Returns the floating-point number adjacent to the first argument in the direction of the second argument. |
static float | nextAfter(float start, double direction) | Returns the floating-point number adjacent to the first argument in the direction of the second argument. |
static double | nextDown(double d) | Returns the floating-point value adjacent to d in the direction of negative infinity. |
static float | nextDown(float f) | Returns the floating-point value adjacent to f in the direction of negative infinity. |
static double | nextUp(double d) | Returns the floating-point value adjacent to d in the direction of positive infinity. |
static float | nextUp(float f) | Returns the floating-point value adjacent to f in the direction of positive infinity. |
static double | pow(double a, double b) | Returns the value of the first argument raised to the power of the second argument. |
static double | random() | Returns a double value with a positive sign, greater than or equal to0.0 and less than1.0. |
static double | rint(double a) | Returns the double value that is closest in value to the argument and is equal to a mathematical integer. |
static long | round(double a) | Returns the closest long to the argument, with ties rounding to positive infinity. |
static int | round(float a) | Returns the closest int to the argument, with ties rounding to positive infinity. |
static double | scalb(double d, int scaleFactor) | Returns d × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply to a member of the double value set. |
static float | scalb(float f, int scaleFactor) | Returns f × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply to a member of the float value set. |
static double | signum(double d) | Returns the signum function of the argument; zero if the argument is zero, 1.0 if the argument is greater than zero, -1.0 if the argument is less than zero. |
static float | signum(float f) | Returns the signum function of the argument; zero if the argument is zero, 1.0f if the argument is greater than zero, -1.0f if the argument is less than zero. |
static double | sin(double a) | Returns the trigonometric sine of an angle. |
static double | sinh(double x) | Returns the hyperbolic sine of a double value. |
static double | sqrt(double a) | Returns the correctly rounded positive square root of a double value. |
static int | subtractExact(int x, int y) | Returns the difference of the arguments, throwing an exception if the result overflows an int. |
static long | subtractExact(long x, long y) | Returns the difference of the arguments, throwing an exception if the result overflows a long. |
static double | tan(double a) | Returns the trigonometric tangent of an angle. |
static double | tanh(double x) | Returns the hyperbolic tangent of a double value. |
static double | toDegrees(double angrad) | Converts an angle measured in radians to an approximately equivalent angle measured in degrees. |
static int | toIntExact(long value) | Returns the value of the long argument; throwing an exception if the value overflows anint. |
static double | toRadians(double angdeg) | Converts an angle measured in degrees to an approximately equivalent angle measured in radians. |
static double | ulp(double d) | Returns the size of an ulp of the argument. |
static float | ulp(float f) | Returns the size of an ulp of the argument. |
public static final double E
double value that is closer than any other toe, the base of the natural logarithms.public static final double PI
double value that is closer than any other topi, the ratio of the circumference of a circle to its diameter.public static double sin(double a)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a - an angle, in radians.public static double cos(double a)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a - an angle, in radians.public static double tan(double a)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a - an angle, in radians.public static double asin(double a)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a - the value whose arc sine is to be returned.public static double acos(double a)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a - the value whose arc cosine is to be returned.public static double atan(double a)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a - the value whose arc tangent is to be returned.public static double toRadians(double angdeg)
angdeg - an angle, in degreesangdeg in radians.public static double toDegrees(double angrad)
cos(toRadians(90.0)) to exactly equal0.0.angrad - an angle, in radiansangrad in degrees.public static double exp(double a)
double value. Special cases:The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a - the exponent to raisee to.a, wheree is the base of the natural logarithms.public static double log(double a)
double value. Special cases:The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a - a valuea, the natural logarithm ofa.public static double log10(double a)
double value. Special cases:The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a - a 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. If the argument is NaN or less than zero, the result is NaN.public static double cbrt(double a)
double value. 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:The computed result must be within 1 ulp of the exact result.
a - a value.a.public static double IEEEremainder(double f1, double f2)
f1 - f2 × n, wheren is the mathematical integer closest to the exact mathematical value of the quotientf1/f2, and if two mathematical integers are equally close tof1/f2, thenn 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 byf2.public static double ceil(double a)
double value that is greater than or equal to the argument and is equal to a mathematical integer. Special cases:Math.ceil(x) is exactly the value of-Math.floor(-x).a - a value.public static double floor(double a)
double value that is less than or equal to the argument and is equal to a mathematical integer. Special cases:a - a value.public static double rint(double a)
double value that is closest in value to the argument and is equal to a mathematical integer. If twodouble values that are mathematical integers are equally close, the result is the integer value that is even. Special cases:a - adouble 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 phasetheta by computing an arc tangent ofy/x in the range of -pi topi. Special cases:double value closest topi.double value closest to -pi.double value closest topi/2.double value closest to -pi/2.double value closest topi/4.double value closest to 3*pi/4.double value closest to -pi/4.double value closest to -3*pi/4.The computed result must be within 2 ulps of the exact result. Results must be semi-monotonic.
y - the ordinate 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 methodceil or, equivalently, a fixed point of the methodfloor. A value is a fixed point of a one-argument method if and only if the result of applying the method to the value is equal to the value.)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
a - the base.b - the exponent.ab.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 ofInteger.MIN_VALUE.Integer.MAX_VALUE, the result is equal to the value ofInteger.MAX_VALUE.a - a floating-point value to be rounded to an integer.int value.Integer.MAX_VALUE,Integer.MIN_VALUEpublic 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 ofLong.MIN_VALUE.Long.MAX_VALUE, the result is equal to the value ofLong.MAX_VALUE.a - a floating-point value to be rounded to along.long value.Long.MAX_VALUE,Long.MIN_VALUEpublic static double random()
double value with a positive sign, greater than or equal to0.0 and 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
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.
double greater than or equal to0.0 and less than1.0.Random.nextDouble()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, long y)
long.x - the first valuey - the second valueArithmeticException - if the result overflows a longpublic static int incrementExact(int a)
int.a - the value to incrementArithmeticException - if the result overflows an intpublic static long incrementExact(long a)
long.a - the value to incrementArithmeticException - if the result overflows a longpublic static int decrementExact(int a)
int.a - the value to decrementArithmeticException - if the result overflows an intpublic static long decrementExact(long a)
long.a - the value to decrementArithmeticException - if the result overflows a longpublic static int negateExact(int a)
int.a - the value to negateArithmeticException - if the result overflows an intpublic static long negateExact(long a)
long.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 anint.value - the long valueArithmeticException - if theargument overflows an intpublic 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 theInteger.MIN_VALUE and the divisor is-1, then integer overflow occurs and the result is equal to theInteger.MIN_VALUE.Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results than truncation when the exact result is negative.
floorDiv and the/ operator are the same.floorDiv(4, 3) == 1 and(4 / 3) == 1.floorDiv returns the integer less than or equal to the quotient and the/ operator returns the integer closest to zero.floorDiv(-4, 3) == -2, whereas(-4 / 3) == -1.x - the dividendy - the divisorint value that is less than or equal to the algebraic quotient.ArithmeticException - if the divisory is zerofloorMod(int, int),floor(double)public static long floorDiv(long x, long y)
long value that is less than or equal to the algebraic quotient. There is one special case, if the dividend is theLong.MIN_VALUE and the divisor is-1, then integer overflow occurs and the result is equal to theLong.MIN_VALUE.Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results than truncation when the exact result is negative.
For examples, seefloorDiv(int, int).
x - the dividendy - the divisorlong value that is less than or equal to the algebraic quotient.ArithmeticException - if the divisory is zerofloorMod(long, long),floor(double)public static int floorMod(int x, int y)
int arguments. The floor modulus isx - (floorDiv(x, y) * y), has the same sign as the divisory, and is in the range of-abs(y) < r < +abs(y).
The relationship betweenfloorDiv andfloorMod is such that:
floorDiv(x, y) * y + floorMod(x, y) == x The difference in values betweenfloorMod and the% operator is due to the difference betweenfloorDiv that returns the integer less than or equal to the quotient and the/ operator that returns the integer closest to zero.
Examples:
floorMod and the% operator are the same.floorMod(4, 3) == 1; and(4 % 3) == 1% operator.floorMod(+4, -3) == -2; and(+4 % -3) == +1floorMod(-4, +3) == +2; and(-4 % +3) == -1floorMod(-4, -3) == -1; and(-4 % -3) == -1 If the signs of arguments are unknown and a positive modulus is needed it can be computed as(floorMod(x, y) + abs(y)) % abs(y).
x - the dividendy - the divisorx - (floorDiv(x, y) * y)ArithmeticException - if the divisory is zerofloorDiv(int, int)public static long floorMod(long x, long y)
long arguments. The floor modulus isx - (floorDiv(x, y) * y), has the same sign as the divisory, and is in the range of-abs(y) < r < +abs(y).
The relationship betweenfloorDiv andfloorMod is such that:
floorDiv(x, y) * y + floorMod(x, y) == x For examples, seefloorMod(int, int).
x - the dividendy - the divisorx - (floorDiv(x, y) * y)ArithmeticException - if the divisory is zerofloorDiv(long, long)public static int abs(int a)
int value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.Note that if the argument is equal to the value ofInteger.MIN_VALUE, the most negative representableint value, the result is that same value, which is negative.
a - the argument whose absolute value is to be determinedpublic 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 ofLong.MIN_VALUE, the most negative representablelong value, the result is that same value, which is negative.
a - the argument whose absolute value is to be determinedpublic static float abs(float a)
float value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))
a - the argument whose absolute value is to be 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.longBitsToDouble((Double.doubleToLongBits(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 ofInteger.MAX_VALUE. If the arguments have the same value, the result is that same value.a - an argument.b - another argument.a andb.public static long max(long a, long b)
long values. 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.a - an argument.b - another argument.a andb.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 andb.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 andb.public static int min(int a, int b)
int values. 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.a - an argument.b - another argument.a andb.public static long min(long a, long b)
long values. 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.a - an argument.b - another argument.a andb.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 andb.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 andb.public static double ulp(double d)
double value is the positive distance between this floating-point value and thedouble value next larger in magnitude. Note that for non-NaNx,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 thefloat value next larger in magnitude. Note that for non-NaNx,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 ofx is defined to be (ex - e-x)/2 wheree isEuler's number.Special cases:
The computed result must be within 2.5 ulps of the exact result.
x - The number whose hyperbolic sine is to be returned.x.public static double cosh(double x)
double value. The hyperbolic cosine ofx is defined to be (ex + e-x)/2 wheree isEuler's number.Special cases:
1.0.The computed result must be within 2.5 ulps of the exact result.
x - The number whose hyperbolic cosine is to be returned.x.public static double tanh(double x)
double value. The hyperbolic tangent ofx is defined to be (ex - e-x)/(ex + e-x), in other words,sinh(x)/cosh(x). Note that the absolute value of the exact tanh is always less than 1.Special cases:
+1.0.-1.0.The computed result must be within 2.5 ulps of the exact result. The result oftanh for any finite input must have an absolute value less than or equal to 1. Note that once the exact result of tanh is within 1/2 of an ulp of the limit value of ±1, correctly signed ±1.0 should be returned.
x - The number whose hyperbolic tangent is to be returned.x.public static double hypot(double x, double y)
Special cases:
The computed result must be within 1 ulp of the exact result. If one parameter is held constant, the results must be semi-monotonic in the other parameter.
x - a valuey - a valuepublic static double expm1(double x)
expm1(x) + 1 is much closer to the true result ofex thanexp(x).Special cases:
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic. The result ofexpm1 for any finite input must be greater than or equal to-1.0. Note that once the exact result ofex - 1 is within 1/2 ulp of the limit value -1,-1.0 should be returned.
x - the exponent to raisee to in the computation ofex -1.x - 1.public static double log1p(double x)
x, 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:
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
x - a valuex + 1), the natural log ofx + 1public static double copySign(double magnitude, double sign)
StrictMath.copySign method, this method does not require NaNsign arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.magnitude - the parameter providing the magnitude of the resultsign - the parameter providing the sign of the resultmagnitude and the sign ofsign.public static float copySign(float magnitude, float sign)
StrictMath.copySign method, this method does not require NaNsign arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.magnitude - the parameter providing the magnitude of the resultsign - the parameter providing the sign of the resultmagnitude and the sign ofsign.public static int getExponent(float f)
float. Special cases:Float.MAX_EXPONENT + 1.Float.MIN_EXPONENT -1.f - afloat valuepublic static int getExponent(double d)
double. Special cases:Double.MAX_EXPONENT + 1.Double.MIN_EXPONENT -1.d - adouble 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 anddirection has a value such that the result should have a smaller magnitude, then a zero with the same sign asstart is returned.start is infinite anddirection has a value such that the result should have a smaller magnitude,Double.MAX_VALUE with the same sign asstart is returned.start is equal to ±Double.MAX_VALUE anddirection has a value such that the result should have a larger magnitude, an infinity with same sign asstart is returned.start - starting floating-point valuedirection - value indicating which ofstart's neighbors orstart should be returnedstart in the direction ofdirection.public static float nextAfter(float start, double direction)
Special cases:
direction is returned.start is ±Float.MIN_VALUE anddirection has a value such that the result should have a smaller magnitude, then a zero with the same sign asstart is returned.start is infinite anddirection has a value such that the result should have a smaller magnitude,Float.MAX_VALUE with the same sign asstart is returned.start is equal to ±Float.MAX_VALUE anddirection has a value such that the result should have a larger magnitude, an infinity with same sign asstart is returned.start - starting floating-point valuedirection - value indicating which ofstart's neighbors orstart should be returnedstart in the direction ofdirection.public static double nextUp(double d)
d in the direction of positive infinity. This method is semantically equivalent tonextAfter(d, Double.POSITIVE_INFINITY); however, anextUp implementation may run faster than its equivalentnextAfter call.Special Cases:
Double.MIN_VALUEd - starting floating-point valuepublic static float nextUp(float f)
f in the direction of positive infinity. This method is semantically equivalent tonextAfter(f, Float.POSITIVE_INFINITY); however, anextUp implementation may run faster than its equivalentnextAfter call.Special Cases:
Float.MIN_VALUEf - starting floating-point valuepublic static double nextDown(double d)
d in the direction of negative infinity. This method is semantically equivalent tonextAfter(d, Double.NEGATIVE_INFINITY); however, anextDown implementation may run faster than its equivalentnextAfter call.Special Cases:
-Double.MIN_VALUEd - starting floating-point valuepublic static float nextDown(float f)
f in the direction of negative infinity. This method is semantically equivalent tonextAfter(f, Float.NEGATIVE_INFINITY); however, anextDown implementation may run faster than its equivalentnextAfter call.Special Cases:
-Float.MIN_VALUEf - 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 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 betweenDouble.MIN_EXPONENT andDouble.MAX_EXPONENT, the answer is calculated exactly. If the exponent of the result would be larger thanDouble.MAX_EXPONENT, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, whenscalb(x, n) is subnormal,scalb(scalb(x, n), -n) may not equalx. When the result is non-NaN, the result has the same sign asd.Special cases:
d - number to be scaled by a power of two.scaleFactor - power of 2 used to scaledd × 2scaleFactorpublic static float scalb(float f, int scaleFactor)
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 betweenFloat.MIN_EXPONENT andFloat.MAX_EXPONENT, the answer is calculated exactly. If the exponent of the result would be larger thanFloat.MAX_EXPONENT, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, whenscalb(x, n) is subnormal,scalb(scalb(x, n), -n) may not equalx. When the result is non-NaN, the result has the same sign asf.Special cases:
f - number to be scaled by a power of two.scaleFactor - power of 2 used to scaleff × 2scaleFactor