Math  |  API reference  |  Android Developers (original) (raw)

public final class Math
extends [Object](/reference/java/lang/Object) ``

The class Math contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.

Unlike some of the numeric methods of class[StrictMath](/reference/java/lang/StrictMath), all implementations of the equivalent functions of class Math are not defined to return the bit-for-bit same results. This relaxation permits better-performing implementations where strict reproducibility is not required.

By default many of the Math methods simply call the equivalent method in StrictMath for their implementation. Code generators are encouraged to use platform-specific native libraries or microprocessor instructions, where available, to provide higher-performance implementations 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-point Math methods is measured in terms of ulps,"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 the Math class, a larger error bound of 1 or 2 ulps is allowed for certain methods. Informally, with a 1 ulp error bound, when the exact result is a representable number, the exact result should be returned as the computed result; otherwise, either of the two floating-point values which bracket the exact result may be returned. For exact results large in magnitude, one of the endpoints of the bracket may be infinite. Besides accuracy at individual arguments, maintaining proper relations between the method at different arguments is also important. Therefore, most methods with more than 0.5 ulp errors are required to be "semi-monotonic": whenever the mathematical function is non-decreasing, so is the floating-point approximation, likewise, whenever the mathematical function is non-increasing, so is the floating-point approximation. Not all approximations that have 1 ulp accuracy will automatically meet the monotonicity requirements.

The platform uses signed two's complement integer arithmetic withint 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.

IEEE 754 Recommended Operations

The 2019 revision of the IEEE 754 floating-point standard includes a section of recommended operations and the semantics of those operations if they are included in a programming environment. The recommended operations present in this class include [sin](/reference/java/lang/Math#sin%28double%29), [cos](/reference/java/lang/Math#cos%28double%29), [tan](/reference/java/lang/Math#tan%28double%29), [asin](/reference/java/lang/Math#asin%28double%29), [acos](/reference/java/lang/Math#acos%28double%29), [atan](/reference/java/lang/Math#atan%28double%29), [exp](/reference/java/lang/Math#exp%28double%29), [expm1](/reference/java/lang/Math#expm1%28double%29), [log](/reference/java/lang/Math#log%28double%29), [log10](/reference/java/lang/Math#log10%28double%29), [log1p](/reference/java/lang/Math#log1p%28double%29),[sinh](/reference/java/lang/Math#sinh%28double%29), [cosh](/reference/java/lang/Math#cosh%28double%29), [tanh](/reference/java/lang/Math#tanh%28double%29), [hypot](/reference/java/lang/Math#hypot%28double,%20double%29), and [pow](/reference/java/lang/Math#pow%28double,%20double%29). (The [sqrt](/reference/java/lang/Math#sqrt%28double%29) operation is a required part of IEEE 754 from a different section of the standard.) The special case behavior of the recommended operations generally follows the guidance of the IEEE 754 standard. However, the pow method defines different behavior for some arguments, as noted in its specification. The IEEE 754 standard defines its operations to be correctly rounded, which is a more stringent quality of implementation condition than required for most of the methods in question that are also included in this class.

Summary

Constants

E

public static final double E

The double value that is closer than any other to_e_, the base of the natural logarithms.

Constant Value: 2.718281828459045

PI

public 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.

Constant Value: 3.141592653589793

TAU

public 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.

Constant Value: 6.283185307179586

Public methods

IEEEremainder

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 tof1 - 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:

• 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.

abs

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](/reference/java/lang/Long#MIN%5FVALUE), the most negative representable long value, the result is that same value, which is negative. In contrast, the [Math.absExact(long)](/reference/java/lang/Math#absExact%28long%29) method throws anArithmeticException for this value.

abs

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](/reference/java/lang/Integer#MIN%5FVALUE), the most negative representable int value, the result is that same value, which is negative. In contrast, the [Math.absExact(int)](/reference/java/lang/Math#absExact%28int%29) method throws anArithmeticException for this value.

abs

public 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:

• 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.

API Note:

• As implied by the above, one valid implementation of this method is given by the expression below which computes adouble 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)

abs

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:

• 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.

API Note:

• As implied by the above, one valid implementation of this method is given by the expression below which computes afloat 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))

absExact

public static long absExact (long a)

Returns the mathematical absolute value of an long value if it is exactly representable as an long, throwingArithmeticException if the result overflows the positive long range.

Since the range of two's complement integers is asymmetric with one additional negative value (JLS {@jls 4.2.1}), the mathematical absolute value of [Long.MIN_VALUE](/reference/java/lang/Long#MIN%5FVALUE) overflows the positive long range, so an exception is thrown for that argument.

absExact

public static int absExact (int a)

Returns the mathematical absolute value of an int value if it is exactly representable as an int, throwingArithmeticException if the result overflows the positive int range.

Since the range of two's complement integers is asymmetric with one additional negative value (JLS {@jls 4.2.1}), the mathematical absolute value of [Integer.MIN_VALUE](/reference/java/lang/Integer#MIN%5FVALUE) overflows the positive int range, so an exception is thrown for that argument.

acos

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:

• If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
• If the argument is 1.0, the result is positive zero.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

addExact

public static int addExact (int x, int y)

Returns the sum of its arguments, throwing an exception if the result overflows an int.

addExact

public static long addExact (long x, long y)

Returns the sum of its arguments, throwing an exception if the result overflows a long.

asin

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:

• 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.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

atan

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:

• 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 infinite, then the result is the closest value to pi/2 with the same sign as the input.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

atan2

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:

• 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 thedouble value 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 thedouble value 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 thedouble value 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 thedouble value closest to -pi/2.
• If both arguments are positive infinity, then the result is thedouble value closest to pi/4.
• If the first argument is positive infinity and the second argument is negative infinity, then the result is the double value closest to 3*pi/4.
• If the first argument is negative infinity and the second argument is positive infinity, then the result is the double value closest to -pi/4.
• If both arguments are negative infinity, then the result is thedouble value closest to -3*pi/4.

The computed result must be within 2 ulps of the exact result. Results must be semi-monotonic.

API Note:

• For y with a positive sign and finite nonzero_x_, the exact mathematical value of atan2 is equal to:
  • If x > 0, atan(abs(y/x))
  • If x < 0, π - atan(abs(y/x))

cbrt

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:

• 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.

The computed result must be within 1 ulp of the exact result.

ceil

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:

• 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.

Note that the value of Math.ceil(x) is exactly the value of -Math.floor(-x).

API Note:

• This method corresponds to the roundToIntegralTowardPositive operation defined in IEEE 754.

ceilDiv

public static long ceilDiv (long x, int y)

Returns the smallest (closest to negative infinity)long value that is greater than or equal to the algebraic quotient. There is one special case: if the dividend isLong.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Long.MIN_VALUE.

Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward positive infinity (ceiling) rounding mode. The ceiling rounding mode gives different results from truncation when the exact result is not an integer and is positive.

For examples, see [ceilDiv(int, int)](/reference/java/lang/Math#ceilDiv%28int,%20int%29).

ceilDiv

public static long ceilDiv (long x, long y)

Returns the smallest (closest to negative infinity)long value that is greater than or equal to the algebraic quotient. There is one special case: if the dividend isLong.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Long.MIN_VALUE.

Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward positive infinity (ceiling) rounding mode. The ceiling rounding mode gives different results from truncation when the exact result is not an integer and is positive.

For examples, see [ceilDiv(int, int)](/reference/java/lang/Math#ceilDiv%28int,%20int%29).

ceilDiv

public static int ceilDiv (int x, int y)

Returns the smallest (closest to negative infinity)int value that is greater than or equal to the algebraic quotient. There is one special case: if the dividend isInteger.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Integer.MIN_VALUE.

Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward positive infinity (ceiling) rounding mode. The ceiling rounding mode gives different results from truncation when the exact quotient is not an integer and is positive.

• If the signs of the arguments are different, the results ofceilDiv and the / operator are the same.
  For example, ceilDiv(-4, 3) == -1 and (-4 / 3) == -1.
• If the signs of the arguments are the same, ceilDiv returns the smallest integer greater than or equal to the quotient while the / operator returns the largest integer less than or equal to the quotient. They differ if and only if the quotient is not an integer.
  For example, ceilDiv(4, 3) == 2, whereas (4 / 3) == 1.

ceilDivExact

public static long ceilDivExact (long x, long y)

Returns the smallest (closest to negative infinity)long value that is greater than or equal to the algebraic quotient. This method is identical to [ceilDiv(long, long)](/reference/java/lang/Math#ceilDiv%28long,%20long%29) except that it throws an ArithmeticException when the dividend isLong.MIN_VALUE and the divisor is-1 instead of ignoring the integer overflow and returningLong.MIN_VALUE.

The ceil modulus method [ceilMod(long, long)](/reference/java/lang/Math#ceilMod%28long,%20long%29) is a suitable counterpart both for this method and for the [ceilDiv(long, long)](/reference/java/lang/Math#ceilDiv%28long,%20long%29) method.

For examples, see [ceilDiv(int, int)](/reference/java/lang/Math#ceilDiv%28int,%20int%29).

ceilDivExact

public static int ceilDivExact (int x, int y)

Returns the smallest (closest to negative infinity)int value that is greater than or equal to the algebraic quotient. This method is identical to [ceilDiv(int, int)](/reference/java/lang/Math#ceilDiv%28int,%20int%29) except that it throws an ArithmeticException when the dividend isInteger.MIN_VALUE and the divisor is-1 instead of ignoring the integer overflow and returningInteger.MIN_VALUE.

The ceil modulus method [ceilMod(int, int)](/reference/java/lang/Math#ceilMod%28int,%20int%29) is a suitable counterpart both for this method and for the [ceilDiv(int, int)](/reference/java/lang/Math#ceilDiv%28int,%20int%29) method.

For examples, see [ceilDiv(int, int)](/reference/java/lang/Math#ceilDiv%28int,%20int%29).

ceilMod

public static long ceilMod (long x, long y)

Returns the ceiling modulus of the 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

For examples, see [ceilMod(int, int)](/reference/java/lang/Math#ceilMod%28int,%20int%29).

ceilMod

public static int ceilMod (int x, int y)

Returns the ceiling modulus of the 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

The difference in values between ceilMod and the % operator is due to the difference between ceilDiv and the / operator, as detailed in ceilDiv(int, int).

Examples:

• Regardless of the signs of the arguments, ceilMod(x, y) is zero exactly when x % y is zero as well.
• If neither ceilMod(x, y) nor x % y is zero, they differ exactly when the signs of the arguments are the same.
  • ceilMod(+4, +3) == -2; and (+4 % +3) == +1
  • ceilMod(-4, -3) == +2; and (-4 % -3) == -1
  • ceilMod(+4, -3) == +1; and (+4 % -3) == +1
  • ceilMod(-4, +3) == -1; and (-4 % +3) == -1

ceilMod

public static int ceilMod (long x, int y)

Returns the ceiling modulus of the 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

For examples, see [ceilMod(int, int)](/reference/java/lang/Math#ceilMod%28int,%20int%29).

clamp

public static double clamp (double value, double min, double max)

Clamps the value to fit between min and max. If the value is less than 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.

clamp

public static float clamp (float value, float min, float max)

Clamps the value to fit between min and max. If the value is less than 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.

clamp

public static int clamp (long value, int min, int max)

Clamps the value to fit between min and max. If the value is less than 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.

clamp

public static long clamp (long value, long min, long max)

Clamps the value to fit between min and max. If the value is less than min, then min is returned. If the value is greater than max, then max is returned. Otherwise, the original value is returned.

copySign

public static float copySign (float magnitude, float sign)

Returns the first floating-point argument with the sign of the second floating-point argument. Note that unlike the [StrictMath.copySign](/reference/java/lang/StrictMath#copySign%28float,%20float%29) method, this method does not require NaN sign arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.

API Note:

• This method corresponds to the copySign operation defined in IEEE 754.

copySign

public static double copySign (double magnitude, double sign)

Returns the first floating-point argument with the sign of the second floating-point argument. Note that unlike the [StrictMath.copySign](/reference/java/lang/StrictMath#copySign%28double,%20double%29) method, this method does not require NaN sign arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.

API Note:

• This method corresponds to the copySign operation defined in IEEE 754.

cos

public static 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.
• If the argument is zero, then the result is 1.0.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

cosh

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:

• 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.

The computed result must be within 2.5 ulps of the exact result.

decrementExact

public static int decrementExact (int a)

Returns the argument decremented by one, throwing an exception if the result overflows an int. The overflow only occurs for the minimum value.

decrementExact

public static long decrementExact (long a)

Returns the argument decremented by one, throwing an exception if the result overflows a long. The overflow only occurs for the minimum value.

divideExact

public static long divideExact (long x, long y)

Returns the quotient of the arguments, throwing an exception if the result overflows a long. Such overflow occurs in this method ifx is [Long.MIN_VALUE](/reference/java/lang/Long#MIN%5FVALUE) 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 {@jls 15.17.2}).

The built-in remainder operator "%" is a suitable counterpart both for this method and for the built-in division operator "/".

divideExact

public static int divideExact (int x, int y)

Returns the quotient of the arguments, throwing an exception if the result overflows an int. Such overflow occurs in this method ifx is [Integer.MIN_VALUE](/reference/java/lang/Integer#MIN%5FVALUE) 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 {@jls 15.17.2}).

The built-in remainder operator "%" is a suitable counterpart both for this method and for the built-in division operator "/".

exp

public static double exp (double a)

Returns Euler's number e raised to the power of adouble value. 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.
• If the argument is zero, then the result is 1.0.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

expm1

public static double expm1 (double x)

Returns e_x −1. Note that for values of_x near 0, the exact sum ofexpm1(x) + 1 is much closer to the true result of _e_x than exp(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.

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 of_e_x - 1 is within 1/2 ulp of the limit value -1, -1.0 should be returned.

floor

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:

• 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.

API Note:

• This method corresponds to the roundToIntegralTowardNegative operation defined in IEEE 754.

floorDiv

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 isInteger.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Integer.MIN_VALUE.

Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results from truncation when the exact quotient is not an integer and is negative.

• If the signs of the arguments are the same, the results offloorDiv and the / operator are the same.
  For example, floorDiv(4, 3) == 1 and (4 / 3) == 1.
• If the signs of the arguments are different, floorDiv returns the largest integer less than or equal to the quotient while the / operator returns the smallest integer greater than or equal to the quotient. They differ if and only if the quotient is not an integer.
  For example, floorDiv(-4, 3) == -2, whereas (-4 / 3) == -1.

floorDiv

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 isLong.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Long.MIN_VALUE.

Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results from truncation when the exact result is not an integer and is negative.

For examples, see [floorDiv(int, int)](/reference/java/lang/Math#floorDiv%28int,%20int%29).

floorDiv

public static long floorDiv (long x, int 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 isLong.MIN_VALUE and the divisor is -1, then integer overflow occurs and the result is equal to Long.MIN_VALUE.

Normal integer division operates under the round to zero rounding mode (truncation). This operation instead acts under the round toward negative infinity (floor) rounding mode. The floor rounding mode gives different results from truncation when the exact result is not an integer and is negative.

For examples, see [floorDiv(int, int)](/reference/java/lang/Math#floorDiv%28int,%20int%29).

floorDivExact

public static long floorDivExact (long x, long y)

Returns the largest (closest to positive infinity)long value that is less than or equal to the algebraic quotient. This method is identical to [floorDiv(long, long)](/reference/java/lang/Math#floorDiv%28long,%20long%29) except that it throws an ArithmeticException when the dividend isLong.MIN_VALUE and the divisor is-1 instead of ignoring the integer overflow and returningLong.MIN_VALUE.

The floor modulus method [floorMod(long, long)](/reference/java/lang/Math#floorMod%28long,%20long%29) is a suitable counterpart both for this method and for the [floorDiv(long, long)](/reference/java/lang/Math#floorDiv%28long,%20long%29) method.

For examples, see [floorDiv(int, int)](/reference/java/lang/Math#floorDiv%28int,%20int%29).

floorDivExact

public static int floorDivExact (int x, int y)

Returns the largest (closest to positive infinity)int value that is less than or equal to the algebraic quotient. This method is identical to [floorDiv(int, int)](/reference/java/lang/Math#floorDiv%28int,%20int%29) except that it throws an ArithmeticException when the dividend isInteger.MIN_VALUE and the divisor is-1 instead of ignoring the integer overflow and returningInteger.MIN_VALUE.

The floor modulus method [floorMod(int, int)](/reference/java/lang/Math#floorMod%28int,%20int%29) is a suitable counterpart both for this method and for the [floorDiv(int, int)](/reference/java/lang/Math#floorDiv%28int,%20int%29) method.

For examples, see [floorDiv(int, int)](/reference/java/lang/Math#floorDiv%28int,%20int%29).

floorMod

public static long floorMod (long x, long y)

Returns the floor modulus of the 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

For examples, see [floorMod(int, int)](/reference/java/lang/Math#floorMod%28int,%20int%29).

floorMod

public static int floorMod (int x, int y)

Returns the floor modulus of the 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

The difference in values between floorMod and the % operator is due to the difference between floorDiv and the / operator, as detailed in floorDiv(int, int).

Examples:

• Regardless of the signs of the arguments, floorMod(x, y) is zero exactly when x % y is zero as well.
• If neither floorMod(x, y) nor x % y is zero, they differ exactly when the signs of the arguments differ.
  • floorMod(+4, +3) == +1; and (+4 % +3) == +1
  • floorMod(-4, -3) == -1; and (-4 % -3) == -1
  • floorMod(+4, -3) == -2; and (+4 % -3) == +1
  • floorMod(-4, +3) == +2; and (-4 % +3) == -1

floorMod

public static int floorMod (long x, int y)

Returns the floor modulus of the 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

For examples, see [floorMod(int, int)](/reference/java/lang/Math#floorMod%28int,%20int%29).

fma

public static double fma (double a, double b, double c)

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 nearestdouble. 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:

• If any argument is NaN, the result is NaN.
• If one of the first two arguments is infinite and the other is zero, the result is NaN.
• If the exact product of the first two arguments is infinite (in other words, at least one of the arguments is infinite and the other is neither zero nor NaN) and the third argument is an infinity of the opposite sign, the result is NaN.

Note that fma(a, 1.0, c) returns the same result as (a + c). However,fma(a, b, +0.0) does not always return the same result as (a * b) sincefma(-0.0, +0.0, +0.0) is +0.0 while (-0.0 * +0.0) is -0.0; fma(a, b, -0.0) is equivalent to (a * b) however.

API Note:

• This method corresponds to the fusedMultiplyAdd operation defined in IEEE 754.

fma

public static float fma (float a, float b, float c)

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 nearestfloat. 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:

• If any argument is NaN, the result is NaN.
• If one of the first two arguments is infinite and the other is zero, the result is NaN.
• If the exact product of the first two arguments is infinite (in other words, at least one of the arguments is infinite and the other is neither zero nor NaN) and the third argument is an infinity of the opposite sign, the result is NaN.

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) sincefma(-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.

API Note:

• This method corresponds to the fusedMultiplyAdd operation defined in IEEE 754.

getExponent

public static int getExponent (double d)

Returns the unbiased exponent used in the representation of adouble. Special cases:

• If the argument is NaN or infinite, then the result is[Double.MAX_EXPONENT](/reference/java/lang/Double#MAX%5FEXPONENT) + 1.
• If the argument is zero or subnormal, then the result is[Double.MIN_EXPONENT](/reference/java/lang/Double#MIN%5FEXPONENT) - 1.

API Note:

• This method is analogous to the logB operation defined in IEEE 754, but returns a different value on subnormal arguments.

getExponent

public static int getExponent (float f)

Returns the unbiased exponent used in the representation of afloat. Special cases:

• If the argument is NaN or infinite, then the result is[Float.MAX_EXPONENT](/reference/java/lang/Float#MAX%5FEXPONENT) + 1.
• If the argument is zero or subnormal, then the result is[Float.MIN_EXPONENT](/reference/java/lang/Float#MIN%5FEXPONENT) - 1.

API Note:

• This method is analogous to the logB operation defined in IEEE 754, but returns a different value on subnormal arguments.

hypot

public static double hypot (double x, double y)

Returns sqrt(_x_2 +_y_2) 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.
• If both arguments are zero, the result is positive zero.

The computed result must be within 1.5 ulps of the exact result. If one parameter is held constant, the results must be semi-monotonic in the other parameter.

incrementExact

public static int incrementExact (int a)

Returns the argument incremented by one, throwing an exception if the result overflows an int. The overflow only occurs for the maximum value.

incrementExact

public static long incrementExact (long a)

Returns the argument incremented by one, throwing an exception if the result overflows a long. The overflow only occurs for the maximum value.

log

public static double log (double a)

Returns the natural logarithm (base e) of a double value. 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 1.0, then the result is positive zero.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

log10

public static double log10 (double a)

Returns the base 10 logarithm of a double value. 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 10_n_ for integer n, then the result is n. In particular, if the argument is 1.0 (100), then the result is positive zero.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

log1p

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 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.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

max

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](/reference/java/lang/Long#MAX%5FVALUE). If the arguments have the same value, the result is that same value.

max

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.

API Note:

• This method corresponds to the maximum operation defined in IEEE 754.

max

public 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](/reference/java/lang/Integer#MAX%5FVALUE). If the arguments have the same value, the result is that same value.

max

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.

API Note:

• This method corresponds to the maximum operation defined in IEEE 754.

min

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.

API Note:

• This method corresponds to the minimum operation defined in IEEE 754.

min

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](/reference/java/lang/Integer#MIN%5FVALUE). If the arguments have the same value, the result is that same value.

min

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](/reference/java/lang/Long#MIN%5FVALUE). If the arguments have the same value, the result is that same value.

min

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.

API Note:

• This method corresponds to the minimum operation defined in IEEE 754.

multiplyExact

public static int multiplyExact (int x, int y)

Returns the product of the arguments, throwing an exception if the result overflows an int.

multiplyExact

public static long multiplyExact (long x, long y)

Returns the product of the arguments, throwing an exception if the result overflows a long.

multiplyExact

public static long multiplyExact (long x, int y)

Returns the product of the arguments, throwing an exception if the result overflows a long.

multiplyFull

public static long multiplyFull (int x, int y)

Returns the exact mathematical product of the arguments.

multiplyHigh

public static long multiplyHigh (long x, long y)

Returns as a long the most significant 64 bits of the 128-bit product of two 64-bit factors.

negateExact

public static int negateExact (int a)

Returns the negation of the argument, throwing an exception if the result overflows an int. The overflow only occurs for the minimum value.

negateExact

public static long negateExact (long a)

Returns the negation of the argument, throwing an exception if the result overflows a long. The overflow only occurs for the minimum value.

nextAfter

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:

• If either argument is a NaN, then NaN is returned.
• If both arguments are signed zeros, a value equivalent to direction is returned.
• If start is ±[Float.MIN_VALUE](/reference/java/lang/Float#MIN%5FVALUE) 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.
• If start is infinite anddirection has a value such that the result should have a smaller magnitude, [Float.MAX_VALUE](/reference/java/lang/Float#MAX%5FVALUE) with the same sign as start is returned.
• If start is equal to ±[Float.MAX_VALUE](/reference/java/lang/Float#MAX%5FVALUE) and direction has a value such that the result should have a larger magnitude, an infinity with same sign as start is returned.

nextAfter

public 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:

• If either argument is a NaN, then NaN is returned.
• If both arguments are signed zeros, direction is returned unchanged (as implied by the requirement of returning the second argument if the arguments compare as equal).
• If start is ±[Double.MIN_VALUE](/reference/java/lang/Double#MIN%5FVALUE) 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.
• If start is infinite anddirection has a value such that the result should have a smaller magnitude, [Double.MAX_VALUE](/reference/java/lang/Double#MAX%5FVALUE) with the same sign as start is returned.
• If start is equal to ±[Double.MAX_VALUE](/reference/java/lang/Double#MAX%5FVALUE) and direction has a value such that the result should have a larger magnitude, an infinity with same sign as start is returned.

nextDown

public 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, anextDown implementation may run faster than its equivalent nextAfter call.

Special Cases:

• If the argument is NaN, the result is NaN.
• If the argument is negative infinity, the result is negative infinity.
• If the argument is zero, the result is-Double.MIN_VALUE

API Note:

• This method corresponds to the nextDown operation defined in IEEE 754.

nextDown

public 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, anextDown implementation may run faster than its equivalent nextAfter call.

Special Cases:

• If the argument is NaN, the result is NaN.
• If the argument is negative infinity, the result is negative infinity.
• If the argument is zero, the result is-Float.MIN_VALUE

API Note:

• This method corresponds to the nextDown operation defined in IEEE 754.

nextUp

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 equivalentnextAfter call.

Special Cases:

• If the argument is NaN, the result is NaN.
• If the argument is positive infinity, the result is positive infinity.
• If the argument is zero, the result is[Double.MIN_VALUE](/reference/java/lang/Double#MIN%5FVALUE)

API Note:

• This method corresponds to the nextUp operation defined in IEEE 754.

nextUp

public 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 equivalentnextAfter call.

Special Cases:

• If the argument is NaN, the result is NaN.
• If the argument is positive infinity, the result is positive infinity.
• If the argument is zero, the result is[Float.MIN_VALUE](/reference/java/lang/Float#MIN%5FVALUE)

API Note:

• This method corresponds to the nextUp operation defined in IEEE 754.

pow

public static 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 first argument is 1.0, then the result is 1.0.
• If the second argument is NaN, then the result is NaN except where the first argument is 1.0.
• 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,
    then the result is positive 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,
    then the result is positive zero.
• If the absolute value of the first argument equals 1 and the second argument is infinite, then the result is 1.0.
• 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,
    then the result is positive 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,
    then the result is positive infinity.
• 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,
    then the result is positive zero.
• 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,
    then the result is negative zero.
• 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,
    then the result is positive infinity.
• 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,
    then the result is negative infinity.
• 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 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](/reference/java/lang/Math#ceil%28double%29) or, equivalently, a fixed point of the method [floor](/reference/java/lang/Math#floor%28double%29). 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.

API Note:

• The special cases definitions of this method differ from the special case definitions of the IEEE 754 recommended 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.

powExact

public static long powExact (long x, int n)

Returns x raised to the power of n, throwing an exception if the result overflows a long. When n is 0, the returned value is 1.

powExact

public static int powExact (int x, int n)

Returns x raised to the power of n, throwing an exception if the result overflows an int. When n is 0, the returned value is 1.

random

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.

API Note:

• As the largest double value less than 1.0 is Math.nextDown(1.0), a value x in the closed range[x1,x2] where x1<=x2 may be defined by the statements

  ```

double f = Math.random()/Math.nextDown(1.0);
double x = x1*(1.0 - f) + x2*f;

rint

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 twodouble values that are mathematical integers are equally close, 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.

API Note:

• This method corresponds to the roundToIntegralTiesToEven operation defined in IEEE 754.

round

public static int round (float a)

Returns the closest int to the argument, with ties rounding to positive infinity.

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 of Integer.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 of Integer.MAX_VALUE.

round

public static long round (double a)

Returns the closest long to the argument, with ties rounding to positive infinity.

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 of Long.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 of Long.MAX_VALUE.

scalb

public static float scalb (float f, int scaleFactor)

Returns 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](/reference/java/lang/Float#MIN%5FEXPONENT) and [Float.MAX_EXPONENT](/reference/java/lang/Float#MAX%5FEXPONENT), 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, whenscalb(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:

• If the first argument is NaN, NaN is returned.
• If the first argument is infinite, then an infinity of the same sign is returned.
• If the first argument is zero, then a zero of the same sign is returned.

API Note:

• This method corresponds to the scaleB operation defined in IEEE 754.

scalb

public static double scalb (double d, int scaleFactor)

Returns 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](/reference/java/lang/Double#MIN%5FEXPONENT) and [Double.MAX_EXPONENT](/reference/java/lang/Double#MAX%5FEXPONENT), 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, whenscalb(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:

• If the first argument is NaN, NaN is returned.
• If the first argument is infinite, then an infinity of the same sign is returned.
• If the first argument is zero, then a zero of the same sign is returned.

API Note:

• This method corresponds to the scaleB operation defined in IEEE 754.

signum

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.

signum

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.

sin

public static 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.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

sinh

public 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:

• 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.

The computed result must be within 2.5 ulps of the exact result.

sqrt

public static double sqrt (double a)

Returns the correctly rounded positive square root of adouble value. 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.

Otherwise, the result is the double value closest to the true mathematical square root of the argument value.

API Note:

• This method corresponds to the squareRoot operation defined in IEEE 754.

subtractExact

public static int subtractExact (int x, int y)

Returns the difference of the arguments, throwing an exception if the result overflows an int.

subtractExact

public static long subtractExact (long x, long y)

Returns the difference of the arguments, throwing an exception if the result overflows a long.

tan

public static 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.

The computed result must be within 1.25 ulps of the exact result. Results must be semi-monotonic.

tanh

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:

• 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.

The computed result must be within 2.5 ulps of the exact result. The result of tanh for any finite input must have an absolute value less than or equal to 1. Note that once the exact result of tanh is within 1/2 of an ulp of the limit value of ±1, correctly signed ±1.0 should be returned.

toDegrees

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.

toIntExact

public static int toIntExact (long value)

Returns the value of the long argument, throwing an exception if the value overflows an int.

toRadians

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.

ulp

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:

• 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 isDouble.MIN_VALUE.
• If the argument is ±Double.MAX_VALUE, then the result is equal to 2971.

ulp

public 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:

• 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 isFloat.MIN_VALUE.
• If the argument is ±Float.MAX_VALUE, then the result is equal to 2104.

unsignedMultiplyExact

public static int unsignedMultiplyExact (int x, int y)

Returns the product of the unsigned arguments, throwing an exception if the result overflows an unsigned int.

unsignedMultiplyExact

public static long unsignedMultiplyExact (long x, long y)

Returns the product of the unsigned arguments, throwing an exception if the result overflows an unsigned long.

unsignedMultiplyExact

public static long unsignedMultiplyExact (long x, int y)

Returns the product of the unsigned arguments, throwing an exception if the result overflows an unsigned long.

unsignedMultiplyHigh

public static long unsignedMultiplyHigh (long x, long y)

Returns as a long the most significant 64 bits of the unsigned 128-bit product of two unsigned 64-bit factors.

unsignedPowExact

public static int unsignedPowExact (int x, int n)

Returns unsigned x raised to the power of n, throwing an exception if the result overflows an unsigned int. When n is 0, the returned value is 1.

unsignedPowExact

public static long unsignedPowExact (long x, int n)

Returns unsigned x raised to the power of n, throwing an exception if the result overflows an unsigned long. When n is 0, the returned value is 1.