Math
class Math
kotlin.Any | |
↳ | java.lang.Math |
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
, 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 of Math
methods. Such higher-performance implementations still must conform to the specification for Math
.
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, an ulp 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 is correctly 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 with int and long primitive types. The developer should choose the primitive type to ensure that arithmetic operations consistently produce correct results, which in some cases means the operations will not overflow the range of values of the computation. The best practice is to choose the primitive type and algorithm to avoid overflow. In cases where the size is int
or long
and overflow errors need to be detected, the methods whose names end with Exact
throw an ArithmeticException
when the results overflow.
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
, cos
, tan
, asin
, acos
, atan
, exp
, expm1
, log
, log10
, log1p
, sinh
, cosh
, tanh
, hypot
, and pow
. (The sqrt
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 | |
---|---|
static Double |
The |
static Double |
The |
static Double |
The |
Public methods | |
---|---|
static Double |
IEEEremainder(f1: Double, f2: Double) Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. |
static Int |
Returns the absolute value of an |
static Long |
Returns the absolute value of a |
static Float |
Returns the absolute value of a |
static Double |
Returns the absolute value of a |
static Int |
Returns the mathematical absolute value of an |
static Long |
Returns the mathematical absolute value of an |
static Double |
Returns the arc cosine of a value; the returned angle is in the range 0. |
static Int |
Returns the sum of its arguments, throwing an exception if the result overflows an |
static Long |
Returns the sum of its arguments, throwing an exception if the result overflows a |
static Double |
Returns the arc sine of a value; the returned angle is in the range -pi/2 through pi/2. |
static Double |
Returns the arc tangent of a value; the returned angle is in the range -pi/2 through pi/2. |
static Double |
Returns the angle theta from the conversion of rectangular coordinates ( |
static Double |
Returns the cube root of a |
static Double |
Returns the smallest (closest to negative infinity) |
static Int |
Returns the smallest (closest to negative infinity) |
static Long |
Returns the smallest (closest to negative infinity) |
static Long |
Returns the smallest (closest to negative infinity) |
static Int |
ceilDivExact(x: Int, y: Int) Returns the smallest (closest to negative infinity) |
static Long |
ceilDivExact(x: Long, y: Long) Returns the smallest (closest to negative infinity) |
static Int |
Returns the ceiling modulus of the |
static Int |
Returns the ceiling modulus of the |
static Long |
Returns the ceiling modulus of the |
static Int |
Clamps the value to fit between min and max. |
static Long |
Clamps the value to fit between min and max. |
static Double |
Clamps the value to fit between min and max. |
static Float |
Clamps the value to fit between min and max. |
static Double |
Returns the first floating-point argument with the sign of the second floating-point argument. |
static Float |
Returns the first floating-point argument with the sign of the second floating-point argument. |
static Double |
Returns the trigonometric cosine of an angle. |
static Double |
Returns the hyperbolic cosine of a |
static Int |
decrementExact(a: Int) Returns the argument decremented by one, throwing an exception if the result overflows an |
static Long |
decrementExact(a: Long) Returns the argument decremented by one, throwing an exception if the result overflows a |
static Int |
divideExact(x: Int, y: Int) Returns the quotient of the arguments, throwing an exception if the result overflows an |
static Long |
divideExact(x: Long, y: Long) Returns the quotient of the arguments, throwing an exception if the result overflows a |
static Double |
Returns Euler's number e raised to the power of a |
static Double |
Returns ex -1. |
static Double |
Returns the largest (closest to positive infinity) |
static Int |
Returns the largest (closest to positive infinity) |
static Long |
Returns the largest (closest to positive infinity) |
static Long |
Returns the largest (closest to positive infinity) |
static Int |
floorDivExact(x: Int, y: Int) Returns the largest (closest to positive infinity) |
static Long |
floorDivExact(x: Long, y: Long) Returns the largest (closest to positive infinity) |
static Int |
Returns the floor modulus of the |
static Int |
Returns the floor modulus of the |
static Long |
Returns the floor modulus of the |
static Double |
Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest |
static Float |
Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest |
static Int |
getExponent(f: Float) Returns the unbiased exponent used in the representation of a |
static Int |
getExponent(d: Double) Returns the unbiased exponent used in the representation of a |
static Double |
Returns sqrt(x2 +y2) without intermediate overflow or underflow. |
static Int |
incrementExact(a: Int) Returns the argument incremented by one, throwing an exception if the result overflows an |
static Long |
incrementExact(a: Long) Returns the argument incremented by one, throwing an exception if the result overflows a |
static Double |
Returns the natural logarithm (base e) of a |
static Double |
Returns the base 10 logarithm of a |
static Double |
Returns the natural logarithm of the sum of the argument and 1. |
static Int |
Returns the greater of two |
static Long |
Returns the greater of two |
static Float |
Returns the greater of two |
static Double |
Returns the greater of two |
static Int |
Returns the smaller of two |
static Long |
Returns the smaller of two |
static Float |
Returns the smaller of two |
static Double |
Returns the smaller of two |
static Int |
multiplyExact(x: Int, y: Int) Returns the product of the arguments, throwing an exception if the result overflows an |
static Long |
multiplyExact(x: Long, y: Int) Returns the product of the arguments, throwing an exception if the result overflows a |
static Long |
multiplyExact(x: Long, y: Long) Returns the product of the arguments, throwing an exception if the result overflows a |
static Long |
multiplyFull(x: Int, y: Int) Returns the exact mathematical product of the arguments. |
static Long |
multiplyHigh(x: Long, y: Long) Returns as a |
static Int |
negateExact(a: Int) Returns the negation of the argument, throwing an exception if the result overflows an |
static Long |
negateExact(a: Long) Returns the negation of the argument, throwing an exception if the result overflows a |
static Double |
Returns the floating-point number adjacent to the first argument in the direction of the second argument. |
static Float |
Returns the floating-point number adjacent to the first argument in the direction of the second argument. |
static Double |
Returns the floating-point value adjacent to |
static Float |
Returns the floating-point value adjacent to |
static Double |
Returns the floating-point value adjacent to |
static Float |
Returns the floating-point value adjacent to |
static Double |
Returns the value of the first argument raised to the power of the second argument. |
static Double |
random() Returns a |
static Double |
Returns the |
static Int |
Returns the closest |
static Long |
Returns the closest |
static Double |
Returns |
static Float |
Returns |
static Double |
Returns the signum function of the argument; zero if the argument is zero, 1. |
static Float |
Returns the signum function of the argument; zero if the argument is zero, 1. |
static Double |
Returns the trigonometric sine of an angle. |
static Double |
Returns the hyperbolic sine of a |
static Double |
Returns the correctly rounded positive square root of a |
static Int |
subtractExact(x: Int, y: Int) Returns the difference of the arguments, throwing an exception if the result overflows an |
static Long |
subtractExact(x: Long, y: Long) Returns the difference of the arguments, throwing an exception if the result overflows a |
static Double |
Returns the trigonometric tangent of an angle. |
static Double |
Returns the hyperbolic tangent of a |
static Double |
Converts an angle measured in radians to an approximately equivalent angle measured in degrees. |
static Int |
toIntExact(value: Long) Returns the value of the |
static Double |
Converts an angle measured in degrees to an approximately equivalent angle measured in radians. |
static Double |
Returns the size of an ulp of the argument. |
static Float |
Returns the size of an ulp of the argument. |
static Long |
unsignedMultiplyHigh(x: Long, y: Long) Returns as a |
Constants
E
static val E: Double
The double
value that is closer than any other to e, the base of the natural logarithms.
Value: 2.718281828459045
PI
static val PI: Double
The double
value that is closer than any other to pi (π), the ratio of the circumference of a circle to its diameter.
Value: 3.141592653589793
TAU
static val TAU: Double
The double
value that is closer than any other to tau (τ), the ratio of the circumference of a circle to its radius.
Value: 6.283185307179586
Public methods
IEEEremainder
static fun IEEEremainder(
f1: Double,
f2: Double
): Double
Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. The remainder value is mathematically equal to f1 - f2
× n, where n is the mathematical integer closest to the exact mathematical value of the quotient f1/f2
, and if two mathematical integers are equally close to f1/f2
, then n is the integer that is even. If the remainder is zero, its sign is the same as the sign of the first argument. Special cases:
- 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.
Parameters | |
---|---|
f1 |
Double: the dividend. |
f2 |
Double: the divisor. |
Return | |
---|---|
Double |
the remainder when f1 is divided by f2 . |
abs
static fun abs(a: Int): Int
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 java.lang.Integer#MIN_VALUE
, the most negative representable int
value, the result is that same value, which is negative. In contrast, the Math#absExact(int)
method throws an ArithmeticException
for this value.
Parameters | |
---|---|
a |
Int: the argument whose absolute value is to be determined |
Return | |
---|---|
Int |
the absolute value of the argument. |
See Also
abs
static fun abs(a: Long): Long
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 java.lang.Long#MIN_VALUE
, the most negative representable long
value, the result is that same value, which is negative. In contrast, the Math#absExact(long)
method throws an ArithmeticException
for this value.
Parameters | |
---|---|
a |
Long: the argument whose absolute value is to be determined |
Return | |
---|---|
Long |
the absolute value of the argument. |
See Also
abs
static fun abs(a: Float): Float
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.
Parameters | |
---|---|
a |
Float: the argument whose absolute value is to be determined |
Return | |
---|---|
Float |
the absolute value of the argument. |
abs
static fun abs(a: Double): Double
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.
Parameters | |
---|---|
a |
Double: the argument whose absolute value is to be determined |
Return | |
---|---|
Double |
the absolute value of the argument. |
absExact
static fun absExact(a: Int): Int
Returns the mathematical absolute value of an int
value if it is exactly representable as an int
, throwing ArithmeticException
if the result overflows the positive int
range.
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
overflows the positive int
range, so an exception is thrown for that argument.
Parameters | |
---|---|
a |
Int: the argument whose absolute value is to be determined |
Return | |
---|---|
Int |
the absolute value of the argument, unless overflow occurs |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the argument is Integer#MIN_VALUE |
See Also
absExact
static fun absExact(a: Long): Long
Returns the mathematical absolute value of an long
value if it is exactly representable as an long
, throwing ArithmeticException
if the result overflows the positive long
range.
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
overflows the positive long
range, so an exception is thrown for that argument.
Parameters | |
---|---|
a |
Long: the argument whose absolute value is to be determined |
Return | |
---|---|
Long |
the absolute value of the argument, unless overflow occurs |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the argument is Long#MIN_VALUE |
See Also
acos
static fun acos(a: Double): Double
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.
Parameters | |
---|---|
a |
Double: the value whose arc cosine is to be returned. |
Return | |
---|---|
Double |
the arc cosine of the argument. |
addExact
static fun addExact(
x: Int,
y: Int
): Int
Returns the sum of its arguments, throwing an exception if the result overflows an int
.
Parameters | |
---|---|
x |
Int: the first value |
y |
Int: the second value |
Return | |
---|---|
Int |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows an int |
addExact
static fun addExact(
x: Long,
y: Long
): Long
Returns the sum of its arguments, throwing an exception if the result overflows a long
.
Parameters | |
---|---|
x |
Long: the first value |
y |
Long: the second value |
Return | |
---|---|
Long |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows a long |
asin
static fun asin(a: Double): Double
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.
Parameters | |
---|---|
a |
Double: the value whose arc sine is to be returned. |
Return | |
---|---|
Double |
the arc sine of the argument. |
atan
static fun atan(a: Double): Double
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 java.lang.Double#isInfinite, 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.
Parameters | |
---|---|
a |
Double: the value whose arc tangent is to be returned. |
Return | |
---|---|
Double |
the arc tangent of the argument. |
atan2
static fun atan2(
y: Double,
x: Double
): Double
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 the
double
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 the
double
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 the
double
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 the
double
value closest to -pi/2. - If both arguments are positive infinity, then the result is the
double
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 the
double
value closest to -3*pi/4.
The computed result must be within 2 ulps of the exact result. Results must be semi-monotonic.
Parameters | |
---|---|
y |
Double: the ordinate coordinate |
x |
Double: the abscissa coordinate |
Return | |
---|---|
Double |
the theta component of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates. |
cbrt
static fun cbrt(a: Double): Double
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.
Parameters | |
---|---|
a |
Double: a value. |
Return | |
---|---|
Double |
the cube root of a . |
ceil
static fun ceil(a: Double): Double
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.
Math.ceil(x)
is exactly the value of -Math.floor(-x)
.
Parameters | |
---|---|
a |
Double: a value. |
Return | |
---|---|
Double |
the smallest (closest to negative infinity) floating-point value that is greater than or equal to the argument and is equal to a mathematical integer. |
ceilDiv
static fun ceilDiv(
x: Int,
y: Int
): Int
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 is Integer.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 of
ceilDiv
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
.
Parameters | |
---|---|
x |
Int: the dividend |
y |
Int: the divisor |
Return | |
---|---|
Int |
the smallest (closest to negative infinity) int value that is greater than or equal to the algebraic quotient. |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero |
See Also
ceilDiv
static fun ceilDiv(
x: Long,
y: Int
): Long
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 is Long.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)
.
Parameters | |
---|---|
x |
Long: the dividend |
y |
Int: the divisor |
Return | |
---|---|
Long |
the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient. |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero |
See Also
ceilDiv
static fun ceilDiv(
x: Long,
y: Long
): Long
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 is Long.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)
.
Parameters | |
---|---|
x |
Long: the dividend |
y |
Long: the divisor |
Return | |
---|---|
Long |
the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient. |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero |
See Also
ceilDivExact
static fun ceilDivExact(
x: Int,
y: Int
): Int
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)
except that it throws an ArithmeticException
when the dividend is Integer.MIN_VALUE and the divisor is -1
instead of ignoring the integer overflow and returning Integer.MIN_VALUE
.
The ceil modulus method ceilMod(int,int)
is a suitable counterpart both for this method and for the ceilDiv(int,int)
method.
For examples, see ceilDiv(int,int)
.
Parameters | |
---|---|
x |
Int: the dividend |
y |
Int: the divisor |
Return | |
---|---|
Int |
the smallest (closest to negative infinity) int value that is greater than or equal to the algebraic quotient. |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero, or the dividend x is Integer.MIN_VALUE and the divisor y is -1 . |
See Also
ceilDivExact
static fun ceilDivExact(
x: Long,
y: Long
): Long
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)
except that it throws an ArithmeticException
when the dividend is Long.MIN_VALUE and the divisor is -1
instead of ignoring the integer overflow and returning Long.MIN_VALUE
.
The ceil modulus method ceilMod(long,long)
is a suitable counterpart both for this method and for the ceilDiv(long,long)
method.
For examples, see ceilDiv(int,int)
.
Parameters | |
---|---|
x |
Long: the dividend |
y |
Long: the divisor |
Return | |
---|---|
Long |
the smallest (closest to negative infinity) long value that is greater than or equal to the algebraic quotient. |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero, or the dividend x is Long.MIN_VALUE and the divisor y is -1 . |
See Also
ceilMod
static fun ceilMod(
x: Int,
y: Int
): Int
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 whenx % y
is zero as well. - If neither
ceilMod
(x, y) norx % 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
Parameters | |
---|---|
x |
Int: the dividend |
y |
Int: the divisor |
Return | |
---|---|
Int |
the ceiling modulus x - (ceilDiv(x, y) * y) |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero |
See Also
ceilMod
static fun ceilMod(
x: Long,
y: Int
): Int
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)
.
Parameters | |
---|---|
x |
Long: the dividend |
y |
Int: the divisor |
Return | |
---|---|
Int |
the ceiling modulus x - (ceilDiv(x, y) * y) |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero |
See Also
ceilMod
static fun ceilMod(
x: Long,
y: Long
): Long
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)
.
Parameters | |
---|---|
x |
Long: the dividend |
y |
Long: the divisor |
Return | |
---|---|
Long |
the ceiling modulus x - (ceilDiv(x, y) * y) |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero |
See Also
clamp
static fun clamp(
value: Long,
min: Int,
max: Int
): Int
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.
Parameters | |
---|---|
value |
Long: value to clamp |
min |
Int: minimal allowed value |
max |
Int: maximal allowed value |
Return | |
---|---|
Int |
a clamped value that fits into min..max interval |
Exceptions | |
---|---|
java.lang.IllegalArgumentException |
if min > max |
clamp
static fun clamp(
value: Long,
min: Long,
max: Long
): Long
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.
Parameters | |
---|---|
value |
Long: value to clamp |
min |
Long: minimal allowed value |
max |
Long: maximal allowed value |
Return | |
---|---|
Long |
a clamped value that fits into min..max interval |
Exceptions | |
---|---|
java.lang.IllegalArgumentException |
if min > max |
clamp
static fun clamp(
value: Double,
min: Double,
max: Double
): Double
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.
Parameters | |
---|---|
value |
Double: value to clamp |
min |
Double: minimal allowed value |
max |
Double: maximal allowed value |
Return | |
---|---|
Double |
a clamped value that fits into min..max interval |
Exceptions | |
---|---|
java.lang.IllegalArgumentException |
if either of min and max arguments is NaN, or min > max , or min is +0.0, and max is -0.0. |
clamp
static fun clamp(
value: Float,
min: Float,
max: Float
): Float
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.
Parameters | |
---|---|
value |
Float: value to clamp |
min |
Float: minimal allowed value |
max |
Float: maximal allowed value |
Return | |
---|---|
Float |
a clamped value that fits into min..max interval |
Exceptions | |
---|---|
java.lang.IllegalArgumentException |
if either of min and max arguments is NaN, or min > max , or min is +0.0f, and max is -0.0f. |
copySign
static fun copySign(
magnitude: Double,
sign: Double
): Double
Returns the first floating-point argument with the sign of the second floating-point argument. Note that unlike the StrictMath.copySign
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.
Parameters | |
---|---|
magnitude |
Double: the parameter providing the magnitude of the result |
sign |
Double: the parameter providing the sign of the result |
Return | |
---|---|
Double |
a value with the magnitude of magnitude and the sign of sign . |
copySign
static fun copySign(
magnitude: Float,
sign: Float
): Float
Returns the first floating-point argument with the sign of the second floating-point argument. Note that unlike the StrictMath.copySign
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.
Parameters | |
---|---|
magnitude |
Float: the parameter providing the magnitude of the result |
sign |
Float: the parameter providing the sign of the result |
Return | |
---|---|
Float |
a value with the magnitude of magnitude and the sign of sign . |
cos
static fun cos(a: Double): Double
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.
Parameters | |
---|---|
a |
Double: an angle, in radians. |
Return | |
---|---|
Double |
the cosine of the argument. |
cosh
static fun cosh(x: Double): Double
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.
Parameters | |
---|---|
x |
Double: The number whose hyperbolic cosine is to be returned. |
Return | |
---|---|
Double |
The hyperbolic cosine of x . |
decrementExact
static fun decrementExact(a: Int): Int
Returns the argument decremented by one, throwing an exception if the result overflows an int
. The overflow only occurs for the minimum value.
Parameters | |
---|---|
a |
Int: the value to decrement |
Return | |
---|---|
Int |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows an int |
decrementExact
static fun decrementExact(a: Long): Long
Returns the argument decremented by one, throwing an exception if the result overflows a long
. The overflow only occurs for the minimum value.
Parameters | |
---|---|
a |
Long: the value to decrement |
Return | |
---|---|
Long |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows a long |
divideExact
static fun divideExact(
x: Int,
y: Int
): Int
Returns the quotient of the arguments, throwing an exception if the result overflows an int
. Such overflow occurs in this method if x
is Integer#MIN_VALUE
and y
is -1
. In contrast, if Integer.MIN_VALUE / -1
were evaluated directly, the result would be Integer.MIN_VALUE
and no exception would be thrown.
If y
is zero, an ArithmeticException
is thrown (JLS {@jls 15.17.2}).
The built-in remainder operator "%
" is a suitable counterpart both for this method and for the built-in division operator "/
".
Parameters | |
---|---|
x |
Int: the dividend |
y |
Int: the divisor |
Return | |
---|---|
Int |
the quotient x / y |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if y is zero or the quotient overflows an int |
divideExact
static fun divideExact(
x: Long,
y: Long
): Long
Returns the quotient of the arguments, throwing an exception if the result overflows a long
. Such overflow occurs in this method if x
is Long#MIN_VALUE
and y
is -1
. In contrast, if Long.MIN_VALUE / -1
were evaluated directly, the result would be Long.MIN_VALUE
and no exception would be thrown.
If y
is zero, an ArithmeticException
is thrown (JLS {@jls 15.17.2}).
The built-in remainder operator "%
" is a suitable counterpart both for this method and for the built-in division operator "/
".
Parameters | |
---|---|
x |
Long: the dividend |
y |
Long: the divisor |
Return | |
---|---|
Long |
the quotient x / y |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if y is zero or the quotient overflows a long |
exp
static fun exp(a: Double): Double
Returns Euler's number e raised to the power of a double
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.
Parameters | |
---|---|
a |
Double: the exponent to raise e to. |
Return | |
---|---|
Double |
the value ea , where e is the base of the natural logarithms. |
expm1
static fun expm1(x: Double): Double
Returns ex -1. Note that for values of x near 0, the exact sum of expm1(x)
+ 1 is much closer to the true result of ex than exp(x)
.
Special cases:
- 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 of expm1
for any finite input must be greater than or equal to -1.0
. Note that once the exact result of ex
- 1 is within 1/2 ulp of the limit value -1, -1.0
should be returned.
Parameters | |
---|---|
x |
Double: the exponent to raise e to in the computation of ex -1. |
Return | |
---|---|
Double |
the value ex - 1. |
floor
static fun floor(a: Double): Double
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.
Parameters | |
---|---|
a |
Double: a value. |
Return | |
---|---|
Double |
the largest (closest to positive infinity) floating-point value that less than or equal to the argument and is equal to a mathematical integer. |
floorDiv
static fun floorDiv(
x: Int,
y: Int
): Int
Returns the largest (closest to positive infinity) int
value that is less than or equal to the algebraic quotient. There is one special case: if the dividend is Integer.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 of
floorDiv
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
.
Parameters | |
---|---|
x |
Int: the dividend |
y |
Int: the divisor |
Return | |
---|---|
Int |
the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient. |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero |
See Also
floorDiv
static fun floorDiv(
x: Long,
y: Int
): Long
Returns the largest (closest to positive infinity) long
value that is less than or equal to the algebraic quotient. There is one special case: if the dividend is Long.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)
.
Parameters | |
---|---|
x |
Long: the dividend |
y |
Int: the divisor |
Return | |
---|---|
Long |
the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero |
See Also
floorDiv
static fun floorDiv(
x: Long,
y: Long
): Long
Returns the largest (closest to positive infinity) long
value that is less than or equal to the algebraic quotient. There is one special case: if the dividend is Long.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)
.
Parameters | |
---|---|
x |
Long: the dividend |
y |
Long: the divisor |
Return | |
---|---|
Long |
the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero |
See Also
floorDivExact
static fun floorDivExact(
x: Int,
y: Int
): Int
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)
except that it throws an ArithmeticException
when the dividend is Integer.MIN_VALUE and the divisor is -1
instead of ignoring the integer overflow and returning Integer.MIN_VALUE
.
The floor modulus method floorMod(int,int)
is a suitable counterpart both for this method and for the floorDiv(int,int)
method.
For examples, see floorDiv(int,int)
.
Parameters | |
---|---|
x |
Int: the dividend |
y |
Int: the divisor |
Return | |
---|---|
Int |
the largest (closest to positive infinity) int value that is less than or equal to the algebraic quotient. |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero, or the dividend x is Integer.MIN_VALUE and the divisor y is -1 . |
See Also
floorDivExact
static fun floorDivExact(
x: Long,
y: Long
): Long
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)
except that it throws an ArithmeticException
when the dividend is Long.MIN_VALUE and the divisor is -1
instead of ignoring the integer overflow and returning Long.MIN_VALUE
.
The floor modulus method floorMod(long,long)
is a suitable counterpart both for this method and for the floorDiv(long,long)
method.
For examples, see floorDiv(int,int)
.
Parameters | |
---|---|
x |
Long: the dividend |
y |
Long: the divisor |
Return | |
---|---|
Long |
the largest (closest to positive infinity) long value that is less than or equal to the algebraic quotient. |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero, or the dividend x is Long.MIN_VALUE and the divisor y is -1 . |
See Also
floorMod
static fun floorMod(
x: Int,
y: Int
): Int
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 whenx % y
is zero as well. - If neither
floorMod
(x, y) norx % 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
Parameters | |
---|---|
x |
Int: the dividend |
y |
Int: the divisor |
Return | |
---|---|
Int |
the floor modulus x - (floorDiv(x, y) * y) |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero |
See Also
floorMod
static fun floorMod(
x: Long,
y: Int
): Int
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)
.
Parameters | |
---|---|
x |
Long: the dividend |
y |
Int: the divisor |
Return | |
---|---|
Int |
the floor modulus x - (floorDiv(x, y) * y) |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero |
See Also
floorMod
static fun floorMod(
x: Long,
y: Long
): Long
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)
.
Parameters | |
---|---|
x |
Long: the dividend |
y |
Long: the divisor |
Return | |
---|---|
Long |
the floor modulus x - (floorDiv(x, y) * y) |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the divisor y is zero |
See Also
fma
static fun fma(
a: Double,
b: Double,
c: Double
): Double
Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest double
. The rounding is done using the round to nearest even. 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
) since fma(-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.
Parameters | |
---|---|
a |
Double: a value |
b |
Double: a value |
c |
Double: a value |
Return | |
---|---|
Double |
(a × b + c) computed, as if with unlimited range and precision, and rounded once to the nearest double value |
fma
static fun fma(
a: Float,
b: Float,
c: Float
): Float
Returns the fused multiply add of the three arguments; that is, returns the exact product of the first two arguments summed with the third argument and then rounded once to the nearest float
. The rounding is done using the round to nearest even. 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
) since fma(-0.0f, +0.0f, +0.0f)
is +0.0f
while (-0.0f * +0.0f
) is -0.0f
; fma(a, b, -0.0f)
is equivalent to (a * b
) however.
Parameters | |
---|---|
a |
Float: a value |
b |
Float: a value |
c |
Float: a value |
Return | |
---|---|
Float |
(a × b + c) computed, as if with unlimited range and precision, and rounded once to the nearest float value |
getExponent
static fun getExponent(f: Float): Int
Returns the unbiased exponent used in the representation of a float
. Special cases:
- If the argument is NaN or infinite, then the result is
Float#MAX_EXPONENT
+ 1. - If the argument is zero or subnormal, then the result is
Float#MIN_EXPONENT
- 1.
Parameters | |
---|---|
f |
Float: a float value |
Return | |
---|---|
Int |
the unbiased exponent of the argument |
getExponent
static fun getExponent(d: Double): Int
Returns the unbiased exponent used in the representation of a double
. Special cases:
- If the argument is NaN or infinite, then the result is
Double#MAX_EXPONENT
+ 1. - If the argument is zero or subnormal, then the result is
Double#MIN_EXPONENT
- 1.
Parameters | |
---|---|
d |
Double: a double value |
Return | |
---|---|
Int |
the unbiased exponent of the argument |
hypot
static fun hypot(
x: Double,
y: Double
): Double
Returns sqrt(x2 +y2) without intermediate overflow or underflow.
Special cases:
- If either argument is infinite, then the result is positive infinity.
- If either argument is NaN and neither argument is infinite, then the result is NaN.
- If both arguments are zero, the result is positive zero.
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.
Parameters | |
---|---|
x |
Double: a value |
y |
Double: a value |
Return | |
---|---|
Double |
sqrt(x2 +y2) without intermediate overflow or underflow |
incrementExact
static fun incrementExact(a: Int): Int
Returns the argument incremented by one, throwing an exception if the result overflows an int
. The overflow only occurs for the maximum value.
Parameters | |
---|---|
a |
Int: the value to increment |
Return | |
---|---|
Int |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows an int |
incrementExact
static fun incrementExact(a: Long): Long
Returns the argument incremented by one, throwing an exception if the result overflows a long
. The overflow only occurs for the maximum value.
Parameters | |
---|---|
a |
Long: the value to increment |
Return | |
---|---|
Long |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows a long |
log
static fun log(a: Double): Double
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.
Parameters | |
---|---|
a |
Double: a value |
Return | |
---|---|
Double |
the value ln a , the natural logarithm of a . |
log10
static fun log10(a: Double): Double
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 10n 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.
Parameters | |
---|---|
a |
Double: a value |
Return | |
---|---|
Double |
the base 10 logarithm of a . |
log1p
static fun log1p(x: Double): Double
Returns the natural logarithm of the sum of the argument and 1. Note that for small values x
, the result of log1p(x)
is much closer to the true result of ln(1 + x
) than the floating-point evaluation of log(1.0+x)
.
Special cases:
- 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.
Parameters | |
---|---|
x |
Double: a value |
Return | |
---|---|
Double |
the value ln(x + 1), the natural log of x + 1 |
max
static fun max(
a: Int,
b: Int
): Int
Returns the greater of two int
values. That is, the result is the argument closer to the value of Integer#MAX_VALUE
. If the arguments have the same value, the result is that same value.
Parameters | |
---|---|
a |
Int: an argument. |
b |
Int: another argument. |
Return | |
---|---|
Int |
the larger of a and b . |
max
static fun max(
a: Long,
b: Long
): Long
Returns the greater of two long
values. That is, the result is the argument closer to the value of Long#MAX_VALUE
. If the arguments have the same value, the result is that same value.
Parameters | |
---|---|
a |
Long: an argument. |
b |
Long: another argument. |
Return | |
---|---|
Long |
the larger of a and b . |
max
static fun max(
a: Float,
b: Float
): Float
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.
Parameters | |
---|---|
a |
Float: an argument. |
b |
Float: another argument. |
Return | |
---|---|
Float |
the larger of a and b . |
max
static fun max(
a: Double,
b: Double
): Double
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.
Parameters | |
---|---|
a |
Double: an argument. |
b |
Double: another argument. |
Return | |
---|---|
Double |
the larger of a and b . |
min
static fun min(
a: Int,
b: Int
): Int
Returns the smaller of two int
values. That is, the result the argument closer to the value of Integer#MIN_VALUE
. If the arguments have the same value, the result is that same value.
Parameters | |
---|---|
a |
Int: an argument. |
b |
Int: another argument. |
Return | |
---|---|
Int |
the smaller of a and b . |
min
static fun min(
a: Long,
b: Long
): Long
Returns the smaller of two long
values. That is, the result is the argument closer to the value of Long#MIN_VALUE
. If the arguments have the same value, the result is that same value.
Parameters | |
---|---|
a |
Long: an argument. |
b |
Long: another argument. |
Return | |
---|---|
Long |
the smaller of a and b . |
min
static fun min(
a: Float,
b: Float
): Float
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.
Parameters | |
---|---|
a |
Float: an argument. |
b |
Float: another argument. |
Return | |
---|---|
Float |
the smaller of a and b . |
min
static fun min(
a: Double,
b: Double
): Double
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.
Parameters | |
---|---|
a |
Double: an argument. |
b |
Double: another argument. |
Return | |
---|---|
Double |
the smaller of a and b . |
multiplyExact
static fun multiplyExact(
x: Int,
y: Int
): Int
Returns the product of the arguments, throwing an exception if the result overflows an int
.
Parameters | |
---|---|
x |
Int: the first value |
y |
Int: the second value |
Return | |
---|---|
Int |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows an int |
multiplyExact
static fun multiplyExact(
x: Long,
y: Int
): Long
Returns the product of the arguments, throwing an exception if the result overflows a long
.
Parameters | |
---|---|
x |
Long: the first value |
y |
Int: the second value |
Return | |
---|---|
Long |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows a long |
multiplyExact
static fun multiplyExact(
x: Long,
y: Long
): Long
Returns the product of the arguments, throwing an exception if the result overflows a long
.
Parameters | |
---|---|
x |
Long: the first value |
y |
Long: the second value |
Return | |
---|---|
Long |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows a long |
multiplyFull
static fun multiplyFull(
x: Int,
y: Int
): Long
Returns the exact mathematical product of the arguments.
Parameters | |
---|---|
x |
Int: the first value |
y |
Int: the second value |
Return | |
---|---|
Long |
the result |
multiplyHigh
static fun multiplyHigh(
x: Long,
y: Long
): Long
Returns as a long
the most significant 64 bits of the 128-bit product of two 64-bit factors.
Parameters | |
---|---|
x |
Long: the first value |
y |
Long: the second value |
Return | |
---|---|
Long |
the result |
See Also
negateExact
static fun negateExact(a: Int): Int
Returns the negation of the argument, throwing an exception if the result overflows an int
. The overflow only occurs for the minimum value.
Parameters | |
---|---|
a |
Int: the value to negate |
Return | |
---|---|
Int |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows an int |
negateExact
static fun negateExact(a: Long): Long
Returns the negation of the argument, throwing an exception if the result overflows a long
. The overflow only occurs for the minimum value.
Parameters | |
---|---|
a |
Long: the value to negate |
Return | |
---|---|
Long |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows a long |
nextAfter
static fun nextAfter(
start: Double,
direction: Double
): Double
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
anddirection
has a value such that the result should have a smaller magnitude, then a zero with the same sign asstart
is returned. - If
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. - If
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.
Parameters | |
---|---|
start |
Double: starting floating-point value |
direction |
Double: value indicating which of start 's neighbors or start should be returned |
Return | |
---|---|
Double |
The floating-point number adjacent to start in the direction of direction . |
nextAfter
static fun nextAfter(
start: Float,
direction: Double
): Float
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
anddirection
has a value such that the result should have a smaller magnitude, then a zero with the same sign asstart
is returned. - If
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. - If
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.
Parameters | |
---|---|
start |
Float: starting floating-point value |
direction |
Double: value indicating which of start 's neighbors or start should be returned |
Return | |
---|---|
Float |
The floating-point number adjacent to start in the direction of direction . |
nextDown
static fun nextDown(d: Double): Double
Returns the floating-point value adjacent to d
in the direction of negative infinity. This method is semantically equivalent to nextAfter(d, Double.NEGATIVE_INFINITY)
; however, a nextDown
implementation may run faster than its equivalent nextAfter
call.
Special Cases:
- 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
Parameters | |
---|---|
d |
Double: starting floating-point value |
Return | |
---|---|
Double |
The adjacent floating-point value closer to negative infinity. |
nextDown
static fun nextDown(f: Float): Float
Returns the floating-point value adjacent to f
in the direction of negative infinity. This method is semantically equivalent to nextAfter(f, Float.NEGATIVE_INFINITY)
; however, a nextDown
implementation may run faster than its equivalent nextAfter
call.
Special Cases:
- 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
Parameters | |
---|---|
f |
Float: starting floating-point value |
Return | |
---|---|
Float |
The adjacent floating-point value closer to negative infinity. |
nextUp
static fun nextUp(d: Double): Double
Returns the floating-point value adjacent to d
in the direction of positive infinity. This method is semantically equivalent to nextAfter(d, Double.POSITIVE_INFINITY)
; however, a nextUp
implementation may run faster than its equivalent nextAfter
call.
Special Cases:
- 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
Parameters | |
---|---|
d |
Double: starting floating-point value |
Return | |
---|---|
Double |
The adjacent floating-point value closer to positive infinity. |
nextUp
static fun nextUp(f: Float): Float
Returns the floating-point value adjacent to f
in the direction of positive infinity. This method is semantically equivalent to nextAfter(f, Float.POSITIVE_INFINITY)
; however, a nextUp
implementation may run faster than its equivalent nextAfter
call.
Special Cases:
- 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
Parameters | |
---|---|
f |
Float: starting floating-point value |
Return | |
---|---|
Float |
The adjacent floating-point value closer to positive infinity. |
pow
static fun pow(
a: Double,
b: Double
): Double
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,
- If
- the absolute value of the first argument is greater than 1 and the second argument is negative infinity, or
- the absolute value of the first argument is less than 1 and the second argument is positive infinity,
- If the absolute value of the first argument equals 1 and the second argument is infinite, then the result is 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,
- If
- the first argument is positive zero and the second argument is less than zero, or
- the first argument is positive infinity and the second argument is greater than zero,
- If
- the first argument is negative zero and the second argument is greater than zero but not a finite odd integer, or
- the first argument is negative infinity and the second argument is less than zero but not a finite odd integer,
- If
- the first argument is negative zero and the second argument is a positive finite odd integer, or
- the first argument is negative infinity and the second argument is a negative finite odd integer,
- If
- the first argument is negative zero and the second argument is less than zero but not a finite odd integer, or
- the first argument is negative infinity and the second argument is greater than zero but not a finite odd integer,
- If
- the first argument is negative zero and the second argument is a negative finite odd integer, or
- the first argument is negative infinity and the second argument is a positive finite odd integer,
- If the first argument is finite and less than zero
- if the second argument is a finite even integer, the result is equal to the result of raising the absolute value of the first argument to the power of the second argument
- if the second argument is a finite odd integer, the result is equal to the negative of the result of raising the absolute value of the first argument to the power of the second argument
- if the second argument is finite and not an integer, then the result is NaN.
- If both arguments are integers, then the result is exactly equal to the mathematical result of raising the first argument to the power of the second argument if that result can in fact be represented exactly as a
double
value.
(In the foregoing descriptions, a floating-point value is considered to be an integer if and only if it is finite and a fixed point of the method ceil
or, equivalently, a fixed point of the method floor
. A value is a fixed point of a one-argument method if and only if the result of applying the method to the value is equal to the value.)
The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.
Parameters | |
---|---|
a |
Double: the base. |
b |
Double: the exponent. |
Return | |
---|---|
Double |
the value a b . |
random
static fun random(): Double
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.
Return | |
---|---|
Double |
a pseudorandom double greater than or equal to 0.0 and less than 1.0 . |
rint
static fun rint(a: Double): Double
Returns the double
value that is closest in value to the argument and is equal to a mathematical integer. If two double
values that are mathematical integers are equally close, 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.
Parameters | |
---|---|
a |
Double: a double value. |
Return | |
---|---|
Double |
the closest floating-point value to a that is equal to a mathematical integer. |
round
static fun round(a: Float): Int
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 ofInteger.MIN_VALUE
. - If the argument is positive infinity or any value greater than or equal to the value of
Integer.MAX_VALUE
, the result is equal to the value ofInteger.MAX_VALUE
.
Parameters | |
---|---|
a |
Float: a floating-point value to be rounded to an integer. |
Return | |
---|---|
Int |
the value of the argument rounded to the nearest int value. |
round
static fun round(a: Double): Long
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 ofLong.MIN_VALUE
. - If the argument is positive infinity or any value greater than or equal to the value of
Long.MAX_VALUE
, the result is equal to the value ofLong.MAX_VALUE
.
Parameters | |
---|---|
a |
Double: a floating-point value to be rounded to a long . |
Return | |
---|---|
Long |
the value of the argument rounded to the nearest long value. |
scalb
static fun scalb(
d: Double,
scaleFactor: Int
): Double
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
and java.lang.Double#MAX_EXPONENT
, the answer is calculated exactly. If the exponent of the result would be larger than Double.MAX_EXPONENT
, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when scalb(x, n)
is subnormal, scalb(scalb(x, n), -n)
may not equal x. When the result is non-NaN, the result has the same sign as d
.
Special cases:
- 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.
Parameters | |
---|---|
d |
Double: number to be scaled by a power of two. |
scaleFactor |
Int: power of 2 used to scale d |
Return | |
---|---|
Double |
d × 2scaleFactor |
scalb
static fun scalb(
f: Float,
scaleFactor: Int
): Float
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
and java.lang.Float#MAX_EXPONENT
, the answer is calculated exactly. If the exponent of the result would be larger than Float.MAX_EXPONENT
, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when scalb(x, n)
is subnormal, scalb(scalb(x, n), -n)
may not equal x. When the result is non-NaN, the result has the same sign as f
.
Special cases:
- 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.
Parameters | |
---|---|
f |
Float: number to be scaled by a power of two. |
scaleFactor |
Int: power of 2 used to scale f |
Return | |
---|---|
Float |
f × 2scaleFactor |
signum
static fun signum(d: Double): Double
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.
Parameters | |
---|---|
d |
Double: the floating-point value whose signum is to be returned |
Return | |
---|---|
Double |
the signum function of the argument |
signum
static fun signum(f: Float): Float
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.
Parameters | |
---|---|
f |
Float: the floating-point value whose signum is to be returned |
Return | |
---|---|
Float |
the signum function of the argument |
sin
static fun sin(a: Double): Double
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.
Parameters | |
---|---|
a |
Double: an angle, in radians. |
Return | |
---|---|
Double |
the sine of the argument. |
sinh
static fun sinh(x: Double): Double
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.
Parameters | |
---|---|
x |
Double: The number whose hyperbolic sine is to be returned. |
Return | |
---|---|
Double |
The hyperbolic sine of x . |
sqrt
static fun sqrt(a: Double): Double
Returns the correctly rounded positive square root 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 the same as the argument.
double
value closest to the true mathematical square root of the argument value.
Parameters | |
---|---|
a |
Double: a value. |
Return | |
---|---|
Double |
the positive square root of a . If the argument is NaN or less than zero, the result is NaN. |
subtractExact
static fun subtractExact(
x: Int,
y: Int
): Int
Returns the difference of the arguments, throwing an exception if the result overflows an int
.
Parameters | |
---|---|
x |
Int: the first value |
y |
Int: the second value to subtract from the first |
Return | |
---|---|
Int |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows an int |
subtractExact
static fun subtractExact(
x: Long,
y: Long
): Long
Returns the difference of the arguments, throwing an exception if the result overflows a long
.
Parameters | |
---|---|
x |
Long: the first value |
y |
Long: the second value to subtract from the first |
Return | |
---|---|
Long |
the result |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the result overflows a long |
tan
static fun tan(a: Double): Double
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 ulp of the exact result. Results must be semi-monotonic.
Parameters | |
---|---|
a |
Double: an angle, in radians. |
Return | |
---|---|
Double |
the tangent of the argument. |
tanh
static fun tanh(x: Double): Double
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.
Parameters | |
---|---|
x |
Double: The number whose hyperbolic tangent is to be returned. |
Return | |
---|---|
Double |
The hyperbolic tangent of x . |
toDegrees
static fun toDegrees(angrad: Double): Double
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
.
Parameters | |
---|---|
angrad |
Double: an angle, in radians |
Return | |
---|---|
Double |
the measurement of the angle angrad in degrees. |
toIntExact
static fun toIntExact(value: Long): Int
Returns the value of the long
argument, throwing an exception if the value overflows an int
.
Parameters | |
---|---|
value |
Long: the long value |
Return | |
---|---|
Int |
the argument as an int |
Exceptions | |
---|---|
java.lang.ArithmeticException |
if the argument overflows an int |
toRadians
static fun toRadians(angdeg: Double): Double
Converts an angle measured in degrees to an approximately equivalent angle measured in radians. The conversion from degrees to radians is generally inexact.
Parameters | |
---|---|
angdeg |
Double: an angle, in degrees |
Return | |
---|---|
Double |
the measurement of the angle angdeg in radians. |
ulp
static fun ulp(d: Double): Double
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 is
Double.MIN_VALUE
. - If the argument is ±
Double.MAX_VALUE
, then the result is equal to 2971.
Parameters | |
---|---|
d |
Double: the floating-point value whose ulp is to be returned |
Return | |
---|---|
Double |
the size of an ulp of the argument |
ulp
static fun ulp(f: Float): Float
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 is
Float.MIN_VALUE
. - If the argument is ±
Float.MAX_VALUE
, then the result is equal to 2104.
Parameters | |
---|---|
f |
Float: the floating-point value whose ulp is to be returned |
Return | |
---|---|
Float |
the size of an ulp of the argument |
unsignedMultiplyHigh
static fun unsignedMultiplyHigh(
x: Long,
y: Long
): Long
Returns as a long
the most significant 64 bits of the unsigned 128-bit product of two unsigned 64-bit factors.
Parameters | |
---|---|
x |
Long: the first value |
y |
Long: the second value |
Return | |
---|---|
Long |
the result |
See Also