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/*
* Copyright 2010-2018 JetBrains s.r.o. and Kotlin Programming Language contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
@file:JvmMultifileClass
@file:JvmName("MathKt")
package kotlin.math
import kotlin.internal.InlineOnly
import kotlin.math.Constants.LN2
import kotlin.math.Constants.taylor_2_bound
import kotlin.math.Constants.taylor_n_bound
import kotlin.math.Constants.upper_taylor_2_bound
import kotlin.math.Constants.upper_taylor_n_bound
import java.lang.Math as nativeMath
private object Constants {
// constants
/** Natural logarithm of 2.0, used to compute [log2] function */
@JvmField
internal val LN2: Double = ln(2.0)
@JvmField
internal val epsilon: Double = nativeMath.ulp(1.0)
@JvmField
internal val taylor_2_bound = nativeMath.sqrt(epsilon)
@JvmField
internal val taylor_n_bound = nativeMath.sqrt(taylor_2_bound)
@JvmField
internal val upper_taylor_2_bound = 1 / taylor_2_bound
@JvmField
internal val upper_taylor_n_bound = 1 / taylor_n_bound
}
// region ================ Double Math ========================================
/** Computes the sine of the angle [x] given in radians.
*
* Special cases:
* - `sin(NaN|+Inf|-Inf)` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun sin(x: Double): Double = nativeMath.sin(x)
/** Computes the cosine of the angle [x] given in radians.
*
* Special cases:
* - `cos(NaN|+Inf|-Inf)` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun cos(x: Double): Double = nativeMath.cos(x)
/** Computes the tangent of the angle [x] given in radians.
*
* Special cases:
* - `tan(NaN|+Inf|-Inf)` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun tan(x: Double): Double = nativeMath.tan(x)
/**
* Computes the arc sine of the value [x];
* the returned value is an angle in the range from `-PI/2` to `PI/2` radians.
*
* Special cases:
* - `asin(x)` is `NaN`, when `abs(x) > 1` or x is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun asin(x: Double): Double = nativeMath.asin(x)
/**
* Computes the arc cosine of the value [x];
* the returned value is an angle in the range from `0.0` to `PI` radians.
*
* Special cases:
* - `acos(x)` is `NaN`, when `abs(x) > 1` or x is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun acos(x: Double): Double = nativeMath.acos(x)
/**
* Computes the arc tangent of the value [x];
* the returned value is an angle in the range from `-PI/2` to `PI/2` radians.
*
* Special cases:
* - `atan(NaN)` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun atan(x: Double): Double = nativeMath.atan(x)
/**
* Returns the angle `theta` of the polar coordinates `(r, theta)` that correspond
* to the rectangular coordinates `(x, y)` by computing the arc tangent of the value [y] / [x];
* the returned value is an angle in the range from `-PI` to `PI` radians.
*
* Special cases:
* - `atan2(0.0, 0.0)` is `0.0`
* - `atan2(0.0, x)` is `0.0` for `x > 0` and `PI` for `x < 0`
* - `atan2(-0.0, x)` is `-0.0` for 'x > 0` and `-PI` for `x < 0`
* - `atan2(y, +Inf)` is `0.0` for `0 < y < +Inf` and `-0.0` for '-Inf < y < 0`
* - `atan2(y, -Inf)` is `PI` for `0 < y < +Inf` and `-PI` for `-Inf < y < 0`
* - `atan2(y, 0.0)` is `PI/2` for `y > 0` and `-PI/2` for `y < 0`
* - `atan2(+Inf, x)` is `PI/2` for finite `x`y
* - `atan2(-Inf, x)` is `-PI/2` for finite `x`
* - `atan2(NaN, x)` and `atan2(y, NaN)` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun atan2(y: Double, x: Double): Double = nativeMath.atan2(y, x)
/**
* Computes the hyperbolic sine of the value [x].
*
* Special cases:
* - `sinh(NaN)` is `NaN`
* - `sinh(+Inf)` is `+Inf`
* - `sinh(-Inf)` is `-Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun sinh(x: Double): Double = nativeMath.sinh(x)
/**
* Computes the hyperbolic cosine of the value [x].
*
* Special cases:
* - `cosh(NaN)` is `NaN`
* - `cosh(+Inf|-Inf)` is `+Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun cosh(x: Double): Double = nativeMath.cosh(x)
/**
* Computes the hyperbolic tangent of the value [x].
*
* Special cases:
* - `tanh(NaN)` is `NaN`
* - `tanh(+Inf)` is `1.0`
* - `tanh(-Inf)` is `-1.0`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun tanh(x: Double): Double = nativeMath.tanh(x)
// Inverse hyperbolic function implementations derived from boost special math functions,
// Copyright Eric Ford & Hubert Holin 2001.
/**
* Computes the inverse hyperbolic sine of the value [x].
*
* The returned value is `y` such that `sinh(y) == x`.
*
* Special cases:
* - `asinh(NaN)` is `NaN`
* - `asinh(+Inf)` is `+Inf`
* - `asinh(-Inf)` is `-Inf`
*/
@SinceKotlin("1.2")
public actual fun asinh(x: Double): Double =
when {
x >= +taylor_n_bound ->
if (x > upper_taylor_n_bound) {
if (x > upper_taylor_2_bound) {
// approximation by laurent series in 1/x at 0+ order from -1 to 0
nativeMath.log(x) + LN2
} else {
// approximation by laurent series in 1/x at 0+ order from -1 to 1
nativeMath.log(x * 2 + (1 / (x * 2)))
}
} else {
nativeMath.log(x + nativeMath.sqrt(x * x + 1))
}
x <= -taylor_n_bound -> -asinh(-x)
else -> {
// approximation by taylor series in x at 0 up to order 2
var result = x;
if (nativeMath.abs(x) >= taylor_2_bound) {
// approximation by taylor series in x at 0 up to order 4
result -= (x * x * x) / 6
}
result
}
}
/**
* Computes the inverse hyperbolic cosine of the value [x].
*
* The returned value is positive `y` such that `cosh(y) == x`.
*
* Special cases:
* - `acosh(NaN)` is `NaN`
* - `acosh(x)` is `NaN` when `x < 1`
* - `acosh(+Inf)` is `+Inf`
*/
@SinceKotlin("1.2")
public actual fun acosh(x: Double): Double =
when {
x < 1 -> Double.NaN
x > upper_taylor_2_bound ->
// approximation by laurent series in 1/x at 0+ order from -1 to 0
nativeMath.log(x) + LN2
x - 1 >= taylor_n_bound ->
nativeMath.log(x + nativeMath.sqrt(x * x - 1))
else -> {
val y = nativeMath.sqrt(x - 1)
// approximation by taylor series in y at 0 up to order 2
var result = y
if (y >= taylor_2_bound) {
// approximation by taylor series in y at 0 up to order 4
result -= (y * y * y) / 12
}
nativeMath.sqrt(2.0) * result
}
}
/**
* Computes the inverse hyperbolic tangent of the value [x].
*
* The returned value is `y` such that `tanh(y) == x`.
*
* Special cases:
* - `tanh(NaN)` is `NaN`
* - `tanh(x)` is `NaN` when `x > 1` or `x < -1`
* - `tanh(1.0)` is `+Inf`
* - `tanh(-1.0)` is `-Inf`
*/
@SinceKotlin("1.2")
public actual fun atanh(x: Double): Double {
if (nativeMath.abs(x) < taylor_n_bound) {
var result = x
if (nativeMath.abs(x) > taylor_2_bound) {
result += (x * x * x) / 3
}
return result
}
return nativeMath.log((1 + x) / (1 - x)) / 2
}
/**
* Computes `sqrt(x^2 + y^2)` without intermediate overflow or underflow.
*
* Special cases:
* - returns `+Inf` if any of arguments is infinite
* - returns `NaN` if any of arguments is `NaN` and the other is not infinite
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun hypot(x: Double, y: Double): Double = nativeMath.hypot(x, y)
/**
* Computes the positive square root of the value [x].
*
* Special cases:
* - `sqrt(x)` is `NaN` when `x < 0` or `x` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun sqrt(x: Double): Double = nativeMath.sqrt(x)
/**
* Computes Euler's number `e` raised to the power of the value [x].
*
* Special cases:
* - `exp(NaN)` is `NaN`
* - `exp(+Inf)` is `+Inf`
* - `exp(-Inf)` is `0.0`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun exp(x: Double): Double = nativeMath.exp(x)
/**
* Computes `exp(x) - 1`.
*
* This function can be implemented to produce more precise result for [x] near zero.
*
* Special cases:
* - `expm1(NaN)` is `NaN`
* - `expm1(+Inf)` is `+Inf`
* - `expm1(-Inf)` is `-1.0`
*
* @see [exp] function.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun expm1(x: Double): Double = nativeMath.expm1(x)
/**
* Computes the logarithm of the value [x] to the given [base].
*
* Special cases:
* - `log(x, b)` is `NaN` if either `x` or `b` are `NaN`
* - `log(x, b)` is `NaN` when `x < 0` or `b <= 0` or `b == 1.0`
* - `log(+Inf, +Inf)` is `NaN`
* - `log(+Inf, b)` is `+Inf` for `b > 1` and `-Inf` for `b < 1`
* - `log(0.0, b)` is `-Inf` for `b > 1` and `+Inf` for `b > 1`
*
* See also logarithm functions for common fixed bases: [ln], [log10] and [log2].
*/
@SinceKotlin("1.2")
public actual fun log(x: Double, base: Double): Double {
if (base <= 0.0 || base == 1.0) return Double.NaN
return nativeMath.log(x) / nativeMath.log(base)
}
/**
* Computes the natural logarithm (base `E`) of the value [x].
*
* Special cases:
* - `ln(NaN)` is `NaN`
* - `ln(x)` is `NaN` when `x < 0.0`
* - `ln(+Inf)` is `+Inf`
* - `ln(0.0)` is `-Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun ln(x: Double): Double = nativeMath.log(x)
/**
* Computes the common logarithm (base 10) of the value [x].
*
* @see [ln] function for special cases.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun log10(x: Double): Double = nativeMath.log10(x)
/**
* Computes the binary logarithm (base 2) of the value [x].
*
* @see [ln] function for special cases.
*/
@SinceKotlin("1.2")
public actual fun log2(x: Double): Double = nativeMath.log(x) / LN2
/**
* Computes `ln(x + 1)`.
*
* This function can be implemented to produce more precise result for [x] near zero.
*
* Special cases:
* - `ln1p(NaN)` is `NaN`
* - `ln1p(x)` is `NaN` where `x < -1.0`
* - `ln1p(-1.0)` is `-Inf`
* - `ln1p(+Inf)` is `+Inf`
*
* @see [ln] function
* @see [expm1] function
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun ln1p(x: Double): Double = nativeMath.log1p(x)
/**
* Rounds the given value [x] to an integer towards positive infinity.
* @return the smallest double value that is greater than or equal to the given value [x] and is a mathematical integer.
*
* Special cases:
* - `ceil(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun ceil(x: Double): Double = nativeMath.ceil(x)
/**
* Rounds the given value [x] to an integer towards negative infinity.
* @return the largest double value that is smaller than or equal to the given value [x] and is a mathematical integer.
*
* Special cases:
* - `floor(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun floor(x: Double): Double = nativeMath.floor(x)
/**
* Rounds the given value [x] to an integer towards zero.
*
* @return the value [x] having its fractional part truncated.
*
* Special cases:
* - `truncate(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
public actual fun truncate(x: Double): Double = when {
x.isNaN() || x.isInfinite() -> x
x > 0 -> floor(x)
else -> ceil(x)
}
/**
* Rounds the given value [x] towards the closest integer with ties rounded towards even integer.
*
* Special cases:
* - `round(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun round(x: Double): Double = nativeMath.rint(x)
/**
* Returns the absolute value of the given value [x].
*
* Special cases:
* - `abs(NaN)` is `NaN`
*
* @see absoluteValue extension property for [Double]
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun abs(x: Double): Double = nativeMath.abs(x)
/**
* Returns the sign of the given value [x]:
* - `-1.0` if the value is negative,
* - zero if the value is zero,
* - `1.0` if the value is positive
*
* Special case:
* - `sign(NaN)` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun sign(x: Double): Double = nativeMath.signum(x)
/**
* Returns the smaller of two values.
*
* If either value is `NaN`, then the result is `NaN`.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun min(a: Double, b: Double): Double = nativeMath.min(a, b)
/**
* Returns the greater of two values.
*
* If either value is `NaN`, then the result is `NaN`.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun max(a: Double, b: Double): Double = nativeMath.max(a, b)
// extensions
/**
* Raises this value to the power [x].
*
* Special cases:
* - `b.pow(0.0)` is `1.0`
* - `b.pow(1.0) == b`
* - `b.pow(NaN)` is `NaN`
* - `NaN.pow(x)` is `NaN` for `x != 0.0`
* - `b.pow(Inf)` is `NaN` for `abs(b) == 1.0`
* - `b.pow(x)` is `NaN` for `b < 0` and `x` is finite and not an integer
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun Double.pow(x: Double): Double = nativeMath.pow(this, x)
/**
* Raises this value to the integer power [n].
*
* See the other overload of [pow] for details.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun Double.pow(n: Int): Double = nativeMath.pow(this, n.toDouble())
/**
* Computes the remainder of division of this value by the [divisor] value according to the IEEE 754 standard.
*
* The result is computed as `r = this - (q * divisor)` where `q` is the quotient of division rounded to the nearest integer,
* `q = round(this / other)`.
*
* Special cases:
* - `x.IEEErem(y)` is `NaN`, when `x` is `NaN` or `y` is `NaN` or `x` is `+Inf|-Inf` or `y` is zero.
* - `x.IEEErem(y) == x` when `x` is finite and `y` is infinite.
*
* @see round
*/
@SinceKotlin("1.2")
@InlineOnly
public inline fun Double.IEEErem(divisor: Double): Double = nativeMath.IEEEremainder(this, divisor)
/**
* Returns the absolute value of this value.
*
* Special cases:
* - `NaN.absoluteValue` is `NaN`
*
* @see abs function
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline val Double.absoluteValue: Double get() = nativeMath.abs(this)
/**
* Returns the sign of this value:
* - `-1.0` if the value is negative,
* - zero if the value is zero,
* - `1.0` if the value is positive
*
* Special case:
* - `NaN.sign` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline val Double.sign: Double get() = nativeMath.signum(this)
/**
* Returns this value with the sign bit same as of the [sign] value.
*
* If [sign] is `NaN` the sign of the result is undefined.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun Double.withSign(sign: Double): Double = nativeMath.copySign(this, sign)
/**
* Returns this value with the sign bit same as of the [sign] value.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun Double.withSign(sign: Int): Double = nativeMath.copySign(this, sign.toDouble())
/**
* Returns the ulp (unit in the last place) of this value.
*
* An ulp is a positive distance between this value and the next nearest [Double] value larger in magnitude.
*
* Special Cases:
* - `NaN.ulp` is `NaN`
* - `x.ulp` is `+Inf` when `x` is `+Inf` or `-Inf`
* - `0.0.ulp` is `Double.MIN_VALUE`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline val Double.ulp: Double get() = nativeMath.ulp(this)
/**
* Returns the [Double] value nearest to this value in direction of positive infinity.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun Double.nextUp(): Double = nativeMath.nextUp(this)
/**
* Returns the [Double] value nearest to this value in direction of negative infinity.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun Double.nextDown(): Double = nativeMath.nextAfter(this, Double.NEGATIVE_INFINITY)
/**
* Returns the [Double] value nearest to this value in direction from this value towards the value [to].
*
* Special cases:
* - `x.nextTowards(y)` is `NaN` if either `x` or `y` are `NaN`
* - `x.nextTowards(x) == x`
*
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun Double.nextTowards(to: Double): Double = nativeMath.nextAfter(this, to)
/**
* Rounds this [Double] value to the nearest integer and converts the result to [Int].
* Ties are rounded towards positive infinity.
*
* Special cases:
* - `x.roundToInt() == Int.MAX_VALUE` when `x > Int.MAX_VALUE`
* - `x.roundToInt() == Int.MIN_VALUE` when `x < Int.MIN_VALUE`
*
* @throws IllegalArgumentException when this value is `NaN`
*/
@SinceKotlin("1.2")
public actual fun Double.roundToInt(): Int = when {
isNaN() -> throw IllegalArgumentException("Cannot round NaN value.")
this > Int.MAX_VALUE -> Int.MAX_VALUE
this < Int.MIN_VALUE -> Int.MIN_VALUE
else -> nativeMath.round(this).toInt()
}
/**
* Rounds this [Double] value to the nearest integer and converts the result to [Long].
* Ties are rounded towards positive infinity.
*
* Special cases:
* - `x.roundToLong() == Long.MAX_VALUE` when `x > Long.MAX_VALUE`
* - `x.roundToLong() == Long.MIN_VALUE` when `x < Long.MIN_VALUE`
*
* @throws IllegalArgumentException when this value is `NaN`
*/
@SinceKotlin("1.2")
public actual fun Double.roundToLong(): Long =
if (isNaN()) throw IllegalArgumentException("Cannot round NaN value.") else nativeMath.round(this)
// endregion
// region ================ Float Math ========================================
/** Computes the sine of the angle [x] given in radians.
*
* Special cases:
* - `sin(NaN|+Inf|-Inf)` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun sin(x: Float): Float = nativeMath.sin(x.toDouble()).toFloat()
/** Computes the cosine of the angle [x] given in radians.
*
* Special cases:
* - `cos(NaN|+Inf|-Inf)` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun cos(x: Float): Float = nativeMath.cos(x.toDouble()).toFloat()
/** Computes the tangent of the angle [x] given in radians.
*
* Special cases:
* - `tan(NaN|+Inf|-Inf)` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun tan(x: Float): Float = nativeMath.tan(x.toDouble()).toFloat()
/**
* Computes the arc sine of the value [x];
* the returned value is an angle in the range from `-PI/2` to `PI/2` radians.
*
* Special cases:
* - `asin(x)` is `NaN`, when `abs(x) > 1` or x is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun asin(x: Float): Float = nativeMath.asin(x.toDouble()).toFloat()
/**
* Computes the arc cosine of the value [x];
* the returned value is an angle in the range from `0.0` to `PI` radians.
*
* Special cases:
* - `acos(x)` is `NaN`, when `abs(x) > 1` or x is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun acos(x: Float): Float = nativeMath.acos(x.toDouble()).toFloat()
/**
* Computes the arc tangent of the value [x];
* the returned value is an angle in the range from `-PI/2` to `PI/2` radians.
*
* Special cases:
* - `atan(NaN)` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun atan(x: Float): Float = nativeMath.atan(x.toDouble()).toFloat()
/**
* Returns the angle `theta` of the polar coordinates `(r, theta)` that correspond
* to the rectangular coordinates `(x, y)` by computing the arc tangent of the value [y] / [x];
* the returned value is an angle in the range from `-PI` to `PI` radians.
*
* Special cases:
* - `atan2(0.0, 0.0)` is `0.0`
* - `atan2(0.0, x)` is `0.0` for `x > 0` and `PI` for `x < 0`
* - `atan2(-0.0, x)` is `-0.0` for 'x > 0` and `-PI` for `x < 0`
* - `atan2(y, +Inf)` is `0.0` for `0 < y < +Inf` and `-0.0` for '-Inf < y < 0`
* - `atan2(y, -Inf)` is `PI` for `0 < y < +Inf` and `-PI` for `-Inf < y < 0`
* - `atan2(y, 0.0)` is `PI/2` for `y > 0` and `-PI/2` for `y < 0`
* - `atan2(+Inf, x)` is `PI/2` for finite `x`y
* - `atan2(-Inf, x)` is `-PI/2` for finite `x`
* - `atan2(NaN, x)` and `atan2(y, NaN)` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun atan2(y: Float, x: Float): Float = nativeMath.atan2(y.toDouble(), x.toDouble()).toFloat()
/**
* Computes the hyperbolic sine of the value [x].
*
* Special cases:
* - `sinh(NaN)` is `NaN`
* - `sinh(+Inf)` is `+Inf`
* - `sinh(-Inf)` is `-Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun sinh(x: Float): Float = nativeMath.sinh(x.toDouble()).toFloat()
/**
* Computes the hyperbolic cosine of the value [x].
*
* Special cases:
* - `cosh(NaN)` is `NaN`
* - `cosh(+Inf|-Inf)` is `+Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun cosh(x: Float): Float = nativeMath.cosh(x.toDouble()).toFloat()
/**
* Computes the hyperbolic tangent of the value [x].
*
* Special cases:
* - `tanh(NaN)` is `NaN`
* - `tanh(+Inf)` is `1.0`
* - `tanh(-Inf)` is `-1.0`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun tanh(x: Float): Float = nativeMath.tanh(x.toDouble()).toFloat()
/**
* Computes the inverse hyperbolic sine of the value [x].
*
* The returned value is `y` such that `sinh(y) == x`.
*
* Special cases:
* - `asinh(NaN)` is `NaN`
* - `asinh(+Inf)` is `+Inf`
* - `asinh(-Inf)` is `-Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun asinh(x: Float): Float = asinh(x.toDouble()).toFloat()
/**
* Computes the inverse hyperbolic cosine of the value [x].
*
* The returned value is positive `y` such that `cosh(y) == x`.
*
* Special cases:
* - `acosh(NaN)` is `NaN`
* - `acosh(x)` is `NaN` when `x < 1`
* - `acosh(+Inf)` is `+Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun acosh(x: Float): Float = acosh(x.toDouble()).toFloat()
/**
* Computes the inverse hyperbolic tangent of the value [x].
*
* The returned value is `y` such that `tanh(y) == x`.
*
* Special cases:
* - `tanh(NaN)` is `NaN`
* - `tanh(x)` is `NaN` when `x > 1` or `x < -1`
* - `tanh(1.0)` is `+Inf`
* - `tanh(-1.0)` is `-Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun atanh(x: Float): Float = atanh(x.toDouble()).toFloat()
/**
* Computes `sqrt(x^2 + y^2)` without intermediate overflow or underflow.
*
* Special cases:
* - returns `+Inf` if any of arguments is infinite
* - returns `NaN` if any of arguments is `NaN` and the other is not infinite
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun hypot(x: Float, y: Float): Float = nativeMath.hypot(x.toDouble(), y.toDouble()).toFloat()
/**
* Computes the positive square root of the value [x].
*
* Special cases:
* - `sqrt(x)` is `NaN` when `x < 0` or `x` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun sqrt(x: Float): Float = nativeMath.sqrt(x.toDouble()).toFloat()
/**
* Computes Euler's number `e` raised to the power of the value [x].
*
* Special cases:
* - `exp(NaN)` is `NaN`
* - `exp(+Inf)` is `+Inf`
* - `exp(-Inf)` is `0.0`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun exp(x: Float): Float = nativeMath.exp(x.toDouble()).toFloat()
/**
* Computes `exp(x) - 1`.
*
* This function can be implemented to produce more precise result for [x] near zero.
*
* Special cases:
* - `expm1(NaN)` is `NaN`
* - `expm1(+Inf)` is `+Inf`
* - `expm1(-Inf)` is `-1.0`
*
* @see [exp] function.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun expm1(x: Float): Float = nativeMath.expm1(x.toDouble()).toFloat()
/**
* Computes the logarithm of the value [x] to the given [base].
*
* Special cases:
* - `log(x, b)` is `NaN` if either `x` or `b` are `NaN`
* - `log(x, b)` is `NaN` when `x < 0` or `b <= 0` or `b == 1.0`
* - `log(+Inf, +Inf)` is `NaN`
* - `log(+Inf, b)` is `+Inf` for `b > 1` and `-Inf` for `b < 1`
* - `log(0.0, b)` is `-Inf` for `b > 1` and `+Inf` for `b > 1`
*
* See also logarithm functions for common fixed bases: [ln], [log10] and [log2].
*/
@SinceKotlin("1.2")
public actual fun log(x: Float, base: Float): Float {
if (base <= 0.0F || base == 1.0F) return Float.NaN
return (nativeMath.log(x.toDouble()) / nativeMath.log(base.toDouble())).toFloat()
}
/**
* Computes the natural logarithm (base `E`) of the value [x].
*
* Special cases:
* - `ln(NaN)` is `NaN`
* - `ln(x)` is `NaN` when `x < 0.0`
* - `ln(+Inf)` is `+Inf`
* - `ln(0.0)` is `-Inf`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun ln(x: Float): Float = nativeMath.log(x.toDouble()).toFloat()
/**
* Computes the common logarithm (base 10) of the value [x].
*
* @see [ln] function for special cases.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun log10(x: Float): Float = nativeMath.log10(x.toDouble()).toFloat()
/**
* Computes the binary logarithm (base 2) of the value [x].
*
* @see [ln] function for special cases.
*/
@SinceKotlin("1.2")
public actual fun log2(x: Float): Float = (nativeMath.log(x.toDouble()) / LN2).toFloat()
/**
* Computes `ln(a + 1)`.
*
* This function can be implemented to produce more precise result for [x] near zero.
*
* Special cases:
* - `ln1p(NaN)` is `NaN`
* - `ln1p(x)` is `NaN` where `x < -1.0`
* - `ln1p(-1.0)` is `-Inf`
* - `ln1p(+Inf)` is `+Inf`
*
* @see [ln] function
* @see [expm1] function
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun ln1p(x: Float): Float = nativeMath.log1p(x.toDouble()).toFloat()
/**
* Rounds the given value [x] to an integer towards positive infinity.
* @return the smallest Float value that is greater than or equal to the given value [x] and is a mathematical integer.
*
* Special cases:
* - `ceil(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun ceil(x: Float): Float = nativeMath.ceil(x.toDouble()).toFloat()
/**
* Rounds the given value [x] to an integer towards negative infinity.
* @return the largest Float value that is smaller than or equal to the given value [x] and is a mathematical integer.
*
* Special cases:
* - `floor(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun floor(x: Float): Float = nativeMath.floor(x.toDouble()).toFloat()
/**
* Rounds the given value [x] to an integer towards zero.
*
* @return the value [x] having its fractional part truncated.
*
* Special cases:
* - `truncate(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
public actual fun truncate(x: Float): Float = when {
x.isNaN() || x.isInfinite() -> x
x > 0 -> floor(x)
else -> ceil(x)
}
/**
* Rounds the given value [x] towards the closest integer with ties rounded towards even integer.
*
* Special cases:
* - `round(x)` is `x` where `x` is `NaN` or `+Inf` or `-Inf` or already a mathematical integer.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun round(x: Float): Float = nativeMath.rint(x.toDouble()).toFloat()
/**
* Returns the absolute value of the given value [x].
*
* Special cases:
* - `abs(NaN)` is `NaN`
*
* @see absoluteValue extension property for [Float]
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun abs(x: Float): Float = nativeMath.abs(x)
/**
* Returns the sign of the given value [x]:
* - `-1.0` if the value is negative,
* - zero if the value is zero,
* - `1.0` if the value is positive
*
* Special case:
* - `sign(NaN)` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun sign(x: Float): Float = nativeMath.signum(x)
/**
* Returns the smaller of two values.
*
* If either value is `NaN`, then the result is `NaN`.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun min(a: Float, b: Float): Float = nativeMath.min(a, b)
/**
* Returns the greater of two values.
*
* If either value is `NaN`, then the result is `NaN`.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun max(a: Float, b: Float): Float = nativeMath.max(a, b)
// extensions
/**
* Raises this value to the power [x].
*
* Special cases:
* - `b.pow(0.0)` is `1.0`
* - `b.pow(1.0) == b`
* - `b.pow(NaN)` is `NaN`
* - `NaN.pow(x)` is `NaN` for `x != 0.0`
* - `b.pow(Inf)` is `NaN` for `abs(b) == 1.0`
* - `b.pow(x)` is `NaN` for `b < 0` and `x` is finite and not an integer
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun Float.pow(x: Float): Float = nativeMath.pow(this.toDouble(), x.toDouble()).toFloat()
/**
* Raises this value to the integer power [n].
*
* See the other overload of [pow] for details.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun Float.pow(n: Int): Float = nativeMath.pow(this.toDouble(), n.toDouble()).toFloat()
/**
* Computes the remainder of division of this value by the [divisor] value according to the IEEE 754 standard.
*
* The result is computed as `r = this - (q * divisor)` where `q` is the quotient of division rounded to the nearest integer,
* `q = round(this / other)`.
*
* Special cases:
* - `x.IEEErem(y)` is `NaN`, when `x` is `NaN` or `y` is `NaN` or `x` is `+Inf|-Inf` or `y` is zero.
* - `x.IEEErem(y) == x` when `x` is finite and `y` is infinite.
*
* @see round
*/
@SinceKotlin("1.2")
@InlineOnly
public inline fun Float.IEEErem(divisor: Float): Float = nativeMath.IEEEremainder(this.toDouble(), divisor.toDouble()).toFloat()
/**
* Returns the absolute value of this value.
*
* Special cases:
* - `NaN.absoluteValue` is `NaN`
*
* @see abs function
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline val Float.absoluteValue: Float get() = nativeMath.abs(this)
/**
* Returns the sign of this value:
* - `-1.0` if the value is negative,
* - zero if the value is zero,
* - `1.0` if the value is positive
*
* Special case:
* - `NaN.sign` is `NaN`
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline val Float.sign: Float get() = nativeMath.signum(this)
/**
* Returns this value with the sign bit same as of the [sign] value.
*
* If [sign] is `NaN` the sign of the result is undefined.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun Float.withSign(sign: Float): Float = nativeMath.copySign(this, sign)
/**
* Returns this value with the sign bit same as of the [sign] value.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun Float.withSign(sign: Int): Float = nativeMath.copySign(this, sign.toFloat())
/**
* Returns the ulp of this value.
*
* An ulp is a positive distance between this value and the next nearest [Float] value larger in magnitude.
*
* Special Cases:
* - `NaN.ulp` is `NaN`
* - `x.ulp` is `+Inf` when `x` is `+Inf` or `-Inf`
* - `0.0.ulp` is `Float.NIN_VALUE`
*/
@SinceKotlin("1.2")
@InlineOnly
public inline val Float.ulp: Float get() = nativeMath.ulp(this)
/**
* Returns the [Float] value nearest to this value in direction of positive infinity.
*/
@SinceKotlin("1.2")
@InlineOnly
public inline fun Float.nextUp(): Float = nativeMath.nextUp(this)
/**
* Returns the [Float] value nearest to this value in direction of negative infinity.
*/
@SinceKotlin("1.2")
@InlineOnly
public inline fun Float.nextDown(): Float = nativeMath.nextAfter(this, Double.NEGATIVE_INFINITY)
/**
* Returns the [Float] value nearest to this value in direction from this value towards the value [to].
*
* Special cases:
* - `x.nextTowards(y)` is `NaN` if either `x` or `y` are `NaN`
* - `x.nextTowards(x) == x`
*
*/
@SinceKotlin("1.2")
@InlineOnly
public inline fun Float.nextTowards(to: Float): Float = nativeMath.nextAfter(this, to.toDouble())
/**
* Rounds this [Float] value to the nearest integer and converts the result to [Int].
* Ties are rounded towards positive infinity.
*
* Special cases:
* - `x.roundToInt() == Int.MAX_VALUE` when `x > Int.MAX_VALUE`
* - `x.roundToInt() == Int.MIN_VALUE` when `x < Int.MIN_VALUE`
*
* @throws IllegalArgumentException when this value is `NaN`
*/
@SinceKotlin("1.2")
public actual fun Float.roundToInt(): Int =
if (isNaN()) throw IllegalArgumentException("Cannot round NaN value.") else nativeMath.round(this)
/**
* Rounds this [Float] value to the nearest integer and converts the result to [Long].
* Ties are rounded towards positive infinity.
*
* Special cases:
* - `x.roundToLong() == Long.MAX_VALUE` when `x > Long.MAX_VALUE`
* - `x.roundToLong() == Long.MIN_VALUE` when `x < Long.MIN_VALUE`
*
* @throws IllegalArgumentException when this value is `NaN`
*/
@SinceKotlin("1.2")
public actual fun Float.roundToLong(): Long = toDouble().roundToLong()
// endregion
// region ================ Integer Math ========================================
/**
* Returns the absolute value of the given value [n].
*
* Special cases:
* - `abs(Int.MIN_VALUE)` is `Int.MIN_VALUE` due to an overflow
*
* @see absoluteValue extension property for [Int]
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun abs(n: Int): Int = nativeMath.abs(n)
/**
* Returns the smaller of two values.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun min(a: Int, b: Int): Int = nativeMath.min(a, b)
/**
* Returns the greater of two values.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun max(a: Int, b: Int): Int = nativeMath.max(a, b)
/**
* Returns the absolute value of this value.
*
* Special cases:
* - `Int.MIN_VALUE.absoluteValue` is `Int.MIN_VALUE` due to an overflow
*
* @see abs function
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline val Int.absoluteValue: Int get() = nativeMath.abs(this)
/**
* Returns the sign of this value:
* - `-1` if the value is negative,
* - `0` if the value is zero,
* - `1` if the value is positive
*/
@SinceKotlin("1.2")
public actual val Int.sign: Int get() = when {
this < 0 -> -1
this > 0 -> 1
else -> 0
}
/**
* Returns the absolute value of the given value [n].
*
* Special cases:
* - `abs(Long.MIN_VALUE)` is `Long.MIN_VALUE` due to an overflow
*
* @see absoluteValue extension property for [Long]
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun abs(n: Long): Long = nativeMath.abs(n)
/**
* Returns the smaller of two values.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun min(a: Long, b: Long): Long = nativeMath.min(a, b)
/**
* Returns the greater of two values.
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline fun max(a: Long, b: Long): Long = nativeMath.max(a, b)
/**
* Returns the absolute value of this value.
*
* Special cases:
* - `Long.MIN_VALUE.absoluteValue` is `Long.MIN_VALUE` due to an overflow
*
* @see abs function
*/
@SinceKotlin("1.2")
@InlineOnly
public actual inline val Long.absoluteValue: Long get() = nativeMath.abs(this)
/**
* Returns the sign of this value:
* - `-1` if the value is negative,
* - `0` if the value is zero,
* - `1` if the value is positive
*/
@SinceKotlin("1.2")
public actual val Long.sign: Int get() = when {
this < 0 -> -1
this > 0 -> 1
else -> 0
}
// endregion