Romain Guy
02a3915fdf
cbrt() is the standard cubic root function that provides several advantages over pow(x, 1.0/3.0): - Better precision - Faster - Behaves better with negative values
744 lines
29 KiB
Kotlin
744 lines
29 KiB
Kotlin
/*
|
|
* 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.
|
|
*/
|
|
|
|
package test.numbers
|
|
|
|
import kotlin.math.*
|
|
import kotlin.test.*
|
|
|
|
fun assertAlmostEquals(expected: Double, actual: Double, tolerance: Double? = null) {
|
|
val tolerance_ = tolerance?.let { abs(it) } ?: 0.000000000001
|
|
if (abs(expected - actual) > tolerance_) {
|
|
assertEquals(expected, actual)
|
|
}
|
|
}
|
|
|
|
fun assertAlmostEquals(expected: Float, actual: Float, tolerance: Double? = null) {
|
|
val tolerance_ = tolerance?.let { abs(it) } ?: 0.0000001
|
|
if (abs(expected - actual) > tolerance_) {
|
|
assertEquals(expected, actual)
|
|
}
|
|
}
|
|
|
|
// For Kotlin JS tests
|
|
private val Float.ulpCommon: Float
|
|
get() = when {
|
|
isNaN() -> Float.NaN
|
|
isInfinite() -> Float.POSITIVE_INFINITY
|
|
this == Float.MAX_VALUE || this == -Float.MAX_VALUE -> 2.0f.pow(104)
|
|
else -> {
|
|
val d = absoluteValue
|
|
// Ensure we never have -0.0f
|
|
val valueOrPositiveZero = (this + 0.0f).toBits();
|
|
Float.fromBits(valueOrPositiveZero + (if (valueOrPositiveZero >= 0) 1 else -1)) - d
|
|
}
|
|
}
|
|
|
|
class DoubleMathTest {
|
|
|
|
@Test fun trigonometric() {
|
|
assertEquals(0.0, sin(0.0))
|
|
assertAlmostEquals(0.0, sin(PI))
|
|
|
|
assertEquals(0.0, asin(0.0))
|
|
assertAlmostEquals(PI / 2, asin(1.0))
|
|
|
|
assertEquals(1.0, cos(0.0))
|
|
assertAlmostEquals(-1.0, cos(PI))
|
|
|
|
assertEquals(0.0, acos(1.0))
|
|
assertAlmostEquals(PI / 2, acos(0.0))
|
|
|
|
assertEquals(0.0, tan(0.0))
|
|
assertAlmostEquals(1.0, tan(PI / 4))
|
|
|
|
assertAlmostEquals(0.0, atan(0.0))
|
|
assertAlmostEquals(PI / 4, atan(1.0))
|
|
|
|
assertAlmostEquals(PI / 4, atan2(10.0, 10.0))
|
|
assertAlmostEquals(-PI / 4, atan2(Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY))
|
|
assertAlmostEquals(0.0, atan2(0.0, 0.0))
|
|
assertAlmostEquals(0.0, atan2(0.0, 10.0))
|
|
assertAlmostEquals(PI / 2, atan2(2.0, 0.0))
|
|
|
|
for (angle in listOf(Double.NaN, Double.POSITIVE_INFINITY, Double.NEGATIVE_INFINITY)) {
|
|
assertTrue(sin(angle).isNaN(), "sin($angle)")
|
|
assertTrue(cos(angle).isNaN(), "cos($angle)")
|
|
assertTrue(tan(angle).isNaN(), "tan($angle)")
|
|
}
|
|
|
|
for (value in listOf(Double.NaN, 1.2, -1.1)) {
|
|
assertTrue(asin(value).isNaN())
|
|
assertTrue(acos(value).isNaN())
|
|
}
|
|
assertTrue(atan(Double.NaN).isNaN())
|
|
assertTrue(atan2(Double.NaN, 0.0).isNaN())
|
|
assertTrue(atan2(0.0, Double.NaN).isNaN())
|
|
}
|
|
|
|
@Test fun hyperbolic() {
|
|
assertEquals(Double.POSITIVE_INFINITY, sinh(Double.POSITIVE_INFINITY))
|
|
assertEquals(Double.NEGATIVE_INFINITY, sinh(Double.NEGATIVE_INFINITY))
|
|
assertTrue(sinh(Double.MIN_VALUE) != 0.0)
|
|
assertTrue(sinh(710.0).isFinite())
|
|
assertTrue(sinh(-710.0).isFinite())
|
|
assertTrue(sinh(Double.NaN).isNaN())
|
|
|
|
assertEquals(Double.POSITIVE_INFINITY, cosh(Double.POSITIVE_INFINITY))
|
|
assertEquals(Double.POSITIVE_INFINITY, cosh(Double.NEGATIVE_INFINITY))
|
|
assertTrue(cosh(710.0).isFinite())
|
|
assertTrue(cosh(-710.0).isFinite())
|
|
assertTrue(cosh(Double.NaN).isNaN())
|
|
|
|
assertAlmostEquals(1.0, tanh(Double.POSITIVE_INFINITY))
|
|
assertAlmostEquals(-1.0, tanh(Double.NEGATIVE_INFINITY))
|
|
assertTrue(tanh(Double.MIN_VALUE) != 0.0)
|
|
assertTrue(tanh(Double.NaN).isNaN())
|
|
}
|
|
|
|
@Test fun inverseHyperbolicSin() {
|
|
for (exact in listOf(Double.POSITIVE_INFINITY, Double.NEGATIVE_INFINITY, 0.0, Double.MIN_VALUE, -Double.MIN_VALUE, 0.00001)) {
|
|
assertEquals(exact, asinh(sinh(exact)))
|
|
}
|
|
for (approx in listOf(Double.MIN_VALUE, 0.1, 1.0, 100.0, 710.0)) {
|
|
assertAlmostEquals(approx, asinh(sinh(approx)))
|
|
assertAlmostEquals(-approx, asinh(sinh(-approx)))
|
|
}
|
|
assertTrue(asinh(Double.NaN).isNaN())
|
|
}
|
|
|
|
@Test fun inverseHyperbolicCos() {
|
|
for (exact in listOf(Double.POSITIVE_INFINITY, Double.NEGATIVE_INFINITY, 0.0)) {
|
|
assertEquals(abs(exact), acosh(cosh(exact)))
|
|
}
|
|
for (approx in listOf(Double.MIN_VALUE, 0.00001, 1.0, 100.0, 710.0)) {
|
|
assertAlmostEquals(approx, acosh(cosh(approx)))
|
|
assertAlmostEquals(approx, acosh(cosh(-approx)))
|
|
}
|
|
for (invalid in listOf(-1.0, 0.0, 0.99999, Double.NaN)) {
|
|
assertTrue(acosh(invalid).isNaN())
|
|
}
|
|
}
|
|
|
|
@Test fun inverseHyperbolicTan() {
|
|
for (exact in listOf(Double.POSITIVE_INFINITY, Double.NEGATIVE_INFINITY, 0.0, Double.MIN_VALUE, -Double.MIN_VALUE)) {
|
|
assertEquals(exact, atanh(tanh(exact)))
|
|
}
|
|
for (approx in listOf(0.00001)) {
|
|
assertAlmostEquals(approx, atanh(tanh(approx)))
|
|
}
|
|
|
|
for (invalid in listOf(-1.00001, 1.00001, Double.NaN, Double.MAX_VALUE, -Double.MAX_VALUE, Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY)) {
|
|
assertTrue(atanh(invalid).isNaN())
|
|
}
|
|
}
|
|
|
|
@Test fun cubeRoots() {
|
|
val testingPairs = mapOf(
|
|
Double.NaN to Double.NaN,
|
|
Double.POSITIVE_INFINITY to Double.POSITIVE_INFINITY,
|
|
Double.NEGATIVE_INFINITY to Double.NEGATIVE_INFINITY,
|
|
Double.fromBits(0x0010000000000000) to 2.812644285236262E-103, // smallest normal value
|
|
Double.fromBits(0x1L) to 1.7031839360032603E-108, // smallest value (denormal)
|
|
Double.MAX_VALUE to 5.643803094122362E102,
|
|
0.0 to 0.0,
|
|
0.9 to 0.9654893846056297,
|
|
9.9 to 2.1472291690189413,
|
|
27.0 to 3.0,
|
|
399.1289 to 7.362710510208026,
|
|
8123.452 to 20.102351976782558,
|
|
21717.639 to 27.9,
|
|
392890.22 to 73.24147345684439
|
|
)
|
|
|
|
for ((x, result) in testingPairs) {
|
|
assertEquals(result, cbrt(x), if (result.isFinite()) 2.0 * result.ulp else 0.0)
|
|
assertEquals(cbrt(-x), -cbrt(x))
|
|
}
|
|
}
|
|
|
|
@Test fun powers() {
|
|
assertEquals(5.0, hypot(3.0, 4.0))
|
|
assertEquals(Double.POSITIVE_INFINITY, hypot(Double.NEGATIVE_INFINITY, Double.NaN))
|
|
assertEquals(Double.POSITIVE_INFINITY, hypot(Double.NaN, Double.POSITIVE_INFINITY))
|
|
assertTrue(hypot(Double.NaN, 0.0).isNaN())
|
|
|
|
assertEquals(1.0, Double.NaN.pow(0.0))
|
|
assertEquals(1.0, Double.POSITIVE_INFINITY.pow(0))
|
|
assertEquals(49.0, 7.0.pow(2))
|
|
assertEquals(0.25, 2.0.pow(-2))
|
|
assertTrue(0.0.pow(Double.NaN).isNaN())
|
|
assertTrue(Double.NaN.pow(-1).isNaN())
|
|
assertTrue((-7.0).pow(1 / 3.0).isNaN())
|
|
assertTrue(1.0.pow(Double.POSITIVE_INFINITY).isNaN())
|
|
assertTrue((-1.0).pow(Double.NEGATIVE_INFINITY).isNaN())
|
|
|
|
assertEquals(5.0, sqrt(9.0 + 16.0))
|
|
assertTrue(sqrt(-1.0).isNaN())
|
|
assertTrue(sqrt(Double.NaN).isNaN())
|
|
|
|
assertTrue(exp(Double.NaN).isNaN())
|
|
assertAlmostEquals(E, exp(1.0))
|
|
assertEquals(1.0, exp(0.0))
|
|
assertEquals(0.0, exp(Double.NEGATIVE_INFINITY))
|
|
assertEquals(Double.POSITIVE_INFINITY, exp(Double.POSITIVE_INFINITY))
|
|
|
|
assertEquals(0.0, expm1(0.0))
|
|
assertEquals(Double.MIN_VALUE, expm1(Double.MIN_VALUE))
|
|
assertEquals(0.00010000500016667084, expm1(1e-4))
|
|
assertEquals(-1.0, expm1(Double.NEGATIVE_INFINITY))
|
|
assertEquals(Double.POSITIVE_INFINITY, expm1(Double.POSITIVE_INFINITY))
|
|
}
|
|
|
|
@Test fun logarithms() {
|
|
assertTrue(log(1.0, Double.NaN).isNaN())
|
|
assertTrue(log(Double.NaN, 1.0).isNaN())
|
|
assertTrue(log(-1.0, 2.0).isNaN())
|
|
assertTrue(log(2.0, -1.0).isNaN())
|
|
assertTrue(log(2.0, 0.0).isNaN())
|
|
assertTrue(log(2.0, 1.0).isNaN())
|
|
assertTrue(log(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY).isNaN())
|
|
assertEquals(-2.0, log(0.25, 2.0))
|
|
assertEquals(-0.5, log(2.0, 0.25))
|
|
assertEquals(Double.NEGATIVE_INFINITY, log(Double.POSITIVE_INFINITY, 0.25))
|
|
assertEquals(Double.POSITIVE_INFINITY, log(Double.POSITIVE_INFINITY, 2.0))
|
|
assertEquals(Double.NEGATIVE_INFINITY, log(0.0, 2.0))
|
|
assertEquals(Double.POSITIVE_INFINITY, log(0.0, 0.25))
|
|
|
|
assertTrue(ln(Double.NaN).isNaN())
|
|
assertTrue(ln(-1.0).isNaN())
|
|
assertEquals(1.0, ln(E))
|
|
assertEquals(Double.NEGATIVE_INFINITY, ln(0.0))
|
|
assertEquals(Double.POSITIVE_INFINITY, ln(Double.POSITIVE_INFINITY))
|
|
|
|
assertEquals(1.0, log10(10.0))
|
|
assertAlmostEquals(-1.0, log10(0.1))
|
|
|
|
assertAlmostEquals(3.0, log2(8.0))
|
|
assertEquals(-1.0, log2(0.5))
|
|
|
|
assertTrue(ln1p(Double.NaN).isNaN())
|
|
assertTrue(ln1p(-1.1).isNaN())
|
|
assertEquals(0.0, ln1p(0.0))
|
|
assertEquals(9.999995000003334e-7, ln1p(1e-6))
|
|
assertEquals(Double.MIN_VALUE, ln1p(Double.MIN_VALUE))
|
|
assertEquals(Double.NEGATIVE_INFINITY, ln1p(-1.0))
|
|
}
|
|
|
|
@Test fun rounding() {
|
|
for (value in listOf(Double.NaN, Double.POSITIVE_INFINITY, Double.NEGATIVE_INFINITY, 0.0, 1.0, -10.0)) {
|
|
assertEquals(value, ceil(value))
|
|
assertEquals(value, floor(value))
|
|
assertEquals(value, truncate(value))
|
|
assertEquals(value, round(value))
|
|
}
|
|
val data = arrayOf( // v floor trunc round ceil
|
|
doubleArrayOf( 1.3, 1.0, 1.0, 1.0, 2.0),
|
|
doubleArrayOf(-1.3, -2.0, -1.0, -1.0, -1.0),
|
|
doubleArrayOf( 1.5, 1.0, 1.0, 2.0, 2.0),
|
|
doubleArrayOf(-1.5, -2.0, -1.0, -2.0, -1.0),
|
|
doubleArrayOf( 1.8, 1.0, 1.0, 2.0, 2.0),
|
|
doubleArrayOf(-1.8, -2.0, -1.0, -2.0, -1.0),
|
|
|
|
doubleArrayOf( 2.3, 2.0, 2.0, 2.0, 3.0),
|
|
doubleArrayOf(-2.3, -3.0, -2.0, -2.0, -2.0),
|
|
doubleArrayOf( 2.5, 2.0, 2.0, 2.0, 3.0),
|
|
doubleArrayOf(-2.5, -3.0, -2.0, -2.0, -2.0),
|
|
doubleArrayOf( 2.8, 2.0, 2.0, 3.0, 3.0),
|
|
doubleArrayOf(-2.8, -3.0, -2.0, -3.0, -2.0)
|
|
)
|
|
for ((v, f, t, r, c) in data) {
|
|
assertEquals(f, floor(v), "floor($v)")
|
|
assertEquals(t, truncate(v), "truncate($v)")
|
|
assertEquals(r, round(v), "round($v)")
|
|
assertEquals(c, ceil(v), "ceil($v)")
|
|
}
|
|
}
|
|
|
|
@Test fun roundingConversion() {
|
|
assertEquals(1L, 1.0.roundToLong())
|
|
assertEquals(1L, 1.1.roundToLong())
|
|
assertEquals(2L, 1.5.roundToLong())
|
|
assertEquals(3L, 2.5.roundToLong())
|
|
assertEquals(-2L, (-2.5).roundToLong())
|
|
assertEquals(-3L, (-2.6).roundToLong())
|
|
assertEquals(9223372036854774784, (9223372036854774800.0).roundToLong())
|
|
assertEquals(Long.MAX_VALUE, Double.MAX_VALUE.roundToLong())
|
|
assertEquals(Long.MIN_VALUE, (-Double.MAX_VALUE).roundToLong())
|
|
assertEquals(Long.MAX_VALUE, Double.POSITIVE_INFINITY.roundToLong())
|
|
assertEquals(Long.MIN_VALUE, Double.NEGATIVE_INFINITY.roundToLong())
|
|
|
|
assertFails { Double.NaN.roundToLong() }
|
|
|
|
assertEquals(1, 1.0.roundToInt())
|
|
assertEquals(1, 1.1.roundToInt())
|
|
assertEquals(2, 1.5.roundToInt())
|
|
assertEquals(3, 2.5.roundToInt())
|
|
assertEquals(-2, (-2.5).roundToInt())
|
|
assertEquals(-3, (-2.6).roundToInt())
|
|
assertEquals(2123456789, (2123456789.0).roundToInt())
|
|
assertEquals(Int.MAX_VALUE, Double.MAX_VALUE.roundToInt())
|
|
assertEquals(Int.MIN_VALUE, (-Double.MAX_VALUE).roundToInt())
|
|
assertEquals(Int.MAX_VALUE, Double.POSITIVE_INFINITY.roundToInt())
|
|
assertEquals(Int.MIN_VALUE, Double.NEGATIVE_INFINITY.roundToInt())
|
|
|
|
assertFails { Double.NaN.roundToInt() }
|
|
}
|
|
|
|
@Test fun absoluteValue() {
|
|
assertTrue(abs(Double.NaN).isNaN())
|
|
assertTrue(Double.NaN.absoluteValue.isNaN())
|
|
|
|
for (value in listOf(0.0, Double.MIN_VALUE, 0.1, 1.0, 1000.0, Double.MAX_VALUE, Double.POSITIVE_INFINITY)) {
|
|
assertEquals(value, value.absoluteValue)
|
|
assertEquals(value, (-value).absoluteValue)
|
|
assertEquals(value, abs(value))
|
|
assertEquals(value, abs(-value))
|
|
}
|
|
}
|
|
|
|
@Test fun signs() {
|
|
assertTrue(sign(Double.NaN).isNaN())
|
|
assertTrue(Double.NaN.sign.isNaN())
|
|
|
|
val negatives = listOf(Double.NEGATIVE_INFINITY, -Double.MAX_VALUE, -1.0, -Double.MIN_VALUE)
|
|
for (value in negatives) {
|
|
assertEquals(-1.0, sign(value))
|
|
assertEquals(-1.0, value.sign)
|
|
}
|
|
|
|
val zeroes = listOf(0.0, -0.0)
|
|
for (value in zeroes) {
|
|
assertEquals(value, sign(value))
|
|
assertEquals(value, value.sign)
|
|
}
|
|
|
|
|
|
val positives = listOf(Double.POSITIVE_INFINITY, Double.MAX_VALUE, 1.0, Double.MIN_VALUE)
|
|
for (value in positives) {
|
|
assertEquals(1.0, sign(value))
|
|
assertEquals(1.0, value.sign)
|
|
}
|
|
|
|
val allValues = negatives + positives
|
|
for (a in allValues) {
|
|
for (b in allValues) {
|
|
val r = a.withSign(b)
|
|
assertEquals(a.absoluteValue, r.absoluteValue)
|
|
assertEquals(b.sign, r.sign, "expected $a with sign bit of $b to have sign ${b.sign}")
|
|
}
|
|
|
|
val rp0 = a.withSign(0.0)
|
|
assertEquals(1.0, rp0.sign)
|
|
assertEquals(a.absoluteValue, rp0.absoluteValue)
|
|
|
|
val rm0 = a.withSign(-0.0)
|
|
assertEquals(-1.0, rm0.sign)
|
|
assertEquals(a.absoluteValue, rm0.absoluteValue)
|
|
|
|
val ri = a.withSign(-1)
|
|
assertEquals(-1.0, ri.sign)
|
|
assertEquals(a.absoluteValue, ri.absoluteValue)
|
|
|
|
val rn = a.withSign(Double.NaN)
|
|
assertEquals(a.absoluteValue, rn.absoluteValue)
|
|
}
|
|
}
|
|
|
|
|
|
@Test fun nextAndPrev() {
|
|
for (value in listOf(0.0, -0.0, Double.MIN_VALUE, -1.0, 2.0.pow(10))) {
|
|
val next = value.nextUp()
|
|
if (next > 0) {
|
|
assertEquals(next, value + value.ulp)
|
|
} else {
|
|
assertEquals(value, next - next.ulp)
|
|
}
|
|
|
|
val prev = value.nextDown()
|
|
if (prev > 0) {
|
|
assertEquals(value, prev + prev.ulp)
|
|
} else {
|
|
assertEquals(prev, value - value.ulp)
|
|
}
|
|
|
|
val toZero = value.nextTowards(0.0)
|
|
if (toZero != 0.0) {
|
|
assertEquals(value, toZero + toZero.ulp.withSign(toZero))
|
|
}
|
|
|
|
assertEquals(Double.POSITIVE_INFINITY, Double.MAX_VALUE.nextUp())
|
|
assertEquals(Double.MAX_VALUE, Double.POSITIVE_INFINITY.nextDown())
|
|
|
|
assertEquals(Double.NEGATIVE_INFINITY, (-Double.MAX_VALUE).nextDown())
|
|
assertEquals((-Double.MAX_VALUE), Double.NEGATIVE_INFINITY.nextUp())
|
|
|
|
assertTrue(Double.NaN.ulp.isNaN())
|
|
assertTrue(Double.NaN.nextDown().isNaN())
|
|
assertTrue(Double.NaN.nextUp().isNaN())
|
|
assertTrue(Double.NaN.nextTowards(0.0).isNaN())
|
|
|
|
assertEquals(Double.MIN_VALUE, (0.0).ulp)
|
|
assertEquals(Double.MIN_VALUE, (-0.0).ulp)
|
|
assertEquals(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY.ulp)
|
|
assertEquals(Double.POSITIVE_INFINITY, Double.NEGATIVE_INFINITY.ulp)
|
|
|
|
val maxUlp = 2.0.pow(971)
|
|
assertEquals(maxUlp, Double.MAX_VALUE.ulp)
|
|
assertEquals(maxUlp, (-Double.MAX_VALUE).ulp)
|
|
}
|
|
}
|
|
}
|
|
|
|
class FloatMathTest {
|
|
|
|
companion object {
|
|
const val PI = kotlin.math.PI.toFloat()
|
|
const val E = kotlin.math.E.toFloat()
|
|
}
|
|
|
|
// TODO: ensure it passes in kotlin-stdlib-js-ir after implementing KT-24975
|
|
@Ignore
|
|
@Test
|
|
fun floatRangeConversion() {
|
|
// expected run-time conversion to produce the same result as compile-time one
|
|
assertEquals(kotlin.math.E.toFloat(), E)
|
|
assertEquals(kotlin.math.PI.toFloat(), PI)
|
|
}
|
|
|
|
@Test fun trigonometric() {
|
|
assertEquals(0.0F, sin(0.0F))
|
|
assertAlmostEquals(0.0F, sin(PI))
|
|
|
|
assertEquals(0.0F, asin(0.0F))
|
|
assertAlmostEquals(PI / 2, asin(1.0F), 0.0000002)
|
|
|
|
assertEquals(1.0F, cos(0.0F))
|
|
assertAlmostEquals(-1.0F, cos(PI))
|
|
|
|
assertEquals(0.0F, acos(1.0F))
|
|
assertAlmostEquals(PI / 2, acos(0.0F))
|
|
|
|
assertEquals(0.0F, tan(0.0F))
|
|
assertAlmostEquals(1.0F, tan(PI / 4))
|
|
|
|
assertAlmostEquals(0.0F, atan(0.0F))
|
|
assertAlmostEquals(PI / 4, atan(1.0F))
|
|
|
|
assertAlmostEquals(PI / 4, atan2(10.0F, 10.0F))
|
|
assertAlmostEquals(-PI / 4, atan2(Float.NEGATIVE_INFINITY, Float.POSITIVE_INFINITY))
|
|
assertAlmostEquals(0.0F, atan2(0.0F, 0.0F))
|
|
assertAlmostEquals(0.0F, atan2(0.0F, 10.0F))
|
|
assertAlmostEquals(PI / 2, atan2(2.0F, 0.0F))
|
|
|
|
for (angle in listOf(Float.NaN, Float.POSITIVE_INFINITY, Float.NEGATIVE_INFINITY)) {
|
|
assertTrue(sin(angle).isNaN(), "sin($angle)")
|
|
assertTrue(cos(angle).isNaN(), "cos($angle)")
|
|
assertTrue(tan(angle).isNaN(), "tan($angle)")
|
|
}
|
|
|
|
for (value in listOf(Float.NaN, 1.2F, -1.1F)) {
|
|
assertTrue(asin(value).isNaN())
|
|
assertTrue(acos(value).isNaN())
|
|
}
|
|
assertTrue(atan(Float.NaN).isNaN())
|
|
assertTrue(atan2(Float.NaN, 0.0F).isNaN())
|
|
assertTrue(atan2(0.0F, Float.NaN).isNaN())
|
|
}
|
|
|
|
@Test fun hyperbolic() {
|
|
assertEquals(Float.POSITIVE_INFINITY, sinh(Float.POSITIVE_INFINITY))
|
|
assertEquals(Float.NEGATIVE_INFINITY, sinh(Float.NEGATIVE_INFINITY))
|
|
assertTrue(sinh(Float.MIN_VALUE) != 0.0F)
|
|
assertTrue(sinh(89.0F).isFinite())
|
|
assertTrue(sinh(-89.0F).isFinite())
|
|
assertTrue(sinh(Float.NaN).isNaN())
|
|
|
|
assertEquals(Float.POSITIVE_INFINITY, cosh(Float.POSITIVE_INFINITY))
|
|
assertEquals(Float.POSITIVE_INFINITY, cosh(Float.NEGATIVE_INFINITY))
|
|
assertTrue(cosh(89.0F).isFinite())
|
|
assertTrue(cosh(-89.0F).isFinite())
|
|
assertTrue(cosh(Float.NaN).isNaN())
|
|
|
|
assertAlmostEquals(1.0F, tanh(Float.POSITIVE_INFINITY))
|
|
assertAlmostEquals(-1.0F, tanh(Float.NEGATIVE_INFINITY))
|
|
assertTrue(tanh(Float.MIN_VALUE) != 0.0F)
|
|
assertTrue(tanh(Float.NaN).isNaN())
|
|
}
|
|
|
|
@Test fun inverseHyperbolicSin() {
|
|
for (exact in listOf(Float.POSITIVE_INFINITY, Float.NEGATIVE_INFINITY, 0.0F, Float.MIN_VALUE, -Float.MIN_VALUE, 0.00001F)) {
|
|
assertEquals(exact, asinh(sinh(exact)))
|
|
}
|
|
for (approx in listOf(Float.MIN_VALUE, 0.1F, 1.0F, 89.0F)) {
|
|
assertAlmostEquals(approx, asinh(sinh(approx)))
|
|
assertAlmostEquals(-approx, asinh(sinh(-approx)))
|
|
}
|
|
assertTrue(asinh(Float.NaN).isNaN())
|
|
}
|
|
|
|
@Test fun inverseHyperbolicCos() {
|
|
for (exact in listOf(Float.POSITIVE_INFINITY, Float.NEGATIVE_INFINITY, 0.0F)) {
|
|
assertEquals(abs(exact), acosh(cosh(exact)))
|
|
}
|
|
for (approx in listOf(Float.MIN_VALUE, 0.1F, 1.0F, 89.0F)) {
|
|
assertAlmostEquals(approx, acosh(cosh(approx)))
|
|
assertAlmostEquals(approx, acosh(cosh(-approx)))
|
|
}
|
|
for (invalid in listOf(-1.0F, 0.0F, 0.99999F, Float.NaN)) {
|
|
assertTrue(acosh(invalid).isNaN())
|
|
}
|
|
}
|
|
|
|
@Test fun inverseHyperbolicTan() {
|
|
for (exact in listOf(Float.POSITIVE_INFINITY, Float.NEGATIVE_INFINITY, 0.0F, Float.MIN_VALUE, -Float.MIN_VALUE)) {
|
|
assertEquals(exact, atanh(tanh(exact)))
|
|
}
|
|
|
|
for (approx in listOf(0.00001F)) {
|
|
assertAlmostEquals(approx, atanh(tanh(approx)))
|
|
}
|
|
|
|
for (invalid in listOf(-1.00001F, 1.00001F, Float.NaN, Float.MAX_VALUE, -Float.MAX_VALUE, Float.NEGATIVE_INFINITY, Float.POSITIVE_INFINITY)) {
|
|
assertTrue(atanh(invalid).isNaN())
|
|
}
|
|
}
|
|
|
|
@Test fun cubeRoots() {
|
|
val testingPairs = mapOf(
|
|
Float.NaN to Float.NaN,
|
|
Float.POSITIVE_INFINITY to Float.POSITIVE_INFINITY,
|
|
Float.NEGATIVE_INFINITY to Float.NEGATIVE_INFINITY,
|
|
Float.fromBits(0x00800000) to 2.2737368E-13f, // smallest normal value
|
|
Float.fromBits(0x1) to 1.1190347E-15f, // smallest value (denormal)
|
|
Float.MAX_VALUE to 6.9814636E12f,
|
|
0.0f to 0.0f,
|
|
0.9f to 0.9654894f,
|
|
9.9f to 2.1472292f,
|
|
27.0f to 3.0f,
|
|
399.1289f to 7.3627105f,
|
|
8123.452f to 20.102352f,
|
|
21717.639f to 27.9f,
|
|
392890.22f to 73.24147f
|
|
)
|
|
|
|
for ((x, result) in testingPairs) {
|
|
assertEquals(result, cbrt(x), if (result.isFinite()) 2.0f * result.ulpCommon else 0.0f)
|
|
assertEquals(cbrt(-x), -cbrt(x))
|
|
}
|
|
}
|
|
|
|
@Test fun powers() {
|
|
assertEquals(5.0F, hypot(3.0F, 4.0F))
|
|
assertEquals(Float.POSITIVE_INFINITY, hypot(Float.NEGATIVE_INFINITY, Float.NaN))
|
|
assertEquals(Float.POSITIVE_INFINITY, hypot(Float.NaN, Float.POSITIVE_INFINITY))
|
|
assertTrue(hypot(Float.NaN, 0.0F).isNaN())
|
|
|
|
assertEquals(1.0F, Float.NaN.pow(0.0F))
|
|
assertEquals(1.0F, Float.POSITIVE_INFINITY.pow(0))
|
|
assertEquals(49.0F, 7.0F.pow(2))
|
|
assertEquals(0.25F, 2.0F.pow(-2))
|
|
assertTrue(0.0F.pow(Float.NaN).isNaN())
|
|
assertTrue(Float.NaN.pow(-1).isNaN())
|
|
assertTrue((-7.0F).pow(1 / 3.0F).isNaN())
|
|
assertTrue(1.0F.pow(Float.POSITIVE_INFINITY).isNaN())
|
|
assertTrue((-1.0F).pow(Float.NEGATIVE_INFINITY).isNaN())
|
|
|
|
assertEquals(5.0F, sqrt(9.0F + 16.0F))
|
|
assertTrue(sqrt(-1.0F).isNaN())
|
|
assertTrue(sqrt(Float.NaN).isNaN())
|
|
|
|
assertTrue(exp(Float.NaN).isNaN())
|
|
assertAlmostEquals(kotlin.math.E.toFloat(), exp(1.0F))
|
|
assertEquals(1.0F, exp(0.0F))
|
|
assertEquals(0.0F, exp(Float.NEGATIVE_INFINITY))
|
|
assertEquals(Float.POSITIVE_INFINITY, exp(Float.POSITIVE_INFINITY))
|
|
|
|
assertEquals(0.0F, expm1(0.0F))
|
|
assertEquals(-1.0F, expm1(Float.NEGATIVE_INFINITY))
|
|
assertEquals(Float.POSITIVE_INFINITY, expm1(Float.POSITIVE_INFINITY))
|
|
}
|
|
|
|
@Test fun logarithms() {
|
|
assertTrue(log(1.0F, Float.NaN).isNaN())
|
|
assertTrue(log(Float.NaN, 1.0F).isNaN())
|
|
assertTrue(log(-1.0F, 2.0F).isNaN())
|
|
assertTrue(log(2.0F, -1.0F).isNaN())
|
|
assertTrue(log(2.0F, 0.0F).isNaN())
|
|
assertTrue(log(2.0F, 1.0F).isNaN())
|
|
assertTrue(log(Float.POSITIVE_INFINITY, Float.POSITIVE_INFINITY).isNaN())
|
|
assertEquals(-2.0F, log(0.25F, 2.0F))
|
|
assertEquals(-0.5F, log(2.0F, 0.25F))
|
|
assertEquals(Float.NEGATIVE_INFINITY, log(Float.POSITIVE_INFINITY, 0.25F))
|
|
assertEquals(Float.POSITIVE_INFINITY, log(Float.POSITIVE_INFINITY, 2.0F))
|
|
assertEquals(Float.NEGATIVE_INFINITY, log(0.0F, 2.0F))
|
|
assertEquals(Float.POSITIVE_INFINITY, log(0.0F, 0.25F))
|
|
|
|
assertTrue(ln(Float.NaN).isNaN())
|
|
assertTrue(ln(-1.0F).isNaN())
|
|
assertAlmostEquals(1.0F, ln(E))
|
|
assertEquals(Float.NEGATIVE_INFINITY, ln(0.0F))
|
|
assertEquals(Float.POSITIVE_INFINITY, ln(Float.POSITIVE_INFINITY))
|
|
|
|
assertEquals(1.0F, log10(10.0F))
|
|
assertAlmostEquals(-1.0F, log10(0.1F))
|
|
|
|
assertAlmostEquals(3.0F, log2(8.0F))
|
|
assertEquals(-1.0F, log2(0.5F))
|
|
|
|
assertTrue(ln1p(Float.NaN).isNaN())
|
|
assertTrue(ln1p(-1.1F).isNaN())
|
|
assertEquals(0.0F, ln1p(0.0F))
|
|
assertEquals(Float.NEGATIVE_INFINITY, ln1p(-1.0F))
|
|
}
|
|
|
|
@Test fun rounding() {
|
|
for (value in listOf(Float.NaN, Float.POSITIVE_INFINITY, Float.NEGATIVE_INFINITY, 0.0F, 1.0F, -10.0F)) {
|
|
assertEquals(value, ceil(value))
|
|
assertEquals(value, floor(value))
|
|
assertEquals(value, truncate(value))
|
|
assertEquals(value, round(value))
|
|
}
|
|
val data = arrayOf( // v floor trunc round ceil
|
|
floatArrayOf( 1.3F, 1.0F, 1.0F, 1.0F, 2.0F),
|
|
floatArrayOf(-1.3F, -2.0F, -1.0F, -1.0F, -1.0F),
|
|
floatArrayOf( 1.5F, 1.0F, 1.0F, 2.0F, 2.0F),
|
|
floatArrayOf(-1.5F, -2.0F, -1.0F, -2.0F, -1.0F),
|
|
floatArrayOf( 1.8F, 1.0F, 1.0F, 2.0F, 2.0F),
|
|
floatArrayOf(-1.8F, -2.0F, -1.0F, -2.0F, -1.0F),
|
|
|
|
floatArrayOf( 2.3F, 2.0F, 2.0F, 2.0F, 3.0F),
|
|
floatArrayOf(-2.3F, -3.0F, -2.0F, -2.0F, -2.0F),
|
|
floatArrayOf( 2.5F, 2.0F, 2.0F, 2.0F, 3.0F),
|
|
floatArrayOf(-2.5F, -3.0F, -2.0F, -2.0F, -2.0F),
|
|
floatArrayOf( 2.8F, 2.0F, 2.0F, 3.0F, 3.0F),
|
|
floatArrayOf(-2.8F, -3.0F, -2.0F, -3.0F, -2.0F)
|
|
)
|
|
for ((v, f, t, r, c) in data) {
|
|
assertEquals(f, floor(v), "floor($v)")
|
|
assertEquals(t, truncate(v), "truncate($v)")
|
|
assertEquals(r, round(v), "round($v)")
|
|
assertEquals(c, ceil(v), "ceil($v)")
|
|
}
|
|
}
|
|
|
|
@Test fun roundingConversion() {
|
|
assertEquals(1L, 1.0F.roundToLong())
|
|
assertEquals(1L, 1.1F.roundToLong())
|
|
assertEquals(2L, 1.5F.roundToLong())
|
|
assertEquals(3L, 2.5F.roundToLong())
|
|
assertEquals(-2L, (-2.5F).roundToLong())
|
|
assertEquals(-3L, (-2.6F).roundToLong())
|
|
// assertEquals(9223372036854774784, (9223372036854774800.0F).roundToLong()) // platform-specific
|
|
assertEquals(Long.MAX_VALUE, Float.MAX_VALUE.roundToLong())
|
|
assertEquals(Long.MIN_VALUE, (-Float.MAX_VALUE).roundToLong())
|
|
assertEquals(Long.MAX_VALUE, Float.POSITIVE_INFINITY.roundToLong())
|
|
assertEquals(Long.MIN_VALUE, Float.NEGATIVE_INFINITY.roundToLong())
|
|
|
|
assertFails { Float.NaN.roundToLong() }
|
|
|
|
assertEquals(1, 1.0F.roundToInt())
|
|
assertEquals(1, 1.1F.roundToInt())
|
|
assertEquals(2, 1.5F.roundToInt())
|
|
assertEquals(3, 2.5F.roundToInt())
|
|
assertEquals(-2, (-2.5F).roundToInt())
|
|
assertEquals(-3, (-2.6F).roundToInt())
|
|
assertEquals(16777218, (16777218F).roundToInt())
|
|
assertEquals(Int.MAX_VALUE, Float.MAX_VALUE.roundToInt())
|
|
assertEquals(Int.MIN_VALUE, (-Float.MAX_VALUE).roundToInt())
|
|
assertEquals(Int.MAX_VALUE, Float.POSITIVE_INFINITY.roundToInt())
|
|
assertEquals(Int.MIN_VALUE, Float.NEGATIVE_INFINITY.roundToInt())
|
|
|
|
assertFails { Float.NaN.roundToInt() }
|
|
}
|
|
|
|
@Test fun absoluteValue() {
|
|
assertTrue(abs(Float.NaN).isNaN())
|
|
assertTrue(Float.NaN.absoluteValue.isNaN())
|
|
|
|
for (value in listOf(0.0F, Float.MIN_VALUE, 0.1F, 1.0F, 1000.0F, Float.MAX_VALUE, Float.POSITIVE_INFINITY)) {
|
|
assertEquals(value, value.absoluteValue)
|
|
assertEquals(value, (-value).absoluteValue)
|
|
assertEquals(value, abs(value))
|
|
assertEquals(value, abs(-value))
|
|
}
|
|
}
|
|
|
|
@Test fun signs() {
|
|
assertTrue(sign(Float.NaN).isNaN())
|
|
assertTrue(Float.NaN.sign.isNaN())
|
|
|
|
val negatives = listOf(Float.NEGATIVE_INFINITY, -Float.MAX_VALUE, -1.0F, -Float.MIN_VALUE)
|
|
for (value in negatives) {
|
|
assertEquals(-1.0F, sign(value))
|
|
assertEquals(-1.0F, value.sign)
|
|
}
|
|
|
|
val zeroes = listOf(0.0F, -0.0F)
|
|
for (value in zeroes) {
|
|
assertEquals(value, sign(value))
|
|
assertEquals(value, value.sign)
|
|
}
|
|
|
|
|
|
val positives = listOf(Float.POSITIVE_INFINITY, Float.MAX_VALUE, 1.0F, Float.MIN_VALUE)
|
|
for (value in positives) {
|
|
assertEquals(1.0F, sign(value))
|
|
assertEquals(1.0F, value.sign)
|
|
}
|
|
|
|
val allValues = negatives + positives
|
|
for (a in allValues) {
|
|
for (b in allValues) {
|
|
val r = a.withSign(b)
|
|
assertEquals(a.absoluteValue, r.absoluteValue)
|
|
assertEquals(b.sign, r.sign)
|
|
}
|
|
|
|
val rp0 = a.withSign(0.0F)
|
|
assertEquals(1.0F, rp0.sign)
|
|
assertEquals(a.absoluteValue, rp0.absoluteValue)
|
|
|
|
val rm0 = a.withSign(-0.0F)
|
|
assertEquals(-1.0F, rm0.sign)
|
|
assertEquals(a.absoluteValue, rm0.absoluteValue)
|
|
|
|
val ri = a.withSign(-1)
|
|
assertEquals(-1.0F, ri.sign)
|
|
assertEquals(a.absoluteValue, ri.absoluteValue)
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
class IntegerMathTest {
|
|
|
|
@Test fun intSigns() {
|
|
val negatives = listOf(Int.MIN_VALUE, -65536, -1)
|
|
val positives = listOf(1, 100, 256, Int.MAX_VALUE)
|
|
negatives.forEach { assertEquals(-1, it.sign) }
|
|
positives.forEach { assertEquals(1, it.sign) }
|
|
assertEquals(0, 0.sign)
|
|
|
|
(negatives - Int.MIN_VALUE).forEach { assertEquals(-it, it.absoluteValue) }
|
|
assertEquals(Int.MIN_VALUE, Int.MIN_VALUE.absoluteValue)
|
|
|
|
positives.forEach { assertEquals(it, it.absoluteValue) }
|
|
}
|
|
|
|
|
|
@Test fun longSigns() {
|
|
val negatives = listOf(Long.MIN_VALUE, -65536L, -1L)
|
|
val positives = listOf(1L, 100L, 256L, Long.MAX_VALUE)
|
|
negatives.forEach { assertEquals(-1, it.sign) }
|
|
positives.forEach { assertEquals(1, it.sign) }
|
|
assertEquals(0, 0L.sign)
|
|
|
|
(negatives - Long.MIN_VALUE).forEach { assertEquals(-it, it.absoluteValue) }
|
|
assertEquals(Long.MIN_VALUE, Long.MIN_VALUE.absoluteValue)
|
|
|
|
positives.forEach { assertEquals(it, it.absoluteValue) }
|
|
}
|
|
} |