问题描述
我有两个功能。一种使用 BigInteger
和 BigDecimal
。我想使用泰勒级数计算 sin(z)
:
这是我的代码:
fun sinus(z: BigDecimal,upperBound: Int = 100): BigDecimal = calcSin(z,upperBound)
fun cosinus(z: BigDecimal,upperBound,false)
fun calcSin(z: BigDecimal,upperBound: Int = 100,isSin: Boolean = true): BigDecimal {
var erg: BigDecimal = BigDecimal.ZERO
for (n in 0..upperBound) {
// val zaehler = (-1.0).pow(n).toBigDecimal() * z.pow(2 * n + (if (isSin) 1 else 0))
// val nenner = fac(2 * n + (if (isSin) 1 else 0)).toBigDecimal()
val zaehler = (-1.0).pow(n).toBigDecimal() * z.pow(2 * n + 1)
val nenner = fac(2 * n + 1).toBigDecimal()
erg += (zaehler / nenner)
}
return erg
}
fun calcSin(z: Double,upperBound: Int = 100): Double {
var res = 0.0
for (n in 0..upperBound) {
val zaehler = (-1.0).pow(n) * z.pow(2 * n + 1)
val nenner = fac(2 * n + 1,true)
res += (zaehler / nenner)
}
return res
}
fun fac(n: Int): BigInteger = if (n == 0 || n == 1) BigInteger.ONE else n.toBigInteger() * fac(n - 1)
fun fac(n: Int,dummy: Boolean): Double = if (n == 0 || n == 1) 1.0 else n.todouble() * fac(n - 1,dummy)
根据 Google 的说法,Sin(1) 是
0.8414709848
然而,以下输出是:
println("Sinus 1: ${sinus(1.0.toBigDecimal())}")
println("Sinus 1: ${sinus(1.0.toBigDecimal()).todouble()}")
println("Sinus 1: ${sinus(1.0.toBigDecimal(),1000)}")
println("Sinus 1: ${calcSin(1.0)}")
输出:
Sinus 1: 0.8414373208078281027995610599000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Sinus 1: 0.8414373208078281
Sinus 1: 0.8414373208078281027995610599000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Sinus 1: 0.8414709848078965
我错过了什么?为什么 Double-Variant 给出了正确的值,而 BigDecimal 没有?即使有 1000 次迭代。 注释掉的代码也用于计算 Cos,但想先解决这个问题,所以我让两个函数看起来一样
解决方法
在 BigDecimal
变体中,尝试将 erg += (zaehler / nenner)
替换为 erg += (zaehler.divide(nenner,20,RoundingMode.HALF_EVEN))
我怀疑缩放除法结果的默认值(如此处 https://docs.oracle.com/en/java/javase/11/docs/api/java.base/java/math/BigDecimal.html 所述)不是您想要的。
顺便说一句 - 我认为性能不是练习的一部分,否则你对阶乘的实现是一个低悬的果实。