Here you can find the source of exp(BigDecimal power)
| Parameter | Description |
|---|---|
| BigDecimal | the input power |
public static BigDecimal exp(BigDecimal power)
//package com.java2s; /**//w w w .j a v a 2 s . com * Licensed to the Apache Software Foundation (ASF) under one * or more contributor license agreements. See the NOTICE file * distributed with this work for additional information * regarding copyright ownership. The ASF licenses this file * to you under the Apache License, Version 2.0 (the * "License"); you may not use this file except in compliance * with the License. You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, * software distributed under the License is distributed on an * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY * KIND, either express or implied. See the License for the * specific language governing permissions and limitations * under the License. */ import java.math.BigDecimal; import java.math.BigInteger; import java.math.MathContext; import java.math.RoundingMode; public class Main { /** * Raises e to the power of the input big decimal. * @param BigDecimal the input power * @return the result */ public static BigDecimal exp(BigDecimal power) { int precision = power.precision(); MathContext context = new MathContext(precision, RoundingMode.HALF_DOWN); return exp(power, context); } /** * Returns e raised to the input power using a Taylor expansion with * @param BigDecimal the power * @param MathContext the math context * @return e raised to the input power */ public static BigDecimal exp(BigDecimal input, MathContext context) { int taylorTerms = 8; if (input.compareTo(BigDecimal.ZERO) < 0) { BigDecimal inverse = exp(input.negate(), context); return BigDecimal.ONE.divide(inverse, context); } else if (input.compareTo(BigDecimal.ZERO) == 0) { return BigDecimal.ONE.setScale(context.getPrecision(), RoundingMode.HALF_DOWN); } else { double inputDouble = input.doubleValue(); double inputUlpDouble = input.ulp().doubleValue(); double taylorNumberCheck1 = Math.pow(inputDouble, taylorTerms); double taylorNumberCheck2 = taylorTerms * (taylorTerms - 1.0) * (taylorTerms - 2.0) * inputUlpDouble; if (taylorNumberCheck1 < taylorNumberCheck2) { BigDecimal result = BigDecimal.ONE; BigDecimal inputPowerNum = BigDecimal.ONE; BigInteger factorialNum = BigInteger.ONE; int taylorPrecision = 1 + (int) (Math.log10(Math.abs(0.5 / (inputUlpDouble / taylorTerms)))); MathContext taylorContext = new MathContext(taylorPrecision); for (int i = 1; i <= taylorTerms; i++) { factorialNum = factorialNum.multiply(new BigInteger(i + "")); inputPowerNum = inputPowerNum.multiply(input); BigDecimal c = inputPowerNum.divide(new BigDecimal(factorialNum), taylorContext); result = result.add(c); double taylorNumberCheck3 = Math.abs(inputPowerNum.doubleValue()); double taylorNumberCheck4 = Math.abs(c.doubleValue()); double taylorNumberCheck5 = inputUlpDouble / 2; if (taylorNumberCheck3 < i && taylorNumberCheck4 < taylorNumberCheck5) { break; } } int finalPrecision = 1 + (int) (Math.log10(Math.abs(0.5 / (inputUlpDouble / 2.0)))); ; MathContext finalContext = new MathContext(finalPrecision); return result.round(finalContext); } else { double taylorProduct = taylorTerms * (taylorTerms - 1.0) * (taylorTerms - 2.0) * inputUlpDouble; double taylorPower = Math.pow(inputDouble, taylorTerms); Double scaleBy10Double = 1.0 - Math.log10(taylorProduct / taylorPower) / (taylorTerms - 1.0); int scaleBy10 = scaleBy10Double.intValue(); BigDecimal inputRaised10 = input.scaleByPowerOfTen(-scaleBy10); BigDecimal expxby10 = exp(inputRaised10, context); MathContext contextRaised10 = new MathContext(expxby10.precision() - scaleBy10); while (scaleBy10 > 0) { int minimum = Math.min(8, scaleBy10); scaleBy10 -= minimum; MathContext minContext = new MathContext(expxby10.precision() - minimum + 2); int precisionMin = 1; while (minimum-- > 0) { precisionMin *= 10; } expxby10 = expxby10.pow(precisionMin, minContext); } return expxby10.round(contextRaised10); } } } /** * Raises the base to the power and returns the result. Calculates the power * by finding the natural log using a Taylor sequence and exp using Newton's * method of approximating the nth root. * @param BigDecimal base the base * @param BigDecimal power the power * @return the result */ static public BigDecimal pow(BigDecimal base, BigDecimal power) { int precisionBase = base.precision(); int precisionPower = power.precision(); int precision = precisionBase < precisionPower ? precisionBase : precisionPower; MathContext context = new MathContext(precision, RoundingMode.HALF_DOWN); return pow(base, power, context); } /** * Raises the base to the power and returns the result. Calculates the power * by finding the natural log using a Taylor sequence and exp using Newton's * method of approximating the nth root. * @param BigDecimal the base * @param BigDecimal the power * @param MathContext the math context * @return the result */ static public BigDecimal pow(BigDecimal base, BigDecimal power, MathContext context) { if (base.compareTo(BigDecimal.ZERO) < 0) { throw new ArithmeticException("Base cannot be negative."); } if (base.compareTo(BigDecimal.ZERO) == 0) { return BigDecimal.ZERO; } BigDecimal result = ln(base); result = power.multiply(result, context); result = exp(result, context); return result; } /** * Calculates the natural logarithm using a Taylor sequqnce. * @param BigDecimal the input big decimal > 0 * @return the natural logarithm */ public static BigDecimal ln(BigDecimal input) { int precision = input.precision(); MathContext context = new MathContext(precision, RoundingMode.HALF_DOWN); return ln(input, context); } /** * Calculates the natural logarithm using a Taylor sequqnce. * @param BigDecimal the input big decimal > 0 * @return the natural logarithm */ public static BigDecimal ln(BigDecimal input, MathContext context) { BigDecimal two = new BigDecimal("2", context); BigDecimal inputMinus = input.subtract(BigDecimal.ONE, context); BigDecimal inputPlus = input.add(BigDecimal.ONE, context); BigDecimal y = inputMinus.divide(inputPlus, context); BigDecimal result = new BigDecimal("0", context); BigDecimal last = new BigDecimal(result.toString(), context); int k = 0; while (true) { BigDecimal argumentOne = BigDecimal.ONE .divide(BigDecimal.ONE.add(two.multiply(new BigDecimal(k), context), context), context); BigDecimal argumentTwo = y.pow(k * 2, context); result = result.add(argumentOne.multiply(argumentTwo, context), context); if (last.equals(result)) { break; } last = new BigDecimal(result.toString(), context); k++; } return y.multiply(two, context).multiply(result, context); } }