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/*
* 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.
*/
package java.math;
/**
* Static library that provides all multiplication of {@link BigInteger} methods.
*/
class Multiplication {
/** Just to denote that this class can't be instantiated. */
private Multiplication() {}
// BEGIN android-removed
// /**
// * Break point in digits (number of {@code int} elements)
// * between Karatsuba and Pencil and Paper multiply.
// */
// static final int whenUseKaratsuba = 63; // an heuristic value
// END android-removed
/**
* An array with powers of ten that fit in the type {@code int}.
* ({@code 10^0,10^1,...,10^9})
*/
static final int[] tenPows = {
1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000
};
/**
* An array with powers of five that fit in the type {@code int}.
* ({@code 5^0,5^1,...,5^13})
*/
static final int[] fivePows = {
1, 5, 25, 125, 625, 3125, 15625, 78125, 390625,
1953125, 9765625, 48828125, 244140625, 1220703125
};
/**
* An array with the first powers of ten in {@code BigInteger} version.
* ({@code 10^0,10^1,...,10^31})
*/
static final BigInteger[] bigTenPows = new BigInteger[32];
/**
* An array with the first powers of five in {@code BigInteger} version.
* ({@code 5^0,5^1,...,5^31})
*/
static final BigInteger bigFivePows[] = new BigInteger[32];
static {
int i;
long fivePow = 1L;
for (i = 0; i <= 18; i++) {
bigFivePows[i] = BigInteger.valueOf(fivePow);
bigTenPows[i] = BigInteger.valueOf(fivePow << i);
fivePow *= 5;
}
for (; i < bigTenPows.length; i++) {
bigFivePows[i] = bigFivePows[i - 1].multiply(bigFivePows[1]);
bigTenPows[i] = bigTenPows[i - 1].multiply(BigInteger.TEN);
}
}
// BEGIN android-note: multiply has been removed in favor of using OpenSSL BIGNUM
// END android-note
/**
* Multiplies a number by a positive integer.
* @param val an arbitrary {@code BigInteger}
* @param factor a positive {@code int} number
* @return {@code val * factor}
*/
static BigInteger multiplyByPositiveInt(BigInteger val, int factor) {
BigInt bi = val.getBigInt().copy();
bi.multiplyByPositiveInt(factor);
return new BigInteger(bi);
}
/**
* Multiplies a number by a power of ten.
* This method is used in {@code BigDecimal} class.
* @param val the number to be multiplied
* @param exp a positive {@code long} exponent
* @return {@code val * 10exp}
*/
static BigInteger multiplyByTenPow(BigInteger val, long exp) {
// PRE: exp >= 0
return ((exp < tenPows.length)
? multiplyByPositiveInt(val, tenPows[(int)exp])
: val.multiply(powerOf10(exp)));
}
/**
* It calculates a power of ten, which exponent could be out of 32-bit range.
* Note that internally this method will be used in the worst case with
* an exponent equals to: {@code Integer.MAX_VALUE - Integer.MIN_VALUE}.
* @param exp the exponent of power of ten, it must be positive.
* @return a {@code BigInteger} with value {@code 10exp}.
*/
static BigInteger powerOf10(long exp) {
// PRE: exp >= 0
int intExp = (int)exp;
// "SMALL POWERS"
if (exp < bigTenPows.length) {
// The largest power that fit in 'long' type
return bigTenPows[intExp];
} else if (exp <= 50) {
// To calculate: 10^exp
return BigInteger.TEN.pow(intExp);
} else if (exp <= 1000) {
// To calculate: 5^exp * 2^exp
return bigFivePows[1].pow(intExp).shiftLeft(intExp);
}
// "LARGE POWERS"
/*
* To check if there is free memory to allocate a BigInteger of the
* estimated size, measured in bytes: 1 + [exp / log10(2)]
*/
long byteArraySize = 1 + (long)(exp / 2.4082399653118496);
// RoboVM note: Start change. It is unreliable to depend on
// Runtime.freeMemory() here. As a workaround we always assume there's
// at least 64k (1<<16) bytes of free memory.
if (byteArraySize > (1 << 16) && byteArraySize > Runtime.getRuntime().freeMemory()) {
throw new ArithmeticException();
}
// RoboVM note: End change.
if (exp <= Integer.MAX_VALUE) {
// To calculate: 5^exp * 2^exp
return bigFivePows[1].pow(intExp).shiftLeft(intExp);
}
/*
* "HUGE POWERS"
*
* This branch probably won't be executed since the power of ten is too
* big.
*/
// To calculate: 5^exp
BigInteger powerOfFive = bigFivePows[1].pow(Integer.MAX_VALUE);
BigInteger res = powerOfFive;
long longExp = exp - Integer.MAX_VALUE;
intExp = (int)(exp % Integer.MAX_VALUE);
while (longExp > Integer.MAX_VALUE) {
res = res.multiply(powerOfFive);
longExp -= Integer.MAX_VALUE;
}
res = res.multiply(bigFivePows[1].pow(intExp));
// To calculate: 5^exp << exp
res = res.shiftLeft(Integer.MAX_VALUE);
longExp = exp - Integer.MAX_VALUE;
while (longExp > Integer.MAX_VALUE) {
res = res.shiftLeft(Integer.MAX_VALUE);
longExp -= Integer.MAX_VALUE;
}
res = res.shiftLeft(intExp);
return res;
}
/**
* Multiplies a number by a power of five.
* This method is used in {@code BigDecimal} class.
* @param val the number to be multiplied
* @param exp a positive {@code int} exponent
* @return {@code val * 5exp}
*/
static BigInteger multiplyByFivePow(BigInteger val, int exp) {
// PRE: exp >= 0
if (exp < fivePows.length) {
return multiplyByPositiveInt(val, fivePows[exp]);
} else if (exp < bigFivePows.length) {
return val.multiply(bigFivePows[exp]);
} else {// Large powers of five
return val.multiply(bigFivePows[1].pow(exp));
}
}
}
