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461 lines (444 loc) · 17.3 KB
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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 {@link BigInteger} base conversion from/to any
* integer represented in an {@link java.lang.String} Object.
*/
class Conversion {
/** Just to denote that this class can't be instantiated */
private Conversion() {}
/**
* Holds the maximal exponent for each radix, so that radix<sup>digitFitInInt[radix]</sup>
* fit in an {@code int} (32 bits).
*/
static final int[] digitFitInInt = { -1, -1, 31, 19, 15, 13, 11,
11, 10, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 5 };
/**
* bigRadices values are precomputed maximal powers of radices (integer
* numbers from 2 to 36) that fit into unsigned int (32 bits). bigRadices[0] =
* 2 ^ 31, bigRadices[8] = 10 ^ 9, etc.
*/
static final int[] bigRadices = { -2147483648, 1162261467,
1073741824, 1220703125, 362797056, 1977326743, 1073741824,
387420489, 1000000000, 214358881, 429981696, 815730721, 1475789056,
170859375, 268435456, 410338673, 612220032, 893871739, 1280000000,
1801088541, 113379904, 148035889, 191102976, 244140625, 308915776,
387420489, 481890304, 594823321, 729000000, 887503681, 1073741824,
1291467969, 1544804416, 1838265625, 60466176 };
/** @see BigInteger#toString(int) */
static String bigInteger2String(BigInteger val, int radix) {
val.prepareJavaRepresentation();
int sign = val.sign;
int numberLength = val.numberLength;
int[] digits = val.digits;
if (sign == 0) {
return "0";
}
if (numberLength == 1) {
int highDigit = digits[numberLength - 1];
long v = highDigit & 0xFFFFFFFFL;
if (sign < 0) {
v = -v;
}
return Long.toString(v, radix);
}
if ((radix == 10) || (radix < Character.MIN_RADIX)
|| (radix > Character.MAX_RADIX)) {
return val.toString();
}
double bitsForRadixDigit;
bitsForRadixDigit = Math.log(radix) / Math.log(2);
int resLengthInChars = (int) (val.abs().bitLength() / bitsForRadixDigit + ((sign < 0) ? 1
: 0)) + 1;
char[] result = new char[resLengthInChars];
int currentChar = resLengthInChars;
int resDigit;
if (radix != 16) {
int[] temp = new int[numberLength];
System.arraycopy(digits, 0, temp, 0, numberLength);
int tempLen = numberLength;
int charsPerInt = digitFitInInt[radix];
int i;
// get the maximal power of radix that fits in int
int bigRadix = bigRadices[radix - 2];
while (true) {
// divide the array of digits by bigRadix and convert remainders
// to characters collecting them in the char array
resDigit = Division.divideArrayByInt(temp, temp, tempLen,
bigRadix);
int previous = currentChar;
do {
result[--currentChar] = Character.forDigit(
resDigit % radix, radix);
} while (((resDigit /= radix) != 0) && (currentChar != 0));
int delta = charsPerInt - previous + currentChar;
for (i = 0; i < delta && currentChar > 0; i++) {
result[--currentChar] = '0';
}
for (i = tempLen - 1; (i > 0) && (temp[i] == 0); i--) {
;
}
tempLen = i + 1;
if ((tempLen == 1) && (temp[0] == 0)) { // the quotient is 0
break;
}
}
} else {
// radix == 16
for (int i = 0; i < numberLength; i++) {
for (int j = 0; (j < 8) && (currentChar > 0); j++) {
resDigit = digits[i] >> (j << 2) & 0xf;
result[--currentChar] = Character.forDigit(resDigit, 16);
}
}
}
while (result[currentChar] == '0') {
currentChar++;
}
if (sign == -1) {
result[--currentChar] = '-';
}
return new String(result, currentChar, resLengthInChars - currentChar);
}
/**
* Builds the correspondent {@code String} representation of {@code val}
* being scaled by {@code scale}.
*
* @see BigInteger#toString()
* @see BigDecimal#toString()
*/
static String toDecimalScaledString(BigInteger val, int scale) {
val.prepareJavaRepresentation();
int sign = val.sign;
int numberLength = val.numberLength;
int[] digits = val.digits;
int resLengthInChars;
int currentChar;
char[] result;
if (sign == 0) {
switch (scale) {
case 0:
return "0";
case 1:
return "0.0";
case 2:
return "0.00";
case 3:
return "0.000";
case 4:
return "0.0000";
case 5:
return "0.00000";
case 6:
return "0.000000";
default:
StringBuilder result1 = new StringBuilder();
if (scale < 0) {
result1.append("0E+");
} else {
result1.append("0E");
}
result1.append(-scale);
return result1.toString();
}
}
// one 32-bit unsigned value may contains 10 decimal digits
resLengthInChars = numberLength * 10 + 1 + 7;
// Explanation why +1+7:
// +1 - one char for sign if needed.
// +7 - For "special case 2" (see below) we have 7 free chars for
// inserting necessary scaled digits.
result = new char[resLengthInChars + 1];
// allocated [resLengthInChars+1] characters.
// a free latest character may be used for "special case 1" (see
// below)
currentChar = resLengthInChars;
if (numberLength == 1) {
int highDigit = digits[0];
if (highDigit < 0) {
long v = highDigit & 0xFFFFFFFFL;
do {
long prev = v;
v /= 10;
result[--currentChar] = (char) (0x0030 + ((int) (prev - v * 10)));
} while (v != 0);
} else {
int v = highDigit;
do {
int prev = v;
v /= 10;
result[--currentChar] = (char) (0x0030 + (prev - v * 10));
} while (v != 0);
}
} else {
int[] temp = new int[numberLength];
int tempLen = numberLength;
System.arraycopy(digits, 0, temp, 0, tempLen);
BIG_LOOP: while (true) {
// divide the array of digits by bigRadix and convert
// remainders
// to characters collecting them in the char array
long result11 = 0;
for (int i1 = tempLen - 1; i1 >= 0; i1--) {
long temp1 = (result11 << 32)
+ (temp[i1] & 0xFFFFFFFFL);
long res = divideLongByBillion(temp1);
temp[i1] = (int) res;
result11 = (int) (res >> 32);
}
int resDigit = (int) result11;
int previous = currentChar;
do {
result[--currentChar] = (char) (0x0030 + (resDigit % 10));
} while (((resDigit /= 10) != 0) && (currentChar != 0));
int delta = 9 - previous + currentChar;
for (int i = 0; (i < delta) && (currentChar > 0); i++) {
result[--currentChar] = '0';
}
int j = tempLen - 1;
for (; temp[j] == 0; j--) {
if (j == 0) { // means temp[0] == 0
break BIG_LOOP;
}
}
tempLen = j + 1;
}
while (result[currentChar] == '0') {
currentChar++;
}
}
boolean negNumber = (sign < 0);
int exponent = resLengthInChars - currentChar - scale - 1;
if (scale == 0) {
if (negNumber) {
result[--currentChar] = '-';
}
return new String(result, currentChar, resLengthInChars
- currentChar);
}
if ((scale > 0) && (exponent >= -6)) {
if (exponent >= 0) {
// special case 1
int insertPoint = currentChar + exponent;
for (int j = resLengthInChars - 1; j >= insertPoint; j--) {
result[j + 1] = result[j];
}
result[++insertPoint] = '.';
if (negNumber) {
result[--currentChar] = '-';
}
return new String(result, currentChar, resLengthInChars
- currentChar + 1);
}
// special case 2
for (int j = 2; j < -exponent + 1; j++) {
result[--currentChar] = '0';
}
result[--currentChar] = '.';
result[--currentChar] = '0';
if (negNumber) {
result[--currentChar] = '-';
}
return new String(result, currentChar, resLengthInChars
- currentChar);
}
int startPoint = currentChar + 1;
int endPoint = resLengthInChars;
StringBuilder result1 = new StringBuilder(16 + endPoint - startPoint);
if (negNumber) {
result1.append('-');
}
if (endPoint - startPoint >= 1) {
result1.append(result[currentChar]);
result1.append('.');
result1.append(result, currentChar + 1, resLengthInChars
- currentChar - 1);
} else {
result1.append(result, currentChar, resLengthInChars
- currentChar);
}
result1.append('E');
if (exponent > 0) {
result1.append('+');
}
result1.append(Integer.toString(exponent));
return result1.toString();
}
/* can process only 32-bit numbers */
static String toDecimalScaledString(long value, int scale) {
int resLengthInChars;
int currentChar;
char[] result;
boolean negNumber = value < 0;
if(negNumber) {
value = -value;
}
if (value == 0) {
switch (scale) {
case 0: return "0";
case 1: return "0.0";
case 2: return "0.00";
case 3: return "0.000";
case 4: return "0.0000";
case 5: return "0.00000";
case 6: return "0.000000";
default:
StringBuilder result1 = new StringBuilder();
if (scale < 0) {
result1.append("0E+");
} else {
result1.append("0E");
}
result1.append( (scale == Integer.MIN_VALUE) ? "2147483648" : Integer.toString(-scale));
return result1.toString();
}
}
// one 32-bit unsigned value may contains 10 decimal digits
resLengthInChars = 18;
// Explanation why +1+7:
// +1 - one char for sign if needed.
// +7 - For "special case 2" (see below) we have 7 free chars for
// inserting necessary scaled digits.
result = new char[resLengthInChars+1];
// Allocated [resLengthInChars+1] characters.
// a free latest character may be used for "special case 1" (see below)
currentChar = resLengthInChars;
long v = value;
do {
long prev = v;
v /= 10;
result[--currentChar] = (char) (0x0030 + (prev - v * 10));
} while (v != 0);
long exponent = (long)resLengthInChars - (long)currentChar - scale - 1L;
if (scale == 0) {
if (negNumber) {
result[--currentChar] = '-';
}
return new String(result, currentChar, resLengthInChars - currentChar);
}
if (scale > 0 && exponent >= -6) {
if (exponent >= 0) {
// special case 1
int insertPoint = currentChar + (int) exponent ;
for(int j=resLengthInChars-1; j>=insertPoint; j--) {
result[j+1] = result[j];
}
result[++insertPoint]='.';
if (negNumber) {
result[--currentChar] = '-';
}
return new String(result, currentChar, resLengthInChars - currentChar + 1);
}
// special case 2
for (int j = 2; j < -exponent + 1; j++) {
result[--currentChar] = '0';
}
result[--currentChar] = '.';
result[--currentChar] = '0';
if (negNumber) {
result[--currentChar] = '-';
}
return new String(result, currentChar, resLengthInChars - currentChar);
}
int startPoint = currentChar + 1;
int endPoint = resLengthInChars;
StringBuilder result1 = new StringBuilder(16 + endPoint - startPoint);
if (negNumber) {
result1.append('-');
}
if (endPoint - startPoint >= 1) {
result1.append(result[currentChar]);
result1.append('.');
result1.append(result,currentChar+1,resLengthInChars - currentChar-1);
} else {
result1.append(result,currentChar,resLengthInChars - currentChar);
}
result1.append('E');
if (exponent > 0) {
result1.append('+');
}
result1.append(Long.toString(exponent));
return result1.toString();
}
static long divideLongByBillion(long a) {
long quot;
long rem;
if (a >= 0) {
long bLong = 1000000000L;
quot = (a / bLong);
rem = (a % bLong);
} else {
/*
* Make the dividend positive shifting it right by 1 bit then get
* the quotient an remainder and correct them properly
*/
long aPos = a >>> 1;
long bPos = 1000000000L >>> 1;
quot = aPos / bPos;
rem = aPos % bPos;
// double the remainder and add 1 if 'a' is odd
rem = (rem << 1) + (a & 1);
}
return ((rem << 32) | (quot & 0xFFFFFFFFL));
}
/** @see BigInteger#doubleValue() */
static double bigInteger2Double(BigInteger val) {
val.prepareJavaRepresentation();
// val.bitLength() < 64
if ((val.numberLength < 2)
|| ((val.numberLength == 2) && (val.digits[1] > 0))) {
return val.longValue();
}
// val.bitLength() >= 33 * 32 > 1024
if (val.numberLength > 32) {
return ((val.sign > 0) ? Double.POSITIVE_INFINITY
: Double.NEGATIVE_INFINITY);
}
int bitLen = val.abs().bitLength();
long exponent = bitLen - 1;
int delta = bitLen - 54;
// We need 54 top bits from this, the 53th bit is always 1 in lVal.
long lVal = val.abs().shiftRight(delta).longValue();
/*
* Take 53 bits from lVal to mantissa. The least significant bit is
* needed for rounding.
*/
long mantissa = lVal & 0x1FFFFFFFFFFFFFL;
if (exponent == 1023) {
if (mantissa == 0X1FFFFFFFFFFFFFL) {
return ((val.sign > 0) ? Double.POSITIVE_INFINITY
: Double.NEGATIVE_INFINITY);
}
if (mantissa == 0x1FFFFFFFFFFFFEL) {
return ((val.sign > 0) ? Double.MAX_VALUE : -Double.MAX_VALUE);
}
}
// Round the mantissa
if (((mantissa & 1) == 1)
&& (((mantissa & 2) == 2) || BitLevel.nonZeroDroppedBits(delta,
val.digits))) {
mantissa += 2;
}
mantissa >>= 1; // drop the rounding bit
long resSign = (val.sign < 0) ? 0x8000000000000000L : 0;
exponent = ((1023 + exponent) << 52) & 0x7FF0000000000000L;
long result = resSign | exponent | mantissa;
return Double.longBitsToDouble(result);
}
}
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