From 936e6f9bd41e192e1ede500ef5aa26dd2a276ec0 Mon Sep 17 00:00:00 2001 From: Brian Jones Date: Mon, 5 Nov 2001 02:56:46 +0000 Subject: * native/jni/awt: renamed native/jni/gtk-peer * native/jni/javaio.h: moved to native/jni/java-io * native/jni/javaio.c: moved to native/jni/java-io * native/jni/java_io_File.c: moved to native/jni/java-io * native/jni/java_io_FileDescriptor.c: moved to native/jni/java-io * native/jni/java_io_FileInputStream.c: moved to native/jni/java-io * native/jni/java_io_FileOutputStream.c: moved to native/jni/java-io * native/jni/java_io_ObjectInputStream.c: moved to native/jni/java-io * native/jni/java_io_ObjectOutputStream.c: moved to native/jni/java-io * native/jni/java_io_RandomAccessFile.c: moved to native/jni/java-io * native/jni/javalang.h: moved to native/jni/java-lang * native/jni/javalang.c: moved to native/jni/java-lang * native/jni/java_lang_Double.c: moved to native/jni/java-lang * native/jni/java_lang_Float.c: moved to native/jni/java-lang * native/jni/java_lang_Object.c: moved to native/jni/java-lang * native/jni/java_lang_System.c: moved to native/jni/java-lang * native/jni/java_lang_reflect_Array.c: moved to native/jni/java-lang * native/jni/javanet.h: moved to native/jni/java-net * native/jni/javanet.c: moved to native/jni/java-net * native/jni/java_net_InetAddress.c: moved to native/jni/java-net * native/jni/java_net_PlainDatagramSocketImpl.c: moved to native/jni/java-net * native/jni/java_net_PlainSocketImpl.c: moved to native/jni/java-net * native/jni/java_util_ResourceBundle.c: moved to native/jni/java-util * native/jni/java_util_TimeZone.c: moved to native/jni/java-util * native/jni/ieeefp.h: moved to native/jni/mprec * native/jni/java-assert.h: moved to native/jni/mprec * native/jni/mprec.c: moved to native/jni/mprec * native/jni/mprec.h: moved to native/jni/mprec * native/jni/acos.c: removed * native/jni/asin.c: removed * native/jni/atan2.c: removed * native/jni/atan.c: removed * native/jni/ceil.c: removed * native/jni/cos.c: removed * native/jni/dtoa.c: removed * native/jni/e_fmod.c: removed * native/jni/exp.c: removed * native/jni/floor.c: removed * native/jni/jcl.c: removed * native/jni/jcl.h: removed * native/jni/k_cos.c: removed * native/jni/k_rem_pio2.c: removed * native/jni/k_sin.c: removed * native/jni/k_tan.c: removed * native/jni/log.c: removed * native/jni/pow.c: removed * native/jni/remainder.c: removed * native/jni/rint.c: removed * native/jni/s_fabs.c: removed * native/jni/sin.c: removed * native/jni/sqrt.c: removed * native/jni/tan.c: removed * native/jni/fdlibm.h: removed * native/jni/java_math_BigInteger.c: no longer needed * native/fdlibm/dtoa.c: added from gcj to sync sources * native/fdlibm/e_acos.c: added from gcj to sync sources * native/fdlibm/e_asin.c: added from gcj to sync sources * native/fdlibm/e_atan2.c: added from gcj to sync sources * native/fdlibm/e_exp.c: added from gcj to sync sources * native/fdlibm/e_fmod.c: added from gcj to sync sources * native/fdlibm/e_log.c: added from gcj to sync sources * native/fdlibm/e_pow.c: added from gcj to sync sources * native/fdlibm/e_remainder.c: added from gcj to sync sources * native/fdlibm/e_rem_pio2.c: added from gcj to sync sources * native/fdlibm/e_scalb.c: added from gcj to sync sources * native/fdlibm/e_sqrt.c: added from gcj to sync sources * native/fdlibm/fdlibm.h: added from gcj to sync sources * native/fdlibm/ieeefp.h: added from gcj to sync sources * native/fdlibm/java-assert.h: added from gcj to sync sources * native/fdlibm/k_cos.c: added from gcj to sync sources * native/fdlibm/k_rem_pio2.c: added from gcj to sync sources * native/fdlibm/k_sin.c: added from gcj to sync sources * native/fdlibm/k_tan.c: added from gcj to sync sources * native/fdlibm/mprec.c: added from gcj to sync sources * native/fdlibm/mprec.h: added from gcj to sync sources * native/fdlibm/s_atan.c: added from gcj to sync sources * native/fdlibm/s_ceil.c: added from gcj to sync sources * native/fdlibm/s_copysign.c: added from gcj to sync sources * native/fdlibm/s_cos.c: added from gcj to sync sources * native/fdlibm/s_fabs.c: added from gcj to sync sources * native/fdlibm/sf_fabs.c: added from gcj to sync sources * native/fdlibm/s_floor.c: added from gcj to sync sources * native/fdlibm/sf_rint.c: added from gcj to sync sources * native/fdlibm/s_rint.c: added from gcj to sync sources * native/fdlibm/s_scalbn.c: added from gcj to sync sources * native/fdlibm/s_sin.c: added from gcj to sync sources * native/fdlibm/s_tan.c: added from gcj to sync sources * native/fdlibm/strtod.c: added from gcj to sync sources * native/fdlibm/w_acos.c: added from gcj to sync sources * native/fdlibm/w_asin.c: added from gcj to sync sources * native/fdlibm/w_atan2.c: added from gcj to sync sources * native/fdlibm/w_exp.c: added from gcj to sync sources * native/fdlibm/w_fmod.c: added from gcj to sync sources * native/fdlibm/w_log.c: added from gcj to sync sources * native/fdlibm/w_pow.c: added from gcj to sync sources * native/fdlibm/w_remainder.c: added from gcj to sync sources * native/fdlibm/w_sqrt.c: added from gcj to sync sources * native/fdlibm/.cvsignore: new file * native/jni/gtk-peer/Makefile.am: added -module to LDFLAGS * native/jni/java-io/Makefile.am: added -module to LDFLAGS * native/jni/java-io/.cvsignore: new file * native/jni/java-lang/Makefile.am: added -module to LDFLAGS * native/jni/java-lang/.cvsignore: new file * native/jni/java-net/Makefile.am: added -module to LDFLAGS * native/jni/java-net/.cvsignore: new file * native/jni/java-util/Makefile.am: added -module to LDFLAGS * native/jni/java-util/.cvsignore: new file * native/fdlibm/Makefile.am: added -module to LDFLAGS * native/jni/Makefile.am: removed rules, SUBDIRS equals java-io, java-lang, java-net, java-util, gtk-peer * native/Makefile.am: prepended fdlibm to SUBDIRS * java/lang/Math.java static(): load libjavalang.so instead of libjavalangmath.so * java/math/BigInteger.java: replaced our native version with pure Java implementation from gcj * gnu/classpath/math: new directory * gnu/classpath/math/MPN.java: new file from gcj, which came from Kawa, and is included with permission from Per Bothner, the author. * README: updated with current information about CVS and the project * THANKYOU: added Per Bothner * TODO: updated with current information as I know it * NEWS: updated with information about a 0.03 release * HACKING: updated with new information * INSTALL: updated with new information * BUGS: added link to Savannah bug reporting page for the project * ltconfig: removed due to upgrade of libtool to 1.4.2 * ltmain.sh: updated with libtool 1.4.2 * depcomp: new file from automake 1.5 upgrade * configure.in: added to OUTPUT native/fdlibm/Makefile, native/jni/java-io/Makefile, native/jni/java-lang/Makefile, native/jni/java-net/Makefile, native/jni/java-util/Makefile, native/jni/gtk-peer/Makefile * install.sh: updated * missing: updated * mkinstalldirs: updated * native/lib/Makefile.am: INCLUDES += changed to just INCLUDES = to avoid automake warning * native/lib/jcl.h: removed TRUE/FALSE #defines, added DBG * native/nsa/: removed, files native_state.* moved to native/lib * native/lib: renamed native/jni/classpath * native/cni/Makefile.am: new file * native/cni/.cvsignore: new file * native/jni/gtk-peer/Makefile.am: LIBADD used to get native_state from a common location * native/jni/java-io/Makefile.am: LIBADD used to get jcl from a common location, source modified to use relevant JCL_* functions * native/jni/java-lang/Makefile.am: LIBADD used to get jcl from a common location * native/jni/java-net/Makefile.am: LIBADD used to get jcl from a common location, source modified to use relevant JCL_* functions * vm/reference/java/lang/Thread.java (Thread): wrongly marked private constructor Thread (ThreadGroup, String) now public * native/jni/java-util/java_util_ResourceBundle.c: removed file * native/jni/java-util/Makefile.am: removed java_util_ResourceBundle.c from library --- java/math/BigInteger.java | 2378 +++++++++++++++++++++++++++++++++++++++++---- 1 file changed, 2166 insertions(+), 212 deletions(-) (limited to 'java/math/BigInteger.java') diff --git a/java/math/BigInteger.java b/java/math/BigInteger.java index 185b75b30..065d5fcf2 100644 --- a/java/math/BigInteger.java +++ b/java/math/BigInteger.java @@ -26,277 +26,2231 @@ executable file might be covered by the GNU General Public License. */ package java.math; +import gnu.classpath.math.*; import java.util.Random; +import java.io.ObjectInputStream; +import java.io.ObjectOutputStream; +import java.io.IOException; -import gnu.classpath.Configuration; +/** + * @author Warren Levy + * @date December 20, 1999. + */ -public class BigInteger implements Comparable { - final int native_state = System.identityHashCode(this); +/** + * Written using on-line Java Platform 1.2 API Specification, as well + * as "The Java Class Libraries", 2nd edition (Addison-Wesley, 1998) and + * "Applied Cryptography, Second Edition" by Bruce Schneier (Wiley, 1996). + * + * Based primarily on IntNum.java BitOps.java by Per Bothner + * (found in Kawa 1.6.62). + * + * Status: Believed complete and correct. + */ - public static final BigInteger ZERO; - public static final BigInteger ONE; +public class BigInteger extends Number implements Comparable +{ + /** All integers are stored in 2's-complement form. + * If words == null, the ival is the value of this BigInteger. + * Otherwise, the first ival elements of words make the value + * of this BigInteger, stored in little-endian order, 2's-complement form. */ + transient private int ival; + transient private int[] words; - static + // Serialization fields. + private int bitCount = -1; + private int bitLength = -1; + private int firstNonzeroByteNum = -2; + private int lowestSetBit = -2; + private byte[] magnitude; + private int signum; + private static final long serialVersionUID = -8287574255936472291L; + + + /** We pre-allocate integers in the range minFixNum..maxFixNum. */ + private static final int minFixNum = -100; + private static final int maxFixNum = 1024; + private static final int numFixNum = maxFixNum-minFixNum+1; + private static final BigInteger[] smallFixNums = new BigInteger[numFixNum]; + + static { + for (int i = numFixNum; --i >= 0; ) + smallFixNums[i] = new BigInteger(i + minFixNum); + } + + // JDK1.2 + public static final BigInteger ZERO = smallFixNums[-minFixNum]; + + // JDK1.2 + public static final BigInteger ONE = smallFixNums[1 - minFixNum]; + + /* Rounding modes: */ + private static final int FLOOR = 1; + private static final int CEILING = 2; + private static final int TRUNCATE = 3; + private static final int ROUND = 4; + + /** When checking the probability of primes, it is most efficient to + * first check the factoring of small primes, so we'll use this array. + */ + private static final int[] primes = + { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, + 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, + 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, + 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251 }; + + private BigInteger() + { + } + + /* Create a new (non-shared) BigInteger, and initialize to an int. */ + private BigInteger(int value) + { + ival = value; + } + + public BigInteger(String val, int radix) { - if (Configuration.INIT_LOAD_LIBRARY) + BigInteger result = valueOf(val, radix); + this.ival = result.ival; + this.words = result.words; + } + + public BigInteger(String val) + { + this(val, 10); + } + + /* Create a new (non-shared) BigInteger, and initialize from a byte array. */ + public BigInteger(byte[] val) + { + if (val == null || val.length < 1) + throw new NumberFormatException(); + + words = byteArrayToIntArray(val, val[0] < 0 ? -1 : 0); + BigInteger result = make(words, words.length); + this.ival = result.ival; + this.words = result.words; + } + + public BigInteger(int signum, byte[] magnitude) + { + if (magnitude == null || signum > 1 || signum < -1) + throw new NumberFormatException(); + + if (signum == 0) { - System.loadLibrary ("bigint"); - initNativeState(); + int i; + for (i = magnitude.length - 1; i >= 0 && magnitude[i] == 0; --i) + ; + if (i >= 0) + throw new NumberFormatException(); + return; } - ZERO = new BigInteger(); - ONE = new BigInteger(1L); + + // Magnitude is always positive, so don't ever pass a sign of -1. + words = byteArrayToIntArray(magnitude, 0); + BigInteger result = make(words, words.length); + this.ival = result.ival; + this.words = result.words; + + if (signum < 0) + setNegative(); } - public BigInteger(String val) { - this(val, 10); + public BigInteger(int numBits, Random rnd) + { + if (numBits < 0) + throw new IllegalArgumentException(); + + init(numBits, rnd); + } + + private void init(int numBits, Random rnd) + { + int highbits = numBits & 31; + if (highbits > 0) + highbits = rnd.nextInt() >>> (32 - highbits); + int nwords = numBits / 32; + + while (highbits == 0 && nwords > 0) + { + highbits = rnd.nextInt(); + --nwords; + } + if (nwords == 0 && highbits >= 0) + { + ival = highbits; + } + else + { + ival = highbits < 0 ? nwords + 2 : nwords + 1; + words = new int[ival]; + words[nwords] = highbits; + while (--nwords >= 0) + words[nwords] = rnd.nextInt(); + } + } + + public BigInteger(int bitLength, int certainty, Random rnd) + { + this(bitLength, rnd); + + // Keep going until we find a probable prime. + while (true) + { + if (isProbablePrime(certainty)) + return; + + init(bitLength, rnd); + } + } + + /** Return a (possibly-shared) BigInteger with a given long value. */ + private static BigInteger make(long value) + { + if (value >= minFixNum && value <= maxFixNum) + return smallFixNums[(int)value - minFixNum]; + int i = (int) value; + if ((long)i == value) + return new BigInteger(i); + BigInteger result = alloc(2); + result.ival = 2; + result.words[0] = i; + result.words[1] = (int) (value >> 32); + return result; + } + + // FIXME: Could simply rename 'make' method above as valueOf while + // changing all instances of 'make'. Don't do this until this class + // is done as the Kawa class this is based on has 'make' methods + // with other parameters; wait to see if they are used in BigInteger. + public static BigInteger valueOf(long val) + { + return make(val); } - public BigInteger(String val, int radix) { - if (!initFromString(forEachDigit(val, radix), radix)) - throw new NumberFormatException(val); + /** Make a canonicalized BigInteger from an array of words. + * The array may be reused (without copying). */ + private static BigInteger make(int[] words, int len) + { + if (words == null) + return make(len); + len = BigInteger.wordsNeeded(words, len); + if (len <= 1) + return len == 0 ? ZERO : make(words[0]); + BigInteger num = new BigInteger(); + num.words = words; + num.ival = len; + return num; + } + + /** Convert a big-endian byte array to a little-endian array of words. */ + private static int[] byteArrayToIntArray(byte[] bytes, int sign) + { + // Determine number of words needed. + int[] words = new int[bytes.length/4 + 1]; + int nwords = words.length; + + // Create a int out of modulo 4 high order bytes. + int bptr = 0; + int word = sign; + for (int i = bytes.length % 4; i > 0; --i, bptr++) + word = (word << 8) | (((int) bytes[bptr]) & 0xff); + words[--nwords] = word; + + // Elements remaining in byte[] are a multiple of 4. + while (nwords > 0) + words[--nwords] = bytes[bptr++] << 24 | + (((int) bytes[bptr++]) & 0xff) << 16 | + (((int) bytes[bptr++]) & 0xff) << 8 | + (((int) bytes[bptr++]) & 0xff); + return words; } - /** - * Canonicalizes each char digit in str, keeping a leading minus - * sign if it exists. + /** Allocate a new non-shared BigInteger. + * @param nwords number of words to allocate */ - static String forEachDigit(String str, int radix) { - char buf[] = new char[str.length()]; - int i = 0; - if (str.charAt(0) == '-') - buf[i++] = '-'; + private static BigInteger alloc(int nwords) + { + if (nwords <= 1) + return new BigInteger(); + BigInteger result = new BigInteger(); + result.words = new int[nwords]; + return result; + } + + /** Change words.length to nwords. + * We allow words.length to be upto nwords+2 without reallocating. + */ + private void realloc(int nwords) + { + if (nwords == 0) + { + if (words != null) + { + if (ival > 0) + ival = words[0]; + words = null; + } + } + else if (words == null + || words.length < nwords + || words.length > nwords + 2) + { + int[] new_words = new int [nwords]; + if (words == null) + { + new_words[0] = ival; + ival = 1; + } + else + { + if (nwords < ival) + ival = nwords; + System.arraycopy(words, 0, new_words, 0, ival); + } + words = new_words; + } + } + + private final boolean isNegative() + { + return (words == null ? ival : words[ival - 1]) < 0; + } + + public int signum() + { + int top = words == null ? ival : words[ival-1]; + if (top == 0 && words == null) + return 0; + return top < 0 ? -1 : 1; + } + + private static int compareTo(BigInteger x, BigInteger y) + { + if (x.words == null && y.words == null) + return x.ival < y.ival ? -1 : x.ival > y.ival ? 1 : 0; + boolean x_negative = x.isNegative(); + boolean y_negative = y.isNegative(); + if (x_negative != y_negative) + return x_negative ? -1 : 1; + int x_len = x.words == null ? 1 : x.ival; + int y_len = y.words == null ? 1 : y.ival; + if (x_len != y_len) + return (x_len > y_len) != x_negative ? 1 : -1; + return MPN.cmp(x.words, y.words, x_len); + } + + // JDK1.2 + public int compareTo(Object obj) + { + if (obj instanceof BigInteger) + return compareTo(this, (BigInteger) obj); + throw new ClassCastException(); + } + + public int compareTo(BigInteger val) + { + return compareTo(this, val); + } + + public BigInteger min(BigInteger val) + { + return compareTo(this, val) < 0 ? this : val; + } + + public BigInteger max(BigInteger val) + { + return compareTo(this, val) > 0 ? this : val; + } + + private final boolean isOdd() + { + int low = words == null ? ival : words[0]; + return (low & 1) != 0; + } + + private final boolean isZero() + { + return words == null && ival == 0; + } + + private final boolean isOne() + { + return words == null && ival == 1; + } + + private final boolean isMinusOne() + { + return words == null && ival == -1; + } + + /** Calculate how many words are significant in words[0:len-1]. + * Returns the least value x such that x>0 && words[0:x-1]==words[0:len-1], + * when words is viewed as a 2's complement integer. + */ + private static int wordsNeeded(int[] words, int len) + { + int i = len; + if (i > 0) + { + int word = words[--i]; + if (word == -1) + { + while (i > 0 && (word = words[i - 1]) < 0) + { + i--; + if (word != -1) break; + } + } + else + { + while (word == 0 && i > 0 && (word = words[i - 1]) >= 0) i--; + } + } + return i + 1; + } - for ( ; i < buf.length; i++) - if ((buf[i] = - Character.forDigit(Character.digit(str.charAt(i), radix), radix)) - == '\u0000') - throw new NumberFormatException(str + " not valid in radix " + radix); + private BigInteger canonicalize() + { + if (words != null + && (ival = BigInteger.wordsNeeded(words, ival)) <= 1) + { + if (ival == 1) + ival = words[0]; + words = null; + } + if (words == null && ival >= minFixNum && ival <= maxFixNum) + return smallFixNums[(int) ival - minFixNum]; + return this; + } - return new String(buf); + /** Add two ints, yielding a BigInteger. */ + private static final BigInteger add(int x, int y) + { + return BigInteger.make((long) x + (long) y); } - public BigInteger(int bitLength, int certainty, Random rnd) { - throw new ArithmeticException("unimplemented"); + /** Add a BigInteger and an int, yielding a new BigInteger. */ + private static BigInteger add(BigInteger x, int y) + { + if (x.words == null) + return BigInteger.add(x.ival, y); + BigInteger result = new BigInteger(0); + result.setAdd(x, y); + return result.canonicalize(); } - public BigInteger(int numBits, Random rnd) { - this(1, getRandomMagnitude(numBits, rnd)); + /** Set this to the sum of x and y. + * OK if x==this. */ + private void setAdd(BigInteger x, int y) + { + if (x.words == null) + { + set((long) x.ival + (long) y); + return; + } + int len = x.ival; + realloc(len + 1); + long carry = y; + for (int i = 0; i < len; i++) + { + carry += ((long) x.words[i] & 0xffffffffL); + words[i] = (int) carry; + carry >>= 32; + } + if (x.words[len - 1] < 0) + carry--; + words[len] = (int) carry; + ival = wordsNeeded(words, len + 1); } - private static byte[] getRandomMagnitude(int numBits, Random rnd) { - int array_size = numBits / 8; - int extra_bits = numBits % 8; - if (extra_bits != 0) - array_size++; + /** Destructively add an int to this. */ + private final void setAdd(int y) + { + setAdd(this, y); + } - byte[] data = new byte[array_size]; - rnd.nextBytes(data); - if (extra_bits != 0) - data[0] &= (1 << extra_bits) - 1; // mask off any extra bits + /** Destructively set the value of this to a long. */ + private final void set(long y) + { + int i = (int) y; + if ((long) i == y) + { + ival = i; + words = null; + } + else + { + realloc(2); + words[0] = i; + words[1] = (int) (y >> 32); + ival = 2; + } + } - return data; + /** Destructively set the value of this to the given words. + * The words array is reused, not copied. */ + private final void set(int[] words, int length) + { + this.ival = length; + this.words = words; } - public BigInteger(byte[] val) { - if (val.length == 0) - throw new NumberFormatException("val.length is 0"); - initFromTwosCompByteArray(val); + /** Destructively set the value of this to that of y. */ + private final void set(BigInteger y) + { + if (y.words == null) + set(y.ival); + else if (this != y) + { + realloc(y.ival); + System.arraycopy(y.words, 0, words, 0, y.ival); + ival = y.ival; + } } - public BigInteger(int signum, byte[] magnitude) { - switch (signum) { - case 0: - for (int i = 0; i < magnitude.length; i++) - if (magnitude[i] != 0) - throw new NumberFormatException("magnitude["+i+"] is non zero"); - initZero(); - break; - case 1: - case -1: - if (magnitude.length == 0) - initZero(); - else - initFromSignedMagnitudeByteArray(signum, magnitude); - break; - default: - throw new NumberFormatException("invalid signum"); - } + /** Add two BigIntegers, yielding their sum as another BigInteger. */ + private static BigInteger add(BigInteger x, BigInteger y, int k) + { + if (x.words == null && y.words == null) + return BigInteger.make((long) k * (long) y.ival + (long) x.ival); + if (k != 1) + { + if (k == -1) + y = BigInteger.neg(y); + else + y = BigInteger.times(y, BigInteger.make(k)); + } + if (x.words == null) + return BigInteger.add(y, x.ival); + if (y.words == null) + return BigInteger.add(x, y.ival); + // Both are big + int len; + if (y.ival > x.ival) + { // Swap so x is longer then y. + BigInteger tmp = x; x = y; y = tmp; + } + BigInteger result = alloc(x.ival + 1); + int i = y.ival; + long carry = MPN.add_n(result.words, x.words, y.words, i); + long y_ext = y.words[i - 1] < 0 ? 0xffffffffL : 0; + for (; i < x.ival; i++) + { + carry += ((long) x.words[i] & 0xffffffffL) + y_ext;; + result.words[i] = (int) carry; + carry >>>= 32; + } + if (x.words[i - 1] < 0) + y_ext--; + result.words[i] = (int) (carry + y_ext); + result.ival = i+1; + return result.canonicalize(); } - private BigInteger(long l) { - initFromLong(l); + public BigInteger add(BigInteger val) + { + return add(this, val, 1); } - private BigInteger() { - initZero(); + public BigInteger subtract(BigInteger val) + { + return add(this, val, -1); } - static public BigInteger valueOf(long l) { - if (l == 0) + private static final BigInteger times(BigInteger x, int y) + { + if (y == 0) return ZERO; - if (l == 1) - return ONE; - return new BigInteger(l); - } - - native public BigInteger abs(); - native public BigInteger add(BigInteger val); - native public BigInteger subtact(BigInteger val); - native public BigInteger multiply(BigInteger val); - native public BigInteger divide(BigInteger val) - throws ArithmeticException; - native public BigInteger remainder(BigInteger val) - throws ArithmeticException; - native public BigInteger gcd(BigInteger val); - - public BigInteger[] divideAndRemainder(BigInteger val) - throws ArithmeticException { - BigInteger res[] = new BigInteger[2]; - res[0] = divide(val); - res[1] = remainder(val); - return res; - } - - native public BigInteger pow(int exponent) - throws ArithmeticException; - native public BigInteger modPow(BigInteger exponent, - BigInteger m) - throws ArithmeticException; - native public BigInteger mod(BigInteger m) - throws ArithmeticException; - native public BigInteger modInverse(BigInteger m) - throws ArithmeticException; - - // bitwise operations - native public BigInteger shiftLeft(int n); - native public BigInteger shiftRight(int n); - native public BigInteger and(BigInteger val); - native public BigInteger or(BigInteger val); - native public BigInteger xor(BigInteger val); - native public BigInteger not(); - native public BigInteger andNot(BigInteger val); - native public int getLowestSetBit(); - native public int bitLength(); - native public int bitCount(); - native public boolean testBit(int n); - native public BigInteger setBit(int n); - native public BigInteger clearBit(int n); - native public BigInteger flipBit(int n); - - native public boolean isProbablePrime(int certainty); - - native public BigInteger negate(); - native public BigInteger subtract(BigInteger val); - native public int compareTo(BigInteger val); - public int compareTo(Object o) throws ClassCastException { - return compareTo((BigInteger)o); - } - native public int signum(); - - public boolean equals(Object o) { - return (o instanceof BigInteger && nativeEquals((BigInteger)o)); - } - - public BigInteger min(BigInteger val) { - switch (compareTo(val)) { - case -1: - case 0: - return this; - default: - return val; - } + if (y == 1) + return x; + int[] xwords = x.words; + int xlen = x.ival; + if (xwords == null) + return BigInteger.make((long) xlen * (long) y); + boolean negative; + BigInteger result = BigInteger.alloc(xlen + 1); + if (xwords[xlen - 1] < 0) + { + negative = true; + negate(result.words, xwords, xlen); + xwords = result.words; + } + else + negative = false; + if (y < 0) + { + negative = !negative; + y = -y; + } + result.words[xlen] = MPN.mul_1(result.words, xwords, xlen, y); + result.ival = xlen + 1; + if (negative) + result.setNegative(); + return result.canonicalize(); } - public BigInteger max(BigInteger val) { - switch (compareTo(val)) { - case -1: - case 0: - return val; - default: - return this; - } + private static final BigInteger times(BigInteger x, BigInteger y) + { + if (y.words == null) + return times(x, y.ival); + if (x.words == null) + return times(y, x.ival); + boolean negative = false; + int[] xwords; + int[] ywords; + int xlen = x.ival; + int ylen = y.ival; + if (x.isNegative()) + { + negative = true; + xwords = new int[xlen]; + negate(xwords, x.words, xlen); + } + else + { + negative = false; + xwords = x.words; + } + if (y.isNegative()) + { + negative = !negative; + ywords = new int[ylen]; + negate(ywords, y.words, ylen); + } + else + ywords = y.words; + // Swap if x is shorter then y. + if (xlen < ylen) + { + int[] twords = xwords; xwords = ywords; ywords = twords; + int tlen = xlen; xlen = ylen; ylen = tlen; + } + BigInteger result = BigInteger.alloc(xlen+ylen); + MPN.mul(result.words, xwords, xlen, ywords, ylen); + result.ival = xlen+ylen; + if (negative) + result.setNegative(); + return result.canonicalize(); + } + + public BigInteger multiply(BigInteger y) + { + return times(this, y); + } + + private static void divide(long x, long y, + BigInteger quotient, BigInteger remainder, + int rounding_mode) + { + boolean xNegative, yNegative; + if (x < 0) + { + xNegative = true; + if (x == Long.MIN_VALUE) + { + divide(BigInteger.make(x), BigInteger.make(y), + quotient, remainder, rounding_mode); + return; + } + x = -x; + } + else + xNegative = false; + + if (y < 0) + { + yNegative = true; + if (y == Long.MIN_VALUE) + { + if (rounding_mode == TRUNCATE) + { // x != Long.Min_VALUE implies abs(x) < abs(y) + if (quotient != null) + quotient.set(0); + if (remainder != null) + remainder.set(x); + } + else + divide(BigInteger.make(x), BigInteger.make(y), + quotient, remainder, rounding_mode); + return; + } + y = -y; + } + else + yNegative = false; + + long q = x / y; + long r = x % y; + boolean qNegative = xNegative ^ yNegative; + + boolean add_one = false; + if (r != 0) + { + switch (rounding_mode) + { + case TRUNCATE: + break; + case CEILING: + case FLOOR: + if (qNegative == (rounding_mode == FLOOR)) + add_one = true; + break; + case ROUND: + add_one = r > ((y - (q & 1)) >> 1); + break; + } + } + if (quotient != null) + { + if (add_one) + q++; + if (qNegative) + q = -q; + quotient.set(q); + } + if (remainder != null) + { + // The remainder is by definition: X-Q*Y + if (add_one) + { + // Subtract the remainder from Y. + r = y - r; + // In this case, abs(Q*Y) > abs(X). + // So sign(remainder) = -sign(X). + xNegative = ! xNegative; + } + else + { + // If !add_one, then: abs(Q*Y) <= abs(X). + // So sign(remainder) = sign(X). + } + if (xNegative) + r = -r; + remainder.set(r); + } + } + + /** Divide two integers, yielding quotient and remainder. + * @param x the numerator in the division + * @param y the denominator in the division + * @param quotient is set to the quotient of the result (iff quotient!=null) + * @param remainder is set to the remainder of the result + * (iff remainder!=null) + * @param rounding_mode one of FLOOR, CEILING, TRUNCATE, or ROUND. + */ + private static void divide(BigInteger x, BigInteger y, + BigInteger quotient, BigInteger remainder, + int rounding_mode) + { + if ((x.words == null || x.ival <= 2) + && (y.words == null || y.ival <= 2)) + { + long x_l = x.longValue(); + long y_l = y.longValue(); + if (x_l != Long.MIN_VALUE && y_l != Long.MIN_VALUE) + { + divide(x_l, y_l, quotient, remainder, rounding_mode); + return; + } + } + + boolean xNegative = x.isNegative(); + boolean yNegative = y.isNegative(); + boolean qNegative = xNegative ^ yNegative; + + int ylen = y.words == null ? 1 : y.ival; + int[] ywords = new int[ylen]; + y.getAbsolute(ywords); + while (ylen > 1 && ywords[ylen - 1] == 0) ylen--; + + int xlen = x.words == null ? 1 : x.ival; + int[] xwords = new int[xlen+2]; + x.getAbsolute(xwords); + while (xlen > 1 && xwords[xlen-1] == 0) xlen--; + + int qlen, rlen; + + int cmpval = MPN.cmp(xwords, xlen, ywords, ylen); + if (cmpval < 0) // abs(x) < abs(y) + { // quotient = 0; remainder = num. + int[] rwords = xwords; xwords = ywords; ywords = rwords; + rlen = xlen; qlen = 1; xwords[0] = 0; + } + else if (cmpval == 0) // abs(x) == abs(y) + { + xwords[0] = 1; qlen = 1; // quotient = 1 + ywords[0] = 0; rlen = 1; // remainder = 0; + } + else if (ylen == 1) + { + qlen = xlen; + // Need to leave room for a word of leading zeros if dividing by 1 + // and the dividend has the high bit set. It might be safe to + // increment qlen in all cases, but it certainly is only necessary + // in the following case. + if (ywords[0] == 1 && xwords[xlen-1] < 0) + qlen++; + rlen = 1; + ywords[0] = MPN.divmod_1(xwords, xwords, xlen, ywords[0]); + } + else // abs(x) > abs(y) + { + // Normalize the denominator, i.e. make its most significant bit set by + // shifting it normalization_steps bits to the left. Also shift the + // numerator the same number of steps (to keep the quotient the same!). + + int nshift = MPN.count_leading_zeros(ywords[ylen - 1]); + if (nshift != 0) + { + // Shift up the denominator setting the most significant bit of + // the most significant word. + MPN.lshift(ywords, 0, ywords, ylen, nshift); + + // Shift up the numerator, possibly introducing a new most + // significant word. + int x_high = MPN.lshift(xwords, 0, xwords, xlen, nshift); + xwords[xlen++] = x_high; + } + + if (xlen == ylen) + xwords[xlen++] = 0; + MPN.divide(xwords, xlen, ywords, ylen); + rlen = ylen; + MPN.rshift0 (ywords, xwords, 0, rlen, nshift); + + qlen = xlen + 1 - ylen; + if (quotient != null) + { + for (int i = 0; i < qlen; i++) + xwords[i] = xwords[i+ylen]; + } + } + + if (ywords[rlen-1] < 0) + { + ywords[rlen] = 0; + rlen++; + } + + // Now the quotient is in xwords, and the remainder is in ywords. + + boolean add_one = false; + if (rlen > 1 || ywords[0] != 0) + { // Non-zero remainder i.e. in-exact quotient. + switch (rounding_mode) + { + case TRUNCATE: + break; + case CEILING: + case FLOOR: + if (qNegative == (rounding_mode == FLOOR)) + add_one = true; + break; + case ROUND: + // int cmp = compareTo(remainder<<1, abs(y)); + BigInteger tmp = remainder == null ? new BigInteger() : remainder; + tmp.set(ywords, rlen); + tmp = shift(tmp, 1); + if (yNegative) + tmp.setNegative(); + int cmp = compareTo(tmp, y); + // Now cmp == compareTo(sign(y)*(remainder<<1), y) + if (yNegative) + cmp = -cmp; + add_one = (cmp == 1) || (cmp == 0 && (xwords[0]&1) != 0); + } + } + if (quotient != null) + { + quotient.set(xwords, qlen); + if (qNegative) + { + if (add_one) // -(quotient + 1) == ~(quotient) + quotient.setInvert(); + else + quotient.setNegative(); + } + else if (add_one) + quotient.setAdd(1); + } + if (remainder != null) + { + // The remainder is by definition: X-Q*Y + remainder.set(ywords, rlen); + if (add_one) + { + // Subtract the remainder from Y: + // abs(R) = abs(Y) - abs(orig_rem) = -(abs(orig_rem) - abs(Y)). + BigInteger tmp; + if (y.words == null) + { + tmp = remainder; + tmp.set(yNegative ? ywords[0] + y.ival : ywords[0] - y.ival); + } + else + tmp = BigInteger.add(remainder, y, yNegative ? 1 : -1); + // Now tmp <= 0. + // In this case, abs(Q) = 1 + floor(abs(X)/abs(Y)). + // Hence, abs(Q*Y) > abs(X). + // So sign(remainder) = -sign(X). + if (xNegative) + remainder.setNegative(tmp); + else + remainder.set(tmp); + } + else + { + // If !add_one, then: abs(Q*Y) <= abs(X). + // So sign(remainder) = sign(X). + if (xNegative) + remainder.setNegative(); + } + } + } + + public BigInteger divide(BigInteger val) + { + if (val.isZero()) + throw new ArithmeticException("divisor is zero"); + + BigInteger quot = new BigInteger(); + divide(this, val, quot, null, TRUNCATE); + return quot.canonicalize(); } - public native int hashCode(); + public BigInteger remainder(BigInteger val) + { + if (val.isZero()) + throw new ArithmeticException("divisor is zero"); - static native void initNativeState(); - native boolean initFromString(String val, int radix); - native void initFromLong(long l); - native void initFromSignedMagnitudeByteArray(int signum, byte[] magnitude); - native void initFromTwosCompByteArray(byte[] array); - native void initZero(); + BigInteger rem = new BigInteger(); + divide(this, val, null, rem, TRUNCATE); + return rem.canonicalize(); + } - public native void print(); - native boolean nativeEquals(BigInteger val); + public BigInteger[] divideAndRemainder(BigInteger val) + { + if (val.isZero()) + throw new ArithmeticException("divisor is zero"); - public native long longValue(); - public int intValue() { - return (int)longValue(); + BigInteger[] result = new BigInteger[2]; + result[0] = new BigInteger(); + result[1] = new BigInteger(); + divide(this, val, result[0], result[1], TRUNCATE); + result[0].canonicalize(); + result[1].canonicalize(); + return result; } - - public native double doubleValue(); - public float floatValue() { - return (float)doubleValue(); + + public BigInteger mod(BigInteger m) + { + if (m.isNegative() || m.isZero()) + throw new ArithmeticException("non-positive modulus"); + + BigInteger rem = new BigInteger(); + divide(this, m, null, rem, FLOOR); + return rem.canonicalize(); } - public native String toString(int radix); - - public String toString() { - return toString(10); + /** Calculate power for BigInteger exponents. + * @param y exponent assumed to be non-negative. */ + private BigInteger pow(BigInteger y) + { + if (isOne()) + return this; + if (isMinusOne()) + return y.isOdd () ? this : ONE; + if (y.words == null && y.ival >= 0) + return pow(y.ival); + + // Assume exponent is non-negative. + if (isZero()) + return this; + + // Implemented by repeated squaring and multiplication. + BigInteger pow2 = this; + BigInteger r = null; + for (;;) // for (i = 0; ; i++) + { + // pow2 == x**(2**i) + // prod = x**(sum(j=0..i-1, (y>>j)&1)) + if (y.isOdd()) + r = r == null ? pow2 : times(r, pow2); // r *= pow2 + y = BigInteger.shift(y, -1); + if (y.isZero()) + break; + // pow2 *= pow2; + pow2 = times(pow2, pow2); + } + return r == null ? ONE : r; + } + + /** Calculate the integral power of a BigInteger. + * @param exponent the exponent (must be non-negative) + */ + public BigInteger pow(int exponent) + { + if (exponent <= 0) + { + if (exponent == 0) + return ONE; + else + throw new ArithmeticException("negative exponent"); + } + if (isZero()) + return this; + int plen = words == null ? 1 : ival; // Length of pow2. + int blen = ((bitLength() * exponent) >> 5) + 2 * plen; + boolean negative = isNegative() && (exponent & 1) != 0; + int[] pow2 = new int [blen]; + int[] rwords = new int [blen]; + int[] work = new int [blen]; + getAbsolute(pow2); // pow2 = abs(this); + int rlen = 1; + rwords[0] = 1; // rwords = 1; + for (;;) // for (i = 0; ; i++) + { + // pow2 == this**(2**i) + // prod = this**(sum(j=0..i-1, (exponent>>j)&1)) + if ((exponent & 1) != 0) + { // r *= pow2 + MPN.mul(work, pow2, plen, rwords, rlen); + int[] temp = work; work = rwords; rwords = temp; + rlen += plen; + while (rwords[rlen - 1] == 0) rlen--; + } + exponent >>= 1; + if (exponent == 0) + break; + // pow2 *= pow2; + MPN.mul(work, pow2, plen, pow2, plen); + int[] temp = work; work = pow2; pow2 = temp; // swap to avoid a copy + plen *= 2; + while (pow2[plen - 1] == 0) plen--; + } + if (rwords[rlen - 1] < 0) + rlen++; + if (negative) + negate(rwords, rwords, rlen); + return BigInteger.make(rwords, rlen); } - public native byte[] toByteArray(); + private static final int[] euclidInv(int a, int b, int prevDiv) + { + // Storage for return values, plus one slot for a temp int (see below). + int[] xy; + + if (b == 0) + throw new ArithmeticException("not invertible"); + else if (b == 1) + { + // Success: values are indeed invertible! + // Bottom of the recursion reached; start unwinding. + xy = new int[3]; + xy[0] = -prevDiv; + xy[1] = 1; + return xy; + } + + xy = euclidInv(b, a % b, a / b); // Recursion happens here. - protected void finalize() throws Throwable { - nativeFinalize(); - super.finalize(); + // xy[2] is just temp storage for intermediate results in the following + // calculation. This saves us a bit of space over having an int + // allocated at every level of this recursive method. + xy[2] = xy[0]; + xy[0] = xy[2] * -prevDiv + xy[1]; + xy[1] = xy[2]; + return xy; } - native void nativeFinalize(); + private static final BigInteger[] + euclidInv(BigInteger a, BigInteger b, BigInteger prevDiv) + { + // FIXME: This method could be more efficient memory-wise and should be + // modified as such since it is recursive. - static public void main(String args[]) { - BigInteger i = new BigInteger(-549755813888L); - BigInteger i2 = new BigInteger ("5"); - BigInteger i3 = new BigInteger ("7"); - byte[] foo = new byte[2]; - foo[0] = 0; - foo[1] = 0; -// BigInteger i4 = new BigInteger(-1, foo); -// System.out.println(i4); - // BigInteger i5 = new BigInteger(20, new Random(5)); + // Storage for return values, plus one slot for a temp int (see below). + BigInteger[] xy; - BigInteger i4 = new BigInteger(-300L); - System.out.println (i4); - byte[] bar = i4.toByteArray(); - for (int z = 0; z < bar.length; z++) - System.out.println(z + ": " + bar[z]); + if (b.isZero()) + throw new ArithmeticException("not invertible"); + else if (b.isOne()) + { + // Success: values are indeed invertible! + // Bottom of the recursion reached; start unwinding. + xy = new BigInteger[3]; + xy[0] = neg(prevDiv); + xy[1] = ONE; + return xy; + } - BigInteger i5 = new BigInteger(bar); - System.out.println (i5); + // Recursion happens in the following conditional! - // System.out.println(i5); - // i.modPow(i2, i3).print(); - // System.out.println(i.toString()); + // If a just contains an int, then use integer math for the rest. + if (a.words == null) + { + int[] xyInt = euclidInv(b.ival, a.ival % b.ival, a.ival / b.ival); + xy = new BigInteger[3]; + xy[0] = new BigInteger(xyInt[0]); + xy[1] = new BigInteger(xyInt[1]); + } + else + { + BigInteger rem = new BigInteger(); + BigInteger quot = new BigInteger(); + divide(a, b, quot, rem, FLOOR); + xy = euclidInv(b, rem, quot); + } - // i3 = i.modInverse(i2); - // i3.print(); - // System.out.println(i.isProbablePrime(50)); + // xy[2] is just temp storage for intermediate results in the following + // calculation. This saves us a bit of space over having a BigInteger + // allocated at every level of this recursive method. + xy[2] = xy[0]; + xy[0] = add(xy[1], times(xy[2], prevDiv), -1); + xy[1] = xy[2]; + return xy; + } - java.math.BigInteger bi = new java.math.BigInteger("11"); - java.math.BigInteger bi2 = new java.math.BigInteger("-8"); - java.math.BigInteger bi3 = new java.math.BigInteger("7"); -// System.out.println(bi.isProbablePrime(50)); + public BigInteger modInverse(BigInteger y) + { + if (y.isNegative() || y.isZero()) + throw new ArithmeticException("non-positive modulo"); + // Degenerate cases. + if (y.isOne()) + return ZERO; + else if (isOne()) + return ONE; -// BigInteger i = new BigInteger("3"); -// BigInteger i2 = new BigInteger ("4"); -// BigInteger i3 = new BigInteger ("7"); -// // i.print(); -// i.modPow(i2, i3).print(); + // Use Euclid's algorithm as in gcd() but do this recursively + // rather than in a loop so we can use the intermediate results as we + // unwind from the recursion. + // Used http://www.math.nmsu.edu/~crypto/EuclideanAlgo.html as reference. + BigInteger result = new BigInteger(); + int xval = ival; + int yval = y.ival; + boolean swapped = false; -// java.math.BigInteger bi = new java.math.BigInteger("3"); -// java.math.BigInteger bi2 = new java.math.BigInteger("4"); -// java.math.BigInteger bi3 = new java.math.BigInteger("7"); -// System.out.println(bi.modPow(bi2, bi3)); + if (y.words == null) + { + // The result is guaranteed to be less than the modulus, y (which is + // an int), so simplify this by working with the int result of this + // modulo y. Also, if this is negative, make it positive via modulo + // math. Note that BigInteger.mod() must be used even if this is + // already an int as the % operator would provide a negative result if + // this is negative, BigInteger.mod() never returns negative values. + if (words != null || isNegative()) + xval = mod(y).ival; + + // Swap values so x > y. + if (yval > xval) + { + int tmp = xval; xval = yval; yval = tmp; + swapped = true; + } + // Normally, the result is in the 2nd element of the array, but + // if originally x < y, then x and y were swapped and the result + // is in the 1st element of the array. + result.ival = + euclidInv(yval, xval % yval, xval / yval)[swapped ? 0 : 1]; + + // Result can't be negative, so make it positive by adding the + // original modulus, y.ival (not the possibly "swapped" yval). + if (result.ival < 0) + result.ival += y.ival; + } + else + { + BigInteger x = this; + + // As above, force this to be a positive value via modulo math. + if (isNegative()) + x = mod(y); + + // Swap values so x > y. + if (x.compareTo(y) < 0) + { + BigInteger tmp = x; x = y; y = tmp; + swapped = true; + } + // As above (for ints), result will be in the 2nd element unless + // the original x and y were swapped. + BigInteger rem = new BigInteger(); + BigInteger quot = new BigInteger(); + divide(x, y, quot, rem, FLOOR); + result = euclidInv(y, rem, quot)[swapped ? 0 : 1]; + + // Result can't be negative, so make it positive by adding the + // original modulus, y (which is now x if they were swapped). + if (result.isNegative()) + result = add(result, swapped ? x : y, 1); + } + + return result; + } + + public BigInteger modPow(BigInteger exponent, BigInteger m) + { + if (m.isNegative() || m.isZero()) + throw new ArithmeticException("non-positive modulo"); + + if (exponent.isNegative()) + return modInverse(m); + if (exponent.isOne()) + return mod(m); + + // To do this naively by first raising this to the power of exponent + // and then performing modulo m would be extremely expensive, especially + // for very large numbers. The solution is found in Number Theory + // where a combination of partial powers and modulos can be done easily. + // + // We'll use the algorithm for Additive Chaining which can be found on + // p. 244 of "Applied Cryptography, Second Edition" by Bruce Schneier. + BigInteger s, t, u; + int i; + + s = ONE; + t = this; + u = exponent; + + while (!u.isZero()) + { + if (u.and(ONE).isOne()) + s = times(s, t).mod(m); + u = u.shiftRight(1); + t = times(t, t).mod(m); + } + + return s; + } + + /** Calculate Greatest Common Divisor for non-negative ints. */ + private static final int gcd(int a, int b) + { + // Euclid's algorithm, copied from libg++. + if (b > a) + { + int tmp = a; a = b; b = tmp; + } + for(;;) + { + if (b == 0) + return a; + else if (b == 1) + return b; + else + { + int tmp = b; + b = a % b; + a = tmp; + } + } + } + + public BigInteger gcd(BigInteger y) + { + int xval = ival; + int yval = y.ival; + if (words == null) + { + if (xval == 0) + return BigInteger.abs(y); + if (y.words == null + && xval != Integer.MIN_VALUE && yval != Integer.MIN_VALUE) + { + if (xval < 0) + xval = -xval; + if (yval < 0) + yval = -yval; + return BigInteger.make(BigInteger.gcd(xval, yval)); + } + xval = 1; + } + if (y.words == null) + { + if (yval == 0) + return BigInteger.abs(this); + yval = 1; + } + int len = (xval > yval ? xval : yval) + 1; + int[] xwords = new int[len]; + int[] ywords = new int[len]; + getAbsolute(xwords); + y.getAbsolute(ywords); + len = MPN.gcd(xwords, ywords, len); + BigInteger result = new BigInteger(0); + result.ival = len; + result.words = xwords; + return result.canonicalize(); + } + + public boolean isProbablePrime(int certainty) + { + /** We'll use the Rabin-Miller algorithm for doing a probabilistic + * primality test. It is fast, easy and has faster decreasing odds of a + * composite passing than with other tests. This means that this + * method will actually have a probability much greater than the + * 1 - .5^certainty specified in the JCL (p. 117), but I don't think + * anyone will complain about better performance with greater certainty. + * + * The Rabin-Miller algorithm can be found on pp. 259-261 of "Applied + * Cryptography, Second Edition" by Bruce Schneier. + */ + + // First rule out small prime factors and assure the number is odd. + for (int i = 0; i < primes.length; i++) + { + if (words == null && ival == primes[i]) + return true; + if (remainder(make(primes[i])).isZero()) + return false; + } + + // Now perform the Rabin-Miller test. + // NB: I know that this can be simplified programatically, but + // I have tried to keep it as close as possible to the algorithm + // as written in the Schneier book for reference purposes. + + // Set b to the number of times 2 evenly divides (this - 1). + // I.e. 2^b is the largest power of 2 that divides (this - 1). + BigInteger pMinus1 = add(this, -1); + int b = pMinus1.getLowestSetBit(); + + // Set m such that this = 1 + 2^b * m. + BigInteger m = pMinus1.divide(make(2L << b - 1)); + + Random rand = new Random(); + while (certainty-- > 0) + { + // Pick a random number greater than 1 and less than this. + // The algorithm says to pick a small number to make the calculations + // go faster, but it doesn't say how small; we'll use 2 to 1024. + int a = rand.nextInt(); + a = (a < 0 ? -a : a) % 1023 + 2; + + BigInteger z = make(a).modPow(m, this); + if (z.isOne() || z.equals(pMinus1)) + continue; // Passes the test; may be prime. + + int i; + for (i = 0; i < b; ) + { + if (z.isOne()) + return false; + i++; + if (z.equals(pMinus1)) + break; // Passes the test; may be prime. + + z = z.modPow(make(2), this); + } + + if (i == b && !z.equals(pMinus1)) + return false; + } + return true; + } + + private void setInvert() + { + if (words == null) + ival = ~ival; + else + { + for (int i = ival; --i >= 0; ) + words[i] = ~words[i]; + } + } + + private void setShiftLeft(BigInteger x, int count) + { + int[] xwords; + int xlen; + if (x.words == null) + { + if (count < 32) + { + set((long) x.ival << count); + return; + } + xwords = new int[1]; + xwords[0] = x.ival; + xlen = 1; + } + else + { + xwords = x.words; + xlen = x.ival; + } + int word_count = count >> 5; + count &= 31; + int new_len = xlen + word_count; + if (count == 0) + { + realloc(new_len); + for (int i = xlen; --i >= 0; ) + words[i+word_count] = xwords[i]; + } + else + { + new_len++; + realloc(new_len); + int shift_out = MPN.lshift(words, word_count, xwords, xlen, count); + count = 32 - count; + words[new_len-1] = (shift_out << count) >> count; // sign-extend. + } + ival = new_len; + for (int i = word_count; --i >= 0; ) + words[i] = 0; + } + + private void setShiftRight(BigInteger x, int count) + { + if (x.words == null) + set(count < 32 ? x.ival >> count : x.ival < 0 ? -1 : 0); + else if (count == 0) + set(x); + else + { + boolean neg = x.isNegative(); + int word_count = count >> 5; + count &= 31; + int d_len = x.ival - word_count; + if (d_len <= 0) + set(neg ? -1 : 0); + else + { + if (words == null || words.length < d_len) + realloc(d_len); + MPN.rshift0 (words, x.words, word_count, d_len, count); + ival = d_len; + if (neg) + words[d_len-1] |= -2 << (31 - count); + } + } + } + + private void setShift(BigInteger x, int count) + { + if (count > 0) + setShiftLeft(x, count); + else + setShiftRight(x, -count); + } + + private static BigInteger shift(BigInteger x, int count) + { + if (x.words == null) + { + if (count <= 0) + return make(count > -32 ? x.ival >> (-count) : x.ival < 0 ? -1 : 0); + if (count < 32) + return make((long) x.ival << count); + } + if (count == 0) + return x; + BigInteger result = new BigInteger(0); + result.setShift(x, count); + return result.canonicalize(); + } + + public BigInteger shiftLeft(int n) + { + return shift(this, n); + } + + public BigInteger shiftRight(int n) + { + return shift(this, -n); + } + + private void format(int radix, StringBuffer buffer) + { + if (words == null) + buffer.append(Integer.toString(ival, radix)); + else if (ival <= 2) + buffer.append(Long.toString(longValue(), radix)); + else + { + boolean neg = isNegative(); + int[] work; + if (neg || radix != 16) + { + work = new int[ival]; + getAbsolute(work); + } + else + work = words; + int len = ival; + + int buf_size = len * (MPN.chars_per_word(radix) + 1); + if (radix == 16) + { + if (neg) + buffer.append('-'); + int buf_start = buffer.length(); + for (int i = len; --i >= 0; ) + { + int word = work[i]; + for (int j = 8; --j >= 0; ) + { + int hex_digit = (word >> (4 * j)) & 0xF; + // Suppress leading zeros: + if (hex_digit > 0 || buffer.length() > buf_start) + buffer.append(Character.forDigit(hex_digit, 16)); + } + } + } + else + { + int i = buffer.length(); + for (;;) + { + int digit = MPN.divmod_1(work, work, len, radix); + buffer.append(Character.forDigit(digit, radix)); + while (len > 0 && work[len-1] == 0) len--; + if (len == 0) + break; + } + if (neg) + buffer.append('-'); + /* Reverse buffer. */ + int j = buffer.length() - 1; + while (i < j) + { + char tmp = buffer.charAt(i); + buffer.setCharAt(i, buffer.charAt(j)); + buffer.setCharAt(j, tmp); + i++; j--; + } + } + } + } + + public String toString() + { + return toString(10); + } + + public String toString(int radix) + { + if (words == null) + return Integer.toString(ival, radix); + else if (ival <= 2) + return Long.toString(longValue(), radix); + int buf_size = ival * (MPN.chars_per_word(radix) + 1); + StringBuffer buffer = new StringBuffer(buf_size); + format(radix, buffer); + return buffer.toString(); + } + + public int intValue() + { + if (words == null) + return ival; + return words[0]; + } + + public long longValue() + { + if (words == null) + return ival; + if (ival == 1) + return words[0]; + return ((long)words[1] << 32) + ((long)words[0] & 0xffffffffL); + } + + public int hashCode() + { + // FIXME: May not match hashcode of JDK. + return words == null ? ival : (words[0] + words[ival - 1]); + } + + /* Assumes x and y are both canonicalized. */ + private static boolean equals(BigInteger x, BigInteger y) + { + if (x.words == null && y.words == null) + return x.ival == y.ival; + if (x.words == null || y.words == null || x.ival != y.ival) + return false; + for (int i = x.ival; --i >= 0; ) + { + if (x.words[i] != y.words[i]) + return false; + } + return true; + } + + /* Assumes this and obj are both canonicalized. */ + public boolean equals(Object obj) + { + if (obj == null || ! (obj instanceof BigInteger)) + return false; + return BigInteger.equals(this, (BigInteger) obj); + } + + private static BigInteger valueOf(String s, int radix) + throws NumberFormatException + { + int len = s.length(); + // Testing (len < MPN.chars_per_word(radix)) would be more accurate, + // but slightly more expensive, for little practical gain. + if (len <= 15 && radix <= 16) + return BigInteger.make(Long.parseLong(s, radix)); + + int byte_len = 0; + byte[] bytes = new byte[len]; + boolean negative = false; + for (int i = 0; i < len; i++) + { + char ch = s.charAt(i); + if (ch == '-') + negative = true; + else if (ch == '_' || (byte_len == 0 && (ch == ' ' || ch == '\t'))) + continue; + else + { + int digit = Character.digit(ch, radix); + if (digit < 0) + break; + bytes[byte_len++] = (byte) digit; + } + } + return valueOf(bytes, byte_len, negative, radix); + } + + private static BigInteger valueOf(byte[] digits, int byte_len, + boolean negative, int radix) + { + int chars_per_word = MPN.chars_per_word(radix); + int[] words = new int[byte_len / chars_per_word + 1]; + int size = MPN.set_str(words, digits, byte_len, radix); + if (size == 0) + return ZERO; + if (words[size-1] < 0) + words[size++] = 0; + if (negative) + negate(words, words, size); + return make(words, size); + } + + public double doubleValue() + { + if (words == null) + return (double) ival; + if (ival <= 2) + return (double) longValue(); + if (isNegative()) + return BigInteger.neg(this).roundToDouble(0, true, false); + else + return roundToDouble(0, false, false); + } + + public float floatValue() + { + return (float) doubleValue(); + } + + /** Return true if any of the lowest n bits are one. + * (false if n is negative). */ + private boolean checkBits(int n) + { + if (n <= 0) + return false; + if (words == null) + return n > 31 || ((ival & ((1 << n) - 1)) != 0); + int i; + for (i = 0; i < (n >> 5) ; i++) + if (words[i] != 0) + return true; + return (n & 31) != 0 && (words[i] & ((1 << (n & 31)) - 1)) != 0; + } + + /** Convert a semi-processed BigInteger to double. + * Number must be non-negative. Multiplies by a power of two, applies sign, + * and converts to double, with the usual java rounding. + * @param exp power of two, positive or negative, by which to multiply + * @param neg true if negative + * @param remainder true if the BigInteger is the result of a truncating + * division that had non-zero remainder. To ensure proper rounding in + * this case, the BigInteger must have at least 54 bits. */ + private double roundToDouble(int exp, boolean neg, boolean remainder) + { + // Compute length. + int il = bitLength(); + + // Exponent when normalized to have decimal point directly after + // leading one. This is stored excess 1023 in the exponent bit field. + exp += il - 1; + + // Gross underflow. If exp == -1075, we let the rounding + // computation determine whether it is minval or 0 (which are just + // 0x0000 0000 0000 0001 and 0x0000 0000 0000 0000 as bit + // patterns). + if (exp < -1075) + return neg ? -0.0 : 0.0; + + // gross overflow + if (exp > 1023) + return neg ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY; + + // number of bits in mantissa, including the leading one. + // 53 unless it's denormalized + int ml = (exp >= -1022 ? 53 : 53 + exp + 1022); + + // Get top ml + 1 bits. The extra one is for rounding. + long m; + int excess_bits = il - (ml + 1); + if (excess_bits > 0) + m = ((words == null) ? ival >> excess_bits + : MPN.rshift_long(words, ival, excess_bits)); + else + m = longValue() << (- excess_bits); + + // Special rounding for maxval. If the number exceeds maxval by + // any amount, even if it's less than half a step, it overflows. + if (exp == 1023 && ((m >> 1) == (1L << 53) - 1)) + { + if (remainder || checkBits(il - ml)) + return neg ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY; + else + return neg ? - Double.MAX_VALUE : Double.MAX_VALUE; + } + + // Normal round-to-even rule: round up if the bit dropped is a one, and + // the bit above it or any of the bits below it is a one. + if ((m & 1) == 1 + && ((m & 2) == 2 || remainder || checkBits(excess_bits))) + { + m += 2; + // Check if we overflowed the mantissa + if ((m & (1L << 54)) != 0) + { + exp++; + // renormalize + m >>= 1; + } + // Check if a denormalized mantissa was just rounded up to a + // normalized one. + else if (ml == 52 && (m & (1L << 53)) != 0) + exp++; + } + + // Discard the rounding bit + m >>= 1; + + long bits_sign = neg ? (1L << 63) : 0; + exp += 1023; + long bits_exp = (exp <= 0) ? 0 : ((long)exp) << 52; + long bits_mant = m & ~(1L << 52); + return Double.longBitsToDouble(bits_sign | bits_exp | bits_mant); + } + + /** Copy the abolute value of this into an array of words. + * Assumes words.length >= (this.words == null ? 1 : this.ival). + * Result is zero-extended, but need not be a valid 2's complement number. + */ + + private void getAbsolute(int[] words) + { + int len; + if (this.words == null) + { + len = 1; + words[0] = this.ival; + } + else + { + len = this.ival; + for (int i = len; --i >= 0; ) + words[i] = this.words[i]; + } + if (words[len - 1] < 0) + negate(words, words, len); + for (int i = words.length; --i > len; ) + words[i] = 0; + } + + /** Set dest[0:len-1] to the negation of src[0:len-1]. + * Return true if overflow (i.e. if src is -2**(32*len-1)). + * Ok for src==dest. */ + private static boolean negate(int[] dest, int[] src, int len) + { + long carry = 1; + boolean negative = src[len-1] < 0; + for (int i = 0; i < len; i++) + { + carry += ((long) (~src[i]) & 0xffffffffL); + dest[i] = (int) carry; + carry >>= 32; + } + return (negative && dest[len-1] < 0); + } + + /** Destructively set this to the negative of x. + * It is OK if x==this.*/ + private void setNegative(BigInteger x) + { + int len = x.ival; + if (x.words == null) + { + if (len == Integer.MIN_VALUE) + set(- (long) len); + else + set(-len); + return; + } + realloc(len + 1); + if (BigInteger.negate(words, x.words, len)) + words[len++] = 0; + ival = len; + } + + /** Destructively negate this. */ + private final void setNegative() + { + setNegative(this); + } + + private static BigInteger abs(BigInteger x) + { + return x.isNegative() ? neg(x) : x; + } + + public BigInteger abs() + { + return abs(this); + } + + private static BigInteger neg(BigInteger x) + { + if (x.words == null && x.ival != Integer.MIN_VALUE) + return make(- x.ival); + BigInteger result = new BigInteger(0); + result.setNegative(x); + return result.canonicalize(); + } + + public BigInteger negate() + { + return BigInteger.neg(this); + } + + /** Calculates ceiling(log2(this < 0 ? -this : this+1)) + * See Common Lisp: the Language, 2nd ed, p. 361. + */ + public int bitLength() + { + if (words == null) + return MPN.intLength(ival); + else + return MPN.intLength(words, ival); + } + + public byte[] toByteArray() + { + // Determine number of bytes needed. The method bitlength returns + // the size without the sign bit, so add one bit for that and then + // add 7 more to emulate the ceil function using integer math. + byte[] bytes = new byte[(bitLength() + 1 + 7) / 8]; + int nbytes = bytes.length; + + int wptr = 0; + int word; + + // Deal with words array until one word or less is left to process. + // If BigInteger is an int, then it is in ival and nbytes will be <= 4. + while (nbytes > 4) + { + word = words[wptr++]; + for (int i = 4; i > 0; --i, word >>= 8) + bytes[--nbytes] = (byte) word; + } + + // Deal with the last few bytes. If BigInteger is an int, use ival. + word = (words == null) ? ival : words[wptr]; + for ( ; nbytes > 0; word >>= 8) + bytes[--nbytes] = (byte) word; + + return bytes; + } + + /** Return the boolean opcode (for bitOp) for swapped operands. + * I.e. bitOp(swappedOp(op), x, y) == bitOp(op, y, x). + */ + private static int swappedOp(int op) + { + return + "\000\001\004\005\002\003\006\007\010\011\014\015\012\013\016\017" + .charAt(op); + } + + /** Do one the the 16 possible bit-wise operations of two BigIntegers. */ + private static BigInteger bitOp(int op, BigInteger x, BigInteger y) + { + switch (op) + { + case 0: return ZERO; + case 1: return x.and(y); + case 3: return x; + case 5: return y; + case 15: return make(-1); + } + BigInteger result = new BigInteger(); + setBitOp(result, op, x, y); + return result.canonicalize(); + } + + /** Do one the the 16 possible bit-wise operations of two BigIntegers. */ + private static void setBitOp(BigInteger result, int op, + BigInteger x, BigInteger y) + { + if (y.words == null) ; + else if (x.words == null || x.ival < y.ival) + { + BigInteger temp = x; x = y; y = temp; + op = swappedOp(op); + } + int xi; + int yi; + int xlen, ylen; + if (y.words == null) + { + yi = y.ival; + ylen = 1; + } + else + { + yi = y.words[0]; + ylen = y.ival; + } + if (x.words == null) + { + xi = x.ival; + xlen = 1; + } + else + { + xi = x.words[0]; + xlen = x.ival; + } + if (xlen > 1) + result.realloc(xlen); + int[] w = result.words; + int i = 0; + // Code for how to handle the remainder of x. + // 0: Truncate to length of y. + // 1: Copy rest of x. + // 2: Invert rest of x. + int finish = 0; + int ni; + switch (op) + { + case 0: // clr + ni = 0; + break; + case 1: // and + for (;;) + { + ni = xi & yi; + if (i+1 >= ylen) break; + w[i++] = ni; xi = x.words[i]; yi = y.words[i]; + } + if (yi < 0) finish = 1; + break; + case 2: // andc2 + for (;;) + { + ni = xi & ~yi; + if (i+1 >= ylen) break; + w[i++] = ni; xi = x.words[i]; yi = y.words[i]; + } + if (yi >= 0) finish = 1; + break; + case 3: // copy x + ni = xi; + finish = 1; // Copy rest + break; + case 4: // andc1 + for (;;) + { + ni = ~xi & yi; + if (i+1 >= ylen) break; + w[i++] = ni; xi = x.words[i]; yi = y.words[i]; + } + if (yi < 0) finish = 2; + break; + case 5: // copy y + for (;;) + { + ni = yi; + if (i+1 >= ylen) break; + w[i++] = ni; xi = x.words[i]; yi = y.words[i]; + } + break; + case 6: // xor + for (;;) + { + ni = xi ^ yi; + if (i+1 >= ylen) break; + w[i++] = ni; xi = x.words[i]; yi = y.words[i]; + } + finish = yi < 0 ? 2 : 1; + break; + case 7: // ior + for (;;) + { + ni = xi | yi; + if (i+1 >= ylen) break; + w[i++] = ni; xi = x.words[i]; yi = y.words[i]; + } + if (yi >= 0) finish = 1; + break; + case 8: // nor + for (;;) + { + ni = ~(xi | yi); + if (i+1 >= ylen) break; + w[i++] = ni; xi = x.words[i]; yi = y.words[i]; + } + if (yi >= 0) finish = 2; + break; + case 9: // eqv [exclusive nor] + for (;;) + { + ni = ~(xi ^ yi); + if (i+1 >= ylen) break; + w[i++] = ni; xi = x.words[i]; yi = y.words[i]; + } + finish = yi >= 0 ? 2 : 1; + break; + case 10: // c2 + for (;;) + { + ni = ~yi; + if (i+1 >= ylen) break; + w[i++] = ni; xi = x.words[i]; yi = y.words[i]; + } + break; + case 11: // orc2 + for (;;) + { + ni = xi | ~yi; + if (i+1 >= ylen) break; + w[i++] = ni; xi = x.words[i]; yi = y.words[i]; + } + if (yi < 0) finish = 1; + break; + case 12: // c1 + ni = ~xi; + finish = 2; + break; + case 13: // orc1 + for (;;) + { + ni = ~xi | yi; + if (i+1 >= ylen) break; + w[i++] = ni; xi = x.words[i]; yi = y.words[i]; + } + if (yi >= 0) finish = 2; + break; + case 14: // nand + for (;;) + { + ni = ~(xi & yi); + if (i+1 >= ylen) break; + w[i++] = ni; xi = x.words[i]; yi = y.words[i]; + } + if (yi < 0) finish = 2; + break; + default: + case 15: // set + ni = -1; + break; + } + // Here i==ylen-1; w[0]..w[i-1] have the correct result; + // and ni contains the correct result for w[i+1]. + if (i+1 == xlen) + finish = 0; + switch (finish) + { + case 0: + if (i == 0 && w == null) + { + result.ival = ni; + return; + } + w[i++] = ni; + break; + case 1: w[i] = ni; while (++i < xlen) w[i] = x.words[i]; break; + case 2: w[i] = ni; while (++i < xlen) w[i] = ~x.words[i]; break; + } + result.ival = i; + } + + /** Return the logical (bit-wise) "and" of a BigInteger and an int. */ + private static BigInteger and(BigInteger x, int y) + { + if (x.words == null) + return BigInteger.make(x.ival & y); + if (y >= 0) + return BigInteger.make(x.words[0] & y); + int len = x.ival; + int[] words = new int[len]; + words[0] = x.words[0] & y; + while (--len > 0) + words[len] = x.words[len]; + return BigInteger.make(words, x.ival); + } + + /** Return the logical (bit-wise) "and" of two BigIntegers. */ + public BigInteger and(BigInteger y) + { + if (y.words == null) + return and(this, y.ival); + else if (words == null) + return and(y, ival); + + BigInteger x = this; + if (ival < y.ival) + { + BigInteger temp = this; x = y; y = temp; + } + int i; + int len = y.isNegative() ? x.ival : y.ival; + int[] words = new int[len]; + for (i = 0; i < y.ival; i++) + words[i] = x.words[i] & y.words[i]; + for ( ; i < len; i++) + words[i] = x.words[i]; + return BigInteger.make(words, len); + } + + /** Return the logical (bit-wise) "(inclusive) or" of two BigIntegers. */ + public BigInteger or(BigInteger y) + { + return bitOp(7, this, y); + } + + /** Return the logical (bit-wise) "exclusive or" of two BigIntegers. */ + public BigInteger xor(BigInteger y) + { + return bitOp(6, this, y); + } + + /** Return the logical (bit-wise) negation of a BigInteger. */ + public BigInteger not() + { + return bitOp(12, this, ZERO); + } + + public BigInteger andNot(BigInteger val) + { + return and(val.not()); + } + + public BigInteger clearBit(int n) + { + if (n < 0) + throw new ArithmeticException(); + + return and(ONE.shiftLeft(n).not()); + } + + public BigInteger setBit(int n) + { + if (n < 0) + throw new ArithmeticException(); + + return or(ONE.shiftLeft(n)); + } + + public boolean testBit(int n) + { + if (n < 0) + throw new ArithmeticException(); + + return !and(ONE.shiftLeft(n)).isZero(); + } + + public BigInteger flipBit(int n) + { + if (n < 0) + throw new ArithmeticException(); + + return xor(ONE.shiftLeft(n)); + } + + public int getLowestSetBit() + { + if (isZero()) + return -1; + + if (words == null) + return MPN.findLowestBit(ival); + else + return MPN.findLowestBit(words); + } + + // bit4count[I] is number of '1' bits in I. + private static final byte[] bit4_count = { 0, 1, 1, 2, 1, 2, 2, 3, + 1, 2, 2, 3, 2, 3, 3, 4}; + + private static int bitCount(int i) + { + int count = 0; + while (i != 0) + { + count += bit4_count[i & 15]; + i >>>= 4; + } + return count; + } + + private static int bitCount(int[] x, int len) + { + int count = 0; + while (--len >= 0) + count += bitCount(x[len]); + return count; + } + + /** Count one bits in a BigInteger. + * If argument is negative, count zero bits instead. */ + public int bitCount() + { + int i, x_len; + int[] x_words = words; + if (x_words == null) + { + x_len = 1; + i = bitCount(ival); + } + else + { + x_len = ival; + i = bitCount(x_words, x_len); + } + return isNegative() ? x_len * 32 - i : i; + } + + private void readObject(ObjectInputStream s) + throws IOException, ClassNotFoundException + { + s.defaultReadObject(); + words = byteArrayToIntArray(magnitude, signum < 0 ? -1 : 0); + BigInteger result = make(words, words.length); + this.ival = result.ival; + this.words = result.words; + } + + private void writeObject(ObjectOutputStream s) + throws IOException, ClassNotFoundException + { + signum = signum(); + magnitude = toByteArray(); + s.defaultWriteObject(); } } -- cgit v1.2.1