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gcc/libjava/classpath/gnu/java/math/MPN.java

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/* gnu.java.math.MPN
Copyright (C) 1999, 2000, 2001, 2004 Free Software Foundation, Inc.
This file is part of GNU Classpath.
GNU Classpath is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.
GNU Classpath is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received a copy of the GNU General Public License
along with GNU Classpath; see the file COPYING. If not, write to the
Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301 USA.
Linking this library statically or dynamically with other modules is
making a combined work based on this library. Thus, the terms and
conditions of the GNU General Public License cover the whole
combination.
As a special exception, the copyright holders of this library give you
permission to link this library with independent modules to produce an
executable, regardless of the license terms of these independent
modules, and to copy and distribute the resulting executable under
terms of your choice, provided that you also meet, for each linked
independent module, the terms and conditions of the license of that
module. An independent module is a module which is not derived from
or based on this library. If you modify this library, you may extend
this exception to your version of the library, but you are not
obligated to do so. If you do not wish to do so, delete this
exception statement from your version. */
// Included from Kawa 1.6.62 with permission of the author,
// Per Bothner <per@bothner.com>.
package gnu.java.math;
/** This contains various low-level routines for unsigned bigints.
* The interfaces match the mpn interfaces in gmp,
* so it should be easy to replace them with fast native functions
* that are trivial wrappers around the mpn_ functions in gmp
* (at least on platforms that use 32-bit "limbs").
*/
public class MPN
{
/** Add x[0:size-1] and y, and write the size least
* significant words of the result to dest.
* Return carry, either 0 or 1.
* All values are unsigned.
* This is basically the same as gmp's mpn_add_1. */
public static int add_1 (int[] dest, int[] x, int size, int y)
{
long carry = (long) y & 0xffffffffL;
for (int i = 0; i < size; i++)
{
carry += ((long) x[i] & 0xffffffffL);
dest[i] = (int) carry;
carry >>= 32;
}
return (int) carry;
}
/** Add x[0:len-1] and y[0:len-1] and write the len least
* significant words of the result to dest[0:len-1].
* All words are treated as unsigned.
* @return the carry, either 0 or 1
* This function is basically the same as gmp's mpn_add_n.
*/
public static int add_n (int dest[], int[] x, int[] y, int len)
{
long carry = 0;
for (int i = 0; i < len; i++)
{
carry += ((long) x[i] & 0xffffffffL)
+ ((long) y[i] & 0xffffffffL);
dest[i] = (int) carry;
carry >>>= 32;
}
return (int) carry;
}
/** Subtract Y[0:size-1] from X[0:size-1], and write
* the size least significant words of the result to dest[0:size-1].
* Return borrow, either 0 or 1.
* This is basically the same as gmp's mpn_sub_n function.
*/
public static int sub_n (int[] dest, int[] X, int[] Y, int size)
{
int cy = 0;
for (int i = 0; i < size; i++)
{
int y = Y[i];
int x = X[i];
y += cy; /* add previous carry to subtrahend */
// Invert the high-order bit, because: (unsigned) X > (unsigned) Y
// iff: (int) (X^0x80000000) > (int) (Y^0x80000000).
cy = (y^0x80000000) < (cy^0x80000000) ? 1 : 0;
y = x - y;
cy += (y^0x80000000) > (x ^ 0x80000000) ? 1 : 0;
dest[i] = y;
}
return cy;
}
/** Multiply x[0:len-1] by y, and write the len least
* significant words of the product to dest[0:len-1].
* Return the most significant word of the product.
* All values are treated as if they were unsigned
* (i.e. masked with 0xffffffffL).
* OK if dest==x (not sure if this is guaranteed for mpn_mul_1).
* This function is basically the same as gmp's mpn_mul_1.
*/
public static int mul_1 (int[] dest, int[] x, int len, int y)
{
long yword = (long) y & 0xffffffffL;
long carry = 0;
for (int j = 0; j < len; j++)
{
carry += ((long) x[j] & 0xffffffffL) * yword;
dest[j] = (int) carry;
carry >>>= 32;
}
return (int) carry;
}
/**
* Multiply x[0:xlen-1] and y[0:ylen-1], and
* write the result to dest[0:xlen+ylen-1].
* The destination has to have space for xlen+ylen words,
* even if the result might be one limb smaller.
* This function requires that xlen >= ylen.
* The destination must be distinct from either input operands.
* All operands are unsigned.
* This function is basically the same gmp's mpn_mul. */
public static void mul (int[] dest,
int[] x, int xlen,
int[] y, int ylen)
{
dest[xlen] = MPN.mul_1 (dest, x, xlen, y[0]);
for (int i = 1; i < ylen; i++)
{
long yword = (long) y[i] & 0xffffffffL;
long carry = 0;
for (int j = 0; j < xlen; j++)
{
carry += ((long) x[j] & 0xffffffffL) * yword
+ ((long) dest[i+j] & 0xffffffffL);
dest[i+j] = (int) carry;
carry >>>= 32;
}
dest[i+xlen] = (int) carry;
}
}
/* Divide (unsigned long) N by (unsigned int) D.
* Returns (remainder << 32)+(unsigned int)(quotient).
* Assumes (unsigned int)(N>>32) < (unsigned int)D.
* Code transcribed from gmp-2.0's mpn_udiv_w_sdiv function.
*/
public static long udiv_qrnnd (long N, int D)
{
long q, r;
long a1 = N >>> 32;
long a0 = N & 0xffffffffL;
if (D >= 0)
{
if (a1 < ((D - a1 - (a0 >>> 31)) & 0xffffffffL))
{
/* dividend, divisor, and quotient are nonnegative */
q = N / D;
r = N % D;
}
else
{
/* Compute c1*2^32 + c0 = a1*2^32 + a0 - 2^31*d */
long c = N - ((long) D << 31);
/* Divide (c1*2^32 + c0) by d */
q = c / D;
r = c % D;
/* Add 2^31 to quotient */
q += 1 << 31;
}
}
else
{
long b1 = D >>> 1; /* d/2, between 2^30 and 2^31 - 1 */
//long c1 = (a1 >> 1); /* A/2 */
//int c0 = (a1 << 31) + (a0 >> 1);
long c = N >>> 1;
if (a1 < b1 || (a1 >> 1) < b1)
{
if (a1 < b1)
{
q = c / b1;
r = c % b1;
}
else /* c1 < b1, so 2^31 <= (A/2)/b1 < 2^32 */
{
c = ~(c - (b1 << 32));
q = c / b1; /* (A/2) / (d/2) */
r = c % b1;
q = (~q) & 0xffffffffL; /* (A/2)/b1 */
r = (b1 - 1) - r; /* r < b1 => new r >= 0 */
}
r = 2 * r + (a0 & 1);
if ((D & 1) != 0)
{
if (r >= q) {
r = r - q;
} else if (q - r <= ((long) D & 0xffffffffL)) {
r = r - q + D;
q -= 1;
} else {
r = r - q + D + D;
q -= 2;
}
}
}
else /* Implies c1 = b1 */
{ /* Hence a1 = d - 1 = 2*b1 - 1 */
if (a0 >= ((long)(-D) & 0xffffffffL))
{
q = -1;
r = a0 + D;
}
else
{
q = -2;
r = a0 + D + D;
}
}
}
return (r << 32) | (q & 0xFFFFFFFFl);
}
/** Divide divident[0:len-1] by (unsigned int)divisor.
* Write result into quotient[0:len-1.
* Return the one-word (unsigned) remainder.
* OK for quotient==dividend.
*/
public static int divmod_1 (int[] quotient, int[] dividend,
int len, int divisor)
{
int i = len - 1;
long r = dividend[i];
if ((r & 0xffffffffL) >= ((long)divisor & 0xffffffffL))
r = 0;
else
{
quotient[i--] = 0;
r <<= 32;
}
for (; i >= 0; i--)
{
int n0 = dividend[i];
r = (r & ~0xffffffffL) | (n0 & 0xffffffffL);
r = udiv_qrnnd (r, divisor);
quotient[i] = (int) r;
}
return (int)(r >> 32);
}
/* Subtract x[0:len-1]*y from dest[offset:offset+len-1].
* All values are treated as if unsigned.
* @return the most significant word of
* the product, minus borrow-out from the subtraction.
*/
public static int submul_1 (int[] dest, int offset, int[] x, int len, int y)
{
long yl = (long) y & 0xffffffffL;
int carry = 0;
int j = 0;
do
{
long prod = ((long) x[j] & 0xffffffffL) * yl;
int prod_low = (int) prod;
int prod_high = (int) (prod >> 32);
prod_low += carry;
// Invert the high-order bit, because: (unsigned) X > (unsigned) Y
// iff: (int) (X^0x80000000) > (int) (Y^0x80000000).
carry = ((prod_low ^ 0x80000000) < (carry ^ 0x80000000) ? 1 : 0)
+ prod_high;
int x_j = dest[offset+j];
prod_low = x_j - prod_low;
if ((prod_low ^ 0x80000000) > (x_j ^ 0x80000000))
carry++;
dest[offset+j] = prod_low;
}
while (++j < len);
return carry;
}
/** Divide zds[0:nx] by y[0:ny-1].
* The remainder ends up in zds[0:ny-1].
* The quotient ends up in zds[ny:nx].
* Assumes: nx>ny.
* (int)y[ny-1] < 0 (i.e. most significant bit set)
*/
public static void divide (int[] zds, int nx, int[] y, int ny)
{
// This is basically Knuth's formulation of the classical algorithm,
// but translated from in scm_divbigbig in Jaffar's SCM implementation.
// Correspondance with Knuth's notation:
// Knuth's u[0:m+n] == zds[nx:0].
// Knuth's v[1:n] == y[ny-1:0]
// Knuth's n == ny.
// Knuth's m == nx-ny.
// Our nx == Knuth's m+n.
// Could be re-implemented using gmp's mpn_divrem:
// zds[nx] = mpn_divrem (&zds[ny], 0, zds, nx, y, ny).
int j = nx;
do
{ // loop over digits of quotient
// Knuth's j == our nx-j.
// Knuth's u[j:j+n] == our zds[j:j-ny].
int qhat; // treated as unsigned
if (zds[j]==y[ny-1])
qhat = -1; // 0xffffffff
else
{
long w = (((long)(zds[j])) << 32) + ((long)zds[j-1] & 0xffffffffL);
qhat = (int) udiv_qrnnd (w, y[ny-1]);
}
if (qhat != 0)
{
int borrow = submul_1 (zds, j - ny, y, ny, qhat);
int save = zds[j];
long num = ((long)save&0xffffffffL) - ((long)borrow&0xffffffffL);
while (num != 0)
{
qhat--;
long carry = 0;
for (int i = 0; i < ny; i++)
{
carry += ((long) zds[j-ny+i] & 0xffffffffL)
+ ((long) y[i] & 0xffffffffL);
zds[j-ny+i] = (int) carry;
carry >>>= 32;
}
zds[j] += carry;
num = carry - 1;
}
}
zds[j] = qhat;
} while (--j >= ny);
}
/** Number of digits in the conversion base that always fits in a word.
* For example, for base 10 this is 9, since 10**9 is the
* largest number that fits into a words (assuming 32-bit words).
* This is the same as gmp's __mp_bases[radix].chars_per_limb.
* @param radix the base
* @return number of digits */
public static int chars_per_word (int radix)
{
if (radix < 10)
{
if (radix < 8)
{
if (radix <= 2)
return 32;
else if (radix == 3)
return 20;
else if (radix == 4)
return 16;
else
return 18 - radix;
}
else
return 10;
}
else if (radix < 12)
return 9;
else if (radix <= 16)
return 8;
else if (radix <= 23)
return 7;
else if (radix <= 40)
return 6;
// The following are conservative, but we don't care.
else if (radix <= 256)
return 4;
else
return 1;
}
/** Count the number of leading zero bits in an int. */
public static int count_leading_zeros (int i)
{
if (i == 0)
return 32;
int count = 0;
for (int k = 16; k > 0; k = k >> 1) {
int j = i >>> k;
if (j == 0)
count += k;
else
i = j;
}
return count;
}
public static int set_str (int dest[], byte[] str, int str_len, int base)
{
int size = 0;
if ((base & (base - 1)) == 0)
{
// The base is a power of 2. Read the input string from
// least to most significant character/digit. */
int next_bitpos = 0;
int bits_per_indigit = 0;
for (int i = base; (i >>= 1) != 0; ) bits_per_indigit++;
int res_digit = 0;
for (int i = str_len; --i >= 0; )
{
int inp_digit = str[i];
res_digit |= inp_digit << next_bitpos;
next_bitpos += bits_per_indigit;
if (next_bitpos >= 32)
{
dest[size++] = res_digit;
next_bitpos -= 32;
res_digit = inp_digit >> (bits_per_indigit - next_bitpos);
}
}
if (res_digit != 0)
dest[size++] = res_digit;
}
else
{
// General case. The base is not a power of 2.
int indigits_per_limb = MPN.chars_per_word (base);
int str_pos = 0;
while (str_pos < str_len)
{
int chunk = str_len - str_pos;
if (chunk > indigits_per_limb)
chunk = indigits_per_limb;
int res_digit = str[str_pos++];
int big_base = base;
while (--chunk > 0)
{
res_digit = res_digit * base + str[str_pos++];
big_base *= base;
}
int cy_limb;
if (size == 0)
cy_limb = res_digit;
else
{
cy_limb = MPN.mul_1 (dest, dest, size, big_base);
cy_limb += MPN.add_1 (dest, dest, size, res_digit);
}
if (cy_limb != 0)
dest[size++] = cy_limb;
}
}
return size;
}
/** Compare x[0:size-1] with y[0:size-1], treating them as unsigned integers.
* @result -1, 0, or 1 depending on if x&lt;y, x==y, or x&gt;y.
* This is basically the same as gmp's mpn_cmp function.
*/
public static int cmp (int[] x, int[] y, int size)
{
while (--size >= 0)
{
int x_word = x[size];
int y_word = y[size];
if (x_word != y_word)
{
// Invert the high-order bit, because:
// (unsigned) X > (unsigned) Y iff
// (int) (X^0x80000000) > (int) (Y^0x80000000).
return (x_word ^ 0x80000000) > (y_word ^0x80000000) ? 1 : -1;
}
}
return 0;
}
/**
* Compare x[0:xlen-1] with y[0:ylen-1], treating them as unsigned integers.
*
* @return -1, 0, or 1 depending on if x&lt;y, x==y, or x&gt;y.
*/
public static int cmp (int[] x, int xlen, int[] y, int ylen)
{
return xlen > ylen ? 1 : xlen < ylen ? -1 : cmp (x, y, xlen);
}
/**
* Shift x[x_start:x_start+len-1] count bits to the "right"
* (i.e. divide by 2**count).
* Store the len least significant words of the result at dest.
* The bits shifted out to the right are returned.
* OK if dest==x.
* Assumes: 0 &lt; count &lt; 32
*/
public static int rshift (int[] dest, int[] x, int x_start,
int len, int count)
{
int count_2 = 32 - count;
int low_word = x[x_start];
int retval = low_word << count_2;
int i = 1;
for (; i < len; i++)
{
int high_word = x[x_start+i];
dest[i-1] = (low_word >>> count) | (high_word << count_2);
low_word = high_word;
}
dest[i-1] = low_word >>> count;
return retval;
}
/**
* Shift x[x_start:x_start+len-1] count bits to the "right"
* (i.e. divide by 2**count).
* Store the len least significant words of the result at dest.
* OK if dest==x.
* Assumes: 0 &lt;= count &lt; 32
* Same as rshift, but handles count==0 (and has no return value).
*/
public static void rshift0 (int[] dest, int[] x, int x_start,
int len, int count)
{
if (count > 0)
rshift(dest, x, x_start, len, count);
else
for (int i = 0; i < len; i++)
dest[i] = x[i + x_start];
}
/** Return the long-truncated value of right shifting.
* @param x a two's-complement "bignum"
* @param len the number of significant words in x
* @param count the shift count
* @return (long)(x[0..len-1] &gt;&gt; count).
*/
public static long rshift_long (int[] x, int len, int count)
{
int wordno = count >> 5;
count &= 31;
int sign = x[len-1] < 0 ? -1 : 0;
int w0 = wordno >= len ? sign : x[wordno];
wordno++;
int w1 = wordno >= len ? sign : x[wordno];
if (count != 0)
{
wordno++;
int w2 = wordno >= len ? sign : x[wordno];
w0 = (w0 >>> count) | (w1 << (32-count));
w1 = (w1 >>> count) | (w2 << (32-count));
}
return ((long)w1 << 32) | ((long)w0 & 0xffffffffL);
}
/* Shift x[0:len-1] left by count bits, and store the len least
* significant words of the result in dest[d_offset:d_offset+len-1].
* Return the bits shifted out from the most significant digit.
* Assumes 0 &lt; count &lt; 32.
* OK if dest==x.
*/
public static int lshift (int[] dest, int d_offset,
int[] x, int len, int count)
{
int count_2 = 32 - count;
int i = len - 1;
int high_word = x[i];
int retval = high_word >>> count_2;
d_offset++;
while (--i >= 0)
{
int low_word = x[i];
dest[d_offset+i] = (high_word << count) | (low_word >>> count_2);
high_word = low_word;
}
dest[d_offset+i] = high_word << count;
return retval;
}
/** Return least i such that word &amp; (1&lt;&lt;i). Assumes word!=0. */
public static int findLowestBit (int word)
{
int i = 0;
while ((word & 0xF) == 0)
{
word >>= 4;
i += 4;
}
if ((word & 3) == 0)
{
word >>= 2;
i += 2;
}
if ((word & 1) == 0)
i += 1;
return i;
}
/** Return least i such that words &amp; (1&lt;&lt;i). Assumes there is such an i. */
public static int findLowestBit (int[] words)
{
for (int i = 0; ; i++)
{
if (words[i] != 0)
return 32 * i + findLowestBit (words[i]);
}
}
/** Calculate Greatest Common Divisior of x[0:len-1] and y[0:len-1].
* Assumes both arguments are non-zero.
* Leaves result in x, and returns len of result.
* Also destroys y (actually sets it to a copy of the result). */
public static int gcd (int[] x, int[] y, int len)
{
int i, word;
// Find sh such that both x and y are divisible by 2**sh.
for (i = 0; ; i++)
{
word = x[i] | y[i];
if (word != 0)
{
// Must terminate, since x and y are non-zero.
break;
}
}
int initShiftWords = i;
int initShiftBits = findLowestBit (word);
// Logically: sh = initShiftWords * 32 + initShiftBits
// Temporarily devide both x and y by 2**sh.
len -= initShiftWords;
MPN.rshift0 (x, x, initShiftWords, len, initShiftBits);
MPN.rshift0 (y, y, initShiftWords, len, initShiftBits);
int[] odd_arg; /* One of x or y which is odd. */
int[] other_arg; /* The other one can be even or odd. */
if ((x[0] & 1) != 0)
{
odd_arg = x;
other_arg = y;
}
else
{
odd_arg = y;
other_arg = x;
}
for (;;)
{
// Shift other_arg until it is odd; this doesn't
// affect the gcd, since we divide by 2**k, which does not
// divide odd_arg.
for (i = 0; other_arg[i] == 0; ) i++;
if (i > 0)
{
int j;
for (j = 0; j < len-i; j++)
other_arg[j] = other_arg[j+i];
for ( ; j < len; j++)
other_arg[j] = 0;
}
i = findLowestBit(other_arg[0]);
if (i > 0)
MPN.rshift (other_arg, other_arg, 0, len, i);
// Now both odd_arg and other_arg are odd.
// Subtract the smaller from the larger.
// This does not change the result, since gcd(a-b,b)==gcd(a,b).
i = MPN.cmp(odd_arg, other_arg, len);
if (i == 0)
break;
if (i > 0)
{ // odd_arg > other_arg
MPN.sub_n (odd_arg, odd_arg, other_arg, len);
// Now odd_arg is even, so swap with other_arg;
int[] tmp = odd_arg; odd_arg = other_arg; other_arg = tmp;
}
else
{ // other_arg > odd_arg
MPN.sub_n (other_arg, other_arg, odd_arg, len);
}
while (odd_arg[len-1] == 0 && other_arg[len-1] == 0)
len--;
}
if (initShiftWords + initShiftBits > 0)
{
if (initShiftBits > 0)
{
int sh_out = MPN.lshift (x, initShiftWords, x, len, initShiftBits);
if (sh_out != 0)
x[(len++)+initShiftWords] = sh_out;
}
else
{
for (i = len; --i >= 0;)
x[i+initShiftWords] = x[i];
}
for (i = initShiftWords; --i >= 0; )
x[i] = 0;
len += initShiftWords;
}
return len;
}
public static int intLength (int i)
{
return 32 - count_leading_zeros (i < 0 ? ~i : i);
}
/** Calcaulte the Common Lisp "integer-length" function.
* Assumes input is canonicalized: len==BigInteger.wordsNeeded(words,len) */
public static int intLength (int[] words, int len)
{
len--;
return intLength (words[len]) + 32 * len;
}
/* DEBUGGING:
public static void dprint (BigInteger x)
{
if (x.words == null)
System.err.print(Long.toString((long) x.ival & 0xffffffffL, 16));
else
dprint (System.err, x.words, x.ival);
}
public static void dprint (int[] x) { dprint (System.err, x, x.length); }
public static void dprint (int[] x, int len) { dprint (System.err, x, len); }
public static void dprint (java.io.PrintStream ps, int[] x, int len)
{
ps.print('(');
for (int i = 0; i < len; i++)
{
if (i > 0)
ps.print (' ');
ps.print ("#x" + Long.toString ((long) x[i] & 0xffffffffL, 16));
}
ps.print(')');
}
*/
}
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