Makefile.am: Added MPN.java and BigInteger.java.

	* Makefile.am: Added MPN.java and BigInteger.java.
	* Makefile.in: Rebuilt.
	* gnu/gcj/math/MPN.java: New file.
	* java/math/BigInteger.java: New file.

From-SVN: r31794

1 files changed, 736 insertions, 0 deletions

diff --git a/libjava/gnu/gcj/math/MPN.java b/libjava/gnu/gcj/math/MPN.java
new file mode 100644
index 0000000..5bbabfd
--- /dev/null
+++ b/libjava/gnu/gcj/math/MPN.java
@@ -0,0 +1,736 @@
+/* Copyright (C) 1999, 2000  Red Hat, Inc.
+
+   This file is part of libgcj.
+
+This software is copyrighted work licensed under the terms of the
+Libgcj License.  Please consult the file "LIBGCJ_LICENSE" for
+details.  */
+
+// Included from Kawa 1.6.62 with permission of the author,
+// Per Bothner <per@bothner.com>.
+
+package gnu.gcj.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<y, x==y, or x>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.
+   * @result -1, 0, or 1 depending on if x<y, x==y, or x>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 < count < 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;
+  }
+
+  /** 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] >> 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]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.
+   * OK if count > 32 (but must be >= 0).
+   */
+  public static void rshift (int[] dest, int[] x, int len, int count)
+  {
+    int word_count = count >> 5;
+    count &= 31;
+    rshift (dest, x, word_count, len, count);
+    while (word_count < len)
+      dest[word_count++] = 0;
+  }
+
+  /* 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 < count < 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&(1<<i). Assumes word!=0. */
+
+  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 & (1<<i). Assumes there is such an i. */
+
+  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.rshift (x, x, initShiftWords, len, initShiftBits);
+    MPN.rshift (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==IntNum.wordsNeeded(words,len) */
+  public static int intLength (int[] words, int len)
+  {
+    len--;
+    return intLength (words[len]) + 32 * len;
+  }
+
+  /* DEBUGGING:
+  public static void dprint (IntNum 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(')');
+  }
+  */
+}