mpn.java

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/* gnu.java.math.MPN
   Copyright (C) 1999, 2000, 2001 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., 59 Temple Place, Suite 330, Boston, MA
02111-1307 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 <[e-mail]>.

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;
	  }