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769 lines
20 KiB
Java
769 lines
20 KiB
Java
/* gnu.java.math.MPN
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Copyright (C) 1999, 2000, 2001 Free Software Foundation, Inc.
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This file is part of GNU Classpath.
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GNU Classpath is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2, or (at your option)
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any later version.
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GNU Classpath is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with GNU Classpath; see the file COPYING. If not, write to the
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Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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02111-1307 USA.
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Linking this library statically or dynamically with other modules is
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making a combined work based on this library. Thus, the terms and
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conditions of the GNU General Public License cover the whole
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combination.
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As a special exception, the copyright holders of this library give you
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permission to link this library with independent modules to produce an
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executable, regardless of the license terms of these independent
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modules, and to copy and distribute the resulting executable under
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terms of your choice, provided that you also meet, for each linked
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independent module, the terms and conditions of the license of that
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module. An independent module is a module which is not derived from
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or based on this library. If you modify this library, you may extend
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this exception to your version of the library, but you are not
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obligated to do so. If you do not wish to do so, delete this
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exception statement from your version. */
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// Included from Kawa 1.6.62 with permission of the author,
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// Per Bothner <per@bothner.com>.
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package gnu.java.math;
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/** This contains various low-level routines for unsigned bigints.
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* The interfaces match the mpn interfaces in gmp,
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* so it should be easy to replace them with fast native functions
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* that are trivial wrappers around the mpn_ functions in gmp
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* (at least on platforms that use 32-bit "limbs").
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*/
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public class MPN
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{
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/** Add x[0:size-1] and y, and write the size least
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* significant words of the result to dest.
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* Return carry, either 0 or 1.
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* All values are unsigned.
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* This is basically the same as gmp's mpn_add_1. */
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public static int add_1 (int[] dest, int[] x, int size, int y)
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{
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long carry = (long) y & 0xffffffffL;
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for (int i = 0; i < size; i++)
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{
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carry += ((long) x[i] & 0xffffffffL);
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dest[i] = (int) carry;
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carry >>= 32;
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}
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return (int) carry;
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}
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/** Add x[0:len-1] and y[0:len-1] and write the len least
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* significant words of the result to dest[0:len-1].
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* All words are treated as unsigned.
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* @return the carry, either 0 or 1
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* This function is basically the same as gmp's mpn_add_n.
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*/
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public static int add_n (int dest[], int[] x, int[] y, int len)
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{
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long carry = 0;
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for (int i = 0; i < len; i++)
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{
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carry += ((long) x[i] & 0xffffffffL)
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+ ((long) y[i] & 0xffffffffL);
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dest[i] = (int) carry;
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carry >>>= 32;
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}
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return (int) carry;
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}
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/** Subtract Y[0:size-1] from X[0:size-1], and write
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* the size least significant words of the result to dest[0:size-1].
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* Return borrow, either 0 or 1.
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* This is basically the same as gmp's mpn_sub_n function.
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*/
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public static int sub_n (int[] dest, int[] X, int[] Y, int size)
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{
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int cy = 0;
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for (int i = 0; i < size; i++)
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{
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int y = Y[i];
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int x = X[i];
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y += cy; /* add previous carry to subtrahend */
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// Invert the high-order bit, because: (unsigned) X > (unsigned) Y
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// iff: (int) (X^0x80000000) > (int) (Y^0x80000000).
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cy = (y^0x80000000) < (cy^0x80000000) ? 1 : 0;
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y = x - y;
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cy += (y^0x80000000) > (x ^ 0x80000000) ? 1 : 0;
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dest[i] = y;
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}
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return cy;
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}
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/** Multiply x[0:len-1] by y, and write the len least
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* significant words of the product to dest[0:len-1].
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* Return the most significant word of the product.
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* All values are treated as if they were unsigned
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* (i.e. masked with 0xffffffffL).
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* OK if dest==x (not sure if this is guaranteed for mpn_mul_1).
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* This function is basically the same as gmp's mpn_mul_1.
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*/
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public static int mul_1 (int[] dest, int[] x, int len, int y)
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{
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long yword = (long) y & 0xffffffffL;
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long carry = 0;
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for (int j = 0; j < len; j++)
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{
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carry += ((long) x[j] & 0xffffffffL) * yword;
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dest[j] = (int) carry;
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carry >>>= 32;
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}
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return (int) carry;
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}
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/**
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* Multiply x[0:xlen-1] and y[0:ylen-1], and
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* write the result to dest[0:xlen+ylen-1].
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* The destination has to have space for xlen+ylen words,
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* even if the result might be one limb smaller.
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* This function requires that xlen >= ylen.
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* The destination must be distinct from either input operands.
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* All operands are unsigned.
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* This function is basically the same gmp's mpn_mul. */
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public static void mul (int[] dest,
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int[] x, int xlen,
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int[] y, int ylen)
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{
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dest[xlen] = MPN.mul_1 (dest, x, xlen, y[0]);
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for (int i = 1; i < ylen; i++)
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{
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long yword = (long) y[i] & 0xffffffffL;
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long carry = 0;
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for (int j = 0; j < xlen; j++)
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{
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carry += ((long) x[j] & 0xffffffffL) * yword
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+ ((long) dest[i+j] & 0xffffffffL);
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dest[i+j] = (int) carry;
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carry >>>= 32;
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}
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dest[i+xlen] = (int) carry;
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}
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}
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/* Divide (unsigned long) N by (unsigned int) D.
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* Returns (remainder << 32)+(unsigned int)(quotient).
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* Assumes (unsigned int)(N>>32) < (unsigned int)D.
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* Code transcribed from gmp-2.0's mpn_udiv_w_sdiv function.
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*/
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public static long udiv_qrnnd (long N, int D)
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{
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long q, r;
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long a1 = N >>> 32;
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long a0 = N & 0xffffffffL;
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if (D >= 0)
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{
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if (a1 < ((D - a1 - (a0 >>> 31)) & 0xffffffffL))
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{
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/* dividend, divisor, and quotient are nonnegative */
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q = N / D;
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r = N % D;
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}
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else
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{
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/* Compute c1*2^32 + c0 = a1*2^32 + a0 - 2^31*d */
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long c = N - ((long) D << 31);
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/* Divide (c1*2^32 + c0) by d */
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q = c / D;
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r = c % D;
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/* Add 2^31 to quotient */
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q += 1 << 31;
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}
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}
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else
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{
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long b1 = D >>> 1; /* d/2, between 2^30 and 2^31 - 1 */
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//long c1 = (a1 >> 1); /* A/2 */
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//int c0 = (a1 << 31) + (a0 >> 1);
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long c = N >>> 1;
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if (a1 < b1 || (a1 >> 1) < b1)
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{
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if (a1 < b1)
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{
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q = c / b1;
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r = c % b1;
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}
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else /* c1 < b1, so 2^31 <= (A/2)/b1 < 2^32 */
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{
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c = ~(c - (b1 << 32));
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q = c / b1; /* (A/2) / (d/2) */
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r = c % b1;
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q = (~q) & 0xffffffffL; /* (A/2)/b1 */
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r = (b1 - 1) - r; /* r < b1 => new r >= 0 */
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}
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r = 2 * r + (a0 & 1);
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if ((D & 1) != 0)
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{
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if (r >= q) {
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r = r - q;
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} else if (q - r <= ((long) D & 0xffffffffL)) {
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r = r - q + D;
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q -= 1;
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} else {
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r = r - q + D + D;
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q -= 2;
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}
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}
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}
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else /* Implies c1 = b1 */
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{ /* Hence a1 = d - 1 = 2*b1 - 1 */
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if (a0 >= ((long)(-D) & 0xffffffffL))
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{
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q = -1;
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r = a0 + D;
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}
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else
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{
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q = -2;
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r = a0 + D + D;
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}
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}
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}
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return (r << 32) | (q & 0xFFFFFFFFl);
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}
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/** Divide divident[0:len-1] by (unsigned int)divisor.
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* Write result into quotient[0:len-1.
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* Return the one-word (unsigned) remainder.
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* OK for quotient==dividend.
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*/
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public static int divmod_1 (int[] quotient, int[] dividend,
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int len, int divisor)
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{
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int i = len - 1;
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long r = dividend[i];
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if ((r & 0xffffffffL) >= ((long)divisor & 0xffffffffL))
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r = 0;
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else
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{
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quotient[i--] = 0;
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r <<= 32;
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}
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for (; i >= 0; i--)
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{
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int n0 = dividend[i];
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r = (r & ~0xffffffffL) | (n0 & 0xffffffffL);
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r = udiv_qrnnd (r, divisor);
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quotient[i] = (int) r;
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}
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return (int)(r >> 32);
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}
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/* Subtract x[0:len-1]*y from dest[offset:offset+len-1].
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* All values are treated as if unsigned.
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* @return the most significant word of
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* the product, minus borrow-out from the subtraction.
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*/
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public static int submul_1 (int[] dest, int offset, int[] x, int len, int y)
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{
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long yl = (long) y & 0xffffffffL;
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int carry = 0;
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int j = 0;
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do
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{
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long prod = ((long) x[j] & 0xffffffffL) * yl;
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int prod_low = (int) prod;
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int prod_high = (int) (prod >> 32);
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prod_low += carry;
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// Invert the high-order bit, because: (unsigned) X > (unsigned) Y
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// iff: (int) (X^0x80000000) > (int) (Y^0x80000000).
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carry = ((prod_low ^ 0x80000000) < (carry ^ 0x80000000) ? 1 : 0)
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+ prod_high;
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int x_j = dest[offset+j];
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prod_low = x_j - prod_low;
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if ((prod_low ^ 0x80000000) > (x_j ^ 0x80000000))
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carry++;
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dest[offset+j] = prod_low;
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}
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while (++j < len);
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return carry;
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}
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/** Divide zds[0:nx] by y[0:ny-1].
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* The remainder ends up in zds[0:ny-1].
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* The quotient ends up in zds[ny:nx].
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* Assumes: nx>ny.
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* (int)y[ny-1] < 0 (i.e. most significant bit set)
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*/
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public static void divide (int[] zds, int nx, int[] y, int ny)
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{
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// This is basically Knuth's formulation of the classical algorithm,
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// but translated from in scm_divbigbig in Jaffar's SCM implementation.
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// Correspondance with Knuth's notation:
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// Knuth's u[0:m+n] == zds[nx:0].
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// Knuth's v[1:n] == y[ny-1:0]
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// Knuth's n == ny.
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// Knuth's m == nx-ny.
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// Our nx == Knuth's m+n.
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// Could be re-implemented using gmp's mpn_divrem:
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// zds[nx] = mpn_divrem (&zds[ny], 0, zds, nx, y, ny).
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int j = nx;
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do
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{ // loop over digits of quotient
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// Knuth's j == our nx-j.
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// Knuth's u[j:j+n] == our zds[j:j-ny].
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int qhat; // treated as unsigned
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if (zds[j]==y[ny-1])
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qhat = -1; // 0xffffffff
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else
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{
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long w = (((long)(zds[j])) << 32) + ((long)zds[j-1] & 0xffffffffL);
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qhat = (int) udiv_qrnnd (w, y[ny-1]);
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}
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if (qhat != 0)
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{
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int borrow = submul_1 (zds, j - ny, y, ny, qhat);
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int save = zds[j];
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long num = ((long)save&0xffffffffL) - ((long)borrow&0xffffffffL);
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while (num != 0)
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{
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qhat--;
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long carry = 0;
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for (int i = 0; i < ny; i++)
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{
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carry += ((long) zds[j-ny+i] & 0xffffffffL)
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+ ((long) y[i] & 0xffffffffL);
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zds[j-ny+i] = (int) carry;
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carry >>>= 32;
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}
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zds[j] += carry;
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num = carry - 1;
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}
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}
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zds[j] = qhat;
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} while (--j >= ny);
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}
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/** Number of digits in the conversion base that always fits in a word.
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* For example, for base 10 this is 9, since 10**9 is the
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* largest number that fits into a words (assuming 32-bit words).
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* This is the same as gmp's __mp_bases[radix].chars_per_limb.
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* @param radix the base
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* @return number of digits */
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public static int chars_per_word (int radix)
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{
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if (radix < 10)
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{
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if (radix < 8)
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{
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if (radix <= 2)
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return 32;
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else if (radix == 3)
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return 20;
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else if (radix == 4)
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return 16;
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else
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return 18 - radix;
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}
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else
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return 10;
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}
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else if (radix < 12)
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return 9;
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else if (radix <= 16)
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return 8;
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else if (radix <= 23)
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return 7;
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else if (radix <= 40)
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return 6;
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// The following are conservative, but we don't care.
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else if (radix <= 256)
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return 4;
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else
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return 1;
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}
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/** Count the number of leading zero bits in an int. */
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public static int count_leading_zeros (int i)
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{
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if (i == 0)
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return 32;
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int count = 0;
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for (int k = 16; k > 0; k = k >> 1) {
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int j = i >>> k;
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if (j == 0)
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count += k;
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else
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i = j;
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}
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return count;
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}
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public static int set_str (int dest[], byte[] str, int str_len, int base)
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{
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int size = 0;
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if ((base & (base - 1)) == 0)
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{
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// The base is a power of 2. Read the input string from
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// least to most significant character/digit. */
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int next_bitpos = 0;
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int bits_per_indigit = 0;
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for (int i = base; (i >>= 1) != 0; ) bits_per_indigit++;
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int res_digit = 0;
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for (int i = str_len; --i >= 0; )
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{
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int inp_digit = str[i];
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res_digit |= inp_digit << next_bitpos;
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next_bitpos += bits_per_indigit;
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if (next_bitpos >= 32)
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{
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dest[size++] = res_digit;
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next_bitpos -= 32;
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res_digit = inp_digit >> (bits_per_indigit - next_bitpos);
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}
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}
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if (res_digit != 0)
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dest[size++] = res_digit;
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}
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else
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{
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// General case. The base is not a power of 2.
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int indigits_per_limb = MPN.chars_per_word (base);
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int str_pos = 0;
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while (str_pos < str_len)
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{
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int chunk = str_len - str_pos;
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if (chunk > indigits_per_limb)
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chunk = indigits_per_limb;
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int res_digit = str[str_pos++];
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int big_base = base;
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while (--chunk > 0)
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{
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res_digit = res_digit * base + str[str_pos++];
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big_base *= base;
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}
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int cy_limb;
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if (size == 0)
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cy_limb = res_digit;
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else
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{
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cy_limb = MPN.mul_1 (dest, dest, size, big_base);
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cy_limb += MPN.add_1 (dest, dest, size, res_digit);
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}
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if (cy_limb != 0)
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dest[size++] = cy_limb;
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}
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}
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return size;
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}
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/** Compare x[0:size-1] with y[0:size-1], treating them as unsigned integers.
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* @result -1, 0, or 1 depending on if x<y, x==y, or x>y.
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* This is basically the same as gmp's mpn_cmp function.
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*/
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public static int cmp (int[] x, int[] y, int size)
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{
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while (--size >= 0)
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{
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int x_word = x[size];
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int y_word = y[size];
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if (x_word != y_word)
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{
|
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// 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;
|
|
}
|
|
|
|
/* 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 <= count < 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] >> 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 < 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. */
|
|
|
|
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 & (1<<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(')');
|
|
}
|
|
*/
|
|
}
|