+++ /dev/null
-/* 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 <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<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;
- }
-
- /* 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(')');
- }
- */
-}
projects / msp430-gcc.git / blobdiff