/* glplib02.c (64-bit arithmetic) */

 /***********************************************************************

 *  This code is part of GLPK (GNU Linear Programming Kit).

 *

 *  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,

 *  2009, 2010 Andrew Makhorin, Department for Applied Informatics,

 *  Moscow Aviation Institute, Moscow, Russia. All rights reserved.

 *  E-mail: <mao@gnu.org>.

 *

 *  GLPK 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 3 of the License, or

 *  (at your option) any later version.

 *

 *  GLPK 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 GLPK. If not, see <http://www.gnu.org/licenses/>.

 ***********************************************************************/

 #include "glpenv.h"

 #include "glplib.h"

 /***********************************************************************

 *  NAME

 *

 *  xlset - expand integer to long integer

 *

 *  SYNOPSIS

 *

 *  #include "glplib.h"

 *  glp_long xlset(int x);

 *

 *  RETURNS

 *

 *  The routine xlset returns x expanded to long integer. */

 glp_long xlset(int x)

 {     glp_long t;

       t.lo = x, t.hi = (x >= 0 ? 0 : -1);

       return t;

 }

 /***********************************************************************

 *  NAME

 *

 *  xlneg - negate long integer

 *

 *  SYNOPSIS

 *

 *  #include "glplib.h"

 *  glp_long xlneg(glp_long x);

 *

 *  RETURNS

 *

 *  The routine xlneg returns the difference  0 - x. */

 glp_long xlneg(glp_long x)

 {     if (x.lo)

          x.lo = - x.lo, x.hi = ~x.hi;

       else

          x.hi = - x.hi;

       return x;

 }

 /***********************************************************************

 *  NAME

 *

 *  xladd - add long integers

 *

 *  SYNOPSIS

 *

 *  #include "glplib.h"

 *  glp_long xladd(glp_long x, glp_long y);

 *

 *  RETURNS

 *

 *  The routine xladd returns the sum x + y. */

 glp_long xladd(glp_long x, glp_long y)

 {     if ((unsigned int)x.lo <= 0xFFFFFFFF - (unsigned int)y.lo)

          x.lo += y.lo, x.hi += y.hi;

       else

          x.lo += y.lo, x.hi += y.hi + 1;

       return x;

 }

 /***********************************************************************

 *  NAME

 *

 *  xlsub - subtract long integers

 *

 *  SYNOPSIS

 *

 *  #include "glplib.h"

 *  glp_long xlsub(glp_long x, glp_long y);

 *

 *  RETURNS

 *

 *  The routine xlsub returns the difference x - y. */

 glp_long xlsub(glp_long x, glp_long y)

 {     return

          xladd(x, xlneg(y));

 }

 /***********************************************************************

 *  NAME

 *

 *  xlcmp - compare long integers

 *

 *  SYNOPSIS

 *

 *  #include "glplib.h"

 *  int xlcmp(glp_long x, glp_long y);

 *

 *  RETURNS

 *

 *  The routine xlcmp returns the sign of the difference x - y. */

 int xlcmp(glp_long x, glp_long y)

 {     if (x.hi >= 0 && y.hi <  0) return +1;

       if (x.hi <  0 && y.hi >= 0) return -1;

       if ((unsigned int)x.hi < (unsigned int)y.hi) return -1;

       if ((unsigned int)x.hi > (unsigned int)y.hi) return +1;

       if ((unsigned int)x.lo < (unsigned int)y.lo) return -1;

       if ((unsigned int)x.lo > (unsigned int)y.lo) return +1;

       return 0;

 }

 /***********************************************************************

 *  NAME

 *

 *  xlmul - multiply long integers

 *

 *  SYNOPSIS

 *

 *  #include "glplib.h"

 *  glp_long xlmul(glp_long x, glp_long y);

 *

 *  RETURNS

 *

 *  The routine xlmul returns the product x * y. */

 glp_long xlmul(glp_long x, glp_long y)

 {     unsigned short xx[8], yy[4];

       xx[4] = (unsigned short)x.lo;

       xx[5] = (unsigned short)(x.lo >> 16);

       xx[6] = (unsigned short)x.hi;

       xx[7] = (unsigned short)(x.hi >> 16);

       yy[0] = (unsigned short)y.lo;

       yy[1] = (unsigned short)(y.lo >> 16);

       yy[2] = (unsigned short)y.hi;

       yy[3] = (unsigned short)(y.hi >> 16);

       bigmul(4, 4, xx, yy);

       x.lo = (unsigned int)xx[0] | ((unsigned int)xx[1] << 16);

       x.hi = (unsigned int)xx[2] | ((unsigned int)xx[3] << 16);

       return x;

 }

 /***********************************************************************

 *  NAME

 *

 *  xldiv - divide long integers

 *

 *  SYNOPSIS

 *

 *  #include "glplib.h"

 *  glp_ldiv xldiv(glp_long x, glp_long y);

 *

 *  RETURNS

 *

 *  The routine xldiv returns a structure of type glp_ldiv containing

 *  members quot (the quotient) and rem (the remainder), both of type

 *  glp_long. */

 glp_ldiv xldiv(glp_long x, glp_long y)

 {     glp_ldiv t;

       int m, sx, sy;

       unsigned short xx[8], yy[4];

       /* sx := sign(x) */

       sx = (x.hi < 0);

       /* sy := sign(y) */

       sy = (y.hi < 0);

       /* x := |x| */

       if (sx) x = xlneg(x);

       /* y := |y| */

       if (sy) y = xlneg(y);

       /* compute x div y and x mod y */

       xx[0] = (unsigned short)x.lo;

       xx[1] = (unsigned short)(x.lo >> 16);

       xx[2] = (unsigned short)x.hi;

       xx[3] = (unsigned short)(x.hi >> 16);

       yy[0] = (unsigned short)y.lo;

       yy[1] = (unsigned short)(y.lo >> 16);

       yy[2] = (unsigned short)y.hi;

       yy[3] = (unsigned short)(y.hi >> 16);

       if (yy[3])

          m = 4;

       else if (yy[2])

          m = 3;

       else if (yy[1])

          m = 2;

       else if (yy[0])

          m = 1;

       else

          xerror("xldiv: divide by zero\n");

       bigdiv(4 - m, m, xx, yy);

       /* remainder in x[0], x[1], ..., x[m-1] */

       t.rem.lo = (unsigned int)xx[0], t.rem.hi = 0;

       if (m >= 2) t.rem.lo |= (unsigned int)xx[1] << 16;

       if (m >= 3) t.rem.hi = (unsigned int)xx[2];

       if (m >= 4) t.rem.hi |= (unsigned int)xx[3] << 16;

       if (sx) t.rem = xlneg(t.rem);

       /* quotient in x[m], x[m+1], ..., x[4] */

       t.quot.lo = (unsigned int)xx[m], t.quot.hi = 0;

       if (m <= 3) t.quot.lo |= (unsigned int)xx[m+1] << 16;

       if (m <= 2) t.quot.hi = (unsigned int)xx[m+2];

       if (m <= 1) t.quot.hi |= (unsigned int)xx[m+3] << 16;

       if (sx ^ sy) t.quot = xlneg(t.quot);

       return t;

 }

 /***********************************************************************

 *  NAME

 *

 *  xltod - convert long integer to double

 *

 *  SYNOPSIS

 *

 *  #include "glplib.h"

 *  double xltod(glp_long x);

 *

 *  RETURNS

 *

 *  The routine xltod returns x converted to double. */

 double xltod(glp_long x)

 {     double s, z;

       if (x.hi >= 0)

          s = +1.0;

       else

          s = -1.0, x = xlneg(x);

       if (x.hi >= 0)

          z = 4294967296.0 * (double)x.hi + (double)(unsigned int)x.lo;

       else

       {  xassert(x.hi == 0x80000000 && x.lo == 0x00000000);

          z = 9223372036854775808.0; /* 2^63 */

       }

       return s * z;

 }

 char *xltoa(glp_long x, char *s)

 {     /* convert long integer to character string */

       static const char *d = "0123456789";

       glp_ldiv t;

       int neg, len;

       if (x.hi >= 0)

          neg = 0;

       else

          neg = 1, x = xlneg(x);

       if (x.hi >= 0)

       {  len = 0;

          while (!(x.hi == 0 && x.lo == 0))

          {  t = xldiv(x, xlset(10));

             xassert(0 <= t.rem.lo && t.rem.lo <= 9);

             s[len++] = d[t.rem.lo];

             x = t.quot;

          }

          if (len == 0) s[len++] = d[0];

          if (neg) s[len++] = '-';

          s[len] = '\0';

          strrev(s);

       }

       else

          strcpy(s, "-9223372036854775808"); /* -2^63 */

       return s;

 }

 /**********************************************************************/

 #if 0

 #include "glprng.h"

 #define N_TEST 1000000

 /* number of tests */

 static glp_long myrand(RNG *rand)

 {     glp_long x;

       int k;

       k = rng_unif_rand(rand, 4);

       xassert(0 <= k && k <= 3);

       x.lo = rng_unif_rand(rand, 65536);

       if (k == 1 || k == 3)

       {  x.lo <<= 16;

          x.lo += rng_unif_rand(rand, 65536);

       }

       if (k <= 1)

          x.hi = 0;

       else

          x.hi = rng_unif_rand(rand, 65536);

       if (k == 3)

       {  x.hi <<= 16;

          x.hi += rng_unif_rand(rand, 65536);

       }

       if (rng_unif_rand(rand, 2)) x = xlneg(x);

       return x;

 }

 int main(void)

 {     RNG *rand;

       glp_long x, y;

       glp_ldiv z;

       int test;

       rand = rng_create_rand();

       for (test = 1; test <= N_TEST; test++)

       {  x = myrand(rand);

          y = myrand(rand);

          if (y.lo == 0 && y.hi == 0) y.lo = 1;

          /* z.quot := x div y, z.rem := x mod y */

          z = xldiv(x, y);

          /* x must be equal to y * z.quot + z.rem */

          xassert(xlcmp(x, xladd(xlmul(y, z.quot), z.rem)) == 0);

       }

       xprintf("%d tests successfully passed\n", N_TEST);

       rng_delete_rand(rand);

       return 0;

 }

 #endif

 /* eof */