/* glplib03.c (miscellaneous library routines) */

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

*  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

*

*  str2int - convert character string to value of int type

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  int str2int(const char *str, int *val);

*

*  DESCRIPTION

*

*  The routine str2int converts the character string str to a value of

*  integer type and stores the value into location, which the parameter

*  val points to (in the case of error content of this location is not

*  changed).

*

*  RETURNS

*

*  The routine returns one of the following error codes:

*

*  0 - no error;

*  1 - value out of range;

*  2 - character string is syntactically incorrect. */

int str2int(const char *str, int *_val)

{     int d, k, s, val = 0;

      /* scan optional sign */

      if (str[0] == '+')

         s = +1, k = 1;

      else if (str[0] == '-')

         s = -1, k = 1;

      else

         s = +1, k = 0;

      /* check for the first digit */

      if (!isdigit((unsigned char)str[k])) return 2;

      /* scan digits */

      while (isdigit((unsigned char)str[k]))

      {  d = str[k++] - '0';

         if (s > 0)

         {  if (val > INT_MAX / 10) return 1;

            val *= 10;

            if (val > INT_MAX - d) return 1;

            val += d;

         }

         else

         {  if (val < INT_MIN / 10) return 1;

            val *= 10;

            if (val < INT_MIN + d) return 1;

            val -= d;

         }

      }

      /* check for terminator */

      if (str[k] != '\0') return 2;

      /* conversion has been done */

      *_val = val;

      return 0;

}

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

*  NAME

*

*  str2num - convert character string to value of double type

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  int str2num(const char *str, double *val);

*

*  DESCRIPTION

*

*  The routine str2num converts the character string str to a value of

*  double type and stores the value into location, which the parameter

*  val points to (in the case of error content of this location is not

*  changed).

*

*  RETURNS

*

*  The routine returns one of the following error codes:

*

*  0 - no error;

*  1 - value out of range;

*  2 - character string is syntactically incorrect. */

int str2num(const char *str, double *_val)

{     int k;

      double val;

      /* scan optional sign */

      k = (str[0] == '+' || str[0] == '-' ? 1 : 0);

      /* check for decimal point */

      if (str[k] == '.')

      {  k++;

         /* a digit should follow it */

         if (!isdigit((unsigned char)str[k])) return 2;

         k++;

         goto frac;

      }

      /* integer part should start with a digit */

      if (!isdigit((unsigned char)str[k])) return 2;

      /* scan integer part */

      while (isdigit((unsigned char)str[k])) k++;

      /* check for decimal point */

      if (str[k] == '.') k++;

frac: /* scan optional fraction part */

      while (isdigit((unsigned char)str[k])) k++;

      /* check for decimal exponent */

      if (str[k] == 'E' || str[k] == 'e')

      {  k++;

         /* scan optional sign */

         if (str[k] == '+' || str[k] == '-') k++;

         /* a digit should follow E, E+ or E- */

         if (!isdigit((unsigned char)str[k])) return 2;

      }

      /* scan optional exponent part */

      while (isdigit((unsigned char)str[k])) k++;

      /* check for terminator */

      if (str[k] != '\0') return 2;

      /* perform conversion */

      {  char *endptr;

         val = strtod(str, &endptr);

         if (*endptr != '\0') return 2;

      }

      /* check for overflow */

      if (!(-DBL_MAX <= val && val <= +DBL_MAX)) return 1;

      /* check for underflow */

      if (-DBL_MIN < val && val < +DBL_MIN) val = 0.0;

      /* conversion has been done */

      *_val = val;

      return 0;

}

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

*  NAME

*

*  strspx - remove all spaces from character string

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  char *strspx(char *str);

*

*  DESCRIPTION

*

*  The routine strspx removes all spaces from the character string str.

*

*  RETURNS

*

*  The routine returns a pointer to the character string.

*

*  EXAMPLES

*

*  strspx("   Errare   humanum   est   ") => "Errarehumanumest"

*

*  strspx("      ")                       => "" */

char *strspx(char *str)

{     char *s, *t;

      for (s = t = str; *s; s++) if (*s != ' ') *t++ = *s;

      *t = '\0';

      return str;

}

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

*  NAME

*

*  strtrim - remove trailing spaces from character string

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  char *strtrim(char *str);

*

*  DESCRIPTION

*

*  The routine strtrim removes trailing spaces from the character

*  string str.

*

*  RETURNS

*

*  The routine returns a pointer to the character string.

*

*  EXAMPLES

*

*  strtrim("Errare humanum est   ") => "Errare humanum est"

*

*  strtrim("      ")                => "" */

char *strtrim(char *str)

{     char *t;

      for (t = strrchr(str, '\0') - 1; t >= str; t--)

      {  if (*t != ' ') break;

         *t = '\0';

      }

      return str;

}

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

*  NAME

*

*  strrev - reverse character string

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  char *strrev(char *s);

*

*  DESCRIPTION

*

*  The routine strrev changes characters in a character string s to the

*  reverse order, except the terminating null character.

*

*  RETURNS

*

*  The routine returns the pointer s.

*

*  EXAMPLES

*

*  strrev("")                => ""

*

*  strrev("Today is Monday") => "yadnoM si yadoT" */

char *strrev(char *s)

{     int i, j;

      char t;

      for (i = 0, j = strlen(s)-1; i < j; i++, j--)

         t = s[i], s[i] = s[j], s[j] = t;

      return s;

}

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

*  NAME

*

*  gcd - find greatest common divisor of two integers

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  int gcd(int x, int y);

*

*  RETURNS

*

*  The routine gcd returns gcd(x, y), the greatest common divisor of

*  the two positive integers given.

*

*  ALGORITHM

*

*  The routine gcd is based on Euclid's algorithm.

*

*  REFERENCES

*

*  Don Knuth, The Art of Computer Programming, Vol.2: Seminumerical

*  Algorithms, 3rd Edition, Addison-Wesley, 1997. Section 4.5.2: The

*  Greatest Common Divisor, pp. 333-56. */

int gcd(int x, int y)

{     int r;

      xassert(x > 0 && y > 0);

      while (y > 0)

         r = x % y, x = y, y = r;

      return x;

}

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

*  NAME

*

*  gcdn - find greatest common divisor of n integers

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  int gcdn(int n, int x[]);

*

*  RETURNS

*

*  The routine gcdn returns gcd(x[1], x[2], ..., x[n]), the greatest

*  common divisor of n positive integers given, n > 0.

*

*  BACKGROUND

*

*  The routine gcdn is based on the following identity:

*

*     gcd(x, y, z) = gcd(gcd(x, y), z).

*

*  REFERENCES

*

*  Don Knuth, The Art of Computer Programming, Vol.2: Seminumerical

*  Algorithms, 3rd Edition, Addison-Wesley, 1997. Section 4.5.2: The

*  Greatest Common Divisor, pp. 333-56. */

int gcdn(int n, int x[])

{     int d, j;

      xassert(n > 0);

      for (j = 1; j <= n; j++)

      {  xassert(x[j] > 0);

         if (j == 1)

            d = x[1];

         else

            d = gcd(d, x[j]);

         if (d == 1) break;

      }

      return d;

}

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

*  NAME

*

*  lcm - find least common multiple of two integers

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  int lcm(int x, int y);

*

*  RETURNS

*

*  The routine lcm returns lcm(x, y), the least common multiple of the

*  two positive integers given. In case of integer overflow the routine

*  returns zero.

*

*  BACKGROUND

*

*  The routine lcm is based on the following identity:

*

*     lcm(x, y) = (x * y) / gcd(x, y) = x * [y / gcd(x, y)],

*

*  where gcd(x, y) is the greatest common divisor of x and y. */

int lcm(int x, int y)

{     xassert(x > 0);

      xassert(y > 0);

      y /= gcd(x, y);

      if (x > INT_MAX / y) return 0;

      return x * y;

}

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

*  NAME

*

*  lcmn - find least common multiple of n integers

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  int lcmn(int n, int x[]);

*

*  RETURNS

*

*  The routine lcmn returns lcm(x[1], x[2], ..., x[n]), the least

*  common multiple of n positive integers given, n > 0. In case of

*  integer overflow the routine returns zero.

*

*  BACKGROUND

*

*  The routine lcmn is based on the following identity:

*

*     lcmn(x, y, z) = lcm(lcm(x, y), z),

*

*  where lcm(x, y) is the least common multiple of x and y. */

int lcmn(int n, int x[])

{     int m, j;

      xassert(n > 0);

      for (j = 1; j <= n; j++)

      {  xassert(x[j] > 0);

         if (j == 1)

            m = x[1];

         else

            m = lcm(m, x[j]);

         if (m == 0) break;

      }

      return m;

}

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

*  NAME

*

*  round2n - round floating-point number to nearest power of two

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  double round2n(double x);

*

*  RETURNS

*

*  Given a positive floating-point value x the routine round2n returns

*  2^n such that |x - 2^n| is minimal.

*

*  EXAMPLES

*

*  round2n(10.1) = 2^3 = 8

*  round2n(15.3) = 2^4 = 16

*  round2n(0.01) = 2^(-7) = 0.0078125

*

*  BACKGROUND

*

*  Let x = f * 2^e, where 0.5 <= f < 1 is a normalized fractional part,

*  e is an integer exponent. Then, obviously, 0.5 * 2^e <= x < 2^e, so

*  if x - 0.5 * 2^e <= 2^e - x, we choose 0.5 * 2^e = 2^(e-1), and 2^e

*  otherwise. The latter condition can be written as 2 * x <= 1.5 * 2^e

*  or 2 * f * 2^e <= 1.5 * 2^e or, finally, f <= 0.75. */

double round2n(double x)

{     int e;

      double f;

      xassert(x > 0.0);

      f = frexp(x, &e);

      return ldexp(1.0, f <= 0.75 ? e-1 : e);

}

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

*  NAME

*

*  fp2rat - convert floating-point number to rational number

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  int fp2rat(double x, double eps, double *p, double *q);

*

*  DESCRIPTION

*

*  Given a floating-point number 0 <= x < 1 the routine fp2rat finds

*  its "best" rational approximation p / q, where p >= 0 and q > 0 are

*  integer numbers, such that |x - p / q| <= eps.

*

*  RETURNS

*

*  The routine fp2rat returns the number of iterations used to achieve

*  the specified precision eps.

*

*  EXAMPLES

*

*  For x = sqrt(2) - 1 = 0.414213562373095 and eps = 1e-6 the routine

*  gives p = 408 and q = 985, where 408 / 985 = 0.414213197969543.

*

*  BACKGROUND

*

*  It is well known that every positive real number x can be expressed

*  as the following continued fraction:

*

*     x = b[0] + a[1]

*                ------------------------

*                b[1] + a[2]

*                       -----------------

*                       b[2] + a[3]

*                              ----------

*                              b[3] + ...

*

*  where:

*

*     a[k] = 1,                  k = 0, 1, 2, ...

*

*     b[k] = floor(x[k]),        k = 0, 1, 2, ...

*

*     x[0] = x,

*

*     x[k] = 1 / frac(x[k-1]),   k = 1, 2, 3, ...

*

*  To find the "best" rational approximation of x the routine computes

*  partial fractions f[k] by dropping after k terms as follows:

*

*     f[k] = A[k] / B[k],

*

*  where:

*

*     A[-1] = 1,   A[0] = b[0],   B[-1] = 0,   B[0] = 1,

*

*     A[k] = b[k] * A[k-1] + a[k] * A[k-2],

*

*     B[k] = b[k] * B[k-1] + a[k] * B[k-2].

*

*  Once the condition

*

*     |x - f[k]| <= eps

*

*  has been satisfied, the routine reports p = A[k] and q = B[k] as the

*  final answer.

*

*  In the table below here is some statistics obtained for one million

*  random numbers uniformly distributed in the range [0, 1).

*

*      eps      max p   mean p      max q    mean q  max k   mean k

*     -------------------------------------------------------------

*     1e-1          8      1.6          9       3.2    3      1.4

*     1e-2         98      6.2         99      12.4    5      2.4

*     1e-3        997     20.7        998      41.5    8      3.4

*     1e-4       9959     66.6       9960     133.5   10      4.4

*     1e-5      97403    211.7      97404     424.2   13      5.3

*     1e-6     479669    669.9     479670    1342.9   15      6.3

*     1e-7    1579030   2127.3    3962146    4257.8   16      7.3

*     1e-8   26188823   6749.4   26188824   13503.4   19      8.2

*

*  REFERENCES

*

*  W. B. Jones and W. J. Thron, "Continued Fractions: Analytic Theory

*  and Applications," Encyclopedia on Mathematics and Its Applications,

*  Addison-Wesley, 1980. */

int fp2rat(double x, double eps, double *p, double *q)

{     int k;

      double xk, Akm1, Ak, Bkm1, Bk, ak, bk, fk, temp;

      if (!(0.0 <= x && x < 1.0))

         xerror("fp2rat: x = %g; number out of range\n", x);

      for (k = 0; ; k++)

      {  xassert(k <= 100);

         if (k == 0)

         {  /* x[0] = x */

            xk = x;

            /* A[-1] = 1 */

            Akm1 = 1.0;

            /* A[0] = b[0] = floor(x[0]) = 0 */

            Ak = 0.0;

            /* B[-1] = 0 */

            Bkm1 = 0.0;

            /* B[0] = 1 */

            Bk = 1.0;

         }

         else

         {  /* x[k] = 1 / frac(x[k-1]) */

            temp = xk - floor(xk);

            xassert(temp != 0.0);

            xk = 1.0 / temp;

            /* a[k] = 1 */

            ak = 1.0;

            /* b[k] = floor(x[k]) */

            bk = floor(xk);

            /* A[k] = b[k] * A[k-1] + a[k] * A[k-2] */

            temp = bk * Ak + ak * Akm1;

            Akm1 = Ak, Ak = temp;

            /* B[k] = b[k] * B[k-1] + a[k] * B[k-2] */

            temp = bk * Bk + ak * Bkm1;

            Bkm1 = Bk, Bk = temp;

         }

         /* f[k] = A[k] / B[k] */

         fk = Ak / Bk;

#if 0

         print("%.*g / %.*g = %.*g", DBL_DIG, Ak, DBL_DIG, Bk, DBL_DIG,

            fk);

#endif

         if (fabs(x - fk) <= eps) break;

      }

      *p = Ak;

      *q = Bk;

      return k;

}

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

*  NAME

*

*  jday - convert calendar date to Julian day number

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  int jday(int d, int m, int y);

*

*  DESCRIPTION

*

*  The routine jday converts a calendar date, Gregorian calendar, to

*  corresponding Julian day number j.

*

*  From the given day d, month m, and year y, the Julian day number j

*  is computed without using tables.

*

*  The routine is valid for 1 <= y <= 4000.

*

*  RETURNS

*

*  The routine jday returns the Julian day number, or negative value if

*  the specified date is incorrect.

*

*  REFERENCES

*

*  R. G. Tantzen, Algorithm 199: conversions between calendar date and

*  Julian day number, Communications of the ACM, vol. 6, no. 8, p. 444,

*  Aug. 1963. */

int jday(int d, int m, int y)

{     int c, ya, j, dd;

      if (!(1 <= d && d <= 31 && 1 <= m && m <= 12 && 1 <= y &&

            y <= 4000))

      {  j = -1;

         goto done;

      }

      if (m >= 3) m -= 3; else m += 9, y--;

      c = y / 100;

      ya = y - 100 * c;

      j = (146097 * c) / 4 + (1461 * ya) / 4 + (153 * m + 2) / 5 + d +

         1721119;

      jdate(j, &dd, NULL, NULL);

      if (d != dd) j = -1;

done: return j;

}

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

*  NAME

*

*  jdate - convert Julian day number to calendar date

*

*  SYNOPSIS

*

*  #include "glplib.h"

*  void jdate(int j, int *d, int *m, int *y);

*

*  DESCRIPTION

*

*  The routine jdate converts a Julian day number j to corresponding

*  calendar date, Gregorian calendar.

*

*  The day d, month m, and year y are computed without using tables and

*  stored in corresponding locations.

*

*  The routine is valid for 1721426 <= j <= 3182395.

*

*  RETURNS

*

*  If the conversion is successful, the routine returns zero, otherwise

*  non-zero.

*

*  REFERENCES

*

*  R. G. Tantzen, Algorithm 199: conversions between calendar date and

*  Julian day number, Communications of the ACM, vol. 6, no. 8, p. 444,

*  Aug. 1963. */

int jdate(int j, int *_d, int *_m, int *_y)

{     int d, m, y, ret = 0;

      if (!(1721426 <= j && j <= 3182395))

      {  ret = 1;

         goto done;

      }

      j -= 1721119;

      y = (4 * j - 1) / 146097;

      j = (4 * j - 1) % 146097;

      d = j / 4;

      j = (4 * d + 3) / 1461;

      d = (4 * d + 3) % 1461;

      d = (d + 4) / 4;

      m = (5 * d - 3) / 153;

      d = (5 * d - 3) % 153;

      d = (d + 5) / 5;

      y = 100 * y + j;

      if (m <= 9) m += 3; else m -= 9, y++;

      if (_d != NULL) *_d = d;

      if (_m != NULL) *_m = m;

      if (_y != NULL) *_y = y;

done: return ret;

}

#if 0

int main(void)

{     int jbeg, jend, j, d, m, y;

      jbeg = jday(1, 1, 1);

      jend = jday(31, 12, 4000);

      for (j = jbeg; j <= jend; j++)

      {  xassert(jdate(j, &d, &m, &y) == 0);

         xassert(jday(d, m, y) == j);

      }

      xprintf("Routines jday and jdate work correctly.\n");

      return 0;

}

#endif

/* eof */