%%	options

copyright owner	=	Dirk Krause
copyright year	=	2014
license		=	bsd



%%	header

/**	@file	dk3mal.h	Mathematical operations on long, long long,
	intmax_t and dk3_im_t.
*/

#include <dk3conf.h>

#include <stdio.h>
#if DK3_HAVE_SYS_TYPES_H
#include <sys/types.h>
#endif
#if DK3_HAVE_STDINT
#include <stdint.h>
#endif
#if DK3_HAVE_INTTYPES_H
#include <inttypes.h>
#endif
#if DK3_HAVE_LIMITS_H
#include <limits.h>
#endif
#if DK3_HAVE_MATH_H
#include <math.h>
#endif
#if DK3_HAVE_FLOAT_H
#include <float.h>
#endif


#ifdef __cplusplus
extern "C" {
#endif

/**	Absolute value.
	@param	a	Original value.
	@param	ec	Pointer to error code variable, may be NULL.
	@return	Non-negative value on success,
	DK3_L_MAX and ec = DK3_ERROR_MATH_OVERFLOW on error.
*/
long
dk3ma_l_abs_ok(long a, int *ec);

/**	Addition.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Summary of a and b.
*/
long
dk3ma_l_add_ok(long a, long b, int *ec);

/**	Substraction.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Difference of a and b.
*/
long
dk3ma_l_sub_ok(long a, long b, int *ec);

/**	Multiplication.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Product of a and b.
*/
long
dk3ma_l_mul_ok(long a, long b, int *ec);

/**	Division.
	@param	a	Left operand (nominator).
	@param	b	Right operand (denominator).
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW or
	DK3_ERROR_MATH_DIVZERO when returning.
	@return	Fraction of a and b.
*/
long
dk3ma_l_div_ok(long a, long b, int *ec);

/**	Greatest common divisor.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Greatest common divisor of a and b on success,
	0L and ec = DK3_ERROR_MATH_OVERFLOW on error.
*/
long
dk3ma_l_gcd_ok(long a, long b, int *ec);



#if DK3_HAVE_LONG_LONG

/**	Absolute value.
	@param	a	Original value.
	@param	ec	Pointer to error code variable, may be NULL.
	@return	Non-negative value on success,
	DK3_L_MAX and ec = DK3_ERROR_MATH_OVERFLOW on error.
*/
long long
dk3ma_ll_abs_ok(long long a, int *ec);

/**	Addition.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Summary of a and b.
*/
long long
dk3ma_ll_add_ok(long long a, long long b, int *ec);

/**	Substraction.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Difference of a and b.
*/
long long
dk3ma_ll_sub_ok(long long a, long long b, int *ec);

/**	Multiplication.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Product of a and b.
*/
long long
dk3ma_ll_mul_ok(long long a, long long b, int *ec);

/**	Division.
	@param	a	Left operand (nominator).
	@param	b	Right operand (denominator).
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW or
	DK3_ERROR_MATH_DIVZERO when returning.
	@return	Fraction of a and b.
*/
long long
dk3ma_ll_div_ok(long long a, long long b, int *ec);

/**	Greatest common divisor.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Greatest common divisor of a and b on success,
	0L and ec = DK3_ERROR_MATH_OVERFLOW on error.
*/
long long
dk3ma_ll_gcd_ok(long long a, long long b, int *ec);

#endif
/* if DK3_HAVE_LONG_LONG */



#if DK3_HAVE_INTMAX_T

/**	Absolute value.
	@param	a	Original value.
	@param	ec	Pointer to error code variable, may be NULL.
	@return	Non-negative value on success,
	DK3_L_MAX and ec = DK3_ERROR_MATH_OVERFLOW on error.
*/
intmax_t
dk3ma_intmax_t_abs_ok(intmax_t a, int *ec);

/**	Addition.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Summary of a and b.
*/
intmax_t
dk3ma_intmax_t_add_ok(intmax_t a, intmax_t b, int *ec);

/**	Substraction.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Difference of a and b.
*/
intmax_t
dk3ma_intmax_t_sub_ok(intmax_t a, intmax_t b, int *ec);

/**	Multiplication.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Product of a and b.
*/
intmax_t
dk3ma_intmax_t_mul_ok(intmax_t a, intmax_t b, int *ec);

/**	Division.
	@param	a	Left operand (nominator).
	@param	b	Right operand (denominator).
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW or
	DK3_ERROR_MATH_DIVZERO when returning.
	@return	Fraction of a and b.
*/
intmax_t
dk3ma_intmax_t_div_ok(intmax_t a, intmax_t b, int *ec);

/**	Greatest common divisor.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Greatest common divisor of a and b on success,
	0L and ec = DK3_ERROR_MATH_OVERFLOW on error.
*/
intmax_t
dk3ma_intmax_t_gcd_ok(intmax_t a, intmax_t b, int *ec);

#endif

/**	Absolute value.
	@param	a	Original value.
	@param	ec	Pointer to error code variable, may be NULL.
	@return	Non-negative value on success,
	DK3_L_MAX and ec = DK3_ERROR_MATH_OVERFLOW on error.
*/
dk3_im_t
dk3ma_im_abs_ok(dk3_im_t a, int *ec);

/**	Addition.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Summary of a and b.
*/
dk3_im_t
dk3ma_im_add_ok(dk3_im_t a, dk3_im_t b, int *ec);

/**	Substraction.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Difference of a and b.
*/
dk3_im_t
dk3ma_im_sub_ok(dk3_im_t a, dk3_im_t b, int *ec);

/**	Multiplication.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Product of a and b.
*/
dk3_im_t
dk3ma_im_mul_ok(dk3_im_t a, dk3_im_t b, int *ec);

/**	Division.
	@param	a	Left operand (nominator).
	@param	b	Right operand (denominator).
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW or
	DK3_ERROR_MATH_DIVZERO when returning.
	@return	Fraction of a and b.
*/
dk3_im_t
dk3ma_im_div_ok(dk3_im_t a, dk3_im_t b, int *ec);

/**	Greatest common divisor.
	@param	a	Left operand.
	@param	b	Right operand.
	@param	ec	Pointer to error code variable, may be NULL.
	The variable may be set to DK3_ERROR_MATH_OVERFLOW when returning.
	@return	Greatest common divisor of a and b on success,
	0L and ec = DK3_ERROR_MATH_OVERFLOW on error.
*/
dk3_im_t
dk3ma_im_gcd_ok(dk3_im_t a, dk3_im_t b, int *ec);

#ifdef __cplusplus
}
#endif



%%	module



#include "dk3ma.h"



$!trace-include



long
dk3ma_l_abs_ok(long a, int *ec)
{
  if (NULL != ec) { if(DK3_L_MIN == a) { *ec = DK3_ERROR_MATH_OVERFLOW; } }
  return ((0L <= a) ? a : (0L - a));
}



long
dk3ma_l_add_ok(long a, long b, int *ec)
{
  if (NULL != ec) {
    if ((0L < a) && (0L < b)) {
      if((DK3_L_MAX - a) < b) { *ec = DK3_ERROR_MATH_OVERFLOW; }
    } else {
      if ((0L > a) && (0L > b)) {
        if (DK3_L_MIN == a) {
	  *ec = DK3_ERROR_MATH_OVERFLOW;
	} else {
	  if ((DK3_L_MIN - a) > b) {
	    *ec = DK3_ERROR_MATH_OVERFLOW;
	  }
	}
      }
    }
  }
  return (a + b);
}



long
dk3ma_l_sub_ok(long a, long b, int *ec)
{
  if (NULL != ec) {
    if ((0L < a) && (0L > b)) {
      if((DK3_L_MAX + b) < a) { *ec = DK3_ERROR_MATH_OVERFLOW; }
    } else {
      if ((0L > a) && (0L < b)) {
        if((DK3_L_MIN + b) > a) { *ec = DK3_ERROR_MATH_OVERFLOW; }
      }
    }
  }
  return (a - b);
}




long
dk3ma_l_mul_ok(long a, long b, int *ec)
{
  if (NULL != ec) {
    if ((0L != a) && (0L != b)) {
      if ((DK3_L_MIN == a) && (1L != b)) {
        *ec = DK3_ERROR_MATH_OVERFLOW;
	goto checksfinished;
      }
      if ((DK3_L_MIN == b) && (1L != a)) {
        *ec = DK3_ERROR_MATH_OVERFLOW;
	goto checksfinished;
      }
      if ((DK3_L_MAX / dk3ma_l_abs_ok(a, ec)) < dk3ma_l_abs_ok(b, ec)) {
        *ec = DK3_ERROR_MATH_OVERFLOW;
	/* goto checksfinished; -- when adding further tests -- */
      }
    }
  }
  checksfinished:
  return (a * b);
}



long
dk3ma_l_div_ok(long a, long b, int *ec)
{
  long		back	= 0L;
  if (0L != b) {
    if ((DK3_L_MIN == a) && (-1L == b)) {
      back = DK3_L_MAX;
      *ec = DK3_ERROR_MATH_OVERFLOW;
    } else {
      back = a / b;
    }
  } else {
    if (NULL != ec) { *ec = DK3_ERROR_MATH_DIVZERO; }
    if (0L <= a) { back = DK3_L_MAX; }
    else         { back = DK3_L_MIN; }
  }
  return back;
}



long
dk3ma_l_gcd_ok(long a, long b, int *ec)
{
  long	h;
  if (0L > a) {
    if (DK3_L_MIN == a) {
      a = 0L;
      if (NULL != ec) { *ec = DK3_ERROR_MATH_OVERFLOW; }
      goto finished;
    } else {
      a = 0L - a;
    }
  }
  if (0L > b) {
    if (DK3_L_MIN == b) {
      a = 0L;
      if (NULL != ec) { *ec = DK3_ERROR_MATH_OVERFLOW; }
      goto finished;
    } else {
      b = 0L - b;
    }
  }
  while (0L < b) {
    h = a % b;
    a = b;
    b = h;
  }
  if (0L == a) { a = 1L; }
  finished:
  return a;
}



#if DK3_HAVE_LONG_LONG



long long
dk3ma_ll_abs_ok(long long a, int *ec)
{
  if (NULL != ec) { if(DK3_LL_MIN == a) { *ec = DK3_ERROR_MATH_OVERFLOW; } }
  return ((0LL <= a) ? a : (0L - a));
}



long long
dk3ma_ll_add_ok(long long a, long long b, int *ec)
{
  if (NULL != ec) {
    if ((0LL < a) && (0LL < b)) {
      if((DK3_LL_MAX - a) < b) { *ec = DK3_ERROR_MATH_OVERFLOW; }
    } else {
      if ((0LL > a) && (0LL > b)) {
        if (DK3_LL_MIN == a) {
	  *ec = DK3_ERROR_MATH_OVERFLOW;
	} else {
	  if ((DK3_LL_MIN - a) > b) {
	    *ec = DK3_ERROR_MATH_OVERFLOW;
	  }
	}
      }
    }
  }
  return (a + b);
}



long long
dk3ma_ll_sub_ok(long long a, long long b, int *ec)
{
  if (NULL != ec) {
    if ((0LL < a) && (0LL > b)) {
      if((DK3_LL_MAX + b) < a) { *ec = DK3_ERROR_MATH_OVERFLOW; }
    } else {
      if ((0LL > a) && (0LL < b)) {
        if((DK3_LL_MIN + b) > a) { *ec = DK3_ERROR_MATH_OVERFLOW; }
      }
    }
  }
  return (a - b);
}




long long
dk3ma_ll_mul_ok(long long a, long long b, int *ec)
{
  if (NULL != ec) {
    if ((0LL != a) && (0LL != b)) {
      if ((DK3_LL_MIN == a) && (1LL != b)) {
        *ec = DK3_ERROR_MATH_OVERFLOW;
	goto checksfinished;
      }
      if ((DK3_LL_MIN == b) && (1LL != a)) {
        *ec = DK3_ERROR_MATH_OVERFLOW;
	goto checksfinished;
      }
      if ((DK3_LL_MAX / dk3ma_ll_abs_ok(a, ec)) < dk3ma_ll_abs_ok(b, ec)) {
        *ec = DK3_ERROR_MATH_OVERFLOW;
	/* goto checksfinished; -- when adding further tests -- */
      }
    }
  }
  checksfinished:
  return (a * b);
}



long long
dk3ma_ll_div_ok(long long a, long long b, int *ec)
{
  long long	back	= 0L;
  if (0LL != b) {
    if ((DK3_LL_MIN == a) && (-1LL == b)) {
      back = DK3_LL_MAX;
      *ec = DK3_ERROR_MATH_OVERFLOW;
    } else {
      back = a / b;
    }
  } else {
    if (NULL != ec) { *ec = DK3_ERROR_MATH_DIVZERO; }
    if (0LL <= a) { back = DK3_LL_MAX; }
    else          { back = DK3_LL_MIN; }
  }
  return back;
}



long long
dk3ma_ll_gcd_ok(long long a, long long b, int *ec)
{
  long long	h;
  if (0LL > a) {
    if (DK3_LL_MIN == a) {
      a = 0LL;
      if (NULL != ec) { *ec = DK3_ERROR_MATH_OVERFLOW; }
      goto finished;
    } else {
      a = 0LL - a;
    }
  }
  if (0LL > b) {
    if (DK3_LL_MIN == b) {
      a = 0LL;
      if (NULL != ec) { *ec = DK3_ERROR_MATH_OVERFLOW; }
      goto finished;
    } else {
      b = 0LL - b;
    }
  }
  while (0LL < b) {
    h = a % b;
    a = b;
    b = h;
  }
  if (0LL == a) { a = 1LL; }
  finished:
  return a;
}


#endif



#if DK3_HAVE_INTMAX_T

intmax_t
dk3ma_intmax_t_abs_ok(intmax_t a, int *ec)
{
  if (ec) { if (DK3_INTMAX_T_MIN == a) { *ec = DK3_ERROR_MATH_OVERFLOW; } }
  return ((DK3_INTMAX_T_0 <= a) ? a : (DK3_INTMAX_T_0 - a));
}



intmax_t
dk3ma_intmax_t_add_ok(intmax_t a, intmax_t b, int *ec)
{
  if (NULL != ec) {
    if ((DK3_INTMAX_T_0 < a) && (DK3_INTMAX_T_0 < b)) {
      if ((DK3_INTMAX_T_MAX - a) < b) { *ec = DK3_ERROR_MATH_OVERFLOW; }
    } else {
      if ((DK3_INTMAX_T_0 > a) && (DK3_INTMAX_T_0 > b)) {
        if (DK3_INTMAX_T_MIN == a) {
	  *ec = DK3_ERROR_MATH_OVERFLOW;
	} else {
	  if ((DK3_INTMAX_T_MIN - a) > b) { *ec = DK3_ERROR_MATH_OVERFLOW; }
	}
      }
    }
  }
  return (a + b);
}



intmax_t
dk3ma_intmax_t_sub_ok(intmax_t a, intmax_t b, int *ec)
{
  if (NULL != ec) {
    if((DK3_INTMAX_T_0 < a) && (DK3_INTMAX_T_0 > b)) {
      if((DK3_INTMAX_T_MAX + b) < a) { *ec = DK3_ERROR_MATH_OVERFLOW; }
    } else {
      if((DK3_INTMAX_T_0 > a) && (DK3_INTMAX_T_0 < b)) {
        if((DK3_INTMAX_T_MIN + b) > a) { *ec = DK3_ERROR_MATH_OVERFLOW; }
      }
    }
  }
  return (a - b);
}



intmax_t
dk3ma_intmax_t_mul_ok(intmax_t a, intmax_t b, int *ec)
{
  if (NULL != ec) {
    if ((DK3_INTMAX_T_0 != a) && (DK3_INTMAX_T_0 != b)) {
      if ((DK3_INTMAX_T_MIN == a) && (DK3_INTMAX_T_1 != b)) {
        *ec = DK3_ERROR_MATH_OVERFLOW;
	goto checksfinished;
      }
      if ((DK3_INTMAX_T_MIN == b) && (DK3_INTMAX_T_1 != a)) {
        *ec = DK3_ERROR_MATH_OVERFLOW;
	goto checksfinished;
      }
      if (
        (DK3_INTMAX_T_MAX / dk3ma_intmax_t_abs_ok(a, ec))
	< dk3ma_intmax_t_abs_ok(b, ec)
      )
      {
        *ec = DK3_ERROR_MATH_OVERFLOW;
	/* goto checksfinished; -- when adding further tests -- */
      }
    }
  }
  checksfinished:
  return (a * b);
}



intmax_t
dk3ma_intmax_t_div_ok(intmax_t a, intmax_t b, int *ec)
{
  intmax_t	back = DK3_INTMAX_T_0;
  if (DK3_INTMAX_T_0 != b) {
    if ((DK3_INTMAX_T_MIN == a) && ((-DK3_INTMAX_T_1) == b)) {
      back = DK3_INTMAX_T_MAX;
      *ec = DK3_ERROR_MATH_OVERFLOW;
    } else {
      back = (a / b);
    }
  } else {
    if (NULL != ec) { *ec = DK3_ERROR_MATH_DIVZERO; }
    if (DK3_INTMAX_T_0 <= a) { back = DK3_INTMAX_T_MAX; }
    else		     { back = DK3_INTMAX_T_MIN; }
  }
  return back;
}



intmax_t
dk3ma_intmax_t_gcd_ok(intmax_t a, intmax_t b, int *ec)
{
  intmax_t	h;
  if (DK3_INTMAX_T_0 > a) {
    if (DK3_INTMAX_T_MIN == a) {
      a = DK3_INTMAX_T_0;
      if (NULL != ec) { *ec = DK3_ERROR_MATH_OVERFLOW; }
      goto finished;
    } else {
      a = DK3_INTMAX_T_0 - a;
    }
  }
  if (DK3_INTMAX_T_0 > b) {
    if (DK3_INTMAX_T_MIN == b) {
      a = DK3_INTMAX_T_0;
      if (NULL != ec) { *ec = DK3_ERROR_MATH_OVERFLOW; }
      goto finished;
    } else {
      b = DK3_INTMAX_T_0 - b;
    }
  }
  while (DK3_INTMAX_T_0 < b) {
    h = a % b;
    a = b;
    b = h;
  }
  if (DK3_INTMAX_T_0 == a) { a = DK3_INTMAX_T_1 ; }
  finished:
  return a;
}

#endif



dk3_im_t
dk3ma_im_abs_ok(dk3_im_t a, int *ec)
{
#if DK3_HAVE_INTMAX_T
  return (dk3ma_intmax_t_abs_ok(a, ec));
#else
#if DK3_HAVE_LONG_LONG
  return (dk3ma_ll_abs_ok(a, ec));
#else
  return (dk3ma_l_abs_ok(a, ec));
#endif
#endif
}



dk3_im_t
dk3ma_im_add_ok(dk3_im_t a, dk3_im_t b, int *ec)
{
#if DK3_HAVE_INTMAX_T
  return (dk3ma_intmax_t_add_ok(a, b, ec));
#else
#if DK3_HAVE_LONG_LONG
  return (dk3ma_ll_add_ok(a, b, ec));
#else
  return (dk3ma_l_add_ok(a, b, ec));
#endif
#endif
}



dk3_im_t
dk3ma_im_sub_ok(dk3_im_t a, dk3_im_t b, int *ec)
{
#if DK3_HAVE_INTMAX_T
  return (dk3ma_intmax_t_sub_ok(a, b, ec));
#else
#if DK3_HAVE_LONG_LONG
  return (dk3ma_ll_sub_ok(a, b, ec));
#else
  return (dk3ma_l_sub_ok(a, b, ec));
#endif
#endif
}



dk3_im_t
dk3ma_im_mul_ok(dk3_im_t a, dk3_im_t b, int *ec)
{
#if DK3_HAVE_INTMAX_T
  return (dk3ma_intmax_t_mul_ok(a, b, ec));
#else
#if DK3_HAVE_LONG_LONG
  return (dk3ma_ll_mul_ok(a, b, ec));
#else
  return (dk3ma_l_mul_ok(a, b, ec));
#endif
#endif
}



dk3_im_t
dk3ma_im_div_ok(dk3_im_t a, dk3_im_t b, int *ec)
{
#if DK3_HAVE_INTMAX_T
  return (dk3ma_intmax_t_div_ok(a, b, ec));
#else
#if DK3_HAVE_LONG_LONG
  return (dk3ma_ll_div_ok(a, b, ec));
#else
  return (dk3ma_l_div_ok(a, b, ec));
#endif
#endif
}



dk3_im_t
dk3ma_im_gcd_ok(dk3_im_t a, dk3_im_t b, int *ec)
{
#if DK3_HAVE_INTMAX_T
  return (dk3ma_intmax_t_gcd_ok(a, b, ec));
#else
#if DK3_HAVE_LONG_LONG
  return (dk3ma_ll_gcd_ok(a, b, ec));
#else
  return (dk3ma_l_gcd_ok(a, b, ec));
#endif
#endif
}