path: root/trionan.c

/*************************************************************************
 *
 * $Id$
 *
 * Copyright (C) 2001 Bjorn Reese <breese@users.sourceforge.net>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR IMPLIED
 * WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED WARRANTIES OF
 * MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE AUTHORS AND
 * CONTRIBUTORS ACCEPT NO RESPONSIBILITY IN ANY CONCEIVABLE MANNER.
 *
 ************************************************************************
 *
 * Functions to handle special quantities in floating-point numbers
 * (that is, NaNs and infinity). They provide the capability to detect
 * and fabricate special quantities.
 *
 * Although written to be as portable as possible, it can never be
 * guaranteed to work on all platforms, as not all hardware supports
 * special quantities.
 *
 * The approach used here (approximately) is to:
 *
 *   1. Use C99 functionality when available.
 *   2. Use IEEE 754 bit-patterns if possible.
 *   3. Use platform-specific techniques.
 *
 * This program has been tested on the following platforms (in
 * alphabetic order)
 *
 *   OS              CPU          Compiler
 * -------------------------------------------------
 *   AIX 4.1.4       PowerPC      gcc
 *   Darwin 1.3.7    PowerPC      gcc
 *   FreeBSD 2.2     x86          gcc
 *   FreeBSD 3.3     x86          gcc
 *   FreeBSD 4.3     x86          gcc
 *   FreeBSD 4.3     Alpha        gcc
 *   HP-UX 10.20     PA-RISC      gcc
 *   HP-UX 10.20     PA-RISC      HP C++
 *   IRIX 6.5        MIPS         MIPSpro C
 *   Linux 2.2       x86          gcc
 *   Linux 2.2       Alpha        gcc
 *   Linux 2.4       IA64         gcc
 *   Linux 2.4       StrongARM    gcc
 *   NetBSD 1.4      x86          gcc
 *   NetBSD 1.4      StrongARM    gcc
 *   NetBSD 1.5      Alpha        gcc
 *   OpenVMS 7.1     Alpha        DEC C 6.0
 *   RISC OS 4       StrongARM    Norcroft C
 *   Solaris 2.5.1   x86          gcc
 *   Solaris 2.5.1   Sparc        gcc
 *   Solaris 2.6     Sparc        WorkShop 4.2
 *   Solaris 8       Sparc        Forte C 6
 *   Tru64 4.0D      Alpha        gcc
 *   Tru64 5.1       Alpha        gcc
 *   WinNT           x86          MSVC 5.0 & 6.0
 *
 ************************************************************************/

static const char rcsid[] = "@(#)$Id$";

/*************************************************************************
 * Include files
 */
#include "triodef.h"
#include "trionan.h"

#include <math.h>
#include <string.h>
#include <limits.h>
#include <float.h>
#if defined(TRIO_PLATFORM_UNIX)
# include <signal.h>
#endif
#if defined(TRIO_COMPILER_DECC)
# include <fp_class.h>
#endif
#include <assert.h>

#if defined(TRIO_DOCUMENTATION)
# include "doc/doc_nan.h"
#endif
/** @addtogroup SpecialQuantities
    @{
*/

/*************************************************************************
 * Definitions
 */

/* We must enable IEEE floating-point on Alpha */
#if defined(__alpha) && !defined(_IEEE_FP)
# if defined(TRIO_COMPILER_DECC)
#  if defined(TRIO_PLATFORM_VMS)
#   error "Must be compiled with option /IEEE_MODE=UNDERFLOW_TO_ZERO/FLOAT=IEEE"
#  else
#   error "Must be compiled with option -ieee"
#  endif
# elif defined(TRIO_COMPILER_GCC) && (defined(__osf__) || defined(__linux__))
#  error "Must be compiled with option -mieee"
# endif
#endif /* __alpha && ! _IEEE_FP */

/*
 * In ANSI/IEEE 754-1985 64-bits double format numbers have the
 * following properties (amoungst others)
 *
 *   o FLT_RADIX == 2: binary encoding
 *   o DBL_MAX_EXP == 1024: 11 bits exponent, where one bit is used
 *     to indicate special numbers (e.g. NaN and Infinity), so the
 *     maximum exponent is 10 bits wide (2^10 == 1024).
 *   o DBL_MANT_DIG == 53: The mantissa is 52 bits wide, but because
 *     numbers are normalized the initial binary 1 is represented
 *     implicitly (the so-called "hidden bit"), which leaves us with
 *     the ability to represent 53 bits wide mantissa.
 */
#if (FLT_RADIX == 2) && (DBL_MAX_EXP == 1024) && (DBL_MANT_DIG == 53)
# define USE_IEEE_754
#endif


/*************************************************************************
 * Data
 */

#if defined(USE_IEEE_754)

/*
 * Endian-agnostic indexing macro.
 *
 * The value of internalEndianMagic, when converted into a 64-bit
 * integer, becomes 0x0706050403020100 (we could have used a 64-bit
 * integer value instead of a double, but not all platforms supports
 * that type). The value is automatically encoded with the correct
 * endianess by the compiler, which means that we can support any
 * kind of endianess. The individual bytes are then used as an index
 * for the IEEE 754 bit-patterns and masks.
 */
#define TRIO_DOUBLE_INDEX(x) (((unsigned char *)&internalEndianMagic)[7-(x)])

static TRIO_CONST double internalEndianMagic = 7.949928895127363e-275;

/* Mask for the sign */
static TRIO_CONST unsigned char ieee_754_sign_mask[] = {
  0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
};

/* Mask for the exponent */
static TRIO_CONST unsigned char ieee_754_exponent_mask[] = {
  0x7F, 0xF0, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
};

/* Mask for the mantissa */
static TRIO_CONST unsigned char ieee_754_mantissa_mask[] = {
  0x00, 0x0F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
};

/* Bit-pattern for negative zero */
static TRIO_CONST unsigned char ieee_754_negzero_array[] = {
  0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
};

/* Bit-pattern for infinity */
static TRIO_CONST unsigned char ieee_754_infinity_array[] = {
  0x7F, 0xF0, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
};

/* Bit-pattern for quiet NaN */
static TRIO_CONST unsigned char ieee_754_qnan_array[] = {
  0x7F, 0xF8, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
};


/*************************************************************************
 * Functions
 */

/*
 * trio_make_double
 */
TRIO_PRIVATE double
trio_make_double(TRIO_CONST unsigned char *values)
{
  TRIO_VOLATILE double result;
  int i;

  for (i = 0; i < (int)sizeof(double); i++) {
    ((TRIO_VOLATILE unsigned char *)&result)[TRIO_DOUBLE_INDEX(i)] = values[i];
  }
  return result;
}

/*
 * trio_examine_double
 */
TRIO_PRIVATE int
trio_is_special_quantity(double number,
			 int *has_mantissa)
{
  unsigned int i;
  unsigned char current;
  int is_special_quantity = (1 == 1);

  *has_mantissa = 0;

  for (i = 0; i < (unsigned int)sizeof(double); i++) {
    current = ((unsigned char *)&number)[TRIO_DOUBLE_INDEX(i)];
    is_special_quantity
      &= ((current & ieee_754_exponent_mask[i]) == ieee_754_exponent_mask[i]);
    *has_mantissa |= (current & ieee_754_mantissa_mask[i]);
  }
  return is_special_quantity;
}

/**
   Get the sign value

   @return 1 for negative, 0 for positive
*/
TRIO_PUBLIC int
trio_get_sign(double number) 
{
  unsigned int i;
  unsigned char current;
  int sign = (1 == 1);

  for (i = 0; i < (unsigned int)sizeof(double); i++) {
    current = ((unsigned char *)&number)[TRIO_DOUBLE_INDEX(i)];
    sign
      &= ((current & ieee_754_sign_mask[i]) == ieee_754_sign_mask[i]);
  }
  return sign;
}

/**
   Generate negative zero

   @return Floating-point representation of negative zero.
*/
TRIO_PUBLIC double
trio_nzero(void) 
{
  return trio_make_double(ieee_754_negzero_array);
}

#endif /* USE_IEEE_754 */


/**
   Generate positive infinity.

   @return Floating-point representation of positive infinity.
*/
TRIO_PUBLIC double
trio_pinf(void)
{
  /* Cache the result */
  static double result = 0.0;

  if (result == 0.0) {
    
#if defined(INFINITY) && defined(__STDC_IEC_559__)
    result = (double)INFINITY;

#elif defined(USE_IEEE_754)
    result = trio_make_double(ieee_754_infinity_array);

#else
    /*
     * If HUGE_VAL is different from DBL_MAX, then HUGE_VAL is used
     * as infinity. Otherwise we have to resort to an overflow
     * operation to generate infinity.
     */
# if defined(TRIO_PLATFORM_UNIX)
    void (*signal_handler)(int) = signal(SIGFPE, SIG_IGN);
# endif

    result = HUGE_VAL;
    if (HUGE_VAL == DBL_MAX) {
      /* Force overflow */
      result += HUGE_VAL;
    }
    
# if defined(TRIO_PLATFORM_UNIX)
    signal(SIGFPE, signal_handler);
# endif

#endif
  }
  return result;
}

/**
   Generate negative infinity.

   @return Floating-point value of negative infinity.
*/
TRIO_PUBLIC double
trio_ninf(void)
{
  static double result = 0.0;

  if (result == 0.0) {
    /*
     * Negative infinity is calculated by negating positive infinity,
     * which can be done because it is legal to do calculations on
     * infinity (for example,  1 / infinity == 0).
     */
    result = -trio_pinf();
  }
  return result;
}

/**
   Generate NaN.

   @return Floating-point representation of NaN.
*/
TRIO_PUBLIC double
trio_nan(void)
{
  /* Cache the result */
  static double result = 0.0;

  if (result == 0.0) {
    
#if defined(TRIO_COMPILER_SUPPORTS_C99)
    result = nan(NULL);

#elif defined(NAN) && defined(__STDC_IEC_559__)
    result = (double)NAN;
  
#elif defined(USE_IEEE_754)
    result = trio_make_double(ieee_754_qnan_array);

#else
    /*
     * There are several ways to generate NaN. The one used here is
     * to divide infinity by infinity. I would have preferred to add
     * negative infinity to positive infinity, but that yields wrong
     * result (infinity) on FreeBSD.
     *
     * This may fail if the hardware does not support NaN, or if
     * the Invalid Operation floating-point exception is unmasked.
     */
# if defined(TRIO_PLATFORM_UNIX)
    void (*signal_handler)(int) = signal(SIGFPE, SIG_IGN);
# endif
    
    result = trio_pinf() / trio_pinf();
    
# if defined(TRIO_PLATFORM_UNIX)
    signal(SIGFPE, signal_handler);
# endif
    
#endif
  }
  return result;
}

/**
   Check for NaN.

   @param number An arbitrary floating-point number.
   @return Boolean value indicating whether or not the number is a NaN.
*/
TRIO_PUBLIC int
trio_isnan(TRIO_VOLATILE double number)
{
#if defined(isnan) || defined(TRIO_COMPILER_SUPPORTS_UNIX95)
  /*
   * C99 defines isnan() as a macro. UNIX95 defines isnan() as a
   * function. This function was already present in XPG4, but this
   * is a bit tricky to detect with compiler defines, so we choose
   * the conservative approach and only use it for UNIX95.
   */
  return isnan(number);
  
#elif defined(TRIO_COMPILER_MSVC)
  /*
   * MSC has an _isnan() function
   */
  return _isnan(number);

#elif defined(USE_IEEE_754)
  /*
   * Examine IEEE 754 bit-pattern. A NaN must have a special exponent
   * pattern, and a non-empty mantissa.
   */
  int has_mantissa;
  int is_special_quantity;

  is_special_quantity = trio_is_special_quantity(number, &has_mantissa);
  
  return (is_special_quantity && has_mantissa);
  
#else
  /*
   * Fallback solution
   */
  int status;
  double integral, fraction;
  
# if defined(TRIO_PLATFORM_UNIX)
  void (*signal_handler)(int) = signal(SIGFPE, SIG_IGN);
# endif
  
  status = (/*
	     * NaN is the only number which does not compare to itself
	     */
	    (number != number) ||
	    /*
	     * Fallback solution if NaN compares to NaN
	     */
	    ((number != 0.0) &&
	     (fraction = modf(number, &integral),
	      integral == fraction)));
  
# if defined(TRIO_PLATFORM_UNIX)
  signal(SIGFPE, signal_handler);
# endif
  
  return status;
  
#endif
}

/**
   Check for infinity.

   @param number An arbitrary floating-point number.
   @return 1 if positive infinity, -1 if negative infinity, 0 otherwise.
*/
TRIO_PUBLIC int
trio_isinf(TRIO_VOLATILE double number)
{
#if defined(TRIO_COMPILER_DECC)
  /*
   * DECC has an isinf() macro, but it works differently than that
   * of C99, so we use the fp_class() function instead.
   */
  return ((fp_class(number) == FP_POS_INF)
	  ? 1
	  : ((fp_class(number) == FP_NEG_INF) ? -1 : 0));
  
#elif defined(isinf)
  /*
   * C99 defines isinf() as a macro.
   */
  return isinf(number);
  
#elif defined(TRIO_COMPILER_MSVC)
  /*
   * MSVC has an _fpclass() function that can be used to detect infinity.
   */
  return ((_fpclass(number) == _FPCLASS_PINF)
	  ? 1
	  : ((_fpclass(number) == _FPCLASS_NINF) ? -1 : 0));

#elif defined(USE_IEEE_754)
  /*
   * Examine IEEE 754 bit-pattern. Infinity must have a special exponent
   * pattern, and an empty mantissa.
   */
  int has_mantissa;
  int is_special_quantity;

  is_special_quantity = trio_is_special_quantity(number, &has_mantissa);
  
  return (is_special_quantity && !has_mantissa)
    ? ((number < 0.0) ? -1 : 1)
    : 0;

#else
  /*
   * Fallback solution.
   */
  int status;
  
# if defined(TRIO_PLATFORM_UNIX)
  void (*signal_handler)(int) = signal(SIGFPE, SIG_IGN);
# endif
  
  double infinity = trio_pinf();
  
  status = ((number == infinity)
	    ? 1
	    : ((number == -infinity) ? -1 : 0));
  
# if defined(TRIO_PLATFORM_UNIX)
  signal(SIGFPE, signal_handler);
# endif
  
  return status;
  
#endif
}

/** @} SpecialQuantities */

/*************************************************************************
 * For test purposes.
 *
 * Add the following compiler option to include this test code.
 *
 *  Unix : -DSTANDALONE
 *  VMS  : /DEFINE=(STANDALONE)
 */
#if defined(STANDALONE)
# include <stdio.h>

int main(void)
{
  double my_nan;
  double my_pinf;
  double my_ninf;
# if defined(TRIO_PLATFORM_UNIX)
  void (*signal_handler)(int);
# endif

  my_nan = trio_nan();
  my_pinf = trio_pinf();
  my_ninf = trio_ninf();

  printf("NaN : %4g 0x%02x%02x%02x%02x%02x%02x%02x%02x (%2d, %2d)\n",
	 my_nan,
	 ((unsigned char *)&my_nan)[0],
	 ((unsigned char *)&my_nan)[1],
	 ((unsigned char *)&my_nan)[2],
	 ((unsigned char *)&my_nan)[3],
	 ((unsigned char *)&my_nan)[4],
	 ((unsigned char *)&my_nan)[5],
	 ((unsigned char *)&my_nan)[6],
	 ((unsigned char *)&my_nan)[7],
	 trio_isnan(my_nan), trio_isinf(my_nan));
  printf("PInf: %4g 0x%02x%02x%02x%02x%02x%02x%02x%02x (%2d, %2d)\n",
	 my_pinf,
	 ((unsigned char *)&my_pinf)[0],
	 ((unsigned char *)&my_pinf)[1],
	 ((unsigned char *)&my_pinf)[2],
	 ((unsigned char *)&my_pinf)[3],
	 ((unsigned char *)&my_pinf)[4],
	 ((unsigned char *)&my_pinf)[5],
	 ((unsigned char *)&my_pinf)[6],
	 ((unsigned char *)&my_pinf)[7],
	 trio_isnan(my_pinf), trio_isinf(my_pinf));
  printf("NInf: %4g 0x%02x%02x%02x%02x%02x%02x%02x%02x (%2d, %2d)\n",
	 my_ninf,
	 ((unsigned char *)&my_ninf)[0],
	 ((unsigned char *)&my_ninf)[1],
	 ((unsigned char *)&my_ninf)[2],
	 ((unsigned char *)&my_ninf)[3],
	 ((unsigned char *)&my_ninf)[4],
	 ((unsigned char *)&my_ninf)[5],
	 ((unsigned char *)&my_ninf)[6],
	 ((unsigned char *)&my_ninf)[7],
	 trio_isnan(my_ninf), trio_isinf(my_ninf));
  
# if defined(TRIO_PLATFORM_UNIX)
  signal_handler = signal(SIGFPE, SIG_IGN);
# endif
  
  my_pinf = DBL_MAX + DBL_MAX;
  my_ninf = -my_pinf;
  my_nan = my_pinf / my_pinf;

# if defined(TRIO_PLATFORM_UNIX)
  signal(SIGFPE, signal_handler);
# endif
  
  printf("NaN : %4g 0x%02x%02x%02x%02x%02x%02x%02x%02x (%2d, %2d)\n",
	 my_nan,
	 ((unsigned char *)&my_nan)[0],
	 ((unsigned char *)&my_nan)[1],
	 ((unsigned char *)&my_nan)[2],
	 ((unsigned char *)&my_nan)[3],
	 ((unsigned char *)&my_nan)[4],
	 ((unsigned char *)&my_nan)[5],
	 ((unsigned char *)&my_nan)[6],
	 ((unsigned char *)&my_nan)[7],
	 trio_isnan(my_nan), trio_isinf(my_nan));
  printf("PInf: %4g 0x%02x%02x%02x%02x%02x%02x%02x%02x (%2d, %2d)\n",
	 my_pinf,
	 ((unsigned char *)&my_pinf)[0],
	 ((unsigned char *)&my_pinf)[1],
	 ((unsigned char *)&my_pinf)[2],
	 ((unsigned char *)&my_pinf)[3],
	 ((unsigned char *)&my_pinf)[4],
	 ((unsigned char *)&my_pinf)[5],
	 ((unsigned char *)&my_pinf)[6],
	 ((unsigned char *)&my_pinf)[7],
	 trio_isnan(my_pinf), trio_isinf(my_pinf));
  printf("NInf: %4g 0x%02x%02x%02x%02x%02x%02x%02x%02x (%2d, %2d)\n",
	 my_ninf,
	 ((unsigned char *)&my_ninf)[0],
	 ((unsigned char *)&my_ninf)[1],
	 ((unsigned char *)&my_ninf)[2],
	 ((unsigned char *)&my_ninf)[3],
	 ((unsigned char *)&my_ninf)[4],
	 ((unsigned char *)&my_ninf)[5],
	 ((unsigned char *)&my_ninf)[6],
	 ((unsigned char *)&my_ninf)[7],
	 trio_isnan(my_ninf), trio_isinf(my_ninf));
	 
  return 0;
}
#endif