gcc/floatlib.c

/*
** libgcc support for software floating point.
** Copyright (C) 1991 by Pipeline Associates, Inc.  All rights reserved.
** Permission is granted to do *anything* you want with this file,
** commercial or otherwise, provided this message remains intact.  So there!
** I would appreciate receiving any updates/patches/changes that anyone
** makes, and am willing to be the repository for said changes (am I
** making a big mistake?).

Warning! Only single-precision is actually implemented.  This file
won't really be much use until double-precision is supported.

However, once that is done, this file might eventually become a
replacement for libgcc1.c.  It might also make possible
cross-compilation for an IEEE target machine from a non-IEEE
host such as a VAX.

If you'd like to work on completing this, please talk to rms@gnu.ai.mit.edu.


**
** Pat Wood
** Pipeline Associates, Inc.
** pipeline!phw@motown.com or
** sun!pipeline!phw or
** uunet!motown!pipeline!phw
**
** 05/01/91 -- V1.0 -- first release to gcc mailing lists
** 05/04/91 -- V1.1 -- added float and double prototypes and return values
**                  -- fixed problems with adding and subtracting zero
**                  -- fixed rounding in truncdfsf2
**                  -- fixed SWAP define and tested on 386
*/

/*
** The following are routines that replace the libgcc soft floating point
** routines that are called automatically when -msoft-float is selected.
** The support single and double precision IEEE format, with provisions
** for byte-swapped machines (tested on 386).  Some of the double-precision
** routines work at full precision, but most of the hard ones simply punt
** and call the single precision routines, producing a loss of accuracy.
** long long support is not assumed or included.
** Overall accuracy is close to IEEE (actually 68882) for single-precision
** arithmetic.  I think there may still be a 1 in 1000 chance of a bit
** being rounded the wrong way during a multiply.  I'm not fussy enough to
** bother with it, but if anyone is, knock yourself out.
**
** Efficiency has only been addressed where it was obvious that something
** would make a big difference.  Anyone who wants to do this right for
** best speed should go in and rewrite in assembler.
**
** I have tested this only on a 68030 workstation and 386/ix integrated
** in with -msoft-float.
*/

/* the following deal with IEEE single-precision numbers */
#define D_PHANTOM_BIT   0x00100000
#define EXCESS		126
#define SIGNBIT		0x80000000
#define HIDDEN		(1 << 23)
#define SIGN(fp)	((fp) & SIGNBIT)
#define EXP(fp)		(((fp) >> 23) & 0xFF)
#define MANT(fp)	(((fp) & 0x7FFFFF) | HIDDEN)
#define PACK(s,e,m)	((s) | ((e) << 23) | (m))

/* the following deal with IEEE double-precision numbers */
#define EXCESSD		1022
#define HIDDEND		(1 << 20)
#define EXPD(fp)	(((fp.l.upper) >> 20) & 0x7FF)
#define SIGND(fp)	((fp.l.upper) & SIGNBIT)
#define MANTD(fp)	(((((fp.l.upper) & 0xFFFFF) | HIDDEND) << 10) | \
				(fp.l.lower >> 22))

/* define SWAP for 386/960 reverse-byte-order brain-damaged CPUs */
union double_long
  {
    double d;
#ifdef SWAP
    struct {
      unsigned long lower;
      long upper;
    } l;
#else
    struct {
      long upper;
      unsigned long lower;
    } l;
#endif
  };

union float_long
  {
    float f;
    long l;
  };

   struct _ieee {
#ifdef SWAP
      unsigned mantissa2 : 32;
      unsigned mantissa1 : 20;
      unsigned exponent  : 11;
      unsigned sign      : 1;
#else
      unsigned exponent  : 11;
      unsigned sign      : 1;
      unsigned mantissa2 : 32;
      unsigned mantissa1 : 20;
#endif
   };

   union _doubleu {
      double d;
      struct _ieee ieee;
#ifdef SWAP
      struct {
         unsigned long lower;
         long upper;
      } l;
#else
      struct {
         long upper;
         unsigned long lower;
      } l;
#endif
   };

/* add two floats */

float
__addsf3 (float a1, float a2)
{
  register long mant1, mant2;
  register union float_long fl1, fl2;
  register int exp1, exp2;
  int sign = 0;

  fl1.f = a1;
  fl2.f = a2;

  /* check for zero args */
  if (!fl1.l)
    return (fl2.f);
  if (!fl2.l)
    return (fl1.f);

  exp1 = EXP (fl1.l);
  exp2 = EXP (fl2.l);

  if (exp1 > exp2 + 25)
    return (fl1.l);
  if (exp2 > exp1 + 25)
    return (fl2.l);

  /* do everything in excess precision so's we can round later */
  mant1 = MANT (fl1.l) << 6;
  mant2 = MANT (fl2.l) << 6;

  if (SIGN (fl1.l))
    mant1 = -mant1;
  if (SIGN (fl2.l))
    mant2 = -mant2;

  if (exp1 > exp2)
    {
      mant2 >>= exp1 - exp2;
    }
  else
    {
      mant1 >>= exp2 - exp1;
      exp1 = exp2;
    }
  mant1 += mant2;

  if (mant1 < 0)
    {
      mant1 = -mant1;
      sign = SIGNBIT;
    }
  else if (!mant1)
    return (0);

  /* normalize up */
  while (!(mant1 & 0xE0000000))
    {
      mant1 <<= 1;
      exp1--;
    }

  /* normalize down? */
  if (mant1 & (1 << 30))
    {
      mant1 >>= 1;
      exp1++;
    }

  /* round to even */
  mant1 += (mant1 & 0x40) ? 0x20 : 0x1F;

  /* normalize down? */
  if (mant1 & (1 << 30))
    {
      mant1 >>= 1;
      exp1++;
    }

  /* lose extra precision */
  mant1 >>= 6;

  /* turn off hidden bit */
  mant1 &= ~HIDDEN;

  /* pack up and go home */
  fl1.l = PACK (sign, exp1, mant1);
  return (fl1.f);
}

/* subtract two floats */

float
__subsf3 (float a1, float a2)
{
  register union float_long fl1, fl2;

  fl1.f = a1;
  fl2.f = a2;

  /* check for zero args */
  if (!fl2.l)
    return (fl1.f);
  if (!fl1.l)
    return (-fl2.f);

  /* twiddle sign bit and add */
  fl2.l ^= SIGNBIT;
  return __addsf3 (a1, fl2.f);
}

/* compare two floats */

long
__cmpsf2 (float a1, float a2)
{
  register union float_long fl1, fl2;

  fl1.f = a1;
  fl2.f = a2;

  if (SIGN (fl1.l) && SIGN (fl2.l))
    {
      fl1.l ^= SIGNBIT;
      fl2.l ^= SIGNBIT;
    }
  if (fl1.l < fl2.l)
    return (-1);
  if (fl1.l > fl2.l)
    return (1);
  return (0);
}

/* multiply two floats */

float
__mulsf3 (float a1, float a2)
{
  register union float_long fl1, fl2;
  register unsigned long result;
  register int exp;
  int sign;

  fl1.f = a1;
  fl2.f = a2;

  if (!fl1.l || !fl2.l)
    return (0);

  /* compute sign and exponent */
  sign = SIGN (fl1.l) ^ SIGN (fl2.l);
  exp = EXP (fl1.l) - EXCESS;
  exp += EXP (fl2.l);

  fl1.l = MANT (fl1.l);
  fl2.l = MANT (fl2.l);

  /* the multiply is done as one 16x16 multiply and two 16x8 multiples */
  result = (fl1.l >> 8) * (fl2.l >> 8);
  result += ((fl1.l & 0xFF) * (fl2.l >> 8)) >> 8;
  result += ((fl2.l & 0xFF) * (fl1.l >> 8)) >> 8;

  if (result & 0x80000000)
    {
      /* round */
      result += 0x80;
      result >>= 8;
    }
  else
    {
      /* round */
      result += 0x40;
      result >>= 7;
      exp--;
    }

  result &= ~HIDDEN;

  /* pack up and go home */
  fl1.l = PACK (sign, exp, result);
  return (fl1.f);
}

/* divide two floats */

float
__divsf3 (float a1, float a2)
{
  register union float_long fl1, fl2;
  register int result;
  register int mask;
  register int exp, sign;

  fl1.f = a1;
  fl2.f = a2;

  /* subtract exponents */
  exp = EXP (fl1.l) - EXP (fl2.l) + EXCESS;

  /* compute sign */
  sign = SIGN (fl1.l) ^ SIGN (fl2.l);

  /* divide by zero??? */
  if (!fl2.l)
    /* return NaN or -NaN */
    return (sign ? 0xFFFFFFFF : 0x7FFFFFFF);

  /* numerator zero??? */
  if (!fl1.l)
    return (0);

  /* now get mantissas */
  fl1.l = MANT (fl1.l);
  fl2.l = MANT (fl2.l);

  /* this assures we have 25 bits of precision in the end */
  if (fl1.l < fl2.l)
    {
      fl1.l <<= 1;
      exp--;
    }

  /* now we perform repeated subtraction of fl2.l from fl1.l */
  mask = 0x1000000;
  result = 0;
  while (mask)
    {
      if (fl1.l >= fl2.l)
	{
	  result |= mask;
	  fl1.l -= fl2.l;
	}
      fl1.l <<= 1;
      mask >>= 1;
    }

  /* round */
  result += 1;

  /* normalize down */
  exp++;
  result >>= 1;

  result &= ~HIDDEN;

  /* pack up and go home */
  fl1.l = PACK (sign, exp, result);
  return (fl1.f);
}

/* convert int to double */

double
__floatsidf (register long a1)
{
  register int sign = 0, exp = 31 + EXCESSD;
  union double_long dl;

  if (!a1)
    {
      dl.l.upper = dl.l.lower = 0;
      return (dl.d);
    }

  if (a1 < 0)
    {
      sign = SIGNBIT;
      a1 = -a1;
    }

  while (a1 < 0x1000000)
    {
      a1 <<= 4;
      exp -= 4;
    }

  while (a1 < 0x40000000)
    {
      a1 <<= 1;
      exp--;
    }

  /* pack up and go home */
  dl.l.upper = sign;
  dl.l.upper |= exp << 20;
  dl.l.upper |= (a1 >> 10) & ~HIDDEND;
  dl.l.lower = a1 << 22;

  return (dl.d);
}

/* negate a float */

float
__negsf2 (float a1)
{
  register union float_long fl1;

  fl1.f = a1;
  if (!fl1.l)
    return (0);

  fl1.l ^= SIGNBIT;
  return (fl1.f);
}

/* negate a double */

double
__negdf2 (double a1)
{
  register union double_long dl1;

  dl1.d = a1;

  if (!dl1.l.upper && !dl1.l.lower)
      return (dl1.d);

  dl1.l.upper ^= SIGNBIT;
  return (dl1.d);
}

/* convert float to double */

double
__extendsfdf2 (float a1)
{
  register union float_long fl1;
  register union double_long dl;
  register int exp;

  fl1.f = a1;

  if (!fl1.l)
    {
      dl.l.upper = dl.l.lower = 0;
      return (dl.d);
    }

  dl.l.upper = SIGN (fl1.l);
  exp = EXP (fl1.l) - EXCESS + EXCESSD;
  dl.l.upper |= exp << 20;
  dl.l.upper |= (MANT (fl1.l) & ~HIDDEN) >> 3;
  dl.l.lower = MANT (fl1.l) << 29;

  return (dl.d);
}

/* convert double to float */

float
__truncdfsf2 (double a1)
{
  register int exp;
  register long mant;
  register union float_long fl;
  register union double_long dl1;

  dl1.d = a1;

  if (!dl1.l.upper && !dl1.l.lower)
    return (0);

  exp = EXPD (dl1) - EXCESSD + EXCESS;

  /* shift double mantissa 6 bits so we can round */
  mant = MANTD (dl1) >> 6;

  /* now round and shift down */
  mant += 1;
  mant >>= 1;

  /* did the round overflow? */
  if (mant & 0xFF000000)
    {
      mant >>= 1;
      exp++;
    }

  mant &= ~HIDDEN;

  /* pack up and go home */
  fl.l = PACK (SIGND (dl1), exp, mant);
  return (fl.f);
}

/* compare two doubles */

long
__cmpdf2 (double a1, double a2)
{
  register union double_long dl1, dl2;

  dl1.d = a1;
  dl2.d = a2;

  if (SIGND (dl1) && SIGND (dl2))
    {
      dl1.l.upper ^= SIGNBIT;
      dl2.l.upper ^= SIGNBIT;
    }
  if (dl1.l.upper < dl2.l.upper)
    return (-1);
  if (dl1.l.upper > dl2.l.upper)
    return (1);
  if (dl1.l.lower < dl2.l.lower)
    return (-1);
  if (dl1.l.lower > dl2.l.lower)
    return (1);
  return (0);
}

/* convert double to int */

long
__fixdfsi (double a1)
{
  register union double_long dl1;
  register int exp;
  register long l;

  dl1.d = a1;

  if (!dl1.l.upper && !dl1.l.lower)
    return (0);

  exp = EXPD (dl1) - EXCESSD - 31;
  l = MANTD (dl1);

  if (exp > 0)
    return (0x7FFFFFFF | SIGND (dl1)); /* largest integer */

  /* shift down until exp = 0 or l = 0 */
  if (exp < 0 && exp > -32 && l)
    l >>= -exp;
  else
    return (0);

  return (SIGND (dl1) ? -l : l);
}

/* convert double to unsigned int */

unsigned
long __fixunsdfsi (double a1)
{
  register union double_long dl1;
  register int exp;
  register unsigned long l;

  dl1.d = a1;

  if (!dl1.l.upper && !dl1.l.lower)
    return (0);

  exp = EXPD (dl1) - EXCESSD - 32;
  l = (((((dl1.l.upper) & 0xFFFFF) | HIDDEND) << 11) | (dl1.l.lower >> 21));

  if (exp > 0)
    return (0xFFFFFFFF);	/* largest integer */

  /* shift down until exp = 0 or l = 0 */
  if (exp < 0 && exp > -32 && l)
    l >>= -exp;
  else
    return (0);

  return (l);
}

/* For now, the hard double-precision routines simply
   punt and do it in single */
/* addtwo doubles */

double
__adddf3 (double a1, double a2)
{
  return ((float) a1 + (float) a2);
}

/* subtract two doubles */

double
__subdf3 (double a1, double a2)
{
  return ((float) a1 - (float) a2);
}

/* multiply two doubles */

double
__muldf3 (double a1, double a2)
{
  return ((float) a1 * (float) a2);
}

/*
 *
 * Name:   Barrett Richardson
 * E-mail: barrett@iglou.com
 * When:   Thu Dec 15 10:31:11 EST 1994
 *
 *    callable function:
 *
 *       double __divdf3(double a1, double a2);
 *
 *       Does software divide of a1 / a2.
 *
 *       Based largely on __divsf3() in floatlib.c in the gcc
 *       distribution.
 *
 *    Purpose: To be used in conjunction with the -msoft-float
 *             option of gcc. You should be able to tack it to the
 *             end of floatlib.c included in the gcc distribution,
 *             and delete the __divdf3() already there which just 
 *             calls the single precision function (or may just
 *             use the floating point processor with some configurations).
 *
 *   You may use this code for whatever your heart desires.
 */




/*
 * Compare the the mantissas of two doubles.
 * Each mantissa is in two longs.
 * 
 *   return      1   if x1's mantissa is greater than x2's
 *              -1   if x1's mantissa is less than x2's
 *               0   if the two mantissa's are equal.
 *
 *   The Mantissas won't fit into a 4 byte word, so they are
 *   broken up into two parts.
 *
 *   This function is used internally by __divdf3()
 */

int
__dcmp (long x1m1, long x1m2, long x2m1, long x2m2)
{
   if (x1m1 > x2m1)
      return 1;

   if (x1m1 < x2m1)
      return -1;

 /*  If the first word in the two mantissas were equal check the second word */

   if (x1m2 > x2m2)
      return 1;

   if (x1m2 < x2m2)
      return -1;

   return 0;
}


/* divide two doubles */

double
__divdf3 (double a1, double a2)
{

   int  sign,
        exponent,
        bit_bucket;

   register unsigned long mantissa1,
                          mantissa2,
                          x1m1,
                          x1m2,
                          x2m1,
                          x2m2,
                          mask;

   union _doubleu x1,
                  x2,
                  result;


   x1.d = a1;
   x2.d = a2;

   exponent = x1.ieee.exponent - x2.ieee.exponent + EXCESSD;

   sign = x1.ieee.sign ^ x2.ieee.sign;

   x2.ieee.sign = 0;  /* don't want the sign bit to affect any zero */
                      /* comparisons when checking for zero divide  */

   if (!x2.l.lower && !x2.l.upper) { /* check for zero divide */
      result.l.lower = 0x0;
      if (sign)
         result.l.upper = 0xFFF00000;   /* negative infinity */
      else
         result.l.upper = 0x7FF00000;   /* positive infinity */
      return result.d;
   }

   if (!x1.l.upper && !x1.l.lower)  /* check for 0.0 numerator */
      return (0.0);

   x1m1 = x1.ieee.mantissa1 | D_PHANTOM_BIT;  /* turn on phantom bit */
   x1m2 = x1.ieee.mantissa2;

   x2m1 = x2.ieee.mantissa1 | D_PHANTOM_BIT;  /* turn on phantom bit */
   x2m2 = x2.ieee.mantissa2;

   if (__dcmp(x1m1,x1m2,x2m1,x2m2) < 0) {

   /* if x1's mantissa is less than x2's shift it left one and decrement */
   /* the exponent to accomodate the change in the mantissa              */

      x1m1 <<= 1;               /*                          */
      bit_bucket = x1m2 >> 31;  /*  Shift mantissa left one */
      x1m1 |= bit_bucket;       /*                          */
      x1m2 <<= 1;               /*                          */

      exponent--;
   }


   mantissa1 = 0;
   mantissa2 = 0;


  /* Get the first part of the results mantissa using successive */
  /* subtraction.                                                */

   mask = 0x00200000;
   while (mask) {

      if (__dcmp(x1m1,x1m2,x2m1,x2m2) >= 0) {

     /* subtract x2's mantissa from x1's */

         mantissa1 |= mask;   /* turn on a bit in the result */

         if (x2m2 > x1m2)
            x1m1--;
         x1m2 -= x2m2; 
         x1m1 -= x2m1;
      }

      x1m1 <<= 1;               /*                          */
      bit_bucket = x1m2 >> 31;  /*  Shift mantissa left one */
      x1m1 |= bit_bucket;       /*                          */
      x1m2 <<= 1;               /*                          */

      mask >>= 1;
   }

  /* Get the second part of the results mantissa using successive */
  /* subtraction.                                                 */

   mask = 0x80000000;
   while (mask) {

      if (__dcmp(x1m1,x1m2,x2m1,x2m2) >= 0) {

     /* subtract x2's mantissa from x1's */

         mantissa2 |= mask;   /* turn on a bit in the result */

         if (x2m2 > x1m2)
            x1m1--;
         x1m2 -= x2m2; 
         x1m1 -= x2m1;
      }
      x1m1 <<= 1;               /*                          */
      bit_bucket = x1m2 >> 31;  /*  Shift mantissa left one */
      x1m1 |= bit_bucket;       /*                          */
      x1m2 <<= 1;               /*                          */

      mask >>= 1;
   }

  /* round up by adding 1 to mantissa */

   if (mantissa2 == 0xFFFFFFFF) {  /* check for over flow */

   /* spill if overflow */

      mantissa2 = 0;
      mantissa1++;
   }
   else
      mantissa2++;

   exponent++;   /* increment exponent (mantissa must be shifted right */
                 /* also)                                              */

 /* shift mantissa right one and assume a phantom bit (which really gives */
 /* 53 bits of precision in the mantissa)                                 */

   mantissa2 >>= 1;
   bit_bucket = mantissa1 & 1;
   mantissa2 |= (bit_bucket << 31);
   mantissa1 >>= 1;

  /* put all the info into the result */

   result.ieee.exponent  = exponent;
   result.ieee.sign      = sign;
   result.ieee.mantissa1 = mantissa1;
   result.ieee.mantissa2 = mantissa2;


   return result.d;
}