g_generic_x87.c

The Valgrind distribution has multiple tools. The most popular is the memory checking tool (called M

   /* If the exponent is 7FFF, this is either an Infinity, a SNaN or
      QNaN, as determined by examining bits 62:0, thus:
          0  ... 0    Inf
          0X ... X    SNaN
          1X ... X    QNaN
      where at least one of the Xs is not zero.
   */
   if (bexp == 0x7FFF) {
      isInf = toBool(
                 (f80[7] & 0x7F) == 0 
                 && f80[6] == 0 && f80[5] == 0 && f80[4] == 0 
                 && f80[3] == 0 && f80[2] == 0 && f80[1] == 0 
                 && f80[0] == 0
              );
      if (isInf) {
         if (0 == (f80[7] & 0x80))
            goto wierd_NaN;
         /* Produce an appropriately signed infinity:
            S 1--1 (11)  0--0 (52)
         */
         f64[7] = toUChar((sign << 7) | 0x7F);
         f64[6] = 0xF0;
         f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0;
         return;
      }
      /* So it's either a QNaN or SNaN.  Distinguish by considering
         bit 62.  Note, this destroys all the trailing bits
         (identity?) of the NaN.  IEEE754 doesn't require preserving
         these (it only requires that there be one QNaN value and one
         SNaN value), but x87 does seem to have some ability to
         preserve them.  Anyway, here, the NaN's identity is
         destroyed.  Could be improved. */
      if (f80[8] & 0x40) {
         /* QNaN.  Make a QNaN:
            S 1--1 (11)  1  1--1 (51) 
         */
         f64[7] = toUChar((sign << 7) | 0x7F);
         f64[6] = 0xFF;
         f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0xFF;
      } else {
         /* SNaN.  Make a SNaN:
            S 1--1 (11)  0  1--1 (51) 
         */
         f64[7] = toUChar((sign << 7) | 0x7F);
         f64[6] = 0xF7;
         f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0xFF;
      }
      return;
   }

   /* If it's not a Zero, NaN or Inf, and the integer part (bit 62) is
      zero, the x87 FPU appears to consider the number denormalised
      and converts it to a QNaN. */
   if (0 == (f80[7] & 0x80)) {
      wierd_NaN:
      /* Strange hardware QNaN:
         S 1--1 (11)  1  0--0 (51) 
      */
      /* On a PIII, these QNaNs always appear with sign==1.  I have
         no idea why. */
      f64[7] = (1 /*sign*/ << 7) | 0x7F;
      f64[6] = 0xF8;
      f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0;
      return;
   }

   /* It's not a zero, denormal, infinity or nan.  So it must be a 
      normalised number.  Rebias the exponent and consider. */
   bexp -= (16383 - 1023);
   if (bexp >= 0x7FF) {
      /* It's too big for a double.  Construct an infinity. */
      f64[7] = toUChar((sign << 7) | 0x7F);
      f64[6] = 0xF0;
      f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0;
      return;
   }

   if (bexp <= 0) {
      /* It's too small for a normalised double.  First construct a
         zero and then see if it can be improved into a denormal.  */
      f64[7] = toUChar(sign << 7);
      f64[6] = f64[5] = f64[4] = f64[3] = f64[2] = f64[1] = f64[0] = 0;

      if (bexp < -52)
         /* Too small even for a denormal. */
         return;

      /* Ok, let's make a denormal.  Note, this is SLOW. */
      /* Copy bits 63, 62, 61, etc of the src mantissa into the dst, 
         indexes 52+bexp, 51+bexp, etc, until k+bexp < 0. */
      /* bexp is in range -52 .. 0 inclusive */
      for (i = 63; i >= 0; i--) {
         j = i - 12 + bexp;
         if (j < 0) break;
         /* We shouldn't really call vassert from generated code. */
         vassert(j >= 0 && j < 52);
         write_bit_array ( f64,
                           j,
                           read_bit_array ( f80, i ) );
      }
      /* and now we might have to round ... */
      if (read_bit_array(f80, 10+1 - bexp) == 1) 
         goto do_rounding;

      return;
   }

   /* Ok, it's a normalised number which is representable as a double.
      Copy the exponent and mantissa into place. */
   /*
   for (i = 0; i < 52; i++)
      write_bit_array ( f64,
                        i,
                        read_bit_array ( f80, i+11 ) );
   */
   f64[0] = toUChar( (f80[1] >> 3) | (f80[2] << 5) );
   f64[1] = toUChar( (f80[2] >> 3) | (f80[3] << 5) );
   f64[2] = toUChar( (f80[3] >> 3) | (f80[4] << 5) );
   f64[3] = toUChar( (f80[4] >> 3) | (f80[5] << 5) );
   f64[4] = toUChar( (f80[5] >> 3) | (f80[6] << 5) );
   f64[5] = toUChar( (f80[6] >> 3) | (f80[7] << 5) );

   f64[6] = toUChar( ((bexp << 4) & 0xF0) | ((f80[7] >> 3) & 0x0F) );

   f64[7] = toUChar( (sign << 7) | ((bexp >> 4) & 0x7F) );

   /* Now consider any rounding that needs to happen as a result of
      truncating the mantissa. */
   if (f80[1] & 4) /* read_bit_array(f80, 10) == 1) */ {

      /* If the bottom bits of f80 are "100 0000 0000", then the
         infinitely precise value is deemed to be mid-way between the
         two closest representable values.  Since we're doing
         round-to-nearest (the default mode), in that case it is the
         bit immediately above which indicates whether we should round
         upwards or not -- if 0, we don't.  All that is encapsulated
         in the following simple test. */
      if ((f80[1] & 0xF) == 4/*0100b*/ && f80[0] == 0)
         return;

      do_rounding:
      /* Round upwards.  This is a kludge.  Once in every 2^24
         roundings (statistically) the bottom three bytes are all 0xFF
         and so we don't round at all.  Could be improved. */
      if (f64[0] != 0xFF) { 
         f64[0]++; 
      }
      else 
      if (f64[0] == 0xFF && f64[1] != 0xFF) {
         f64[0] = 0;
         f64[1]++;
      }
      else      
      if (f64[0] == 0xFF && f64[1] == 0xFF && f64[2] != 0xFF) {
         f64[0] = 0;
         f64[1] = 0;
         f64[2]++;
      }
      /* else we don't round, but we should. */
   }
}


/* CALLED FROM GENERATED CODE: CLEAN HELPER */
/* Extract the signed significand or exponent component as per
   fxtract.  Arg and result are doubles travelling under the guise of
   ULongs.  Returns significand when getExp is zero and exponent
   otherwise. */
ULong x86amd64g_calculate_FXTRACT ( ULong arg, HWord getExp )
{
   ULong  uSig, uExp;
   /* Long   sSig; */
   Int    sExp, i;
   UInt   sign, expExp;

   /*
    S  7FF    0------0   infinity
    S  7FF    0X-----X   snan
    S  7FF    1X-----X   qnan
   */
   const ULong posInf  = 0x7FF0000000000000ULL;
   const ULong negInf  = 0xFFF0000000000000ULL;
   const ULong nanMask = 0x7FF0000000000000ULL;
   const ULong qNan    = 0x7FF8000000000000ULL;
   const ULong posZero = 0x0000000000000000ULL;
   const ULong negZero = 0x8000000000000000ULL;
   const ULong bit51   = 1ULL << 51;
   const ULong bit52   = 1ULL << 52;
   const ULong sigMask = bit52 - 1;

   /* Mimic PIII behaviour for special cases. */
   if (arg == posInf)
      return getExp ? posInf : posInf;
   if (arg == negInf)
      return getExp ? posInf : negInf;
   if ((arg & nanMask) == nanMask)
      return qNan;
   if (arg == posZero)
      return getExp ? negInf : posZero;
   if (arg == negZero)
      return getExp ? negInf : negZero;

   /* Split into sign, exponent and significand. */
   sign = ((UInt)(arg >> 63)) & 1;

   /* Mask off exponent & sign. uSig is in range 0 .. 2^52-1. */
   uSig = arg & sigMask;

   /* Get the exponent. */
   sExp = ((Int)(arg >> 52)) & 0x7FF;

   /* Deal with denormals: if the exponent is zero, then the
      significand cannot possibly be zero (negZero/posZero are handled
      above).  Shift the significand left until bit 51 of it becomes
      1, and decrease the exponent accordingly.
   */
   if (sExp == 0) {
      for (i = 0; i < 52; i++) {
         if (uSig & bit51)
            break;
         uSig <<= 1;
         sExp--;
      }
      uSig <<= 1;
   } else {
      /* Add the implied leading-1 in the significand. */
      uSig |= bit52;
   }

   /* Roll in the sign. */
   /* sSig = uSig; */
   /* if (sign) sSig =- sSig; */

   /* Convert sig into a double.  This should be an exact conversion.
      Then divide by 2^52, which should give a value in the range 1.0
      to 2.0-epsilon, at least for normalised args. */
   /* dSig = (Double)sSig; */
   /* dSig /= 67108864.0;  */ /* 2^26 */
   /* dSig /= 67108864.0;  */ /* 2^26 */
   uSig &= sigMask;
   uSig |= 0x3FF0000000000000ULL;
   if (sign)
      uSig ^= negZero;

   /* Convert exp into a double.  Also an exact conversion. */
   /* dExp = (Double)(sExp - 1023); */
   sExp -= 1023;
   if (sExp == 0) {
      uExp = 0;
   } else {
      uExp   = sExp < 0 ? -sExp : sExp;
      expExp = 0x3FF +52;
      /* 1 <= uExp <= 1074 */
      /* Skip first 42 iterations of normalisation loop as we know they
         will always happen */
      uExp <<= 42;
      expExp -= 42;
      for (i = 0; i < 52-42; i++) {
         if (uExp & bit52)
            break;
         uExp <<= 1;
         expExp--;
      }
      uExp &= sigMask;
      uExp |= ((ULong)expExp) << 52;
      if (sExp < 0) uExp ^= negZero;
   }

   return getExp ? uExp : uSig;
}


/*---------------------------------------------------------------*/
/*--- end                       guest-generic/h_generic_x87.c ---*/
/*---------------------------------------------------------------*/