text: /* -----------------------------------------------------------------------------
   *
   * (c) Lennart Augustsson
   * (c) The GHC Team, 1998-2000
   *
   * Miscellaneous support for floating-point primitives
   *
   * ---------------------------------------------------------------------------*/
  
  #include "PosixSource.h"
  #include "Rts.h"
  
  #include "StgPrimFloat.h"
  
  #include <math.h>
  #include <float.h>
  #include <limits.h>
  
  #define IEEE_FLOATING_POINT 1
  
  #if FLT_RADIX != 2
  # error FLT_RADIX != 2 not supported
  #endif
  
  /*
   * Encoding and decoding Doubles.  Code based on the HBC code
   * (lib/fltcode.c).
   */
  
  #if IEEE_FLOATING_POINT
  #define MY_DMINEXP  ((DBL_MIN_EXP) - (DBL_MANT_DIG) - 1)
  /* DMINEXP is defined in values.h on Linux (for example) */
  #define DHIGHBIT 0x00100000
  #define DMSBIT   0x80000000
  
  #define MY_FMINEXP  ((FLT_MIN_EXP) - (FLT_MANT_DIG) - 1)
  #define FHIGHBIT 0x00800000
  #define FMSBIT   0x80000000
  #endif
  
  #if defined(WORDS_BIGENDIAN) || defined(FLOAT_WORDS_BIGENDIAN)
  #define L 1
  #define H 0
  #else
  #define L 0
  #define H 1
  #endif
  
  #define __abs(a)                (( (a) >= 0 ) ? (a) : (-(a)))
  
  /** #15271: Some large ratios are converted into double incorrectly.
    * This occurs when StgInt has 64 bits and C int has 32 bits, where wrapping
    * occurs and an incorrect signed value is passed into ldexp */
  STATIC_INLINE int
  truncExponent(I_ e)
  {
  #if INT_MAX < STG_INT_MAX
    if (RTS_UNLIKELY(e > INT_MAX))
      e = INT_MAX;
  #endif
  #if INT_MIN > STG_INT_MIN
    if (RTS_UNLIKELY(e < INT_MIN))
      e = INT_MIN;
  #endif
    return e;
  }
  
  /* Special version for words */
  StgDouble
  __word_encodeDouble (W_ j, I_ e)
  {
    StgDouble r;
  
    r = (StgDouble)j;
  
    /* Now raise to the exponent */
    if ( r != 0.0 ) /* Lennart suggests this avoids a bug in MIPS's ldexp */
      r = ldexp(r, truncExponent(e));
  
    return r;
  }
  
  /* Special version for small Integers */
  StgDouble
  __int_encodeDouble (I_ j, I_ e)
  {
    StgDouble r;
  
    r = (StgDouble)__abs(j);
  
    /* Now raise to the exponent */
    if ( r != 0.0 ) /* Lennart suggests this avoids a bug in MIPS's ldexp */
      r = ldexp(r, truncExponent(e));
  
    /* sign is encoded in the size */
    if (j < 0)
      r = -r;
  
    return r;
  }
  
  /* Special version for small Integers */
  StgFloat
  __int_encodeFloat (I_ j, I_ e)
  {
    StgFloat r;
  
    r = (StgFloat)__abs(j);
  
    /* Now raise to the exponent */
    if ( r != 0.0 ) /* Lennart suggests this avoids a bug in MIPS's ldexp */
      r = ldexp(r, truncExponent(e));
  
    /* sign is encoded in the size */
    if (j < 0)
      r = -r;
  
    return r;
  }
  
  /* Special version for small positive Integers */
  StgFloat
  __word_encodeFloat (W_ j, I_ e)
  {
    StgFloat r;
  
    r = (StgFloat)j;
  
    /* Now raise to the exponent */
    if ( r != 0.0 ) /* Lennart suggests this avoids a bug in MIPS's ldexp */
      r = ldexp(r, truncExponent(e));
  
    return r;
  }
  
  /* This only supports IEEE floating point */
  
  void
  __decodeDouble_2Int (I_ *man_sign, W_ *man_high, W_ *man_low, I_ *exp, StgDouble dbl)
  {
      /* Do some bit fiddling on IEEE */
      unsigned int low, high;             /* assuming 32 bit ints */
      int sign, iexp;
      union { double d; unsigned int i[2]; } u;   /* assuming 32 bit ints, 64 bit double */
  
      ASSERT(sizeof(unsigned int ) == 4            );
      ASSERT(sizeof(dbl          ) == 8            );
      ASSERT(sizeof(dbl          ) == SIZEOF_DOUBLE);
  
      u.d = dbl;      /* grab chunks of the double */
      low = u.i[L];
      high = u.i[H];
  
      if (low == 0 && (high & ~DMSBIT) == 0) {
          *man_low = 0;
          *man_high = 0;
          *exp = 0L;
      } else {
          iexp = ((high >> 20) & 0x7ff) + MY_DMINEXP;
          sign = high;
  
          high &= DHIGHBIT-1;
          if (iexp != MY_DMINEXP) /* don't add hidden bit to denorms */
              high |= DHIGHBIT;
          else {
              iexp++;
              /* A denorm, normalize the mantissa */
              while (! (high & DHIGHBIT)) {
                  high <<= 1;
                  if (low & DMSBIT)
                      high++;
                  low <<= 1;
                  iexp--;
              }
          }
          *exp = (I_) iexp;
          *man_low = low;
          *man_high = high;
          *man_sign = (sign < 0) ? -1 : 1;
      }
  }
  
  /* This is expected to replace uses of __decodeDouble_2Int() in the long run */
  StgInt
  __decodeDouble_Int64 (StgInt64 *const mantissa, const StgDouble dbl)
  {
  #if 0
      // We can't use this yet as-is, see ticket #9810
      if (dbl) {
          int exp = 0;
          *mantissa = (StgInt64)scalbn(frexp(dbl, &exp), DBL_MANT_DIG);
          return exp-DBL_MANT_DIG;
      } else {
          *mantissa = 0;
          return 0;
      }
  #else
      I_ man_sign = 0;
      W_ man_high = 0, man_low = 0;
      I_ exp = 0;
  
      __decodeDouble_2Int (&man_sign, &man_high, &man_low, &exp, dbl);
      ASSIGN_Int64((W_*)mantissa, ((((StgInt64)man_high << 32)
                                    | (StgInt64)man_low)
                                   * (StgInt64)man_sign));
      return exp;
  #endif
  }
  
  /* Convenient union types for checking the layout of IEEE 754 types -
     based on defs in GNU libc <ieee754.h>
  */
  
  void
  __decodeFloat_Int (I_ *man, I_ *exp, StgFloat flt)
  {
      /* Do some bit fiddling on IEEE */
      int high, sign;                 /* assuming 32 bit ints */
      union { float f; int i; } u;    /* assuming 32 bit float and int */
  
      ASSERT(sizeof(int          ) == 4            );
      ASSERT(sizeof(flt          ) == 4            );
      ASSERT(sizeof(flt          ) == SIZEOF_FLOAT );
  
      u.f = flt;      /* grab the float */
      high = u.i;
  
      if ((high & ~FMSBIT) == 0) {
          *man = 0;
          *exp = 0;
      } else {
          *exp = ((high >> 23) & 0xff) + MY_FMINEXP;
          sign = high;
  
          high &= FHIGHBIT-1;
          if (*exp != MY_FMINEXP) /* don't add hidden bit to denorms */
              high |= FHIGHBIT;
          else {
              (*exp)++;
              /* A denorm, normalize the mantissa */
              while (! (high & FHIGHBIT)) {
                  high <<= 1;
                  (*exp)--;
              }
          }
          *man = high;
          if (sign < 0)
              *man = - *man;
      }
  }
  
  