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op-1.h

/*
 * Basic one-word fraction declaration and manipulation.
 */

#define _FP_FRAC_DECL_1(X)    _FP_W_TYPE X##_f
#define _FP_FRAC_COPY_1(D,S)  (D##_f = S##_f)
#define _FP_FRAC_SET_1(X,I)   (X##_f = I)
#define _FP_FRAC_HIGH_1(X)    (X##_f)
#define _FP_FRAC_LOW_1(X)     (X##_f)
#define _FP_FRAC_WORD_1(X,w)  (X##_f)

#define _FP_FRAC_ADDI_1(X,I)  (X##_f += I)
#define _FP_FRAC_SLL_1(X,N)               \
  do {                                    \
    if (__builtin_constant_p(N) && (N) == 1)    \
      X##_f += X##_f;                     \
    else                            \
      X##_f <<= (N);                      \
  } while (0)
#define _FP_FRAC_SRL_1(X,N)   (X##_f >>= N)

/* Right shift with sticky-lsb.  */
#define _FP_FRAC_SRS_1(X,N,sz)      __FP_FRAC_SRS_1(X##_f, N, sz)

#define __FP_FRAC_SRS_1(X,N,sz)                                   \
   (X = (X >> (N) | (__builtin_constant_p(N) && (N) == 1          \
                 ? X & 1 : (X << (_FP_W_TYPE_SIZE - (N))) != 0)))

#define _FP_FRAC_ADD_1(R,X,Y) (R##_f = X##_f + Y##_f)
#define _FP_FRAC_SUB_1(R,X,Y) (R##_f = X##_f - Y##_f)
#define _FP_FRAC_CLZ_1(z, X)  __FP_CLZ(z, X##_f)

/* Predicates */
#define _FP_FRAC_NEGP_1(X)    ((_FP_WS_TYPE)X##_f < 0)
#define _FP_FRAC_ZEROP_1(X)   (X##_f == 0)
#define _FP_FRAC_OVERP_1(fs,X)      (X##_f & _FP_OVERFLOW_##fs)
#define _FP_FRAC_EQ_1(X, Y)   (X##_f == Y##_f)
#define _FP_FRAC_GE_1(X, Y)   (X##_f >= Y##_f)
#define _FP_FRAC_GT_1(X, Y)   (X##_f > Y##_f)

#define _FP_ZEROFRAC_1        0
#define _FP_MINFRAC_1         1

/*
 * Unpack the raw bits of a native fp value.  Do not classify or
 * normalize the data.
 */

#define _FP_UNPACK_RAW_1(fs, X, val)                        \
  do {                                                \
    union _FP_UNION_##fs _flo; _flo.flt = (val);            \
                                                \
    X##_f = _flo.bits.frac;                           \
    X##_e = _flo.bits.exp;                            \
    X##_s = _flo.bits.sign;                           \
  } while (0)


/*
 * Repack the raw bits of a native fp value.
 */

#define _FP_PACK_RAW_1(fs, val, X)                    \
  do {                                                \
    union _FP_UNION_##fs _flo;                              \
                                                \
    _flo.bits.frac = X##_f;                           \
    _flo.bits.exp  = X##_e;                           \
    _flo.bits.sign = X##_s;                           \
                                                \
    (val) = _flo.flt;                                 \
  } while (0)


/*
 * Multiplication algorithms:
 */

/* Basic.  Assuming the host word size is >= 2*FRACBITS, we can do the
   multiplication immediately.  */

#define _FP_MUL_MEAT_1_imm(fs, R, X, Y)                           \
  do {                                                      \
    R##_f = X##_f * Y##_f;                                  \
    /* Normalize since we know where the msb of the multiplicands \
       were (bit B), we know that the msb of the of the product is      \
       at either 2B or 2B-1.  */                            \
    _FP_FRAC_SRS_1(R, _FP_WFRACBITS_##fs-1, 2*_FP_WFRACBITS_##fs);      \
  } while (0)

/* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */

#define _FP_MUL_MEAT_1_wide(fs, R, X, Y, doit)                    \
  do {                                                      \
    _FP_W_TYPE _Z_f0, _Z_f1;                                \
    doit(_Z_f1, _Z_f0, X##_f, Y##_f);                             \
    /* Normalize since we know where the msb of the multiplicands \
       were (bit B), we know that the msb of the of the product is      \
       at either 2B or 2B-1.  */                            \
    _FP_FRAC_SRS_2(_Z, _FP_WFRACBITS_##fs-1, 2*_FP_WFRACBITS_##fs);     \
    R##_f = _Z_f0;                                          \
  } while (0)

/* Finally, a simple widening multiply algorithm.  What fun!  */

#define _FP_MUL_MEAT_1_hard(fs, R, X, Y)                    \
  do {                                                      \
    _FP_W_TYPE _xh, _xl, _yh, _yl, _z_f0, _z_f1, _a_f0, _a_f1;          \
                                                      \
    /* split the words in half */                           \
    _xh = X##_f >> (_FP_W_TYPE_SIZE/2);                           \
    _xl = X##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1);         \
    _yh = Y##_f >> (_FP_W_TYPE_SIZE/2);                           \
    _yl = Y##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1);         \
                                                      \
    /* multiply the pieces */                               \
    _z_f0 = _xl * _yl;                                      \
    _a_f0 = _xh * _yl;                                      \
    _a_f1 = _xl * _yh;                                      \
    _z_f1 = _xh * _yh;                                      \
                                                      \
    /* reassemble into two full words */                    \
    if ((_a_f0 += _a_f1) < _a_f1)                           \
      _z_f1 += (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2);              \
    _a_f1 = _a_f0 >> (_FP_W_TYPE_SIZE/2);                   \
    _a_f0 = _a_f0 << (_FP_W_TYPE_SIZE/2);                   \
    _FP_FRAC_ADD_2(_z, _z, _a);                                   \
                                                      \
    /* normalize */                                         \
    _FP_FRAC_SRS_2(_z, _FP_WFRACBITS_##fs - 1, 2*_FP_WFRACBITS_##fs);   \
    R##_f = _z_f0;                                          \
  } while (0)


/*
 * Division algorithms:
 */

/* Basic.  Assuming the host word size is >= 2*FRACBITS, we can do the
   division immediately.  Give this macro either _FP_DIV_HELP_imm for
   C primitives or _FP_DIV_HELP_ldiv for the ISO function.  Which you
   choose will depend on what the compiler does with divrem4.  */

#define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit)         \
  do {                                          \
    _FP_W_TYPE _q, _r;                          \
    X##_f <<= (X##_f < Y##_f                    \
             ? R##_e--, _FP_WFRACBITS_##fs            \
             : _FP_WFRACBITS_##fs - 1);         \
    doit(_q, _r, X##_f, Y##_f);                       \
    R##_f = _q | (_r != 0);                     \
  } while (0)

/* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd
   that may be useful in this situation.  This first is for a primitive
   that requires normalization, the second for one that does not.  Look
   for UDIV_NEEDS_NORMALIZATION to tell which your machine needs.  */

#define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y)                     \
  do {                                                      \
    _FP_W_TYPE _nh, _nl, _q, _r;                            \
                                                      \
    /* Normalize Y -- i.e. make the most significant bit set.  */ \
    Y##_f <<= _FP_WFRACXBITS_##fs - 1;                            \
                                                      \
    /* Shift X op correspondingly high, that is, up one full word.  */  \
    if (X##_f <= Y##_f)                                     \
      {                                                     \
      _nl = 0;                                        \
      _nh = X##_f;                                          \
      }                                                     \
    else                                              \
      {                                                     \
      R##_e++;                                        \
      _nl = X##_f << (_FP_W_TYPE_SIZE-1);                   \
      _nh = X##_f >> 1;                               \
      }                                                     \
                                                      \
    udiv_qrnnd(_q, _r, _nh, _nl, Y##_f);                    \
    R##_f = _q | (_r != 0);                                 \
  } while (0)

#define _FP_DIV_MEAT_1_udiv(fs, R, X, Y)        \
  do {                                          \
    _FP_W_TYPE _nh, _nl, _q, _r;                \
    if (X##_f < Y##_f)                          \
      {                                         \
      R##_e--;                            \
      _nl = X##_f << _FP_WFRACBITS_##fs;        \
      _nh = X##_f >> _FP_WFRACXBITS_##fs;       \
      }                                         \
    else                                  \
      {                                         \
      _nl = X##_f << (_FP_WFRACBITS_##fs - 1);  \
      _nh = X##_f >> (_FP_WFRACXBITS_##fs + 1); \
      }                                         \
    udiv_qrnnd(_q, _r, _nh, _nl, Y##_f);        \
    R##_f = _q | (_r != 0);                     \
  } while (0)


/*
 * Square root algorithms:
 * We have just one right now, maybe Newton approximation
 * should be added for those machines where division is fast.
 */

#define _FP_SQRT_MEAT_1(R, S, T, X, q)                \
  do {                                          \
    while (q)                                   \
      {                                         \
        T##_f = S##_f + q;                      \
        if (T##_f <= X##_f)                     \
          {                               \
            S##_f = T##_f + q;                        \
            X##_f -= T##_f;                     \
            R##_f += q;                         \
          }                               \
        _FP_FRAC_SLL_1(X, 1);                   \
        q >>= 1;                          \
      }                                         \
  } while (0)

/*
 * Assembly/disassembly for converting to/from integral types.
 * No shifting or overflow handled here.
 */

#define _FP_FRAC_ASSEMBLE_1(r, X, rsize)  (r = X##_f)
#define _FP_FRAC_DISASSEMBLE_1(X, r, rsize)     (X##_f = r)


/*
 * Convert FP values between word sizes
 */

#define _FP_FRAC_CONV_1_1(dfs, sfs, D, S)                   \
  do {                                                      \
    D##_f = S##_f;                                          \
    if (_FP_WFRACBITS_##sfs > _FP_WFRACBITS_##dfs)                \
      _FP_FRAC_SRS_1(D, (_FP_WFRACBITS_##sfs-_FP_WFRACBITS_##dfs),      \
                 _FP_WFRACBITS_##sfs);                      \
    else                                              \
      D##_f <<= _FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs;        \
  } while (0)

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