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/*
* 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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