/*
* Basic two-word fraction declaration and manipulation.
*/
#define _FP_FRAC_DECL_2(X) _FP_W_TYPE X##_f0, X##_f1
#define _FP_FRAC_COPY_2(D,S) (D##_f0 = S##_f0, D##_f1 = S##_f1)
#define _FP_FRAC_SET_2(X,I) __FP_FRAC_SET_2(X, I)
#define _FP_FRAC_HIGH_2(X) (X##_f1)
#define _FP_FRAC_LOW_2(X) (X##_f0)
#define _FP_FRAC_WORD_2(X,w) (X##_f##w)
#define _FP_FRAC_SLL_2(X,N) \
do { \
if ((N) < _FP_W_TYPE_SIZE) \
{ \
if (__builtin_constant_p(N) && (N) == 1) \
{ \
X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0); \
X##_f0 += X##_f0; \
} \
else \
{ \
X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \
X##_f0 <<= (N); \
} \
} \
else \
{ \
X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \
X##_f0 = 0; \
} \
} while (0)
#define _FP_FRAC_SRL_2(X,N) \
do { \
if ((N) < _FP_W_TYPE_SIZE) \
{ \
X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \
X##_f1 >>= (N); \
} \
else \
{ \
X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \
X##_f1 = 0; \
} \
} while (0)
/* Right shift with sticky-lsb. */
#define _FP_FRAC_SRS_2(X,N,sz) \
do { \
if ((N) < _FP_W_TYPE_SIZE) \
{ \
X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) | \
(__builtin_constant_p(N) && (N) == 1 \
? X##_f0 & 1 \
: (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \
X##_f1 >>= (N); \
} \
else \
{ \
X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) | \
(((X##_f1 << (2 * _FP_W_TYPE_SIZE - (N))) | \
X##_f0) != 0)); \
X##_f1 = 0; \
} \
} while (0)
#define _FP_FRAC_ADDI_2(X,I) \
__FP_FRAC_ADDI_2(X##_f1, X##_f0, I)
#define _FP_FRAC_ADD_2(R,X,Y) \
__FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
#define _FP_FRAC_SUB_2(R,X,Y) \
__FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
#define _FP_FRAC_CLZ_2(R,X) \
do { \
if (X##_f1) \
__FP_CLZ(R,X##_f1); \
else \
{ \
__FP_CLZ(R,X##_f0); \
R += _FP_W_TYPE_SIZE; \
} \
} while(0)
/* Predicates */
#define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0)
#define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0)
#define _FP_FRAC_OVERP_2(fs,X) (X##_f1 & _FP_OVERFLOW_##fs)
#define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0)
#define _FP_FRAC_GT_2(X, Y) \
((X##_f1 > Y##_f1) || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0))
#define _FP_FRAC_GE_2(X, Y) \
((X##_f1 > Y##_f1) || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0))
#define _FP_ZEROFRAC_2 0, 0
#define _FP_MINFRAC_2 0, 1
/*
* Internals
*/
#define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1)
#define __FP_CLZ_2(R, xh, xl) \
do { \
if (xh) \
__FP_CLZ(R,xl); \
else \
{ \
__FP_CLZ(R,xl); \
R += _FP_W_TYPE_SIZE; \
} \
} while(0)
#if 0
#ifndef __FP_FRAC_ADDI_2
#define __FP_FRAC_ADDI_2(xh, xl, i) \
(xh += ((xl += i) < i))
#endif
#ifndef __FP_FRAC_ADD_2
#define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \
(rh = xh + yh + ((rl = xl + yl) < xl))
#endif
#ifndef __FP_FRAC_SUB_2
#define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \
(rh = xh - yh - ((rl = xl - yl) > xl))
#endif
#else
#undef __FP_FRAC_ADDI_2
#define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i)
#undef __FP_FRAC_ADD_2
#define __FP_FRAC_ADD_2 add_ssaaaa
#undef __FP_FRAC_SUB_2
#define __FP_FRAC_SUB_2 sub_ddmmss
#endif
/*
* Unpack the raw bits of a native fp value. Do not classify or
* normalize the data.
*/
#define _FP_UNPACK_RAW_2(fs, X, val) \
do { \
union _FP_UNION_##fs _flo; _flo.flt = (val); \
\
X##_f0 = _flo.bits.frac0; \
X##_f1 = _flo.bits.frac1; \
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_2(fs, val, X) \
do { \
union _FP_UNION_##fs _flo; \
\
_flo.bits.frac0 = X##_f0; \
_flo.bits.frac1 = X##_f1; \
_flo.bits.exp = X##_e; \
_flo.bits.sign = X##_s; \
\
(val) = _flo.flt; \
} while (0)
/*
* Multiplication algorithms:
*/
/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
#define _FP_MUL_MEAT_2_wide(fs, R, X, Y, doit) \
do { \
_FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
\
doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \
doit(_b_f1, _b_f0, X##_f0, Y##_f1); \
doit(_c_f1, _c_f0, X##_f1, Y##_f0); \
doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \
\
__FP_FRAC_ADD_4(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
_FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0), \
0, _b_f1, _b_f0, 0, \
_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
_FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0)); \
__FP_FRAC_ADD_4(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
_FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0), \
0, _c_f1, _c_f0, 0, \
_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
_FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0)); \
\
/* 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_4(_z, _FP_WFRACBITS_##fs-1, 2*_FP_WFRACBITS_##fs); \
R##_f0 = _FP_FRAC_WORD_4(_z,0); \
R##_f1 = _FP_FRAC_WORD_4(_z,1); \
} while (0)
/* This next macro appears to be totally broken. Fortunately nowhere
* seems to use it :-> The problem is that we define _z[4] but
* then use it in _FP_FRAC_SRS_4, which will attempt to access
* _z_f[n] which will cause an error. The fix probably involves
* declaring it with _FP_FRAC_DECL_4, see previous macro. -- PMM 02/1998
*/
#define _FP_MUL_MEAT_2_gmp(fs, R, X, Y) \
do { \
_FP_W_TYPE _x[2], _y[2], _z[4]; \
_x[0] = X##_f0; _x[1] = X##_f1; \
_y[0] = Y##_f0; _y[1] = Y##_f1; \
\
mpn_mul_n(_z, _x, _y, 2); \
\
/* 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_4(_z, _FP_WFRACBITS##_fs-1, 2*_FP_WFRACBITS_##fs); \
R##_f0 = _z[0]; \
R##_f1 = _z[1]; \
} while (0)
/*
* Division algorithms:
* This seems to be giving me difficulties -- PMM
* Look, NetBSD seems to be able to comment algorithms. Can't you?
* I've thrown printks at the problem.
* This now appears to work, but I still don't really know why.
* Also, I don't think the result is properly normalised...
*/
#define _FP_DIV_MEAT_2_udiv_64(fs, R, X, Y) \
do { \
extern void _fp_udivmodti4(_FP_W_TYPE q[2], _FP_W_TYPE r[2], \
_FP_W_TYPE n1, _FP_W_TYPE n0, \
_FP_W_TYPE d1, _FP_W_TYPE d0); \
_FP_W_TYPE _n_f3, _n_f2, _n_f1, _n_f0, _r_f1, _r_f0; \
_FP_W_TYPE _q_f1, _q_f0, _m_f1, _m_f0; \
_FP_W_TYPE _rmem[2], _qmem[2]; \
/* I think this check is to ensure that the result is normalised. \
* Assuming X,Y normalised (ie in [1.0,2.0)) X/Y will be in \
* [0.5,2.0). Furthermore, it will be less than 1.0 iff X < Y. \
* In this case we tweak things. (this is based on comments in \
* the NetBSD FPU emulation code. ) \
* We know X,Y are normalised because we ensure this as part of \
* the unpacking process. -- PMM \
*/ \
if (_FP_FRAC_GT_2(X, Y)) \
{ \
/* R##_e++; */ \
_n_f3 = X##_f1 >> 1; \
_n_f2 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \
_n_f1 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \
_n_f0 = 0; \
} \
else \
{ \
R##_e--; \
_n_f3 = X##_f1; \
_n_f2 = X##_f0; \
_n_f1 = _n_f0 = 0; \
} \
\
/* Normalize, i.e. make the most significant bit of the \
denominator set. CHANGED: - 1 to nothing -- PMM */ \
_FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs /* -1 */); \
\
/* Do the 256/128 bit division given the 128-bit _fp_udivmodtf4 \
primitive snagged from libgcc2.c. */ \
\
_fp_udivmodti4(_qmem, _rmem, _n_f3, _n_f2, 0, Y##_f1); \
_q_f1 = _qmem[0]; \
umul_ppmm(_m_f1, _m_f0, _q_f1, Y##_f0); \
_r_f1 = _rmem[0]; \
_r_f0 = _n_f1; \
if (_FP_FRAC_GT_2(_m, _r)) \
{ \
_q_f1--; \
_FP_FRAC_ADD_2(_r, _r, Y); \
if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
{ \
_q_f1--; \
_FP_FRAC_ADD_2(_r, _r, Y); \
} \
} \
_FP_FRAC_SUB_2(_r, _r, _m); \
\
_fp_udivmodti4(_qmem, _rmem, _r_f1, _r_f0, 0, Y##_f1); \
_q_f0 = _qmem[0]; \
umul_ppmm(_m_f1, _m_f0, _q_f0, Y##_f0); \
_r_f1 = _rmem[0]; \
_r_f0 = _n_f0; \
if (_FP_FRAC_GT_2(_m, _r)) \
{ \
_q_f0--; \
_FP_FRAC_ADD_2(_r, _r, Y); \
if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
{ \
_q_f0--; \
_FP_FRAC_ADD_2(_r, _r, Y); \
} \
} \
_FP_FRAC_SUB_2(_r, _r, _m); \
\
R##_f1 = _q_f1; \
R##_f0 = _q_f0 | ((_r_f1 | _r_f0) != 0); \
/* adjust so answer is normalized again. I'm not sure what the \
* final sz param should be. In practice it's never used since \
* N is 1 which is always going to be < _FP_W_TYPE_SIZE... \
*/ \
/* _FP_FRAC_SRS_2(R,1,_FP_WFRACBITS_##fs); */ \
} while (0)
#define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \
do { \
_FP_W_TYPE _x[4], _y[2], _z[4]; \
_y[0] = Y##_f0; _y[1] = Y##_f1; \
_x[0] = _x[3] = 0; \
if (_FP_FRAC_GT_2(X, Y)) \
{ \
R##_e++; \
_x[1] = (X##_f0 << (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE) | \
X##_f1 >> (_FP_W_TYPE_SIZE - \
(_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE))); \
_x[2] = X##_f1 << (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE); \
} \
else \
{ \
_x[1] = (X##_f0 << (_FP_WFRACBITS - _FP_W_TYPE_SIZE) | \
X##_f1 >> (_FP_W_TYPE_SIZE - \
(_FP_WFRACBITS - _FP_W_TYPE_SIZE))); \
_x[2] = X##_f1 << (_FP_WFRACBITS - _FP_W_TYPE_SIZE); \
} \
\
(void) mpn_divrem (_z, 0, _x, 4, _y, 2); \
R##_f1 = _z[1]; \
R##_f0 = _z[0] | ((_x[0] | _x[1]) != 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_2(R, S, T, X, q) \
do { \
while (q) \
{ \
T##_f1 = S##_f1 + q; \
if (T##_f1 <= X##_f1) \
{ \
S##_f1 = T##_f1 + q; \
X##_f1 -= T##_f1; \
R##_f1 += q; \
} \
_FP_FRAC_SLL_2(X, 1); \
q >>= 1; \
} \
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
while (q) \
{ \
T##_f0 = S##_f0 + q; \
T##_f1 = S##_f1; \
if (T##_f1 < X##_f1 || \
(T##_f1 == X##_f1 && T##_f0 < X##_f0)) \
{ \
S##_f0 = T##_f0 + q; \
if (((_FP_WS_TYPE)T##_f0) < 0 && \
((_FP_WS_TYPE)S##_f0) >= 0) \
S##_f1++; \
_FP_FRAC_SUB_2(X, X, T); \
R##_f0 += q; \
} \
_FP_FRAC_SLL_2(X, 1); \
q >>= 1; \
} \
} while (0)
/*
* Assembly/disassembly for converting to/from integral types.
* No shifting or overflow handled here.
*/
#define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \
do { \
if (rsize <= _FP_W_TYPE_SIZE) \
r = X##_f0; \
else \
{ \
r = X##_f1; \
r <<= _FP_W_TYPE_SIZE; \
r += X##_f0; \
} \
} while (0)
#define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \
do { \
X##_f0 = r; \
X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \
} while (0)
/*
* Convert FP values between word sizes
*/
#define _FP_FRAC_CONV_1_2(dfs, sfs, D, S) \
do { \
_FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \
_FP_WFRACBITS_##sfs); \
D##_f = S##_f0; \
} while (0)
#define _FP_FRAC_CONV_2_1(dfs, sfs, D, S) \
do { \
D##_f0 = S##_f; \
D##_f1 = 0; \
_FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \
} while (0)
