1da177e4c3
Initial git repository build. I'm not bothering with the full history, even though we have it. We can create a separate "historical" git archive of that later if we want to, and in the meantime it's about 3.2GB when imported into git - space that would just make the early git days unnecessarily complicated, when we don't have a lot of good infrastructure for it. Let it rip!
433 lines
13 KiB
C
433 lines
13 KiB
C
/*
|
|
* 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 << (sz - (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)
|
|
|