op-2.h
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上传日期:2013-02-24
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- /*
- * BK Id: SCCS/s.op-2.h 1.5 05/17/01 18:14:23 cort
- */
- /*
- * 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)