| /* |
| * 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) |
| |
