| /* |
| * 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) |