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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 | /* * 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) |