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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 | /* * 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) |