1 /* 2 * Basic two-word fraction declaration and manipulation. 3 */ 4 5 #define _FP_FRAC_DECL_2(X) _FP_W_TYPE X##_f0, X##_f1 6 #define _FP_FRAC_COPY_2(D,S) (D##_f0 = S##_f0, D##_f1 = S##_f1) 7 #define _FP_FRAC_SET_2(X,I) __FP_FRAC_SET_2(X, I) 8 #define _FP_FRAC_HIGH_2(X) (X##_f1) 9 #define _FP_FRAC_LOW_2(X) (X##_f0) 10 #define _FP_FRAC_WORD_2(X,w) (X##_f##w) 11 12 #define _FP_FRAC_SLL_2(X,N) \ 13 do { \ 14 if ((N) < _FP_W_TYPE_SIZE) \ 15 { \ 16 if (__builtin_constant_p(N) && (N) == 1) \ 17 { \ 18 X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0); \ 19 X##_f0 += X##_f0; \ 20 } \ 21 else \ 22 { \ 23 X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \ 24 X##_f0 <<= (N); \ 25 } \ 26 } \ 27 else \ 28 { \ 29 X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \ 30 X##_f0 = 0; \ 31 } \ 32 } while (0) 33 34 #define _FP_FRAC_SRL_2(X,N) \ 35 do { \ 36 if ((N) < _FP_W_TYPE_SIZE) \ 37 { \ 38 X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \ 39 X##_f1 >>= (N); \ 40 } \ 41 else \ 42 { \ 43 X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \ 44 X##_f1 = 0; \ 45 } \ 46 } while (0) 47 48 /* Right shift with sticky-lsb. */ 49 #define _FP_FRAC_SRS_2(X,N,sz) \ 50 do { \ 51 if ((N) < _FP_W_TYPE_SIZE) \ 52 { \ 53 X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) | \ 54 (__builtin_constant_p(N) && (N) == 1 \ 55 ? X##_f0 & 1 \ 56 : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \ 57 X##_f1 >>= (N); \ 58 } \ 59 else \ 60 { \ 61 X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) | \ 62 (((X##_f1 << (sz - (N))) | X##_f0) != 0)); \ 63 X##_f1 = 0; \ 64 } \ 65 } while (0) 66 67 #define _FP_FRAC_ADDI_2(X,I) \ 68 __FP_FRAC_ADDI_2(X##_f1, X##_f0, I) 69 70 #define _FP_FRAC_ADD_2(R,X,Y) \ 71 __FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) 72 73 #define _FP_FRAC_SUB_2(R,X,Y) \ 74 __FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) 75 76 #define _FP_FRAC_CLZ_2(R,X) \ 77 do { \ 78 if (X##_f1) \ 79 __FP_CLZ(R,X##_f1); \ 80 else \ 81 { \ 82 __FP_CLZ(R,X##_f0); \ 83 R += _FP_W_TYPE_SIZE; \ 84 } \ 85 } while(0) 86 87 /* Predicates */ 88 #define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0) 89 #define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0) 90 #define _FP_FRAC_OVERP_2(fs,X) (X##_f1 & _FP_OVERFLOW_##fs) 91 #define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0) 92 #define _FP_FRAC_GT_2(X, Y) \ 93 ((X##_f1 > Y##_f1) || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0)) 94 #define _FP_FRAC_GE_2(X, Y) \ 95 ((X##_f1 > Y##_f1) || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0)) 96 97 #define _FP_ZEROFRAC_2 0, 0 98 #define _FP_MINFRAC_2 0, 1 99 100 /* 101 * Internals 102 */ 103 104 #define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1) 105 106 #define __FP_CLZ_2(R, xh, xl) \ 107 do { \ 108 if (xh) \ 109 __FP_CLZ(R,xl); \ 110 else \ 111 { \ 112 __FP_CLZ(R,xl); \ 113 R += _FP_W_TYPE_SIZE; \ 114 } \ 115 } while(0) 116 117 #if 0 118 119 #ifndef __FP_FRAC_ADDI_2 120 #define __FP_FRAC_ADDI_2(xh, xl, i) \ 121 (xh += ((xl += i) < i)) 122 #endif 123 #ifndef __FP_FRAC_ADD_2 124 #define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \ 125 (rh = xh + yh + ((rl = xl + yl) < xl)) 126 #endif 127 #ifndef __FP_FRAC_SUB_2 128 #define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \ 129 (rh = xh - yh - ((rl = xl - yl) > xl)) 130 #endif 131 132 #else 133 134 #undef __FP_FRAC_ADDI_2 135 #define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i) 136 #undef __FP_FRAC_ADD_2 137 #define __FP_FRAC_ADD_2 add_ssaaaa 138 #undef __FP_FRAC_SUB_2 139 #define __FP_FRAC_SUB_2 sub_ddmmss 140 141 #endif 142 143 /* 144 * Unpack the raw bits of a native fp value. Do not classify or 145 * normalize the data. 146 */ 147 148 #define _FP_UNPACK_RAW_2(fs, X, val) \ 149 do { \ 150 union _FP_UNION_##fs _flo; _flo.flt = (val); \ 151 \ 152 X##_f0 = _flo.bits.frac0; \ 153 X##_f1 = _flo.bits.frac1; \ 154 X##_e = _flo.bits.exp; \ 155 X##_s = _flo.bits.sign; \ 156 } while (0) 157 158 159 /* 160 * Repack the raw bits of a native fp value. 161 */ 162 163 #define _FP_PACK_RAW_2(fs, val, X) \ 164 do { \ 165 union _FP_UNION_##fs _flo; \ 166 \ 167 _flo.bits.frac0 = X##_f0; \ 168 _flo.bits.frac1 = X##_f1; \ 169 _flo.bits.exp = X##_e; \ 170 _flo.bits.sign = X##_s; \ 171 \ 172 (val) = _flo.flt; \ 173 } while (0) 174 175 176 /* 177 * Multiplication algorithms: 178 */ 179 180 /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ 181 182 #define _FP_MUL_MEAT_2_wide(fs, R, X, Y, doit) \ 183 do { \ 184 _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ 185 \ 186 doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \ 187 doit(_b_f1, _b_f0, X##_f0, Y##_f1); \ 188 doit(_c_f1, _c_f0, X##_f1, Y##_f0); \ 189 doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \ 190 \ 191 __FP_FRAC_ADD_4(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 192 _FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0), \ 193 0, _b_f1, _b_f0, 0, \ 194 _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 195 _FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0)); \ 196 __FP_FRAC_ADD_4(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 197 _FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0), \ 198 0, _c_f1, _c_f0, 0, \ 199 _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 200 _FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0)); \ 201 \ 202 /* Normalize since we know where the msb of the multiplicands \ 203 were (bit B), we know that the msb of the of the product is \ 204 at either 2B or 2B-1. */ \ 205 _FP_FRAC_SRS_4(_z, _FP_WFRACBITS_##fs-1, 2*_FP_WFRACBITS_##fs); \ 206 R##_f0 = _FP_FRAC_WORD_4(_z,0); \ 207 R##_f1 = _FP_FRAC_WORD_4(_z,1); \ 208 } while (0) 209 210 /* This next macro appears to be totally broken. Fortunately nowhere 211 * seems to use it :-> The problem is that we define _z[4] but 212 * then use it in _FP_FRAC_SRS_4, which will attempt to access 213 * _z_f[n] which will cause an error. The fix probably involves 214 * declaring it with _FP_FRAC_DECL_4, see previous macro. -- PMM 02/1998 215 */ 216 #define _FP_MUL_MEAT_2_gmp(fs, R, X, Y) \ 217 do { \ 218 _FP_W_TYPE _x[2], _y[2], _z[4]; \ 219 _x[0] = X##_f0; _x[1] = X##_f1; \ 220 _y[0] = Y##_f0; _y[1] = Y##_f1; \ 221 \ 222 mpn_mul_n(_z, _x, _y, 2); \ 223 \ 224 /* Normalize since we know where the msb of the multiplicands \ 225 were (bit B), we know that the msb of the of the product is \ 226 at either 2B or 2B-1. */ \ 227 _FP_FRAC_SRS_4(_z, _FP_WFRACBITS##_fs-1, 2*_FP_WFRACBITS_##fs); \ 228 R##_f0 = _z[0]; \ 229 R##_f1 = _z[1]; \ 230 } while (0) 231 232 233 /* 234 * Division algorithms: 235 * This seems to be giving me difficulties -- PMM 236 * Look, NetBSD seems to be able to comment algorithms. Can't you? 237 * I've thrown printks at the problem. 238 * This now appears to work, but I still don't really know why. 239 * Also, I don't think the result is properly normalised... 240 */ 241 242 #define _FP_DIV_MEAT_2_udiv_64(fs, R, X, Y) \ 243 do { \ 244 extern void _fp_udivmodti4(_FP_W_TYPE q[2], _FP_W_TYPE r[2], \ 245 _FP_W_TYPE n1, _FP_W_TYPE n0, \ 246 _FP_W_TYPE d1, _FP_W_TYPE d0); \ 247 _FP_W_TYPE _n_f3, _n_f2, _n_f1, _n_f0, _r_f1, _r_f0; \ 248 _FP_W_TYPE _q_f1, _q_f0, _m_f1, _m_f0; \ 249 _FP_W_TYPE _rmem[2], _qmem[2]; \ 250 /* I think this check is to ensure that the result is normalised. \ 251 * Assuming X,Y normalised (ie in [1.0,2.0)) X/Y will be in \ 252 * [0.5,2.0). Furthermore, it will be less than 1.0 iff X < Y. \ 253 * In this case we tweak things. (this is based on comments in \ 254 * the NetBSD FPU emulation code. ) \ 255 * We know X,Y are normalised because we ensure this as part of \ 256 * the unpacking process. -- PMM \ 257 */ \ 258 if (_FP_FRAC_GT_2(X, Y)) \ 259 { \ 260 /* R##_e++; */ \ 261 _n_f3 = X##_f1 >> 1; \ 262 _n_f2 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \ 263 _n_f1 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \ 264 _n_f0 = 0; \ 265 } \ 266 else \ 267 { \ 268 R##_e--; \ 269 _n_f3 = X##_f1; \ 270 _n_f2 = X##_f0; \ 271 _n_f1 = _n_f0 = 0; \ 272 } \ 273 \ 274 /* Normalize, i.e. make the most significant bit of the \ 275 denominator set. CHANGED: - 1 to nothing -- PMM */ \ 276 _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs /* -1 */); \ 277 \ 278 /* Do the 256/128 bit division given the 128-bit _fp_udivmodtf4 \ 279 primitive snagged from libgcc2.c. */ \ 280 \ 281 _fp_udivmodti4(_qmem, _rmem, _n_f3, _n_f2, 0, Y##_f1); \ 282 _q_f1 = _qmem[0]; \ 283 umul_ppmm(_m_f1, _m_f0, _q_f1, Y##_f0); \ 284 _r_f1 = _rmem[0]; \ 285 _r_f0 = _n_f1; \ 286 if (_FP_FRAC_GT_2(_m, _r)) \ 287 { \ 288 _q_f1--; \ 289 _FP_FRAC_ADD_2(_r, _r, Y); \ 290 if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ 291 { \ 292 _q_f1--; \ 293 _FP_FRAC_ADD_2(_r, _r, Y); \ 294 } \ 295 } \ 296 _FP_FRAC_SUB_2(_r, _r, _m); \ 297 \ 298 _fp_udivmodti4(_qmem, _rmem, _r_f1, _r_f0, 0, Y##_f1); \ 299 _q_f0 = _qmem[0]; \ 300 umul_ppmm(_m_f1, _m_f0, _q_f0, Y##_f0); \ 301 _r_f1 = _rmem[0]; \ 302 _r_f0 = _n_f0; \ 303 if (_FP_FRAC_GT_2(_m, _r)) \ 304 { \ 305 _q_f0--; \ 306 _FP_FRAC_ADD_2(_r, _r, Y); \ 307 if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ 308 { \ 309 _q_f0--; \ 310 _FP_FRAC_ADD_2(_r, _r, Y); \ 311 } \ 312 } \ 313 _FP_FRAC_SUB_2(_r, _r, _m); \ 314 \ 315 R##_f1 = _q_f1; \ 316 R##_f0 = _q_f0 | ((_r_f1 | _r_f0) != 0); \ 317 /* adjust so answer is normalized again. I'm not sure what the \ 318 * final sz param should be. In practice it's never used since \ 319 * N is 1 which is always going to be < _FP_W_TYPE_SIZE... \ 320 */ \ 321 /* _FP_FRAC_SRS_2(R,1,_FP_WFRACBITS_##fs); */ \ 322 } while (0) 323 324 325 #define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \ 326 do { \ 327 _FP_W_TYPE _x[4], _y[2], _z[4]; \ 328 _y[0] = Y##_f0; _y[1] = Y##_f1; \ 329 _x[0] = _x[3] = 0; \ 330 if (_FP_FRAC_GT_2(X, Y)) \ 331 { \ 332 R##_e++; \ 333 _x[1] = (X##_f0 << (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE) | \ 334 X##_f1 >> (_FP_W_TYPE_SIZE - \ 335 (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE))); \ 336 _x[2] = X##_f1 << (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE); \ 337 } \ 338 else \ 339 { \ 340 _x[1] = (X##_f0 << (_FP_WFRACBITS - _FP_W_TYPE_SIZE) | \ 341 X##_f1 >> (_FP_W_TYPE_SIZE - \ 342 (_FP_WFRACBITS - _FP_W_TYPE_SIZE))); \ 343 _x[2] = X##_f1 << (_FP_WFRACBITS - _FP_W_TYPE_SIZE); \ 344 } \ 345 \ 346 (void) mpn_divrem (_z, 0, _x, 4, _y, 2); \ 347 R##_f1 = _z[1]; \ 348 R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \ 349 } while (0) 350 351 352 /* 353 * Square root algorithms: 354 * We have just one right now, maybe Newton approximation 355 * should be added for those machines where division is fast. 356 */ 357 358 #define _FP_SQRT_MEAT_2(R, S, T, X, q) \ 359 do { \ 360 while (q) \ 361 { \ 362 T##_f1 = S##_f1 + q; \ 363 if (T##_f1 <= X##_f1) \ 364 { \ 365 S##_f1 = T##_f1 + q; \ 366 X##_f1 -= T##_f1; \ 367 R##_f1 += q; \ 368 } \ 369 _FP_FRAC_SLL_2(X, 1); \ 370 q >>= 1; \ 371 } \ 372 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ 373 while (q) \ 374 { \ 375 T##_f0 = S##_f0 + q; \ 376 T##_f1 = S##_f1; \ 377 if (T##_f1 < X##_f1 || \ 378 (T##_f1 == X##_f1 && T##_f0 < X##_f0)) \ 379 { \ 380 S##_f0 = T##_f0 + q; \ 381 if (((_FP_WS_TYPE)T##_f0) < 0 && \ 382 ((_FP_WS_TYPE)S##_f0) >= 0) \ 383 S##_f1++; \ 384 _FP_FRAC_SUB_2(X, X, T); \ 385 R##_f0 += q; \ 386 } \ 387 _FP_FRAC_SLL_2(X, 1); \ 388 q >>= 1; \ 389 } \ 390 } while (0) 391 392 393 /* 394 * Assembly/disassembly for converting to/from integral types. 395 * No shifting or overflow handled here. 396 */ 397 398 #define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \ 399 do { \ 400 if (rsize <= _FP_W_TYPE_SIZE) \ 401 r = X##_f0; \ 402 else \ 403 { \ 404 r = X##_f1; \ 405 r <<= _FP_W_TYPE_SIZE; \ 406 r += X##_f0; \ 407 } \ 408 } while (0) 409 410 #define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \ 411 do { \ 412 X##_f0 = r; \ 413 X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \ 414 } while (0) 415 416 /* 417 * Convert FP values between word sizes 418 */ 419 420 #define _FP_FRAC_CONV_1_2(dfs, sfs, D, S) \ 421 do { \ 422 _FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \ 423 _FP_WFRACBITS_##sfs); \ 424 D##_f = S##_f0; \ 425 } while (0) 426 427 #define _FP_FRAC_CONV_2_1(dfs, sfs, D, S) \ 428 do { \ 429 D##_f0 = S##_f; \ 430 D##_f1 = 0; \ 431 _FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \ 432 } while (0) 433 434