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) 116 117 118#undef __FP_FRAC_ADDI_2 119#define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i) 120#undef __FP_FRAC_ADD_2 121#define __FP_FRAC_ADD_2 add_ssaaaa 122#undef __FP_FRAC_SUB_2 123#define __FP_FRAC_SUB_2 sub_ddmmss 124 125 126/* 127 * Unpack the raw bits of a native fp value. Do not classify or 128 * normalize the data. 129 */ 130 131#define _FP_UNPACK_RAW_2(fs, X, val) \ 132 do { \ 133 union _FP_UNION_##fs _flo; _flo.flt = (val); \ 134 \ 135 X##_f0 = _flo.bits.frac0; \ 136 X##_f1 = _flo.bits.frac1; \ 137 X##_e = _flo.bits.exp; \ 138 X##_s = _flo.bits.sign; \ 139 } while (0) 140 141 142/* 143 * Repack the raw bits of a native fp value. 144 */ 145 146#define _FP_PACK_RAW_2(fs, val, X) \ 147 do { \ 148 union _FP_UNION_##fs _flo; \ 149 \ 150 _flo.bits.frac0 = X##_f0; \ 151 _flo.bits.frac1 = X##_f1; \ 152 _flo.bits.exp = X##_e; \ 153 _flo.bits.sign = X##_s; \ 154 \ 155 (val) = _flo.flt; \ 156 } while (0) 157 158 159/* 160 * Multiplication algorithms: 161 */ 162 163/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ 164 165#define _FP_MUL_MEAT_2_wide(fs, R, X, Y, doit) \ 166 do { \ 167 _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ 168 \ 169 doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \ 170 doit(_b_f1, _b_f0, X##_f0, Y##_f1); \ 171 doit(_c_f1, _c_f0, X##_f1, Y##_f0); \ 172 doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \ 173 \ 174 __FP_FRAC_ADD_4(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 175 _FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0), \ 176 0, _b_f1, _b_f0, 0, \ 177 _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 178 _FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0)); \ 179 __FP_FRAC_ADD_4(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 180 _FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0), \ 181 0, _c_f1, _c_f0, 0, \ 182 _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 183 _FP_FRAC_WORD_4(_z,1),_FP_FRAC_WORD_4(_z,0)); \ 184 \ 185 /* Normalize since we know where the msb of the multiplicands \ 186 were (bit B), we know that the msb of the of the product is \ 187 at either 2B or 2B-1. */ \ 188 _FP_FRAC_SRS_4(_z, _FP_WFRACBITS_##fs-1, 2*_FP_WFRACBITS_##fs); \ 189 R##_f0 = _FP_FRAC_WORD_4(_z,0); \ 190 R##_f1 = _FP_FRAC_WORD_4(_z,1); \ 191 } while (0) 192 193/* This next macro appears to be totally broken. Fortunately nowhere 194 * seems to use it :-> The problem is that we define _z[4] but 195 * then use it in _FP_FRAC_SRS_4, which will attempt to access 196 * _z_f[n] which will cause an error. The fix probably involves 197 * declaring it with _FP_FRAC_DECL_4, see previous macro. -- PMM 02/1998 198 */ 199#define _FP_MUL_MEAT_2_gmp(fs, R, X, Y) \ 200 do { \ 201 _FP_W_TYPE _x[2], _y[2], _z[4]; \ 202 _x[0] = X##_f0; _x[1] = X##_f1; \ 203 _y[0] = Y##_f0; _y[1] = Y##_f1; \ 204 \ 205 mpn_mul_n(_z, _x, _y, 2); \ 206 \ 207 /* Normalize since we know where the msb of the multiplicands \ 208 were (bit B), we know that the msb of the of the product is \ 209 at either 2B or 2B-1. */ \ 210 _FP_FRAC_SRS_4(_z, _FP_WFRACBITS##_fs-1, 2*_FP_WFRACBITS_##fs); \ 211 R##_f0 = _z[0]; \ 212 R##_f1 = _z[1]; \ 213 } while (0) 214 215 216/* 217 * Division algorithms: 218 * This seems to be giving me difficulties -- PMM 219 * Look, NetBSD seems to be able to comment algorithms. Can't you? 220 * I've thrown printks at the problem. 221 * This now appears to work, but I still don't really know why. 222 * Also, I don't think the result is properly normalised... 223 */ 224 225#define _FP_DIV_MEAT_2_udiv_64(fs, R, X, Y) \ 226 do { \ 227 extern void _fp_udivmodti4(_FP_W_TYPE q[2], _FP_W_TYPE r[2], \ 228 _FP_W_TYPE n1, _FP_W_TYPE n0, \ 229 _FP_W_TYPE d1, _FP_W_TYPE d0); \ 230 _FP_W_TYPE _n_f3, _n_f2, _n_f1, _n_f0, _r_f1, _r_f0; \ 231 _FP_W_TYPE _q_f1, _q_f0, _m_f1, _m_f0; \ 232 _FP_W_TYPE _rmem[2], _qmem[2]; \ 233 /* I think this check is to ensure that the result is normalised. \ 234 * Assuming X,Y normalised (ie in [1.0,2.0)) X/Y will be in \ 235 * [0.5,2.0). Furthermore, it will be less than 1.0 iff X < Y. \ 236 * In this case we tweak things. (this is based on comments in \ 237 * the NetBSD FPU emulation code. ) \ 238 * We know X,Y are normalised because we ensure this as part of \ 239 * the unpacking process. -- PMM \ 240 */ \ 241 if (_FP_FRAC_GT_2(X, Y)) \ 242 { \ 243/* R##_e++; */ \ 244 _n_f3 = X##_f1 >> 1; \ 245 _n_f2 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \ 246 _n_f1 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \ 247 _n_f0 = 0; \ 248 } \ 249 else \ 250 { \ 251 R##_e--; \ 252 _n_f3 = X##_f1; \ 253 _n_f2 = X##_f0; \ 254 _n_f1 = _n_f0 = 0; \ 255 } \ 256 \ 257 /* Normalize, i.e. make the most significant bit of the \ 258 denominator set. CHANGED: - 1 to nothing -- PMM */ \ 259 _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs /* -1 */); \ 260 \ 261 /* Do the 256/128 bit division given the 128-bit _fp_udivmodtf4 \ 262 primitive snagged from libgcc2.c. */ \ 263 \ 264 _fp_udivmodti4(_qmem, _rmem, _n_f3, _n_f2, 0, Y##_f1); \ 265 _q_f1 = _qmem[0]; \ 266 umul_ppmm(_m_f1, _m_f0, _q_f1, Y##_f0); \ 267 _r_f1 = _rmem[0]; \ 268 _r_f0 = _n_f1; \ 269 if (_FP_FRAC_GT_2(_m, _r)) \ 270 { \ 271 _q_f1--; \ 272 _FP_FRAC_ADD_2(_r, _r, Y); \ 273 if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ 274 { \ 275 _q_f1--; \ 276 _FP_FRAC_ADD_2(_r, _r, Y); \ 277 } \ 278 } \ 279 _FP_FRAC_SUB_2(_r, _r, _m); \ 280 \ 281 _fp_udivmodti4(_qmem, _rmem, _r_f1, _r_f0, 0, Y##_f1); \ 282 _q_f0 = _qmem[0]; \ 283 umul_ppmm(_m_f1, _m_f0, _q_f0, Y##_f0); \ 284 _r_f1 = _rmem[0]; \ 285 _r_f0 = _n_f0; \ 286 if (_FP_FRAC_GT_2(_m, _r)) \ 287 { \ 288 _q_f0--; \ 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_f0--; \ 293 _FP_FRAC_ADD_2(_r, _r, Y); \ 294 } \ 295 } \ 296 _FP_FRAC_SUB_2(_r, _r, _m); \ 297 \ 298 R##_f1 = _q_f1; \ 299 R##_f0 = _q_f0 | ((_r_f1 | _r_f0) != 0); \ 300 /* adjust so answer is normalized again. I'm not sure what the \ 301 * final sz param should be. In practice it's never used since \ 302 * N is 1 which is always going to be < _FP_W_TYPE_SIZE... \ 303 */ \ 304 /* _FP_FRAC_SRS_2(R,1,_FP_WFRACBITS_##fs); */ \ 305 } while (0) 306 307 308#define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \ 309 do { \ 310 _FP_W_TYPE _x[4], _y[2], _z[4]; \ 311 _y[0] = Y##_f0; _y[1] = Y##_f1; \ 312 _x[0] = _x[3] = 0; \ 313 if (_FP_FRAC_GT_2(X, Y)) \ 314 { \ 315 R##_e++; \ 316 _x[1] = (X##_f0 << (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE) | \ 317 X##_f1 >> (_FP_W_TYPE_SIZE - \ 318 (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE))); \ 319 _x[2] = X##_f1 << (_FP_WFRACBITS-1 - _FP_W_TYPE_SIZE); \ 320 } \ 321 else \ 322 { \ 323 _x[1] = (X##_f0 << (_FP_WFRACBITS - _FP_W_TYPE_SIZE) | \ 324 X##_f1 >> (_FP_W_TYPE_SIZE - \ 325 (_FP_WFRACBITS - _FP_W_TYPE_SIZE))); \ 326 _x[2] = X##_f1 << (_FP_WFRACBITS - _FP_W_TYPE_SIZE); \ 327 } \ 328 \ 329 (void) mpn_divrem (_z, 0, _x, 4, _y, 2); \ 330 R##_f1 = _z[1]; \ 331 R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \ 332 } while (0) 333 334 335/* 336 * Square root algorithms: 337 * We have just one right now, maybe Newton approximation 338 * should be added for those machines where division is fast. 339 */ 340 341#define _FP_SQRT_MEAT_2(R, S, T, X, q) \ 342 do { \ 343 while (q) \ 344 { \ 345 T##_f1 = S##_f1 + q; \ 346 if (T##_f1 <= X##_f1) \ 347 { \ 348 S##_f1 = T##_f1 + q; \ 349 X##_f1 -= T##_f1; \ 350 R##_f1 += q; \ 351 } \ 352 _FP_FRAC_SLL_2(X, 1); \ 353 q >>= 1; \ 354 } \ 355 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ 356 while (q) \ 357 { \ 358 T##_f0 = S##_f0 + q; \ 359 T##_f1 = S##_f1; \ 360 if (T##_f1 < X##_f1 || \ 361 (T##_f1 == X##_f1 && T##_f0 < X##_f0)) \ 362 { \ 363 S##_f0 = T##_f0 + q; \ 364 if (((_FP_WS_TYPE)T##_f0) < 0 && \ 365 ((_FP_WS_TYPE)S##_f0) >= 0) \ 366 S##_f1++; \ 367 _FP_FRAC_SUB_2(X, X, T); \ 368 R##_f0 += q; \ 369 } \ 370 _FP_FRAC_SLL_2(X, 1); \ 371 q >>= 1; \ 372 } \ 373 } while (0) 374 375 376/* 377 * Assembly/disassembly for converting to/from integral types. 378 * No shifting or overflow handled here. 379 */ 380 381#define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \ 382 do { \ 383 if (rsize <= _FP_W_TYPE_SIZE) \ 384 r = X##_f0; \ 385 else \ 386 { \ 387 r = X##_f1; \ 388 r <<= _FP_W_TYPE_SIZE; \ 389 r += X##_f0; \ 390 } \ 391 } while (0) 392 393#define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \ 394 do { \ 395 X##_f0 = r; \ 396 X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \ 397 } while (0) 398 399/* 400 * Convert FP values between word sizes 401 */ 402 403#define _FP_FRAC_CONV_1_2(dfs, sfs, D, S) \ 404 do { \ 405 _FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \ 406 _FP_WFRACBITS_##sfs); \ 407 D##_f = S##_f0; \ 408 } while (0) 409 410#define _FP_FRAC_CONV_2_1(dfs, sfs, D, S) \ 411 do { \ 412 D##_f0 = S##_f; \ 413 D##_f1 = 0; \ 414 _FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \ 415 } while (0) 416