1 /* Software floating-point emulation. 2 Basic two-word fraction declaration and manipulation. 3 Copyright (C) 1997,1998,1999 Free Software Foundation, Inc. 4 This file is part of the GNU C Library. 5 Contributed by Richard Henderson (rth@cygnus.com), 6 Jakub Jelinek (jj@ultra.linux.cz), 7 David S. Miller (davem@redhat.com) and 8 Peter Maydell (pmaydell@chiark.greenend.org.uk). 9 10 The GNU C Library is free software; you can redistribute it and/or 11 modify it under the terms of the GNU Library General Public License as 12 published by the Free Software Foundation; either version 2 of the 13 License, or (at your option) any later version. 14 15 The GNU C Library is distributed in the hope that it will be useful, 16 but WITHOUT ANY WARRANTY; without even the implied warranty of 17 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 18 Library General Public License for more details. 19 20 You should have received a copy of the GNU Library General Public 21 License along with the GNU C Library; see the file COPYING.LIB. If 22 not, write to the Free Software Foundation, Inc., 23 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ 24 25 #ifndef __MATH_EMU_OP_2_H__ 26 #define __MATH_EMU_OP_2_H__ 27 28 #define _FP_FRAC_DECL_2(X) _FP_W_TYPE X##_f0 = 0, X##_f1 = 0 29 #define _FP_FRAC_COPY_2(D,S) (D##_f0 = S##_f0, D##_f1 = S##_f1) 30 #define _FP_FRAC_SET_2(X,I) __FP_FRAC_SET_2(X, I) 31 #define _FP_FRAC_HIGH_2(X) (X##_f1) 32 #define _FP_FRAC_LOW_2(X) (X##_f0) 33 #define _FP_FRAC_WORD_2(X,w) (X##_f##w) 34 #define _FP_FRAC_SLL_2(X, N) ( \ 35 (void) (((N) < _FP_W_TYPE_SIZE) \ 36 ? ({ \ 37 if (__builtin_constant_p(N) && (N) == 1) { \ 38 X##_f1 = X##_f1 + X##_f1 + \ 39 (((_FP_WS_TYPE) (X##_f0)) < 0); \ 40 X##_f0 += X##_f0; \ 41 } else { \ 42 X##_f1 = X##_f1 << (N) | X##_f0 >> \ 43 (_FP_W_TYPE_SIZE - (N)); \ 44 X##_f0 <<= (N); \ 45 } \ 46 0; \ 47 }) \ 48 : ({ \ 49 X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \ 50 X##_f0 = 0; \ 51 }))) 52 53 54 #define _FP_FRAC_SRL_2(X, N) ( \ 55 (void) (((N) < _FP_W_TYPE_SIZE) \ 56 ? ({ \ 57 X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \ 58 X##_f1 >>= (N); \ 59 }) \ 60 : ({ \ 61 X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \ 62 X##_f1 = 0; \ 63 }))) 64 65 66 /* Right shift with sticky-lsb. */ 67 #define _FP_FRAC_SRS_2(X, N, sz) ( \ 68 (void) (((N) < _FP_W_TYPE_SIZE) \ 69 ? ({ \ 70 X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) \ 71 | (__builtin_constant_p(N) && (N) == 1 \ 72 ? X##_f0 & 1 \ 73 : (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \ 74 X##_f1 >>= (N); \ 75 }) \ 76 : ({ \ 77 X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) \ 78 | ((((N) == _FP_W_TYPE_SIZE \ 79 ? 0 \ 80 : (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \ 81 | X##_f0) != 0)); \ 82 X##_f1 = 0; \ 83 }))) 84 85 #define _FP_FRAC_ADDI_2(X,I) \ 86 __FP_FRAC_ADDI_2(X##_f1, X##_f0, I) 87 88 #define _FP_FRAC_ADD_2(R,X,Y) \ 89 __FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) 90 91 #define _FP_FRAC_SUB_2(R,X,Y) \ 92 __FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0) 93 94 #define _FP_FRAC_DEC_2(X,Y) \ 95 __FP_FRAC_DEC_2(X##_f1, X##_f0, Y##_f1, Y##_f0) 96 97 #define _FP_FRAC_CLZ_2(R,X) \ 98 do { \ 99 if (X##_f1) \ 100 __FP_CLZ(R,X##_f1); \ 101 else \ 102 { \ 103 __FP_CLZ(R,X##_f0); \ 104 R += _FP_W_TYPE_SIZE; \ 105 } \ 106 } while(0) 107 108 /* Predicates */ 109 #define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0) 110 #define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0) 111 #define _FP_FRAC_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs) 112 #define _FP_FRAC_CLEAR_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs) 113 #define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0) 114 #define _FP_FRAC_GT_2(X, Y) \ 115 (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0)) 116 #define _FP_FRAC_GE_2(X, Y) \ 117 (X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0)) 118 119 #define _FP_ZEROFRAC_2 0, 0 120 #define _FP_MINFRAC_2 0, 1 121 #define _FP_MAXFRAC_2 (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0) 122 123 /* 124 * Internals 125 */ 126 127 #define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1) 128 129 #define __FP_CLZ_2(R, xh, xl) \ 130 do { \ 131 if (xh) \ 132 __FP_CLZ(R,xh); \ 133 else \ 134 { \ 135 __FP_CLZ(R,xl); \ 136 R += _FP_W_TYPE_SIZE; \ 137 } \ 138 } while(0) 139 140 #if 0 141 142 #ifndef __FP_FRAC_ADDI_2 143 #define __FP_FRAC_ADDI_2(xh, xl, i) \ 144 (xh += ((xl += i) < i)) 145 #endif 146 #ifndef __FP_FRAC_ADD_2 147 #define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \ 148 (rh = xh + yh + ((rl = xl + yl) < xl)) 149 #endif 150 #ifndef __FP_FRAC_SUB_2 151 #define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \ 152 (rh = xh - yh - ((rl = xl - yl) > xl)) 153 #endif 154 #ifndef __FP_FRAC_DEC_2 155 #define __FP_FRAC_DEC_2(xh, xl, yh, yl) \ 156 do { \ 157 UWtype _t = xl; \ 158 xh -= yh + ((xl -= yl) > _t); \ 159 } while (0) 160 #endif 161 162 #else 163 164 #undef __FP_FRAC_ADDI_2 165 #define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i) 166 #undef __FP_FRAC_ADD_2 167 #define __FP_FRAC_ADD_2 add_ssaaaa 168 #undef __FP_FRAC_SUB_2 169 #define __FP_FRAC_SUB_2 sub_ddmmss 170 #undef __FP_FRAC_DEC_2 171 #define __FP_FRAC_DEC_2(xh, xl, yh, yl) sub_ddmmss(xh, xl, xh, xl, yh, yl) 172 173 #endif 174 175 /* 176 * Unpack the raw bits of a native fp value. Do not classify or 177 * normalize the data. 178 */ 179 180 #define _FP_UNPACK_RAW_2(fs, X, val) \ 181 do { \ 182 union _FP_UNION_##fs _flo; _flo.flt = (val); \ 183 \ 184 X##_f0 = _flo.bits.frac0; \ 185 X##_f1 = _flo.bits.frac1; \ 186 X##_e = _flo.bits.exp; \ 187 X##_s = _flo.bits.sign; \ 188 } while (0) 189 190 #define _FP_UNPACK_RAW_2_P(fs, X, val) \ 191 do { \ 192 union _FP_UNION_##fs *_flo = \ 193 (union _FP_UNION_##fs *)(val); \ 194 \ 195 X##_f0 = _flo->bits.frac0; \ 196 X##_f1 = _flo->bits.frac1; \ 197 X##_e = _flo->bits.exp; \ 198 X##_s = _flo->bits.sign; \ 199 } while (0) 200 201 202 /* 203 * Repack the raw bits of a native fp value. 204 */ 205 206 #define _FP_PACK_RAW_2(fs, val, X) \ 207 do { \ 208 union _FP_UNION_##fs _flo; \ 209 \ 210 _flo.bits.frac0 = X##_f0; \ 211 _flo.bits.frac1 = X##_f1; \ 212 _flo.bits.exp = X##_e; \ 213 _flo.bits.sign = X##_s; \ 214 \ 215 (val) = _flo.flt; \ 216 } while (0) 217 218 #define _FP_PACK_RAW_2_P(fs, val, X) \ 219 do { \ 220 union _FP_UNION_##fs *_flo = \ 221 (union _FP_UNION_##fs *)(val); \ 222 \ 223 _flo->bits.frac0 = X##_f0; \ 224 _flo->bits.frac1 = X##_f1; \ 225 _flo->bits.exp = X##_e; \ 226 _flo->bits.sign = X##_s; \ 227 } while (0) 228 229 230 /* 231 * Multiplication algorithms: 232 */ 233 234 /* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ 235 236 #define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit) \ 237 do { \ 238 _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ 239 \ 240 doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \ 241 doit(_b_f1, _b_f0, X##_f0, Y##_f1); \ 242 doit(_c_f1, _c_f0, X##_f1, Y##_f0); \ 243 doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \ 244 \ 245 __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 246 _FP_FRAC_WORD_4(_z,1), 0, _b_f1, _b_f0, \ 247 _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 248 _FP_FRAC_WORD_4(_z,1)); \ 249 __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 250 _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0, \ 251 _FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 252 _FP_FRAC_WORD_4(_z,1)); \ 253 \ 254 /* Normalize since we know where the msb of the multiplicands \ 255 were (bit B), we know that the msb of the of the product is \ 256 at either 2B or 2B-1. */ \ 257 _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ 258 R##_f0 = _FP_FRAC_WORD_4(_z,0); \ 259 R##_f1 = _FP_FRAC_WORD_4(_z,1); \ 260 } while (0) 261 262 /* Given a 1W * 1W => 2W primitive, do the extended multiplication. 263 Do only 3 multiplications instead of four. This one is for machines 264 where multiplication is much more expensive than subtraction. */ 265 266 #define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit) \ 267 do { \ 268 _FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \ 269 _FP_W_TYPE _d; \ 270 int _c1, _c2; \ 271 \ 272 _b_f0 = X##_f0 + X##_f1; \ 273 _c1 = _b_f0 < X##_f0; \ 274 _b_f1 = Y##_f0 + Y##_f1; \ 275 _c2 = _b_f1 < Y##_f0; \ 276 doit(_d, _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \ 277 doit(_FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1), _b_f0, _b_f1); \ 278 doit(_c_f1, _c_f0, X##_f1, Y##_f1); \ 279 \ 280 _b_f0 &= -_c2; \ 281 _b_f1 &= -_c1; \ 282 __FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 283 _FP_FRAC_WORD_4(_z,1), (_c1 & _c2), 0, _d, \ 284 0, _FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1)); \ 285 __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 286 _b_f0); \ 287 __FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 288 _b_f1); \ 289 __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 290 _FP_FRAC_WORD_4(_z,1), \ 291 0, _d, _FP_FRAC_WORD_4(_z,0)); \ 292 __FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \ 293 _FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0); \ 294 __FP_FRAC_ADD_2(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), \ 295 _c_f1, _c_f0, \ 296 _FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2)); \ 297 \ 298 /* Normalize since we know where the msb of the multiplicands \ 299 were (bit B), we know that the msb of the of the product is \ 300 at either 2B or 2B-1. */ \ 301 _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ 302 R##_f0 = _FP_FRAC_WORD_4(_z,0); \ 303 R##_f1 = _FP_FRAC_WORD_4(_z,1); \ 304 } while (0) 305 306 #define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \ 307 do { \ 308 _FP_FRAC_DECL_4(_z); \ 309 _FP_W_TYPE _x[2], _y[2]; \ 310 _x[0] = X##_f0; _x[1] = X##_f1; \ 311 _y[0] = Y##_f0; _y[1] = Y##_f1; \ 312 \ 313 mpn_mul_n(_z_f, _x, _y, 2); \ 314 \ 315 /* Normalize since we know where the msb of the multiplicands \ 316 were (bit B), we know that the msb of the of the product is \ 317 at either 2B or 2B-1. */ \ 318 _FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \ 319 R##_f0 = _z_f[0]; \ 320 R##_f1 = _z_f[1]; \ 321 } while (0) 322 323 /* Do at most 120x120=240 bits multiplication using double floating 324 point multiplication. This is useful if floating point 325 multiplication has much bigger throughput than integer multiply. 326 It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits 327 between 106 and 120 only. 328 Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set. 329 SETFETZ is a macro which will disable all FPU exceptions and set rounding 330 towards zero, RESETFE should optionally reset it back. */ 331 332 #define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \ 333 do { \ 334 static const double _const[] = { \ 335 /* 2^-24 */ 5.9604644775390625e-08, \ 336 /* 2^-48 */ 3.5527136788005009e-15, \ 337 /* 2^-72 */ 2.1175823681357508e-22, \ 338 /* 2^-96 */ 1.2621774483536189e-29, \ 339 /* 2^28 */ 2.68435456e+08, \ 340 /* 2^4 */ 1.600000e+01, \ 341 /* 2^-20 */ 9.5367431640625e-07, \ 342 /* 2^-44 */ 5.6843418860808015e-14, \ 343 /* 2^-68 */ 3.3881317890172014e-21, \ 344 /* 2^-92 */ 2.0194839173657902e-28, \ 345 /* 2^-116 */ 1.2037062152420224e-35}; \ 346 double _a240, _b240, _c240, _d240, _e240, _f240, \ 347 _g240, _h240, _i240, _j240, _k240; \ 348 union { double d; UDItype i; } _l240, _m240, _n240, _o240, \ 349 _p240, _q240, _r240, _s240; \ 350 UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \ 351 \ 352 if (wfracbits < 106 || wfracbits > 120) \ 353 abort(); \ 354 \ 355 setfetz; \ 356 \ 357 _e240 = (double)(long)(X##_f0 & 0xffffff); \ 358 _j240 = (double)(long)(Y##_f0 & 0xffffff); \ 359 _d240 = (double)(long)((X##_f0 >> 24) & 0xffffff); \ 360 _i240 = (double)(long)((Y##_f0 >> 24) & 0xffffff); \ 361 _c240 = (double)(long)(((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \ 362 _h240 = (double)(long)(((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \ 363 _b240 = (double)(long)((X##_f1 >> 8) & 0xffffff); \ 364 _g240 = (double)(long)((Y##_f1 >> 8) & 0xffffff); \ 365 _a240 = (double)(long)(X##_f1 >> 32); \ 366 _f240 = (double)(long)(Y##_f1 >> 32); \ 367 _e240 *= _const[3]; \ 368 _j240 *= _const[3]; \ 369 _d240 *= _const[2]; \ 370 _i240 *= _const[2]; \ 371 _c240 *= _const[1]; \ 372 _h240 *= _const[1]; \ 373 _b240 *= _const[0]; \ 374 _g240 *= _const[0]; \ 375 _s240.d = _e240*_j240;\ 376 _r240.d = _d240*_j240 + _e240*_i240;\ 377 _q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240;\ 378 _p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240;\ 379 _o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240;\ 380 _n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \ 381 _m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \ 382 _l240.d = _a240*_g240 + _b240*_f240; \ 383 _k240 = _a240*_f240; \ 384 _r240.d += _s240.d; \ 385 _q240.d += _r240.d; \ 386 _p240.d += _q240.d; \ 387 _o240.d += _p240.d; \ 388 _n240.d += _o240.d; \ 389 _m240.d += _n240.d; \ 390 _l240.d += _m240.d; \ 391 _k240 += _l240.d; \ 392 _s240.d -= ((_const[10]+_s240.d)-_const[10]); \ 393 _r240.d -= ((_const[9]+_r240.d)-_const[9]); \ 394 _q240.d -= ((_const[8]+_q240.d)-_const[8]); \ 395 _p240.d -= ((_const[7]+_p240.d)-_const[7]); \ 396 _o240.d += _const[7]; \ 397 _n240.d += _const[6]; \ 398 _m240.d += _const[5]; \ 399 _l240.d += _const[4]; \ 400 if (_s240.d != 0.0) _y240 = 1; \ 401 if (_r240.d != 0.0) _y240 = 1; \ 402 if (_q240.d != 0.0) _y240 = 1; \ 403 if (_p240.d != 0.0) _y240 = 1; \ 404 _t240 = (DItype)_k240; \ 405 _u240 = _l240.i; \ 406 _v240 = _m240.i; \ 407 _w240 = _n240.i; \ 408 _x240 = _o240.i; \ 409 R##_f1 = (_t240 << (128 - (wfracbits - 1))) \ 410 | ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104)); \ 411 R##_f0 = ((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \ 412 | ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \ 413 | ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \ 414 | ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \ 415 | _y240; \ 416 resetfe; \ 417 } while (0) 418 419 /* 420 * Division algorithms: 421 */ 422 423 #define _FP_DIV_MEAT_2_udiv(fs, R, X, Y) \ 424 do { \ 425 _FP_W_TYPE _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0; \ 426 if (_FP_FRAC_GT_2(X, Y)) \ 427 { \ 428 _n_f2 = X##_f1 >> 1; \ 429 _n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \ 430 _n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \ 431 } \ 432 else \ 433 { \ 434 R##_e--; \ 435 _n_f2 = X##_f1; \ 436 _n_f1 = X##_f0; \ 437 _n_f0 = 0; \ 438 } \ 439 \ 440 /* Normalize, i.e. make the most significant bit of the \ 441 denominator set. */ \ 442 _FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs); \ 443 \ 444 udiv_qrnnd(R##_f1, _r_f1, _n_f2, _n_f1, Y##_f1); \ 445 umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0); \ 446 _r_f0 = _n_f0; \ 447 if (_FP_FRAC_GT_2(_m, _r)) \ 448 { \ 449 R##_f1--; \ 450 _FP_FRAC_ADD_2(_r, Y, _r); \ 451 if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ 452 { \ 453 R##_f1--; \ 454 _FP_FRAC_ADD_2(_r, Y, _r); \ 455 } \ 456 } \ 457 _FP_FRAC_DEC_2(_r, _m); \ 458 \ 459 if (_r_f1 == Y##_f1) \ 460 { \ 461 /* This is a special case, not an optimization \ 462 (_r/Y##_f1 would not fit into UWtype). \ 463 As _r is guaranteed to be < Y, R##_f0 can be either \ 464 (UWtype)-1 or (UWtype)-2. But as we know what kind \ 465 of bits it is (sticky, guard, round), we don't care. \ 466 We also don't care what the reminder is, because the \ 467 guard bit will be set anyway. -jj */ \ 468 R##_f0 = -1; \ 469 } \ 470 else \ 471 { \ 472 udiv_qrnnd(R##_f0, _r_f1, _r_f1, _r_f0, Y##_f1); \ 473 umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0); \ 474 _r_f0 = 0; \ 475 if (_FP_FRAC_GT_2(_m, _r)) \ 476 { \ 477 R##_f0--; \ 478 _FP_FRAC_ADD_2(_r, Y, _r); \ 479 if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \ 480 { \ 481 R##_f0--; \ 482 _FP_FRAC_ADD_2(_r, Y, _r); \ 483 } \ 484 } \ 485 if (!_FP_FRAC_EQ_2(_r, _m)) \ 486 R##_f0 |= _FP_WORK_STICKY; \ 487 } \ 488 } while (0) 489 490 491 #define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \ 492 do { \ 493 _FP_W_TYPE _x[4], _y[2], _z[4]; \ 494 _y[0] = Y##_f0; _y[1] = Y##_f1; \ 495 _x[0] = _x[3] = 0; \ 496 if (_FP_FRAC_GT_2(X, Y)) \ 497 { \ 498 R##_e++; \ 499 _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) | \ 500 X##_f1 >> (_FP_W_TYPE_SIZE - \ 501 (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE))); \ 502 _x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE); \ 503 } \ 504 else \ 505 { \ 506 _x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) | \ 507 X##_f1 >> (_FP_W_TYPE_SIZE - \ 508 (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE))); \ 509 _x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE); \ 510 } \ 511 \ 512 (void) mpn_divrem (_z, 0, _x, 4, _y, 2); \ 513 R##_f1 = _z[1]; \ 514 R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \ 515 } while (0) 516 517 518 /* 519 * Square root algorithms: 520 * We have just one right now, maybe Newton approximation 521 * should be added for those machines where division is fast. 522 */ 523 524 #define _FP_SQRT_MEAT_2(R, S, T, X, q) \ 525 do { \ 526 while (q) \ 527 { \ 528 T##_f1 = S##_f1 + q; \ 529 if (T##_f1 <= X##_f1) \ 530 { \ 531 S##_f1 = T##_f1 + q; \ 532 X##_f1 -= T##_f1; \ 533 R##_f1 += q; \ 534 } \ 535 _FP_FRAC_SLL_2(X, 1); \ 536 q >>= 1; \ 537 } \ 538 q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \ 539 while (q != _FP_WORK_ROUND) \ 540 { \ 541 T##_f0 = S##_f0 + q; \ 542 T##_f1 = S##_f1; \ 543 if (T##_f1 < X##_f1 || \ 544 (T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \ 545 { \ 546 S##_f0 = T##_f0 + q; \ 547 S##_f1 += (T##_f0 > S##_f0); \ 548 _FP_FRAC_DEC_2(X, T); \ 549 R##_f0 += q; \ 550 } \ 551 _FP_FRAC_SLL_2(X, 1); \ 552 q >>= 1; \ 553 } \ 554 if (X##_f0 | X##_f1) \ 555 { \ 556 if (S##_f1 < X##_f1 || \ 557 (S##_f1 == X##_f1 && S##_f0 < X##_f0)) \ 558 R##_f0 |= _FP_WORK_ROUND; \ 559 R##_f0 |= _FP_WORK_STICKY; \ 560 } \ 561 } while (0) 562 563 564 /* 565 * Assembly/disassembly for converting to/from integral types. 566 * No shifting or overflow handled here. 567 */ 568 569 #define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \ 570 (void) (((rsize) <= _FP_W_TYPE_SIZE) \ 571 ? ({ (r) = X##_f0; }) \ 572 : ({ \ 573 (r) = X##_f1; \ 574 (r) <<= _FP_W_TYPE_SIZE; \ 575 (r) += X##_f0; \ 576 })) 577 578 #define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \ 579 do { \ 580 X##_f0 = r; \ 581 X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \ 582 } while (0) 583 584 /* 585 * Convert FP values between word sizes 586 */ 587 588 #define _FP_FRAC_CONV_1_2(dfs, sfs, D, S) \ 589 do { \ 590 if (S##_c != FP_CLS_NAN) \ 591 _FP_FRAC_SRS_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs), \ 592 _FP_WFRACBITS_##sfs); \ 593 else \ 594 _FP_FRAC_SRL_2(S, (_FP_WFRACBITS_##sfs - _FP_WFRACBITS_##dfs)); \ 595 D##_f = S##_f0; \ 596 } while (0) 597 598 #define _FP_FRAC_CONV_2_1(dfs, sfs, D, S) \ 599 do { \ 600 D##_f0 = S##_f; \ 601 D##_f1 = 0; \ 602 _FP_FRAC_SLL_2(D, (_FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs)); \ 603 } while (0) 604 605 #endif 606