1/* Software floating-point emulation. 2 Basic one-word fraction declaration and manipulation. 3 Copyright (C) 1997-2014 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 Lesser General Public 12 License as published by the Free Software Foundation; either 13 version 2.1 of the License, or (at your option) any later version. 14 15 In addition to the permissions in the GNU Lesser General Public 16 License, the Free Software Foundation gives you unlimited 17 permission to link the compiled version of this file into 18 combinations with other programs, and to distribute those 19 combinations without any restriction coming from the use of this 20 file. (The Lesser General Public License restrictions do apply in 21 other respects; for example, they cover modification of the file, 22 and distribution when not linked into a combine executable.) 23 24 The GNU C Library is distributed in the hope that it will be useful, 25 but WITHOUT ANY WARRANTY; without even the implied warranty of 26 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 27 Lesser General Public License for more details. 28 29 You should have received a copy of the GNU Lesser General Public 30 License along with the GNU C Library; if not, see 31 <http://www.gnu.org/licenses/>. */ 32 33#define _FP_FRAC_DECL_1(X) _FP_W_TYPE X##_f 34#define _FP_FRAC_COPY_1(D, S) (D##_f = S##_f) 35#define _FP_FRAC_SET_1(X, I) (X##_f = I) 36#define _FP_FRAC_HIGH_1(X) (X##_f) 37#define _FP_FRAC_LOW_1(X) (X##_f) 38#define _FP_FRAC_WORD_1(X, w) (X##_f) 39 40#define _FP_FRAC_ADDI_1(X, I) (X##_f += I) 41#define _FP_FRAC_SLL_1(X, N) \ 42 do \ 43 { \ 44 if (__builtin_constant_p (N) && (N) == 1) \ 45 X##_f += X##_f; \ 46 else \ 47 X##_f <<= (N); \ 48 } \ 49 while (0) 50#define _FP_FRAC_SRL_1(X, N) (X##_f >>= N) 51 52/* Right shift with sticky-lsb. */ 53#define _FP_FRAC_SRST_1(X, S, N, sz) __FP_FRAC_SRST_1 (X##_f, S, (N), (sz)) 54#define _FP_FRAC_SRS_1(X, N, sz) __FP_FRAC_SRS_1 (X##_f, (N), (sz)) 55 56#define __FP_FRAC_SRST_1(X, S, N, sz) \ 57 do \ 58 { \ 59 S = (__builtin_constant_p (N) && (N) == 1 \ 60 ? X & 1 \ 61 : (X << (_FP_W_TYPE_SIZE - (N))) != 0); \ 62 X = X >> (N); \ 63 } \ 64 while (0) 65 66#define __FP_FRAC_SRS_1(X, N, sz) \ 67 (X = (X >> (N) | (__builtin_constant_p (N) && (N) == 1 \ 68 ? X & 1 \ 69 : (X << (_FP_W_TYPE_SIZE - (N))) != 0))) 70 71#define _FP_FRAC_ADD_1(R, X, Y) (R##_f = X##_f + Y##_f) 72#define _FP_FRAC_SUB_1(R, X, Y) (R##_f = X##_f - Y##_f) 73#define _FP_FRAC_DEC_1(X, Y) (X##_f -= Y##_f) 74#define _FP_FRAC_CLZ_1(z, X) __FP_CLZ ((z), X##_f) 75 76/* Predicates. */ 77#define _FP_FRAC_NEGP_1(X) ((_FP_WS_TYPE) X##_f < 0) 78#define _FP_FRAC_ZEROP_1(X) (X##_f == 0) 79#define _FP_FRAC_OVERP_1(fs, X) (X##_f & _FP_OVERFLOW_##fs) 80#define _FP_FRAC_CLEAR_OVERP_1(fs, X) (X##_f &= ~_FP_OVERFLOW_##fs) 81#define _FP_FRAC_HIGHBIT_DW_1(fs, X) (X##_f & _FP_HIGHBIT_DW_##fs) 82#define _FP_FRAC_EQ_1(X, Y) (X##_f == Y##_f) 83#define _FP_FRAC_GE_1(X, Y) (X##_f >= Y##_f) 84#define _FP_FRAC_GT_1(X, Y) (X##_f > Y##_f) 85 86#define _FP_ZEROFRAC_1 0 87#define _FP_MINFRAC_1 1 88#define _FP_MAXFRAC_1 (~(_FP_WS_TYPE) 0) 89 90/* Unpack the raw bits of a native fp value. Do not classify or 91 normalize the data. */ 92 93#define _FP_UNPACK_RAW_1(fs, X, val) \ 94 do \ 95 { \ 96 union _FP_UNION_##fs _FP_UNPACK_RAW_1_flo; \ 97 _FP_UNPACK_RAW_1_flo.flt = (val); \ 98 \ 99 X##_f = _FP_UNPACK_RAW_1_flo.bits.frac; \ 100 X##_e = _FP_UNPACK_RAW_1_flo.bits.exp; \ 101 X##_s = _FP_UNPACK_RAW_1_flo.bits.sign; \ 102 } \ 103 while (0) 104 105#define _FP_UNPACK_RAW_1_P(fs, X, val) \ 106 do \ 107 { \ 108 union _FP_UNION_##fs *_FP_UNPACK_RAW_1_P_flo \ 109 = (union _FP_UNION_##fs *) (val); \ 110 \ 111 X##_f = _FP_UNPACK_RAW_1_P_flo->bits.frac; \ 112 X##_e = _FP_UNPACK_RAW_1_P_flo->bits.exp; \ 113 X##_s = _FP_UNPACK_RAW_1_P_flo->bits.sign; \ 114 } \ 115 while (0) 116 117/* Repack the raw bits of a native fp value. */ 118 119#define _FP_PACK_RAW_1(fs, val, X) \ 120 do \ 121 { \ 122 union _FP_UNION_##fs _FP_PACK_RAW_1_flo; \ 123 \ 124 _FP_PACK_RAW_1_flo.bits.frac = X##_f; \ 125 _FP_PACK_RAW_1_flo.bits.exp = X##_e; \ 126 _FP_PACK_RAW_1_flo.bits.sign = X##_s; \ 127 \ 128 (val) = _FP_PACK_RAW_1_flo.flt; \ 129 } \ 130 while (0) 131 132#define _FP_PACK_RAW_1_P(fs, val, X) \ 133 do \ 134 { \ 135 union _FP_UNION_##fs *_FP_PACK_RAW_1_P_flo \ 136 = (union _FP_UNION_##fs *) (val); \ 137 \ 138 _FP_PACK_RAW_1_P_flo->bits.frac = X##_f; \ 139 _FP_PACK_RAW_1_P_flo->bits.exp = X##_e; \ 140 _FP_PACK_RAW_1_P_flo->bits.sign = X##_s; \ 141 } \ 142 while (0) 143 144 145/* Multiplication algorithms: */ 146 147/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the 148 multiplication immediately. */ 149 150#define _FP_MUL_MEAT_DW_1_imm(wfracbits, R, X, Y) \ 151 do \ 152 { \ 153 R##_f = X##_f * Y##_f; \ 154 } \ 155 while (0) 156 157#define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y) \ 158 do \ 159 { \ 160 _FP_MUL_MEAT_DW_1_imm ((wfracbits), R, X, Y); \ 161 /* Normalize since we know where the msb of the multiplicands \ 162 were (bit B), we know that the msb of the of the product is \ 163 at either 2B or 2B-1. */ \ 164 _FP_FRAC_SRS_1 (R, (wfracbits)-1, 2*(wfracbits)); \ 165 } \ 166 while (0) 167 168/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */ 169 170#define _FP_MUL_MEAT_DW_1_wide(wfracbits, R, X, Y, doit) \ 171 do \ 172 { \ 173 doit (R##_f1, R##_f0, X##_f, Y##_f); \ 174 } \ 175 while (0) 176 177#define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit) \ 178 do \ 179 { \ 180 _FP_FRAC_DECL_2 (_FP_MUL_MEAT_1_wide_Z); \ 181 _FP_MUL_MEAT_DW_1_wide ((wfracbits), _FP_MUL_MEAT_1_wide_Z, \ 182 X, Y, doit); \ 183 /* Normalize since we know where the msb of the multiplicands \ 184 were (bit B), we know that the msb of the of the product is \ 185 at either 2B or 2B-1. */ \ 186 _FP_FRAC_SRS_2 (_FP_MUL_MEAT_1_wide_Z, (wfracbits)-1, \ 187 2*(wfracbits)); \ 188 R##_f = _FP_MUL_MEAT_1_wide_Z_f0; \ 189 } \ 190 while (0) 191 192/* Finally, a simple widening multiply algorithm. What fun! */ 193 194#define _FP_MUL_MEAT_DW_1_hard(wfracbits, R, X, Y) \ 195 do \ 196 { \ 197 _FP_W_TYPE _FP_MUL_MEAT_DW_1_hard_xh, _FP_MUL_MEAT_DW_1_hard_xl; \ 198 _FP_W_TYPE _FP_MUL_MEAT_DW_1_hard_yh, _FP_MUL_MEAT_DW_1_hard_yl; \ 199 _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_1_hard_a); \ 200 \ 201 /* Split the words in half. */ \ 202 _FP_MUL_MEAT_DW_1_hard_xh = X##_f >> (_FP_W_TYPE_SIZE/2); \ 203 _FP_MUL_MEAT_DW_1_hard_xl \ 204 = X##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1); \ 205 _FP_MUL_MEAT_DW_1_hard_yh = Y##_f >> (_FP_W_TYPE_SIZE/2); \ 206 _FP_MUL_MEAT_DW_1_hard_yl \ 207 = Y##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1); \ 208 \ 209 /* Multiply the pieces. */ \ 210 R##_f0 = _FP_MUL_MEAT_DW_1_hard_xl * _FP_MUL_MEAT_DW_1_hard_yl; \ 211 _FP_MUL_MEAT_DW_1_hard_a_f0 \ 212 = _FP_MUL_MEAT_DW_1_hard_xh * _FP_MUL_MEAT_DW_1_hard_yl; \ 213 _FP_MUL_MEAT_DW_1_hard_a_f1 \ 214 = _FP_MUL_MEAT_DW_1_hard_xl * _FP_MUL_MEAT_DW_1_hard_yh; \ 215 R##_f1 = _FP_MUL_MEAT_DW_1_hard_xh * _FP_MUL_MEAT_DW_1_hard_yh; \ 216 \ 217 /* Reassemble into two full words. */ \ 218 if ((_FP_MUL_MEAT_DW_1_hard_a_f0 += _FP_MUL_MEAT_DW_1_hard_a_f1) \ 219 < _FP_MUL_MEAT_DW_1_hard_a_f1) \ 220 R##_f1 += (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2); \ 221 _FP_MUL_MEAT_DW_1_hard_a_f1 \ 222 = _FP_MUL_MEAT_DW_1_hard_a_f0 >> (_FP_W_TYPE_SIZE/2); \ 223 _FP_MUL_MEAT_DW_1_hard_a_f0 \ 224 = _FP_MUL_MEAT_DW_1_hard_a_f0 << (_FP_W_TYPE_SIZE/2); \ 225 _FP_FRAC_ADD_2 (R, R, _FP_MUL_MEAT_DW_1_hard_a); \ 226 } \ 227 while (0) 228 229#define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y) \ 230 do \ 231 { \ 232 _FP_FRAC_DECL_2 (_FP_MUL_MEAT_1_hard_z); \ 233 _FP_MUL_MEAT_DW_1_hard ((wfracbits), \ 234 _FP_MUL_MEAT_1_hard_z, X, Y); \ 235 \ 236 /* Normalize. */ \ 237 _FP_FRAC_SRS_2 (_FP_MUL_MEAT_1_hard_z, \ 238 (wfracbits) - 1, 2*(wfracbits)); \ 239 R##_f = _FP_MUL_MEAT_1_hard_z_f0; \ 240 } \ 241 while (0) 242 243 244/* Division algorithms: */ 245 246/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the 247 division immediately. Give this macro either _FP_DIV_HELP_imm for 248 C primitives or _FP_DIV_HELP_ldiv for the ISO function. Which you 249 choose will depend on what the compiler does with divrem4. */ 250 251#define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit) \ 252 do \ 253 { \ 254 _FP_W_TYPE _FP_DIV_MEAT_1_imm_q, _FP_DIV_MEAT_1_imm_r; \ 255 X##_f <<= (X##_f < Y##_f \ 256 ? R##_e--, _FP_WFRACBITS_##fs \ 257 : _FP_WFRACBITS_##fs - 1); \ 258 doit (_FP_DIV_MEAT_1_imm_q, _FP_DIV_MEAT_1_imm_r, X##_f, Y##_f); \ 259 R##_f = _FP_DIV_MEAT_1_imm_q | (_FP_DIV_MEAT_1_imm_r != 0); \ 260 } \ 261 while (0) 262 263/* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd 264 that may be useful in this situation. This first is for a primitive 265 that requires normalization, the second for one that does not. Look 266 for UDIV_NEEDS_NORMALIZATION to tell which your machine needs. */ 267 268#define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y) \ 269 do \ 270 { \ 271 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_nh; \ 272 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_nl; \ 273 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_q; \ 274 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_r; \ 275 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_y; \ 276 \ 277 /* Normalize Y -- i.e. make the most significant bit set. */ \ 278 _FP_DIV_MEAT_1_udiv_norm_y = Y##_f << _FP_WFRACXBITS_##fs; \ 279 \ 280 /* Shift X op correspondingly high, that is, up one full word. */ \ 281 if (X##_f < Y##_f) \ 282 { \ 283 R##_e--; \ 284 _FP_DIV_MEAT_1_udiv_norm_nl = 0; \ 285 _FP_DIV_MEAT_1_udiv_norm_nh = X##_f; \ 286 } \ 287 else \ 288 { \ 289 _FP_DIV_MEAT_1_udiv_norm_nl = X##_f << (_FP_W_TYPE_SIZE - 1); \ 290 _FP_DIV_MEAT_1_udiv_norm_nh = X##_f >> 1; \ 291 } \ 292 \ 293 udiv_qrnnd (_FP_DIV_MEAT_1_udiv_norm_q, \ 294 _FP_DIV_MEAT_1_udiv_norm_r, \ 295 _FP_DIV_MEAT_1_udiv_norm_nh, \ 296 _FP_DIV_MEAT_1_udiv_norm_nl, \ 297 _FP_DIV_MEAT_1_udiv_norm_y); \ 298 R##_f = (_FP_DIV_MEAT_1_udiv_norm_q \ 299 | (_FP_DIV_MEAT_1_udiv_norm_r != 0)); \ 300 } \ 301 while (0) 302 303#define _FP_DIV_MEAT_1_udiv(fs, R, X, Y) \ 304 do \ 305 { \ 306 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_nh, _FP_DIV_MEAT_1_udiv_nl; \ 307 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_q, _FP_DIV_MEAT_1_udiv_r; \ 308 if (X##_f < Y##_f) \ 309 { \ 310 R##_e--; \ 311 _FP_DIV_MEAT_1_udiv_nl = X##_f << _FP_WFRACBITS_##fs; \ 312 _FP_DIV_MEAT_1_udiv_nh = X##_f >> _FP_WFRACXBITS_##fs; \ 313 } \ 314 else \ 315 { \ 316 _FP_DIV_MEAT_1_udiv_nl = X##_f << (_FP_WFRACBITS_##fs - 1); \ 317 _FP_DIV_MEAT_1_udiv_nh = X##_f >> (_FP_WFRACXBITS_##fs + 1); \ 318 } \ 319 udiv_qrnnd (_FP_DIV_MEAT_1_udiv_q, _FP_DIV_MEAT_1_udiv_r, \ 320 _FP_DIV_MEAT_1_udiv_nh, _FP_DIV_MEAT_1_udiv_nl, \ 321 Y##_f); \ 322 R##_f = _FP_DIV_MEAT_1_udiv_q | (_FP_DIV_MEAT_1_udiv_r != 0); \ 323 } \ 324 while (0) 325 326 327/* Square root algorithms: 328 We have just one right now, maybe Newton approximation 329 should be added for those machines where division is fast. */ 330 331#define _FP_SQRT_MEAT_1(R, S, T, X, q) \ 332 do \ 333 { \ 334 while ((q) != _FP_WORK_ROUND) \ 335 { \ 336 T##_f = S##_f + (q); \ 337 if (T##_f <= X##_f) \ 338 { \ 339 S##_f = T##_f + (q); \ 340 X##_f -= T##_f; \ 341 R##_f += (q); \ 342 } \ 343 _FP_FRAC_SLL_1 (X, 1); \ 344 (q) >>= 1; \ 345 } \ 346 if (X##_f) \ 347 { \ 348 if (S##_f < X##_f) \ 349 R##_f |= _FP_WORK_ROUND; \ 350 R##_f |= _FP_WORK_STICKY; \ 351 } \ 352 } \ 353 while (0) 354 355/* Assembly/disassembly for converting to/from integral types. 356 No shifting or overflow handled here. */ 357 358#define _FP_FRAC_ASSEMBLE_1(r, X, rsize) ((r) = X##_f) 359#define _FP_FRAC_DISASSEMBLE_1(X, r, rsize) (X##_f = (r)) 360 361 362/* Convert FP values between word sizes. */ 363 364#define _FP_FRAC_COPY_1_1(D, S) (D##_f = S##_f) 365