1/* Software floating-point emulation.
2 Basic one-word fraction declaration and manipulation.
3 Copyright (C) 1997-2021 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 <https://www.gnu.org/licenses/>. */
32
33#ifndef SOFT_FP_OP_1_H
34#define SOFT_FP_OP_1_H 1
35
36#define _FP_FRAC_DECL_1(X) _FP_W_TYPE X##_f _FP_ZERO_INIT
37#define _FP_FRAC_COPY_1(D, S) (D##_f = S##_f)
38#define _FP_FRAC_SET_1(X, I) (X##_f = I)
39#define _FP_FRAC_HIGH_1(X) (X##_f)
40#define _FP_FRAC_LOW_1(X) (X##_f)
41#define _FP_FRAC_WORD_1(X, w) (X##_f)
42
43#define _FP_FRAC_ADDI_1(X, I) (X##_f += I)
44#define _FP_FRAC_SLL_1(X, N) \
45 do \
46 { \
47 if (__builtin_constant_p (N) && (N) == 1) \
48 X##_f += X##_f; \
49 else \
50 X##_f <<= (N); \
51 } \
52 while (0)
53#define _FP_FRAC_SRL_1(X, N) (X##_f >>= N)
54
55/* Right shift with sticky-lsb. */
56#define _FP_FRAC_SRST_1(X, S, N, sz) __FP_FRAC_SRST_1 (X##_f, S, (N), (sz))
57#define _FP_FRAC_SRS_1(X, N, sz) __FP_FRAC_SRS_1 (X##_f, (N), (sz))
58
59#define __FP_FRAC_SRST_1(X, S, N, sz) \
60 do \
61 { \
62 S = (__builtin_constant_p (N) && (N) == 1 \
63 ? X & 1 \
64 : (X << (_FP_W_TYPE_SIZE - (N))) != 0); \
65 X = X >> (N); \
66 } \
67 while (0)
68
69#define __FP_FRAC_SRS_1(X, N, sz) \
70 (X = (X >> (N) | (__builtin_constant_p (N) && (N) == 1 \
71 ? X & 1 \
72 : (X << (_FP_W_TYPE_SIZE - (N))) != 0)))
73
74#define _FP_FRAC_ADD_1(R, X, Y) (R##_f = X##_f + Y##_f)
75#define _FP_FRAC_SUB_1(R, X, Y) (R##_f = X##_f - Y##_f)
76#define _FP_FRAC_DEC_1(X, Y) (X##_f -= Y##_f)
77#define _FP_FRAC_CLZ_1(z, X) __FP_CLZ ((z), X##_f)
78
79/* Predicates. */
80#define _FP_FRAC_NEGP_1(X) ((_FP_WS_TYPE) X##_f < 0)
81#define _FP_FRAC_ZEROP_1(X) (X##_f == 0)
82#define _FP_FRAC_OVERP_1(fs, X) (X##_f & _FP_OVERFLOW_##fs)
83#define _FP_FRAC_CLEAR_OVERP_1(fs, X) (X##_f &= ~_FP_OVERFLOW_##fs)
84#define _FP_FRAC_HIGHBIT_DW_1(fs, X) (X##_f & _FP_HIGHBIT_DW_##fs)
85#define _FP_FRAC_EQ_1(X, Y) (X##_f == Y##_f)
86#define _FP_FRAC_GE_1(X, Y) (X##_f >= Y##_f)
87#define _FP_FRAC_GT_1(X, Y) (X##_f > Y##_f)
88
89#define _FP_ZEROFRAC_1 0
90#define _FP_MINFRAC_1 1
91#define _FP_MAXFRAC_1 (~(_FP_WS_TYPE) 0)
92
93/* Unpack the raw bits of a native fp value. Do not classify or
94 normalize the data. */
95
96#define _FP_UNPACK_RAW_1(fs, X, val) \
97 do \
98 { \
99 union _FP_UNION_##fs _FP_UNPACK_RAW_1_flo; \
100 _FP_UNPACK_RAW_1_flo.flt = (val); \
101 \
102 X##_f = _FP_UNPACK_RAW_1_flo.bits.frac; \
103 X##_e = _FP_UNPACK_RAW_1_flo.bits.exp; \
104 X##_s = _FP_UNPACK_RAW_1_flo.bits.sign; \
105 } \
106 while (0)
107
108#define _FP_UNPACK_RAW_1_P(fs, X, val) \
109 do \
110 { \
111 union _FP_UNION_##fs *_FP_UNPACK_RAW_1_P_flo \
112 = (union _FP_UNION_##fs *) (val); \
113 \
114 X##_f = _FP_UNPACK_RAW_1_P_flo->bits.frac; \
115 X##_e = _FP_UNPACK_RAW_1_P_flo->bits.exp; \
116 X##_s = _FP_UNPACK_RAW_1_P_flo->bits.sign; \
117 } \
118 while (0)
119
120/* Repack the raw bits of a native fp value. */
121
122#define _FP_PACK_RAW_1(fs, val, X) \
123 do \
124 { \
125 union _FP_UNION_##fs _FP_PACK_RAW_1_flo; \
126 \
127 _FP_PACK_RAW_1_flo.bits.frac = X##_f; \
128 _FP_PACK_RAW_1_flo.bits.exp = X##_e; \
129 _FP_PACK_RAW_1_flo.bits.sign = X##_s; \
130 \
131 (val) = _FP_PACK_RAW_1_flo.flt; \
132 } \
133 while (0)
134
135#define _FP_PACK_RAW_1_P(fs, val, X) \
136 do \
137 { \
138 union _FP_UNION_##fs *_FP_PACK_RAW_1_P_flo \
139 = (union _FP_UNION_##fs *) (val); \
140 \
141 _FP_PACK_RAW_1_P_flo->bits.frac = X##_f; \
142 _FP_PACK_RAW_1_P_flo->bits.exp = X##_e; \
143 _FP_PACK_RAW_1_P_flo->bits.sign = X##_s; \
144 } \
145 while (0)
146
147
148/* Multiplication algorithms: */
149
150/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the
151 multiplication immediately. */
152
153#define _FP_MUL_MEAT_DW_1_imm(wfracbits, R, X, Y) \
154 do \
155 { \
156 R##_f = X##_f * Y##_f; \
157 } \
158 while (0)
159
160#define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y) \
161 do \
162 { \
163 _FP_MUL_MEAT_DW_1_imm ((wfracbits), R, X, Y); \
164 /* Normalize since we know where the msb of the multiplicands \
165 were (bit B), we know that the msb of the of the product is \
166 at either 2B or 2B-1. */ \
167 _FP_FRAC_SRS_1 (R, (wfracbits)-1, 2*(wfracbits)); \
168 } \
169 while (0)
170
171/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
172
173#define _FP_MUL_MEAT_DW_1_wide(wfracbits, R, X, Y, doit) \
174 do \
175 { \
176 doit (R##_f1, R##_f0, X##_f, Y##_f); \
177 } \
178 while (0)
179
180#define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit) \
181 do \
182 { \
183 _FP_FRAC_DECL_2 (_FP_MUL_MEAT_1_wide_Z); \
184 _FP_MUL_MEAT_DW_1_wide ((wfracbits), _FP_MUL_MEAT_1_wide_Z, \
185 X, Y, doit); \
186 /* Normalize since we know where the msb of the multiplicands \
187 were (bit B), we know that the msb of the of the product is \
188 at either 2B or 2B-1. */ \
189 _FP_FRAC_SRS_2 (_FP_MUL_MEAT_1_wide_Z, (wfracbits)-1, \
190 2*(wfracbits)); \
191 R##_f = _FP_MUL_MEAT_1_wide_Z_f0; \
192 } \
193 while (0)
194
195/* Finally, a simple widening multiply algorithm. What fun! */
196
197#define _FP_MUL_MEAT_DW_1_hard(wfracbits, R, X, Y) \
198 do \
199 { \
200 _FP_W_TYPE _FP_MUL_MEAT_DW_1_hard_xh, _FP_MUL_MEAT_DW_1_hard_xl; \
201 _FP_W_TYPE _FP_MUL_MEAT_DW_1_hard_yh, _FP_MUL_MEAT_DW_1_hard_yl; \
202 _FP_FRAC_DECL_2 (_FP_MUL_MEAT_DW_1_hard_a); \
203 \
204 /* Split the words in half. */ \
205 _FP_MUL_MEAT_DW_1_hard_xh = X##_f >> (_FP_W_TYPE_SIZE/2); \
206 _FP_MUL_MEAT_DW_1_hard_xl \
207 = X##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1); \
208 _FP_MUL_MEAT_DW_1_hard_yh = Y##_f >> (_FP_W_TYPE_SIZE/2); \
209 _FP_MUL_MEAT_DW_1_hard_yl \
210 = Y##_f & (((_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2)) - 1); \
211 \
212 /* Multiply the pieces. */ \
213 R##_f0 = _FP_MUL_MEAT_DW_1_hard_xl * _FP_MUL_MEAT_DW_1_hard_yl; \
214 _FP_MUL_MEAT_DW_1_hard_a_f0 \
215 = _FP_MUL_MEAT_DW_1_hard_xh * _FP_MUL_MEAT_DW_1_hard_yl; \
216 _FP_MUL_MEAT_DW_1_hard_a_f1 \
217 = _FP_MUL_MEAT_DW_1_hard_xl * _FP_MUL_MEAT_DW_1_hard_yh; \
218 R##_f1 = _FP_MUL_MEAT_DW_1_hard_xh * _FP_MUL_MEAT_DW_1_hard_yh; \
219 \
220 /* Reassemble into two full words. */ \
221 if ((_FP_MUL_MEAT_DW_1_hard_a_f0 += _FP_MUL_MEAT_DW_1_hard_a_f1) \
222 < _FP_MUL_MEAT_DW_1_hard_a_f1) \
223 R##_f1 += (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE/2); \
224 _FP_MUL_MEAT_DW_1_hard_a_f1 \
225 = _FP_MUL_MEAT_DW_1_hard_a_f0 >> (_FP_W_TYPE_SIZE/2); \
226 _FP_MUL_MEAT_DW_1_hard_a_f0 \
227 = _FP_MUL_MEAT_DW_1_hard_a_f0 << (_FP_W_TYPE_SIZE/2); \
228 _FP_FRAC_ADD_2 (R, R, _FP_MUL_MEAT_DW_1_hard_a); \
229 } \
230 while (0)
231
232#define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y) \
233 do \
234 { \
235 _FP_FRAC_DECL_2 (_FP_MUL_MEAT_1_hard_z); \
236 _FP_MUL_MEAT_DW_1_hard ((wfracbits), \
237 _FP_MUL_MEAT_1_hard_z, X, Y); \
238 \
239 /* Normalize. */ \
240 _FP_FRAC_SRS_2 (_FP_MUL_MEAT_1_hard_z, \
241 (wfracbits) - 1, 2*(wfracbits)); \
242 R##_f = _FP_MUL_MEAT_1_hard_z_f0; \
243 } \
244 while (0)
245
246
247/* Division algorithms: */
248
249/* Basic. Assuming the host word size is >= 2*FRACBITS, we can do the
250 division immediately. Give this macro either _FP_DIV_HELP_imm for
251 C primitives or _FP_DIV_HELP_ldiv for the ISO function. Which you
252 choose will depend on what the compiler does with divrem4. */
253
254#define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit) \
255 do \
256 { \
257 _FP_W_TYPE _FP_DIV_MEAT_1_imm_q, _FP_DIV_MEAT_1_imm_r; \
258 X##_f <<= (X##_f < Y##_f \
259 ? R##_e--, _FP_WFRACBITS_##fs \
260 : _FP_WFRACBITS_##fs - 1); \
261 doit (_FP_DIV_MEAT_1_imm_q, _FP_DIV_MEAT_1_imm_r, X##_f, Y##_f); \
262 R##_f = _FP_DIV_MEAT_1_imm_q | (_FP_DIV_MEAT_1_imm_r != 0); \
263 } \
264 while (0)
265
266/* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd
267 that may be useful in this situation. This first is for a primitive
268 that requires normalization, the second for one that does not. Look
269 for UDIV_NEEDS_NORMALIZATION to tell which your machine needs. */
270
271#define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y) \
272 do \
273 { \
274 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_nh; \
275 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_nl; \
276 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_q; \
277 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_r; \
278 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_norm_y; \
279 \
280 /* Normalize Y -- i.e. make the most significant bit set. */ \
281 _FP_DIV_MEAT_1_udiv_norm_y = Y##_f << _FP_WFRACXBITS_##fs; \
282 \
283 /* Shift X op correspondingly high, that is, up one full word. */ \
284 if (X##_f < Y##_f) \
285 { \
286 R##_e--; \
287 _FP_DIV_MEAT_1_udiv_norm_nl = 0; \
288 _FP_DIV_MEAT_1_udiv_norm_nh = X##_f; \
289 } \
290 else \
291 { \
292 _FP_DIV_MEAT_1_udiv_norm_nl = X##_f << (_FP_W_TYPE_SIZE - 1); \
293 _FP_DIV_MEAT_1_udiv_norm_nh = X##_f >> 1; \
294 } \
295 \
296 udiv_qrnnd (_FP_DIV_MEAT_1_udiv_norm_q, \
297 _FP_DIV_MEAT_1_udiv_norm_r, \
298 _FP_DIV_MEAT_1_udiv_norm_nh, \
299 _FP_DIV_MEAT_1_udiv_norm_nl, \
300 _FP_DIV_MEAT_1_udiv_norm_y); \
301 R##_f = (_FP_DIV_MEAT_1_udiv_norm_q \
302 | (_FP_DIV_MEAT_1_udiv_norm_r != 0)); \
303 } \
304 while (0)
305
306#define _FP_DIV_MEAT_1_udiv(fs, R, X, Y) \
307 do \
308 { \
309 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_nh, _FP_DIV_MEAT_1_udiv_nl; \
310 _FP_W_TYPE _FP_DIV_MEAT_1_udiv_q, _FP_DIV_MEAT_1_udiv_r; \
311 if (X##_f < Y##_f) \
312 { \
313 R##_e--; \
314 _FP_DIV_MEAT_1_udiv_nl = X##_f << _FP_WFRACBITS_##fs; \
315 _FP_DIV_MEAT_1_udiv_nh = X##_f >> _FP_WFRACXBITS_##fs; \
316 } \
317 else \
318 { \
319 _FP_DIV_MEAT_1_udiv_nl = X##_f << (_FP_WFRACBITS_##fs - 1); \
320 _FP_DIV_MEAT_1_udiv_nh = X##_f >> (_FP_WFRACXBITS_##fs + 1); \
321 } \
322 udiv_qrnnd (_FP_DIV_MEAT_1_udiv_q, _FP_DIV_MEAT_1_udiv_r, \
323 _FP_DIV_MEAT_1_udiv_nh, _FP_DIV_MEAT_1_udiv_nl, \
324 Y##_f); \
325 R##_f = _FP_DIV_MEAT_1_udiv_q | (_FP_DIV_MEAT_1_udiv_r != 0); \
326 } \
327 while (0)
328
329
330/* Square root algorithms:
331 We have just one right now, maybe Newton approximation
332 should be added for those machines where division is fast. */
333
334#define _FP_SQRT_MEAT_1(R, S, T, X, q) \
335 do \
336 { \
337 while ((q) != _FP_WORK_ROUND) \
338 { \
339 T##_f = S##_f + (q); \
340 if (T##_f <= X##_f) \
341 { \
342 S##_f = T##_f + (q); \
343 X##_f -= T##_f; \
344 R##_f += (q); \
345 } \
346 _FP_FRAC_SLL_1 (X, 1); \
347 (q) >>= 1; \
348 } \
349 if (X##_f) \
350 { \
351 if (S##_f < X##_f) \
352 R##_f |= _FP_WORK_ROUND; \
353 R##_f |= _FP_WORK_STICKY; \
354 } \
355 } \
356 while (0)
357
358/* Assembly/disassembly for converting to/from integral types.
359 No shifting or overflow handled here. */
360
361#define _FP_FRAC_ASSEMBLE_1(r, X, rsize) ((r) = X##_f)
362#define _FP_FRAC_DISASSEMBLE_1(X, r, rsize) (X##_f = (r))
363
364
365/* Convert FP values between word sizes. */
366
367#define _FP_FRAC_COPY_1_1(D, S) (D##_f = S##_f)
368
369#endif /* !SOFT_FP_OP_1_H */
370