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1 /* Software floating-point emulation.
2    Basic one-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_1_H__
26 #define    __MATH_EMU_OP_1_H__
27 
28 #define _FP_FRAC_DECL_1(X)	_FP_W_TYPE X##_f=0
29 #define _FP_FRAC_COPY_1(D,S)	(D##_f = S##_f)
30 #define _FP_FRAC_SET_1(X,I)	(X##_f = I)
31 #define _FP_FRAC_HIGH_1(X)	(X##_f)
32 #define _FP_FRAC_LOW_1(X)	(X##_f)
33 #define _FP_FRAC_WORD_1(X,w)	(X##_f)
34 
35 #define _FP_FRAC_ADDI_1(X,I)	(X##_f += I)
36 #define _FP_FRAC_SLL_1(X,N)			\
37   do {						\
38     if (__builtin_constant_p(N) && (N) == 1)	\
39       X##_f += X##_f;				\
40     else					\
41       X##_f <<= (N);				\
42   } while (0)
43 #define _FP_FRAC_SRL_1(X,N)	(X##_f >>= N)
44 
45 /* Right shift with sticky-lsb.  */
46 #define _FP_FRAC_SRS_1(X,N,sz)	__FP_FRAC_SRS_1(X##_f, N, sz)
47 
48 #define __FP_FRAC_SRS_1(X,N,sz)						\
49    (X = (X >> (N) | (__builtin_constant_p(N) && (N) == 1		\
50 		     ? X & 1 : (X << (_FP_W_TYPE_SIZE - (N))) != 0)))
51 
52 #define _FP_FRAC_ADD_1(R,X,Y)	(R##_f = X##_f + Y##_f)
53 #define _FP_FRAC_SUB_1(R,X,Y)	(R##_f = X##_f - Y##_f)
54 #define _FP_FRAC_DEC_1(X,Y)	(X##_f -= Y##_f)
55 #define _FP_FRAC_CLZ_1(z, X)	__FP_CLZ(z, X##_f)
56 
57 /* Predicates */
58 #define _FP_FRAC_NEGP_1(X)	((_FP_WS_TYPE)X##_f < 0)
59 #define _FP_FRAC_ZEROP_1(X)	(X##_f == 0)
60 #define _FP_FRAC_OVERP_1(fs,X)	(X##_f & _FP_OVERFLOW_##fs)
61 #define _FP_FRAC_CLEAR_OVERP_1(fs,X)	(X##_f &= ~_FP_OVERFLOW_##fs)
62 #define _FP_FRAC_EQ_1(X, Y)	(X##_f == Y##_f)
63 #define _FP_FRAC_GE_1(X, Y)	(X##_f >= Y##_f)
64 #define _FP_FRAC_GT_1(X, Y)	(X##_f > Y##_f)
65 
66 #define _FP_ZEROFRAC_1		0
67 #define _FP_MINFRAC_1		1
68 #define _FP_MAXFRAC_1		(~(_FP_WS_TYPE)0)
69 
70 /*
71  * Unpack the raw bits of a native fp value.  Do not classify or
72  * normalize the data.
73  */
74 
75 #define _FP_UNPACK_RAW_1(fs, X, val)				\
76   do {								\
77     union _FP_UNION_##fs _flo; _flo.flt = (val);		\
78 								\
79     X##_f = _flo.bits.frac;					\
80     X##_e = _flo.bits.exp;					\
81     X##_s = _flo.bits.sign;					\
82   } while (0)
83 
84 #define _FP_UNPACK_RAW_1_P(fs, X, val)				\
85   do {								\
86     union _FP_UNION_##fs *_flo =				\
87       (union _FP_UNION_##fs *)(val);				\
88 								\
89     X##_f = _flo->bits.frac;					\
90     X##_e = _flo->bits.exp;					\
91     X##_s = _flo->bits.sign;					\
92   } while (0)
93 
94 /*
95  * Repack the raw bits of a native fp value.
96  */
97 
98 #define _FP_PACK_RAW_1(fs, val, X)				\
99   do {								\
100     union _FP_UNION_##fs _flo;					\
101 								\
102     _flo.bits.frac = X##_f;					\
103     _flo.bits.exp  = X##_e;					\
104     _flo.bits.sign = X##_s;					\
105 								\
106     (val) = _flo.flt;						\
107   } while (0)
108 
109 #define _FP_PACK_RAW_1_P(fs, val, X)				\
110   do {								\
111     union _FP_UNION_##fs *_flo =				\
112       (union _FP_UNION_##fs *)(val);				\
113 								\
114     _flo->bits.frac = X##_f;					\
115     _flo->bits.exp  = X##_e;					\
116     _flo->bits.sign = X##_s;					\
117   } while (0)
118 
119 
120 /*
121  * Multiplication algorithms:
122  */
123 
124 /* Basic.  Assuming the host word size is >= 2*FRACBITS, we can do the
125    multiplication immediately.  */
126 
127 #define _FP_MUL_MEAT_1_imm(wfracbits, R, X, Y)				\
128   do {									\
129     R##_f = X##_f * Y##_f;						\
130     /* Normalize since we know where the msb of the multiplicands	\
131        were (bit B), we know that the msb of the of the product is	\
132        at either 2B or 2B-1.  */					\
133     _FP_FRAC_SRS_1(R, wfracbits-1, 2*wfracbits);			\
134   } while (0)
135 
136 /* Given a 1W * 1W => 2W primitive, do the extended multiplication.  */
137 
138 #define _FP_MUL_MEAT_1_wide(wfracbits, R, X, Y, doit)			\
139   do {									\
140     _FP_W_TYPE _Z_f0, _Z_f1;						\
141     doit(_Z_f1, _Z_f0, X##_f, Y##_f);					\
142     /* Normalize since we know where the msb of the multiplicands	\
143        were (bit B), we know that the msb of the of the product is	\
144        at either 2B or 2B-1.  */					\
145     _FP_FRAC_SRS_2(_Z, wfracbits-1, 2*wfracbits);			\
146     R##_f = _Z_f0;							\
147   } while (0)
148 
149 /* Finally, a simple widening multiply algorithm.  What fun!  */
150 
151 #define _FP_MUL_MEAT_1_hard(wfracbits, R, X, Y)				\
152   do {									\
153     _FP_W_TYPE _xh, _xl, _yh, _yl, _z_f0, _z_f1, _a_f0, _a_f1;		\
154 									\
155     /* split the words in half */					\
156     _xh = X##_f >> (_FP_W_TYPE_SIZE/2);					\
157     _xl = X##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1);		\
158     _yh = Y##_f >> (_FP_W_TYPE_SIZE/2);					\
159     _yl = Y##_f & (((_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2)) - 1);		\
160 									\
161     /* multiply the pieces */						\
162     _z_f0 = _xl * _yl;							\
163     _a_f0 = _xh * _yl;							\
164     _a_f1 = _xl * _yh;							\
165     _z_f1 = _xh * _yh;							\
166 									\
167     /* reassemble into two full words */				\
168     if ((_a_f0 += _a_f1) < _a_f1)					\
169       _z_f1 += (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE/2);			\
170     _a_f1 = _a_f0 >> (_FP_W_TYPE_SIZE/2);				\
171     _a_f0 = _a_f0 << (_FP_W_TYPE_SIZE/2);				\
172     _FP_FRAC_ADD_2(_z, _z, _a);						\
173 									\
174     /* normalize */							\
175     _FP_FRAC_SRS_2(_z, wfracbits - 1, 2*wfracbits);			\
176     R##_f = _z_f0;							\
177   } while (0)
178 
179 
180 /*
181  * Division algorithms:
182  */
183 
184 /* Basic.  Assuming the host word size is >= 2*FRACBITS, we can do the
185    division immediately.  Give this macro either _FP_DIV_HELP_imm for
186    C primitives or _FP_DIV_HELP_ldiv for the ISO function.  Which you
187    choose will depend on what the compiler does with divrem4.  */
188 
189 #define _FP_DIV_MEAT_1_imm(fs, R, X, Y, doit)		\
190   do {							\
191     _FP_W_TYPE _q, _r;					\
192     X##_f <<= (X##_f < Y##_f				\
193 	       ? R##_e--, _FP_WFRACBITS_##fs		\
194 	       : _FP_WFRACBITS_##fs - 1);		\
195     doit(_q, _r, X##_f, Y##_f);				\
196     R##_f = _q | (_r != 0);				\
197   } while (0)
198 
199 /* GCC's longlong.h defines a 2W / 1W => (1W,1W) primitive udiv_qrnnd
200    that may be useful in this situation.  This first is for a primitive
201    that requires normalization, the second for one that does not.  Look
202    for UDIV_NEEDS_NORMALIZATION to tell which your machine needs.  */
203 
204 #define _FP_DIV_MEAT_1_udiv_norm(fs, R, X, Y)				\
205   do {									\
206     _FP_W_TYPE _nh, _nl, _q, _r, _y;					\
207 									\
208     /* Normalize Y -- i.e. make the most significant bit set.  */	\
209     _y = Y##_f << _FP_WFRACXBITS_##fs;					\
210 									\
211     /* Shift X op correspondingly high, that is, up one full word.  */	\
212     if (X##_f < Y##_f)							\
213       {									\
214 	R##_e--;							\
215 	_nl = 0;							\
216 	_nh = X##_f;							\
217       }									\
218     else								\
219       {									\
220 	_nl = X##_f << (_FP_W_TYPE_SIZE - 1);				\
221 	_nh = X##_f >> 1;						\
222       }									\
223     									\
224     udiv_qrnnd(_q, _r, _nh, _nl, _y);					\
225     R##_f = _q | (_r != 0);						\
226   } while (0)
227 
228 #define _FP_DIV_MEAT_1_udiv(fs, R, X, Y)		\
229   do {							\
230     _FP_W_TYPE _nh, _nl, _q, _r;			\
231     if (X##_f < Y##_f)					\
232       {							\
233 	R##_e--;					\
234 	_nl = X##_f << _FP_WFRACBITS_##fs;		\
235 	_nh = X##_f >> _FP_WFRACXBITS_##fs;		\
236       }							\
237     else						\
238       {							\
239 	_nl = X##_f << (_FP_WFRACBITS_##fs - 1);	\
240 	_nh = X##_f >> (_FP_WFRACXBITS_##fs + 1);	\
241       }							\
242     udiv_qrnnd(_q, _r, _nh, _nl, Y##_f);		\
243     R##_f = _q | (_r != 0);				\
244   } while (0)
245 
246 
247 /*
248  * Square root algorithms:
249  * We have just one right now, maybe Newton approximation
250  * should be added for those machines where division is fast.
251  */
252 
253 #define _FP_SQRT_MEAT_1(R, S, T, X, q)			\
254   do {							\
255     while (q != _FP_WORK_ROUND)				\
256       {							\
257         T##_f = S##_f + q;				\
258         if (T##_f <= X##_f)				\
259           {						\
260             S##_f = T##_f + q;				\
261             X##_f -= T##_f;				\
262             R##_f += q;					\
263           }						\
264         _FP_FRAC_SLL_1(X, 1);				\
265         q >>= 1;					\
266       }							\
267     if (X##_f)						\
268       {							\
269 	if (S##_f < X##_f)				\
270 	  R##_f |= _FP_WORK_ROUND;			\
271 	R##_f |= _FP_WORK_STICKY;			\
272       }							\
273   } while (0)
274 
275 /*
276  * Assembly/disassembly for converting to/from integral types.
277  * No shifting or overflow handled here.
278  */
279 
280 #define _FP_FRAC_ASSEMBLE_1(r, X, rsize)	(r = X##_f)
281 #define _FP_FRAC_DISASSEMBLE_1(X, r, rsize)	(X##_f = r)
282 
283 
284 /*
285  * Convert FP values between word sizes
286  */
287 
288 #define _FP_FRAC_CONV_1_1(dfs, sfs, D, S)				\
289   do {									\
290     D##_f = S##_f;							\
291     if (_FP_WFRACBITS_##sfs > _FP_WFRACBITS_##dfs)			\
292       {									\
293 	if (S##_c != FP_CLS_NAN)					\
294 	  _FP_FRAC_SRS_1(D, (_FP_WFRACBITS_##sfs-_FP_WFRACBITS_##dfs),	\
295 			 _FP_WFRACBITS_##sfs);				\
296 	else								\
297 	  _FP_FRAC_SRL_1(D, (_FP_WFRACBITS_##sfs-_FP_WFRACBITS_##dfs));	\
298       }									\
299     else								\
300       D##_f <<= _FP_WFRACBITS_##dfs - _FP_WFRACBITS_##sfs;		\
301   } while (0)
302 
303 #endif /* __MATH_EMU_OP_1_H__ */
304