1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
|
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#ifndef _MATH_PRIVATE_H_
#define _MATH_PRIVATE_H_
#include <endian.h>
#include <sys/types.h>
/* The original fdlibm code used statements like:
n0 = ((*(int*)&one)>>29)^1; * index of high word *
ix0 = *(n0+(int*)&x); * high word of x *
ix1 = *((1-n0)+(int*)&x); * low word of x *
to dig two 32 bit words out of the 64 bit IEEE floating point
value. That is non-ANSI, and, moreover, the gcc instruction
scheduler gets it wrong. We instead use the following macros.
Unlike the original code, we determine the endianness at compile
time, not at run time; I don't see much benefit to selecting
endianness at run time. */
/* A union which permits us to convert between a double and two 32 bit
ints. */
/*
* Math on arm is special (read: stupid):
* For FPA, float words are always big-endian.
* For VFP, float words follow the memory system mode.
* For Maverick, float words are always little-endian.
*/
#if !defined(__MAVERICK__) && ((__BYTE_ORDER == __BIG_ENDIAN) || \
(!defined(__VFP_FP__) && (defined(__arm__) || defined(__thumb__))))
typedef union
{
double value;
struct
{
u_int32_t msw;
u_int32_t lsw;
} parts;
} ieee_double_shape_type;
#else
typedef union
{
double value;
struct
{
u_int32_t lsw;
u_int32_t msw;
} parts;
} ieee_double_shape_type;
#endif
/* Get two 32 bit ints from a double. */
#define EXTRACT_WORDS(ix0,ix1,d) \
do { \
ieee_double_shape_type ew_u; \
ew_u.value = (d); \
(ix0) = ew_u.parts.msw; \
(ix1) = ew_u.parts.lsw; \
} while (0)
/* Get the more significant 32 bit int from a double. */
#define GET_HIGH_WORD(i,d) \
do { \
ieee_double_shape_type gh_u; \
gh_u.value = (d); \
(i) = gh_u.parts.msw; \
} while (0)
/* Get the less significant 32 bit int from a double. */
#define GET_LOW_WORD(i,d) \
do { \
ieee_double_shape_type gl_u; \
gl_u.value = (d); \
(i) = gl_u.parts.lsw; \
} while (0)
/* Set a double from two 32 bit ints. */
#define INSERT_WORDS(d,ix0,ix1) \
do { \
ieee_double_shape_type iw_u; \
iw_u.parts.msw = (ix0); \
iw_u.parts.lsw = (ix1); \
(d) = iw_u.value; \
} while (0)
/* Set the more significant 32 bits of a double from an int. */
#define SET_HIGH_WORD(d,v) \
do { \
ieee_double_shape_type sh_u; \
sh_u.value = (d); \
sh_u.parts.msw = (v); \
(d) = sh_u.value; \
} while (0)
/* Set the less significant 32 bits of a double from an int. */
#define SET_LOW_WORD(d,v) \
do { \
ieee_double_shape_type sl_u; \
sl_u.value = (d); \
sl_u.parts.lsw = (v); \
(d) = sl_u.value; \
} while (0)
/* A union which permits us to convert between a float and a 32 bit
int. */
typedef union
{
float value;
u_int32_t word;
} ieee_float_shape_type;
/* Get a 32 bit int from a float. */
#define GET_FLOAT_WORD(i,d) \
do { \
ieee_float_shape_type gf_u; \
gf_u.value = (d); \
(i) = gf_u.word; \
} while (0)
/* Set a float from a 32 bit int. */
#define SET_FLOAT_WORD(d,i) \
do { \
ieee_float_shape_type sf_u; \
sf_u.word = (i); \
(d) = sf_u.value; \
} while (0)
/* ieee style elementary functions */
extern double __ieee754_sqrt (double) attribute_hidden;
extern double __ieee754_acos (double) attribute_hidden;
extern double __ieee754_acosh (double) attribute_hidden;
extern double __ieee754_log (double) attribute_hidden;
extern double __ieee754_log2 (double) attribute_hidden;
extern double __ieee754_atanh (double) attribute_hidden;
extern double __ieee754_asin (double) attribute_hidden;
extern double __ieee754_atan2 (double,double) attribute_hidden;
extern double __ieee754_exp (double) attribute_hidden;
extern double __ieee754_exp10 (double) attribute_hidden;
extern double __ieee754_cosh (double) attribute_hidden;
extern double __ieee754_fmod (double,double) attribute_hidden;
extern double __ieee754_pow (double,double) attribute_hidden;
extern double __ieee754_lgamma_r (double,int *) attribute_hidden;
/*extern double __ieee754_gamma_r (double,int *) attribute_hidden;*/
extern double __ieee754_lgamma (double) attribute_hidden;
/*extern double __ieee754_gamma (double) attribute_hidden;*/
extern double __ieee754_log10 (double) attribute_hidden;
extern double __ieee754_sinh (double) attribute_hidden;
extern double __ieee754_hypot (double,double) attribute_hidden;
extern double __ieee754_j0 (double) attribute_hidden;
extern double __ieee754_j1 (double) attribute_hidden;
extern double __ieee754_y0 (double) attribute_hidden;
extern double __ieee754_y1 (double) attribute_hidden;
extern double __ieee754_jn (int,double) attribute_hidden;
extern double __ieee754_yn (int,double) attribute_hidden;
extern double __ieee754_remainder (double,double) attribute_hidden;
extern int __ieee754_rem_pio2 (double,double*) attribute_hidden;
extern double __ieee754_scalb (double,double) attribute_hidden;
/* fdlibm kernel function */
extern double __kernel_sin (double,double,int) attribute_hidden;
extern double __kernel_cos (double,double) attribute_hidden;
extern double __kernel_tan (double,double,int) attribute_hidden;
extern int __kernel_rem_pio2 (double*,double*,int,int,int,const int*) attribute_hidden;
/*
* math_opt_barrier(x): safely load x, even if it was manipulated
* by non-floationg point operations. This macro returns the value of x.
* This ensures compiler does not (ab)use its knowledge about x value
* and don't optimize future operations. Example:
* float x;
* SET_FLOAT_WORD(x, 0x80000001); // sets a bit pattern
* y = math_opt_barrier(x); // "compiler, do not cheat!"
* y = y * y; // compiler can't optimize, must use real multiply insn
*
* math_force_eval(x): force expression x to be evaluated.
* Useful if otherwise compiler may eliminate the expression
* as unused. This macro returns no value.
* Example: "void fn(float f) { f = f * f; }"
* versus "void fn(float f) { f = f * f; math_force_eval(f); }"
*
* Currently, math_force_eval(x) stores x into
* a floating point register or memory *of the appropriate size*.
* There is no guarantee this will not change.
*/
#if defined(__i386__)
#define math_opt_barrier(x) ({ \
__typeof(x) __x = (x); \
/* "t": load x into top-of-stack fpreg */ \
__asm__ ("" : "=t" (__x) : "0" (__x)); \
__x; \
})
#define math_force_eval(x) do { \
__typeof(x) __x = (x); \
if (sizeof(__x) <= sizeof(double)) \
/* "m": store x into a memory location */ \
__asm__ __volatile__ ("" : : "m" (__x)); \
else /* long double */ \
/* "f": load x into (any) fpreg */ \
__asm__ __volatile__ ("" : : "f" (__x)); \
} while (0)
#endif
#if defined(__x86_64__)
#define math_opt_barrier(x) ({ \
__typeof(x) __x = (x); \
if (sizeof(__x) <= sizeof(double)) \
/* "x": load into XMM SSE register */ \
__asm__ ("" : "=x" (__x) : "0" (__x)); \
else /* long double */ \
/* "t": load x into top-of-stack fpreg */ \
__asm__ ("" : "=t" (__x) : "0" (__x)); \
__x; \
})
#define math_force_eval(x) do { \
__typeof(x) __x = (x); \
if (sizeof(__x) <= sizeof(double)) \
/* "x": load into XMM SSE register */ \
__asm__ __volatile__ ("" : : "x" (__x)); \
else /* long double */ \
/* "f": load x into (any) fpreg */ \
__asm__ __volatile__ ("" : : "f" (__x)); \
} while (0)
#endif
/* Default implementations force store to a memory location */
#ifndef math_opt_barrier
#define math_opt_barrier(x) ({ __typeof(x) __x = (x); __asm__ ("" : "+m" (__x)); __x; })
#endif
#ifndef math_force_eval
#define math_force_eval(x) do { __typeof(x) __x = (x); __asm__ __volatile__ ("" : : "m" (__x)); } while (0)
#endif
#endif /* _MATH_PRIVATE_H_ */
|
