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
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
|
#ifndef _LIBM_H
#define _LIBM_H
#include <stdint.h>
#include <float.h>
#include <math.h>
#include <endian.h>
#include "fp_arch.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __LITTLE_ENDIAN
union ldshape {
long double f;
struct {
uint64_t m;
uint16_t se;
} i;
};
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __BIG_ENDIAN
/* This is the m68k variant of 80-bit long double, and this definition only works
* on archs where the alignment requirement of uint64_t is <= 4. */
union ldshape {
long double f;
struct {
uint16_t se;
uint16_t pad;
uint64_t m;
} i;
};
#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __LITTLE_ENDIAN
union ldshape {
long double f;
struct {
uint64_t lo;
uint32_t mid;
uint16_t top;
uint16_t se;
} i;
struct {
uint64_t lo;
uint64_t hi;
} i2;
};
#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __BIG_ENDIAN
union ldshape {
long double f;
struct {
uint16_t se;
uint16_t top;
uint32_t mid;
uint64_t lo;
} i;
struct {
uint64_t hi;
uint64_t lo;
} i2;
};
#else
#error Unsupported long double representation
#endif
/* Support non-nearest rounding mode. */
#define WANT_ROUNDING 1
/* Support signaling NaNs. */
#define WANT_SNAN 0
#if WANT_SNAN
#error SNaN is unsupported
#else
#define issignalingf_inline(x) 0
#define issignaling_inline(x) 0
#endif
#ifndef TOINT_INTRINSICS
#define TOINT_INTRINSICS 0
#endif
#if TOINT_INTRINSICS
/* Round x to nearest int in all rounding modes, ties have to be rounded
consistently with converttoint so the results match. If the result
would be outside of [-2^31, 2^31-1] then the semantics is unspecified. */
static double_t roundtoint(double_t);
/* Convert x to nearest int in all rounding modes, ties have to be rounded
consistently with roundtoint. If the result is not representible in an
int32_t then the semantics is unspecified. */
static int32_t converttoint(double_t);
#endif
/* Helps static branch prediction so hot path can be better optimized. */
#ifdef __GNUC__
#define predict_true(x) __builtin_expect(!!(x), 1)
#define predict_false(x) __builtin_expect(x, 0)
#else
#define predict_true(x) (x)
#define predict_false(x) (x)
#endif
/* Evaluate an expression as the specified type. With standard excess
precision handling a type cast or assignment is enough (with
-ffloat-store an assignment is required, in old compilers argument
passing and return statement may not drop excess precision). */
static inline float eval_as_float(float x)
{
float y = x;
return y;
}
static inline double eval_as_double(double x)
{
double y = x;
return y;
}
/* fp_barrier returns its input, but limits code transformations
as if it had a side-effect (e.g. observable io) and returned
an arbitrary value. */
#ifndef fp_barrierf
#define fp_barrierf fp_barrierf
static inline float fp_barrierf(float x)
{
volatile float y = x;
return y;
}
#endif
#ifndef fp_barrier
#define fp_barrier fp_barrier
static inline double fp_barrier(double x)
{
volatile double y = x;
return y;
}
#endif
#ifndef fp_barrierl
#define fp_barrierl fp_barrierl
static inline long double fp_barrierl(long double x)
{
volatile long double y = x;
return y;
}
#endif
/* fp_force_eval ensures that the input value is computed when that's
otherwise unused. To prevent the constant folding of the input
expression, an additional fp_barrier may be needed or a compilation
mode that does so (e.g. -frounding-math in gcc). Then it can be
used to evaluate an expression for its fenv side-effects only. */
#ifndef fp_force_evalf
#define fp_force_evalf fp_force_evalf
static inline void fp_force_evalf(float x)
{
volatile float y;
y = x;
}
#endif
#ifndef fp_force_eval
#define fp_force_eval fp_force_eval
static inline void fp_force_eval(double x)
{
volatile double y;
y = x;
}
#endif
#ifndef fp_force_evall
#define fp_force_evall fp_force_evall
static inline void fp_force_evall(long double x)
{
volatile long double y;
y = x;
}
#endif
#define FORCE_EVAL(x) do { \
if (sizeof(x) == sizeof(float)) { \
fp_force_evalf(x); \
} else if (sizeof(x) == sizeof(double)) { \
fp_force_eval(x); \
} else { \
fp_force_evall(x); \
} \
} while(0)
#define asuint(f) ((union{float _f; uint32_t _i;}){f})._i
#define asfloat(i) ((union{uint32_t _i; float _f;}){i})._f
#define asuint64(f) ((union{double _f; uint64_t _i;}){f})._i
#define asdouble(i) ((union{uint64_t _i; double _f;}){i})._f
#define EXTRACT_WORDS(hi,lo,d) \
do { \
uint64_t __u = asuint64(d); \
(hi) = __u >> 32; \
(lo) = (uint32_t)__u; \
} while (0)
#define GET_HIGH_WORD(hi,d) \
do { \
(hi) = asuint64(d) >> 32; \
} while (0)
#define GET_LOW_WORD(lo,d) \
do { \
(lo) = (uint32_t)asuint64(d); \
} while (0)
#define INSERT_WORDS(d,hi,lo) \
do { \
(d) = asdouble(((uint64_t)(hi)<<32) | (uint32_t)(lo)); \
} while (0)
#define SET_HIGH_WORD(d,hi) \
INSERT_WORDS(d, hi, (uint32_t)asuint64(d))
#define SET_LOW_WORD(d,lo) \
INSERT_WORDS(d, asuint64(d)>>32, lo)
#define GET_FLOAT_WORD(w,d) \
do { \
(w) = asuint(d); \
} while (0)
#define SET_FLOAT_WORD(d,w) \
do { \
(d) = asfloat(w); \
} while (0)
hidden int __rem_pio2_large(double*,double*,int,int,int);
hidden int __rem_pio2(double,double*);
hidden double __sin(double,double,int);
hidden double __cos(double,double);
hidden double __tan(double,double,int);
hidden double __expo2(double,double);
hidden int __rem_pio2f(float,double*);
hidden float __sindf(double);
hidden float __cosdf(double);
hidden float __tandf(double,int);
hidden float __expo2f(float,float);
hidden int __rem_pio2l(long double, long double *);
hidden long double __sinl(long double, long double, int);
hidden long double __cosl(long double, long double);
hidden long double __tanl(long double, long double, int);
hidden long double __polevll(long double, const long double *, int);
hidden long double __p1evll(long double, const long double *, int);
extern int __signgam;
hidden double __lgamma_r(double, int *);
hidden float __lgammaf_r(float, int *);
/* error handling functions */
hidden float __math_xflowf(uint32_t, float);
hidden float __math_uflowf(uint32_t);
hidden float __math_oflowf(uint32_t);
hidden float __math_divzerof(uint32_t);
hidden float __math_invalidf(float);
hidden double __math_xflow(uint32_t, double);
hidden double __math_uflow(uint32_t);
hidden double __math_oflow(uint32_t);
hidden double __math_divzero(uint32_t);
hidden double __math_invalid(double);
#if LDBL_MANT_DIG != DBL_MANT_DIG
hidden long double __math_invalidl(long double);
#endif
#endif
|
