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
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
|
/* Inline math functions for i387 and SSE.
Copyright (C) 1995-2018 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#ifndef _MATH_H
# error "Never use <bits/mathinline.h> directly; include <math.h> instead."
#endif
#ifndef __extern_always_inline
# define __MATH_INLINE __inline
#else
# define __MATH_INLINE __extern_always_inline
#endif
/* Disable x87 inlines when -fpmath=sse is passed and also when we're building
on x86_64. Older gcc (gcc-3.2 for example) does not define __SSE2_MATH__
for x86_64. */
#if !defined __SSE2_MATH__ && !defined __x86_64__
# if ((!defined __NO_MATH_INLINES || defined __LIBC_INTERNAL_MATH_INLINES) \
&& defined __OPTIMIZE__)
/* The inline functions do not set errno or raise necessarily the
correct exceptions. */
# undef math_errhandling
/* A macro to define float, double, and long double versions of various
math functions for the ix87 FPU. FUNC is the function name (which will
be suffixed with f and l for the float and long double version,
respectively). OP is the name of the FPU operation.
We define two sets of macros. The set with the additional NP
doesn't add a prototype declaration. */
# ifdef __USE_ISOC99
# define __inline_mathop(func, op) \
__inline_mathop_ (double, func, op) \
__inline_mathop_ (float, __CONCAT(func,f), op) \
__inline_mathop_ (long double, __CONCAT(func,l), op)
# define __inline_mathopNP(func, op) \
__inline_mathopNP_ (double, func, op) \
__inline_mathopNP_ (float, __CONCAT(func,f), op) \
__inline_mathopNP_ (long double, __CONCAT(func,l), op)
# else
# define __inline_mathop(func, op) \
__inline_mathop_ (double, func, op)
# define __inline_mathopNP(func, op) \
__inline_mathopNP_ (double, func, op)
# endif
# define __inline_mathop_(float_type, func, op) \
__inline_mathop_decl_ (float_type, func, op, "0" (__x))
# define __inline_mathopNP_(float_type, func, op) \
__inline_mathop_declNP_ (float_type, func, op, "0" (__x))
# ifdef __USE_ISOC99
# define __inline_mathop_decl(func, op, params...) \
__inline_mathop_decl_ (double, func, op, params) \
__inline_mathop_decl_ (float, __CONCAT(func,f), op, params) \
__inline_mathop_decl_ (long double, __CONCAT(func,l), op, params)
# define __inline_mathop_declNP(func, op, params...) \
__inline_mathop_declNP_ (double, func, op, params) \
__inline_mathop_declNP_ (float, __CONCAT(func,f), op, params) \
__inline_mathop_declNP_ (long double, __CONCAT(func,l), op, params)
# else
# define __inline_mathop_decl(func, op, params...) \
__inline_mathop_decl_ (double, func, op, params)
# define __inline_mathop_declNP(func, op, params...) \
__inline_mathop_declNP_ (double, func, op, params)
# endif
# define __inline_mathop_decl_(float_type, func, op, params...) \
__MATH_INLINE float_type func (float_type) __THROW; \
__inline_mathop_declNP_ (float_type, func, op, params)
# define __inline_mathop_declNP_(float_type, func, op, params...) \
__MATH_INLINE float_type __NTH (func (float_type __x)) \
{ \
register float_type __result; \
__asm __volatile__ (op : "=t" (__result) : params); \
return __result; \
}
# ifdef __USE_ISOC99
# define __inline_mathcode(func, arg, code) \
__inline_mathcode_ (double, func, arg, code) \
__inline_mathcode_ (float, __CONCAT(func,f), arg, code) \
__inline_mathcode_ (long double, __CONCAT(func,l), arg, code)
# define __inline_mathcodeNP(func, arg, code) \
__inline_mathcodeNP_ (double, func, arg, code) \
__inline_mathcodeNP_ (float, __CONCAT(func,f), arg, code) \
__inline_mathcodeNP_ (long double, __CONCAT(func,l), arg, code)
# define __inline_mathcode2(func, arg1, arg2, code) \
__inline_mathcode2_ (double, func, arg1, arg2, code) \
__inline_mathcode2_ (float, __CONCAT(func,f), arg1, arg2, code) \
__inline_mathcode2_ (long double, __CONCAT(func,l), arg1, arg2, code)
# define __inline_mathcodeNP2(func, arg1, arg2, code) \
__inline_mathcodeNP2_ (double, func, arg1, arg2, code) \
__inline_mathcodeNP2_ (float, __CONCAT(func,f), arg1, arg2, code) \
__inline_mathcodeNP2_ (long double, __CONCAT(func,l), arg1, arg2, code)
# define __inline_mathcode3(func, arg1, arg2, arg3, code) \
__inline_mathcode3_ (double, func, arg1, arg2, arg3, code) \
__inline_mathcode3_ (float, __CONCAT(func,f), arg1, arg2, arg3, code) \
__inline_mathcode3_ (long double, __CONCAT(func,l), arg1, arg2, arg3, code)
# define __inline_mathcodeNP3(func, arg1, arg2, arg3, code) \
__inline_mathcodeNP3_ (double, func, arg1, arg2, arg3, code) \
__inline_mathcodeNP3_ (float, __CONCAT(func,f), arg1, arg2, arg3, code) \
__inline_mathcodeNP3_ (long double, __CONCAT(func,l), arg1, arg2, arg3, code)
# else
# define __inline_mathcode(func, arg, code) \
__inline_mathcode_ (double, func, (arg), code)
# define __inline_mathcodeNP(func, arg, code) \
__inline_mathcodeNP_ (double, func, (arg), code)
# define __inline_mathcode2(func, arg1, arg2, code) \
__inline_mathcode2_ (double, func, arg1, arg2, code)
# define __inline_mathcodeNP2(func, arg1, arg2, code) \
__inline_mathcodeNP2_ (double, func, arg1, arg2, code)
# define __inline_mathcode3(func, arg1, arg2, arg3, code) \
__inline_mathcode3_ (double, func, arg1, arg2, arg3, code)
# define __inline_mathcodeNP3(func, arg1, arg2, arg3, code) \
__inline_mathcodeNP3_ (double, func, arg1, arg2, arg3, code)
# endif
# define __inline_mathcode_(float_type, func, arg, code) \
__MATH_INLINE float_type func (float_type) __THROW; \
__inline_mathcodeNP_(float_type, func, arg, code)
# define __inline_mathcodeNP_(float_type, func, arg, code) \
__MATH_INLINE float_type __NTH (func (float_type arg)) \
{ \
code; \
}
# define __inline_mathcode2_(float_type, func, arg1, arg2, code) \
__MATH_INLINE float_type func (float_type, float_type) __THROW; \
__inline_mathcodeNP2_ (float_type, func, arg1, arg2, code)
# define __inline_mathcodeNP2_(float_type, func, arg1, arg2, code) \
__MATH_INLINE float_type __NTH (func (float_type arg1, float_type arg2)) \
{ \
code; \
}
# define __inline_mathcode3_(float_type, func, arg1, arg2, arg3, code) \
__MATH_INLINE float_type func (float_type, float_type, float_type) __THROW; \
__inline_mathcodeNP3_(float_type, func, arg1, arg2, arg3, code)
# define __inline_mathcodeNP3_(float_type, func, arg1, arg2, arg3, code) \
__MATH_INLINE float_type __NTH (func (float_type arg1, float_type arg2, \
float_type arg3)) \
{ \
code; \
}
# endif
# if !defined __NO_MATH_INLINES && defined __OPTIMIZE__
/* Miscellaneous functions */
/* __FAST_MATH__ is defined by gcc -ffast-math. */
# ifdef __FAST_MATH__
/* Optimized inline implementation, sometimes with reduced precision
and/or argument range. */
# if __GNUC_PREREQ (3, 5)
# define __expm1_code \
register long double __temp; \
__temp = __builtin_expm1l (__x); \
return __temp ? __temp : __x
# else
# define __expm1_code \
register long double __value; \
register long double __exponent; \
register long double __temp; \
__asm __volatile__ \
("fldl2e # e^x - 1 = 2^(x * log2(e)) - 1\n\t" \
"fmul %%st(1) # x * log2(e)\n\t" \
"fst %%st(1)\n\t" \
"frndint # int(x * log2(e))\n\t" \
"fxch\n\t" \
"fsub %%st(1) # fract(x * log2(e))\n\t" \
"f2xm1 # 2^(fract(x * log2(e))) - 1\n\t" \
"fscale # 2^(x * log2(e)) - 2^(int(x * log2(e)))\n\t" \
: "=t" (__value), "=u" (__exponent) : "0" (__x)); \
__asm __volatile__ \
("fscale # 2^int(x * log2(e))\n\t" \
: "=t" (__temp) : "0" (1.0), "u" (__exponent)); \
__temp -= 1.0; \
__temp += __value; \
return __temp ? __temp : __x
# endif
__inline_mathcodeNP_ (long double, __expm1l, __x, __expm1_code)
# if __GNUC_PREREQ (3, 4)
__inline_mathcodeNP_ (long double, __expl, __x, return __builtin_expl (__x))
# else
# define __exp_code \
register long double __value; \
register long double __exponent; \
__asm __volatile__ \
("fldl2e # e^x = 2^(x * log2(e))\n\t" \
"fmul %%st(1) # x * log2(e)\n\t" \
"fst %%st(1)\n\t" \
"frndint # int(x * log2(e))\n\t" \
"fxch\n\t" \
"fsub %%st(1) # fract(x * log2(e))\n\t" \
"f2xm1 # 2^(fract(x * log2(e))) - 1\n\t" \
: "=t" (__value), "=u" (__exponent) : "0" (__x)); \
__value += 1.0; \
__asm __volatile__ \
("fscale" \
: "=t" (__value) : "0" (__value), "u" (__exponent)); \
return __value
__inline_mathcodeNP (exp, __x, __exp_code)
__inline_mathcodeNP_ (long double, __expl, __x, __exp_code)
# endif
# endif /* __FAST_MATH__ */
# ifdef __FAST_MATH__
# if !__GNUC_PREREQ (3,3)
__inline_mathopNP (sqrt, "fsqrt")
__inline_mathopNP_ (long double, __sqrtl, "fsqrt")
# define __libc_sqrtl(n) __sqrtl (n)
# else
# define __libc_sqrtl(n) __builtin_sqrtl (n)
# endif
# endif
# if __GNUC_PREREQ (2, 8)
__inline_mathcodeNP_ (double, fabs, __x, return __builtin_fabs (__x))
# ifdef __USE_ISOC99
__inline_mathcodeNP_ (float, fabsf, __x, return __builtin_fabsf (__x))
__inline_mathcodeNP_ (long double, fabsl, __x, return __builtin_fabsl (__x))
# endif
__inline_mathcodeNP_ (long double, __fabsl, __x, return __builtin_fabsl (__x))
# else
__inline_mathop (fabs, "fabs")
__inline_mathop_ (long double, __fabsl, "fabs")
# endif
__inline_mathcode_ (long double, __sgn1l, __x, \
__extension__ union { long double __xld; unsigned int __xi[3]; } __n = \
{ __xld: __x }; \
__n.__xi[2] = (__n.__xi[2] & 0x8000) | 0x3fff; \
__n.__xi[1] = 0x80000000; \
__n.__xi[0] = 0; \
return __n.__xld)
# ifdef __FAST_MATH__
/* The argument range of the inline version of sinhl is slightly reduced. */
__inline_mathcodeNP (sinh, __x, \
register long double __exm1 = __expm1l (__fabsl (__x)); \
return 0.5 * (__exm1 / (__exm1 + 1.0) + __exm1) * __sgn1l (__x))
__inline_mathcodeNP (cosh, __x, \
register long double __ex = __expl (__x); \
return 0.5 * (__ex + 1.0 / __ex))
__inline_mathcodeNP (tanh, __x, \
register long double __exm1 = __expm1l (-__fabsl (__x + __x)); \
return __exm1 / (__exm1 + 2.0) * __sgn1l (-__x))
# endif
/* Optimized versions for some non-standardized functions. */
# ifdef __USE_ISOC99
# ifdef __FAST_MATH__
__inline_mathcodeNP (expm1, __x, __expm1_code)
# endif
# endif
/* Undefine some of the large macros which are not used anymore. */
# ifdef __FAST_MATH__
# undef __expm1_code
# undef __exp_code
# endif /* __FAST_MATH__ */
# endif /* __NO_MATH_INLINES */
/* This code is used internally in the GNU libc. */
# ifdef __LIBC_INTERNAL_MATH_INLINES
__inline_mathcode2_ (long double, __ieee754_atan2l, __y, __x,
register long double __value;
__asm __volatile__ ("fpatan\n\t"
: "=t" (__value)
: "0" (__x), "u" (__y) : "st(1)");
return __value;)
# endif
#endif /* !__SSE2_MATH__ && !__x86_64__ */
|
