libm.h raw
1 #ifndef _LIBM_H
2 #define _LIBM_H
3
4 #include <stdint.h>
5 #include <float.h>
6 #include <math.h>
7 #include <endian.h>
8 #include "fp_arch.h"
9
10 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
11 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __LITTLE_ENDIAN
12 union ldshape {
13 long double f;
14 struct {
15 uint64_t m;
16 uint16_t se;
17 } i;
18 };
19 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __BIG_ENDIAN
20 /* This is the m68k variant of 80-bit long double, and this definition only works
21 * on archs where the alignment requirement of uint64_t is <= 4. */
22 union ldshape {
23 long double f;
24 struct {
25 uint16_t se;
26 uint16_t pad;
27 uint64_t m;
28 } i;
29 };
30 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __LITTLE_ENDIAN
31 union ldshape {
32 long double f;
33 struct {
34 uint64_t lo;
35 uint32_t mid;
36 uint16_t top;
37 uint16_t se;
38 } i;
39 struct {
40 uint64_t lo;
41 uint64_t hi;
42 } i2;
43 };
44 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384 && __BYTE_ORDER == __BIG_ENDIAN
45 union ldshape {
46 long double f;
47 struct {
48 uint16_t se;
49 uint16_t top;
50 uint32_t mid;
51 uint64_t lo;
52 } i;
53 struct {
54 uint64_t hi;
55 uint64_t lo;
56 } i2;
57 };
58 #else
59 #error Unsupported long double representation
60 #endif
61
62 /* Support non-nearest rounding mode. */
63 #define WANT_ROUNDING 1
64 /* Support signaling NaNs. */
65 #define WANT_SNAN 0
66
67 #if WANT_SNAN
68 #error SNaN is unsupported
69 #else
70 #define issignalingf_inline(x) 0
71 #define issignaling_inline(x) 0
72 #endif
73
74 #ifndef TOINT_INTRINSICS
75 #define TOINT_INTRINSICS 0
76 #endif
77
78 #if TOINT_INTRINSICS
79 /* Round x to nearest int in all rounding modes, ties have to be rounded
80 consistently with converttoint so the results match. If the result
81 would be outside of [-2^31, 2^31-1] then the semantics is unspecified. */
82 static double_t roundtoint(double_t);
83
84 /* Convert x to nearest int in all rounding modes, ties have to be rounded
85 consistently with roundtoint. If the result is not representible in an
86 int32_t then the semantics is unspecified. */
87 static int32_t converttoint(double_t);
88 #endif
89
90 /* Helps static branch prediction so hot path can be better optimized. */
91 #ifdef __GNUC__
92 #define predict_true(x) __builtin_expect(!!(x), 1)
93 #define predict_false(x) __builtin_expect(x, 0)
94 #else
95 #define predict_true(x) (x)
96 #define predict_false(x) (x)
97 #endif
98
99 /* Evaluate an expression as the specified type. With standard excess
100 precision handling a type cast or assignment is enough (with
101 -ffloat-store an assignment is required, in old compilers argument
102 passing and return statement may not drop excess precision). */
103
104 static inline float eval_as_float(float x)
105 {
106 float y = x;
107 return y;
108 }
109
110 static inline double eval_as_double(double x)
111 {
112 double y = x;
113 return y;
114 }
115
116 /* fp_barrier returns its input, but limits code transformations
117 as if it had a side-effect (e.g. observable io) and returned
118 an arbitrary value. */
119
120 #ifndef fp_barrierf
121 #define fp_barrierf fp_barrierf
122 static inline float fp_barrierf(float x)
123 {
124 volatile float y = x;
125 return y;
126 }
127 #endif
128
129 #ifndef fp_barrier
130 #define fp_barrier fp_barrier
131 static inline double fp_barrier(double x)
132 {
133 volatile double y = x;
134 return y;
135 }
136 #endif
137
138 #ifndef fp_barrierl
139 #define fp_barrierl fp_barrierl
140 static inline long double fp_barrierl(long double x)
141 {
142 volatile long double y = x;
143 return y;
144 }
145 #endif
146
147 /* fp_force_eval ensures that the input value is computed when that's
148 otherwise unused. To prevent the constant folding of the input
149 expression, an additional fp_barrier may be needed or a compilation
150 mode that does so (e.g. -frounding-math in gcc). Then it can be
151 used to evaluate an expression for its fenv side-effects only. */
152
153 #ifndef fp_force_evalf
154 #define fp_force_evalf fp_force_evalf
155 static inline void fp_force_evalf(float x)
156 {
157 volatile float y;
158 y = x;
159 }
160 #endif
161
162 #ifndef fp_force_eval
163 #define fp_force_eval fp_force_eval
164 static inline void fp_force_eval(double x)
165 {
166 volatile double y;
167 y = x;
168 }
169 #endif
170
171 #ifndef fp_force_evall
172 #define fp_force_evall fp_force_evall
173 static inline void fp_force_evall(long double x)
174 {
175 volatile long double y;
176 y = x;
177 }
178 #endif
179
180 #define FORCE_EVAL(x) do { \
181 if (sizeof(x) == sizeof(float)) { \
182 fp_force_evalf(x); \
183 } else if (sizeof(x) == sizeof(double)) { \
184 fp_force_eval(x); \
185 } else { \
186 fp_force_evall(x); \
187 } \
188 } while(0)
189
190 #define asuint(f) ((union{float _f; uint32_t _i;}){f})._i
191 #define asfloat(i) ((union{uint32_t _i; float _f;}){i})._f
192 #define asuint64(f) ((union{double _f; uint64_t _i;}){f})._i
193 #define asdouble(i) ((union{uint64_t _i; double _f;}){i})._f
194
195 #define EXTRACT_WORDS(hi,lo,d) \
196 do { \
197 uint64_t __u = asuint64(d); \
198 (hi) = __u >> 32; \
199 (lo) = (uint32_t)__u; \
200 } while (0)
201
202 #define GET_HIGH_WORD(hi,d) \
203 do { \
204 (hi) = asuint64(d) >> 32; \
205 } while (0)
206
207 #define GET_LOW_WORD(lo,d) \
208 do { \
209 (lo) = (uint32_t)asuint64(d); \
210 } while (0)
211
212 #define INSERT_WORDS(d,hi,lo) \
213 do { \
214 (d) = asdouble(((uint64_t)(hi)<<32) | (uint32_t)(lo)); \
215 } while (0)
216
217 #define SET_HIGH_WORD(d,hi) \
218 INSERT_WORDS(d, hi, (uint32_t)asuint64(d))
219
220 #define SET_LOW_WORD(d,lo) \
221 INSERT_WORDS(d, asuint64(d)>>32, lo)
222
223 #define GET_FLOAT_WORD(w,d) \
224 do { \
225 (w) = asuint(d); \
226 } while (0)
227
228 #define SET_FLOAT_WORD(d,w) \
229 do { \
230 (d) = asfloat(w); \
231 } while (0)
232
233 hidden int __rem_pio2_large(double*,double*,int,int,int);
234
235 hidden int __rem_pio2(double,double*);
236 hidden double __sin(double,double,int);
237 hidden double __cos(double,double);
238 hidden double __tan(double,double,int);
239 hidden double __expo2(double,double);
240
241 hidden int __rem_pio2f(float,double*);
242 hidden float __sindf(double);
243 hidden float __cosdf(double);
244 hidden float __tandf(double,int);
245 hidden float __expo2f(float,float);
246
247 hidden int __rem_pio2l(long double, long double *);
248 hidden long double __sinl(long double, long double, int);
249 hidden long double __cosl(long double, long double);
250 hidden long double __tanl(long double, long double, int);
251
252 hidden long double __polevll(long double, const long double *, int);
253 hidden long double __p1evll(long double, const long double *, int);
254
255 extern int __signgam;
256 hidden double __lgamma_r(double, int *);
257 hidden float __lgammaf_r(float, int *);
258
259 /* error handling functions */
260 hidden float __math_xflowf(uint32_t, float);
261 hidden float __math_uflowf(uint32_t);
262 hidden float __math_oflowf(uint32_t);
263 hidden float __math_divzerof(uint32_t);
264 hidden float __math_invalidf(float);
265 hidden double __math_xflow(uint32_t, double);
266 hidden double __math_uflow(uint32_t);
267 hidden double __math_oflow(uint32_t);
268 hidden double __math_divzero(uint32_t);
269 hidden double __math_invalid(double);
270 #if LDBL_MANT_DIG != DBL_MANT_DIG
271 hidden long double __math_invalidl(long double);
272 #endif
273
274 #endif
275