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
|
#ifndef _TGMATH_H
#define _TGMATH_H
/*
the return types are only correct with gcc (__GNUC__)
otherwise they are long double or long double complex
the long double version of a function is never chosen when
sizeof(double) == sizeof(long double)
(but the return type is set correctly with gcc)
*/
#include <math.h>
#include <complex.h>
#define __IS_FP(x) !!((1?1:(x))/2)
#define __IS_CX(x) (__IS_FP(x) && sizeof(x) == sizeof((x)+I))
#define __IS_REAL(x) (__IS_FP(x) && 2*sizeof(x) == sizeof((x)+I))
#define __FLT(x) (__IS_REAL(x) && sizeof(x) == sizeof(float))
#define __LDBL(x) (__IS_REAL(x) && sizeof(x) == sizeof(long double) && sizeof(long double) != sizeof(double))
#define __FLTCX(x) (__IS_CX(x) && sizeof(x) == sizeof(float complex))
#define __DBLCX(x) (__IS_CX(x) && sizeof(x) == sizeof(double complex))
#define __LDBLCX(x) (__IS_CX(x) && sizeof(x) == sizeof(long double complex) && sizeof(long double) != sizeof(double))
/* return type */
#ifdef __GNUC__
/* cast to double when x is integral, otherwise use typeof(x) */
#define __RETCAST(x) (__typeof__(*( \
0 ? (__typeof__(0 ? (double *)0 : (void *)__IS_FP(x)))0 : \
(__typeof__(0 ? (__typeof__(x) *)0 : (void *)!__IS_FP(x)))0 )))
/* 2 args case, consider complex types (for cpow) */
#define __RETCAST_2(x, y) (__typeof__(*( \
0 ? (__typeof__(0 ? (double *)0 : \
(void *)!((!__IS_FP(x) || !__IS_FP(y)) && __FLT((x)+(y)+1.0f))))0 : \
0 ? (__typeof__(0 ? (double complex *)0 : \
(void *)!((!__IS_FP(x) || !__IS_FP(y)) && __FLTCX((x)+(y)))))0 : \
(__typeof__(0 ? (__typeof__((x)+(y)) *)0 : \
(void *)((!__IS_FP(x) || !__IS_FP(y)) && (__FLT((x)+(y)+1.0f) || __FLTCX((x)+(y))))))0 )))
/* 3 args case, don't consider complex types (fma only) */
#define __RETCAST_3(x, y, z) (__typeof__(*( \
0 ? (__typeof__(0 ? (double *)0 : \
(void *)!((!__IS_FP(x) || !__IS_FP(y) || !__IS_FP(z)) && __FLT((x)+(y)+(z)+1.0f))))0 : \
(__typeof__(0 ? (__typeof__((x)+(y)) *)0 : \
(void *)((!__IS_FP(x) || !__IS_FP(y) || !__IS_FP(z)) && __FLT((x)+(y)+(z)+1.0f))))0 )))
/* drop complex from the type of x */
#define __TO_REAL(x) *( \
0 ? (__typeof__(0 ? (double *)0 : (void *)!__DBLCX(x)))0 : \
0 ? (__typeof__(0 ? (float *)0 : (void *)!__FLTCX(x)))0 : \
0 ? (__typeof__(0 ? (long double *)0 : (void *)!__LDBLCX(x)))0 : \
(__typeof__(0 ? (__typeof__(x) *)0 : (void *)__IS_CX(x)))0 )
#else
#define __RETCAST(x)
#define __RETCAST_2(x, y)
#define __RETCAST_3(x, y, z)
#endif
/* function selection */
#define __tg_real(fun, x) (__RETCAST(x)( \
__FLT(x) ? fun ## f (x) : \
__LDBL(x) ? fun ## l (x) : \
fun(x) ))
#define __tg_real_2_1(fun, x, y) (__RETCAST(x)( \
__FLT(x) ? fun ## f (x, y) : \
__LDBL(x) ? fun ## l (x, y) : \
fun(x, y) ))
#define __tg_real_2(fun, x, y) (__RETCAST_2(x, y)( \
__FLT(x) && __FLT(y) ? fun ## f (x, y) : \
__LDBL((x)+(y)) ? fun ## l (x, y) : \
fun(x, y) ))
#define __tg_complex(fun, x) (__RETCAST((x)+I)( \
__FLTCX((x)+I) && __IS_FP(x) ? fun ## f (x) : \
__LDBLCX((x)+I) ? fun ## l (x) : \
fun(x) ))
#define __tg_complex_retreal(fun, x) (__RETCAST(__TO_REAL(x))( \
__FLTCX((x)+I) && __IS_FP(x) ? fun ## f (x) : \
__LDBLCX((x)+I) ? fun ## l (x) : \
fun(x) ))
#define __tg_real_complex(fun, x) (__RETCAST(x)( \
__FLTCX(x) ? c ## fun ## f (x) : \
__DBLCX(x) ? c ## fun (x) : \
__LDBLCX(x) ? c ## fun ## l (x) : \
__FLT(x) ? fun ## f (x) : \
__LDBL(x) ? fun ## l (x) : \
fun(x) ))
/* special cases */
#define __tg_real_remquo(x, y, z) (__RETCAST_2(x, y)( \
__FLT(x) && __FLT(y) ? remquof(x, y, z) : \
__LDBL((x)+(y)) ? remquol(x, y, z) : \
remquo(x, y, z) ))
#define __tg_real_fma(x, y, z) (__RETCAST_3(x, y, z)( \
__FLT(x) && __FLT(y) && __FLT(z) ? fmaf(x, y, z) : \
__LDBL((x)+(y)+(z)) ? fmal(x, y, z) : \
fma(x, y, z) ))
#define __tg_real_complex_pow(x, y) (__RETCAST_2(x, y)( \
__FLTCX((x)+(y)) && __IS_FP(x) && __IS_FP(y) ? cpowf(x, y) : \
__FLTCX((x)+(y)) ? cpow(x, y) : \
__DBLCX((x)+(y)) ? cpow(x, y) : \
__LDBLCX((x)+(y)) ? cpowl(x, y) : \
__FLT(x) && __FLT(y) ? powf(x, y) : \
__LDBL((x)+(y)) ? powl(x, y) : \
pow(x, y) ))
#define __tg_real_complex_fabs(x) (__RETCAST(__TO_REAL(x))( \
__FLTCX(x) ? cabsf(x) : \
__DBLCX(x) ? cabs(x) : \
__LDBLCX(x) ? cabsl(x) : \
__FLT(x) ? fabsf(x) : \
__LDBL(x) ? fabsl(x) : \
fabs(x) ))
/* suppress any macros in math.h or complex.h */
#undef acos
#undef acosh
#undef asin
#undef asinh
#undef atan
#undef atan2
#undef atanh
#undef carg
#undef cbrt
#undef ceil
#undef cimag
#undef conj
#undef copysign
#undef cos
#undef cosh
#undef cproj
#undef creal
#undef erf
#undef erfc
#undef exp
#undef exp2
#undef expm1
#undef fabs
#undef fdim
#undef floor
#undef fma
#undef fmax
#undef fmin
#undef fmod
#undef frexp
#undef hypot
#undef ilogb
#undef ldexp
#undef lgamma
#undef llrint
#undef llround
#undef log
#undef log10
#undef log1p
#undef log2
#undef logb
#undef lrint
#undef lround
#undef nearbyint
#undef nextafter
#undef nexttoward
#undef pow
#undef remainder
#undef remquo
#undef rint
#undef round
#undef scalbln
#undef scalbn
#undef sin
#undef sinh
#undef sqrt
#undef tan
#undef tanh
#undef tgamma
#undef trunc
/* tg functions */
#define acos(x) __tg_real_complex(acos, (x))
#define acosh(x) __tg_real_complex(acosh, (x))
#define asin(x) __tg_real_complex(asin, (x))
#define asinh(x) __tg_real_complex(asinh, (x))
#define atan(x) __tg_real_complex(atan, (x))
#define atan2(x,y) __tg_real_2(atan2, (x), (y))
#define atanh(x) __tg_real_complex(atanh, (x))
#define carg(x) __tg_complex_retreal(carg, (x))
#define cbrt(x) __tg_real(cbrt, (x))
#define ceil(x) __tg_real(ceil, (x))
#define cimag(x) __tg_complex_retreal(cimag, (x))
#define conj(x) __tg_complex(conj, (x))
#define copysign(x,y) __tg_real_2(copysign, (x), (y))
#define cos(x) __tg_real_complex(cos, (x))
#define cosh(x) __tg_real_complex(cosh, (x))
#define cproj(x) __tg_complex(cproj, (x))
#define creal(x) __tg_complex_retreal(creal, (x))
#define erf(x) __tg_real(erf, (x))
#define erfc(x) __tg_real(erfc, (x))
#define exp(x) __tg_real_complex(exp, (x))
#define exp2(x) __tg_real(exp2, (x))
#define expm1(x) __tg_real(expm1, (x))
#define fabs(x) __tg_real_complex_fabs(x)
#define fdim(x,y) __tg_real_2(fdim, (x), (y))
#define floor(x) __tg_real(floor, (x))
#define fma(x,y,z) __tg_real_fma((x), (y), (z))
#define fmax(x,y) __tg_real_2(fmax, (x), (y))
#define fmin(x,y) __tg_real_2(fmin, (x), (y))
#define fmod(x,y) __tg_real_2(fmod, (x), (y))
#define frexp(x,y) __tg_real_2_1(frexp, (x), (y))
#define hypot(x,y) __tg_real_2(hypot, (x), (y))
#define ilogb(x) __tg_real(ilogb, (x))
#define ldexp(x,y) __tg_real_2_1(ldexp, (x), (y))
#define lgamma(x) __tg_real(lgamma, (x))
#define llrint(x) __tg_real(llrint, (x))
#define llround(x) __tg_real(llround, (x))
#define log(x) __tg_real_complex(log, (x))
#define log10(x) __tg_real(log10, (x))
#define log1p(x) __tg_real(log1p, (x))
#define log2(x) __tg_real(log2, (x))
#define logb(x) __tg_real(logb, (x))
#define lrint(x) __tg_real(lrint, (x))
#define lround(x) __tg_real(lround, (x))
#define nearbyint(x) __tg_real(nearbyint, (x))
#define nextafter(x,y) __tg_real_2(nextafter, (x), (y))
#define nexttoward(x,y) __tg_real_2(nexttoward, (x), (y))
#define pow(x,y) __tg_real_complex_pow((x), (y))
#define remainder(x,y) __tg_real_2(remainder, (x), (y))
#define remquo(x,y,z) __tg_real_remquo((x), (y), (z))
#define rint(x) __tg_real(rint, (x))
#define round(x) __tg_real(round, (x))
#define scalbln(x,y) __tg_real_2_1(scalbln, (x), (y))
#define scalbn(x,y) __tg_real_2_1(scalbn, (x), (y))
#define sin(x) __tg_real_complex(sin, (x))
#define sinh(x) __tg_real_complex(sinh, (x))
#define sqrt(x) __tg_real_complex(sqrt, (x))
#define tan(x) __tg_real_complex(tan, (x))
#define tanh(x) __tg_real_complex(tanh, (x))
#define tgamma(x) __tg_real(tgamma, (x))
#define trunc(x) __tg_real(trunc, (x))
#endif
|
