1 /*
2  * ====================================================
3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4  *
5  * Developed at SunPro, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  */
11 
12 /*
13  * from: @(#)fdlibm.h 5.1 93/09/24
14  * $FreeBSD: stable/9/lib/msun/src/math_private.h 239529 2012-08-21 19:45:48Z dim $
15  */
16 
17 #ifndef _MATH_PRIVATE_H_
18 #define	_MATH_PRIVATE_H_
19 
20 #include <sys/types.h>
21 #include <machine/endian.h>
22 
23 /*
24  * The original fdlibm code used statements like:
25  *	n0 = ((*(int*)&one)>>29)^1;		* index of high word *
26  *	ix0 = *(n0+(int*)&x);			* high word of x *
27  *	ix1 = *((1-n0)+(int*)&x);		* low word of x *
28  * to dig two 32 bit words out of the 64 bit IEEE floating point
29  * value.  That is non-ANSI, and, moreover, the gcc instruction
30  * scheduler gets it wrong.  We instead use the following macros.
31  * Unlike the original code, we determine the endianness at compile
32  * time, not at run time; I don't see much benefit to selecting
33  * endianness at run time.
34  */
35 
36 /*
37  * A union which permits us to convert between a double and two 32 bit
38  * ints.
39  */
40 
41 #ifdef __arm__
42 #if defined(__VFP_FP__)
43 #define	IEEE_WORD_ORDER	BYTE_ORDER
44 #else
45 #define	IEEE_WORD_ORDER	BIG_ENDIAN
46 #endif
47 #else /* __arm__ */
48 #define	IEEE_WORD_ORDER	BYTE_ORDER
49 #endif
50 
51 #if IEEE_WORD_ORDER == BIG_ENDIAN
52 
53 typedef union
54 {
55   double value;
56   struct
57   {
58     u_int32_t msw;
59     u_int32_t lsw;
60   } parts;
61   struct
62   {
63     u_int64_t w;
64   } xparts;
65 } ieee_double_shape_type;
66 
67 #endif
68 
69 #if IEEE_WORD_ORDER == LITTLE_ENDIAN
70 
71 typedef union
72 {
73   double value;
74   struct
75   {
76     u_int32_t lsw;
77     u_int32_t msw;
78   } parts;
79   struct
80   {
81     u_int64_t w;
82   } xparts;
83 } ieee_double_shape_type;
84 
85 #endif
86 
87 /* Get two 32 bit ints from a double.  */
88 
89 #define EXTRACT_WORDS(ix0,ix1,d)				\
90 do {								\
91   ieee_double_shape_type ew_u;					\
92   ew_u.value = (d);						\
93   (ix0) = ew_u.parts.msw;					\
94   (ix1) = ew_u.parts.lsw;					\
95 } while (0)
96 
97 /* Get a 64-bit int from a double. */
98 #define EXTRACT_WORD64(ix,d)					\
99 do {								\
100   ieee_double_shape_type ew_u;					\
101   ew_u.value = (d);						\
102   (ix) = ew_u.xparts.w;						\
103 } while (0)
104 
105 /* Get the more significant 32 bit int from a double.  */
106 
107 #define GET_HIGH_WORD(i,d)					\
108 do {								\
109   ieee_double_shape_type gh_u;					\
110   gh_u.value = (d);						\
111   (i) = gh_u.parts.msw;						\
112 } while (0)
113 
114 /* Get the less significant 32 bit int from a double.  */
115 
116 #define GET_LOW_WORD(i,d)					\
117 do {								\
118   ieee_double_shape_type gl_u;					\
119   gl_u.value = (d);						\
120   (i) = gl_u.parts.lsw;						\
121 } while (0)
122 
123 /* Set a double from two 32 bit ints.  */
124 
125 #define INSERT_WORDS(d,ix0,ix1)					\
126 do {								\
127   ieee_double_shape_type iw_u;					\
128   iw_u.parts.msw = (ix0);					\
129   iw_u.parts.lsw = (ix1);					\
130   (d) = iw_u.value;						\
131 } while (0)
132 
133 /* Set a double from a 64-bit int. */
134 #define INSERT_WORD64(d,ix)					\
135 do {								\
136   ieee_double_shape_type iw_u;					\
137   iw_u.xparts.w = (ix);						\
138   (d) = iw_u.value;						\
139 } while (0)
140 
141 /* Set the more significant 32 bits of a double from an int.  */
142 
143 #define SET_HIGH_WORD(d,v)					\
144 do {								\
145   ieee_double_shape_type sh_u;					\
146   sh_u.value = (d);						\
147   sh_u.parts.msw = (v);						\
148   (d) = sh_u.value;						\
149 } while (0)
150 
151 /* Set the less significant 32 bits of a double from an int.  */
152 
153 #define SET_LOW_WORD(d,v)					\
154 do {								\
155   ieee_double_shape_type sl_u;					\
156   sl_u.value = (d);						\
157   sl_u.parts.lsw = (v);						\
158   (d) = sl_u.value;						\
159 } while (0)
160 
161 /*
162  * A union which permits us to convert between a float and a 32 bit
163  * int.
164  */
165 
166 typedef union
167 {
168   float value;
169   /* FIXME: Assumes 32 bit int.  */
170   unsigned int word;
171 } ieee_float_shape_type;
172 
173 /* Get a 32 bit int from a float.  */
174 
175 #define GET_FLOAT_WORD(i,d)					\
176 do {								\
177   ieee_float_shape_type gf_u;					\
178   gf_u.value = (d);						\
179   (i) = gf_u.word;						\
180 } while (0)
181 
182 /* Set a float from a 32 bit int.  */
183 
184 #define SET_FLOAT_WORD(d,i)					\
185 do {								\
186   ieee_float_shape_type sf_u;					\
187   sf_u.word = (i);						\
188   (d) = sf_u.value;						\
189 } while (0)
190 
191 #ifdef FLT_EVAL_METHOD
192 /*
193  * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
194  */
195 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
196 #define	STRICT_ASSIGN(type, lval, rval)	((lval) = (rval))
197 #else
198 #define	STRICT_ASSIGN(type, lval, rval) do {	\
199 	volatile type __lval;			\
200 						\
201 	if (sizeof(type) >= sizeof(double))	\
202 		(lval) = (rval);		\
203 	else {					\
204 		__lval = (rval);		\
205 		(lval) = __lval;		\
206 	}					\
207 } while (0)
208 #endif
209 #endif
210 
211 /*
212  * Common routine to process the arguments to nan(), nanf(), and nanl().
213  */
214 void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
215 
216 #ifdef _COMPLEX_H
217 
218 /*
219  * C99 specifies that complex numbers have the same representation as
220  * an array of two elements, where the first element is the real part
221  * and the second element is the imaginary part.
222  */
223 typedef union {
224 	float complex f;
225 	float a[2];
226 } float_complex;
227 typedef union {
228 	double complex f;
229 	double a[2];
230 } double_complex;
231 typedef union {
232 	long double complex f;
233 	long double a[2];
234 } long_double_complex;
235 #define	REALPART(z)	((z).a[0])
236 #define	IMAGPART(z)	((z).a[1])
237 
238 /*
239  * Inline functions that can be used to construct complex values.
240  *
241  * The C99 standard intends x+I*y to be used for this, but x+I*y is
242  * currently unusable in general since gcc introduces many overflow,
243  * underflow, sign and efficiency bugs by rewriting I*y as
244  * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
245  * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
246  * to -0.0+I*0.0.
247  */
248 static __inline float complex
cpackf(float x,float y)249 cpackf(float x, float y)
250 {
251 	float_complex z;
252 
253 	REALPART(z) = x;
254 	IMAGPART(z) = y;
255 	return (z.f);
256 }
257 
258 static __inline double complex
cpack(double x,double y)259 cpack(double x, double y)
260 {
261 	double_complex z;
262 
263 	REALPART(z) = x;
264 	IMAGPART(z) = y;
265 	return (z.f);
266 }
267 
268 static __inline long double complex
cpackl(long double x,long double y)269 cpackl(long double x, long double y)
270 {
271 	long_double_complex z;
272 
273 	REALPART(z) = x;
274 	IMAGPART(z) = y;
275 	return (z.f);
276 }
277 #endif /* _COMPLEX_H */
278 
279 #ifdef __GNUCLIKE_ASM
280 
281 /* Asm versions of some functions. */
282 
283 #ifdef __amd64__
284 static __inline int
irint(double x)285 irint(double x)
286 {
287 	int n;
288 
289 	asm("cvtsd2si %1,%0" : "=r" (n) : "x" (x));
290 	return (n);
291 }
292 #define	HAVE_EFFICIENT_IRINT
293 #endif
294 
295 #ifdef __i386__
296 static __inline int
irint(double x)297 irint(double x)
298 {
299 	int n;
300 
301 	asm("fistl %0" : "=m" (n) : "t" (x));
302 	return (n);
303 }
304 #define	HAVE_EFFICIENT_IRINT
305 #endif
306 
307 #endif /* __GNUCLIKE_ASM */
308 
309 /*
310  * ieee style elementary functions
311  *
312  * We rename functions here to improve other sources' diffability
313  * against fdlibm.
314  */
315 #define	__ieee754_sqrt	sqrt
316 #define	__ieee754_acos	acos
317 #define	__ieee754_acosh	acosh
318 #define	__ieee754_log	log
319 #define	__ieee754_log2	log2
320 #define	__ieee754_atanh	atanh
321 #define	__ieee754_asin	asin
322 #define	__ieee754_atan2	atan2
323 #define	__ieee754_exp	exp
324 #define	__ieee754_cosh	cosh
325 #define	__ieee754_fmod	fmod
326 #define	__ieee754_pow	pow
327 #define	__ieee754_lgamma lgamma
328 #define	__ieee754_gamma	gamma
329 #define	__ieee754_lgamma_r lgamma_r
330 #define	__ieee754_gamma_r gamma_r
331 #define	__ieee754_log10	log10
332 #define	__ieee754_sinh	sinh
333 #define	__ieee754_hypot	hypot
334 #define	__ieee754_j0	j0
335 #define	__ieee754_j1	j1
336 #define	__ieee754_y0	y0
337 #define	__ieee754_y1	y1
338 #define	__ieee754_jn	jn
339 #define	__ieee754_yn	yn
340 #define	__ieee754_remainder remainder
341 #define	__ieee754_scalb	scalb
342 #define	__ieee754_sqrtf	sqrtf
343 #define	__ieee754_acosf	acosf
344 #define	__ieee754_acoshf acoshf
345 #define	__ieee754_logf	logf
346 #define	__ieee754_atanhf atanhf
347 #define	__ieee754_asinf	asinf
348 #define	__ieee754_atan2f atan2f
349 #define	__ieee754_expf	expf
350 #define	__ieee754_coshf	coshf
351 #define	__ieee754_fmodf	fmodf
352 #define	__ieee754_powf	powf
353 #define	__ieee754_lgammaf lgammaf
354 #define	__ieee754_gammaf gammaf
355 #define	__ieee754_lgammaf_r lgammaf_r
356 #define	__ieee754_gammaf_r gammaf_r
357 #define	__ieee754_log10f log10f
358 #define	__ieee754_log2f log2f
359 #define	__ieee754_sinhf	sinhf
360 #define	__ieee754_hypotf hypotf
361 #define	__ieee754_j0f	j0f
362 #define	__ieee754_j1f	j1f
363 #define	__ieee754_y0f	y0f
364 #define	__ieee754_y1f	y1f
365 #define	__ieee754_jnf	jnf
366 #define	__ieee754_ynf	ynf
367 #define	__ieee754_remainderf remainderf
368 #define	__ieee754_scalbf scalbf
369 
370 /* fdlibm kernel function */
371 int	__kernel_rem_pio2(double*,double*,int,int,int);
372 
373 /* double precision kernel functions */
374 #ifndef INLINE_REM_PIO2
375 int	__ieee754_rem_pio2(double,double*);
376 #endif
377 double	__kernel_sin(double,double,int);
378 double	__kernel_cos(double,double);
379 double	__kernel_tan(double,double,int);
380 
381 /* float precision kernel functions */
382 #ifndef INLINE_REM_PIO2F
383 int	__ieee754_rem_pio2f(float,double*);
384 #endif
385 #ifndef INLINE_KERNEL_SINDF
386 float	__kernel_sindf(double);
387 #endif
388 #ifndef INLINE_KERNEL_COSDF
389 float	__kernel_cosdf(double);
390 #endif
391 #ifndef INLINE_KERNEL_TANDF
392 float	__kernel_tandf(double,int);
393 #endif
394 
395 /* long double precision kernel functions */
396 long double __kernel_sinl(long double, long double, int);
397 long double __kernel_cosl(long double, long double);
398 long double __kernel_tanl(long double, long double, int);
399 
400 #endif /* !_MATH_PRIVATE_H_ */
401