1 /*	$OpenBSD: math_private.h,v 1.18 2016/09/12 19:47:02 guenther Exp $	*/
2 /*
3  * ====================================================
4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5  *
6  * Developed at SunPro, a Sun Microsystems, Inc. business.
7  * Permission to use, copy, modify, and distribute this
8  * software is freely granted, provided that this notice
9  * is preserved.
10  * ====================================================
11  */
12 
13 /*
14  * from: @(#)fdlibm.h 5.1 93/09/24
15  */
16 
17 #ifndef _MATH_PRIVATE_H_
18 #define _MATH_PRIVATE_H_
19 
20 #include <sys/types.h>
21 
22 /* The original fdlibm code used statements like:
23 	n0 = ((*(int*)&one)>>29)^1;		* index of high word *
24 	ix0 = *(n0+(int*)&x);			* high word of x *
25 	ix1 = *((1-n0)+(int*)&x);		* low word of x *
26    to dig two 32 bit words out of the 64 bit IEEE floating point
27    value.  That is non-ANSI, and, moreover, the gcc instruction
28    scheduler gets it wrong.  We instead use the following macros.
29    Unlike the original code, we determine the endianness at compile
30    time, not at run time; I don't see much benefit to selecting
31    endianness at run time.  */
32 
33 /* A union which permits us to convert between a long double and
34    four 32 bit ints.  */
35 
36 #if BYTE_ORDER == BIG_ENDIAN
37 
38 typedef union
39 {
40   long double value;
41   struct {
42     u_int32_t mswhi;
43     u_int32_t mswlo;
44     u_int32_t lswhi;
45     u_int32_t lswlo;
46   } parts32;
47   struct {
48     u_int64_t msw;
49     u_int64_t lsw;
50   } parts64;
51 } ieee_quad_shape_type;
52 
53 #endif
54 
55 #if BYTE_ORDER == LITTLE_ENDIAN
56 
57 typedef union
58 {
59   long double value;
60   struct {
61     u_int32_t lswlo;
62     u_int32_t lswhi;
63     u_int32_t mswlo;
64     u_int32_t mswhi;
65   } parts32;
66   struct {
67     u_int64_t lsw;
68     u_int64_t msw;
69   } parts64;
70 } ieee_quad_shape_type;
71 
72 #endif
73 
74 /* Get two 64 bit ints from a long double.  */
75 
76 #define GET_LDOUBLE_WORDS64(ix0,ix1,d)				\
77 do {								\
78   ieee_quad_shape_type qw_u;					\
79   qw_u.value = (d);						\
80   (ix0) = qw_u.parts64.msw;					\
81   (ix1) = qw_u.parts64.lsw;					\
82 } while (0)
83 
84 /* Set a long double from two 64 bit ints.  */
85 
86 #define SET_LDOUBLE_WORDS64(d,ix0,ix1)				\
87 do {								\
88   ieee_quad_shape_type qw_u;					\
89   qw_u.parts64.msw = (ix0);					\
90   qw_u.parts64.lsw = (ix1);					\
91   (d) = qw_u.value;						\
92 } while (0)
93 
94 /* Get the more significant 64 bits of a long double mantissa.  */
95 
96 #define GET_LDOUBLE_MSW64(v,d)					\
97 do {								\
98   ieee_quad_shape_type sh_u;					\
99   sh_u.value = (d);						\
100   (v) = sh_u.parts64.msw;					\
101 } while (0)
102 
103 /* Set the more significant 64 bits of a long double mantissa from an int.  */
104 
105 #define SET_LDOUBLE_MSW64(d,v)					\
106 do {								\
107   ieee_quad_shape_type sh_u;					\
108   sh_u.value = (d);						\
109   sh_u.parts64.msw = (v);					\
110   (d) = sh_u.value;						\
111 } while (0)
112 
113 /* Get the least significant 64 bits of a long double mantissa.  */
114 
115 #define GET_LDOUBLE_LSW64(v,d)					\
116 do {								\
117   ieee_quad_shape_type sh_u;					\
118   sh_u.value = (d);						\
119   (v) = sh_u.parts64.lsw;					\
120 } while (0)
121 
122 /* A union which permits us to convert between a long double and
123    three 32 bit ints.  */
124 
125 #if BYTE_ORDER == BIG_ENDIAN
126 
127 typedef union
128 {
129   long double value;
130   struct {
131 #ifdef __LP64__
132     int padh:32;
133 #endif
134     int exp:16;
135     int padl:16;
136     u_int32_t msw;
137     u_int32_t lsw;
138   } parts;
139 } ieee_extended_shape_type;
140 
141 #endif
142 
143 #if BYTE_ORDER == LITTLE_ENDIAN
144 
145 typedef union
146 {
147   long double value;
148   struct {
149     u_int32_t lsw;
150     u_int32_t msw;
151     int exp:16;
152     int padl:16;
153 #ifdef __LP64__
154     int padh:32;
155 #endif
156   } parts;
157 } ieee_extended_shape_type;
158 
159 #endif
160 
161 /* Get three 32 bit ints from a double.  */
162 
163 #define GET_LDOUBLE_WORDS(se,ix0,ix1,d)				\
164 do {								\
165   ieee_extended_shape_type ew_u;				\
166   ew_u.value = (d);						\
167   (se) = ew_u.parts.exp;					\
168   (ix0) = ew_u.parts.msw;					\
169   (ix1) = ew_u.parts.lsw;					\
170 } while (0)
171 
172 /* Set a double from two 32 bit ints.  */
173 
174 #define SET_LDOUBLE_WORDS(d,se,ix0,ix1)				\
175 do {								\
176   ieee_extended_shape_type iw_u;				\
177   iw_u.parts.exp = (se);					\
178   iw_u.parts.msw = (ix0);					\
179   iw_u.parts.lsw = (ix1);					\
180   (d) = iw_u.value;						\
181 } while (0)
182 
183 /* Get the more significant 32 bits of a long double mantissa.  */
184 
185 #define GET_LDOUBLE_MSW(v,d)					\
186 do {								\
187   ieee_extended_shape_type sh_u;				\
188   sh_u.value = (d);						\
189   (v) = sh_u.parts.msw;						\
190 } while (0)
191 
192 /* Set the more significant 32 bits of a long double mantissa from an int.  */
193 
194 #define SET_LDOUBLE_MSW(d,v)					\
195 do {								\
196   ieee_extended_shape_type sh_u;				\
197   sh_u.value = (d);						\
198   sh_u.parts.msw = (v);						\
199   (d) = sh_u.value;						\
200 } while (0)
201 
202 /* Get int from the exponent of a long double.  */
203 
204 #define GET_LDOUBLE_EXP(se,d)					\
205 do {								\
206   ieee_extended_shape_type ge_u;				\
207   ge_u.value = (d);						\
208   (se) = ge_u.parts.exp;					\
209 } while (0)
210 
211 /* Set exponent of a long double from an int.  */
212 
213 #define SET_LDOUBLE_EXP(d,se)					\
214 do {								\
215   ieee_extended_shape_type se_u;				\
216   se_u.value = (d);						\
217   se_u.parts.exp = (se);					\
218   (d) = se_u.value;						\
219 } while (0)
220 
221 /* A union which permits us to convert between a double and two 32 bit
222    ints.  */
223 
224 /*
225  * The arm port is little endian except for the FP word order which is
226  * big endian.
227  */
228 
229 #if (BYTE_ORDER == BIG_ENDIAN) || (defined(__arm__) && !defined(__VFP_FP__))
230 
231 typedef union
232 {
233   double value;
234   struct
235   {
236     u_int32_t msw;
237     u_int32_t lsw;
238   } parts;
239 } ieee_double_shape_type;
240 
241 #endif
242 
243 #if (BYTE_ORDER == LITTLE_ENDIAN) && !(defined(__arm__) && !defined(__VFP_FP__))
244 
245 typedef union
246 {
247   double value;
248   struct
249   {
250     u_int32_t lsw;
251     u_int32_t msw;
252   } parts;
253 } ieee_double_shape_type;
254 
255 #endif
256 
257 /* Get two 32 bit ints from a double.  */
258 
259 #define EXTRACT_WORDS(ix0,ix1,d)				\
260 do {								\
261   ieee_double_shape_type ew_u;					\
262   ew_u.value = (d);						\
263   (ix0) = ew_u.parts.msw;					\
264   (ix1) = ew_u.parts.lsw;					\
265 } while (0)
266 
267 /* Get the more significant 32 bit int from a double.  */
268 
269 #define GET_HIGH_WORD(i,d)					\
270 do {								\
271   ieee_double_shape_type gh_u;					\
272   gh_u.value = (d);						\
273   (i) = gh_u.parts.msw;						\
274 } while (0)
275 
276 /* Get the less significant 32 bit int from a double.  */
277 
278 #define GET_LOW_WORD(i,d)					\
279 do {								\
280   ieee_double_shape_type gl_u;					\
281   gl_u.value = (d);						\
282   (i) = gl_u.parts.lsw;						\
283 } while (0)
284 
285 /* Set a double from two 32 bit ints.  */
286 
287 #define INSERT_WORDS(d,ix0,ix1)					\
288 do {								\
289   ieee_double_shape_type iw_u;					\
290   iw_u.parts.msw = (ix0);					\
291   iw_u.parts.lsw = (ix1);					\
292   (d) = iw_u.value;						\
293 } while (0)
294 
295 /* Set the more significant 32 bits of a double from an int.  */
296 
297 #define SET_HIGH_WORD(d,v)					\
298 do {								\
299   ieee_double_shape_type sh_u;					\
300   sh_u.value = (d);						\
301   sh_u.parts.msw = (v);						\
302   (d) = sh_u.value;						\
303 } while (0)
304 
305 /* Set the less significant 32 bits of a double from an int.  */
306 
307 #define SET_LOW_WORD(d,v)					\
308 do {								\
309   ieee_double_shape_type sl_u;					\
310   sl_u.value = (d);						\
311   sl_u.parts.lsw = (v);						\
312   (d) = sl_u.value;						\
313 } while (0)
314 
315 /* A union which permits us to convert between a float and a 32 bit
316    int.  */
317 
318 typedef union
319 {
320   float value;
321   u_int32_t word;
322 } ieee_float_shape_type;
323 
324 /* Get a 32 bit int from a float.  */
325 
326 #define GET_FLOAT_WORD(i,d)					\
327 do {								\
328   ieee_float_shape_type gf_u;					\
329   gf_u.value = (d);						\
330   (i) = gf_u.word;						\
331 } while (0)
332 
333 /* Set a float from a 32 bit int.  */
334 
335 #define SET_FLOAT_WORD(d,i)					\
336 do {								\
337   ieee_float_shape_type sf_u;					\
338   sf_u.word = (i);						\
339   (d) = sf_u.value;						\
340 } while (0)
341 
342 #ifdef FLT_EVAL_METHOD
343 /*
344  * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
345  */
346 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
347 #define	STRICT_ASSIGN(type, lval, rval)	((lval) = (rval))
348 #else /* FLT_EVAL_METHOD == 0 || __GNUC__ == 0 */
349 #define	STRICT_ASSIGN(type, lval, rval) do {	\
350 	volatile type __lval;			\
351 						\
352 	if (sizeof(type) >= sizeof(long double))	\
353 		(lval) = (rval);		\
354 	else {					\
355 		__lval = (rval);		\
356 		(lval) = __lval;		\
357 	}					\
358 } while (0)
359 #endif /* FLT_EVAL_METHOD == 0 || __GNUC__ == 0 */
360 #endif /* FLT_EVAL_METHOD */
361 
362 __BEGIN_HIDDEN_DECLS
363 /* fdlibm kernel function */
364 extern int    __ieee754_rem_pio2(double,double*);
365 extern double __kernel_sin(double,double,int);
366 extern double __kernel_cos(double,double);
367 extern double __kernel_tan(double,double,int);
368 extern int    __kernel_rem_pio2(double*,double*,int,int,int);
369 
370 /* float versions of fdlibm kernel functions */
371 extern int   __ieee754_rem_pio2f(float,float*);
372 extern float __kernel_sinf(float,float,int);
373 extern float __kernel_cosf(float,float);
374 extern float __kernel_tanf(float,float,int);
375 extern int   __kernel_rem_pio2f(float*,float*,int,int,int,const int*);
376 
377 /* long double precision kernel functions */
378 long double __kernel_sinl(long double, long double, int);
379 long double __kernel_cosl(long double, long double);
380 long double __kernel_tanl(long double, long double, int);
381 
382 /*
383  * Common routine to process the arguments to nan(), nanf(), and nanl().
384  */
385 void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
386 __END_HIDDEN_DECLS
387 
388 /*
389  * TRUNC() is a macro that sets the trailing 27 bits in the mantissa
390  * of an IEEE double variable to zero.  It must be expression-like
391  * for syntactic reasons, and we implement this expression using
392  * an inline function instead of a pure macro to avoid depending
393  * on the gcc feature of statement-expressions.
394  */
395 #define TRUNC(d)	(_b_trunc(&(d)))
396 
397 static __inline void
398 _b_trunc(volatile double *_dp)
399 {
400 	uint32_t _lw;
401 
402 	GET_LOW_WORD(_lw, *_dp);
403 	SET_LOW_WORD(*_dp, _lw & 0xf8000000);
404 }
405 
406 struct Double {
407 	double	a;
408 	double	b;
409 };
410 
411 /*
412  * Functions internal to the math package, yet not static.
413  */
414 __BEGIN_HIDDEN_DECLS
415 double __exp__D(double, double);
416 struct Double __log__D(double);
417 long double __p1evll(long double, void *, int);
418 long double __polevll(long double, void *, int);
419 __END_HIDDEN_DECLS
420 
421 #endif /* _MATH_PRIVATE_H_ */
422