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  * $FreeBSD$
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__) || defined(__ARM_EABI__)
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 /*
192  * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
193  * double.
194  */
195 
196 #define	EXTRACT_LDBL80_WORDS(ix0,ix1,d)				\
197 do {								\
198   union IEEEl2bits ew_u;					\
199   ew_u.e = (d);							\
200   (ix0) = ew_u.xbits.expsign;					\
201   (ix1) = ew_u.xbits.man;					\
202 } while (0)
203 
204 /*
205  * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
206  * long double.
207  */
208 
209 #define	EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d)			\
210 do {								\
211   union IEEEl2bits ew_u;					\
212   ew_u.e = (d);							\
213   (ix0) = ew_u.xbits.expsign;					\
214   (ix1) = ew_u.xbits.manh;					\
215   (ix2) = ew_u.xbits.manl;					\
216 } while (0)
217 
218 /* Get expsign as a 16 bit int from a long double.  */
219 
220 #define	GET_LDBL_EXPSIGN(i,d)					\
221 do {								\
222   union IEEEl2bits ge_u;					\
223   ge_u.e = (d);							\
224   (i) = ge_u.xbits.expsign;					\
225 } while (0)
226 
227 /*
228  * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
229  * mantissa.
230  */
231 
232 #define	INSERT_LDBL80_WORDS(d,ix0,ix1)				\
233 do {								\
234   union IEEEl2bits iw_u;					\
235   iw_u.xbits.expsign = (ix0);					\
236   iw_u.xbits.man = (ix1);					\
237   (d) = iw_u.e;							\
238 } while (0)
239 
240 /*
241  * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
242  * comprising the mantissa.
243  */
244 
245 #define	INSERT_LDBL128_WORDS(d,ix0,ix1,ix2)			\
246 do {								\
247   union IEEEl2bits iw_u;					\
248   iw_u.xbits.expsign = (ix0);					\
249   iw_u.xbits.manh = (ix1);					\
250   iw_u.xbits.manl = (ix2);					\
251   (d) = iw_u.e;							\
252 } while (0)
253 
254 /* Set expsign of a long double from a 16 bit int.  */
255 
256 #define	SET_LDBL_EXPSIGN(d,v)					\
257 do {								\
258   union IEEEl2bits se_u;					\
259   se_u.e = (d);							\
260   se_u.xbits.expsign = (v);					\
261   (d) = se_u.e;							\
262 } while (0)
263 
264 #ifdef __i386__
265 /* Long double constants are broken on i386. */
266 #define	LD80C(m, ex, v) {						\
267 	.xbits.man = __CONCAT(m, ULL),					\
268 	.xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0),	\
269 }
270 #else
271 /* The above works on non-i386 too, but we use this to check v. */
272 #define	LD80C(m, ex, v)	{ .e = (v), }
273 #endif
274 
275 #ifdef FLT_EVAL_METHOD
276 /*
277  * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
278  */
279 #if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
280 #define	STRICT_ASSIGN(type, lval, rval)	((lval) = (rval))
281 #else
282 #define	STRICT_ASSIGN(type, lval, rval) do {	\
283 	volatile type __lval;			\
284 						\
285 	if (sizeof(type) >= sizeof(long double))	\
286 		(lval) = (rval);		\
287 	else {					\
288 		__lval = (rval);		\
289 		(lval) = __lval;		\
290 	}					\
291 } while (0)
292 #endif
293 #endif /* FLT_EVAL_METHOD */
294 
295 /* Support switching the mode to FP_PE if necessary. */
296 #if defined(__i386__) && !defined(NO_FPSETPREC)
297 #define	ENTERI()				\
298 	long double __retval;			\
299 	fp_prec_t __oprec;			\
300 						\
301 	if ((__oprec = fpgetprec()) != FP_PE)	\
302 		fpsetprec(FP_PE)
303 #define	RETURNI(x) do {				\
304 	__retval = (x);				\
305 	if (__oprec != FP_PE)			\
306 		fpsetprec(__oprec);		\
307 	RETURNF(__retval);			\
308 } while (0)
309 #else
310 #define	ENTERI(x)
311 #define	RETURNI(x)	RETURNF(x)
312 #endif
313 
314 /* Default return statement if hack*_t() is not used. */
315 #define      RETURNF(v)      return (v)
316 
317 /*
318  * 2sum gives the same result as 2sumF without requiring |a| >= |b| or
319  * a == 0, but is slower.
320  */
321 #define	_2sum(a, b) do {	\
322 	__typeof(a) __s, __w;	\
323 				\
324 	__w = (a) + (b);	\
325 	__s = __w - (a);	\
326 	(b) = ((a) - (__w - __s)) + ((b) - __s); \
327 	(a) = __w;		\
328 } while (0)
329 
330 /*
331  * 2sumF algorithm.
332  *
333  * "Normalize" the terms in the infinite-precision expression a + b for
334  * the sum of 2 floating point values so that b is as small as possible
335  * relative to 'a'.  (The resulting 'a' is the value of the expression in
336  * the same precision as 'a' and the resulting b is the rounding error.)
337  * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
338  * exponent overflow or underflow must not occur.  This uses a Theorem of
339  * Dekker (1971).  See Knuth (1981) 4.2.2 Theorem C.  The name "TwoSum"
340  * is apparently due to Skewchuk (1997).
341  *
342  * For this to always work, assignment of a + b to 'a' must not retain any
343  * extra precision in a + b.  This is required by C standards but broken
344  * in many compilers.  The brokenness cannot be worked around using
345  * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
346  * algorithm would be destroyed by non-null strict assignments.  (The
347  * compilers are correct to be broken -- the efficiency of all floating
348  * point code calculations would be destroyed similarly if they forced the
349  * conversions.)
350  *
351  * Fortunately, a case that works well can usually be arranged by building
352  * any extra precision into the type of 'a' -- 'a' should have type float_t,
353  * double_t or long double.  b's type should be no larger than 'a's type.
354  * Callers should use these types with scopes as large as possible, to
355  * reduce their own extra-precision and efficiciency problems.  In
356  * particular, they shouldn't convert back and forth just to call here.
357  */
358 #ifdef DEBUG
359 #define	_2sumF(a, b) do {				\
360 	__typeof(a) __w;				\
361 	volatile __typeof(a) __ia, __ib, __r, __vw;	\
362 							\
363 	__ia = (a);					\
364 	__ib = (b);					\
365 	assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib));	\
366 							\
367 	__w = (a) + (b);				\
368 	(b) = ((a) - __w) + (b);			\
369 	(a) = __w;					\
370 							\
371 	/* The next 2 assertions are weak if (a) is already long double. */ \
372 	assert((long double)__ia + __ib == (long double)(a) + (b));	\
373 	__vw = __ia + __ib;				\
374 	__r = __ia - __vw;				\
375 	__r += __ib;					\
376 	assert(__vw == (a) && __r == (b));		\
377 } while (0)
378 #else /* !DEBUG */
379 #define	_2sumF(a, b) do {	\
380 	__typeof(a) __w;	\
381 				\
382 	__w = (a) + (b);	\
383 	(b) = ((a) - __w) + (b); \
384 	(a) = __w;		\
385 } while (0)
386 #endif /* DEBUG */
387 
388 /*
389  * Set x += c, where x is represented in extra precision as a + b.
390  * x must be sufficiently normalized and sufficiently larger than c,
391  * and the result is then sufficiently normalized.
392  *
393  * The details of ordering are that |a| must be >= |c| (so that (a, c)
394  * can be normalized without extra work to swap 'a' with c).  The details of
395  * the normalization are that b must be small relative to the normalized 'a'.
396  * Normalization of (a, c) makes the normalized c tiny relative to the
397  * normalized a, so b remains small relative to 'a' in the result.  However,
398  * b need not ever be tiny relative to 'a'.  For example, b might be about
399  * 2**20 times smaller than 'a' to give about 20 extra bits of precision.
400  * That is usually enough, and adding c (which by normalization is about
401  * 2**53 times smaller than a) cannot change b significantly.  However,
402  * cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
403  * significantly relative to b.  The caller must ensure that significant
404  * cancellation doesn't occur, either by having c of the same sign as 'a',
405  * or by having |c| a few percent smaller than |a|.  Pre-normalization of
406  * (a, b) may help.
407  *
408  * This is is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
409  * exercise 19).  We gain considerable efficiency by requiring the terms to
410  * be sufficiently normalized and sufficiently increasing.
411  */
412 #define	_3sumF(a, b, c) do {	\
413 	__typeof(a) __tmp;	\
414 				\
415 	__tmp = (c);		\
416 	_2sumF(__tmp, (a));	\
417 	(b) += (a);		\
418 	(a) = __tmp;		\
419 } while (0)
420 
421 /*
422  * Common routine to process the arguments to nan(), nanf(), and nanl().
423  */
424 void _scan_nan(uint32_t *__words, int __num_words, const char *__s);
425 
426 #ifdef _COMPLEX_H
427 
428 /*
429  * C99 specifies that complex numbers have the same representation as
430  * an array of two elements, where the first element is the real part
431  * and the second element is the imaginary part.
432  */
433 typedef union {
434 	float complex f;
435 	float a[2];
436 } float_complex;
437 typedef union {
438 	double complex f;
439 	double a[2];
440 } double_complex;
441 typedef union {
442 	long double complex f;
443 	long double a[2];
444 } long_double_complex;
445 #define	REALPART(z)	((z).a[0])
446 #define	IMAGPART(z)	((z).a[1])
447 
448 /*
449  * Inline functions that can be used to construct complex values.
450  *
451  * The C99 standard intends x+I*y to be used for this, but x+I*y is
452  * currently unusable in general since gcc introduces many overflow,
453  * underflow, sign and efficiency bugs by rewriting I*y as
454  * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
455  * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
456  * to -0.0+I*0.0.
457  */
458 static __inline float complex
cpackf(float x,float y)459 cpackf(float x, float y)
460 {
461 	float_complex z;
462 
463 	REALPART(z) = x;
464 	IMAGPART(z) = y;
465 	return (z.f);
466 }
467 
468 static __inline double complex
cpack(double x,double y)469 cpack(double x, double y)
470 {
471 	double_complex z;
472 
473 	REALPART(z) = x;
474 	IMAGPART(z) = y;
475 	return (z.f);
476 }
477 
478 static __inline long double complex
cpackl(long double x,long double y)479 cpackl(long double x, long double y)
480 {
481 	long_double_complex z;
482 
483 	REALPART(z) = x;
484 	IMAGPART(z) = y;
485 	return (z.f);
486 }
487 #endif /* _COMPLEX_H */
488 
489 #ifdef __GNUCLIKE_ASM
490 
491 /* Asm versions of some functions. */
492 
493 #ifdef __amd64__
494 static __inline int
irint(double x)495 irint(double x)
496 {
497 	int n;
498 
499 	asm("cvtsd2si %1,%0" : "=r" (n) : "x" (x));
500 	return (n);
501 }
502 #define	HAVE_EFFICIENT_IRINT
503 #endif
504 
505 #ifdef __i386__
506 static __inline int
irint(double x)507 irint(double x)
508 {
509 	int n;
510 
511 	asm("fistl %0" : "=m" (n) : "t" (x));
512 	return (n);
513 }
514 #define	HAVE_EFFICIENT_IRINT
515 #endif
516 
517 #if defined(__amd64__) || defined(__i386__)
518 static __inline int
irintl(long double x)519 irintl(long double x)
520 {
521 	int n;
522 
523 	asm("fistl %0" : "=m" (n) : "t" (x));
524 	return (n);
525 }
526 #define	HAVE_EFFICIENT_IRINTL
527 #endif
528 
529 #endif /* __GNUCLIKE_ASM */
530 
531 #ifdef DEBUG
532 #if defined(__amd64__) || defined(__i386__)
533 #define	breakpoint()	asm("int $3")
534 #else
535 #include <signal.h>
536 
537 #define	breakpoint()	raise(SIGTRAP)
538 #endif
539 #endif
540 
541 /* Write a pari script to test things externally. */
542 #ifdef DOPRINT
543 #include <stdio.h>
544 
545 #ifndef DOPRINT_SWIZZLE
546 #define	DOPRINT_SWIZZLE		0
547 #endif
548 
549 #ifdef DOPRINT_LD80
550 
551 #define	DOPRINT_START(xp) do {						\
552 	uint64_t __lx;							\
553 	uint16_t __hx;							\
554 									\
555 	/* Hack to give more-problematic args. */			\
556 	EXTRACT_LDBL80_WORDS(__hx, __lx, *xp);				\
557 	__lx ^= DOPRINT_SWIZZLE;					\
558 	INSERT_LDBL80_WORDS(*xp, __hx, __lx);				\
559 	printf("x = %.21Lg; ", (long double)*xp);			\
560 } while (0)
561 #define	DOPRINT_END1(v)							\
562 	printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
563 #define	DOPRINT_END2(hi, lo)						\
564 	printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",		\
565 	    (long double)(hi), (long double)(lo))
566 
567 #elif defined(DOPRINT_D64)
568 
569 #define	DOPRINT_START(xp) do {						\
570 	uint32_t __hx, __lx;						\
571 									\
572 	EXTRACT_WORDS(__hx, __lx, *xp);					\
573 	__lx ^= DOPRINT_SWIZZLE;					\
574 	INSERT_WORDS(*xp, __hx, __lx);					\
575 	printf("x = %.21Lg; ", (long double)*xp);			\
576 } while (0)
577 #define	DOPRINT_END1(v)							\
578 	printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
579 #define	DOPRINT_END2(hi, lo)						\
580 	printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",		\
581 	    (long double)(hi), (long double)(lo))
582 
583 #elif defined(DOPRINT_F32)
584 
585 #define	DOPRINT_START(xp) do {						\
586 	uint32_t __hx;							\
587 									\
588 	GET_FLOAT_WORD(__hx, *xp);					\
589 	__hx ^= DOPRINT_SWIZZLE;					\
590 	SET_FLOAT_WORD(*xp, __hx);					\
591 	printf("x = %.21Lg; ", (long double)*xp);			\
592 } while (0)
593 #define	DOPRINT_END1(v)							\
594 	printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
595 #define	DOPRINT_END2(hi, lo)						\
596 	printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",		\
597 	    (long double)(hi), (long double)(lo))
598 
599 #else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */
600 
601 #ifndef DOPRINT_SWIZZLE_HIGH
602 #define	DOPRINT_SWIZZLE_HIGH	0
603 #endif
604 
605 #define	DOPRINT_START(xp) do {						\
606 	uint64_t __lx, __llx;						\
607 	uint16_t __hx;							\
608 									\
609 	EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp);			\
610 	__llx ^= DOPRINT_SWIZZLE;					\
611 	__lx ^= DOPRINT_SWIZZLE_HIGH;					\
612 	INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx);			\
613 	printf("x = %.36Lg; ", (long double)*xp);					\
614 } while (0)
615 #define	DOPRINT_END1(v)							\
616 	printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v))
617 #define	DOPRINT_END2(hi, lo)						\
618 	printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n",		\
619 	    (long double)(hi), (long double)(lo))
620 
621 #endif /* DOPRINT_LD80 */
622 
623 #else /* !DOPRINT */
624 #define	DOPRINT_START(xp)
625 #define	DOPRINT_END1(v)
626 #define	DOPRINT_END2(hi, lo)
627 #endif /* DOPRINT */
628 
629 #define	RETURNP(x) do {			\
630 	DOPRINT_END1(x);		\
631 	RETURNF(x);			\
632 } while (0)
633 #define	RETURNPI(x) do {		\
634 	DOPRINT_END1(x);		\
635 	RETURNI(x);			\
636 } while (0)
637 #define	RETURN2P(x, y) do {		\
638 	DOPRINT_END2((x), (y));		\
639 	RETURNF((x) + (y));		\
640 } while (0)
641 #define	RETURN2PI(x, y) do {		\
642 	DOPRINT_END2((x), (y));		\
643 	RETURNI((x) + (y));		\
644 } while (0)
645 #ifdef STRUCT_RETURN
646 #define	RETURNSP(rp) do {		\
647 	if (!(rp)->lo_set)		\
648 		RETURNP((rp)->hi);	\
649 	RETURN2P((rp)->hi, (rp)->lo);	\
650 } while (0)
651 #define	RETURNSPI(rp) do {		\
652 	if (!(rp)->lo_set)		\
653 		RETURNPI((rp)->hi);	\
654 	RETURN2PI((rp)->hi, (rp)->lo);	\
655 } while (0)
656 #endif
657 #define	SUM2P(x, y) ({			\
658 	const __typeof (x) __x = (x);	\
659 	const __typeof (y) __y = (y);	\
660 					\
661 	DOPRINT_END2(__x, __y);		\
662 	__x + __y;			\
663 })
664 
665 /*
666  * ieee style elementary functions
667  *
668  * We rename functions here to improve other sources' diffability
669  * against fdlibm.
670  */
671 #define	__ieee754_sqrt	sqrt
672 #define	__ieee754_acos	acos
673 #define	__ieee754_acosh	acosh
674 #define	__ieee754_log	log
675 #define	__ieee754_log2	log2
676 #define	__ieee754_atanh	atanh
677 #define	__ieee754_asin	asin
678 #define	__ieee754_atan2	atan2
679 #define	__ieee754_exp	exp
680 #define	__ieee754_cosh	cosh
681 #define	__ieee754_fmod	fmod
682 #define	__ieee754_pow	pow
683 #define	__ieee754_lgamma lgamma
684 #define	__ieee754_gamma	gamma
685 #define	__ieee754_lgamma_r lgamma_r
686 #define	__ieee754_gamma_r gamma_r
687 #define	__ieee754_log10	log10
688 #define	__ieee754_sinh	sinh
689 #define	__ieee754_hypot	hypot
690 #define	__ieee754_j0	j0
691 #define	__ieee754_j1	j1
692 #define	__ieee754_y0	y0
693 #define	__ieee754_y1	y1
694 #define	__ieee754_jn	jn
695 #define	__ieee754_yn	yn
696 #define	__ieee754_remainder remainder
697 #define	__ieee754_scalb	scalb
698 #define	__ieee754_sqrtf	sqrtf
699 #define	__ieee754_acosf	acosf
700 #define	__ieee754_acoshf acoshf
701 #define	__ieee754_logf	logf
702 #define	__ieee754_atanhf atanhf
703 #define	__ieee754_asinf	asinf
704 #define	__ieee754_atan2f atan2f
705 #define	__ieee754_expf	expf
706 #define	__ieee754_coshf	coshf
707 #define	__ieee754_fmodf	fmodf
708 #define	__ieee754_powf	powf
709 #define	__ieee754_lgammaf lgammaf
710 #define	__ieee754_gammaf gammaf
711 #define	__ieee754_lgammaf_r lgammaf_r
712 #define	__ieee754_gammaf_r gammaf_r
713 #define	__ieee754_log10f log10f
714 #define	__ieee754_log2f log2f
715 #define	__ieee754_sinhf	sinhf
716 #define	__ieee754_hypotf hypotf
717 #define	__ieee754_j0f	j0f
718 #define	__ieee754_j1f	j1f
719 #define	__ieee754_y0f	y0f
720 #define	__ieee754_y1f	y1f
721 #define	__ieee754_jnf	jnf
722 #define	__ieee754_ynf	ynf
723 #define	__ieee754_remainderf remainderf
724 #define	__ieee754_scalbf scalbf
725 
726 /* fdlibm kernel function */
727 int	__kernel_rem_pio2(double*,double*,int,int,int);
728 
729 /* double precision kernel functions */
730 #ifndef INLINE_REM_PIO2
731 int	__ieee754_rem_pio2(double,double*);
732 #endif
733 double	__kernel_sin(double,double,int);
734 double	__kernel_cos(double,double);
735 double	__kernel_tan(double,double,int);
736 double	__ldexp_exp(double,int);
737 #ifdef _COMPLEX_H
738 double complex __ldexp_cexp(double complex,int);
739 #endif
740 
741 /* float precision kernel functions */
742 #ifndef INLINE_REM_PIO2F
743 int	__ieee754_rem_pio2f(float,double*);
744 #endif
745 #ifndef INLINE_KERNEL_SINDF
746 float	__kernel_sindf(double);
747 #endif
748 #ifndef INLINE_KERNEL_COSDF
749 float	__kernel_cosdf(double);
750 #endif
751 #ifndef INLINE_KERNEL_TANDF
752 float	__kernel_tandf(double,int);
753 #endif
754 float	__ldexp_expf(float,int);
755 #ifdef _COMPLEX_H
756 float complex __ldexp_cexpf(float complex,int);
757 #endif
758 
759 /* long double precision kernel functions */
760 long double __kernel_sinl(long double, long double, int);
761 long double __kernel_cosl(long double, long double);
762 long double __kernel_tanl(long double, long double, int);
763 
764 #endif /* !_MATH_PRIVATE_H_ */
765