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 */
14
15#ifndef _MATH_H_
16#define	_MATH_H_
17
18#include <sys/_types.h>
19#include <machine/_limits.h>
20
21/*
22 * ANSI/POSIX
23 */
24extern const union __infinity_un {
25	unsigned char	__uc[8];
26	double		__ud;
27} __infinity;
28
29extern const union __nan_un {
30	unsigned char	__uc[sizeof(float)];
31	float		__uf;
32} __nan;
33
34#if __GNUC_PREREQ__(3, 3)
35#define	__MATH_BUILTIN_CONSTANTS
36#endif
37
38#if __GNUC_PREREQ__(3, 0)
39#define	__MATH_BUILTIN_RELOPS
40#endif
41
42#ifdef __MATH_BUILTIN_CONSTANTS
43#define	HUGE_VAL	__builtin_huge_val()
44#else
45#define	HUGE_VAL	(__infinity.__ud)
46#endif
47
48#if __ISO_C_VISIBLE >= 1999
49#define	FP_ILOGB0	(-__INT_MAX)
50#define	FP_ILOGBNAN	__INT_MAX
51
52#ifdef __MATH_BUILTIN_CONSTANTS
53#define	HUGE_VALF	__builtin_huge_valf()
54#define	HUGE_VALL	__builtin_huge_vall()
55#define	INFINITY	__builtin_inff()
56#define	NAN		__builtin_nanf("")
57#else
58#define	HUGE_VALF	(float)HUGE_VAL
59#define	HUGE_VALL	(long double)HUGE_VAL
60#define	INFINITY	HUGE_VALF
61#define	NAN		(__nan.__uf)
62#endif /* __MATH_BUILTIN_CONSTANTS */
63
64#define	MATH_ERRNO	1
65#define	MATH_ERREXCEPT	2
66#define	math_errhandling	MATH_ERREXCEPT
67
68#define	FP_FAST_FMAF	1
69
70/* Symbolic constants to classify floating point numbers. */
71#define	FP_INFINITE	0x01
72#define	FP_NAN		0x02
73#define	FP_NORMAL	0x04
74#define	FP_SUBNORMAL	0x08
75#define	FP_ZERO		0x10
76
77#if __STDC_VERSION__ >= 201112L || __has_extension(c_generic_selections)
78#define	__fp_type_select(x, f, d, ld) __extension__ _Generic((x),	\
79    float: f,								\
80    double: d,								\
81    long double: ld)(x)
82#elif __GNUC_PREREQ__(3, 1) && !defined(__cplusplus)
83#define	__fp_type_select(x, f, d, ld) __builtin_choose_expr(		\
84    __builtin_types_compatible_p(__typeof(x), long double), ld(x),	\
85    __builtin_choose_expr(						\
86    __builtin_types_compatible_p(__typeof(x), double), d(x),		\
87    __builtin_choose_expr(						\
88    __builtin_types_compatible_p(__typeof(x), float), f(x), (void)0)))
89#else
90#define	 __fp_type_select(x, f, d, ld)					\
91    ((sizeof(x) == sizeof(float)) ? f(x)				\
92    : (sizeof(x) == sizeof(double)) ? d(x)				\
93    : ld(x))
94#endif
95
96#define	fpclassify(x) \
97	__fp_type_select(x, __fpclassifyf, __fpclassifyd, __fpclassifyl)
98#define	isfinite(x) __fp_type_select(x, __isfinitef, __isfinite, __isfinitel)
99#define	isinf(x) __fp_type_select(x, __isinff, __isinf, __isinfl)
100#define	isnan(x) \
101	__fp_type_select(x, __inline_isnanf, __inline_isnan, __inline_isnanl)
102#define	isnormal(x) __fp_type_select(x, __isnormalf, __isnormal, __isnormall)
103
104#ifdef __MATH_BUILTIN_RELOPS
105#define	isgreater(x, y)		__builtin_isgreater((x), (y))
106#define	isgreaterequal(x, y)	__builtin_isgreaterequal((x), (y))
107#define	isless(x, y)		__builtin_isless((x), (y))
108#define	islessequal(x, y)	__builtin_islessequal((x), (y))
109#define	islessgreater(x, y)	__builtin_islessgreater((x), (y))
110#define	isunordered(x, y)	__builtin_isunordered((x), (y))
111#else
112#define	isgreater(x, y)		(!isunordered((x), (y)) && (x) > (y))
113#define	isgreaterequal(x, y)	(!isunordered((x), (y)) && (x) >= (y))
114#define	isless(x, y)		(!isunordered((x), (y)) && (x) < (y))
115#define	islessequal(x, y)	(!isunordered((x), (y)) && (x) <= (y))
116#define	islessgreater(x, y)	(!isunordered((x), (y)) && \
117					((x) > (y) || (y) > (x)))
118#define	isunordered(x, y)	(isnan(x) || isnan(y))
119#endif /* __MATH_BUILTIN_RELOPS */
120
121#define	signbit(x) __fp_type_select(x, __signbitf, __signbit, __signbitl)
122
123typedef	__double_t	double_t;
124typedef	__float_t	float_t;
125#endif /* __ISO_C_VISIBLE >= 1999 */
126
127/*
128 * XOPEN/SVID
129 */
130#if __BSD_VISIBLE || __XSI_VISIBLE
131#define	M_E		2.7182818284590452354	/* e */
132#define	M_LOG2E		1.4426950408889634074	/* log 2e */
133#define	M_LOG10E	0.43429448190325182765	/* log 10e */
134#define	M_LN2		0.69314718055994530942	/* log e2 */
135#define	M_LN10		2.30258509299404568402	/* log e10 */
136#define	M_PI		3.14159265358979323846	/* pi */
137#define	M_PI_2		1.57079632679489661923	/* pi/2 */
138#define	M_PI_4		0.78539816339744830962	/* pi/4 */
139#define	M_1_PI		0.31830988618379067154	/* 1/pi */
140#define	M_2_PI		0.63661977236758134308	/* 2/pi */
141#define	M_2_SQRTPI	1.12837916709551257390	/* 2/sqrt(pi) */
142#define	M_SQRT2		1.41421356237309504880	/* sqrt(2) */
143#define	M_SQRT1_2	0.70710678118654752440	/* 1/sqrt(2) */
144
145#if __BSD_VISIBLE || __XSI_VISIBLE >= 800
146#define	M_El		2.718281828459045235360287471352662498L	/* e */
147#define	M_LOG2El	1.442695040888963407359924681001892137L	/* log_2 e */
148#define	M_LOG10El	0.434294481903251827651128918916605082L	/* log_10 e */
149#define	M_LN2l		0.693147180559945309417232121458176568L	/* log_e 2 */
150#define	M_LN10l		2.302585092994045684017991454684364208L	/* log_e 10 */
151#define	M_PIl		3.141592653589793238462643383279502884L	/* pi */
152#define	M_PI_2l		1.570796326794896619231321691639751442L	/* pi/2 */
153#define	M_PI_4l		0.785398163397448309615660845819875721L	/* pi/4 */
154#define	M_1_PIl		0.318309886183790671537767526745028724L	/* 1/pi */
155#define	M_2_PIl		0.636619772367581343075535053490057448L	/* 2/pi */
156#define	M_2_SQRTPIl	1.128379167095512573896158903121545172L	/* 2/sqrt(pi) */
157#define	M_SQRT2l	1.414213562373095048801688724209698079L	/* sqrt(2) */
158#define	M_SQRT1_2l	0.707106781186547524400844362104849039L	/* 1/sqrt(2) */
159#endif /* __BSD_VISIBLE || __XSI_VISIBLE >= 800 */
160
161#define	MAXFLOAT	((float)3.40282346638528860e+38)
162extern int signgam;
163#endif /* __BSD_VISIBLE || __XSI_VISIBLE */
164
165#if __BSD_VISIBLE
166#if 0
167/* Old value from 4.4BSD-Lite math.h; this is probably better. */
168#define	HUGE		HUGE_VAL
169#else
170#define	HUGE		MAXFLOAT
171#endif
172#endif /* __BSD_VISIBLE */
173
174/*
175 * Most of these functions depend on the rounding mode and have the side
176 * effect of raising floating-point exceptions, so they are not declared
177 * as __pure2.  In C99, FENV_ACCESS affects the purity of these functions.
178 */
179__BEGIN_DECLS
180/*
181 * ANSI/POSIX
182 */
183int	__fpclassifyd(double) __pure2;
184int	__fpclassifyf(float) __pure2;
185int	__fpclassifyl(long double) __pure2;
186int	__isfinitef(float) __pure2;
187int	__isfinite(double) __pure2;
188int	__isfinitel(long double) __pure2;
189int	__isinff(float) __pure2;
190int	__isinf(double) __pure2;
191int	__isinfl(long double) __pure2;
192int	__isnormalf(float) __pure2;
193int	__isnormal(double) __pure2;
194int	__isnormall(long double) __pure2;
195int	__signbit(double) __pure2;
196int	__signbitf(float) __pure2;
197int	__signbitl(long double) __pure2;
198
199static __inline int
200__inline_isnan(const double __x)
201{
202
203	return (__x != __x);
204}
205
206static __inline int
207__inline_isnanf(const float __x)
208{
209
210	return (__x != __x);
211}
212
213static __inline int
214__inline_isnanl(const long double __x)
215{
216
217	return (__x != __x);
218}
219
220/*
221 * Define the following aliases, for compatibility with glibc and CUDA.
222 */
223#define __isnan __inline_isnan
224#define __isnanf __inline_isnanf
225
226/*
227 * Version 2 of the Single UNIX Specification (UNIX98) defined isnan() and
228 * isinf() as functions taking double.  C99, and the subsequent POSIX revisions
229 * (SUSv3, POSIX.1-2001, define it as a macro that accepts any real floating
230 * point type.  If we are targeting SUSv2 and C99 or C11 (or C++11) then we
231 * expose the newer definition, assuming that the language spec takes
232 * precedence over the operating system interface spec.
233 */
234#if	__XSI_VISIBLE > 0 && __XSI_VISIBLE < 600 && __ISO_C_VISIBLE < 1999
235#undef isinf
236#undef isnan
237int	isinf(double);
238int	isnan(double);
239#endif
240
241double	acos(double);
242double	asin(double);
243double	atan(double);
244double	atan2(double, double);
245double	cos(double);
246double	sin(double);
247double	tan(double);
248
249double	cosh(double);
250double	sinh(double);
251double	tanh(double);
252
253double	exp(double);
254double	frexp(double, int *);	/* fundamentally !__pure2 */
255double	ldexp(double, int);
256double	log(double);
257double	log10(double);
258double	modf(double, double *);	/* fundamentally !__pure2 */
259
260double	pow(double, double);
261double	sqrt(double);
262
263double	ceil(double);
264double	fabs(double) __pure2;
265double	floor(double);
266double	fmod(double, double);
267
268/*
269 * These functions are not in C90.
270 */
271#if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE
272double	acosh(double);
273double	asinh(double);
274double	atanh(double);
275double	cbrt(double);
276double	erf(double);
277double	erfc(double);
278double	exp2(double);
279double	expm1(double);
280double	fma(double, double, double);
281double	hypot(double, double);
282int	ilogb(double) __pure2;
283double	lgamma(double);
284long long llrint(double);
285long long llround(double);
286double	log1p(double);
287double	log2(double);
288double	logb(double);
289long	lrint(double);
290long	lround(double);
291double	nan(const char *) __pure2;
292double	nextafter(double, double);
293double	remainder(double, double);
294double	remquo(double, double, int *);
295double	rint(double);
296#endif /* __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */
297
298#if __BSD_VISIBLE || __XSI_VISIBLE
299double	j0(double);
300double	j1(double);
301double	jn(int, double);
302double	y0(double);
303double	y1(double);
304double	yn(int, double);
305
306#if __XSI_VISIBLE <= 500 || __BSD_VISIBLE
307double	gamma(double);
308#endif
309
310#if __XSI_VISIBLE <= 600 || __BSD_VISIBLE
311double	scalb(double, double);
312#endif
313#endif /* __BSD_VISIBLE || __XSI_VISIBLE */
314
315#if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999
316double	copysign(double, double) __pure2;
317double	fdim(double, double);
318double	fmax(double, double) __pure2;
319double	fmin(double, double) __pure2;
320double	nearbyint(double);
321double	round(double);
322double	scalbln(double, long);
323double	scalbn(double, int);
324double	tgamma(double);
325double	trunc(double);
326#endif
327
328/*
329 * BSD math library entry points
330 */
331#if __BSD_VISIBLE
332double	drem(double, double);
333int	finite(double) __pure2;
334int	isnanf(float) __pure2;
335
336/*
337 * Reentrant version of gamma & lgamma; passes signgam back by reference
338 * as the second argument; user must allocate space for signgam.
339 */
340double	gamma_r(double, int *);
341double	lgamma_r(double, int *);
342
343/*
344 * IEEE Test Vector
345 */
346double	significand(double);
347#endif /* __BSD_VISIBLE */
348
349/* float versions of ANSI/POSIX functions */
350#if __ISO_C_VISIBLE >= 1999
351float	acosf(float);
352float	asinf(float);
353float	atanf(float);
354float	atan2f(float, float);
355float	cosf(float);
356float	sinf(float);
357float	tanf(float);
358
359float	coshf(float);
360float	sinhf(float);
361float	tanhf(float);
362
363float	exp2f(float);
364float	expf(float);
365float	expm1f(float);
366float	frexpf(float, int *);	/* fundamentally !__pure2 */
367int	ilogbf(float) __pure2;
368float	ldexpf(float, int);
369float	log10f(float);
370float	log1pf(float);
371float	log2f(float);
372float	logf(float);
373float	modff(float, float *);	/* fundamentally !__pure2 */
374
375float	powf(float, float);
376float	sqrtf(float);
377
378float	ceilf(float);
379float	fabsf(float) __pure2;
380float	floorf(float);
381float	fmodf(float, float);
382float	roundf(float);
383
384float	erff(float);
385float	erfcf(float);
386float	hypotf(float, float);
387float	lgammaf(float);
388float	tgammaf(float);
389
390float	acoshf(float);
391float	asinhf(float);
392float	atanhf(float);
393float	cbrtf(float);
394float	logbf(float);
395float	copysignf(float, float) __pure2;
396long long llrintf(float);
397long long llroundf(float);
398long	lrintf(float);
399long	lroundf(float);
400float	nanf(const char *) __pure2;
401float	nearbyintf(float);
402float	nextafterf(float, float);
403float	remainderf(float, float);
404float	remquof(float, float, int *);
405float	rintf(float);
406float	scalblnf(float, long);
407float	scalbnf(float, int);
408float	truncf(float);
409
410float	fdimf(float, float);
411float	fmaf(float, float, float);
412float	fmaxf(float, float) __pure2;
413float	fminf(float, float) __pure2;
414#endif
415
416/*
417 * float versions of BSD math library entry points
418 */
419#if __BSD_VISIBLE
420float	dremf(float, float);
421int	finitef(float) __pure2;
422float	gammaf(float);
423float	j0f(float);
424float	j1f(float);
425float	jnf(int, float);
426float	scalbf(float, float);
427float	y0f(float);
428float	y1f(float);
429float	ynf(int, float);
430
431/*
432 * Float versions of reentrant version of gamma & lgamma; passes
433 * signgam back by reference as the second argument; user must
434 * allocate space for signgam.
435 */
436float	gammaf_r(float, int *);
437float	lgammaf_r(float, int *);
438
439/*
440 * float version of IEEE Test Vector
441 */
442float	significandf(float);
443#endif	/* __BSD_VISIBLE */
444
445/*
446 * long double versions of ISO/POSIX math functions
447 */
448#if __ISO_C_VISIBLE >= 1999
449long double	acoshl(long double);
450long double	acosl(long double);
451long double	asinhl(long double);
452long double	asinl(long double);
453long double	atan2l(long double, long double);
454long double	atanhl(long double);
455long double	atanl(long double);
456long double	cbrtl(long double);
457long double	ceill(long double);
458long double	copysignl(long double, long double) __pure2;
459long double	coshl(long double);
460long double	cosl(long double);
461long double	erfcl(long double);
462long double	erfl(long double);
463long double	exp2l(long double);
464long double	expl(long double);
465long double	expm1l(long double);
466long double	fabsl(long double) __pure2;
467long double	fdiml(long double, long double);
468long double	floorl(long double);
469long double	fmal(long double, long double, long double);
470long double	fmaxl(long double, long double) __pure2;
471long double	fminl(long double, long double) __pure2;
472long double	fmodl(long double, long double);
473long double	frexpl(long double, int *); /* fundamentally !__pure2 */
474long double	hypotl(long double, long double);
475int		ilogbl(long double) __pure2;
476long double	ldexpl(long double, int);
477long double	lgammal(long double);
478long long	llrintl(long double);
479long long	llroundl(long double);
480long double	log10l(long double);
481long double	log1pl(long double);
482long double	log2l(long double);
483long double	logbl(long double);
484long double	logl(long double);
485long		lrintl(long double);
486long		lroundl(long double);
487long double	modfl(long double, long double *); /* fundamentally !__pure2 */
488long double	nanl(const char *) __pure2;
489long double	nearbyintl(long double);
490long double	nextafterl(long double, long double);
491double		nexttoward(double, long double);
492float		nexttowardf(float, long double);
493long double	nexttowardl(long double, long double);
494long double	powl(long double, long double);
495long double	remainderl(long double, long double);
496long double	remquol(long double, long double, int *);
497long double	rintl(long double);
498long double	roundl(long double);
499long double	scalblnl(long double, long);
500long double	scalbnl(long double, int);
501long double	sinhl(long double);
502long double	sinl(long double);
503long double	sqrtl(long double);
504long double	tanhl(long double);
505long double	tanl(long double);
506long double	tgammal(long double);
507long double	truncl(long double);
508#endif /* __ISO_C_VISIBLE >= 1999 */
509
510#if __BSD_VISIBLE
511long double	lgammal_r(long double, int *);
512void		sincos(double, double *, double *);
513void		sincosf(float, float *, float *);
514void		sincosl(long double, long double *, long double *);
515double		cospi(double);
516float		cospif(float);
517long double 	cospil(long double);
518double		sinpi(double);
519float		sinpif(float);
520long double 	sinpil(long double);
521double		tanpi(double);
522float		tanpif(float);
523long double	tanpil(long double);
524#endif
525
526__END_DECLS
527
528#endif /* !_MATH_H_ */
529