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_H_
18#define	_MATH_H_
19
20#include <sys/cdefs.h>
21#include <sys/_types.h>
22#include <limits.h>
23
24/*
25 * ANSI/POSIX
26 */
27extern const union __infinity_un {
28	unsigned char	__uc[8];
29	double		__ud;
30} __infinity;
31
32extern const union __nan_un {
33	unsigned char	__uc[sizeof(float)];
34	float		__uf;
35} __nan;
36
37#if __GNUC_PREREQ__(3, 3) || (defined(__INTEL_COMPILER) && __INTEL_COMPILER >= 800)
38#define	__MATH_BUILTIN_CONSTANTS
39#endif
40
41#if __GNUC_PREREQ__(3, 0) && !defined(__INTEL_COMPILER)
42#define	__MATH_BUILTIN_RELOPS
43#endif
44
45#ifdef __MATH_BUILTIN_CONSTANTS
46#define	HUGE_VAL	__builtin_huge_val()
47#else
48#define	HUGE_VAL	(__infinity.__ud)
49#endif
50
51#if __ISO_C_VISIBLE >= 1999
52#define	FP_ILOGB0	(-INT_MAX) /* Android-changed */
53#define	FP_ILOGBNAN	INT_MAX /* Android-changed */
54
55#ifdef __MATH_BUILTIN_CONSTANTS
56#define	HUGE_VALF	__builtin_huge_valf()
57#define	HUGE_VALL	__builtin_huge_vall()
58#define	INFINITY	__builtin_inff()
59#define	NAN		__builtin_nanf("")
60#else
61#define	HUGE_VALF	(float)HUGE_VAL
62#define	HUGE_VALL	(long double)HUGE_VAL
63#define	INFINITY	HUGE_VALF
64#define	NAN		(__nan.__uf)
65#endif /* __MATH_BUILTIN_CONSTANTS */
66
67#define	MATH_ERRNO	1
68#define	MATH_ERREXCEPT	2
69#define	math_errhandling	MATH_ERREXCEPT
70
71#define	FP_FAST_FMAF	1
72#ifdef __ia64__
73#define	FP_FAST_FMA	1
74#define	FP_FAST_FMAL	1
75#endif
76
77/* Symbolic constants to classify floating point numbers. */
78#define	FP_INFINITE	0x01
79#define	FP_NAN		0x02
80#define	FP_NORMAL	0x04
81#define	FP_SUBNORMAL	0x08
82#define	FP_ZERO		0x10
83#define	fpclassify(x) \
84    ((sizeof (x) == sizeof (float)) ? __fpclassifyf(x) \
85    : (sizeof (x) == sizeof (double)) ? __fpclassifyd(x) \
86    : __fpclassifyl(x))
87
88#define	isfinite(x)					\
89    ((sizeof (x) == sizeof (float)) ? __isfinitef(x)	\
90    : (sizeof (x) == sizeof (double)) ? __isfinite(x)	\
91    : __isfinitel(x))
92#define	isinf(x)					\
93    ((sizeof (x) == sizeof (float)) ? __isinff(x)	\
94    : (sizeof (x) == sizeof (double)) ? isinf(x)	\
95    : __isinfl(x))
96#define	isnan(x)					\
97    ((sizeof (x) == sizeof (float)) ? __isnanf(x)	\
98    : (sizeof (x) == sizeof (double)) ? isnan(x)	\
99    : __isnanl(x))
100#define	isnormal(x)					\
101    ((sizeof (x) == sizeof (float)) ? __isnormalf(x)	\
102    : (sizeof (x) == sizeof (double)) ? __isnormal(x)	\
103    : __isnormall(x))
104
105#ifdef __MATH_BUILTIN_RELOPS
106#define	isgreater(x, y)		__builtin_isgreater((x), (y))
107#define	isgreaterequal(x, y)	__builtin_isgreaterequal((x), (y))
108#define	isless(x, y)		__builtin_isless((x), (y))
109#define	islessequal(x, y)	__builtin_islessequal((x), (y))
110#define	islessgreater(x, y)	__builtin_islessgreater((x), (y))
111#define	isunordered(x, y)	__builtin_isunordered((x), (y))
112#else
113#define	isgreater(x, y)		(!isunordered((x), (y)) && (x) > (y))
114#define	isgreaterequal(x, y)	(!isunordered((x), (y)) && (x) >= (y))
115#define	isless(x, y)		(!isunordered((x), (y)) && (x) < (y))
116#define	islessequal(x, y)	(!isunordered((x), (y)) && (x) <= (y))
117#define	islessgreater(x, y)	(!isunordered((x), (y)) && \
118					((x) > (y) || (y) > (x)))
119#define	isunordered(x, y)	(isnan(x) || isnan(y))
120#endif /* __MATH_BUILTIN_RELOPS */
121
122#define	signbit(x)					\
123    ((sizeof (x) == sizeof (float)) ? __signbitf(x)	\
124    : (sizeof (x) == sizeof (double)) ? __signbit(x)	\
125    : __signbitl(x))
126
127typedef	__double_t	double_t;
128typedef	__float_t	float_t;
129#endif /* __ISO_C_VISIBLE >= 1999 */
130
131/*
132 * XOPEN/SVID
133 */
134#if __BSD_VISIBLE || __XSI_VISIBLE
135#define	M_E		2.7182818284590452354	/* e */
136#define	M_LOG2E		1.4426950408889634074	/* log 2e */
137#define	M_LOG10E	0.43429448190325182765	/* log 10e */
138#define	M_LN2		0.69314718055994530942	/* log e2 */
139#define	M_LN10		2.30258509299404568402	/* log e10 */
140#define	M_PI		3.14159265358979323846	/* pi */
141#define	M_PI_2		1.57079632679489661923	/* pi/2 */
142#define	M_PI_4		0.78539816339744830962	/* pi/4 */
143#define	M_1_PI		0.31830988618379067154	/* 1/pi */
144#define	M_2_PI		0.63661977236758134308	/* 2/pi */
145#define	M_2_SQRTPI	1.12837916709551257390	/* 2/sqrt(pi) */
146#define	M_SQRT2		1.41421356237309504880	/* sqrt(2) */
147#define	M_SQRT1_2	0.70710678118654752440	/* 1/sqrt(2) */
148
149#define	MAXFLOAT	((float)3.40282346638528860e+38)
150extern int signgam;
151#endif /* __BSD_VISIBLE || __XSI_VISIBLE */
152
153#if __BSD_VISIBLE
154#if 0
155/* Old value from 4.4BSD-Lite math.h; this is probably better. */
156#define	HUGE		HUGE_VAL
157#else
158#define	HUGE		MAXFLOAT
159#endif
160#endif /* __BSD_VISIBLE */
161
162/*
163 * Most of these functions depend on the rounding mode and have the side
164 * effect of raising floating-point exceptions, so they are not declared
165 * as __pure2.  In C99, FENV_ACCESS affects the purity of these functions.
166 */
167__BEGIN_DECLS
168/*
169 * ANSI/POSIX
170 */
171int	__fpclassifyd(double) __pure2;
172int	__fpclassifyf(float) __pure2;
173int	__fpclassifyl(long double) __pure2;
174int	__isfinitef(float) __pure2;
175int	__isfinite(double) __pure2;
176int	__isfinitel(long double) __pure2;
177int	__isinff(float) __pure2;
178int	__isinfl(long double) __pure2;
179int	__isnanf(float) __pure2;
180int	__isnanl(long double) __pure2;
181int	__isnormalf(float) __pure2;
182int	__isnormal(double) __pure2;
183int	__isnormall(long double) __pure2;
184int	__signbit(double) __pure2;
185int	__signbitf(float) __pure2;
186int	__signbitl(long double) __pure2;
187
188double	acos(double);
189double	asin(double);
190double	atan(double);
191double	atan2(double, double);
192double	cos(double);
193double	sin(double);
194double	tan(double);
195
196double	cosh(double);
197double	sinh(double);
198double	tanh(double);
199
200double	exp(double);
201double	frexp(double, int *);	/* fundamentally !__pure2 */
202double	ldexp(double, int);
203double	log(double);
204double	log10(double);
205double	modf(double, double *);	/* fundamentally !__pure2 */
206
207double	pow(double, double);
208double	sqrt(double);
209
210double	ceil(double);
211double	fabs(double) __pure2;
212double	floor(double);
213double	fmod(double, double);
214
215/*
216 * These functions are not in C90.
217 */
218#if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE
219double	acosh(double);
220double	asinh(double);
221double	atanh(double);
222double	cbrt(double);
223double	erf(double);
224double	erfc(double);
225double	exp2(double);
226double	expm1(double);
227double	fma(double, double, double);
228double	hypot(double, double);
229int	ilogb(double) __pure2;
230int	(isinf)(double) __pure2;
231int	(isnan)(double) __pure2;
232double	lgamma(double);
233long long llrint(double);
234long long llround(double);
235double	log1p(double);
236double	log2(double);
237double	logb(double);
238long	lrint(double);
239long	lround(double);
240double	nan(const char *) __pure2;
241double	nextafter(double, double);
242double	remainder(double, double);
243double	remquo(double, double, int *);
244double	rint(double);
245#endif /* __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999 || __XSI_VISIBLE */
246
247#if __BSD_VISIBLE || __XSI_VISIBLE
248double	j0(double);
249double	j1(double);
250double	jn(int, double);
251double	y0(double);
252double	y1(double);
253double	yn(int, double);
254
255#if __XSI_VISIBLE <= 500 || __BSD_VISIBLE
256double	gamma(double);
257#endif
258
259#if __XSI_VISIBLE <= 600 || __BSD_VISIBLE
260double	scalb(double, double);
261#endif
262#endif /* __BSD_VISIBLE || __XSI_VISIBLE */
263
264#if __BSD_VISIBLE || __ISO_C_VISIBLE >= 1999
265double	copysign(double, double) __pure2;
266double	fdim(double, double);
267double	fmax(double, double) __pure2;
268double	fmin(double, double) __pure2;
269double	nearbyint(double);
270double	round(double);
271double	scalbln(double, long);
272double	scalbn(double, int);
273double	tgamma(double);
274double	trunc(double);
275#endif
276
277/*
278 * BSD math library entry points
279 */
280#if __BSD_VISIBLE
281double	drem(double, double);
282int	finite(double) __pure2;
283int	isnanf(float) __pure2;
284
285/*
286 * Reentrant version of gamma & lgamma; passes signgam back by reference
287 * as the second argument; user must allocate space for signgam.
288 */
289double	gamma_r(double, int *);
290double	lgamma_r(double, int *);
291
292/*
293 * IEEE Test Vector
294 */
295double	significand(double);
296#endif /* __BSD_VISIBLE */
297
298/* float versions of ANSI/POSIX functions */
299#if __ISO_C_VISIBLE >= 1999
300float	acosf(float);
301float	asinf(float);
302float	atanf(float);
303float	atan2f(float, float);
304float	cosf(float);
305float	sinf(float);
306float	tanf(float);
307
308float	coshf(float);
309float	sinhf(float);
310float	tanhf(float);
311
312float	exp2f(float);
313float	expf(float);
314float	expm1f(float);
315float	frexpf(float, int *);	/* fundamentally !__pure2 */
316int	ilogbf(float) __pure2;
317float	ldexpf(float, int);
318float	log10f(float);
319float	log1pf(float);
320float	log2f(float);
321float	logf(float);
322float	modff(float, float *);	/* fundamentally !__pure2 */
323
324float	powf(float, float);
325float	sqrtf(float);
326
327float	ceilf(float);
328float	fabsf(float) __pure2;
329float	floorf(float);
330float	fmodf(float, float);
331float	roundf(float);
332
333float	erff(float);
334float	erfcf(float);
335float	hypotf(float, float);
336float	lgammaf(float);
337float	tgammaf(float);
338
339float	acoshf(float);
340float	asinhf(float);
341float	atanhf(float);
342float	cbrtf(float);
343float	logbf(float);
344float	copysignf(float, float) __pure2;
345long long llrintf(float);
346long long llroundf(float);
347long	lrintf(float);
348long	lroundf(float);
349float	nanf(const char *) __pure2;
350float	nearbyintf(float);
351float	nextafterf(float, float);
352float	remainderf(float, float);
353float	remquof(float, float, int *);
354float	rintf(float);
355float	scalblnf(float, long);
356float	scalbnf(float, int);
357float	truncf(float);
358
359float	fdimf(float, float);
360float	fmaf(float, float, float);
361float	fmaxf(float, float) __pure2;
362float	fminf(float, float) __pure2;
363#endif
364
365/*
366 * float versions of BSD math library entry points
367 */
368#if __BSD_VISIBLE
369float	dremf(float, float);
370int	finitef(float) __pure2;
371float	gammaf(float);
372float	j0f(float);
373float	j1f(float);
374float	jnf(int, float);
375float	scalbf(float, float);
376float	y0f(float);
377float	y1f(float);
378float	ynf(int, float);
379
380/*
381 * Float versions of reentrant version of gamma & lgamma; passes
382 * signgam back by reference as the second argument; user must
383 * allocate space for signgam.
384 */
385float	gammaf_r(float, int *);
386float	lgammaf_r(float, int *);
387
388/*
389 * float version of IEEE Test Vector
390 */
391float	significandf(float);
392#endif	/* __BSD_VISIBLE */
393
394/*
395 * long double versions of ISO/POSIX math functions
396 */
397#if __ISO_C_VISIBLE >= 1999
398long double	acosl(long double);
399long double	asinl(long double);
400long double	atan2l(long double, long double);
401long double	atanl(long double);
402long double	cbrtl(long double);
403long double	ceill(long double);
404long double	copysignl(long double, long double) __pure2;
405long double	cosl(long double);
406long double	exp2l(long double);
407long double	expl(long double);
408long double	fabsl(long double) __pure2;
409long double	fdiml(long double, long double);
410long double	floorl(long double);
411long double	fmal(long double, long double, long double);
412long double	fmaxl(long double, long double) __pure2;
413long double	fminl(long double, long double) __pure2;
414long double	fmodl(long double, long double);
415long double	frexpl(long double value, int *); /* fundamentally !__pure2 */
416long double	hypotl(long double, long double);
417int		ilogbl(long double) __pure2;
418long double	ldexpl(long double, int);
419long long	llrintl(long double);
420long long	llroundl(long double);
421long double	logbl(long double);
422long		lrintl(long double);
423long		lroundl(long double);
424long double	modfl(long double, long double *); /* fundamentally !__pure2 */
425long double	nanl(const char *) __pure2;
426long double	nearbyintl(long double);
427long double	nextafterl(long double, long double);
428double		nexttoward(double, long double);
429float		nexttowardf(float, long double);
430long double	nexttowardl(long double, long double);
431long double	remainderl(long double, long double);
432long double	remquol(long double, long double, int *);
433long double	rintl(long double);
434long double	roundl(long double);
435long double	scalblnl(long double, long);
436long double	scalbnl(long double, int);
437long double	sinl(long double);
438long double	sqrtl(long double);
439long double	tanl(long double);
440long double	truncl(long double);
441
442#endif /* __ISO_C_VISIBLE >= 1999 */
443__END_DECLS
444
445#endif /* !_MATH_H_ */
446
447/* separate header for cmath */
448#ifndef _MATH_EXTRA_H_
449#if __ISO_C_VISIBLE >= 1999
450#if _DECLARE_C99_LDBL_MATH
451
452#define _MATH_EXTRA_H_
453
454/*
455 * extra long double versions of math functions for C99 and cmath
456 */
457__BEGIN_DECLS
458
459long double	acoshl(long double);
460long double	asinhl(long double);
461long double	atanhl(long double);
462long double	coshl(long double);
463long double	erfcl(long double);
464long double	erfl(long double);
465long double	expm1l(long double);
466long double	lgammal(long double);
467long double	log10l(long double);
468long double	log1pl(long double);
469long double	log2l(long double);
470long double	logl(long double);
471long double	powl(long double, long double);
472long double	sinhl(long double);
473long double	tanhl(long double);
474long double	tgammal(long double);
475
476__END_DECLS
477
478#endif /* !_DECLARE_C99_LDBL_MATH */
479#endif /* __ISO_C_VISIBLE >= 1999 */
480#endif /* !_MATH_EXTRA_H_ */
481