[termux-packages] / disabled-packages / mono / math_private.h

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

/*
 * from: @(#)fdlibm.h 5.1 93/09/24
 * $FreeBSD$
 */

#ifndef _MATH_PRIVATE_H_
#define	_MATH_PRIVATE_H_

#include <sys/types.h>
#include <machine/endian.h>

/*
 * The original fdlibm code used statements like:
 *	n0 = ((*(int*)&one)>>29)^1;		* index of high word *
 *	ix0 = *(n0+(int*)&x);			* high word of x *
 *	ix1 = *((1-n0)+(int*)&x);		* low word of x *
 * to dig two 32 bit words out of the 64 bit IEEE floating point
 * value.  That is non-ANSI, and, moreover, the gcc instruction
 * scheduler gets it wrong.  We instead use the following macros.
 * Unlike the original code, we determine the endianness at compile
 * time, not at run time; I don't see much benefit to selecting
 * endianness at run time.
 */

/*
 * A union which permits us to convert between a double and two 32 bit
 * ints.
 */

#ifdef __arm__
#if defined(__VFP_FP__) || defined(__ARM_EABI__)
#define	IEEE_WORD_ORDER	BYTE_ORDER
#else
#define	IEEE_WORD_ORDER	BIG_ENDIAN
#endif
#else /* __arm__ */
#define	IEEE_WORD_ORDER	BYTE_ORDER
#endif

#if IEEE_WORD_ORDER == BIG_ENDIAN

typedef union
{
  double value;
  struct
  {
    u_int32_t msw;
    u_int32_t lsw;
  } parts;
  struct
  {
    u_int64_t w;
  } xparts;
} ieee_double_shape_type;

#endif

#if IEEE_WORD_ORDER == LITTLE_ENDIAN

typedef union
{
  double value;
  struct
  {
    u_int32_t lsw;
    u_int32_t msw;
  } parts;
  struct
  {
    u_int64_t w;
  } xparts;
} ieee_double_shape_type;

#endif

/* Get two 32 bit ints from a double.  */

#define EXTRACT_WORDS(ix0,ix1,d)				\
do {								\
  ieee_double_shape_type ew_u;					\
  ew_u.value = (d);						\
  (ix0) = ew_u.parts.msw;					\
  (ix1) = ew_u.parts.lsw;					\
} while (0)

/* Get a 64-bit int from a double. */
#define EXTRACT_WORD64(ix,d)					\
do {								\
  ieee_double_shape_type ew_u;					\
  ew_u.value = (d);						\
  (ix) = ew_u.xparts.w;						\
} while (0)

/* Get the more significant 32 bit int from a double.  */

#define GET_HIGH_WORD(i,d)					\
do {								\
  ieee_double_shape_type gh_u;					\
  gh_u.value = (d);						\
  (i) = gh_u.parts.msw;						\
} while (0)

/* Get the less significant 32 bit int from a double.  */

#define GET_LOW_WORD(i,d)					\
do {								\
  ieee_double_shape_type gl_u;					\
  gl_u.value = (d);						\
  (i) = gl_u.parts.lsw;						\
} while (0)

/* Set a double from two 32 bit ints.  */

#define INSERT_WORDS(d,ix0,ix1)					\
do {								\
  ieee_double_shape_type iw_u;					\
  iw_u.parts.msw = (ix0);					\
  iw_u.parts.lsw = (ix1);					\
  (d) = iw_u.value;						\
} while (0)

/* Set a double from a 64-bit int. */
#define INSERT_WORD64(d,ix)					\
do {								\
  ieee_double_shape_type iw_u;					\
  iw_u.xparts.w = (ix);						\
  (d) = iw_u.value;						\
} while (0)

/* Set the more significant 32 bits of a double from an int.  */

#define SET_HIGH_WORD(d,v)					\
do {								\
  ieee_double_shape_type sh_u;					\
  sh_u.value = (d);						\
  sh_u.parts.msw = (v);						\
  (d) = sh_u.value;						\
} while (0)

/* Set the less significant 32 bits of a double from an int.  */

#define SET_LOW_WORD(d,v)					\
do {								\
  ieee_double_shape_type sl_u;					\
  sl_u.value = (d);						\
  sl_u.parts.lsw = (v);						\
  (d) = sl_u.value;						\
} while (0)

/*
 * A union which permits us to convert between a float and a 32 bit
 * int.
 */

typedef union
{
  float value;
  /* FIXME: Assumes 32 bit int.  */
  unsigned int word;
} ieee_float_shape_type;

/* Get a 32 bit int from a float.  */

#define GET_FLOAT_WORD(i,d)					\
do {								\
  ieee_float_shape_type gf_u;					\
  gf_u.value = (d);						\
  (i) = gf_u.word;						\
} while (0)

/* Set a float from a 32 bit int.  */

#define SET_FLOAT_WORD(d,i)					\
do {								\
  ieee_float_shape_type sf_u;					\
  sf_u.word = (i);						\
  (d) = sf_u.value;						\
} while (0)

/*
 * Get expsign and mantissa as 16 bit and 64 bit ints from an 80 bit long
 * double.
 */

#define	EXTRACT_LDBL80_WORDS(ix0,ix1,d)				\
do {								\
  union IEEEl2bits ew_u;					\
  ew_u.e = (d);							\
  (ix0) = ew_u.xbits.expsign;					\
  (ix1) = ew_u.xbits.man;					\
} while (0)

/*
 * Get expsign and mantissa as one 16 bit and two 64 bit ints from a 128 bit
 * long double.
 */

#define	EXTRACT_LDBL128_WORDS(ix0,ix1,ix2,d)			\
do {								\
  union IEEEl2bits ew_u;					\
  ew_u.e = (d);							\
  (ix0) = ew_u.xbits.expsign;					\
  (ix1) = ew_u.xbits.manh;					\
  (ix2) = ew_u.xbits.manl;					\
} while (0)

/* Get expsign as a 16 bit int from a long double.  */

#define	GET_LDBL_EXPSIGN(i,d)					\
do {								\
  union IEEEl2bits ge_u;					\
  ge_u.e = (d);							\
  (i) = ge_u.xbits.expsign;					\
} while (0)

/*
 * Set an 80 bit long double from a 16 bit int expsign and a 64 bit int
 * mantissa.
 */

#define	INSERT_LDBL80_WORDS(d,ix0,ix1)				\
do {								\
  union IEEEl2bits iw_u;					\
  iw_u.xbits.expsign = (ix0);					\
  iw_u.xbits.man = (ix1);					\
  (d) = iw_u.e;							\
} while (0)

/*
 * Set a 128 bit long double from a 16 bit int expsign and two 64 bit ints
 * comprising the mantissa.
 */

#define	INSERT_LDBL128_WORDS(d,ix0,ix1,ix2)			\
do {								\
  union IEEEl2bits iw_u;					\
  iw_u.xbits.expsign = (ix0);					\
  iw_u.xbits.manh = (ix1);					\
  iw_u.xbits.manl = (ix2);					\
  (d) = iw_u.e;							\
} while (0)

/* Set expsign of a long double from a 16 bit int.  */

#define	SET_LDBL_EXPSIGN(d,v)					\
do {								\
  union IEEEl2bits se_u;					\
  se_u.e = (d);							\
  se_u.xbits.expsign = (v);					\
  (d) = se_u.e;							\
} while (0)

#ifdef __i386__
/* Long double constants are broken on i386. */
#define	LD80C(m, ex, v) {						\
	.xbits.man = __CONCAT(m, ULL),					\
	.xbits.expsign = (0x3fff + (ex)) | ((v) < 0 ? 0x8000 : 0),	\
}
#else
/* The above works on non-i386 too, but we use this to check v. */
#define	LD80C(m, ex, v)	{ .e = (v), }
#endif

#ifdef FLT_EVAL_METHOD
/*
 * Attempt to get strict C99 semantics for assignment with non-C99 compilers.
 */
#if FLT_EVAL_METHOD == 0 || __GNUC__ == 0
#define	STRICT_ASSIGN(type, lval, rval)	((lval) = (rval))
#else
#define	STRICT_ASSIGN(type, lval, rval) do {	\
	volatile type __lval;			\
						\
	if (sizeof(type) >= sizeof(long double))	\
		(lval) = (rval);		\
	else {					\
		__lval = (rval);		\
		(lval) = __lval;		\
	}					\
} while (0)
#endif
#endif /* FLT_EVAL_METHOD */

/* Support switching the mode to FP_PE if necessary. */
#if defined(__i386__) && !defined(NO_FPSETPREC)
#define	ENTERI()				\
	long double __retval;			\
	fp_prec_t __oprec;			\
						\
	if ((__oprec = fpgetprec()) != FP_PE)	\
		fpsetprec(FP_PE)
#define	RETURNI(x) do {				\
	__retval = (x);				\
	if (__oprec != FP_PE)			\
		fpsetprec(__oprec);		\
	RETURNF(__retval);			\
} while (0)
#else
#define	ENTERI(x)
#define	RETURNI(x)	RETURNF(x)
#endif

/* Default return statement if hack*_t() is not used. */
#define      RETURNF(v)      return (v)

/*
 * 2sum gives the same result as 2sumF without requiring |a| >= |b| or
 * a == 0, but is slower.
 */
#define	_2sum(a, b) do {	\
	__typeof(a) __s, __w;	\
				\
	__w = (a) + (b);	\
	__s = __w - (a);	\
	(b) = ((a) - (__w - __s)) + ((b) - __s); \
	(a) = __w;		\
} while (0)

/*
 * 2sumF algorithm.
 *
 * "Normalize" the terms in the infinite-precision expression a + b for
 * the sum of 2 floating point values so that b is as small as possible
 * relative to 'a'.  (The resulting 'a' is the value of the expression in
 * the same precision as 'a' and the resulting b is the rounding error.)
 * |a| must be >= |b| or 0, b's type must be no larger than 'a's type, and
 * exponent overflow or underflow must not occur.  This uses a Theorem of
 * Dekker (1971).  See Knuth (1981) 4.2.2 Theorem C.  The name "TwoSum"
 * is apparently due to Skewchuk (1997).
 *
 * For this to always work, assignment of a + b to 'a' must not retain any
 * extra precision in a + b.  This is required by C standards but broken
 * in many compilers.  The brokenness cannot be worked around using
 * STRICT_ASSIGN() like we do elsewhere, since the efficiency of this
 * algorithm would be destroyed by non-null strict assignments.  (The
 * compilers are correct to be broken -- the efficiency of all floating
 * point code calculations would be destroyed similarly if they forced the
 * conversions.)
 *
 * Fortunately, a case that works well can usually be arranged by building
 * any extra precision into the type of 'a' -- 'a' should have type float_t,
 * double_t or long double.  b's type should be no larger than 'a's type.
 * Callers should use these types with scopes as large as possible, to
 * reduce their own extra-precision and efficiciency problems.  In
 * particular, they shouldn't convert back and forth just to call here.
 */
#ifdef DEBUG
#define	_2sumF(a, b) do {				\
	__typeof(a) __w;				\
	volatile __typeof(a) __ia, __ib, __r, __vw;	\
							\
	__ia = (a);					\
	__ib = (b);					\
	assert(__ia == 0 || fabsl(__ia) >= fabsl(__ib));	\
							\
	__w = (a) + (b);				\
	(b) = ((a) - __w) + (b);			\
	(a) = __w;					\
							\
	/* The next 2 assertions are weak if (a) is already long double. */ \
	assert((long double)__ia + __ib == (long double)(a) + (b));	\
	__vw = __ia + __ib;				\
	__r = __ia - __vw;				\
	__r += __ib;					\
	assert(__vw == (a) && __r == (b));		\
} while (0)
#else /* !DEBUG */
#define	_2sumF(a, b) do {	\
	__typeof(a) __w;	\
				\
	__w = (a) + (b);	\
	(b) = ((a) - __w) + (b); \
	(a) = __w;		\
} while (0)
#endif /* DEBUG */

/*
 * Set x += c, where x is represented in extra precision as a + b.
 * x must be sufficiently normalized and sufficiently larger than c,
 * and the result is then sufficiently normalized.
 *
 * The details of ordering are that |a| must be >= |c| (so that (a, c)
 * can be normalized without extra work to swap 'a' with c).  The details of
 * the normalization are that b must be small relative to the normalized 'a'.
 * Normalization of (a, c) makes the normalized c tiny relative to the
 * normalized a, so b remains small relative to 'a' in the result.  However,
 * b need not ever be tiny relative to 'a'.  For example, b might be about
 * 2**20 times smaller than 'a' to give about 20 extra bits of precision.
 * That is usually enough, and adding c (which by normalization is about
 * 2**53 times smaller than a) cannot change b significantly.  However,
 * cancellation of 'a' with c in normalization of (a, c) may reduce 'a'
 * significantly relative to b.  The caller must ensure that significant
 * cancellation doesn't occur, either by having c of the same sign as 'a',
 * or by having |c| a few percent smaller than |a|.  Pre-normalization of
 * (a, b) may help.
 *
 * This is is a variant of an algorithm of Kahan (see Knuth (1981) 4.2.2
 * exercise 19).  We gain considerable efficiency by requiring the terms to
 * be sufficiently normalized and sufficiently increasing.
 */
#define	_3sumF(a, b, c) do {	\
	__typeof(a) __tmp;	\
				\
	__tmp = (c);		\
	_2sumF(__tmp, (a));	\
	(b) += (a);		\
	(a) = __tmp;		\
} while (0)

/*
 * Common routine to process the arguments to nan(), nanf(), and nanl().
 */
void _scan_nan(uint32_t *__words, int __num_words, const char *__s);

#ifdef _COMPLEX_H

/*
 * C99 specifies that complex numbers have the same representation as
 * an array of two elements, where the first element is the real part
 * and the second element is the imaginary part.
 */
typedef union {
	float complex f;
	float a[2];
} float_complex;
typedef union {
	double complex f;
	double a[2];
} double_complex;
typedef union {
	long double complex f;
	long double a[2];
} long_double_complex;
#define	REALPART(z)	((z).a[0])
#define	IMAGPART(z)	((z).a[1])

/*
 * Inline functions that can be used to construct complex values.
 *
 * The C99 standard intends x+I*y to be used for this, but x+I*y is
 * currently unusable in general since gcc introduces many overflow,
 * underflow, sign and efficiency bugs by rewriting I*y as
 * (0.0+I)*(y+0.0*I) and laboriously computing the full complex product.
 * In particular, I*Inf is corrupted to NaN+I*Inf, and I*-0 is corrupted
 * to -0.0+I*0.0.
 */
static __inline float complex
cpackf(float x, float y)
{
	float_complex z;

	REALPART(z) = x;
	IMAGPART(z) = y;
	return (z.f);
}

static __inline double complex
cpack(double x, double y)
{
	double_complex z;

	REALPART(z) = x;
	IMAGPART(z) = y;
	return (z.f);
}

static __inline long double complex
cpackl(long double x, long double y)
{
	long_double_complex z;

	REALPART(z) = x;
	IMAGPART(z) = y;
	return (z.f);
}
#endif /* _COMPLEX_H */
 
#ifdef __GNUCLIKE_ASM

/* Asm versions of some functions. */

#ifdef __amd64__
static __inline int
irint(double x)
{
	int n;

	asm("cvtsd2si %1,%0" : "=r" (n) : "x" (x));
	return (n);
}
#define	HAVE_EFFICIENT_IRINT
#endif

#ifdef __i386__
static __inline int
irint(double x)
{
	int n;

	asm("fistl %0" : "=m" (n) : "t" (x));
	return (n);
}
#define	HAVE_EFFICIENT_IRINT
#endif

#if defined(__amd64__) || defined(__i386__)
static __inline int
irintl(long double x)
{
	int n;

	asm("fistl %0" : "=m" (n) : "t" (x));
	return (n);
}
#define	HAVE_EFFICIENT_IRINTL
#endif

#endif /* __GNUCLIKE_ASM */

#ifdef DEBUG
#if defined(__amd64__) || defined(__i386__)
#define	breakpoint()	asm("int $3")
#else
#include <signal.h>

#define	breakpoint()	raise(SIGTRAP)
#endif
#endif

/* Write a pari script to test things externally. */
#ifdef DOPRINT
#include <stdio.h>

#ifndef DOPRINT_SWIZZLE
#define	DOPRINT_SWIZZLE		0
#endif

#ifdef DOPRINT_LD80

#define	DOPRINT_START(xp) do {						\
	uint64_t __lx;							\
	uint16_t __hx;							\
									\
	/* Hack to give more-problematic args. */			\
	EXTRACT_LDBL80_WORDS(__hx, __lx, *xp);				\
	__lx ^= DOPRINT_SWIZZLE;					\
	INSERT_LDBL80_WORDS(*xp, __hx, __lx);				\
	printf("x = %.21Lg; ", (long double)*xp);			\
} while (0)
#define	DOPRINT_END1(v)							\
	printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
#define	DOPRINT_END2(hi, lo)						\
	printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",		\
	    (long double)(hi), (long double)(lo))

#elif defined(DOPRINT_D64)

#define	DOPRINT_START(xp) do {						\
	uint32_t __hx, __lx;						\
									\
	EXTRACT_WORDS(__hx, __lx, *xp);					\
	__lx ^= DOPRINT_SWIZZLE;					\
	INSERT_WORDS(*xp, __hx, __lx);					\
	printf("x = %.21Lg; ", (long double)*xp);			\
} while (0)
#define	DOPRINT_END1(v)							\
	printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
#define	DOPRINT_END2(hi, lo)						\
	printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",		\
	    (long double)(hi), (long double)(lo))

#elif defined(DOPRINT_F32)

#define	DOPRINT_START(xp) do {						\
	uint32_t __hx;							\
									\
	GET_FLOAT_WORD(__hx, *xp);					\
	__hx ^= DOPRINT_SWIZZLE;					\
	SET_FLOAT_WORD(*xp, __hx);					\
	printf("x = %.21Lg; ", (long double)*xp);			\
} while (0)
#define	DOPRINT_END1(v)							\
	printf("y = %.21Lg; z = 0; show(x, y, z);\n", (long double)(v))
#define	DOPRINT_END2(hi, lo)						\
	printf("y = %.21Lg; z = %.21Lg; show(x, y, z);\n",		\
	    (long double)(hi), (long double)(lo))

#else /* !DOPRINT_LD80 && !DOPRINT_D64 (LD128 only) */

#ifndef DOPRINT_SWIZZLE_HIGH
#define	DOPRINT_SWIZZLE_HIGH	0
#endif

#define	DOPRINT_START(xp) do {						\
	uint64_t __lx, __llx;						\
	uint16_t __hx;							\
									\
	EXTRACT_LDBL128_WORDS(__hx, __lx, __llx, *xp);			\
	__llx ^= DOPRINT_SWIZZLE;					\
	__lx ^= DOPRINT_SWIZZLE_HIGH;					\
	INSERT_LDBL128_WORDS(*xp, __hx, __lx, __llx);			\
	printf("x = %.36Lg; ", (long double)*xp);					\
} while (0)
#define	DOPRINT_END1(v)							\
	printf("y = %.36Lg; z = 0; show(x, y, z);\n", (long double)(v))
#define	DOPRINT_END2(hi, lo)						\
	printf("y = %.36Lg; z = %.36Lg; show(x, y, z);\n",		\
	    (long double)(hi), (long double)(lo))

#endif /* DOPRINT_LD80 */

#else /* !DOPRINT */
#define	DOPRINT_START(xp)
#define	DOPRINT_END1(v)
#define	DOPRINT_END2(hi, lo)
#endif /* DOPRINT */

#define	RETURNP(x) do {			\
	DOPRINT_END1(x);		\
	RETURNF(x);			\
} while (0)
#define	RETURNPI(x) do {		\
	DOPRINT_END1(x);		\
	RETURNI(x);			\
} while (0)
#define	RETURN2P(x, y) do {		\
	DOPRINT_END2((x), (y));		\
	RETURNF((x) + (y));		\
} while (0)
#define	RETURN2PI(x, y) do {		\
	DOPRINT_END2((x), (y));		\
	RETURNI((x) + (y));		\
} while (0)
#ifdef STRUCT_RETURN
#define	RETURNSP(rp) do {		\
	if (!(rp)->lo_set)		\
		RETURNP((rp)->hi);	\
	RETURN2P((rp)->hi, (rp)->lo);	\
} while (0)
#define	RETURNSPI(rp) do {		\
	if (!(rp)->lo_set)		\
		RETURNPI((rp)->hi);	\
	RETURN2PI((rp)->hi, (rp)->lo);	\
} while (0)
#endif
#define	SUM2P(x, y) ({			\
	const __typeof (x) __x = (x);	\
	const __typeof (y) __y = (y);	\
					\
	DOPRINT_END2(__x, __y);		\
	__x + __y;			\
})

/*
 * ieee style elementary functions
 *
 * We rename functions here to improve other sources' diffability
 * against fdlibm.
 */
#define	__ieee754_sqrt	sqrt
#define	__ieee754_acos	acos
#define	__ieee754_acosh	acosh
#define	__ieee754_log	log
#define	__ieee754_log2	log2
#define	__ieee754_atanh	atanh
#define	__ieee754_asin	asin
#define	__ieee754_atan2	atan2
#define	__ieee754_exp	exp
#define	__ieee754_cosh	cosh
#define	__ieee754_fmod	fmod
#define	__ieee754_pow	pow
#define	__ieee754_lgamma lgamma
#define	__ieee754_gamma	gamma
#define	__ieee754_lgamma_r lgamma_r
#define	__ieee754_gamma_r gamma_r
#define	__ieee754_log10	log10
#define	__ieee754_sinh	sinh
#define	__ieee754_hypot	hypot
#define	__ieee754_j0	j0
#define	__ieee754_j1	j1
#define	__ieee754_y0	y0
#define	__ieee754_y1	y1
#define	__ieee754_jn	jn
#define	__ieee754_yn	yn
#define	__ieee754_remainder remainder
#define	__ieee754_scalb	scalb
#define	__ieee754_sqrtf	sqrtf
#define	__ieee754_acosf	acosf
#define	__ieee754_acoshf acoshf
#define	__ieee754_logf	logf
#define	__ieee754_atanhf atanhf
#define	__ieee754_asinf	asinf
#define	__ieee754_atan2f atan2f
#define	__ieee754_expf	expf
#define	__ieee754_coshf	coshf
#define	__ieee754_fmodf	fmodf
#define	__ieee754_powf	powf
#define	__ieee754_lgammaf lgammaf
#define	__ieee754_gammaf gammaf
#define	__ieee754_lgammaf_r lgammaf_r
#define	__ieee754_gammaf_r gammaf_r
#define	__ieee754_log10f log10f
#define	__ieee754_log2f log2f
#define	__ieee754_sinhf	sinhf
#define	__ieee754_hypotf hypotf
#define	__ieee754_j0f	j0f
#define	__ieee754_j1f	j1f
#define	__ieee754_y0f	y0f
#define	__ieee754_y1f	y1f
#define	__ieee754_jnf	jnf
#define	__ieee754_ynf	ynf
#define	__ieee754_remainderf remainderf
#define	__ieee754_scalbf scalbf

/* fdlibm kernel function */
int	__kernel_rem_pio2(double*,double*,int,int,int);

/* double precision kernel functions */
#ifndef INLINE_REM_PIO2
int	__ieee754_rem_pio2(double,double*);
#endif
double	__kernel_sin(double,double,int);
double	__kernel_cos(double,double);
double	__kernel_tan(double,double,int);
double	__ldexp_exp(double,int);
#ifdef _COMPLEX_H
double complex __ldexp_cexp(double complex,int);
#endif

/* float precision kernel functions */
#ifndef INLINE_REM_PIO2F
int	__ieee754_rem_pio2f(float,double*);
#endif
#ifndef INLINE_KERNEL_SINDF
float	__kernel_sindf(double);
#endif
#ifndef INLINE_KERNEL_COSDF
float	__kernel_cosdf(double);
#endif
#ifndef INLINE_KERNEL_TANDF
float	__kernel_tandf(double,int);
#endif
float	__ldexp_expf(float,int);
#ifdef _COMPLEX_H
float complex __ldexp_cexpf(float complex,int);
#endif

/* long double precision kernel functions */
long double __kernel_sinl(long double, long double, int);
long double __kernel_cosl(long double, long double);
long double __kernel_tanl(long double, long double, int);

#endif /* !_MATH_PRIVATE_H_ */
Commit	Line	Data
698b1561 VB	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+Iy to be used for this, but x+Iy 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+0.0I) and laboriously computing the full complex product.
455	* In particular, IInf is corrupted to NaN+IInf, and I*-0 is corrupted
456	* to -0.0+I*0.0.
457	*/
458	static __inline float complex
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
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
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
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
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
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_ */