mathinline.h

glibc 库, 不仅可以学习使用库函数,还可以学习函数的具体实现,是提高功力的好资料

  __asm __volatile__							      \
    ("fscale			# 2^int(x * log2(e))\n\t"		      \
     : "=t" (__temp) : "0" (1.0), "u" (__exponent));			      \
  __temp -= 1.0;							      \
  __temp += __value;							      \
  return __temp ? __temp : __x
# endif
__inline_mathcodeNP_ (long double, __expm1l, __x, __expm1_code)

# if __GNUC_PREREQ (3, 4)
__inline_mathcodeNP_ (long double, __expl, __x, return __builtin_expl (__x))
# else
#  define __exp_code \
  register long double __value;						      \
  register long double __exponent;					      \
  __asm __volatile__							      \
    ("fldl2e			# e^x = 2^(x * log2(e))\n\t"		      \
     "fmul	%%st(1)		# x * log2(e)\n\t"			      \
     "fst	%%st(1)\n\t"						      \
     "frndint			# int(x * log2(e))\n\t"			      \
     "fxch\n\t"								      \
     "fsub	%%st(1)		# fract(x * log2(e))\n\t"		      \
     "f2xm1			# 2^(fract(x * log2(e))) - 1\n\t"	      \
     : "=t" (__value), "=u" (__exponent) : "0" (__x));			      \
  __value += 1.0;							      \
  __asm __volatile__							      \
    ("fscale"								      \
     : "=t" (__value) : "0" (__value), "u" (__exponent));		      \
  return __value
__inline_mathcodeNP (exp, __x, __exp_code)
__inline_mathcodeNP_ (long double, __expl, __x, __exp_code)
# endif


# if !__GNUC_PREREQ (3, 5)
__inline_mathcodeNP (tan, __x, \
  register long double __value;						      \
  register long double __value2 __attribute__ ((__unused__));		      \
  __asm __volatile__							      \
    ("fptan"								      \
     : "=t" (__value2), "=u" (__value) : "0" (__x));			      \
  return __value)
# endif
#endif /* __FAST_MATH__ */


#if __GNUC_PREREQ (3, 4)
__inline_mathcodeNP2_ (long double, __atan2l, __y, __x,
		       return __builtin_atan2l (__y, __x))
#else
# define __atan2_code \
  register long double __value;						      \
  __asm __volatile__							      \
    ("fpatan"								      \
     : "=t" (__value) : "0" (__x), "u" (__y) : "st(1)");		      \
  return __value
# ifdef __FAST_MATH__
__inline_mathcodeNP2 (atan2, __y, __x, __atan2_code)
# endif
__inline_mathcodeNP2_ (long double, __atan2l, __y, __x, __atan2_code)
#endif


#if defined __FAST_MATH__ && !__GNUC_PREREQ (3, 5)
__inline_mathcodeNP2 (fmod, __x, __y, \
  register long double __value;						      \
  __asm __volatile__							      \
    ("1:	fprem\n\t"						      \
     "fnstsw	%%ax\n\t"						      \
     "sahf\n\t"								      \
     "jp	1b"							      \
     : "=t" (__value) : "0" (__x), "u" (__y) : "ax", "cc");		      \
  return __value)
#endif


#ifdef __FAST_MATH__
# if !__GNUC_PREREQ (3,3)
__inline_mathopNP (sqrt, "fsqrt")
__inline_mathopNP_ (long double, __sqrtl, "fsqrt")
#  define __libc_sqrtl(n) __sqrtl (n)
# else
#  define __libc_sqrtl(n) __builtin_sqrtl (n)
# endif
#endif

#if __GNUC_PREREQ (2, 8)
__inline_mathcodeNP_ (double, fabs, __x, return __builtin_fabs (__x))
# if defined __USE_MISC || defined __USE_ISOC99
__inline_mathcodeNP_ (float, fabsf, __x, return __builtin_fabsf (__x))
__inline_mathcodeNP_ (long double, fabsl, __x, return __builtin_fabsl (__x))
# endif
__inline_mathcodeNP_ (long double, __fabsl, __x, return __builtin_fabsl (__x))
#else
__inline_mathop (fabs, "fabs")
__inline_mathop_ (long double, __fabsl, "fabs")
#endif

#ifdef __FAST_MATH__
# if !__GNUC_PREREQ (3, 4)
/* The argument range of this inline version is reduced.  */
__inline_mathopNP (sin, "fsin")
/* The argument range of this inline version is reduced.  */
__inline_mathopNP (cos, "fcos")

__inline_mathop_declNP (log, "fldln2; fxch; fyl2x", "0" (__x) : "st(1)")
# endif

# if !__GNUC_PREREQ (3, 5)
__inline_mathop_declNP (log10, "fldlg2; fxch; fyl2x", "0" (__x) : "st(1)")

__inline_mathcodeNP (asin, __x, return __atan2l (__x, __libc_sqrtl (1.0 - __x * __x)))
__inline_mathcodeNP (acos, __x, return __atan2l (__libc_sqrtl (1.0 - __x * __x), __x))
# endif

# if !__GNUC_PREREQ (3, 4)
__inline_mathop_declNP (atan, "fld1; fpatan", "0" (__x) : "st(1)")
# endif
#endif /* __FAST_MATH__ */

__inline_mathcode_ (long double, __sgn1l, __x, \
  __extension__ union { long double __xld; unsigned int __xi[3]; } __n =      \
    { __xld: __x };							      \
  __n.__xi[2] = (__n.__xi[2] & 0x8000) | 0x3fff;			      \
  __n.__xi[1] = 0x80000000;						      \
  __n.__xi[0] = 0;							      \
  return __n.__xld)


#ifdef __FAST_MATH__
/* The argument range of the inline version of sinhl is slightly reduced.  */
__inline_mathcodeNP (sinh, __x, \
  register long double __exm1 = __expm1l (__fabsl (__x));		      \
  return 0.5 * (__exm1 / (__exm1 + 1.0) + __exm1) * __sgn1l (__x))

__inline_mathcodeNP (cosh, __x, \
  register long double __ex = __expl (__x);				      \
  return 0.5 * (__ex + 1.0 / __ex))

__inline_mathcodeNP (tanh, __x, \
  register long double __exm1 = __expm1l (-__fabsl (__x + __x));	      \
  return __exm1 / (__exm1 + 2.0) * __sgn1l (-__x))
#endif

__inline_mathcodeNP (floor, __x, \
  register long double __value;						      \
  register int __ignore;						      \
  unsigned short int __cw;						      \
  unsigned short int __cwtmp;						      \
  __asm __volatile ("fnstcw %3\n\t"					      \
		    "movzwl %3, %1\n\t"					      \
		    "andl $0xf3ff, %1\n\t"				      \
		    "orl $0x0400, %1\n\t"	/* rounding down */	      \
		    "movw %w1, %2\n\t"					      \
		    "fldcw %2\n\t"					      \
		    "frndint\n\t"					      \
		    "fldcw %3"						      \
		    : "=t" (__value), "=&q" (__ignore), "=m" (__cwtmp),	      \
		      "=m" (__cw)					      \
		    : "0" (__x));					      \
  return __value)

__inline_mathcodeNP (ceil, __x, \
  register long double __value;						      \
  register int __ignore;						      \
  unsigned short int __cw;						      \
  unsigned short int __cwtmp;						      \
  __asm __volatile ("fnstcw %3\n\t"					      \
		    "movzwl %3, %1\n\t"					      \
		    "andl $0xf3ff, %1\n\t"				      \
		    "orl $0x0800, %1\n\t"	/* rounding up */	      \
		    "movw %w1, %2\n\t"					      \
		    "fldcw %2\n\t"					      \
		    "frndint\n\t"					      \
		    "fldcw %3"						      \
		    : "=t" (__value), "=&q" (__ignore), "=m" (__cwtmp),	      \
		      "=m" (__cw)					      \
		    : "0" (__x));					      \
  return __value)

#ifdef __FAST_MATH__
# define __ldexp_code \
  register long double __value;						      \
  __asm __volatile__							      \
    ("fscale"								      \
     : "=t" (__value) : "0" (__x), "u" ((long double) __y));		      \
  return __value

__MATH_INLINE double
__NTH (ldexp (double __x, int __y))
{
  __ldexp_code;
}
#endif


/* Optimized versions for some non-standardized functions.  */
#if defined __USE_ISOC99 || defined __USE_MISC

# ifdef __FAST_MATH__
__inline_mathcodeNP (expm1, __x, __expm1_code)

/* We cannot rely on M_SQRT being defined.  So we do it for ourself
   here.  */
#  define __M_SQRT2	1.41421356237309504880L	/* sqrt(2) */

#  if !__GNUC_PREREQ (3, 5)
__inline_mathcodeNP (log1p, __x, \
  register long double __value;						      \
  if (__fabsl (__x) >= 1.0 - 0.5 * __M_SQRT2)				      \
    __value = logl (1.0 + __x);						      \
  else									      \
    __asm __volatile__							      \
      ("fldln2\n\t"							      \
       "fxch\n\t"							      \
       "fyl2xp1"							      \
       : "=t" (__value) : "0" (__x) : "st(1)");				      \
  return __value)
#  endif


/* The argument range of the inline version of asinhl is slightly reduced.  */
__inline_mathcodeNP (asinh, __x, \
  register long double  __y = __fabsl (__x);				      \
  return (log1pl (__y * __y / (__libc_sqrtl (__y * __y + 1.0) + 1.0) + __y)   \
	  * __sgn1l (__x)))

__inline_mathcodeNP (acosh, __x, \
  return logl (__x + __libc_sqrtl (__x - 1.0) * __libc_sqrtl (__x + 1.0)))

__inline_mathcodeNP (atanh, __x, \
  register long double __y = __fabsl (__x);				      \
  return -0.5 * log1pl (-(__y + __y) / (1.0 + __y)) * __sgn1l (__x))

/* The argument range of the inline version of hypotl is slightly reduced.  */
__inline_mathcodeNP2 (hypot, __x, __y,
		      return __libc_sqrtl (__x * __x + __y * __y))

#  if !__GNUC_PREREQ (3, 5)
__inline_mathcodeNP(logb, __x, \
  register long double __value;						      \
  register long double __junk;						      \
  __asm __volatile__							      \
    ("fxtract\n\t"							      \
     : "=t" (__junk), "=u" (__value) : "0" (__x));			      \
  return __value)
#  endif

# endif
#endif

#ifdef __USE_ISOC99
# ifdef __FAST_MATH__

#  if !__GNUC_PREREQ (3, 5)
__inline_mathop_declNP (log2, "fld1; fxch; fyl2x", "0" (__x) : "st(1)")
#  endif

__MATH_INLINE float
__NTH (ldexpf (float __x, int __y))
{
  __ldexp_code;
}

__MATH_INLINE long double
__NTH (ldexpl (long double __x, int __y))
{
  __ldexp_code;
}

__inline_mathcodeNP3 (fma, __x, __y, __z, return (__x * __y) + __z)

__inline_mathopNP (rint, "frndint")
# endif /* __FAST_MATH__ */

# define __lrint_code \
  long int __lrintres;							      \
  __asm__ __volatile__							      \
    ("fistpl %0"							      \
     : "=m" (__lrintres) : "t" (__x) : "st");				      \
  return __lrintres
__MATH_INLINE long int
__NTH (lrintf (float __x))
{
  __lrint_code;
}
__MATH_INLINE long int
__NTH (lrint (double __x))
{
  __lrint_code;
}
__MATH_INLINE long int
__NTH (lrintl (long double __x))
{
  __lrint_code;
}
# undef __lrint_code

# define __llrint_code \
  long long int __llrintres;						      \
  __asm__ __volatile__							      \
    ("fistpll %0"							      \
     : "=m" (__llrintres) : "t" (__x) : "st");				      \
  return __llrintres
__MATH_INLINE long long int
__NTH (llrintf (float __x))
{
  __llrint_code;
}
__MATH_INLINE long long int
__NTH (llrint (double __x))
{
  __llrint_code;
}
__MATH_INLINE long long int
__NTH (llrintl (long double __x))
{
  __llrint_code;
}
# undef __llrint_code

#endif


#ifdef __USE_MISC

# if defined __FAST_MATH__ && !__GNUC_PREREQ (3, 5)
__inline_mathcodeNP2 (drem, __x, __y, \
  register double __value;						      \
  register int __clobbered;						      \
  __asm __volatile__							      \
    ("1:	fprem1\n\t"						      \
     "fstsw	%%ax\n\t"						      \
     "sahf\n\t"								      \
     "jp	1b"							      \
     : "=t" (__value), "=&a" (__clobbered) : "0" (__x), "u" (__y) : "cc");    \
  return __value)
# endif


/* This function is used in the `isfinite' macro.  */
__MATH_INLINE int
__NTH (__finite (double __x))
{
  return (__extension__
	  (((((union { double __d; int __i[2]; }) {__d: __x}).__i[1]
	     | 0x800fffffu) + 1) >> 31));
}

/* Miscellaneous functions */
# ifdef __FAST_MATH__
__inline_mathcode (__coshm1, __x, \
  register long double __exm1 = __expm1l (__fabsl (__x));		      \
  return 0.5 * (__exm1 / (__exm1 + 1.0)) * __exm1)

__inline_mathcode (__acosh1p, __x, \
  return log1pl (__x + __libc_sqrtl (__x) * __libc_sqrtl (__x + 2.0)))

# endif /* __FAST_MATH__ */
#endif /* __USE_MISC  */

/* Undefine some of the large macros which are not used anymore.  */
#undef __atan2_code
#ifdef __FAST_MATH__
# undef __expm1_code
# undef __exp_code
# undef __sincos_code
#endif /* __FAST_MATH__ */

#endif /* __NO_MATH_INLINES  */


/* This code is used internally in the GNU libc.  */
#ifdef __LIBC_INTERNAL_MATH_INLINES
__inline_mathop (__ieee754_sqrt, "fsqrt")
__inline_mathcode2 (__ieee754_atan2, __y, __x,
		    register long double __value;
		    __asm __volatile__ ("fpatan\n\t"
					: "=t" (__value)
					: "0" (__x), "u" (__y) : "st(1)");
		    return __value;)
#endif

#endif /* __GNUC__  */