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612 lines
19 KiB
612 lines
19 KiB
#ifndef _MATH_H_ |
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#define _MATH_H_ |
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//#include <sys/reent.h> |
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#include <machine/ieeefp.h> |
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#include "_ansi.h" |
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//#define _PARAMS(_x) _x |
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_BEGIN_STD_C |
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#if 0 |
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/* __dmath, __fmath, and __ldmath are only here for backwards compatibility |
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* in case any code used them. They are no longer used by Newlib, itself, |
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* other than legacy. */ |
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union __dmath |
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{ |
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double d; |
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__ULong i[2]; |
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}; |
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union __fmath |
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{ |
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float f; |
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__ULong i[1]; |
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}; |
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#if defined(_HAVE_LONG_DOUBLE) |
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union __ldmath |
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{ |
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long double ld; |
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__ULong i[4]; |
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}; |
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#endif |
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#endif |
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/* Natural log of 2 */ |
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#define _M_LN2 0.693147180559945309417 |
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#if defined(__GNUC__) && \ |
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( (__GNUC__ >= 4) || \ |
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( (__GNUC__ >= 3) && defined(__GNUC_MINOR__) && (__GNUC_MINOR__ >= 3) ) ) |
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/* gcc >= 3.3 implicitly defines builtins for HUGE_VALx values. */ |
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# ifndef HUGE_VAL |
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# define HUGE_VAL (__builtin_huge_val()) |
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# endif |
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# ifndef HUGE_VALF |
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# define HUGE_VALF (__builtin_huge_valf()) |
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# endif |
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# ifndef HUGE_VALL |
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# define HUGE_VALL (__builtin_huge_vall()) |
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# endif |
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# ifndef INFINITY |
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# define INFINITY (__builtin_inff()) |
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# endif |
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# ifndef NAN |
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# define NAN (__builtin_nanf("")) |
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# endif |
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#else /* !gcc >= 3.3 */ |
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/* No builtins. Use fixed defines instead. (All 3 HUGE plus the INFINITY |
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* and NAN macros are required to be constant expressions. Using a variable-- |
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* even a static const--does not meet this requirement, as it cannot be |
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* evaluated at translation time.) |
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* The infinities are done using numbers that are far in excess of |
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* something that would be expected to be encountered in a floating-point |
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* implementation. (A more certain way uses values from float.h, but that is |
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* avoided because system includes are not supposed to include each other.) |
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* This method might produce warnings from some compilers. (It does in |
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* newer GCCs, but not for ones that would hit this #else.) If this happens, |
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* please report details to the Newlib mailing list. */ |
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#ifndef HUGE_VAL |
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#define HUGE_VAL (1.0e999999999) |
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#endif |
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#ifndef HUGE_VALF |
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#define HUGE_VALF (1.0e999999999F) |
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#endif |
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#if !defined(HUGE_VALL) && defined(_HAVE_LONG_DOUBLE) |
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#define HUGE_VALL (1.0e999999999L) |
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#endif |
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#if !defined(INFINITY) |
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#define INFINITY (HUGE_VALF) |
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#endif |
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#if !defined(NAN) |
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#if defined(__GNUC__) && defined(__cplusplus) |
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/* Exception: older g++ versions warn about the divide by 0 used in the |
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* normal case (even though older gccs do not). This trick suppresses the |
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* warning, but causes errors for plain gcc, so is only used in the one |
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* special case. */ |
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static const union { __ULong __i[1]; float __d; } __Nanf = {0x7FC00000}; |
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#define NAN (__Nanf.__d) |
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#else |
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#define NAN (0.0F/0.0F) |
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#endif |
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#endif |
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#endif /* !gcc >= 3.3 */ |
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/* Reentrant ANSI C functions. */ |
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#ifndef __math_68881 |
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extern double atan _PARAMS((double)); |
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extern double cos _PARAMS((double)); |
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extern double sin _PARAMS((double)); |
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extern double tan _PARAMS((double)); |
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extern double tanh _PARAMS((double)); |
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extern double frexp _PARAMS((double, int *)); |
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extern double modf _PARAMS((double, double *)); |
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extern double ceil _PARAMS((double)); |
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extern double fabs _PARAMS((double)); |
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extern double floor _PARAMS((double)); |
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#endif /* ! defined (__math_68881) */ |
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/* Non reentrant ANSI C functions. */ |
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#ifndef _REENT_ONLY |
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#ifndef __math_68881 |
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extern double acos _PARAMS((double)); |
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extern double asin _PARAMS((double)); |
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extern double atan2 _PARAMS((double, double)); |
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extern double cosh _PARAMS((double)); |
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extern double sinh _PARAMS((double)); |
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extern double exp _PARAMS((double)); |
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extern double ldexp _PARAMS((double, int)); |
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extern double log _PARAMS((double)); |
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extern double log10 _PARAMS((double)); |
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extern double pow _PARAMS((double, double)); |
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extern double sqrt _PARAMS((double)); |
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extern double fmod _PARAMS((double, double)); |
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#endif /* ! defined (__math_68881) */ |
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#endif /* ! defined (_REENT_ONLY) */ |
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#if !defined(__STRICT_ANSI__) || defined(__cplusplus) || __STDC_VERSION__ >= 199901L |
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/* ISO C99 types and macros. */ |
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#ifndef FLT_EVAL_METHOD |
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#define FLT_EVAL_METHOD 0 |
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typedef float float_t; |
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typedef double double_t; |
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#endif /* FLT_EVAL_METHOD */ |
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#define FP_NAN 0 |
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#define FP_INFINITE 1 |
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#define FP_ZERO 2 |
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#define FP_SUBNORMAL 3 |
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#define FP_NORMAL 4 |
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#ifndef FP_ILOGB0 |
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# define FP_ILOGB0 (-INT_MAX) |
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#endif |
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#ifndef FP_ILOGBNAN |
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# define FP_ILOGBNAN INT_MAX |
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#endif |
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#ifndef MATH_ERRNO |
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# define MATH_ERRNO 1 |
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#endif |
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#ifndef MATH_ERREXCEPT |
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# define MATH_ERREXCEPT 2 |
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#endif |
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#ifndef math_errhandling |
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# define math_errhandling MATH_ERRNO |
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#endif |
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extern int __isinff (float x); |
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extern int __isinfd (double x); |
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extern int __isnanf (float x); |
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extern int __isnand (double x); |
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extern int __fpclassifyf (float x); |
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extern int __fpclassifyd (double x); |
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extern int __signbitf (float x); |
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extern int __signbitd (double x); |
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#define fpclassify(__x) \ |
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((sizeof(__x) == sizeof(float)) ? __fpclassifyf(__x) : \ |
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__fpclassifyd(__x)) |
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#ifndef isfinite |
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#define isfinite(__y) \ |
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(__extension__ ({int __cy = fpclassify(__y); \ |
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__cy != FP_INFINITE && __cy != FP_NAN;})) |
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#endif |
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/* Note: isinf and isnan were once functions in newlib that took double |
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* arguments. C99 specifies that these names are reserved for macros |
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* supporting multiple floating point types. Thus, they are |
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* now defined as macros. Implementations of the old functions |
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* taking double arguments still exist for compatibility purposes |
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* (prototypes for them are in <ieeefp.h>). */ |
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#ifndef isinf |
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#define isinf(y) (fpclassify(y) == FP_INFINITE) |
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#endif |
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#ifndef isnan |
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#define isnan(y) (fpclassify(y) == FP_NAN) |
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#endif |
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#define isnormal(y) (fpclassify(y) == FP_NORMAL) |
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#define signbit(__x) \ |
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((sizeof(__x) == sizeof(float)) ? __signbitf(__x) : \ |
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__signbitd(__x)) |
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#define isgreater(x,y) \ |
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(__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \ |
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!isunordered(__x,__y) && (__x > __y);})) |
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#define isgreaterequal(x,y) \ |
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(__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \ |
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!isunordered(__x,__y) && (__x >= __y);})) |
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#define isless(x,y) \ |
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(__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \ |
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!isunordered(__x,__y) && (__x < __y);})) |
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#define islessequal(x,y) \ |
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(__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \ |
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!isunordered(__x,__y) && (__x <= __y);})) |
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#define islessgreater(x,y) \ |
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(__extension__ ({__typeof__(x) __x = (x); __typeof__(y) __y = (y); \ |
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!isunordered(__x,__y) && (__x < __y || __x > __y);})) |
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#define isunordered(a,b) \ |
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(__extension__ ({__typeof__(a) __a = (a); __typeof__(b) __b = (b); \ |
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fpclassify(__a) == FP_NAN || fpclassify(__b) == FP_NAN;})) |
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/* Non ANSI double precision functions. */ |
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extern double infinity _PARAMS((void)); |
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extern double nan _PARAMS((const char *)); |
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extern int finite _PARAMS((double)); |
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extern double copysign _PARAMS((double, double)); |
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extern double logb _PARAMS((double)); |
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extern int ilogb _PARAMS((double)); |
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extern double asinh _PARAMS((double)); |
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extern double cbrt _PARAMS((double)); |
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extern double nextafter _PARAMS((double, double)); |
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extern double rint _PARAMS((double)); |
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extern double scalbn _PARAMS((double, int)); |
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extern double exp2 _PARAMS((double)); |
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extern double scalbln _PARAMS((double, long int)); |
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extern double tgamma _PARAMS((double)); |
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extern double nearbyint _PARAMS((double)); |
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extern long int lrint _PARAMS((double)); |
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extern _LONG_LONG_TYPE int llrint _PARAMS((double)); |
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extern double round _PARAMS((double)); |
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extern long int lround _PARAMS((double)); |
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extern long long int llround _PARAMS((double)); |
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extern double trunc _PARAMS((double)); |
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extern double remquo _PARAMS((double, double, int *)); |
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extern double fdim _PARAMS((double, double)); |
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extern double fmax _PARAMS((double, double)); |
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extern double fmin _PARAMS((double, double)); |
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extern double fma _PARAMS((double, double, double)); |
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#ifndef __math_68881 |
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extern double log1p _PARAMS((double)); |
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extern double expm1 _PARAMS((double)); |
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#endif /* ! defined (__math_68881) */ |
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#ifndef _REENT_ONLY |
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extern double acosh _PARAMS((double)); |
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extern double atanh _PARAMS((double)); |
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extern double remainder _PARAMS((double, double)); |
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extern double gamma _PARAMS((double)); |
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extern double lgamma _PARAMS((double)); |
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extern double erf _PARAMS((double)); |
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extern double erfc _PARAMS((double)); |
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extern double log2 _PARAMS((double)); |
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#if !defined(__cplusplus) |
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#define log2(x) (log (x) / _M_LN2) |
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#endif |
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#ifndef __math_68881 |
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extern double hypot _PARAMS((double, double)); |
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#endif |
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#endif /* ! defined (_REENT_ONLY) */ |
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/* Single precision versions of ANSI functions. */ |
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extern float atanf _PARAMS((float)); |
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extern float cosf _PARAMS((float)); |
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extern float sinf _PARAMS((float)); |
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extern float tanf _PARAMS((float)); |
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extern float tanhf _PARAMS((float)); |
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extern float frexpf _PARAMS((float, int *)); |
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extern float modff _PARAMS((float, float *)); |
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extern float ceilf _PARAMS((float)); |
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extern float fabsf _PARAMS((float)); |
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extern float floorf _PARAMS((float)); |
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#ifndef _REENT_ONLY |
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extern float acosf _PARAMS((float)); |
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extern float asinf _PARAMS((float)); |
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extern float atan2f _PARAMS((float, float)); |
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extern float coshf _PARAMS((float)); |
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extern float sinhf _PARAMS((float)); |
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extern float expf _PARAMS((float)); |
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extern float ldexpf _PARAMS((float, int)); |
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extern float logf _PARAMS((float)); |
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extern float log10f _PARAMS((float)); |
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extern float powf _PARAMS((float, float)); |
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extern float sqrtf _PARAMS((float)); |
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extern float fmodf _PARAMS((float, float)); |
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#endif /* ! defined (_REENT_ONLY) */ |
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/* Other single precision functions. */ |
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extern float exp2f _PARAMS((float)); |
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extern float scalblnf _PARAMS((float, long int)); |
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extern float tgammaf _PARAMS((float)); |
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extern float nearbyintf _PARAMS((float)); |
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extern long int lrintf _PARAMS((float)); |
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extern _LONG_LONG_TYPE llrintf _PARAMS((float)); |
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extern float roundf _PARAMS((float)); |
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extern long int lroundf _PARAMS((float)); |
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extern long long int llroundf _PARAMS((float)); |
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extern float truncf _PARAMS((float)); |
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extern float remquof _PARAMS((float, float, int *)); |
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extern float fdimf _PARAMS((float, float)); |
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extern float fmaxf _PARAMS((float, float)); |
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extern float fminf _PARAMS((float, float)); |
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extern float fmaf _PARAMS((float, float, float)); |
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extern float infinityf _PARAMS((void)); |
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extern float nanf _PARAMS((const char *)); |
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extern int finitef _PARAMS((float)); |
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extern float copysignf _PARAMS((float, float)); |
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extern float logbf _PARAMS((float)); |
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extern int ilogbf _PARAMS((float)); |
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extern float asinhf _PARAMS((float)); |
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extern float cbrtf _PARAMS((float)); |
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extern float nextafterf _PARAMS((float, float)); |
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extern float rintf _PARAMS((float)); |
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extern float scalbnf _PARAMS((float, int)); |
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extern float log1pf _PARAMS((float)); |
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extern float expm1f _PARAMS((float)); |
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#ifndef _REENT_ONLY |
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extern float acoshf _PARAMS((float)); |
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extern float atanhf _PARAMS((float)); |
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extern float remainderf _PARAMS((float, float)); |
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extern float gammaf _PARAMS((float)); |
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extern float lgammaf _PARAMS((float)); |
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extern float erff _PARAMS((float)); |
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extern float erfcf _PARAMS((float)); |
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extern float log2f _PARAMS((float)); |
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#if !defined(__cplusplus) |
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#define log2f(x) (logf (x) / (float_t) _M_LN2) |
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#endif |
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extern float hypotf _PARAMS((float, float)); |
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#endif /* ! defined (_REENT_ONLY) */ |
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/* On platforms where long double equals double. */ |
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#ifdef _LDBL_EQ_DBL |
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/* Reentrant ANSI C functions. */ |
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#ifndef __math_68881 |
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extern long double atanl _PARAMS((long double)); |
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extern long double cosl _PARAMS((long double)); |
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extern long double sinl _PARAMS((long double)); |
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extern long double tanl _PARAMS((long double)); |
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extern long double tanhl _PARAMS((long double)); |
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extern long double frexpl _PARAMS((long double value, int *)); |
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extern long double modfl _PARAMS((long double, long double *)); |
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extern long double ceill _PARAMS((long double)); |
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extern long double fabsl _PARAMS((long double)); |
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extern long double floorl _PARAMS((long double)); |
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extern long double log1pl _PARAMS((long double)); |
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extern long double expm1l _PARAMS((long double)); |
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#endif /* ! defined (__math_68881) */ |
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/* Non reentrant ANSI C functions. */ |
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#ifndef _REENT_ONLY |
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#ifndef __math_68881 |
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extern long double acosl _PARAMS((long double)); |
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extern long double asinl _PARAMS((long double)); |
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extern long double atan2l _PARAMS((long double, long double)); |
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extern long double coshl _PARAMS((long double)); |
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extern long double sinhl _PARAMS((long double)); |
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extern long double expl _PARAMS((long double)); |
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extern long double ldexpl _PARAMS((long double, int)); |
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extern long double logl _PARAMS((long double)); |
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extern long double log10l _PARAMS((long double)); |
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extern long double powl _PARAMS((long double, long double)); |
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extern long double sqrtl _PARAMS((long double)); |
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extern long double fmodl _PARAMS((long double, long double)); |
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extern long double hypotl _PARAMS((long double, long double)); |
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#endif /* ! defined (__math_68881) */ |
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#endif /* ! defined (_REENT_ONLY) */ |
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extern long double copysignl _PARAMS((long double, long double)); |
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extern long double nanl _PARAMS((const char *)); |
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extern int ilogbl _PARAMS((long double)); |
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extern long double asinhl _PARAMS((long double)); |
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extern long double cbrtl _PARAMS((long double)); |
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extern long double nextafterl _PARAMS((long double, long double)); |
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extern long double rintl _PARAMS((long double)); |
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extern long double scalbnl _PARAMS((long double, int)); |
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extern long double exp2l _PARAMS((long double)); |
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extern long double scalblnl _PARAMS((long double, long)); |
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extern long double tgammal _PARAMS((long double)); |
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extern long double nearbyintl _PARAMS((long double)); |
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extern long int lrintl _PARAMS((long double)); |
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extern long long int llrintl _PARAMS((long double)); |
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extern long double roundl _PARAMS((long double)); |
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extern long lroundl _PARAMS((long double)); |
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extern _LONG_LONG_TYPE int llroundl _PARAMS((long double)); |
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extern long double truncl _PARAMS((long double)); |
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extern long double remquol _PARAMS((long double, long double, int *)); |
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extern long double fdiml _PARAMS((long double, long double)); |
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extern long double fmaxl _PARAMS((long double, long double)); |
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extern long double fminl _PARAMS((long double, long double)); |
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extern long double fmal _PARAMS((long double, long double, long double)); |
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#ifndef _REENT_ONLY |
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extern long double acoshl _PARAMS((long double)); |
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extern long double atanhl _PARAMS((long double)); |
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extern long double remainderl _PARAMS((long double, long double)); |
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extern long double lgammal _PARAMS((long double)); |
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extern long double erfl _PARAMS((long double)); |
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extern long double erfcl _PARAMS((long double)); |
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#endif /* ! defined (_REENT_ONLY) */ |
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#else /* !_LDBL_EQ_DBL */ |
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#ifdef __i386__ |
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/* Other long double precision functions. */ |
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extern _LONG_DOUBLE rintl _PARAMS((_LONG_DOUBLE)); |
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extern long int lrintl _PARAMS((_LONG_DOUBLE)); |
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extern _LONG_LONG_TYPE llrintl _PARAMS((_LONG_DOUBLE)); |
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#endif /* __i386__ */ |
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#endif /* !_LDBL_EQ_DBL */ |
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#endif /* !defined (__STRICT_ANSI__) || defined(__cplusplus) || __STDC_VERSION__ >= 199901L */ |
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#if !defined (__STRICT_ANSI__) || defined(__cplusplus) |
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extern double drem _PARAMS((double, double)); |
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extern void sincos _PARAMS((double, double *, double *)); |
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extern double gamma_r _PARAMS((double, int *)); |
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extern double lgamma_r _PARAMS((double, int *)); |
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extern double y0 _PARAMS((double)); |
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extern double y1 _PARAMS((double)); |
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extern double yn _PARAMS((int, double)); |
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extern double j0 _PARAMS((double)); |
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extern double j1 _PARAMS((double)); |
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extern double jn _PARAMS((int, double)); |
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extern float dremf _PARAMS((float, float)); |
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extern void sincosf _PARAMS((float, float *, float *)); |
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extern float gammaf_r _PARAMS((float, int *)); |
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extern float lgammaf_r _PARAMS((float, int *)); |
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extern float y0f _PARAMS((float)); |
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extern float y1f _PARAMS((float)); |
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extern float ynf _PARAMS((int, float)); |
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extern float j0f _PARAMS((float)); |
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extern float j1f _PARAMS((float)); |
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extern float jnf _PARAMS((int, float)); |
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/* GNU extensions */ |
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# ifndef exp10 |
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extern double exp10 _PARAMS((double)); |
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# endif |
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# ifndef pow10 |
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extern double pow10 _PARAMS((double)); |
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# endif |
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# ifndef exp10f |
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extern float exp10f _PARAMS((float)); |
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# endif |
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# ifndef pow10f |
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extern float pow10f _PARAMS((float)); |
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# endif |
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#endif /* !defined (__STRICT_ANSI__) || defined(__cplusplus) */ |
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#ifndef __STRICT_ANSI__ |
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/* The gamma functions use a global variable, signgam. */ |
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#ifndef _REENT_ONLY |
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#define signgam (*__signgam()) |
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extern int *__signgam _PARAMS((void)); |
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#endif /* ! defined (_REENT_ONLY) */ |
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#define __signgam_r(ptr) _REENT_SIGNGAM(ptr) |
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/* The exception structure passed to the matherr routine. */ |
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/* We have a problem when using C++ since `exception' is a reserved |
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name in C++. */ |
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#ifdef __cplusplus |
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struct __exception |
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#else |
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struct exception |
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#endif |
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{ |
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int type; |
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char *name; |
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double arg1; |
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double arg2; |
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double retval; |
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int err; |
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}; |
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#ifdef __cplusplus |
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extern int matherr _PARAMS((struct __exception *e)); |
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#else |
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extern int matherr _PARAMS((struct exception *e)); |
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#endif |
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/* Values for the type field of struct exception. */ |
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#define DOMAIN 1 |
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#define SING 2 |
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#define OVERFLOW 3 |
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#define UNDERFLOW 4 |
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#define TLOSS 5 |
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#define PLOSS 6 |
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/* Useful constants. */ |
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#define MAXFLOAT 3.40282347e+38F |
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#define M_E 2.7182818284590452354 |
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#define M_LOG2E 1.4426950408889634074 |
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#define M_LOG10E 0.43429448190325182765 |
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#define M_LN2 _M_LN2 |
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#define M_LN10 2.30258509299404568402 |
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#define M_PI 3.14159265358979323846 |
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#define M_TWOPI (M_PI * 2.0) |
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#define M_PI_2 1.57079632679489661923 |
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#define M_PI_4 0.78539816339744830962 |
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#define M_3PI_4 2.3561944901923448370E0 |
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#define M_SQRTPI 1.77245385090551602792981 |
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#define M_1_PI 0.31830988618379067154 |
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#define M_2_PI 0.63661977236758134308 |
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#define M_2_SQRTPI 1.12837916709551257390 |
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#define M_DEG_TO_RAD 0.01745329251994 |
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#define M_RAD_TO_DEG 57.2957795130823 |
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#define M_SQRT2 1.41421356237309504880 |
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#define M_SQRT1_2 0.70710678118654752440 |
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#define M_LN2LO 1.9082149292705877000E-10 |
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#define M_LN2HI 6.9314718036912381649E-1 |
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#define M_SQRT3 1.73205080756887719000 |
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#define M_IVLN10 0.43429448190325182765 /* 1 / log(10) */ |
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#define M_LOG2_E _M_LN2 |
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#define M_INVLN2 1.4426950408889633870E0 /* 1 / log(2) */ |
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#define M_E_F 2.7182818284590452354f |
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#define M_LOG2E_F 1.4426950408889634074f |
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#define M_LOG10E_F 0.43429448190325182765f |
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#define M_LN2_F _M_LN2_F |
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#define M_LN10_F 2.30258509299404568402f |
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#define M_PI_F 3.14159265358979323846f |
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#define M_TWOPI_F (M_PI_F * 2.0f) |
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#define M_PI_2_F 1.57079632679489661923f |
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#define M_PI_4_F 0.78539816339744830962f |
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#define M_3PI_4_F 2.3561944901923448370E0f |
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#define M_SQRTPI_F 1.77245385090551602792981f |
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#define M_1_PI_F 0.31830988618379067154f |
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#define M_2_PI_F 0.63661977236758134308f |
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#define M_2_SQRTPI_F 1.12837916709551257390f |
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#define M_DEG_TO_RAD_F 0.01745329251994f |
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#define M_RAD_TO_DEG_F 57.2957795130823f |
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#define M_SQRT2_F 1.41421356237309504880f |
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#define M_SQRT1_2_F 0.70710678118654752440f |
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#define M_LN2LO_F 1.9082149292705877000E-10f |
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#define M_LN2HI_F 6.9314718036912381649E-1f |
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#define M_SQRT3_F 1.73205080756887719000f |
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#define M_IVLN10_F 0.43429448190325182765f /* 1 / log(10) */ |
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#define M_LOG2_E_F _M_LN2_F |
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#define M_INVLN2_F 1.4426950408889633870E0f /* 1 / log(2) */ |
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/* Global control over fdlibm error handling. */ |
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enum __fdlibm_version |
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{ |
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__fdlibm_ieee = -1, |
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__fdlibm_svid, |
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__fdlibm_xopen, |
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__fdlibm_posix |
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}; |
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#define _LIB_VERSION_TYPE enum __fdlibm_version |
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#define _LIB_VERSION __fdlib_version |
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extern __IMPORT _LIB_VERSION_TYPE _LIB_VERSION; |
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#define _IEEE_ __fdlibm_ieee |
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#define _SVID_ __fdlibm_svid |
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#define _XOPEN_ __fdlibm_xopen |
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#define _POSIX_ __fdlibm_posix |
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#endif /* ! defined (__STRICT_ANSI__) */ |
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_END_STD_C |
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#ifdef __FAST_MATH__ |
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#include <machine/fastmath.h> |
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#endif |
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#endif /* _MATH_H_ */
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