math.h

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/*
 * math.h: ANSI 'C' (X3J11 Oct 88) library header, section 4.5
 * Copyright (C) Codemist Ltd., 1988
 * Copyright 1991-1998 ARM Limited. All rights reserved
 */

/*
 * RCS $Revision: 1.34.2.1 $ Codemist 0.03
 * Checkin $Date: 2001/02/22 16:23:35 $
 * Revising $Author: cadeniyi $
 */


#ifndef __math_h
#define __math_h

  #ifndef __MATH_DECLS
  #define __MATH_DECLS

    #undef __CLIBNS

    #ifdef __cplusplus
      #ifdef __EDG_RUNTIME_USES_NAMESPACES
        namespace std {
        #define __CLIBNS std::
      #else
        #define __CLIBNS ::
      #endif /* ifdef __EDG_RUNTIME_USES_NAMESPACES */

      extern "C" {
    #else
      #define __CLIBNS
    #endif  /* __cplusplus */


#ifndef HUGE_VAL
#ifndef __STRICT_ANSI__
#define HUGE_VAL (0d_7FF0000000000000)
#else
extern const double __huge_val;
#define HUGE_VAL (__huge_val)
#endif
#endif

#ifndef __STRICT_ANSI__                /* C99 extensions: */
#define INFINITY (0f_7F800000)         /* positive float infinity */
#define NAN (0f_7FC00001)              /* float quiet NaN */
#endif

extern double acos(double /*x*/);
   /* computes the principal value of the arc cosine of x */
   /* a domain error occurs for arguments not in the range -1 to 1 */
   /* Returns: the arc cosine in the range 0 to Pi. */
extern double asin(double /*x*/);
   /* computes the principal value of the arc sine of x */
   /* a domain error occurs for arguments not in the range -1 to 1 */
   /* and -HUGE_VAL is returned. */
   /* Returns: the arc sine in the range -Pi/2 to Pi/2. */

extern __pure double atan(double /*x*/);
   /* computes the principal value of the arc tangent of x */
   /* Returns: the arc tangent in the range -Pi/2 to Pi/2. */

extern double atan2(double /*y*/, double /*x*/);
   /* computes the principal value of the arc tangent of y/x, using the */
   /* signs of both arguments to determine the quadrant of the return value */
   /* a domain error occurs if both args are zero, and -HUGE_VAL returned. */
   /* Returns: the arc tangent of y/x, in the range -Pi to Pi. */


extern __pure double cos(double /*x*/);
   /* computes the cosine of x (measured in radians). A large magnitude */
   /* argument may yield a result with little or no significance */
   /* Returns: the cosine value. */
extern __pure double sin(double /*x*/);
   /* computes the sine of x (measured in radians). A large magnitude */
   /* argument may yield a result with little or no significance */
   /* Returns: the sine value. */

extern void __use_accurate_range_reduction(void);
   /* reference this to select the larger, slower, but more accurate */
   /* range reduction in sin, cos and tan */

extern double tan(double /*x*/);
   /* computes the tangent of x (measured in radians). A large magnitude */
   /* argument may yield a result with little or no significance */
   /* Returns: the tangent value. */
   /*          if range error; returns HUGE_VAL. */

extern double cosh(double /*x*/);
   /* computes the hyperbolic cosine of x. A range error occurs if the */
   /* magnitude of x is too large. */
   /* Returns: the hyperbolic cosine value. */
   /*          if range error; returns HUGE_VAL. */
extern double sinh(double /*x*/);
   /* computes the hyperbolic sine of x. A range error occurs if the */
   /* magnitude of x is too large. */
   /* Returns: the hyperbolic sine value. */
   /*          if range error; returns -HUGE_VAL or HUGE_VAL depending */
   /*          on the sign of the argument */

extern __pure double tanh(double /*x*/);
   /* computes the hyperbolic tangent of x. */
   /* Returns: the hyperbolic tangent value. */

extern double exp(double /*x*/);
   /* computes the exponential function of x. A range error occurs if the */
   /* magnitude of x is too large. */
   /* Returns: the exponential value. */
   /*          if underflow range error; 0 is returned. */
   /*          if overflow range error; HUGE_VAL is returned. */

extern double frexp(double /*value*/, int * /*exp*/);
   /* breaks a floating-point number into a normalised fraction and an */
   /* integral power of 2. It stores the integer in the int object pointed */
   /* to by exp. */
   /* Returns: the value x, such that x is a double with magnitude in the */
   /* interval 0.5 to 1.0 or zero, and value equals x times 2 raised to the */
   /* power *exp. If value is zero, both parts of the result are zero. */

extern double ldexp(double /*x*/, int /*exp*/);
   /* multiplies a floating-point number by an integral power of 2. */
   /* A range error may occur. */
   /* Returns: the value of x times 2 raised to the power of exp. */
   /*          if range error; HUGE_VAL is returned. */
extern double log(double /*x*/);
   /* computes the natural logarithm of x. A domain error occurs if the */
   /* argument is negative, and -HUGE_VAL is returned. A range error occurs */
   /* if the argument is zero. */
   /* Returns: the natural logarithm. */
   /*          if range error; -HUGE_VAL is returned. */
extern double log10(double /*x*/);
   /* computes the base-ten logarithm of x. A domain error occurs if the */
   /* argument is negative. A range error occurs if the argument is zero. */
   /* Returns: the base-ten logarithm. */
extern double modf(double /*value*/, double * /*iptr*/);
   /* breaks the argument value into integral and fraction parts, each of */
   /* which has the same sign as the argument. It stores the integral part */
   /* as a double in the object pointed to by iptr. */
   /* Returns: the signed fractional part of value. */

extern double pow(double /*x*/, double /*y*/);
   /* computes x raised to the power of y. A domain error occurs if x is */
   /* zero and y is less than or equal to zero, or if x is negative and y */
   /* is not an integer, and -HUGE_VAL returned. A range error may occur. */
   /* Returns: the value of x raised to the power of y. */
   /*          if underflow range error; 0 is returned. */
   /*          if overflow range error; HUGE_VAL is returned. */
extern double sqrt(double /*x*/);
   /* computes the non-negative square root of x. A domain error occurs */
   /* if the argument is negative, and -HUGE_VAL returned. */
   /* Returns: the value of the square root. */
#ifdef __TARGET_FPU_VFP
    extern double _sqrt(double);    /* native VFP double precision sqrt */
    extern float _sqrtf(float);     /* native VFP single precision sqrt */
#else
    __inline double _sqrt(double __x) { return sqrt(__x); }
    __inline float _sqrtf(float __x) { return (float)sqrt(__x); }
#endif

extern __pure double ceil(double /*x*/);
   /* computes the smallest integer not less than x. */
   /* Returns: the smallest integer not less than x, expressed as a double. */
extern __pure double fabs(double /*x*/);
   /* computes the absolute value of the floating-point number x. */
   /* Returns: the absolute value of x. */

extern float (_fabsf)(float);
#ifndef __STRICT_ANSI__
   #define fabsf (_fabsf) /* C99 */
#endif

extern __pure double floor(double /*d*/);
   /* computes the largest integer not greater than x. */
   /* Returns: the largest integer not greater than x, expressed as a double */

extern double fmod(double /*x*/, double /*y*/);
   /* computes the floating-point remainder of x/y. */
   /* Returns: the value x - i * y, for some integer i such that, if y is */
   /*          nonzero, the result has the same sign as x and magnitude */
   /*          less than the magnitude of y. If y is zero, a domain error */
   /*          occurs and -HUGE_VAL is returned. */

    /* Additional Mathlib functions not defined by the ANSI standard.
     * Not guaranteed, and not necessarily very well tested.
     * C99 requires the user to include <math.h> to use these functions
     * declaring them "by hand" is not sufficient
     */
#ifndef __STRICT_ANSI__

#if defined __thumb || defined __TARGET_FPU_SOFTVFP || defined __TARGET_FPU_SOFTVFP_VFP || \
                       defined __TARGET_FPU_SOFTFPA || defined __TARGET_FPU_SOFTFPA_FPA
#define _FPMANGLE(name) __softfp_ ## name
#else
#define _FPMANGLE(name) __hardfp_ ## name
#endif

extern double _FPMANGLE(acosh) (double /*x*/);
__inline double acosh(double __x) { return _FPMANGLE(acosh)(__x); }
    /*
     * Inverse cosh. EDOM if argument < 1.0
     */
extern double _FPMANGLE(asinh) (double /*x*/);
__inline double asinh(double __x) { return _FPMANGLE(asinh)(__x); }
    /*
     * Inverse sinh.
     */
extern double _FPMANGLE(atanh) (double /*x*/);
__inline double atanh(double __x) { return _FPMANGLE(atanh)(__x); }
    /*
     * Inverse tanh. EDOM if |argument| > 1.0
     */
extern double _FPMANGLE(cbrt) (double /*x*/);
__inline double cbrt(double __x) { return _FPMANGLE(cbrt)(__x); }
    /*
     * Cube root.
     */
extern double _FPMANGLE(copysign) (double /*x*/, double /*y*/);
__inline double copysign(double __x, double __y) { return _FPMANGLE(copysign)(__x,__y); }
    /*
     * Returns x with sign bit replaced by sign of y.
     */
extern double _FPMANGLE(erf) (double /*x*/);
__inline double erf(double __x) { return _FPMANGLE(erf)(__x); }
    /*
     * Error function. (2/sqrt(pi)) * integral from 0 to x of exp(-t*t) dt.
     */
extern double _FPMANGLE(erfc) (double /*x*/);
__inline double erfc(double __x) { return _FPMANGLE(erfc)(__x); }
    /*
     * 1-erf(x). (More accurate than just coding 1-erf(x), for large x.)
     */
extern double _FPMANGLE(expm1) (double /*x*/);
__inline double expm1(double __x) { return _FPMANGLE(expm1)(__x); }
    /*
     * exp(x)-1. (More accurate than just coding exp(x)-1, for small x.)
     */
extern int _FPMANGLE(finite) (double /*x*/);
__inline double finite(double __x) { return _FPMANGLE(finite)(__x); }
    /*
     * TRUE if argument is finite (ie not infinity or NaN).
     */
extern double _FPMANGLE(gamma) (double /*x*/);
__inline double gamma(double __x) { return _FPMANGLE(gamma)(__x); }
    /*
     * The log of the absolute value of the gamma function of x. The sign
     * of the gamma function of x is returned in the global `signgam'.
     */
extern double _FPMANGLE(gamma_r) (double /*x*/, int * /*signgam*/);
__inline double gamma_r(double __x, int *__p) { return _FPMANGLE(gamma_r)(__x,__p); }
    /*
     * The log of the absolute value of the gamma function of x. The sign
     * of the gamma function of x is returned in the second argument.
     */
extern double _FPMANGLE(hypot) (double /*x*/, double /*y*/);
__inline double hypot(double __x, double __y) { return _FPMANGLE(hypot)(__x,__y); }
    /*
     * sqrt(x*x+y*y), ie the length of the vector (x,y) or the
     * hypotenuse of a right triangle whose other two sides are x
     * and y. Won't overflow unless the _answer_ is too big, even
     * if the intermediate x*x+y*y is too big.
     */
extern int _FPMANGLE(ilogb) (double /*x*/);
__inline int ilogb(double __x) { return _FPMANGLE(ilogb)(__x); }
    /*
     * Exponent of x (returns 0 for 1.0, 1 for 2.0, -1 for 0.5, etc.)
     */
extern int _FPMANGLE(isnan) (double /*x*/);
__inline double isnan(double __x) { return _FPMANGLE(isnan)(__x); }
    /*
     * Returns TRUE if x is a NaN.
     */
extern double _FPMANGLE(j0) (double /*x*/);
__inline double j0(double __x) { return _FPMANGLE(j0)(__x); }
    /*
     * Bessel function of the first kind, order 0. Returns ERANGE
     * if |x| > 2^52 (total loss of significance).
     */
extern double _FPMANGLE(j1) (double /*x*/);