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/* Copyright (C) 1993 by Zardoz Software, Inc. */
/*******************************************************************************
* FILE NAME: MATH.h
*
* TITLE: This function prototypes and data type definitions for the Math Functions.
*
* DATA_RIGHTS: Western Design Center and R & C Services Proprietary
* Copyright(C) 1980-2004
* All rights reserved. Reproduction in any manner,
* in whole or in part, is strictly prohibited without
* the prior written approval of R & C Services or
* Western Design Center.
*
* DESCRIPTION: This file describes function prototypes and data type
* definitions used for General purpose Math functions.
*
* Double precison floating point format:
*
* 6 6 5 5 0
* 3 2 2 1 0
* ___________________________
* |s|exponent| fraction |
* +-+--------+--------------+
*
*
* Single/Float precison floating point format:
*
* 3 3 2 2 0
* 1 0 X X 0
* ___________________________
* |s|exponent| fraction |
* +-+--------+--------------+
*
*
* Long Double precison floating point format:
*
* 1 1 1
* 2 2 X X 0
* 7 6 X X 0
* ___________________________
* |s|exponent| fraction |
* +-+--------+--------------+
*
*
*
*
* SPECIAL CONSIDERATIONS:
* <None>
*
* AUTHOR: R. Greenthal
*
*
* CREATION DATE: November 17,2003
*
* REVISION HISTORY
* Name Date Description
* ------------ ---------- ----------------------------------------------
* Jim Goodnow 1993 Initial
* R. Greenthal 11/17/2003 Added Single Precision Math Functions
* And templates for "long double" - 128 bit Math
*
* 01/21/2004 Added cadd, asinh, rad2deg, etc.
* 01/29/2004 Added constants
* 02/05/2004 Added more Gamma, FFT, & Bessel Functions
* 02/18/2004 Added Integra...
* 03/08/2004 Added Transcendental with built in Rad/Deg/Grad
* 0x/xx/2004 Added
*
*******************************************************************************
*/
#ifndef _MATH_H
#define _MATH_H
#include <sys/types.h>
/*
*=========================== CONSTANTS & MACROS ===============================
*/
#ifndef _FLOAT_T
#define _FLOAT_T
typedef float float_t;
#endif
#ifndef _DOUBLE_T
#define _DOUBLE_T
typedef double double_t;
#endif
#define FP_INFINITE 2
#define FP_NAN 3
#define FP_NORMAL 1
#define FP_SUBNORMAL 1
#define FP_ZERO 4
#define FP_FAST_FMA
#define FP_FAST_FMAF FP_FAST_FMA
#define FP_FAST_FMAL FP_FAST_FMA
#define FP_ILOGB0 -INT_MAX
#define FP_ILOGBNAN INT_MAX
#define fpclassify(x) _fpclassify(x)
#define isfinite(x) _isfinite(x)
#define isinf(x) _isinf(x)
#define isnan(x) _isnan(x)
#define isnormal(x) _isfinite(x)
#define signbit(x) _signbit(x)
#define NAN nan("255")
#define SIGDIGLEN 36 // significant decimal digits
#define DECSTROUTLEN 80 // max length for dec2str output
#define FLOATDECIMAL ((char)(0))
#define FIXEDDECIMAL ((char)(1))
/***********************************
Limiting Constants Used by
Double Precision Functions
************************************/
#define HUGE_VAL 1.797693134862316E+308
#define LOGHUGE (709.778)
#define TINY_VAL (2.2e-308)
#define LOGTINY (-708.396)
// We are currently EQUATING long double & double
//#define LONG_DOUBLE_SIZE 16 // 128 Bits/16 Bytes
#define LONG_DOUBLE_SIZE 8 // 64 Bits/8 Bytes
#define DOUBLE_SIZE 8 // 64 Bits/8 Bytes
//#define HUGE_VAL __inf()
#define INFINITY __inf()
//#define HUGE_VAL INFINITY
#define HUGE_VALF HUGE_VAL
#define HUGE_VALL HUGE_VAL
/***********************************
General Math Constants Used by
Double Precision Functions
(20 places to the Right of
the Decimal point)
************************************/
#define PI 3.14159265358979323846
#define PIOVR2 1.57079632679489661923 // PI/2
#define M_1_PI 0.318309886183790671538 // 1/PI
#define PI2 6.28318530717958647692 // 2*PI
#define SIN45 0.70710678118654752440 // SIN(45 degrees)
#define SQRT2 1.41421356237309504880 // SQRT(2)
#define LN2 0.69314718055994530942 // Ln 2 constant
#define EULER 0.577215664901532860607 // Euler number
#define LN10 2.30258509299404568402 // ln(10)
#define SQRTPI 1.77245385090551602730 // sqrt(PI)
#define LOG10E 0.43429448190325182765 // Log(e)
//#define 180_PI 57.2957795130823208768 // One Radian in degrees = 180/PI
//#define
//#define M_3PI_4 2.35619449019234492884698253745962716
//#define M_3PI_8 1.17809724509617246442349126872981358
//#define M_PI_4 0.78539816339744830961566084581987572
//#define M_PI_8 0.39269908169872415480783042290993786
//#define M_1_PI 0.31830988618379067153776752674502872
//#define M_2_PI 0.63661977236758134307553505349005744
//#define M_4_PI 1.27323954473516268615107010698011488
#define M_E 2.71828182845904523536028747135266250 //constant "e"
//#define M_1_SQRT2 0.70710678118654752440084436210484904
#define LOGPI 1.14472988584940017414
/***********************************
Limiting Constants Used by
Single Precision Functions
************************************/
#define FLT_HUGE_VAL 1.797693135E+308f
#define FLT_LOGHUGE 709.778f
#define FLT_TINY_VAL 2.2e-308f
#define FLT_LOGTINY -708.396f
/***********************************
General Math Constants Used by
Double Precision Functions
(xx places to the Right of
the Decimal point)
************************************/
#define F_PI 3.141592653f
#define F_PIOVR2 1.570796327f // PI/2
#define F_PI2 6.283185307f // 2*PI
#define F_SIN45 0.707106781f // SIN()
#define F_SQRT2 1.414213562f // SQRT(2)
#define F_LN2 0.693147181f // Ln 2 constant
#define F_LN10 2.302585092f // ln(10)
#define F_LOG10E 0.434294481f // Log(e)
/***********************************
Limiting Constants Used by
Long Double Precision Functions
************************************/
#define LDBL_HUGE_VAL 1.797693134862316E+308L
#define LDBL_LOGHUGE 709.778L
#define LDBL_TINY_VAL 2.2e-308L
#define LDBL_LOGTINY -708.396L
/***********************************
General Math Constants Used by
Long Double Precision Functions
(xx places to the Right of
the Decimal point)
************************************/
#define LDBL_PI 3.14159265358979323846L
#define LDBL_PI2 6.28318530717958647692L // 2*PI
#define LDBL_PIOVR2 1.57079632679489661923L // PI/2
#define LDBL_SIN45 0.70710678118654752440L // SIN()
#define LDBL_SQRT2 1.41421356237309504880L // SQRT(2)
#define LDBL_LN2 0.69314718055994530942L // Ln 2 constant
#define LDBL_LN10 2.30258509299404568402L // ln(10)
#define LDBL_LOG10E 0.43429448190325182765L // Log(e)
//#define M_PI 3.14159265358979323846264338327950288
//#define M_2PI 6.28318530717958647692528676655900576
//#define M_3PI_4 2.35619449019234492884698253745962716
//#define M_PI_2 1.57079632679489661923132169163975144
//#define M_3PI_8 1.17809724509617246442349126872981358
//#define M_PI_4 0.78539816339744830961566084581987572
//#define M_PI_8 0.39269908169872415480783042290993786
//#define M_1_PI 0.31830988618379067153776752674502872
//#define M_2_PI 0.63661977236758134307553505349005744
//#define M_4_PI 1.27323954473516268615107010698011488
#define M_E 2.71828182845904523536028747135266250 //constant "e"
//#define M_LOG2E 1.44269504088896340735992468100189213
//#define M_LOG10E 0.43429448190325182765112891891660508
//#define M_LN2 0.69314718055994530941723212145817657
//#define M_LN10 2.30258509299404568401799145468436421
//#define M_SQRT2 1.41421356237309504880168872420969808
//#define M_1_SQRT2 0.70710678118654752440084436210484904
/*
*================================== TYPES =====================================
*/
#ifndef ERRNO
extern int errno;
#endif
struct exception {
int type; /* type of exception */
char *name; /* name of function */
double arg1; /* first argument to function */
double arg2; /* second argument to function */
double retval; /* value to be returned if error is not fatal */
};
/* exception types */
#define DOMAIN 1 /* not in domain of function (i.e. number passed either to small or too large) */
#define SING 2 /* singularity (function not defined)(i.e. x/0) */
#define OVERFLOW 3 /* result too large */
#define UNDERFLOW 4 /* result too small */
#define TLOSS 5 /* total loss of precision */
#define PLOSS 6 /* partial loss of precision */
/*
*============================= FUNCTION CALL PROTOTYPES ============================
*/
/************************************************************************************
************************************************************************************
Double Precision Math Functions - (General ANSI Standard Functions)
*************************************************************************************
*************************************************************************************/
double acos(double); // Arc Cosine
float acosf(float);
long double acosl(long double);
double acosh(double); // Arc Hyperbolic Cosine
float acoshf(float);
long double acoshl(long double);
double asin(double); // Arc Sine
float asinf(float);
long double asinl(long double);
double asinh(double); // Arc Hyperbolic Sine
float asinhf(float);
long double asinhl(long double);
double atan(double); // Arc Tangent
float atanf(float);
long double atanl(long double);
double atanh(double); // Arc Hyperbolic Tangent
float atanhf(float);
long double atanhl(long double);
double atan2(double, double); // Inverse tangent of y/x
float atan2f(float, float);
long double atan2l(long double, long double);
double atof(const char *); // ASCII to Float
double cbrt(double ); // Cube Root
float cbrtf(float );
long double cbrtl(long double );
double ceil(double); // Smallest integer >= argument (as double)
float ceilf(float );
long double ceill(long double );
double cos(double); // Cosine of a Radian
float cosf(float);
long double cosl(long double);
double cosh(double); // Hyperbolic Cosine
float coshf(float);
long double coshl(long double);
double cotan(double); // Cotangent
float cotanf(float);
long double cotanl(long double);
double deg2rad(double ); // Degrees to Radians
float deg2radf(float );
long double deg2radl(long double);
//double drand(int n); //
double exp(double); // Natural ("e") Exponential (e^x)
float expf(float);
long double expl(long double);
double fabs(double); // Floating Absolute value
float fabsf(float);
long double fabsl(long double);
double floor(double); // Largest integer <= argument
float floorf(float );
long double floorl(long double );
double fma(double x, double y, double z); // Calculate (x * y) + z
float fmaf(float x, float y, float z); // Calculate (x * y) + z
long double fmal(long double x, long double y, long double z);
double fmod(double, double); // Floating modulus
float fmodf(float, float);
long double fmodl(long double, long double);
double frexp(double, int *); // Returns the mantissa of the floating point number
float frexpf(float, int *);
long double frexpl(long double, int *);
double hypot(double x, double y); // Calculate the Hypotenuse
float hypotf(float x, float y); //
long double hypotl(long double x, long double y); //
double ipow(double x, int n); // return x^n where n is an integer???????????????
double ldexp(double, int); // Returns the value of x times 2 raised to the exp power
float ldexpf(float, int);
long double ldexpl(long double, int);
//long _lrand()
double log(double); // Logarithm base "e" or natural
float logf(float);
long double logl(long double);
double log10(double); // Logarithm base 10
float log10f(float);
long double log10l(long double);
double modf(double, double *); // Return integer and fractional parts of number
float modff(float, float *);
long double modfl(long double, long double *);
double pseries(double , double coef[], unsigned ); // Expand polynomial series - sum = coef[0]+x*coef[1]+x^2*coef[2]+...+x^(n-1)*coef[n-1]
#if 0
#define pow(x,y) power(x,y) // same as "pow"
#endif
#if 0
#define powf(x,y) powerf(x,y)
#endif
#if 0
#define powl(x,y) powerl(x,y)
#endif
double pow(double, double); // Calculates "x" to the "y" power
float powf(float, float);
long double powl(long double, long double);
double rad2deg(double ); // Radians to Degrees
float rad2degf(float );
long double rad2degl(long double);
double sin(double); // Sine of a Radian
float sinf(float);
long double sinl(long double);
double sinh(double); // Hyperbolic Sine
float sinhf(float);
long double sinhl(long double);
double sqrt(double); // Square Root
float sqrtf(float);
long double sqrtl(long double);
double tan(double); // Tangent (Sine/Cosine)
float tanf(float);
long double tanl(long double);
double tanh(double); // Hyperbolic Tangent
float tanhf(float);
long double tanhl(long double);
double tgamma(double x); // gamma function of the argument
float tgammaf(float x);
long double tgammal(long double x);
//long double atoldl(const char *);
//*******************************************************************
// Gamma & Error Functions
//*******************************************************************
double erf(double ); // Error Function
float erff(float );
double erfc(double ); // Error Function
float erfcf(float );
double ierfc(double ); // Inverse Error Function
float ierfcf(float );
double gamma(double ); // Gamma function
float gammaf(float );
double lgamma(double ); // Log Gamma function
float lgammaf(float );
//******************
// Bessel Functions
//******************
double j0(double x); // First Bessel function of the first kind (Order 0)
double j1(double x); // Second Bessel function of the first kind (Order 1)
double jn(int n, double x); // Bessel Function Order n of the first kind
double y0(double x); // First Bessel function of the second Kind (Order 0)
double y1(double x); // Second Bessel function of the second Kind
double yn(int n, double x); // Bessel Function Order n of the second kind
double besi0_(double x); // Zeroth order modified bessel function of first kind.
//*************************
// Error handling Functions
//*************************
double _domerr(char *name, double arg1, double arg2);
double _tloss(char *name, double arg1, double arg2);
double _ploss(char *name, double arg1, double arg2);
double _rangerr(char *name, double arg1, double arg2, double dflt);
int matherr(struct exception *x);
void matherr_(char *funcname, int errnum);
/************************************************************************************
************************************************************************************
************************************************************************************
N O N A N S I
************************************************************************************
************************************************************************************
************************************************************************************
***********************************************************************************/
//*******************
// Calculus Functions
//*******************
double *convolve(double *data, int ndata, double weights[], int nweights,
int ndec, int itype, int isym, int *length);
double *deriv(double *data, double delta, int ndata);
double *integrat(double *xin, double dx, int ndata);
//******************
// Lowpass Filter Functions
// Smoothing Functions
//******************
void lowpass(double weights[], int nweights, double fc, double dB, int half); // Digital Lowpass filter of uniform time intervals (a Kaiser-Bessel window)
double *smooth(double *data, int ndata, int factor); // a Kaiser lowpass filter (Reduces the high frequency noise)
//******************
// DSP/FFT Functions
//******************
double stopbnd_(double ); // Used by bandpass()
void bandpass(double weights[], int nweights, double fh, double fl,
double dB, int half);
// Subroutine computes power spectral density of complex array v[] of length
// nv and returns it in the real array pw[] length npw.
//double *powspec(double *v, unsigned nv, unsigned npw, double *w);
// Computes power spectral density of real array
/********************************************************************/
/* This library is concerned entirely with angles in general and */
/* trigonometric functions in particular. */
/********************************************************************/
#ifndef ANGLE_TYPE
#define ANGLE_TYPE
enum angle_type {RAD, DEG, GRAD};
#endif
/********************************************************************/
/* The following three routines 'normalize' the supplied angle to */
/* be within limits appropiate for the trigonemetric routines. */
/* normalize_radians ensures that the supplied angle is between -PI */
/* and +PI, normalize_degrees between -180.0 and +180.0 and */
/* normalize_grade between -200.0 and +200.0. NOTE - ALL the */
/* normal trigonometric functions normalize the angle before use, */
/* and the inverse functions after. */
/********************************************************************/
void normalize_radians(double *radians);
void normalize_radiansf(float *radians);
void normalize_radiansl(long double *radians);
void normalize_degrees(double *degrees);
void normalize_degreesf(float *degrees);
void normalize_degreesl(long double *degrees);
void normalize_grade(double *grade);
void normalize_gradef(float *grade);
void normalize_gradel(long double *grade);
/********************************************************************/
/* These six routines enable conversion, of angles, between */
/* radians, degrees and grade. NOTE there is no need to normalize */
/* the angle to be converted before calling any of these routines */
/* as they all call the appropriate normalisation routine. */
/********************************************************************/
double radians_to_degrees(double radians);
float radians_to_degreesf(float radians);
long double radians_to_degreesl(long double radians);
double radians_to_grade(double radians);
float radians_to_gradef(float radians);
long double radians_to_gradel(long double radians);
double degrees_to_radians(double degrees);
float degrees_to_radiansf(float degrees);
long double degrees_to_radiansl(long double degrees);
double degrees_to_grade(double degrees);
float degrees_to_gradef(float degrees);
long double degrees_to_gradel(long double degrees);
double grade_to_radians(double grade);
float grade_to_radiansf(float grade);
long double grade_to_radiansl(long double grade);
double grade_to_degrees(double grade);
float grade_to_degreesf(float grade);
long double grade_to_degreesl(long double grade);
/********************************************************************/
/* The following six routines are the normal trigonometric */
/* functions. */
/********************************************************************/
double sine(double angle, enum angle_type atype);
float sinef(float angle, enum angle_type atype);
long double sinel(long double angle, enum angle_type atype);
double cosine(double angle, enum angle_type atype);
float cosinef(float angle, enum angle_type atype);
long double cosinel(long double angle, enum angle_type atype);
double tangent(double angle, enum angle_type atype);
float tangentf(float angle, enum angle_type atype);
long double tangentl(long double angle, enum angle_type atype);
double secant(double angle, enum angle_type atype);
float secantf(float angle, enum angle_type atype);
long double secantl(long double angle, enum angle_type atype);
double cosecant(double angle, enum angle_type atype);
float cosecantf(float angle, enum angle_type atype);
long double cosecantl(long double angle, enum angle_type atype);
double cotangent(double angle, enum angle_type atype);
float cotangentf(float angle, enum angle_type atype);
long double cotangentl(long double angle, enum angle_type atype);
/********************************************************************/
/* The following six routines are the normal inverse trigonometric */
/* functions. */
/********************************************************************/
double arc_sine(double x, enum angle_type outtype);
float arc_sinef(float x, enum angle_type outtype);
long double arc_sinel(long double x, enum angle_type outtype);
double arc_cosine(double x, enum angle_type outtype);
float arc_cosinef(float x, enum angle_type outtype);
long double arc_cosinel(long double x, enum angle_type outtype);
double arc_tangent(double x, enum angle_type outtype);
float arc_tangentf(float x, enum angle_type outtype);
long double arc_tangentl(long double x, enum angle_type outtype);
double arc_secant(double x, enum angle_type outtype);
float arc_secantf(float x, enum angle_type outtype);
long double arc_secantl(long double x, enum angle_type outtype);
double arc_cosecant(double x, enum angle_type outtype);
float arc_cosecantf(float x, enum angle_type outtype);
long double arc_cosecantl(long double x, enum angle_type outtype);
double arc_cotangent(double x, enum angle_type outtype);
float arc_cotangentf(float x, enum angle_type outtype);
long double arc_cotangentl(long double x, enum angle_type outtype);
/********************************************************************/
/* The following six routines are the hyperbolic trigonometric */
/* functions. */
/********************************************************************/
double hyperbolic_sine(double angle, enum angle_type atype);
float hyperbolic_sinef(float angle, enum angle_type atype);
long double hyperbolic_sinel(long double angle, enum angle_type atype);
double hyperbolic_cosine(double angle, enum angle_type atype);
float hyperbolic_cosinef(float angle, enum angle_type atype);
long double hyperbolic_cosinel(long double angle, enum angle_type atype);
double hyperbolic_tangent(double angle, enum angle_type atype);
float hyperbolic_tangentf(float angle, enum angle_type atype);
long double hyperbolic_tangentl(long double angle, enum angle_type atype);
double hyperbolic_secant(double angle, enum angle_type atype);
float hyperbolic_secantf(float angle, enum angle_type atype);
long double hyperbolic_secantl(long double angle, enum angle_type atype);
double hyperbolic_cosecant(double angle, enum angle_type atype);
float hyperbolic_cosecantf(float angle, enum angle_type atype);
long double hyperbolic_cosecantl(long double angle, enum angle_type atype);
double hyperbolic_cotangent(double angle, enum angle_type atype);
float hyperbolic_cotangentf(float angle, enum angle_type atype);
long double hyperbolic_cotangentl(long double angle, enum angle_type atype);
/********************************************************************/
/* The following six routines are the hyperbolic inverse */
/* trigonometric functions. */
/********************************************************************/
double hyperbolic_arc_sine(double x, enum angle_type outtype);
float hyperbolic_arc_sinef(float x, enum angle_type outtype);
long double hyperbolic_arc_sinel(long double x, enum angle_type outtype);
double hyperbolic_arc_cosine(double x, enum angle_type outtype);
float hyperbolic_arc_cosinef(float x, enum angle_type outtype);
long double hyperbolic_arc_cosinel(long double x, enum angle_type outtype);
double hyperbolic_arc_tangent(double x, enum angle_type outtype);
float hyperbolic_arc_tangentf(float x, enum angle_type outtype);
long double hyperbolic_arc_tangentl(long double x, enum angle_type outtype);
double hyperbolic_arc_secant(double x, enum angle_type outtype);
float hyperbolic_arc_secantf(float x, enum angle_type outtype);
long double hyperbolic_arc_secantl(long double x, enum angle_type outtype);
double hyperbolic_arc_cosecant(double x, enum angle_type outtype);
float hyperbolic_arc_cosecantf(float x, enum angle_type outtype);
long double hyperbolic_arc_cosecantl(long double x, enum angle_type outtype);
double hyperbolic_arc_cotangent(double x, enum angle_type outtype);
float hyperbolic_arc_cotangentf(float x, enum angle_type outtype);
long double hyperbolic_arc_cotangentl(long double x, enum angle_type outtype);
/********************************************************************/
/* The following four routines "complete" the standard library */
/* functions. */
/********************************************************************/
double sech(double x);
float sechf(float x);
long double sechl(long double x);
double csch(double x);
float cschf(float x);
long double cschl(long double x);
double coth(double x);
float cothf(float x);
long double cothl(long double x);
double acoth(double x);
float acothf(float x);
long double acothl(long double x);
/************************************************************************************
************************************************************************************
(Special Embedded Functions)
NON ANSI
*************************************************************************************
*************************************************************************************/
char *ecvt(double x, int digits, int *decimal, int *sign); // Convert the Double Precision number to Character string
char *fcvt(double x, int digits, int *decimal, int *sign); // Convert the Double Precision number to Character string - almost same as ecvt - digits arg is diff
char *gcvt(double x, int digits, char *buffer); // Convert the Float Precision number to Character string
BOOL dtoa(char *szLabel, double dNumber, int nChars, BOOL bUseSciNot );
long Gcd(long a, long b); // Greatest common divisor of a and b
//long long Gcd(long long a, long long b);
double Fac(long number); // Factorial of a number
float Facf(int number);
//long double Facl(long long number);
#endif /* End of _MATH_H */
#pragma Pop (List)
/**************************************
End of File MATH.H
***************************************/
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