[Easycalc-commits] PPCport/compat MathLib.cpp, NONE, 1.1 MathLib.h, NONE, 1.1 Preferences.cpp, NONE, 1.1 Preferences.h, NONE, 1.1

[Mapi B. <ma...@us...>]

Update of /cvsroot/easycalc/PPCport/compat
In directory 23jxhf1.ch3.sourceforge.com:/tmp/cvs-serv17350

Added Files:
	MathLib.cpp MathLib.h Preferences.cpp Preferences.h 
Log Message:
MathLib compatibility

--- NEW FILE: Preferences.cpp ---
#include "StdAfx.h"
#include "Preferences.h"
#include <winnls.h>

#define DEC_DOT 0
#define DEC_COM 1
#define TH_SPC  0
#define TH_COM  1
#define TH_DOT  2
#define TH_APO  3

unsigned int PrefGetPreference(SystemPreferencesChoice choice) {
    unsigned int returnVal;

    switch (choice) {
        case prefNumberFormat:
            {
            int dec, th;
            TCHAR cdec[10], cth[10];
            int rcdec = GetLocaleInfo(LOCALE_USER_DEFAULT, 
                                      LOCALE_SDECIMAL, 
                                      cdec, 
                                      9 
                                     );
            int rcth = GetLocaleInfo(LOCALE_USER_DEFAULT, 
                                     LOCALE_STHOUSAND, 
                                     cth, 
                                     9 
                                    );
            if (rcdec <= 0)   dec = DEC_DOT;    // By default ..
            else {
                cdec[rcdec] = 0;
                if (_tcsstr(cdec, _T(",")) != NULL) {
                    dec = DEC_COM;
                } else {
                    dec = DEC_DOT; // By default
                }
            }

            if (rcth <= 0)   th = TH_SPC;       // By default ..
            else {
                cth[rcth] = 0;
                if (_tcsstr(cth, _T("'")) != NULL) {
                    th = TH_APO;
                } else if (_tcsstr(cth, _T(".")) != NULL) {
                    th = TH_DOT;
                } else if (_tcsstr(cth, _T(",")) != NULL) {
                    th = TH_COM;
                } else {
                    th = TH_SPC; // By default
                }
            }

            if ((th == TH_APO) && (dec == DEC_COM))   returnVal = nfApostropheComma;
            else if ((th == TH_APO) && (dec == DEC_DOT))   returnVal = nfApostrophePeriod;
            else if ((th == TH_SPC) && (dec == DEC_COM))   returnVal = nfSpaceComma;
            else if ((th == TH_DOT) && (dec == DEC_COM))   returnVal = nfPeriodComma;
            else    returnVal = nfCommaPeriod;
            }
            break;

        default:
            returnVal = 0;
    }

    return (returnVal);
}
--- NEW FILE: Preferences.h ---
#pragma once

#ifndef PREFERENCES_H
#define PREFERENCES_H 1

typedef enum {
    nfCommaPeriod,
    nfPeriodComma,
    nfSpaceComma,
    nfApostrophePeriod,
    nfApostropheComma
} NumberFormatType;

typedef enum {
    prefNumberFormat
} SystemPreferencesChoice;

unsigned int PrefGetPreference(SystemPreferencesChoice choice);

#endif
--- NEW FILE: MathLib.h ---
/* MathLib: Pilot shared library of IEEE-754 double math functions
 *
 * Library function prototypes for the calling application.  This is
 * the file that the calling application should include in order to
 * get access to the routines in the library; it serves the same
 * function as the file "math.h" normally used on systems with
 * standard math libraries.  Each function in the library has two
 * prototypes listed; the first is for the programmer-friendly
 * wrapper function in MathLib.c, the second is for the raw SYS_TRAP()
 * invocation that actually calls the library routine.
 *
 * Copyright (C) 1997 Rick Huebner
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Library General Public License as
 * published by the Free Software Foundation; either version 2 of
 * the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Library General Public License for more details.
 *
 * You should have received a copy of the GNU Library General Public License
 * along with this program; see file COPYING.LIB.  If not, write to the
 * Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, 
 * Boston, MA 02110-1301, USA
 *
 * Version 1.01, 23 August 1997, Rick Huebner
 */
#ifndef __MATHLIB_H__
#define __MATHLIB_H__

// This is the major version number of the library.  If new functions
// are added to this library, this version number must be incremented
// to protect programs which are compiled with this header from trying
// to invoke the new functions in an old version of MathLib.prc,
// which would be fatal.  Do NOT delete any functions from this list,
// or any older programs which try to use them will die.  Any changes
// other than adding new functions should be reflected in the minor
// part of the version number, e.g. 1.1 if a bug fix, 2.0 if new
// functions added.
#define MathLibVersion 1

// Possible Err values from MathLib functions
typedef enum MathLibErrorCode {
	mlErrNone = 0,
	mlErrOldVersion,	// library is older than version passed to open()
	mlErrNotOpen,		// close() without having called open() first
	mlErrNoMemory		// can't allocate global data block
} MathLibErrorCode;

// Library reference returned by SysLibFind() or SysLibLoad()
extern UInt16 MathLibRef;

/*****************************
 * Library control functions *
 *****************************/
Err MathLibOpen(UInt16 refnum, UInt16 version)		// Initialize library for use
	SYS_TRAP(sysLibTrapOpen);
Err MathLibClose(UInt16 refnum, UInt16 *usecountP)// Free library resources when finished
	SYS_TRAP(sysLibTrapClose);
Err MathLibSleep(UInt16 refnum)					// Called by OS when Pilot sleeps
	SYS_TRAP(sysLibTrapSleep);
Err MathLibWake(UInt16 refnum)					// Called by OS when Pilot wakes
	SYS_TRAP(sysLibTrapWake);

/***************************
 * Trigonometric functions *
 ***************************/
//double acos(double x);				// Arc cosine of x 
//double asin(double x);				// Arc sine of x	
//double atan(double x);				// Arc tangent of x	
//double atan2(double y, double x);	// Arc tangent of y/x	
//double cos(double x);				// Cosine of x	
//double sin(double x);				// Sine of x	
//double tan(double x);				// Tangent of x	
void   sincos(double x, double *sinx, double *cosx); 	// Sine and cosine of x	

/************************	
 * Hyperbolic functions	*
 ************************/ 
//double cosh(double x);				// Hyperbolic cosine of x 
//double sinh(double x);				// Hyperbolic sine of x
//double tanh(double x);				// Hyperbolic tangent of x
double acosh(double x);				// Hyperbolic arc cosine of x
double asinh(double x);				// Hyperbolic arc sine of x
double atanh(double x);				// Hyperbolic arc tangent of x

/*****************************************
 * Exponential and logarithmic functions *
 *****************************************/
//double exp(double x);					// Exponential function of x [pow(e,x)]
//double frexp(double x, Int16 *exponent);	// Break x into normalized fraction and an integral power of 2
//double ldexp(double x, Int16 exponent);	// x * pow(2,exponent)
//double log(double x);					// Natural logarithm of x
//double log10(double x);					// Base 10 logarithm of x
//double modf(double x, double *intpart);	// Break x into integral and fractional parts
double expm1(double x);					// exp(x) - 1
double log1p(double x);					// log(1+x)
//double logb(double x);					// Base 2 signed integral exponent of x
#define logb(x) _logb(x)
double log2(double x);					// Base 2 logarithm of x

/*******************
 * Power functions *
 *******************/	
//double pow(double x, double y);		// x to the y power [x**y]
//double sqrt(double x);				// Square root of x [x**0.5]
//double hypot(double x, double y);	// sqrt(x*x + y*y)	[hypotenuse of right triangle]
#define hypot(x,y) _hypot(x,y)
double cbrt(double x);				// Cube root of x	[x**(1/3)]

/************************************************************
 * Nearest integer, absolute value, and remainder functions *
 ************************************************************/
//double ceil(double x);				// Smallest integral value not less than x
//double fabs(double x);				// Absolute value of x
//double floor(double x);				// Largest integral value not greater than x
//double fmod(double x, double y);	// Modulo remainder of x/y

/***************************
 * Miscellaneous functions *
 ***************************/
//Int16  isinf(double x);					// Return 0 if x is finite or NaN, +1 if +Infinity, or -1 if -Infinity
int isinf(double x);
//Int16  finite(double x);				// Return nonzero if x is finite and not NaN
#define finite(x) _finite(x)
//double scalbn(double x, Int16 exponent);	// x * pow(2,exponent)
#define scalbn(x,exponent) _scalb(x,(long)exponent)
double drem(double x, double y);		// Remainder of x/y
double significand(double x);			// Fractional part of x after dividing out ilogb(x)
//double copysign(double x, double y);	// Return x with its sign changed to match y's
#define copysign(x,y) _copysign(x,y)
//Int16  isnan(double x);					// Return nonzero if x is NaN (Not a Number)
#define isnan(x) _isnan(x)
//Int16  ilogb(double x);					// Binary exponent of non-zero x
int ilogb(double x);
double rint(double x);					// Integral value nearest x in direction of prevailing rounding mode
//double nextafter(double x, double y);	// Next machine double value after x in the direction towards y
#define nextafter(x,y) _nextafter(x,y)
//double remainder(double x, double y);	// Remainder of integer division x/y with infinite precision
#define remainder(x,y) drem(x,y)
// Not used by EasyCalc, and not worth a fudge ...
//double scalb(double x, double exponent);// x * pow(2,exponent)
double round(double x);					// Round x to nearest integral value away from zero
double trunc(double x);					// Round x to nearest integral value not larger than x
//UInt32 signbit(double x);				// Return signbit of x's machine representation
#define signbit(x) ((_fpclass(x) & (_FPCLASS_NINF | _FPCLASS_NN | _FPCLASS_ND | _FPCLASS_NZ) != 0)
 
#endif // __MATHLIB_H__

--- NEW FILE: MathLib.cpp ---
/* MathLib: Pilot shared library of IEEE-754 double math functions
 *
 * Convenience functions for the calling application.  These functions
 * provide a programmer-friendly wrapper around the raw system trap
 * invocations which actually call the library routines.  The idea
 * is to allow the programmer to say:
 *    y = sqrt(x);
 * instead of requiring:
 *     MathLibSqrt(MathLibRef, x, &y);
 * like the system trap interface requires.  The system trap form is
 * not only harder to read, but can't directly replace the traditional
 * function call in ported code, and can't be nested inside an expression.
 * Just add this source file to your project or makefile, and include
 * "MathLib.h" in any source file that needs to call these.
 *
 * The downside to these routines is that they'll take up some space
 * in your program, though CodeWarrior at least is smart enough to
 * only link in the ones which you actually use, so it doesn't really
 * cost you that much.  In fact, if you call these enough they'll pay
 * for themselves, since "x=sqrt(x)" generates much less code than
 * calling MathLibSqrt() directly.
 *
 * Copyright (C) 1997 Rick Huebner
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Library General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Library General Public License for more details.
 *
 * You should have received a copy of the GNU Library General Public License
 * along with this program; see file COPYING.LIB.  If not, write to the
 * Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
 * Boston, MA  02110-1301, USA.
 *
 * Version 1.01, 23 August 1997, Rick Huebner
 */
#include "stdafx.h"

#include "PalmOS.h"

#include "MathLib.h"
#include "defuns.h"

// Library reference returned by SysLibFind() or SysLibLoad()
UInt16 MathLibRef;



//double acos(double x) {
//    double result;
//    MathLibACos(MathLibRef, x, &result);
//    return result;
//}

//double asin(double x) {
//    double result;
//    MathLibASin(MathLibRef, x, &result);
//    return result;
//}

//double atan(double x) {
//    double result;
//    MathLibATan(MathLibRef, x, &result);
//    return result;
//}

//double atan2(double y, double x) {
//    double result;
//    MathLibATan2(MathLibRef, y, x, &result);
//    return result;
//}

//double cos(double x) {
//    double result;
//    MathLibCos(MathLibRef, x, &result);
//    return result;
//}

//double sin(double x) {
//    double result;
//    MathLibSin(MathLibRef, x, &result);
//    return result;
//}

//double tan(double x) {
//    double result;
//    MathLibTan(MathLibRef, x, &result);
//    return result;
//}

//void sincos(double x, double *sinx, double *cosx) {
//    MathLibSinCos(MathLibRef, x, sinx, cosx);
//}
void sincos(double x, double *sinx, double *cosx) {
    // Note: could also be calculated with:
    //1. Reduce the angle x to the range (0, pi/2)
    //2. Let z = tan(x/2),
    //   then sin(x) = 2*z/(1+z*z), cos(x) = (1-z*z)/(1+z*z) .
    // But with a floating point unit around ... not sure that
    // the perf/accuracy tradeoff is so beneficial.
    // The ARM processor does not have a sincos function like on Intel/AMD.
    *sinx = sin(x);
    *cosx = cos(x);
}

//double cosh(double x) {
//    double result;
//    MathLibCosH(MathLibRef, x, &result);
//    return result;
//}

//double sinh(double x) {
//    double result;
//    MathLibSinH(MathLibRef, x, &result);
//    return result;
//}

//double tanh(double x) {
//    double result;
//    MathLibTanH(MathLibRef, x, &result);
//    return result;
//}

//double acosh(double x) {
//    double result;
//    MathLibACosH(MathLibRef, x, &result);
//    return result;
//}
double acosh(double x) {
    //acosh(x) = ln(x + sqrt(x-1) * sqrt(x+1))
    //         = ln(x + sqrt(x*x-1))
    //for x > 1
    //Note: acosh(1) = 0
    double result = 0.0;
    if (x < 1.0)
        result = NaN;
    else if (isinf(x))
        result = x;
    else if (x > 1.0)
        result = log(x + sqrt(x*x - 1.0));
    return (result);
}

//double asinh(double x) {
//    double result;
//    MathLibASinH(MathLibRef, x, &result);
//    return result;
//}
double asinh(double x) {
    //asinh(x) = ln(x + sqrt(x*x+1))
    //for x > 0
    //asinh(0) = 0
    //If x<0, take the opposite or the result calculated with -x.
    double result = 0.0;
    if (isinf(x) || _isnan(x))
        result = x;
    else if (x > 0.0)
        result = log(x + sqrt(x*x + 1.0));
    else if (x < 0.0)
        result = -log(-x + sqrt(x*x + 1.0));
    return (result);
}

//double atanh(double x) {
//    double result;
//    MathLibATanH(MathLibRef, x, &result);
//    return result;
//}
double atanh(double x) {
    //atan(x) = 1/2 * ln((1+x)/(1-x))
    //for -1 < x < 1
    //atanh(-1) = -infinity
    //atanh(1) = +infinity
    double result = 0.0;
    if (_isnan(x) || (x < -1.0) || (x > 1.0))
        result = NaN;
    else if ((x == 1.0) || (x == -1.0))
        result = x / 0.0;
    else if (x != 0.0)
//        result = 0.5 * log((1.0 + x) * (1.0 - x));
        result = _scalb(log((1.0 + x) * (1.0 - x)), -1);
    return (result);
}

//double exp(double x) {
//    double result;
//    MathLibExp(MathLibRef, x, &result);
//    return result;
//}

//double frexp(double x, Int16 *exponent) {
//    double fraction;
//    MathLibFrExp(MathLibRef, x, &fraction, exponent);
//    return fraction;
//}

//double ldexp(double x, Int16 exponent) {
//    double result;
//    MathLibLdExp(MathLibRef, x, exponent, &result);
//    return result;
//}

//double log(double x) {
//    double result;
//    MathLibLog(MathLibRef, x, &result);
//    return result;
//}

//double log10(double x) {
//    double result;
//    MathLibLog10(MathLibRef, x, &result);
//    return result;
//}

//double modf(double x, double *intpart) {
//    double fraction;
//    MathLibModF(MathLibRef, x, intpart, &fraction);
//    return fraction;
//}

//double expm1(double x) {
//    double result;
//    MathLibExpM1(MathLibRef, x, &result);
//    return result;
//}

/***************************************************************
 * The following is imported from the Free42 source code 1.4.50 at
 * http://free42.sourceforge.net/ , from pocketpc/mathfudge.c,
 * itself borrowing the log1p() and expm1() parts from the GNU C
 * Library, version 2.2.5, originally donated by Sun Microsystems.
 * Indeed, the Microsoft Visual series are missing those functions.
 ***************************************************************/
static double
//one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
//ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
ln2_hi  =  6.93147180369123816490e-01,	/* 3fe62e42 fee00000 */
ln2_lo  =  1.90821492927058770002e-10,	/* 3dea39ef 35793c76 */
//two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
vast=  1.00000000000000000000e+300;

#define int32_t int
#define u_int32_t unsigned int

/* __FLOAT_WORD_ORDER == LITTLE_ENDIAN */
typedef union {
    double d;
    struct {
		int lx, hx;
    } w;
} double_words;

/* Get the more significant 32 bit int from a double.  */
typedef union
{
  double value;
  struct
  {
    u_int32_t lsw;
    u_int32_t msw;
  } parts;
} ieee_double_shape_type;

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

/* Get the less significant 32 bit int from a double.  */
#define GET_LOW_WORD(i,d)					\
do {								\
  ieee_double_shape_type gl_u;					\
  gl_u.value = (d);						\
  (i) = gl_u.parts.lsw;						\
} while (0)

/* Set the more significant 32 bits of a double from an int.  */
#define SET_HIGH_WORD(d,v)					\
do {								\
  ieee_double_shape_type sh_u;					\
  sh_u.value = (d);						\
  sh_u.parts.msw = (v);						\
  (d) = sh_u.value;						\
} while (0)

/*---------------------------------------------------------------------------*/
/* @(#)s_expm1.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */
/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
   for performance improvement on pipelined processors.
*/

/* expm1(x)
 * Returns exp(x)-1, the exponential of x minus 1.
 *
 * Method
 *   1. Argument reduction:
 *	Given x, find r and integer k such that
 *
 *               x = k*ln2 + r,  |r| <= 0.5*ln2 ~ 0.34658
 *
 *      Here a correction term c will be computed to compensate
 *	the error in r when rounded to a floating-point number.
 *
 *   2. Approximating expm1(r) by a special rational function on
 *	the interval [0,0.34658]:
 *	Since
 *	    r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
 *	we define R1(r*r) by
 *	    r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
 *	That is,
 *	    R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
 *		     = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
 *		     = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
 *      We use a special Reme algorithm on [0,0.347] to generate
 * 	a polynomial of degree 5 in r*r to approximate R1. The
 *	maximum error of this polynomial approximation is bounded
 *	by 2**-61. In other words,
 *	    R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
 *	where 	Q1  =  -1.6666666666666567384E-2,
 * 		Q2  =   3.9682539681370365873E-4,
 * 		Q3  =  -9.9206344733435987357E-6,
 * 		Q4  =   2.5051361420808517002E-7,
 * 		Q5  =  -6.2843505682382617102E-9;
 *  	(where z=r*r, and the values of Q1 to Q5 are listed below)
 *	with error bounded by
 *	    |                  5           |     -61
 *	    | 1.0+Q1*z+...+Q5*z   -  R1(z) | <= 2
 *	    |                              |
 *
 *	expm1(r) = exp(r)-1 is then computed by the following
 * 	specific way which minimize the accumulation rounding error:
 *			       2     3
 *			      r     r    [ 3 - (R1 + R1*r/2)  ]
 *	      expm1(r) = r + --- + --- * [--------------------]
 *		              2     2    [ 6 - r*(3 - R1*r/2) ]
 *
 *	To compensate the error in the argument reduction, we use
 *		expm1(r+c) = expm1(r) + c + expm1(r)*c
 *			   ~ expm1(r) + c + r*c
 *	Thus c+r*c will be added in as the correction terms for
 *	expm1(r+c). Now rearrange the term to avoid optimization
 * 	screw up:
 *		        (      2                                    2 )
 *		        ({  ( r    [ R1 -  (3 - R1*r/2) ]  )  }    r  )
 *	 expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
 *	                ({  ( 2    [ 6 - r*(3 - R1*r/2) ]  )  }    2  )
 *                      (                                             )
 *
 *		   = r - E
 *   3. Scale back to obtain expm1(x):
 *	From step 1, we have
 *	   expm1(x) = either 2^k*[expm1(r)+1] - 1
 *		    = or     2^k*[expm1(r) + (1-2^-k)]
 *   4. Implementation notes:
 *	(A). To save one multiplication, we scale the coefficient Qi
 *	     to Qi*2^i, and replace z by (x^2)/2.
 *	(B). To achieve maximum accuracy, we compute expm1(x) by
 *	  (i)   if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
 *	  (ii)  if k=0, return r-E
 *	  (iii) if k=-1, return 0.5*(r-E)-0.5
 *        (iv)	if k=1 if r < -0.25, return 2*((r+0.5)- E)
 *	       	       else	     return  1.0+2.0*(r-E);
 *	  (v)   if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
 *	  (vi)  if k <= 20, return 2^k((1-2^-k)-(E-r)), else
 *	  (vii) return 2^k(1-((E+2^-k)-r))
 *
 * Special cases:
 *	expm1(INF) is INF, expm1(NaN) is NaN;
 *	expm1(-INF) is -1, and
 *	for finite argument, only expm1(0)=0 is exact.
 *
 * Accuracy:
 *	according to an error analysis, the error is always less than
 *	1 ulp (unit in the last place).
 *
 * Misc. info.
 *	For IEEE double
 *	    if x >  7.09782712893383973096e+02 then expm1(x) overflow
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following
 * constants. The decimal values may be used, provided that the
 * compiler will convert from decimal to binary accurately enough
 * to produce the hexadecimal values shown.
 */
#define one Q[0]
static double
/*vast		= 1.0e+300,*/
tiny		= 1.0e-300,
o_threshold	= 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
/*ln2_hi		= 6.93147180369123816490e-01,*/ /* 0x3fe62e42, 0xfee00000 */
/*ln2_lo		= 1.90821492927058770002e-10,*/ /* 0x3dea39ef, 0x35793c76 */
invln2		= 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
	/* scaled coefficients related to expm1 */
Q[]  =  {1.0, -3.33333333333331316428e-02, /* BFA11111 111110F4 */
   1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
  -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
   4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
  -2.01099218183624371326e-07}; /* BE8AFDB7 6E09C32D */

double expm1(double x)
{
	double y,hi,lo,c,t,e,hxs,hfx,r1,h2,h4,R1,R2,R3;
	int32_t k,xsb;
	u_int32_t hx;

	GET_HIGH_WORD(hx,x);
	xsb = hx&0x80000000;		/* sign bit of x */
	if(xsb==0) y=x; else y= -x;	/* y = |x| */
	hx &= 0x7fffffff;		/* high word of |x| */

    /* filter out vast and non-finite argument */
	if(hx >= 0x4043687A) {			/* if |x|>=56*ln2 */
	    if(hx >= 0x40862E42) {		/* if |x|>=709.78... */
                if(hx>=0x7ff00000) {
		    u_int32_t low;
		    GET_LOW_WORD(low,x);
		    if(((hx&0xfffff)|low)!=0)
		         return x+x; 	 /* NaN */
		    else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
	        }
	        if(x > o_threshold) return vast*vast; /* overflow */
	    }
	    if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
		if(x+tiny<0.0)		/* raise inexact */
		return tiny-one;	/* return -1 */
	    }
	}

    /* argument reduction */
	if(hx > 0x3fd62e42) {		/* if  |x| > 0.5 ln2 */
	    if(hx < 0x3FF0A2B2) {	/* and |x| < 1.5 ln2 */
		if(xsb==0)
		    {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
		else
		    {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
	    } else {
		k  = (int32_t) (invln2*x+((xsb==0)?0.5:-0.5));
		t  = k;
		hi = x - t*ln2_hi;	/* t*ln2_hi is exact here */
		lo = t*ln2_lo;
	    }
	    x  = hi - lo;
	    c  = (hi-x)-lo;
	}
	else if(hx < 0x3c900000) {  	/* when |x|<2**-54, return x */
	    t = vast+x;	/* return x with inexact flags when x!=0 */
	    return x - (t-(vast+x));
	}
	else k = 0;

    /* x is now in primary range */
	hfx = 0.5*x;
	hxs = x*hfx;
#ifdef DO_NOT_USE_THIS
	r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
#else
	R1 = one+hxs*Q[1]; h2 = hxs*hxs;
	R2 = Q[2]+hxs*Q[3]; h4 = h2*h2;
	R3 = Q[4]+hxs*Q[5];
	r1 = R1 + h2*R2 + h4*R3;
#endif
	t  = 3.0-r1*hfx;
	e  = hxs*((r1-t)/(6.0 - x*t));
	if(k==0) return x - (x*e-hxs);		/* c is 0 */
	else {
	    e  = (x*(e-c)-c);
	    e -= hxs;
	    if(k== -1) return 0.5*(x-e)-0.5;
	    if(k==1) {
	       	if(x < -0.25) return -2.0*(e-(x+0.5));
	       	else 	      return  one+2.0*(x-e);
	    }
	    if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
	        u_int32_t high;
	        y = one-(e-x);
		GET_HIGH_WORD(high,y);
		SET_HIGH_WORD(y,high+(k<<20));	/* add k to y's exponent */
	        return y-one;
	    }
	    t = one;
	    if(k<20) {
	        u_int32_t high;
	        SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k));  /* t=1-2^-k */
	       	y = t-(e-x);
		GET_HIGH_WORD(high,y);
		SET_HIGH_WORD(y,high+(k<<20));	/* add k to y's exponent */
	   } else {
	        u_int32_t high;
		SET_HIGH_WORD(t,((0x3ff-k)<<20));	/* 2^-k */
	       	y = x-(e+t);
	       	y += one;
		GET_HIGH_WORD(high,y);
		SET_HIGH_WORD(y,high+(k<<20));	/* add k to y's exponent */
	    }
	}
	return y;
}

//double log1p(double x) {
//    double result;
//    MathLibLog1P(MathLibRef, x, &result);
//    return result;
//}
/*---------------------------------------------------------------------------*/
/* @(#)s_log1p.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */
/* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
   for performance improvement on pipelined processors.
*/

/* double log1p(double x)
 *
 * Method :
 *   1. Argument Reduction: find k and f such that
 *			1+x = 2^k * (1+f),
 *	   where  sqrt(2)/2 < 1+f < sqrt(2) .
 *
 *      Note. If k=0, then f=x is exact. However, if k!=0, then f
 *	may not be representable exactly. In that case, a correction
 *	term is need. Let u=1+x rounded. Let c = (1+x)-u, then
 *	log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
 *	and add back the correction term c/u.
 *	(Note: when x > 2**53, one can simply return log(x))
 *
 *   2. Approximation of log1p(f).
 *	Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
 *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
 *	     	 = 2s + s*R
 *      We use a special Reme algorithm on [0,0.1716] to generate
 * 	a polynomial of degree 14 to approximate R The maximum error
 *	of this polynomial approximation is bounded by 2**-58.45. In
 *	other words,
 *		        2      4      6      8      10      12      14
 *	    R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s  +Lp6*s  +Lp7*s
 *  	(the values of Lp1 to Lp7 are listed in the program)
 *	and
 *	    |      2          14          |     -58.45
 *	    | Lp1*s +...+Lp7*s    -  R(z) | <= 2
 *	    |                             |
 *	Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
 *	In order to guarantee error in log below 1ulp, we compute log
 *	by
 *		log1p(f) = f - (hfsq - s*(hfsq+R)).
 *
 *	3. Finally, log1p(x) = k*ln2 + log1p(f).
 *		 	     = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
 *	   Here ln2 is split into two floating point number:
 *			ln2_hi + ln2_lo,
 *	   where n*ln2_hi is always exact for |n| < 2000.
 *
 * Special cases:
 *	log1p(x) is NaN with signal if x < -1 (including -INF) ;
 *	log1p(+INF) is +INF; log1p(-1) is -INF with signal;
 *	log1p(NaN) is that NaN with no signal.
 *
 * Accuracy:
 *	according to an error analysis, the error is always less than
 *	1 ulp (unit in the last place).
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following
 * constants. The decimal values may be used, provided that the
 * compiler will convert from decimal to binary accurately enough
 * to produce the hexadecimal values shown.
 *
 * Note: Assuming log() return accurate answer, the following
 * 	 algorithm can be used to compute log1p(x) to within a few ULP:
 *
 *		u = 1+x;
 *		if(u==1.0) return x ; else
 *			   return log(u)*(x/(u-1.0));
 *
 *	 See HP-15C Advanced Functions Handbook, p.193.
 */
static double
//ln2_hi  =  6.93147180369123816490e-01,	/* 3fe62e42 fee00000 */
//ln2_lo  =  1.90821492927058770002e-10,	/* 3dea39ef 35793c76 */
two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
Lp[] = {0.0, 6.666666666666735130e-01,  /* 3FE55555 55555593 */
 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
 2.857142874366239149e-01,  /* 3FD24924 94229359 */
 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
 1.479819860511658591e-01};  /* 3FC2F112 DF3E5244 */

static double zero = 0.0;

double log1p(double x)
{
	double hfsq,f,c,s,z,R,u,z2,z4,z6,R1,R2,R3,R4;
	int32_t k,hx,hu,ax;

	GET_HIGH_WORD(hx,x);
	ax = hx&0x7fffffff;

	k = 1;
	if (hx < 0x3FDA827A) {			/* x < 0.41422  */
	    if(ax>=0x3ff00000) {		/* x <= -1.0 */
		if(x==-1.0) return -two54/(x-x);/* log1p(-1)=+inf */
		else return (x-x)/(x-x);	/* log1p(x<-1)=NaN */
	    }
	    if(ax<0x3e200000) {			/* |x| < 2**-29 */
		if(two54+x>zero			/* raise inexact */
	            &&ax<0x3c900000) 		/* |x| < 2**-54 */
		    return x;
		else
		    return x - x*x*0.5;
	    }
	    if(hx>0||hx<=((int32_t)0xbfd2bec3)) {
		k=0;f=x;hu=1;}	/* -0.2929<x<0.41422 */
	}
	if (hx >= 0x7ff00000) return x+x;
	if(k!=0) {
	    if(hx<0x43400000) {
		u  = 1.0+x;
		GET_HIGH_WORD(hu,u);
	        k  = (hu>>20)-1023;
	        c  = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */
		c /= u;
	    } else {
		u  = x;
		GET_HIGH_WORD(hu,u);
	        k  = (hu>>20)-1023;
		c  = 0;
	    }
	    hu &= 0x000fffff;
	    if(hu<0x6a09e) {
	        SET_HIGH_WORD(u,hu|0x3ff00000);	/* normalize u */
	    } else {
	        k += 1;
		SET_HIGH_WORD(u,hu|0x3fe00000);	/* normalize u/2 */
	        hu = (0x00100000-hu)>>2;
	    }
	    f = u-1.0;
	}
	hfsq=0.5*f*f;
	if(hu==0) {	/* |f| < 2**-20 */
	    if(f==zero) {
	      if(k==0) return zero;
			else {c += k*ln2_lo; return k*ln2_hi+c;}
	    }
	    R = hfsq*(1.0-0.66666666666666666*f);
	    if(k==0) return f-R; else
	    	     return k*ln2_hi-((R-(k*ln2_lo+c))-f);
	}
 	s = f/(2.0+f);
	z = s*s;
#ifdef DO_NOT_USE_THIS
	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
#else
	R1 = z*Lp[1]; z2=z*z;
	R2 = Lp[2]+z*Lp[3]; z4=z2*z2;
	R3 = Lp[4]+z*Lp[5]; z6=z4*z2;
	R4 = Lp[6]+z*Lp[7];
	R = R1 + z2*R2 + z4*R3 + z6*R4;
#endif
	if(k==0) return f-(hfsq-s*(hfsq+R)); else
		 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
}

//double logb(double x) {
//    double result;
//    MathLibLogB(MathLibRef, x, &result);
//    return result;
//}

//double log2(double x) {
//    double result;
//    MathLibLog2(MathLibRef, x, &result);
//    return result;
//}
double log2(double x) {
    //log2(x) = ln(x)/ln(2)
    //for x > 0
    //Note: log2(1) = 0, log2(0) = -infinity, log2(+infinity) = +infinity
    double result = 0.0;
    if (x < 0.0)
        result = NaN;
    else if (x == 0.0)
        result = -1.0 / x;
    else if (isinf(x))
        result = x;
    else   result = log(x) / log(2.0);
    return (result);
}

//double pow(double x, double y) {
//    double result;
//    MathLibPow(MathLibRef, x, y, &result);
//    return result;
//}

//double sqrt(double x) {
//    double result;
//    MathLibSqrt(MathLibRef, x, &result);
//    return result;
//}

//double hypot(double x, double y) {
//    double result;
//    MathLibHypot(MathLibRef, x, y, &result);
//    return result;
//}

//double cbrt(double x) {
//    double result;
//    MathLibCbrt(MathLibRef, x, &result);
//    return result;
//}
double cbrt(double x) {
    //cbrt(x) = x**(1/3) = exp(ln(x)/3)
    double result;
    if (_isnan(x) || (x == 0.0) || (x == 1.0) || (x == -1.0) || isinf(x))
        result = x;
    else   result = pow(x, 1.0/3.0);
//    else if (x > 0.0)
//        result = exp(log(x)/3.0);
//    else   result = - exp(log(-x)/3.0);
    return (result);
}

//double ceil(double x) {
//    double result;
//    MathLibCeil(MathLibRef, x, &result);
//    return result;
//}

//double fabs(double x) {
//    double result;
//    MathLibFAbs(MathLibRef, x, &result);
//    return result;
//}

//double floor(double x) {
//    double result;
//    MathLibFloor(MathLibRef, x, &result);
//    return result;
//}

//double fmod(double x, double y) {
//    double result;
//    MathLibFMod(MathLibRef, x, y, &result);
//    return result;
//}

//Int16 isinf(double x) {
//    Int16 result;
//    MathLibIsInf(MathLibRef, x, &result);
//    return result;
//}
int isinf(double x) {
    int rc = _fpclass(x);
    if ((rc & _FPCLASS_NINF) != 0)   return (-1);
    else if ((rc & _FPCLASS_PINF) != 0)   return (1);
    else   return (0);
}

//Int16 finite(double x) {
//    Int16 result;
//    MathLibFinite(MathLibRef, x, &result);
//    return result;
//}

//double scalbn(double x, Int16 exponent) {
//    double result;
//    MathLibScalBN(MathLibRef, x, exponent, &result);
//    return result;
//}

//double drem(double x, double y) {
//    double result;
//        MathLibDRem(MathLibRef, x, y, &result);
//    return result;
//}
double drem(double x, double y) {
    // The function drem is like fmod and compute the remainder r = x - ny when y is nonzero
    // except that it rounds the internal quotient n to the nearest integer
    // instead of towards zero to an integer.
    // For example, drem (6.5, 2.3) returns -0.4, which is 6.5 minus 6.9.
    // The absolute value of the result is less than or equal to half the absolute value
    // of the denominator. The difference between fmod (numerator, denominator)
    // and drem (numerator, denominator) is always either denominator, minus denominator,
    // or zero.
    // If the absolute value |n-x/y| = 0.5, n is chosen to be even.
    // For example, drem (5.5, 2.2) returns 1.1, which is 5.5 minus 2 * 2.2 = 4.4,
    // and drem (7.7, 2.2) returns -1.1, which is 7.7 minus 4 * 2.2 = 8.8.
    // If denominator is zero, drem returns NaN, just like fmod.
    // If x or y is a NaN, a NaN is returned.
    // If x is an infinity, a NaN is returned.
    // If y is an infinity, x is returned.
    double result;
    if ((y == 0.0) || _isnan(x) || _isnan(y) || isinf(x))
        result = NaN;
    else if (isinf(y))
        result = x;
    else {
//        result = fmod(x, y);
//        double r1 = result - y; // Takes care of the positive case, with n+1
//        double r2 = result + y; // Takes care of the negative case, with n-1
//        double fr = fabs(result);
//        double fr1 = fabs(r1);
//        double fr2 = fabs(r2);
//        if (fr1 < fr) { // Keep the one with lowest absolute value
//            result = r1;
//            fr = fr1;
//        } else if (fr2 < fr) {
//            result = r2;
//            fr = fr2;
//        } else if (fr1 == fr) { // Equidistant
//        } else if (fr2 == fr) { // Equidistant
//        }
        double q = x / y;
        int n = (int) rint(q);
        result = x - (double) n * y;
    }
    return (result);
}

//double significand(double x) {
//    double result;
//    MathLibSignificand(MathLibRef, x, &result);
//    return result;
//}
double significand(double x) {
    //The Math.significand() function returns the mantissa of x scaled to the range [1,2].
    //It is equivalent to scalb(x, (double) -ilogb(x)).
    //This function exists mainly for use in certain standardized tests for IEEE 754 conformance.
    //The function significand(x) isn't defined when x is one of:
    //* 0,
    //* positive or negative infinity,
    //* NAN.
    double result;
    if ((x == 0.0) || _isnan(x) || isinf(x))
        result = NaN;
    else   result = _scalb(x, (long) ilogb(x));
    return result;
}

//double copysign(double x, double y) {
//    double result;
//    MathLibCopySign(MathLibRef, x, y, &result);
//    return result;
//}

//Int16 isnan(double x) {
//    Int16 result;
//    MathLibIsNaN(MathLibRef, x, &result);
//    return result;
//}

//Int16 ilogb(double x) {
//    Int16 result;
//    MathLibILogB(MathLibRef, x, &result);
//    return result;
//}
int ilogb(double x) {
    //The ilogb() function returns the exponent part of x.
    //Formally, the return value is the integral part of logr|x| as a signed integral value,
    //for non-zero x, where r is the radix of the machine's floating point arithmetic.
    //The call ilogb(x) is equivalent to (int)logb(x). 
    //If x is 0, then ilogb() returns INT_MIN.
    //If x is NaN or ±Inf, then ilogb() returns INT_MAX. 
    int result;
    if (_isnan(x) || isinf(x))
        result = INT_MAX;
    else if (x == 0.0)
        result = INT_MIN;
    else   result = (int) _logb(x);
    return result;
}

//double rint(double x) {
//    double result;
//    MathLibRInt16(MathLibRef, x, &result);
//    return result;
//}
double rint(double x) {
    //Round x to an integer value according to the current rounding mode.
    //The default rounding mode is to round to the nearest integer.
    //Some machines support other modes, but round-to-nearest is always used unless
    //you explicitly select another.
    //This implementation will use round-to-nearest.
    //Note: for halfway numbers, rint() is to pick the even closest integer.
    double result;
    if (_isnan(x) || isinf(x) || (x == 0.0))
        result = x;
    else {
        double fract, n;
        int nn, nn1;
        fract = modf(x, &n);
        nn = (int) n;
        nn1 = nn >> 1;
        nn1 <<= 1;
        if (x > 0.0) {
            if (fract > 0.5)
                n += 1.0;
            else if (fract == 0.5) {
                if (nn != nn1)
                    n += 1.0;
            }
        } else {
            if (fract < -0.5)
                n -= 1.0;
            else if (fract == -0.5) {
                if (nn != nn1)
                    n -= 1.0;
            }
        }
        result = n;
    }
    return (result);
}

//double nextafter(double x, double y) {
//    double result;
//    MathLibNextAfter(MathLibRef, x, y, &result);
//    return result;
//}

//double remainder(double x, double y) {
//    double result;
//    MathLibRemainder(MathLibRef, x, y, &result);
//    return result;
//}

//double scalb(double x, double exponent) {
//    double result;
//    MathLibScalB(MathLibRef, x, exponent, &result);
//    return result;
//}

//double round(double x) {
//    double result;
//    MathLibRound(MathLibRef, x, &result);
//    return result;floor
//}
double round(double x) {
    double result;
    if (_isnan(x) || isinf(x))
        result = NaN;
    else if (x == trunc(x))
        result = x;
    else if (x < 0.0)
        result = trunc(x-0.5);
    else
        result = trunc(x+0.5);
    return (result);
}

//double trunc(double x) {
//    double result;
//    MathLibTrunc(MathLibRef, x, &result);
//    return result;
//}
double trunc(double x) {
    double result;
    if (_isnan(x) || isinf(x))
        result = NaN;
    modf(x, &result);
    return (result);
}

//UInt32 signbit(double x) {
//    UInt32 result;
//    MathLibSignBit(MathLibRef, x, &result);
//    return result;
//}