/* @(#)mathlib.h 1.2 90/02/02
*
* Definitions used with the portable math library.
*
* This is being done because libm.a doesn't appear to be as portable
* as originally assumed.
*
* These routines are taken from two sources:
*
* 1/ Fred Fishs' portable maths library which was posted to the
* comp.sources.unix newsgroup on April 1987.
*
* acos, acosh, asin, asinh, atan, atanh, cos, cosh, fabs,
* exp, log, log10, mod, poly, sin, sinh, sqrt, tan, tanh.
*
* 2/ The BSD4.3 maths library found on uunet in
* bsd_sources/src/usr.lib/libm.
*
* pow, pow_p, scalb, logb, copysign, finite, drem, exp__E,
* log__L.
*
* Customised and condensed by Rich Burridge,
* Sun Microsystems, Australia.
*
* Permission is given to distribute these sources, as long as the
* copyright messages are not removed, and no monies are exchanged.
*
* No responsibility is taken for any errors or inaccuracies inherent
* either to the comments or the code of this program, but if
* reported to me then an attempt will be made to fix them.
*/
/************************************************************************
* *
* N O T I C E *
* *
* Copyright Abandoned, 1987, Fred Fish *
* *
* This previously copyrighted work has been placed into the *
* public domain by the author (Fred Fish) and may be freely used *
* for any purpose, private or commercial. I would appreciate *
* it, as a courtesy, if this notice is left in all copies and *
* derivative works. Thank you, and enjoy... *
* *
* The author makes no warranty of any kind with respect to this *
* product and explicitly disclaims any implied warranties of *
* merchantability or fitness for any particular purpose. *
* *
************************************************************************
*/
/* This file gets included with all of the floating point math
* library routines when they are compiled. Note that
* this is the proper place to put machine dependencies
* whenever possible.
*
* It should be pointed out that for simplicity's sake, the
* environment parameters are defined as floating point constants,
* rather than octal or hexadecimal initializations of allocated
* storage areas. This means that the range of allowed numbers
* may not exactly match the hardware's capabilities. For example,
* if the maximum positive double precision floating point number
* is EXACTLY 1.11...E100 and the constant "MAXDOUBLE is
* defined to be 1.11E100 then the numbers between 1.11E100 and
* 1.11...E100 are considered to be undefined. For most
* applications, this will cause no problems.
*
* An alternate method is to allocate a global static "double" variable,
* say "maxdouble", and use a union declaration and initialization
* to initialize it with the proper bits for the EXACT maximum value.
* This was not done because the only compilers available to the
* author did not fully support union initialization features.
*/
extern double acos(), acosh(), asin(), asinh(), atan(), atanh() ;
extern double cos(), cosh(), exp(), fabs(), log(), log10(), pow() ;
extern double sin(), sinh(), sqrt(), tan(), tanh() ;
/*START============start of definitions from <values.h>============START
*
* If your system has a /usr/include/values.h, or has another include
* file which defines:
* MAXDOUBLE => Maximum double precision number
* MINDOUBLE => Minimum double precision number
* DMAXEXP => Maximum exponent of a double
* DMINEXP => Minimum exponent of a double
*
* you can comment out these definitions down to the END line below.
*/
#ifndef BITSPERBYTE
/* These values work with any binary representation of integers
* where the high-order bit contains the sign. */
/* a number used normally for size of a shift */
#if gcos
#define BITSPERBYTE 9
#else
#define BITSPERBYTE 8
#endif
#define BITS(type) (BITSPERBYTE * (int)sizeof(type))
/* Various values that describe the binary floating-point representation
* MAXDOUBLE - the largest double
* ((_EXPBASE ** DMAXEXP) * (1 - (_EXPBASE ** -DSIGNIF)))
* MINDOUBLE - the smallest double (_EXPBASE ** (DMINEXP - 1))
* DMAXEXP - the maximum exponent of a double (as returned by frexp())
* DMINEXP - the minimum exponent of a double (as returned by frexp())
* DSIGNIF - the number of significant bits in a double
* _IEEE - 1 if IEEE standard representation is used
* _DEXPLEN - the number of bits for the exponent of a double
* _HIDDENBIT - 1 if high-significance bit of mantissa is implicit
*/
#if u3b || u3b5 || sun
#define MAXDOUBLE 1.79769313486231470e+308
#define MINDOUBLE 4.94065645841246544e-324
#define _IEEE 1
#define _DEXPLEN 11
#define _HIDDENBIT 1
#define DMINEXP (-(DMAXEXP + DSIGNIF - _HIDDENBIT - 3))
#endif
#if pdp11 || vax
#define MAXDOUBLE 1.701411834604692293e+38
#define MINDOUBLE (0.01 * 2.938735877055718770e-37)
#define _IEEE 0
#define _DEXPLEN 8
#define _HIDDENBIT 1
#define DMINEXP (-DMAXEXP)
#endif
#if gcos
#define MAXDOUBLE 1.7014118346046923171e+38
#define MINDOUBLE 2.9387358770557187699e-39
#define _IEEE 0
#define _DEXPLEN 8
#define _HIDDENBIT 0
#define DMINEXP (-(DMAXEXP + 1))
#endif
#define DSIGNIF (BITS(double) - _DEXPLEN + _HIDDENBIT - 1)
#define DMAXEXP ((1 << _DEXPLEN - 1) - 1 + _IEEE)
#endif /*BITSPERBYTE*/
/*END==============end of definitions from <values.h>==================END*/
#define LOG2_MAXDOUBLE (DMAXEXP + 1)
#define LOG2_MINDOUBLE (DMINEXP - 1)
#define LOGE_MAXDOUBLE (LOG2_MAXDOUBLE / LOG2E)
#define LOGE_MINDOUBLE (LOG2_MINDOUBLE / LOG2E)
/*
* The following are hacks which should be fixed when I understand all
* the issues a little better. |tanh(TANH_MAXARG)| = 1.0
*/
#define TANH_MAXARG 16
#define SQRT_MAXDOUBLE 1.304380e19
#define TWOPI (2.0 * PI)
#define HALFPI (PI / 2.0)
#define FOURTHPI (PI / 4.0)
#define SIXTHPI (PI / 6.0)
#define LOG2E 1.4426950408889634074 /* Log to base 2 of e */
#define LOG10E 0.4342944819032518276
#define SQRT2 1.4142135623730950488
#define SQRT3 1.7320508075688772935
#define LN2 0.6931471805599453094
#define LNSQRT2 0.3465735902799726547
/* MC68000 HARDWARE DEPENDENCIES
*
* cc -DIEEE => uses IEEE floating point format
*
* Apologies for the double negative. I want as few definitions
* needed in the default case as possible.
*/
#ifndef NOIEEE
#define X6_UNDERFLOWS (4.209340e-52) /* X**6 almost underflows */
#define X16_UNDERFLOWS (5.421010e-20) /* X**16 almost underflows */
#endif /*NOIEEE*/
/* It is hoped that your system supplies all the mathematical functions
* required by calctool. If not then, it is possible to use the needed
* ones from the portable math library routines that comes with these
* sources.
*
* There is one definition for each routine used by calctool. These are
* commented out by default to signify that this system has that routine.
* If you are missing any, then uncomment the appropriate definitions.
*/
/*#define NEED_ACOS */
/*#define NEED_ACOSH */
/*#define NEED_ASIN */
/*#define NEED_ASINH */
/*#define NEED_ATAN */
/*#define NEED_ATANH */
/*#define NEED_COS */
/*#define NEED_COSH */
/*#define NEED_EXP */
/*#define NEED_LOG */
/*#define NEED_LOG10 */
/*#define NEED_POW */
/*#define NEED_SIN */
/*#define NEED_SINH */
/*#define NEED_SQRT */
/*#define NEED_TAN */
/*#define NEED_TANH */
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