ieee.c

win32program disassembler

#include <stdio.h>

/* Include file for extended precision arithmetic programs.
 */

/* Number of 16 bit words in external x type format */
#define NE 10

/* Number of 16 bit words in internal format */
#define NI (NE+3)

/* Array offset to exponent */
#define E 1

/* Array offset to high guard word */
#define M 2

/* Number of bits of precision */
#define NBITS ((NI-4)*16)

/* Maximum number of decimal digits in ASCII conversion
 * = NBITS*log10(2)
 */
#define NDEC (NBITS*8/27)

/* The exponent of 1.0 */
#define EXONE (0x3fff)

void eadd(), esub(), emul(), ediv();
int ecmp(), enormlz(), eshift();
void eshup1(), eshup8(), eshup6(), eshdn1(), eshdn8(), eshdn6();
void eabs(), eneg(), emov(), eclear(), einfin(), efloor();
void eldexp(), efrexp(), eifrac(), ltoe();
void esqrt(), elog(), eexp(), etanh(), epow();
void asctoe(), asctoe24(), asctoe53(), asctoe64();
void etoasc(), e24toasc(), e53toasc(), e64toasc();
void etoe64(), etoe53(), etoe24(), e64toe(), e53toe(), e24toe();
int mtherr();
extern unsigned short ezero[], ehalf[], eone[], etwo[];
extern unsigned short elog2[], esqrt2[];


/* by Stephen L. Moshier. */

/*							mconf.h
 *
 *	Common include file for math routines
 *
 *
 *
 * SYNOPSIS:
 *
 * #include "mconf.h"
 *
 *
 *
 * DESCRIPTION:
 *
 * This file contains definitions for error codes that are
 * passed to the common error handling routine mtherr()
 * (which see).
 *
 * The file also includes a conditional assembly definition
 * for the type of computer arithmetic (IEEE, DEC, Motorola
 * IEEE, or UNKnown).
 * 
 * For Digital Equipment PDP-11 and VAX computers, certain
 * IBM systems, and others that use numbers with a 56-bit
 * significand, the symbol DEC should be defined.  In this
 * mode, most floating point constants are given as arrays
 * of octal integers to eliminate decimal to binary conversion
 * errors that might be introduced by the compiler.
 *
 * For little-endian computers, such as IBM PC, that follow the
 * IEEE Standard for Binary Floating Point Arithmetic (ANSI/IEEE
 * Std 754-1985), the symbol IBMPC should be defined.  These
 * numbers have 53-bit significands.  In this mode, constants
 * are provided as arrays of hexadecimal 16 bit integers.
 *
 * Big-endian IEEE format is denoted MIEEE.  On some RISC
 * systems such as Sun SPARC, double precision constants
 * must be stored on 8-byte address boundaries.  Since integer
 * arrays may be aligned differently, the MIEEE configuration
 * may fail on such machines.
 *
 * To accommodate other types of computer arithmetic, all
 * constants are also provided in a normal decimal radix
 * which one can hope are correctly converted to a suitable
 * format by the available C language compiler.  To invoke
 * this mode, define the symbol UNK.
 *
 * An important difference among these modes is a predefined
 * set of machine arithmetic constants for each.  The numbers
 * MACHEP (the machine roundoff error), MAXNUM (largest number
 * represented), and several other parameters are preset by
 * the configuration symbol.  Check the file const.c to
 * ensure that these values are correct for your computer.
 *
 * Configurations NANS, INFINITIES, MINUSZERO, and DENORMAL
 * may fail on many systems.  Verify that they are supposed
 * to work on your computer.
 */

/*
Cephes Math Library Release 2.3:  June, 1995
Copyright 1984, 1987, 1989, 1995 by Stephen L. Moshier
*/


/* Constant definitions for math error conditions
 */

#define DOMAIN		1	/* argument domain error */
#define SING		2	/* argument singularity */
#define OVERFLOW	3	/* overflow range error */
#define UNDERFLOW	4	/* underflow range error */
#define TLOSS		5	/* total loss of precision */
#define PLOSS		6	/* partial loss of precision */

#define EDOM		33
#define ERANGE		34

/* Complex numeral.  */
typedef struct
	{
	double r;
	double i;
	} cmplx;

/* Long double complex numeral.  */
typedef struct
	{
	double r;
	double i;
	} cmplxl;

/* Type of computer arithmetic */

/* PDP-11, Pro350, VAX:
 */
/* #define DEC 1 */

/* Intel IEEE, low order words come first:
 */
/* #define IBMPC 1 */

/* Motorola IEEE, high order words come first
 * (Sun 680x0 workstation):
 */
/* #define MIEEE 1 */

/* UNKnown arithmetic, invokes coefficients given in
 * normal decimal format.  Beware of range boundary
 * problems (MACHEP, MAXLOG, etc. in const.c) and
 * roundoff problems in pow.c:
 * (Sun SPARCstation)
 */
#define UNK 1

/* If you define UNK, then be sure to set BIGENDIAN properly. */
#define BIGENDIAN 0

/* Define this `volatile' if your compiler thinks
 * that floating point arithmetic obeys the associative
 * and distributive laws.  It will defeat some optimizations
 * (but probably not enough of them).
 *
 * #define VOLATILE volatile
 */
#define VOLATILE

/* For 12-byte long doubles on an i386, pad a 16-bit short 0
 * to the end of real constants initialized by integer arrays.
 *
 * #define XPD 0,
 *
 * Otherwise, the type is 10 bytes long and XPD should be
 * defined blank (e.g., Microsoft C).
 *
 * #define XPD
 */
#define XPD 0,

/* Define to support tiny denormal numbers, else undefine. */
#define DENORMAL 1

/* Define to ask for infinity support, else undefine. */
#define INFINITIES 1

/* Define to ask for support of numbers that are Not-a-Number,
   else undefine.  This may automatically define INFINITIES in some files. */
#define NANS 1

/* Define to distinguish between -0.0 and +0.0.  */
#define MINUSZERO 1

/* Define 1 for ANSI C atan2() function
   See atan.c and clog.c. */
#define ANSIC 1

int mtherr();

/* Variable for error reporting.  See mtherr.c.  */
extern int merror;


/*							econst.c	*/
/*  e type constants used by high precision check routines */

#if NE == 10
/* 0.0 */
unsigned short ezero[NE] =
 {0x0000, 0x0000, 0x0000, 0x0000,
  0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,};

/* 5.0E-1 */
unsigned short ehalf[NE] =
 {0x0000, 0x0000, 0x0000, 0x0000,
  0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3ffe,};

/* 1.0E0 */
unsigned short eone[NE] =
 {0x0000, 0x0000, 0x0000, 0x0000,
  0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,};

/* 2.0E0 */
unsigned short etwo[NE] =
 {0x0000, 0x0000, 0x0000, 0x0000,
  0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4000,};

/* 3.2E1 */
unsigned short e32[NE] =
 {0x0000, 0x0000, 0x0000, 0x0000,
  0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4004,};

/* 6.93147180559945309417232121458176568075500134360255E-1 */
unsigned short elog2[NE] =
 {0x40f3, 0xf6af, 0x03f2, 0xb398,
  0xc9e3, 0x79ab, 0150717, 0013767, 0130562, 0x3ffe,};

/* 1.41421356237309504880168872420969807856967187537695E0 */
unsigned short esqrt2[NE] =
 {0x1d6f, 0xbe9f, 0x754a, 0x89b3,
  0x597d, 0x6484, 0174736, 0171463, 0132404, 0x3fff,};

/* 3.14159265358979323846264338327950288419716939937511E0 */
unsigned short epi[NE] =
 {0x2902, 0x1cd1, 0x80dc, 0x628b,
  0xc4c6, 0xc234, 0020550, 0155242, 0144417, 0040000,};
  
/* 5.7721566490153286060651209008240243104215933593992E-1 */
unsigned short eeul[NE] = {
0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,};

#else

/* 0.0 */
unsigned short ezero[NE] = {
0, 0000000,0000000,0000000,0000000,0000000,};
/* 5.0E-1 */
unsigned short ehalf[NE] = {
0, 0000000,0000000,0000000,0100000,0x3ffe,};
/* 1.0E0 */
unsigned short eone[NE] = {
0, 0000000,0000000,0000000,0100000,0x3fff,};
/* 2.0E0 */
unsigned short etwo[NE] = {
0, 0000000,0000000,0000000,0100000,0040000,};
/* 3.2E1 */
unsigned short e32[NE] = {
0, 0000000,0000000,0000000,0100000,0040004,};
/* 6.93147180559945309417232121458176568075500134360255E-1 */
unsigned short elog2[NE] = {
0xc9e4,0x79ab,0150717,0013767,0130562,0x3ffe,};
/* 1.41421356237309504880168872420969807856967187537695E0 */
unsigned short esqrt2[NE] = {
0x597e,0x6484,0174736,0171463,0132404,0x3fff,};
/* 2/sqrt(PI) =
 * 1.12837916709551257389615890312154517168810125865800E0 */
unsigned short eoneopi[NE] = {
0x71d5,0x688d,0012333,0135202,0110156,0x3fff,};
/* 3.14159265358979323846264338327950288419716939937511E0 */
unsigned short epi[NE] = {
0xc4c6,0xc234,0020550,0155242,0144417,0040000,};
/* 5.7721566490153286060651209008240243104215933593992E-1 */
unsigned short eeul[NE] = {
0xd1be,0xc7a4,0076660,0063743,0111704,0x3ffe,};
#endif
extern unsigned short ezero[];
extern unsigned short ehalf[];
extern unsigned short eone[];
extern unsigned short etwo[];
extern unsigned short e32[];
extern unsigned short elog2[];
extern unsigned short esqrt2[];
extern unsigned short eoneopi[];
extern unsigned short epi[];
extern unsigned short eeul[];


/*							ieee.c
 *
 *    Extended precision IEEE binary floating point arithmetic routines
 *
 * Numbers are stored in C language as arrays of 16-bit unsigned
 * short integers.  The arguments of the routines are pointers to
 * the arrays.
 *
 *
 * External e type data structure, simulates Intel 8087 chip
 * temporary real format but possibly with a larger significand:
 *
 *	NE-1 significand words	(least significant word first,
 *				 most significant bit is normally set)
 *	exponent		(value = EXONE for 1.0,
 *				top bit is the sign)
 *
 *
 * Internal data structure of a number (a "word" is 16 bits):
 *
 * ei[0]	sign word	(0 for positive, 0xffff for negative)
 * ei[1]	biased exponent	(value = EXONE for the number 1.0)
 * ei[2]	high guard word	(always zero after normalization)
 * ei[3]
 * to ei[NI-2]	significand	(NI-4 significand words,
 *				 most significant word first,
 *				 most significant bit is set)
 * ei[NI-1]	low guard word	(0x8000 bit is rounding place)
 *
 *
 *
 *		Routines for external format numbers
 *
 *	asctoe( string, e )	ASCII string to extended double e type
 *	asctoe64( string, &d )	ASCII string to long double
 *	asctoe53( string, &d )	ASCII string to double
 *	asctoe24( string, &f )	ASCII string to single
 *	asctoeg( string, e, prec ) ASCII string to specified precision
 *	e24toe( &f, e )		IEEE single precision to e type
 *	e53toe( &d, e )		IEEE double precision to e type
 *	e64toe( &d, e )		IEEE long double precision to e type
 *	eabs(e)			absolute value
 *	eadd( a, b, c )		c = b + a
 *	eclear(e)		e = 0
 *	ecmp (a, b)		Returns 1 if a > b, 0 if a == b,
 *				-1 if a < b, -2 if either a or b is a NaN.
 *	ediv( a, b, c )		c = b / a
 *	efloor( a, b )		truncate to integer, toward -infinity
 *	efrexp( a, exp, s )	extract exponent and significand
 *	eifrac( e, &l, frac )   e to long integer and e type fraction
 *	euifrac( e, &l, frac )  e to unsigned long integer and e type fraction
 *	einfin( e )		set e to infinity, leaving its sign alone
 *	eldexp( a, n, b )	multiply by 2**n
 *	emov( a, b )		b = a
 *	emul( a, b, c )		c = b * a
 *	eneg(e)			e = -e
 *	eround( a, b )		b = nearest integer value to a
 *	esub( a, b, c )		c = b - a
 *	e24toasc( &f, str, n )	single to ASCII string, n digits after decimal
 *	e53toasc( &d, str, n )	double to ASCII string, n digits after decimal
 *	e64toasc( &d, str, n )	long double to ASCII string
 *	etoasc( e, str, n )	e to ASCII string, n digits after decimal
 *	etoe24( e, &f )		convert e type to IEEE single precision
 *	etoe53( e, &d )		convert e type to IEEE double precision
 *	etoe64( e, &d )		convert e type to IEEE long double precision
 *	ltoe( &l, e )		long (32 bit) integer to e type
 *	ultoe( &l, e )		unsigned long (32 bit) integer to e type
 *      eisneg( e )             1 if sign bit of e != 0, else 0
 *      eisinf( e )             1 if e has maximum exponent (non-IEEE)
 *				or is infinite (IEEE)
 *      eisnan( e )             1 if e is a NaN
 *	esqrt( a, b )		b = square root of a
 *
 *
 *		Routines for internal format numbers
 *
 *	eaddm( ai, bi )		add significands, bi = bi + ai
 *	ecleaz(ei)		ei = 0
 *	ecleazs(ei)		set ei = 0 but leave its sign alone
 *	ecmpm( ai, bi )		compare significands, return 1, 0, or -1
 *	edivm( ai, bi )		divide  significands, bi = bi / ai
 *	emdnorm(ai,l,s,exp)	normalize and round off
 *	emovi( a, ai )		convert external a to internal ai
 *	emovo( ai, a )		convert internal ai to external a
 *	emovz( ai, bi )		bi = ai, low guard word of bi = 0
 *	emulm( ai, bi )		multiply significands, bi = bi * ai
 *	enormlz(ei)		left-justify the significand
 *	eshdn1( ai )		shift significand and guards down 1 bit
 *	eshdn8( ai )		shift down 8 bits
 *	eshdn6( ai )		shift down 16 bits
 *	eshift( ai, n )		shift ai n bits up (or down if n < 0)
 *	eshup1( ai )		shift significand and guards up 1 bit
 *	eshup8( ai )		shift up 8 bits
 *	eshup6( ai )		shift up 16 bits
 *	esubm( ai, bi )		subtract significands, bi = bi - ai
 *
 *
 * The result is always normalized and rounded to NI-4 word precision
 * after each arithmetic operation.
 *
 * Exception flags are NOT fully supported.
 *
 * Define INFINITY in mconf.h for support of infinity; otherwise a
 * saturation arithmetic is implemented.
 *
 * Define NANS for support of Not-a-Number items; otherwise the
 * arithmetic will never produce a NaN output, and might be confused
 * by a NaN input.
 * If NaN's are supported, the output of ecmp(a,b) is -2 if
 * either a or b is a NaN. This means asking if(ecmp(a,b) < 0)
 * may not be legitimate. Use if(ecmp(a,b) == -1) for less-than
 * if in doubt.
 * Signaling NaN's are NOT supported; they are treated the same
 * as quiet NaN's.
 *
 * Denormals are always supported here where appropriate (e.g., not
 * for conversion to DEC numbers).
 */

/*
 * Revision history:
 *
 *  5 Jan 84	PDP-11 assembly language version
 *  2 Mar 86	fixed bug in asctoq()
 *  6 Dec 86	C language version
 * 30 Aug 88	100 digit version, improved rounding
 * 15 May 92    80-bit long double support
 *
 * Author:  S. L. Moshier.
 */


/* Change UNK into something else. */
#ifdef UNK
#undef UNK
#if BIGENDIAN
#define MIEEE 1
#else
#define IBMPC 1
#endif
#endif

/* NaN's require infinity support. */
#ifdef NANS
#ifndef INFINITY
#define INFINITY
#endif
#endif

/* This handles 64-bit long ints. */
#define LONGBITS (8 * sizeof(long))

/* Control register for rounding precision.
 * This can be set to 80 (if NE=6), 64, 56, 53, or 24 bits.
 */
int rndprc = NBITS;
extern int rndprc;

void eaddm(), esubm(), emdnorm(), asctoeg(), enan();
static void toe24(), toe53(), toe64(), toe113();
void eremain(), einit(), eiremain();
int ecmpm(), edivm(), emulm(), eisneg(), eisinf();
void emovi(), emovo(), emovz(), ecleaz(), eadd1();
void etodec(), todec(), dectoe();
int eisnan(), eiisnan();



void einit()
{
}

/*
; Clear out entire external format number.
;
; unsigned short x[];
; eclear( x );
*/

void eclear( x )
register unsigned short *x;
{
register int i;

for( i=0; i<NE; i++ )
	*x++ = 0;
}



/* Move external format number from a to b.
 *
 * emov( a, b );
 */

void emov( a, b )
register unsigned short *a, *b;
{
register int i;

for( i=0; i<NE; i++ )
	*b++ = *a++;
}


/*
;	Absolute value of external format number
;
;	short x[NE];
;	eabs( x );
*/

void eabs(x)
unsigned short x[];	/* x is the memory address of a short */
{

x[NE-1] &= 0x7fff; /* sign is top bit of last word of external format */
}




/*
;	Negate external format number
;
;	unsigned short x[NE];
;	eneg( x );
*/

void eneg(x)
unsigned short x[];
{

#ifdef NANS
if( eisnan(x) )
	return;
#endif
x[NE-1] ^= 0x8000; /* Toggle the sign bit */
}



/* Return 1 if external format number is negative,
 * else return zero.
 */
int eisneg(x)
unsigned short x[];
{

#ifdef NANS
if( eisnan(x) )
	return( 0 );
#endif
if( x[NE-1] & 0x8000 )
	return( 1 );
else
	return( 0 );
}


/* Return 1 if external format number has maximum possible exponent,
 * else return zero.
 */
int eisinf(x)
unsigned short x[];
{

if( (x[NE-1] & 0x7fff) == 0x7fff )
	{
#ifdef NANS
	if( eisnan(x) )
		return( 0 );
#endif
	return( 1 );
	}
else
	return( 0 );
}

/* Check if e-type number is not a number.
 */
int eisnan(x)
unsigned short x[];
{

#ifdef NANS
int i;
/* NaN has maximum exponent */
if( (x[NE-1] & 0x7fff) != 0x7fff )
	return (0);
/* ... and non-zero significand field. */
for( i=0; i<NE-1; i++ )
	{
	if( *x++ != 0 )
		return (1);
	}
#endif
return (0);
}

/*
; Fill entire number, including exponent and significand, with
; largest possible number.  These programs implement a saturation
; value that is an ordinary, legal number.  A special value
; "infinity" may also be implemented; this would require tests
; for that value and implementation of special rules for arithmetic
; operations involving inifinity.
*/

void einfin(x)
register unsigned short *x;
{
register int i;

#ifdef INFINITY
for( i=0; i<NE-1; i++ )
	*x++ = 0;
*x |= 32767;
#else
for( i=0; i<NE-1; i++ )
	*x++ = 0xffff;
*x |= 32766;
if( rndprc < NBITS )
	{
	if (rndprc == 113)
		{
		*(x - 9) = 0;
		*(x - 8) = 0;
		}
	if( rndprc == 64 )
		{
		*(x-5) = 0;
		}
	if( rndprc == 53 )
		{
		*(x-4) = 0xf800;
		}
	else
		{
		*(x-4) = 0;
		*(x-3) = 0;
		*(x-2) = 0xff00;
		}
	}
#endif
}



/* Move in external format number,
 * converting it to internal format.
 */
void emovi( a, b )
unsigned short *a, *b;
{
register unsigned short *p, *q;
int i;

q = b;
p = a + (NE-1);	/* point to last word of external number */
/* get the sign bit */
if( *p & 0x8000 )
	*q++ = 0xffff;
else
	*q++ = 0;
/* get the exponent */
*q = *p--;
*q++ &= 0x7fff;	/* delete the sign bit */
#ifdef INFINITY
if( (*(q-1) & 0x7fff) == 0x7fff )
	{
#ifdef NANS
	if( eisnan(a) )
		{
		*q++ = 0;
		for( i=3; i<NI; i++ )
			*q++ = *p--;
		return;
		}
#endif
	for( i=2; i<NI; i++ )
		*q++ = 0;
	return;
	}
#endif
/* clear high guard word */
*q++ = 0;
/* move in the significand */
for( i=0; i<NE-1; i++ )
	*q++ = *p--;
/* clear low guard word */
*q = 0;
}


/* Move internal format number out,
 * converting it to external format.
 */
void emovo( a, b )
unsigned short *a, *b;
{
register unsigned short *p, *q;
unsigned short i;