#ifndef _CEPHES_EMATH_H
#define _CEPHES_EMATH_H
/* This file is extracted from S L Moshier's ioldoubl.c,
* modified for use in MinGW
*
* Extended precision arithmetic functions for long double I/O.
* This program has been placed in the public domain.
*/
/*
* Revision history:
*
* 5 Jan 84 PDP-11 assembly language version
* 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.
*
* 6 Oct 02 Modified for MinGW by inlining utility routines,
* removing global variables, and splitting out strtold
* from _IO_ldtoa and _IO_ldtostr.
*
* Danny Smith <dannysmith@users.sourceforge.net>
*
*/
/* 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
*
* __asctoe64( string, &d ) ASCII string to long double
* __asctoeg( string, e, prec ) ASCII string to specified precision
* __e64toe( &d, e ) IEEE long double precision to e type
* __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
* __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).
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <errno.h>
#include <math.h>
#include <locale.h>
#include <ctype.h>
#define alloca __builtin_alloca
/* Don't build non-ANSI _IO_ldtoa. It is not thread safe. */
#ifndef USE_LDTOA
#define USE_LDTOA 0
#endif
/* Number of 16 bit words in external x type format */
#define NE 6
/* 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)
#define mtherr(x,y)
extern long double strtold (const char * __restrict__ s, char ** __restrict__ se);
extern int __asctoe64(const char * __restrict__ ss,
short unsigned int * __restrict__ y);
extern void __emul(const short unsigned int * a,
const short unsigned int * b,
short unsigned int * c);
extern int __ecmp(const short unsigned int * __restrict__ a,
const short unsigned int * __restrict__ b);
extern int __enormlz(short unsigned int *x);
extern int __eshift(short unsigned int *x, int sc);
extern void __eaddm(const short unsigned int * __restrict__ x,
short unsigned int * __restrict__ y);
extern void __esubm(const short unsigned int * __restrict__ x,
short unsigned int * __restrict__ y);
extern void __emdnorm(short unsigned int *s, int lost, int subflg,
long int exp, int rcntrl, const int rndprc);
extern void __toe64(short unsigned int * __restrict__ a,
short unsigned int * __restrict__ b);
extern int __edivm(short unsigned int * __restrict__ den,
short unsigned int * __restrict__ num);
extern int __emulm(const short unsigned int * __restrict__ a,
short unsigned int * __restrict__ b);
extern void __emovi(const short unsigned int * __restrict__ a,
short unsigned int * __restrict__ b);
extern void __emovo(const short unsigned int * __restrict__ a,
short unsigned int * __restrict__ b);
#if USE_LDTOA
extern char * _IO_ldtoa(long double, int, int, int *, int *, char **);
extern void _IO_ldtostr(long double *x, char *string, int ndigs,
int flags, char fmt);
extern void __eiremain(short unsigned int * __restrict__ den,
short unsigned int *__restrict__ num,
short unsigned int *__restrict__ equot);
extern void __efloor(short unsigned int *x, short unsigned int *y);
extern void __eadd1(const short unsigned int * __restrict__ a,
const short unsigned int * __restrict__ b,
short unsigned int * __restrict__ c,
int subflg);
extern void __esub(const short unsigned int *a, const short unsigned int *b,
short unsigned int *c);
extern void __ediv(const short unsigned int *a, const short unsigned int *b,
short unsigned int *c);
extern void __e64toe(short unsigned int *pe, short unsigned int *y);
#endif
static __inline__ int __eisneg(const short unsigned int *x);
static __inline__ int __eisinf(const short unsigned int *x);
static __inline__ int __eisnan(const short unsigned int *x);
static __inline__ int __eiszero(const short unsigned int *a);
static __inline__ void __emovz(register const short unsigned int * __restrict__ a,
register short unsigned int * __restrict__ b);
static __inline__ void __eclear(register short unsigned int *x);
static __inline__ void __ecleaz(register short unsigned int *xi);
static __inline__ void __ecleazs(register short unsigned int *xi);
static __inline__ int __eiisinf(const short unsigned int *x);
static __inline__ int __eiisnan(const short unsigned int *x);
static __inline__ int __eiiszero(const short unsigned int *x);
static __inline__ void __enan_64(short unsigned int *nan);
static __inline__ void __enan_NBITS (short unsigned int *nan);
static __inline__ void __enan_NI16 (short unsigned int *nan);
static __inline__ void __einfin(register short unsigned int *x);
static __inline__ void __eneg(short unsigned int *x);
static __inline__ void __eshup1(register short unsigned int *x);
static __inline__ void __eshup8(register short unsigned int *x);
static __inline__ void __eshup6(register short unsigned int *x);
static __inline__ void __eshdn1(register short unsigned int *x);
static __inline__ void __eshdn8(register short unsigned int *x);
static __inline__ void __eshdn6(register short unsigned int *x);
/* Intel IEEE, low order words come first:
*/
#define IBMPC 1
/* Define 1 for ANSI C atan2() function
* See atan.c and clog.c.
*/
#define ANSIC 1
/*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.
*
* #define XPD
*/
#define XPD 0,
/* #define XPD */
#define NANS
/* NaN's require infinity support. */
#ifdef NANS
#ifndef INFINITY
#define INFINITY
#endif
#endif
/* This handles 64-bit long ints. */
#define LONGBITS (8 * sizeof(long))
#define NTEN 12
#define MAXP 4096
/*
; Clear out entire external format number.
;
; unsigned short x[];
; eclear( x );
*/
static __inline__ void __eclear(register short unsigned int *x)
{
memset(x, 0, NE * sizeof(unsigned short));
}
/* Move external format number from a to b.
*
* emov( a, b );
*/
static __inline__ void __emov(register const short unsigned int * __restrict__ a,
register short unsigned int * __restrict__ b)
{
memcpy(b, a, NE * sizeof(unsigned short));
}
/*
; Negate external format number
;
; unsigned short x[NE];
; eneg( x );
*/
static __inline__ void __eneg(short unsigned int *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.
*/
static __inline__ int __eisneg(const short unsigned int *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.
*/
static __inline__ int __eisinf(const short unsigned int *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.
*/
static __inline__ int __eisnan(const short unsigned int *x)
{
#ifdef NANS
int i;
/* NaN has maximum __exponent */
if( (x[NE-1] & 0x7fff) == 0x7fff )
/* ... 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.
*/
static __inline__ void __einfin(register short unsigned int *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;
*(x-5) = 0;
#endif
}
/* Clear out internal format number.
*/
static __inline__ void __ecleaz(register short unsigned int *xi)
{
memset(xi, 0, NI * sizeof(unsigned short));
}
/* same, but don't touch the sign. */
static __inline__ void __ecleazs(register short unsigned int *xi)
{
++xi;
memset(xi, 0, (NI-1) * sizeof(unsigned short));
}
/* Move internal format number from a to b.
*/
static __inline__ void __emovz(register const short unsigned int * __restrict__ a,
register short unsigned int * __restrict__ b)
{
memcpy(b, a, (NI-1) * sizeof(unsigned short));
b[NI-1]=0;
}
/* Return nonzero if internal format number is a NaN.
*/
static __inline__ int __eiisnan (const short unsigned int *x)
{
int i;
if( (x[E] & 0x7fff) == 0x7fff )
{
for( i=M+1; i<NI; i++ )
{
if( x[i] != 0 )
return(1);
}
}
return(0);
}
/* Return nonzero if external format number is zero. */
static __inline__ int
__eiszero(const short unsigned int * a)
{
if (*((long double*) a) == 0)
return (1);
return (0);
}
/* Return nonzero if internal format number is zero. */
static __inline__ int
__eiiszero(const short unsigned int * ai)
{
int i;
/* skip the sign word */
for( i=1; i<NI-1; i++ )
{
if( ai[i] != 0 )
return (0);
}
return (1);
}
/* Return nonzero if internal format number is infinite. */
static __inline__ int
__eiisinf (const unsigned short *x)
{
#ifdef NANS
if (__eiisnan (x))
return (0);
#endif
if ((x[E] & 0x7fff) == 0x7fff)
return (1);
return (0);
}
/*
; Compare significands of numbers in internal format.
; Guard words are included in the comparison.
;
; unsigned short a[NI], b[NI];
; cmpm( a, b );
;
; for the significands:
; returns +1 if a > b
; 0 if a == b
; -1 if a < b
*/
static __inline__ int __ecmpm(register const short unsigned int * __restrict__ a,
register const short unsigned int * __restrict__ b)
{
int i;
a += M; /* skip up to significand area */
b += M;
for( i=M; i<NI; i++ )
{
if( *a++ != *b++ )
goto difrnt;
}
return(0);
difrnt:
if( *(--a) > *(--b) )
return(1);
else
return(-1);
}
/*
; Shift significand down by 1 bit
*/
static __inline__ void __eshdn1(register short unsigned int *x)
{
register unsigned short bits;
int i;
x += M; /* point to significand area */
bits = 0;
for( i=M; i<NI; i++ )
{
if( *x & 1 )
bits |= 1;
*x >>= 1;
if( bits & 2 )
*x |= 0x8000;
bits <<= 1;
++x;
}
}
/*
; Shift significand up by 1 bit
*/
static __inline__ void __eshup1(register short unsigned int *x)
{
register unsigned short bits;
int i;
x += NI-1;
bits = 0;
for( i=M; i<NI; i++ )
{
if( *x & 0x8000 )
bits |= 1;
*x <<= 1;
if( bits & 2 )
*x |= 1;
bits <<= 1;
--x;
}
}
/*
; Shift significand down by 8 bits
*/
static __inline__ void __eshdn8(register short unsigned int *x)
{
register unsigned short newbyt, oldbyt;
int i;
x += M;
oldbyt = 0;
for( i=M; i<NI; i++ )
{
newbyt = *x << 8;
*x >>= 8;
*x |= oldbyt;
oldbyt = newbyt;
++x;
}
}
/*
; Shift significand up by 8 bits
*/
static __inline__ void __eshup8(register short unsigned int *x)
{
int i;
register unsigned short newbyt, oldbyt;
x += NI-1;
oldbyt = 0;
for( i=M; i<NI; i++ )
{
newbyt = *x >> 8;
*x <<= 8;
*x |= oldbyt;
oldbyt = newbyt;
--x;
}
}
/*
; Shift significand up by 16 bits
*/
static __inline__ void __eshup6(register short unsigned int *x)
{
int i;
register unsigned short *p;
p = x + M;
x += M + 1;
for( i=M; i<NI-1; i++ )
*p++ = *x++;
*p = 0;
}
/*
; Shift significand down by 16 bits
*/
static __inline__ void __eshdn6(register short unsigned int *x)
{
int i;
register unsigned short *p;
x += NI-1;
p = x + 1;
for( i=M; i<NI-1; i++ )
*(--p) = *(--x);
*(--p) = 0;
}
/*
; Add significands
; x + y replaces y
*/
static __inline__ void __enan_64(unsigned short* nan)
{
int i;
for( i=0; i<3; i++ )
*nan++ = 0;
*nan++ = 0xc000;
*nan++ = 0x7fff;
*nan = 0;
return;
}
static __inline__ void __enan_NBITS(unsigned short* nan)
{
int i;
for( i=0; i<NE-2; i++ )
*nan++ = 0;
*nan++ = 0xc000;
*nan = 0x7fff;
return;
}
static __inline__ void __enan_NI16(unsigned short* nan)
{
int i;
*nan++ = 0;
*nan++ = 0x7fff;
*nan++ = 0;
*nan++ = 0xc000;
for( i=4; i<NI; i++ )
*nan++ = 0;
return;
}
#endif /* _CEPHES_EMATH_H */