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/* real.c - implementation of REAL_ARITHMETIC, REAL_VALUE_ATOF,
and support for XFmode IEEE extended real floating point arithmetic.
Copyright (C) 1993, 1994 Free Software Foundation, Inc.
Contributed by Stephen L. Moshier (moshier@world.std.com).
This file is part of GNU CC.
GNU CC is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.
GNU CC 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with GNU CC; see the file COPYING. If not, write to
the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. */
#include <stdio.h>
#include <errno.h>
#include "config.h"
#include "tree.h"
#ifndef errno
extern int errno;
#endif
/* To enable support of XFmode extended real floating point, define
LONG_DOUBLE_TYPE_SIZE 96 in the tm.h file (m68k.h or i386.h).
To support cross compilation between IEEE, VAX and IBM floating
point formats, define REAL_ARITHMETIC in the tm.h file.
In either case the machine files (tm.h) must not contain any code
that tries to use host floating point arithmetic to convert
REAL_VALUE_TYPEs from `double' to `float', pass them to fprintf,
etc. In cross-compile situations a REAL_VALUE_TYPE may not
be intelligible to the host computer's native arithmetic.
The emulator defaults to the host's floating point format so that
its decimal conversion functions can be used if desired (see
real.h).
The first part of this file interfaces gcc to ieee.c, which is a
floating point arithmetic suite that was not written with gcc in
mind. The interface is followed by ieee.c itself and related
items. Avoid changing ieee.c unless you have suitable test
programs available. A special version of the PARANOIA floating
point arithmetic tester, modified for this purpose, can be found
on usc.edu : /pub/C-numanal/ieeetest.zoo. Some tutorial
information on ieee.c is given in my book: S. L. Moshier,
_Methods and Programs for Mathematical Functions_, Prentice-Hall
or Simon & Schuster Int'l, 1989. A library of XFmode elementary
transcendental functions can be obtained by ftp from
research.att.com: netlib/cephes/ldouble.shar.Z */
/* Type of computer arithmetic.
Only one of DEC, IBM, MIEEE, IBMPC, or UNK should get defined.
`MIEEE' refers generically to big-endian IEEE floating-point data
structure. This definition should work in SFmode `float' type and
DFmode `double' type on virtually all big-endian IEEE machines.
If LONG_DOUBLE_TYPE_SIZE has been defined to be 96, then MIEEE
also invokes the particular XFmode (`long double' type) data
structure used by the Motorola 680x0 series processors.
`IBMPC' refers generally to little-endian IEEE machines. In this
case, if LONG_DOUBLE_TYPE_SIZE has been defined to be 96, then
IBMPC also invokes the particular XFmode `long double' data
structure used by the Intel 80x86 series processors.
`DEC' refers specifically to the Digital Equipment Corp PDP-11
and VAX floating point data structure. This model currently
supports no type wider than DFmode.
`IBM' refers specifically to the IBM System/370 and compatible
floating point data structure. This model currently supports
no type wider than DFmode. The IBM conversions were contributed by
frank@atom.ansto.gov.au (Frank Crawford).
If LONG_DOUBLE_TYPE_SIZE = 64 (the default, unless tm.h defines it)
then `long double' and `double' are both implemented, but they
both mean DFmode. In this case, the software floating-point
support available here is activated by writing
#define REAL_ARITHMETIC
in tm.h.
The case LONG_DOUBLE_TYPE_SIZE = 128 activates TFmode support
and may deactivate XFmode since `long double' is used to refer
to both modes.
The macros FLOAT_WORDS_BIG_ENDIAN, HOST_FLOAT_WORDS_BIG_ENDIAN,
contributed by Richard Earnshaw <Richard.Earnshaw@cl.cam.ac.uk>,
separate the floating point unit's endian-ness from that of
the integer addressing. This permits one to define a big-endian
FPU on a little-endian machine (e.g., ARM). An extension to
BYTES_BIG_ENDIAN may be required for some machines in the future.
These optional macros may be defined in tm.h. In real.h, they
default to WORDS_BIG_ENDIAN, etc., so there is no need to define
them for any normal host or target machine on which the floats
and the integers have the same endian-ness. */
/* The following converts gcc macros into the ones used by this file. */
/* REAL_ARITHMETIC defined means that macros in real.h are
defined to call emulator functions. */
#ifdef REAL_ARITHMETIC
#if TARGET_FLOAT_FORMAT == VAX_FLOAT_FORMAT
/* PDP-11, Pro350, VAX: */
#define DEC 1
#else /* it's not VAX */
#if TARGET_FLOAT_FORMAT == IBM_FLOAT_FORMAT
/* IBM System/370 style */
#define IBM 1
#else /* it's also not an IBM */
#if TARGET_FLOAT_FORMAT == IEEE_FLOAT_FORMAT
#if FLOAT_WORDS_BIG_ENDIAN
/* Motorola IEEE, high order words come first (Sun workstation): */
#define MIEEE 1
#else /* not big-endian */
/* Intel IEEE, low order words come first:
*/
#define IBMPC 1
#endif /* big-endian */
#else /* it's not IEEE either */
/* UNKnown arithmetic. We don't support this and can't go on. */
unknown arithmetic type
#define UNK 1
#endif /* not IEEE */
#endif /* not IBM */
#endif /* not VAX */
#else
/* REAL_ARITHMETIC not defined means that the *host's* data
structure will be used. It may differ by endian-ness from the
target machine's structure and will get its ends swapped
accordingly (but not here). Probably only the decimal <-> binary
functions in this file will actually be used in this case. */
#if HOST_FLOAT_FORMAT == VAX_FLOAT_FORMAT
#define DEC 1
#else /* it's not VAX */
#if HOST_FLOAT_FORMAT == IBM_FLOAT_FORMAT
/* IBM System/370 style */
#define IBM 1
#else /* it's also not an IBM */
#if HOST_FLOAT_FORMAT == IEEE_FLOAT_FORMAT
#if HOST_FLOAT_WORDS_BIG_ENDIAN
#define MIEEE 1
#else /* not big-endian */
#define IBMPC 1
#endif /* big-endian */
#else /* it's not IEEE either */
unknown arithmetic type
#define UNK 1
#endif /* not IEEE */
#endif /* not IBM */
#endif /* not VAX */
#endif /* REAL_ARITHMETIC not defined */
/* Define INFINITY for support of infinity.
Define NANS for support of Not-a-Number's (NaN's). */
#if !defined(DEC) && !defined(IBM)
#define INFINITY
#define NANS
#endif
/* Support of NaNs requires support of infinity. */
#ifdef NANS
#ifndef INFINITY
#define INFINITY
#endif
#endif
/* Find a host integer type that is at least 16 bits wide,
and another type at least twice whatever that size is. */
#if HOST_BITS_PER_CHAR >= 16
#define EMUSHORT char
#define EMUSHORT_SIZE HOST_BITS_PER_CHAR
#define EMULONG_SIZE (2 * HOST_BITS_PER_CHAR)
#else
#if HOST_BITS_PER_SHORT >= 16
#define EMUSHORT short
#define EMUSHORT_SIZE HOST_BITS_PER_SHORT
#define EMULONG_SIZE (2 * HOST_BITS_PER_SHORT)
#else
#if HOST_BITS_PER_INT >= 16
#define EMUSHORT int
#define EMUSHORT_SIZE HOST_BITS_PER_INT
#define EMULONG_SIZE (2 * HOST_BITS_PER_INT)
#else
#if HOST_BITS_PER_LONG >= 16
#define EMUSHORT long
#define EMUSHORT_SIZE HOST_BITS_PER_LONG
#define EMULONG_SIZE (2 * HOST_BITS_PER_LONG)
#else
/* You will have to modify this program to have a smaller unit size. */
#define EMU_NON_COMPILE
#endif
#endif
#endif
#endif
#if HOST_BITS_PER_SHORT >= EMULONG_SIZE
#define EMULONG short
#else
#if HOST_BITS_PER_INT >= EMULONG_SIZE
#define EMULONG int
#else
#if HOST_BITS_PER_LONG >= EMULONG_SIZE
#define EMULONG long
#else
#if HOST_BITS_PER_LONG_LONG >= EMULONG_SIZE
#define EMULONG long long int
#else
/* You will have to modify this program to have a smaller unit size. */
#define EMU_NON_COMPILE
#endif
#endif
#endif
#endif
/* The host interface doesn't work if no 16-bit size exists. */
#if EMUSHORT_SIZE != 16
#define EMU_NON_COMPILE
#endif
/* OK to continue compilation. */
#ifndef EMU_NON_COMPILE
/* Construct macros to translate between REAL_VALUE_TYPE and e type.
In GET_REAL and PUT_REAL, r and e are pointers.
A REAL_VALUE_TYPE is guaranteed to occupy contiguous locations
in memory, with no holes. */
#if LONG_DOUBLE_TYPE_SIZE == 96
/* Number of 16 bit words in external e type format */
#define NE 6
#define MAXDECEXP 4932
#define MINDECEXP -4956
#define GET_REAL(r,e) bcopy (r, e, 2*NE)
#define PUT_REAL(e,r) bcopy (e, r, 2*NE)
#else /* no XFmode */
#if LONG_DOUBLE_TYPE_SIZE == 128
#define NE 10
#define MAXDECEXP 4932
#define MINDECEXP -4977
#define GET_REAL(r,e) bcopy (r, e, 2*NE)
#define PUT_REAL(e,r) bcopy (e, r, 2*NE)
#else
#define NE 6
#define MAXDECEXP 4932
#define MINDECEXP -4956
#ifdef REAL_ARITHMETIC
/* Emulator uses target format internally
but host stores it in host endian-ness. */
#if HOST_FLOAT_WORDS_BIG_ENDIAN == FLOAT_WORDS_BIG_ENDIAN
#define GET_REAL(r,e) e53toe ((unsigned EMUSHORT*) (r), (e))
#define PUT_REAL(e,r) etoe53 ((e), (unsigned EMUSHORT *) (r))
#else /* endian-ness differs */
/* emulator uses target endian-ness internally */
#define GET_REAL(r,e) \
do { unsigned EMUSHORT w[4]; \
w[3] = ((EMUSHORT *) r)[0]; \
w[2] = ((EMUSHORT *) r)[1]; \
w[1] = ((EMUSHORT *) r)[2]; \
w[0] = ((EMUSHORT *) r)[3]; \
e53toe (w, (e)); } while (0)
#define PUT_REAL(e,r) \
do { unsigned EMUSHORT w[4]; \
etoe53 ((e), w); \
*((EMUSHORT *) r) = w[3]; \
*((EMUSHORT *) r + 1) = w[2]; \
*((EMUSHORT *) r + 2) = w[1]; \
*((EMUSHORT *) r + 3) = w[0]; } while (0)
#endif /* endian-ness differs */
#else /* not REAL_ARITHMETIC */
/* emulator uses host format */
#define GET_REAL(r,e) e53toe ((unsigned EMUSHORT *) (r), (e))
#define PUT_REAL(e,r) etoe53 ((e), (unsigned EMUSHORT *) (r))
#endif /* not REAL_ARITHMETIC */
#endif /* not TFmode */
#endif /* no XFmode */
/* 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)
extern int extra_warnings;
extern unsigned EMUSHORT ezero[], ehalf[], eone[], etwo[];
extern unsigned EMUSHORT elog2[], esqrt2[];
static void endian PROTO((unsigned EMUSHORT *, long *,
enum machine_mode));
static void eclear PROTO((unsigned EMUSHORT *));
static void emov PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void eabs PROTO((unsigned EMUSHORT *));
static void eneg PROTO((unsigned EMUSHORT *));
static int eisneg PROTO((unsigned EMUSHORT *));
static int eisinf PROTO((unsigned EMUSHORT *));
static int eisnan PROTO((unsigned EMUSHORT *));
static void einfin PROTO((unsigned EMUSHORT *));
static void enan PROTO((unsigned EMUSHORT *, int));
static void emovi PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void emovo PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void ecleaz PROTO((unsigned EMUSHORT *));
static void ecleazs PROTO((unsigned EMUSHORT *));
static void emovz PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void einan PROTO((unsigned EMUSHORT *));
static int eiisnan PROTO((unsigned EMUSHORT *));
static int eiisneg PROTO((unsigned EMUSHORT *));
static void eiinfin PROTO((unsigned EMUSHORT *));
static int eiisinf PROTO((unsigned EMUSHORT *));
static int ecmpm PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void eshdn1 PROTO((unsigned EMUSHORT *));
static void eshup1 PROTO((unsigned EMUSHORT *));
static void eshdn8 PROTO((unsigned EMUSHORT *));
static void eshup8 PROTO((unsigned EMUSHORT *));
static void eshup6 PROTO((unsigned EMUSHORT *));
static void eshdn6 PROTO((unsigned EMUSHORT *));
static void eaddm PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void esubm PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void m16m PROTO((unsigned int, unsigned short *,
unsigned short *));
static int edivm PROTO((unsigned short *, unsigned short *));
static int emulm PROTO((unsigned short *, unsigned short *));
static void emdnorm PROTO((unsigned EMUSHORT *, int, int, EMULONG, int));
static void esub PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *,
unsigned EMUSHORT *));
static void eadd PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *,
unsigned EMUSHORT *));
static void eadd1 PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *,
unsigned EMUSHORT *));
static void ediv PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *,
unsigned EMUSHORT *));
static void emul PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *,
unsigned EMUSHORT *));
static void e53toe PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void e64toe PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void e113toe PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void e24toe PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void etoe113 PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void toe113 PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void etoe64 PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void toe64 PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void etoe53 PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void toe53 PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void etoe24 PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void toe24 PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static int ecmp PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void eround PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void ltoe PROTO((HOST_WIDE_INT *, unsigned EMUSHORT *));
static void ultoe PROTO((unsigned HOST_WIDE_INT *, unsigned EMUSHORT *));
static void eifrac PROTO((unsigned EMUSHORT *, HOST_WIDE_INT *,
unsigned EMUSHORT *));
static void euifrac PROTO((unsigned EMUSHORT *, unsigned HOST_WIDE_INT *,
unsigned EMUSHORT *));
static int eshift PROTO((unsigned EMUSHORT *, int));
static int enormlz PROTO((unsigned EMUSHORT *));
static void e24toasc PROTO((unsigned EMUSHORT *, char *, int));
static void e53toasc PROTO((unsigned EMUSHORT *, char *, int));
static void e64toasc PROTO((unsigned EMUSHORT *, char *, int));
static void e113toasc PROTO((unsigned EMUSHORT *, char *, int));
static void etoasc PROTO((unsigned EMUSHORT *, char *, int));
static void asctoe24 PROTO((char *, unsigned EMUSHORT *));
static void asctoe53 PROTO((char *, unsigned EMUSHORT *));
static void asctoe64 PROTO((char *, unsigned EMUSHORT *));
static void asctoe113 PROTO((char *, unsigned EMUSHORT *));
static void asctoe PROTO((char *, unsigned EMUSHORT *));
static void asctoeg PROTO((char *, unsigned EMUSHORT *, int));
static void efloor PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void efrexp PROTO((unsigned EMUSHORT *, int *,
unsigned EMUSHORT *));
static void eldexp PROTO((unsigned EMUSHORT *, int, unsigned EMUSHORT *));
static void eremain PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *,
unsigned EMUSHORT *));
static void eiremain PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void mtherr PROTO((char *, int));
static void dectoe PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void etodec PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void todec PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void ibmtoe PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *,
enum machine_mode));
static void etoibm PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *,
enum machine_mode));
static void toibm PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *,
enum machine_mode));
static void make_nan PROTO((unsigned EMUSHORT *, int, enum machine_mode));
static void uditoe PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void ditoe PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void etoudi PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void etodi PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
static void esqrt PROTO((unsigned EMUSHORT *, unsigned EMUSHORT *));
/* Copy 32-bit numbers obtained from array containing 16-bit numbers,
swapping ends if required, into output array of longs. The
result is normally passed to fprintf by the ASM_OUTPUT_ macros. */
static void
endian (e, x, mode)
unsigned EMUSHORT e[];
long x[];
enum machine_mode mode;
{
unsigned long th, t;
#if FLOAT_WORDS_BIG_ENDIAN
switch (mode)
{
case TFmode:
/* Swap halfwords in the fourth long. */
th = (unsigned long) e[6] & 0xffff;
t = (unsigned long) e[7] & 0xffff;
t |= th << 16;
x[3] = (long) t;
case XFmode:
/* Swap halfwords in the third long. */
th = (unsigned long) e[4] & 0xffff;
t = (unsigned long) e[5] & 0xffff;
t |= th << 16;
x[2] = (long) t;
/* fall into the double case */
case DFmode:
/* swap halfwords in the second word */
th = (unsigned long) e[2] & 0xffff;
t = (unsigned long) e[3] & 0xffff;
t |= th << 16;
x[1] = (long) t;
/* fall into the float case */
case HFmode:
case SFmode:
/* swap halfwords in the first word */
th = (unsigned long) e[0] & 0xffff;
t = (unsigned long) e[1] & 0xffff;
t |= th << 16;
x[0] = t;
break;
default:
abort ();
}
#else
/* Pack the output array without swapping. */
switch (mode)
{
case TFmode:
/* Pack the fourth long. */
th = (unsigned long) e[7] & 0xffff;
t = (unsigned long) e[6] & 0xffff;
t |= th << 16;
x[3] = (long) t;
case XFmode:
/* Pack the third long.
Each element of the input REAL_VALUE_TYPE array has 16 useful bits
in it. */
th = (unsigned long) e[5] & 0xffff;
t = (unsigned long) e[4] & 0xffff;
t |= th << 16;
x[2] = (long) t;
/* fall into the double case */
case DFmode:
/* pack the second long */
th = (unsigned long) e[3] & 0xffff;
t = (unsigned long) e[2] & 0xffff;
t |= th << 16;
x[1] = (long) t;
/* fall into the float case */
case HFmode:
case SFmode:
/* pack the first long */
th = (unsigned long) e[1] & 0xffff;
t = (unsigned long) e[0] & 0xffff;
t |= th << 16;
x[0] = t;
break;
default:
abort ();
}
#endif
}
/* This is the implementation of the REAL_ARITHMETIC macro. */
void
earith (value, icode, r1, r2)
REAL_VALUE_TYPE *value;
int icode;
REAL_VALUE_TYPE *r1;
REAL_VALUE_TYPE *r2;
{
unsigned EMUSHORT d1[NE], d2[NE], v[NE];
enum tree_code code;
GET_REAL (r1, d1);
GET_REAL (r2, d2);
#ifdef NANS
/* Return NaN input back to the caller. */
if (eisnan (d1))
{
PUT_REAL (d1, value);
return;
}
if (eisnan (d2))
{
PUT_REAL (d2, value);
return;
}
#endif
code = (enum tree_code) icode;
switch (code)
{
case PLUS_EXPR:
eadd (d2, d1, v);
break;
case MINUS_EXPR:
esub (d2, d1, v); /* d1 - d2 */
break;
case MULT_EXPR:
emul (d2, d1, v);
break;
case RDIV_EXPR:
#ifndef REAL_INFINITY
if (ecmp (d2, ezero) == 0)
{
#ifdef NANS
enan (v, eisneg (d1) ^ eisneg (d2));
break;
#else
abort ();
#endif
}
#endif
ediv (d2, d1, v); /* d1/d2 */
break;
case MIN_EXPR: /* min (d1,d2) */
if (ecmp (d1, d2) < 0)
emov (d1, v);
else
emov (d2, v);
break;
case MAX_EXPR: /* max (d1,d2) */
if (ecmp (d1, d2) > 0)
emov (d1, v);
else
emov (d2, v);
break;
default:
emov (ezero, v);
break;
}
PUT_REAL (v, value);
}
/* Truncate REAL_VALUE_TYPE toward zero to signed HOST_WIDE_INT.
implements REAL_VALUE_RNDZINT (x) (etrunci (x)). */
REAL_VALUE_TYPE
etrunci (x)
REAL_VALUE_TYPE x;
{
unsigned EMUSHORT f[NE], g[NE];
REAL_VALUE_TYPE r;
HOST_WIDE_INT l;
GET_REAL (&x, g);
#ifdef NANS
if (eisnan (g))
return (x);
#endif
eifrac (g, &l, f);
ltoe (&l, g);
PUT_REAL (g, &r);
return (r);
}
/* Truncate REAL_VALUE_TYPE toward zero to unsigned HOST_WIDE_INT;
implements REAL_VALUE_UNSIGNED_RNDZINT (x) (etruncui (x)). */
REAL_VALUE_TYPE
etruncui (x)
REAL_VALUE_TYPE x;
{
unsigned EMUSHORT f[NE], g[NE];
REAL_VALUE_TYPE r;
unsigned HOST_WIDE_INT l;
GET_REAL (&x, g);
#ifdef NANS
if (eisnan (g))
return (x);
#endif
euifrac (g, &l, f);
ultoe (&l, g);
PUT_REAL (g, &r);
return (r);
}
/* This is the REAL_VALUE_ATOF function. It converts a decimal string to
binary, rounding off as indicated by the machine_mode argument. Then it
promotes the rounded value to REAL_VALUE_TYPE. */
REAL_VALUE_TYPE
ereal_atof (s, t)
char *s;
enum machine_mode t;
{
unsigned EMUSHORT tem[NE], e[NE];
REAL_VALUE_TYPE r;
switch (t)
{
case HFmode:
case SFmode:
asctoe24 (s, tem);
e24toe (tem, e);
break;
case DFmode:
asctoe53 (s, tem);
e53toe (tem, e);
break;
case XFmode:
asctoe64 (s, tem);
e64toe (tem, e);
break;
case TFmode:
asctoe113 (s, tem);
e113toe (tem, e);
break;
default:
asctoe (s, e);
}
PUT_REAL (e, &r);
return (r);
}
/* Expansion of REAL_NEGATE. */
REAL_VALUE_TYPE
ereal_negate (x)
REAL_VALUE_TYPE x;
{
unsigned EMUSHORT e[NE];
REAL_VALUE_TYPE r;
GET_REAL (&x, e);
eneg (e);
PUT_REAL (e, &r);
return (r);
}
/* Round real toward zero to HOST_WIDE_INT;
implements REAL_VALUE_FIX (x). */
HOST_WIDE_INT
efixi (x)
REAL_VALUE_TYPE x;
{
unsigned EMUSHORT f[NE], g[NE];
HOST_WIDE_INT l;
GET_REAL (&x, f);
#ifdef NANS
if (eisnan (f))
{
warning ("conversion from NaN to int");
return (-1);
}
#endif
eifrac (f, &l, g);
return l;
}
/* Round real toward zero to unsigned HOST_WIDE_INT
implements REAL_VALUE_UNSIGNED_FIX (x).
Negative input returns zero. */
unsigned HOST_WIDE_INT
efixui (x)
REAL_VALUE_TYPE x;
{
unsigned EMUSHORT f[NE], g[NE];
unsigned HOST_WIDE_INT l;
GET_REAL (&x, f);
#ifdef NANS
if (eisnan (f))
{
warning ("conversion from NaN to unsigned int");
return (-1);
}
#endif
euifrac (f, &l, g);
return l;
}
/* REAL_VALUE_FROM_INT macro. */
void
ereal_from_int (d, i, j)
REAL_VALUE_TYPE *d;
HOST_WIDE_INT i, j;
{
unsigned EMUSHORT df[NE], dg[NE];
HOST_WIDE_INT low, high;
int sign;
sign = 0;
low = i;
if ((high = j) < 0)
{
sign = 1;
/* complement and add 1 */
high = ~high;
if (low)
low = -low;
else
high += 1;
}
eldexp (eone, HOST_BITS_PER_WIDE_INT, df);
ultoe ((unsigned HOST_WIDE_INT *) &high, dg);
emul (dg, df, dg);
ultoe ((unsigned HOST_WIDE_INT *) &low, df);
eadd (df, dg, dg);
if (sign)
eneg (dg);
PUT_REAL (dg, d);
}
/* REAL_VALUE_FROM_UNSIGNED_INT macro. */
void
ereal_from_uint (d, i, j)
REAL_VALUE_TYPE *d;
unsigned HOST_WIDE_INT i, j;
{
unsigned EMUSHORT df[NE], dg[NE];
unsigned HOST_WIDE_INT low, high;
low = i;
high = j;
eldexp (eone, HOST_BITS_PER_WIDE_INT, df);
ultoe (&high, dg);
emul (dg, df, dg);
ultoe (&low, df);
eadd (df, dg, dg);
PUT_REAL (dg, d);
}
/* REAL_VALUE_TO_INT macro. */
void
ereal_to_int (low, high, rr)
HOST_WIDE_INT *low, *high;
REAL_VALUE_TYPE rr;
{
unsigned EMUSHORT d[NE], df[NE], dg[NE], dh[NE];
int s;
GET_REAL (&rr, d);
#ifdef NANS
if (eisnan (d))
{
warning ("conversion from NaN to int");
*low = -1;
*high = -1;
return;
}
#endif
/* convert positive value */
s = 0;
if (eisneg (d))
{
eneg (d);
s = 1;
}
eldexp (eone, HOST_BITS_PER_WIDE_INT, df);
ediv (df, d, dg); /* dg = d / 2^32 is the high word */
euifrac (dg, (unsigned HOST_WIDE_INT *) high, dh);
emul (df, dh, dg); /* fractional part is the low word */
euifrac (dg, (unsigned HOST_WIDE_INT *)low, dh);
if (s)
{
/* complement and add 1 */
*high = ~(*high);
if (*low)
*low = -(*low);
else
*high += 1;
}
}
/* REAL_VALUE_LDEXP macro. */
REAL_VALUE_TYPE
ereal_ldexp (x, n)
REAL_VALUE_TYPE x;
int n;
{
unsigned EMUSHORT e[NE], y[NE];
REAL_VALUE_TYPE r;
GET_REAL (&x, e);
#ifdef NANS
if (eisnan (e))
return (x);
#endif
eldexp (e, n, y);
PUT_REAL (y, &r);
return (r);
}
/* These routines are conditionally compiled because functions
of the same names may be defined in fold-const.c. */
#ifdef REAL_ARITHMETIC
/* Check for infinity in a REAL_VALUE_TYPE. */
int
target_isinf (x)
REAL_VALUE_TYPE x;
{
unsigned EMUSHORT e[NE];
#ifdef INFINITY
GET_REAL (&x, e);
return (eisinf (e));
#else
return 0;
#endif
}
/* Check whether a REAL_VALUE_TYPE item is a NaN. */
int
target_isnan (x)
REAL_VALUE_TYPE x;
{
unsigned EMUSHORT e[NE];
#ifdef NANS
GET_REAL (&x, e);
return (eisnan (e));
#else
return (0);
#endif
}
/* Check for a negative REAL_VALUE_TYPE number.
This just checks the sign bit, so that -0 counts as negative. */
int
target_negative (x)
REAL_VALUE_TYPE x;
{
return ereal_isneg (x);
}
/* Expansion of REAL_VALUE_TRUNCATE.
The result is in floating point, rounded to nearest or even. */
REAL_VALUE_TYPE
real_value_truncate (mode, arg)
enum machine_mode mode;
REAL_VALUE_TYPE arg;
{
unsigned EMUSHORT e[NE], t[NE];
REAL_VALUE_TYPE r;
GET_REAL (&arg, e);
#ifdef NANS
if (eisnan (e))
return (arg);
#endif
eclear (t);
switch (mode)
{
case TFmode:
etoe113 (e, t);
e113toe (t, t);
break;
case XFmode:
etoe64 (e, t);
e64toe (t, t);
break;
case DFmode:
etoe53 (e, t);
e53toe (t, t);
break;
case HFmode:
case SFmode:
etoe24 (e, t);
e24toe (t, t);
break;
case SImode:
r = etrunci (arg);
return (r);
/* If an unsupported type was requested, presume that
the machine files know something useful to do with
the unmodified value. */
default:
return (arg);
}
PUT_REAL (t, &r);
return (r);
}
#endif /* REAL_ARITHMETIC defined */
/* Used for debugging--print the value of R in human-readable format
on stderr. */
void
debug_real (r)
REAL_VALUE_TYPE r;
{
char dstr[30];
REAL_VALUE_TO_DECIMAL (r, "%.20g", dstr);
fprintf (stderr, "%s", dstr);
}
/* Target values are arrays of host longs. A long is guaranteed
to be at least 32 bits wide. */
/* 128-bit long double */
void
etartdouble (r, l)
REAL_VALUE_TYPE r;
long l[];
{
unsigned EMUSHORT e[NE];
GET_REAL (&r, e);
etoe113 (e, e);
endian (e, l, TFmode);
}
/* 80-bit long double */
void
etarldouble (r, l)
REAL_VALUE_TYPE r;
long l[];
{
unsigned EMUSHORT e[NE];
GET_REAL (&r, e);
etoe64 (e, e);
endian (e, l, XFmode);
}
void
etardouble (r, l)
REAL_VALUE_TYPE r;
long l[];
{
unsigned EMUSHORT e[NE];
GET_REAL (&r, e);
etoe53 (e, e);
endian (e, l, DFmode);
}
long
etarsingle (r)
REAL_VALUE_TYPE r;
{
unsigned EMUSHORT e[NE];
long l;
GET_REAL (&r, e);
etoe24 (e, e);
endian (e, &l, SFmode);
return ((long) l);
}
void
ereal_to_decimal (x, s)
REAL_VALUE_TYPE x;
char *s;
{
unsigned EMUSHORT e[NE];
GET_REAL (&x, e);
etoasc (e, s, 20);
}
int
ereal_cmp (x, y)
REAL_VALUE_TYPE x, y;
{
unsigned EMUSHORT ex[NE], ey[NE];
GET_REAL (&x, ex);
GET_REAL (&y, ey);
return (ecmp (ex, ey));
}
int
ereal_isneg (x)
REAL_VALUE_TYPE x;
{
unsigned EMUSHORT ex[NE];
GET_REAL (&x, ex);
return (eisneg (ex));
}
/* End of REAL_ARITHMETIC interface */
/*
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
e113toe (&d, e) 128-bit 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 HOST_WIDE_INT and e type fraction
euifrac (e, &l, frac) e to unsigned HOST_WIDE_INT 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) 80-bit long double to ASCII string
e113toasc (&d, str, n) 128-bit 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) HOST_WIDE_INT to e type
ultoe (&l, e) unsigned HOST_WIDE_INT 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
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
eiisinf (ai) 1 if infinite
eiisnan (ai) 1 if a NaN
eiisneg (ai) 1 if sign bit of ai != 0, else 0
einan (ai) set ai = NaN
eiinfin (ai) set ai = infinity
The result is always normalized and rounded to NI-4 word precision
after each arithmetic operation.
Exception flags are NOT fully supported.
Signaling NaN's are NOT supported; they are treated the same
as quiet NaN's.
Define INFINITY 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.
Denormals are always supported here where appropriate (e.g., not
for conversion to DEC numbers). */
/* Definitions for error codes that are passed to the common error handling
routine mtherr.
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 computers, such as IBM PC, that follow the IEEE
Standard for Binary Floating Point Arithmetic (ANSI/IEEE
Std 754-1985), the symbol IBMPC or MIEEE should be defined.
These numbers have 53-bit significands. In this mode, constants
are provided as arrays of hexadecimal 16 bit integers.
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, the symbol UNK is defined.
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.
For ANSI C compatibility, define ANSIC equal to 1. Currently
this affects only the atan2 function and others that use it. */
/* 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 INVALID 7 /* NaN-producing operation */
/* e type constants used by high precision check routines */
#if LONG_DOUBLE_TYPE_SIZE == 128
/* 0.0 */
unsigned EMUSHORT ezero[NE] =
{0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,};
extern unsigned EMUSHORT ezero[];
/* 5.0E-1 */
unsigned EMUSHORT ehalf[NE] =
{0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3ffe,};
extern unsigned EMUSHORT ehalf[];
/* 1.0E0 */
unsigned EMUSHORT eone[NE] =
{0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,};
extern unsigned EMUSHORT eone[];
/* 2.0E0 */
unsigned EMUSHORT etwo[NE] =
{0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4000,};
extern unsigned EMUSHORT etwo[];
/* 3.2E1 */
unsigned EMUSHORT e32[NE] =
{0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x4004,};
extern unsigned EMUSHORT e32[];
/* 6.93147180559945309417232121458176568075500134360255E-1 */
unsigned EMUSHORT elog2[NE] =
{0x40f3, 0xf6af, 0x03f2, 0xb398,
0xc9e3, 0x79ab, 0150717, 0013767, 0130562, 0x3ffe,};
extern unsigned EMUSHORT elog2[];
/* 1.41421356237309504880168872420969807856967187537695E0 */
unsigned EMUSHORT esqrt2[NE] =
{0x1d6f, 0xbe9f, 0x754a, 0x89b3,
0x597d, 0x6484, 0174736, 0171463, 0132404, 0x3fff,};
extern unsigned EMUSHORT esqrt2[];
/* 3.14159265358979323846264338327950288419716939937511E0 */
unsigned EMUSHORT epi[NE] =
{0x2902, 0x1cd1, 0x80dc, 0x628b,
0xc4c6, 0xc234, 0020550, 0155242, 0144417, 0040000,};
extern unsigned EMUSHORT epi[];
#else
/* LONG_DOUBLE_TYPE_SIZE is other than 128 */
unsigned EMUSHORT ezero[NE] =
{0, 0000000, 0000000, 0000000, 0000000, 0000000,};
unsigned EMUSHORT ehalf[NE] =
{0, 0000000, 0000000, 0000000, 0100000, 0x3ffe,};
unsigned EMUSHORT eone[NE] =
{0, 0000000, 0000000, 0000000, 0100000, 0x3fff,};
unsigned EMUSHORT etwo[NE] =
{0, 0000000, 0000000, 0000000, 0100000, 0040000,};
unsigned EMUSHORT e32[NE] =
{0, 0000000, 0000000, 0000000, 0100000, 0040004,};
unsigned EMUSHORT elog2[NE] =
{0xc9e4, 0x79ab, 0150717, 0013767, 0130562, 0x3ffe,};
unsigned EMUSHORT esqrt2[NE] =
{0x597e, 0x6484, 0174736, 0171463, 0132404, 0x3fff,};
unsigned EMUSHORT epi[NE] =
{0xc4c6, 0xc234, 0020550, 0155242, 0144417, 0040000,};
#endif
/* Control register for rounding precision.
This can be set to 113 (if NE=10), 80 (if NE=6), 64, 56, 53, or 24 bits. */
int rndprc = NBITS;
extern int rndprc;
/* Clear out entire external format number. */
static void
eclear (x)
register unsigned EMUSHORT *x;
{
register int i;
for (i = 0; i < NE; i++)
*x++ = 0;
}
/* Move external format number from a to b. */
static void
emov (a, b)
register unsigned EMUSHORT *a, *b;
{
register int i;
for (i = 0; i < NE; i++)
*b++ = *a++;
}
/* Absolute value of external format number. */
static void
eabs (x)
unsigned EMUSHORT x[];
{
/* sign is top bit of last word of external format */
x[NE - 1] &= 0x7fff;
}
/* Negate external format number. */
static void
eneg (x)
unsigned EMUSHORT x[];
{
x[NE - 1] ^= 0x8000; /* Toggle the sign bit */
}
/* Return 1 if sign bit of external format number is nonzero, else zero. */
static int
eisneg (x)
unsigned EMUSHORT x[];
{
if (x[NE - 1] & 0x8000)
return (1);
else
return (0);
}
/* Return 1 if external format number is infinity, else return zero. */
static int
eisinf (x)
unsigned EMUSHORT x[];
{
#ifdef NANS
if (eisnan (x))
return (0);
#endif
if ((x[NE - 1] & 0x7fff) == 0x7fff)
return (1);
else
return (0);
}
/* Check if e-type number is not a number. The bit pattern is one that we
defined, so we know for sure how to detect it. */
static int
eisnan (x)
unsigned EMUSHORT 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 external format number with infinity pattern (IEEE)
or largest possible number (non-IEEE). */
static void
einfin (x)
register unsigned EMUSHORT *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
}
/* Output an e-type NaN.
This generates Intel's quiet NaN pattern for extended real.
The exponent is 7fff, the leading mantissa word is c000. */
static void
enan (x, sign)
register unsigned EMUSHORT *x;
int sign;
{
register int i;
for (i = 0; i < NE - 2; i++)
*x++ = 0;
*x++ = 0xc000;
*x = (sign << 15) | 0x7fff;
}
/* Move in external format number, converting it to internal format. */
static void
emovi (a, b)
unsigned EMUSHORT *a, *b;
{
register unsigned EMUSHORT *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. */
static void
emovo (a, b)
unsigned EMUSHORT *a, *b;
{
register unsigned EMUSHORT *p, *q;
unsigned EMUSHORT i;
int j;
p = a;
q = b + (NE - 1); /* point to output exponent */
/* combine sign and exponent */
i = *p++;
if (i)
*q-- = *p++ | 0x8000;
else
*q-- = *p++;
#ifdef INFINITY
if (*(p - 1) == 0x7fff)
{
#ifdef NANS
if (eiisnan (a))
{
enan (b, eiisneg (a));
return;
}
#endif
einfin (b);
return;
}
#endif
/* skip over guard word */
++p;
/* move the significand */
for (j = 0; j < NE - 1; j++)
*q-- = *p++;
}
/* Clear out internal format number. */
static void
ecleaz (xi)
register unsigned EMUSHORT *xi;
{
register int i;
for (i = 0; i < NI; i++)
*xi++ = 0;
}
/* Same, but don't touch the sign. */
static void
ecleazs (xi)
register unsigned EMUSHORT *xi;
{
register int i;
++xi;
for (i = 0; i < NI - 1; i++)
*xi++ = 0;
}
/* Move internal format number from a to b. */
static void
emovz (a, b)
register unsigned EMUSHORT *a, *b;
{
register int i;
for (i = 0; i < NI - 1; i++)
*b++ = *a++;
/* clear low guard word */
*b = 0;
}
/* Generate internal format NaN.
The explicit pattern for this is maximum exponent and
top two significant bits set. */
static void
einan (x)
unsigned EMUSHORT x[];
{
ecleaz (x);
x[E] = 0x7fff;
x[M + 1] = 0xc000;
}
/* Return nonzero if internal format number is a NaN. */
static int
eiisnan (x)
unsigned EMUSHORT 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 sign of internal format number is nonzero. */
static int
eiisneg (x)
unsigned EMUSHORT x[];
{
return x[0] != 0;
}
/* Fill internal format number with infinity pattern.
This has maximum exponent and significand all zeros. */
static void
eiinfin (x)
unsigned EMUSHORT x[];
{
ecleaz (x);
x[E] = 0x7fff;
}
/* Return nonzero if internal format number is infinite. */
static int
eiisinf (x)
unsigned EMUSHORT 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.
Returns +1 if a > b
0 if a == b
-1 if a < b */
static int
ecmpm (a, b)
register unsigned EMUSHORT *a, *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 void
eshdn1 (x)
register unsigned EMUSHORT *x;
{
register unsigned EMUSHORT 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 void
eshup1 (x)
register unsigned EMUSHORT *x;
{
register unsigned EMUSHORT 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 void
eshdn8 (x)
register unsigned EMUSHORT *x;
{
register unsigned EMUSHORT 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 void
eshup8 (x)
register unsigned EMUSHORT *x;
{
int i;
register unsigned EMUSHORT 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 void
eshup6 (x)
register unsigned EMUSHORT *x;
{
int i;
register unsigned EMUSHORT *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 void
eshdn6 (x)
register unsigned EMUSHORT *x;
{
int i;
register unsigned EMUSHORT *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 void
eaddm (x, y)
unsigned EMUSHORT *x, *y;
{
register unsigned EMULONG a;
int i;
unsigned int carry;
x += NI - 1;
y += NI - 1;
carry = 0;
for (i = M; i < NI; i++)
{
a = (unsigned EMULONG) (*x) + (unsigned EMULONG) (*y) + carry;
if (a & 0x10000)
carry = 1;
else
carry = 0;
*y = (unsigned EMUSHORT) a;
--x;
--y;
}
}
/* Subtract significands. y - x replaces y. */
static void
esubm (x, y)
unsigned EMUSHORT *x, *y;
{
unsigned EMULONG a;
int i;
unsigned int carry;
x += NI - 1;
y += NI - 1;
carry = 0;
for (i = M; i < NI; i++)
{
a = (unsigned EMULONG) (*y) - (unsigned EMULONG) (*x) - carry;
if (a & 0x10000)
carry = 1;
else
carry = 0;
*y = (unsigned EMUSHORT) a;
--x;
--y;
}
}
static unsigned EMUSHORT equot[NI];
#if 0
/* Radix 2 shift-and-add versions of multiply and divide */
/* Divide significands */
int
edivm (den, num)
unsigned EMUSHORT den[], num[];
{
int i;
register unsigned EMUSHORT *p, *q;
unsigned EMUSHORT j;
p = &equot[0];
*p++ = num[0];
*p++ = num[1];
for (i = M; i < NI; i++)
{
*p++ = 0;
}
/* Use faster compare and subtraction if denominator has only 15 bits of
significance. */
p = &den[M + 2];
if (*p++ == 0)
{
for (i = M + 3; i < NI; i++)
{
if (*p++ != 0)
goto fulldiv;
}
if ((den[M + 1] & 1) != 0)
goto fulldiv;
eshdn1 (num);
eshdn1 (den);
p = &den[M + 1];
q = &num[M + 1];
for (i = 0; i < NBITS + 2; i++)
{
if (*p <= *q)
{
*q -= *p;
j = 1;
}
else
{
j = 0;
}
eshup1 (equot);
equot[NI - 2] |= j;
eshup1 (num);
}
goto divdon;
}
/* The number of quotient bits to calculate is NBITS + 1 scaling guard
bit + 1 roundoff bit. */
fulldiv:
p = &equot[NI - 2];
for (i = 0; i < NBITS + 2; i++)
{
if (ecmpm (den, num) <= 0)
{
esubm (den, num);
j = 1; /* quotient bit = 1 */
}
else
j = 0;
eshup1 (equot);
*p |= j;
eshup1 (num);
}
divdon:
eshdn1 (equot);
eshdn1 (equot);
/* test for nonzero remainder after roundoff bit */
p = &num[M];
j = 0;
for (i = M; i < NI; i++)
{
j |= *p++;
}
if (j)
j = 1;
for (i = 0; i < NI; i++)
num[i] = equot[i];
return ((int) j);
}
/* Multiply significands */
int
emulm (a, b)
unsigned EMUSHORT a[], b[];
{
unsigned EMUSHORT *p, *q;
int i, j, k;
equot[0] = b[0];
equot[1] = b[1];
for (i = M; i < NI; i++)
equot[i] = 0;
p = &a[NI - 2];
k = NBITS;
while (*p == 0) /* significand is not supposed to be zero */
{
eshdn6 (a);
k -= 16;
}
if ((*p & 0xff) == 0)
{
eshdn8 (a);
k -= 8;
}
q = &equot[NI - 1];
j = 0;
for (i = 0; i < k; i++)
{
if (*p & 1)
eaddm (b, equot);
/* remember if there were any nonzero bits shifted out */
if (*q & 1)
j |= 1;
eshdn1 (a);
eshdn1 (equot);
}
for (i = 0; i < NI; i++)
b[i] = equot[i];
/* return flag for lost nonzero bits */
return (j);
}
#else
/* Radix 65536 versions of multiply and divide */
/* Multiply significand of e-type number b
by 16-bit quantity a, e-type result to c. */
static void
m16m (a, b, c)
unsigned int a;
unsigned short b[], c[];
{
register unsigned short *pp;
register unsigned long carry;
unsigned short *ps;
unsigned short p[NI];
unsigned long aa, m;
int i;
aa = a;
pp = &p[NI-2];
*pp++ = 0;
*pp = 0;
ps = &b[NI-1];
for (i=M+1; i<NI; i++)
{
if (*ps == 0)
{
--ps;
--pp;
*(pp-1) = 0;
}
else
{
m = (unsigned long) aa * *ps--;
carry = (m & 0xffff) + *pp;
*pp-- = (unsigned short)carry;
carry = (carry >> 16) + (m >> 16) + *pp;
*pp = (unsigned short)carry;
*(pp-1) = carry >> 16;
}
}
for (i=M; i<NI; i++)
c[i] = p[i];
}
/* Divide significands. Neither the numerator nor the denominator
is permitted to have its high guard word nonzero. */
static int
edivm (den, num)
unsigned short den[], num[];
{
int i;
register unsigned short *p;
unsigned long tnum;
unsigned short j, tdenm, tquot;
unsigned short tprod[NI+1];
p = &equot[0];
*p++ = num[0];
*p++ = num[1];
for (i=M; i<NI; i++)
{
*p++ = 0;
}
eshdn1 (num);
tdenm = den[M+1];
for (i=M; i<NI; i++)
{
/* Find trial quotient digit (the radix is 65536). */
tnum = (((unsigned long) num[M]) << 16) + num[M+1];
/* Do not execute the divide instruction if it will overflow. */
if ((tdenm * 0xffffL) < tnum)
tquot = 0xffff;
else
tquot = tnum / tdenm;
/* Multiply denominator by trial quotient digit. */
m16m ((unsigned int)tquot, den, tprod);
/* The quotient digit may have been overestimated. */
if (ecmpm (tprod, num) > 0)
{
tquot -= 1;
esubm (den, tprod);
if (ecmpm (tprod, num) > 0)
{
tquot -= 1;
esubm (den, tprod);
}
}
esubm (tprod, num);
equot[i] = tquot;
eshup6(num);
}
/* test for nonzero remainder after roundoff bit */
p = &num[M];
j = 0;
for (i=M; i<NI; i++)
{
j |= *p++;
}
if (j)
j = 1;
for (i=0; i<NI; i++)
num[i] = equot[i];
return ((int)j);
}
/* Multiply significands */
static int
emulm (a, b)
unsigned short a[], b[];
{
unsigned short *p, *q;
unsigned short pprod[NI];
unsigned short j;
int i;
equot[0] = b[0];
equot[1] = b[1];
for (i=M; i<NI; i++)
equot[i] = 0;
j = 0;
p = &a[NI-1];
q = &equot[NI-1];
for (i=M+1; i<NI; i++)
{
if (*p == 0)
{
--p;
}
else
{
m16m ((unsigned int) *p--, b, pprod);
eaddm(pprod, equot);
}
j |= *q;
eshdn6(equot);
}
for (i=0; i<NI; i++)
b[i] = equot[i];
/* return flag for lost nonzero bits */
return ((int)j);
}
#endif
/* Normalize and round off.
The internal format number to be rounded is "s".
Input "lost" indicates whether or not the number is exact.
This is the so-called sticky bit.
Input "subflg" indicates whether the number was obtained
by a subtraction operation. In that case if lost is nonzero
then the number is slightly smaller than indicated.
Input "exp" is the biased exponent, which may be negative.
the exponent field of "s" is ignored but is replaced by
"exp" as adjusted by normalization and rounding.
Input "rcntrl" is the rounding control.
For future reference: In order for emdnorm to round off denormal
significands at the right point, the input exponent must be
adjusted to be the actual value it would have after conversion to
the final floating point type. This adjustment has been
implemented for all type conversions (etoe53, etc.) and decimal
conversions, but not for the arithmetic functions (eadd, etc.).
Data types having standard 15-bit exponents are not affected by
this, but SFmode and DFmode are affected. For example, ediv with
rndprc = 24 will not round correctly to 24-bit precision if the
result is denormal. */
static int rlast = -1;
static int rw = 0;
static unsigned EMUSHORT rmsk = 0;
static unsigned EMUSHORT rmbit = 0;
static unsigned EMUSHORT rebit = 0;
static int re = 0;
static unsigned EMUSHORT rbit[NI];
static void
emdnorm (s, lost, subflg, exp, rcntrl)
unsigned EMUSHORT s[];
int lost;
int subflg;
EMULONG exp;
int rcntrl;
{
int i, j;
unsigned EMUSHORT r;
/* Normalize */
j = enormlz (s);
/* a blank significand could mean either zero or infinity. */
#ifndef INFINITY
if (j > NBITS)
{
ecleazs (s);
return;
}
#endif
exp -= j;
#ifndef INFINITY
if (exp >= 32767L)
goto overf;
#else
if ((j > NBITS) && (exp < 32767))
{
ecleazs (s);
return;
}
#endif
if (exp < 0L)
{
if (exp > (EMULONG) (-NBITS - 1))
{
j = (int) exp;
i = eshift (s, j);
if (i)
lost = 1;
}
else
{
ecleazs (s);
return;
}
}
/* Round off, unless told not to by rcntrl. */
if (rcntrl == 0)
goto mdfin;
/* Set up rounding parameters if the control register changed. */
if (rndprc != rlast)
{
ecleaz (rbit);
switch (rndprc)
{
default:
case NBITS:
rw = NI - 1; /* low guard word */
rmsk = 0xffff;
rmbit = 0x8000;
re = rw - 1;
rebit = 1;
break;
case 113:
rw = 10;
rmsk = 0x7fff;
rmbit = 0x4000;
rebit = 0x8000;
re = rw;
break;
case 64:
rw = 7;
rmsk = 0xffff;
rmbit = 0x8000;
re = rw - 1;
rebit = 1;
break;
/* For DEC or IBM arithmetic */
case 56:
rw = 6;
rmsk = 0xff;
rmbit = 0x80;
rebit = 0x100;
re = rw;
break;
case 53:
rw = 6;
rmsk = 0x7ff;
rmbit = 0x0400;
rebit = 0x800;
re = rw;
break;
case 24:
rw = 4;
rmsk = 0xff;
rmbit = 0x80;
rebit = 0x100;
re = rw;
break;
}
rbit[re] = rebit;
rlast = rndprc;
}
/* Shift down 1 temporarily if the data structure has an implied
most significant bit and the number is denormal. */
if ((exp <= 0) && (rndprc != 64) && (rndprc != NBITS))
{
lost |= s[NI - 1] & 1;
eshdn1 (s);
}
/* Clear out all bits below the rounding bit,
remembering in r if any were nonzero. */
r = s[rw] & rmsk;
if (rndprc < NBITS)
{
i = rw + 1;
while (i < NI)
{
if (s[i])
r |= 1;
s[i] = 0;
++i;
}
}
s[rw] &= ~rmsk;
if ((r & rmbit) != 0)
{
if (r == rmbit)
{
if (lost == 0)
{ /* round to even */
if ((s[re] & rebit) == 0)
goto mddone;
}
else
{
if (subflg != 0)
goto mddone;
}
}
eaddm (rbit, s);
}
mddone:
if ((exp <= 0) && (rndprc != 64) && (rndprc != NBITS))
{
eshup1 (s);
}
if (s[2] != 0)
{ /* overflow on roundoff */
eshdn1 (s);
exp += 1;
}
mdfin:
s[NI - 1] = 0;
if (exp >= 32767L)
{
#ifndef INFINITY
overf:
#endif
#ifdef INFINITY
s[1] = 32767;
for (i = 2; i < NI - 1; i++)
s[i] = 0;
if (extra_warnings)
warning ("floating point overflow");
#else
s[1] = 32766;
s[2] = 0;
for (i = M + 1; i < NI - 1; i++)
s[i] = 0xffff;
s[NI - 1] = 0;
if ((rndprc < 64) || (rndprc == 113))
{
s[rw] &= ~rmsk;
if (rndprc == 24)
{
s[5] = 0;
s[6] = 0;
}
}
#endif
return;
}
if (exp < 0)
s[1] = 0;
else
s[1] = (unsigned EMUSHORT) exp;
}
/* Subtract external format numbers. */
static int subflg = 0;
static void
esub (a, b, c)
unsigned EMUSHORT *a, *b, *c;
{
#ifdef NANS
if (eisnan (a))
{
emov (a, c);
return;
}
if (eisnan (b))
{
emov (b, c);
return;
}
/* Infinity minus infinity is a NaN.
Test for subtracting infinities of the same sign. */
if (eisinf (a) && eisinf (b)
&& ((eisneg (a) ^ eisneg (b)) == 0))
{
mtherr ("esub", INVALID);
enan (c, 0);
return;
}
#endif
subflg = 1;
eadd1 (a, b, c);
}
/* Add. */
static void
eadd (a, b, c)
unsigned EMUSHORT *a, *b, *c;
{
#ifdef NANS
/* NaN plus anything is a NaN. */
if (eisnan (a))
{
emov (a, c);
return;
}
if (eisnan (b))
{
emov (b, c);
return;
}
/* Infinity minus infinity is a NaN.
Test for adding infinities of opposite signs. */
if (eisinf (a) && eisinf (b)
&& ((eisneg (a) ^ eisneg (b)) != 0))
{
mtherr ("esub", INVALID);
enan (c, 0);
return;
}
#endif
subflg = 0;
eadd1 (a, b, c);
}
static void
eadd1 (a, b, c)
unsigned EMUSHORT *a, *b, *c;
{
unsigned EMUSHORT ai[NI], bi[NI], ci[NI];
int i, lost, j, k;
EMULONG lt, lta, ltb;
#ifdef INFINITY
if (eisinf (a))
{
emov (a, c);
if (subflg)
eneg (c);
return;
}
if (eisinf (b))
{
emov (b, c);
return;
}
#endif
emovi (a, ai);
emovi (b, bi);
if (subflg)
ai[0] = ~ai[0];
/* compare exponents */
lta = ai[E];
ltb = bi[E];
lt = lta - ltb;
if (lt > 0L)
{ /* put the larger number in bi */
emovz (bi, ci);
emovz (ai, bi);
emovz (ci, ai);
ltb = bi[E];
lt = -lt;
}
lost = 0;
if (lt != 0L)
{
if (lt < (EMULONG) (-NBITS - 1))
goto done; /* answer same as larger addend */
k = (int) lt;
lost = eshift (ai, k); /* shift the smaller number down */
}
else
{
/* exponents were the same, so must compare significands */
i = ecmpm (ai, bi);
if (i == 0)
{ /* the numbers are identical in magnitude */
/* if different signs, result is zero */
if (ai[0] != bi[0])
{
eclear (c);
return;
}
/* if same sign, result is double */
/* double denomalized tiny number */
if ((bi[E] == 0) && ((bi[3] & 0x8000) == 0))
{
eshup1 (bi);
goto done;
}
/* add 1 to exponent unless both are zero! */
for (j = 1; j < NI - 1; j++)
{
if (bi[j] != 0)
{
/* This could overflow, but let emovo take care of that. */
ltb += 1;
break;
}
}
bi[E] = (unsigned EMUSHORT) ltb;
goto done;
}
if (i > 0)
{ /* put the larger number in bi */
emovz (bi, ci);
emovz (ai, bi);
emovz (ci, ai);
}
}
if (ai[0] == bi[0])
{
eaddm (ai, bi);
subflg = 0;
}
else
{
esubm (ai, bi);
subflg = 1;
}
emdnorm (bi, lost, subflg, ltb, 64);
done:
emovo (bi, c);
}
/* Divide. */
static void
ediv (a, b, c)
unsigned EMUSHORT *a, *b, *c;
{
unsigned EMUSHORT ai[NI], bi[NI];
int i;
EMULONG lt, lta, ltb;
#ifdef NANS
/* Return any NaN input. */
if (eisnan (a))
{
emov (a, c);
return;
}
if (eisnan (b))
{
emov (b, c);
return;
}
/* Zero over zero, or infinity over infinity, is a NaN. */
if (((ecmp (a, ezero) == 0) && (ecmp (b, ezero) == 0))
|| (eisinf (a) && eisinf (b)))
{
mtherr ("ediv", INVALID);
enan (c, eisneg (a) ^ eisneg (b));
return;
}
#endif
/* Infinity over anything else is infinity. */
#ifdef INFINITY
if (eisinf (b))
{
if (eisneg (a) ^ eisneg (b))
*(c + (NE - 1)) = 0x8000;
else
*(c + (NE - 1)) = 0;
einfin (c);
return;
}
/* Anything else over infinity is zero. */
if (eisinf (a))
{
eclear (c);
return;
}
#endif
emovi (a, ai);
emovi (b, bi);
lta = ai[E];
ltb = bi[E];
if (bi[E] == 0)
{ /* See if numerator is zero. */
for (i = 1; i < NI - 1; i++)
{
if (bi[i] != 0)
{
ltb -= enormlz (bi);
goto dnzro1;
}
}
eclear (c);
return;
}
dnzro1:
if (ai[E] == 0)
{ /* possible divide by zero */
for (i = 1; i < NI - 1; i++)
{
if (ai[i] != 0)
{
lta -= enormlz (ai);
goto dnzro2;
}
}
if (ai[0] == bi[0])
*(c + (NE - 1)) = 0;
else
*(c + (NE - 1)) = 0x8000;
/* Divide by zero is not an invalid operation.
It is a divide-by-zero operation! */
einfin (c);
mtherr ("ediv", SING);
return;
}
dnzro2:
i = edivm (ai, bi);
/* calculate exponent */
lt = ltb - lta + EXONE;
emdnorm (bi, i, 0, lt, 64);
/* set the sign */
if (ai[0] == bi[0])
bi[0] = 0;
else
bi[0] = 0Xffff;
emovo (bi, c);
}
/* Multiply. */
static void
emul (a, b, c)
unsigned EMUSHORT *a, *b, *c;
{
unsigned EMUSHORT ai[NI], bi[NI];
int i, j;
EMULONG lt, lta, ltb;
#ifdef NANS
/* NaN times anything is the same NaN. */
if (eisnan (a))
{
emov (a, c);
return;
}
if (eisnan (b))
{
emov (b, c);
return;
}
/* Zero times infinity is a NaN. */
if ((eisinf (a) && (ecmp (b, ezero) == 0))
|| (eisinf (b) && (ecmp (a, ezero) == 0)))
{
mtherr ("emul", INVALID);
enan (c, eisneg (a) ^ eisneg (b));
return;
}
#endif
/* Infinity times anything else is infinity. */
#ifdef INFINITY
if (eisinf (a) || eisinf (b))
{
if (eisneg (a) ^ eisneg (b))
*(c + (NE - 1)) = 0x8000;
else
*(c + (NE - 1)) = 0;
einfin (c);
return;
}
#endif
emovi (a, ai);
emovi (b, bi);
lta = ai[E];
ltb = bi[E];
if (ai[E] == 0)
{
for (i = 1; i < NI - 1; i++)
{
if (ai[i] != 0)
{
lta -= enormlz (ai);
goto mnzer1;
}
}
eclear (c);
return;
}
mnzer1:
if (bi[E] == 0)
{
for (i = 1; i < NI - 1; i++)
{
if (bi[i] != 0)
{
ltb -= enormlz (bi);
goto mnzer2;
}
}
eclear (c);
return;
}
mnzer2:
/* Multiply significands */
j = emulm (ai, bi);
/* calculate exponent */
lt = lta + ltb - (EXONE - 1);
emdnorm (bi, j, 0, lt, 64);
/* calculate sign of product */
if (ai[0] == bi[0])
bi[0] = 0;
else
bi[0] = 0xffff;
emovo (bi, c);
}
/* Convert IEEE double precision to e type. */
static void
e53toe (pe, y)
unsigned EMUSHORT *pe, *y;
{
#ifdef DEC
dectoe (pe, y); /* see etodec.c */
#else
#ifdef IBM
ibmtoe (pe, y, DFmode);
#else
register unsigned EMUSHORT r;
register unsigned EMUSHORT *e, *p;
unsigned EMUSHORT yy[NI];
int denorm, k;
e = pe;
denorm = 0; /* flag if denormalized number */
ecleaz (yy);
#ifdef IBMPC
e += 3;
#endif
r = *e;
yy[0] = 0;
if (r & 0x8000)
yy[0] = 0xffff;
yy[M] = (r & 0x0f) | 0x10;
r &= ~0x800f; /* strip sign and 4 significand bits */
#ifdef INFINITY
if (r == 0x7ff0)
{
#ifdef NANS
#ifdef IBMPC
if (((pe[3] & 0xf) != 0) || (pe[2] != 0)
|| (pe[1] != 0) || (pe[0] != 0))
{
enan (y, yy[0] != 0);
return;
}
#else
if (((pe[0] & 0xf) != 0) || (pe[1] != 0)
|| (pe[2] != 0) || (pe[3] != 0))
{
enan (y, yy[0] != 0);
return;
}
#endif
#endif /* NANS */
eclear (y);
einfin (y);
if (yy[0])
eneg (y);
return;
}
#endif /* INFINITY */
r >>= 4;
/* If zero exponent, then the significand is denormalized.
So take back the understood high significand bit. */
if (r == 0)
{
denorm = 1;
yy[M] &= ~0x10;
}
r += EXONE - 01777;
yy[E] = r;
p = &yy[M + 1];
#ifdef IBMPC
*p++ = *(--e);
*p++ = *(--e);
*p++ = *(--e);
#endif
#ifdef MIEEE
++e;
*p++ = *e++;
*p++ = *e++;
*p++ = *e++;
#endif
eshift (yy, -5);
if (denorm)
{ /* if zero exponent, then normalize the significand */
if ((k = enormlz (yy)) > NBITS)
ecleazs (yy);
else
yy[E] -= (unsigned EMUSHORT) (k - 1);
}
emovo (yy, y);
#endif /* not IBM */
#endif /* not DEC */
}
static void
e64toe (pe, y)
unsigned EMUSHORT *pe, *y;
{
unsigned EMUSHORT yy[NI];
unsigned EMUSHORT *e, *p, *q;
int i;
e = pe;
p = yy;
for (i = 0; i < NE - 5; i++)
*p++ = 0;
#ifdef IBMPC
for (i = 0; i < 5; i++)
*p++ = *e++;
#endif
/* This precision is not ordinarily supported on DEC or IBM. */
#ifdef DEC
for (i = 0; i < 5; i++)
*p++ = *e++;
#endif
#ifdef IBM
p = &yy[0] + (NE - 1);
*p-- = *e++;
++e;
for (i = 0; i < 5; i++)
*p-- = *e++;
#endif
#ifdef MIEEE
p = &yy[0] + (NE - 1);
*p-- = *e++;
++e;
for (i = 0; i < 4; i++)
*p-- = *e++;
#endif
p = yy;
q = y;
#ifdef INFINITY
if (*p == 0x7fff)
{
#ifdef NANS
#ifdef IBMPC
for (i = 0; i < 4; i++)
{
if (pe[i] != 0)
{
enan (y, (*p & 0x8000) != 0);
return;
}
}
#else
for (i = 1; i <= 4; i++)
{
if (pe[i] != 0)
{
enan (y, (*p & 0x8000) != 0);
return;
}
}
#endif
#endif /* NANS */
eclear (y);
einfin (y);
if (*p & 0x8000)
eneg (y);
return;
}
#endif /* INFINITY */
for (i = 0; i < NE; i++)
*q++ = *p++;
}
static void
e113toe (pe, y)
unsigned EMUSHORT *pe, *y;
{
register unsigned EMUSHORT r;
unsigned EMUSHORT *e, *p;
unsigned EMUSHORT yy[NI];
int denorm, i;
e = pe;
denorm = 0;
ecleaz (yy);
#ifdef IBMPC
e += 7;
#endif
r = *e;
yy[0] = 0;
if (r & 0x8000)
yy[0] = 0xffff;
r &= 0x7fff;
#ifdef INFINITY
if (r == 0x7fff)
{
#ifdef NANS
#ifdef IBMPC
for (i = 0; i < 7; i++)
{
if (pe[i] != 0)
{
enan (y, yy[0] != 0);
return;
}
}
#else
for (i = 1; i < 8; i++)
{
if (pe[i] != 0)
{
enan (y, yy[0] != 0);
return;
}
}
#endif
#endif /* NANS */
eclear (y);
einfin (y);
if (yy[0])
eneg (y);
return;
}
#endif /* INFINITY */
yy[E] = r;
p = &yy[M + 1];
#ifdef IBMPC
for (i = 0; i < 7; i++)
*p++ = *(--e);
#endif
#ifdef MIEEE
++e;
for (i = 0; i < 7; i++)
*p++ = *e++;
#endif
/* If denormal, remove the implied bit; else shift down 1. */
if (r == 0)
{
yy[M] = 0;
}
else
{
yy[M] = 1;
eshift (yy, -1);
}
emovo (yy, y);
}
/* Convert IEEE single precision to e type. */
static void
e24toe (pe, y)
unsigned EMUSHORT *pe, *y;
{
#ifdef IBM
ibmtoe (pe, y, SFmode);
#else
register unsigned EMUSHORT r;
register unsigned EMUSHORT *e, *p;
unsigned EMUSHORT yy[NI];
int denorm, k;
e = pe;
denorm = 0; /* flag if denormalized number */
ecleaz (yy);
#ifdef IBMPC
e += 1;
#endif
#ifdef DEC
e += 1;
#endif
r = *e;
yy[0] = 0;
if (r & 0x8000)
yy[0] = 0xffff;
yy[M] = (r & 0x7f) | 0200;
r &= ~0x807f; /* strip sign and 7 significand bits */
#ifdef INFINITY
if (r == 0x7f80)
{
#ifdef NANS
#ifdef MIEEE
if (((pe[0] & 0x7f) != 0) || (pe[1] != 0))
{
enan (y, yy[0] != 0);
return;
}
#else
if (((pe[1] & 0x7f) != 0) || (pe[0] != 0))
{
enan (y, yy[0] != 0);
return;
}
#endif
#endif /* NANS */
eclear (y);
einfin (y);
if (yy[0])
eneg (y);
return;
}
#endif /* INFINITY */
r >>= 7;
/* If zero exponent, then the significand is denormalized.
So take back the understood high significand bit. */
if (r == 0)
{
denorm = 1;
yy[M] &= ~0200;
}
r += EXONE - 0177;
yy[E] = r;
p = &yy[M + 1];
#ifdef IBMPC
*p++ = *(--e);
#endif
#ifdef DEC
*p++ = *(--e);
#endif
#ifdef MIEEE
++e;
*p++ = *e++;
#endif
eshift (yy, -8);
if (denorm)
{ /* if zero exponent, then normalize the significand */
if ((k = enormlz (yy)) > NBITS)
ecleazs (yy);
else
yy[E] -= (unsigned EMUSHORT) (k - 1);
}
emovo (yy, y);
#endif /* not IBM */
}
static void
etoe113 (x, e)
unsigned EMUSHORT *x, *e;
{
unsigned EMUSHORT xi[NI];
EMULONG exp;
int rndsav;
#ifdef NANS
if (eisnan (x))
{
make_nan (e, eisneg (x), TFmode);
return;
}
#endif
emovi (x, xi);
exp = (EMULONG) xi[E];
#ifdef INFINITY
if (eisinf (x))
goto nonorm;
#endif
/* round off to nearest or even */
rndsav = rndprc;
rndprc = 113;
emdnorm (xi, 0, 0, exp, 64);
rndprc = rndsav;
nonorm:
toe113 (xi, e);
}
/* Move out internal format to ieee long double */
static void
toe113 (a, b)
unsigned EMUSHORT *a, *b;
{
register unsigned EMUSHORT *p, *q;
unsigned EMUSHORT i;
#ifdef NANS
if (eiisnan (a))
{
make_nan (b, eiisneg (a), TFmode);
return;
}
#endif
p = a;
#ifdef MIEEE
q = b;
#else
q = b + 7; /* point to output exponent */
#endif
/* If not denormal, delete the implied bit. */
if (a[E] != 0)
{
eshup1 (a);
}
/* combine sign and exponent */
i = *p++;
#ifdef MIEEE
if (i)
*q++ = *p++ | 0x8000;
else
*q++ = *p++;
#else
if (i)
*q-- = *p++ | 0x8000;
else
*q-- = *p++;
#endif
/* skip over guard word */
++p;
/* move the significand */
#ifdef MIEEE
for (i = 0; i < 7; i++)
*q++ = *p++;
#else
for (i = 0; i < 7; i++)
*q-- = *p++;
#endif
}
static void
etoe64 (x, e)
unsigned EMUSHORT *x, *e;
{
unsigned EMUSHORT xi[NI];
EMULONG exp;
int rndsav;
#ifdef NANS
if (eisnan (x))
{
make_nan (e, eisneg (x), XFmode);
return;
}
#endif
emovi (x, xi);
/* adjust exponent for offset */
exp = (EMULONG) xi[E];
#ifdef INFINITY
if (eisinf (x))
goto nonorm;
#endif
/* round off to nearest or even */
rndsav = rndprc;
rndprc = 64;
emdnorm (xi, 0, 0, exp, 64);
rndprc = rndsav;
nonorm:
toe64 (xi, e);
}
/* Move out internal format to ieee long double. */
static void
toe64 (a, b)
unsigned EMUSHORT *a, *b;
{
register unsigned EMUSHORT *p, *q;
unsigned EMUSHORT i;
#ifdef NANS
if (eiisnan (a))
{
make_nan (b, eiisneg (a), XFmode);
return;
}
#endif
p = a;
#if defined(MIEEE) || defined(IBM)
q = b;
#else
q = b + 4; /* point to output exponent */
#if LONG_DOUBLE_TYPE_SIZE == 96
/* Clear the last two bytes of 12-byte Intel format */
*(q+1) = 0;
#endif
#endif
/* combine sign and exponent */
i = *p++;
#if defined(MIEEE) || defined(IBM)
if (i)
*q++ = *p++ | 0x8000;
else
*q++ = *p++;
*q++ = 0;
#else
if (i)
*q-- = *p++ | 0x8000;
else
*q-- = *p++;
#endif
/* skip over guard word */
++p;
/* move the significand */
#if defined(MIEEE) || defined(IBM)
for (i = 0; i < 4; i++)
*q++ = *p++;
#else
for (i = 0; i < 4; i++)
*q-- = *p++;
#endif
}
/* e type to IEEE double precision. */
#ifdef DEC
static void
etoe53 (x, e)
unsigned EMUSHORT *x, *e;
{
etodec (x, e); /* see etodec.c */
}
static void
toe53 (x, y)
unsigned EMUSHORT *x, *y;
{
todec (x, y);
}
#else
#ifdef IBM
static void
etoe53 (x, e)
unsigned EMUSHORT *x, *e;
{
etoibm (x, e, DFmode);
}
static void
toe53 (x, y)
unsigned EMUSHORT *x, *y;
{
toibm (x, y, DFmode);
}
#else /* it's neither DEC nor IBM */
static void
etoe53 (x, e)
unsigned EMUSHORT *x, *e;
{
unsigned EMUSHORT xi[NI];
EMULONG exp;
int rndsav;
#ifdef NANS
if (eisnan (x))
{
make_nan (e, eisneg (x), DFmode);
return;
}
#endif
emovi (x, xi);
/* adjust exponent for offsets */
exp = (EMULONG) xi[E] - (EXONE - 0x3ff);
#ifdef INFINITY
if (eisinf (x))
goto nonorm;
#endif
/* round off to nearest or even */
rndsav = rndprc;
rndprc = 53;
emdnorm (xi, 0, 0, exp, 64);
rndprc = rndsav;
nonorm:
toe53 (xi, e);
}
static void
toe53 (x, y)
unsigned EMUSHORT *x, *y;
{
unsigned EMUSHORT i;
unsigned EMUSHORT *p;
#ifdef NANS
if (eiisnan (x))
{
make_nan (y, eiisneg (x), DFmode);
return;
}
#endif
p = &x[0];
#ifdef IBMPC
y += 3;
#endif
*y = 0; /* output high order */
if (*p++)
*y = 0x8000; /* output sign bit */
i = *p++;
if (i >= (unsigned int) 2047)
{ /* Saturate at largest number less than infinity. */
#ifdef INFINITY
*y |= 0x7ff0;
#ifdef IBMPC
*(--y) = 0;
*(--y) = 0;
*(--y) = 0;
#endif
#ifdef MIEEE
++y;
*y++ = 0;
*y++ = 0;
*y++ = 0;
#endif
#else
*y |= (unsigned EMUSHORT) 0x7fef;
#ifdef IBMPC
*(--y) = 0xffff;
*(--y) = 0xffff;
*(--y) = 0xffff;
#endif
#ifdef MIEEE
++y;
*y++ = 0xffff;
*y++ = 0xffff;
*y++ = 0xffff;
#endif
#endif
return;
}
if (i == 0)
{
eshift (x, 4);
}
else
{
i <<= 4;
eshift (x, 5);
}
i |= *p++ & (unsigned EMUSHORT) 0x0f; /* *p = xi[M] */
*y |= (unsigned EMUSHORT) i; /* high order output already has sign bit set */
#ifdef IBMPC
*(--y) = *p++;
*(--y) = *p++;
*(--y) = *p;
#endif
#ifdef MIEEE
++y;
*y++ = *p++;
*y++ = *p++;
*y++ = *p++;
#endif
}
#endif /* not IBM */
#endif /* not DEC */
/* e type to IEEE single precision. */
#ifdef IBM
static void
etoe24 (x, e)
unsigned EMUSHORT *x, *e;
{
etoibm (x, e, SFmode);
}
static void
toe24 (x, y)
unsigned EMUSHORT *x, *y;
{
toibm (x, y, SFmode);
}
#else
static void
etoe24 (x, e)
unsigned EMUSHORT *x, *e;
{
EMULONG exp;
unsigned EMUSHORT xi[NI];
int rndsav;
#ifdef NANS
if (eisnan (x))
{
make_nan (e, eisneg (x), SFmode);
return;
}
#endif
emovi (x, xi);
/* adjust exponent for offsets */
exp = (EMULONG) xi[E] - (EXONE - 0177);
#ifdef INFINITY
if (eisinf (x))
goto nonorm;
#endif
/* round off to nearest or even */
rndsav = rndprc;
rndprc = 24;
emdnorm (xi, 0, 0, exp, 64);
rndprc = rndsav;
nonorm:
toe24 (xi, e);
}
static void
toe24 (x, y)
unsigned EMUSHORT *x, *y;
{
unsigned EMUSHORT i;
unsigned EMUSHORT *p;
#ifdef NANS
if (eiisnan (x))
{
make_nan (y, eiisneg (x), SFmode);
return;
}
#endif
p = &x[0];
#ifdef IBMPC
y += 1;
#endif
#ifdef DEC
y += 1;
#endif
*y = 0; /* output high order */
if (*p++)
*y = 0x8000; /* output sign bit */
i = *p++;
/* Handle overflow cases. */
if (i >= 255)
{
#ifdef INFINITY
*y |= (unsigned EMUSHORT) 0x7f80;
#ifdef IBMPC
*(--y) = 0;
#endif
#ifdef DEC
*(--y) = 0;
#endif
#ifdef MIEEE
++y;
*y = 0;
#endif
#else /* no INFINITY */
*y |= (unsigned EMUSHORT) 0x7f7f;
#ifdef IBMPC
*(--y) = 0xffff;
#endif
#ifdef DEC
*(--y) = 0xffff;
#endif
#ifdef MIEEE
++y;
*y = 0xffff;
#endif
#ifdef ERANGE
errno = ERANGE;
#endif
#endif /* no INFINITY */
return;
}
if (i == 0)
{
eshift (x, 7);
}
else
{
i <<= 7;
eshift (x, 8);
}
i |= *p++ & (unsigned EMUSHORT) 0x7f; /* *p = xi[M] */
*y |= i; /* high order output already has sign bit set */
#ifdef IBMPC
*(--y) = *p;
#endif
#ifdef DEC
*(--y) = *p;
#endif
#ifdef MIEEE
++y;
*y = *p;
#endif
}
#endif /* not IBM */
/* Compare two e type numbers.
Return +1 if a > b
0 if a == b
-1 if a < b
-2 if either a or b is a NaN. */
static int
ecmp (a, b)
unsigned EMUSHORT *a, *b;
{
unsigned EMUSHORT ai[NI], bi[NI];
register unsigned EMUSHORT *p, *q;
register int i;
int msign;
#ifdef NANS
if (eisnan (a) || eisnan (b))
return (-2);
#endif
emovi (a, ai);
p = ai;
emovi (b, bi);
q = bi;
if (*p != *q)
{ /* the signs are different */
/* -0 equals + 0 */
for (i = 1; i < NI - 1; i++)
{
if (ai[i] != 0)
goto nzro;
if (bi[i] != 0)
goto nzro;
}
return (0);
nzro:
if (*p == 0)
return (1);
else
return (-1);
}
/* both are the same sign */
if (*p == 0)
msign = 1;
else
msign = -1;
i = NI - 1;
do
{
if (*p++ != *q++)
{
goto diff;
}
}
while (--i > 0);
return (0); /* equality */
diff:
if (*(--p) > *(--q))
return (msign); /* p is bigger */
else
return (-msign); /* p is littler */
}
/* Find nearest integer to x = floor (x + 0.5). */
static void
eround (x, y)
unsigned EMUSHORT *x, *y;
{
eadd (ehalf, x, y);
efloor (y, y);
}
/* Convert HOST_WIDE_INT to e type. */
static void
ltoe (lp, y)
HOST_WIDE_INT *lp;
unsigned EMUSHORT *y;
{
unsigned EMUSHORT yi[NI];
unsigned HOST_WIDE_INT ll;
int k;
ecleaz (yi);
if (*lp < 0)
{
/* make it positive */
ll = (unsigned HOST_WIDE_INT) (-(*lp));
yi[0] = 0xffff; /* put correct sign in the e type number */
}
else
{
ll = (unsigned HOST_WIDE_INT) (*lp);
}
/* move the long integer to yi significand area */
#if HOST_BITS_PER_WIDE_INT == 64
yi[M] = (unsigned EMUSHORT) (ll >> 48);
yi[M + 1] = (unsigned EMUSHORT) (ll >> 32);
yi[M + 2] = (unsigned EMUSHORT) (ll >> 16);
yi[M + 3] = (unsigned EMUSHORT) ll;
yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
#else
yi[M] = (unsigned EMUSHORT) (ll >> 16);
yi[M + 1] = (unsigned EMUSHORT) ll;
yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
#endif
if ((k = enormlz (yi)) > NBITS)/* normalize the significand */
ecleaz (yi); /* it was zero */
else
yi[E] -= (unsigned EMUSHORT) k;/* subtract shift count from exponent */
emovo (yi, y); /* output the answer */
}
/* Convert unsigned HOST_WIDE_INT to e type. */
static void
ultoe (lp, y)
unsigned HOST_WIDE_INT *lp;
unsigned EMUSHORT *y;
{
unsigned EMUSHORT yi[NI];
unsigned HOST_WIDE_INT ll;
int k;
ecleaz (yi);
ll = *lp;
/* move the long integer to ayi significand area */
#if HOST_BITS_PER_WIDE_INT == 64
yi[M] = (unsigned EMUSHORT) (ll >> 48);
yi[M + 1] = (unsigned EMUSHORT) (ll >> 32);
yi[M + 2] = (unsigned EMUSHORT) (ll >> 16);
yi[M + 3] = (unsigned EMUSHORT) ll;
yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
#else
yi[M] = (unsigned EMUSHORT) (ll >> 16);
yi[M + 1] = (unsigned EMUSHORT) ll;
yi[E] = EXONE + 15; /* exponent if normalize shift count were 0 */
#endif
if ((k = enormlz (yi)) > NBITS)/* normalize the significand */
ecleaz (yi); /* it was zero */
else
yi[E] -= (unsigned EMUSHORT) k; /* subtract shift count from exponent */
emovo (yi, y); /* output the answer */
}
/* Find signed HOST_WIDE_INT integer and floating point fractional
parts of e-type (packed internal format) floating point input X.
The integer output I has the sign of the input, except that
positive overflow is permitted if FIXUNS_TRUNC_LIKE_FIX_TRUNC.
The output e-type fraction FRAC is the positive fractional
part of abs (X). */
static void
eifrac (x, i, frac)
unsigned EMUSHORT *x;
HOST_WIDE_INT *i;
unsigned EMUSHORT *frac;
{
unsigned EMUSHORT xi[NI];
int j, k;
unsigned HOST_WIDE_INT ll;
emovi (x, xi);
k = (int) xi[E] - (EXONE - 1);
if (k <= 0)
{
/* if exponent <= 0, integer = 0 and real output is fraction */
*i = 0L;
emovo (xi, frac);
return;
}
if (k > (HOST_BITS_PER_WIDE_INT - 1))
{
/* long integer overflow: output large integer
and correct fraction */
if (xi[0])
*i = ((unsigned HOST_WIDE_INT) 1) << (HOST_BITS_PER_WIDE_INT - 1);
else
{
#ifdef FIXUNS_TRUNC_LIKE_FIX_TRUNC
/* In this case, let it overflow and convert as if unsigned. */
euifrac (x, &ll, frac);
*i = (HOST_WIDE_INT) ll;
return;
#else
/* In other cases, return the largest positive integer. */
*i = (((unsigned HOST_WIDE_INT) 1) << (HOST_BITS_PER_WIDE_INT - 1)) - 1;
#endif
}
eshift (xi, k);
if (extra_warnings)
warning ("overflow on truncation to integer");
}
else if (k > 16)
{
/* Shift more than 16 bits: first shift up k-16 mod 16,
then shift up by 16's. */
j = k - ((k >> 4) << 4);
eshift (xi, j);
ll = xi[M];
k -= j;
do
{
eshup6 (xi);
ll = (ll << 16) | xi[M];
}
while ((k -= 16) > 0);
*i = ll;
if (xi[0])
*i = -(*i);
}
else
{
/* shift not more than 16 bits */
eshift (xi, k);
*i = (HOST_WIDE_INT) xi[M] & 0xffff;
if (xi[0])
*i = -(*i);
}
xi[0] = 0;
xi[E] = EXONE - 1;
xi[M] = 0;
if ((k = enormlz (xi)) > NBITS)
ecleaz (xi);
else
xi[E] -= (unsigned EMUSHORT) k;
emovo (xi, frac);
}
/* Find unsigned HOST_WIDE_INT integer and floating point fractional parts.
A negative e type input yields integer output = 0
but correct fraction. */
static void
euifrac (x, i, frac)
unsigned EMUSHORT *x;
unsigned HOST_WIDE_INT *i;
unsigned EMUSHORT *frac;
{
unsigned HOST_WIDE_INT ll;
unsigned EMUSHORT xi[NI];
int j, k;
emovi (x, xi);
k = (int) xi[E] - (EXONE - 1);
if (k <= 0)
{
/* if exponent <= 0, integer = 0 and argument is fraction */
*i = 0L;
emovo (xi, frac);
return;
}
if (k > HOST_BITS_PER_WIDE_INT)
{
/* Long integer overflow: output large integer
and correct fraction.
Note, the BSD microvax compiler says that ~(0UL)
is a syntax error. */
*i = ~(0L);
eshift (xi, k);
if (extra_warnings)
warning ("overflow on truncation to unsigned integer");
}
else if (k > 16)
{
/* Shift more than 16 bits: first shift up k-16 mod 16,
then shift up by 16's. */
j = k - ((k >> 4) << 4);
eshift (xi, j);
ll = xi[M];
k -= j;
do
{
eshup6 (xi);
ll = (ll << 16) | xi[M];
}
while ((k -= 16) > 0);
*i = ll;
}
else
{
/* shift not more than 16 bits */
eshift (xi, k);
*i = (HOST_WIDE_INT) xi[M] & 0xffff;
}
if (xi[0]) /* A negative value yields unsigned integer 0. */
*i = 0L;
xi[0] = 0;
xi[E] = EXONE - 1;
xi[M] = 0;
if ((k = enormlz (xi)) > NBITS)
ecleaz (xi);
else
xi[E] -= (unsigned EMUSHORT) k;
emovo (xi, frac);
}
/* Shift significand area up or down by the number of bits given by SC. */
static int
eshift (x, sc)
unsigned EMUSHORT *x;
int sc;
{
unsigned EMUSHORT lost;
unsigned EMUSHORT *p;
if (sc == 0)
return (0);
lost = 0;
p = x + NI - 1;
if (sc < 0)
{
sc = -sc;
while (sc >= 16)
{
lost |= *p; /* remember lost bits */
eshdn6 (x);
sc -= 16;
}
while (sc >= 8)
{
lost |= *p & 0xff;
eshdn8 (x);
sc -= 8;
}
while (sc > 0)
{
lost |= *p & 1;
eshdn1 (x);
sc -= 1;
}
}
else
{
while (sc >= 16)
{
eshup6 (x);
sc -= 16;
}
while (sc >= 8)
{
eshup8 (x);
sc -= 8;
}
while (sc > 0)
{
eshup1 (x);
sc -= 1;
}
}
if (lost)
lost = 1;
return ((int) lost);
}
/* Shift normalize the significand area pointed to by argument.
Shift count (up = positive) is returned. */
static int
enormlz (x)
unsigned EMUSHORT x[];
{
register unsigned EMUSHORT *p;
int sc;
sc = 0;
p = &x[M];
if (*p != 0)
goto normdn;
++p;
if (*p & 0x8000)
return (0); /* already normalized */
while (*p == 0)
{
eshup6 (x);
sc += 16;
/* With guard word, there are NBITS+16 bits available.
Return true if all are zero. */
if (sc > NBITS)
return (sc);
}
/* see if high byte is zero */
while ((*p & 0xff00) == 0)
{
eshup8 (x);
sc += 8;
}
/* now shift 1 bit at a time */
while ((*p & 0x8000) == 0)
{
eshup1 (x);
sc += 1;
if (sc > NBITS)
{
mtherr ("enormlz", UNDERFLOW);
return (sc);
}
}
return (sc);
/* Normalize by shifting down out of the high guard word
of the significand */
normdn:
if (*p & 0xff00)
{
eshdn8 (x);
sc -= 8;
}
while (*p != 0)
{
eshdn1 (x);
sc -= 1;
if (sc < -NBITS)
{
mtherr ("enormlz", OVERFLOW);
return (sc);
}
}
return (sc);
}
/* Convert e type number to decimal format ASCII string.
The constants are for 64 bit precision. */
#define NTEN 12
#define MAXP 4096
#if LONG_DOUBLE_TYPE_SIZE == 128
static unsigned EMUSHORT etens[NTEN + 1][NE] =
{
{0x6576, 0x4a92, 0x804a, 0x153f,
0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,}, /* 10**4096 */
{0x6a32, 0xce52, 0x329a, 0x28ce,
0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,}, /* 10**2048 */
{0x526c, 0x50ce, 0xf18b, 0x3d28,
0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,},
{0x9c66, 0x58f8, 0xbc50, 0x5c54,
0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,},
{0x851e, 0xeab7, 0x98fe, 0x901b,
0xddbb, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,},
{0x0235, 0x0137, 0x36b1, 0x336c,
0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,},
{0x50f8, 0x25fb, 0xc76b, 0x6b71,
0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,},
{0x0000, 0x0000, 0x0000, 0x0000,
0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,},
{0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,},
{0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,},
{0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,},
{0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,},
{0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,}, /* 10**1 */
};
static unsigned EMUSHORT emtens[NTEN + 1][NE] =
{
{0x2030, 0xcffc, 0xa1c3, 0x8123,
0x2de3, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,}, /* 10**-4096 */
{0x8264, 0xd2cb, 0xf2ea, 0x12d4,
0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,}, /* 10**-2048 */
{0xf53f, 0xf698, 0x6bd3, 0x0158,
0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,},
{0xe731, 0x04d4, 0xe3f2, 0xd332,
0x7132, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,},
{0xa23e, 0x5308, 0xfefb, 0x1155,
0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,},
{0xe26d, 0xdbde, 0xd05d, 0xb3f6,
0xac7c, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,},
{0x2a20, 0x6224, 0x47b3, 0x98d7,
0x3f23, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,},
{0x0b5b, 0x4af2, 0xa581, 0x18ed,
0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,},
{0xbf71, 0xa9b3, 0x7989, 0xbe68,
0x4c2e, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,},
{0x3d4d, 0x7c3d, 0x36ba, 0x0d2b,
0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,},
{0xc155, 0xa4a8, 0x404e, 0x6113,
0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,},
{0xd70a, 0x70a3, 0x0a3d, 0xa3d7,
0x3d70, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,},
{0xcccd, 0xcccc, 0xcccc, 0xcccc,
0xcccc, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,}, /* 10**-1 */
};
#else
/* LONG_DOUBLE_TYPE_SIZE is other than 128 */
static unsigned EMUSHORT etens[NTEN + 1][NE] =
{
{0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,}, /* 10**4096 */
{0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,}, /* 10**2048 */
{0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,},
{0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,},
{0xddbc, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,},
{0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,},
{0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,},
{0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,},
{0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,},
{0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,},
{0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,},
{0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,},
{0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,}, /* 10**1 */
};
static unsigned EMUSHORT emtens[NTEN + 1][NE] =
{
{0x2de4, 0x9fde, 0xd2ce, 0x04c8, 0xa6dd, 0x0ad8,}, /* 10**-4096 */
{0x4925, 0x2de4, 0x3436, 0x534f, 0xceae, 0x256b,}, /* 10**-2048 */
{0x87a6, 0xc0bd, 0xda57, 0x82a5, 0xa2a6, 0x32b5,},
{0x7133, 0xd21c, 0xdb23, 0xee32, 0x9049, 0x395a,},
{0xfa91, 0x1939, 0x637a, 0x4325, 0xc031, 0x3cac,},
{0xac7d, 0xe4a0, 0x64bc, 0x467c, 0xddd0, 0x3e55,},
{0x3f24, 0xe9a5, 0xa539, 0xea27, 0xa87f, 0x3f2a,},
{0x67de, 0x94ba, 0x4539, 0x1ead, 0xcfb1, 0x3f94,},
{0x4c2f, 0xe15b, 0xc44d, 0x94be, 0xe695, 0x3fc9,},
{0xfdc2, 0xcefc, 0x8461, 0x7711, 0xabcc, 0x3fe4,},
{0xd3c3, 0x652b, 0xe219, 0x1758, 0xd1b7, 0x3ff1,},
{0x3d71, 0xd70a, 0x70a3, 0x0a3d, 0xa3d7, 0x3ff8,},
{0xcccd, 0xcccc, 0xcccc, 0xcccc, 0xcccc, 0x3ffb,}, /* 10**-1 */
};
#endif
static void
e24toasc (x, string, ndigs)
unsigned EMUSHORT x[];
char *string;
int ndigs;
{
unsigned EMUSHORT w[NI];
e24toe (x, w);
etoasc (w, string, ndigs);
}
static void
e53toasc (x, string, ndigs)
unsigned EMUSHORT x[];
char *string;
int ndigs;
{
unsigned EMUSHORT w[NI];
e53toe (x, w);
etoasc (w, string, ndigs);
}
static void
e64toasc (x, string, ndigs)
unsigned EMUSHORT x[];
char *string;
int ndigs;
{
unsigned EMUSHORT w[NI];
e64toe (x, w);
etoasc (w, string, ndigs);
}
static void
e113toasc (x, string, ndigs)
unsigned EMUSHORT x[];
char *string;
int ndigs;
{
unsigned EMUSHORT w[NI];
e113toe (x, w);
etoasc (w, string, ndigs);
}
static char wstring[80]; /* working storage for ASCII output */
static void
etoasc (x, string, ndigs)
unsigned EMUSHORT x[];
char *string;
int ndigs;
{
EMUSHORT digit;
unsigned EMUSHORT y[NI], t[NI], u[NI], w[NI];
unsigned EMUSHORT *p, *r, *ten;
unsigned EMUSHORT sign;
int i, j, k, expon, rndsav;
char *s, *ss;
unsigned EMUSHORT m;
rndsav = rndprc;
ss = string;
s = wstring;
*ss = '\0';
*s = '\0';
#ifdef NANS
if (eisnan (x))
{
sprintf (wstring, " NaN ");
goto bxit;
}
#endif
rndprc = NBITS; /* set to full precision */
emov (x, y); /* retain external format */
if (y[NE - 1] & 0x8000)
{
sign = 0xffff;
y[NE - 1] &= 0x7fff;
}
else
{
sign = 0;
}
expon = 0;
ten = &etens[NTEN][0];
emov (eone, t);
/* Test for zero exponent */
if (y[NE - 1] == 0)
{
for (k = 0; k < NE - 1; k++)
{
if (y[k] != 0)
goto tnzro; /* denormalized number */
}
goto isone; /* legal all zeros */
}
tnzro:
/* Test for infinity. */
if (y[NE - 1] == 0x7fff)
{
if (sign)
sprintf (wstring, " -Infinity ");
else
sprintf (wstring, " Infinity ");
goto bxit;
}
/* Test for exponent nonzero but significand denormalized.
* This is an error condition.
*/
if ((y[NE - 1] != 0) && ((y[NE - 2] & 0x8000) == 0))
{
mtherr ("etoasc", DOMAIN);
sprintf (wstring, "NaN");
goto bxit;
}
/* Compare to 1.0 */
i = ecmp (eone, y);
if (i == 0)
goto isone;
if (i == -2)
abort ();
if (i < 0)
{ /* Number is greater than 1 */
/* Convert significand to an integer and strip trailing decimal zeros. */
emov (y, u);
u[NE - 1] = EXONE + NBITS - 1;
p = &etens[NTEN - 4][0];
m = 16;
do
{
ediv (p, u, t);
efloor (t, w);
for (j = 0; j < NE - 1; j++)
{
if (t[j] != w[j])
goto noint;
}
emov (t, u);
expon += (int) m;
noint:
p += NE;
m >>= 1;
}
while (m != 0);
/* Rescale from integer significand */
u[NE - 1] += y[NE - 1] - (unsigned int) (EXONE + NBITS - 1);
emov (u, y);
/* Find power of 10 */
emov (eone, t);
m = MAXP;
p = &etens[0][0];
/* An unordered compare result shouldn't happen here. */
while (ecmp (ten, u) <= 0)
{
if (ecmp (p, u) <= 0)
{
ediv (p, u, u);
emul (p, t, t);
expon += (int) m;
}
m >>= 1;
if (m == 0)
break;
p += NE;
}
}
else
{ /* Number is less than 1.0 */
/* Pad significand with trailing decimal zeros. */
if (y[NE - 1] == 0)
{
while ((y[NE - 2] & 0x8000) == 0)
{
emul (ten, y, y);
expon -= 1;
}
}
else
{
emovi (y, w);
for (i = 0; i < NDEC + 1; i++)
{
if ((w[NI - 1] & 0x7) != 0)
break;
/* multiply by 10 */
emovz (w, u);
eshdn1 (u);
eshdn1 (u);
eaddm (w, u);
u[1] += 3;
while (u[2] != 0)
{
eshdn1 (u);
u[1] += 1;
}
if (u[NI - 1] != 0)
break;
if (eone[NE - 1] <= u[1])
break;
emovz (u, w);
expon -= 1;
}
emovo (w, y);
}
k = -MAXP;
p = &emtens[0][0];
r = &etens[0][0];
emov (y, w);
emov (eone, t);
while (ecmp (eone, w) > 0)
{
if (ecmp (p, w) >= 0)
{
emul (r, w, w);
emul (r, t, t);
expon += k;
}
k /= 2;
if (k == 0)
break;
p += NE;
r += NE;
}
ediv (t, eone, t);
}
isone:
/* Find the first (leading) digit. */
emovi (t, w);
emovz (w, t);
emovi (y, w);
emovz (w, y);
eiremain (t, y);
digit = equot[NI - 1];
while ((digit == 0) && (ecmp (y, ezero) != 0))
{
eshup1 (y);
emovz (y, u);
eshup1 (u);
eshup1 (u);
eaddm (u, y);
eiremain (t, y);
digit = equot[NI - 1];
expon -= 1;
}
s = wstring;
if (sign)
*s++ = '-';
else
*s++ = ' ';
/* Examine number of digits requested by caller. */
if (ndigs < 0)
ndigs = 0;
if (ndigs > NDEC)
ndigs = NDEC;
if (digit == 10)
{
*s++ = '1';
*s++ = '.';
if (ndigs > 0)
{
*s++ = '0';
ndigs -= 1;
}
expon += 1;
}
else
{
*s++ = (char)digit + '0';
*s++ = '.';
}
/* Generate digits after the decimal point. */
for (k = 0; k <= ndigs; k++)
{
/* multiply current number by 10, without normalizing */
eshup1 (y);
emovz (y, u);
eshup1 (u);
eshup1 (u);
eaddm (u, y);
eiremain (t, y);
*s++ = (char) equot[NI - 1] + '0';
}
digit = equot[NI - 1];
--s;
ss = s;
/* round off the ASCII string */
if (digit > 4)
{
/* Test for critical rounding case in ASCII output. */
if (digit == 5)
{
emovo (y, t);
if (ecmp (t, ezero) != 0)
goto roun; /* round to nearest */
if ((*(s - 1) & 1) == 0)
goto doexp; /* round to even */
}
/* Round up and propagate carry-outs */
roun:
--s;
k = *s & 0x7f;
/* Carry out to most significant digit? */
if (k == '.')
{
--s;
k = *s;
k += 1;
*s = (char) k;
/* Most significant digit carries to 10? */
if (k > '9')
{
expon += 1;
*s = '1';
}
goto doexp;
}
/* Round up and carry out from less significant digits */
k += 1;
*s = (char) k;
if (k > '9')
{
*s = '0';
goto roun;
}
}
doexp:
/*
if (expon >= 0)
sprintf (ss, "e+%d", expon);
else
sprintf (ss, "e%d", expon);
*/
sprintf (ss, "e%d", expon);
bxit:
rndprc = rndsav;
/* copy out the working string */
s = string;
ss = wstring;
while (*ss == ' ') /* strip possible leading space */
++ss;
while ((*s++ = *ss++) != '\0')
;
}
/* Convert ASCII string to quadruple precision floating point
Numeric input is free field decimal number with max of 15 digits with or
without decimal point entered as ASCII from teletype. Entering E after
the number followed by a second number causes the second number to be
interpreted as a power of 10 to be multiplied by the first number
(i.e., "scientific" notation). */
/* ASCII to single */
static void
asctoe24 (s, y)
char *s;
unsigned EMUSHORT *y;
{
asctoeg (s, y, 24);
}
/* ASCII to double */
static void
asctoe53 (s, y)
char *s;
unsigned EMUSHORT *y;
{
#if defined(DEC) || defined(IBM)
asctoeg (s, y, 56);
#else
asctoeg (s, y, 53);
#endif
}
/* ASCII to long double */
static void
asctoe64 (s, y)
char *s;
unsigned EMUSHORT *y;
{
asctoeg (s, y, 64);
}
/* ASCII to 128-bit long double */
static void
asctoe113 (s, y)
char *s;
unsigned EMUSHORT *y;
{
asctoeg (s, y, 113);
}
/* ASCII to super double */
static void
asctoe (s, y)
char *s;
unsigned EMUSHORT *y;
{
asctoeg (s, y, NBITS);
}
/* ASCII to e type, with specified rounding precision = oprec. */
static void
asctoeg (ss, y, oprec)
char *ss;
unsigned EMUSHORT *y;
int oprec;
{
unsigned EMUSHORT yy[NI], xt[NI], tt[NI];
int esign, decflg, sgnflg, nexp, exp, prec, lost;
int k, trail, c, rndsav;
EMULONG lexp;
unsigned EMUSHORT nsign, *p;
char *sp, *s, *lstr;
/* Copy the input string. */
lstr = (char *) alloca (strlen (ss) + 1);
s = ss;
while (*s == ' ') /* skip leading spaces */
++s;
sp = lstr;
while ((*sp++ = *s++) != '\0')
;
s = lstr;
rndsav = rndprc;
rndprc = NBITS; /* Set to full precision */
lost = 0;
nsign = 0;
decflg = 0;
sgnflg = 0;
nexp = 0;
exp = 0;
prec = 0;
ecleaz (yy);
trail = 0;
nxtcom:
k = *s - '0';
if ((k >= 0) && (k <= 9))
{
/* Ignore leading zeros */
if ((prec == 0) && (decflg == 0) && (k == 0))
goto donchr;
/* Identify and strip trailing zeros after the decimal point. */
if ((trail == 0) && (decflg != 0))
{
sp = s;
while ((*sp >= '0') && (*sp <= '9'))
++sp;
/* Check for syntax error */
c = *sp & 0x7f;
if ((c != 'e') && (c != 'E') && (c != '\0')
&& (c != '\n') && (c != '\r') && (c != ' ')
&& (c != ','))
goto error;
--sp;
while (*sp == '0')
*sp-- = 'z';
trail = 1;
if (*s == 'z')
goto donchr;
}
/* If enough digits were given to more than fill up the yy register,
continuing until overflow into the high guard word yy[2]
guarantees that there will be a roundoff bit at the top
of the low guard word after normalization. */
if (yy[2] == 0)
{
if (decflg)
nexp += 1; /* count digits after decimal point */
eshup1 (yy); /* multiply current number by 10 */
emovz (yy, xt);
eshup1 (xt);
eshup1 (xt);
eaddm (xt, yy);
ecleaz (xt);
xt[NI - 2] = (unsigned EMUSHORT) k;
eaddm (xt, yy);
}
else
{
/* Mark any lost non-zero digit. */
lost |= k;
/* Count lost digits before the decimal point. */
if (decflg == 0)
nexp -= 1;
}
prec += 1;
goto donchr;
}
switch (*s)
{
case 'z':
break;
case 'E':
case 'e':
goto expnt;
case '.': /* decimal point */
if (decflg)
goto error;
++decflg;
break;
case '-':
nsign = 0xffff;
if (sgnflg)
goto error;
++sgnflg;
break;
case '+':
if (sgnflg)
goto error;
++sgnflg;
break;
case ',':
case ' ':
case '\0':
case '\n':
case '\r':
goto daldone;
case 'i':
case 'I':
goto infinite;
default:
error:
#ifdef NANS
einan (yy);
#else
mtherr ("asctoe", DOMAIN);
eclear (yy);
#endif
goto aexit;
}
donchr:
++s;
goto nxtcom;
/* Exponent interpretation */
expnt:
esign = 1;
exp = 0;
++s;
/* check for + or - */
if (*s == '-')
{
esign = -1;
++s;
}
if (*s == '+')
++s;
while ((*s >= '0') && (*s <= '9'))
{
exp *= 10;
exp += *s++ - '0';
if (exp > -(MINDECEXP))
{
if (esign < 0)
goto zero;
else
goto infinite;
}
}
if (esign < 0)
exp = -exp;
if (exp > MAXDECEXP)
{
infinite:
ecleaz (yy);
yy[E] = 0x7fff; /* infinity */
goto aexit;
}
if (exp < MINDECEXP)
{
zero:
ecleaz (yy);
goto aexit;
}
daldone:
nexp = exp - nexp;
/* Pad trailing zeros to minimize power of 10, per IEEE spec. */
while ((nexp > 0) && (yy[2] == 0))
{
emovz (yy, xt);
eshup1 (xt);
eshup1 (xt);
eaddm (yy, xt);
eshup1 (xt);
if (xt[2] != 0)
break;
nexp -= 1;
emovz (xt, yy);
}
if ((k = enormlz (yy)) > NBITS)
{
ecleaz (yy);
goto aexit;
}
lexp = (EXONE - 1 + NBITS) - k;
emdnorm (yy, lost, 0, lexp, 64);
/* Convert to external format:
Multiply by 10**nexp. If precision is 64 bits,
the maximum relative error incurred in forming 10**n
for 0 <= n <= 324 is 8.2e-20, at 10**180.
For 0 <= n <= 999, the peak relative error is 1.4e-19 at 10**947.
For 0 >= n >= -999, it is -1.55e-19 at 10**-435. */
lexp = yy[E];
if (nexp == 0)
{
k = 0;
goto expdon;
}
esign = 1;
if (nexp < 0)
{
nexp = -nexp;
esign = -1;
if (nexp > 4096)
{
/* Punt. Can't handle this without 2 divides. */
emovi (etens[0], tt);
lexp -= tt[E];
k = edivm (tt, yy);
lexp += EXONE;
nexp -= 4096;
}
}
p = &etens[NTEN][0];
emov (eone, xt);
exp = 1;
do
{
if (exp & nexp)
emul (p, xt, xt);
p -= NE;
exp = exp + exp;
}
while (exp <= MAXP);
emovi (xt, tt);
if (esign < 0)
{
lexp -= tt[E];
k = edivm (tt, yy);
lexp += EXONE;
}
else
{
lexp += tt[E];
k = emulm (tt, yy);
lexp -= EXONE - 1;
}
expdon:
/* Round and convert directly to the destination type */
if (oprec == 53)
lexp -= EXONE - 0x3ff;
#ifdef IBM
else if (oprec == 24 || oprec == 56)
lexp -= EXONE - (0x41 << 2);
#else
else if (oprec == 24)
lexp -= EXONE - 0177;
#endif
#ifdef DEC
else if (oprec == 56)
lexp -= EXONE - 0201;
#endif
rndprc = oprec;
emdnorm (yy, k, 0, lexp, 64);
aexit:
rndprc = rndsav;
yy[0] = nsign;
switch (oprec)
{
#ifdef DEC
case 56:
todec (yy, y); /* see etodec.c */
break;
#endif
#ifdef IBM
case 56:
toibm (yy, y, DFmode);
break;
#endif
case 53:
toe53 (yy, y);
break;
case 24:
toe24 (yy, y);
break;
case 64:
toe64 (yy, y);
break;
case 113:
toe113 (yy, y);
break;
case NBITS:
emovo (yy, y);
break;
}
}
/* y = largest integer not greater than x (truncated toward minus infinity) */
static unsigned EMUSHORT bmask[] =
{
0xffff,
0xfffe,
0xfffc,
0xfff8,
0xfff0,
0xffe0,
0xffc0,
0xff80,
0xff00,
0xfe00,
0xfc00,
0xf800,
0xf000,
0xe000,
0xc000,
0x8000,
0x0000,
};
static void
efloor (x, y)
unsigned EMUSHORT x[], y[];
{
register unsigned EMUSHORT *p;
int e, expon, i;
unsigned EMUSHORT f[NE];
emov (x, f); /* leave in external format */
expon = (int) f[NE - 1];
e = (expon & 0x7fff) - (EXONE - 1);
if (e <= 0)
{
eclear (y);
goto isitneg;
}
/* number of bits to clear out */
e = NBITS - e;
emov (f, y);
if (e <= 0)
return;
p = &y[0];
while (e >= 16)
{
*p++ = 0;
e -= 16;
}
/* clear the remaining bits */
*p &= bmask[e];
/* truncate negatives toward minus infinity */
isitneg:
if ((unsigned EMUSHORT) expon & (unsigned EMUSHORT) 0x8000)
{
for (i = 0; i < NE - 1; i++)
{
if (f[i] != y[i])
{
esub (eone, y, y);
break;
}
}
}
}
/* Returns s and exp such that s * 2**exp = x and .5 <= s < 1.
For example, 1.1 = 0.55 * 2**1
Handles denormalized numbers properly using long integer exp. */
static void
efrexp (x, exp, s)
unsigned EMUSHORT x[];
int *exp;
unsigned EMUSHORT s[];
{
unsigned EMUSHORT xi[NI];
EMULONG li;
emovi (x, xi);
li = (EMULONG) ((EMUSHORT) xi[1]);
if (li == 0)
{
li -= enormlz (xi);
}
xi[1] = 0x3ffe;
emovo (xi, s);
*exp = (int) (li - 0x3ffe);
}
/* Return y = x * 2**pwr2. */
static void
eldexp (x, pwr2, y)
unsigned EMUSHORT x[];
int pwr2;
unsigned EMUSHORT y[];
{
unsigned EMUSHORT xi[NI];
EMULONG li;
int i;
emovi (x, xi);
li = xi[1];
li += pwr2;
i = 0;
emdnorm (xi, i, i, li, 64);
emovo (xi, y);
}
/* c = remainder after dividing b by a
Least significant integer quotient bits left in equot[]. */
static void
eremain (a, b, c)
unsigned EMUSHORT a[], b[], c[];
{
unsigned EMUSHORT den[NI], num[NI];
#ifdef NANS
if (eisinf (b)
|| (ecmp (a, ezero) == 0)
|| eisnan (a)
|| eisnan (b))
{
enan (c, 0);
return;
}
#endif
if (ecmp (a, ezero) == 0)
{
mtherr ("eremain", SING);
eclear (c);
return;
}
emovi (a, den);
emovi (b, num);
eiremain (den, num);
/* Sign of remainder = sign of quotient */
if (a[0] == b[0])
num[0] = 0;
else
num[0] = 0xffff;
emovo (num, c);
}
static void
eiremain (den, num)
unsigned EMUSHORT den[], num[];
{
EMULONG ld, ln;
unsigned EMUSHORT j;
ld = den[E];
ld -= enormlz (den);
ln = num[E];
ln -= enormlz (num);
ecleaz (equot);
while (ln >= ld)
{
if (ecmpm (den, num) <= 0)
{
esubm (den, num);
j = 1;
}
else
{
j = 0;
}
eshup1 (equot);
equot[NI - 1] |= j;
eshup1 (num);
ln -= 1;
}
emdnorm (num, 0, 0, ln, 0);
}
/* This routine may be called to report one of the following
error conditions (in the include file mconf.h).
Mnemonic Value Significance
DOMAIN 1 argument domain error
SING 2 function singularity
OVERFLOW 3 overflow range error
UNDERFLOW 4 underflow range error
TLOSS 5 total loss of precision
PLOSS 6 partial loss of precision
INVALID 7 NaN - producing operation
EDOM 33 Unix domain error code
ERANGE 34 Unix range error code
The default version of the file prints the function name,
passed to it by the pointer fctnam, followed by the
error condition. The display is directed to the standard
output device. The routine then returns to the calling
program. Users may wish to modify the program to abort by
calling exit under severe error conditions such as domain
errors.
Since all error conditions pass control to this function,
the display may be easily changed, eliminated, or directed
to an error logging device. */
/* Note: the order of appearance of the following messages is bound to the
error codes defined above. */
#define NMSGS 8
static char *ermsg[NMSGS] =
{
"unknown", /* error code 0 */
"domain", /* error code 1 */
"singularity", /* et seq. */
"overflow",
"underflow",
"total loss of precision",
"partial loss of precision",
"invalid operation"
};
int merror = 0;
extern int merror;
static void
mtherr (name, code)
char *name;
int code;
{
char errstr[80];
/* Display string passed by calling program, which is supposed to be the
name of the function in which the error occurred.
Display error message defined by the code argument. */
if ((code <= 0) || (code >= NMSGS))
code = 0;
sprintf (errstr, " %s %s error", name, ermsg[code]);
if (extra_warnings)
warning (errstr);
/* Set global error message word */
merror = code + 1;
}
#ifdef DEC
/* Convert DEC double precision to e type. */
static void
dectoe (d, e)
unsigned EMUSHORT *d;
unsigned EMUSHORT *e;
{
unsigned EMUSHORT y[NI];
register unsigned EMUSHORT r, *p;
ecleaz (y); /* start with a zero */
p = y; /* point to our number */
r = *d; /* get DEC exponent word */
if (*d & (unsigned int) 0x8000)
*p = 0xffff; /* fill in our sign */
++p; /* bump pointer to our exponent word */
r &= 0x7fff; /* strip the sign bit */
if (r == 0) /* answer = 0 if high order DEC word = 0 */
goto done;
r >>= 7; /* shift exponent word down 7 bits */
r += EXONE - 0201; /* subtract DEC exponent offset */
/* add our e type exponent offset */
*p++ = r; /* to form our exponent */
r = *d++; /* now do the high order mantissa */
r &= 0177; /* strip off the DEC exponent and sign bits */
r |= 0200; /* the DEC understood high order mantissa bit */
*p++ = r; /* put result in our high guard word */
*p++ = *d++; /* fill in the rest of our mantissa */
*p++ = *d++;
*p = *d;
eshdn8 (y); /* shift our mantissa down 8 bits */
done:
emovo (y, e);
}
/*
; convert e type to DEC double precision
; double d;
; EMUSHORT e[NE];
; etodec (e, &d);
*/
static void
etodec (x, d)
unsigned EMUSHORT *x, *d;
{
unsigned EMUSHORT xi[NI];
EMULONG exp;
int rndsav;
emovi (x, xi);
exp = (EMULONG) xi[E] - (EXONE - 0201); /* adjust exponent for offsets */
/* round off to nearest or even */
rndsav = rndprc;
rndprc = 56;
emdnorm (xi, 0, 0, exp, 64);
rndprc = rndsav;
todec (xi, d);
}
static void
todec (x, y)
unsigned EMUSHORT *x, *y;
{
unsigned EMUSHORT i;
unsigned EMUSHORT *p;
p = x;
*y = 0;
if (*p++)
*y = 0100000;
i = *p++;
if (i == 0)
{
*y++ = 0;
*y++ = 0;
*y++ = 0;
*y++ = 0;
return;
}
if (i > 0377)
{
*y++ |= 077777;
*y++ = 0xffff;
*y++ = 0xffff;
*y++ = 0xffff;
#ifdef ERANGE
errno = ERANGE;
#endif
return;
}
i &= 0377;
i <<= 7;
eshup8 (x);
x[M] &= 0177;
i |= x[M];
*y++ |= i;
*y++ = x[M + 1];
*y++ = x[M + 2];
*y++ = x[M + 3];
}
#endif /* DEC */
#ifdef IBM
/* Convert IBM single/double precision to e type. */
static void
ibmtoe (d, e, mode)
unsigned EMUSHORT *d;
unsigned EMUSHORT *e;
enum machine_mode mode;
{
unsigned EMUSHORT y[NI];
register unsigned EMUSHORT r, *p;
int rndsav;
ecleaz (y); /* start with a zero */
p = y; /* point to our number */
r = *d; /* get IBM exponent word */
if (*d & (unsigned int) 0x8000)
*p = 0xffff; /* fill in our sign */
++p; /* bump pointer to our exponent word */
r &= 0x7f00; /* strip the sign bit */
r >>= 6; /* shift exponent word down 6 bits */
/* in fact shift by 8 right and 2 left */
r += EXONE - (0x41 << 2); /* subtract IBM exponent offset */
/* add our e type exponent offset */
*p++ = r; /* to form our exponent */
*p++ = *d++ & 0xff; /* now do the high order mantissa */
/* strip off the IBM exponent and sign bits */
if (mode != SFmode) /* there are only 2 words in SFmode */
{
*p++ = *d++; /* fill in the rest of our mantissa */
*p++ = *d++;
}
*p = *d;
if (y[M] == 0 && y[M+1] == 0 && y[M+2] == 0 && y[M+3] == 0)
y[0] = y[E] = 0;
else
y[E] -= 5 + enormlz (y); /* now normalise the mantissa */
/* handle change in RADIX */
emovo (y, e);
}
/* Convert e type to IBM single/double precision. */
static void
etoibm (x, d, mode)
unsigned EMUSHORT *x, *d;
enum machine_mode mode;
{
unsigned EMUSHORT xi[NI];
EMULONG exp;
int rndsav;
emovi (x, xi);
exp = (EMULONG) xi[E] - (EXONE - (0x41 << 2)); /* adjust exponent for offsets */
/* round off to nearest or even */
rndsav = rndprc;
rndprc = 56;
emdnorm (xi, 0, 0, exp, 64);
rndprc = rndsav;
toibm (xi, d, mode);
}
static void
toibm (x, y, mode)
unsigned EMUSHORT *x, *y;
enum machine_mode mode;
{
unsigned EMUSHORT i;
unsigned EMUSHORT *p;
int r;
p = x;
*y = 0;
if (*p++)
*y = 0x8000;
i = *p++;
if (i == 0)
{
*y++ = 0;
*y++ = 0;
if (mode != SFmode)
{
*y++ = 0;
*y++ = 0;
}
return;
}
r = i & 0x3;
i >>= 2;
if (i > 0x7f)
{
*y++ |= 0x7fff;
*y++ = 0xffff;
if (mode != SFmode)
{
*y++ = 0xffff;
*y++ = 0xffff;
}
#ifdef ERANGE
errno = ERANGE;
#endif
return;
}
i &= 0x7f;
*y |= (i << 8);
eshift (x, r + 5);
*y++ |= x[M];
*y++ = x[M + 1];
if (mode != SFmode)
{
*y++ = x[M + 2];
*y++ = x[M + 3];
}
}
#endif /* IBM */
/* Output a binary NaN bit pattern in the target machine's format. */
/* If special NaN bit patterns are required, define them in tm.h
as arrays of unsigned 16-bit shorts. Otherwise, use the default
patterns here. */
#ifdef TFMODE_NAN
TFMODE_NAN;
#else
#ifdef MIEEE
unsigned EMUSHORT TFnan[8] =
{0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff};
#endif
#ifdef IBMPC
unsigned EMUSHORT TFnan[8] = {0, 0, 0, 0, 0, 0, 0x8000, 0xffff};
#endif
#endif
#ifdef XFMODE_NAN
XFMODE_NAN;
#else
#ifdef MIEEE
unsigned EMUSHORT XFnan[6] = {0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff};
#endif
#ifdef IBMPC
unsigned EMUSHORT XFnan[6] = {0, 0, 0, 0xc000, 0xffff, 0};
#endif
#endif
#ifdef DFMODE_NAN
DFMODE_NAN;
#else
#ifdef MIEEE
unsigned EMUSHORT DFnan[4] = {0x7fff, 0xffff, 0xffff, 0xffff};
#endif
#ifdef IBMPC
unsigned EMUSHORT DFnan[4] = {0, 0, 0, 0xfff8};
#endif
#endif
#ifdef SFMODE_NAN
SFMODE_NAN;
#else
#ifdef MIEEE
unsigned EMUSHORT SFnan[2] = {0x7fff, 0xffff};
#endif
#ifdef IBMPC
unsigned EMUSHORT SFnan[2] = {0, 0xffc0};
#endif
#endif
static void
make_nan (nan, sign, mode)
unsigned EMUSHORT *nan;
int sign;
enum machine_mode mode;
{
int n;
unsigned EMUSHORT *p;
switch (mode)
{
/* Possibly the `reserved operand' patterns on a VAX can be
used like NaN's, but probably not in the same way as IEEE. */
#if !defined(DEC) && !defined(IBM)
case TFmode:
n = 8;
p = TFnan;
break;
case XFmode:
n = 6;
p = XFnan;
break;
case DFmode:
n = 4;
p = DFnan;
break;
case HFmode:
case SFmode:
n = 2;
p = SFnan;
break;
#endif
default:
abort ();
}
#ifdef MIEEE
*nan++ = (sign << 15) | *p++;
#endif
while (--n != 0)
*nan++ = *p++;
#ifndef MIEEE
*nan = (sign << 15) | *p;
#endif
}
/* Convert an SFmode target `float' value to a REAL_VALUE_TYPE.
This is the inverse of the function `etarsingle' invoked by
REAL_VALUE_TO_TARGET_SINGLE. */
REAL_VALUE_TYPE
ereal_from_float (f)
HOST_WIDE_INT f;
{
REAL_VALUE_TYPE r;
unsigned EMUSHORT s[2];
unsigned EMUSHORT e[NE];
/* Convert 32 bit integer to array of 16 bit pieces in target machine order.
This is the inverse operation to what the function `endian' does. */
#if FLOAT_WORDS_BIG_ENDIAN
s[0] = (unsigned EMUSHORT) (f >> 16);
s[1] = (unsigned EMUSHORT) f;
#else
s[0] = (unsigned EMUSHORT) f;
s[1] = (unsigned EMUSHORT) (f >> 16);
#endif
/* Convert and promote the target float to E-type. */
e24toe (s, e);
/* Output E-type to REAL_VALUE_TYPE. */
PUT_REAL (e, &r);
return r;
}
/* Convert a DFmode target `double' value to a REAL_VALUE_TYPE.
This is the inverse of the function `etardouble' invoked by
REAL_VALUE_TO_TARGET_DOUBLE.
The DFmode is stored as an array of HOST_WIDE_INT in the target's
data format, with no holes in the bit packing. The first element
of the input array holds the bits that would come first in the
target computer's memory. */
REAL_VALUE_TYPE
ereal_from_double (d)
HOST_WIDE_INT d[];
{
REAL_VALUE_TYPE r;
unsigned EMUSHORT s[4];
unsigned EMUSHORT e[NE];
/* Convert array of HOST_WIDE_INT to equivalent array of 16-bit pieces. */
#if FLOAT_WORDS_BIG_ENDIAN
s[0] = (unsigned EMUSHORT) (d[0] >> 16);
s[1] = (unsigned EMUSHORT) d[0];
#if HOST_BITS_PER_WIDE_INT == 32
s[2] = (unsigned EMUSHORT) (d[1] >> 16);
s[3] = (unsigned EMUSHORT) d[1];
#else
/* In this case the entire target double is contained in the
first array element. The second element of the input is ignored. */
s[2] = (unsigned EMUSHORT) (d[0] >> 48);
s[3] = (unsigned EMUSHORT) (d[0] >> 32);
#endif
#else
/* Target float words are little-endian. */
s[0] = (unsigned EMUSHORT) d[0];
s[1] = (unsigned EMUSHORT) (d[0] >> 16);
#if HOST_BITS_PER_WIDE_INT == 32
s[2] = (unsigned EMUSHORT) d[1];
s[3] = (unsigned EMUSHORT) (d[1] >> 16);
#else
s[2] = (unsigned EMUSHORT) (d[0] >> 32);
s[3] = (unsigned EMUSHORT) (d[0] >> 48);
#endif
#endif
/* Convert target double to E-type. */
e53toe (s, e);
/* Output E-type to REAL_VALUE_TYPE. */
PUT_REAL (e, &r);
return r;
}
/* Convert target computer unsigned 64-bit integer to e-type.
The endian-ness of DImode follows the convention for integers,
so we use WORDS_BIG_ENDIAN here, not FLOAT_WORDS_BIG_ENDIAN. */
static void
uditoe (di, e)
unsigned EMUSHORT *di; /* Address of the 64-bit int. */
unsigned EMUSHORT *e;
{
unsigned EMUSHORT yi[NI];
int k;
ecleaz (yi);
#if WORDS_BIG_ENDIAN
for (k = M; k < M + 4; k++)
yi[k] = *di++;
#else
for (k = M + 3; k >= M; k--)
yi[k] = *di++;
#endif
yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
if ((k = enormlz (yi)) > NBITS)/* normalize the significand */
ecleaz (yi); /* it was zero */
else
yi[E] -= (unsigned EMUSHORT) k;/* subtract shift count from exponent */
emovo (yi, e);
}
/* Convert target computer signed 64-bit integer to e-type. */
static void
ditoe (di, e)
unsigned EMUSHORT *di; /* Address of the 64-bit int. */
unsigned EMUSHORT *e;
{
unsigned EMULONG acc;
unsigned EMUSHORT yi[NI];
unsigned EMUSHORT carry;
int k, sign;
ecleaz (yi);
#if WORDS_BIG_ENDIAN
for (k = M; k < M + 4; k++)
yi[k] = *di++;
#else
for (k = M + 3; k >= M; k--)
yi[k] = *di++;
#endif
/* Take absolute value */
sign = 0;
if (yi[M] & 0x8000)
{
sign = 1;
carry = 0;
for (k = M + 3; k >= M; k--)
{
acc = (unsigned EMULONG) (~yi[k] & 0xffff) + carry;
yi[k] = acc;
carry = 0;
if (acc & 0x10000)
carry = 1;
}
}
yi[E] = EXONE + 47; /* exponent if normalize shift count were 0 */
if ((k = enormlz (yi)) > NBITS)/* normalize the significand */
ecleaz (yi); /* it was zero */
else
yi[E] -= (unsigned EMUSHORT) k;/* subtract shift count from exponent */
emovo (yi, e);
if (sign)
eneg (e);
}
/* Convert e-type to unsigned 64-bit int. */
static void
etoudi (x, i)
unsigned EMUSHORT *x;
unsigned EMUSHORT *i;
{
unsigned EMUSHORT xi[NI];
int j, k;
emovi (x, xi);
if (xi[0])
{
xi[M] = 0;
goto noshift;
}
k = (int) xi[E] - (EXONE - 1);
if (k <= 0)
{
for (j = 0; j < 4; j++)
*i++ = 0;
return;
}
if (k > 64)
{
for (j = 0; j < 4; j++)
*i++ = 0xffff;
if (extra_warnings)
warning ("overflow on truncation to integer");
return;
}
if (k > 16)
{
/* Shift more than 16 bits: first shift up k-16 mod 16,
then shift up by 16's. */
j = k - ((k >> 4) << 4);
if (j == 0)
j = 16;
eshift (xi, j);
#if WORDS_BIG_ENDIAN
*i++ = xi[M];
#else
i += 3;
*i-- = xi[M];
#endif
k -= j;
do
{
eshup6 (xi);
#if WORDS_BIG_ENDIAN
*i++ = xi[M];
#else
*i-- = xi[M];
#endif
}
while ((k -= 16) > 0);
}
else
{
/* shift not more than 16 bits */
eshift (xi, k);
noshift:
#if WORDS_BIG_ENDIAN
i += 3;
*i-- = xi[M];
*i-- = 0;
*i-- = 0;
*i = 0;
#else
*i++ = xi[M];
*i++ = 0;
*i++ = 0;
*i = 0;
#endif
}
}
/* Convert e-type to signed 64-bit int. */
static void
etodi (x, i)
unsigned EMUSHORT *x;
unsigned EMUSHORT *i;
{
unsigned EMULONG acc;
unsigned EMUSHORT xi[NI];
unsigned EMUSHORT carry;
unsigned EMUSHORT *isave;
int j, k;
emovi (x, xi);
k = (int) xi[E] - (EXONE - 1);
if (k <= 0)
{
for (j = 0; j < 4; j++)
*i++ = 0;
return;
}
if (k > 64)
{
for (j = 0; j < 4; j++)
*i++ = 0xffff;
if (extra_warnings)
warning ("overflow on truncation to integer");
return;
}
isave = i;
if (k > 16)
{
/* Shift more than 16 bits: first shift up k-16 mod 16,
then shift up by 16's. */
j = k - ((k >> 4) << 4);
if (j == 0)
j = 16;
eshift (xi, j);
#if WORDS_BIG_ENDIAN
*i++ = xi[M];
#else
i += 3;
*i-- = xi[M];
#endif
k -= j;
do
{
eshup6 (xi);
#if WORDS_BIG_ENDIAN
*i++ = xi[M];
#else
*i-- = xi[M];
#endif
}
while ((k -= 16) > 0);
}
else
{
/* shift not more than 16 bits */
eshift (xi, k);
#if WORDS_BIG_ENDIAN
i += 3;
*i = xi[M];
*i-- = 0;
*i-- = 0;
*i = 0;
#else
*i++ = xi[M];
*i++ = 0;
*i++ = 0;
*i = 0;
#endif
}
/* Negate if negative */
if (xi[0])
{
carry = 0;
#if WORDS_BIG_ENDIAN
isave += 3;
#endif
for (k = 0; k < 4; k++)
{
acc = (unsigned EMULONG) (~(*isave) & 0xffff) + carry;
#if WORDS_BIG_ENDIAN
*isave-- = acc;
#else
*isave++ = acc;
#endif
carry = 0;
if (acc & 0x10000)
carry = 1;
}
}
}
/* Longhand square root routine. */
static int esqinited = 0;
static unsigned short sqrndbit[NI];
static void
esqrt (x, y)
unsigned EMUSHORT *x, *y;
{
unsigned EMUSHORT temp[NI], num[NI], sq[NI], xx[NI];
EMULONG m, exp;
int i, j, k, n, nlups;
if (esqinited == 0)
{
ecleaz (sqrndbit);
sqrndbit[NI - 2] = 1;
esqinited = 1;
}
/* Check for arg <= 0 */
i = ecmp (x, ezero);
if (i <= 0)
{
if (i == -1)
{
mtherr ("esqrt", DOMAIN);
eclear (y);
}
else
emov (x, y);
return;
}
#ifdef INFINITY
if (eisinf (x))
{
eclear (y);
einfin (y);
return;
}
#endif
/* Bring in the arg and renormalize if it is denormal. */
emovi (x, xx);
m = (EMULONG) xx[1]; /* local long word exponent */
if (m == 0)
m -= enormlz (xx);
/* Divide exponent by 2 */
m -= 0x3ffe;
exp = (unsigned short) ((m / 2) + 0x3ffe);
/* Adjust if exponent odd */
if ((m & 1) != 0)
{
if (m > 0)
exp += 1;
eshdn1 (xx);
}
ecleaz (sq);
ecleaz (num);
n = 8; /* get 8 bits of result per inner loop */
nlups = rndprc;
j = 0;
while (nlups > 0)
{
/* bring in next word of arg */
if (j < NE)
num[NI - 1] = xx[j + 3];
/* Do additional bit on last outer loop, for roundoff. */
if (nlups <= 8)
n = nlups + 1;
for (i = 0; i < n; i++)
{
/* Next 2 bits of arg */
eshup1 (num);
eshup1 (num);
/* Shift up answer */
eshup1 (sq);
/* Make trial divisor */
for (k = 0; k < NI; k++)
temp[k] = sq[k];
eshup1 (temp);
eaddm (sqrndbit, temp);
/* Subtract and insert answer bit if it goes in */
if (ecmpm (temp, num) <= 0)
{
esubm (temp, num);
sq[NI - 2] |= 1;
}
}
nlups -= n;
j += 1;
}
/* Adjust for extra, roundoff loop done. */
exp += (NBITS - 1) - rndprc;
/* Sticky bit = 1 if the remainder is nonzero. */
k = 0;
for (i = 3; i < NI; i++)
k |= (int) num[i];
/* Renormalize and round off. */
emdnorm (sq, k, 0, exp, 64);
emovo (sq, y);
}
#endif /* EMU_NON_COMPILE not defined */
/* Return the binary precision of the significand for a given
floating point mode. The mode can hold an integer value
that many bits wide, without losing any bits. */
int
significand_size (mode)
enum machine_mode mode;
{
switch (mode)
{
case SFmode:
return 24;
case DFmode:
#if TARGET_FLOAT_FORMAT == IEEE_FLOAT_FORMAT
return 53;
#else
#if TARGET_FLOAT_FORMAT == IBM_FLOAT_FORMAT
return 56;
#else
#if TARGET_FLOAT_FORMAT == VAX_FLOAT_FORMAT
return 56;
#else
abort ();
#endif
#endif
#endif
case XFmode:
return 64;
case TFmode:
return 113;
default:
abort ();
}
}
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.