/* Extended precision arithmetic functions for long double I/O.
* This program has been placed in the public domain.
*/
#include <newlib.h>
#include <sys/config.h>
#ifndef _USE_GDTOA
#include <_ansi.h>
#include <reent.h>
#include <string.h>
#include <stdlib.h>
#include "mprec.h"
/* These are the externally visible entries. */
/* linux name: long double _IO_strtold (char *, char **); */
long double _strtold (char *, char **);
char *_ldtoa_r (struct _reent *, long double, int, int, int *, int *,
char **);
int _ldcheck (long double *);
#if 0
void _IO_ldtostr (long double *, char *, int, int, char);
#endif
/* Number of 16 bit words in external x type format */
#define NE 10
/* Number of 16 bit words in internal format */
#define NI (NE+3)
/* Array offset to exponent */
#define E 1
/* Array offset to high guard word */
#define M 2
/* Number of bits of precision */
#define NBITS ((NI-4)*16)
/* Maximum number of decimal digits in ASCII conversion */
#define NDEC 1023
/* Use static stack buffer for up to 44 digits */
#define NDEC_SML 44
/* The exponent of 1.0 */
#define EXONE (0x3fff)
/* Maximum exponent digits - base 10 */
#define MAX_EXP_DIGITS 5
/* Control structure for long double conversion including rounding precision values.
* rndprc can be set to 80 (if NE=6), 64, 56, 53, or 24 bits.
*/
typedef struct
{
int rlast;
int rndprc;
int rw;
int re;
int outexpon;
unsigned short rmsk;
unsigned short rmbit;
unsigned short rebit;
unsigned short rbit[NI];
unsigned short equot[NI];
} LDPARMS;
static void esub (const short unsigned int *a, const short unsigned int *b,
short unsigned int *c, LDPARMS * ldp);
static void emul (const short unsigned int *a, const short unsigned int *b,
short unsigned int *c, LDPARMS * ldp);
static void ediv (const short unsigned int *a, const short unsigned int *b,
short unsigned int *c, LDPARMS * ldp);
static int ecmp (const short unsigned int *a, const short unsigned int *b);
static int enormlz (short unsigned int *x);
static int eshift (short unsigned int *x, int sc);
static void eshup1 (register short unsigned int *x);
static void eshup8 (register short unsigned int *x);
static void eshup6 (register short unsigned int *x);
static void eshdn1 (register short unsigned int *x);
static void eshdn8 (register short unsigned int *x);
static void eshdn6 (register short unsigned int *x);
static void eneg (short unsigned int *x);
static void emov (register const short unsigned int *a,
register short unsigned int *b);
static void eclear (register short unsigned int *x);
static void einfin (register short unsigned int *x, register LDPARMS * ldp);
static void efloor (short unsigned int *x, short unsigned int *y,
LDPARMS * ldp);
static void etoasc (short unsigned int *x, char *string, int ndec, int ndigs,
int outformat, LDPARMS * ldp);
union uconv
{
unsigned short pe;
long double d;
};
#if LDBL_MANT_DIG == 24
static void e24toe (short unsigned int *pe, short unsigned int *y,
LDPARMS * ldp);
#elif LDBL_MANT_DIG == 53
static void e53toe (short unsigned int *pe, short unsigned int *y,
LDPARMS * ldp);
#elif LDBL_MANT_DIG == 64
static void e64toe (short unsigned int *pe, short unsigned int *y,
LDPARMS * ldp);
#else
static void e113toe (short unsigned int *pe, short unsigned int *y,
LDPARMS * ldp);
#endif
/* econst.c */
/* e type constants used by high precision check routines */
#if NE == 10
/* 0.0 */
static const unsigned short ezero[NE] = { 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
};
/* 1.0E0 */
static const unsigned short eone[NE] = { 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,
};
#else
/* 0.0 */
static const unsigned short ezero[NE] = {
0, 0000000, 0000000, 0000000, 0000000, 0000000,
};
/* 1.0E0 */
static const unsigned short eone[NE] = {
0, 0000000, 0000000, 0000000, 0100000, 0x3fff,
};
#endif
/* Debugging routine for displaying errors */
#ifdef DEBUG
/* Notice: the order of appearance of the following
* messages is bound to the error codes defined
* in mconf.h.
*/
static const char *const ermsg[7] = {
"unknown", /* error code 0 */
"domain", /* error code 1 */
"singularity", /* et seq. */
"overflow",
"underflow",
"total loss of precision",
"partial loss of precision"
};
#define mtherr(name, code) printf( "\n%s %s error\n", name, ermsg[code] );
#else
#define mtherr(name, code)
#endif
/* ieee.c
*
* Extended precision IEEE binary floating point arithmetic routines
*
* Numbers are stored in C language as arrays of 16-bit unsigned
* short integers. The arguments of the routines are pointers to
* the arrays.
*
*
* External e type data structure, simulates Intel 8087 chip
* temporary real format but possibly with a larger significand:
*
* NE-1 significand words (least significant word first,
* most significant bit is normally set)
* exponent (value = EXONE for 1.0,
* top bit is the sign)
*
*
* Internal data structure of a number (a "word" is 16 bits):
*
* ei[0] sign word (0 for positive, 0xffff for negative)
* ei[1] biased exponent (value = EXONE for the number 1.0)
* ei[2] high guard word (always zero after normalization)
* ei[3]
* to ei[NI-2] significand (NI-4 significand words,
* most significant word first,
* most significant bit is set)
* ei[NI-1] low guard word (0x8000 bit is rounding place)
*
*
*
* Routines for external format numbers
*
* asctoe( string, e ) ASCII string to extended double e type
* asctoe64( string, &d ) ASCII string to long double
* asctoe53( string, &d ) ASCII string to double
* asctoe24( string, &f ) ASCII string to single
* asctoeg( string, e, prec, ldp ) ASCII string to specified precision
* e24toe( &f, e, ldp ) IEEE single precision to e type
* e53toe( &d, e, ldp ) IEEE double precision to e type
* e64toe( &d, e, ldp ) IEEE long double precision to e type
* e113toe( &d, e, ldp ) IEEE long double precision to e type
* eabs(e) absolute value
* eadd( a, b, c ) c = b + a
* eclear(e) e = 0
* ecmp (a, b) Returns 1 if a > b, 0 if a == b,
* -1 if a < b, -2 if either a or b is a NaN.
* ediv( a, b, c, ldp ) c = b / a
* efloor( a, b, ldp ) truncate to integer, toward -infinity
* efrexp( a, exp, s ) extract exponent and significand
* eifrac( e, &l, frac ) e to long integer and e type fraction
* euifrac( e, &l, frac ) e to unsigned long integer and e type fraction
* einfin( e, ldp ) 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, ldp ) c = b * a
* eneg(e) e = -e
* eround( a, b ) b = nearest integer value to a
* esub( a, b, c, ldp ) c = b - a
* e24toasc( &f, str, n ) single to ASCII string, n digits after decimal
* e53toasc( &d, str, n ) double to ASCII string, n digits after decimal
* e64toasc( &d, str, n ) long double to ASCII string
* etoasc(e,str,ndec,n,fmt,ldp)e to ASCII string, n digits after decimal
* etoe24( e, &f ) convert e type to IEEE single precision
* etoe53( e, &d ) convert e type to IEEE double precision
* etoe64( e, &d ) convert e type to IEEE long double precision
* ltoe( &l, e ) long (32 bit) integer to e type
* ultoe( &l, e ) unsigned long (32 bit) integer to e type
* eisneg( e ) 1 if sign bit of e != 0, else 0
* eisinf( e ) 1 if e has maximum exponent (non-IEEE)
* or is infinite (IEEE)
* eisnan( e ) 1 if e is a NaN
* esqrt( a, b ) b = square root of a
*
*
* Routines for internal format numbers
*
* eaddm( ai, bi ) add significands, bi = bi + ai
* ecleaz(ei) ei = 0
* ecleazs(ei) set ei = 0 but leave its sign alone
* ecmpm( ai, bi ) compare significands, return 1, 0, or -1
* edivm( ai, bi, ldp ) divide significands, bi = bi / ai
* emdnorm(ai,l,s,exp,ldp) normalize and round off
* emovi( a, ai ) convert external a to internal ai
* emovo( ai, a, ldp ) convert internal ai to external a
* emovz( ai, bi ) bi = ai, low guard word of bi = 0
* emulm( ai, bi, ldp ) multiply significands, bi = bi * ai
* enormlz(ei) left-justify the significand
* eshdn1( ai ) shift significand and guards down 1 bit
* eshdn8( ai ) shift down 8 bits
* eshdn6( ai ) shift down 16 bits
* eshift( ai, n ) shift ai n bits up (or down if n < 0)
* eshup1( ai ) shift significand and guards up 1 bit
* eshup8( ai ) shift up 8 bits
* eshup6( ai ) shift up 16 bits
* esubm( ai, bi ) subtract significands, bi = bi - ai
*
*
* The result is always normalized and rounded to NI-4 word precision
* after each arithmetic operation.
*
* Exception flags are NOT fully supported.
*
* Define USE_INFINITY in mconf.h for support of infinity; otherwise a
* saturation arithmetic is implemented.
*
* Define NANS for support of Not-a-Number items; otherwise the
* arithmetic will never produce a NaN output, and might be confused
* by a NaN input.
* If NaN's are supported, the output of ecmp(a,b) is -2 if
* either a or b is a NaN. This means asking if(ecmp(a,b) < 0)
* may not be legitimate. Use if(ecmp(a,b) == -1) for less-than
* if in doubt.
* Signaling NaN's are NOT supported; they are treated the same
* as quiet NaN's.
*
* Denormals are always supported here where appropriate (e.g., not
* for conversion to DEC numbers).
*/
/*
* Revision history:
*
* 5 Jan 84 PDP-11 assembly language version
* 6 Dec 86 C language version
* 30 Aug 88 100 digit version, improved rounding
* 15 May 92 80-bit long double support
* 22 Nov 00 Revised to fit into newlib by Jeff Johnston <jjohnstn@redhat.com>
*
* Author: S. L. Moshier.
*
* Copyright (c) 1984,2000 S.L. Moshier
*
* Permission to use, copy, modify, and distribute this software for any
* purpose without fee is hereby granted, provided that this entire notice
* is included in all copies of any software which is or includes a copy
* or modification of this software and in all copies of the supporting
* documentation for such software.
*
* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
* WARRANTY. IN PARTICULAR, THE AUTHOR MAKES NO REPRESENTATION
* OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY OF THIS
* SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
*
*/
#include <stdio.h>
/* #include "\usr\include\stdio.h" */
/*#include "ehead.h"*/
/*#include "mconf.h"*/
/* mconf.h
*
* Common include file for math routines
*
*
*
* SYNOPSIS:
*
* #include "mconf.h"
*
*
*
* DESCRIPTION:
*
* This file contains definitions for error codes that are
* passed to the common error handling routine mtherr()
* (which see).
*
* The file also includes a conditional assembly definition
* for the type of computer arithmetic (IEEE, DEC, Motorola
* IEEE, or UNKnown).
*
* For Digital Equipment PDP-11 and VAX computers, certain
* IBM systems, and others that use numbers with a 56-bit
* significand, the symbol DEC should be defined. In this
* mode, most floating point constants are given as arrays
* of octal integers to eliminate decimal to binary conversion
* errors that might be introduced by the compiler.
*
* For computers, such as IBM PC, that follow the IEEE
* Standard for Binary Floating Point Arithmetic (ANSI/IEEE
* Std 754-1985), the symbol IBMPC should be defined. These
* numbers have 53-bit significands. In this mode, constants
* are provided as arrays of hexadecimal 16 bit integers.
*
* 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 EDOM 33
#define ERANGE 34
typedef struct
{
double r;
double i;
} cmplx;
/* Type of computer arithmetic */
#ifndef DEC
#ifdef __IEEE_LITTLE_ENDIAN
#define IBMPC 1
#else /* !__IEEE_LITTLE_ENDIAN */
#define MIEEE 1
#endif /* !__IEEE_LITTLE_ENDIAN */
#endif /* !DEC */
/* Define 1 for ANSI C atan2() function
* See atan.c and clog.c.
*/
#define ANSIC 1
/*define VOLATILE volatile*/
#define VOLATILE
#define NANS
#define USE_INFINITY
/* NaN's require infinity support. */
#ifdef NANS
#ifndef INFINITY
#define USE_INFINITY
#endif
#endif
/* This handles 64-bit long ints. */
#define LONGBITS (8 * sizeof(long))
static void eaddm (short unsigned int *x, short unsigned int *y);
static void esubm (short unsigned int *x, short unsigned int *y);
static void emdnorm (short unsigned int *s, int lost, int subflg,
long int exp, int rcntrl, LDPARMS * ldp);
#if 0 /* Broken, unusable implementation of strtold */
static int asctoeg (char *ss, short unsigned int *y, int oprec,
LDPARMS * ldp);
#endif
static void enan (short unsigned int *nan, int size);
#if LDBL_MANT_DIG == 24
static void toe24 (short unsigned int *x, short unsigned int *y);
#elif LDBL_MANT_DIG == 53
static void toe53 (short unsigned int *x, short unsigned int *y);
#elif LDBL_MANT_DIG == 64
static void toe64 (short unsigned int *a, short unsigned int *b);
#else
static void toe113 (short unsigned int *a, short unsigned int *b);
#endif
static void eiremain (short unsigned int *den, short unsigned int *num,
LDPARMS * ldp);
static int ecmpm (register short unsigned int *a,
register short unsigned int *b);
static int edivm (short unsigned int *den, short unsigned int *num,
LDPARMS * ldp);
static int emulm (short unsigned int *a, short unsigned int *b,
LDPARMS * ldp);
static int eisneg (const short unsigned int *x);
static int eisinf (const short unsigned int *x);
static void emovi (const short unsigned int *a, short unsigned int *b);
static void emovo (short unsigned int *a, short unsigned int *b,
LDPARMS * ldp);
static void emovz (register short unsigned int *a,
register short unsigned int *b);
static void ecleaz (register short unsigned int *xi);
static void eadd1 (const short unsigned int *a, const short unsigned int *b,
short unsigned int *c, int subflg, LDPARMS * ldp);
static int eisnan (const short unsigned int *x);
static int eiisnan (short unsigned int *x);
#ifdef DEC
static void etodec (), todec (), dectoe ();
#endif
/*
; Clear out entire external format number.
;
; unsigned short x[];
; eclear( x );
*/
static void
eclear (register short unsigned int *x)
{
register int i;
for (i = 0; i < NE; i++)
*x++ = 0;
}
/* Move external format number from a to b.
*
* emov( a, b );
*/
static void
emov (register const short unsigned int *a, register short unsigned int *b)
{
register int i;
for (i = 0; i < NE; i++)
*b++ = *a++;
}
/*
; Negate external format number
;
; unsigned short x[NE];
; eneg( x );
*/
static void
eneg (short unsigned int *x)
{
#ifdef NANS
if (eisnan (x))
return;
#endif
x[NE - 1] ^= 0x8000; /* Toggle the sign bit */
}
/* Return 1 if external format number is negative,
* else return zero.
*/
static int
eisneg (const short unsigned int *x)
{
#ifdef NANS
if (eisnan (x))
return (0);
#endif
if (x[NE - 1] & 0x8000)
return (1);
else
return (0);
}
/* Return 1 if external format number has maximum possible exponent,
* else return zero.
*/
static int
eisinf (const short unsigned int *x)
{
if ((x[NE - 1] & 0x7fff) == 0x7fff)
{
#ifdef NANS
if (eisnan (x))
return (0);
#endif
return (1);
}
else
return (0);
}
/* Check if e-type number is not a number.
*/
static int
eisnan (const short unsigned int *x)
{
#ifdef NANS
int i;
/* NaN has maximum exponent */
if ((x[NE - 1] & 0x7fff) != 0x7fff)
return (0);
/* ... and non-zero significand field. */
for (i = 0; i < NE - 1; i++)
{
if (*x++ != 0)
return (1);
}
#endif
return (0);
}
/*
; Fill entire number, including exponent and significand, with
; largest possible number. These programs implement a saturation
; value that is an ordinary, legal number. A special value
; "infinity" may also be implemented; this would require tests
; for that value and implementation of special rules for arithmetic
; operations involving inifinity.
*/
static void
einfin (register short unsigned int *x, register LDPARMS * ldp)
{
register int i;
#ifdef USE_INFINITY
for (i = 0; i < NE - 1; i++)
*x++ = 0;
*x |= 32767;
ldp = ldp;
#else
for (i = 0; i < NE - 1; i++)
*x++ = 0xffff;
*x |= 32766;
if (ldp->rndprc < NBITS)
{
if (ldp->rndprc == 113)
{
*(x - 9) = 0;
*(x - 8) = 0;
}
if (ldp->rndprc == 64)
{
*(x - 5) = 0;
}
if (ldp->rndprc == 53)
{
*(x - 4) = 0xf800;
}
else
{
*(x - 4) = 0;
*(x - 3) = 0;
*(x - 2) = 0xff00;
}
}
#endif
}
/* Move in external format number,
* converting it to internal format.
*/
static void
emovi (const short unsigned int *a, short unsigned int *b)
{
register const unsigned short *p;
register unsigned short *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 USE_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 (short unsigned int *a, short unsigned int *b, LDPARMS * ldp)
{
register unsigned short *p, *q;
unsigned short i;
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 USE_INFINITY
if (*(p - 1) == 0x7fff)
{
#ifdef NANS
if (eiisnan (a))
{
enan (b, NBITS);
return;
}
#endif
einfin (b, ldp);
return;
}
#endif
/* skip over guard word */
++p;
/* move the significand */
for (i = 0; i < NE - 1; i++)
*q-- = *p++;
}
/* Clear out internal format number.
*/
static void
ecleaz (register short unsigned int *xi)
{
register int i;
for (i = 0; i < NI; i++)
*xi++ = 0;
}
/* same, but don't touch the sign. */
static void
ecleazs (register short unsigned int *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 (register short unsigned int *a, register short unsigned int *b)
{
register int i;
for (i = 0; i < NI - 1; i++)
*b++ = *a++;
/* clear low guard word */
*b = 0;
}
/* Return nonzero if internal format number is a NaN.
*/
static int
eiisnan (short unsigned int *x)
{
int i;
if ((x[E] & 0x7fff) == 0x7fff)
{
for (i = M + 1; i < NI; i++)
{
if (x[i] != 0)
return (1);
}
}
return (0);
}
#if LDBL_MANT_DIG == 64
/* Return nonzero if internal format number is infinite. */
static int
eiisinf (unsigned short x[])
{
#ifdef NANS
if (eiisnan (x))
return (0);
#endif
if ((x[E] & 0x7fff) == 0x7fff)
return (1);
return (0);
}
#endif /* LDBL_MANT_DIG == 64 */
/*
; Compare significands of numbers in internal format.
; Guard words are included in the comparison.
;
; unsigned short a[NI], b[NI];
; cmpm( a, b );
;
; for the significands:
; returns +1 if a > b
; 0 if a == b
; -1 if a < b
*/
static int
ecmpm (register short unsigned int *a, register short unsigned int *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 (register short unsigned int *x)
{
register unsigned short bits;
int i;
x += M; /* point to significand area */
bits = 0;
for (i = M; i < NI; i++)
{
if (*x & 1)
bits |= 1;
*x >>= 1;
if (bits & 2)
*x |= 0x8000;
bits <<= 1;
++x;
}
}
/*
; Shift significand up by 1 bit
*/
static void
eshup1 (register short unsigned int *x)
{
register unsigned short bits;
int i;
x += NI - 1;
bits = 0;
for (i = M; i < NI; i++)
{
if (*x & 0x8000)
bits |= 1;
*x <<= 1;
if (bits & 2)
*x |= 1;
bits <<= 1;
--x;
}
}
/*
; Shift significand down by 8 bits
*/
static void
eshdn8 (register short unsigned int *x)
{
register unsigned short newbyt, oldbyt;
int i;
x += M;
oldbyt = 0;
for (i = M; i < NI; i++)
{
newbyt = *x << 8;
*x >>= 8;
*x |= oldbyt;
oldbyt = newbyt;
++x;
}
}
/*
; Shift significand up by 8 bits
*/
static void
eshup8 (register short unsigned int *x)
{
int i;
register unsigned short newbyt, oldbyt;
x += NI - 1;
oldbyt = 0;
for (i = M; i < NI; i++)
{
newbyt = *x >> 8;
*x <<= 8;
*x |= oldbyt;
oldbyt = newbyt;
--x;
}
}
/*
; Shift significand up by 16 bits
*/
static void
eshup6 (register short unsigned int *x)
{
int i;
register unsigned short *p;
p = x + M;
x += M + 1;
for (i = M; i < NI - 1; i++)
*p++ = *x++;
*p = 0;
}
/*
; Shift significand down by 16 bits
*/
static void
eshdn6 (register short unsigned int *x)
{
int i;
register unsigned short *p;
x += NI - 1;
p = x + 1;
for (i = M; i < NI - 1; i++)
*(--p) = *(--x);
*(--p) = 0;
}
/*
; Add significands
; x + y replaces y
*/
static void
eaddm (short unsigned int *x, short unsigned int *y)
{
register unsigned long a;
int i;
unsigned int carry;
x += NI - 1;
y += NI - 1;
carry = 0;
for (i = M; i < NI; i++)
{
a = (unsigned long) (*x) + (unsigned long) (*y) + carry;
if (a & 0x10000)
carry = 1;
else
carry = 0;
*y = (unsigned short) a;
--x;
--y;
}
}
/*
; Subtract significands
; y - x replaces y
*/
static void
esubm (short unsigned int *x, short unsigned int *y)
{
unsigned long a;
int i;
unsigned int carry;
x += NI - 1;
y += NI - 1;
carry = 0;
for (i = M; i < NI; i++)
{
a = (unsigned long) (*y) - (unsigned long) (*x) - carry;
if (a & 0x10000)
carry = 1;
else
carry = 0;
*y = (unsigned short) a;
--x;
--y;
}
}
/* Divide significands */
/* Multiply significand of e-type number b
by 16-bit quantity a, e-type result to c. */
static void
m16m (short unsigned int a, short unsigned int *b, short unsigned int *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 (short unsigned int *den, short unsigned int *num, LDPARMS * ldp)
{
int i;
register unsigned short *p;
unsigned long tnum;
unsigned short j, tdenm, tquot;
unsigned short tprod[NI + 1];
unsigned short *equot = ldp->equot;
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 * 0xffffUL) < tnum)
tquot = 0xffff;
else
tquot = tnum / tdenm;
/* Prove that the divide worked. */
/*
tcheck = (unsigned long )tquot * tdenm;
if( tnum - tcheck > tdenm )
tquot = 0xffff;
*/
/* Multiply denominator by trial quotient digit. */
m16m (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);
}
}
/*
if( ecmpm( tprod, num ) > 0 )
{
eshow( "tprod", tprod );
eshow( "num ", num );
printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
tnum, den[M+1], tquot );
}
*/
esubm (tprod, num);
/*
if( ecmpm( num, den ) >= 0 )
{
eshow( "num ", num );
eshow( "den ", den );
printf( "tnum = %08lx, tden = %04x, tquot = %04x\n",
tnum, den[M+1], tquot );
}
*/
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 (short unsigned int *a, short unsigned int *b, LDPARMS * ldp)
{
unsigned short *p, *q;
unsigned short pprod[NI];
unsigned short j;
int i;
unsigned short *equot = ldp->equot;
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 (*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);
}
/*
static void eshow(str, x)
char *str;
unsigned short *x;
{
int i;
printf( "%s ", str );
for( i=0; i<NI; i++ )
printf( "%04x ", *x++ );
printf( "\n" );
}
*/
/*
* Normalize and round off.
*
* The internal format number to be rounded is "s".
* Input "lost" indicates whether 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.
*/
static void
emdnorm (short unsigned int *s, int lost, int subflg, long int exp,
int rcntrl, LDPARMS * ldp)
{
int i, j;
unsigned short r;
/* Normalize */
j = enormlz (s);
/* a blank significand could mean either zero or infinity. */
#ifndef USE_INFINITY
if (j > NBITS)
{
ecleazs (s);
return;
}
#endif
exp -= j;
#ifndef USE_INFINITY
if (exp >= 32767L)
goto overf;
#else
if ((j > NBITS) && (exp < 32767L))
{
ecleazs (s);
return;
}
#endif
if (exp < 0L)
{
if (exp > (long) (-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 (ldp->rndprc != ldp->rlast)
{
ecleaz (ldp->rbit);
switch (ldp->rndprc)
{
default:
case NBITS:
ldp->rw = NI - 1; /* low guard word */
ldp->rmsk = 0xffff;
ldp->rmbit = 0x8000;
ldp->rebit = 1;
ldp->re = ldp->rw - 1;
break;
case 113:
ldp->rw = 10;
ldp->rmsk = 0x7fff;
ldp->rmbit = 0x4000;
ldp->rebit = 0x8000;
ldp->re = ldp->rw;
break;
case 64:
ldp->rw = 7;
ldp->rmsk = 0xffff;
ldp->rmbit = 0x8000;
ldp->rebit = 1;
ldp->re = ldp->rw - 1;
break;
/* For DEC arithmetic */
case 56:
ldp->rw = 6;
ldp->rmsk = 0xff;
ldp->rmbit = 0x80;
ldp->rebit = 0x100;
ldp->re = ldp->rw;
break;
case 53:
ldp->rw = 6;
ldp->rmsk = 0x7ff;
ldp->rmbit = 0x0400;
ldp->rebit = 0x800;
ldp->re = ldp->rw;
break;
case 24:
ldp->rw = 4;
ldp->rmsk = 0xff;
ldp->rmbit = 0x80;
ldp->rebit = 0x100;
ldp->re = ldp->rw;
break;
}
ldp->rbit[ldp->re] = ldp->rebit;
ldp->rlast = ldp->rndprc;
}
/* Shift down 1 temporarily if the data structure has an implied
* most significant bit and the number is denormal.
* For rndprc = 64 or NBITS, there is no implied bit.
* But Intel long double denormals lose one bit of significance even so.
*/
#if IBMPC
if ((exp <= 0) && (ldp->rndprc != NBITS))
#else
if ((exp <= 0) && (ldp->rndprc != 64) && (ldp->rndprc != NBITS))
#endif
{
lost |= s[NI - 1] & 1;
eshdn1 (s);
}
/* Clear out all bits below the rounding bit,
* remembering in r if any were nonzero.
*/
r = s[ldp->rw] & ldp->rmsk;
if (ldp->rndprc < NBITS)
{
i = ldp->rw + 1;
while (i < NI)
{
if (s[i])
r |= 1;
s[i] = 0;
++i;
}
}
s[ldp->rw] &= ~ldp->rmsk;
if ((r & ldp->rmbit) != 0)
{
if (r == ldp->rmbit)
{
if (lost == 0)
{ /* round to even */
if ((s[ldp->re] & ldp->rebit) == 0)
goto mddone;
}
else
{
if (subflg != 0)
goto mddone;
}
}
eaddm (ldp->rbit, s);
}
mddone:
#if IBMPC
if ((exp <= 0) && (ldp->rndprc != NBITS))
#else
if ((exp <= 0) && (ldp->rndprc != 64) && (ldp->rndprc != NBITS))
#endif
{
eshup1 (s);
}
if (s[2] != 0)
{ /* overflow on roundoff */
eshdn1 (s);
exp += 1;
}
mdfin:
s[NI - 1] = 0;
if (exp >= 32767L)
{
#ifndef USE_INFINITY
overf:
#endif
#ifdef USE_INFINITY
s[1] = 32767;
for (i = 2; i < NI - 1; i++)
s[i] = 0;
#else
s[1] = 32766;
s[2] = 0;
for (i = M + 1; i < NI - 1; i++)
s[i] = 0xffff;
s[NI - 1] = 0;
if ((ldp->rndprc < 64) || (ldp->rndprc == 113))
{
s[ldp->rw] &= ~ldp->rmsk;
if (ldp->rndprc == 24)
{
s[5] = 0;
s[6] = 0;
}
}
#endif
return;
}
if (exp < 0)
s[1] = 0;
else
s[1] = (unsigned short) exp;
}
/*
; Subtract external format numbers.
;
; unsigned short a[NE], b[NE], c[NE];
; LDPARMS *ldp;
; esub( a, b, c, ldp ); c = b - a
*/
static void
esub (const short unsigned int *a, const short unsigned int *b,
short unsigned int *c, LDPARMS * ldp)
{
#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", DOMAIN);
enan (c, NBITS);
return;
}
#endif
eadd1 (a, b, c, 1, ldp);
}
static void
eadd1 (const short unsigned int *a, const short unsigned int *b,
short unsigned int *c, int subflg, LDPARMS * ldp)
{
unsigned short ai[NI], bi[NI], ci[NI];
int i, lost, j, k;
long lt, lta, ltb;
#ifdef USE_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 < (long) (-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 short) 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, ldp);
done:
emovo (bi, c, ldp);
}
/*
; Divide.
;
; unsigned short a[NE], b[NE], c[NE];
; LDPARMS *ldp;
; ediv( a, b, c, ldp ); c = b / a
*/
static void
ediv (const short unsigned int *a, const short unsigned int *b,
short unsigned int *c, LDPARMS * ldp)
{
unsigned short ai[NI], bi[NI];
int i;
long 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", DOMAIN);
enan (c, NBITS);
return;
}
#endif
/* Infinity over anything else is infinity. */
#ifdef USE_INFINITY
if (eisinf (b))
{
if (eisneg (a) ^ eisneg (b))
*(c + (NE - 1)) = 0x8000;
else
*(c + (NE - 1)) = 0;
einfin (c, ldp);
return;
}
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;
einfin (c, ldp);
mtherr ("ediv", SING);
return;
}
dnzro2:
i = edivm (ai, bi, ldp);
/* calculate exponent */
lt = ltb - lta + EXONE;
emdnorm (bi, i, 0, lt, 64, ldp);
/* set the sign */
if (ai[0] == bi[0])
bi[0] = 0;
else
bi[0] = 0Xffff;
emovo (bi, c, ldp);
}
/*
; Multiply.
;
; unsigned short a[NE], b[NE], c[NE];
; LDPARMS *ldp
; emul( a, b, c, ldp ); c = b * a
*/
static void
emul (const short unsigned int *a, const short unsigned int *b,
short unsigned int *c, LDPARMS * ldp)
{
unsigned short ai[NI], bi[NI];
int i, j;
long 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", DOMAIN);
enan (c, NBITS);
return;
}
#endif
/* Infinity times anything else is infinity. */
#ifdef USE_INFINITY
if (eisinf (a) || eisinf (b))
{
if (eisneg (a) ^ eisneg (b))
*(c + (NE - 1)) = 0x8000;
else
*(c + (NE - 1)) = 0;
einfin (c, ldp);
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, ldp);
/* calculate exponent */
lt = lta + ltb - (EXONE - 1);
emdnorm (bi, j, 0, lt, 64, ldp);
/* calculate sign of product */
if (ai[0] == bi[0])
bi[0] = 0;
else
bi[0] = 0xffff;
emovo (bi, c, ldp);
}
#if LDBL_MANT_DIG > 64
static void
e113toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp)
{
register unsigned short r;
unsigned short *e, *p;
unsigned short 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 USE_INFINITY
if (r == 0x7fff)
{
#ifdef NANS
#ifdef IBMPC
for (i = 0; i < 7; i++)
{
if (pe[i] != 0)
{
enan (y, NBITS);
return;
}
}
#else /* !IBMPC */
for (i = 1; i < 8; i++)
{
if (pe[i] != 0)
{
enan (y, NBITS);
return;
}
}
#endif /* !IBMPC */
#endif /* NANS */
eclear (y);
einfin (y, ldp);
if (*e & 0x8000)
eneg (y);
return;
}
#endif /* INFINITY */
yy[E] = r;
p = &yy[M + 1];
#ifdef IBMPC
for (i = 0; i < 7; i++)
*p++ = *(--e);
#else /* IBMPC */
++e;
for (i = 0; i < 7; i++)
*p++ = *e++;
#endif /* IBMPC */
/* 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, ldp);
}
/* move out internal format to ieee long double */
static void
__attribute__ ((__unused__))
toe113 (short unsigned int *a, short unsigned int *b)
{
register unsigned short *p, *q;
unsigned short i;
#ifdef NANS
if (eiisnan (a))
{
enan (b, 113);
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
}
#endif /* LDBL_MANT_DIG > 64 */
#if LDBL_MANT_DIG == 64
static void
e64toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp)
{
unsigned short yy[NI];
unsigned short *p, *q, *e;
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
#ifdef DEC
for (i = 0; i < 5; i++)
*p++ = *e++;
#endif
#ifdef MIEEE
p = &yy[0] + (NE - 1);
*p-- = *e++;
++e; /* MIEEE skips over 2nd short */
for (i = 0; i < 4; i++)
*p-- = *e++;
#endif
#ifdef IBMPC
/* For Intel long double, shift denormal significand up 1
-- but only if the top significand bit is zero. */
if ((yy[NE - 1] & 0x7fff) == 0 && (yy[NE - 2] & 0x8000) == 0)
{
unsigned short temp[NI + 1];
emovi (yy, temp);
eshup1 (temp);
emovo (temp, y, ldp);
return;
}
#endif
#ifdef USE_INFINITY
/* Point to the exponent field. */
p = &yy[NE - 1];
if ((*p & 0x7fff) == 0x7fff)
{
#ifdef NANS
#ifdef IBMPC
for (i = 0; i < 4; i++)
{
if ((i != 3 && pe[i] != 0)
/* Check for Intel long double infinity pattern. */
|| (i == 3 && pe[i] != 0x8000))
{
enan (y, NBITS);
return;
}
}
#endif
#ifdef MIEEE
for (i = 2; i <= 5; i++)
{
if (pe[i] != 0)
{
enan (y, NBITS);
return;
}
}
#endif
#endif /* NANS */
eclear (y);
einfin (y, ldp);
if (*p & 0x8000)
eneg (y);
return;
}
#endif /* USE_INFINITY */
p = yy;
q = y;
for (i = 0; i < NE; i++)
*q++ = *p++;
}
/* move out internal format to ieee long double */
static void
__attribute__ ((__unused__))
toe64 (short unsigned int *a, short unsigned int *b)
{
register unsigned short *p, *q;
unsigned short i;
#ifdef NANS
if (eiisnan (a))
{
enan (b, 64);
return;
}
#endif
#ifdef IBMPC
/* Shift Intel denormal significand down 1. */
if (a[E] == 0)
eshdn1 (a);
#endif
p = a;
#ifdef MIEEE
q = b;
#else
q = b + 4; /* point to output exponent */
/* NOTE: Intel data type is 96 bits wide, clear the last word here. */
*(q + 1) = 0;
#endif
/* combine sign and exponent */
i = *p++;
#ifdef MIEEE
if (i)
*q++ = *p++ | 0x8000;
else
*q++ = *p++;
*q++ = 0; /* leave 2nd short blank */
#else
if (i)
*q-- = *p++ | 0x8000;
else
*q-- = *p++;
#endif
/* skip over guard word */
++p;
/* move the significand */
#ifdef MIEEE
for (i = 0; i < 4; i++)
*q++ = *p++;
#else
#ifdef USE_INFINITY
#ifdef IBMPC
if (eiisinf (a))
{
/* Intel long double infinity. */
*q-- = 0x8000;
*q-- = 0;
*q-- = 0;
*q = 0;
return;
}
#endif /* IBMPC */
#endif /* USE_INFINITY */
for (i = 0; i < 4; i++)
*q-- = *p++;
#endif
}
#endif /* LDBL_MANT_DIG == 64 */
#if LDBL_MANT_DIG == 53
/*
; Convert IEEE double precision to e type
; double d;
; unsigned short x[N+2];
; e53toe( &d, x );
*/
static void
e53toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp)
{
#ifdef DEC
dectoe (pe, y); /* see etodec.c */
#else
register unsigned short r;
register unsigned short *p, *e;
unsigned short yy[NI];
int denorm, k;
e = pe;
denorm = 0; /* flag if denormalized number */
ecleaz (yy);
#ifdef IBMPC
e += 3;
#endif
#ifdef DEC
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 USE_INFINITY
if (r == 0x7ff0)
{
#ifdef NANS
#ifdef IBMPC
if (((pe[3] & 0xf) != 0) || (pe[2] != 0)
|| (pe[1] != 0) || (pe[0] != 0))
{
enan (y, NBITS);
return;
}
#else /* !IBMPC */
if (((pe[0] & 0xf) != 0) || (pe[1] != 0)
|| (pe[2] != 0) || (pe[3] != 0))
{
enan (y, NBITS);
return;
}
#endif /* !IBMPC */
#endif /* NANS */
eclear (y);
einfin (y, ldp);
if (yy[0])
eneg (y);
return;
}
#endif
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);
#else /* !IBMPC */
++e;
*p++ = *e++;
*p++ = *e++;
*p++ = *e++;
#endif /* !IBMPC */
(void) eshift (yy, -5);
if (denorm)
{ /* if zero exponent, then normalize the significand */
if ((k = enormlz (yy)) > NBITS)
ecleazs (yy);
else
yy[E] -= (unsigned short) (k - 1);
}
emovo (yy, y, ldp);
#endif /* !DEC */
}
/*
; e type to IEEE double precision
; double d;
; unsigned short x[NE];
; etoe53( x, &d );
*/
#ifdef DEC
static void
etoe53 (x, e)
unsigned short *x, *e;
{
etodec (x, e); /* see etodec.c */
}
static void
__attribute__ ((__unused__))
toe53 (x, y)
unsigned short *x, *y;
{
todec (x, y);
}
#else
static void
__attribute__ ((__unused__))
toe53 (short unsigned int *x, short unsigned int *y)
{
unsigned short i;
unsigned short *p;
#ifdef NANS
if (eiisnan (x))
{
enan (y, 53);
return;
}
#endif
p = &x[0];
#ifdef IBMPC
y += 3;
#endif
#ifdef DEC
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 USE_INFINITY
*y |= 0x7ff0;
#ifdef IBMPC
*(--y) = 0;
*(--y) = 0;
*(--y) = 0;
#else /* !IBMPC */
++y;
*y++ = 0;
*y++ = 0;
*y++ = 0;
#endif /* IBMPC */
#else /* !USE_INFINITY */
*y |= (unsigned short) 0x7fef;
#ifdef IBMPC
*(--y) = 0xffff;
*(--y) = 0xffff;
*(--y) = 0xffff;
#else /* !IBMPC */
++y;
*y++ = 0xffff;
*y++ = 0xffff;
*y++ = 0xffff;
#endif
#endif /* !USE_INFINITY */
return;
}
if (i == 0)
{
(void) eshift (x, 4);
}
else
{
i <<= 4;
(void) eshift (x, 5);
}
i |= *p++ & (unsigned short) 0x0f; /* *p = xi[M] */
*y |= (unsigned short) i; /* high order output already has sign bit set */
#ifdef IBMPC
*(--y) = *p++;
*(--y) = *p++;
*(--y) = *p;
#else /* !IBMPC */
++y;
*y++ = *p++;
*y++ = *p++;
*y++ = *p++;
#endif /* !IBMPC */
}
#endif /* not DEC */
#endif /* LDBL_MANT_DIG == 53 */
#if LDBL_MANT_DIG == 24
/*
; Convert IEEE single precision to e type
; float d;
; unsigned short x[N+2];
; dtox( &d, x );
*/
void
e24toe (short unsigned int *pe, short unsigned int *y, LDPARMS * ldp)
{
register unsigned short r;
register unsigned short *p, *e;
unsigned short 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 USE_INFINITY
if (r == 0x7f80)
{
#ifdef NANS
#ifdef MIEEE
if (((pe[0] & 0x7f) != 0) || (pe[1] != 0))
{
enan (y, NBITS);
return;
}
#else /* !MIEEE */
if (((pe[1] & 0x7f) != 0) || (pe[0] != 0))
{
enan (y, NBITS);
return;
}
#endif /* !MIEEE */
#endif /* NANS */
eclear (y);
einfin (y, ldp);
if (yy[0])
eneg (y);
return;
}
#endif
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
(void) eshift (yy, -8);
if (denorm)
{ /* if zero exponent, then normalize the significand */
if ((k = enormlz (yy)) > NBITS)
ecleazs (yy);
else
yy[E] -= (unsigned short) (k - 1);
}
emovo (yy, y, ldp);
}
static void
__attribute__ ((__unused__))
toe24 (short unsigned int *x, short unsigned int *y)
{
unsigned short i;
unsigned short *p;
#ifdef NANS
if (eiisnan (x))
{
enan (y, 24);
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++;
if (i >= 255)
{ /* Saturate at largest number less than infinity. */
#ifdef USE_INFINITY
*y |= (unsigned short) 0x7f80;
#ifdef IBMPC
*(--y) = 0;
#endif
#ifdef DEC
*(--y) = 0;
#endif
#ifdef MIEEE
++y;
*y = 0;
#endif
#else /* !USE_INFINITY */
*y |= (unsigned short) 0x7f7f;
#ifdef IBMPC
*(--y) = 0xffff;
#endif
#ifdef DEC
*(--y) = 0xffff;
#endif
#ifdef MIEEE
++y;
*y = 0xffff;
#endif
#endif /* !USE_INFINITY */
return;
}
if (i == 0)
{
(void) eshift (x, 7);
}
else
{
i <<= 7;
(void) eshift (x, 8);
}
i |= *p++ & (unsigned short) 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 /* LDBL_MANT_DIG == 24 */
/* Compare two e type numbers.
*
* unsigned short a[NE], b[NE];
* 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.
*/
static int
ecmp (const short unsigned int *a, const short unsigned int *b)
{
unsigned short ai[NI], bi[NI];
register unsigned short *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 */
}
/*
; Shift significand
;
; Shifts significand area up or down by the number of bits
; given by the variable sc.
*/
static int
eshift (short unsigned int *x, int sc)
{
unsigned short lost;
unsigned short *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);
}
/*
; normalize
;
; Shift normalizes the significand area pointed to by argument
; shift count (up = positive) is returned.
*/
static int
enormlz (short unsigned int *x)
{
register unsigned short *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 + 16))
{
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 NE == 10
static const unsigned short 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 const unsigned short 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
static const unsigned short 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 const unsigned short 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
/* ASCII string outputs for unix */
#if 0
void
_IO_ldtostr (x, string, ndigs, flags, fmt)
long double *x;
char *string;
int ndigs;
int flags;
char fmt;
{
unsigned short w[NI];
char *t, *u;
LDPARMS rnd;
LDPARMS *ldp = &rnd;
rnd.rlast = -1;
rnd.rndprc = NBITS;
if (sizeof (long double) == 16)
e113toe ((unsigned short *) x, w, ldp);
else
e64toe ((unsigned short *) x, w, ldp);
etoasc (w, string, ndigs, -1, ldp);
if (ndigs == 0 && flags == 0)
{
/* Delete the decimal point unless alternate format. */
t = string;
while (*t != '.')
++t;
u = t + 1;
while (*t != '\0')
*t++ = *u++;
}
if (*string == ' ')
{
t = string;
u = t + 1;
while (*t != '\0')
*t++ = *u++;
}
if (fmt == 'E')
{
t = string;
while (*t != 'e')
++t;
*t = 'E';
}
}
#endif
/* This routine will not return more than NDEC+1 digits. */
char *
_ldtoa_r (struct _reent *ptr, long double d, int mode, int ndigits,
int *decpt, int *sign, char **rve)
{
unsigned short e[NI];
char *s, *p;
int i, j, k;
int orig_ndigits;
LDPARMS rnd;
LDPARMS *ldp = &rnd;
char *outstr;
char outbuf_sml[NDEC_SML + MAX_EXP_DIGITS + 10];
char *outbuf = outbuf_sml;
union uconv du;
du.d = d;
orig_ndigits = ndigits;
rnd.rlast = -1;
rnd.rndprc = NBITS;
_REENT_CHECK_MP (ptr);
/* reentrancy addition to use mprec storage pool */
if (_REENT_MP_RESULT (ptr))
{
_REENT_MP_RESULT (ptr)->_k = _REENT_MP_RESULT_K (ptr);
_REENT_MP_RESULT (ptr)->_maxwds = 1 << _REENT_MP_RESULT_K (ptr);
Bfree (ptr, _REENT_MP_RESULT (ptr));
_REENT_MP_RESULT (ptr) = 0;
}
#if LDBL_MANT_DIG == 24
e24toe (&du.pe, e, ldp);
#elif LDBL_MANT_DIG == 53
e53toe (&du.pe, e, ldp);
#elif LDBL_MANT_DIG == 64
e64toe (&du.pe, e, ldp);
#else
e113toe (&du.pe, e, ldp);
#endif
if (eisneg (e))
*sign = 1;
else
*sign = 0;
/* Mode 3 is "f" format. */
if (mode != 3)
ndigits -= 1;
/* Mode 0 is for %.999 format, which is supposed to give a
minimum length string that will convert back to the same binary value.
For now, just ask for 20 digits which is enough but sometimes too many. */
if (mode == 0)
ndigits = 20;
/* This sanity limit must agree with the corresponding one in etoasc, to
keep straight the returned value of outexpon. Note that we use a dynamic
limit now, either ndec (<= NDEC) or NDEC_SML, depending on ndigits. */
__int32_t ndec;
if (mode == 3) /* %f */
{
__int32_t expon = (e[NE - 1] & 0x7fff) - (EXONE - 1); /* exponent part */
/* log2(10) approximately 485/146 */
ndec = expon * 146 / 485 + ndigits;
}
else /* %g/%e */
ndec = ndigits;
if (ndec < 0)
ndec = 0;
if (ndec > NDEC)
ndec = NDEC;
/* Allocate buffer if more than NDEC_SML digits are requested. */
if (ndec > NDEC_SML)
{
outbuf = (char *) _malloc_r (ptr, ndec + MAX_EXP_DIGITS + 10);
if (!outbuf)
{
ndec = NDEC_SML;
outbuf = outbuf_sml;
}
}
etoasc (e, outbuf, (int) ndec, ndigits, mode, ldp);
s = outbuf;
if (eisinf (e) || eisnan (e))
{
*decpt = 9999;
goto stripspaces;
}
*decpt = ldp->outexpon + 1;
/* Transform the string returned by etoasc into what the caller wants. */
/* Look for decimal point and delete it from the string. */
s = outbuf;
while (*s != '\0')
{
if (*s == '.')
goto yesdecpt;
++s;
}
goto nodecpt;
yesdecpt:
/* Delete the decimal point. */
while (*s != '\0')
{
*s = *(s + 1);
++s;
}
nodecpt:
/* Back up over the exponent field. */
while (*s != 'E' && s > outbuf)
--s;
*s = '\0';
stripspaces:
/* Strip leading spaces and sign. */
p = outbuf;
while (*p == ' ' || *p == '-')
++p;
/* Find new end of string. */
s = outbuf;
while ((*s++ = *p++) != '\0')
;
--s;
/* Strip trailing zeros. */
if (mode == 2)
k = 1;
else if (ndigits > ldp->outexpon)
k = ndigits;
else
k = ldp->outexpon;
while (*(s - 1) == '0' && ((s - outbuf) > k))
*(--s) = '\0';
/* In f format, flush small off-scale values to zero.
Rounding has been taken care of by etoasc. */
if (mode == 3 && ((ndigits + ldp->outexpon) < 0))
{
s = outbuf;
*s = '\0';
*decpt = 0;
}
/* reentrancy addition to use mprec storage pool */
/* we want to have enough space to hold the formatted result */
if (mode == 3) /* f format, account for sign + dec digits + decpt + frac */
i = *decpt + orig_ndigits + 3;
else /* account for sign + max precision digs + E + exp sign + exponent */
i = orig_ndigits + MAX_EXP_DIGITS + 4;
j = sizeof (__ULong);
for (_REENT_MP_RESULT_K (ptr) = 0;
sizeof (_Bigint) - sizeof (__ULong) + j <= i; j <<= 1)
_REENT_MP_RESULT_K (ptr)++;
_REENT_MP_RESULT (ptr) = eBalloc (ptr, _REENT_MP_RESULT_K (ptr));
/* Copy from internal temporary buffer to permanent buffer. */
outstr = (char *) _REENT_MP_RESULT (ptr);
strcpy (outstr, outbuf);
if (rve)
*rve = outstr + (s - outbuf);
if (outbuf != outbuf_sml)
_free_r (ptr, outbuf);
return outstr;
}
/* Routine used to tell if long double is NaN or Infinity or regular number.
Returns: 0 = regular number
1 = Nan
2 = Infinity
*/
int
_ldcheck (long double *d)
{
unsigned short e[NI];
LDPARMS rnd;
LDPARMS *ldp = &rnd;
union uconv du;
rnd.rlast = -1;
rnd.rndprc = NBITS;
du.d = *d;
#if LDBL_MANT_DIG == 24
e24toe (&du.pe, e, ldp);
#elif LDBL_MANT_DIG == 53
e53toe (&du.pe, e, ldp);
#elif LDBL_MANT_DIG == 64
e64toe (&du.pe, e, ldp);
#else
e113toe (&du.pe, e, ldp);
#endif
if ((e[NE - 1] & 0x7fff) == 0x7fff)
{
#ifdef NANS
if (eisnan (e))
return (1);
#endif
return (2);
}
else
return (0);
} /* _ldcheck */
static void
etoasc (short unsigned int *x, char *string, int ndec, int ndigits,
int outformat, LDPARMS * ldp)
{
long digit;
unsigned short y[NI], t[NI], u[NI], w[NI];
const unsigned short *p, *r, *ten;
unsigned short sign;
int i, j, k, expon, rndsav, ndigs;
char *s, *ss;
unsigned short m;
unsigned short *equot = ldp->equot;
ndigs = ndigits;
rndsav = ldp->rndprc;
#ifdef NANS
if (eisnan (x))
{
sprintf (string, " NaN ");
expon = 9999;
goto bxit;
}
#endif
ldp->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 (string, " -Infinity ");
else
sprintf (string, " Infinity ");
expon = 9999;
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 (string, "NaN");
expon = 9999;
goto bxit;
}
/* Compare to 1.0 */
i = ecmp (eone, y);
if (i == 0)
goto isone;
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, ldp);
efloor (t, w, ldp);
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];
while (ecmp (ten, u) <= 0)
{
if (ecmp (p, u) <= 0)
{
ediv (p, u, u, ldp);
emul (p, t, t, ldp);
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, ldp);
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, ldp);
}
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, ldp);
emul (r, t, t, ldp);
expon += k;
}
k /= 2;
if (k == 0)
break;
p += NE;
r += NE;
}
ediv (t, eone, t, ldp);
}
isone:
/* Find the first (leading) digit. */
emovi (t, w);
emovz (w, t);
emovi (y, w);
emovz (w, y);
eiremain (t, y, ldp);
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, ldp);
digit = equot[NI - 1];
expon -= 1;
}
s = string;
if (sign)
*s++ = '-';
else
*s++ = ' ';
/* Examine number of digits requested by caller. */
if (outformat == 3)
ndigs += expon;
/*
else 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;
if (ndigs < 0)
{
ss = s;
goto doexp;
}
}
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, ldp);
*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, ldp);
if (ecmp (t, ezero) != 0)
goto roun; /* round to nearest */
if (ndigs < 0 || (*(s - 1 - (*(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 (ndigs < 0)
{
/* This will print like "1E-6". */
*s = '1';
expon += 1;
goto doexp;
}
else 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:
#ifdef __GO32__
if (expon >= 0)
sprintf (ss, "e+%02d", expon);
else
sprintf (ss, "e-%02d", -expon);
#else
sprintf (ss, "E%d", expon);
#endif
bxit:
ldp->rndprc = rndsav;
ldp->outexpon = expon;
}
#if 0 /* Broken, unusable implementation of strtold */
/*
; ASCTOQ
; ASCTOQ.MAC LATEST REV: 11 JAN 84
; SLM, 3 JAN 78
;
; 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).
;
; Usage:
; asctoq( string, q );
*/
long double
_strtold (char *s, char **se)
{
union uconv x;
LDPARMS rnd;
LDPARMS *ldp = &rnd;
int lenldstr;
rnd.rlast = -1;
rnd.rndprc = NBITS;
lenldstr = asctoeg (s, &x.pe, LDBL_MANT_DIG, ldp);
if (se)
*se = s + lenldstr;
return x.d;
}
#define REASONABLE_LEN 200
static int
asctoeg (char *ss, short unsigned int *y, int oprec, LDPARMS * ldp)
{
unsigned short yy[NI], xt[NI], tt[NI];
int esign, decflg, sgnflg, nexp, exp, prec, lost;
int k, trail, c, rndsav;
long lexp;
unsigned short nsign;
const unsigned short *p;
char *sp, *s, *lstr;
int lenldstr;
int mflag = 0;
char tmpstr[REASONABLE_LEN];
/* Copy the input string. */
c = strlen (ss) + 2;
if (c <= REASONABLE_LEN)
lstr = tmpstr;
else
{
lstr = (char *) calloc (c, 1);
mflag = 1;
}
s = ss;
lenldstr = 0;
while (*s == ' ') /* skip leading spaces */
{
++s;
++lenldstr;
}
sp = lstr;
for (k = 0; k < c; k++)
{
if ((*sp++ = *s++) == '\0')
break;
}
*sp = '\0';
s = lstr;
rndsav = ldp->rndprc;
ldp->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 short) 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
enan (yy, NI * 16);
#else
mtherr ("asctoe", DOMAIN);
ecleaz (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 > 4977)
{
if (esign < 0)
goto zero;
else
goto infinite;
}
}
if (esign < 0)
exp = -exp;
if (exp > 4932)
{
infinite:
ecleaz (yy);
yy[E] = 0x7fff; /* infinity */
goto aexit;
}
if (exp < -4977)
{
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, ldp);
/* 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, ldp);
lexp += EXONE;
nexp -= 4096;
}
}
p = &etens[NTEN][0];
emov (eone, xt);
exp = 1;
do
{
if (exp & nexp)
emul (p, xt, xt, ldp);
p -= NE;
exp = exp + exp;
}
while (exp <= MAXP);
emovi (xt, tt);
if (esign < 0)
{
lexp -= tt[E];
k = edivm (tt, yy, ldp);
lexp += EXONE;
}
else
{
lexp += tt[E];
k = emulm (tt, yy, ldp);
lexp -= EXONE - 1;
}
expdon:
/* Round and convert directly to the destination type */
if (oprec == 53)
lexp -= EXONE - 0x3ff;
else if (oprec == 24)
lexp -= EXONE - 0177;
#ifdef DEC
else if (oprec == 56)
lexp -= EXONE - 0201;
#endif
ldp->rndprc = oprec;
emdnorm (yy, k, 0, lexp, 64, ldp);
aexit:
ldp->rndprc = rndsav;
yy[0] = nsign;
switch (oprec)
{
#ifdef DEC
case 56:
todec (yy, y); /* see etodec.c */
break;
#endif
#if LDBL_MANT_DIG == 53
case 53:
toe53 (yy, y);
break;
#elif LDBL_MANT_DIG == 24
case 24:
toe24 (yy, y);
break;
#elif LDBL_MANT_DIG == 64
case 64:
toe64 (yy, y);
break;
#elif LDBL_MANT_DIG == 113
case 113:
toe113 (yy, y);
break;
#else
case NBITS:
emovo (yy, y, ldp);
break;
#endif
}
lenldstr += s - lstr;
if (mflag)
free (lstr);
return lenldstr;
}
#endif
/* y = largest integer not greater than x
* (truncated toward minus infinity)
*
* unsigned short x[NE], y[NE]
* LDPARMS *ldp
*
* efloor( x, y, ldp );
*/
static const unsigned short bmask[] = {
0xffff,
0xfffe,
0xfffc,
0xfff8,
0xfff0,
0xffe0,
0xffc0,
0xff80,
0xff00,
0xfe00,
0xfc00,
0xf800,
0xf000,
0xe000,
0xc000,
0x8000,
0x0000,
};
static void
efloor (short unsigned int *x, short unsigned int *y, LDPARMS * ldp)
{
register unsigned short *p;
int e, expon, i;
unsigned short 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 short) expon & (unsigned short) 0x8000)
{
for (i = 0; i < NE - 1; i++)
{
if (f[i] != y[i])
{
esub (eone, y, y, ldp);
break;
}
}
}
}
static void
eiremain (short unsigned int *den, short unsigned int *num, LDPARMS * ldp)
{
long ld, ln;
unsigned short j;
unsigned short *equot = ldp->equot;
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, ldp);
}
/* NaN bit patterns
*/
#ifdef MIEEE
#if !defined(__mips)
static const unsigned short nan113[8] = {
0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff
};
static const unsigned short nan64[6] = {
0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff
};
static const unsigned short nan53[4] = { 0x7fff, 0xffff, 0xffff, 0xffff };
static const unsigned short nan24[2] = { 0x7fff, 0xffff };
#elif defined(__mips_nan2008) /* __mips */
static const unsigned short nan113[8] = { 0x7fff, 0x8000, 0, 0, 0, 0, 0, 0 };
static const unsigned short nan64[6] = { 0x7fff, 0xc000, 0, 0, 0, 0 };
static const unsigned short nan53[4] = { 0x7ff8, 0, 0, 0 };
static const unsigned short nan24[2] = { 0x7fc0, 0 };
#else /* __mips && !__mips_nan2008 */
static const unsigned short nan113[8] = {
0x7fff, 0x7fff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff
};
static const unsigned short nan64[6] = {
0x7fff, 0xbfff, 0xffff, 0xffff, 0xffff, 0xffff
};
static const unsigned short nan53[4] = { 0x7ff7, 0xffff, 0xffff, 0xffff };
static const unsigned short nan24[2] = { 0x7fbf, 0xffff };
#endif /* __mips && !__mips_nan2008 */
#else /* !MIEEE */
#if !defined(__mips) || defined(__mips_nan2008)
static const unsigned short nan113[8] = { 0, 0, 0, 0, 0, 0, 0x8000, 0x7fff };
static const unsigned short nan64[6] = { 0, 0, 0, 0, 0xc000, 0x7fff };
static const unsigned short nan53[4] = { 0, 0, 0, 0x7ff8 };
static const unsigned short nan24[2] = { 0, 0x7fc0 };
#else /* __mips && !__mips_nan2008 */
static const unsigned short nan113[8] = {
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0x7fff, 0x7fff
};
static const unsigned short nan64[6] = {
0xffff, 0xffff, 0xffff, 0xffff, 0xbfff, 0x7fff
};
static const unsigned short nan53[4] = { 0xffff, 0xffff, 0xffff, 0x7ff7 };
static const unsigned short nan24[2] = { 0xffff, 0x7fbf };
#endif /* __mips && !__mips_nan2008 */
#endif /* !MIEEE */
static void
enan (short unsigned int *nan, int size)
{
int i, n;
const unsigned short *p;
switch (size)
{
#ifndef DEC
case 113:
n = 8;
p = nan113;
break;
case 64:
n = 6;
p = nan64;
break;
case 53:
n = 4;
p = nan53;
break;
case 24:
n = 2;
p = nan24;
break;
case NBITS:
#if !defined(__mips) || defined(__mips_nan2008)
for (i = 0; i < NE - 2; i++)
*nan++ = 0;
*nan++ = 0xc000;
#else /* __mips && !__mips_nan2008 */
for (i = 0; i < NE - 2; i++)
*nan++ = 0xffff;
*nan++ = 0xbfff;
#endif /* __mips && !__mips_nan2008 */
*nan++ = 0x7fff;
return;
case NI * 16:
*nan++ = 0;
*nan++ = 0x7fff;
*nan++ = 0;
#if !defined(__mips) || defined(__mips_nan2008)
*nan++ = 0xc000;
for (i = 4; i < NI - 1; i++)
*nan++ = 0;
#else /* __mips && !__mips_nan2008 */
*nan++ = 0xbfff;
for (i = 4; i < NI - 1; i++)
*nan++ = 0xffff;
#endif /* __mips && !__mips_nan2008 */
*nan++ = 0;
return;
#endif
default:
mtherr ("enan", DOMAIN);
return;
}
for (i = 0; i < n; i++)
*nan++ = *p++;
}
#endif /* !_USE_GDTOA */