422 lines
8.5 KiB
C
422 lines
8.5 KiB
C
/* This file is extracted from S L Moshier's ioldoubl.c,
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* modified for use in MinGW
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*
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* Extended precision arithmetic functions for long double I/O.
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* This program has been placed in the public domain.
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*/
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/*
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* Revision history:
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*
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* 5 Jan 84 PDP-11 assembly language version
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* 6 Dec 86 C language version
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* 30 Aug 88 100 digit version, improved rounding
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* 15 May 92 80-bit long double support
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*
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* Author: S. L. Moshier.
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*
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* 6 Oct 02 Modified for MinGW by inlining utility routines,
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* removing global variables and splitting out strtold
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* from _IO_ldtoa and _IO_ldtostr.
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*
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* 4 Feb 04 Reorganize __asctoe64 to fix setting error codes,
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* and handling special chars.
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*
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* Danny Smith <dannysmith@users.sourceforge.net>
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*/
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#include "math/cephes_emath.h"
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#if NE == 10
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/* 1.0E0 */
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static const unsigned short __eone[NE] =
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{0x0000, 0x0000, 0x0000, 0x0000,
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0x0000, 0x0000, 0x0000, 0x0000, 0x8000, 0x3fff,};
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#else
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static const unsigned short __eone[NE] = {
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0, 0000000,0000000,0000000,0100000,0x3fff,};
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#endif
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#if NE == 10
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static const unsigned short __etens[NTEN + 1][NE] =
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{
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{0x6576, 0x4a92, 0x804a, 0x153f,
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0xc94c, 0x979a, 0x8a20, 0x5202, 0xc460, 0x7525,}, /* 10**4096 */
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{0x6a32, 0xce52, 0x329a, 0x28ce,
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0xa74d, 0x5de4, 0xc53d, 0x3b5d, 0x9e8b, 0x5a92,}, /* 10**2048 */
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{0x526c, 0x50ce, 0xf18b, 0x3d28,
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0x650d, 0x0c17, 0x8175, 0x7586, 0xc976, 0x4d48,},
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{0x9c66, 0x58f8, 0xbc50, 0x5c54,
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0xcc65, 0x91c6, 0xa60e, 0xa0ae, 0xe319, 0x46a3,},
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{0x851e, 0xeab7, 0x98fe, 0x901b,
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0xddbb, 0xde8d, 0x9df9, 0xebfb, 0xaa7e, 0x4351,},
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{0x0235, 0x0137, 0x36b1, 0x336c,
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0xc66f, 0x8cdf, 0x80e9, 0x47c9, 0x93ba, 0x41a8,},
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{0x50f8, 0x25fb, 0xc76b, 0x6b71,
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0x3cbf, 0xa6d5, 0xffcf, 0x1f49, 0xc278, 0x40d3,},
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{0x0000, 0x0000, 0x0000, 0x0000,
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0xf020, 0xb59d, 0x2b70, 0xada8, 0x9dc5, 0x4069,},
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{0x0000, 0x0000, 0x0000, 0x0000,
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0x0000, 0x0000, 0x0400, 0xc9bf, 0x8e1b, 0x4034,},
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{0x0000, 0x0000, 0x0000, 0x0000,
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0x0000, 0x0000, 0x0000, 0x2000, 0xbebc, 0x4019,},
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{0x0000, 0x0000, 0x0000, 0x0000,
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0x0000, 0x0000, 0x0000, 0x0000, 0x9c40, 0x400c,},
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{0x0000, 0x0000, 0x0000, 0x0000,
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0x0000, 0x0000, 0x0000, 0x0000, 0xc800, 0x4005,},
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{0x0000, 0x0000, 0x0000, 0x0000,
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0x0000, 0x0000, 0x0000, 0x0000, 0xa000, 0x4002,}, /* 10**1 */
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};
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#else
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static const unsigned short __etens[NTEN+1][NE] = {
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{0xc94c,0x979a,0x8a20,0x5202,0xc460,0x7525,},/* 10**4096 */
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{0xa74d,0x5de4,0xc53d,0x3b5d,0x9e8b,0x5a92,},/* 10**2048 */
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{0x650d,0x0c17,0x8175,0x7586,0xc976,0x4d48,},
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{0xcc65,0x91c6,0xa60e,0xa0ae,0xe319,0x46a3,},
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{0xddbc,0xde8d,0x9df9,0xebfb,0xaa7e,0x4351,},
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{0xc66f,0x8cdf,0x80e9,0x47c9,0x93ba,0x41a8,},
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{0x3cbf,0xa6d5,0xffcf,0x1f49,0xc278,0x40d3,},
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{0xf020,0xb59d,0x2b70,0xada8,0x9dc5,0x4069,},
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{0x0000,0x0000,0x0400,0xc9bf,0x8e1b,0x4034,},
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{0x0000,0x0000,0x0000,0x2000,0xbebc,0x4019,},
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{0x0000,0x0000,0x0000,0x0000,0x9c40,0x400c,},
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{0x0000,0x0000,0x0000,0x0000,0xc800,0x4005,},
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{0x0000,0x0000,0x0000,0x0000,0xa000,0x4002,}, /* 10**1 */
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};
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#endif
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int __asctoe64(const char * __restrict__ ss, short unsigned int * __restrict__ y)
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{
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unsigned short yy[NI], xt[NI], tt[NI];
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int esign, decflg, nexp, exp, lost;
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int k, c;
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int valid_lead_string = 0;
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int have_non_zero_mant = 0;
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int prec = 0;
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/* int trail = 0; */
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long lexp;
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unsigned short nsign = 0;
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const unsigned short *p;
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char *sp, *lstr;
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char *s;
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const char dec_sym = *(localeconv ()->decimal_point);
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int lenldstr = 0;
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/* Copy the input string. */
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c = strlen (ss) + 2;
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lstr = (char *) alloca (c);
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s = (char *) ss;
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while( isspace ((int)(unsigned char)*s)) /* skip leading spaces */
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{
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++s;
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++lenldstr;
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}
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sp = lstr;
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for( k=0; k<c; k++ )
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{
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if( (*sp++ = *s++) == '\0' )
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break;
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}
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*sp = '\0';
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s = lstr;
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if (*s == '-')
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{
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nsign = 0xffff;
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++s;
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}
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else if (*s == '+')
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{
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++s;
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}
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if (_strnicmp("INF", s , 3) == 0)
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{
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valid_lead_string = 1;
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s += 3;
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if ( _strnicmp ("INITY", s, 5) == 0)
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s += 5;
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__ecleaz(yy);
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yy[E] = 0x7fff; /* infinity */
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goto aexit;
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}
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else if(_strnicmp ("NAN", s, 3) == 0)
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{
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valid_lead_string = 1;
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s += 3;
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__enan_NI16( yy );
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goto aexit;
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}
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/* FIXME: Handle case of strtold ("NAN(n_char_seq)",endptr) */
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/* Now get some digits. */
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lost = 0;
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decflg = 0;
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nexp = 0;
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exp = 0;
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__ecleaz( yy );
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/* Ignore leading zeros */
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while (*s == '0')
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{
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valid_lead_string = 1;
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s++;
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}
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nxtcom:
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k = *s - '0';
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if( (k >= 0) && (k <= 9) )
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{
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#if 0
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/* The use of a special char as a flag for trailing zeroes causes problems when input
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actually contains the char */
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/* Identify and strip trailing zeros after the decimal point. */
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if( (trail == 0) && (decflg != 0) )
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{
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sp = s;
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while( (*sp >= '0') && (*sp <= '9') )
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++sp;
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--sp;
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while( *sp == '0' )
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{
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*sp-- = (char)-1;
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trail++;
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}
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if( *s == (char)-1 )
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goto donchr;
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}
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#endif
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/* If enough digits were given to more than fill up the yy register,
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* continuing until overflow into the high guard word yy[2]
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* guarantees that there will be a roundoff bit at the top
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* of the low guard word after normalization.
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*/
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if( yy[2] == 0 )
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{
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if( decflg )
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nexp += 1; /* count digits after decimal point */
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__eshup1( yy ); /* multiply current number by 10 */
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__emovz( yy, xt );
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__eshup1( xt );
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__eshup1( xt );
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__eaddm( xt, yy );
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__ecleaz( xt );
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xt[NI-2] = (unsigned short )k;
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__eaddm( xt, yy );
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}
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else
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{
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/* Mark any lost non-zero digit. */
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lost |= k;
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/* Count lost digits before the decimal point. */
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if (decflg == 0)
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nexp -= 1;
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}
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have_non_zero_mant |= k;
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prec ++;
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/* goto donchr; */
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}
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else if (*s == dec_sym)
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{
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if( decflg )
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goto daldone;
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++decflg;
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}
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else if ((*s == 'E') || (*s == 'e') )
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{
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if (prec || valid_lead_string)
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goto expnt;
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else
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goto daldone;
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}
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#if 0
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else if (*s == (char)-1)
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goto donchr;
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#endif
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else /* an invalid char */
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goto daldone;
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/* donchr: */
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++s;
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goto nxtcom;
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/* Exponent interpretation */
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expnt:
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esign = 1;
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exp = 0;
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/* Save position in case we need to fall back. */
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sp = s;
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++s;
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/* check for + or - */
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if( *s == '-' )
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{
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esign = -1;
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++s;
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}
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if( *s == '+' )
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++s;
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/* Check for valid exponent. */
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if (!(*s >= '0' && *s <= '9'))
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{
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s = sp;
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goto daldone;
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}
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while( (*s >= '0') && (*s <= '9') )
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{
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/* Stop modifying exp if we are going to overflow anyway,
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but keep parsing the string. */
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if (exp < 4978)
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{
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exp *= 10;
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exp += *s - '0';
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}
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s++;
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}
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if( esign < 0 )
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exp = -exp;
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if (exp > 4977) /* maybe overflow */
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{
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__ecleaz(yy);
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if (have_non_zero_mant)
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yy[E] = 0x7fff;
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goto aexit;
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}
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else if (exp < -4977) /* underflow */
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{
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__ecleaz(yy);
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goto aexit;
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}
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daldone:
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nexp = exp - nexp;
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/* Pad trailing zeros to minimize power of 10, per IEEE spec. */
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while( (nexp > 0) && (yy[2] == 0) )
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{
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__emovz( yy, xt );
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__eshup1( xt );
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__eshup1( xt );
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__eaddm( yy, xt );
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__eshup1( xt );
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if( xt[2] != 0 )
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break;
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nexp -= 1;
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__emovz( xt, yy );
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}
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if( (k = __enormlz(yy)) > NBITS )
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{
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__ecleaz(yy);
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goto aexit;
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}
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lexp = (EXONE - 1 + NBITS) - k;
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__emdnorm( yy, lost, 0, lexp, 64, NBITS );
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/* convert to external format */
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/* Multiply by 10**nexp. If precision is 64 bits,
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* the maximum relative error incurred in forming 10**n
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* for 0 <= n <= 324 is 8.2e-20, at 10**180.
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* For 0 <= n <= 999, the peak relative error is 1.4e-19 at 10**947.
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* For 0 >= n >= -999, it is -1.55e-19 at 10**-435.
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*/
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lexp = yy[E];
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if( nexp == 0 )
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{
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k = 0;
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goto expdon;
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}
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esign = 1;
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if( nexp < 0 )
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{
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nexp = -nexp;
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esign = -1;
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if( nexp > 4096 )
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{ /* Punt. Can't handle this without 2 divides. */
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__emovi( __etens[0], tt );
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lexp -= tt[E];
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k = __edivm( tt, yy );
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lexp += EXONE;
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nexp -= 4096;
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}
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}
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p = &__etens[NTEN][0];
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__emov( __eone, xt );
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exp = 1;
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do
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{
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if( exp & nexp )
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__emul( p, xt, xt );
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p -= NE;
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exp = exp + exp;
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}
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while( exp <= MAXP );
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__emovi( xt, tt );
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if( esign < 0 )
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{
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lexp -= tt[E];
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k = __edivm( tt, yy );
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lexp += EXONE;
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}
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else
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{
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lexp += tt[E];
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k = __emulm( tt, yy );
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lexp -= EXONE - 1;
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}
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expdon:
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/* Round and convert directly to the destination type */
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__emdnorm( yy, k, 0, lexp, 64, 64 );
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aexit:
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yy[0] = nsign;
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__toe64( yy, y );
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/* Check for overflow, undeflow */
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if (have_non_zero_mant &&
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(*((long double*) y) == 0.0L || isinf (*((long double*) y))))
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errno = ERANGE;
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if (prec || valid_lead_string)
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return (lenldstr + (s - lstr));
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return 0;
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}
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long double strtold (const char * __restrict__ s, char ** __restrict__ se)
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{
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int lenldstr;
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union
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{
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unsigned short int us[6];
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long double ld;
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} xx = {{0}};
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lenldstr = __asctoe64( s, xx.us);
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if (se)
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*se = (char*)s + lenldstr;
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return xx.ld;
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}
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