447 lines
12 KiB
C
447 lines
12 KiB
C
/****************************************************************
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*
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* The author of this software is David M. Gay.
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*
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* Copyright (c) 1991 by AT&T.
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose without fee is hereby granted, provided that this entire notice
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* is included in all copies of any software which is or includes a copy
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* or modification of this software and in all copies of the supporting
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* documentation for such software.
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*
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* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
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* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
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* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
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* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
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*
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***************************************************************/
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/* Please send bug reports to
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David M. Gay
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AT&T Bell Laboratories, Room 2C-463
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600 Mountain Avenue
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Murray Hill, NJ 07974-2070
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U.S.A.
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dmg@research.att.com or research!dmg
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*/
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#include <ieeefp.h>
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#include <math.h>
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#include <float.h>
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#include <errno.h>
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#include <sys/config.h>
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#include <sys/types.h>
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#ifdef __IEEE_LITTLE_ENDIAN
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#define IEEE_8087
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#endif
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#ifdef __IEEE_BIG_ENDIAN
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#define IEEE_MC68k
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#endif
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#ifdef __Z8000__
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#define Just_16
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#endif
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#ifdef DEBUG
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#include "stdio.h"
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#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
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#endif
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#ifdef Unsigned_Shifts
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#define Sign_Extend(a,b) if (b < 0) a |= (__uint32_t)0xffff0000;
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#else
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#define Sign_Extend(a,b) /*no-op*/
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#endif
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#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
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Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
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#endif
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/* If we are going to examine or modify specific bits in a double using
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the word0 and/or word1 macros, then we must wrap the double inside
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a union. This is necessary to avoid undefined behavior according to
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the ANSI C spec. */
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union double_union
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{
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double d;
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__uint32_t i[2];
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};
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#ifdef IEEE_8087
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#define word0(x) (x.i[1])
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#define word1(x) (x.i[0])
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#else
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#define word0(x) (x.i[0])
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#define word1(x) (x.i[1])
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#endif
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/* The following is taken from gdtoaimp.h for use with new strtod. */
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typedef __int32_t Long;
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typedef union { double d; __ULong L[2]; } U;
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#ifdef YES_ALIAS
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#define dval(x) x
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#ifdef IEEE_8087
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#define dword0(x) ((__ULong *)&x)[1]
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#define dword1(x) ((__ULong *)&x)[0]
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#else
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#define dword0(x) ((__ULong *)&x)[0]
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#define dword1(x) ((__ULong *)&x)[1]
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#endif
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#else /* !YES_ALIAS */
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#ifdef IEEE_8087
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#define dword0(x) ((U*)&x)->L[1]
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#define dword1(x) ((U*)&x)->L[0]
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#else
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#define dword0(x) ((U*)&x)->L[0]
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#define dword1(x) ((U*)&x)->L[1]
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#endif
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#define dval(x) ((U*)&x)->d
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#endif /* YES_ALIAS */
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#undef SI
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#ifdef Sudden_Underflow
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#define SI 1
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#else
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#define SI 0
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#endif
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/* The following definition of Storeinc is appropriate for MIPS processors.
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* An alternative that might be better on some machines is
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* #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
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*/
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#if defined (__IEEE_BYTES_LITTLE_ENDIAN) + defined (IEEE_8087) + defined (VAX)
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#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
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((unsigned short *)a)[0] = (unsigned short)c, a++)
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#else
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#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
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((unsigned short *)a)[1] = (unsigned short)c, a++)
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#endif
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/* #define P DBL_MANT_DIG */
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/* Ten_pmax = floor(P*log(2)/log(5)) */
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/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
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/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
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/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
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#if defined(IEEE_8087) + defined(IEEE_MC68k)
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#if defined (_DOUBLE_IS_32BITS)
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#define Exp_shift 23
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#define Exp_shift1 23
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#define Exp_msk1 ((__uint32_t)0x00800000L)
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#define Exp_msk11 ((__uint32_t)0x00800000L)
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#define Exp_mask ((__uint32_t)0x7f800000L)
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#define P 24
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#define Bias 127
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#define NO_HEX_FP /* not supported in this case */
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#if 0
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#define IEEE_Arith /* it is, but the code doesn't handle IEEE singles yet */
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#endif
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/* Following is needed due to IEEE_Arith not being set on above. */
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#if defined(__v800)
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#define n_bigtens 2
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#else
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#define n_bigtens 5
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#endif
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#define Emin (-126)
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#define Exp_1 ((__uint32_t)0x3f800000L)
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#define Exp_11 ((__uint32_t)0x3f800000L)
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#define Ebits 8
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#define Frac_mask ((__uint32_t)0x007fffffL)
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#define Frac_mask1 ((__uint32_t)0x007fffffL)
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#define Ten_pmax 10
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#define Sign_bit ((__uint32_t)0x80000000L)
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#define Ten_pmax 10
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#define Bletch 2
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#define Bndry_mask ((__uint32_t)0x007fffffL)
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#define Bndry_mask1 ((__uint32_t)0x007fffffL)
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#define LSB 1
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#define Sign_bit ((__uint32_t)0x80000000L)
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#define Log2P 1
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#define Tiny0 0
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#define Tiny1 1
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#define Quick_max 5
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#define Int_max 6
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#define Infinite(x) (word0(x) == ((__uint32_t)0x7f800000L))
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#undef word0
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#undef word1
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#undef dword0
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#undef dword1
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#define word0(x) (x.i[0])
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#define word1(x) 0
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#define dword0(x) ((__ULong *)&x)[0]
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#define dword1(x) 0
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#else
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#define Exp_shift 20
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#define Exp_shift1 20
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#define Exp_msk1 ((__uint32_t)0x100000L)
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#define Exp_msk11 ((__uint32_t)0x100000L)
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#define Exp_mask ((__uint32_t)0x7ff00000L)
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#define P 53
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#define Bias 1023
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#define IEEE_Arith
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#define Emin (-1022)
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#define Exp_1 ((__uint32_t)0x3ff00000L)
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#define Exp_11 ((__uint32_t)0x3ff00000L)
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#define Ebits 11
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#define Frac_mask ((__uint32_t)0xfffffL)
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#define Frac_mask1 ((__uint32_t)0xfffffL)
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#define Ten_pmax 22
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#define Bletch 0x10
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#define Bndry_mask ((__uint32_t)0xfffffL)
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#define Bndry_mask1 ((__uint32_t)0xfffffL)
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#define LSB 1
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#define Sign_bit ((__uint32_t)0x80000000L)
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#define Log2P 1
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#define Tiny0 0
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#define Tiny1 1
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#define Quick_max 14
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#define Int_max 14
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#define Infinite(x) (word0(x) == ((__uint32_t)0x7ff00000L)) /* sufficient test for here */
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#endif /* !_DOUBLE_IS_32BITS */
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#ifndef Flt_Rounds
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#ifdef FLT_ROUNDS
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#define Flt_Rounds FLT_ROUNDS
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#else
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#define Flt_Rounds 1
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#endif
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#endif /*Flt_Rounds*/
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#else /* !IEEE_8087 && !IEEE_MC68k */
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#undef Sudden_Underflow
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#define Sudden_Underflow
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#ifdef IBM
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#define Flt_Rounds 0
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#define Exp_shift 24
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#define Exp_shift1 24
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#define Exp_msk1 ((__uint32_t)0x1000000L)
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#define Exp_msk11 ((__uint32_t)0x1000000L)
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#define Exp_mask ((__uint32_t)0x7f000000L)
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#define P 14
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#define Bias 65
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#define Exp_1 ((__uint32_t)0x41000000L)
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#define Exp_11 ((__uint32_t)0x41000000L)
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#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
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#define Frac_mask ((__uint32_t)0xffffffL)
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#define Frac_mask1 ((__uint32_t)0xffffffL)
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#define Bletch 4
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#define Ten_pmax 22
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#define Bndry_mask ((__uint32_t)0xefffffL)
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#define Bndry_mask1 ((__uint32_t)0xffffffL)
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#define LSB 1
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#define Sign_bit ((__uint32_t)0x80000000L)
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#define Log2P 4
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#define Tiny0 ((__uint32_t)0x100000L)
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#define Tiny1 0
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#define Quick_max 14
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#define Int_max 15
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#else /* VAX */
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#define Flt_Rounds 1
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#define Exp_shift 23
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#define Exp_shift1 7
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#define Exp_msk1 0x80
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#define Exp_msk11 ((__uint32_t)0x800000L)
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#define Exp_mask ((__uint32_t)0x7f80L)
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#define P 56
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#define Bias 129
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#define Exp_1 ((__uint32_t)0x40800000L)
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#define Exp_11 ((__uint32_t)0x4080L)
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#define Ebits 8
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#define Frac_mask ((__uint32_t)0x7fffffL)
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#define Frac_mask1 ((__uint32_t)0xffff007fL)
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#define Ten_pmax 24
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#define Bletch 2
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#define Bndry_mask ((__uint32_t)0xffff007fL)
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#define Bndry_mask1 ((__uint32_t)0xffff007fL)
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#define LSB ((__uint32_t)0x10000L)
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#define Sign_bit ((__uint32_t)0x8000L)
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#define Log2P 1
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#define Tiny0 0x80
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#define Tiny1 0
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#define Quick_max 15
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#define Int_max 15
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#endif
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#endif
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#ifndef IEEE_Arith
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#define ROUND_BIASED
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#else
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#define Scale_Bit 0x10
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#if defined(_DOUBLE_IS_32BITS) && defined(__v800)
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#define n_bigtens 2
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#else
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#define n_bigtens 5
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#endif
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#endif
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#ifdef IBM
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#define n_bigtens 3
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#endif
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#ifdef VAX
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#define n_bigtens 2
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#endif
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#ifndef __NO_INFNAN_CHECK
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#define INFNAN_CHECK
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#endif
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/*
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* NAN_WORD0 and NAN_WORD1 are only referenced in strtod.c. Prior to
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* 20050115, they used to be hard-wired here (to 0x7ff80000 and 0,
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* respectively), but now are determined by compiling and running
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* qnan.c to generate gd_qnan.h, which specifies d_QNAN0 and d_QNAN1.
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* Formerly gdtoaimp.h recommended supplying suitable -DNAN_WORD0=...
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* and -DNAN_WORD1=... values if necessary. This should still work.
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* (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
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*/
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#ifdef IEEE_Arith
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#ifdef IEEE_MC68k
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#define _0 0
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#define _1 1
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#ifndef NAN_WORD0
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#define NAN_WORD0 d_QNAN0
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#endif
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#ifndef NAN_WORD1
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#define NAN_WORD1 d_QNAN1
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#endif
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#else
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#define _0 1
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#define _1 0
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#ifndef NAN_WORD0
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#define NAN_WORD0 d_QNAN1
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#endif
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#ifndef NAN_WORD1
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#define NAN_WORD1 d_QNAN0
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#endif
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#endif
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#else
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#undef INFNAN_CHECK
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#endif
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#ifdef RND_PRODQUOT
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#define rounded_product(a,b) a = rnd_prod(a, b)
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#define rounded_quotient(a,b) a = rnd_quot(a, b)
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#ifdef KR_headers
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extern double rnd_prod(), rnd_quot();
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#else
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extern double rnd_prod(double, double), rnd_quot(double, double);
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#endif
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#else
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#define rounded_product(a,b) a *= b
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#define rounded_quotient(a,b) a /= b
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#endif
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#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
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#define Big1 ((__uint32_t)0xffffffffL)
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#ifndef Just_16
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/* When Pack_32 is not defined, we store 16 bits per 32-bit long.
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* This makes some inner loops simpler and sometimes saves work
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* during multiplications, but it often seems to make things slightly
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* slower. Hence the default is now to store 32 bits per long.
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*/
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#ifndef Pack_32
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#define Pack_32
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#endif
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#else /* Just_16 */
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#ifndef Pack_16
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#define Pack_16
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#endif
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#endif /* Just_16 */
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#ifdef Pack_32
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#define ULbits 32
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#define kshift 5
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#define kmask 31
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#define ALL_ON 0xffffffff
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#else
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#define ULbits 16
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#define kshift 4
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#define kmask 15
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#define ALL_ON 0xffff
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#endif
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#ifdef __cplusplus
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extern "C" double strtod(const char *s00, char **se);
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extern "C" char *dtoa(double d, int mode, int ndigits,
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int *decpt, int *sign, char **rve);
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#endif
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typedef struct _Bigint _Bigint;
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#define Balloc _Balloc
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#define Bfree _Bfree
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#define multadd __multadd
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#define s2b __s2b
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#define lo0bits __lo0bits
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#define hi0bits __hi0bits
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#define i2b __i2b
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#define mult __multiply
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#define pow5mult __pow5mult
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#define lshift __lshift
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#define cmp __mcmp
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#define diff __mdiff
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#define ulp __ulp
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#define b2d __b2d
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#define d2b __d2b
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#define ratio __ratio
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#define any_on __any_on
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#define gethex __gethex
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#define copybits __copybits
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#define hexnan __hexnan
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#define hexdig_init __hexdig_init
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#define hexdig __hexdig
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#define tens __mprec_tens
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#define bigtens __mprec_bigtens
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#define tinytens __mprec_tinytens
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struct _reent ;
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struct FPI;
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double _EXFUN(ulp,(double x));
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double _EXFUN(b2d,(_Bigint *a , int *e));
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_Bigint * _EXFUN(Balloc,(struct _reent *p, int k));
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void _EXFUN(Bfree,(struct _reent *p, _Bigint *v));
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_Bigint * _EXFUN(multadd,(struct _reent *p, _Bigint *, int, int));
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_Bigint * _EXFUN(s2b,(struct _reent *, const char*, int, int, __ULong));
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_Bigint * _EXFUN(i2b,(struct _reent *,int));
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_Bigint * _EXFUN(mult, (struct _reent *, _Bigint *, _Bigint *));
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_Bigint * _EXFUN(pow5mult, (struct _reent *, _Bigint *, int k));
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int _EXFUN(hi0bits,(__ULong));
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int _EXFUN(lo0bits,(__ULong *));
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_Bigint * _EXFUN(d2b,(struct _reent *p, double d, int *e, int *bits));
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_Bigint * _EXFUN(lshift,(struct _reent *p, _Bigint *b, int k));
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_Bigint * _EXFUN(diff,(struct _reent *p, _Bigint *a, _Bigint *b));
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int _EXFUN(cmp,(_Bigint *a, _Bigint *b));
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int _EXFUN(gethex,(struct _reent *p, _CONST char **sp, struct FPI *fpi, Long *exp, _Bigint **bp, int sign));
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double _EXFUN(ratio,(_Bigint *a, _Bigint *b));
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__ULong _EXFUN(any_on,(_Bigint *b, int k));
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void _EXFUN(copybits,(__ULong *c, int n, _Bigint *b));
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void _EXFUN(hexdig_init,(void));
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#ifdef INFNAN_CHECK
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int _EXFUN(hexnan,(_CONST char **sp, struct FPI *fpi, __ULong *x0));
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#endif
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#define Bcopy(x,y) memcpy((char *)&x->_sign, (char *)&y->_sign, y->_wds*sizeof(__Long) + 2*sizeof(int))
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extern _CONST double tinytens[];
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extern _CONST double bigtens[];
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extern _CONST double tens[];
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extern unsigned char hexdig[];
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double _EXFUN(_mprec_log10,(int));
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